1,0,0,0,0.000000," ","integrate((b*x^6+a*x^3)^(5/3),x, algorithm=""giac"")","\int {\left(b x^{6} + a x^{3}\right)}^{\frac{5}{3}}\,{d x}"," ",0,"integrate((b*x^6 + a*x^3)^(5/3), x)","F",0
2,0,0,0,0.000000," ","integrate((b*x^6+a*x^3)^(2/3),x, algorithm=""giac"")","\int {\left(b x^{6} + a x^{3}\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*x^6 + a*x^3)^(2/3), x)","F",0
3,1,14,0,24.995861," ","integrate(1/(b*x^6+a*x^3)^(2/3),x, algorithm=""giac"")","-\frac{{\left(b + \frac{a}{x^{3}}\right)}^{\frac{1}{3}}}{a}"," ",0,"-(b + a/x^3)^(1/3)/a","A",0
4,1,52,0,23.788821," ","integrate(1/(b*x^6+a*x^3)^(5/3),x, algorithm=""giac"")","\frac{b^{2}}{2 \, a^{3} {\left(b + \frac{a}{x^{3}}\right)}^{\frac{2}{3}}} - \frac{a^{9} {\left(b + \frac{a}{x^{3}}\right)}^{\frac{4}{3}} - 8 \, a^{9} {\left(b + \frac{a}{x^{3}}\right)}^{\frac{1}{3}} b}{4 \, a^{12}}"," ",0,"1/2*b^2/(a^3*(b + a/x^3)^(2/3)) - 1/4*(a^9*(b + a/x^3)^(4/3) - 8*a^9*(b + a/x^3)^(1/3)*b)/a^12","A",0
5,1,38,0,0.315896," ","integrate(1/(x^6-x^3),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{2 \, x^{2}} - \frac{1}{6} \, \log\left(x^{2} + x + 1\right) + \frac{1}{3} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/2/x^2 - 1/6*log(x^2 + x + 1) + 1/3*log(abs(x - 1))","A",0
6,1,23,0,0.395479," ","integrate(x^5*((b*x^3+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{18} \, {\left(2 \, b x^{9} + 3 \, a x^{6}\right)} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/18*(2*b*x^9 + 3*a*x^6)*sgn(b*x^3 + a)","A",0
7,1,29,0,0.371369," ","integrate(x^4*((b*x^3+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, b x^{8} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{5} \, a x^{5} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/8*b*x^8*sgn(b*x^3 + a) + 1/5*a*x^5*sgn(b*x^3 + a)","A",0
8,1,29,0,0.388431," ","integrate(x^3*((b*x^3+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{7} \, b x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{4} \, a x^{4} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/7*b*x^7*sgn(b*x^3 + a) + 1/4*a*x^4*sgn(b*x^3 + a)","A",0
9,1,22,0,0.361909," ","integrate(x^2*((b*x^3+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(b x^{6} + 2 \, a x^{3}\right)} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/6*(b*x^6 + 2*a*x^3)*sgn(b*x^3 + a)","A",0
10,1,29,0,0.326445," ","integrate(x*((b*x^3+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, b x^{5} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{2} \, a x^{2} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/5*b*x^5*sgn(b*x^3 + a) + 1/2*a*x^2*sgn(b*x^3 + a)","A",0
11,1,20,0,0.378752," ","integrate(((b*x^3+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, {\left(b x^{4} + 4 \, a x\right)} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/4*(b*x^4 + 4*a*x)*sgn(b*x^3 + a)","A",0
12,1,28,0,0.289090," ","integrate(((b*x^3+a)^2)^(1/2)/x,x, algorithm=""giac"")","\frac{1}{3} \, b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + a \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/3*b*x^3*sgn(b*x^3 + a) + a*log(abs(x))*sgn(b*x^3 + a)","A",0
13,1,29,0,0.323199," ","integrate(((b*x^3+a)^2)^(1/2)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, b x^{2} \mathrm{sgn}\left(b x^{3} + a\right) - \frac{a \mathrm{sgn}\left(b x^{3} + a\right)}{x}"," ",0,"1/2*b*x^2*sgn(b*x^3 + a) - a*sgn(b*x^3 + a)/x","A",0
14,1,26,0,0.402900," ","integrate(((b*x^3+a)^2)^(1/2)/x^3,x, algorithm=""giac"")","b x \mathrm{sgn}\left(b x^{3} + a\right) - \frac{a \mathrm{sgn}\left(b x^{3} + a\right)}{2 \, x^{2}}"," ",0,"b*x*sgn(b*x^3 + a) - 1/2*a*sgn(b*x^3 + a)/x^2","A",0
15,1,43,0,0.346405," ","integrate(((b*x^3+a)^2)^(1/2)/x^4,x, algorithm=""giac"")","b \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x^{3} + a\right) - \frac{b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + a \mathrm{sgn}\left(b x^{3} + a\right)}{3 \, x^{3}}"," ",0,"b*log(abs(x))*sgn(b*x^3 + a) - 1/3*(b*x^3*sgn(b*x^3 + a) + a*sgn(b*x^3 + a))/x^3","A",0
16,1,30,0,0.353819," ","integrate(((b*x^3+a)^2)^(1/2)/x^5,x, algorithm=""giac"")","-\frac{4 \, b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + a \mathrm{sgn}\left(b x^{3} + a\right)}{4 \, x^{4}}"," ",0,"-1/4*(4*b*x^3*sgn(b*x^3 + a) + a*sgn(b*x^3 + a))/x^4","A",0
17,1,31,0,0.348267," ","integrate(((b*x^3+a)^2)^(1/2)/x^6,x, algorithm=""giac"")","-\frac{5 \, b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 2 \, a \mathrm{sgn}\left(b x^{3} + a\right)}{10 \, x^{5}}"," ",0,"-1/10*(5*b*x^3*sgn(b*x^3 + a) + 2*a*sgn(b*x^3 + a))/x^5","A",0
18,1,30,0,0.336355," ","integrate(((b*x^3+a)^2)^(1/2)/x^7,x, algorithm=""giac"")","-\frac{2 \, b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + a \mathrm{sgn}\left(b x^{3} + a\right)}{6 \, x^{6}}"," ",0,"-1/6*(2*b*x^3*sgn(b*x^3 + a) + a*sgn(b*x^3 + a))/x^6","A",0
19,1,31,0,0.339365," ","integrate(((b*x^3+a)^2)^(1/2)/x^8,x, algorithm=""giac"")","-\frac{7 \, b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 4 \, a \mathrm{sgn}\left(b x^{3} + a\right)}{28 \, x^{7}}"," ",0,"-1/28*(7*b*x^3*sgn(b*x^3 + a) + 4*a*sgn(b*x^3 + a))/x^7","A",0
20,1,31,0,0.378773," ","integrate(((b*x^3+a)^2)^(1/2)/x^9,x, algorithm=""giac"")","-\frac{8 \, b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 5 \, a \mathrm{sgn}\left(b x^{3} + a\right)}{40 \, x^{8}}"," ",0,"-1/40*(8*b*x^3*sgn(b*x^3 + a) + 5*a*sgn(b*x^3 + a))/x^8","A",0
21,1,31,0,0.356530," ","integrate(((b*x^3+a)^2)^(1/2)/x^10,x, algorithm=""giac"")","-\frac{3 \, b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 2 \, a \mathrm{sgn}\left(b x^{3} + a\right)}{18 \, x^{9}}"," ",0,"-1/18*(3*b*x^3*sgn(b*x^3 + a) + 2*a*sgn(b*x^3 + a))/x^9","A",0
22,1,31,0,0.306698," ","integrate(((b*x^3+a)^2)^(1/2)/x^11,x, algorithm=""giac"")","-\frac{10 \, b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 7 \, a \mathrm{sgn}\left(b x^{3} + a\right)}{70 \, x^{10}}"," ",0,"-1/70*(10*b*x^3*sgn(b*x^3 + a) + 7*a*sgn(b*x^3 + a))/x^10","A",0
23,1,67,0,0.385067," ","integrate(x^9*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{19} \, b^{3} x^{19} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{16} \, a b^{2} x^{16} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{13} \, a^{2} b x^{13} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{10} \, a^{3} x^{10} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/19*b^3*x^19*sgn(b*x^3 + a) + 3/16*a*b^2*x^16*sgn(b*x^3 + a) + 3/13*a^2*b*x^13*sgn(b*x^3 + a) + 1/10*a^3*x^10*sgn(b*x^3 + a)","A",0
24,1,67,0,0.302515," ","integrate(x^8*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{18} \, b^{3} x^{18} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{5} \, a b^{2} x^{15} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{4} \, a^{2} b x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{9} \, a^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/18*b^3*x^18*sgn(b*x^3 + a) + 1/5*a*b^2*x^15*sgn(b*x^3 + a) + 1/4*a^2*b*x^12*sgn(b*x^3 + a) + 1/9*a^3*x^9*sgn(b*x^3 + a)","A",0
25,1,67,0,0.294943," ","integrate(x^7*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{17} \, b^{3} x^{17} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{14} \, a b^{2} x^{14} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{11} \, a^{2} b x^{11} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{8} \, a^{3} x^{8} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/17*b^3*x^17*sgn(b*x^3 + a) + 3/14*a*b^2*x^14*sgn(b*x^3 + a) + 3/11*a^2*b*x^11*sgn(b*x^3 + a) + 1/8*a^3*x^8*sgn(b*x^3 + a)","A",0
26,1,67,0,0.359154," ","integrate(x^6*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{16} \, b^{3} x^{16} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{13} \, a b^{2} x^{13} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{10} \, a^{2} b x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{7} \, a^{3} x^{7} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/16*b^3*x^16*sgn(b*x^3 + a) + 3/13*a*b^2*x^13*sgn(b*x^3 + a) + 3/10*a^2*b*x^10*sgn(b*x^3 + a) + 1/7*a^3*x^7*sgn(b*x^3 + a)","A",0
27,1,45,0,0.436953," ","integrate(x^5*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{60} \, {\left(4 \, b^{3} x^{15} + 15 \, a b^{2} x^{12} + 20 \, a^{2} b x^{9} + 10 \, a^{3} x^{6}\right)} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/60*(4*b^3*x^15 + 15*a*b^2*x^12 + 20*a^2*b*x^9 + 10*a^3*x^6)*sgn(b*x^3 + a)","A",0
28,1,67,0,0.368131," ","integrate(x^4*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{14} \, b^{3} x^{14} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{11} \, a b^{2} x^{11} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{8} \, a^{2} b x^{8} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{5} \, a^{3} x^{5} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/14*b^3*x^14*sgn(b*x^3 + a) + 3/11*a*b^2*x^11*sgn(b*x^3 + a) + 3/8*a^2*b*x^8*sgn(b*x^3 + a) + 1/5*a^3*x^5*sgn(b*x^3 + a)","A",0
29,1,67,0,0.447137," ","integrate(x^3*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{13} \, b^{3} x^{13} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{10} \, a b^{2} x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{7} \, a^{2} b x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{4} \, a^{3} x^{4} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/13*b^3*x^13*sgn(b*x^3 + a) + 3/10*a*b^2*x^10*sgn(b*x^3 + a) + 3/7*a^2*b*x^7*sgn(b*x^3 + a) + 1/4*a^3*x^4*sgn(b*x^3 + a)","A",0
30,1,44,0,0.412543," ","integrate(x^2*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{12} \, {\left(2 \, {\left(b x^{6} + 2 \, a x^{3}\right)} a^{2} + {\left(b x^{6} + 2 \, a x^{3}\right)}^{2} b\right)} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/12*(2*(b*x^6 + 2*a*x^3)*a^2 + (b*x^6 + 2*a*x^3)^2*b)*sgn(b*x^3 + a)","A",0
31,1,67,0,0.374296," ","integrate(x*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{11} \, b^{3} x^{11} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{8} \, a b^{2} x^{8} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{5} \, a^{2} b x^{5} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{2} \, a^{3} x^{2} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/11*b^3*x^11*sgn(b*x^3 + a) + 3/8*a*b^2*x^8*sgn(b*x^3 + a) + 3/5*a^2*b*x^5*sgn(b*x^3 + a) + 1/2*a^3*x^2*sgn(b*x^3 + a)","A",0
32,1,64,0,0.359748," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{10} \, b^{3} x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{7} \, a b^{2} x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{4} \, a^{2} b x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + a^{3} x \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/10*b^3*x^10*sgn(b*x^3 + a) + 3/7*a*b^2*x^7*sgn(b*x^3 + a) + 3/4*a^2*b*x^4*sgn(b*x^3 + a) + a^3*x*sgn(b*x^3 + a)","A",0
33,1,65,0,0.426450," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x,x, algorithm=""giac"")","\frac{1}{9} \, b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{2} \, a b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + a^{2} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + a^{3} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/9*b^3*x^9*sgn(b*x^3 + a) + 1/2*a*b^2*x^6*sgn(b*x^3 + a) + a^2*b*x^3*sgn(b*x^3 + a) + a^3*log(abs(x))*sgn(b*x^3 + a)","A",0
34,1,67,0,0.336597," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^2,x, algorithm=""giac"")","\frac{1}{8} \, b^{3} x^{8} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{5} \, a b^{2} x^{5} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{2} \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{3} + a\right) - \frac{a^{3} \mathrm{sgn}\left(b x^{3} + a\right)}{x}"," ",0,"1/8*b^3*x^8*sgn(b*x^3 + a) + 3/5*a*b^2*x^5*sgn(b*x^3 + a) + 3/2*a^2*b*x^2*sgn(b*x^3 + a) - a^3*sgn(b*x^3 + a)/x","A",0
35,1,65,0,0.383584," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^3,x, algorithm=""giac"")","\frac{1}{7} \, b^{3} x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{4} \, a b^{2} x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + 3 \, a^{2} b x \mathrm{sgn}\left(b x^{3} + a\right) - \frac{a^{3} \mathrm{sgn}\left(b x^{3} + a\right)}{2 \, x^{2}}"," ",0,"1/7*b^3*x^7*sgn(b*x^3 + a) + 3/4*a*b^2*x^4*sgn(b*x^3 + a) + 3*a^2*b*x*sgn(b*x^3 + a) - 1/2*a^3*sgn(b*x^3 + a)/x^2","A",0
36,1,85,0,0.365207," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^4,x, algorithm=""giac"")","\frac{1}{6} \, b^{3} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + a b^{2} x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 3 \, a^{2} b \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x^{3} + a\right) - \frac{3 \, a^{2} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + a^{3} \mathrm{sgn}\left(b x^{3} + a\right)}{3 \, x^{3}}"," ",0,"1/6*b^3*x^6*sgn(b*x^3 + a) + a*b^2*x^3*sgn(b*x^3 + a) + 3*a^2*b*log(abs(x))*sgn(b*x^3 + a) - 1/3*(3*a^2*b*x^3*sgn(b*x^3 + a) + a^3*sgn(b*x^3 + a))/x^3","A",0
37,1,69,0,0.361634," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^5,x, algorithm=""giac"")","\frac{1}{5} \, b^{3} x^{5} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{3}{2} \, a b^{2} x^{2} \mathrm{sgn}\left(b x^{3} + a\right) - \frac{12 \, a^{2} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + a^{3} \mathrm{sgn}\left(b x^{3} + a\right)}{4 \, x^{4}}"," ",0,"1/5*b^3*x^5*sgn(b*x^3 + a) + 3/2*a*b^2*x^2*sgn(b*x^3 + a) - 1/4*(12*a^2*b*x^3*sgn(b*x^3 + a) + a^3*sgn(b*x^3 + a))/x^4","A",0
38,1,68,0,0.292711," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^6,x, algorithm=""giac"")","\frac{1}{4} \, b^{3} x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + 3 \, a b^{2} x \mathrm{sgn}\left(b x^{3} + a\right) - \frac{15 \, a^{2} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 2 \, a^{3} \mathrm{sgn}\left(b x^{3} + a\right)}{10 \, x^{5}}"," ",0,"1/4*b^3*x^4*sgn(b*x^3 + a) + 3*a*b^2*x*sgn(b*x^3 + a) - 1/10*(15*a^2*b*x^3*sgn(b*x^3 + a) + 2*a^3*sgn(b*x^3 + a))/x^5","A",0
39,1,86,0,0.340020," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^7,x, algorithm=""giac"")","\frac{1}{3} \, b^{3} x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 3 \, a b^{2} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x^{3} + a\right) - \frac{9 \, a b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 6 \, a^{2} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + a^{3} \mathrm{sgn}\left(b x^{3} + a\right)}{6 \, x^{6}}"," ",0,"1/3*b^3*x^3*sgn(b*x^3 + a) + 3*a*b^2*log(abs(x))*sgn(b*x^3 + a) - 1/6*(9*a*b^2*x^6*sgn(b*x^3 + a) + 6*a^2*b*x^3*sgn(b*x^3 + a) + a^3*sgn(b*x^3 + a))/x^6","A",0
40,1,70,0,0.470019," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^8,x, algorithm=""giac"")","\frac{1}{2} \, b^{3} x^{2} \mathrm{sgn}\left(b x^{3} + a\right) - \frac{84 \, a b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 21 \, a^{2} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 4 \, a^{3} \mathrm{sgn}\left(b x^{3} + a\right)}{28 \, x^{7}}"," ",0,"1/2*b^3*x^2*sgn(b*x^3 + a) - 1/28*(84*a*b^2*x^6*sgn(b*x^3 + a) + 21*a^2*b*x^3*sgn(b*x^3 + a) + 4*a^3*sgn(b*x^3 + a))/x^7","A",0
41,1,67,0,0.391068," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^9,x, algorithm=""giac"")","b^{3} x \mathrm{sgn}\left(b x^{3} + a\right) - \frac{60 \, a b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 24 \, a^{2} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 5 \, a^{3} \mathrm{sgn}\left(b x^{3} + a\right)}{40 \, x^{8}}"," ",0,"b^3*x*sgn(b*x^3 + a) - 1/40*(60*a*b^2*x^6*sgn(b*x^3 + a) + 24*a^2*b*x^3*sgn(b*x^3 + a) + 5*a^3*sgn(b*x^3 + a))/x^8","A",0
42,1,85,0,0.376595," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^10,x, algorithm=""giac"")","b^{3} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x^{3} + a\right) - \frac{11 \, b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 18 \, a b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 9 \, a^{2} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 2 \, a^{3} \mathrm{sgn}\left(b x^{3} + a\right)}{18 \, x^{9}}"," ",0,"b^3*log(abs(x))*sgn(b*x^3 + a) - 1/18*(11*b^3*x^9*sgn(b*x^3 + a) + 18*a*b^2*x^6*sgn(b*x^3 + a) + 9*a^2*b*x^3*sgn(b*x^3 + a) + 2*a^3*sgn(b*x^3 + a))/x^9","A",0
43,1,69,0,0.361011," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^11,x, algorithm=""giac"")","-\frac{140 \, b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 105 \, a b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 60 \, a^{2} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 14 \, a^{3} \mathrm{sgn}\left(b x^{3} + a\right)}{140 \, x^{10}}"," ",0,"-1/140*(140*b^3*x^9*sgn(b*x^3 + a) + 105*a*b^2*x^6*sgn(b*x^3 + a) + 60*a^2*b*x^3*sgn(b*x^3 + a) + 14*a^3*sgn(b*x^3 + a))/x^10","A",0
44,1,69,0,0.418980," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^12,x, algorithm=""giac"")","-\frac{220 \, b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 264 \, a b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 165 \, a^{2} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 40 \, a^{3} \mathrm{sgn}\left(b x^{3} + a\right)}{440 \, x^{11}}"," ",0,"-1/440*(220*b^3*x^9*sgn(b*x^3 + a) + 264*a*b^2*x^6*sgn(b*x^3 + a) + 165*a^2*b*x^3*sgn(b*x^3 + a) + 40*a^3*sgn(b*x^3 + a))/x^11","A",0
45,1,68,0,0.356949," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^13,x, algorithm=""giac"")","-\frac{4 \, b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 6 \, a b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 4 \, a^{2} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + a^{3} \mathrm{sgn}\left(b x^{3} + a\right)}{12 \, x^{12}}"," ",0,"-1/12*(4*b^3*x^9*sgn(b*x^3 + a) + 6*a*b^2*x^6*sgn(b*x^3 + a) + 4*a^2*b*x^3*sgn(b*x^3 + a) + a^3*sgn(b*x^3 + a))/x^12","B",0
46,1,69,0,0.358054," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^14,x, algorithm=""giac"")","-\frac{455 \, b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 780 \, a b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 546 \, a^{2} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 140 \, a^{3} \mathrm{sgn}\left(b x^{3} + a\right)}{1820 \, x^{13}}"," ",0,"-1/1820*(455*b^3*x^9*sgn(b*x^3 + a) + 780*a*b^2*x^6*sgn(b*x^3 + a) + 546*a^2*b*x^3*sgn(b*x^3 + a) + 140*a^3*sgn(b*x^3 + a))/x^13","A",0
47,1,69,0,0.360121," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^15,x, algorithm=""giac"")","-\frac{616 \, b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 1155 \, a b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 840 \, a^{2} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 220 \, a^{3} \mathrm{sgn}\left(b x^{3} + a\right)}{3080 \, x^{14}}"," ",0,"-1/3080*(616*b^3*x^9*sgn(b*x^3 + a) + 1155*a*b^2*x^6*sgn(b*x^3 + a) + 840*a^2*b*x^3*sgn(b*x^3 + a) + 220*a^3*sgn(b*x^3 + a))/x^14","A",0
48,1,69,0,0.414457," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^16,x, algorithm=""giac"")","-\frac{10 \, b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 20 \, a b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 15 \, a^{2} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 4 \, a^{3} \mathrm{sgn}\left(b x^{3} + a\right)}{60 \, x^{15}}"," ",0,"-1/60*(10*b^3*x^9*sgn(b*x^3 + a) + 20*a*b^2*x^6*sgn(b*x^3 + a) + 15*a^2*b*x^3*sgn(b*x^3 + a) + 4*a^3*sgn(b*x^3 + a))/x^15","A",0
49,1,69,0,0.303653," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^17,x, algorithm=""giac"")","-\frac{1040 \, b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 2184 \, a b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 1680 \, a^{2} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 455 \, a^{3} \mathrm{sgn}\left(b x^{3} + a\right)}{7280 \, x^{16}}"," ",0,"-1/7280*(1040*b^3*x^9*sgn(b*x^3 + a) + 2184*a*b^2*x^6*sgn(b*x^3 + a) + 1680*a^2*b*x^3*sgn(b*x^3 + a) + 455*a^3*sgn(b*x^3 + a))/x^16","A",0
50,1,105,0,0.326225," ","integrate(x^13*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{29} \, b^{5} x^{29} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{26} \, a b^{4} x^{26} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{10}{23} \, a^{2} b^{3} x^{23} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{2} \, a^{3} b^{2} x^{20} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{17} \, a^{4} b x^{17} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{14} \, a^{5} x^{14} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/29*b^5*x^29*sgn(b*x^3 + a) + 5/26*a*b^4*x^26*sgn(b*x^3 + a) + 10/23*a^2*b^3*x^23*sgn(b*x^3 + a) + 1/2*a^3*b^2*x^20*sgn(b*x^3 + a) + 5/17*a^4*b*x^17*sgn(b*x^3 + a) + 1/14*a^5*x^14*sgn(b*x^3 + a)","A",0
51,1,105,0,0.322436," ","integrate(x^12*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{28} \, b^{5} x^{28} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{5} \, a b^{4} x^{25} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{11} \, a^{2} b^{3} x^{22} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{10}{19} \, a^{3} b^{2} x^{19} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{16} \, a^{4} b x^{16} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{13} \, a^{5} x^{13} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/28*b^5*x^28*sgn(b*x^3 + a) + 1/5*a*b^4*x^25*sgn(b*x^3 + a) + 5/11*a^2*b^3*x^22*sgn(b*x^3 + a) + 10/19*a^3*b^2*x^19*sgn(b*x^3 + a) + 5/16*a^4*b*x^16*sgn(b*x^3 + a) + 1/13*a^5*x^13*sgn(b*x^3 + a)","A",0
52,1,105,0,0.350985," ","integrate(x^11*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{27} \, b^{5} x^{27} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{24} \, a b^{4} x^{24} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{10}{21} \, a^{2} b^{3} x^{21} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{9} \, a^{3} b^{2} x^{18} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{3} \, a^{4} b x^{15} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{12} \, a^{5} x^{12} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/27*b^5*x^27*sgn(b*x^3 + a) + 5/24*a*b^4*x^24*sgn(b*x^3 + a) + 10/21*a^2*b^3*x^21*sgn(b*x^3 + a) + 5/9*a^3*b^2*x^18*sgn(b*x^3 + a) + 1/3*a^4*b*x^15*sgn(b*x^3 + a) + 1/12*a^5*x^12*sgn(b*x^3 + a)","A",0
53,1,105,0,0.442517," ","integrate(x^10*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{26} \, b^{5} x^{26} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{23} \, a b^{4} x^{23} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{2} \, a^{2} b^{3} x^{20} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{10}{17} \, a^{3} b^{2} x^{17} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{14} \, a^{4} b x^{14} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{11} \, a^{5} x^{11} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/26*b^5*x^26*sgn(b*x^3 + a) + 5/23*a*b^4*x^23*sgn(b*x^3 + a) + 1/2*a^2*b^3*x^20*sgn(b*x^3 + a) + 10/17*a^3*b^2*x^17*sgn(b*x^3 + a) + 5/14*a^4*b*x^14*sgn(b*x^3 + a) + 1/11*a^5*x^11*sgn(b*x^3 + a)","A",0
54,1,105,0,0.401464," ","integrate(x^9*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{25} \, b^{5} x^{25} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{22} \, a b^{4} x^{22} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{10}{19} \, a^{2} b^{3} x^{19} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{8} \, a^{3} b^{2} x^{16} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{13} \, a^{4} b x^{13} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{10} \, a^{5} x^{10} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/25*b^5*x^25*sgn(b*x^3 + a) + 5/22*a*b^4*x^22*sgn(b*x^3 + a) + 10/19*a^2*b^3*x^19*sgn(b*x^3 + a) + 5/8*a^3*b^2*x^16*sgn(b*x^3 + a) + 5/13*a^4*b*x^13*sgn(b*x^3 + a) + 1/10*a^5*x^10*sgn(b*x^3 + a)","A",0
55,1,105,0,0.377395," ","integrate(x^8*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{24} \, b^{5} x^{24} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{21} \, a b^{4} x^{21} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{9} \, a^{2} b^{3} x^{18} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{2}{3} \, a^{3} b^{2} x^{15} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{12} \, a^{4} b x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{9} \, a^{5} x^{9} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/24*b^5*x^24*sgn(b*x^3 + a) + 5/21*a*b^4*x^21*sgn(b*x^3 + a) + 5/9*a^2*b^3*x^18*sgn(b*x^3 + a) + 2/3*a^3*b^2*x^15*sgn(b*x^3 + a) + 5/12*a^4*b*x^12*sgn(b*x^3 + a) + 1/9*a^5*x^9*sgn(b*x^3 + a)","A",0
56,1,105,0,0.339049," ","integrate(x^7*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{23} \, b^{5} x^{23} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{4} \, a b^{4} x^{20} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{10}{17} \, a^{2} b^{3} x^{17} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{7} \, a^{3} b^{2} x^{14} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{11} \, a^{4} b x^{11} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{8} \, a^{5} x^{8} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/23*b^5*x^23*sgn(b*x^3 + a) + 1/4*a*b^4*x^20*sgn(b*x^3 + a) + 10/17*a^2*b^3*x^17*sgn(b*x^3 + a) + 5/7*a^3*b^2*x^14*sgn(b*x^3 + a) + 5/11*a^4*b*x^11*sgn(b*x^3 + a) + 1/8*a^5*x^8*sgn(b*x^3 + a)","A",0
57,1,105,0,0.344625," ","integrate(x^6*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{22} \, b^{5} x^{22} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{19} \, a b^{4} x^{19} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{8} \, a^{2} b^{3} x^{16} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{10}{13} \, a^{3} b^{2} x^{13} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{2} \, a^{4} b x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{7} \, a^{5} x^{7} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/22*b^5*x^22*sgn(b*x^3 + a) + 5/19*a*b^4*x^19*sgn(b*x^3 + a) + 5/8*a^2*b^3*x^16*sgn(b*x^3 + a) + 10/13*a^3*b^2*x^13*sgn(b*x^3 + a) + 1/2*a^4*b*x^10*sgn(b*x^3 + a) + 1/7*a^5*x^7*sgn(b*x^3 + a)","A",0
58,1,67,0,0.290681," ","integrate(x^5*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{126} \, {\left(6 \, b^{5} x^{21} + 35 \, a b^{4} x^{18} + 84 \, a^{2} b^{3} x^{15} + 105 \, a^{3} b^{2} x^{12} + 70 \, a^{4} b x^{9} + 21 \, a^{5} x^{6}\right)} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/126*(6*b^5*x^21 + 35*a*b^4*x^18 + 84*a^2*b^3*x^15 + 105*a^3*b^2*x^12 + 70*a^4*b*x^9 + 21*a^5*x^6)*sgn(b*x^3 + a)","A",0
59,1,105,0,0.416302," ","integrate(x^4*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{20} \, b^{5} x^{20} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{17} \, a b^{4} x^{17} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{7} \, a^{2} b^{3} x^{14} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{10}{11} \, a^{3} b^{2} x^{11} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{8} \, a^{4} b x^{8} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{5} \, a^{5} x^{5} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/20*b^5*x^20*sgn(b*x^3 + a) + 5/17*a*b^4*x^17*sgn(b*x^3 + a) + 5/7*a^2*b^3*x^14*sgn(b*x^3 + a) + 10/11*a^3*b^2*x^11*sgn(b*x^3 + a) + 5/8*a^4*b*x^8*sgn(b*x^3 + a) + 1/5*a^5*x^5*sgn(b*x^3 + a)","A",0
60,1,104,0,0.317320," ","integrate(x^3*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{19} \, b^{5} x^{19} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{16} \, a b^{4} x^{16} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{10}{13} \, a^{2} b^{3} x^{13} \mathrm{sgn}\left(b x^{3} + a\right) + a^{3} b^{2} x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{7} \, a^{4} b x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{4} \, a^{5} x^{4} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/19*b^5*x^19*sgn(b*x^3 + a) + 5/16*a*b^4*x^16*sgn(b*x^3 + a) + 10/13*a^2*b^3*x^13*sgn(b*x^3 + a) + a^3*b^2*x^10*sgn(b*x^3 + a) + 5/7*a^4*b*x^7*sgn(b*x^3 + a) + 1/4*a^5*x^4*sgn(b*x^3 + a)","A",0
61,1,66,0,0.372932," ","integrate(x^2*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{18} \, {\left(3 \, {\left(b x^{6} + 2 \, a x^{3}\right)} a^{4} + 3 \, {\left(b x^{6} + 2 \, a x^{3}\right)}^{2} a^{2} b + {\left(b x^{6} + 2 \, a x^{3}\right)}^{3} b^{2}\right)} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/18*(3*(b*x^6 + 2*a*x^3)*a^4 + 3*(b*x^6 + 2*a*x^3)^2*a^2*b + (b*x^6 + 2*a*x^3)^3*b^2)*sgn(b*x^3 + a)","B",0
62,1,104,0,0.367716," ","integrate(x*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{17} \, b^{5} x^{17} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{14} \, a b^{4} x^{14} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{10}{11} \, a^{2} b^{3} x^{11} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{4} \, a^{3} b^{2} x^{8} \mathrm{sgn}\left(b x^{3} + a\right) + a^{4} b x^{5} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{2} \, a^{5} x^{2} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/17*b^5*x^17*sgn(b*x^3 + a) + 5/14*a*b^4*x^14*sgn(b*x^3 + a) + 10/11*a^2*b^3*x^11*sgn(b*x^3 + a) + 5/4*a^3*b^2*x^8*sgn(b*x^3 + a) + a^4*b*x^5*sgn(b*x^3 + a) + 1/2*a^5*x^2*sgn(b*x^3 + a)","A",0
63,1,101,0,0.375833," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{16} \, b^{5} x^{16} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{13} \, a b^{4} x^{13} \mathrm{sgn}\left(b x^{3} + a\right) + a^{2} b^{3} x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{10}{7} \, a^{3} b^{2} x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{4} \, a^{4} b x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + a^{5} x \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/16*b^5*x^16*sgn(b*x^3 + a) + 5/13*a*b^4*x^13*sgn(b*x^3 + a) + a^2*b^3*x^10*sgn(b*x^3 + a) + 10/7*a^3*b^2*x^7*sgn(b*x^3 + a) + 5/4*a^4*b*x^4*sgn(b*x^3 + a) + a^5*x*sgn(b*x^3 + a)","A",0
64,1,104,0,0.351903," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x,x, algorithm=""giac"")","\frac{1}{15} \, b^{5} x^{15} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{12} \, a b^{4} x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{10}{9} \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{3} \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{3} \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + a^{5} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/15*b^5*x^15*sgn(b*x^3 + a) + 5/12*a*b^4*x^12*sgn(b*x^3 + a) + 10/9*a^2*b^3*x^9*sgn(b*x^3 + a) + 5/3*a^3*b^2*x^6*sgn(b*x^3 + a) + 5/3*a^4*b*x^3*sgn(b*x^3 + a) + a^5*log(abs(x))*sgn(b*x^3 + a)","A",0
65,1,105,0,0.334270," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^2,x, algorithm=""giac"")","\frac{1}{14} \, b^{5} x^{14} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{11} \, a b^{4} x^{11} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{4} \, a^{2} b^{3} x^{8} \mathrm{sgn}\left(b x^{3} + a\right) + 2 \, a^{3} b^{2} x^{5} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{2} \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{3} + a\right) - \frac{a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{x}"," ",0,"1/14*b^5*x^14*sgn(b*x^3 + a) + 5/11*a*b^4*x^11*sgn(b*x^3 + a) + 5/4*a^2*b^3*x^8*sgn(b*x^3 + a) + 2*a^3*b^2*x^5*sgn(b*x^3 + a) + 5/2*a^4*b*x^2*sgn(b*x^3 + a) - a^5*sgn(b*x^3 + a)/x","A",0
66,1,103,0,0.362017," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^3,x, algorithm=""giac"")","\frac{1}{13} \, b^{5} x^{13} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{1}{2} \, a b^{4} x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{10}{7} \, a^{2} b^{3} x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{2} \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + 5 \, a^{4} b x \mathrm{sgn}\left(b x^{3} + a\right) - \frac{a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{2 \, x^{2}}"," ",0,"1/13*b^5*x^13*sgn(b*x^3 + a) + 1/2*a*b^4*x^10*sgn(b*x^3 + a) + 10/7*a^2*b^3*x^7*sgn(b*x^3 + a) + 5/2*a^3*b^2*x^4*sgn(b*x^3 + a) + 5*a^4*b*x*sgn(b*x^3 + a) - 1/2*a^5*sgn(b*x^3 + a)/x^2","A",0
67,1,124,0,0.307552," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^4,x, algorithm=""giac"")","\frac{1}{12} \, b^{5} x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{9} \, a b^{4} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{3} \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{10}{3} \, a^{3} b^{2} x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 5 \, a^{4} b \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x^{3} + a\right) - \frac{5 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{3 \, x^{3}}"," ",0,"1/12*b^5*x^12*sgn(b*x^3 + a) + 5/9*a*b^4*x^9*sgn(b*x^3 + a) + 5/3*a^2*b^3*x^6*sgn(b*x^3 + a) + 10/3*a^3*b^2*x^3*sgn(b*x^3 + a) + 5*a^4*b*log(abs(x))*sgn(b*x^3 + a) - 1/3*(5*a^4*b*x^3*sgn(b*x^3 + a) + a^5*sgn(b*x^3 + a))/x^3","A",0
68,1,107,0,0.351143," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^5,x, algorithm=""giac"")","\frac{1}{11} \, b^{5} x^{11} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{8} \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{3} + a\right) + 2 \, a^{2} b^{3} x^{5} \mathrm{sgn}\left(b x^{3} + a\right) + 5 \, a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x^{3} + a\right) - \frac{20 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{4 \, x^{4}}"," ",0,"1/11*b^5*x^11*sgn(b*x^3 + a) + 5/8*a*b^4*x^8*sgn(b*x^3 + a) + 2*a^2*b^3*x^5*sgn(b*x^3 + a) + 5*a^3*b^2*x^2*sgn(b*x^3 + a) - 1/4*(20*a^4*b*x^3*sgn(b*x^3 + a) + a^5*sgn(b*x^3 + a))/x^4","A",0
69,1,106,0,0.340809," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^6,x, algorithm=""giac"")","\frac{1}{10} \, b^{5} x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{7} \, a b^{4} x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{2} \, a^{2} b^{3} x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + 10 \, a^{3} b^{2} x \mathrm{sgn}\left(b x^{3} + a\right) - \frac{25 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 2 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{10 \, x^{5}}"," ",0,"1/10*b^5*x^10*sgn(b*x^3 + a) + 5/7*a*b^4*x^7*sgn(b*x^3 + a) + 5/2*a^2*b^3*x^4*sgn(b*x^3 + a) + 10*a^3*b^2*x*sgn(b*x^3 + a) - 1/10*(25*a^4*b*x^3*sgn(b*x^3 + a) + 2*a^5*sgn(b*x^3 + a))/x^5","A",0
70,1,126,0,0.366976," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^7,x, algorithm=""giac"")","\frac{1}{9} \, b^{5} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{6} \, a b^{4} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{10}{3} \, a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 10 \, a^{3} b^{2} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x^{3} + a\right) - \frac{30 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 10 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{6 \, x^{6}}"," ",0,"1/9*b^5*x^9*sgn(b*x^3 + a) + 5/6*a*b^4*x^6*sgn(b*x^3 + a) + 10/3*a^2*b^3*x^3*sgn(b*x^3 + a) + 10*a^3*b^2*log(abs(x))*sgn(b*x^3 + a) - 1/6*(30*a^3*b^2*x^6*sgn(b*x^3 + a) + 10*a^4*b*x^3*sgn(b*x^3 + a) + a^5*sgn(b*x^3 + a))/x^6","A",0
71,1,107,0,0.325503," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^8,x, algorithm=""giac"")","\frac{1}{8} \, b^{5} x^{8} \mathrm{sgn}\left(b x^{3} + a\right) + a b^{4} x^{5} \mathrm{sgn}\left(b x^{3} + a\right) + 5 \, a^{2} b^{3} x^{2} \mathrm{sgn}\left(b x^{3} + a\right) - \frac{280 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 35 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 4 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{28 \, x^{7}}"," ",0,"1/8*b^5*x^8*sgn(b*x^3 + a) + a*b^4*x^5*sgn(b*x^3 + a) + 5*a^2*b^3*x^2*sgn(b*x^3 + a) - 1/28*(280*a^3*b^2*x^6*sgn(b*x^3 + a) + 35*a^4*b*x^3*sgn(b*x^3 + a) + 4*a^5*sgn(b*x^3 + a))/x^7","A",0
72,1,105,0,0.336109," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^9,x, algorithm=""giac"")","\frac{1}{7} \, b^{5} x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{4} \, a b^{4} x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + 10 \, a^{2} b^{3} x \mathrm{sgn}\left(b x^{3} + a\right) - \frac{40 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 8 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{8 \, x^{8}}"," ",0,"1/7*b^5*x^7*sgn(b*x^3 + a) + 5/4*a*b^4*x^4*sgn(b*x^3 + a) + 10*a^2*b^3*x*sgn(b*x^3 + a) - 1/8*(40*a^3*b^2*x^6*sgn(b*x^3 + a) + 8*a^4*b*x^3*sgn(b*x^3 + a) + a^5*sgn(b*x^3 + a))/x^8","A",0
73,1,127,0,0.397490," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^10,x, algorithm=""giac"")","\frac{1}{6} \, b^{5} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{3} \, a b^{4} x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 10 \, a^{2} b^{3} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x^{3} + a\right) - \frac{110 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 60 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 15 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 2 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{18 \, x^{9}}"," ",0,"1/6*b^5*x^6*sgn(b*x^3 + a) + 5/3*a*b^4*x^3*sgn(b*x^3 + a) + 10*a^2*b^3*log(abs(x))*sgn(b*x^3 + a) - 1/18*(110*a^2*b^3*x^9*sgn(b*x^3 + a) + 60*a^3*b^2*x^6*sgn(b*x^3 + a) + 15*a^4*b*x^3*sgn(b*x^3 + a) + 2*a^5*sgn(b*x^3 + a))/x^9","A",0
74,1,108,0,0.396834," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^11,x, algorithm=""giac"")","\frac{1}{5} \, b^{5} x^{5} \mathrm{sgn}\left(b x^{3} + a\right) + \frac{5}{2} \, a b^{4} x^{2} \mathrm{sgn}\left(b x^{3} + a\right) - \frac{700 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 175 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 50 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 7 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{70 \, x^{10}}"," ",0,"1/5*b^5*x^5*sgn(b*x^3 + a) + 5/2*a*b^4*x^2*sgn(b*x^3 + a) - 1/70*(700*a^2*b^3*x^9*sgn(b*x^3 + a) + 175*a^3*b^2*x^6*sgn(b*x^3 + a) + 50*a^4*b*x^3*sgn(b*x^3 + a) + 7*a^5*sgn(b*x^3 + a))/x^10","A",0
75,1,106,0,0.350375," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^12,x, algorithm=""giac"")","\frac{1}{4} \, b^{5} x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + 5 \, a b^{4} x \mathrm{sgn}\left(b x^{3} + a\right) - \frac{440 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 176 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 55 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 8 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{88 \, x^{11}}"," ",0,"1/4*b^5*x^4*sgn(b*x^3 + a) + 5*a*b^4*x*sgn(b*x^3 + a) - 1/88*(440*a^2*b^3*x^9*sgn(b*x^3 + a) + 176*a^3*b^2*x^6*sgn(b*x^3 + a) + 55*a^4*b*x^3*sgn(b*x^3 + a) + 8*a^5*sgn(b*x^3 + a))/x^11","A",0
76,1,125,0,0.378394," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^13,x, algorithm=""giac"")","\frac{1}{3} \, b^{5} x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 5 \, a b^{4} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x^{3} + a\right) - \frac{125 \, a b^{4} x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + 120 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 60 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 20 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 3 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{36 \, x^{12}}"," ",0,"1/3*b^5*x^3*sgn(b*x^3 + a) + 5*a*b^4*log(abs(x))*sgn(b*x^3 + a) - 1/36*(125*a*b^4*x^12*sgn(b*x^3 + a) + 120*a^2*b^3*x^9*sgn(b*x^3 + a) + 60*a^3*b^2*x^6*sgn(b*x^3 + a) + 20*a^4*b*x^3*sgn(b*x^3 + a) + 3*a^5*sgn(b*x^3 + a))/x^12","A",0
77,1,108,0,0.334902," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^14,x, algorithm=""giac"")","\frac{1}{2} \, b^{5} x^{2} \mathrm{sgn}\left(b x^{3} + a\right) - \frac{910 \, a b^{4} x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + 455 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 260 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 91 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 14 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{182 \, x^{13}}"," ",0,"1/2*b^5*x^2*sgn(b*x^3 + a) - 1/182*(910*a*b^4*x^12*sgn(b*x^3 + a) + 455*a^2*b^3*x^9*sgn(b*x^3 + a) + 260*a^3*b^2*x^6*sgn(b*x^3 + a) + 91*a^4*b*x^3*sgn(b*x^3 + a) + 14*a^5*sgn(b*x^3 + a))/x^13","A",0
78,1,105,0,0.346018," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^15,x, algorithm=""giac"")","b^{5} x \mathrm{sgn}\left(b x^{3} + a\right) - \frac{770 \, a b^{4} x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + 616 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 385 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 140 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 22 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{308 \, x^{14}}"," ",0,"b^5*x*sgn(b*x^3 + a) - 1/308*(770*a*b^4*x^12*sgn(b*x^3 + a) + 616*a^2*b^3*x^9*sgn(b*x^3 + a) + 385*a^3*b^2*x^6*sgn(b*x^3 + a) + 140*a^4*b*x^3*sgn(b*x^3 + a) + 22*a^5*sgn(b*x^3 + a))/x^14","A",0
79,1,123,0,0.370100," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^16,x, algorithm=""giac"")","b^{5} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x^{3} + a\right) - \frac{137 \, b^{5} x^{15} \mathrm{sgn}\left(b x^{3} + a\right) + 300 \, a b^{4} x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + 300 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 200 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 75 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 12 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{180 \, x^{15}}"," ",0,"b^5*log(abs(x))*sgn(b*x^3 + a) - 1/180*(137*b^5*x^15*sgn(b*x^3 + a) + 300*a*b^4*x^12*sgn(b*x^3 + a) + 300*a^2*b^3*x^9*sgn(b*x^3 + a) + 200*a^3*b^2*x^6*sgn(b*x^3 + a) + 75*a^4*b*x^3*sgn(b*x^3 + a) + 12*a^5*sgn(b*x^3 + a))/x^15","A",0
80,1,107,0,0.340098," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^17,x, algorithm=""giac"")","-\frac{1456 \, b^{5} x^{15} \mathrm{sgn}\left(b x^{3} + a\right) + 1820 \, a b^{4} x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + 2080 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 1456 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 560 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 91 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{1456 \, x^{16}}"," ",0,"-1/1456*(1456*b^5*x^15*sgn(b*x^3 + a) + 1820*a*b^4*x^12*sgn(b*x^3 + a) + 2080*a^2*b^3*x^9*sgn(b*x^3 + a) + 1456*a^3*b^2*x^6*sgn(b*x^3 + a) + 560*a^4*b*x^3*sgn(b*x^3 + a) + 91*a^5*sgn(b*x^3 + a))/x^16","A",0
81,1,107,0,0.447581," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^18,x, algorithm=""giac"")","-\frac{2618 \, b^{5} x^{15} \mathrm{sgn}\left(b x^{3} + a\right) + 5236 \, a b^{4} x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + 6545 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 4760 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 1870 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 308 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{5236 \, x^{17}}"," ",0,"-1/5236*(2618*b^5*x^15*sgn(b*x^3 + a) + 5236*a*b^4*x^12*sgn(b*x^3 + a) + 6545*a^2*b^3*x^9*sgn(b*x^3 + a) + 4760*a^3*b^2*x^6*sgn(b*x^3 + a) + 1870*a^4*b*x^3*sgn(b*x^3 + a) + 308*a^5*sgn(b*x^3 + a))/x^17","A",0
82,1,106,0,0.291257," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^19,x, algorithm=""giac"")","-\frac{6 \, b^{5} x^{15} \mathrm{sgn}\left(b x^{3} + a\right) + 15 \, a b^{4} x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + 20 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 15 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 6 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{18 \, x^{18}}"," ",0,"-1/18*(6*b^5*x^15*sgn(b*x^3 + a) + 15*a*b^4*x^12*sgn(b*x^3 + a) + 20*a^2*b^3*x^9*sgn(b*x^3 + a) + 15*a^3*b^2*x^6*sgn(b*x^3 + a) + 6*a^4*b*x^3*sgn(b*x^3 + a) + a^5*sgn(b*x^3 + a))/x^18","B",0
83,1,107,0,0.361017," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^20,x, algorithm=""giac"")","-\frac{6916 \, b^{5} x^{15} \mathrm{sgn}\left(b x^{3} + a\right) + 19760 \, a b^{4} x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + 27664 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 21280 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 8645 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 1456 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{27664 \, x^{19}}"," ",0,"-1/27664*(6916*b^5*x^15*sgn(b*x^3 + a) + 19760*a*b^4*x^12*sgn(b*x^3 + a) + 27664*a^2*b^3*x^9*sgn(b*x^3 + a) + 21280*a^3*b^2*x^6*sgn(b*x^3 + a) + 8645*a^4*b*x^3*sgn(b*x^3 + a) + 1456*a^5*sgn(b*x^3 + a))/x^19","A",0
84,1,107,0,0.318336," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^21,x, algorithm=""giac"")","-\frac{10472 \, b^{5} x^{15} \mathrm{sgn}\left(b x^{3} + a\right) + 32725 \, a b^{4} x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + 47600 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 37400 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 15400 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 2618 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{52360 \, x^{20}}"," ",0,"-1/52360*(10472*b^5*x^15*sgn(b*x^3 + a) + 32725*a*b^4*x^12*sgn(b*x^3 + a) + 47600*a^2*b^3*x^9*sgn(b*x^3 + a) + 37400*a^3*b^2*x^6*sgn(b*x^3 + a) + 15400*a^4*b*x^3*sgn(b*x^3 + a) + 2618*a^5*sgn(b*x^3 + a))/x^20","A",0
85,1,107,0,0.321762," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^22,x, algorithm=""giac"")","-\frac{21 \, b^{5} x^{15} \mathrm{sgn}\left(b x^{3} + a\right) + 70 \, a b^{4} x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + 105 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 84 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 35 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 6 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{126 \, x^{21}}"," ",0,"-1/126*(21*b^5*x^15*sgn(b*x^3 + a) + 70*a*b^4*x^12*sgn(b*x^3 + a) + 105*a^2*b^3*x^9*sgn(b*x^3 + a) + 84*a^3*b^2*x^6*sgn(b*x^3 + a) + 35*a^4*b*x^3*sgn(b*x^3 + a) + 6*a^5*sgn(b*x^3 + a))/x^21","A",0
86,1,107,0,0.329787," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^23,x, algorithm=""giac"")","-\frac{21736 \, b^{5} x^{15} \mathrm{sgn}\left(b x^{3} + a\right) + 76076 \, a b^{4} x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + 117040 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 95095 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 40040 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 6916 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{152152 \, x^{22}}"," ",0,"-1/152152*(21736*b^5*x^15*sgn(b*x^3 + a) + 76076*a*b^4*x^12*sgn(b*x^3 + a) + 117040*a^2*b^3*x^9*sgn(b*x^3 + a) + 95095*a^3*b^2*x^6*sgn(b*x^3 + a) + 40040*a^4*b*x^3*sgn(b*x^3 + a) + 6916*a^5*sgn(b*x^3 + a))/x^22","A",0
87,1,107,0,0.340446," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^24,x, algorithm=""giac"")","-\frac{30107 \, b^{5} x^{15} \mathrm{sgn}\left(b x^{3} + a\right) + 109480 \, a b^{4} x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + 172040 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 141680 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 60214 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 10472 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{240856 \, x^{23}}"," ",0,"-1/240856*(30107*b^5*x^15*sgn(b*x^3 + a) + 109480*a*b^4*x^12*sgn(b*x^3 + a) + 172040*a^2*b^3*x^9*sgn(b*x^3 + a) + 141680*a^3*b^2*x^6*sgn(b*x^3 + a) + 60214*a^4*b*x^3*sgn(b*x^3 + a) + 10472*a^5*sgn(b*x^3 + a))/x^23","A",0
88,1,107,0,0.394662," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^25,x, algorithm=""giac"")","-\frac{56 \, b^{5} x^{15} \mathrm{sgn}\left(b x^{3} + a\right) + 210 \, a b^{4} x^{12} \mathrm{sgn}\left(b x^{3} + a\right) + 336 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{3} + a\right) + 280 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{3} + a\right) + 120 \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{3} + a\right) + 21 \, a^{5} \mathrm{sgn}\left(b x^{3} + a\right)}{504 \, x^{24}}"," ",0,"-1/504*(56*b^5*x^15*sgn(b*x^3 + a) + 210*a*b^4*x^12*sgn(b*x^3 + a) + 336*a^2*b^3*x^9*sgn(b*x^3 + a) + 280*a^3*b^2*x^6*sgn(b*x^3 + a) + 120*a^4*b*x^3*sgn(b*x^3 + a) + 21*a^5*sgn(b*x^3 + a))/x^24","A",0
89,1,146,0,0.370812," ","integrate(x^4/((b*x^3+a)^2)^(1/2),x, algorithm=""giac"")","\frac{x^{2} \mathrm{sgn}\left(b x^{3} + a\right)}{2 \, b} + \frac{\left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right) \mathrm{sgn}\left(b x^{3} + a\right)}{3 \, b} + \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right) \mathrm{sgn}\left(b x^{3} + a\right)}{3 \, b^{3}} - \frac{\left(-a b^{2}\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right) \mathrm{sgn}\left(b x^{3} + a\right)}{6 \, b^{3}}"," ",0,"1/2*x^2*sgn(b*x^3 + a)/b + 1/3*(-a/b)^(2/3)*log(abs(x - (-a/b)^(1/3)))*sgn(b*x^3 + a)/b + 1/3*sqrt(3)*(-a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))*sgn(b*x^3 + a)/b^3 - 1/6*(-a*b^2)^(2/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))*sgn(b*x^3 + a)/b^3","A",0
90,1,143,0,0.408695," ","integrate(x^3/((b*x^3+a)^2)^(1/2),x, algorithm=""giac"")","\frac{\left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right) \mathrm{sgn}\left(b x^{3} + a\right)}{3 \, b} + \frac{x \mathrm{sgn}\left(b x^{3} + a\right)}{b} - \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right) \mathrm{sgn}\left(b x^{3} + a\right)}{3 \, b^{2}} - \frac{\left(-a b^{2}\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) \mathrm{sgn}\left(b x^{3} + a\right)}{6 \, b^{2}}"," ",0,"1/3*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))*sgn(b*x^3 + a)/b + x*sgn(b*x^3 + a)/b - 1/3*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))*sgn(b*x^3 + a)/b^2 - 1/6*(-a*b^2)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))*sgn(b*x^3 + a)/b^2","A",0
91,1,22,0,0.340159," ","integrate(x^2/((b*x^3+a)^2)^(1/2),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{3} + a \right|}\right) \mathrm{sgn}\left(b x^{3} + a\right)}{3 \, b}"," ",0,"1/3*log(abs(b*x^3 + a))*sgn(b*x^3 + a)/b","A",0
92,1,124,0,0.416991," ","integrate(x/((b*x^3+a)^2)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right) \mathrm{sgn}\left(b x^{3} + a\right)}{3 \, \left(-a b^{2}\right)^{\frac{1}{3}}} - \frac{\log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right) \mathrm{sgn}\left(b x^{3} + a\right)}{6 \, \left(-a b^{2}\right)^{\frac{1}{3}}} - \frac{\left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right) \mathrm{sgn}\left(b x^{3} + a\right)}{3 \, a}"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))*sgn(b*x^3 + a)/(-a*b^2)^(1/3) - 1/6*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))*sgn(b*x^3 + a)/(-a*b^2)^(1/3) - 1/3*(-a/b)^(2/3)*log(abs(x - (-a/b)^(1/3)))*sgn(b*x^3 + a)/a","A",0
93,1,122,0,0.364794," ","integrate(1/((b*x^3+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{6} \, {\left(\frac{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{a} - \frac{2 \, \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{a b} - \frac{\left(-a b^{2}\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)}{a b}\right)} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"-1/6*(2*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a - 2*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a*b) - (-a*b^2)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a*b))*sgn(b*x^3 + a)","A",0
94,1,32,0,0.342953," ","integrate(1/x/((b*x^3+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{3} \, {\left(\frac{\log\left({\left| b x^{3} + a \right|}\right)}{a} - \frac{3 \, \log\left({\left| x \right|}\right)}{a}\right)} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"-1/3*(log(abs(b*x^3 + a))/a - 3*log(abs(x))/a)*sgn(b*x^3 + a)","A",0
95,1,131,0,0.370752," ","integrate(1/x^2/((b*x^3+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(\frac{2 \, b \left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{a^{2}} + \frac{2 \, \sqrt{3} \left(-a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{a^{2} b} - \frac{\left(-a b^{2}\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{a^{2} b} - \frac{6}{a x}\right)} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/6*(2*b*(-a/b)^(2/3)*log(abs(x - (-a/b)^(1/3)))/a^2 + 2*sqrt(3)*(-a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^2*b) - (-a*b^2)^(2/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^2*b) - 6/(a*x))*sgn(b*x^3 + a)","A",0
96,1,125,0,0.334245," ","integrate(1/x^3/((b*x^3+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(\frac{2 \, b \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{a^{2}} - \frac{2 \, \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{a^{2}} - \frac{\left(-a b^{2}\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)}{a^{2}} - \frac{3}{a x^{2}}\right)} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/6*(2*b*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^2 - 2*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/a^2 - (-a*b^2)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/a^2 - 3/(a*x^2))*sgn(b*x^3 + a)","A",0
97,1,50,0,0.367438," ","integrate(1/x^4/((b*x^3+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, {\left(\frac{b \log\left({\left| b x^{3} + a \right|}\right)}{a^{2}} - \frac{3 \, b \log\left({\left| x \right|}\right)}{a^{2}} + \frac{b x^{3} - a}{a^{2} x^{3}}\right)} \mathrm{sgn}\left(b x^{3} + a\right)"," ",0,"1/3*(b*log(abs(b*x^3 + a))/a^2 - 3*b*log(abs(x))/a^2 + (b*x^3 - a)/(a^2*x^3))*sgn(b*x^3 + a)","A",0
98,0,0,0,0.000000," ","integrate(x^4/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
99,0,0,0,0.000000," ","integrate(x^3/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
100,0,0,0,0.000000," ","integrate(x^2/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
101,0,0,0,0.000000," ","integrate(x/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
102,0,0,0,0.000000," ","integrate(1/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
103,0,0,0,0.000000," ","integrate(1/x/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
104,0,0,0,0.000000," ","integrate(1/x^2/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
105,0,0,0,0.000000," ","integrate(1/x^3/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
106,0,0,0,0.000000," ","integrate(1/x^4/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
107,0,0,0,0.000000," ","integrate(x^6/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
108,0,0,0,0.000000," ","integrate(x^5/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
109,0,0,0,0.000000," ","integrate(x^4/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
110,0,0,0,0.000000," ","integrate(x^3/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
111,0,0,0,0.000000," ","integrate(x^2/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
112,0,0,0,0.000000," ","integrate(x/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
113,0,0,0,0.000000," ","integrate(1/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
114,0,0,0,0.000000," ","integrate(1/x/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
115,0,0,0,0.000000," ","integrate(1/x^2/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
116,0,0,0,0.000000," ","integrate(1/x^3/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
117,0,0,0,0.000000," ","integrate(1/x^4/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
118,1,900,0,0.672951," ","integrate((d*x)^m*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\frac{\left(d x\right)^{m} b^{5} m^{5} x^{16} \mathrm{sgn}\left(b x^{3} + a\right) + 35 \, \left(d x\right)^{m} b^{5} m^{4} x^{16} \mathrm{sgn}\left(b x^{3} + a\right) + 445 \, \left(d x\right)^{m} b^{5} m^{3} x^{16} \mathrm{sgn}\left(b x^{3} + a\right) + 5 \, \left(d x\right)^{m} a b^{4} m^{5} x^{13} \mathrm{sgn}\left(b x^{3} + a\right) + 2485 \, \left(d x\right)^{m} b^{5} m^{2} x^{16} \mathrm{sgn}\left(b x^{3} + a\right) + 190 \, \left(d x\right)^{m} a b^{4} m^{4} x^{13} \mathrm{sgn}\left(b x^{3} + a\right) + 5714 \, \left(d x\right)^{m} b^{5} m x^{16} \mathrm{sgn}\left(b x^{3} + a\right) + 2555 \, \left(d x\right)^{m} a b^{4} m^{3} x^{13} \mathrm{sgn}\left(b x^{3} + a\right) + 3640 \, \left(d x\right)^{m} b^{5} x^{16} \mathrm{sgn}\left(b x^{3} + a\right) + 10 \, \left(d x\right)^{m} a^{2} b^{3} m^{5} x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + 14810 \, \left(d x\right)^{m} a b^{4} m^{2} x^{13} \mathrm{sgn}\left(b x^{3} + a\right) + 410 \, \left(d x\right)^{m} a^{2} b^{3} m^{4} x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + 34840 \, \left(d x\right)^{m} a b^{4} m x^{13} \mathrm{sgn}\left(b x^{3} + a\right) + 5950 \, \left(d x\right)^{m} a^{2} b^{3} m^{3} x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + 22400 \, \left(d x\right)^{m} a b^{4} x^{13} \mathrm{sgn}\left(b x^{3} + a\right) + 10 \, \left(d x\right)^{m} a^{3} b^{2} m^{5} x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + 36550 \, \left(d x\right)^{m} a^{2} b^{3} m^{2} x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + 440 \, \left(d x\right)^{m} a^{3} b^{2} m^{4} x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + 89240 \, \left(d x\right)^{m} a^{2} b^{3} m x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + 6970 \, \left(d x\right)^{m} a^{3} b^{2} m^{3} x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + 58240 \, \left(d x\right)^{m} a^{2} b^{3} x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + 5 \, \left(d x\right)^{m} a^{4} b m^{5} x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + 47260 \, \left(d x\right)^{m} a^{3} b^{2} m^{2} x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + 235 \, \left(d x\right)^{m} a^{4} b m^{4} x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + 123920 \, \left(d x\right)^{m} a^{3} b^{2} m x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + 4085 \, \left(d x\right)^{m} a^{4} b m^{3} x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + 83200 \, \left(d x\right)^{m} a^{3} b^{2} x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + \left(d x\right)^{m} a^{5} m^{5} x \mathrm{sgn}\left(b x^{3} + a\right) + 31685 \, \left(d x\right)^{m} a^{4} b m^{2} x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + 50 \, \left(d x\right)^{m} a^{5} m^{4} x \mathrm{sgn}\left(b x^{3} + a\right) + 100630 \, \left(d x\right)^{m} a^{4} b m x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + 955 \, \left(d x\right)^{m} a^{5} m^{3} x \mathrm{sgn}\left(b x^{3} + a\right) + 72800 \, \left(d x\right)^{m} a^{4} b x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + 8650 \, \left(d x\right)^{m} a^{5} m^{2} x \mathrm{sgn}\left(b x^{3} + a\right) + 36824 \, \left(d x\right)^{m} a^{5} m x \mathrm{sgn}\left(b x^{3} + a\right) + 58240 \, \left(d x\right)^{m} a^{5} x \mathrm{sgn}\left(b x^{3} + a\right)}{m^{6} + 51 \, m^{5} + 1005 \, m^{4} + 9605 \, m^{3} + 45474 \, m^{2} + 95064 \, m + 58240}"," ",0,"((d*x)^m*b^5*m^5*x^16*sgn(b*x^3 + a) + 35*(d*x)^m*b^5*m^4*x^16*sgn(b*x^3 + a) + 445*(d*x)^m*b^5*m^3*x^16*sgn(b*x^3 + a) + 5*(d*x)^m*a*b^4*m^5*x^13*sgn(b*x^3 + a) + 2485*(d*x)^m*b^5*m^2*x^16*sgn(b*x^3 + a) + 190*(d*x)^m*a*b^4*m^4*x^13*sgn(b*x^3 + a) + 5714*(d*x)^m*b^5*m*x^16*sgn(b*x^3 + a) + 2555*(d*x)^m*a*b^4*m^3*x^13*sgn(b*x^3 + a) + 3640*(d*x)^m*b^5*x^16*sgn(b*x^3 + a) + 10*(d*x)^m*a^2*b^3*m^5*x^10*sgn(b*x^3 + a) + 14810*(d*x)^m*a*b^4*m^2*x^13*sgn(b*x^3 + a) + 410*(d*x)^m*a^2*b^3*m^4*x^10*sgn(b*x^3 + a) + 34840*(d*x)^m*a*b^4*m*x^13*sgn(b*x^3 + a) + 5950*(d*x)^m*a^2*b^3*m^3*x^10*sgn(b*x^3 + a) + 22400*(d*x)^m*a*b^4*x^13*sgn(b*x^3 + a) + 10*(d*x)^m*a^3*b^2*m^5*x^7*sgn(b*x^3 + a) + 36550*(d*x)^m*a^2*b^3*m^2*x^10*sgn(b*x^3 + a) + 440*(d*x)^m*a^3*b^2*m^4*x^7*sgn(b*x^3 + a) + 89240*(d*x)^m*a^2*b^3*m*x^10*sgn(b*x^3 + a) + 6970*(d*x)^m*a^3*b^2*m^3*x^7*sgn(b*x^3 + a) + 58240*(d*x)^m*a^2*b^3*x^10*sgn(b*x^3 + a) + 5*(d*x)^m*a^4*b*m^5*x^4*sgn(b*x^3 + a) + 47260*(d*x)^m*a^3*b^2*m^2*x^7*sgn(b*x^3 + a) + 235*(d*x)^m*a^4*b*m^4*x^4*sgn(b*x^3 + a) + 123920*(d*x)^m*a^3*b^2*m*x^7*sgn(b*x^3 + a) + 4085*(d*x)^m*a^4*b*m^3*x^4*sgn(b*x^3 + a) + 83200*(d*x)^m*a^3*b^2*x^7*sgn(b*x^3 + a) + (d*x)^m*a^5*m^5*x*sgn(b*x^3 + a) + 31685*(d*x)^m*a^4*b*m^2*x^4*sgn(b*x^3 + a) + 50*(d*x)^m*a^5*m^4*x*sgn(b*x^3 + a) + 100630*(d*x)^m*a^4*b*m*x^4*sgn(b*x^3 + a) + 955*(d*x)^m*a^5*m^3*x*sgn(b*x^3 + a) + 72800*(d*x)^m*a^4*b*x^4*sgn(b*x^3 + a) + 8650*(d*x)^m*a^5*m^2*x*sgn(b*x^3 + a) + 36824*(d*x)^m*a^5*m*x*sgn(b*x^3 + a) + 58240*(d*x)^m*a^5*x*sgn(b*x^3 + a))/(m^6 + 51*m^5 + 1005*m^4 + 9605*m^3 + 45474*m^2 + 95064*m + 58240)","B",0
119,1,384,0,0.523957," ","integrate((d*x)^m*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\frac{\left(d x\right)^{m} b^{3} m^{3} x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + 12 \, \left(d x\right)^{m} b^{3} m^{2} x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + 39 \, \left(d x\right)^{m} b^{3} m x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + 3 \, \left(d x\right)^{m} a b^{2} m^{3} x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + 28 \, \left(d x\right)^{m} b^{3} x^{10} \mathrm{sgn}\left(b x^{3} + a\right) + 45 \, \left(d x\right)^{m} a b^{2} m^{2} x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + 162 \, \left(d x\right)^{m} a b^{2} m x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + 3 \, \left(d x\right)^{m} a^{2} b m^{3} x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + 120 \, \left(d x\right)^{m} a b^{2} x^{7} \mathrm{sgn}\left(b x^{3} + a\right) + 54 \, \left(d x\right)^{m} a^{2} b m^{2} x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + 261 \, \left(d x\right)^{m} a^{2} b m x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + \left(d x\right)^{m} a^{3} m^{3} x \mathrm{sgn}\left(b x^{3} + a\right) + 210 \, \left(d x\right)^{m} a^{2} b x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + 21 \, \left(d x\right)^{m} a^{3} m^{2} x \mathrm{sgn}\left(b x^{3} + a\right) + 138 \, \left(d x\right)^{m} a^{3} m x \mathrm{sgn}\left(b x^{3} + a\right) + 280 \, \left(d x\right)^{m} a^{3} x \mathrm{sgn}\left(b x^{3} + a\right)}{m^{4} + 22 \, m^{3} + 159 \, m^{2} + 418 \, m + 280}"," ",0,"((d*x)^m*b^3*m^3*x^10*sgn(b*x^3 + a) + 12*(d*x)^m*b^3*m^2*x^10*sgn(b*x^3 + a) + 39*(d*x)^m*b^3*m*x^10*sgn(b*x^3 + a) + 3*(d*x)^m*a*b^2*m^3*x^7*sgn(b*x^3 + a) + 28*(d*x)^m*b^3*x^10*sgn(b*x^3 + a) + 45*(d*x)^m*a*b^2*m^2*x^7*sgn(b*x^3 + a) + 162*(d*x)^m*a*b^2*m*x^7*sgn(b*x^3 + a) + 3*(d*x)^m*a^2*b*m^3*x^4*sgn(b*x^3 + a) + 120*(d*x)^m*a*b^2*x^7*sgn(b*x^3 + a) + 54*(d*x)^m*a^2*b*m^2*x^4*sgn(b*x^3 + a) + 261*(d*x)^m*a^2*b*m*x^4*sgn(b*x^3 + a) + (d*x)^m*a^3*m^3*x*sgn(b*x^3 + a) + 210*(d*x)^m*a^2*b*x^4*sgn(b*x^3 + a) + 21*(d*x)^m*a^3*m^2*x*sgn(b*x^3 + a) + 138*(d*x)^m*a^3*m*x*sgn(b*x^3 + a) + 280*(d*x)^m*a^3*x*sgn(b*x^3 + a))/(m^4 + 22*m^3 + 159*m^2 + 418*m + 280)","B",0
120,1,83,0,0.451740," ","integrate((d*x)^m*(b^2*x^6+2*a*b*x^3+a^2)^(1/2),x, algorithm=""giac"")","\frac{\left(d x\right)^{m} b m x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + \left(d x\right)^{m} b x^{4} \mathrm{sgn}\left(b x^{3} + a\right) + \left(d x\right)^{m} a m x \mathrm{sgn}\left(b x^{3} + a\right) + 4 \, \left(d x\right)^{m} a x \mathrm{sgn}\left(b x^{3} + a\right)}{m^{2} + 5 \, m + 4}"," ",0,"((d*x)^m*b*m*x^4*sgn(b*x^3 + a) + (d*x)^m*b*x^4*sgn(b*x^3 + a) + (d*x)^m*a*m*x*sgn(b*x^3 + a) + 4*(d*x)^m*a*x*sgn(b*x^3 + a))/(m^2 + 5*m + 4)","A",0
121,0,0,0,0.000000," ","integrate((d*x)^m/(b^2*x^6+2*a*b*x^3+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{\sqrt{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}}\,{d x}"," ",0,"integrate((d*x)^m/sqrt(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
122,0,0,0,0.000000," ","integrate((d*x)^m/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*x)^m/(b^2*x^6 + 2*a*b*x^3 + a^2)^(3/2), x)","F",0
123,0,0,0,0.000000," ","integrate((d*x)^m/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*x)^m/(b^2*x^6 + 2*a*b*x^3 + a^2)^(5/2), x)","F",0
124,0,0,0,0.000000," ","integrate((d*x)^m*(b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""giac"")","\int {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b^2*x^6 + 2*a*b*x^3 + a^2)^p*(d*x)^m, x)","F",0
125,1,375,0,0.529830," ","integrate(x^11*(b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""giac"")","\frac{4 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} b^{4} p^{3} x^{12} + 12 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} b^{4} p^{2} x^{12} + 11 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} b^{4} p x^{12} + 4 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} a b^{3} p^{3} x^{9} + 3 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} b^{4} x^{12} + 6 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} a b^{3} p^{2} x^{9} + 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} a b^{3} p x^{9} - 6 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} a^{2} b^{2} p^{2} x^{6} - 3 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} a^{2} b^{2} p x^{6} + 6 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} a^{3} b p x^{3} - 3 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} a^{4}}{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^2*x^6 + 2*a*b*x^3 + a^2)^p*b^4*p^3*x^12 + 12*(b^2*x^6 + 2*a*b*x^3 + a^2)^p*b^4*p^2*x^12 + 11*(b^2*x^6 + 2*a*b*x^3 + a^2)^p*b^4*p*x^12 + 4*(b^2*x^6 + 2*a*b*x^3 + a^2)^p*a*b^3*p^3*x^9 + 3*(b^2*x^6 + 2*a*b*x^3 + a^2)^p*b^4*x^12 + 6*(b^2*x^6 + 2*a*b*x^3 + a^2)^p*a*b^3*p^2*x^9 + 2*(b^2*x^6 + 2*a*b*x^3 + a^2)^p*a*b^3*p*x^9 - 6*(b^2*x^6 + 2*a*b*x^3 + a^2)^p*a^2*b^2*p^2*x^6 - 3*(b^2*x^6 + 2*a*b*x^3 + a^2)^p*a^2*b^2*p*x^6 + 6*(b^2*x^6 + 2*a*b*x^3 + a^2)^p*a^3*b*p*x^3 - 3*(b^2*x^6 + 2*a*b*x^3 + a^2)^p*a^4)/(4*b^4*p^4 + 20*b^4*p^3 + 35*b^4*p^2 + 25*b^4*p + 6*b^4)","B",0
126,1,235,0,0.438673," ","integrate(x^8*(b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""giac"")","\frac{2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} b^{3} p^{2} x^{9} + 3 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} b^{3} p x^{9} + {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} b^{3} x^{9} + 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} a b^{2} p^{2} x^{6} + {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} a b^{2} p x^{6} - 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} a^{2} b p x^{3} + {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} a^{3}}{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^2*x^6 + 2*a*b*x^3 + a^2)^p*b^3*p^2*x^9 + 3*(b^2*x^6 + 2*a*b*x^3 + a^2)^p*b^3*p*x^9 + (b^2*x^6 + 2*a*b*x^3 + a^2)^p*b^3*x^9 + 2*(b^2*x^6 + 2*a*b*x^3 + a^2)^p*a*b^2*p^2*x^6 + (b^2*x^6 + 2*a*b*x^3 + a^2)^p*a*b^2*p*x^6 - 2*(b^2*x^6 + 2*a*b*x^3 + a^2)^p*a^2*b*p*x^3 + (b^2*x^6 + 2*a*b*x^3 + a^2)^p*a^3)/(4*b^3*p^3 + 12*b^3*p^2 + 11*b^3*p + 3*b^3)","A",0
127,1,132,0,0.479063," ","integrate(x^5*(b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""giac"")","\frac{2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} b^{2} p x^{6} + {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} b^{2} x^{6} + 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} a b p x^{3} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} a^{2}}{6 \, {\left(2 \, b^{2} p^{2} + 3 \, b^{2} p + b^{2}\right)}}"," ",0,"1/6*(2*(b^2*x^6 + 2*a*b*x^3 + a^2)^p*b^2*p*x^6 + (b^2*x^6 + 2*a*b*x^3 + a^2)^p*b^2*x^6 + 2*(b^2*x^6 + 2*a*b*x^3 + a^2)^p*a*b*p*x^3 - (b^2*x^6 + 2*a*b*x^3 + a^2)^p*a^2)/(2*b^2*p^2 + 3*b^2*p + b^2)","A",0
128,0,0,0,0.000000," ","integrate(x^4*(b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""giac"")","\int {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} x^{4}\,{d x}"," ",0,"integrate((b^2*x^6 + 2*a*b*x^3 + a^2)^p*x^4, x)","F",0
129,0,0,0,0.000000," ","integrate(x^3*(b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""giac"")","\int {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} x^{3}\,{d x}"," ",0,"integrate((b^2*x^6 + 2*a*b*x^3 + a^2)^p*x^3, x)","F",0
130,1,58,0,0.482265," ","integrate(x^2*(b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""giac"")","\frac{{\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} b x^{3} + {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} a}{3 \, {\left(2 \, b p + b\right)}}"," ",0,"1/3*((b^2*x^6 + 2*a*b*x^3 + a^2)^p*b*x^3 + (b^2*x^6 + 2*a*b*x^3 + a^2)^p*a)/(2*b*p + b)","A",0
131,0,0,0,0.000000," ","integrate(x*(b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""giac"")","\int {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} x\,{d x}"," ",0,"integrate((b^2*x^6 + 2*a*b*x^3 + a^2)^p*x, x)","F",0
132,0,0,0,0.000000," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""giac"")","\int {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p}\,{d x}"," ",0,"integrate((b^2*x^6 + 2*a*b*x^3 + a^2)^p, x)","F",0
133,0,0,0,0.000000," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^p/x,x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p}}{x}\,{d x}"," ",0,"integrate((b^2*x^6 + 2*a*b*x^3 + a^2)^p/x, x)","F",0
134,0,0,0,0.000000," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^p/x^2,x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate((b^2*x^6 + 2*a*b*x^3 + a^2)^p/x^2, x)","F",0
135,0,0,0,0.000000," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^p/x^3,x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p}}{x^{3}}\,{d x}"," ",0,"integrate((b^2*x^6 + 2*a*b*x^3 + a^2)^p/x^3, x)","F",0
136,0,0,0,0.000000," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^p/x^4,x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p}}{x^{4}}\,{d x}"," ",0,"integrate((b^2*x^6 + 2*a*b*x^3 + a^2)^p/x^4, x)","F",0
137,0,0,0,0.000000," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^p/x^5,x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p}}{x^{5}}\,{d x}"," ",0,"integrate((b^2*x^6 + 2*a*b*x^3 + a^2)^p/x^5, x)","F",0
138,1,75,0,1.138244," ","integrate(x^8/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\frac{x^{3}}{3 \, c} - \frac{b \log\left(c x^{6} + b x^{3} + a\right)}{6 \, c^{2}} + \frac{{\left(b^{2} - 2 \, a c\right)} \arctan\left(\frac{2 \, c x^{3} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{3 \, \sqrt{-b^{2} + 4 \, a c} c^{2}}"," ",0,"1/3*x^3/c - 1/6*b*log(c*x^6 + b*x^3 + a)/c^2 + 1/3*(b^2 - 2*a*c)*arctan((2*c*x^3 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2)","A",0
139,1,59,0,1.185996," ","integrate(x^5/(c*x^6+b*x^3+a),x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{2 \, c x^{3} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{3 \, \sqrt{-b^{2} + 4 \, a c} c} + \frac{\log\left(c x^{6} + b x^{3} + a\right)}{6 \, c}"," ",0,"-1/3*b*arctan((2*c*x^3 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c) + 1/6*log(c*x^6 + b*x^3 + a)/c","A",0
140,1,36,0,0.982797," ","integrate(x^2/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{2 \, c x^{3} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{3 \, \sqrt{-b^{2} + 4 \, a c}}"," ",0,"2/3*arctan((2*c*x^3 + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c)","A",0
141,1,66,0,1.002780," ","integrate(1/x/(c*x^6+b*x^3+a),x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{2 \, c x^{3} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{3 \, \sqrt{-b^{2} + 4 \, a c} a} - \frac{\log\left(c x^{6} + b x^{3} + a\right)}{6 \, a} + \frac{\log\left({\left| x \right|}\right)}{a}"," ",0,"-1/3*b*arctan((2*c*x^3 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a) - 1/6*log(c*x^6 + b*x^3 + a)/a + log(abs(x))/a","A",0
142,1,93,0,1.137469," ","integrate(1/x^4/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\frac{b \log\left(c x^{6} + b x^{3} + a\right)}{6 \, a^{2}} - \frac{b \log\left({\left| x \right|}\right)}{a^{2}} + \frac{{\left(b^{2} - 2 \, a c\right)} \arctan\left(\frac{2 \, c x^{3} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{3 \, \sqrt{-b^{2} + 4 \, a c} a^{2}} + \frac{b x^{3} - a}{3 \, a^{2} x^{3}}"," ",0,"1/6*b*log(c*x^6 + b*x^3 + a)/a^2 - b*log(abs(x))/a^2 + 1/3*(b^2 - 2*a*c)*arctan((2*c*x^3 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a^2) + 1/3*(b*x^3 - a)/(a^2*x^3)","A",0
143,0,0,0,0.000000," ","integrate(x^7/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int \frac{x^{7}}{c x^{6} + b x^{3} + a}\,{d x}"," ",0,"integrate(x^7/(c*x^6 + b*x^3 + a), x)","F",0
144,0,0,0,0.000000," ","integrate(x^6/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int \frac{x^{6}}{c x^{6} + b x^{3} + a}\,{d x}"," ",0,"integrate(x^6/(c*x^6 + b*x^3 + a), x)","F",0
145,0,0,0,0.000000," ","integrate(x^4/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int \frac{x^{4}}{c x^{6} + b x^{3} + a}\,{d x}"," ",0,"integrate(x^4/(c*x^6 + b*x^3 + a), x)","F",0
146,0,0,0,0.000000," ","integrate(x^3/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int \frac{x^{3}}{c x^{6} + b x^{3} + a}\,{d x}"," ",0,"integrate(x^3/(c*x^6 + b*x^3 + a), x)","F",0
147,0,0,0,0.000000," ","integrate(x/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int \frac{x}{c x^{6} + b x^{3} + a}\,{d x}"," ",0,"integrate(x/(c*x^6 + b*x^3 + a), x)","F",0
148,0,0,0,0.000000," ","integrate(1/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int \frac{1}{c x^{6} + b x^{3} + a}\,{d x}"," ",0,"integrate(1/(c*x^6 + b*x^3 + a), x)","F",0
149,0,0,0,0.000000," ","integrate(1/x^2/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{6} + b x^{3} + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((c*x^6 + b*x^3 + a)*x^2), x)","F",0
150,0,0,0,0.000000," ","integrate(1/x^3/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{6} + b x^{3} + a\right)} x^{3}}\,{d x}"," ",0,"integrate(1/((c*x^6 + b*x^3 + a)*x^3), x)","F",0
151,1,29,0,0.394119," ","integrate(x^11/(x^6+4*x^3+3),x, algorithm=""giac"")","\frac{1}{6} \, x^{6} - \frac{4}{3} \, x^{3} + \frac{9}{2} \, \log\left({\left| x^{3} + 3 \right|}\right) - \frac{1}{6} \, \log\left({\left| x^{3} + 1 \right|}\right)"," ",0,"1/6*x^6 - 4/3*x^3 + 9/2*log(abs(x^3 + 3)) - 1/6*log(abs(x^3 + 1))","A",0
152,1,24,0,0.343449," ","integrate(x^8/(x^6+4*x^3+3),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} - \frac{3}{2} \, \log\left({\left| x^{3} + 3 \right|}\right) + \frac{1}{6} \, \log\left({\left| x^{3} + 1 \right|}\right)"," ",0,"1/3*x^3 - 3/2*log(abs(x^3 + 3)) + 1/6*log(abs(x^3 + 1))","A",0
153,1,19,0,0.363705," ","integrate(x^5/(x^6+4*x^3+3),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| x^{3} + 3 \right|}\right) - \frac{1}{6} \, \log\left({\left| x^{3} + 1 \right|}\right)"," ",0,"1/2*log(abs(x^3 + 3)) - 1/6*log(abs(x^3 + 1))","A",0
154,1,19,0,0.327892," ","integrate(x^2/(x^6+4*x^3+3),x, algorithm=""giac"")","-\frac{1}{6} \, \log\left({\left| x^{3} + 3 \right|}\right) + \frac{1}{6} \, \log\left({\left| x^{3} + 1 \right|}\right)"," ",0,"-1/6*log(abs(x^3 + 3)) + 1/6*log(abs(x^3 + 1))","B",0
155,1,24,0,0.352796," ","integrate(1/x/(x^6+4*x^3+3),x, algorithm=""giac"")","\frac{1}{18} \, \log\left({\left| x^{3} + 3 \right|}\right) - \frac{1}{6} \, \log\left({\left| x^{3} + 1 \right|}\right) + \frac{1}{3} \, \log\left({\left| x \right|}\right)"," ",0,"1/18*log(abs(x^3 + 3)) - 1/6*log(abs(x^3 + 1)) + 1/3*log(abs(x))","A",0
156,1,36,0,0.300835," ","integrate(1/x^4/(x^6+4*x^3+3),x, algorithm=""giac"")","\frac{4 \, x^{3} - 3}{27 \, x^{3}} - \frac{1}{54} \, \log\left({\left| x^{3} + 3 \right|}\right) + \frac{1}{6} \, \log\left({\left| x^{3} + 1 \right|}\right) - \frac{4}{9} \, \log\left({\left| x \right|}\right)"," ",0,"1/27*(4*x^3 - 3)/x^3 - 1/54*log(abs(x^3 + 3)) + 1/6*log(abs(x^3 + 1)) - 4/9*log(abs(x))","A",0
157,1,41,0,0.365373," ","integrate(1/x^7/(x^6+4*x^3+3),x, algorithm=""giac"")","-\frac{13 \, x^{6} - 8 \, x^{3} + 3}{54 \, x^{6}} + \frac{1}{162} \, \log\left({\left| x^{3} + 3 \right|}\right) - \frac{1}{6} \, \log\left({\left| x^{3} + 1 \right|}\right) + \frac{13}{27} \, \log\left({\left| x \right|}\right)"," ",0,"-1/54*(13*x^6 - 8*x^3 + 3)/x^6 + 1/162*log(abs(x^3 + 3)) - 1/6*log(abs(x^3 + 1)) + 13/27*log(abs(x))","A",0
158,1,96,0,0.365194," ","integrate(x^10/(x^6+4*x^3+3),x, algorithm=""giac"")","\frac{1}{5} \, x^{5} - 2 \, x^{2} + \frac{3}{4} \cdot 3^{\frac{2}{3}} \log\left(x^{2} - 3^{\frac{1}{3}} x + 3^{\frac{2}{3}}\right) - \frac{3}{2} \cdot 3^{\frac{2}{3}} \log\left({\left| x + 3^{\frac{1}{3}} \right|}\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{9}{2} \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({\left| x + 1 \right|}\right)"," ",0,"1/5*x^5 - 2*x^2 + 3/4*3^(2/3)*log(x^2 - 3^(1/3)*x + 3^(2/3)) - 3/2*3^(2/3)*log(abs(x + 3^(1/3))) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 9/2*3^(1/6)*arctan(1/3*3^(1/6)*(2*x - 3^(1/3))) - 1/12*log(x^2 - x + 1) + 1/6*log(abs(x + 1))","A",0
159,1,94,0,0.432005," ","integrate(x^9/(x^6+4*x^3+3),x, algorithm=""giac"")","\frac{1}{4} \, x^{4} + \frac{3}{2} \cdot 3^{\frac{5}{6}} \arctan\left(\frac{1}{3} \cdot 3^{\frac{1}{6}} {\left(2 \, x - 3^{\frac{1}{3}}\right)}\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({\left| x + 3^{\frac{1}{3}} \right|}\right) - 4 \, x + \frac{1}{12} \, \log\left(x^{2} - x + 1\right) - \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/4*x^4 + 3/2*3^(5/6)*arctan(1/3*3^(1/6)*(2*x - 3^(1/3))) - 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(abs(x + 3^(1/3))) - 4*x + 1/12*log(x^2 - x + 1) - 1/6*log(abs(x + 1))","A",0
160,1,91,0,0.336090," ","integrate(x^7/(x^6+4*x^3+3),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - \frac{1}{4} \cdot 3^{\frac{2}{3}} \log\left(x^{2} - 3^{\frac{1}{3}} x + 3^{\frac{2}{3}}\right) + \frac{1}{2} \cdot 3^{\frac{2}{3}} \log\left({\left| x + 3^{\frac{1}{3}} \right|}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{3}{2} \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({\left| x + 1 \right|}\right)"," ",0,"1/2*x^2 - 1/4*3^(2/3)*log(x^2 - 3^(1/3)*x + 3^(2/3)) + 1/2*3^(2/3)*log(abs(x + 3^(1/3))) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 3/2*3^(1/6)*arctan(1/3*3^(1/6)*(2*x - 3^(1/3))) + 1/12*log(x^2 - x + 1) - 1/6*log(abs(x + 1))","A",0
161,1,87,0,0.453932," ","integrate(x^6/(x^6+4*x^3+3),x, algorithm=""giac"")","-\frac{1}{2} \cdot 3^{\frac{5}{6}} \arctan\left(\frac{1}{3} \cdot 3^{\frac{1}{6}} {\left(2 \, x - 3^{\frac{1}{3}}\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{4} \cdot 3^{\frac{1}{3}} \log\left(x^{2} - 3^{\frac{1}{3}} x + 3^{\frac{2}{3}}\right) - \frac{1}{2} \cdot 3^{\frac{1}{3}} \log\left({\left| x + 3^{\frac{1}{3}} \right|}\right) + x - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/2*3^(5/6)*arctan(1/3*3^(1/6)*(2*x - 3^(1/3))) + 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(abs(x + 3^(1/3))) + x - 1/12*log(x^2 - x + 1) + 1/6*log(abs(x + 1))","A",0
162,1,86,0,0.303176," ","integrate(x^4/(x^6+4*x^3+3),x, algorithm=""giac"")","\frac{1}{12} \cdot 3^{\frac{2}{3}} \log\left(x^{2} - 3^{\frac{1}{3}} x + 3^{\frac{2}{3}}\right) - \frac{1}{6} \cdot 3^{\frac{2}{3}} \log\left({\left| x + 3^{\frac{1}{3}} \right|}\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}} \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({\left| x + 1 \right|}\right)"," ",0,"1/12*3^(2/3)*log(x^2 - 3^(1/3)*x + 3^(2/3)) - 1/6*3^(2/3)*log(abs(x + 3^(1/3))) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/2*3^(1/6)*arctan(1/3*3^(1/6)*(2*x - 3^(1/3))) - 1/12*log(x^2 - x + 1) + 1/6*log(abs(x + 1))","A",0
163,1,86,0,0.335174," ","integrate(x^3/(x^6+4*x^3+3),x, algorithm=""giac"")","\frac{1}{6} \cdot 3^{\frac{5}{6}} \arctan\left(\frac{1}{3} \cdot 3^{\frac{1}{6}} {\left(2 \, x - 3^{\frac{1}{3}}\right)}\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{12} \cdot 3^{\frac{1}{3}} \log\left(x^{2} - 3^{\frac{1}{3}} x + 3^{\frac{2}{3}}\right) + \frac{1}{6} \cdot 3^{\frac{1}{3}} \log\left({\left| x + 3^{\frac{1}{3}} \right|}\right) + \frac{1}{12} \, \log\left(x^{2} - x + 1\right) - \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/6*3^(5/6)*arctan(1/3*3^(1/6)*(2*x - 3^(1/3))) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/12*3^(1/3)*log(x^2 - 3^(1/3)*x + 3^(2/3)) + 1/6*3^(1/3)*log(abs(x + 3^(1/3))) + 1/12*log(x^2 - x + 1) - 1/6*log(abs(x + 1))","A",0
164,1,86,0,0.363355," ","integrate(x/(x^6+4*x^3+3),x, algorithm=""giac"")","-\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({\left| x + 3^{\frac{1}{3}} \right|}\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({\left| x + 1 \right|}\right)"," ",0,"-1/36*3^(2/3)*log(x^2 - 3^(1/3)*x + 3^(2/3)) + 1/18*3^(2/3)*log(abs(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(abs(x + 1))","A",0
165,1,86,0,0.339127," ","integrate(1/(x^6+4*x^3+3),x, algorithm=""giac"")","-\frac{1}{18} \cdot 3^{\frac{5}{6}} \arctan\left(\frac{1}{3} \cdot 3^{\frac{1}{6}} {\left(2 \, x - 3^{\frac{1}{3}}\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{36} \cdot 3^{\frac{1}{3}} \log\left(x^{2} - 3^{\frac{1}{3}} x + 3^{\frac{2}{3}}\right) - \frac{1}{18} \cdot 3^{\frac{1}{3}} \log\left({\left| x + 3^{\frac{1}{3}} \right|}\right) - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/18*3^(5/6)*arctan(1/3*3^(1/6)*(2*x - 3^(1/3))) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/36*3^(1/3)*log(x^2 - 3^(1/3)*x + 3^(2/3)) - 1/18*3^(1/3)*log(abs(x + 3^(1/3))) - 1/12*log(x^2 - x + 1) + 1/6*log(abs(x + 1))","A",0
166,1,91,0,0.413688," ","integrate(1/x^2/(x^6+4*x^3+3),x, algorithm=""giac"")","\frac{1}{108} \cdot 3^{\frac{2}{3}} \log\left(x^{2} - 3^{\frac{1}{3}} x + 3^{\frac{2}{3}}\right) - \frac{1}{54} \cdot 3^{\frac{2}{3}} \log\left({\left| x + 3^{\frac{1}{3}} \right|}\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{18} \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}{3 \, x} - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/108*3^(2/3)*log(x^2 - 3^(1/3)*x + 3^(2/3)) - 1/54*3^(2/3)*log(abs(x + 3^(1/3))) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/18*3^(1/6)*arctan(1/3*3^(1/6)*(2*x - 3^(1/3))) - 1/3/x - 1/12*log(x^2 - x + 1) + 1/6*log(abs(x + 1))","A",0
167,1,91,0,0.410532," ","integrate(1/x^3/(x^6+4*x^3+3),x, algorithm=""giac"")","\frac{1}{54} \cdot 3^{\frac{5}{6}} \arctan\left(\frac{1}{3} \cdot 3^{\frac{1}{6}} {\left(2 \, x - 3^{\frac{1}{3}}\right)}\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{108} \cdot 3^{\frac{1}{3}} \log\left(x^{2} - 3^{\frac{1}{3}} x + 3^{\frac{2}{3}}\right) + \frac{1}{54} \cdot 3^{\frac{1}{3}} \log\left({\left| x + 3^{\frac{1}{3}} \right|}\right) - \frac{1}{6 \, x^{2}} + \frac{1}{12} \, \log\left(x^{2} - x + 1\right) - \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/54*3^(5/6)*arctan(1/3*3^(1/6)*(2*x - 3^(1/3))) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/108*3^(1/3)*log(x^2 - 3^(1/3)*x + 3^(2/3)) + 1/54*3^(1/3)*log(abs(x + 3^(1/3))) - 1/6/x^2 + 1/12*log(x^2 - x + 1) - 1/6*log(abs(x + 1))","A",0
168,1,98,0,0.363103," ","integrate(1/x^5/(x^6+4*x^3+3),x, algorithm=""giac"")","-\frac{1}{324} \cdot 3^{\frac{2}{3}} \log\left(x^{2} - 3^{\frac{1}{3}} x + 3^{\frac{2}{3}}\right) + \frac{1}{162} \cdot 3^{\frac{2}{3}} \log\left({\left| x + 3^{\frac{1}{3}} \right|}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{54} \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{16 \, x^{3} - 3}{36 \, x^{4}} + \frac{1}{12} \, \log\left(x^{2} - x + 1\right) - \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/324*3^(2/3)*log(x^2 - 3^(1/3)*x + 3^(2/3)) + 1/162*3^(2/3)*log(abs(x + 3^(1/3))) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/54*3^(1/6)*arctan(1/3*3^(1/6)*(2*x - 3^(1/3))) + 1/36*(16*x^3 - 3)/x^4 + 1/12*log(x^2 - x + 1) - 1/6*log(abs(x + 1))","A",0
169,1,98,0,0.357971," ","integrate(1/x^6/(x^6+4*x^3+3),x, algorithm=""giac"")","-\frac{1}{162} \cdot 3^{\frac{5}{6}} \arctan\left(\frac{1}{3} \cdot 3^{\frac{1}{6}} {\left(2 \, x - 3^{\frac{1}{3}}\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{324} \cdot 3^{\frac{1}{3}} \log\left(x^{2} - 3^{\frac{1}{3}} x + 3^{\frac{2}{3}}\right) - \frac{1}{162} \cdot 3^{\frac{1}{3}} \log\left({\left| x + 3^{\frac{1}{3}} \right|}\right) + \frac{10 \, x^{3} - 3}{45 \, x^{5}} - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/162*3^(5/6)*arctan(1/3*3^(1/6)*(2*x - 3^(1/3))) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/324*3^(1/3)*log(x^2 - 3^(1/3)*x + 3^(2/3)) - 1/162*3^(1/3)*log(abs(x + 3^(1/3))) + 1/45*(10*x^3 - 3)/x^5 - 1/12*log(x^2 - x + 1) + 1/6*log(abs(x + 1))","A",0
170,1,638,0,0.524924," ","integrate(x^6/(x^6-x^3+1),x, algorithm=""giac"")","-\frac{1}{9} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} - 6 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{4} + 4 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right) - 4 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{3} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) + 2 \, \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{4}{9} \, \pi\right) - 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) - \frac{1}{9} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} - 6 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{4} + 4 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right) - 4 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{3} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) + 2 \, \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{2}{9} \, \pi\right) - 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) - \frac{1}{9} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} - 6 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{4} - 4 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right) + 4 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{3} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + 2 \, \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{1}{9} \, \pi\right) + 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) - \frac{1}{18} \, {\left(4 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right) - 4 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{3} - \cos\left(\frac{4}{9} \, \pi\right)^{4} + 6 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right) - 2 \, \cos\left(\frac{4}{9} \, \pi\right)\right)} \log\left(-{\left(\sqrt{3} i \cos\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)\right)} x + x^{2} + 1\right) - \frac{1}{18} \, {\left(4 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right) - 4 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{3} - \cos\left(\frac{2}{9} \, \pi\right)^{4} + 6 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right) - 2 \, \cos\left(\frac{2}{9} \, \pi\right)\right)} \log\left(-{\left(\sqrt{3} i \cos\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)\right)} x + x^{2} + 1\right) + \frac{1}{18} \, {\left(4 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right) - 4 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{3} + \cos\left(\frac{1}{9} \, \pi\right)^{4} - 6 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{2} + \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right) - 2 \, \cos\left(\frac{1}{9} \, \pi\right)\right)} \log\left({\left(\sqrt{3} i \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} x + x^{2} + 1\right) + x"," ",0,"-1/9*(sqrt(3)*cos(4/9*pi)^4 - 6*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^2 + sqrt(3)*sin(4/9*pi)^4 + 4*cos(4/9*pi)^3*sin(4/9*pi) - 4*cos(4/9*pi)*sin(4/9*pi)^3 + 2*sqrt(3)*cos(4/9*pi) + 2*sin(4/9*pi))*arctan(-((sqrt(3)*i + 1)*cos(4/9*pi) - 2*x)/((sqrt(3)*i + 1)*sin(4/9*pi))) - 1/9*(sqrt(3)*cos(2/9*pi)^4 - 6*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^2 + sqrt(3)*sin(2/9*pi)^4 + 4*cos(2/9*pi)^3*sin(2/9*pi) - 4*cos(2/9*pi)*sin(2/9*pi)^3 + 2*sqrt(3)*cos(2/9*pi) + 2*sin(2/9*pi))*arctan(-((sqrt(3)*i + 1)*cos(2/9*pi) - 2*x)/((sqrt(3)*i + 1)*sin(2/9*pi))) - 1/9*(sqrt(3)*cos(1/9*pi)^4 - 6*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^4 - 4*cos(1/9*pi)^3*sin(1/9*pi) + 4*cos(1/9*pi)*sin(1/9*pi)^3 - 2*sqrt(3)*cos(1/9*pi) + 2*sin(1/9*pi))*arctan(((sqrt(3)*i + 1)*cos(1/9*pi) + 2*x)/((sqrt(3)*i + 1)*sin(1/9*pi))) - 1/18*(4*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi) - 4*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^3 - cos(4/9*pi)^4 + 6*cos(4/9*pi)^2*sin(4/9*pi)^2 - sin(4/9*pi)^4 + 2*sqrt(3)*sin(4/9*pi) - 2*cos(4/9*pi))*log(-(sqrt(3)*i*cos(4/9*pi) + cos(4/9*pi))*x + x^2 + 1) - 1/18*(4*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi) - 4*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^3 - cos(2/9*pi)^4 + 6*cos(2/9*pi)^2*sin(2/9*pi)^2 - sin(2/9*pi)^4 + 2*sqrt(3)*sin(2/9*pi) - 2*cos(2/9*pi))*log(-(sqrt(3)*i*cos(2/9*pi) + cos(2/9*pi))*x + x^2 + 1) + 1/18*(4*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi) - 4*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^3 + cos(1/9*pi)^4 - 6*cos(1/9*pi)^2*sin(1/9*pi)^2 + sin(1/9*pi)^4 - 2*sqrt(3)*sin(1/9*pi) - 2*cos(1/9*pi))*log((sqrt(3)*i*cos(1/9*pi) + cos(1/9*pi))*x + x^2 + 1) + x","B",0
171,1,32,0,0.433372," ","integrate(x^5/(x^6-x^3+1),x, algorithm=""giac"")","\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
172,1,824,0,0.688236," ","integrate(x^4/(x^6-x^3+1),x, algorithm=""giac"")","-\frac{1}{9} \, {\left(2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 20 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 20 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - 2 \, \sin\left(\frac{4}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{4}{9} \, \pi\right) - 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) - \frac{1}{9} \, {\left(2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 20 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 20 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - 2 \, \sin\left(\frac{2}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{2}{9} \, \pi\right) - 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) + \frac{1}{9} \, {\left(2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 20 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 20 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + 2 \, \sin\left(\frac{1}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{1}{9} \, \pi\right) + 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) - \frac{1}{18} \, {\left(10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 20 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + 2 \, \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + 2 \, \cos\left(\frac{4}{9} \, \pi\right)^{5} - 20 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 10 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left(-{\left(\sqrt{3} i \cos\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)\right)} x + x^{2} + 1\right) - \frac{1}{18} \, {\left(10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 20 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + 2 \, \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + 2 \, \cos\left(\frac{2}{9} \, \pi\right)^{5} - 20 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 10 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left(-{\left(\sqrt{3} i \cos\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)\right)} x + x^{2} + 1\right) - \frac{1}{18} \, {\left(10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 20 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + 2 \, \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - 2 \, \cos\left(\frac{1}{9} \, \pi\right)^{5} + 20 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 10 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)^{2} - \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(\sqrt{3} i \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} x + x^{2} + 1\right)"," ",0,"-1/9*(2*sqrt(3)*cos(4/9*pi)^5 - 20*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 10*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 10*cos(4/9*pi)^4*sin(4/9*pi) + 20*cos(4/9*pi)^2*sin(4/9*pi)^3 - 2*sin(4/9*pi)^5 + sqrt(3)*cos(4/9*pi)^2 - sqrt(3)*sin(4/9*pi)^2 - 2*cos(4/9*pi)*sin(4/9*pi))*arctan(-((sqrt(3)*i + 1)*cos(4/9*pi) - 2*x)/((sqrt(3)*i + 1)*sin(4/9*pi))) - 1/9*(2*sqrt(3)*cos(2/9*pi)^5 - 20*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 10*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 10*cos(2/9*pi)^4*sin(2/9*pi) + 20*cos(2/9*pi)^2*sin(2/9*pi)^3 - 2*sin(2/9*pi)^5 + sqrt(3)*cos(2/9*pi)^2 - sqrt(3)*sin(2/9*pi)^2 - 2*cos(2/9*pi)*sin(2/9*pi))*arctan(-((sqrt(3)*i + 1)*cos(2/9*pi) - 2*x)/((sqrt(3)*i + 1)*sin(2/9*pi))) + 1/9*(2*sqrt(3)*cos(1/9*pi)^5 - 20*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 10*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 10*cos(1/9*pi)^4*sin(1/9*pi) - 20*cos(1/9*pi)^2*sin(1/9*pi)^3 + 2*sin(1/9*pi)^5 - sqrt(3)*cos(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi))*arctan(((sqrt(3)*i + 1)*cos(1/9*pi) + 2*x)/((sqrt(3)*i + 1)*sin(1/9*pi))) - 1/18*(10*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 20*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + 2*sqrt(3)*sin(4/9*pi)^5 + 2*cos(4/9*pi)^5 - 20*cos(4/9*pi)^3*sin(4/9*pi)^2 + 10*cos(4/9*pi)*sin(4/9*pi)^4 + 2*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) + cos(4/9*pi)^2 - sin(4/9*pi)^2)*log(-(sqrt(3)*i*cos(4/9*pi) + cos(4/9*pi))*x + x^2 + 1) - 1/18*(10*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 20*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + 2*sqrt(3)*sin(2/9*pi)^5 + 2*cos(2/9*pi)^5 - 20*cos(2/9*pi)^3*sin(2/9*pi)^2 + 10*cos(2/9*pi)*sin(2/9*pi)^4 + 2*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) + cos(2/9*pi)^2 - sin(2/9*pi)^2)*log(-(sqrt(3)*i*cos(2/9*pi) + cos(2/9*pi))*x + x^2 + 1) - 1/18*(10*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 20*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + 2*sqrt(3)*sin(1/9*pi)^5 - 2*cos(1/9*pi)^5 + 20*cos(1/9*pi)^3*sin(1/9*pi)^2 - 10*cos(1/9*pi)*sin(1/9*pi)^4 - 2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + cos(1/9*pi)^2 - sin(1/9*pi)^2)*log((sqrt(3)*i*cos(1/9*pi) + cos(1/9*pi))*x + x^2 + 1)","B",0
173,1,637,0,0.573956," ","integrate(x^3/(x^6-x^3+1),x, algorithm=""giac"")","-\frac{1}{9} \, {\left(2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} - 12 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 2 \, \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{4} + 8 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right) - 8 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{3} + \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) + \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{4}{9} \, \pi\right) - 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) - \frac{1}{9} \, {\left(2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} - 12 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 2 \, \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{4} + 8 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right) - 8 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{3} + \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) + \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{2}{9} \, \pi\right) - 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) - \frac{1}{9} \, {\left(2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} - 12 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 2 \, \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{4} - 8 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right) + 8 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{3} - \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{1}{9} \, \pi\right) + 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) - \frac{1}{18} \, {\left(8 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right) - 8 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{3} - 2 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} + 12 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \sin\left(\frac{4}{9} \, \pi\right)^{4} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right) - \cos\left(\frac{4}{9} \, \pi\right)\right)} \log\left(-{\left(\sqrt{3} i \cos\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)\right)} x + x^{2} + 1\right) - \frac{1}{18} \, {\left(8 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right) - 8 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{3} - 2 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} + 12 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \sin\left(\frac{2}{9} \, \pi\right)^{4} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right) - \cos\left(\frac{2}{9} \, \pi\right)\right)} \log\left(-{\left(\sqrt{3} i \cos\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)\right)} x + x^{2} + 1\right) + \frac{1}{18} \, {\left(8 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right) - 8 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{3} + 2 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} - 12 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 2 \, \sin\left(\frac{1}{9} \, \pi\right)^{4} - \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right) - \cos\left(\frac{1}{9} \, \pi\right)\right)} \log\left({\left(\sqrt{3} i \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} x + x^{2} + 1\right)"," ",0,"-1/9*(2*sqrt(3)*cos(4/9*pi)^4 - 12*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^2 + 2*sqrt(3)*sin(4/9*pi)^4 + 8*cos(4/9*pi)^3*sin(4/9*pi) - 8*cos(4/9*pi)*sin(4/9*pi)^3 + sqrt(3)*cos(4/9*pi) + sin(4/9*pi))*arctan(-((sqrt(3)*i + 1)*cos(4/9*pi) - 2*x)/((sqrt(3)*i + 1)*sin(4/9*pi))) - 1/9*(2*sqrt(3)*cos(2/9*pi)^4 - 12*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^2 + 2*sqrt(3)*sin(2/9*pi)^4 + 8*cos(2/9*pi)^3*sin(2/9*pi) - 8*cos(2/9*pi)*sin(2/9*pi)^3 + sqrt(3)*cos(2/9*pi) + sin(2/9*pi))*arctan(-((sqrt(3)*i + 1)*cos(2/9*pi) - 2*x)/((sqrt(3)*i + 1)*sin(2/9*pi))) - 1/9*(2*sqrt(3)*cos(1/9*pi)^4 - 12*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^2 + 2*sqrt(3)*sin(1/9*pi)^4 - 8*cos(1/9*pi)^3*sin(1/9*pi) + 8*cos(1/9*pi)*sin(1/9*pi)^3 - sqrt(3)*cos(1/9*pi) + sin(1/9*pi))*arctan(((sqrt(3)*i + 1)*cos(1/9*pi) + 2*x)/((sqrt(3)*i + 1)*sin(1/9*pi))) - 1/18*(8*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi) - 8*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^3 - 2*cos(4/9*pi)^4 + 12*cos(4/9*pi)^2*sin(4/9*pi)^2 - 2*sin(4/9*pi)^4 + sqrt(3)*sin(4/9*pi) - cos(4/9*pi))*log(-(sqrt(3)*i*cos(4/9*pi) + cos(4/9*pi))*x + x^2 + 1) - 1/18*(8*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi) - 8*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^3 - 2*cos(2/9*pi)^4 + 12*cos(2/9*pi)^2*sin(2/9*pi)^2 - 2*sin(2/9*pi)^4 + sqrt(3)*sin(2/9*pi) - cos(2/9*pi))*log(-(sqrt(3)*i*cos(2/9*pi) + cos(2/9*pi))*x + x^2 + 1) + 1/18*(8*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi) - 8*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^3 + 2*cos(1/9*pi)^4 - 12*cos(1/9*pi)^2*sin(1/9*pi)^2 + 2*sin(1/9*pi)^4 - sqrt(3)*sin(1/9*pi) - cos(1/9*pi))*log((sqrt(3)*i*cos(1/9*pi) + cos(1/9*pi))*x + x^2 + 1)","B",0
174,1,18,0,0.494751," ","integrate(x^2/(x^6-x^3+1),x, algorithm=""giac"")","\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
175,1,812,0,0.570084," ","integrate(x/(x^6-x^3+1),x, algorithm=""giac"")","-\frac{1}{9} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - \sin\left(\frac{4}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 2 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{4}{9} \, \pi\right) - 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) - \frac{1}{9} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - \sin\left(\frac{2}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 2 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{2}{9} \, \pi\right) - 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) + \frac{1}{9} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 5 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sin\left(\frac{1}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{1}{9} \, \pi\right) + 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) - \frac{1}{18} \, {\left(5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) - \cos\left(\frac{4}{9} \, \pi\right)^{2} + \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left(-{\left(\sqrt{3} i \cos\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)\right)} x + x^{2} + 1\right) - \frac{1}{18} \, {\left(5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) - \cos\left(\frac{2}{9} \, \pi\right)^{2} + \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left(-{\left(\sqrt{3} i \cos\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)\right)} x + x^{2} + 1\right) - \frac{1}{18} \, {\left(5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - \cos\left(\frac{1}{9} \, \pi\right)^{5} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 5 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) - \cos\left(\frac{1}{9} \, \pi\right)^{2} + \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(\sqrt{3} i \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} x + x^{2} + 1\right)"," ",0,"-1/9*(sqrt(3)*cos(4/9*pi)^5 - 10*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 5*cos(4/9*pi)^4*sin(4/9*pi) + 10*cos(4/9*pi)^2*sin(4/9*pi)^3 - sin(4/9*pi)^5 - sqrt(3)*cos(4/9*pi)^2 + sqrt(3)*sin(4/9*pi)^2 + 2*cos(4/9*pi)*sin(4/9*pi))*arctan(-((sqrt(3)*i + 1)*cos(4/9*pi) - 2*x)/((sqrt(3)*i + 1)*sin(4/9*pi))) - 1/9*(sqrt(3)*cos(2/9*pi)^5 - 10*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 5*cos(2/9*pi)^4*sin(2/9*pi) + 10*cos(2/9*pi)^2*sin(2/9*pi)^3 - sin(2/9*pi)^5 - sqrt(3)*cos(2/9*pi)^2 + sqrt(3)*sin(2/9*pi)^2 + 2*cos(2/9*pi)*sin(2/9*pi))*arctan(-((sqrt(3)*i + 1)*cos(2/9*pi) - 2*x)/((sqrt(3)*i + 1)*sin(2/9*pi))) + 1/9*(sqrt(3)*cos(1/9*pi)^5 - 10*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 5*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 5*cos(1/9*pi)^4*sin(1/9*pi) - 10*cos(1/9*pi)^2*sin(1/9*pi)^3 + sin(1/9*pi)^5 + sqrt(3)*cos(1/9*pi)^2 - sqrt(3)*sin(1/9*pi)^2 + 2*cos(1/9*pi)*sin(1/9*pi))*arctan(((sqrt(3)*i + 1)*cos(1/9*pi) + 2*x)/((sqrt(3)*i + 1)*sin(1/9*pi))) - 1/18*(5*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 10*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + sqrt(3)*sin(4/9*pi)^5 + cos(4/9*pi)^5 - 10*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*cos(4/9*pi)*sin(4/9*pi)^4 - 2*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) - cos(4/9*pi)^2 + sin(4/9*pi)^2)*log(-(sqrt(3)*i*cos(4/9*pi) + cos(4/9*pi))*x + x^2 + 1) - 1/18*(5*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 10*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + sqrt(3)*sin(2/9*pi)^5 + cos(2/9*pi)^5 - 10*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*cos(2/9*pi)*sin(2/9*pi)^4 - 2*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) - cos(2/9*pi)^2 + sin(2/9*pi)^2)*log(-(sqrt(3)*i*cos(2/9*pi) + cos(2/9*pi))*x + x^2 + 1) - 1/18*(5*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 10*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + sqrt(3)*sin(1/9*pi)^5 - cos(1/9*pi)^5 + 10*cos(1/9*pi)^3*sin(1/9*pi)^2 - 5*cos(1/9*pi)*sin(1/9*pi)^4 + 2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) - cos(1/9*pi)^2 + sin(1/9*pi)^2)*log((sqrt(3)*i*cos(1/9*pi) + cos(1/9*pi))*x + x^2 + 1)","B",0
176,1,629,0,0.499377," ","integrate(1/(x^6-x^3+1),x, algorithm=""giac"")","-\frac{1}{9} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} - 6 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{4} + 4 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right) - 4 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{3} - \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) - \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{4}{9} \, \pi\right) - 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) - \frac{1}{9} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} - 6 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{4} + 4 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right) - 4 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{3} - \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) - \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{2}{9} \, \pi\right) - 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) - \frac{1}{9} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} - 6 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{4} - 4 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right) + 4 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) - \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{1}{9} \, \pi\right) + 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) - \frac{1}{18} \, {\left(4 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right) - 4 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{3} - \cos\left(\frac{4}{9} \, \pi\right)^{4} + 6 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{4} - \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)\right)} \log\left(-{\left(\sqrt{3} i \cos\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)\right)} x + x^{2} + 1\right) - \frac{1}{18} \, {\left(4 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right) - 4 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{3} - \cos\left(\frac{2}{9} \, \pi\right)^{4} + 6 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{4} - \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)\right)} \log\left(-{\left(\sqrt{3} i \cos\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)\right)} x + x^{2} + 1\right) + \frac{1}{18} \, {\left(4 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right) - 4 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{3} + \cos\left(\frac{1}{9} \, \pi\right)^{4} - 6 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{2} + \sin\left(\frac{1}{9} \, \pi\right)^{4} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} \log\left({\left(\sqrt{3} i \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} x + x^{2} + 1\right)"," ",0,"-1/9*(sqrt(3)*cos(4/9*pi)^4 - 6*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^2 + sqrt(3)*sin(4/9*pi)^4 + 4*cos(4/9*pi)^3*sin(4/9*pi) - 4*cos(4/9*pi)*sin(4/9*pi)^3 - sqrt(3)*cos(4/9*pi) - sin(4/9*pi))*arctan(-((sqrt(3)*i + 1)*cos(4/9*pi) - 2*x)/((sqrt(3)*i + 1)*sin(4/9*pi))) - 1/9*(sqrt(3)*cos(2/9*pi)^4 - 6*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^2 + sqrt(3)*sin(2/9*pi)^4 + 4*cos(2/9*pi)^3*sin(2/9*pi) - 4*cos(2/9*pi)*sin(2/9*pi)^3 - sqrt(3)*cos(2/9*pi) - sin(2/9*pi))*arctan(-((sqrt(3)*i + 1)*cos(2/9*pi) - 2*x)/((sqrt(3)*i + 1)*sin(2/9*pi))) - 1/9*(sqrt(3)*cos(1/9*pi)^4 - 6*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^4 - 4*cos(1/9*pi)^3*sin(1/9*pi) + 4*cos(1/9*pi)*sin(1/9*pi)^3 + sqrt(3)*cos(1/9*pi) - sin(1/9*pi))*arctan(((sqrt(3)*i + 1)*cos(1/9*pi) + 2*x)/((sqrt(3)*i + 1)*sin(1/9*pi))) - 1/18*(4*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi) - 4*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^3 - cos(4/9*pi)^4 + 6*cos(4/9*pi)^2*sin(4/9*pi)^2 - sin(4/9*pi)^4 - sqrt(3)*sin(4/9*pi) + cos(4/9*pi))*log(-(sqrt(3)*i*cos(4/9*pi) + cos(4/9*pi))*x + x^2 + 1) - 1/18*(4*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi) - 4*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^3 - cos(2/9*pi)^4 + 6*cos(2/9*pi)^2*sin(2/9*pi)^2 - sin(2/9*pi)^4 - sqrt(3)*sin(2/9*pi) + cos(2/9*pi))*log(-(sqrt(3)*i*cos(2/9*pi) + cos(2/9*pi))*x + x^2 + 1) + 1/18*(4*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi) - 4*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^3 + cos(1/9*pi)^4 - 6*cos(1/9*pi)^2*sin(1/9*pi)^2 + sin(1/9*pi)^4 + sqrt(3)*sin(1/9*pi) + cos(1/9*pi))*log((sqrt(3)*i*cos(1/9*pi) + cos(1/9*pi))*x + x^2 + 1)","B",0
177,1,35,0,0.351659," ","integrate(1/x/(x^6-x^3+1),x, algorithm=""giac"")","\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({\left| x \right|}\right)"," ",0,"1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1)) - 1/6*log(x^6 - x^3 + 1) + log(abs(x))","A",0
178,1,826,0,0.549708," ","integrate(1/x^2/(x^6-x^3+1),x, algorithm=""giac"")","\frac{1}{9} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - \sin\left(\frac{4}{9} \, \pi\right)^{5} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 4 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{4}{9} \, \pi\right) - 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) + \frac{1}{9} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - \sin\left(\frac{2}{9} \, \pi\right)^{5} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 4 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{2}{9} \, \pi\right) - 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) - \frac{1}{9} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 5 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sin\left(\frac{1}{9} \, \pi\right)^{5} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + 2 \, \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 4 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{1}{9} \, \pi\right) + 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) + \frac{1}{18} \, {\left(5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} + 4 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + 2 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left(-{\left(\sqrt{3} i \cos\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)\right)} x + x^{2} + 1\right) + \frac{1}{18} \, {\left(5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} + 4 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) + 2 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left(-{\left(\sqrt{3} i \cos\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)\right)} x + x^{2} + 1\right) + \frac{1}{18} \, {\left(5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - \cos\left(\frac{1}{9} \, \pi\right)^{5} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 5 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} - 4 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + 2 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(\sqrt{3} i \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} x + x^{2} + 1\right) - \frac{1}{x}"," ",0,"1/9*(sqrt(3)*cos(4/9*pi)^5 - 10*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 5*cos(4/9*pi)^4*sin(4/9*pi) + 10*cos(4/9*pi)^2*sin(4/9*pi)^3 - sin(4/9*pi)^5 + 2*sqrt(3)*cos(4/9*pi)^2 - 2*sqrt(3)*sin(4/9*pi)^2 - 4*cos(4/9*pi)*sin(4/9*pi))*arctan(-((sqrt(3)*i + 1)*cos(4/9*pi) - 2*x)/((sqrt(3)*i + 1)*sin(4/9*pi))) + 1/9*(sqrt(3)*cos(2/9*pi)^5 - 10*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 5*cos(2/9*pi)^4*sin(2/9*pi) + 10*cos(2/9*pi)^2*sin(2/9*pi)^3 - sin(2/9*pi)^5 + 2*sqrt(3)*cos(2/9*pi)^2 - 2*sqrt(3)*sin(2/9*pi)^2 - 4*cos(2/9*pi)*sin(2/9*pi))*arctan(-((sqrt(3)*i + 1)*cos(2/9*pi) - 2*x)/((sqrt(3)*i + 1)*sin(2/9*pi))) - 1/9*(sqrt(3)*cos(1/9*pi)^5 - 10*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 5*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 5*cos(1/9*pi)^4*sin(1/9*pi) - 10*cos(1/9*pi)^2*sin(1/9*pi)^3 + sin(1/9*pi)^5 - 2*sqrt(3)*cos(1/9*pi)^2 + 2*sqrt(3)*sin(1/9*pi)^2 - 4*cos(1/9*pi)*sin(1/9*pi))*arctan(((sqrt(3)*i + 1)*cos(1/9*pi) + 2*x)/((sqrt(3)*i + 1)*sin(1/9*pi))) + 1/18*(5*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 10*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + sqrt(3)*sin(4/9*pi)^5 + cos(4/9*pi)^5 - 10*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*cos(4/9*pi)*sin(4/9*pi)^4 + 4*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) + 2*cos(4/9*pi)^2 - 2*sin(4/9*pi)^2)*log(-(sqrt(3)*i*cos(4/9*pi) + cos(4/9*pi))*x + x^2 + 1) + 1/18*(5*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 10*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + sqrt(3)*sin(2/9*pi)^5 + cos(2/9*pi)^5 - 10*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*cos(2/9*pi)*sin(2/9*pi)^4 + 4*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) + 2*cos(2/9*pi)^2 - 2*sin(2/9*pi)^2)*log(-(sqrt(3)*i*cos(2/9*pi) + cos(2/9*pi))*x + x^2 + 1) + 1/18*(5*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 10*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + sqrt(3)*sin(1/9*pi)^5 - cos(1/9*pi)^5 + 10*cos(1/9*pi)^3*sin(1/9*pi)^2 - 5*cos(1/9*pi)*sin(1/9*pi)^4 - 4*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + 2*cos(1/9*pi)^2 - 2*sin(1/9*pi)^2)*log((sqrt(3)*i*cos(1/9*pi) + cos(1/9*pi))*x + x^2 + 1) - 1/x","B",0
179,1,642,0,0.551090," ","integrate(1/x^3/(x^6-x^3+1),x, algorithm=""giac"")","\frac{1}{9} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} - 6 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{4} + 4 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right) - 4 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{3} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) + 2 \, \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{4}{9} \, \pi\right) - 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) + \frac{1}{9} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} - 6 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{4} + 4 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right) - 4 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{3} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) + 2 \, \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{2}{9} \, \pi\right) - 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) + \frac{1}{9} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} - 6 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{4} - 4 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right) + 4 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{3} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + 2 \, \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{1}{9} \, \pi\right) + 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) + \frac{1}{18} \, {\left(4 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right) - 4 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{3} - \cos\left(\frac{4}{9} \, \pi\right)^{4} + 6 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right) - 2 \, \cos\left(\frac{4}{9} \, \pi\right)\right)} \log\left(-{\left(\sqrt{3} i \cos\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)\right)} x + x^{2} + 1\right) + \frac{1}{18} \, {\left(4 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right) - 4 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{3} - \cos\left(\frac{2}{9} \, \pi\right)^{4} + 6 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right) - 2 \, \cos\left(\frac{2}{9} \, \pi\right)\right)} \log\left(-{\left(\sqrt{3} i \cos\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)\right)} x + x^{2} + 1\right) - \frac{1}{18} \, {\left(4 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right) - 4 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{3} + \cos\left(\frac{1}{9} \, \pi\right)^{4} - 6 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{2} + \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right) - 2 \, \cos\left(\frac{1}{9} \, \pi\right)\right)} \log\left({\left(\sqrt{3} i \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} x + x^{2} + 1\right) - \frac{1}{2 \, x^{2}}"," ",0,"1/9*(sqrt(3)*cos(4/9*pi)^4 - 6*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^2 + sqrt(3)*sin(4/9*pi)^4 + 4*cos(4/9*pi)^3*sin(4/9*pi) - 4*cos(4/9*pi)*sin(4/9*pi)^3 + 2*sqrt(3)*cos(4/9*pi) + 2*sin(4/9*pi))*arctan(-((sqrt(3)*i + 1)*cos(4/9*pi) - 2*x)/((sqrt(3)*i + 1)*sin(4/9*pi))) + 1/9*(sqrt(3)*cos(2/9*pi)^4 - 6*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^2 + sqrt(3)*sin(2/9*pi)^4 + 4*cos(2/9*pi)^3*sin(2/9*pi) - 4*cos(2/9*pi)*sin(2/9*pi)^3 + 2*sqrt(3)*cos(2/9*pi) + 2*sin(2/9*pi))*arctan(-((sqrt(3)*i + 1)*cos(2/9*pi) - 2*x)/((sqrt(3)*i + 1)*sin(2/9*pi))) + 1/9*(sqrt(3)*cos(1/9*pi)^4 - 6*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^4 - 4*cos(1/9*pi)^3*sin(1/9*pi) + 4*cos(1/9*pi)*sin(1/9*pi)^3 - 2*sqrt(3)*cos(1/9*pi) + 2*sin(1/9*pi))*arctan(((sqrt(3)*i + 1)*cos(1/9*pi) + 2*x)/((sqrt(3)*i + 1)*sin(1/9*pi))) + 1/18*(4*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi) - 4*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^3 - cos(4/9*pi)^4 + 6*cos(4/9*pi)^2*sin(4/9*pi)^2 - sin(4/9*pi)^4 + 2*sqrt(3)*sin(4/9*pi) - 2*cos(4/9*pi))*log(-(sqrt(3)*i*cos(4/9*pi) + cos(4/9*pi))*x + x^2 + 1) + 1/18*(4*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi) - 4*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^3 - cos(2/9*pi)^4 + 6*cos(2/9*pi)^2*sin(2/9*pi)^2 - sin(2/9*pi)^4 + 2*sqrt(3)*sin(2/9*pi) - 2*cos(2/9*pi))*log(-(sqrt(3)*i*cos(2/9*pi) + cos(2/9*pi))*x + x^2 + 1) - 1/18*(4*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi) - 4*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^3 + cos(1/9*pi)^4 - 6*cos(1/9*pi)^2*sin(1/9*pi)^2 + sin(1/9*pi)^4 - 2*sqrt(3)*sin(1/9*pi) - 2*cos(1/9*pi))*log((sqrt(3)*i*cos(1/9*pi) + cos(1/9*pi))*x + x^2 + 1) - 1/2/x^2","B",0
180,1,45,0,0.417214," ","integrate(1/x^4/(x^6-x^3+1),x, algorithm=""giac"")","-\frac{1}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{3} - 1\right)}\right) - \frac{x^{3} + 1}{3 \, x^{3}} - \frac{1}{6} \, \log\left(x^{6} - x^{3} + 1\right) + \log\left({\left| x \right|}\right)"," ",0,"-1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1)) - 1/3*(x^3 + 1)/x^3 - 1/6*log(x^6 - x^3 + 1) + log(abs(x))","A",0
181,1,836,0,0.548776," ","integrate(1/x^5/(x^6-x^3+1),x, algorithm=""giac"")","\frac{1}{9} \, {\left(2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 20 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 20 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - 2 \, \sin\left(\frac{4}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{4}{9} \, \pi\right) - 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) + \frac{1}{9} \, {\left(2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 20 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 20 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - 2 \, \sin\left(\frac{2}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{2}{9} \, \pi\right) - 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) - \frac{1}{9} \, {\left(2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 20 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 20 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + 2 \, \sin\left(\frac{1}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(\sqrt{3} i + 1\right)} \cos\left(\frac{1}{9} \, \pi\right) + 2 \, x}{{\left(\sqrt{3} i + 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) + \frac{1}{18} \, {\left(10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 20 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + 2 \, \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + 2 \, \cos\left(\frac{4}{9} \, \pi\right)^{5} - 20 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 10 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left(-{\left(\sqrt{3} i \cos\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)\right)} x + x^{2} + 1\right) + \frac{1}{18} \, {\left(10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 20 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + 2 \, \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + 2 \, \cos\left(\frac{2}{9} \, \pi\right)^{5} - 20 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 10 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left(-{\left(\sqrt{3} i \cos\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)\right)} x + x^{2} + 1\right) + \frac{1}{18} \, {\left(10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 20 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + 2 \, \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - 2 \, \cos\left(\frac{1}{9} \, \pi\right)^{5} + 20 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 10 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)^{2} - \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(\sqrt{3} i \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} x + x^{2} + 1\right) - \frac{4 \, x^{3} + 1}{4 \, x^{4}}"," ",0,"1/9*(2*sqrt(3)*cos(4/9*pi)^5 - 20*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 10*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 10*cos(4/9*pi)^4*sin(4/9*pi) + 20*cos(4/9*pi)^2*sin(4/9*pi)^3 - 2*sin(4/9*pi)^5 + sqrt(3)*cos(4/9*pi)^2 - sqrt(3)*sin(4/9*pi)^2 - 2*cos(4/9*pi)*sin(4/9*pi))*arctan(-((sqrt(3)*i + 1)*cos(4/9*pi) - 2*x)/((sqrt(3)*i + 1)*sin(4/9*pi))) + 1/9*(2*sqrt(3)*cos(2/9*pi)^5 - 20*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 10*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 10*cos(2/9*pi)^4*sin(2/9*pi) + 20*cos(2/9*pi)^2*sin(2/9*pi)^3 - 2*sin(2/9*pi)^5 + sqrt(3)*cos(2/9*pi)^2 - sqrt(3)*sin(2/9*pi)^2 - 2*cos(2/9*pi)*sin(2/9*pi))*arctan(-((sqrt(3)*i + 1)*cos(2/9*pi) - 2*x)/((sqrt(3)*i + 1)*sin(2/9*pi))) - 1/9*(2*sqrt(3)*cos(1/9*pi)^5 - 20*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 10*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 10*cos(1/9*pi)^4*sin(1/9*pi) - 20*cos(1/9*pi)^2*sin(1/9*pi)^3 + 2*sin(1/9*pi)^5 - sqrt(3)*cos(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi))*arctan(((sqrt(3)*i + 1)*cos(1/9*pi) + 2*x)/((sqrt(3)*i + 1)*sin(1/9*pi))) + 1/18*(10*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 20*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + 2*sqrt(3)*sin(4/9*pi)^5 + 2*cos(4/9*pi)^5 - 20*cos(4/9*pi)^3*sin(4/9*pi)^2 + 10*cos(4/9*pi)*sin(4/9*pi)^4 + 2*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) + cos(4/9*pi)^2 - sin(4/9*pi)^2)*log(-(sqrt(3)*i*cos(4/9*pi) + cos(4/9*pi))*x + x^2 + 1) + 1/18*(10*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 20*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + 2*sqrt(3)*sin(2/9*pi)^5 + 2*cos(2/9*pi)^5 - 20*cos(2/9*pi)^3*sin(2/9*pi)^2 + 10*cos(2/9*pi)*sin(2/9*pi)^4 + 2*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) + cos(2/9*pi)^2 - sin(2/9*pi)^2)*log(-(sqrt(3)*i*cos(2/9*pi) + cos(2/9*pi))*x + x^2 + 1) + 1/18*(10*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 20*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + 2*sqrt(3)*sin(1/9*pi)^5 - 2*cos(1/9*pi)^5 + 20*cos(1/9*pi)^3*sin(1/9*pi)^2 - 10*cos(1/9*pi)*sin(1/9*pi)^4 - 2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + cos(1/9*pi)^2 - sin(1/9*pi)^2)*log((sqrt(3)*i*cos(1/9*pi) + cos(1/9*pi))*x + x^2 + 1) - 1/4*(4*x^3 + 1)/x^4","B",0
182,0,0,0,0.000000," ","integrate(1/(x^6+x^3+2),x, algorithm=""giac"")","\int \frac{1}{x^{6} + x^{3} + 2}\,{d x}"," ",0,"integrate(1/(x^6 + x^3 + 2), x)","F",0
183,1,18,0,0.503854," ","integrate(x^2/(x^6+x^3+2),x, algorithm=""giac"")","\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
184,0,0,0,0.000000," ","integrate(x^3/(x^6+x^3+2),x, algorithm=""giac"")","\int \frac{x^{3}}{x^{6} + x^{3} + 2}\,{d x}"," ",0,"integrate(x^3/(x^6 + x^3 + 2), x)","F",0
185,0,0,0,0.000000," ","integrate(x^14*(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{6} + b x^{3} + a} x^{14}\,{d x}"," ",0,"integrate(sqrt(c*x^6 + b*x^3 + a)*x^14, x)","F",0
186,0,0,0,0.000000," ","integrate(x^11*(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{6} + b x^{3} + a} x^{11}\,{d x}"," ",0,"integrate(sqrt(c*x^6 + b*x^3 + a)*x^11, x)","F",0
187,0,0,0,0.000000," ","integrate(x^8*(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{6} + b x^{3} + a} x^{8}\,{d x}"," ",0,"integrate(sqrt(c*x^6 + b*x^3 + a)*x^8, x)","F",0
188,1,98,0,0.490617," ","integrate(x^5*(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\frac{1}{72} \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, {\left(4 \, x^{3} + \frac{b}{c}\right)} x^{3} - \frac{3 \, b^{2} - 8 \, a c}{c^{2}}\right)} - \frac{{\left(b^{3} - 4 \, a b c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{3} - \sqrt{c x^{6} + b x^{3} + a}\right)} \sqrt{c} - b \right|}\right)}{48 \, c^{\frac{5}{2}}}"," ",0,"1/72*sqrt(c*x^6 + b*x^3 + a)*(2*(4*x^3 + b/c)*x^3 - (3*b^2 - 8*a*c)/c^2) - 1/48*(b^3 - 4*a*b*c)*log(abs(-2*(sqrt(c)*x^3 - sqrt(c*x^6 + b*x^3 + a))*sqrt(c) - b))/c^(5/2)","A",0
189,1,76,0,0.556323," ","integrate(x^2*(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, x^{3} + \frac{b}{c}\right)} + \frac{{\left(b^{2} - 4 \, a c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{3} - \sqrt{c x^{6} + b x^{3} + a}\right)} \sqrt{c} - b \right|}\right)}{24 \, c^{\frac{3}{2}}}"," ",0,"1/12*sqrt(c*x^6 + b*x^3 + a)*(2*x^3 + b/c) + 1/24*(b^2 - 4*a*c)*log(abs(-2*(sqrt(c)*x^3 - sqrt(c*x^6 + b*x^3 + a))*sqrt(c) - b))/c^(3/2)","A",0
190,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{6} + b x^{3} + a}}{x}\,{d x}"," ",0,"integrate(sqrt(c*x^6 + b*x^3 + a)/x, x)","F",0
191,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{6} + b x^{3} + a}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(c*x^6 + b*x^3 + a)/x^4, x)","F",0
192,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(1/2)/x^7,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{6} + b x^{3} + a}}{x^{7}}\,{d x}"," ",0,"integrate(sqrt(c*x^6 + b*x^3 + a)/x^7, x)","F",0
193,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(1/2)/x^10,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{6} + b x^{3} + a}}{x^{10}}\,{d x}"," ",0,"integrate(sqrt(c*x^6 + b*x^3 + a)/x^10, x)","F",0
194,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(1/2)/x^13,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{6} + b x^{3} + a}}{x^{13}}\,{d x}"," ",0,"integrate(sqrt(c*x^6 + b*x^3 + a)/x^13, x)","F",0
195,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(1/2)/x^16,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{6} + b x^{3} + a}}{x^{16}}\,{d x}"," ",0,"integrate(sqrt(c*x^6 + b*x^3 + a)/x^16, x)","F",0
196,0,0,0,0.000000," ","integrate(x^3*(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{6} + b x^{3} + a} x^{3}\,{d x}"," ",0,"integrate(sqrt(c*x^6 + b*x^3 + a)*x^3, x)","F",0
197,0,0,0,0.000000," ","integrate(x*(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{6} + b x^{3} + a} x\,{d x}"," ",0,"integrate(sqrt(c*x^6 + b*x^3 + a)*x, x)","F",0
198,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{6} + b x^{3} + a}\,{d x}"," ",0,"integrate(sqrt(c*x^6 + b*x^3 + a), x)","F",0
199,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{6} + b x^{3} + a}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^6 + b*x^3 + a)/x^2, x)","F",0
200,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{6} + b x^{3} + a}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(c*x^6 + b*x^3 + a)/x^3, x)","F",0
201,0,0,0,0.000000," ","integrate(x^14*(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}} x^{14}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2)*x^14, x)","F",0
202,0,0,0,0.000000," ","integrate(x^11*(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}} x^{11}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2)*x^11, x)","F",0
203,0,0,0,0.000000," ","integrate(x^8*(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}} x^{8}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2)*x^8, x)","F",0
204,1,172,0,0.561200," ","integrate(x^5*(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\frac{1}{1920} \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, c x^{3} + 11 \, b\right)} x^{3} + \frac{b^{2} c^{3} + 32 \, a c^{4}}{c^{4}}\right)} x^{3} - \frac{5 \, b^{3} c^{2} - 28 \, a b c^{3}}{c^{4}}\right)} x^{3} + \frac{15 \, b^{4} c - 100 \, a b^{2} c^{2} + 128 \, a^{2} c^{3}}{c^{4}}\right)} + \frac{{\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{3} - \sqrt{c x^{6} + b x^{3} + a}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{7}{2}}}"," ",0,"1/1920*sqrt(c*x^6 + b*x^3 + a)*(2*(4*(2*(8*c*x^3 + 11*b)*x^3 + (b^2*c^3 + 32*a*c^4)/c^4)*x^3 - (5*b^3*c^2 - 28*a*b*c^3)/c^4)*x^3 + (15*b^4*c - 100*a*b^2*c^2 + 128*a^2*c^3)/c^4) + 1/256*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*log(abs(-2*(sqrt(c)*x^3 - sqrt(c*x^6 + b*x^3 + a))*sqrt(c) - b))/c^(7/2)","A",0
205,1,135,0,0.610980," ","integrate(x^2*(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, {\left(4 \, {\left(2 \, c x^{3} + 3 \, b\right)} x^{3} + \frac{b^{2} c^{2} + 20 \, a c^{3}}{c^{3}}\right)} x^{3} - \frac{3 \, b^{3} c - 20 \, a b c^{2}}{c^{3}}\right)} - \frac{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{3} - \sqrt{c x^{6} + b x^{3} + a}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{5}{2}}}"," ",0,"1/192*sqrt(c*x^6 + b*x^3 + a)*(2*(4*(2*c*x^3 + 3*b)*x^3 + (b^2*c^2 + 20*a*c^3)/c^3)*x^3 - (3*b^3*c - 20*a*b*c^2)/c^3) - 1/128*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*log(abs(-2*(sqrt(c)*x^3 - sqrt(c*x^6 + b*x^3 + a))*sqrt(c) - b))/c^(5/2)","A",0
206,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(3/2)/x,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2)/x, x)","F",0
207,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^4,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2)/x^4, x)","F",0
208,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^7,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}{x^{7}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2)/x^7, x)","F",0
209,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^10,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}{x^{10}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2)/x^10, x)","F",0
210,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^13,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}{x^{13}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2)/x^13, x)","F",0
211,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^16,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}{x^{16}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2)/x^16, x)","F",0
212,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^19,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}{x^{19}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2)/x^19, x)","F",0
213,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^22,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}{x^{22}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2)/x^22, x)","F",0
214,0,0,0,0.000000," ","integrate(x^3*(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}} x^{3}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2)*x^3, x)","F",0
215,0,0,0,0.000000," ","integrate(x*(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}} x\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2)*x, x)","F",0
216,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2), x)","F",0
217,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2)/x^2, x)","F",0
218,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^3,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2)/x^3, x)","F",0
219,0,0,0,0.000000," ","integrate(x^14/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{14}}{\sqrt{c x^{6} + b x^{3} + a}}\,{d x}"," ",0,"integrate(x^14/sqrt(c*x^6 + b*x^3 + a), x)","F",0
220,0,0,0,0.000000," ","integrate(x^11/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{11}}{\sqrt{c x^{6} + b x^{3} + a}}\,{d x}"," ",0,"integrate(x^11/sqrt(c*x^6 + b*x^3 + a), x)","F",0
221,0,0,0,0.000000," ","integrate(x^8/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{8}}{\sqrt{c x^{6} + b x^{3} + a}}\,{d x}"," ",0,"integrate(x^8/sqrt(c*x^6 + b*x^3 + a), x)","F",0
222,1,61,0,0.674360," ","integrate(x^5/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\frac{b \log\left({\left| -2 \, {\left(\sqrt{c} x^{3} - \sqrt{c x^{6} + b x^{3} + a}\right)} \sqrt{c} - b \right|}\right)}{6 \, c^{\frac{3}{2}}} + \frac{\sqrt{c x^{6} + b x^{3} + a}}{3 \, c}"," ",0,"1/6*b*log(abs(-2*(sqrt(c)*x^3 - sqrt(c*x^6 + b*x^3 + a))*sqrt(c) - b))/c^(3/2) + 1/3*sqrt(c*x^6 + b*x^3 + a)/c","A",0
223,1,40,0,0.676051," ","integrate(x^2/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -2 \, {\left(\sqrt{c} x^{3} - \sqrt{c x^{6} + b x^{3} + a}\right)} \sqrt{c} - b \right|}\right)}{3 \, \sqrt{c}}"," ",0,"-1/3*log(abs(-2*(sqrt(c)*x^3 - sqrt(c*x^6 + b*x^3 + a))*sqrt(c) - b))/sqrt(c)","A",0
224,0,0,0,0.000000," ","integrate(1/x/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{6} + b x^{3} + a} x}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^6 + b*x^3 + a)*x), x)","F",0
225,0,0,0,0.000000," ","integrate(1/x^4/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{6} + b x^{3} + a} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^6 + b*x^3 + a)*x^4), x)","F",0
226,0,0,0,0.000000," ","integrate(1/x^7/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{6} + b x^{3} + a} x^{7}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^6 + b*x^3 + a)*x^7), x)","F",0
227,0,0,0,0.000000," ","integrate(1/x^10/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{6} + b x^{3} + a} x^{10}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^6 + b*x^3 + a)*x^10), x)","F",0
228,0,0,0,0.000000," ","integrate(1/x^13/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{6} + b x^{3} + a} x^{13}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^6 + b*x^3 + a)*x^13), x)","F",0
229,0,0,0,0.000000," ","integrate(x^3/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{3}}{\sqrt{c x^{6} + b x^{3} + a}}\,{d x}"," ",0,"integrate(x^3/sqrt(c*x^6 + b*x^3 + a), x)","F",0
230,0,0,0,0.000000," ","integrate(x/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{c x^{6} + b x^{3} + a}}\,{d x}"," ",0,"integrate(x/sqrt(c*x^6 + b*x^3 + a), x)","F",0
231,0,0,0,0.000000," ","integrate(1/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{6} + b x^{3} + a}}\,{d x}"," ",0,"integrate(1/sqrt(c*x^6 + b*x^3 + a), x)","F",0
232,0,0,0,0.000000," ","integrate(1/x^2/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{6} + b x^{3} + a} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^6 + b*x^3 + a)*x^2), x)","F",0
233,0,0,0,0.000000," ","integrate(1/x^3/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{6} + b x^{3} + a} x^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^6 + b*x^3 + a)*x^3), x)","F",0
234,0,0,0,0.000000," ","integrate(x^14/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{14}}{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^14/(c*x^6 + b*x^3 + a)^(3/2), x)","F",0
235,0,0,0,0.000000," ","integrate(x^11/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{11}}{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^11/(c*x^6 + b*x^3 + a)^(3/2), x)","F",0
236,0,0,0,0.000000," ","integrate(x^8/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{8}}{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^8/(c*x^6 + b*x^3 + a)^(3/2), x)","F",0
237,1,45,0,1.321374," ","integrate(x^5/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{b x^{3}}{b^{2} - 4 \, a c} + \frac{2 \, a}{b^{2} - 4 \, a c}\right)}}{3 \, \sqrt{c x^{6} + b x^{3} + a}}"," ",0,"2/3*(b*x^3/(b^2 - 4*a*c) + 2*a/(b^2 - 4*a*c))/sqrt(c*x^6 + b*x^3 + a)","A",0
238,1,45,0,1.407277," ","integrate(x^2/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{2 \, c x^{3}}{b^{2} - 4 \, a c} + \frac{b}{b^{2} - 4 \, a c}\right)}}{3 \, \sqrt{c x^{6} + b x^{3} + a}}"," ",0,"-2/3*(2*c*x^3/(b^2 - 4*a*c) + b/(b^2 - 4*a*c))/sqrt(c*x^6 + b*x^3 + a)","A",0
239,0,0,0,0.000000," ","integrate(1/x/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(1/((c*x^6 + b*x^3 + a)^(3/2)*x), x)","F",0
240,0,0,0,0.000000," ","integrate(1/x^4/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate(1/((c*x^6 + b*x^3 + a)^(3/2)*x^4), x)","F",0
241,0,0,0,0.000000," ","integrate(1/x^7/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}} x^{7}}\,{d x}"," ",0,"integrate(1/((c*x^6 + b*x^3 + a)^(3/2)*x^7), x)","F",0
242,0,0,0,0.000000," ","integrate(1/x^10/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}} x^{10}}\,{d x}"," ",0,"integrate(1/((c*x^6 + b*x^3 + a)^(3/2)*x^10), x)","F",0
243,0,0,0,0.000000," ","integrate(x^3/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^3/(c*x^6 + b*x^3 + a)^(3/2), x)","F",0
244,0,0,0,0.000000," ","integrate(x/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{x}{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/(c*x^6 + b*x^3 + a)^(3/2), x)","F",0
245,0,0,0,0.000000," ","integrate(1/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(-3/2), x)","F",0
246,0,0,0,0.000000," ","integrate(1/x^2/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((c*x^6 + b*x^3 + a)^(3/2)*x^2), x)","F",0
247,0,0,0,0.000000," ","integrate(1/x^3/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(1/((c*x^6 + b*x^3 + a)^(3/2)*x^3), x)","F",0
248,1,449,0,0.465453," ","integrate((d*x)^m*(c*x^6+b*x^3+a)^2,x, algorithm=""giac"")","\frac{\left(d x\right)^{m} c^{2} m^{4} x^{13} + 22 \, \left(d x\right)^{m} c^{2} m^{3} x^{13} + 159 \, \left(d x\right)^{m} c^{2} m^{2} x^{13} + 2 \, \left(d x\right)^{m} b c m^{4} x^{10} + 418 \, \left(d x\right)^{m} c^{2} m x^{13} + 50 \, \left(d x\right)^{m} b c m^{3} x^{10} + 280 \, \left(d x\right)^{m} c^{2} x^{13} + 390 \, \left(d x\right)^{m} b c m^{2} x^{10} + \left(d x\right)^{m} b^{2} m^{4} x^{7} + 2 \, \left(d x\right)^{m} a c m^{4} x^{7} + 1070 \, \left(d x\right)^{m} b c m x^{10} + 28 \, \left(d x\right)^{m} b^{2} m^{3} x^{7} + 56 \, \left(d x\right)^{m} a c m^{3} x^{7} + 728 \, \left(d x\right)^{m} b c x^{10} + 249 \, \left(d x\right)^{m} b^{2} m^{2} x^{7} + 498 \, \left(d x\right)^{m} a c m^{2} x^{7} + 2 \, \left(d x\right)^{m} a b m^{4} x^{4} + 742 \, \left(d x\right)^{m} b^{2} m x^{7} + 1484 \, \left(d x\right)^{m} a c m x^{7} + 62 \, \left(d x\right)^{m} a b m^{3} x^{4} + 520 \, \left(d x\right)^{m} b^{2} x^{7} + 1040 \, \left(d x\right)^{m} a c x^{7} + 642 \, \left(d x\right)^{m} a b m^{2} x^{4} + \left(d x\right)^{m} a^{2} m^{4} x + 2402 \, \left(d x\right)^{m} a b m x^{4} + 34 \, \left(d x\right)^{m} a^{2} m^{3} x + 1820 \, \left(d x\right)^{m} a b x^{4} + 411 \, \left(d x\right)^{m} a^{2} m^{2} x + 2074 \, \left(d x\right)^{m} a^{2} m x + 3640 \, \left(d x\right)^{m} a^{2} x}{m^{5} + 35 \, m^{4} + 445 \, m^{3} + 2485 \, m^{2} + 5714 \, m + 3640}"," ",0,"((d*x)^m*c^2*m^4*x^13 + 22*(d*x)^m*c^2*m^3*x^13 + 159*(d*x)^m*c^2*m^2*x^13 + 2*(d*x)^m*b*c*m^4*x^10 + 418*(d*x)^m*c^2*m*x^13 + 50*(d*x)^m*b*c*m^3*x^10 + 280*(d*x)^m*c^2*x^13 + 390*(d*x)^m*b*c*m^2*x^10 + (d*x)^m*b^2*m^4*x^7 + 2*(d*x)^m*a*c*m^4*x^7 + 1070*(d*x)^m*b*c*m*x^10 + 28*(d*x)^m*b^2*m^3*x^7 + 56*(d*x)^m*a*c*m^3*x^7 + 728*(d*x)^m*b*c*x^10 + 249*(d*x)^m*b^2*m^2*x^7 + 498*(d*x)^m*a*c*m^2*x^7 + 2*(d*x)^m*a*b*m^4*x^4 + 742*(d*x)^m*b^2*m*x^7 + 1484*(d*x)^m*a*c*m*x^7 + 62*(d*x)^m*a*b*m^3*x^4 + 520*(d*x)^m*b^2*x^7 + 1040*(d*x)^m*a*c*x^7 + 642*(d*x)^m*a*b*m^2*x^4 + (d*x)^m*a^2*m^4*x + 2402*(d*x)^m*a*b*m*x^4 + 34*(d*x)^m*a^2*m^3*x + 1820*(d*x)^m*a*b*x^4 + 411*(d*x)^m*a^2*m^2*x + 2074*(d*x)^m*a^2*m*x + 3640*(d*x)^m*a^2*x)/(m^5 + 35*m^4 + 445*m^3 + 2485*m^2 + 5714*m + 3640)","B",0
249,1,119,0,0.346378," ","integrate((d*x)^m*(c*x^6+b*x^3+a),x, algorithm=""giac"")","\frac{\left(d x\right)^{m} c m^{2} x^{7} + 5 \, \left(d x\right)^{m} c m x^{7} + 4 \, \left(d x\right)^{m} c x^{7} + \left(d x\right)^{m} b m^{2} x^{4} + 8 \, \left(d x\right)^{m} b m x^{4} + 7 \, \left(d x\right)^{m} b x^{4} + \left(d x\right)^{m} a m^{2} x + 11 \, \left(d x\right)^{m} a m x + 28 \, \left(d x\right)^{m} a x}{m^{3} + 12 \, m^{2} + 39 \, m + 28}"," ",0,"((d*x)^m*c*m^2*x^7 + 5*(d*x)^m*c*m*x^7 + 4*(d*x)^m*c*x^7 + (d*x)^m*b*m^2*x^4 + 8*(d*x)^m*b*m*x^4 + 7*(d*x)^m*b*x^4 + (d*x)^m*a*m^2*x + 11*(d*x)^m*a*m*x + 28*(d*x)^m*a*x)/(m^3 + 12*m^2 + 39*m + 28)","B",0
250,0,0,0,0.000000," ","integrate((d*x)^m/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{c x^{6} + b x^{3} + a}\,{d x}"," ",0,"integrate((d*x)^m/(c*x^6 + b*x^3 + a), x)","F",0
251,0,0,0,0.000000," ","integrate((d*x)^m/(c*x^6+b*x^3+a)^2,x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(c x^{6} + b x^{3} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x)^m/(c*x^6 + b*x^3 + a)^2, x)","F",0
252,0,0,0,0.000000," ","integrate((d*x)^m*(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^(3/2)*(d*x)^m, x)","F",0
253,0,0,0,0.000000," ","integrate((d*x)^m*(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{6} + b x^{3} + a} \left(d x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(c*x^6 + b*x^3 + a)*(d*x)^m, x)","F",0
254,0,0,0,0.000000," ","integrate((d*x)^m/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{\sqrt{c x^{6} + b x^{3} + a}}\,{d x}"," ",0,"integrate((d*x)^m/sqrt(c*x^6 + b*x^3 + a), x)","F",0
255,0,0,0,0.000000," ","integrate((d*x)^m/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*x)^m/(c*x^6 + b*x^3 + a)^(3/2), x)","F",0
256,0,0,0,0.000000," ","integrate((d*x)^m*(c*x^6+b*x^3+a)^p,x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)}^{p} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^p*(d*x)^m, x)","F",0
257,0,0,0,0.000000," ","integrate(x^8*(c*x^6+b*x^3+a)^p,x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)}^{p} x^{8}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^p*x^8, x)","F",0
258,0,0,0,0.000000," ","integrate(x^5*(c*x^6+b*x^3+a)^p,x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)}^{p} x^{5}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^p*x^5, x)","F",0
259,0,0,0,0.000000," ","integrate(x^2*(c*x^6+b*x^3+a)^p,x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)}^{p} x^{2}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^p*x^2, x)","F",0
260,0,0,0,0.000000," ","integrate(x^4*(c*x^6+b*x^3+a)^p,x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)}^{p} x^{4}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^p*x^4, x)","F",0
261,0,0,0,0.000000," ","integrate(x^3*(c*x^6+b*x^3+a)^p,x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)}^{p} x^{3}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^p*x^3, x)","F",0
262,0,0,0,0.000000," ","integrate(x*(c*x^6+b*x^3+a)^p,x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)}^{p} x\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^p*x, x)","F",0
263,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^p,x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)}^{p}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^p, x)","F",0
264,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^p/x,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{p}}{x}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^p/x, x)","F",0
265,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^p/x^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^p/x^2, x)","F",0
266,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^p/x^3,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{p}}{x^{3}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^p/x^3, x)","F",0
267,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^p/x^4,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{p}}{x^{4}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^p/x^4, x)","F",0
268,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^p/x^5,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{p}}{x^{5}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^p/x^5, x)","F",0
269,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^p/x^6,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{p}}{x^{6}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^p/x^6, x)","F",0
270,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)^p/x^7,x, algorithm=""giac"")","\int \frac{{\left(c x^{6} + b x^{3} + a\right)}^{p}}{x^{7}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)^p/x^7, x)","F",0
271,0,0,0,0.000000," ","integrate(x^m/(x^8+2*x^4+1),x, algorithm=""giac"")","\int \frac{x^{m}}{x^{8} + 2 \, x^{4} + 1}\,{d x}"," ",0,"integrate(x^m/(x^8 + 2*x^4 + 1), x)","F",0
272,1,24,0,0.340380," ","integrate(x^9/(x^8+2*x^4+1),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + \frac{x^{2}}{4 \, {\left(x^{4} + 1\right)}} - \frac{3}{4} \, \arctan\left(x^{2}\right)"," ",0,"1/2*x^2 + 1/4*x^2/(x^4 + 1) - 3/4*arctan(x^2)","A",0
273,1,18,0,0.279205," ","integrate(x^7/(x^8+2*x^4+1),x, algorithm=""giac"")","\frac{1}{4 \, {\left(x^{4} + 1\right)}} + \frac{1}{4} \, \log\left(x^{4} + 1\right)"," ",0,"1/4/(x^4 + 1) + 1/4*log(x^4 + 1)","A",0
274,1,19,0,0.371902," ","integrate(x^5/(x^8+2*x^4+1),x, algorithm=""giac"")","-\frac{x^{2}}{4 \, {\left(x^{4} + 1\right)}} + \frac{1}{4} \, \arctan\left(x^{2}\right)"," ",0,"-1/4*x^2/(x^4 + 1) + 1/4*arctan(x^2)","A",0
275,1,9,0,0.355315," ","integrate(x^3/(x^8+2*x^4+1),x, algorithm=""giac"")","-\frac{1}{4 \, {\left(x^{4} + 1\right)}}"," ",0,"-1/4/(x^4 + 1)","A",0
276,1,19,0,0.392055," ","integrate(x/(x^8+2*x^4+1),x, algorithm=""giac"")","\frac{x^{2}}{4 \, {\left(x^{4} + 1\right)}} + \frac{1}{4} \, \arctan\left(x^{2}\right)"," ",0,"1/4*x^2/(x^4 + 1) + 1/4*arctan(x^2)","A",0
277,1,29,0,0.360545," ","integrate(1/x/(x^8+2*x^4+1),x, algorithm=""giac"")","\frac{x^{4} + 2}{4 \, {\left(x^{4} + 1\right)}} - \frac{1}{4} \, \log\left(x^{4} + 1\right) + \frac{1}{4} \, \log\left(x^{4}\right)"," ",0,"1/4*(x^4 + 2)/(x^4 + 1) - 1/4*log(x^4 + 1) + 1/4*log(x^4)","A",0
278,1,25,0,0.335381," ","integrate(1/x^3/(x^8+2*x^4+1),x, algorithm=""giac"")","-\frac{3 \, x^{4} + 2}{4 \, {\left(x^{6} + x^{2}\right)}} - \frac{3}{4} \, \arctan\left(x^{2}\right)"," ",0,"-1/4*(3*x^4 + 2)/(x^6 + x^2) - 3/4*arctan(x^2)","A",0
279,1,33,0,0.354867," ","integrate(1/x^5/(x^8+2*x^4+1),x, algorithm=""giac"")","-\frac{2 \, x^{4} + 1}{4 \, {\left(x^{8} + x^{4}\right)}} + \frac{1}{2} \, \log\left(x^{4} + 1\right) - \frac{1}{2} \, \log\left(x^{4}\right)"," ",0,"-1/4*(2*x^4 + 1)/(x^8 + x^4) + 1/2*log(x^4 + 1) - 1/2*log(x^4)","A",0
280,1,31,0,0.296091," ","integrate(1/x^7/(x^8+2*x^4+1),x, algorithm=""giac"")","\frac{x^{2}}{4 \, {\left(x^{4} + 1\right)}} + \frac{6 \, x^{4} - 1}{6 \, x^{6}} + \frac{5}{4} \, \arctan\left(x^{2}\right)"," ",0,"1/4*x^2/(x^4 + 1) + 1/6*(6*x^4 - 1)/x^6 + 5/4*arctan(x^2)","A",0
281,1,83,0,0.339039," ","integrate(x^8/(x^8+2*x^4+1),x, algorithm=""giac"")","-\frac{5}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) - \frac{5}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) - \frac{5}{32} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) + \frac{5}{32} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) + x + \frac{x}{4 \, {\left(x^{4} + 1\right)}}"," ",0,"-5/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) - 5/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) - 5/32*sqrt(2)*log(x^2 + sqrt(2)*x + 1) + 5/32*sqrt(2)*log(x^2 - sqrt(2)*x + 1) + x + 1/4*x/(x^4 + 1)","A",0
282,1,84,0,0.293062," ","integrate(x^6/(x^8+2*x^4+1),x, algorithm=""giac"")","-\frac{x^{3}}{4 \, {\left(x^{4} + 1\right)}} + \frac{3}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{3}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) - \frac{3}{32} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) + \frac{3}{32} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right)"," ",0,"-1/4*x^3/(x^4 + 1) + 3/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 3/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) - 3/32*sqrt(2)*log(x^2 + sqrt(2)*x + 1) + 3/32*sqrt(2)*log(x^2 - sqrt(2)*x + 1)","A",0
283,1,82,0,0.356593," ","integrate(x^4/(x^8+2*x^4+1),x, algorithm=""giac"")","\frac{1}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{1}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) + \frac{1}{32} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{1}{32} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) - \frac{x}{4 \, {\left(x^{4} + 1\right)}}"," ",0,"1/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 1/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) + 1/32*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 1/32*sqrt(2)*log(x^2 - sqrt(2)*x + 1) - 1/4*x/(x^4 + 1)","A",0
284,1,84,0,0.345411," ","integrate(x^2/(x^8+2*x^4+1),x, algorithm=""giac"")","\frac{x^{3}}{4 \, {\left(x^{4} + 1\right)}} + \frac{1}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{1}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) - \frac{1}{32} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) + \frac{1}{32} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right)"," ",0,"1/4*x^3/(x^4 + 1) + 1/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 1/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) - 1/32*sqrt(2)*log(x^2 + sqrt(2)*x + 1) + 1/32*sqrt(2)*log(x^2 - sqrt(2)*x + 1)","A",0
285,1,82,0,0.335863," ","integrate(1/(x^8+2*x^4+1),x, algorithm=""giac"")","\frac{3}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{3}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) + \frac{3}{32} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{3}{32} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) + \frac{x}{4 \, {\left(x^{4} + 1\right)}}"," ",0,"3/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 3/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) + 3/32*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 3/32*sqrt(2)*log(x^2 - sqrt(2)*x + 1) + 1/4*x/(x^4 + 1)","A",0
286,1,88,0,0.357770," ","integrate(1/x^2/(x^8+2*x^4+1),x, algorithm=""giac"")","-\frac{5}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) - \frac{5}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) + \frac{5}{32} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{5}{32} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) - \frac{5 \, x^{4} + 4}{4 \, {\left(x^{5} + x\right)}}"," ",0,"-5/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) - 5/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) + 5/32*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 5/32*sqrt(2)*log(x^2 - sqrt(2)*x + 1) - 1/4*(5*x^4 + 4)/(x^5 + x)","A",0
287,1,87,0,0.442886," ","integrate(1/x^4/(x^8+2*x^4+1),x, algorithm=""giac"")","-\frac{7}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) - \frac{7}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) - \frac{7}{32} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) + \frac{7}{32} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) - \frac{x}{4 \, {\left(x^{4} + 1\right)}} - \frac{1}{3 \, x^{3}}"," ",0,"-7/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) - 7/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) - 7/32*sqrt(2)*log(x^2 + sqrt(2)*x + 1) + 7/32*sqrt(2)*log(x^2 - sqrt(2)*x + 1) - 1/4*x/(x^4 + 1) - 1/3/x^3","A",0
288,1,96,0,0.297177," ","integrate(1/x^6/(x^8+2*x^4+1),x, algorithm=""giac"")","\frac{x^{3}}{4 \, {\left(x^{4} + 1\right)}} + \frac{9}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{9}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) - \frac{9}{32} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) + \frac{9}{32} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) + \frac{10 \, x^{4} - 1}{5 \, x^{5}}"," ",0,"1/4*x^3/(x^4 + 1) + 9/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 9/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) - 9/32*sqrt(2)*log(x^2 + sqrt(2)*x + 1) + 9/32*sqrt(2)*log(x^2 - sqrt(2)*x + 1) + 1/5*(10*x^4 - 1)/x^5","A",0
289,1,94,0,0.364040," ","integrate(1/x^8/(x^8+2*x^4+1),x, algorithm=""giac"")","\frac{11}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{11}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) + \frac{11}{32} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{11}{32} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) + \frac{x}{4 \, {\left(x^{4} + 1\right)}} + \frac{14 \, x^{4} - 3}{21 \, x^{7}}"," ",0,"11/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 11/16*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) + 11/32*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 11/32*sqrt(2)*log(x^2 - sqrt(2)*x + 1) + 1/4*x/(x^4 + 1) + 1/21*(14*x^4 - 3)/x^7","A",0
290,0,0,0,0.000000," ","integrate(x^m/(x^8-2*x^4+1),x, algorithm=""giac"")","\int \frac{x^{m}}{x^{8} - 2 \, x^{4} + 1}\,{d x}"," ",0,"integrate(x^m/(x^8 - 2*x^4 + 1), x)","F",0
291,1,35,0,0.326126," ","integrate(x^9/(x^8-2*x^4+1),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - \frac{x^{2}}{4 \, {\left(x^{4} - 1\right)}} - \frac{3}{8} \, \log\left(x^{2} + 1\right) + \frac{3}{8} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"1/2*x^2 - 1/4*x^2/(x^4 - 1) - 3/8*log(x^2 + 1) + 3/8*log(abs(x^2 - 1))","A",0
292,1,19,0,0.410336," ","integrate(x^7/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{1}{4 \, {\left(x^{4} - 1\right)}} + \frac{1}{4} \, \log\left({\left| x^{4} - 1 \right|}\right)"," ",0,"-1/4/(x^4 - 1) + 1/4*log(abs(x^4 - 1))","A",0
293,1,30,0,0.496471," ","integrate(x^5/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{x^{2}}{4 \, {\left(x^{4} - 1\right)}} - \frac{1}{8} \, \log\left(x^{2} + 1\right) + \frac{1}{8} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"-1/4*x^2/(x^4 - 1) - 1/8*log(x^2 + 1) + 1/8*log(abs(x^2 - 1))","A",0
294,1,9,0,0.499343," ","integrate(x^3/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{1}{4 \, {\left(x^{4} - 1\right)}}"," ",0,"-1/4/(x^4 - 1)","A",0
295,1,30,0,0.471184," ","integrate(x/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{x^{2}}{4 \, {\left(x^{4} - 1\right)}} + \frac{1}{8} \, \log\left(x^{2} + 1\right) - \frac{1}{8} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"-1/4*x^2/(x^4 - 1) + 1/8*log(x^2 + 1) - 1/8*log(abs(x^2 - 1))","A",0
296,1,30,0,0.380508," ","integrate(1/x/(x^8-2*x^4+1),x, algorithm=""giac"")","\frac{x^{4} - 2}{4 \, {\left(x^{4} - 1\right)}} + \frac{1}{4} \, \log\left(x^{4}\right) - \frac{1}{4} \, \log\left({\left| x^{4} - 1 \right|}\right)"," ",0,"1/4*(x^4 - 2)/(x^4 - 1) + 1/4*log(x^4) - 1/4*log(abs(x^4 - 1))","A",0
297,1,38,0,0.413845," ","integrate(1/x^3/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{3 \, x^{4} - 2}{4 \, {\left(x^{6} - x^{2}\right)}} + \frac{3}{8} \, \log\left(x^{2} + 1\right) - \frac{3}{8} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"-1/4*(3*x^4 - 2)/(x^6 - x^2) + 3/8*log(x^2 + 1) - 3/8*log(abs(x^2 - 1))","A",0
298,1,36,0,0.452593," ","integrate(1/x^5/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{2 \, x^{4} - 1}{4 \, {\left(x^{8} - x^{4}\right)}} + \frac{1}{2} \, \log\left(x^{4}\right) - \frac{1}{2} \, \log\left({\left| x^{4} - 1 \right|}\right)"," ",0,"-1/4*(2*x^4 - 1)/(x^8 - x^4) + 1/2*log(x^4) - 1/2*log(abs(x^4 - 1))","A",0
299,1,42,0,0.328304," ","integrate(1/x^7/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{x^{2}}{4 \, {\left(x^{4} - 1\right)}} - \frac{6 \, x^{4} + 1}{6 \, x^{6}} + \frac{5}{8} \, \log\left(x^{2} + 1\right) - \frac{5}{8} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"-1/4*x^2/(x^4 - 1) - 1/6*(6*x^4 + 1)/x^6 + 5/8*log(x^2 + 1) - 5/8*log(abs(x^2 - 1))","A",0
300,1,30,0,0.279852," ","integrate(x^8/(x^8-2*x^4+1),x, algorithm=""giac"")","x - \frac{x}{4 \, {\left(x^{4} - 1\right)}} - \frac{5}{8} \, \arctan\left(x\right) - \frac{5}{16} \, \log\left({\left| x + 1 \right|}\right) + \frac{5}{16} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"x - 1/4*x/(x^4 - 1) - 5/8*arctan(x) - 5/16*log(abs(x + 1)) + 5/16*log(abs(x - 1))","A",0
301,1,31,0,0.399680," ","integrate(x^6/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{x^{3}}{4 \, {\left(x^{4} - 1\right)}} + \frac{3}{8} \, \arctan\left(x\right) - \frac{3}{16} \, \log\left({\left| x + 1 \right|}\right) + \frac{3}{16} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/4*x^3/(x^4 - 1) + 3/8*arctan(x) - 3/16*log(abs(x + 1)) + 3/16*log(abs(x - 1))","A",0
302,1,29,0,0.511535," ","integrate(x^4/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{x}{4 \, {\left(x^{4} - 1\right)}} - \frac{1}{8} \, \arctan\left(x\right) - \frac{1}{16} \, \log\left({\left| x + 1 \right|}\right) + \frac{1}{16} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/4*x/(x^4 - 1) - 1/8*arctan(x) - 1/16*log(abs(x + 1)) + 1/16*log(abs(x - 1))","A",0
303,1,31,0,0.335298," ","integrate(x^2/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{x^{3}}{4 \, {\left(x^{4} - 1\right)}} - \frac{1}{8} \, \arctan\left(x\right) + \frac{1}{16} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{16} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/4*x^3/(x^4 - 1) - 1/8*arctan(x) + 1/16*log(abs(x + 1)) - 1/16*log(abs(x - 1))","A",0
304,1,29,0,0.365673," ","integrate(1/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{x}{4 \, {\left(x^{4} - 1\right)}} + \frac{3}{8} \, \arctan\left(x\right) + \frac{3}{16} \, \log\left({\left| x + 1 \right|}\right) - \frac{3}{16} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/4*x/(x^4 - 1) + 3/8*arctan(x) + 3/16*log(abs(x + 1)) - 3/16*log(abs(x - 1))","A",0
305,1,37,0,0.374571," ","integrate(1/x^2/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{5 \, x^{4} - 4}{4 \, {\left(x^{5} - x\right)}} - \frac{5}{8} \, \arctan\left(x\right) + \frac{5}{16} \, \log\left({\left| x + 1 \right|}\right) - \frac{5}{16} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/4*(5*x^4 - 4)/(x^5 - x) - 5/8*arctan(x) + 5/16*log(abs(x + 1)) - 5/16*log(abs(x - 1))","A",0
306,1,34,0,0.457074," ","integrate(1/x^4/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{x}{4 \, {\left(x^{4} - 1\right)}} - \frac{1}{3 \, x^{3}} + \frac{7}{8} \, \arctan\left(x\right) + \frac{7}{16} \, \log\left({\left| x + 1 \right|}\right) - \frac{7}{16} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/4*x/(x^4 - 1) - 1/3/x^3 + 7/8*arctan(x) + 7/16*log(abs(x + 1)) - 7/16*log(abs(x - 1))","A",0
307,1,43,0,0.450842," ","integrate(1/x^6/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{x^{3}}{4 \, {\left(x^{4} - 1\right)}} - \frac{10 \, x^{4} + 1}{5 \, x^{5}} - \frac{9}{8} \, \arctan\left(x\right) + \frac{9}{16} \, \log\left({\left| x + 1 \right|}\right) - \frac{9}{16} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/4*x^3/(x^4 - 1) - 1/5*(10*x^4 + 1)/x^5 - 9/8*arctan(x) + 9/16*log(abs(x + 1)) - 9/16*log(abs(x - 1))","A",0
308,1,41,0,0.451664," ","integrate(1/x^8/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{x}{4 \, {\left(x^{4} - 1\right)}} - \frac{14 \, x^{4} + 3}{21 \, x^{7}} + \frac{11}{8} \, \arctan\left(x\right) + \frac{11}{16} \, \log\left({\left| x + 1 \right|}\right) - \frac{11}{16} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/4*x/(x^4 - 1) - 1/21*(14*x^4 + 3)/x^7 + 11/8*arctan(x) + 11/16*log(abs(x + 1)) - 11/16*log(abs(x - 1))","A",0
309,0,0,0,0.000000," ","integrate(x^m/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\int \frac{x^{m}}{c x^{8} + b x^{4} + a}\,{d x}"," ",0,"integrate(x^m/(c*x^8 + b*x^4 + a), x)","F",0
310,1,75,0,17.068797," ","integrate(x^11/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\frac{x^{4}}{4 \, c} - \frac{b \log\left(c x^{8} + b x^{4} + a\right)}{8 \, c^{2}} + \frac{{\left(b^{2} - 2 \, a c\right)} \arctan\left(\frac{2 \, c x^{4} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{4 \, \sqrt{-b^{2} + 4 \, a c} c^{2}}"," ",0,"1/4*x^4/c - 1/8*b*log(c*x^8 + b*x^4 + a)/c^2 + 1/4*(b^2 - 2*a*c)*arctan((2*c*x^4 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2)","A",0
311,1,2043,0,18.166279," ","integrate(x^9/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\frac{x^{2}}{2 \, c} + \frac{{\left(2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3} - {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 2 \, b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, a b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 32 \, a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} x^{4} {\left| c \right|} + {\left(2 \, b^{4} c^{3} - 8 \, a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3}\right)} x^{4} - {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, a b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 16 \, a^{2} b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 32 \, a^{3} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{2}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x^{2}}{\sqrt{\frac{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\right)}{8 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} - 2 \, a b^{3} c^{2} + 16 \, a^{3} c^{3} + 8 \, a^{2} b c^{3} + a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} c^{2}} + \frac{{\left(2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3} - {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 2 \, b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 16 \, a b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 32 \, a^{2} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} x^{4} {\left| c \right|} + {\left(2 \, b^{4} c^{3} - 8 \, a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3}\right)} x^{4} - {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, a b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 16 \, a^{2} b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 32 \, a^{3} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{2}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x^{2}}{\sqrt{\frac{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\right)}{8 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} - 2 \, a b^{3} c^{2} + 16 \, a^{3} c^{3} + 8 \, a^{2} b c^{3} + a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} c^{2}}"," ",0,"1/2*x^2/c + 1/8*(2*a*b^3*c^3 - 8*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*a*b*c^3 - (sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c + 2*b^5*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 16*a*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 + 32*a^2*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c + 8*(b^2 - 4*a*c)*a*b*c^2)*x^4*abs(c) + (2*b^4*c^3 - 8*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^3 - 2*(b^2 - 4*a*c)*b^2*c^3)*x^4 - (sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*a*b^4*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 16*a^2*b^2*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 + 32*a^3*c^3 - 2*(b^2 - 4*a*c)*a*b^2*c + 8*(b^2 - 4*a*c)*a^2*c^2)*abs(c))*arctan(2*sqrt(1/2)*x^2/sqrt((b*c + sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((a*b^4*c - 8*a^2*b^2*c^2 - 2*a*b^3*c^2 + 16*a^3*c^3 + 8*a^2*b*c^3 + a*b^2*c^3 - 4*a^2*c^4)*c^2) + 1/8*(2*a*b^3*c^3 - 8*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*a*b*c^3 - (sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 2*b^5*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 16*a*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 32*a^2*b*c^3 + 2*(b^2 - 4*a*c)*b^3*c - 8*(b^2 - 4*a*c)*a*b*c^2)*x^4*abs(c) + (2*b^4*c^3 - 8*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^3 - 2*(b^2 - 4*a*c)*b^2*c^3)*x^4 - (sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 2*a*b^4*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 16*a^2*b^2*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 32*a^3*c^3 + 2*(b^2 - 4*a*c)*a*b^2*c - 8*(b^2 - 4*a*c)*a^2*c^2)*abs(c))*arctan(2*sqrt(1/2)*x^2/sqrt((b*c - sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((a*b^4*c - 8*a^2*b^2*c^2 - 2*a*b^3*c^2 + 16*a^3*c^3 + 8*a^2*b*c^3 + a*b^2*c^3 - 4*a^2*c^4)*c^2)","B",0
312,1,59,0,17.121122," ","integrate(x^7/(c*x^8+b*x^4+a),x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{2 \, c x^{4} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{4 \, \sqrt{-b^{2} + 4 \, a c} c} + \frac{\log\left(c x^{8} + b x^{4} + a\right)}{8 \, c}"," ",0,"-1/4*b*arctan((2*c*x^4 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c) + 1/8*log(c*x^8 + b*x^4 + a)/c","A",0
313,1,1036,0,18.740700," ","integrate(x^5/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\frac{{\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 16 \, a b^{2} c^{2} + 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 32 \, a^{2} c^{3} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} x^{4} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x^{2}}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{8 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}} + \frac{{\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 16 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 32 \, a^{2} c^{3} + 8 \, a b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} x^{4} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x^{2}}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{8 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}}"," ",0,"1/8*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 2*b^4*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 16*a*b^2*c^2 + 2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 32*a^2*c^3 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 + 2*(b^2 - 4*a*c)*b^2*c - 8*(b^2 - 4*a*c)*a*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*x^4*arctan(2*sqrt(1/2)*x^2/sqrt((b + sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c - 2*a*b^3*c + 16*a^3*c^2 + 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c)) + 1/8*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c + 2*b^4*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - 16*a*b^2*c^2 - 2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 + 32*a^2*c^3 + 8*a*b*c^3 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b^2*c + 8*(b^2 - 4*a*c)*a*c^2 + 2*(b^2 - 4*a*c)*b*c^2)*x^4*arctan(2*sqrt(1/2)*x^2/sqrt((b - sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c - 2*a*b^3*c + 16*a^3*c^2 + 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c))","B",0
314,1,36,0,17.344963," ","integrate(x^3/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\frac{\arctan\left(\frac{2 \, c x^{4} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c}}"," ",0,"1/2*arctan((2*c*x^4 + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c)","A",0
315,1,1030,0,19.496390," ","integrate(x/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\frac{{\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 16 \, a b^{2} c^{2} + 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 32 \, a^{2} c^{3} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x^{2}}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{8 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}} + \frac{{\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 16 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 32 \, a^{2} c^{3} + 8 \, a b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x^{2}}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{8 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}}"," ",0,"1/8*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 2*b^4*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 16*a*b^2*c^2 + 2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 32*a^2*c^3 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 + 2*(b^2 - 4*a*c)*b^2*c - 8*(b^2 - 4*a*c)*a*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*arctan(2*sqrt(1/2)*x^2/sqrt((b + sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c - 2*a*b^3*c + 16*a^3*c^2 + 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c)) + 1/8*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c + 2*b^4*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - 16*a*b^2*c^2 - 2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 + 32*a^2*c^3 + 8*a*b*c^3 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b^2*c + 8*(b^2 - 4*a*c)*a*c^2 + 2*(b^2 - 4*a*c)*b*c^2)*arctan(2*sqrt(1/2)*x^2/sqrt((b - sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c - 2*a*b^3*c + 16*a^3*c^2 + 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c))","B",0
316,1,68,0,16.281019," ","integrate(1/x/(c*x^8+b*x^4+a),x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{2 \, c x^{4} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{4 \, \sqrt{-b^{2} + 4 \, a c} a} - \frac{\log\left(c x^{8} + b x^{4} + a\right)}{8 \, a} + \frac{\log\left(x^{4}\right)}{4 \, a}"," ",0,"-1/4*b*arctan((2*c*x^4 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a) - 1/8*log(c*x^8 + b*x^4 + a)/a + 1/4*log(x^4)/a","A",0
317,1,2055,0,15.890506," ","integrate(1/x^3/(c*x^8+b*x^4+a),x, algorithm=""giac"")","-\frac{{\left(2 \, a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 2 \, b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 16 \, a b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 32 \, a^{2} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} x^{4} {\left| a \right|} + {\left(2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} x^{4} + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 2 \, b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 16 \, a b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 32 \, a^{2} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} {\left| a \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x^{2}}{\sqrt{\frac{a b + \sqrt{a^{2} b^{2} - 4 \, a^{3} c}}{a c}}}\right)}{8 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c - 2 \, a^{2} b^{3} c + 16 \, a^{4} c^{2} + 8 \, a^{3} b c^{2} + a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} {\left| a \right|} {\left| c \right|}} + \frac{{\left(2 \, a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 2 \, b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} - 16 \, a b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{4} + 32 \, a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} x^{4} {\left| a \right|} + {\left(2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} x^{4} - {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 2 \, b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, a b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 32 \, a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} {\left| a \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x^{2}}{\sqrt{\frac{a b - \sqrt{a^{2} b^{2} - 4 \, a^{3} c}}{a c}}}\right)}{8 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c - 2 \, a^{2} b^{3} c + 16 \, a^{4} c^{2} + 8 \, a^{3} b c^{2} + a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} {\left| a \right|} {\left| c \right|}} - \frac{1}{2 \, a x^{2}}"," ",0,"-1/8*(2*a*b^4*c^2 - 8*a^2*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 2*(b^2 - 4*a*c)*a*b^2*c^2 + (sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 2*b^4*c^2 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^3 + 16*a*b^2*c^3 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^4 - 32*a^2*c^4 + 2*(b^2 - 4*a*c)*b^2*c^2 - 8*(b^2 - 4*a*c)*a*c^3)*x^4*abs(a) + (2*a*b^3*c^3 - 8*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*a*b*c^3)*x^4 + (sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 2*b^5*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 16*a*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 32*a^2*b*c^3 + 2*(b^2 - 4*a*c)*b^3*c - 8*(b^2 - 4*a*c)*a*b*c^2)*abs(a))*arctan(2*sqrt(1/2)*x^2/sqrt((a*b + sqrt(a^2*b^2 - 4*a^3*c))/(a*c)))/((a^2*b^4 - 8*a^3*b^2*c - 2*a^2*b^3*c + 16*a^4*c^2 + 8*a^3*b*c^2 + a^2*b^2*c^2 - 4*a^3*c^3)*abs(a)*abs(c)) + 1/8*(2*a*b^4*c^2 - 8*a^2*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 2*(b^2 - 4*a*c)*a*b^2*c^2 - (sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 2*b^4*c^2 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^3 - 16*a*b^2*c^3 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^4 + 32*a^2*c^4 - 2*(b^2 - 4*a*c)*b^2*c^2 + 8*(b^2 - 4*a*c)*a*c^3)*x^4*abs(a) + (2*a*b^3*c^3 - 8*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*a*b*c^3)*x^4 - (sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c + 2*b^5*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 16*a*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 + 32*a^2*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c + 8*(b^2 - 4*a*c)*a*b*c^2)*abs(a))*arctan(2*sqrt(1/2)*x^2/sqrt((a*b - sqrt(a^2*b^2 - 4*a^3*c))/(a*c)))/((a^2*b^4 - 8*a^3*b^2*c - 2*a^2*b^3*c + 16*a^4*c^2 + 8*a^3*b*c^2 + a^2*b^2*c^2 - 4*a^3*c^3)*abs(a)*abs(c)) - 1/2/(a*x^2)","B",0
318,1,94,0,14.500921," ","integrate(1/x^5/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\frac{b \log\left(c x^{8} + b x^{4} + a\right)}{8 \, a^{2}} - \frac{b \log\left(x^{4}\right)}{4 \, a^{2}} + \frac{{\left(b^{2} - 2 \, a c\right)} \arctan\left(\frac{2 \, c x^{4} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{4 \, \sqrt{-b^{2} + 4 \, a c} a^{2}} + \frac{b x^{4} - a}{4 \, a^{2} x^{4}}"," ",0,"1/8*b*log(c*x^8 + b*x^4 + a)/a^2 - 1/4*b*log(x^4)/a^2 + 1/4*(b^2 - 2*a*c)*arctan((2*c*x^4 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a^2) + 1/4*(b*x^4 - a)/(a^2*x^4)","A",0
319,-2,0,0,0.000000," ","integrate(x^10/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 19.53Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
320,-2,0,0,0.000000," ","integrate(x^8/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 14.73Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
321,0,0,0,0.000000," ","integrate(x^6/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\int \frac{x^{6}}{c x^{8} + b x^{4} + a}\,{d x}"," ",0,"integrate(x^6/(c*x^8 + b*x^4 + a), x)","F",0
322,0,0,0,0.000000," ","integrate(x^4/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\int \frac{x^{4}}{c x^{8} + b x^{4} + a}\,{d x}"," ",0,"integrate(x^4/(c*x^8 + b*x^4 + a), x)","F",0
323,0,0,0,0.000000," ","integrate(x^2/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\int \frac{x^{2}}{c x^{8} + b x^{4} + a}\,{d x}"," ",0,"integrate(x^2/(c*x^8 + b*x^4 + a), x)","F",0
324,0,0,0,0.000000," ","integrate(1/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\int \frac{1}{c x^{8} + b x^{4} + a}\,{d x}"," ",0,"integrate(1/(c*x^8 + b*x^4 + a), x)","F",0
325,-2,0,0,0.000000," ","integrate(1/x^2/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 14.78Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
326,-2,0,0,0.000000," ","integrate(1/x^4/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 21.84Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
327,0,0,0,0.000000," ","integrate(x^m/(x^8+x^4+1),x, algorithm=""giac"")","\int \frac{x^{m}}{x^{8} + x^{4} + 1}\,{d x}"," ",0,"integrate(x^m/(x^8 + x^4 + 1), x)","F",0
328,1,35,0,0.342140," ","integrate(x^11/(x^8+x^4+1),x, algorithm=""giac"")","\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
329,1,42,0,0.315234," ","integrate(x^9/(x^8+x^4+1),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right)"," ",0,"1/2*x^2 - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1)) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1))","A",0
330,1,30,0,0.389854," ","integrate(x^7/(x^8+x^4+1),x, algorithm=""giac"")","-\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
331,1,61,0,0.388614," ","integrate(x^5/(x^8+x^4+1),x, algorithm=""giac"")","\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
332,1,18,0,0.360948," ","integrate(x^3/(x^8+x^4+1),x, algorithm=""giac"")","\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
333,1,61,0,0.308843," ","integrate(x/(x^8+x^4+1),x, algorithm=""giac"")","\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
334,1,36,0,0.383324," ","integrate(1/x/(x^8+x^4+1),x, algorithm=""giac"")","-\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) + \frac{1}{4} \, \log\left(x^{4}\right)"," ",0,"-1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^4 + 1)) - 1/8*log(x^8 + x^4 + 1) + 1/4*log(x^4)","A",0
335,1,42,0,0.377750," ","integrate(1/x^3/(x^8+x^4+1),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) - \frac{1}{2 \, x^{2}}"," ",0,"-1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1)) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) - 1/2/x^2","A",0
336,1,46,0,0.305828," ","integrate(1/x^5/(x^8+x^4+1),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{4} + 1\right)}\right) + \frac{x^{4} - 1}{4 \, x^{4}} + \frac{1}{8} \, \log\left(x^{8} + x^{4} + 1\right) - \frac{1}{4} \, \log\left(x^{4}\right)"," ",0,"-1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^4 + 1)) + 1/4*(x^4 - 1)/x^4 + 1/8*log(x^8 + x^4 + 1) - 1/4*log(x^4)","A",0
337,1,73,0,0.266077," ","integrate(1/x^7/(x^8+x^4+1),x, algorithm=""giac"")","\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{3 \, x^{4} - 1}{6 \, x^{6}} - \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)) + 1/6*(3*x^4 - 1)/x^6 - 1/8*log(x^4 + x^2 + 1) + 1/8*log(x^4 - x^2 + 1)","A",0
338,1,109,0,0.394558," ","integrate(x^8/(x^8+x^4+1),x, algorithm=""giac"")","-\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}{24} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) + \frac{1}{24} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) + x - \frac{1}{4} \, \arctan\left(2 \, x + \sqrt{3}\right) - \frac{1}{4} \, \arctan\left(2 \, x - \sqrt{3}\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(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/24*sqrt(3)*log(x^2 + sqrt(3)*x + 1) + 1/24*sqrt(3)*log(x^2 - sqrt(3)*x + 1) + x - 1/4*arctan(2*x + sqrt(3)) - 1/4*arctan(2*x - sqrt(3)) - 1/8*log(x^2 + x + 1) + 1/8*log(x^2 - x + 1)","A",0
339,1,66,0,0.326357," ","integrate(x^6/(x^8+x^4+1),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{12} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) + \frac{1}{12} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/12*sqrt(3)*log(x^2 + sqrt(3)*x + 1) + 1/12*sqrt(3)*log(x^2 - sqrt(3)*x + 1)","A",0
340,1,108,0,0.404194," ","integrate(x^4/(x^8+x^4+1),x, algorithm=""giac"")","-\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}{24} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) + \frac{1}{24} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) + \frac{1}{4} \, \arctan\left(2 \, x + \sqrt{3}\right) + \frac{1}{4} \, \arctan\left(2 \, x - \sqrt{3}\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(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/24*sqrt(3)*log(x^2 + sqrt(3)*x + 1) + 1/24*sqrt(3)*log(x^2 - sqrt(3)*x + 1) + 1/4*arctan(2*x + sqrt(3)) + 1/4*arctan(2*x - sqrt(3)) + 1/8*log(x^2 + x + 1) - 1/8*log(x^2 - x + 1)","A",0
341,1,108,0,0.335073," ","integrate(x^2/(x^8+x^4+1),x, algorithm=""giac"")","-\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}{24} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) - \frac{1}{24} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) + \frac{1}{4} \, \arctan\left(2 \, x + \sqrt{3}\right) + \frac{1}{4} \, \arctan\left(2 \, x - \sqrt{3}\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(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/24*sqrt(3)*log(x^2 + sqrt(3)*x + 1) - 1/24*sqrt(3)*log(x^2 - sqrt(3)*x + 1) + 1/4*arctan(2*x + sqrt(3)) + 1/4*arctan(2*x - sqrt(3)) - 1/8*log(x^2 + x + 1) + 1/8*log(x^2 - x + 1)","A",0
342,1,66,0,0.387199," ","integrate(1/(x^8+x^4+1),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{12} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) - \frac{1}{12} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/12*sqrt(3)*log(x^2 + sqrt(3)*x + 1) - 1/12*sqrt(3)*log(x^2 - sqrt(3)*x + 1)","A",0
343,1,113,0,0.329867," ","integrate(1/x^2/(x^8+x^4+1),x, algorithm=""giac"")","-\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}{24} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) - \frac{1}{24} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) - \frac{1}{x} - \frac{1}{4} \, \arctan\left(2 \, x + \sqrt{3}\right) - \frac{1}{4} \, \arctan\left(2 \, x - \sqrt{3}\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(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/24*sqrt(3)*log(x^2 + sqrt(3)*x + 1) - 1/24*sqrt(3)*log(x^2 - sqrt(3)*x + 1) - 1/x - 1/4*arctan(2*x + sqrt(3)) - 1/4*arctan(2*x - sqrt(3)) + 1/8*log(x^2 + x + 1) - 1/8*log(x^2 - x + 1)","A",0
344,1,113,0,0.376592," ","integrate(1/x^4/(x^8+x^4+1),x, algorithm=""giac"")","-\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}{24} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) + \frac{1}{24} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) - \frac{1}{3 \, x^{3}} - \frac{1}{4} \, \arctan\left(2 \, x + \sqrt{3}\right) - \frac{1}{4} \, \arctan\left(2 \, x - \sqrt{3}\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(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/24*sqrt(3)*log(x^2 + sqrt(3)*x + 1) + 1/24*sqrt(3)*log(x^2 - sqrt(3)*x + 1) - 1/3/x^3 - 1/4*arctan(2*x + sqrt(3)) - 1/4*arctan(2*x - sqrt(3)) - 1/8*log(x^2 + x + 1) + 1/8*log(x^2 - x + 1)","A",0
345,1,100,0,0.403792," ","integrate(1/x^6/(x^8+x^4+1),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{24} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) + \frac{1}{24} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) + \frac{5 \, x^{4} - 1}{5 \, x^{5}} + \frac{1}{4} \, \arctan\left(2 \, x + \sqrt{3}\right) + \frac{1}{4} \, \arctan\left(2 \, x - \sqrt{3}\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/24*sqrt(3)*log(x^2 + sqrt(3)*x + 1) + 1/24*sqrt(3)*log(x^2 - sqrt(3)*x + 1) + 1/5*(5*x^4 - 1)/x^5 + 1/4*arctan(2*x + sqrt(3)) + 1/4*arctan(2*x - sqrt(3))","A",0
346,1,120,0,0.426016," ","integrate(1/x^8/(x^8+x^4+1),x, algorithm=""giac"")","-\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}{24} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) + \frac{1}{24} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) + \frac{7 \, x^{4} - 3}{21 \, x^{7}} + \frac{1}{4} \, \arctan\left(2 \, x + \sqrt{3}\right) + \frac{1}{4} \, \arctan\left(2 \, x - \sqrt{3}\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(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/24*sqrt(3)*log(x^2 + sqrt(3)*x + 1) + 1/24*sqrt(3)*log(x^2 - sqrt(3)*x + 1) + 1/21*(7*x^4 - 3)/x^7 + 1/4*arctan(2*x + sqrt(3)) + 1/4*arctan(2*x - sqrt(3)) + 1/8*log(x^2 + x + 1) - 1/8*log(x^2 - x + 1)","A",0
347,0,0,0,0.000000," ","integrate(x^m/(x^8-x^4+1),x, algorithm=""giac"")","\int \frac{x^{m}}{x^{8} - x^{4} + 1}\,{d x}"," ",0,"integrate(x^m/(x^8 - x^4 + 1), x)","F",0
348,1,37,0,0.342389," ","integrate(x^11/(x^8-x^4+1),x, algorithm=""giac"")","\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
349,1,99,0,0.321435," ","integrate(x^9/(x^8-x^4+1),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + \frac{1}{4} \, {\left(x^{4} - 1\right)} \arctan\left(2 \, x^{2} + \sqrt{3}\right) + \frac{1}{4} \, {\left(x^{4} - 1\right)} \arctan\left(2 \, x^{2} - \sqrt{3}\right) + \frac{1}{24} \, {\left(\sqrt{3} x^{4} - \sqrt{3}\right)} \log\left(x^{4} + \sqrt{3} x^{2} + 1\right) - \frac{1}{24} \, {\left(\sqrt{3} x^{4} - \sqrt{3}\right)} \log\left(x^{4} - \sqrt{3} x^{2} + 1\right)"," ",0,"1/2*x^2 + 1/4*(x^4 - 1)*arctan(2*x^2 + sqrt(3)) + 1/4*(x^4 - 1)*arctan(2*x^2 - sqrt(3)) + 1/24*(sqrt(3)*x^4 - sqrt(3))*log(x^4 + sqrt(3)*x^2 + 1) - 1/24*(sqrt(3)*x^4 - sqrt(3))*log(x^4 - sqrt(3)*x^2 + 1)","B",0
350,1,32,0,0.422914," ","integrate(x^7/(x^8-x^4+1),x, algorithm=""giac"")","\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
351,1,76,0,0.348098," ","integrate(x^5/(x^8-x^4+1),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{3} x^{4} \log\left(x^{4} + \sqrt{3} x^{2} + 1\right) - \frac{1}{24} \, \sqrt{3} x^{4} \log\left(x^{4} - \sqrt{3} x^{2} + 1\right) + \frac{1}{4} \, x^{4} \arctan\left(2 \, x^{2} + \sqrt{3}\right) + \frac{1}{4} \, x^{4} \arctan\left(2 \, x^{2} - \sqrt{3}\right)"," ",0,"1/24*sqrt(3)*x^4*log(x^4 + sqrt(3)*x^2 + 1) - 1/24*sqrt(3)*x^4*log(x^4 - sqrt(3)*x^2 + 1) + 1/4*x^4*arctan(2*x^2 + sqrt(3)) + 1/4*x^4*arctan(2*x^2 - sqrt(3))","A",0
352,1,18,0,0.409568," ","integrate(x^3/(x^8-x^4+1),x, algorithm=""giac"")","\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
353,1,64,0,0.407219," ","integrate(x/(x^8-x^4+1),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{3} \log\left(x^{4} + \sqrt{3} x^{2} + 1\right) - \frac{1}{24} \, \sqrt{3} \log\left(x^{4} - \sqrt{3} x^{2} + 1\right) + \frac{1}{4} \, \arctan\left(2 \, x^{2} + \sqrt{3}\right) + \frac{1}{4} \, \arctan\left(2 \, x^{2} - \sqrt{3}\right)"," ",0,"1/24*sqrt(3)*log(x^4 + sqrt(3)*x^2 + 1) - 1/24*sqrt(3)*log(x^4 - sqrt(3)*x^2 + 1) + 1/4*arctan(2*x^2 + sqrt(3)) + 1/4*arctan(2*x^2 - sqrt(3))","A",0
354,1,38,0,0.346261," ","integrate(1/x/(x^8-x^4+1),x, algorithm=""giac"")","\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) + \frac{1}{4} \, \log\left(x^{4}\right)"," ",0,"1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^4 - 1)) - 1/8*log(x^8 - x^4 + 1) + 1/4*log(x^4)","A",0
355,1,99,0,0.314329," ","integrate(1/x^3/(x^8-x^4+1),x, algorithm=""giac"")","-\frac{1}{4} \, {\left(x^{4} - 1\right)} \arctan\left(2 \, x^{2} + \sqrt{3}\right) - \frac{1}{4} \, {\left(x^{4} - 1\right)} \arctan\left(2 \, x^{2} - \sqrt{3}\right) - \frac{1}{24} \, {\left(\sqrt{3} x^{4} - \sqrt{3}\right)} \log\left(x^{4} + \sqrt{3} x^{2} + 1\right) + \frac{1}{24} \, {\left(\sqrt{3} x^{4} - \sqrt{3}\right)} \log\left(x^{4} - \sqrt{3} x^{2} + 1\right) - \frac{1}{2 \, x^{2}}"," ",0,"-1/4*(x^4 - 1)*arctan(2*x^2 + sqrt(3)) - 1/4*(x^4 - 1)*arctan(2*x^2 - sqrt(3)) - 1/24*(sqrt(3)*x^4 - sqrt(3))*log(x^4 + sqrt(3)*x^2 + 1) + 1/24*(sqrt(3)*x^4 - sqrt(3))*log(x^4 - sqrt(3)*x^2 + 1) - 1/2/x^2","B",0
356,1,48,0,0.404249," ","integrate(1/x^5/(x^8-x^4+1),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{4} - 1\right)}\right) - \frac{x^{4} + 1}{4 \, x^{4}} - \frac{1}{8} \, \log\left(x^{8} - x^{4} + 1\right) + \frac{1}{4} \, \log\left(x^{4}\right)"," ",0,"-1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^4 - 1)) - 1/4*(x^4 + 1)/x^4 - 1/8*log(x^8 - x^4 + 1) + 1/4*log(x^4)","A",0
357,1,56,0,0.415174," ","integrate(1/x^7/(x^8-x^4+1),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{3} x^{4} \log\left(x^{4} + \sqrt{3} x^{2} + 1\right) + \frac{1}{12} \, \sqrt{3} x^{4} \log\left(x^{4} - \sqrt{3} x^{2} + 1\right) - \frac{3 \, x^{4} + 1}{6 \, x^{6}}"," ",0,"-1/12*sqrt(3)*x^4*log(x^4 + sqrt(3)*x^2 + 1) + 1/12*sqrt(3)*x^4*log(x^4 - sqrt(3)*x^2 + 1) - 1/6*(3*x^4 + 1)/x^6","A",0
358,1,254,0,0.346514," ","integrate(x^8/(x^8-x^4+1),x, algorithm=""giac"")","-\frac{1}{24} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} - \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) - \frac{1}{24} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} + \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) - \frac{1}{24} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} + \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) - \frac{1}{24} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) - \frac{1}{48} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) + \frac{1}{48} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) - \frac{1}{48} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) + \frac{1}{48} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) + x"," ",0,"-1/24*(sqrt(6) + 3*sqrt(2))*arctan((4*x + sqrt(6) - sqrt(2))/(sqrt(6) + sqrt(2))) - 1/24*(sqrt(6) + 3*sqrt(2))*arctan((4*x - sqrt(6) + sqrt(2))/(sqrt(6) + sqrt(2))) - 1/24*(sqrt(6) - 3*sqrt(2))*arctan((4*x + sqrt(6) + sqrt(2))/(sqrt(6) - sqrt(2))) - 1/24*(sqrt(6) - 3*sqrt(2))*arctan((4*x - sqrt(6) - sqrt(2))/(sqrt(6) - sqrt(2))) - 1/48*(sqrt(6) + 3*sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) + sqrt(2)) + 1) + 1/48*(sqrt(6) + 3*sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) + sqrt(2)) + 1) - 1/48*(sqrt(6) - 3*sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) - sqrt(2)) + 1) + 1/48*(sqrt(6) - 3*sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) - sqrt(2)) + 1) + x","A",0
359,1,205,0,0.397840," ","integrate(x^6/(x^8-x^4+1),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{6} \arctan\left(\frac{4 \, x + \sqrt{6} - \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{12} \, \sqrt{6} \arctan\left(\frac{4 \, x - \sqrt{6} + \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{12} \, \sqrt{6} \arctan\left(\frac{4 \, x + \sqrt{6} + \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{12} \, \sqrt{6} \arctan\left(\frac{4 \, x - \sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) - \frac{1}{24} \, \sqrt{6} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) + \frac{1}{24} \, \sqrt{6} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) - \frac{1}{24} \, \sqrt{6} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) + \frac{1}{24} \, \sqrt{6} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right)"," ",0,"1/12*sqrt(6)*arctan((4*x + sqrt(6) - sqrt(2))/(sqrt(6) + sqrt(2))) + 1/12*sqrt(6)*arctan((4*x - sqrt(6) + sqrt(2))/(sqrt(6) + sqrt(2))) + 1/12*sqrt(6)*arctan((4*x + sqrt(6) + sqrt(2))/(sqrt(6) - sqrt(2))) + 1/12*sqrt(6)*arctan((4*x - sqrt(6) - sqrt(2))/(sqrt(6) - sqrt(2))) - 1/24*sqrt(6)*log(x^2 + 1/2*x*(sqrt(6) + sqrt(2)) + 1) + 1/24*sqrt(6)*log(x^2 - 1/2*x*(sqrt(6) + sqrt(2)) + 1) - 1/24*sqrt(6)*log(x^2 + 1/2*x*(sqrt(6) - sqrt(2)) + 1) + 1/24*sqrt(6)*log(x^2 - 1/2*x*(sqrt(6) - sqrt(2)) + 1)","A",0
360,1,253,0,0.479650," ","integrate(x^4/(x^8-x^4+1),x, algorithm=""giac"")","\frac{1}{24} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} - \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{24} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} + \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{24} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} + \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{24} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{48} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) - \frac{1}{48} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) + \frac{1}{48} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) - \frac{1}{48} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right)"," ",0,"1/24*(sqrt(6) - 3*sqrt(2))*arctan((4*x + sqrt(6) - sqrt(2))/(sqrt(6) + sqrt(2))) + 1/24*(sqrt(6) - 3*sqrt(2))*arctan((4*x - sqrt(6) + sqrt(2))/(sqrt(6) + sqrt(2))) + 1/24*(sqrt(6) + 3*sqrt(2))*arctan((4*x + sqrt(6) + sqrt(2))/(sqrt(6) - sqrt(2))) + 1/24*(sqrt(6) + 3*sqrt(2))*arctan((4*x - sqrt(6) - sqrt(2))/(sqrt(6) - sqrt(2))) + 1/48*(sqrt(6) - 3*sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) + sqrt(2)) + 1) - 1/48*(sqrt(6) - 3*sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) + sqrt(2)) + 1) + 1/48*(sqrt(6) + 3*sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) - sqrt(2)) + 1) - 1/48*(sqrt(6) + 3*sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) - sqrt(2)) + 1)","A",0
361,1,253,0,0.457428," ","integrate(x^2/(x^8-x^4+1),x, algorithm=""giac"")","\frac{1}{24} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} - \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{24} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} + \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{24} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} + \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{24} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) - \frac{1}{48} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) + \frac{1}{48} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) - \frac{1}{48} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) + \frac{1}{48} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right)"," ",0,"1/24*(sqrt(6) - 3*sqrt(2))*arctan((4*x + sqrt(6) - sqrt(2))/(sqrt(6) + sqrt(2))) + 1/24*(sqrt(6) - 3*sqrt(2))*arctan((4*x - sqrt(6) + sqrt(2))/(sqrt(6) + sqrt(2))) + 1/24*(sqrt(6) + 3*sqrt(2))*arctan((4*x + sqrt(6) + sqrt(2))/(sqrt(6) - sqrt(2))) + 1/24*(sqrt(6) + 3*sqrt(2))*arctan((4*x - sqrt(6) - sqrt(2))/(sqrt(6) - sqrt(2))) - 1/48*(sqrt(6) - 3*sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) + sqrt(2)) + 1) + 1/48*(sqrt(6) - 3*sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) + sqrt(2)) + 1) - 1/48*(sqrt(6) + 3*sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) - sqrt(2)) + 1) + 1/48*(sqrt(6) + 3*sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) - sqrt(2)) + 1)","A",0
362,1,205,0,0.400272," ","integrate(1/(x^8-x^4+1),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{6} \arctan\left(\frac{4 \, x + \sqrt{6} - \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{12} \, \sqrt{6} \arctan\left(\frac{4 \, x - \sqrt{6} + \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{12} \, \sqrt{6} \arctan\left(\frac{4 \, x + \sqrt{6} + \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{12} \, \sqrt{6} \arctan\left(\frac{4 \, x - \sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{24} \, \sqrt{6} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) - \frac{1}{24} \, \sqrt{6} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) + \frac{1}{24} \, \sqrt{6} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) - \frac{1}{24} \, \sqrt{6} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right)"," ",0,"1/12*sqrt(6)*arctan((4*x + sqrt(6) - sqrt(2))/(sqrt(6) + sqrt(2))) + 1/12*sqrt(6)*arctan((4*x - sqrt(6) + sqrt(2))/(sqrt(6) + sqrt(2))) + 1/12*sqrt(6)*arctan((4*x + sqrt(6) + sqrt(2))/(sqrt(6) - sqrt(2))) + 1/12*sqrt(6)*arctan((4*x - sqrt(6) - sqrt(2))/(sqrt(6) - sqrt(2))) + 1/24*sqrt(6)*log(x^2 + 1/2*x*(sqrt(6) + sqrt(2)) + 1) - 1/24*sqrt(6)*log(x^2 - 1/2*x*(sqrt(6) + sqrt(2)) + 1) + 1/24*sqrt(6)*log(x^2 + 1/2*x*(sqrt(6) - sqrt(2)) + 1) - 1/24*sqrt(6)*log(x^2 - 1/2*x*(sqrt(6) - sqrt(2)) + 1)","A",0
363,1,258,0,0.462241," ","integrate(1/x^2/(x^8-x^4+1),x, algorithm=""giac"")","-\frac{1}{24} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} - \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) - \frac{1}{24} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} + \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) - \frac{1}{24} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} + \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) - \frac{1}{24} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{48} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) - \frac{1}{48} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) + \frac{1}{48} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) - \frac{1}{48} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) - \frac{1}{x}"," ",0,"-1/24*(sqrt(6) + 3*sqrt(2))*arctan((4*x + sqrt(6) - sqrt(2))/(sqrt(6) + sqrt(2))) - 1/24*(sqrt(6) + 3*sqrt(2))*arctan((4*x - sqrt(6) + sqrt(2))/(sqrt(6) + sqrt(2))) - 1/24*(sqrt(6) - 3*sqrt(2))*arctan((4*x + sqrt(6) + sqrt(2))/(sqrt(6) - sqrt(2))) - 1/24*(sqrt(6) - 3*sqrt(2))*arctan((4*x - sqrt(6) - sqrt(2))/(sqrt(6) - sqrt(2))) + 1/48*(sqrt(6) + 3*sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) + sqrt(2)) + 1) - 1/48*(sqrt(6) + 3*sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) + sqrt(2)) + 1) + 1/48*(sqrt(6) - 3*sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) - sqrt(2)) + 1) - 1/48*(sqrt(6) - 3*sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) - sqrt(2)) + 1) - 1/x","A",0
364,1,258,0,0.353032," ","integrate(1/x^4/(x^8-x^4+1),x, algorithm=""giac"")","\frac{1}{24} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} - \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{24} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} + \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{24} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} + \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{24} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{48} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) - \frac{1}{48} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) + \frac{1}{48} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) - \frac{1}{48} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) - \frac{1}{3 \, x^{3}}"," ",0,"1/24*(sqrt(6) + 3*sqrt(2))*arctan((4*x + sqrt(6) - sqrt(2))/(sqrt(6) + sqrt(2))) + 1/24*(sqrt(6) + 3*sqrt(2))*arctan((4*x - sqrt(6) + sqrt(2))/(sqrt(6) + sqrt(2))) + 1/24*(sqrt(6) - 3*sqrt(2))*arctan((4*x + sqrt(6) + sqrt(2))/(sqrt(6) - sqrt(2))) + 1/24*(sqrt(6) - 3*sqrt(2))*arctan((4*x - sqrt(6) - sqrt(2))/(sqrt(6) - sqrt(2))) + 1/48*(sqrt(6) + 3*sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) + sqrt(2)) + 1) - 1/48*(sqrt(6) + 3*sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) + sqrt(2)) + 1) + 1/48*(sqrt(6) - 3*sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) - sqrt(2)) + 1) - 1/48*(sqrt(6) - 3*sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) - sqrt(2)) + 1) - 1/3/x^3","A",0
365,1,217,0,0.383175," ","integrate(1/x^6/(x^8-x^4+1),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{6} \arctan\left(\frac{4 \, x + \sqrt{6} - \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) - \frac{1}{12} \, \sqrt{6} \arctan\left(\frac{4 \, x - \sqrt{6} + \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) - \frac{1}{12} \, \sqrt{6} \arctan\left(\frac{4 \, x + \sqrt{6} + \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) - \frac{1}{12} \, \sqrt{6} \arctan\left(\frac{4 \, x - \sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{24} \, \sqrt{6} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) - \frac{1}{24} \, \sqrt{6} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) + \frac{1}{24} \, \sqrt{6} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) - \frac{1}{24} \, \sqrt{6} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) - \frac{5 \, x^{4} + 1}{5 \, x^{5}}"," ",0,"-1/12*sqrt(6)*arctan((4*x + sqrt(6) - sqrt(2))/(sqrt(6) + sqrt(2))) - 1/12*sqrt(6)*arctan((4*x - sqrt(6) + sqrt(2))/(sqrt(6) + sqrt(2))) - 1/12*sqrt(6)*arctan((4*x + sqrt(6) + sqrt(2))/(sqrt(6) - sqrt(2))) - 1/12*sqrt(6)*arctan((4*x - sqrt(6) - sqrt(2))/(sqrt(6) - sqrt(2))) + 1/24*sqrt(6)*log(x^2 + 1/2*x*(sqrt(6) + sqrt(2)) + 1) - 1/24*sqrt(6)*log(x^2 - 1/2*x*(sqrt(6) + sqrt(2)) + 1) + 1/24*sqrt(6)*log(x^2 + 1/2*x*(sqrt(6) - sqrt(2)) + 1) - 1/24*sqrt(6)*log(x^2 - 1/2*x*(sqrt(6) - sqrt(2)) + 1) - 1/5*(5*x^4 + 1)/x^5","A",0
366,1,265,0,0.380841," ","integrate(1/x^8/(x^8-x^4+1),x, algorithm=""giac"")","-\frac{1}{24} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} - \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) - \frac{1}{24} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} + \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) - \frac{1}{24} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} + \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) - \frac{1}{24} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) - \frac{1}{48} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) + \frac{1}{48} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) - \frac{1}{48} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) + \frac{1}{48} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) - \frac{7 \, x^{4} + 3}{21 \, x^{7}}"," ",0,"-1/24*(sqrt(6) - 3*sqrt(2))*arctan((4*x + sqrt(6) - sqrt(2))/(sqrt(6) + sqrt(2))) - 1/24*(sqrt(6) - 3*sqrt(2))*arctan((4*x - sqrt(6) + sqrt(2))/(sqrt(6) + sqrt(2))) - 1/24*(sqrt(6) + 3*sqrt(2))*arctan((4*x + sqrt(6) + sqrt(2))/(sqrt(6) - sqrt(2))) - 1/24*(sqrt(6) + 3*sqrt(2))*arctan((4*x - sqrt(6) - sqrt(2))/(sqrt(6) - sqrt(2))) - 1/48*(sqrt(6) - 3*sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) + sqrt(2)) + 1) + 1/48*(sqrt(6) - 3*sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) + sqrt(2)) + 1) - 1/48*(sqrt(6) + 3*sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) - sqrt(2)) + 1) + 1/48*(sqrt(6) + 3*sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) - sqrt(2)) + 1) - 1/21*(7*x^4 + 3)/x^7","A",0
367,0,0,0,0.000000," ","integrate(x^m/(x^8+3*x^4+1),x, algorithm=""giac"")","\int \frac{x^{m}}{x^{8} + 3 \, x^{4} + 1}\,{d x}"," ",0,"integrate(x^m/(x^8 + 3*x^4 + 1), x)","F",0
368,1,50,0,0.497410," ","integrate(x^11/(x^8+3*x^4+1),x, algorithm=""giac"")","\frac{1}{4} \, x^{4} + \frac{7}{40} \, \sqrt{5} \log\left(\frac{2 \, x^{4} - \sqrt{5} + 3}{2 \, x^{4} + \sqrt{5} + 3}\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^4 - sqrt(5) + 3)/(2*x^4 + sqrt(5) + 3)) - 3/8*log(x^8 + 3*x^4 + 1)","A",0
369,1,66,0,0.561275," ","integrate(x^9/(x^8+3*x^4+1),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - \frac{1}{20} \, {\left(3 \, x^{4} {\left(\sqrt{5} - 5\right)} + \sqrt{5} - 5\right)} \arctan\left(\frac{2 \, x^{2}}{\sqrt{5} + 1}\right) - \frac{1}{20} \, {\left(3 \, x^{4} {\left(\sqrt{5} + 5\right)} + \sqrt{5} + 5\right)} \arctan\left(\frac{2 \, x^{2}}{\sqrt{5} - 1}\right)"," ",0,"1/2*x^2 - 1/20*(3*x^4*(sqrt(5) - 5) + sqrt(5) - 5)*arctan(2*x^2/(sqrt(5) + 1)) - 1/20*(3*x^4*(sqrt(5) + 5) + sqrt(5) + 5)*arctan(2*x^2/(sqrt(5) - 1))","A",0
370,1,45,0,0.497433," ","integrate(x^7/(x^8+3*x^4+1),x, algorithm=""giac"")","-\frac{3}{40} \, \sqrt{5} \log\left(\frac{2 \, x^{4} - \sqrt{5} + 3}{2 \, x^{4} + \sqrt{5} + 3}\right) + \frac{1}{8} \, \log\left(x^{8} + 3 \, x^{4} + 1\right)"," ",0,"-3/40*sqrt(5)*log((2*x^4 - sqrt(5) + 3)/(2*x^4 + sqrt(5) + 3)) + 1/8*log(x^8 + 3*x^4 + 1)","A",0
371,1,47,0,0.551321," ","integrate(x^5/(x^8+3*x^4+1),x, algorithm=""giac"")","\frac{1}{20} \, x^{4} {\left(\sqrt{5} - 5\right)} \arctan\left(\frac{2 \, x^{2}}{\sqrt{5} + 1}\right) + \frac{1}{20} \, x^{4} {\left(\sqrt{5} + 5\right)} \arctan\left(\frac{2 \, x^{2}}{\sqrt{5} - 1}\right)"," ",0,"1/20*x^4*(sqrt(5) - 5)*arctan(2*x^2/(sqrt(5) + 1)) + 1/20*x^4*(sqrt(5) + 5)*arctan(2*x^2/(sqrt(5) - 1))","A",0
372,1,31,0,0.601105," ","integrate(x^3/(x^8+3*x^4+1),x, algorithm=""giac"")","\frac{1}{20} \, \sqrt{5} \log\left(\frac{2 \, x^{4} - \sqrt{5} + 3}{2 \, x^{4} + \sqrt{5} + 3}\right)"," ",0,"1/20*sqrt(5)*log((2*x^4 - sqrt(5) + 3)/(2*x^4 + sqrt(5) + 3))","A",0
373,1,41,0,0.419398," ","integrate(x/(x^8+3*x^4+1),x, algorithm=""giac"")","\frac{1}{20} \, {\left(\sqrt{5} - 5\right)} \arctan\left(\frac{2 \, x^{2}}{\sqrt{5} + 1}\right) + \frac{1}{20} \, {\left(\sqrt{5} + 5\right)} \arctan\left(\frac{2 \, x^{2}}{\sqrt{5} - 1}\right)"," ",0,"1/20*(sqrt(5) - 5)*arctan(2*x^2/(sqrt(5) + 1)) + 1/20*(sqrt(5) + 5)*arctan(2*x^2/(sqrt(5) - 1))","A",0
374,1,51,0,0.484036," ","integrate(1/x/(x^8+3*x^4+1),x, algorithm=""giac"")","-\frac{3}{40} \, \sqrt{5} \log\left(\frac{2 \, x^{4} - \sqrt{5} + 3}{2 \, x^{4} + \sqrt{5} + 3}\right) - \frac{1}{8} \, \log\left(x^{8} + 3 \, x^{4} + 1\right) + \frac{1}{4} \, \log\left(x^{4}\right)"," ",0,"-3/40*sqrt(5)*log((2*x^4 - sqrt(5) + 3)/(2*x^4 + sqrt(5) + 3)) - 1/8*log(x^8 + 3*x^4 + 1) + 1/4*log(x^4)","A",0
375,1,68,0,0.456485," ","integrate(1/x^3/(x^8+3*x^4+1),x, algorithm=""giac"")","-\frac{1}{20} \, {\left(x^{4} {\left(\sqrt{5} - 5\right)} + 3 \, \sqrt{5} - 15\right)} \arctan\left(\frac{2 \, x^{2}}{\sqrt{5} + 1}\right) - \frac{1}{20} \, {\left(x^{4} {\left(\sqrt{5} + 5\right)} + 3 \, \sqrt{5} + 15\right)} \arctan\left(\frac{2 \, x^{2}}{\sqrt{5} - 1}\right) - \frac{1}{2 \, x^{2}}"," ",0,"-1/20*(x^4*(sqrt(5) - 5) + 3*sqrt(5) - 15)*arctan(2*x^2/(sqrt(5) + 1)) - 1/20*(x^4*(sqrt(5) + 5) + 3*sqrt(5) + 15)*arctan(2*x^2/(sqrt(5) - 1)) - 1/2/x^2","A",0
376,1,63,0,0.550792," ","integrate(1/x^5/(x^8+3*x^4+1),x, algorithm=""giac"")","\frac{7}{40} \, \sqrt{5} \log\left(\frac{2 \, x^{4} - \sqrt{5} + 3}{2 \, x^{4} + \sqrt{5} + 3}\right) + \frac{3 \, x^{4} - 1}{4 \, x^{4}} + \frac{3}{8} \, \log\left(x^{8} + 3 \, x^{4} + 1\right) - \frac{3}{4} \, \log\left(x^{4}\right)"," ",0,"7/40*sqrt(5)*log((2*x^4 - sqrt(5) + 3)/(2*x^4 + sqrt(5) + 3)) + 1/4*(3*x^4 - 1)/x^4 + 3/8*log(x^8 + 3*x^4 + 1) - 3/4*log(x^4)","A",0
377,1,77,0,0.509025," ","integrate(1/x^7/(x^8+3*x^4+1),x, algorithm=""giac"")","\frac{1}{20} \, {\left(3 \, x^{4} {\left(\sqrt{5} - 5\right)} + 8 \, \sqrt{5} - 40\right)} \arctan\left(\frac{2 \, x^{2}}{\sqrt{5} + 1}\right) + \frac{1}{20} \, {\left(3 \, x^{4} {\left(\sqrt{5} + 5\right)} + 8 \, \sqrt{5} + 40\right)} \arctan\left(\frac{2 \, x^{2}}{\sqrt{5} - 1}\right) + \frac{9 \, x^{4} - 1}{6 \, x^{6}}"," ",0,"1/20*(3*x^4*(sqrt(5) - 5) + 8*sqrt(5) - 40)*arctan(2*x^2/(sqrt(5) + 1)) + 1/20*(3*x^4*(sqrt(5) + 5) + 8*sqrt(5) + 40)*arctan(2*x^2/(sqrt(5) - 1)) + 1/6*(9*x^4 - 1)/x^6","A",0
378,1,240,0,0.725110," ","integrate(x^8/(x^8+3*x^4+1),x, algorithm=""giac"")","-\frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} - 1} + 1\right)\right)} \sqrt{25 \, \sqrt{5} + 55} + \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} - 1} + 1\right)\right)} \sqrt{25 \, \sqrt{5} + 55} + \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} + 1} - 1\right)\right)} \sqrt{25 \, \sqrt{5} - 55} - \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} + 1} - 1\right)\right)} \sqrt{25 \, \sqrt{5} - 55} - \frac{1}{40} \, \sqrt{25 \, \sqrt{5} + 55} \log\left(722500 \, {\left(x + \sqrt{\sqrt{5} + 1}\right)}^{2} + 722500 \, x^{2}\right) + \frac{1}{40} \, \sqrt{25 \, \sqrt{5} + 55} \log\left(722500 \, {\left(x - \sqrt{\sqrt{5} + 1}\right)}^{2} + 722500 \, x^{2}\right) + \frac{1}{40} \, \sqrt{25 \, \sqrt{5} - 55} \log\left(2992900 \, {\left(x + \sqrt{\sqrt{5} - 1}\right)}^{2} + 2992900 \, x^{2}\right) - \frac{1}{40} \, \sqrt{25 \, \sqrt{5} - 55} \log\left(2992900 \, {\left(x - \sqrt{\sqrt{5} - 1}\right)}^{2} + 2992900 \, x^{2}\right) + x"," ",0,"-1/80*(pi + 4*arctan(x*sqrt(sqrt(5) - 1) + 1))*sqrt(25*sqrt(5) + 55) + 1/80*(pi + 4*arctan(-x*sqrt(sqrt(5) - 1) + 1))*sqrt(25*sqrt(5) + 55) + 1/80*(pi + 4*arctan(x*sqrt(sqrt(5) + 1) - 1))*sqrt(25*sqrt(5) - 55) - 1/80*(pi + 4*arctan(-x*sqrt(sqrt(5) + 1) - 1))*sqrt(25*sqrt(5) - 55) - 1/40*sqrt(25*sqrt(5) + 55)*log(722500*(x + sqrt(sqrt(5) + 1))^2 + 722500*x^2) + 1/40*sqrt(25*sqrt(5) + 55)*log(722500*(x - sqrt(sqrt(5) + 1))^2 + 722500*x^2) + 1/40*sqrt(25*sqrt(5) - 55)*log(2992900*(x + sqrt(sqrt(5) - 1))^2 + 2992900*x^2) - 1/40*sqrt(25*sqrt(5) - 55)*log(2992900*(x - sqrt(sqrt(5) - 1))^2 + 2992900*x^2) + x","A",0
379,1,239,0,0.663473," ","integrate(x^6/(x^8+3*x^4+1),x, algorithm=""giac"")","\frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} - 1} - 1\right)\right)} \sqrt{10 \, \sqrt{5} + 20} - \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} - 1} - 1\right)\right)} \sqrt{10 \, \sqrt{5} + 20} - \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} + 1} + 1\right)\right)} \sqrt{10 \, \sqrt{5} - 20} + \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} + 1} + 1\right)\right)} \sqrt{10 \, \sqrt{5} - 20} - \frac{1}{40} \, \sqrt{10 \, \sqrt{5} + 20} \log\left(400 \, {\left(x + \sqrt{\sqrt{5} + 1}\right)}^{2} + 400 \, x^{2}\right) + \frac{1}{40} \, \sqrt{10 \, \sqrt{5} + 20} \log\left(400 \, {\left(x - \sqrt{\sqrt{5} + 1}\right)}^{2} + 400 \, x^{2}\right) + \frac{1}{40} \, \sqrt{10 \, \sqrt{5} - 20} \log\left(10000 \, {\left(x + \sqrt{\sqrt{5} - 1}\right)}^{2} + 10000 \, x^{2}\right) - \frac{1}{40} \, \sqrt{10 \, \sqrt{5} - 20} \log\left(10000 \, {\left(x - \sqrt{\sqrt{5} - 1}\right)}^{2} + 10000 \, x^{2}\right)"," ",0,"1/80*(pi + 4*arctan(x*sqrt(sqrt(5) - 1) - 1))*sqrt(10*sqrt(5) + 20) - 1/80*(pi + 4*arctan(-x*sqrt(sqrt(5) - 1) - 1))*sqrt(10*sqrt(5) + 20) - 1/80*(pi + 4*arctan(x*sqrt(sqrt(5) + 1) + 1))*sqrt(10*sqrt(5) - 20) + 1/80*(pi + 4*arctan(-x*sqrt(sqrt(5) + 1) + 1))*sqrt(10*sqrt(5) - 20) - 1/40*sqrt(10*sqrt(5) + 20)*log(400*(x + sqrt(sqrt(5) + 1))^2 + 400*x^2) + 1/40*sqrt(10*sqrt(5) + 20)*log(400*(x - sqrt(sqrt(5) + 1))^2 + 400*x^2) + 1/40*sqrt(10*sqrt(5) - 20)*log(10000*(x + sqrt(sqrt(5) - 1))^2 + 10000*x^2) - 1/40*sqrt(10*sqrt(5) - 20)*log(10000*(x - sqrt(sqrt(5) - 1))^2 + 10000*x^2)","A",0
380,1,239,0,0.765143," ","integrate(x^4/(x^8+3*x^4+1),x, algorithm=""giac"")","\frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} - 1} + 1\right)\right)} \sqrt{5 \, \sqrt{5} + 5} - \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} - 1} + 1\right)\right)} \sqrt{5 \, \sqrt{5} + 5} - \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} + 1} - 1\right)\right)} \sqrt{5 \, \sqrt{5} - 5} + \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} + 1} - 1\right)\right)} \sqrt{5 \, \sqrt{5} - 5} + \frac{1}{40} \, \sqrt{5 \, \sqrt{5} + 5} \log\left(625 \, {\left(x + \sqrt{\sqrt{5} + 1}\right)}^{2} + 625 \, x^{2}\right) - \frac{1}{40} \, \sqrt{5 \, \sqrt{5} + 5} \log\left(625 \, {\left(x - \sqrt{\sqrt{5} + 1}\right)}^{2} + 625 \, x^{2}\right) - \frac{1}{40} \, \sqrt{5 \, \sqrt{5} - 5} \log\left(4225 \, {\left(x + \sqrt{\sqrt{5} - 1}\right)}^{2} + 4225 \, x^{2}\right) + \frac{1}{40} \, \sqrt{5 \, \sqrt{5} - 5} \log\left(4225 \, {\left(x - \sqrt{\sqrt{5} - 1}\right)}^{2} + 4225 \, x^{2}\right)"," ",0,"1/80*(pi + 4*arctan(x*sqrt(sqrt(5) - 1) + 1))*sqrt(5*sqrt(5) + 5) - 1/80*(pi + 4*arctan(-x*sqrt(sqrt(5) - 1) + 1))*sqrt(5*sqrt(5) + 5) - 1/80*(pi + 4*arctan(x*sqrt(sqrt(5) + 1) - 1))*sqrt(5*sqrt(5) - 5) + 1/80*(pi + 4*arctan(-x*sqrt(sqrt(5) + 1) - 1))*sqrt(5*sqrt(5) - 5) + 1/40*sqrt(5*sqrt(5) + 5)*log(625*(x + sqrt(sqrt(5) + 1))^2 + 625*x^2) - 1/40*sqrt(5*sqrt(5) + 5)*log(625*(x - sqrt(sqrt(5) + 1))^2 + 625*x^2) - 1/40*sqrt(5*sqrt(5) - 5)*log(4225*(x + sqrt(sqrt(5) - 1))^2 + 4225*x^2) + 1/40*sqrt(5*sqrt(5) - 5)*log(4225*(x - sqrt(sqrt(5) - 1))^2 + 4225*x^2)","A",0
381,1,239,0,0.592777," ","integrate(x^2/(x^8+3*x^4+1),x, algorithm=""giac"")","\frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} + 1} - 1\right)\right)} \sqrt{5 \, \sqrt{5} + 5} - \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} + 1} - 1\right)\right)} \sqrt{5 \, \sqrt{5} + 5} - \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} - 1} + 1\right)\right)} \sqrt{5 \, \sqrt{5} - 5} + \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} - 1} + 1\right)\right)} \sqrt{5 \, \sqrt{5} - 5} + \frac{1}{40} \, \sqrt{5 \, \sqrt{5} - 5} \log\left(16900 \, {\left(x + \sqrt{\sqrt{5} + 1}\right)}^{2} + 16900 \, x^{2}\right) - \frac{1}{40} \, \sqrt{5 \, \sqrt{5} - 5} \log\left(16900 \, {\left(x - \sqrt{\sqrt{5} + 1}\right)}^{2} + 16900 \, x^{2}\right) - \frac{1}{40} \, \sqrt{5 \, \sqrt{5} + 5} \log\left(2500 \, {\left(x + \sqrt{\sqrt{5} - 1}\right)}^{2} + 2500 \, x^{2}\right) + \frac{1}{40} \, \sqrt{5 \, \sqrt{5} + 5} \log\left(2500 \, {\left(x - \sqrt{\sqrt{5} - 1}\right)}^{2} + 2500 \, x^{2}\right)"," ",0,"1/80*(pi + 4*arctan(x*sqrt(sqrt(5) + 1) - 1))*sqrt(5*sqrt(5) + 5) - 1/80*(pi + 4*arctan(-x*sqrt(sqrt(5) + 1) - 1))*sqrt(5*sqrt(5) + 5) - 1/80*(pi + 4*arctan(x*sqrt(sqrt(5) - 1) + 1))*sqrt(5*sqrt(5) - 5) + 1/80*(pi + 4*arctan(-x*sqrt(sqrt(5) - 1) + 1))*sqrt(5*sqrt(5) - 5) + 1/40*sqrt(5*sqrt(5) - 5)*log(16900*(x + sqrt(sqrt(5) + 1))^2 + 16900*x^2) - 1/40*sqrt(5*sqrt(5) - 5)*log(16900*(x - sqrt(sqrt(5) + 1))^2 + 16900*x^2) - 1/40*sqrt(5*sqrt(5) + 5)*log(2500*(x + sqrt(sqrt(5) - 1))^2 + 2500*x^2) + 1/40*sqrt(5*sqrt(5) + 5)*log(2500*(x - sqrt(sqrt(5) - 1))^2 + 2500*x^2)","A",0
382,1,239,0,0.528450," ","integrate(1/(x^8+3*x^4+1),x, algorithm=""giac"")","\frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} + 1} + 1\right)\right)} \sqrt{10 \, \sqrt{5} + 20} - \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} + 1} + 1\right)\right)} \sqrt{10 \, \sqrt{5} + 20} - \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} - 1} - 1\right)\right)} \sqrt{10 \, \sqrt{5} - 20} + \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} - 1} - 1\right)\right)} \sqrt{10 \, \sqrt{5} - 20} - \frac{1}{40} \, \sqrt{10 \, \sqrt{5} - 20} \log\left(10000 \, {\left(x + \sqrt{\sqrt{5} + 1}\right)}^{2} + 10000 \, x^{2}\right) + \frac{1}{40} \, \sqrt{10 \, \sqrt{5} - 20} \log\left(10000 \, {\left(x - \sqrt{\sqrt{5} + 1}\right)}^{2} + 10000 \, x^{2}\right) + \frac{1}{40} \, \sqrt{10 \, \sqrt{5} + 20} \log\left(400 \, {\left(x + \sqrt{\sqrt{5} - 1}\right)}^{2} + 400 \, x^{2}\right) - \frac{1}{40} \, \sqrt{10 \, \sqrt{5} + 20} \log\left(400 \, {\left(x - \sqrt{\sqrt{5} - 1}\right)}^{2} + 400 \, x^{2}\right)"," ",0,"1/80*(pi + 4*arctan(x*sqrt(sqrt(5) + 1) + 1))*sqrt(10*sqrt(5) + 20) - 1/80*(pi + 4*arctan(-x*sqrt(sqrt(5) + 1) + 1))*sqrt(10*sqrt(5) + 20) - 1/80*(pi + 4*arctan(x*sqrt(sqrt(5) - 1) - 1))*sqrt(10*sqrt(5) - 20) + 1/80*(pi + 4*arctan(-x*sqrt(sqrt(5) - 1) - 1))*sqrt(10*sqrt(5) - 20) - 1/40*sqrt(10*sqrt(5) - 20)*log(10000*(x + sqrt(sqrt(5) + 1))^2 + 10000*x^2) + 1/40*sqrt(10*sqrt(5) - 20)*log(10000*(x - sqrt(sqrt(5) + 1))^2 + 10000*x^2) + 1/40*sqrt(10*sqrt(5) + 20)*log(400*(x + sqrt(sqrt(5) - 1))^2 + 400*x^2) - 1/40*sqrt(10*sqrt(5) + 20)*log(400*(x - sqrt(sqrt(5) - 1))^2 + 400*x^2)","A",0
383,1,244,0,0.603155," ","integrate(1/x^2/(x^8+3*x^4+1),x, algorithm=""giac"")","-\frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} + 1} - 1\right)\right)} \sqrt{25 \, \sqrt{5} + 55} + \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} + 1} - 1\right)\right)} \sqrt{25 \, \sqrt{5} + 55} + \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} - 1} + 1\right)\right)} \sqrt{25 \, \sqrt{5} - 55} - \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} - 1} + 1\right)\right)} \sqrt{25 \, \sqrt{5} - 55} - \frac{1}{40} \, \sqrt{25 \, \sqrt{5} - 55} \log\left(748225 \, {\left(x + \sqrt{\sqrt{5} + 1}\right)}^{2} + 748225 \, x^{2}\right) + \frac{1}{40} \, \sqrt{25 \, \sqrt{5} - 55} \log\left(748225 \, {\left(x - \sqrt{\sqrt{5} + 1}\right)}^{2} + 748225 \, x^{2}\right) + \frac{1}{40} \, \sqrt{25 \, \sqrt{5} + 55} \log\left(180625 \, {\left(x + \sqrt{\sqrt{5} - 1}\right)}^{2} + 180625 \, x^{2}\right) - \frac{1}{40} \, \sqrt{25 \, \sqrt{5} + 55} \log\left(180625 \, {\left(x - \sqrt{\sqrt{5} - 1}\right)}^{2} + 180625 \, x^{2}\right) - \frac{1}{x}"," ",0,"-1/80*(pi + 4*arctan(x*sqrt(sqrt(5) + 1) - 1))*sqrt(25*sqrt(5) + 55) + 1/80*(pi + 4*arctan(-x*sqrt(sqrt(5) + 1) - 1))*sqrt(25*sqrt(5) + 55) + 1/80*(pi + 4*arctan(x*sqrt(sqrt(5) - 1) + 1))*sqrt(25*sqrt(5) - 55) - 1/80*(pi + 4*arctan(-x*sqrt(sqrt(5) - 1) + 1))*sqrt(25*sqrt(5) - 55) - 1/40*sqrt(25*sqrt(5) - 55)*log(748225*(x + sqrt(sqrt(5) + 1))^2 + 748225*x^2) + 1/40*sqrt(25*sqrt(5) - 55)*log(748225*(x - sqrt(sqrt(5) + 1))^2 + 748225*x^2) + 1/40*sqrt(25*sqrt(5) + 55)*log(180625*(x + sqrt(sqrt(5) - 1))^2 + 180625*x^2) - 1/40*sqrt(25*sqrt(5) + 55)*log(180625*(x - sqrt(sqrt(5) - 1))^2 + 180625*x^2) - 1/x","A",0
384,1,244,0,0.701915," ","integrate(1/x^4/(x^8+3*x^4+1),x, algorithm=""giac"")","-\frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} + 1} + 1\right)\right)} \sqrt{65 \, \sqrt{5} + 145} + \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} + 1} + 1\right)\right)} \sqrt{65 \, \sqrt{5} + 145} + \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} - 1} - 1\right)\right)} \sqrt{65 \, \sqrt{5} - 145} - \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} - 1} - 1\right)\right)} \sqrt{65 \, \sqrt{5} - 145} + \frac{1}{40} \, \sqrt{65 \, \sqrt{5} - 145} \log\left(93122500 \, {\left(x + \sqrt{\sqrt{5} + 1}\right)}^{2} + 93122500 \, x^{2}\right) - \frac{1}{40} \, \sqrt{65 \, \sqrt{5} - 145} \log\left(93122500 \, {\left(x - \sqrt{\sqrt{5} + 1}\right)}^{2} + 93122500 \, x^{2}\right) - \frac{1}{40} \, \sqrt{65 \, \sqrt{5} + 145} \log\left(53728900 \, {\left(x + \sqrt{\sqrt{5} - 1}\right)}^{2} + 53728900 \, x^{2}\right) + \frac{1}{40} \, \sqrt{65 \, \sqrt{5} + 145} \log\left(53728900 \, {\left(x - \sqrt{\sqrt{5} - 1}\right)}^{2} + 53728900 \, x^{2}\right) - \frac{1}{3 \, x^{3}}"," ",0,"-1/80*(pi + 4*arctan(x*sqrt(sqrt(5) + 1) + 1))*sqrt(65*sqrt(5) + 145) + 1/80*(pi + 4*arctan(-x*sqrt(sqrt(5) + 1) + 1))*sqrt(65*sqrt(5) + 145) + 1/80*(pi + 4*arctan(x*sqrt(sqrt(5) - 1) - 1))*sqrt(65*sqrt(5) - 145) - 1/80*(pi + 4*arctan(-x*sqrt(sqrt(5) - 1) - 1))*sqrt(65*sqrt(5) - 145) + 1/40*sqrt(65*sqrt(5) - 145)*log(93122500*(x + sqrt(sqrt(5) + 1))^2 + 93122500*x^2) - 1/40*sqrt(65*sqrt(5) - 145)*log(93122500*(x - sqrt(sqrt(5) + 1))^2 + 93122500*x^2) - 1/40*sqrt(65*sqrt(5) + 145)*log(53728900*(x + sqrt(sqrt(5) - 1))^2 + 53728900*x^2) + 1/40*sqrt(65*sqrt(5) + 145)*log(53728900*(x - sqrt(sqrt(5) - 1))^2 + 53728900*x^2) - 1/3/x^3","A",0
385,0,0,0,0.000000," ","integrate(x^m/(x^8-3*x^4+1),x, algorithm=""giac"")","\int \frac{x^{m}}{x^{8} - 3 \, x^{4} + 1}\,{d x}"," ",0,"integrate(x^m/(x^8 - 3*x^4 + 1), x)","F",0
386,1,53,0,0.415942," ","integrate(x^11/(x^8-3*x^4+1),x, algorithm=""giac"")","\frac{1}{4} \, x^{4} + \frac{7}{40} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x^{4} - \sqrt{5} - 3 \right|}}{{\left| 2 \, x^{4} + \sqrt{5} - 3 \right|}}\right) + \frac{3}{8} \, \log\left({\left| x^{8} - 3 \, x^{4} + 1 \right|}\right)"," ",0,"1/4*x^4 + 7/40*sqrt(5)*log(abs(2*x^4 - sqrt(5) - 3)/abs(2*x^4 + sqrt(5) - 3)) + 3/8*log(abs(x^8 - 3*x^4 + 1))","A",0
387,1,97,0,0.463482," ","integrate(x^9/(x^8-3*x^4+1),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + \frac{1}{10} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x^{2} - \sqrt{5} + 1 \right|}}{2 \, x^{2} + \sqrt{5} + 1}\right) + \frac{1}{10} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x^{2} - \sqrt{5} - 1 \right|}}{{\left| 2 \, x^{2} + \sqrt{5} - 1 \right|}}\right) - \frac{1}{4} \, \log\left({\left| x^{4} + x^{2} - 1 \right|}\right) + \frac{1}{4} \, \log\left({\left| x^{4} - x^{2} - 1 \right|}\right)"," ",0,"1/2*x^2 + 1/10*sqrt(5)*log(abs(2*x^2 - sqrt(5) + 1)/(2*x^2 + sqrt(5) + 1)) + 1/10*sqrt(5)*log(abs(2*x^2 - sqrt(5) - 1)/abs(2*x^2 + sqrt(5) - 1)) - 1/4*log(abs(x^4 + x^2 - 1)) + 1/4*log(abs(x^4 - x^2 - 1))","A",0
388,1,48,0,0.424716," ","integrate(x^7/(x^8-3*x^4+1),x, algorithm=""giac"")","\frac{3}{40} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x^{4} - \sqrt{5} - 3 \right|}}{{\left| 2 \, x^{4} + \sqrt{5} - 3 \right|}}\right) + \frac{1}{8} \, \log\left({\left| x^{8} - 3 \, x^{4} + 1 \right|}\right)"," ",0,"3/40*sqrt(5)*log(abs(2*x^4 - sqrt(5) - 3)/abs(2*x^4 + sqrt(5) - 3)) + 1/8*log(abs(x^8 - 3*x^4 + 1))","A",0
389,1,92,0,0.444912," ","integrate(x^5/(x^8-3*x^4+1),x, algorithm=""giac"")","\frac{1}{40} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x^{2} - \sqrt{5} + 1 \right|}}{2 \, x^{2} + \sqrt{5} + 1}\right) + \frac{1}{40} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x^{2} - \sqrt{5} - 1 \right|}}{{\left| 2 \, x^{2} + \sqrt{5} - 1 \right|}}\right) - \frac{1}{8} \, \log\left({\left| x^{4} + x^{2} - 1 \right|}\right) + \frac{1}{8} \, \log\left({\left| x^{4} - x^{2} - 1 \right|}\right)"," ",0,"1/40*sqrt(5)*log(abs(2*x^2 - sqrt(5) + 1)/(2*x^2 + sqrt(5) + 1)) + 1/40*sqrt(5)*log(abs(2*x^2 - sqrt(5) - 1)/abs(2*x^2 + sqrt(5) - 1)) - 1/8*log(abs(x^4 + x^2 - 1)) + 1/8*log(abs(x^4 - x^2 - 1))","B",0
390,1,33,0,0.537001," ","integrate(x^3/(x^8-3*x^4+1),x, algorithm=""giac"")","\frac{1}{20} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x^{4} - \sqrt{5} - 3 \right|}}{{\left| 2 \, x^{4} + \sqrt{5} - 3 \right|}}\right)"," ",0,"1/20*sqrt(5)*log(abs(2*x^4 - sqrt(5) - 3)/abs(2*x^4 + sqrt(5) - 3))","A",0
391,1,92,0,0.433272," ","integrate(x/(x^8-3*x^4+1),x, algorithm=""giac"")","-\frac{1}{40} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x^{2} - \sqrt{5} + 1 \right|}}{2 \, x^{2} + \sqrt{5} + 1}\right) - \frac{1}{40} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x^{2} - \sqrt{5} - 1 \right|}}{{\left| 2 \, x^{2} + \sqrt{5} - 1 \right|}}\right) - \frac{1}{8} \, \log\left({\left| x^{4} + x^{2} - 1 \right|}\right) + \frac{1}{8} \, \log\left({\left| x^{4} - x^{2} - 1 \right|}\right)"," ",0,"-1/40*sqrt(5)*log(abs(2*x^2 - sqrt(5) + 1)/(2*x^2 + sqrt(5) + 1)) - 1/40*sqrt(5)*log(abs(2*x^2 - sqrt(5) - 1)/abs(2*x^2 + sqrt(5) - 1)) - 1/8*log(abs(x^4 + x^2 - 1)) + 1/8*log(abs(x^4 - x^2 - 1))","B",0
392,1,54,0,0.477083," ","integrate(1/x/(x^8-3*x^4+1),x, algorithm=""giac"")","\frac{3}{40} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x^{4} - \sqrt{5} - 3 \right|}}{{\left| 2 \, x^{4} + \sqrt{5} - 3 \right|}}\right) + \frac{1}{4} \, \log\left(x^{4}\right) - \frac{1}{8} \, \log\left({\left| x^{8} - 3 \, x^{4} + 1 \right|}\right)"," ",0,"3/40*sqrt(5)*log(abs(2*x^4 - sqrt(5) - 3)/abs(2*x^4 + sqrt(5) - 3)) + 1/4*log(x^4) - 1/8*log(abs(x^8 - 3*x^4 + 1))","A",0
393,1,97,0,0.384189," ","integrate(1/x^3/(x^8-3*x^4+1),x, algorithm=""giac"")","-\frac{1}{10} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x^{2} - \sqrt{5} + 1 \right|}}{2 \, x^{2} + \sqrt{5} + 1}\right) - \frac{1}{10} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x^{2} - \sqrt{5} - 1 \right|}}{{\left| 2 \, x^{2} + \sqrt{5} - 1 \right|}}\right) - \frac{1}{2 \, x^{2}} - \frac{1}{4} \, \log\left({\left| x^{4} + x^{2} - 1 \right|}\right) + \frac{1}{4} \, \log\left({\left| x^{4} - x^{2} - 1 \right|}\right)"," ",0,"-1/10*sqrt(5)*log(abs(2*x^2 - sqrt(5) + 1)/(2*x^2 + sqrt(5) + 1)) - 1/10*sqrt(5)*log(abs(2*x^2 - sqrt(5) - 1)/abs(2*x^2 + sqrt(5) - 1)) - 1/2/x^2 - 1/4*log(abs(x^4 + x^2 - 1)) + 1/4*log(abs(x^4 - x^2 - 1))","A",0
394,1,66,0,0.505482," ","integrate(1/x^5/(x^8-3*x^4+1),x, algorithm=""giac"")","\frac{7}{40} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x^{4} - \sqrt{5} - 3 \right|}}{{\left| 2 \, x^{4} + \sqrt{5} - 3 \right|}}\right) - \frac{3 \, x^{4} + 1}{4 \, x^{4}} + \frac{3}{4} \, \log\left(x^{4}\right) - \frac{3}{8} \, \log\left({\left| x^{8} - 3 \, x^{4} + 1 \right|}\right)"," ",0,"7/40*sqrt(5)*log(abs(2*x^4 - sqrt(5) - 3)/abs(2*x^4 + sqrt(5) - 3)) - 1/4*(3*x^4 + 1)/x^4 + 3/4*log(x^4) - 3/8*log(abs(x^8 - 3*x^4 + 1))","A",0
395,1,104,0,0.409027," ","integrate(1/x^7/(x^8-3*x^4+1),x, algorithm=""giac"")","-\frac{11}{40} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x^{2} - \sqrt{5} + 1 \right|}}{2 \, x^{2} + \sqrt{5} + 1}\right) - \frac{11}{40} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x^{2} - \sqrt{5} - 1 \right|}}{{\left| 2 \, x^{2} + \sqrt{5} - 1 \right|}}\right) - \frac{9 \, x^{4} + 1}{6 \, x^{6}} - \frac{5}{8} \, \log\left({\left| x^{4} + x^{2} - 1 \right|}\right) + \frac{5}{8} \, \log\left({\left| x^{4} - x^{2} - 1 \right|}\right)"," ",0,"-11/40*sqrt(5)*log(abs(2*x^2 - sqrt(5) + 1)/(2*x^2 + sqrt(5) + 1)) - 11/40*sqrt(5)*log(abs(2*x^2 - sqrt(5) - 1)/abs(2*x^2 + sqrt(5) - 1)) - 1/6*(9*x^4 + 1)/x^6 - 5/8*log(abs(x^4 + x^2 - 1)) + 5/8*log(abs(x^4 - x^2 - 1))","A",0
396,1,148,0,0.675853," ","integrate(x^8/(x^8-3*x^4+1),x, algorithm=""giac"")","-\frac{1}{20} \, \sqrt{50 \, \sqrt{5} + 110} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) + \frac{1}{20} \, \sqrt{50 \, \sqrt{5} - 110} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) - \frac{1}{40} \, \sqrt{50 \, \sqrt{5} + 110} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{40} \, \sqrt{50 \, \sqrt{5} + 110} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{40} \, \sqrt{50 \, \sqrt{5} - 110} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) - \frac{1}{40} \, \sqrt{50 \, \sqrt{5} - 110} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) + x"," ",0,"-1/20*sqrt(50*sqrt(5) + 110)*arctan(x/sqrt(1/2*sqrt(5) + 1/2)) + 1/20*sqrt(50*sqrt(5) - 110)*arctan(x/sqrt(1/2*sqrt(5) - 1/2)) - 1/40*sqrt(50*sqrt(5) + 110)*log(abs(x + sqrt(1/2*sqrt(5) + 1/2))) + 1/40*sqrt(50*sqrt(5) + 110)*log(abs(x - sqrt(1/2*sqrt(5) + 1/2))) + 1/40*sqrt(50*sqrt(5) - 110)*log(abs(x + sqrt(1/2*sqrt(5) - 1/2))) - 1/40*sqrt(50*sqrt(5) - 110)*log(abs(x - sqrt(1/2*sqrt(5) - 1/2))) + x","A",0
397,1,147,0,0.748005," ","integrate(x^6/(x^8-3*x^4+1),x, algorithm=""giac"")","\frac{1}{10} \, \sqrt{5 \, \sqrt{5} + 10} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) - \frac{1}{10} \, \sqrt{5 \, \sqrt{5} - 10} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) - \frac{1}{20} \, \sqrt{5 \, \sqrt{5} + 10} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{20} \, \sqrt{5 \, \sqrt{5} + 10} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{20} \, \sqrt{5 \, \sqrt{5} - 10} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) - \frac{1}{20} \, \sqrt{5 \, \sqrt{5} - 10} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right)"," ",0,"1/10*sqrt(5*sqrt(5) + 10)*arctan(x/sqrt(1/2*sqrt(5) + 1/2)) - 1/10*sqrt(5*sqrt(5) - 10)*arctan(x/sqrt(1/2*sqrt(5) - 1/2)) - 1/20*sqrt(5*sqrt(5) + 10)*log(abs(x + sqrt(1/2*sqrt(5) + 1/2))) + 1/20*sqrt(5*sqrt(5) + 10)*log(abs(x - sqrt(1/2*sqrt(5) + 1/2))) + 1/20*sqrt(5*sqrt(5) - 10)*log(abs(x + sqrt(1/2*sqrt(5) - 1/2))) - 1/20*sqrt(5*sqrt(5) - 10)*log(abs(x - sqrt(1/2*sqrt(5) - 1/2)))","A",0
398,1,147,0,0.614530," ","integrate(x^4/(x^8-3*x^4+1),x, algorithm=""giac"")","-\frac{1}{20} \, \sqrt{10 \, \sqrt{5} + 10} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) + \frac{1}{20} \, \sqrt{10 \, \sqrt{5} - 10} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) - \frac{1}{40} \, \sqrt{10 \, \sqrt{5} + 10} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{40} \, \sqrt{10 \, \sqrt{5} + 10} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{40} \, \sqrt{10 \, \sqrt{5} - 10} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) - \frac{1}{40} \, \sqrt{10 \, \sqrt{5} - 10} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right)"," ",0,"-1/20*sqrt(10*sqrt(5) + 10)*arctan(x/sqrt(1/2*sqrt(5) + 1/2)) + 1/20*sqrt(10*sqrt(5) - 10)*arctan(x/sqrt(1/2*sqrt(5) - 1/2)) - 1/40*sqrt(10*sqrt(5) + 10)*log(abs(x + sqrt(1/2*sqrt(5) + 1/2))) + 1/40*sqrt(10*sqrt(5) + 10)*log(abs(x - sqrt(1/2*sqrt(5) + 1/2))) + 1/40*sqrt(10*sqrt(5) - 10)*log(abs(x + sqrt(1/2*sqrt(5) - 1/2))) - 1/40*sqrt(10*sqrt(5) - 10)*log(abs(x - sqrt(1/2*sqrt(5) - 1/2)))","A",0
399,1,147,0,0.623738," ","integrate(x^2/(x^8-3*x^4+1),x, algorithm=""giac"")","\frac{1}{20} \, \sqrt{10 \, \sqrt{5} - 10} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) - \frac{1}{20} \, \sqrt{10 \, \sqrt{5} + 10} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) - \frac{1}{40} \, \sqrt{10 \, \sqrt{5} - 10} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{40} \, \sqrt{10 \, \sqrt{5} - 10} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{40} \, \sqrt{10 \, \sqrt{5} + 10} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) - \frac{1}{40} \, \sqrt{10 \, \sqrt{5} + 10} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right)"," ",0,"1/20*sqrt(10*sqrt(5) - 10)*arctan(x/sqrt(1/2*sqrt(5) + 1/2)) - 1/20*sqrt(10*sqrt(5) + 10)*arctan(x/sqrt(1/2*sqrt(5) - 1/2)) - 1/40*sqrt(10*sqrt(5) - 10)*log(abs(x + sqrt(1/2*sqrt(5) + 1/2))) + 1/40*sqrt(10*sqrt(5) - 10)*log(abs(x - sqrt(1/2*sqrt(5) + 1/2))) + 1/40*sqrt(10*sqrt(5) + 10)*log(abs(x + sqrt(1/2*sqrt(5) - 1/2))) - 1/40*sqrt(10*sqrt(5) + 10)*log(abs(x - sqrt(1/2*sqrt(5) - 1/2)))","A",0
400,1,147,0,0.481573," ","integrate(1/(x^8-3*x^4+1),x, algorithm=""giac"")","-\frac{1}{10} \, \sqrt{5 \, \sqrt{5} - 10} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) + \frac{1}{10} \, \sqrt{5 \, \sqrt{5} + 10} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) - \frac{1}{20} \, \sqrt{5 \, \sqrt{5} - 10} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{20} \, \sqrt{5 \, \sqrt{5} - 10} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{20} \, \sqrt{5 \, \sqrt{5} + 10} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) - \frac{1}{20} \, \sqrt{5 \, \sqrt{5} + 10} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right)"," ",0,"-1/10*sqrt(5*sqrt(5) - 10)*arctan(x/sqrt(1/2*sqrt(5) + 1/2)) + 1/10*sqrt(5*sqrt(5) + 10)*arctan(x/sqrt(1/2*sqrt(5) - 1/2)) - 1/20*sqrt(5*sqrt(5) - 10)*log(abs(x + sqrt(1/2*sqrt(5) + 1/2))) + 1/20*sqrt(5*sqrt(5) - 10)*log(abs(x - sqrt(1/2*sqrt(5) + 1/2))) + 1/20*sqrt(5*sqrt(5) + 10)*log(abs(x + sqrt(1/2*sqrt(5) - 1/2))) - 1/20*sqrt(5*sqrt(5) + 10)*log(abs(x - sqrt(1/2*sqrt(5) - 1/2)))","A",0
401,1,152,0,0.541734," ","integrate(1/x^2/(x^8-3*x^4+1),x, algorithm=""giac"")","\frac{1}{20} \, \sqrt{50 \, \sqrt{5} - 110} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) - \frac{1}{20} \, \sqrt{50 \, \sqrt{5} + 110} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) - \frac{1}{40} \, \sqrt{50 \, \sqrt{5} - 110} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{40} \, \sqrt{50 \, \sqrt{5} - 110} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{40} \, \sqrt{50 \, \sqrt{5} + 110} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) - \frac{1}{40} \, \sqrt{50 \, \sqrt{5} + 110} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) - \frac{1}{x}"," ",0,"1/20*sqrt(50*sqrt(5) - 110)*arctan(x/sqrt(1/2*sqrt(5) + 1/2)) - 1/20*sqrt(50*sqrt(5) + 110)*arctan(x/sqrt(1/2*sqrt(5) - 1/2)) - 1/40*sqrt(50*sqrt(5) - 110)*log(abs(x + sqrt(1/2*sqrt(5) + 1/2))) + 1/40*sqrt(50*sqrt(5) - 110)*log(abs(x - sqrt(1/2*sqrt(5) + 1/2))) + 1/40*sqrt(50*sqrt(5) + 110)*log(abs(x + sqrt(1/2*sqrt(5) - 1/2))) - 1/40*sqrt(50*sqrt(5) + 110)*log(abs(x - sqrt(1/2*sqrt(5) - 1/2))) - 1/x","A",0
402,1,152,0,0.669285," ","integrate(1/x^4/(x^8-3*x^4+1),x, algorithm=""giac"")","-\frac{1}{20} \, \sqrt{130 \, \sqrt{5} - 290} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) + \frac{1}{20} \, \sqrt{130 \, \sqrt{5} + 290} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) - \frac{1}{40} \, \sqrt{130 \, \sqrt{5} - 290} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{40} \, \sqrt{130 \, \sqrt{5} - 290} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{40} \, \sqrt{130 \, \sqrt{5} + 290} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) - \frac{1}{40} \, \sqrt{130 \, \sqrt{5} + 290} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) - \frac{1}{3 \, x^{3}}"," ",0,"-1/20*sqrt(130*sqrt(5) - 290)*arctan(x/sqrt(1/2*sqrt(5) + 1/2)) + 1/20*sqrt(130*sqrt(5) + 290)*arctan(x/sqrt(1/2*sqrt(5) - 1/2)) - 1/40*sqrt(130*sqrt(5) - 290)*log(abs(x + sqrt(1/2*sqrt(5) + 1/2))) + 1/40*sqrt(130*sqrt(5) - 290)*log(abs(x - sqrt(1/2*sqrt(5) + 1/2))) + 1/40*sqrt(130*sqrt(5) + 290)*log(abs(x + sqrt(1/2*sqrt(5) - 1/2))) - 1/40*sqrt(130*sqrt(5) + 290)*log(abs(x - sqrt(1/2*sqrt(5) - 1/2))) - 1/3/x^3","A",0
403,1,159,0,0.539434," ","integrate(1/x^6/(x^8-3*x^4+1),x, algorithm=""giac"")","\frac{1}{10} \, \sqrt{85 \, \sqrt{5} - 190} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) - \frac{1}{10} \, \sqrt{85 \, \sqrt{5} + 190} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) - \frac{1}{20} \, \sqrt{85 \, \sqrt{5} - 190} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{20} \, \sqrt{85 \, \sqrt{5} - 190} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{20} \, \sqrt{85 \, \sqrt{5} + 190} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) - \frac{1}{20} \, \sqrt{85 \, \sqrt{5} + 190} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) - \frac{15 \, x^{4} + 1}{5 \, x^{5}}"," ",0,"1/10*sqrt(85*sqrt(5) - 190)*arctan(x/sqrt(1/2*sqrt(5) + 1/2)) - 1/10*sqrt(85*sqrt(5) + 190)*arctan(x/sqrt(1/2*sqrt(5) - 1/2)) - 1/20*sqrt(85*sqrt(5) - 190)*log(abs(x + sqrt(1/2*sqrt(5) + 1/2))) + 1/20*sqrt(85*sqrt(5) - 190)*log(abs(x - sqrt(1/2*sqrt(5) + 1/2))) + 1/20*sqrt(85*sqrt(5) + 190)*log(abs(x + sqrt(1/2*sqrt(5) - 1/2))) - 1/20*sqrt(85*sqrt(5) + 190)*log(abs(x - sqrt(1/2*sqrt(5) - 1/2))) - 1/5*(15*x^4 + 1)/x^5","A",0
404,1,159,0,0.555503," ","integrate(1/x^8/(x^8-3*x^4+1),x, algorithm=""giac"")","-\frac{1}{20} \, \sqrt{890 \, \sqrt{5} - 1990} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) + \frac{1}{20} \, \sqrt{890 \, \sqrt{5} + 1990} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) - \frac{1}{40} \, \sqrt{890 \, \sqrt{5} - 1990} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{40} \, \sqrt{890 \, \sqrt{5} - 1990} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{40} \, \sqrt{890 \, \sqrt{5} + 1990} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) - \frac{1}{40} \, \sqrt{890 \, \sqrt{5} + 1990} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) - \frac{7 \, x^{4} + 1}{7 \, x^{7}}"," ",0,"-1/20*sqrt(890*sqrt(5) - 1990)*arctan(x/sqrt(1/2*sqrt(5) + 1/2)) + 1/20*sqrt(890*sqrt(5) + 1990)*arctan(x/sqrt(1/2*sqrt(5) - 1/2)) - 1/40*sqrt(890*sqrt(5) - 1990)*log(abs(x + sqrt(1/2*sqrt(5) + 1/2))) + 1/40*sqrt(890*sqrt(5) - 1990)*log(abs(x - sqrt(1/2*sqrt(5) + 1/2))) + 1/40*sqrt(890*sqrt(5) + 1990)*log(abs(x + sqrt(1/2*sqrt(5) - 1/2))) - 1/40*sqrt(890*sqrt(5) + 1990)*log(abs(x - sqrt(1/2*sqrt(5) - 1/2))) - 1/7*(7*x^4 + 1)/x^7","A",0
405,1,17,0,0.282395," ","integrate(x^3/(x^8+3*x^4+2),x, algorithm=""giac"")","-\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
406,1,22,0,0.363667," ","integrate(x^11/(x^8+3*x^4+2),x, algorithm=""giac"")","\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
407,1,30,0,2.720980," ","integrate(x^9/(x^10+x^5+2),x, algorithm=""giac"")","-\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
408,1,18,0,2.962292," ","integrate(x^4/(x^10+x^5+2),x, algorithm=""giac"")","\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
409,1,33,0,0.408440," ","integrate(1/x/(x^10+x^5+1),x, algorithm=""giac"")","-\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({\left| x \right|}\right)"," ",0,"-1/15*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^5 + 1)) - 1/10*log(x^10 + x^5 + 1) + log(abs(x))","A",0
410,1,45,0,0.251424," ","integrate(1/x^6/(x^10+x^5+1),x, algorithm=""giac"")","-\frac{1}{15} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{5} + 1\right)}\right) + \frac{x^{5} - 1}{5 \, x^{5}} + \frac{1}{10} \, \log\left(x^{10} + x^{5} + 1\right) - \log\left({\left| x \right|}\right)"," ",0,"-1/15*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^5 + 1)) + 1/5*(x^5 - 1)/x^5 + 1/10*log(x^10 + x^5 + 1) - log(abs(x))","A",0
411,1,33,0,0.350234," ","integrate(1/(x^11+x^6+x),x, algorithm=""giac"")","-\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({\left| x \right|}\right)"," ",0,"-1/15*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^5 + 1)) - 1/10*log(x^10 + x^5 + 1) + log(abs(x))","A",0
412,1,145,0,0.291356," ","integrate(x^3/(c+a/x^2+b/x),x, algorithm=""giac"")","\frac{3 \, c^{3} x^{4} - 4 \, b c^{2} x^{3} + 6 \, b^{2} c x^{2} - 6 \, a c^{2} x^{2} - 12 \, b^{3} x + 24 \, a b c x}{12 \, c^{4}} + \frac{{\left(b^{4} - 3 \, a b^{2} c + a^{2} c^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{5}} - \frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{5}}"," ",0,"1/12*(3*c^3*x^4 - 4*b*c^2*x^3 + 6*b^2*c*x^2 - 6*a*c^2*x^2 - 12*b^3*x + 24*a*b*c*x)/c^4 + 1/2*(b^4 - 3*a*b^2*c + a^2*c^2)*log(c*x^2 + b*x + a)/c^5 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^5)","A",0
413,1,113,0,0.392039," ","integrate(x^2/(c+a/x^2+b/x),x, algorithm=""giac"")","\frac{2 \, c^{2} x^{3} - 3 \, b c x^{2} + 6 \, b^{2} x - 6 \, a c x}{6 \, c^{3}} - \frac{{\left(b^{3} - 2 \, a b c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{4}} + \frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{4}}"," ",0,"1/6*(2*c^2*x^3 - 3*b*c*x^2 + 6*b^2*x - 6*a*c*x)/c^3 - 1/2*(b^3 - 2*a*b*c)*log(c*x^2 + b*x + a)/c^4 + (b^4 - 4*a*b^2*c + 2*a^2*c^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^4)","A",0
414,1,86,0,0.257469," ","integrate(x/(c+a/x^2+b/x),x, algorithm=""giac"")","\frac{c x^{2} - 2 \, b x}{2 \, c^{2}} + \frac{{\left(b^{2} - a c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{3}} - \frac{{\left(b^{3} - 3 \, a b c\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{3}}"," ",0,"1/2*(c*x^2 - 2*b*x)/c^2 + 1/2*(b^2 - a*c)*log(c*x^2 + b*x + a)/c^3 - (b^3 - 3*a*b*c)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^3)","A",0
415,1,67,0,0.274364," ","integrate(1/(c+a/x^2+b/x),x, algorithm=""giac"")","\frac{x}{c} - \frac{b \log\left(c x^{2} + b x + a\right)}{2 \, c^{2}} + \frac{{\left(b^{2} - 2 \, a c\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{2}}"," ",0,"x/c - 1/2*b*log(c*x^2 + b*x + a)/c^2 + (b^2 - 2*a*c)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2)","A",0
416,1,55,0,0.291080," ","integrate(1/(c+a/x^2+b/x)/x,x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c} + \frac{\log\left(c x^{2} + b x + a\right)}{2 \, c}"," ",0,"-b*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c) + 1/2*log(c*x^2 + b*x + a)/c","A",0
417,1,34,0,0.345074," ","integrate(1/(c+a/x^2+b/x)/x^2,x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}}"," ",0,"2*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c)","A",0
418,1,62,0,0.296701," ","integrate(1/(c+a/x^2+b/x)/x^3,x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} a} - \frac{\log\left(c x^{2} + b x + a\right)}{2 \, a} + \frac{\log\left({\left| x \right|}\right)}{a}"," ",0,"-b*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a) - 1/2*log(c*x^2 + b*x + a)/a + log(abs(x))/a","A",0
419,1,79,0,0.385669," ","integrate(1/(c+a/x^2+b/x)/x^4,x, algorithm=""giac"")","\frac{b \log\left(c x^{2} + b x + a\right)}{2 \, a^{2}} - \frac{b \log\left({\left| x \right|}\right)}{a^{2}} + \frac{{\left(b^{2} - 2 \, a c\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} a^{2}} - \frac{1}{a x}"," ",0,"1/2*b*log(c*x^2 + b*x + a)/a^2 - b*log(abs(x))/a^2 + (b^2 - 2*a*c)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a^2) - 1/(a*x)","A",0
420,1,105,0,0.314151," ","integrate(1/(c+a/x^2+b/x)/x^5,x, algorithm=""giac"")","-\frac{{\left(b^{2} - a c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, a^{3}} + \frac{{\left(b^{2} - a c\right)} \log\left({\left| x \right|}\right)}{a^{3}} - \frac{{\left(b^{3} - 3 \, a b c\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} a^{3}} + \frac{2 \, a b x - a^{2}}{2 \, a^{3} x^{2}}"," ",0,"-1/2*(b^2 - a*c)*log(c*x^2 + b*x + a)/a^3 + (b^2 - a*c)*log(abs(x))/a^3 - (b^3 - 3*a*b*c)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a^3) + 1/2*(2*a*b*x - a^2)/(a^3*x^2)","A",0
421,1,136,0,0.381632," ","integrate(1/(c+a/x^2+b/x)/x^6,x, algorithm=""giac"")","\frac{{\left(b^{3} - 2 \, a b c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, a^{4}} - \frac{{\left(b^{3} - 2 \, a b c\right)} \log\left({\left| x \right|}\right)}{a^{4}} + \frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} a^{4}} + \frac{3 \, a^{2} b x - 2 \, a^{3} - 6 \, {\left(a b^{2} - a^{2} c\right)} x^{2}}{6 \, a^{4} x^{3}}"," ",0,"1/2*(b^3 - 2*a*b*c)*log(c*x^2 + b*x + a)/a^4 - (b^3 - 2*a*b*c)*log(abs(x))/a^4 + (b^4 - 4*a*b^2*c + 2*a^2*c^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a^4) + 1/6*(3*a^2*b*x - 2*a^3 - 6*(a*b^2 - a^2*c)*x^2)/(a^4*x^3)","A",0
422,1,188,0,0.330065," ","integrate(x/(c+a/x^2+b/x)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, b^{5} - 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(3 \, b^{2} - 2 \, a c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{4}} + \frac{c^{2} x^{2} - 4 \, b c x}{2 \, c^{4}} + \frac{a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2} + {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} x}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} c^{4}}"," ",0,"-(3*b^5 - 20*a*b^3*c + 30*a^2*b*c^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^4 - 4*a*c^5)*sqrt(-b^2 + 4*a*c)) + 1/2*(3*b^2 - 2*a*c)*log(c*x^2 + b*x + a)/c^4 + 1/2*(c^2*x^2 - 4*b*c*x)/c^4 + (a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2 + (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*x)/((c*x^2 + b*x + a)*(b^2 - 4*a*c)*c^4)","A",0
423,1,161,0,0.369267," ","integrate(1/(c+a/x^2+b/x)^2,x, algorithm=""giac"")","\frac{2 \, {\left(b^{4} - 6 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{x}{c^{2}} - \frac{b \log\left(c x^{2} + b x + a\right)}{c^{3}} - \frac{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} x}{c} + \frac{a b^{3} - 3 \, a^{2} b c}{c}}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} c^{2}}"," ",0,"2*(b^4 - 6*a*b^2*c + 6*a^2*c^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^3 - 4*a*c^4)*sqrt(-b^2 + 4*a*c)) + x/c^2 - b*log(c*x^2 + b*x + a)/c^3 - ((b^4 - 4*a*b^2*c + 2*a^2*c^2)*x/c + (a*b^3 - 3*a^2*b*c)/c)/((c*x^2 + b*x + a)*(b^2 - 4*a*c)*c^2)","A",0
424,1,125,0,0.361951," ","integrate(1/(c+a/x^2+b/x)^2/x,x, algorithm=""giac"")","-\frac{{\left(b^{3} - 6 \, a b c\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{\log\left(c x^{2} + b x + a\right)}{2 \, c^{2}} + \frac{a b^{2} - 2 \, a^{2} c + {\left(b^{3} - 3 \, a b c\right)} x}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} c^{2}}"," ",0,"-(b^3 - 6*a*b*c)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^2 - 4*a*c^3)*sqrt(-b^2 + 4*a*c)) + 1/2*log(c*x^2 + b*x + a)/c^2 + (a*b^2 - 2*a^2*c + (b^3 - 3*a*b*c)*x)/((c*x^2 + b*x + a)*(b^2 - 4*a*c)*c^2)","A",0
425,1,88,0,0.378967," ","integrate(1/(c+a/x^2+b/x)^2/x^2,x, algorithm=""giac"")","-\frac{4 \, a \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{b^{2} x - 2 \, a c x + a b}{{\left(b^{2} c - 4 \, a c^{2}\right)} {\left(c x^{2} + b x + a\right)}}"," ",0,"-4*a*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - (b^2*x - 2*a*c*x + a*b)/((b^2*c - 4*a*c^2)*(c*x^2 + b*x + a))","A",0
426,1,76,0,0.371457," ","integrate(1/(c+a/x^2+b/x)^2/x^3,x, algorithm=""giac"")","\frac{2 \, b \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{b x + 2 \, a}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"2*b*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) + (b*x + 2*a)/((c*x^2 + b*x + a)*(b^2 - 4*a*c))","A",0
427,1,76,0,0.394644," ","integrate(1/(c+a/x^2+b/x)^2/x^4,x, algorithm=""giac"")","-\frac{4 \, c \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, c x + b}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"-4*c*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - (2*c*x + b)/((c*x^2 + b*x + a)*(b^2 - 4*a*c))","A",0
428,1,126,0,0.359169," ","integrate(1/(c+a/x^2+b/x)^2/x^5,x, algorithm=""giac"")","-\frac{{\left(b^{3} - 6 \, a b c\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{\log\left(c x^{2} + b x + a\right)}{2 \, a^{2}} + \frac{\log\left({\left| x \right|}\right)}{a^{2}} + \frac{a b c x + a b^{2} - 2 \, a^{2} c}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} a^{2}}"," ",0,"-(b^3 - 6*a*b*c)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((a^2*b^2 - 4*a^3*c)*sqrt(-b^2 + 4*a*c)) - 1/2*log(c*x^2 + b*x + a)/a^2 + log(abs(x))/a^2 + (a*b*c*x + a*b^2 - 2*a^2*c)/((c*x^2 + b*x + a)*(b^2 - 4*a*c)*a^2)","A",0
429,1,171,0,0.423029," ","integrate(1/(c+a/x^2+b/x)^2/x^6,x, algorithm=""giac"")","\frac{2 \, {\left(b^{4} - 6 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, b^{2} c x^{2} - 6 \, a c^{2} x^{2} + 2 \, b^{3} x - 7 \, a b c x + a b^{2} - 4 \, a^{2} c}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(c x^{3} + b x^{2} + a x\right)}} + \frac{b \log\left(c x^{2} + b x + a\right)}{a^{3}} - \frac{2 \, b \log\left({\left| x \right|}\right)}{a^{3}}"," ",0,"2*(b^4 - 6*a*b^2*c + 6*a^2*c^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((a^3*b^2 - 4*a^4*c)*sqrt(-b^2 + 4*a*c)) - (2*b^2*c*x^2 - 6*a*c^2*x^2 + 2*b^3*x - 7*a*b*c*x + a*b^2 - 4*a^2*c)/((a^2*b^2 - 4*a^3*c)*(c*x^3 + b*x^2 + a*x)) + b*log(c*x^2 + b*x + a)/a^3 - 2*b*log(abs(x))/a^3","A",0
430,1,229,0,0.329890," ","integrate(1/(c+a/x^2+b/x)^2/x^7,x, algorithm=""giac"")","-\frac{{\left(3 \, b^{5} - 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{{\left(3 \, b^{2} - 2 \, a c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, a^{4}} + \frac{{\left(3 \, b^{2} - 2 \, a c\right)} \log\left({\left| x \right|}\right)}{a^{4}} - \frac{a^{3} b^{2} - 4 \, a^{4} c - 2 \, {\left(3 \, a b^{3} c - 11 \, a^{2} b c^{2}\right)} x^{3} - {\left(6 \, a b^{4} - 25 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} x^{2} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x}{2 \, {\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} a^{4} x^{2}}"," ",0,"-(3*b^5 - 20*a*b^3*c + 30*a^2*b*c^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((a^4*b^2 - 4*a^5*c)*sqrt(-b^2 + 4*a*c)) - 1/2*(3*b^2 - 2*a*c)*log(c*x^2 + b*x + a)/a^4 + (3*b^2 - 2*a*c)*log(abs(x))/a^4 - 1/2*(a^3*b^2 - 4*a^4*c - 2*(3*a*b^3*c - 11*a^2*b*c^2)*x^3 - (6*a*b^4 - 25*a^2*b^2*c + 8*a^3*c^2)*x^2 - 3*(a^2*b^3 - 4*a^3*b*c)*x)/((c*x^2 + b*x + a)*(b^2 - 4*a*c)*a^4*x^2)","A",0
431,1,282,0,0.378871," ","integrate(1/(c+a/x^2+b/x)^3,x, algorithm=""giac"")","\frac{3 \, {\left(b^{6} - 10 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2} - 20 \, a^{3} c^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{x}{c^{3}} - \frac{3 \, b \log\left(c x^{2} + b x + a\right)}{2 \, c^{4}} - \frac{5 \, a^{2} b^{5} - 36 \, a^{3} b^{3} c + 58 \, a^{4} b c^{2} + 6 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 17 \, a^{2} b^{2} c^{3} - 6 \, a^{3} c^{4}\right)} x^{3} + {\left(5 \, b^{7} - 34 \, a b^{5} c + 41 \, a^{2} b^{3} c^{2} + 42 \, a^{3} b c^{3}\right)} x^{2} + 2 \, {\left(5 \, a b^{6} - 38 \, a^{2} b^{4} c + 71 \, a^{3} b^{2} c^{2} - 14 \, a^{4} c^{3}\right)} x}{2 \, {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}^{2} c^{4}}"," ",0,"3*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*sqrt(-b^2 + 4*a*c)) + x/c^3 - 3/2*b*log(c*x^2 + b*x + a)/c^4 - 1/2*(5*a^2*b^5 - 36*a^3*b^3*c + 58*a^4*b*c^2 + 6*(b^6*c - 8*a*b^4*c^2 + 17*a^2*b^2*c^3 - 6*a^3*c^4)*x^3 + (5*b^7 - 34*a*b^5*c + 41*a^2*b^3*c^2 + 42*a^3*b*c^3)*x^2 + 2*(5*a*b^6 - 38*a^2*b^4*c + 71*a^3*b^2*c^2 - 14*a^4*c^3)*x)/((c*x^2 + b*x + a)^2*(b^2 - 4*a*c)^2*c^4)","A",0
432,1,245,0,0.397586," ","integrate(1/(c+a/x^2+b/x)^3/x,x, algorithm=""giac"")","-\frac{{\left(b^{5} - 10 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{\log\left(c x^{2} + b x + a\right)}{2 \, c^{3}} + \frac{3 \, a^{2} b^{4} - 21 \, a^{3} b^{2} c + 24 \, a^{4} c^{2} + 2 \, {\left(2 \, b^{5} c - 15 \, a b^{3} c^{2} + 25 \, a^{2} b c^{3}\right)} x^{3} + {\left(3 \, b^{6} - 19 \, a b^{4} c + 11 \, a^{2} b^{2} c^{2} + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(3 \, a b^{5} - 22 \, a^{2} b^{3} c + 31 \, a^{3} b c^{2}\right)} x}{2 \, {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}^{2} c^{3}}"," ",0,"-(b^5 - 10*a*b^3*c + 30*a^2*b*c^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt(-b^2 + 4*a*c)) + 1/2*log(c*x^2 + b*x + a)/c^3 + 1/2*(3*a^2*b^4 - 21*a^3*b^2*c + 24*a^4*c^2 + 2*(2*b^5*c - 15*a*b^3*c^2 + 25*a^2*b*c^3)*x^3 + (3*b^6 - 19*a*b^4*c + 11*a^2*b^2*c^2 + 32*a^3*c^3)*x^2 + 2*(3*a*b^5 - 22*a^2*b^3*c + 31*a^3*b*c^2)*x)/((c*x^2 + b*x + a)^2*(b^2 - 4*a*c)^2*c^3)","A",0
433,1,202,0,0.416134," ","integrate(1/(c+a/x^2+b/x)^3/x^2,x, algorithm=""giac"")","\frac{12 \, a^{2} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, b^{4} c x^{3} - 16 \, a b^{2} c^{2} x^{3} + 20 \, a^{2} c^{3} x^{3} + b^{5} x^{2} - 8 \, a b^{3} c x^{2} - 2 \, a^{2} b c^{2} x^{2} + 2 \, a b^{4} x - 20 \, a^{2} b^{2} c x + 12 \, a^{3} c^{2} x + a^{2} b^{3} - 10 \, a^{3} b c}{2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"12*a^2*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) - 1/2*(2*b^4*c*x^3 - 16*a*b^2*c^2*x^3 + 20*a^2*c^3*x^3 + b^5*x^2 - 8*a*b^3*c*x^2 - 2*a^2*b*c^2*x^2 + 2*a*b^4*x - 20*a^2*b^2*c*x + 12*a^3*c^2*x + a^2*b^3 - 10*a^3*b*c)/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*(c*x^2 + b*x + a)^2)","A",0
434,1,163,0,0.307571," ","integrate(1/(c+a/x^2+b/x)^3/x^3,x, algorithm=""giac"")","-\frac{6 \, a b \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{6 \, a b c^{2} x^{3} + b^{4} x^{2} + a b^{2} c x^{2} + 16 \, a^{2} c^{2} x^{2} + 2 \, a b^{3} x + 10 \, a^{2} b c x + a^{2} b^{2} + 8 \, a^{3} c}{2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"-6*a*b*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) - 1/2*(6*a*b*c^2*x^3 + b^4*x^2 + a*b^2*c*x^2 + 16*a^2*c^2*x^2 + 2*a*b^3*x + 10*a^2*b*c*x + a^2*b^2 + 8*a^3*c)/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*(c*x^2 + b*x + a)^2)","A",0
435,1,154,0,0.435567," ","integrate(1/(c+a/x^2+b/x)^3/x^4,x, algorithm=""giac"")","\frac{2 \, {\left(b^{2} + 2 \, a c\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{2 \, b^{2} c x^{3} + 4 \, a c^{2} x^{3} + 3 \, b^{3} x^{2} + 6 \, a b c x^{2} + 10 \, a b^{2} x - 4 \, a^{2} c x + 6 \, a^{2} b}{2 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"2*(b^2 + 2*a*c)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/2*(2*b^2*c*x^3 + 4*a*c^2*x^3 + 3*b^3*x^2 + 6*a*b*c*x^2 + 10*a*b^2*x - 4*a^2*c*x + 6*a^2*b)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*(c*x^2 + b*x + a)^2)","A",0
436,1,135,0,0.409271," ","integrate(1/(c+a/x^2+b/x)^3/x^5,x, algorithm=""giac"")","-\frac{6 \, b c \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{6 \, b c^{2} x^{3} + 9 \, b^{2} c x^{2} + 2 \, b^{3} x + 10 \, a b c x + a b^{2} + 8 \, a^{2} c}{2 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"-6*b*c*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) - 1/2*(6*b*c^2*x^3 + 9*b^2*c*x^2 + 2*b^3*x + 10*a*b*c*x + a*b^2 + 8*a^2*c)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*(c*x^2 + b*x + a)^2)","A",0
437,1,136,0,0.336971," ","integrate(1/(c+a/x^2+b/x)^3/x^6,x, algorithm=""giac"")","\frac{12 \, c^{2} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{12 \, c^{3} x^{3} + 18 \, b c^{2} x^{2} + 4 \, b^{2} c x + 20 \, a c^{2} x - b^{3} + 10 \, a b c}{2 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"12*c^2*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/2*(12*c^3*x^3 + 18*b*c^2*x^2 + 4*b^2*c*x + 20*a*c^2*x - b^3 + 10*a*b*c)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*(c*x^2 + b*x + a)^2)","A",0
438,1,239,0,0.315268," ","integrate(1/(c+a/x^2+b/x)^3/x^7,x, algorithm=""giac"")","-\frac{{\left(b^{5} - 10 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{\log\left(c x^{2} + b x + a\right)}{2 \, a^{3}} + \frac{\log\left({\left| x \right|}\right)}{a^{3}} + \frac{3 \, a^{2} b^{4} - 21 \, a^{3} b^{2} c + 24 \, a^{4} c^{2} + 2 \, {\left(a b^{3} c^{2} - 7 \, a^{2} b c^{3}\right)} x^{3} + {\left(4 \, a b^{4} c - 29 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 6 \, a^{2} b^{3} c - a^{3} b c^{2}\right)} x}{2 \, {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}^{2} a^{3}}"," ",0,"-(b^5 - 10*a*b^3*c + 30*a^2*b*c^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt(-b^2 + 4*a*c)) - 1/2*log(c*x^2 + b*x + a)/a^3 + log(abs(x))/a^3 + 1/2*(3*a^2*b^4 - 21*a^3*b^2*c + 24*a^4*c^2 + 2*(a*b^3*c^2 - 7*a^2*b*c^3)*x^3 + (4*a*b^4*c - 29*a^2*b^2*c^2 + 16*a^3*c^3)*x^2 + 2*(a*b^5 - 6*a^2*b^3*c - a^3*b*c^2)*x)/((c*x^2 + b*x + a)^2*(b^2 - 4*a*c)^2*a^3)","A",0
439,1,309,0,0.467647," ","integrate(1/(c+a/x^2+b/x)^3/x^8,x, algorithm=""giac"")","\frac{3 \, {\left(b^{6} - 10 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2} - 20 \, a^{3} c^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{3 \, b \log\left(c x^{2} + b x + a\right)}{2 \, a^{4}} - \frac{3 \, b \log\left({\left| x \right|}\right)}{a^{4}} - \frac{2 \, a^{3} b^{4} - 16 \, a^{4} b^{2} c + 32 \, a^{5} c^{2} + 6 \, {\left(a b^{4} c^{2} - 7 \, a^{2} b^{2} c^{3} + 10 \, a^{3} c^{4}\right)} x^{4} + 3 \, {\left(4 \, a b^{5} c - 29 \, a^{2} b^{3} c^{2} + 46 \, a^{3} b c^{3}\right)} x^{3} + 2 \, {\left(3 \, a b^{6} - 18 \, a^{2} b^{4} c + 7 \, a^{3} b^{2} c^{2} + 50 \, a^{4} c^{3}\right)} x^{2} + {\left(9 \, a^{2} b^{5} - 68 \, a^{3} b^{3} c + 122 \, a^{4} b c^{2}\right)} x}{2 \, {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}^{2} a^{4} x}"," ",0,"3*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*sqrt(-b^2 + 4*a*c)) + 3/2*b*log(c*x^2 + b*x + a)/a^4 - 3*b*log(abs(x))/a^4 - 1/2*(2*a^3*b^4 - 16*a^4*b^2*c + 32*a^5*c^2 + 6*(a*b^4*c^2 - 7*a^2*b^2*c^3 + 10*a^3*c^4)*x^4 + 3*(4*a*b^5*c - 29*a^2*b^3*c^2 + 46*a^3*b*c^3)*x^3 + 2*(3*a*b^6 - 18*a^2*b^4*c + 7*a^3*b^2*c^2 + 50*a^4*c^3)*x^2 + (9*a^2*b^5 - 68*a^3*b^3*c + 122*a^4*b*c^2)*x)/((c*x^2 + b*x + a)^2*(b^2 - 4*a*c)^2*a^4*x)","A",0
440,1,32,0,0.255129," ","integrate(x^2/(15+2/x^2+13/x),x, algorithm=""giac"")","\frac{1}{45} \, x^{3} - \frac{13}{450} \, x^{2} + \frac{139}{3375} \, x + \frac{1}{4375} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{16}{567} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/45*x^3 - 13/450*x^2 + 139/3375*x + 1/4375*log(abs(5*x + 1)) - 16/567*log(abs(3*x + 2))","A",0
441,1,27,0,0.280035," ","integrate(x/(15+2/x^2+13/x),x, algorithm=""giac"")","\frac{1}{30} \, x^{2} - \frac{13}{225} \, x - \frac{1}{875} \, \log\left({\left| 5 \, x + 1 \right|}\right) + \frac{8}{189} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/30*x^2 - 13/225*x - 1/875*log(abs(5*x + 1)) + 8/189*log(abs(3*x + 2))","A",0
442,1,22,0,0.277296," ","integrate(1/(15+2/x^2+13/x),x, algorithm=""giac"")","\frac{1}{15} \, x + \frac{1}{175} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{4}{63} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/15*x + 1/175*log(abs(5*x + 1)) - 4/63*log(abs(3*x + 2))","A",0
443,1,19,0,0.275114," ","integrate(1/(15+2/x^2+13/x)/x,x, algorithm=""giac"")","-\frac{1}{35} \, \log\left({\left| 5 \, x + 1 \right|}\right) + \frac{2}{21} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"-1/35*log(abs(5*x + 1)) + 2/21*log(abs(3*x + 2))","A",0
444,1,19,0,0.224082," ","integrate(1/(15+2/x^2+13/x)/x^2,x, algorithm=""giac"")","\frac{1}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{1}{7} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/7*log(abs(5*x + 1)) - 1/7*log(abs(3*x + 2))","A",0
445,1,24,0,0.249931," ","integrate(1/(15+2/x^2+13/x)/x^3,x, algorithm=""giac"")","-\frac{5}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) + \frac{3}{14} \, \log\left({\left| 3 \, x + 2 \right|}\right) + \frac{1}{2} \, \log\left({\left| x \right|}\right)"," ",0,"-5/7*log(abs(5*x + 1)) + 3/14*log(abs(3*x + 2)) + 1/2*log(abs(x))","A",0
446,1,29,0,0.307707," ","integrate(1/(15+2/x^2+13/x)/x^4,x, algorithm=""giac"")","-\frac{1}{2 \, x} + \frac{25}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{9}{28} \, \log\left({\left| 3 \, x + 2 \right|}\right) - \frac{13}{4} \, \log\left({\left| x \right|}\right)"," ",0,"-1/2/x + 25/7*log(abs(5*x + 1)) - 9/28*log(abs(3*x + 2)) - 13/4*log(abs(x))","A",0
447,1,34,0,0.298209," ","integrate(1/(15+2/x^2+13/x)/x^5,x, algorithm=""giac"")","\frac{13 \, x - 1}{4 \, x^{2}} - \frac{125}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) + \frac{27}{56} \, \log\left({\left| 3 \, x + 2 \right|}\right) + \frac{139}{8} \, \log\left({\left| x \right|}\right)"," ",0,"1/4*(13*x - 1)/x^2 - 125/7*log(abs(5*x + 1)) + 27/56*log(abs(3*x + 2)) + 139/8*log(abs(x))","A",0
448,1,39,0,0.294446," ","integrate(1/(15+2/x^2+13/x)/x^6,x, algorithm=""giac"")","-\frac{417 \, x^{2} - 39 \, x + 4}{24 \, x^{3}} + \frac{625}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{81}{112} \, \log\left({\left| 3 \, x + 2 \right|}\right) - \frac{1417}{16} \, \log\left({\left| x \right|}\right)"," ",0,"-1/24*(417*x^2 - 39*x + 4)/x^3 + 625/7*log(abs(5*x + 1)) - 81/112*log(abs(3*x + 2)) - 1417/16*log(abs(x))","A",0
449,-1,0,0,0.000000," ","integrate((a+c/x^2+b/x)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-1,0,0,0.000000," ","integrate((a+c/x^2+b/x)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,-2,0,0,0.000000," ","integrate((a+c/x^2+b/x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
452,-2,0,0,0.000000," ","integrate(1/(a+c/x^2+b/x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
453,-2,0,0,0.000000," ","integrate(1/(a+c/x^2+b/x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
454,-2,0,0,0.000000," ","integrate(1/(a+c/x^2+b/x)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
455,1,29,0,0.340792," ","integrate((a^2+b^2/x^2+2*a*b/x)^(1/2),x, algorithm=""giac"")","a x \mathrm{sgn}\left(a x^{2} + b x\right) + b \log\left({\left| x \right|}\right) \mathrm{sgn}\left(a x^{2} + b x\right)"," ",0,"a*x*sgn(a*x^2 + b*x) + b*log(abs(x))*sgn(a*x^2 + b*x)","A",0
456,1,2109,0,1.663439," ","integrate(1/(c+a/x^4+b/x^2),x, algorithm=""giac"")","\frac{x}{c} + \frac{{\left(2 \, b^{5} c^{4} - 12 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5} - {\left(2 \, b^{5} c^{2} - 16 \, a b^{3} c^{3} + 32 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} c^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, a b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 16 \, a^{2} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 32 \, a^{3} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\right)}{8 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} - 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} c^{2}} - \frac{{\left(2 \, b^{5} c^{4} - 12 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5} - {\left(2 \, b^{5} c^{2} - 16 \, a b^{3} c^{3} + 32 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} c^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 2 \, a b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 16 \, a^{2} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 32 \, a^{3} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\right)}{8 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} - 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} c^{2}}"," ",0,"x/c + 1/8*(2*b^5*c^4 - 12*a*b^3*c^5 + 16*a^2*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5 - (2*b^5*c^2 - 16*a*b^3*c^3 + 32*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*c^2 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*a*b^4*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 16*a^2*b^2*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 + 32*a^3*c^5 - 2*(b^2 - 4*a*c)*a*b^2*c^3 + 8*(b^2 - 4*a*c)*a^2*c^4)*abs(c))*arctan(2*sqrt(1/2)*x/sqrt((b*c + sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((a*b^4*c^3 - 8*a^2*b^2*c^4 - 2*a*b^3*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2) - 1/8*(2*b^5*c^4 - 12*a*b^3*c^5 + 16*a^2*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5 - (2*b^5*c^2 - 16*a*b^3*c^3 + 32*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*c^2 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 2*a*b^4*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 16*a^2*b^2*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 32*a^3*c^5 + 2*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*abs(c))*arctan(2*sqrt(1/2)*x/sqrt((b*c - sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((a*b^4*c^3 - 8*a^2*b^2*c^4 - 2*a*b^3*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2)","B",0
457,0,0,0,0.000000," ","integrate(1/(c+a/x^6+b/x^3),x, algorithm=""giac"")","\int \frac{1}{c + \frac{b}{x^{3}} + \frac{a}{x^{6}}}\,{d x}"," ",0,"integrate(1/(c + b/x^3 + a/x^6), x)","F",0
458,-2,0,0,0.000000," ","integrate(1/(c+a/x^8+b/x^4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 6.96Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
459,-2,0,0,0.000000," ","integrate((a+c*x+b*x^(1/2))^(1/2)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
460,1,49,0,0.331796," ","integrate((1/4/c*b^2+c*x+b*x^(1/2))^2,x, algorithm=""giac"")","\frac{80 \, c^{4} x^{3} + 192 \, b c^{3} x^{\frac{5}{2}} + 180 \, b^{2} c^{2} x^{2} + 80 \, b^{3} c x^{\frac{3}{2}} + 15 \, b^{4} x}{240 \, c^{2}}"," ",0,"1/240*(80*c^4*x^3 + 192*b*c^3*x^(5/2) + 180*b^2*c^2*x^2 + 80*b^3*c*x^(3/2) + 15*b^4*x)/c^2","A",0
461,1,45,0,0.397411," ","integrate(1/(a^2+b^2*x+2*a*b*x^(1/2))^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left| a \right|} \log\left({\left| \sqrt{b^{2} x} \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right) + {\left| a \right|} \right|}\right)}{b^{2}} + \frac{2 \, \sqrt{b^{2} x}}{b^{2} \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right)}"," ",0,"-2*abs(a)*log(abs(sqrt(b^2*x)*sgn(a)*sgn(b) + abs(a)))/b^2 + 2*sqrt(b^2*x)/(b^2*sgn(a)*sgn(b))","A",0
462,1,140,0,0.511080," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(7/2),x, algorithm=""giac"")","\frac{3}{10} \, b^{7} x^{\frac{10}{3}} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) + \frac{7}{3} \, a b^{6} x^{3} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) + \frac{63}{8} \, a^{2} b^{5} x^{\frac{8}{3}} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) + 15 \, a^{3} b^{4} x^{\frac{7}{3}} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) + \frac{35}{2} \, a^{4} b^{3} x^{2} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) + \frac{63}{5} \, a^{5} b^{2} x^{\frac{5}{3}} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) + \frac{21}{4} \, a^{6} b x^{\frac{4}{3}} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) + a^{7} x \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right)"," ",0,"3/10*b^7*x^(10/3)*sgn(b*x^(1/3) + a) + 7/3*a*b^6*x^3*sgn(b*x^(1/3) + a) + 63/8*a^2*b^5*x^(8/3)*sgn(b*x^(1/3) + a) + 15*a^3*b^4*x^(7/3)*sgn(b*x^(1/3) + a) + 35/2*a^4*b^3*x^2*sgn(b*x^(1/3) + a) + 63/5*a^5*b^2*x^(5/3)*sgn(b*x^(1/3) + a) + 21/4*a^6*b*x^(4/3)*sgn(b*x^(1/3) + a) + a^7*x*sgn(b*x^(1/3) + a)","A",0
463,1,102,0,0.534304," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(5/2),x, algorithm=""giac"")","\frac{3}{8} \, b^{5} x^{\frac{8}{3}} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) + \frac{15}{7} \, a b^{4} x^{\frac{7}{3}} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) + 5 \, a^{2} b^{3} x^{2} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) + 6 \, a^{3} b^{2} x^{\frac{5}{3}} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) + \frac{15}{4} \, a^{4} b x^{\frac{4}{3}} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) + a^{5} x \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right)"," ",0,"3/8*b^5*x^(8/3)*sgn(b*x^(1/3) + a) + 15/7*a*b^4*x^(7/3)*sgn(b*x^(1/3) + a) + 5*a^2*b^3*x^2*sgn(b*x^(1/3) + a) + 6*a^3*b^2*x^(5/3)*sgn(b*x^(1/3) + a) + 15/4*a^4*b*x^(4/3)*sgn(b*x^(1/3) + a) + a^5*x*sgn(b*x^(1/3) + a)","A",0
464,1,64,0,0.368052," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(3/2),x, algorithm=""giac"")","\frac{1}{2} \, b^{3} x^{2} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) + \frac{9}{5} \, a b^{2} x^{\frac{5}{3}} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) + \frac{9}{4} \, a^{2} b x^{\frac{4}{3}} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) + a^{3} x \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right)"," ",0,"1/2*b^3*x^2*sgn(b*x^(1/3) + a) + 9/5*a*b^2*x^(5/3)*sgn(b*x^(1/3) + a) + 9/4*a^2*b*x^(4/3)*sgn(b*x^(1/3) + a) + a^3*x*sgn(b*x^(1/3) + a)","A",0
465,1,26,0,0.388663," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(1/2),x, algorithm=""giac"")","\frac{3}{4} \, b x^{\frac{4}{3}} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) + a x \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right)"," ",0,"3/4*b*x^(4/3)*sgn(b*x^(1/3) + a) + a*x*sgn(b*x^(1/3) + a)","A",0
466,1,61,0,0.489225," ","integrate(1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(b x^{\frac{2}{3}} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right) - 2 \, a x^{\frac{1}{3}} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right)\right)}}{2 \, b^{2}} + \frac{3 \, a^{2} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{b^{3} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right)}"," ",0,"3/2*(b*x^(2/3)*sgn(b*x^(1/3) + a) - 2*a*x^(1/3)*sgn(b*x^(1/3) + a))/b^2 + 3*a^2*log(abs(b*x^(1/3) + a))/(b^3*sgn(b*x^(1/3) + a))","A",0
467,1,64,0,0.531895," ","integrate(1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(3/2),x, algorithm=""giac"")","\frac{3 \, \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{b^{3} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right)} + \frac{3 \, {\left(4 \, a x^{\frac{1}{3}} + \frac{3 \, a^{2}}{b}\right)}}{2 \, {\left(b x^{\frac{1}{3}} + a\right)}^{2} b^{2} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right)}"," ",0,"3*log(abs(b*x^(1/3) + a))/(b^3*sgn(b*x^(1/3) + a)) + 3/2*(4*a*x^(1/3) + 3*a^2/b)/((b*x^(1/3) + a)^2*b^2*sgn(b*x^(1/3) + a))","A",0
468,1,43,0,0.545496," ","integrate(1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(5/2),x, algorithm=""giac"")","-\frac{6 \, b^{2} x^{\frac{2}{3}} + 4 \, a b x^{\frac{1}{3}} + a^{2}}{4 \, {\left(b x^{\frac{1}{3}} + a\right)}^{4} b^{3} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right)}"," ",0,"-1/4*(6*b^2*x^(2/3) + 4*a*b*x^(1/3) + a^2)/((b*x^(1/3) + a)^4*b^3*sgn(b*x^(1/3) + a))","A",0
469,1,43,0,0.589046," ","integrate(1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(7/2),x, algorithm=""giac"")","-\frac{15 \, b^{2} x^{\frac{2}{3}} + 6 \, a b x^{\frac{1}{3}} + a^{2}}{20 \, {\left(b x^{\frac{1}{3}} + a\right)}^{6} b^{3} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right)}"," ",0,"-1/20*(15*b^2*x^(2/3) + 6*a*b*x^(1/3) + a^2)/((b*x^(1/3) + a)^6*b^3*sgn(b*x^(1/3) + a))","A",0
470,1,43,0,0.648541," ","integrate(1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(9/2),x, algorithm=""giac"")","-\frac{28 \, b^{2} x^{\frac{2}{3}} + 8 \, a b x^{\frac{1}{3}} + a^{2}}{56 \, {\left(b x^{\frac{1}{3}} + a\right)}^{8} b^{3} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right)}"," ",0,"-1/56*(28*b^2*x^(2/3) + 8*a*b*x^(1/3) + a^2)/((b*x^(1/3) + a)^8*b^3*sgn(b*x^(1/3) + a))","A",0
471,1,43,0,0.743287," ","integrate(1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(11/2),x, algorithm=""giac"")","-\frac{45 \, b^{2} x^{\frac{2}{3}} + 10 \, a b x^{\frac{1}{3}} + a^{2}}{120 \, {\left(b x^{\frac{1}{3}} + a\right)}^{10} b^{3} \mathrm{sgn}\left(b x^{\frac{1}{3}} + a\right)}"," ",0,"-1/120*(45*b^2*x^(2/3) + 10*a*b*x^(1/3) + a^2)/((b*x^(1/3) + a)^10*b^3*sgn(b*x^(1/3) + a))","A",0
472,0,0,0,0.000000," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p*(d*x)^m,x, algorithm=""giac"")","\int {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*(d*x)^m, x)","F",0
473,1,1564,0,0.626811," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p*x^2,x, algorithm=""giac"")","\frac{3 \, {\left(16 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{9} p^{8} x^{3} + 16 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a b^{8} p^{8} x^{\frac{8}{3}} + 288 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{9} p^{7} x^{3} + 224 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a b^{8} p^{7} x^{\frac{8}{3}} - 64 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{2} b^{7} p^{7} x^{\frac{7}{3}} + 2184 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{9} p^{6} x^{3} + 1288 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a b^{8} p^{6} x^{\frac{8}{3}} - 672 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{2} b^{7} p^{6} x^{\frac{7}{3}} + 224 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{3} b^{6} p^{6} x^{2} + 9072 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{9} p^{5} x^{3} + 3920 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a b^{8} p^{5} x^{\frac{8}{3}} - 2800 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{2} b^{7} p^{5} x^{\frac{7}{3}} + 1680 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{3} b^{6} p^{5} x^{2} + 22449 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{9} p^{4} x^{3} - 672 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{4} b^{5} p^{5} x^{\frac{5}{3}} + 6769 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a b^{8} p^{4} x^{\frac{8}{3}} - 5880 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{2} b^{7} p^{4} x^{\frac{7}{3}} + 4760 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{3} b^{6} p^{4} x^{2} + 33642 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{9} p^{3} x^{3} - 3360 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{4} b^{5} p^{4} x^{\frac{5}{3}} + 6566 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a b^{8} p^{3} x^{\frac{8}{3}} + 1680 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{5} b^{4} p^{4} x^{\frac{4}{3}} - 6496 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{2} b^{7} p^{3} x^{\frac{7}{3}} + 6300 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{3} b^{6} p^{3} x^{2} + 29531 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{9} p^{2} x^{3} - 5880 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{4} b^{5} p^{3} x^{\frac{5}{3}} + 3267 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a b^{8} p^{2} x^{\frac{8}{3}} + 5040 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{5} b^{4} p^{3} x^{\frac{4}{3}} - 3528 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{2} b^{7} p^{2} x^{\frac{7}{3}} - 3360 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{6} b^{3} p^{3} x + 3836 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{3} b^{6} p^{2} x^{2} + 13698 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{9} p x^{3} - 4200 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{4} b^{5} p^{2} x^{\frac{5}{3}} + 630 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a b^{8} p x^{\frac{8}{3}} + 4620 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{5} b^{4} p^{2} x^{\frac{4}{3}} - 720 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{2} b^{7} p x^{\frac{7}{3}} - 5040 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{6} b^{3} p^{2} x + 840 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{3} b^{6} p x^{2} + 2520 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{9} x^{3} + 5040 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{7} b^{2} p^{2} x^{\frac{2}{3}} - 1008 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{4} b^{5} p x^{\frac{5}{3}} + 1260 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{5} b^{4} p x^{\frac{4}{3}} - 1680 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{6} b^{3} p x + 2520 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{7} b^{2} p x^{\frac{2}{3}} - 5040 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{8} b p x^{\frac{1}{3}} + 2520 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{9}\right)}}{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*(16*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^9*p^8*x^3 + 16*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a*b^8*p^8*x^(8/3) + 288*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^9*p^7*x^3 + 224*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a*b^8*p^7*x^(8/3) - 64*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^2*b^7*p^7*x^(7/3) + 2184*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^9*p^6*x^3 + 1288*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a*b^8*p^6*x^(8/3) - 672*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^2*b^7*p^6*x^(7/3) + 224*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^3*b^6*p^6*x^2 + 9072*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^9*p^5*x^3 + 3920*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a*b^8*p^5*x^(8/3) - 2800*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^2*b^7*p^5*x^(7/3) + 1680*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^3*b^6*p^5*x^2 + 22449*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^9*p^4*x^3 - 672*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^4*b^5*p^5*x^(5/3) + 6769*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a*b^8*p^4*x^(8/3) - 5880*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^2*b^7*p^4*x^(7/3) + 4760*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^3*b^6*p^4*x^2 + 33642*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^9*p^3*x^3 - 3360*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^4*b^5*p^4*x^(5/3) + 6566*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a*b^8*p^3*x^(8/3) + 1680*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^5*b^4*p^4*x^(4/3) - 6496*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^2*b^7*p^3*x^(7/3) + 6300*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^3*b^6*p^3*x^2 + 29531*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^9*p^2*x^3 - 5880*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^4*b^5*p^3*x^(5/3) + 3267*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a*b^8*p^2*x^(8/3) + 5040*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^5*b^4*p^3*x^(4/3) - 3528*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^2*b^7*p^2*x^(7/3) - 3360*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^6*b^3*p^3*x + 3836*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^3*b^6*p^2*x^2 + 13698*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^9*p*x^3 - 4200*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^4*b^5*p^2*x^(5/3) + 630*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a*b^8*p*x^(8/3) + 4620*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^5*b^4*p^2*x^(4/3) - 720*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^2*b^7*p*x^(7/3) - 5040*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^6*b^3*p^2*x + 840*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^3*b^6*p*x^2 + 2520*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^9*x^3 + 5040*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^7*b^2*p^2*x^(2/3) - 1008*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^4*b^5*p*x^(5/3) + 1260*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^5*b^4*p*x^(4/3) - 1680*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^6*b^3*p*x + 2520*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^7*b^2*p*x^(2/3) - 5040*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^8*b*p*x^(1/3) + 2520*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^9)/(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)","B",0
474,1,745,0,0.480990," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p*x,x, algorithm=""giac"")","\frac{3 \, {\left(8 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{6} p^{5} x^{2} + 8 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a b^{5} p^{5} x^{\frac{5}{3}} + 60 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{6} p^{4} x^{2} + 40 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a b^{5} p^{4} x^{\frac{5}{3}} - 20 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{2} b^{4} p^{4} x^{\frac{4}{3}} + 170 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{6} p^{3} x^{2} + 70 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a b^{5} p^{3} x^{\frac{5}{3}} - 60 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{2} b^{4} p^{3} x^{\frac{4}{3}} + 40 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{3} b^{3} p^{3} x + 225 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{6} p^{2} x^{2} + 50 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a b^{5} p^{2} x^{\frac{5}{3}} - 55 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{2} b^{4} p^{2} x^{\frac{4}{3}} + 60 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{3} b^{3} p^{2} x + 137 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{6} p x^{2} - 60 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{4} b^{2} p^{2} x^{\frac{2}{3}} + 12 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a b^{5} p x^{\frac{5}{3}} - 15 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{2} b^{4} p x^{\frac{4}{3}} + 20 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{3} b^{3} p x + 30 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{6} x^{2} - 30 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{4} b^{2} p x^{\frac{2}{3}} + 60 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{5} b p x^{\frac{1}{3}} - 30 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{6}\right)}}{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*(8*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^6*p^5*x^2 + 8*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a*b^5*p^5*x^(5/3) + 60*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^6*p^4*x^2 + 40*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a*b^5*p^4*x^(5/3) - 20*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^2*b^4*p^4*x^(4/3) + 170*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^6*p^3*x^2 + 70*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a*b^5*p^3*x^(5/3) - 60*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^2*b^4*p^3*x^(4/3) + 40*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^3*b^3*p^3*x + 225*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^6*p^2*x^2 + 50*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a*b^5*p^2*x^(5/3) - 55*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^2*b^4*p^2*x^(4/3) + 60*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^3*b^3*p^2*x + 137*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^6*p*x^2 - 60*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^4*b^2*p^2*x^(2/3) + 12*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a*b^5*p*x^(5/3) - 15*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^2*b^4*p*x^(4/3) + 20*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^3*b^3*p*x + 30*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^6*x^2 - 30*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^4*b^2*p*x^(2/3) + 60*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^5*b*p*x^(1/3) - 30*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^6)/(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)","B",0
475,1,229,0,0.483495," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{3} p^{2} x + 2 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a b^{2} p^{2} x^{\frac{2}{3}} + 3 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{3} p x + {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a b^{2} p x^{\frac{2}{3}} - 2 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{2} b p x^{\frac{1}{3}} + {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{3} x + {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} a^{3}\right)}}{4 \, b^{3} p^{3} + 12 \, b^{3} p^{2} + 11 \, b^{3} p + 3 \, b^{3}}"," ",0,"3*(2*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^3*p^2*x + 2*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a*b^2*p^2*x^(2/3) + 3*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^3*p*x + (b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a*b^2*p*x^(2/3) - 2*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^2*b*p*x^(1/3) + (b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^3*x + (b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*a^3)/(4*b^3*p^3 + 12*b^3*p^2 + 11*b^3*p + 3*b^3)","A",0
476,0,0,0,0.000000," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p/x,x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p}}{x}\,{d x}"," ",0,"integrate((b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p/x, x)","F",0
477,0,0,0,0.000000," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p/x^2,x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate((b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p/x^2, x)","F",0
478,0,0,0,0.000000," ","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=""giac"")","\int -\frac{2 \, {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p} b^{3} {\left(2 \, p - 1\right)} {\left(p - 1\right)} p}{3 \, a^{3} x} + \frac{{\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate(-2/3*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p*b^3*(2*p - 1)*(p - 1)*p/(a^3*x) + (b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p/x^2, x)","F",0
479,-1,0,0,0.000000," ","integrate(1/(a^2+2*a*b*x^(1/4)+b^2*x^(1/2))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
480,1,237,0,0.865606," ","integrate(1/(a^2+2*a*b*x^(1/6)+b^2*x^(1/3))^(5/2),x, algorithm=""giac"")","\frac{3 \, a^{4} {\left| a \right|} \log\left({\left| x^{\frac{1}{6}} {\left| b \right|} \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right) + {\left| a \right|} \right|}\right)}{4 \, {\left(a^{3} b^{5} {\left| a \right|} {\left| b \right|} \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right) - a^{4} b^{6}\right)}} + \frac{3 \, {\left(24 \, a^{5} b^{2} {\left| b \right|} \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right) - 25 \, a^{4} b^{3} {\left| a \right|}\right)} \log\left({\left| b x^{\frac{1}{6}} + a \right|}\right)}{4 \, {\left(a^{3} b^{8} {\left| a \right|} {\left| b \right|} \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right) - a^{4} b^{9}\right)}} + \frac{6 \, x^{\frac{1}{6}}}{b^{4} {\left| b \right|} \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right)} + \frac{70 \, a^{5} {\left| b \right|} \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right) - 70 \, a^{4} b {\left| a \right|} + 93 \, {\left(a^{3} b^{2} {\left| b \right|} \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right) - a^{2} b^{3} {\left| a \right|}\right)} x^{\frac{1}{3}} + 159 \, {\left(a^{4} b {\left| b \right|} \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right) - a^{3} b^{2} {\left| a \right|}\right)} x^{\frac{1}{6}}}{4 \, {\left({\left| a \right|} {\left| b \right|} \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right) - a b\right)} {\left(b x^{\frac{1}{6}} + a\right)}^{3} b^{6}}"," ",0,"3/4*a^4*abs(a)*log(abs(x^(1/6)*abs(b)*sgn(a)*sgn(b) + abs(a)))/(a^3*b^5*abs(a)*abs(b)*sgn(a)*sgn(b) - a^4*b^6) + 3/4*(24*a^5*b^2*abs(b)*sgn(a)*sgn(b) - 25*a^4*b^3*abs(a))*log(abs(b*x^(1/6) + a))/(a^3*b^8*abs(a)*abs(b)*sgn(a)*sgn(b) - a^4*b^9) + 6*x^(1/6)/(b^4*abs(b)*sgn(a)*sgn(b)) + 1/4*(70*a^5*abs(b)*sgn(a)*sgn(b) - 70*a^4*b*abs(a) + 93*(a^3*b^2*abs(b)*sgn(a)*sgn(b) - a^2*b^3*abs(a))*x^(1/3) + 159*(a^4*b*abs(b)*sgn(a)*sgn(b) - a^3*b^2*abs(a))*x^(1/6))/((abs(a)*abs(b)*sgn(a)*sgn(b) - a*b)*(b*x^(1/6) + a)^3*b^6)","A",0
481,1,80,0,0.390340," ","integrate((a^2+b^2/x+2*a*b/x^(1/2))^(3/2),x, algorithm=""giac"")","a^{3} x \mathrm{sgn}\left(a x + b \sqrt{x}\right) \mathrm{sgn}\left(x\right) + 3 \, a b^{2} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(a x + b \sqrt{x}\right) \mathrm{sgn}\left(x\right) + 6 \, a^{2} b \sqrt{x} \mathrm{sgn}\left(a x + b \sqrt{x}\right) \mathrm{sgn}\left(x\right) - \frac{2 \, b^{3} \mathrm{sgn}\left(a x + b \sqrt{x}\right) \mathrm{sgn}\left(x\right)}{\sqrt{x}}"," ",0,"a^3*x*sgn(a*x + b*sqrt(x))*sgn(x) + 3*a*b^2*log(abs(x))*sgn(a*x + b*sqrt(x))*sgn(x) + 6*a^2*b*sqrt(x)*sgn(a*x + b*sqrt(x))*sgn(x) - 2*b^3*sgn(a*x + b*sqrt(x))*sgn(x)/sqrt(x)","A",0
482,1,173,0,0.541316," ","integrate((a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(7/2),x, algorithm=""giac"")","a^{7} x \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right) + 35 \, a^{4} b^{3} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right) + \frac{21}{2} \, a^{6} b x^{\frac{2}{3}} \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right) + 63 \, a^{5} b^{2} x^{\frac{1}{3}} \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right) - \frac{420 \, a^{3} b^{4} x \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right) + 126 \, a^{2} b^{5} x^{\frac{2}{3}} \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right) + 28 \, a b^{6} x^{\frac{1}{3}} \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right) + 3 \, b^{7} \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right)}{4 \, x^{\frac{4}{3}}}"," ",0,"a^7*x*sgn(a*x + b*x^(2/3))*sgn(x) + 35*a^4*b^3*log(abs(x))*sgn(a*x + b*x^(2/3))*sgn(x) + 21/2*a^6*b*x^(2/3)*sgn(a*x + b*x^(2/3))*sgn(x) + 63*a^5*b^2*x^(1/3)*sgn(a*x + b*x^(2/3))*sgn(x) - 1/4*(420*a^3*b^4*x*sgn(a*x + b*x^(2/3))*sgn(x) + 126*a^2*b^5*x^(2/3)*sgn(a*x + b*x^(2/3))*sgn(x) + 28*a*b^6*x^(1/3)*sgn(a*x + b*x^(2/3))*sgn(x) + 3*b^7*sgn(a*x + b*x^(2/3))*sgn(x))/x^(4/3)","A",0
483,1,128,0,0.505489," ","integrate((a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(5/2),x, algorithm=""giac"")","a^{5} x \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right) + 10 \, a^{2} b^{3} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right) + \frac{15}{2} \, a^{4} b x^{\frac{2}{3}} \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right) + 30 \, a^{3} b^{2} x^{\frac{1}{3}} \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right) - \frac{3 \, {\left(10 \, a b^{4} x^{\frac{1}{3}} \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right) + b^{5} \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right)\right)}}{2 \, x^{\frac{2}{3}}}"," ",0,"a^5*x*sgn(a*x + b*x^(2/3))*sgn(x) + 10*a^2*b^3*log(abs(x))*sgn(a*x + b*x^(2/3))*sgn(x) + 15/2*a^4*b*x^(2/3)*sgn(a*x + b*x^(2/3))*sgn(x) + 30*a^3*b^2*x^(1/3)*sgn(a*x + b*x^(2/3))*sgn(x) - 3/2*(10*a*b^4*x^(1/3)*sgn(a*x + b*x^(2/3))*sgn(x) + b^5*sgn(a*x + b*x^(2/3))*sgn(x))/x^(2/3)","A",0
484,1,79,0,0.412291," ","integrate((a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(3/2),x, algorithm=""giac"")","a^{3} x \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right) + b^{3} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right) + \frac{9}{2} \, a^{2} b x^{\frac{2}{3}} \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right) + 9 \, a b^{2} x^{\frac{1}{3}} \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right)"," ",0,"a^3*x*sgn(a*x + b*x^(2/3))*sgn(x) + b^3*log(abs(x))*sgn(a*x + b*x^(2/3))*sgn(x) + 9/2*a^2*b*x^(2/3)*sgn(a*x + b*x^(2/3))*sgn(x) + 9*a*b^2*x^(1/3)*sgn(a*x + b*x^(2/3))*sgn(x)","A",0
485,1,34,0,0.396981," ","integrate((a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(1/2),x, algorithm=""giac"")","a x \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right) + \frac{3}{2} \, b x^{\frac{2}{3}} \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right)"," ",0,"a*x*sgn(a*x + b*x^(2/3))*sgn(x) + 3/2*b*x^(2/3)*sgn(a*x + b*x^(2/3))*sgn(x)","A",0
486,1,77,0,0.592291," ","integrate(1/(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(1/2),x, algorithm=""giac"")","-\frac{3 \, b^{3} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{a^{4} \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right)} + \frac{2 \, a^{2} x - 3 \, a b x^{\frac{2}{3}} + 6 \, b^{2} x^{\frac{1}{3}}}{2 \, a^{3} \mathrm{sgn}\left(a x + b x^{\frac{2}{3}}\right) \mathrm{sgn}\left(x\right)}"," ",0,"-3*b^3*log(abs(a*x^(1/3) + b))/(a^4*sgn(a*x + b*x^(2/3))*sgn(x)) + 1/2*(2*a^2*x - 3*a*b*x^(2/3) + 6*b^2*x^(1/3))/(a^3*sgn(a*x + b*x^(2/3))*sgn(x))","A",0
487,1,121,0,0.660134," ","integrate(1/(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(3/2),x, algorithm=""giac"")","-\frac{30 \, b^{3} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{a^{6} \mathrm{sgn}\left(a x^{\frac{2}{3}} + b x^{\frac{1}{3}}\right)} - \frac{3 \, {\left(10 \, a b^{4} x^{\frac{1}{3}} + 9 \, b^{5}\right)}}{2 \, {\left(a x^{\frac{1}{3}} + b\right)}^{2} a^{6} \mathrm{sgn}\left(a x^{\frac{2}{3}} + b x^{\frac{1}{3}}\right)} + \frac{2 \, a^{6} x - 9 \, a^{5} b x^{\frac{2}{3}} + 36 \, a^{4} b^{2} x^{\frac{1}{3}}}{2 \, a^{9} \mathrm{sgn}\left(a x^{\frac{2}{3}} + b x^{\frac{1}{3}}\right)}"," ",0,"-30*b^3*log(abs(a*x^(1/3) + b))/(a^6*sgn(a*x^(2/3) + b*x^(1/3))) - 3/2*(10*a*b^4*x^(1/3) + 9*b^5)/((a*x^(1/3) + b)^2*a^6*sgn(a*x^(2/3) + b*x^(1/3))) + 1/2*(2*a^6*x - 9*a^5*b*x^(2/3) + 36*a^4*b^2*x^(1/3))/(a^9*sgn(a*x^(2/3) + b*x^(1/3)))","A",0
488,1,141,0,0.716670," ","integrate(1/(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(5/2),x, algorithm=""giac"")","-\frac{105 \, b^{3} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{a^{8} \mathrm{sgn}\left(a x^{\frac{2}{3}} + b x^{\frac{1}{3}}\right)} - \frac{420 \, a^{3} b^{4} x + 1134 \, a^{2} b^{5} x^{\frac{2}{3}} + 1036 \, a b^{6} x^{\frac{1}{3}} + 319 \, b^{7}}{4 \, {\left(a x^{\frac{1}{3}} + b\right)}^{4} a^{8} \mathrm{sgn}\left(a x^{\frac{2}{3}} + b x^{\frac{1}{3}}\right)} + \frac{2 \, a^{10} x - 15 \, a^{9} b x^{\frac{2}{3}} + 90 \, a^{8} b^{2} x^{\frac{1}{3}}}{2 \, a^{15} \mathrm{sgn}\left(a x^{\frac{2}{3}} + b x^{\frac{1}{3}}\right)}"," ",0,"-105*b^3*log(abs(a*x^(1/3) + b))/(a^8*sgn(a*x^(2/3) + b*x^(1/3))) - 1/4*(420*a^3*b^4*x + 1134*a^2*b^5*x^(2/3) + 1036*a*b^6*x^(1/3) + 319*b^7)/((a*x^(1/3) + b)^4*a^8*sgn(a*x^(2/3) + b*x^(1/3))) + 1/2*(2*a^10*x - 15*a^9*b*x^(2/3) + 90*a^8*b^2*x^(1/3))/(a^15*sgn(a*x^(2/3) + b*x^(1/3)))","A",0
489,1,126,0,0.485946," ","integrate((a^2+2*a*b/x^(1/4)+b^2/x^(1/2))^(5/2),x, algorithm=""giac"")","a^{5} x \mathrm{sgn}\left(a x + b x^{\frac{3}{4}}\right) \mathrm{sgn}\left(x\right) + 5 \, a b^{4} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(a x + b x^{\frac{3}{4}}\right) \mathrm{sgn}\left(x\right) + \frac{20}{3} \, a^{4} b x^{\frac{3}{4}} \mathrm{sgn}\left(a x + b x^{\frac{3}{4}}\right) \mathrm{sgn}\left(x\right) + 20 \, a^{3} b^{2} \sqrt{x} \mathrm{sgn}\left(a x + b x^{\frac{3}{4}}\right) \mathrm{sgn}\left(x\right) + 40 \, a^{2} b^{3} x^{\frac{1}{4}} \mathrm{sgn}\left(a x + b x^{\frac{3}{4}}\right) \mathrm{sgn}\left(x\right) - \frac{4 \, b^{5} \mathrm{sgn}\left(a x + b x^{\frac{3}{4}}\right) \mathrm{sgn}\left(x\right)}{x^{\frac{1}{4}}}"," ",0,"a^5*x*sgn(a*x + b*x^(3/4))*sgn(x) + 5*a*b^4*log(abs(x))*sgn(a*x + b*x^(3/4))*sgn(x) + 20/3*a^4*b*x^(3/4)*sgn(a*x + b*x^(3/4))*sgn(x) + 20*a^3*b^2*sqrt(x)*sgn(a*x + b*x^(3/4))*sgn(x) + 40*a^2*b^3*x^(1/4)*sgn(a*x + b*x^(3/4))*sgn(x) - 4*b^5*sgn(a*x + b*x^(3/4))*sgn(x)/x^(1/4)","A",0
490,1,125,0,0.481408," ","integrate((a^2+b^2/x^(2/5)+2*a*b/x^(1/5))^(5/2),x, algorithm=""giac"")","a^{5} x \mathrm{sgn}\left(a x + b x^{\frac{4}{5}}\right) \mathrm{sgn}\left(x\right) + b^{5} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(a x + b x^{\frac{4}{5}}\right) \mathrm{sgn}\left(x\right) + \frac{25}{4} \, a^{4} b x^{\frac{4}{5}} \mathrm{sgn}\left(a x + b x^{\frac{4}{5}}\right) \mathrm{sgn}\left(x\right) + \frac{50}{3} \, a^{3} b^{2} x^{\frac{3}{5}} \mathrm{sgn}\left(a x + b x^{\frac{4}{5}}\right) \mathrm{sgn}\left(x\right) + 25 \, a^{2} b^{3} x^{\frac{2}{5}} \mathrm{sgn}\left(a x + b x^{\frac{4}{5}}\right) \mathrm{sgn}\left(x\right) + 25 \, a b^{4} x^{\frac{1}{5}} \mathrm{sgn}\left(a x + b x^{\frac{4}{5}}\right) \mathrm{sgn}\left(x\right)"," ",0,"a^5*x*sgn(a*x + b*x^(4/5))*sgn(x) + b^5*log(abs(x))*sgn(a*x + b*x^(4/5))*sgn(x) + 25/4*a^4*b*x^(4/5)*sgn(a*x + b*x^(4/5))*sgn(x) + 50/3*a^3*b^2*x^(3/5)*sgn(a*x + b*x^(4/5))*sgn(x) + 25*a^2*b^3*x^(2/5)*sgn(a*x + b*x^(4/5))*sgn(x) + 25*a*b^4*x^(1/5)*sgn(a*x + b*x^(4/5))*sgn(x)","A",0
491,1,84,0,0.589845," ","integrate(1/(a^2+2*a*b*x^(1/5)+b^2*x^(2/5))^(5/2),x, algorithm=""giac"")","\frac{5 \, \log\left({\left| b x^{\frac{1}{5}} + a \right|}\right)}{b^{5} \mathrm{sgn}\left(b x^{\frac{1}{5}} + a\right)} + \frac{5 \, {\left(48 \, a b^{2} x^{\frac{3}{5}} + 108 \, a^{2} b x^{\frac{2}{5}} + 88 \, a^{3} x^{\frac{1}{5}} + \frac{25 \, a^{4}}{b}\right)}}{12 \, {\left(b x^{\frac{1}{5}} + a\right)}^{4} b^{4} \mathrm{sgn}\left(b x^{\frac{1}{5}} + a\right)}"," ",0,"5*log(abs(b*x^(1/5) + a))/(b^5*sgn(b*x^(1/5) + a)) + 5/12*(48*a*b^2*x^(3/5) + 108*a^2*b*x^(2/5) + 88*a^3*x^(1/5) + 25*a^4/b)/((b*x^(1/5) + a)^4*b^4*sgn(b*x^(1/5) + a))","A",0
492,1,172,0,0.460715," ","integrate((a^2+b^2/x^(1/3)+2*a*b/x^(1/6))^(7/2),x, algorithm=""giac"")","a^{7} x \mathrm{sgn}\left(a x + b x^{\frac{5}{6}}\right) \mathrm{sgn}\left(x\right) + 7 \, a b^{6} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(a x + b x^{\frac{5}{6}}\right) \mathrm{sgn}\left(x\right) + \frac{42}{5} \, a^{6} b x^{\frac{5}{6}} \mathrm{sgn}\left(a x + b x^{\frac{5}{6}}\right) \mathrm{sgn}\left(x\right) + \frac{63}{2} \, a^{5} b^{2} x^{\frac{2}{3}} \mathrm{sgn}\left(a x + b x^{\frac{5}{6}}\right) \mathrm{sgn}\left(x\right) + 70 \, a^{4} b^{3} \sqrt{x} \mathrm{sgn}\left(a x + b x^{\frac{5}{6}}\right) \mathrm{sgn}\left(x\right) + 105 \, a^{3} b^{4} x^{\frac{1}{3}} \mathrm{sgn}\left(a x + b x^{\frac{5}{6}}\right) \mathrm{sgn}\left(x\right) + 126 \, a^{2} b^{5} x^{\frac{1}{6}} \mathrm{sgn}\left(a x + b x^{\frac{5}{6}}\right) \mathrm{sgn}\left(x\right) - \frac{6 \, b^{7} \mathrm{sgn}\left(a x + b x^{\frac{5}{6}}\right) \mathrm{sgn}\left(x\right)}{x^{\frac{1}{6}}}"," ",0,"a^7*x*sgn(a*x + b*x^(5/6))*sgn(x) + 7*a*b^6*log(abs(x))*sgn(a*x + b*x^(5/6))*sgn(x) + 42/5*a^6*b*x^(5/6)*sgn(a*x + b*x^(5/6))*sgn(x) + 63/2*a^5*b^2*x^(2/3)*sgn(a*x + b*x^(5/6))*sgn(x) + 70*a^4*b^3*sqrt(x)*sgn(a*x + b*x^(5/6))*sgn(x) + 105*a^3*b^4*x^(1/3)*sgn(a*x + b*x^(5/6))*sgn(x) + 126*a^2*b^5*x^(1/6)*sgn(a*x + b*x^(5/6))*sgn(x) - 6*b^7*sgn(a*x + b*x^(5/6))*sgn(x)/x^(1/6)","A",0
493,0,0,0,0.000000," ","integrate(x^(-1+4*n)/(b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{4 \, n - 1}}{c x^{2 \, n} + b x^{n}}\,{d x}"," ",0,"integrate(x^(4*n - 1)/(c*x^(2*n) + b*x^n), x)","F",0
494,0,0,0,0.000000," ","integrate(x^(-1+3*n)/(b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{3 \, n - 1}}{c x^{2 \, n} + b x^{n}}\,{d x}"," ",0,"integrate(x^(3*n - 1)/(c*x^(2*n) + b*x^n), x)","F",0
495,0,0,0,0.000000," ","integrate(x^(-1+2*n)/(b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{2 \, n - 1}}{c x^{2 \, n} + b x^{n}}\,{d x}"," ",0,"integrate(x^(2*n - 1)/(c*x^(2*n) + b*x^n), x)","F",0
496,1,25,0,0.250893," ","integrate(x^(-1+n)/(b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\frac{\log\left({\left| x \right|}\right)}{b} - \frac{\log\left({\left| c x^{n} + b \right|}\right)}{b n}"," ",0,"log(abs(x))/b - log(abs(c*x^n + b))/(b*n)","A",0
497,0,0,0,0.000000," ","integrate(x^(-1-n)/(b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{-n - 1}}{c x^{2 \, n} + b x^{n}}\,{d x}"," ",0,"integrate(x^(-n - 1)/(c*x^(2*n) + b*x^n), x)","F",0
498,0,0,0,0.000000," ","integrate(x^(-1-2*n)/(b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{-2 \, n - 1}}{c x^{2 \, n} + b x^{n}}\,{d x}"," ",0,"integrate(x^(-2*n - 1)/(c*x^(2*n) + b*x^n), x)","F",0
499,0,0,0,0.000000," ","integrate(x^(-1-3*n)/(b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{-3 \, n - 1}}{c x^{2 \, n} + b x^{n}}\,{d x}"," ",0,"integrate(x^(-3*n - 1)/(c*x^(2*n) + b*x^n), x)","F",0
500,1,203,0,0.347555," ","integrate(x^(-1+1/4*n)/(b*x^n+c*x^(2*n)),x, algorithm=""giac"")","-\frac{\frac{6 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, {\left(x^{n}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{b^{2}} + \frac{6 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, {\left(x^{n}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{b^{2}} + \frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(x^{\frac{1}{2} \, n} + \sqrt{2} {\left(x^{n}\right)}^{\frac{1}{4}} \left(\frac{b}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{b}{c}}\right)}{b^{2}} - \frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(x^{\frac{1}{2} \, n} - \sqrt{2} {\left(x^{n}\right)}^{\frac{1}{4}} \left(\frac{b}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{b}{c}}\right)}{b^{2}} + \frac{8}{b x^{\frac{3}{4} \, n}}}{6 \, n}"," ",0,"-1/6*(6*sqrt(2)*(b*c^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*(x^n)^(1/4))/(b/c)^(1/4))/b^2 + 6*sqrt(2)*(b*c^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*(x^n)^(1/4))/(b/c)^(1/4))/b^2 + 3*sqrt(2)*(b*c^3)^(1/4)*log(x^(1/2*n) + sqrt(2)*(x^n)^(1/4)*(b/c)^(1/4) + sqrt(b/c))/b^2 - 3*sqrt(2)*(b*c^3)^(1/4)*log(x^(1/2*n) - sqrt(2)*(x^n)^(1/4)*(b/c)^(1/4) + sqrt(b/c))/b^2 + 8/(b*x^(3/4*n)))/n","A",0
501,1,136,0,0.418749," ","integrate(x^(-1+1/3*n)/(b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\frac{\frac{2 \, c \left(-\frac{b}{c}\right)^{\frac{1}{3}} \log\left({\left| x^{\frac{1}{3} \, n} - \left(-\frac{b}{c}\right)^{\frac{1}{3}} \right|}\right)}{b^{2}} - \frac{2 \, \sqrt{3} \left(-b c^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x^{\frac{1}{3} \, n} + \left(-\frac{b}{c}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{c}\right)^{\frac{1}{3}}}\right)}{b^{2}} - \frac{\left(-b c^{2}\right)^{\frac{1}{3}} \log\left(x^{\frac{1}{3} \, n} \left(-\frac{b}{c}\right)^{\frac{1}{3}} + {\left(x^{n}\right)}^{\frac{2}{3}} + \left(-\frac{b}{c}\right)^{\frac{2}{3}}\right)}{b^{2}} - \frac{3}{b {\left(x^{n}\right)}^{\frac{2}{3}}}}{2 \, n}"," ",0,"1/2*(2*c*(-b/c)^(1/3)*log(abs(x^(1/3*n) - (-b/c)^(1/3)))/b^2 - 2*sqrt(3)*(-b*c^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x^(1/3*n) + (-b/c)^(1/3))/(-b/c)^(1/3))/b^2 - (-b*c^2)^(1/3)*log(x^(1/3*n)*(-b/c)^(1/3) + (x^n)^(2/3) + (-b/c)^(2/3))/b^2 - 3/(b*(x^n)^(2/3)))/n","A",0
502,1,38,0,0.375452," ","integrate(x^(-1+1/2*n)/(b*x^n+c*x^(2*n)),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{c \arctan\left(\frac{c \sqrt{x^{n}}}{\sqrt{b c}}\right)}{\sqrt{b c} b} + \frac{1}{b \sqrt{x^{n}}}\right)}}{n}"," ",0,"-2*(c*arctan(c*sqrt(x^n)/sqrt(b*c))/(sqrt(b*c)*b) + 1/(b*sqrt(x^n)))/n","A",0
503,0,0,0,0.000000," ","integrate(x^(-1-1/2*n)/(b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{-\frac{1}{2} \, n - 1}}{c x^{2 \, n} + b x^{n}}\,{d x}"," ",0,"integrate(x^(-1/2*n - 1)/(c*x^(2*n) + b*x^n), x)","F",0
504,0,0,0,0.000000," ","integrate(x^(-1-1/3*n)/(b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{-\frac{1}{3} \, n - 1}}{c x^{2 \, n} + b x^{n}}\,{d x}"," ",0,"integrate(x^(-1/3*n - 1)/(c*x^(2*n) + b*x^n), x)","F",0
505,0,0,0,0.000000," ","integrate(x^(-1-1/4*n)/(b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{-\frac{1}{4} \, n - 1}}{c x^{2 \, n} + b x^{n}}\,{d x}"," ",0,"integrate(x^(-1/4*n - 1)/(c*x^(2*n) + b*x^n), x)","F",0
506,0,0,0,0.000000," ","integrate(x^(-1-n*(-1+p))*(b*x^n+c*x^(2*n))^p,x, algorithm=""giac"")","\int {\left(c x^{2 \, n} + b x^{n}\right)}^{p} x^{-n {\left(p - 1\right)} - 1}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n)^p*x^(-n*(p - 1) - 1), x)","F",0
507,0,0,0,0.000000," ","integrate(x^(-1-n*(1+2*p))*(b*x^n+c*x^(2*n))^p,x, algorithm=""giac"")","\int {\left(c x^{2 \, n} + b x^{n}\right)}^{p} x^{-n {\left(2 \, p + 1\right)} - 1}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n)^p*x^(-n*(2*p + 1) - 1), x)","F",0
508,0,0,0,0.000000," ","integrate(x^(-1+2*n)*(a^2+2*a*b*x^n+b^2*x^(2*n))^(5/2),x, algorithm=""giac"")","\int {\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{5}{2}} x^{2 \, n - 1}\,{d x}"," ",0,"integrate((b^2*x^(2*n) + 2*a*b*x^n + a^2)^(5/2)*x^(2*n - 1), x)","F",0
509,0,0,0,0.000000," ","integrate(x^(-1+2*n)*(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""giac"")","\int {\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{3}{2}} x^{2 \, n - 1}\,{d x}"," ",0,"integrate((b^2*x^(2*n) + 2*a*b*x^n + a^2)^(3/2)*x^(2*n - 1), x)","F",0
510,0,0,0,0.000000," ","integrate(x^(-1+2*n)*(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}} x^{2 \, n - 1}\,{d x}"," ",0,"integrate(sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2)*x^(2*n - 1), x)","F",0
511,0,0,0,0.000000," ","integrate(x^(-1+2*n)/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2 \, n - 1}}{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}\,{d x}"," ",0,"integrate(x^(2*n - 1)/sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
512,0,0,0,0.000000," ","integrate(x^(-1+2*n)/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{x^{2 \, n - 1}}{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^(2*n - 1)/(b^2*x^(2*n) + 2*a*b*x^n + a^2)^(3/2), x)","F",0
513,0,0,0,0.000000," ","integrate(x^(-1+2*n)/(a^2+2*a*b*x^n+b^2*x^(2*n))^(5/2),x, algorithm=""giac"")","\int \frac{x^{2 \, n - 1}}{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^(2*n - 1)/(b^2*x^(2*n) + 2*a*b*x^n + a^2)^(5/2), x)","F",0
514,0,0,0,0.000000," ","integrate(x^(-1+2*n)/(a^2+2*a*b*x^n+b^2*x^(2*n))^(7/2),x, algorithm=""giac"")","\int \frac{x^{2 \, n - 1}}{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(x^(2*n - 1)/(b^2*x^(2*n) + 2*a*b*x^n + a^2)^(7/2), x)","F",0
515,1,173,0,0.350452," ","integrate((d*x)^m*(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""giac"")","\frac{b m x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + a m x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + b m x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + a n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + b x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + a x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + b x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right)}{m^{2} + m n + 2 \, m + n + 1}"," ",0,"(b*m*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + a*m*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + b*m*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + a*n*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + b*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + a*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + b*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a))/(m^2 + m*n + 2*m + n + 1)","A",0
516,1,53,0,0.257608," ","integrate(x^2*(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""giac"")","\frac{3 \, b x^{3} x^{n} \mathrm{sgn}\left(b x^{n} + a\right) + a n x^{3} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, a x^{3} \mathrm{sgn}\left(b x^{n} + a\right)}{3 \, {\left(n + 3\right)}}"," ",0,"1/3*(3*b*x^3*x^n*sgn(b*x^n + a) + a*n*x^3*sgn(b*x^n + a) + 3*a*x^3*sgn(b*x^n + a))/(n + 3)","A",0
517,1,53,0,0.294598," ","integrate(x*(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""giac"")","\frac{2 \, b x^{2} x^{n} \mathrm{sgn}\left(b x^{n} + a\right) + a n x^{2} \mathrm{sgn}\left(b x^{n} + a\right) + 2 \, a x^{2} \mathrm{sgn}\left(b x^{n} + a\right)}{2 \, {\left(n + 2\right)}}"," ",0,"1/2*(2*b*x^2*x^n*sgn(b*x^n + a) + a*n*x^2*sgn(b*x^n + a) + 2*a*x^2*sgn(b*x^n + a))/(n + 2)","A",0
518,1,25,0,0.219113," ","integrate((a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""giac"")","{\left(a x + \frac{b x^{n + 1}}{n + 1}\right)} \mathrm{sgn}\left(b x^{n} + a\right)"," ",0,"(a*x + b*x^(n + 1)/(n + 1))*sgn(b*x^n + a)","A",0
519,0,0,0,0.000000," ","integrate((a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}{x}\,{d x}"," ",0,"integrate(sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2)/x, x)","F",0
520,0,0,0,0.000000," ","integrate((a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2)/x^2, x)","F",0
521,0,0,0,0.000000," ","integrate((a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2)/x^3, x)","F",0
522,1,2719,0,0.954552," ","integrate((d*x)^m*(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""giac"")","\frac{b^{3} m^{3} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} m^{2} n x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 2 \, b^{3} m n^{2} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, a b^{2} m^{3} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + b^{3} m^{3} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 12 \, a b^{2} m^{2} n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} m^{2} n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a b^{2} m n^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 2 \, b^{3} m n^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, a^{2} b m^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, a b^{2} m^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + b^{3} m^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 15 \, a^{2} b m^{2} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 12 \, a b^{2} m^{2} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} m^{2} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 18 \, a^{2} b m n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a b^{2} m n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 2 \, b^{3} m n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + a^{3} m^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, a^{2} b m^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, a b^{2} m^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + b^{3} m^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 6 \, a^{3} m^{2} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 15 \, a^{2} b m^{2} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 12 \, a b^{2} m^{2} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} m^{2} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 11 \, a^{3} m n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 18 \, a^{2} b m n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a b^{2} m n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 2 \, b^{3} m n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 6 \, a^{3} n^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} m^{2} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 6 \, b^{3} m n x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 2 \, b^{3} n^{2} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a b^{2} m^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} m^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 24 \, a b^{2} m n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 6 \, b^{3} m n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a b^{2} n^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 2 \, b^{3} n^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a^{2} b m^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a b^{2} m^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} m^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 30 \, a^{2} b m n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 24 \, a b^{2} m n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 6 \, b^{3} m n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 18 \, a^{2} b n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a b^{2} n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 2 \, b^{3} n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, a^{3} m^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a^{2} b m^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a b^{2} m^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} m^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 12 \, a^{3} m n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 30 \, a^{2} b m n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 24 \, a b^{2} m n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 6 \, b^{3} m n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 11 \, a^{3} n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 18 \, a^{2} b n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a b^{2} n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 2 \, b^{3} n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} m x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} n x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a b^{2} m x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} m x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 12 \, a b^{2} n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a^{2} b m x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a b^{2} m x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} m x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 15 \, a^{2} b n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 12 \, a b^{2} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, a^{3} m x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a^{2} b m x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a b^{2} m x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} m x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 6 \, a^{3} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 15 \, a^{2} b n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 12 \, a b^{2} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + b^{3} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, a b^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + b^{3} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, a^{2} b x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, a b^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + b^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + a^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, a^{2} b x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, a b^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right) + b^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} \mathrm{sgn}\left(b x^{n} + a\right)}{m^{4} + 6 \, m^{3} n + 11 \, m^{2} n^{2} + 6 \, m n^{3} + 4 \, m^{3} + 18 \, m^{2} n + 22 \, m n^{2} + 6 \, n^{3} + 6 \, m^{2} + 18 \, m n + 11 \, n^{2} + 4 \, m + 6 \, n + 1}"," ",0,"(b^3*m^3*x*x^(3*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*b^3*m^2*n*x*x^(3*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 2*b^3*m*n^2*x*x^(3*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*a*b^2*m^3*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + b^3*m^3*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 12*a*b^2*m^2*n*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*b^3*m^2*n*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 9*a*b^2*m*n^2*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 2*b^3*m*n^2*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*a^2*b*m^3*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*a*b^2*m^3*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + b^3*m^3*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 15*a^2*b*m^2*n*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 12*a*b^2*m^2*n*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*b^3*m^2*n*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 18*a^2*b*m*n^2*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 9*a*b^2*m*n^2*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 2*b^3*m*n^2*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + a^3*m^3*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*a^2*b*m^3*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*a*b^2*m^3*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + b^3*m^3*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 6*a^3*m^2*n*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 15*a^2*b*m^2*n*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 12*a*b^2*m^2*n*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*b^3*m^2*n*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 11*a^3*m*n^2*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 18*a^2*b*m*n^2*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 9*a*b^2*m*n^2*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 2*b^3*m*n^2*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 6*a^3*n^3*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*b^3*m^2*x*x^(3*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 6*b^3*m*n*x*x^(3*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 2*b^3*n^2*x*x^(3*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 9*a*b^2*m^2*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*b^3*m^2*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 24*a*b^2*m*n*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 6*b^3*m*n*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 9*a*b^2*n^2*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 2*b^3*n^2*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 9*a^2*b*m^2*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 9*a*b^2*m^2*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*b^3*m^2*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 30*a^2*b*m*n*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 24*a*b^2*m*n*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 6*b^3*m*n*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 18*a^2*b*n^2*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 9*a*b^2*n^2*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 2*b^3*n^2*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*a^3*m^2*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 9*a^2*b*m^2*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 9*a*b^2*m^2*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*b^3*m^2*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 12*a^3*m*n*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 30*a^2*b*m*n*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 24*a*b^2*m*n*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 6*b^3*m*n*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 11*a^3*n^2*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 18*a^2*b*n^2*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 9*a*b^2*n^2*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 2*b^3*n^2*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*b^3*m*x*x^(3*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*b^3*n*x*x^(3*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 9*a*b^2*m*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*b^3*m*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 12*a*b^2*n*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*b^3*n*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 9*a^2*b*m*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 9*a*b^2*m*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*b^3*m*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 15*a^2*b*n*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 12*a*b^2*n*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*b^3*n*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*a^3*m*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 9*a^2*b*m*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 9*a*b^2*m*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*b^3*m*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 6*a^3*n*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 15*a^2*b*n*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 12*a*b^2*n*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*b^3*n*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + b^3*x*x^(3*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*a*b^2*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + b^3*x*x^(2*n)*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*a^2*b*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*a*b^2*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + b^3*x*x^n*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + a^3*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*a^2*b*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + 3*a*b^2*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a) + b^3*x*e^(m*log(d) + m*log(x))*sgn(b*x^n + a))/(m^4 + 6*m^3*n + 11*m^2*n^2 + 6*m*n^3 + 4*m^3 + 18*m^2*n + 22*m*n^2 + 6*n^3 + 6*m^2 + 18*m*n + 11*n^2 + 4*m + 6*n + 1)","B",0
523,1,292,0,0.433811," ","integrate(x^2*(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""giac"")","\frac{2 \, b^{3} n^{2} x^{3} x^{3 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a b^{2} n^{2} x^{3} x^{2 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 18 \, a^{2} b n^{2} x^{3} x^{n} \mathrm{sgn}\left(b x^{n} + a\right) + 2 \, a^{3} n^{3} x^{3} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, b^{3} n x^{3} x^{3 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 36 \, a b^{2} n x^{3} x^{2 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 45 \, a^{2} b n x^{3} x^{n} \mathrm{sgn}\left(b x^{n} + a\right) + 11 \, a^{3} n^{2} x^{3} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, b^{3} x^{3} x^{3 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 27 \, a b^{2} x^{3} x^{2 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 27 \, a^{2} b x^{3} x^{n} \mathrm{sgn}\left(b x^{n} + a\right) + 18 \, a^{3} n x^{3} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a^{3} x^{3} \mathrm{sgn}\left(b x^{n} + a\right)}{3 \, {\left(2 \, n^{3} + 11 \, n^{2} + 18 \, n + 9\right)}}"," ",0,"1/3*(2*b^3*n^2*x^3*x^(3*n)*sgn(b*x^n + a) + 9*a*b^2*n^2*x^3*x^(2*n)*sgn(b*x^n + a) + 18*a^2*b*n^2*x^3*x^n*sgn(b*x^n + a) + 2*a^3*n^3*x^3*sgn(b*x^n + a) + 9*b^3*n*x^3*x^(3*n)*sgn(b*x^n + a) + 36*a*b^2*n*x^3*x^(2*n)*sgn(b*x^n + a) + 45*a^2*b*n*x^3*x^n*sgn(b*x^n + a) + 11*a^3*n^2*x^3*sgn(b*x^n + a) + 9*b^3*x^3*x^(3*n)*sgn(b*x^n + a) + 27*a*b^2*x^3*x^(2*n)*sgn(b*x^n + a) + 27*a^2*b*x^3*x^n*sgn(b*x^n + a) + 18*a^3*n*x^3*sgn(b*x^n + a) + 9*a^3*x^3*sgn(b*x^n + a))/(2*n^3 + 11*n^2 + 18*n + 9)","A",0
524,1,292,0,0.373438," ","integrate(x*(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""giac"")","\frac{2 \, b^{3} n^{2} x^{2} x^{3 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a b^{2} n^{2} x^{2} x^{2 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 18 \, a^{2} b n^{2} x^{2} x^{n} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, a^{3} n^{3} x^{2} \mathrm{sgn}\left(b x^{n} + a\right) + 6 \, b^{3} n x^{2} x^{3 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 24 \, a b^{2} n x^{2} x^{2 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 30 \, a^{2} b n x^{2} x^{n} \mathrm{sgn}\left(b x^{n} + a\right) + 11 \, a^{3} n^{2} x^{2} \mathrm{sgn}\left(b x^{n} + a\right) + 4 \, b^{3} x^{2} x^{3 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 12 \, a b^{2} x^{2} x^{2 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 12 \, a^{2} b x^{2} x^{n} \mathrm{sgn}\left(b x^{n} + a\right) + 12 \, a^{3} n x^{2} \mathrm{sgn}\left(b x^{n} + a\right) + 4 \, a^{3} x^{2} \mathrm{sgn}\left(b x^{n} + a\right)}{2 \, {\left(3 \, n^{3} + 11 \, n^{2} + 12 \, n + 4\right)}}"," ",0,"1/2*(2*b^3*n^2*x^2*x^(3*n)*sgn(b*x^n + a) + 9*a*b^2*n^2*x^2*x^(2*n)*sgn(b*x^n + a) + 18*a^2*b*n^2*x^2*x^n*sgn(b*x^n + a) + 3*a^3*n^3*x^2*sgn(b*x^n + a) + 6*b^3*n*x^2*x^(3*n)*sgn(b*x^n + a) + 24*a*b^2*n*x^2*x^(2*n)*sgn(b*x^n + a) + 30*a^2*b*n*x^2*x^n*sgn(b*x^n + a) + 11*a^3*n^2*x^2*sgn(b*x^n + a) + 4*b^3*x^2*x^(3*n)*sgn(b*x^n + a) + 12*a*b^2*x^2*x^(2*n)*sgn(b*x^n + a) + 12*a^2*b*x^2*x^n*sgn(b*x^n + a) + 12*a^3*n*x^2*sgn(b*x^n + a) + 4*a^3*x^2*sgn(b*x^n + a))/(3*n^3 + 11*n^2 + 12*n + 4)","A",0
525,1,263,0,0.488801," ","integrate((a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""giac"")","\frac{6 \, a^{3} n^{3} x \mathrm{sgn}\left(b x^{n} + a\right) + 2 \, b^{3} n^{2} x x^{3 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 9 \, a b^{2} n^{2} x x^{2 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 18 \, a^{2} b n^{2} x x^{n} \mathrm{sgn}\left(b x^{n} + a\right) + 11 \, a^{3} n^{2} x \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, b^{3} n x x^{3 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 12 \, a b^{2} n x x^{2 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 15 \, a^{2} b n x x^{n} \mathrm{sgn}\left(b x^{n} + a\right) + 6 \, a^{3} n x \mathrm{sgn}\left(b x^{n} + a\right) + b^{3} x x^{3 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, a b^{2} x x^{2 \, n} \mathrm{sgn}\left(b x^{n} + a\right) + 3 \, a^{2} b x x^{n} \mathrm{sgn}\left(b x^{n} + a\right) + a^{3} x \mathrm{sgn}\left(b x^{n} + a\right)}{6 \, n^{3} + 11 \, n^{2} + 6 \, n + 1}"," ",0,"(6*a^3*n^3*x*sgn(b*x^n + a) + 2*b^3*n^2*x*x^(3*n)*sgn(b*x^n + a) + 9*a*b^2*n^2*x*x^(2*n)*sgn(b*x^n + a) + 18*a^2*b*n^2*x*x^n*sgn(b*x^n + a) + 11*a^3*n^2*x*sgn(b*x^n + a) + 3*b^3*n*x*x^(3*n)*sgn(b*x^n + a) + 12*a*b^2*n*x*x^(2*n)*sgn(b*x^n + a) + 15*a^2*b*n*x*x^n*sgn(b*x^n + a) + 6*a^3*n*x*sgn(b*x^n + a) + b^3*x*x^(3*n)*sgn(b*x^n + a) + 3*a*b^2*x*x^(2*n)*sgn(b*x^n + a) + 3*a^2*b*x*x^n*sgn(b*x^n + a) + a^3*x*sgn(b*x^n + a))/(6*n^3 + 11*n^2 + 6*n + 1)","A",0
526,0,0,0,0.000000," ","integrate((a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2)/x,x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate((b^2*x^(2*n) + 2*a*b*x^n + a^2)^(3/2)/x, x)","F",0
527,0,0,0,0.000000," ","integrate((a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate((b^2*x^(2*n) + 2*a*b*x^n + a^2)^(3/2)/x^2, x)","F",0
528,0,0,0,0.000000," ","integrate((a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2)/x^3,x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate((b^2*x^(2*n) + 2*a*b*x^n + a^2)^(3/2)/x^3, x)","F",0
529,0,0,0,0.000000," ","integrate((d*x)^m/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}\,{d x}"," ",0,"integrate((d*x)^m/sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
530,0,0,0,0.000000," ","integrate(x^2/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}\,{d x}"," ",0,"integrate(x^2/sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
531,0,0,0,0.000000," ","integrate(x/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}\,{d x}"," ",0,"integrate(x/sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
532,0,0,0,0.000000," ","integrate(1/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}\,{d x}"," ",0,"integrate(1/sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
533,0,0,0,0.000000," ","integrate(1/x/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}} x}\,{d x}"," ",0,"integrate(1/(sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2)*x), x)","F",0
534,0,0,0,0.000000," ","integrate(1/x^2/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2)*x^2), x)","F",0
535,0,0,0,0.000000," ","integrate(1/x^3/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}} x^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2)*x^3), x)","F",0
536,0,0,0,0.000000," ","integrate((d*x)^m/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*x)^m/(b^2*x^(2*n) + 2*a*b*x^n + a^2)^(3/2), x)","F",0
537,0,0,0,0.000000," ","integrate(x^2/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/(b^2*x^(2*n) + 2*a*b*x^n + a^2)^(3/2), x)","F",0
538,0,0,0,0.000000," ","integrate(x/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{x}{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/(b^2*x^(2*n) + 2*a*b*x^n + a^2)^(3/2), x)","F",0
539,0,0,0,0.000000," ","integrate(1/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b^2*x^(2*n) + 2*a*b*x^n + a^2)^(-3/2), x)","F",0
540,0,0,0,0.000000," ","integrate(1/x/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(1/((b^2*x^(2*n) + 2*a*b*x^n + a^2)^(3/2)*x), x)","F",0
541,0,0,0,0.000000," ","integrate(1/x^2/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((b^2*x^(2*n) + 2*a*b*x^n + a^2)^(3/2)*x^2), x)","F",0
542,0,0,0,0.000000," ","integrate(1/x^3/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(1/((b^2*x^(2*n) + 2*a*b*x^n + a^2)^(3/2)*x^3), x)","F",0
543,0,0,0,0.000000," ","integrate((a^2+b^2/(x^(2/(1+2*p)))+2*a*b/(x^(1/(1+2*p))))^p,x, algorithm=""giac"")","\int {\left(a^{2} + \frac{b^{2}}{x^{\frac{2}{2 \, p + 1}}} + \frac{2 \, a b}{x^{\left(\frac{1}{2 \, p + 1}\right)}}\right)}^{p}\,{d x}"," ",0,"integrate((a^2 + b^2/x^(2/(2*p + 1)) + 2*a*b/x^(1/(2*p + 1)))^p, x)","F",0
544,0,0,0,0.000000," ","integrate(1/((a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2*(1+n)/n)),x, algorithm=""giac"")","\int \frac{1}{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{n + 1}{2 \, n}}}\,{d x}"," ",0,"integrate(1/((b^2*x^(2*n) + 2*a*b*x^n + a^2)^(1/2*(n + 1)/n)), x)","F",0
545,0,0,0,0.000000," ","integrate((a^2+b^2/(x^(1/(1+p)))+2*a*b/(x^(1/2/(1+p))))^p,x, algorithm=""giac"")","\int {\left(a^{2} + \frac{2 \, a b}{x^{\frac{1}{2 \, {\left(p + 1\right)}}}} + \frac{b^{2}}{x^{\left(\frac{1}{p + 1}\right)}}\right)}^{p}\,{d x}"," ",0,"integrate((a^2 + 2*a*b/x^(1/2/(p + 1)) + b^2/x^(1/(p + 1)))^p, x)","F",0
546,0,0,0,0.000000," ","integrate(1/((a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2*(1+2*n)/n)),x, algorithm=""giac"")","\int \frac{1}{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{2 \, n + 1}{2 \, n}}}\,{d x}"," ",0,"integrate(1/((b^2*x^(2*n) + 2*a*b*x^n + a^2)^(1/2*(2*n + 1)/n)), x)","F",0
547,0,0,0,0.000000," ","integrate((d*x)^(-1-2*n*(1+p))*(a^2+2*a*b*x^n+b^2*x^(2*n))^p,x, algorithm=""giac"")","\int {\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{p} \left(d x\right)^{-2 \, n {\left(p + 1\right)} - 1}\,{d x}"," ",0,"integrate((b^2*x^(2*n) + 2*a*b*x^n + a^2)^p*(d*x)^(-2*n*(p + 1) - 1), x)","F",0
548,0,0,0,0.000000," ","integrate(x^(-1+2*n)*(a^2+2*a*b*x^n+b^2*x^(2*n))^p,x, algorithm=""giac"")","\int {\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{p} x^{2 \, n - 1}\,{d x}"," ",0,"integrate((b^2*x^(2*n) + 2*a*b*x^n + a^2)^p*x^(2*n - 1), x)","F",0
549,0,0,0,0.000000," ","integrate(x^(-1+4*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{4 \, n - 1}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate(x^(4*n - 1)/(c*x^(2*n) + b*x^n + a), x)","F",0
550,0,0,0,0.000000," ","integrate(x^(-1+3*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{3 \, n - 1}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate(x^(3*n - 1)/(c*x^(2*n) + b*x^n + a), x)","F",0
551,0,0,0,0.000000," ","integrate(x^(-1+2*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{2 \, n - 1}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate(x^(2*n - 1)/(c*x^(2*n) + b*x^n + a), x)","F",0
552,1,39,0,0.413665," ","integrate(x^(-1+n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{2 \, c x^{n} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} n}"," ",0,"2*arctan((2*c*x^n + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*n)","A",0
553,0,0,0,0.000000," ","integrate(x^(-1-n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{-n - 1}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-n - 1)/(c*x^(2*n) + b*x^n + a), x)","F",0
554,0,0,0,0.000000," ","integrate(x^(-1-2*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{-2 \, n - 1}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-2*n - 1)/(c*x^(2*n) + b*x^n + a), x)","F",0
555,0,0,0,0.000000," ","integrate(x^(-1-3*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{-3 \, n - 1}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-3*n - 1)/(c*x^(2*n) + b*x^n + a), x)","F",0
556,0,0,0,0.000000," ","integrate(x^(-1+1/4*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{\frac{1}{4} \, n - 1}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate(x^(1/4*n - 1)/(c*x^(2*n) + b*x^n + a), x)","F",0
557,0,0,0,0.000000," ","integrate(x^(-1+1/3*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{\frac{1}{3} \, n - 1}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate(x^(1/3*n - 1)/(c*x^(2*n) + b*x^n + a), x)","F",0
558,1,1035,0,1.845741," ","integrate(x^(-1+1/2*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\frac{\frac{{\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 16 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 32 \, a^{2} c^{3} + 8 \, a b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{n}}}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{{\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}} + \frac{{\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 16 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 32 \, a^{2} c^{3} + 8 \, a b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{n}}}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{{\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}}}{2 \, n}"," ",0,"1/2*((sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 2*b^4*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 16*a*b^2*c^2 - 2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 32*a^2*c^3 + 8*a*b*c^3 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 + 2*(b^2 - 4*a*c)*b^2*c - 8*(b^2 - 4*a*c)*a*c^2 + 2*(b^2 - 4*a*c)*b*c^2)*arctan(2*sqrt(1/2)*sqrt(x^n)/sqrt((b + sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c - 2*a*b^3*c + 16*a^3*c^2 + 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c)) + (sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c + 2*b^4*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - 16*a*b^2*c^2 - 2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 + 32*a^2*c^3 + 8*a*b*c^3 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b^2*c + 8*(b^2 - 4*a*c)*a*c^2 + 2*(b^2 - 4*a*c)*b*c^2)*arctan(2*sqrt(1/2)*sqrt(x^n)/sqrt((b - sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c - 2*a*b^3*c + 16*a^3*c^2 + 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c)))/n","B",0
559,0,0,0,0.000000," ","integrate(x^(-1-1/2*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{-\frac{1}{2} \, n - 1}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-1/2*n - 1)/(c*x^(2*n) + b*x^n + a), x)","F",0
560,0,0,0,0.000000," ","integrate(x^(-1-1/3*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{-\frac{1}{3} \, n - 1}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-1/3*n - 1)/(c*x^(2*n) + b*x^n + a), x)","F",0
561,0,0,0,0.000000," ","integrate(x^(-1-1/4*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{-\frac{1}{4} \, n - 1}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-1/4*n - 1)/(c*x^(2*n) + b*x^n + a), x)","F",0
562,0,0,0,0.000000," ","integrate(x^2/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x^{2}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate(x^2/(c*x^(2*n) + b*x^n + a), x)","F",0
563,0,0,0,0.000000," ","integrate(x/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{x}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate(x/(c*x^(2*n) + b*x^n + a), x)","F",0
564,0,0,0,0.000000," ","integrate(1/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{1}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate(1/(c*x^(2*n) + b*x^n + a), x)","F",0
565,0,0,0,0.000000," ","integrate(1/x/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + b x^{n} + a\right)} x}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + b*x^n + a)*x), x)","F",0
566,0,0,0,0.000000," ","integrate(1/x^2/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + b x^{n} + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + b*x^n + a)*x^2), x)","F",0
567,0,0,0,0.000000," ","integrate(1/x^3/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + b x^{n} + a\right)} x^{3}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + b*x^n + a)*x^3), x)","F",0
568,0,0,0,0.000000," ","integrate(x^3*(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2 \, n} + b x^{n} + a} x^{3}\,{d x}"," ",0,"integrate(sqrt(c*x^(2*n) + b*x^n + a)*x^3, x)","F",0
569,0,0,0,0.000000," ","integrate(x^2*(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2 \, n} + b x^{n} + a} x^{2}\,{d x}"," ",0,"integrate(sqrt(c*x^(2*n) + b*x^n + a)*x^2, x)","F",0
570,0,0,0,0.000000," ","integrate(x*(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2 \, n} + b x^{n} + a} x\,{d x}"," ",0,"integrate(sqrt(c*x^(2*n) + b*x^n + a)*x, x)","F",0
571,0,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate(sqrt(c*x^(2*n) + b*x^n + a), x)","F",0
572,0,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2 \, n} + b x^{n} + a}}{x}\,{d x}"," ",0,"integrate(sqrt(c*x^(2*n) + b*x^n + a)/x, x)","F",0
573,0,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2 \, n} + b x^{n} + a}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^(2*n) + b*x^n + a)/x^2, x)","F",0
574,0,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2 \, n} + b x^{n} + a}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(c*x^(2*n) + b*x^n + a)/x^3, x)","F",0
575,0,0,0,0.000000," ","integrate(x^3*(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}} x^{3}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^(3/2)*x^3, x)","F",0
576,0,0,0,0.000000," ","integrate(x^2*(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}} x^{2}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^(3/2)*x^2, x)","F",0
577,0,0,0,0.000000," ","integrate(x*(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}} x\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^(3/2)*x, x)","F",0
578,0,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^(3/2), x)","F",0
579,0,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^(3/2)/x,x, algorithm=""giac"")","\int \frac{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^(3/2)/x, x)","F",0
580,0,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^(3/2)/x^2, x)","F",0
581,0,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^(3/2)/x^3,x, algorithm=""giac"")","\int \frac{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^(3/2)/x^3, x)","F",0
582,0,0,0,0.000000," ","integrate(x^3/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{x^{3}}{\sqrt{c x^{2 \, n} + b x^{n} + a}}\,{d x}"," ",0,"integrate(x^3/sqrt(c*x^(2*n) + b*x^n + a), x)","F",0
583,0,0,0,0.000000," ","integrate(x^2/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{c x^{2 \, n} + b x^{n} + a}}\,{d x}"," ",0,"integrate(x^2/sqrt(c*x^(2*n) + b*x^n + a), x)","F",0
584,0,0,0,0.000000," ","integrate(x/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{c x^{2 \, n} + b x^{n} + a}}\,{d x}"," ",0,"integrate(x/sqrt(c*x^(2*n) + b*x^n + a), x)","F",0
585,0,0,0,0.000000," ","integrate(1/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2 \, n} + b x^{n} + a}}\,{d x}"," ",0,"integrate(1/sqrt(c*x^(2*n) + b*x^n + a), x)","F",0
586,0,0,0,0.000000," ","integrate(1/x/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2 \, n} + b x^{n} + a} x}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^(2*n) + b*x^n + a)*x), x)","F",0
587,0,0,0,0.000000," ","integrate(1/x^2/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2 \, n} + b x^{n} + a} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^(2*n) + b*x^n + a)*x^2), x)","F",0
588,0,0,0,0.000000," ","integrate(1/x^3/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2 \, n} + b x^{n} + a} x^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^(2*n) + b*x^n + a)*x^3), x)","F",0
589,0,0,0,0.000000," ","integrate(x^3/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^3/(c*x^(2*n) + b*x^n + a)^(3/2), x)","F",0
590,0,0,0,0.000000," ","integrate(x^2/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/(c*x^(2*n) + b*x^n + a)^(3/2), x)","F",0
591,0,0,0,0.000000," ","integrate(x/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{x}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/(c*x^(2*n) + b*x^n + a)^(3/2), x)","F",0
592,0,0,0,0.000000," ","integrate(1/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^(-3/2), x)","F",0
593,0,0,0,0.000000," ","integrate(1/x/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + b*x^n + a)^(3/2)*x), x)","F",0
594,0,0,0,0.000000," ","integrate(1/x^2/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + b*x^n + a)^(3/2)*x^2), x)","F",0
595,0,0,0,0.000000," ","integrate(1/x^3/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + b*x^n + a)^(3/2)*x^3), x)","F",0
596,-1,0,0,0.000000," ","integrate((d*x)^m*(a+b*x^n+c*x^(2*n))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
597,1,5454,0,0.803147," ","integrate((d*x)^m*(a+b*x^n+c*x^(2*n))^2,x, algorithm=""giac"")","\frac{c^{2} m^{4} x x^{4 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} m^{3} n x x^{4 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 11 \, c^{2} m^{2} n^{2} x x^{4 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} m n^{3} x x^{4 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, b c m^{4} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c^{2} m^{4} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 14 \, b c m^{3} n x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} m^{3} n x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 28 \, b c m^{2} n^{2} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 11 \, c^{2} m^{2} n^{2} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 16 \, b c m n^{3} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} m n^{3} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + b^{2} m^{4} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, a c m^{4} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, b c m^{4} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c^{2} m^{4} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, b^{2} m^{3} n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 16 \, a c m^{3} n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 14 \, b c m^{3} n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} m^{3} n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 19 \, b^{2} m^{2} n^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 38 \, a c m^{2} n^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 28 \, b c m^{2} n^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 11 \, c^{2} m^{2} n^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 12 \, b^{2} m n^{3} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 24 \, a c m n^{3} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 16 \, b c m n^{3} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} m n^{3} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, a b m^{4} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + b^{2} m^{4} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, a c m^{4} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, b c m^{4} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c^{2} m^{4} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 18 \, a b m^{3} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, b^{2} m^{3} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 16 \, a c m^{3} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 14 \, b c m^{3} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} m^{3} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 52 \, a b m^{2} n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 19 \, b^{2} m^{2} n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 38 \, a c m^{2} n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 28 \, b c m^{2} n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 11 \, c^{2} m^{2} n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 48 \, a b m n^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 12 \, b^{2} m n^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 24 \, a c m n^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 16 \, b c m n^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} m n^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + a^{2} m^{4} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, a b m^{4} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + b^{2} m^{4} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, a c m^{4} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, b c m^{4} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c^{2} m^{4} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 10 \, a^{2} m^{3} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 18 \, a b m^{3} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, b^{2} m^{3} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 16 \, a c m^{3} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 14 \, b c m^{3} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} m^{3} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 35 \, a^{2} m^{2} n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 52 \, a b m^{2} n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 19 \, b^{2} m^{2} n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 38 \, a c m^{2} n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 28 \, b c m^{2} n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 11 \, c^{2} m^{2} n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 50 \, a^{2} m n^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 48 \, a b m n^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 12 \, b^{2} m n^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 24 \, a c m n^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 16 \, b c m n^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} m n^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 24 \, a^{2} n^{4} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, c^{2} m^{3} x x^{4 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 18 \, c^{2} m^{2} n x x^{4 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 22 \, c^{2} m n^{2} x x^{4 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} n^{3} x x^{4 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, b c m^{3} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, c^{2} m^{3} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 42 \, b c m^{2} n x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 18 \, c^{2} m^{2} n x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 56 \, b c m n^{2} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 22 \, c^{2} m n^{2} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 16 \, b c n^{3} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} n^{3} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, b^{2} m^{3} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, a c m^{3} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, b c m^{3} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, c^{2} m^{3} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 24 \, b^{2} m^{2} n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 48 \, a c m^{2} n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 42 \, b c m^{2} n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 18 \, c^{2} m^{2} n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 38 \, b^{2} m n^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 76 \, a c m n^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 56 \, b c m n^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 22 \, c^{2} m n^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 12 \, b^{2} n^{3} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 24 \, a c n^{3} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 16 \, b c n^{3} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} n^{3} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, a b m^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, b^{2} m^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, a c m^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, b c m^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, c^{2} m^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 54 \, a b m^{2} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 24 \, b^{2} m^{2} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 48 \, a c m^{2} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 42 \, b c m^{2} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 18 \, c^{2} m^{2} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 104 \, a b m n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 38 \, b^{2} m n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 76 \, a c m n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 56 \, b c m n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 22 \, c^{2} m n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 48 \, a b n^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 12 \, b^{2} n^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 24 \, a c n^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 16 \, b c n^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} n^{3} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, a^{2} m^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, a b m^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, b^{2} m^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, a c m^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, b c m^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, c^{2} m^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 30 \, a^{2} m^{2} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 54 \, a b m^{2} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 24 \, b^{2} m^{2} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 48 \, a c m^{2} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 42 \, b c m^{2} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 18 \, c^{2} m^{2} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 70 \, a^{2} m n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 104 \, a b m n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 38 \, b^{2} m n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 76 \, a c m n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 56 \, b c m n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 22 \, c^{2} m n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 50 \, a^{2} n^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 48 \, a b n^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 12 \, b^{2} n^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 24 \, a c n^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 16 \, b c n^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} n^{3} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} m^{2} x x^{4 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 18 \, c^{2} m n x x^{4 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 11 \, c^{2} n^{2} x x^{4 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 12 \, b c m^{2} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} m^{2} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 42 \, b c m n x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 18 \, c^{2} m n x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 28 \, b c n^{2} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 11 \, c^{2} n^{2} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, b^{2} m^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 12 \, a c m^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 12 \, b c m^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} m^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 24 \, b^{2} m n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 48 \, a c m n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 42 \, b c m n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 18 \, c^{2} m n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 19 \, b^{2} n^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 38 \, a c n^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 28 \, b c n^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 11 \, c^{2} n^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 12 \, a b m^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, b^{2} m^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 12 \, a c m^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 12 \, b c m^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} m^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 54 \, a b m n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 24 \, b^{2} m n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 48 \, a c m n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 42 \, b c m n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 18 \, c^{2} m n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 52 \, a b n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 19 \, b^{2} n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 38 \, a c n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 28 \, b c n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 11 \, c^{2} n^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, a^{2} m^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 12 \, a b m^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, b^{2} m^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 12 \, a c m^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 12 \, b c m^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} m^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 30 \, a^{2} m n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 54 \, a b m n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 24 \, b^{2} m n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 48 \, a c m n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 42 \, b c m n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 18 \, c^{2} m n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 35 \, a^{2} n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 52 \, a b n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 19 \, b^{2} n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 38 \, a c n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 28 \, b c n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 11 \, c^{2} n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, c^{2} m x x^{4 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} n x x^{4 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, b c m x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, c^{2} m x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 14 \, b c n x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} n x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, b^{2} m x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, a c m x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, b c m x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, c^{2} m x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, b^{2} n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 16 \, a c n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 14 \, b c n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, a b m x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, b^{2} m x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, a c m x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, b c m x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, c^{2} m x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 18 \, a b n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, b^{2} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 16 \, a c n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 14 \, b c n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, a^{2} m x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, a b m x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, b^{2} m x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, a c m x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, b c m x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 4 \, c^{2} m x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 10 \, a^{2} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 18 \, a b n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 8 \, b^{2} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 16 \, a c n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 14 \, b c n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 6 \, c^{2} n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c^{2} x x^{4 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, b c x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c^{2} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + b^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, a c x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, b c x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, a b x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + b^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, a c x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, b c x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + a^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, a b x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + b^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, a c x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, b c x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)}}{m^{5} + 10 \, m^{4} n + 35 \, m^{3} n^{2} + 50 \, m^{2} n^{3} + 24 \, m n^{4} + 5 \, m^{4} + 40 \, m^{3} n + 105 \, m^{2} n^{2} + 100 \, m n^{3} + 24 \, n^{4} + 10 \, m^{3} + 60 \, m^{2} n + 105 \, m n^{2} + 50 \, n^{3} + 10 \, m^{2} + 40 \, m n + 35 \, n^{2} + 5 \, m + 10 \, n + 1}"," ",0,"(c^2*m^4*x*x^(4*n)*e^(m*log(d) + m*log(x)) + 6*c^2*m^3*n*x*x^(4*n)*e^(m*log(d) + m*log(x)) + 11*c^2*m^2*n^2*x*x^(4*n)*e^(m*log(d) + m*log(x)) + 6*c^2*m*n^3*x*x^(4*n)*e^(m*log(d) + m*log(x)) + 2*b*c*m^4*x*x^(3*n)*e^(m*log(d) + m*log(x)) + c^2*m^4*x*x^(3*n)*e^(m*log(d) + m*log(x)) + 14*b*c*m^3*n*x*x^(3*n)*e^(m*log(d) + m*log(x)) + 6*c^2*m^3*n*x*x^(3*n)*e^(m*log(d) + m*log(x)) + 28*b*c*m^2*n^2*x*x^(3*n)*e^(m*log(d) + m*log(x)) 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11*c^2*n^2*x*x^(2*n)*e^(m*log(d) + m*log(x)) + 12*a*b*m^2*x*x^n*e^(m*log(d) + m*log(x)) + 6*b^2*m^2*x*x^n*e^(m*log(d) + m*log(x)) + 12*a*c*m^2*x*x^n*e^(m*log(d) + m*log(x)) + 12*b*c*m^2*x*x^n*e^(m*log(d) + m*log(x)) + 6*c^2*m^2*x*x^n*e^(m*log(d) + m*log(x)) + 54*a*b*m*n*x*x^n*e^(m*log(d) + m*log(x)) + 24*b^2*m*n*x*x^n*e^(m*log(d) + m*log(x)) + 48*a*c*m*n*x*x^n*e^(m*log(d) + m*log(x)) + 42*b*c*m*n*x*x^n*e^(m*log(d) + m*log(x)) + 18*c^2*m*n*x*x^n*e^(m*log(d) + m*log(x)) + 52*a*b*n^2*x*x^n*e^(m*log(d) + m*log(x)) + 19*b^2*n^2*x*x^n*e^(m*log(d) + m*log(x)) + 38*a*c*n^2*x*x^n*e^(m*log(d) + m*log(x)) + 28*b*c*n^2*x*x^n*e^(m*log(d) + m*log(x)) + 11*c^2*n^2*x*x^n*e^(m*log(d) + m*log(x)) + 6*a^2*m^2*x*e^(m*log(d) + m*log(x)) + 12*a*b*m^2*x*e^(m*log(d) + m*log(x)) + 6*b^2*m^2*x*e^(m*log(d) + m*log(x)) + 12*a*c*m^2*x*e^(m*log(d) + m*log(x)) + 12*b*c*m^2*x*e^(m*log(d) + m*log(x)) + 6*c^2*m^2*x*e^(m*log(d) + m*log(x)) + 30*a^2*m*n*x*e^(m*log(d) + m*log(x)) + 54*a*b*m*n*x*e^(m*log(d) + m*log(x)) + 24*b^2*m*n*x*e^(m*log(d) + m*log(x)) + 48*a*c*m*n*x*e^(m*log(d) + m*log(x)) + 42*b*c*m*n*x*e^(m*log(d) + m*log(x)) + 18*c^2*m*n*x*e^(m*log(d) + m*log(x)) + 35*a^2*n^2*x*e^(m*log(d) + m*log(x)) + 52*a*b*n^2*x*e^(m*log(d) + m*log(x)) + 19*b^2*n^2*x*e^(m*log(d) + m*log(x)) + 38*a*c*n^2*x*e^(m*log(d) + m*log(x)) + 28*b*c*n^2*x*e^(m*log(d) + m*log(x)) + 11*c^2*n^2*x*e^(m*log(d) + m*log(x)) + 4*c^2*m*x*x^(4*n)*e^(m*log(d) + m*log(x)) + 6*c^2*n*x*x^(4*n)*e^(m*log(d) + m*log(x)) + 8*b*c*m*x*x^(3*n)*e^(m*log(d) + m*log(x)) + 4*c^2*m*x*x^(3*n)*e^(m*log(d) + m*log(x)) + 14*b*c*n*x*x^(3*n)*e^(m*log(d) + m*log(x)) + 6*c^2*n*x*x^(3*n)*e^(m*log(d) + m*log(x)) + 4*b^2*m*x*x^(2*n)*e^(m*log(d) + m*log(x)) + 8*a*c*m*x*x^(2*n)*e^(m*log(d) + m*log(x)) + 8*b*c*m*x*x^(2*n)*e^(m*log(d) + m*log(x)) + 4*c^2*m*x*x^(2*n)*e^(m*log(d) + m*log(x)) + 8*b^2*n*x*x^(2*n)*e^(m*log(d) + m*log(x)) + 16*a*c*n*x*x^(2*n)*e^(m*log(d) + m*log(x)) + 14*b*c*n*x*x^(2*n)*e^(m*log(d) + m*log(x)) + 6*c^2*n*x*x^(2*n)*e^(m*log(d) + m*log(x)) + 8*a*b*m*x*x^n*e^(m*log(d) + m*log(x)) + 4*b^2*m*x*x^n*e^(m*log(d) + m*log(x)) + 8*a*c*m*x*x^n*e^(m*log(d) + m*log(x)) + 8*b*c*m*x*x^n*e^(m*log(d) + m*log(x)) + 4*c^2*m*x*x^n*e^(m*log(d) + m*log(x)) + 18*a*b*n*x*x^n*e^(m*log(d) + m*log(x)) + 8*b^2*n*x*x^n*e^(m*log(d) + m*log(x)) + 16*a*c*n*x*x^n*e^(m*log(d) + m*log(x)) + 14*b*c*n*x*x^n*e^(m*log(d) + m*log(x)) + 6*c^2*n*x*x^n*e^(m*log(d) + m*log(x)) + 4*a^2*m*x*e^(m*log(d) + m*log(x)) + 8*a*b*m*x*e^(m*log(d) + m*log(x)) + 4*b^2*m*x*e^(m*log(d) + m*log(x)) + 8*a*c*m*x*e^(m*log(d) + m*log(x)) + 8*b*c*m*x*e^(m*log(d) + m*log(x)) + 4*c^2*m*x*e^(m*log(d) + m*log(x)) + 10*a^2*n*x*e^(m*log(d) + m*log(x)) + 18*a*b*n*x*e^(m*log(d) + m*log(x)) + 8*b^2*n*x*e^(m*log(d) + m*log(x)) + 16*a*c*n*x*e^(m*log(d) + m*log(x)) + 14*b*c*n*x*e^(m*log(d) + m*log(x)) + 6*c^2*n*x*e^(m*log(d) + m*log(x)) + c^2*x*x^(4*n)*e^(m*log(d) + m*log(x)) + 2*b*c*x*x^(3*n)*e^(m*log(d) + m*log(x)) + c^2*x*x^(3*n)*e^(m*log(d) + m*log(x)) + b^2*x*x^(2*n)*e^(m*log(d) + m*log(x)) + 2*a*c*x*x^(2*n)*e^(m*log(d) + m*log(x)) + 2*b*c*x*x^(2*n)*e^(m*log(d) + m*log(x)) + c^2*x*x^(2*n)*e^(m*log(d) + m*log(x)) + 2*a*b*x*x^n*e^(m*log(d) + m*log(x)) + b^2*x*x^n*e^(m*log(d) + m*log(x)) + 2*a*c*x*x^n*e^(m*log(d) + m*log(x)) + 2*b*c*x*x^n*e^(m*log(d) + m*log(x)) + c^2*x*x^n*e^(m*log(d) + m*log(x)) + a^2*x*e^(m*log(d) + m*log(x)) + 2*a*b*x*e^(m*log(d) + m*log(x)) + b^2*x*e^(m*log(d) + m*log(x)) + 2*a*c*x*e^(m*log(d) + m*log(x)) + 2*b*c*x*e^(m*log(d) + m*log(x)) + c^2*x*e^(m*log(d) + m*log(x)))/(m^5 + 10*m^4*n + 35*m^3*n^2 + 50*m^2*n^3 + 24*m*n^4 + 5*m^4 + 40*m^3*n + 105*m^2*n^2 + 100*m*n^3 + 24*n^4 + 10*m^3 + 60*m^2*n + 105*m*n^2 + 50*n^3 + 10*m^2 + 40*m*n + 35*n^2 + 5*m + 10*n + 1)","B",0
598,1,557,0,0.403066," ","integrate((d*x)^m*(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\frac{c m^{2} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c m n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + b m^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c m^{2} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, b m n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c m n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + a m^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + b m^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c m^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 3 \, a m n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, b m n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c m n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, a n^{2} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, c m x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c n x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, b m x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, c m x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, b n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c n x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, a m x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, b m x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, c m x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 3 \, a n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, b n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c n x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + b x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + a x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + b x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + c x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)}}{m^{3} + 3 \, m^{2} n + 2 \, m n^{2} + 3 \, m^{2} + 6 \, m n + 2 \, n^{2} + 3 \, m + 3 \, n + 1}"," ",0,"(c*m^2*x*x^(2*n)*e^(m*log(d) + m*log(x)) + c*m*n*x*x^(2*n)*e^(m*log(d) + m*log(x)) + b*m^2*x*x^n*e^(m*log(d) + m*log(x)) + c*m^2*x*x^n*e^(m*log(d) + m*log(x)) + 2*b*m*n*x*x^n*e^(m*log(d) + m*log(x)) + c*m*n*x*x^n*e^(m*log(d) + m*log(x)) + a*m^2*x*e^(m*log(d) + m*log(x)) + b*m^2*x*e^(m*log(d) + m*log(x)) + c*m^2*x*e^(m*log(d) + m*log(x)) + 3*a*m*n*x*e^(m*log(d) + m*log(x)) + 2*b*m*n*x*e^(m*log(d) + m*log(x)) + c*m*n*x*e^(m*log(d) + m*log(x)) + 2*a*n^2*x*e^(m*log(d) + m*log(x)) + 2*c*m*x*x^(2*n)*e^(m*log(d) + m*log(x)) + c*n*x*x^(2*n)*e^(m*log(d) + m*log(x)) + 2*b*m*x*x^n*e^(m*log(d) + m*log(x)) + 2*c*m*x*x^n*e^(m*log(d) + m*log(x)) + 2*b*n*x*x^n*e^(m*log(d) + m*log(x)) + c*n*x*x^n*e^(m*log(d) + m*log(x)) + 2*a*m*x*e^(m*log(d) + m*log(x)) + 2*b*m*x*e^(m*log(d) + m*log(x)) + 2*c*m*x*e^(m*log(d) + m*log(x)) + 3*a*n*x*e^(m*log(d) + m*log(x)) + 2*b*n*x*e^(m*log(d) + m*log(x)) + c*n*x*e^(m*log(d) + m*log(x)) + c*x*x^(2*n)*e^(m*log(d) + m*log(x)) + b*x*x^n*e^(m*log(d) + m*log(x)) + c*x*x^n*e^(m*log(d) + m*log(x)) + a*x*e^(m*log(d) + m*log(x)) + b*x*e^(m*log(d) + m*log(x)) + c*x*e^(m*log(d) + m*log(x)))/(m^3 + 3*m^2*n + 2*m*n^2 + 3*m^2 + 6*m*n + 2*n^2 + 3*m + 3*n + 1)","B",0
599,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate((d*x)^m/(c*x^(2*n) + b*x^n + a), x)","F",0
600,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x)^m/(c*x^(2*n) + b*x^n + a)^2, x)","F",0
601,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*x)^m/(c*x^(2*n) + b*x^n + a)^3, x)","F",0
602,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^(3/2)*(d*x)^m, x)","F",0
603,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2 \, n} + b x^{n} + a} \left(d x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(c*x^(2*n) + b*x^n + a)*(d*x)^m, x)","F",0
604,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{\sqrt{c x^{2 \, n} + b x^{n} + a}}\,{d x}"," ",0,"integrate((d*x)^m/sqrt(c*x^(2*n) + b*x^n + a), x)","F",0
605,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*x)^m/(c*x^(2*n) + b*x^n + a)^(3/2), x)","F",0
606,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""giac"")","\int {\left(c x^{2 \, n} + b x^{n} + a\right)}^{p} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^p*(d*x)^m, x)","F",0
607,1,169,0,0.408053," ","integrate((e*x+d)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","\frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)} c d^{6} + \frac{3}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{2} c d^{4} e + \frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{3} c d^{2} e^{2} + \frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)} b d^{4} + \frac{1}{8} \, {\left(x^{2} e + 2 \, d x\right)}^{4} c e^{3} + \frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{2} b d^{2} e + \frac{1}{6} \, {\left(x^{2} e + 2 \, d x\right)}^{3} b e^{2} + \frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)} a d^{2} + \frac{1}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{2} a e"," ",0,"1/2*(x^2*e + 2*d*x)*c*d^6 + 3/4*(x^2*e + 2*d*x)^2*c*d^4*e + 1/2*(x^2*e + 2*d*x)^3*c*d^2*e^2 + 1/2*(x^2*e + 2*d*x)*b*d^4 + 1/8*(x^2*e + 2*d*x)^4*c*e^3 + 1/2*(x^2*e + 2*d*x)^2*b*d^2*e + 1/6*(x^2*e + 2*d*x)^3*b*e^2 + 1/2*(x^2*e + 2*d*x)*a*d^2 + 1/4*(x^2*e + 2*d*x)^2*a*e","B",0
608,1,493,0,0.409503," ","integrate((e*x+d)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)} c^{2} d^{10} + \frac{5}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{2} c^{2} d^{8} e + \frac{5}{3} \, {\left(x^{2} e + 2 \, d x\right)}^{3} c^{2} d^{6} e^{2} + {\left(x^{2} e + 2 \, d x\right)} b c d^{8} + \frac{5}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{4} c^{2} d^{4} e^{3} + 2 \, {\left(x^{2} e + 2 \, d x\right)}^{2} b c d^{6} e + \frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{5} c^{2} d^{2} e^{4} + 2 \, {\left(x^{2} e + 2 \, d x\right)}^{3} b c d^{4} e^{2} + \frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)} b^{2} d^{6} + {\left(x^{2} e + 2 \, d x\right)} a c d^{6} + \frac{1}{12} \, {\left(x^{2} e + 2 \, d x\right)}^{6} c^{2} e^{5} + {\left(x^{2} e + 2 \, d x\right)}^{4} b c d^{2} e^{3} + \frac{3}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{2} b^{2} d^{4} e + \frac{3}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{2} a c d^{4} e + \frac{1}{5} \, {\left(x^{2} e + 2 \, d x\right)}^{5} b c e^{4} + \frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{3} b^{2} d^{2} e^{2} + {\left(x^{2} e + 2 \, d x\right)}^{3} a c d^{2} e^{2} + {\left(x^{2} e + 2 \, d x\right)} a b d^{4} + \frac{1}{8} \, {\left(x^{2} e + 2 \, d x\right)}^{4} b^{2} e^{3} + \frac{1}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{4} a c e^{3} + {\left(x^{2} e + 2 \, d x\right)}^{2} a b d^{2} e + \frac{1}{3} \, {\left(x^{2} e + 2 \, d x\right)}^{3} a b e^{2} + \frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)} a^{2} d^{2} + \frac{1}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{2} a^{2} e"," ",0,"1/2*(x^2*e + 2*d*x)*c^2*d^10 + 5/4*(x^2*e + 2*d*x)^2*c^2*d^8*e + 5/3*(x^2*e + 2*d*x)^3*c^2*d^6*e^2 + (x^2*e + 2*d*x)*b*c*d^8 + 5/4*(x^2*e + 2*d*x)^4*c^2*d^4*e^3 + 2*(x^2*e + 2*d*x)^2*b*c*d^6*e + 1/2*(x^2*e + 2*d*x)^5*c^2*d^2*e^4 + 2*(x^2*e + 2*d*x)^3*b*c*d^4*e^2 + 1/2*(x^2*e + 2*d*x)*b^2*d^6 + (x^2*e + 2*d*x)*a*c*d^6 + 1/12*(x^2*e + 2*d*x)^6*c^2*e^5 + (x^2*e + 2*d*x)^4*b*c*d^2*e^3 + 3/4*(x^2*e + 2*d*x)^2*b^2*d^4*e + 3/2*(x^2*e + 2*d*x)^2*a*c*d^4*e + 1/5*(x^2*e + 2*d*x)^5*b*c*e^4 + 1/2*(x^2*e + 2*d*x)^3*b^2*d^2*e^2 + (x^2*e + 2*d*x)^3*a*c*d^2*e^2 + (x^2*e + 2*d*x)*a*b*d^4 + 1/8*(x^2*e + 2*d*x)^4*b^2*e^3 + 1/4*(x^2*e + 2*d*x)^4*a*c*e^3 + (x^2*e + 2*d*x)^2*a*b*d^2*e + 1/3*(x^2*e + 2*d*x)^3*a*b*e^2 + 1/2*(x^2*e + 2*d*x)*a^2*d^2 + 1/4*(x^2*e + 2*d*x)^2*a^2*e","B",0
609,1,1109,0,0.616650," ","integrate((e*x+d)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","\frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)} c^{3} d^{14} + \frac{7}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{2} c^{3} d^{12} e + \frac{7}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{3} c^{3} d^{10} e^{2} + \frac{3}{2} \, {\left(x^{2} e + 2 \, d x\right)} b c^{2} d^{12} + \frac{35}{8} \, {\left(x^{2} e + 2 \, d x\right)}^{4} c^{3} d^{8} e^{3} + \frac{9}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{2} b c^{2} d^{10} e + \frac{7}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{5} c^{3} d^{6} e^{4} + \frac{15}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{3} b c^{2} d^{8} e^{2} + \frac{3}{2} \, {\left(x^{2} e + 2 \, d x\right)} b^{2} c d^{10} + \frac{3}{2} \, {\left(x^{2} e + 2 \, d x\right)} a c^{2} d^{10} + \frac{7}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{6} c^{3} d^{4} e^{5} + \frac{15}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{4} b c^{2} d^{6} e^{3} + \frac{15}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{2} b^{2} c d^{8} e + \frac{15}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{2} a c^{2} d^{8} e + \frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{7} c^{3} d^{2} e^{6} + \frac{9}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{5} b c^{2} d^{4} e^{4} + 5 \, {\left(x^{2} e + 2 \, d x\right)}^{3} b^{2} c d^{6} e^{2} + 5 \, {\left(x^{2} e + 2 \, d x\right)}^{3} a c^{2} d^{6} e^{2} + \frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)} b^{3} d^{8} + 3 \, {\left(x^{2} e + 2 \, d x\right)} a b c d^{8} + \frac{1}{16} \, {\left(x^{2} e + 2 \, d x\right)}^{8} c^{3} e^{7} + \frac{3}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{6} b c^{2} d^{2} e^{5} + \frac{15}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{4} b^{2} c d^{4} e^{3} + \frac{15}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{4} a c^{2} d^{4} e^{3} + {\left(x^{2} e + 2 \, d x\right)}^{2} b^{3} d^{6} e + 6 \, {\left(x^{2} e + 2 \, d x\right)}^{2} a b c d^{6} e + \frac{3}{14} \, {\left(x^{2} e + 2 \, d x\right)}^{7} b c^{2} e^{6} + \frac{3}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{5} b^{2} c d^{2} e^{4} + \frac{3}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{5} a c^{2} d^{2} e^{4} + {\left(x^{2} e + 2 \, d x\right)}^{3} b^{3} d^{4} e^{2} + 6 \, {\left(x^{2} e + 2 \, d x\right)}^{3} a b c d^{4} e^{2} + \frac{3}{2} \, {\left(x^{2} e + 2 \, d x\right)} a b^{2} d^{6} + \frac{3}{2} \, {\left(x^{2} e + 2 \, d x\right)} a^{2} c d^{6} + \frac{1}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{6} b^{2} c e^{5} + \frac{1}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{6} a c^{2} e^{5} + \frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{4} b^{3} d^{2} e^{3} + 3 \, {\left(x^{2} e + 2 \, d x\right)}^{4} a b c d^{2} e^{3} + \frac{9}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{2} a b^{2} d^{4} e + \frac{9}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{2} a^{2} c d^{4} e + \frac{1}{10} \, {\left(x^{2} e + 2 \, d x\right)}^{5} b^{3} e^{4} + \frac{3}{5} \, {\left(x^{2} e + 2 \, d x\right)}^{5} a b c e^{4} + \frac{3}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{3} a b^{2} d^{2} e^{2} + \frac{3}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{3} a^{2} c d^{2} e^{2} + \frac{3}{2} \, {\left(x^{2} e + 2 \, d x\right)} a^{2} b d^{4} + \frac{3}{8} \, {\left(x^{2} e + 2 \, d x\right)}^{4} a b^{2} e^{3} + \frac{3}{8} \, {\left(x^{2} e + 2 \, d x\right)}^{4} a^{2} c e^{3} + \frac{3}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{2} a^{2} b d^{2} e + \frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)}^{3} a^{2} b e^{2} + \frac{1}{2} \, {\left(x^{2} e + 2 \, d x\right)} a^{3} d^{2} + \frac{1}{4} \, {\left(x^{2} e + 2 \, d x\right)}^{2} a^{3} e"," ",0,"1/2*(x^2*e + 2*d*x)*c^3*d^14 + 7/4*(x^2*e + 2*d*x)^2*c^3*d^12*e + 7/2*(x^2*e + 2*d*x)^3*c^3*d^10*e^2 + 3/2*(x^2*e + 2*d*x)*b*c^2*d^12 + 35/8*(x^2*e + 2*d*x)^4*c^3*d^8*e^3 + 9/2*(x^2*e + 2*d*x)^2*b*c^2*d^10*e + 7/2*(x^2*e + 2*d*x)^5*c^3*d^6*e^4 + 15/2*(x^2*e + 2*d*x)^3*b*c^2*d^8*e^2 + 3/2*(x^2*e + 2*d*x)*b^2*c*d^10 + 3/2*(x^2*e + 2*d*x)*a*c^2*d^10 + 7/4*(x^2*e + 2*d*x)^6*c^3*d^4*e^5 + 15/2*(x^2*e + 2*d*x)^4*b*c^2*d^6*e^3 + 15/4*(x^2*e + 2*d*x)^2*b^2*c*d^8*e + 15/4*(x^2*e + 2*d*x)^2*a*c^2*d^8*e + 1/2*(x^2*e + 2*d*x)^7*c^3*d^2*e^6 + 9/2*(x^2*e + 2*d*x)^5*b*c^2*d^4*e^4 + 5*(x^2*e + 2*d*x)^3*b^2*c*d^6*e^2 + 5*(x^2*e + 2*d*x)^3*a*c^2*d^6*e^2 + 1/2*(x^2*e + 2*d*x)*b^3*d^8 + 3*(x^2*e + 2*d*x)*a*b*c*d^8 + 1/16*(x^2*e + 2*d*x)^8*c^3*e^7 + 3/2*(x^2*e + 2*d*x)^6*b*c^2*d^2*e^5 + 15/4*(x^2*e + 2*d*x)^4*b^2*c*d^4*e^3 + 15/4*(x^2*e + 2*d*x)^4*a*c^2*d^4*e^3 + (x^2*e + 2*d*x)^2*b^3*d^6*e + 6*(x^2*e + 2*d*x)^2*a*b*c*d^6*e + 3/14*(x^2*e + 2*d*x)^7*b*c^2*e^6 + 3/2*(x^2*e + 2*d*x)^5*b^2*c*d^2*e^4 + 3/2*(x^2*e + 2*d*x)^5*a*c^2*d^2*e^4 + (x^2*e + 2*d*x)^3*b^3*d^4*e^2 + 6*(x^2*e + 2*d*x)^3*a*b*c*d^4*e^2 + 3/2*(x^2*e + 2*d*x)*a*b^2*d^6 + 3/2*(x^2*e + 2*d*x)*a^2*c*d^6 + 1/4*(x^2*e + 2*d*x)^6*b^2*c*e^5 + 1/4*(x^2*e + 2*d*x)^6*a*c^2*e^5 + 1/2*(x^2*e + 2*d*x)^4*b^3*d^2*e^3 + 3*(x^2*e + 2*d*x)^4*a*b*c*d^2*e^3 + 9/4*(x^2*e + 2*d*x)^2*a*b^2*d^4*e + 9/4*(x^2*e + 2*d*x)^2*a^2*c*d^4*e + 1/10*(x^2*e + 2*d*x)^5*b^3*e^4 + 3/5*(x^2*e + 2*d*x)^5*a*b*c*e^4 + 3/2*(x^2*e + 2*d*x)^3*a*b^2*d^2*e^2 + 3/2*(x^2*e + 2*d*x)^3*a^2*c*d^2*e^2 + 3/2*(x^2*e + 2*d*x)*a^2*b*d^4 + 3/8*(x^2*e + 2*d*x)^4*a*b^2*e^3 + 3/8*(x^2*e + 2*d*x)^4*a^2*c*e^3 + 3/2*(x^2*e + 2*d*x)^2*a^2*b*d^2*e + 1/2*(x^2*e + 2*d*x)^3*a^2*b*e^2 + 1/2*(x^2*e + 2*d*x)*a^3*d^2 + 1/4*(x^2*e + 2*d*x)^2*a^3*e","B",0
610,1,213,0,0.300236," ","integrate((e*f*x+d*f)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","\frac{1}{2} \, {\left(f x^{2} e + 2 \, d f x\right)} c d^{6} f^{2} + \frac{1}{2} \, {\left(f x^{2} e + 2 \, d f x\right)} b d^{4} f^{2} + \frac{1}{2} \, {\left(f x^{2} e + 2 \, d f x\right)} a d^{2} f^{2} + \frac{18 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} c d^{4} f^{2} e + 12 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} c d^{2} f e^{2} + 12 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} b d^{2} f^{2} e + 3 \, {\left(f x^{2} e + 2 \, d f x\right)}^{4} c e^{3} + 4 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} b f e^{2} + 6 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} a f^{2} e}{24 \, f}"," ",0,"1/2*(f*x^2*e + 2*d*f*x)*c*d^6*f^2 + 1/2*(f*x^2*e + 2*d*f*x)*b*d^4*f^2 + 1/2*(f*x^2*e + 2*d*f*x)*a*d^2*f^2 + 1/24*(18*(f*x^2*e + 2*d*f*x)^2*c*d^4*f^2*e + 12*(f*x^2*e + 2*d*f*x)^3*c*d^2*f*e^2 + 12*(f*x^2*e + 2*d*f*x)^2*b*d^2*f^2*e + 3*(f*x^2*e + 2*d*f*x)^4*c*e^3 + 4*(f*x^2*e + 2*d*f*x)^3*b*f*e^2 + 6*(f*x^2*e + 2*d*f*x)^2*a*f^2*e)/f","B",0
611,1,615,0,0.433012," ","integrate((e*f*x+d*f)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(f x^{2} e + 2 \, d f x\right)} c^{2} d^{10} f^{2} + {\left(f x^{2} e + 2 \, d f x\right)} b c d^{8} f^{2} + \frac{1}{2} \, {\left(f x^{2} e + 2 \, d f x\right)} b^{2} d^{6} f^{2} + {\left(f x^{2} e + 2 \, d f x\right)} a c d^{6} f^{2} + {\left(f x^{2} e + 2 \, d f x\right)} a b d^{4} f^{2} + \frac{1}{2} \, {\left(f x^{2} e + 2 \, d f x\right)} a^{2} d^{2} f^{2} + \frac{150 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} c^{2} d^{8} f^{4} e + 200 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} c^{2} d^{6} f^{3} e^{2} + 240 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} b c d^{6} f^{4} e + 150 \, {\left(f x^{2} e + 2 \, d f x\right)}^{4} c^{2} d^{4} f^{2} e^{3} + 240 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} b c d^{4} f^{3} e^{2} + 90 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} b^{2} d^{4} f^{4} e + 180 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} a c d^{4} f^{4} e + 60 \, {\left(f x^{2} e + 2 \, d f x\right)}^{5} c^{2} d^{2} f e^{4} + 120 \, {\left(f x^{2} e + 2 \, d f x\right)}^{4} b c d^{2} f^{2} e^{3} + 60 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} b^{2} d^{2} f^{3} e^{2} + 120 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} a c d^{2} f^{3} e^{2} + 120 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} a b d^{2} f^{4} e + 10 \, {\left(f x^{2} e + 2 \, d f x\right)}^{6} c^{2} e^{5} + 24 \, {\left(f x^{2} e + 2 \, d f x\right)}^{5} b c f e^{4} + 15 \, {\left(f x^{2} e + 2 \, d f x\right)}^{4} b^{2} f^{2} e^{3} + 30 \, {\left(f x^{2} e + 2 \, d f x\right)}^{4} a c f^{2} e^{3} + 40 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} a b f^{3} e^{2} + 30 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} a^{2} f^{4} e}{120 \, f^{3}}"," ",0,"1/2*(f*x^2*e + 2*d*f*x)*c^2*d^10*f^2 + (f*x^2*e + 2*d*f*x)*b*c*d^8*f^2 + 1/2*(f*x^2*e + 2*d*f*x)*b^2*d^6*f^2 + (f*x^2*e + 2*d*f*x)*a*c*d^6*f^2 + (f*x^2*e + 2*d*f*x)*a*b*d^4*f^2 + 1/2*(f*x^2*e + 2*d*f*x)*a^2*d^2*f^2 + 1/120*(150*(f*x^2*e + 2*d*f*x)^2*c^2*d^8*f^4*e + 200*(f*x^2*e + 2*d*f*x)^3*c^2*d^6*f^3*e^2 + 240*(f*x^2*e + 2*d*f*x)^2*b*c*d^6*f^4*e + 150*(f*x^2*e + 2*d*f*x)^4*c^2*d^4*f^2*e^3 + 240*(f*x^2*e + 2*d*f*x)^3*b*c*d^4*f^3*e^2 + 90*(f*x^2*e + 2*d*f*x)^2*b^2*d^4*f^4*e + 180*(f*x^2*e + 2*d*f*x)^2*a*c*d^4*f^4*e + 60*(f*x^2*e + 2*d*f*x)^5*c^2*d^2*f*e^4 + 120*(f*x^2*e + 2*d*f*x)^4*b*c*d^2*f^2*e^3 + 60*(f*x^2*e + 2*d*f*x)^3*b^2*d^2*f^3*e^2 + 120*(f*x^2*e + 2*d*f*x)^3*a*c*d^2*f^3*e^2 + 120*(f*x^2*e + 2*d*f*x)^2*a*b*d^2*f^4*e + 10*(f*x^2*e + 2*d*f*x)^6*c^2*e^5 + 24*(f*x^2*e + 2*d*f*x)^5*b*c*f*e^4 + 15*(f*x^2*e + 2*d*f*x)^4*b^2*f^2*e^3 + 30*(f*x^2*e + 2*d*f*x)^4*a*c*f^2*e^3 + 40*(f*x^2*e + 2*d*f*x)^3*a*b*f^3*e^2 + 30*(f*x^2*e + 2*d*f*x)^2*a^2*f^4*e)/f^3","B",0
612,1,1360,0,0.514289," ","integrate((e*f*x+d*f)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","\frac{1}{2} \, {\left(f x^{2} e + 2 \, d f x\right)} c^{3} d^{14} f^{2} + \frac{3}{2} \, {\left(f x^{2} e + 2 \, d f x\right)} b c^{2} d^{12} f^{2} + \frac{3}{2} \, {\left(f x^{2} e + 2 \, d f x\right)} b^{2} c d^{10} f^{2} + \frac{3}{2} \, {\left(f x^{2} e + 2 \, d f x\right)} a c^{2} d^{10} f^{2} + \frac{1}{2} \, {\left(f x^{2} e + 2 \, d f x\right)} b^{3} d^{8} f^{2} + 3 \, {\left(f x^{2} e + 2 \, d f x\right)} a b c d^{8} f^{2} + \frac{3}{2} \, {\left(f x^{2} e + 2 \, d f x\right)} a b^{2} d^{6} f^{2} + \frac{3}{2} \, {\left(f x^{2} e + 2 \, d f x\right)} a^{2} c d^{6} f^{2} + \frac{3}{2} \, {\left(f x^{2} e + 2 \, d f x\right)} a^{2} b d^{4} f^{2} + \frac{1}{2} \, {\left(f x^{2} e + 2 \, d f x\right)} a^{3} d^{2} f^{2} + \frac{980 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} c^{3} d^{12} f^{6} e + 1960 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} c^{3} d^{10} f^{5} e^{2} + 2520 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} b c^{2} d^{10} f^{6} e + 2450 \, {\left(f x^{2} e + 2 \, d f x\right)}^{4} c^{3} d^{8} f^{4} e^{3} + 4200 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} b c^{2} d^{8} f^{5} e^{2} + 2100 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} b^{2} c d^{8} f^{6} e + 2100 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} a c^{2} d^{8} f^{6} e + 1960 \, {\left(f x^{2} e + 2 \, d f x\right)}^{5} c^{3} d^{6} f^{3} e^{4} + 4200 \, {\left(f x^{2} e + 2 \, d f x\right)}^{4} b c^{2} d^{6} f^{4} e^{3} + 2800 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} b^{2} c d^{6} f^{5} e^{2} + 2800 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} a c^{2} d^{6} f^{5} e^{2} + 560 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} b^{3} d^{6} f^{6} e + 3360 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} a b c d^{6} f^{6} e + 980 \, {\left(f x^{2} e + 2 \, d f x\right)}^{6} c^{3} d^{4} f^{2} e^{5} + 2520 \, {\left(f x^{2} e + 2 \, d f x\right)}^{5} b c^{2} d^{4} f^{3} e^{4} + 2100 \, {\left(f x^{2} e + 2 \, d f x\right)}^{4} b^{2} c d^{4} f^{4} e^{3} + 2100 \, {\left(f x^{2} e + 2 \, d f x\right)}^{4} a c^{2} d^{4} f^{4} e^{3} + 560 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} b^{3} d^{4} f^{5} e^{2} + 3360 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} a b c d^{4} f^{5} e^{2} + 1260 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} a b^{2} d^{4} f^{6} e + 1260 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} a^{2} c d^{4} f^{6} e + 280 \, {\left(f x^{2} e + 2 \, d f x\right)}^{7} c^{3} d^{2} f e^{6} + 840 \, {\left(f x^{2} e + 2 \, d f x\right)}^{6} b c^{2} d^{2} f^{2} e^{5} + 840 \, {\left(f x^{2} e + 2 \, d f x\right)}^{5} b^{2} c d^{2} f^{3} e^{4} + 840 \, {\left(f x^{2} e + 2 \, d f x\right)}^{5} a c^{2} d^{2} f^{3} e^{4} + 280 \, {\left(f x^{2} e + 2 \, d f x\right)}^{4} b^{3} d^{2} f^{4} e^{3} + 1680 \, {\left(f x^{2} e + 2 \, d f x\right)}^{4} a b c d^{2} f^{4} e^{3} + 840 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} a b^{2} d^{2} f^{5} e^{2} + 840 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} a^{2} c d^{2} f^{5} e^{2} + 840 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} a^{2} b d^{2} f^{6} e + 35 \, {\left(f x^{2} e + 2 \, d f x\right)}^{8} c^{3} e^{7} + 120 \, {\left(f x^{2} e + 2 \, d f x\right)}^{7} b c^{2} f e^{6} + 140 \, {\left(f x^{2} e + 2 \, d f x\right)}^{6} b^{2} c f^{2} e^{5} + 140 \, {\left(f x^{2} e + 2 \, d f x\right)}^{6} a c^{2} f^{2} e^{5} + 56 \, {\left(f x^{2} e + 2 \, d f x\right)}^{5} b^{3} f^{3} e^{4} + 336 \, {\left(f x^{2} e + 2 \, d f x\right)}^{5} a b c f^{3} e^{4} + 210 \, {\left(f x^{2} e + 2 \, d f x\right)}^{4} a b^{2} f^{4} e^{3} + 210 \, {\left(f x^{2} e + 2 \, d f x\right)}^{4} a^{2} c f^{4} e^{3} + 280 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} a^{2} b f^{5} e^{2} + 140 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} a^{3} f^{6} e}{560 \, f^{5}}"," ",0,"1/2*(f*x^2*e + 2*d*f*x)*c^3*d^14*f^2 + 3/2*(f*x^2*e + 2*d*f*x)*b*c^2*d^12*f^2 + 3/2*(f*x^2*e + 2*d*f*x)*b^2*c*d^10*f^2 + 3/2*(f*x^2*e + 2*d*f*x)*a*c^2*d^10*f^2 + 1/2*(f*x^2*e + 2*d*f*x)*b^3*d^8*f^2 + 3*(f*x^2*e + 2*d*f*x)*a*b*c*d^8*f^2 + 3/2*(f*x^2*e + 2*d*f*x)*a*b^2*d^6*f^2 + 3/2*(f*x^2*e + 2*d*f*x)*a^2*c*d^6*f^2 + 3/2*(f*x^2*e + 2*d*f*x)*a^2*b*d^4*f^2 + 1/2*(f*x^2*e + 2*d*f*x)*a^3*d^2*f^2 + 1/560*(980*(f*x^2*e + 2*d*f*x)^2*c^3*d^12*f^6*e + 1960*(f*x^2*e + 2*d*f*x)^3*c^3*d^10*f^5*e^2 + 2520*(f*x^2*e + 2*d*f*x)^2*b*c^2*d^10*f^6*e + 2450*(f*x^2*e + 2*d*f*x)^4*c^3*d^8*f^4*e^3 + 4200*(f*x^2*e + 2*d*f*x)^3*b*c^2*d^8*f^5*e^2 + 2100*(f*x^2*e + 2*d*f*x)^2*b^2*c*d^8*f^6*e + 2100*(f*x^2*e + 2*d*f*x)^2*a*c^2*d^8*f^6*e + 1960*(f*x^2*e + 2*d*f*x)^5*c^3*d^6*f^3*e^4 + 4200*(f*x^2*e + 2*d*f*x)^4*b*c^2*d^6*f^4*e^3 + 2800*(f*x^2*e + 2*d*f*x)^3*b^2*c*d^6*f^5*e^2 + 2800*(f*x^2*e + 2*d*f*x)^3*a*c^2*d^6*f^5*e^2 + 560*(f*x^2*e + 2*d*f*x)^2*b^3*d^6*f^6*e + 3360*(f*x^2*e + 2*d*f*x)^2*a*b*c*d^6*f^6*e + 980*(f*x^2*e + 2*d*f*x)^6*c^3*d^4*f^2*e^5 + 2520*(f*x^2*e + 2*d*f*x)^5*b*c^2*d^4*f^3*e^4 + 2100*(f*x^2*e + 2*d*f*x)^4*b^2*c*d^4*f^4*e^3 + 2100*(f*x^2*e + 2*d*f*x)^4*a*c^2*d^4*f^4*e^3 + 560*(f*x^2*e + 2*d*f*x)^3*b^3*d^4*f^5*e^2 + 3360*(f*x^2*e + 2*d*f*x)^3*a*b*c*d^4*f^5*e^2 + 1260*(f*x^2*e + 2*d*f*x)^2*a*b^2*d^4*f^6*e + 1260*(f*x^2*e + 2*d*f*x)^2*a^2*c*d^4*f^6*e + 280*(f*x^2*e + 2*d*f*x)^7*c^3*d^2*f*e^6 + 840*(f*x^2*e + 2*d*f*x)^6*b*c^2*d^2*f^2*e^5 + 840*(f*x^2*e + 2*d*f*x)^5*b^2*c*d^2*f^3*e^4 + 840*(f*x^2*e + 2*d*f*x)^5*a*c^2*d^2*f^3*e^4 + 280*(f*x^2*e + 2*d*f*x)^4*b^3*d^2*f^4*e^3 + 1680*(f*x^2*e + 2*d*f*x)^4*a*b*c*d^2*f^4*e^3 + 840*(f*x^2*e + 2*d*f*x)^3*a*b^2*d^2*f^5*e^2 + 840*(f*x^2*e + 2*d*f*x)^3*a^2*c*d^2*f^5*e^2 + 840*(f*x^2*e + 2*d*f*x)^2*a^2*b*d^2*f^6*e + 35*(f*x^2*e + 2*d*f*x)^8*c^3*e^7 + 120*(f*x^2*e + 2*d*f*x)^7*b*c^2*f*e^6 + 140*(f*x^2*e + 2*d*f*x)^6*b^2*c*f^2*e^5 + 140*(f*x^2*e + 2*d*f*x)^6*a*c^2*f^2*e^5 + 56*(f*x^2*e + 2*d*f*x)^5*b^3*f^3*e^4 + 336*(f*x^2*e + 2*d*f*x)^5*a*b*c*f^3*e^4 + 210*(f*x^2*e + 2*d*f*x)^4*a*b^2*f^4*e^3 + 210*(f*x^2*e + 2*d*f*x)^4*a^2*c*f^4*e^3 + 280*(f*x^2*e + 2*d*f*x)^3*a^2*b*f^5*e^2 + 140*(f*x^2*e + 2*d*f*x)^2*a^3*f^6*e)/f^5","B",0
613,1,1194,0,0.431442," ","integrate((e*x+d)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","\frac{{\left(\frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b e^{6} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b d e^{5} + b d^{2} e^{4} + a e^{4}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b e^{6} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b d e^{5} + b d^{2} e^{4} + a e^{4}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b e^{6} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b d e^{5} + b d^{2} e^{4} + a e^{4}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b e^{6} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b d e^{5} + b d^{2} e^{4} + a e^{4}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}}\right)} e^{\left(-4\right)}}{2 \, c} + \frac{x}{c}"," ",0,"1/2*(((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*e^6 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*d*e^5 + b*d^2*e^4 + a*e^4)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*e^6 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*d*e^5 + b*d^2*e^4 + a*e^4)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*e^6 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*d*e^5 + b*d^2*e^4 + a*e^4)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*e^6 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*d*e^5 + b*d^2*e^4 + a*e^4)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))))*e^(-4)/c + x/c","B",0
614,1,130,0,0.404811," ","integrate((e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{2 \, c d^{2} + 2 \, {\left(x^{2} e + 2 \, d x\right)} c e + b}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-1\right)}}{2 \, \sqrt{-b^{2} + 4 \, a c} c} + \frac{e^{\left(-1\right)} \log\left(c d^{4} + 2 \, {\left(x^{2} e + 2 \, d x\right)} c d^{2} e + {\left(x^{2} e + 2 \, d x\right)}^{2} c e^{2} + b d^{2} + {\left(x^{2} e + 2 \, d x\right)} b e + a\right)}{4 \, c}"," ",0,"-1/2*b*arctan((2*c*d^2 + 2*(x^2*e + 2*d*x)*c*e + b)/sqrt(-b^2 + 4*a*c))*e^(-1)/(sqrt(-b^2 + 4*a*c)*c) + 1/4*e^(-1)*log(c*d^4 + 2*(x^2*e + 2*d*x)*c*d^2*e + (x^2*e + 2*d*x)^2*c*e^2 + b*d^2 + (x^2*e + 2*d*x)*b*e + a)/c","A",0
615,1,1285,0,0.454582," ","integrate((e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","-\frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} d e + d^{2}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} + 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} c d^{2} e^{2} - 2 \, c d^{3} e + {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b e^{2} - b d e\right)}} - \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} d e + d^{2}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} + 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} c d^{2} e^{2} - 2 \, c d^{3} e + {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b e^{2} - b d e\right)}} - \frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} d e + d^{2}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} + 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} c d^{2} e^{2} - 2 \, c d^{3} e + {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b e^{2} - b d e\right)}} - \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} d e + d^{2}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} + 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} c d^{2} e^{2} - 2 \, c d^{3} e + {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b e^{2} - b d e\right)}}"," ",0,"-1/2*((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*d*e + d^2)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 + 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*c*d^2*e^2 - 2*c*d^3*e + (d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*e^2 - b*d*e) - 1/2*((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*d*e + d^2)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 + 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*c*d^2*e^2 - 2*c*d^3*e + (d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*e^2 - b*d*e) - 1/2*((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*d*e + d^2)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 + 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*c*d^2*e^2 - 2*c*d^3*e + (d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*e^2 - b*d*e) - 1/2*((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*d*e + d^2)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 + 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*c*d^2*e^2 - 2*c*d^3*e + (d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*e^2 - b*d*e)","B",0
616,1,53,0,0.451993," ","integrate((e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","\frac{\arctan\left(\frac{2 \, c d^{2} + 2 \, {\left(x^{2} e + 2 \, d x\right)} c e + b}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}"," ",0,"arctan((2*c*d^2 + 2*(x^2*e + 2*d*x)*c*e + b)/sqrt(-b^2 + 4*a*c))*e^(-1)/sqrt(-b^2 + 4*a*c)","A",0
617,1,274,0,1.147080," ","integrate(1/(e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","-\frac{e^{\left(-1\right)} \log\left({\left| c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a \right|}\right)}{4 \, a} + \frac{e^{\left(-1\right)} \log\left({\left| x e + d \right|}\right)}{a} - \frac{{\left(\frac{a b c e^{3} \log\left({\left| b x^{2} e^{2} + 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e + b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} + 2 \, a \right|}\right)}{\sqrt{b^{2} - 4 \, a c}} - \frac{a b c e^{3} \log\left({\left| -b x^{2} e^{2} - 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e - b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} - 2 \, a \right|}\right)}{\sqrt{b^{2} - 4 \, a c}}\right)} e^{\left(-4\right)}}{4 \, a^{2} c}"," ",0,"-1/4*e^(-1)*log(abs(c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a))/a + e^(-1)*log(abs(x*e + d))/a - 1/4*(a*b*c*e^3*log(abs(b*x^2*e^2 + 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e + b*d^2 + sqrt(b^2 - 4*a*c)*d^2 + 2*a))/sqrt(b^2 - 4*a*c) - a*b*c*e^3*log(abs(-b*x^2*e^2 - 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e - b*d^2 + sqrt(b^2 - 4*a*c)*d^2 - 2*a))/sqrt(b^2 - 4*a*c))*e^(-4)/(a^2*c)","B",0
618,-2,0,0,0.000000," ","integrate(1/(e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument ValueDone","F(-2)",0
619,1,102,0,0.402419," ","integrate(1/(e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","\frac{b e^{\left(-1\right)} \log\left(c + \frac{b}{{\left(x e + d\right)}^{2}} + \frac{a}{{\left(x e + d\right)}^{4}}\right)}{4 \, a^{2}} + \frac{{\left(b^{2} - 2 \, a c\right)} \arctan\left(-\frac{b + \frac{2 \, a}{{\left(x e + d\right)}^{2}}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-1\right)}}{2 \, \sqrt{-b^{2} + 4 \, a c} a^{2}} - \frac{e^{\left(-1\right)}}{2 \, {\left(x e + d\right)}^{2} a}"," ",0,"1/4*b*e^(-1)*log(c + b/(x*e + d)^2 + a/(x*e + d)^4)/a^2 + 1/2*(b^2 - 2*a*c)*arctan(-(b + 2*a/(x*e + d)^2)/sqrt(-b^2 + 4*a*c))*e^(-1)/(sqrt(-b^2 + 4*a*c)*a^2) - 1/2*e^(-1)/((x*e + d)^2*a)","A",0
620,1,1243,0,0.494787," ","integrate(1/(e*x+d)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","-\frac{\frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d e + b c d^{2} + b^{2} - a c\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d e + b c d^{2} + b^{2} - a c\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d e + b c d^{2} + b^{2} - a c\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d e + b c d^{2} + b^{2} - a c\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}}}{2 \, a^{2}} + \frac{{\left(3 \, b x^{2} e^{2} + 6 \, b d x e + 3 \, b d^{2} - a\right)} e^{\left(-1\right)}}{3 \, {\left(x e + d\right)}^{3} a^{2}}"," ",0,"-1/2*(((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*e + b*c*d^2 + b^2 - a*c)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*e + b*c*d^2 + b^2 - a*c)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*e + b*c*d^2 + b^2 - a*c)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*e + b*c*d^2 + b^2 - a*c)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))))/a^2 + 1/3*(3*b*x^2*e^2 + 6*b*d*x*e + 3*b*d^2 - a)*e^(-1)/((x*e + d)^3*a^2)","B",0
621,1,1304,0,0.523714," ","integrate((e*x+d)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","-\frac{\frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b d e + b d^{2} - 2 \, a\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b d e + b d^{2} - 2 \, a\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b d e + b d^{2} - 2 \, a\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b d e + b d^{2} - 2 \, a\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}}}{4 \, {\left(b^{2} - 4 \, a c\right)}} + \frac{b x^{3} e^{3} + 3 \, b d x^{2} e^{2} + 3 \, b d^{2} x e + b d^{3} + 2 \, a x e + 2 \, a d}{2 \, {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)} {\left(b^{2} e - 4 \, a c e\right)}}"," ",0,"-1/4*(((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*d*e + b*d^2 - 2*a)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*d*e + b*d^2 - 2*a)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*d*e + b*d^2 - 2*a)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*d*e + b*d^2 - 2*a)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))))/(b^2 - 4*a*c) + 1/2*(b*x^3*e^3 + 3*b*d*x^2*e^2 + 3*b*d^2*x*e + b*d^3 + 2*a*x*e + 2*a*d)/((c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)*(b^2*e - 4*a*c*e))","B",0
622,1,171,0,0.565377," ","integrate((e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","\frac{b \arctan\left(\frac{2 \, c d^{2} + 2 \, {\left(x^{2} e + 2 \, d x\right)} c e + b}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-1\right)}}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{b d^{2} + {\left(x^{2} e + 2 \, d x\right)} b e + 2 \, a}{2 \, {\left(c d^{4} + 2 \, {\left(x^{2} e + 2 \, d x\right)} c d^{2} e + {\left(x^{2} e + 2 \, d x\right)}^{2} c e^{2} + b d^{2} + {\left(x^{2} e + 2 \, d x\right)} b e + a\right)} {\left(b^{2} e - 4 \, a c e\right)}}"," ",0,"b*arctan((2*c*d^2 + 2*(x^2*e + 2*d*x)*c*e + b)/sqrt(-b^2 + 4*a*c))*e^(-1)/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) + 1/2*(b*d^2 + (x^2*e + 2*d*x)*b*e + 2*a)/((c*d^4 + 2*(x^2*e + 2*d*x)*c*d^2*e + (x^2*e + 2*d*x)^2*c*e^2 + b*d^2 + (x^2*e + 2*d*x)*b*e + a)*(b^2*e - 4*a*c*e))","A",0
623,1,1312,0,0.528780," ","integrate((e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c e^{2} - 4 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} c d e + 2 \, c d^{2} - b\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c e^{2} - 4 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} c d e + 2 \, c d^{2} - b\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c e^{2} - 4 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} c d e + 2 \, c d^{2} - b\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c e^{2} - 4 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} c d e + 2 \, c d^{2} - b\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}}}{4 \, {\left(b^{2} - 4 \, a c\right)}} - \frac{2 \, c x^{3} e^{3} + 6 \, c d x^{2} e^{2} + 6 \, c d^{2} x e + 2 \, c d^{3} + b x e + b d}{2 \, {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)} {\left(b^{2} e - 4 \, a c e\right)}}"," ",0,"1/4*((2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*e^2 - 4*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*c*d*e + 2*c*d^2 - b)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*e^2 - 4*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*c*d*e + 2*c*d^2 - b)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*e^2 - 4*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*c*d*e + 2*c*d^2 - b)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*e^2 - 4*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*c*d*e + 2*c*d^2 - b)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))))/(b^2 - 4*a*c) - 1/2*(2*c*x^3*e^3 + 6*c*d*x^2*e^2 + 6*c*d^2*x*e + 2*c*d^3 + b*x*e + b*d)/((c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)*(b^2*e - 4*a*c*e))","B",0
624,1,172,0,0.461934," ","integrate((e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","-\frac{2 \, c \arctan\left(\frac{2 \, c d^{2} + 2 \, {\left(x^{2} e + 2 \, d x\right)} c e + b}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-1\right)}}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, c d^{2} + 2 \, {\left(x^{2} e + 2 \, d x\right)} c e + b}{2 \, {\left(c d^{4} + 2 \, {\left(x^{2} e + 2 \, d x\right)} c d^{2} e + {\left(x^{2} e + 2 \, d x\right)}^{2} c e^{2} + b d^{2} + {\left(x^{2} e + 2 \, d x\right)} b e + a\right)} {\left(b^{2} e - 4 \, a c e\right)}}"," ",0,"-2*c*arctan((2*c*d^2 + 2*(x^2*e + 2*d*x)*c*e + b)/sqrt(-b^2 + 4*a*c))*e^(-1)/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - 1/2*(2*c*d^2 + 2*(x^2*e + 2*d*x)*c*e + b)/((c*d^4 + 2*(x^2*e + 2*d*x)*c*d^2*e + (x^2*e + 2*d*x)^2*c*e^2 + b*d^2 + (x^2*e + 2*d*x)*b*e + a)*(b^2*e - 4*a*c*e))","A",0
625,1,1357,0,0.463326," ","integrate(1/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","-\frac{\frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d e + b c d^{2} + b^{2} - 6 \, a c\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d e + b c d^{2} + b^{2} - 6 \, a c\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d e + b c d^{2} + b^{2} - 6 \, a c\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d e + b c d^{2} + b^{2} - 6 \, a c\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}}}{4 \, {\left(a b^{2} - 4 \, a^{2} c\right)}} + \frac{b c x^{3} e^{3} + 3 \, b c d x^{2} e^{2} + 3 \, b c d^{2} x e + b c d^{3} + b^{2} x e - 2 \, a c x e + b^{2} d - 2 \, a c d}{2 \, {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)} {\left(a b^{2} e - 4 \, a^{2} c e\right)}}"," ",0,"-1/4*(((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*e + b*c*d^2 + b^2 - 6*a*c)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*e + b*c*d^2 + b^2 - 6*a*c)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*e + b*c*d^2 + b^2 - 6*a*c)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*e + b*c*d^2 + b^2 - 6*a*c)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))))/(a*b^2 - 4*a^2*c) + 1/2*(b*c*x^3*e^3 + 3*b*c*d*x^2*e^2 + 3*b*c*d^2*x*e + b*c*d^3 + b^2*x*e - 2*a*c*x*e + b^2*d - 2*a*c*d)/((c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)*(a*b^2*e - 4*a^2*c*e))","B",0
626,1,454,0,1.252506," ","integrate(1/(e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","-\frac{{\left(a^{2} b^{3} c e^{3} - 6 \, a^{3} b c^{2} e^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left({\left| b x^{2} e^{2} + 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e + b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} + 2 \, a \right|}\right) - {\left(a^{2} b^{3} c e^{3} - 6 \, a^{3} b c^{2} e^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left({\left| -b x^{2} e^{2} - 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e - b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} - 2 \, a \right|}\right)}{4 \, {\left(a^{4} b^{4} c e^{4} - 8 \, a^{5} b^{2} c^{2} e^{4} + 16 \, a^{6} c^{3} e^{4}\right)}} - \frac{e^{\left(-1\right)} \log\left({\left| c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a \right|}\right)}{4 \, a^{2}} + \frac{e^{\left(-1\right)} \log\left({\left| x e + d \right|}\right)}{a^{2}} + \frac{{\left(a b c x^{2} e^{2} + 2 \, a b c d x e + a b c d^{2} + a b^{2} - 2 \, a^{2} c\right)} e^{\left(-1\right)}}{2 \, {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)} a^{2}}"," ",0,"-1/4*((a^2*b^3*c*e^3 - 6*a^3*b*c^2*e^3)*sqrt(b^2 - 4*a*c)*log(abs(b*x^2*e^2 + 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e + b*d^2 + sqrt(b^2 - 4*a*c)*d^2 + 2*a)) - (a^2*b^3*c*e^3 - 6*a^3*b*c^2*e^3)*sqrt(b^2 - 4*a*c)*log(abs(-b*x^2*e^2 - 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e - b*d^2 + sqrt(b^2 - 4*a*c)*d^2 - 2*a)))/(a^4*b^4*c*e^4 - 8*a^5*b^2*c^2*e^4 + 16*a^6*c^3*e^4) - 1/4*e^(-1)*log(abs(c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a))/a^2 + e^(-1)*log(abs(x*e + d))/a^2 + 1/2*(a*b*c*x^2*e^2 + 2*a*b*c*d*x*e + a*b*c*d^2 + a*b^2 - 2*a^2*c)*e^(-1)/((c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)*(b^2 - 4*a*c)*a^2)","B",0
627,1,847,0,0.786815," ","integrate(1/(e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","\frac{{\left(2 \, {\left(3 \, a^{3} b^{2} c - 10 \, a^{4} c^{2}\right)} \sqrt{2 \, a b + 2 \, \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} {\left| a^{2} b^{2} e^{2} - 4 \, a^{3} c e^{2} \right|} e^{2} - {\left(a^{2} b^{2} e^{2} - 4 \, a^{3} c e^{2}\right)}^{2} {\left(3 \, b^{3} - 13 \, a b c\right)} \sqrt{2 \, a b + 2 \, \sqrt{b^{2} - 4 \, a c} a} + {\left(3 \, a^{4} b^{7} - 31 \, a^{5} b^{5} c + 96 \, a^{6} b^{3} c^{2} - 80 \, a^{7} b c^{3}\right)} \sqrt{2 \, a b + 2 \, \sqrt{b^{2} - 4 \, a c} a} e^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} e^{\left(-1\right)}}{{\left(x e + d\right)} \sqrt{\frac{a^{2} b^{3} e^{2} - 4 \, a^{3} b c e^{2} + \sqrt{{\left(a^{2} b^{3} e^{2} - 4 \, a^{3} b c e^{2}\right)}^{2} - 4 \, {\left(a^{3} b^{2} e^{4} - 4 \, a^{4} c e^{4}\right)} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)}}}{a^{3} b^{2} e^{4} - 4 \, a^{4} c e^{4}}}}\right) e^{\left(-3\right)}}{16 \, {\left(a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} {\left| a^{2} b^{2} e^{2} - 4 \, a^{3} c e^{2} \right|} {\left| a \right|}} + \frac{{\left(2 \, {\left(3 \, a^{3} b^{2} c - 10 \, a^{4} c^{2}\right)} \sqrt{2 \, a b - 2 \, \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} {\left| a^{2} b^{2} e^{2} - 4 \, a^{3} c e^{2} \right|} e^{2} + {\left(a^{2} b^{2} e^{2} - 4 \, a^{3} c e^{2}\right)}^{2} {\left(3 \, b^{3} - 13 \, a b c\right)} \sqrt{2 \, a b - 2 \, \sqrt{b^{2} - 4 \, a c} a} - {\left(3 \, a^{4} b^{7} - 31 \, a^{5} b^{5} c + 96 \, a^{6} b^{3} c^{2} - 80 \, a^{7} b c^{3}\right)} \sqrt{2 \, a b - 2 \, \sqrt{b^{2} - 4 \, a c} a} e^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} e^{\left(-1\right)}}{{\left(x e + d\right)} \sqrt{\frac{a^{2} b^{3} e^{2} - 4 \, a^{3} b c e^{2} - \sqrt{{\left(a^{2} b^{3} e^{2} - 4 \, a^{3} b c e^{2}\right)}^{2} - 4 \, {\left(a^{3} b^{2} e^{4} - 4 \, a^{4} c e^{4}\right)} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)}}}{a^{3} b^{2} e^{4} - 4 \, a^{4} c e^{4}}}}\right) e^{\left(-3\right)}}{16 \, {\left(a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} {\left| a^{2} b^{2} e^{2} - 4 \, a^{3} c e^{2} \right|} {\left| a \right|}} - \frac{\frac{b^{2} c e^{\left(-1\right)}}{x e + d} - \frac{2 \, a c^{2} e^{\left(-1\right)}}{x e + d} + \frac{b^{3} e^{\left(-1\right)}}{{\left(x e + d\right)}^{3}} - \frac{3 \, a b c e^{\left(-1\right)}}{{\left(x e + d\right)}^{3}}}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(c + \frac{b}{{\left(x e + d\right)}^{2}} + \frac{a}{{\left(x e + d\right)}^{4}}\right)}} - \frac{e^{\left(-1\right)}}{{\left(x e + d\right)} a^{2}}"," ",0,"1/16*(2*(3*a^3*b^2*c - 10*a^4*c^2)*sqrt(2*a*b + 2*sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*abs(a^2*b^2*e^2 - 4*a^3*c*e^2)*e^2 - (a^2*b^2*e^2 - 4*a^3*c*e^2)^2*(3*b^3 - 13*a*b*c)*sqrt(2*a*b + 2*sqrt(b^2 - 4*a*c)*a) + (3*a^4*b^7 - 31*a^5*b^5*c + 96*a^6*b^3*c^2 - 80*a^7*b*c^3)*sqrt(2*a*b + 2*sqrt(b^2 - 4*a*c)*a)*e^4)*arctan(2*sqrt(1/2)*e^(-1)/((x*e + d)*sqrt((a^2*b^3*e^2 - 4*a^3*b*c*e^2 + sqrt((a^2*b^3*e^2 - 4*a^3*b*c*e^2)^2 - 4*(a^3*b^2*e^4 - 4*a^4*c*e^4)*(a^2*b^2*c - 4*a^3*c^2)))/(a^3*b^2*e^4 - 4*a^4*c*e^4))))*e^(-3)/((a^5*b^2*c - 4*a^6*c^2)*sqrt(b^2 - 4*a*c)*abs(a^2*b^2*e^2 - 4*a^3*c*e^2)*abs(a)) + 1/16*(2*(3*a^3*b^2*c - 10*a^4*c^2)*sqrt(2*a*b - 2*sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*abs(a^2*b^2*e^2 - 4*a^3*c*e^2)*e^2 + (a^2*b^2*e^2 - 4*a^3*c*e^2)^2*(3*b^3 - 13*a*b*c)*sqrt(2*a*b - 2*sqrt(b^2 - 4*a*c)*a) - (3*a^4*b^7 - 31*a^5*b^5*c + 96*a^6*b^3*c^2 - 80*a^7*b*c^3)*sqrt(2*a*b - 2*sqrt(b^2 - 4*a*c)*a)*e^4)*arctan(2*sqrt(1/2)*e^(-1)/((x*e + d)*sqrt((a^2*b^3*e^2 - 4*a^3*b*c*e^2 - sqrt((a^2*b^3*e^2 - 4*a^3*b*c*e^2)^2 - 4*(a^3*b^2*e^4 - 4*a^4*c*e^4)*(a^2*b^2*c - 4*a^3*c^2)))/(a^3*b^2*e^4 - 4*a^4*c*e^4))))*e^(-3)/((a^5*b^2*c - 4*a^6*c^2)*sqrt(b^2 - 4*a*c)*abs(a^2*b^2*e^2 - 4*a^3*c*e^2)*abs(a)) - 1/2*(b^2*c*e^(-1)/(x*e + d) - 2*a*c^2*e^(-1)/(x*e + d) + b^3*e^(-1)/(x*e + d)^3 - 3*a*b*c*e^(-1)/(x*e + d)^3)/((a^2*b^2 - 4*a^3*c)*(c + b/(x*e + d)^2 + a/(x*e + d)^4)) - e^(-1)/((x*e + d)*a^2)","B",0
628,1,224,0,0.429692," ","integrate(1/(e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","\frac{{\left(b^{4} - 6 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} \arctan\left(-\frac{b + \frac{2 \, a}{{\left(x e + d\right)}^{2}}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-1\right)}}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{b e^{\left(-1\right)} \log\left(c + \frac{b}{{\left(x e + d\right)}^{2}} + \frac{a}{{\left(x e + d\right)}^{4}}\right)}{2 \, a^{3}} + \frac{{\left(\frac{b^{3} c - 3 \, a b c^{2}}{a} + \frac{{\left(b^{4} e - 4 \, a b^{2} c e + 2 \, a^{2} c^{2} e\right)} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2} a}\right)} e^{\left(-1\right)}}{2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} {\left(c + \frac{b}{{\left(x e + d\right)}^{2}} + \frac{a}{{\left(x e + d\right)}^{4}}\right)}} - \frac{e^{\left(-1\right)}}{2 \, {\left(x e + d\right)}^{2} a^{2}}"," ",0,"(b^4 - 6*a*b^2*c + 6*a^2*c^2)*arctan(-(b + 2*a/(x*e + d)^2)/sqrt(-b^2 + 4*a*c))*e^(-1)/((a^3*b^2 - 4*a^4*c)*sqrt(-b^2 + 4*a*c)) + 1/2*b*e^(-1)*log(c + b/(x*e + d)^2 + a/(x*e + d)^4)/a^3 + 1/2*((b^3*c - 3*a*b*c^2)/a + (b^4*e - 4*a*b^2*c*e + 2*a^2*c^2*e)*e^(-1)/((x*e + d)^2*a))*e^(-1)/((b^2 - 4*a*c)*a^2*(c + b/(x*e + d)^2 + a/(x*e + d)^4)) - 1/2*e^(-1)/((x*e + d)^2*a^2)","A",0
629,1,1987,0,0.548095," ","integrate(1/(e*x+d)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(5 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{3} c e^{2} - 19 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a b c^{2} e^{2} - 10 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{3} c d e + 38 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a b c^{2} d e + 5 \, b^{3} c d^{2} - 19 \, a b c^{2} d^{2} + 5 \, b^{4} - 24 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(5 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{3} c e^{2} - 19 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a b c^{2} e^{2} - 10 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{3} c d e + 38 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a b c^{2} d e + 5 \, b^{3} c d^{2} - 19 \, a b c^{2} d^{2} + 5 \, b^{4} - 24 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(5 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{3} c e^{2} - 19 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a b c^{2} e^{2} - 10 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{3} c d e + 38 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a b c^{2} d e + 5 \, b^{3} c d^{2} - 19 \, a b c^{2} d^{2} + 5 \, b^{4} - 24 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(5 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{3} c e^{2} - 19 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a b c^{2} e^{2} - 10 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{3} c d e + 38 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a b c^{2} d e + 5 \, b^{3} c d^{2} - 19 \, a b c^{2} d^{2} + 5 \, b^{4} - 24 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}}}{4 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}} + \frac{b^{3} c x^{3} e^{3} - 3 \, a b c^{2} x^{3} e^{3} + 3 \, b^{3} c d x^{2} e^{2} - 9 \, a b c^{2} d x^{2} e^{2} + 3 \, b^{3} c d^{2} x e - 9 \, a b c^{2} d^{2} x e + b^{3} c d^{3} - 3 \, a b c^{2} d^{3} + b^{4} x e - 4 \, a b^{2} c x e + 2 \, a^{2} c^{2} x e + b^{4} d - 4 \, a b^{2} c d + 2 \, a^{2} c^{2} d}{2 \, {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)} {\left(a^{3} b^{2} e - 4 \, a^{4} c e\right)}} + \frac{{\left(6 \, b x^{2} e^{2} + 12 \, b d x e + 6 \, b d^{2} - a\right)} e^{\left(-1\right)}}{3 \, {\left(x e + d\right)}^{3} a^{3}}"," ",0,"-1/4*((5*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^3*c*e^2 - 19*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*b*c^2*e^2 - 10*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^3*c*d*e + 38*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*b*c^2*d*e + 5*b^3*c*d^2 - 19*a*b*c^2*d^2 + 5*b^4 - 24*a*b^2*c + 14*a^2*c^2)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (5*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^3*c*e^2 - 19*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*b*c^2*e^2 - 10*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^3*c*d*e + 38*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*b*c^2*d*e + 5*b^3*c*d^2 - 19*a*b*c^2*d^2 + 5*b^4 - 24*a*b^2*c + 14*a^2*c^2)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (5*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^3*c*e^2 - 19*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*b*c^2*e^2 - 10*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^3*c*d*e + 38*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*b*c^2*d*e + 5*b^3*c*d^2 - 19*a*b*c^2*d^2 + 5*b^4 - 24*a*b^2*c + 14*a^2*c^2)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (5*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^3*c*e^2 - 19*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*b*c^2*e^2 - 10*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^3*c*d*e + 38*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*b*c^2*d*e + 5*b^3*c*d^2 - 19*a*b*c^2*d^2 + 5*b^4 - 24*a*b^2*c + 14*a^2*c^2)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))))/(a^3*b^2 - 4*a^4*c) + 1/2*(b^3*c*x^3*e^3 - 3*a*b*c^2*x^3*e^3 + 3*b^3*c*d*x^2*e^2 - 9*a*b*c^2*d*x^2*e^2 + 3*b^3*c*d^2*x*e - 9*a*b*c^2*d^2*x*e + b^3*c*d^3 - 3*a*b*c^2*d^3 + b^4*x*e - 4*a*b^2*c*x*e + 2*a^2*c^2*x*e + b^4*d - 4*a*b^2*c*d + 2*a^2*c^2*d)/((c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)*(a^3*b^2*e - 4*a^4*c*e)) + 1/3*(6*b*x^2*e^2 + 12*b*d*x*e + 6*b*d^2 - a)*e^(-1)/((x*e + d)^3*a^3)","B",0
630,1,1688,0,0.746374," ","integrate((e*x+d)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","\frac{3 \, {\left(\frac{{\left(4 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c e^{2} - 8 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d e + 4 \, b c d^{2} - b^{2} - 4 \, a c\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(4 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c e^{2} - 8 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d e + 4 \, b c d^{2} - b^{2} - 4 \, a c\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(4 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c e^{2} - 8 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d e + 4 \, b c d^{2} - b^{2} - 4 \, a c\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(4 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c e^{2} - 8 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d e + 4 \, b c d^{2} - b^{2} - 4 \, a c\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}}\right)}}{16 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}} - \frac{12 \, b c^{2} x^{7} e^{7} + 84 \, b c^{2} d x^{6} e^{6} + 252 \, b c^{2} d^{2} x^{5} e^{5} + 420 \, b c^{2} d^{3} x^{4} e^{4} + 420 \, b c^{2} d^{4} x^{3} e^{3} + 252 \, b c^{2} d^{5} x^{2} e^{2} + 84 \, b c^{2} d^{6} x e + 12 \, b c^{2} d^{7} + 19 \, b^{2} c x^{5} e^{5} - 4 \, a c^{2} x^{5} e^{5} + 95 \, b^{2} c d x^{4} e^{4} - 20 \, a c^{2} d x^{4} e^{4} + 190 \, b^{2} c d^{2} x^{3} e^{3} - 40 \, a c^{2} d^{2} x^{3} e^{3} + 190 \, b^{2} c d^{3} x^{2} e^{2} - 40 \, a c^{2} d^{3} x^{2} e^{2} + 95 \, b^{2} c d^{4} x e - 20 \, a c^{2} d^{4} x e + 19 \, b^{2} c d^{5} - 4 \, a c^{2} d^{5} + 5 \, b^{3} x^{3} e^{3} + 16 \, a b c x^{3} e^{3} + 15 \, b^{3} d x^{2} e^{2} + 48 \, a b c d x^{2} e^{2} + 15 \, b^{3} d^{2} x e + 48 \, a b c d^{2} x e + 5 \, b^{3} d^{3} + 16 \, a b c d^{3} + 3 \, a b^{2} x e + 12 \, a^{2} c x e + 3 \, a b^{2} d + 12 \, a^{2} c d}{8 \, {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)}^{2} {\left(b^{4} e - 8 \, a b^{2} c e + 16 \, a^{2} c^{2} e\right)}}"," ",0,"3/16*((4*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*e^2 - 8*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*e + 4*b*c*d^2 - b^2 - 4*a*c)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (4*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*e^2 - 8*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*e + 4*b*c*d^2 - b^2 - 4*a*c)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (4*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*e^2 - 8*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*e + 4*b*c*d^2 - b^2 - 4*a*c)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (4*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*e^2 - 8*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*e + 4*b*c*d^2 - b^2 - 4*a*c)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))))/(b^4 - 8*a*b^2*c + 16*a^2*c^2) - 1/8*(12*b*c^2*x^7*e^7 + 84*b*c^2*d*x^6*e^6 + 252*b*c^2*d^2*x^5*e^5 + 420*b*c^2*d^3*x^4*e^4 + 420*b*c^2*d^4*x^3*e^3 + 252*b*c^2*d^5*x^2*e^2 + 84*b*c^2*d^6*x*e + 12*b*c^2*d^7 + 19*b^2*c*x^5*e^5 - 4*a*c^2*x^5*e^5 + 95*b^2*c*d*x^4*e^4 - 20*a*c^2*d*x^4*e^4 + 190*b^2*c*d^2*x^3*e^3 - 40*a*c^2*d^2*x^3*e^3 + 190*b^2*c*d^3*x^2*e^2 - 40*a*c^2*d^3*x^2*e^2 + 95*b^2*c*d^4*x*e - 20*a*c^2*d^4*x*e + 19*b^2*c*d^5 - 4*a*c^2*d^5 + 5*b^3*x^3*e^3 + 16*a*b*c*x^3*e^3 + 15*b^3*d*x^2*e^2 + 48*a*b*c*d*x^2*e^2 + 15*b^3*d^2*x*e + 48*a*b*c*d^2*x*e + 5*b^3*d^3 + 16*a*b*c*d^3 + 3*a*b^2*x*e + 12*a^2*c*x*e + 3*a*b^2*d + 12*a^2*c*d)/((c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)^2*(b^4*e - 8*a*b^2*c*e + 16*a^2*c^2*e))","B",0
631,1,365,0,0.692688," ","integrate((e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","-\frac{3 \, b c \arctan\left(\frac{2 \, c d^{2} + 2 \, {\left(x^{2} e + 2 \, d x\right)} c e + b}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-1\right)}}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{6 \, b c^{2} d^{6} + 18 \, {\left(x^{2} e + 2 \, d x\right)} b c^{2} d^{4} e + 18 \, {\left(x^{2} e + 2 \, d x\right)}^{2} b c^{2} d^{2} e^{2} + 9 \, b^{2} c d^{4} + 6 \, {\left(x^{2} e + 2 \, d x\right)}^{3} b c^{2} e^{3} + 18 \, {\left(x^{2} e + 2 \, d x\right)} b^{2} c d^{2} e + 9 \, {\left(x^{2} e + 2 \, d x\right)}^{2} b^{2} c e^{2} + 2 \, b^{3} d^{2} + 10 \, a b c d^{2} + 2 \, {\left(x^{2} e + 2 \, d x\right)} b^{3} e + 10 \, {\left(x^{2} e + 2 \, d x\right)} a b c e + a b^{2} + 8 \, a^{2} c}{4 \, {\left(c d^{4} + 2 \, {\left(x^{2} e + 2 \, d x\right)} c d^{2} e + {\left(x^{2} e + 2 \, d x\right)}^{2} c e^{2} + b d^{2} + {\left(x^{2} e + 2 \, d x\right)} b e + a\right)}^{2} {\left(b^{4} e - 8 \, a b^{2} c e + 16 \, a^{2} c^{2} e\right)}}"," ",0,"-3*b*c*arctan((2*c*d^2 + 2*(x^2*e + 2*d*x)*c*e + b)/sqrt(-b^2 + 4*a*c))*e^(-1)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) - 1/4*(6*b*c^2*d^6 + 18*(x^2*e + 2*d*x)*b*c^2*d^4*e + 18*(x^2*e + 2*d*x)^2*b*c^2*d^2*e^2 + 9*b^2*c*d^4 + 6*(x^2*e + 2*d*x)^3*b*c^2*e^3 + 18*(x^2*e + 2*d*x)*b^2*c*d^2*e + 9*(x^2*e + 2*d*x)^2*b^2*c*e^2 + 2*b^3*d^2 + 10*a*b*c*d^2 + 2*(x^2*e + 2*d*x)*b^3*e + 10*(x^2*e + 2*d*x)*a*b*c*e + a*b^2 + 8*a^2*c)/((c*d^4 + 2*(x^2*e + 2*d*x)*c*d^2*e + (x^2*e + 2*d*x)^2*c*e^2 + b*d^2 + (x^2*e + 2*d*x)*b*e + a)^2*(b^4*e - 8*a*b^2*c*e + 16*a^2*c^2*e))","B",0
632,1,2295,0,0.865505," ","integrate((e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","-\frac{\frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{2} c e^{2} + 20 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a c^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{2} c d e - 40 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a c^{2} d e + b^{2} c d^{2} + 20 \, a c^{2} d^{2} + b^{3} - 16 \, a b c\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{2} c e^{2} + 20 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a c^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{2} c d e - 40 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a c^{2} d e + b^{2} c d^{2} + 20 \, a c^{2} d^{2} + b^{3} - 16 \, a b c\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{2} c e^{2} + 20 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a c^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{2} c d e - 40 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a c^{2} d e + b^{2} c d^{2} + 20 \, a c^{2} d^{2} + b^{3} - 16 \, a b c\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{2} c e^{2} + 20 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a c^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{2} c d e - 40 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a c^{2} d e + b^{2} c d^{2} + 20 \, a c^{2} d^{2} + b^{3} - 16 \, a b c\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}}}{16 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)}} + \frac{b^{2} c^{2} x^{7} e^{7} + 20 \, a c^{3} x^{7} e^{7} + 7 \, b^{2} c^{2} d x^{6} e^{6} + 140 \, a c^{3} d x^{6} e^{6} + 21 \, b^{2} c^{2} d^{2} x^{5} e^{5} + 420 \, a c^{3} d^{2} x^{5} e^{5} + 35 \, b^{2} c^{2} d^{3} x^{4} e^{4} + 700 \, a c^{3} d^{3} x^{4} e^{4} + 35 \, b^{2} c^{2} d^{4} x^{3} e^{3} + 700 \, a c^{3} d^{4} x^{3} e^{3} + 21 \, b^{2} c^{2} d^{5} x^{2} e^{2} + 420 \, a c^{3} d^{5} x^{2} e^{2} + 7 \, b^{2} c^{2} d^{6} x e + 140 \, a c^{3} d^{6} x e + b^{2} c^{2} d^{7} + 20 \, a c^{3} d^{7} + 2 \, b^{3} c x^{5} e^{5} + 28 \, a b c^{2} x^{5} e^{5} + 10 \, b^{3} c d x^{4} e^{4} + 140 \, a b c^{2} d x^{4} e^{4} + 20 \, b^{3} c d^{2} x^{3} e^{3} + 280 \, a b c^{2} d^{2} x^{3} e^{3} + 20 \, b^{3} c d^{3} x^{2} e^{2} + 280 \, a b c^{2} d^{3} x^{2} e^{2} + 10 \, b^{3} c d^{4} x e + 140 \, a b c^{2} d^{4} x e + 2 \, b^{3} c d^{5} + 28 \, a b c^{2} d^{5} + b^{4} x^{3} e^{3} + 5 \, a b^{2} c x^{3} e^{3} + 36 \, a^{2} c^{2} x^{3} e^{3} + 3 \, b^{4} d x^{2} e^{2} + 15 \, a b^{2} c d x^{2} e^{2} + 108 \, a^{2} c^{2} d x^{2} e^{2} + 3 \, b^{4} d^{2} x e + 15 \, a b^{2} c d^{2} x e + 108 \, a^{2} c^{2} d^{2} x e + b^{4} d^{3} + 5 \, a b^{2} c d^{3} + 36 \, a^{2} c^{2} d^{3} - a b^{3} x e + 16 \, a^{2} b c x e - a b^{3} d + 16 \, a^{2} b c d}{8 \, {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)}^{2} {\left(a b^{4} e - 8 \, a^{2} b^{2} c e + 16 \, a^{3} c^{2} e\right)}}"," ",0,"-1/16*(((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^2*c*e^2 + 20*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*c^2*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^2*c*d*e - 40*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*c^2*d*e + b^2*c*d^2 + 20*a*c^2*d^2 + b^3 - 16*a*b*c)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^2*c*e^2 + 20*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*c^2*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^2*c*d*e - 40*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*c^2*d*e + b^2*c*d^2 + 20*a*c^2*d^2 + b^3 - 16*a*b*c)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^2*c*e^2 + 20*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*c^2*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^2*c*d*e - 40*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*c^2*d*e + b^2*c*d^2 + 20*a*c^2*d^2 + b^3 - 16*a*b*c)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^2*c*e^2 + 20*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*c^2*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^2*c*d*e - 40*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*c^2*d*e + b^2*c*d^2 + 20*a*c^2*d^2 + b^3 - 16*a*b*c)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2) + 1/8*(b^2*c^2*x^7*e^7 + 20*a*c^3*x^7*e^7 + 7*b^2*c^2*d*x^6*e^6 + 140*a*c^3*d*x^6*e^6 + 21*b^2*c^2*d^2*x^5*e^5 + 420*a*c^3*d^2*x^5*e^5 + 35*b^2*c^2*d^3*x^4*e^4 + 700*a*c^3*d^3*x^4*e^4 + 35*b^2*c^2*d^4*x^3*e^3 + 700*a*c^3*d^4*x^3*e^3 + 21*b^2*c^2*d^5*x^2*e^2 + 420*a*c^3*d^5*x^2*e^2 + 7*b^2*c^2*d^6*x*e + 140*a*c^3*d^6*x*e + b^2*c^2*d^7 + 20*a*c^3*d^7 + 2*b^3*c*x^5*e^5 + 28*a*b*c^2*x^5*e^5 + 10*b^3*c*d*x^4*e^4 + 140*a*b*c^2*d*x^4*e^4 + 20*b^3*c*d^2*x^3*e^3 + 280*a*b*c^2*d^2*x^3*e^3 + 20*b^3*c*d^3*x^2*e^2 + 280*a*b*c^2*d^3*x^2*e^2 + 10*b^3*c*d^4*x*e + 140*a*b*c^2*d^4*x*e + 2*b^3*c*d^5 + 28*a*b*c^2*d^5 + b^4*x^3*e^3 + 5*a*b^2*c*x^3*e^3 + 36*a^2*c^2*x^3*e^3 + 3*b^4*d*x^2*e^2 + 15*a*b^2*c*d*x^2*e^2 + 108*a^2*c^2*d*x^2*e^2 + 3*b^4*d^2*x*e + 15*a*b^2*c*d^2*x*e + 108*a^2*c^2*d^2*x*e + b^4*d^3 + 5*a*b^2*c*d^3 + 36*a^2*c^2*d^3 - a*b^3*x*e + 16*a^2*b*c*x*e - a*b^3*d + 16*a^2*b*c*d)/((c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)^2*(a*b^4*e - 8*a^2*b^2*c*e + 16*a^3*c^2*e))","B",0
633,1,365,0,0.632921," ","integrate((e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","\frac{6 \, c^{2} \arctan\left(\frac{2 \, c d^{2} + 2 \, {\left(x^{2} e + 2 \, d x\right)} c e + b}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-1\right)}}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{12 \, c^{3} d^{6} + 36 \, {\left(x^{2} e + 2 \, d x\right)} c^{3} d^{4} e + 36 \, {\left(x^{2} e + 2 \, d x\right)}^{2} c^{3} d^{2} e^{2} + 18 \, b c^{2} d^{4} + 12 \, {\left(x^{2} e + 2 \, d x\right)}^{3} c^{3} e^{3} + 36 \, {\left(x^{2} e + 2 \, d x\right)} b c^{2} d^{2} e + 18 \, {\left(x^{2} e + 2 \, d x\right)}^{2} b c^{2} e^{2} + 4 \, b^{2} c d^{2} + 20 \, a c^{2} d^{2} + 4 \, {\left(x^{2} e + 2 \, d x\right)} b^{2} c e + 20 \, {\left(x^{2} e + 2 \, d x\right)} a c^{2} e - b^{3} + 10 \, a b c}{4 \, {\left(c d^{4} + 2 \, {\left(x^{2} e + 2 \, d x\right)} c d^{2} e + {\left(x^{2} e + 2 \, d x\right)}^{2} c e^{2} + b d^{2} + {\left(x^{2} e + 2 \, d x\right)} b e + a\right)}^{2} {\left(b^{4} e - 8 \, a b^{2} c e + 16 \, a^{2} c^{2} e\right)}}"," ",0,"6*c^2*arctan((2*c*d^2 + 2*(x^2*e + 2*d*x)*c*e + b)/sqrt(-b^2 + 4*a*c))*e^(-1)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/4*(12*c^3*d^6 + 36*(x^2*e + 2*d*x)*c^3*d^4*e + 36*(x^2*e + 2*d*x)^2*c^3*d^2*e^2 + 18*b*c^2*d^4 + 12*(x^2*e + 2*d*x)^3*c^3*e^3 + 36*(x^2*e + 2*d*x)*b*c^2*d^2*e + 18*(x^2*e + 2*d*x)^2*b*c^2*e^2 + 4*b^2*c*d^2 + 20*a*c^2*d^2 + 4*(x^2*e + 2*d*x)*b^2*c*e + 20*(x^2*e + 2*d*x)*a*c^2*e - b^3 + 10*a*b*c)/((c*d^4 + 2*(x^2*e + 2*d*x)*c*d^2*e + (x^2*e + 2*d*x)^2*c*e^2 + b*d^2 + (x^2*e + 2*d*x)*b*e + a)^2*(b^4*e - 8*a*b^2*c*e + 16*a^2*c^2*e))","B",0
634,1,2487,0,0.563383," ","integrate(1/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(\frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{3} c e^{2} - 8 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a b c^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{3} c d e + 16 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a b c^{2} d e + b^{3} c d^{2} - 8 \, a b c^{2} d^{2} + b^{4} - 9 \, a b^{2} c + 28 \, a^{2} c^{2}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{3} c e^{2} - 8 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a b c^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{3} c d e + 16 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a b c^{2} d e + b^{3} c d^{2} - 8 \, a b c^{2} d^{2} + b^{4} - 9 \, a b^{2} c + 28 \, a^{2} c^{2}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{3} c e^{2} - 8 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a b c^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{3} c d e + 16 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a b c^{2} d e + b^{3} c d^{2} - 8 \, a b c^{2} d^{2} + b^{4} - 9 \, a b^{2} c + 28 \, a^{2} c^{2}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{3} c e^{2} - 8 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a b c^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{3} c d e + 16 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a b c^{2} d e + b^{3} c d^{2} - 8 \, a b c^{2} d^{2} + b^{4} - 9 \, a b^{2} c + 28 \, a^{2} c^{2}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}}\right)}}{16 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)}} + \frac{3 \, b^{3} c^{2} x^{7} e^{7} - 24 \, a b c^{3} x^{7} e^{7} + 21 \, b^{3} c^{2} d x^{6} e^{6} - 168 \, a b c^{3} d x^{6} e^{6} + 63 \, b^{3} c^{2} d^{2} x^{5} e^{5} - 504 \, a b c^{3} d^{2} x^{5} e^{5} + 105 \, b^{3} c^{2} d^{3} x^{4} e^{4} - 840 \, a b c^{3} d^{3} x^{4} e^{4} + 105 \, b^{3} c^{2} d^{4} x^{3} e^{3} - 840 \, a b c^{3} d^{4} x^{3} e^{3} + 63 \, b^{3} c^{2} d^{5} x^{2} e^{2} - 504 \, a b c^{3} d^{5} x^{2} e^{2} + 21 \, b^{3} c^{2} d^{6} x e - 168 \, a b c^{3} d^{6} x e + 3 \, b^{3} c^{2} d^{7} - 24 \, a b c^{3} d^{7} + 6 \, b^{4} c x^{5} e^{5} - 49 \, a b^{2} c^{2} x^{5} e^{5} + 28 \, a^{2} c^{3} x^{5} e^{5} + 30 \, b^{4} c d x^{4} e^{4} - 245 \, a b^{2} c^{2} d x^{4} e^{4} + 140 \, a^{2} c^{3} d x^{4} e^{4} + 60 \, b^{4} c d^{2} x^{3} e^{3} - 490 \, a b^{2} c^{2} d^{2} x^{3} e^{3} + 280 \, a^{2} c^{3} d^{2} x^{3} e^{3} + 60 \, b^{4} c d^{3} x^{2} e^{2} - 490 \, a b^{2} c^{2} d^{3} x^{2} e^{2} + 280 \, a^{2} c^{3} d^{3} x^{2} e^{2} + 30 \, b^{4} c d^{4} x e - 245 \, a b^{2} c^{2} d^{4} x e + 140 \, a^{2} c^{3} d^{4} x e + 6 \, b^{4} c d^{5} - 49 \, a b^{2} c^{2} d^{5} + 28 \, a^{2} c^{3} d^{5} + 3 \, b^{5} x^{3} e^{3} - 20 \, a b^{3} c x^{3} e^{3} - 4 \, a^{2} b c^{2} x^{3} e^{3} + 9 \, b^{5} d x^{2} e^{2} - 60 \, a b^{3} c d x^{2} e^{2} - 12 \, a^{2} b c^{2} d x^{2} e^{2} + 9 \, b^{5} d^{2} x e - 60 \, a b^{3} c d^{2} x e - 12 \, a^{2} b c^{2} d^{2} x e + 3 \, b^{5} d^{3} - 20 \, a b^{3} c d^{3} - 4 \, a^{2} b c^{2} d^{3} + 5 \, a b^{4} x e - 37 \, a^{2} b^{2} c x e + 44 \, a^{3} c^{2} x e + 5 \, a b^{4} d - 37 \, a^{2} b^{2} c d + 44 \, a^{3} c^{2} d}{8 \, {\left(a^{2} b^{4} e - 8 \, a^{3} b^{2} c e + 16 \, a^{4} c^{2} e\right)} {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)}^{2}}"," ",0,"-3/16*(((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^3*c*e^2 - 8*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*b*c^2*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^3*c*d*e + 16*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*b*c^2*d*e + b^3*c*d^2 - 8*a*b*c^2*d^2 + b^4 - 9*a*b^2*c + 28*a^2*c^2)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^3*c*e^2 - 8*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*b*c^2*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^3*c*d*e + 16*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*b*c^2*d*e + b^3*c*d^2 - 8*a*b*c^2*d^2 + b^4 - 9*a*b^2*c + 28*a^2*c^2)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^3*c*e^2 - 8*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*b*c^2*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^3*c*d*e + 16*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*b*c^2*d*e + b^3*c*d^2 - 8*a*b*c^2*d^2 + b^4 - 9*a*b^2*c + 28*a^2*c^2)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^3*c*e^2 - 8*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*b*c^2*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^3*c*d*e + 16*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*b*c^2*d*e + b^3*c*d^2 - 8*a*b*c^2*d^2 + b^4 - 9*a*b^2*c + 28*a^2*c^2)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))))/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2) + 1/8*(3*b^3*c^2*x^7*e^7 - 24*a*b*c^3*x^7*e^7 + 21*b^3*c^2*d*x^6*e^6 - 168*a*b*c^3*d*x^6*e^6 + 63*b^3*c^2*d^2*x^5*e^5 - 504*a*b*c^3*d^2*x^5*e^5 + 105*b^3*c^2*d^3*x^4*e^4 - 840*a*b*c^3*d^3*x^4*e^4 + 105*b^3*c^2*d^4*x^3*e^3 - 840*a*b*c^3*d^4*x^3*e^3 + 63*b^3*c^2*d^5*x^2*e^2 - 504*a*b*c^3*d^5*x^2*e^2 + 21*b^3*c^2*d^6*x*e - 168*a*b*c^3*d^6*x*e + 3*b^3*c^2*d^7 - 24*a*b*c^3*d^7 + 6*b^4*c*x^5*e^5 - 49*a*b^2*c^2*x^5*e^5 + 28*a^2*c^3*x^5*e^5 + 30*b^4*c*d*x^4*e^4 - 245*a*b^2*c^2*d*x^4*e^4 + 140*a^2*c^3*d*x^4*e^4 + 60*b^4*c*d^2*x^3*e^3 - 490*a*b^2*c^2*d^2*x^3*e^3 + 280*a^2*c^3*d^2*x^3*e^3 + 60*b^4*c*d^3*x^2*e^2 - 490*a*b^2*c^2*d^3*x^2*e^2 + 280*a^2*c^3*d^3*x^2*e^2 + 30*b^4*c*d^4*x*e - 245*a*b^2*c^2*d^4*x*e + 140*a^2*c^3*d^4*x*e + 6*b^4*c*d^5 - 49*a*b^2*c^2*d^5 + 28*a^2*c^3*d^5 + 3*b^5*x^3*e^3 - 20*a*b^3*c*x^3*e^3 - 4*a^2*b*c^2*x^3*e^3 + 9*b^5*d*x^2*e^2 - 60*a*b^3*c*d*x^2*e^2 - 12*a^2*b*c^2*d*x^2*e^2 + 9*b^5*d^2*x*e - 60*a*b^3*c*d^2*x*e - 12*a^2*b*c^2*d^2*x*e + 3*b^5*d^3 - 20*a*b^3*c*d^3 - 4*a^2*b*c^2*d^3 + 5*a*b^4*x*e - 37*a^2*b^2*c*x*e + 44*a^3*c^2*x*e + 5*a*b^4*d - 37*a^2*b^2*c*d + 44*a^3*c^2*d)/((a^2*b^4*e - 8*a^3*b^2*c*e + 16*a^4*c^2*e)*(c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)^2)","B",0
635,1,1012,0,1.716350," ","integrate(1/(e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","-\frac{{\left(a^{3} b^{7} c e^{3} - 14 \, a^{4} b^{5} c^{2} e^{3} + 70 \, a^{5} b^{3} c^{3} e^{3} - 120 \, a^{6} b c^{4} e^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left({\left| b x^{2} e^{2} + 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e + b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} + 2 \, a \right|}\right) - {\left(a^{3} b^{7} c e^{3} - 14 \, a^{4} b^{5} c^{2} e^{3} + 70 \, a^{5} b^{3} c^{3} e^{3} - 120 \, a^{6} b c^{4} e^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left({\left| -b x^{2} e^{2} - 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e - b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} - 2 \, a \right|}\right)}{4 \, {\left(a^{6} b^{8} c e^{4} - 16 \, a^{7} b^{6} c^{2} e^{4} + 96 \, a^{8} b^{4} c^{3} e^{4} - 256 \, a^{9} b^{2} c^{4} e^{4} + 256 \, a^{10} c^{5} e^{4}\right)}} - \frac{e^{\left(-1\right)} \log\left({\left| c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a \right|}\right)}{4 \, a^{3}} + \frac{e^{\left(-1\right)} \log\left({\left| x e + d \right|}\right)}{a^{3}} + \frac{{\left(2 \, a b^{3} c^{2} d^{6} - 14 \, a^{2} b c^{3} d^{6} + 4 \, a b^{4} c d^{4} - 29 \, a^{2} b^{2} c^{2} d^{4} + 16 \, a^{3} c^{3} d^{4} + 2 \, a b^{5} d^{2} - 12 \, a^{2} b^{3} c d^{2} - 2 \, a^{3} b c^{2} d^{2} + 2 \, {\left(a b^{3} c^{2} e^{6} - 7 \, a^{2} b c^{3} e^{6}\right)} x^{6} + 3 \, a^{2} b^{4} - 21 \, a^{3} b^{2} c + 24 \, a^{4} c^{2} + 12 \, {\left(a b^{3} c^{2} d e^{5} - 7 \, a^{2} b c^{3} d e^{5}\right)} x^{5} + {\left(30 \, a b^{3} c^{2} d^{2} e^{4} - 210 \, a^{2} b c^{3} d^{2} e^{4} + 4 \, a b^{4} c e^{4} - 29 \, a^{2} b^{2} c^{2} e^{4} + 16 \, a^{3} c^{3} e^{4}\right)} x^{4} + 4 \, {\left(10 \, a b^{3} c^{2} d^{3} e^{3} - 70 \, a^{2} b c^{3} d^{3} e^{3} + 4 \, a b^{4} c d e^{3} - 29 \, a^{2} b^{2} c^{2} d e^{3} + 16 \, a^{3} c^{3} d e^{3}\right)} x^{3} + 2 \, {\left(15 \, a b^{3} c^{2} d^{4} e^{2} - 105 \, a^{2} b c^{3} d^{4} e^{2} + 12 \, a b^{4} c d^{2} e^{2} - 87 \, a^{2} b^{2} c^{2} d^{2} e^{2} + 48 \, a^{3} c^{3} d^{2} e^{2} + a b^{5} e^{2} - 6 \, a^{2} b^{3} c e^{2} - a^{3} b c^{2} e^{2}\right)} x^{2} + 4 \, {\left(3 \, a b^{3} c^{2} d^{5} e - 21 \, a^{2} b c^{3} d^{5} e + 4 \, a b^{4} c d^{3} e - 29 \, a^{2} b^{2} c^{2} d^{3} e + 16 \, a^{3} c^{3} d^{3} e + a b^{5} d e - 6 \, a^{2} b^{3} c d e - a^{3} b c^{2} d e\right)} x\right)} e^{\left(-1\right)}}{4 \, {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}^{2} a^{3}}"," ",0,"-1/4*((a^3*b^7*c*e^3 - 14*a^4*b^5*c^2*e^3 + 70*a^5*b^3*c^3*e^3 - 120*a^6*b*c^4*e^3)*sqrt(b^2 - 4*a*c)*log(abs(b*x^2*e^2 + 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e + b*d^2 + sqrt(b^2 - 4*a*c)*d^2 + 2*a)) - (a^3*b^7*c*e^3 - 14*a^4*b^5*c^2*e^3 + 70*a^5*b^3*c^3*e^3 - 120*a^6*b*c^4*e^3)*sqrt(b^2 - 4*a*c)*log(abs(-b*x^2*e^2 - 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e - b*d^2 + sqrt(b^2 - 4*a*c)*d^2 - 2*a)))/(a^6*b^8*c*e^4 - 16*a^7*b^6*c^2*e^4 + 96*a^8*b^4*c^3*e^4 - 256*a^9*b^2*c^4*e^4 + 256*a^10*c^5*e^4) - 1/4*e^(-1)*log(abs(c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a))/a^3 + e^(-1)*log(abs(x*e + d))/a^3 + 1/4*(2*a*b^3*c^2*d^6 - 14*a^2*b*c^3*d^6 + 4*a*b^4*c*d^4 - 29*a^2*b^2*c^2*d^4 + 16*a^3*c^3*d^4 + 2*a*b^5*d^2 - 12*a^2*b^3*c*d^2 - 2*a^3*b*c^2*d^2 + 2*(a*b^3*c^2*e^6 - 7*a^2*b*c^3*e^6)*x^6 + 3*a^2*b^4 - 21*a^3*b^2*c + 24*a^4*c^2 + 12*(a*b^3*c^2*d*e^5 - 7*a^2*b*c^3*d*e^5)*x^5 + (30*a*b^3*c^2*d^2*e^4 - 210*a^2*b*c^3*d^2*e^4 + 4*a*b^4*c*e^4 - 29*a^2*b^2*c^2*e^4 + 16*a^3*c^3*e^4)*x^4 + 4*(10*a*b^3*c^2*d^3*e^3 - 70*a^2*b*c^3*d^3*e^3 + 4*a*b^4*c*d*e^3 - 29*a^2*b^2*c^2*d*e^3 + 16*a^3*c^3*d*e^3)*x^3 + 2*(15*a*b^3*c^2*d^4*e^2 - 105*a^2*b*c^3*d^4*e^2 + 12*a*b^4*c*d^2*e^2 - 87*a^2*b^2*c^2*d^2*e^2 + 48*a^3*c^3*d^2*e^2 + a*b^5*e^2 - 6*a^2*b^3*c*e^2 - a^3*b*c^2*e^2)*x^2 + 4*(3*a*b^3*c^2*d^5*e - 21*a^2*b*c^3*d^5*e + 4*a*b^4*c*d^3*e - 29*a^2*b^2*c^2*d^3*e + 16*a^3*c^3*d^3*e + a*b^5*d*e - 6*a^2*b^3*c*d*e - a^3*b*c^2*d*e)*x)*e^(-1)/((c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)^2*(b^2 - 4*a*c)^2*a^3)","B",0
636,1,1412,0,1.220400," ","integrate(1/(e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, {\left(5 \, a^{4} b^{6} c - 57 \, a^{5} b^{4} c^{2} + 208 \, a^{6} b^{2} c^{3} - 240 \, a^{7} c^{4}\right)} \sqrt{2 \, a b + 2 \, \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} {\left| a^{3} b^{4} e^{2} - 8 \, a^{4} b^{2} c e^{2} + 16 \, a^{5} c^{2} e^{2} \right|} e^{2} - {\left(a^{3} b^{4} e^{2} - 8 \, a^{4} b^{2} c e^{2} + 16 \, a^{5} c^{2} e^{2}\right)}^{2} {\left(5 \, b^{5} - 42 \, a b^{3} c + 92 \, a^{2} b c^{2}\right)} \sqrt{2 \, a b + 2 \, \sqrt{b^{2} - 4 \, a c} a} + {\left(5 \, a^{6} b^{13} - 112 \, a^{7} b^{11} c + 1030 \, a^{8} b^{9} c^{2} - 4928 \, a^{9} b^{7} c^{3} + 12736 \, a^{10} b^{5} c^{4} - 16384 \, a^{11} b^{3} c^{5} + 7680 \, a^{12} b c^{6}\right)} \sqrt{2 \, a b + 2 \, \sqrt{b^{2} - 4 \, a c} a} e^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} e^{\left(-1\right)}}{{\left(x e + d\right)} \sqrt{\frac{a^{3} b^{5} e^{2} - 8 \, a^{4} b^{3} c e^{2} + 16 \, a^{5} b c^{2} e^{2} + \sqrt{{\left(a^{3} b^{5} e^{2} - 8 \, a^{4} b^{3} c e^{2} + 16 \, a^{5} b c^{2} e^{2}\right)}^{2} - 4 \, {\left(a^{4} b^{4} e^{4} - 8 \, a^{5} b^{2} c e^{4} + 16 \, a^{6} c^{2} e^{4}\right)} {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)}}}{a^{4} b^{4} e^{4} - 8 \, a^{5} b^{2} c e^{4} + 16 \, a^{6} c^{2} e^{4}}}}\right) e^{\left(-3\right)}}{64 \, {\left(a^{7} b^{6} c - 12 \, a^{8} b^{4} c^{2} + 48 \, a^{9} b^{2} c^{3} - 64 \, a^{10} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} {\left| a^{3} b^{4} e^{2} - 8 \, a^{4} b^{2} c e^{2} + 16 \, a^{5} c^{2} e^{2} \right|} {\left| a \right|}} + \frac{3 \, {\left(2 \, {\left(5 \, a^{4} b^{6} c - 57 \, a^{5} b^{4} c^{2} + 208 \, a^{6} b^{2} c^{3} - 240 \, a^{7} c^{4}\right)} \sqrt{2 \, a b - 2 \, \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} {\left| a^{3} b^{4} e^{2} - 8 \, a^{4} b^{2} c e^{2} + 16 \, a^{5} c^{2} e^{2} \right|} e^{2} + {\left(a^{3} b^{4} e^{2} - 8 \, a^{4} b^{2} c e^{2} + 16 \, a^{5} c^{2} e^{2}\right)}^{2} {\left(5 \, b^{5} - 42 \, a b^{3} c + 92 \, a^{2} b c^{2}\right)} \sqrt{2 \, a b - 2 \, \sqrt{b^{2} - 4 \, a c} a} - {\left(5 \, a^{6} b^{13} - 112 \, a^{7} b^{11} c + 1030 \, a^{8} b^{9} c^{2} - 4928 \, a^{9} b^{7} c^{3} + 12736 \, a^{10} b^{5} c^{4} - 16384 \, a^{11} b^{3} c^{5} + 7680 \, a^{12} b c^{6}\right)} \sqrt{2 \, a b - 2 \, \sqrt{b^{2} - 4 \, a c} a} e^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} e^{\left(-1\right)}}{{\left(x e + d\right)} \sqrt{\frac{a^{3} b^{5} e^{2} - 8 \, a^{4} b^{3} c e^{2} + 16 \, a^{5} b c^{2} e^{2} - \sqrt{{\left(a^{3} b^{5} e^{2} - 8 \, a^{4} b^{3} c e^{2} + 16 \, a^{5} b c^{2} e^{2}\right)}^{2} - 4 \, {\left(a^{4} b^{4} e^{4} - 8 \, a^{5} b^{2} c e^{4} + 16 \, a^{6} c^{2} e^{4}\right)} {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)}}}{a^{4} b^{4} e^{4} - 8 \, a^{5} b^{2} c e^{4} + 16 \, a^{6} c^{2} e^{4}}}}\right) e^{\left(-3\right)}}{64 \, {\left(a^{7} b^{6} c - 12 \, a^{8} b^{4} c^{2} + 48 \, a^{9} b^{2} c^{3} - 64 \, a^{10} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} {\left| a^{3} b^{4} e^{2} - 8 \, a^{4} b^{2} c e^{2} + 16 \, a^{5} c^{2} e^{2} \right|} {\left| a \right|}} - \frac{\frac{7 \, b^{4} c^{2} e^{\left(-1\right)}}{x e + d} - \frac{47 \, a b^{2} c^{3} e^{\left(-1\right)}}{x e + d} + \frac{52 \, a^{2} c^{4} e^{\left(-1\right)}}{x e + d} + \frac{14 \, b^{5} c e^{\left(-1\right)}}{{\left(x e + d\right)}^{3}} - \frac{99 \, a b^{3} c^{2} e^{\left(-1\right)}}{{\left(x e + d\right)}^{3}} + \frac{136 \, a^{2} b c^{3} e^{\left(-1\right)}}{{\left(x e + d\right)}^{3}} + \frac{7 \, b^{6} e^{\left(-1\right)}}{{\left(x e + d\right)}^{5}} - \frac{43 \, a b^{4} c e^{\left(-1\right)}}{{\left(x e + d\right)}^{5}} + \frac{25 \, a^{2} b^{2} c^{2} e^{\left(-1\right)}}{{\left(x e + d\right)}^{5}} + \frac{68 \, a^{3} c^{3} e^{\left(-1\right)}}{{\left(x e + d\right)}^{5}} + \frac{9 \, a b^{5} e^{\left(-1\right)}}{{\left(x e + d\right)}^{7}} - \frac{66 \, a^{2} b^{3} c e^{\left(-1\right)}}{{\left(x e + d\right)}^{7}} + \frac{108 \, a^{3} b c^{2} e^{\left(-1\right)}}{{\left(x e + d\right)}^{7}}}{8 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} {\left(c + \frac{b}{{\left(x e + d\right)}^{2}} + \frac{a}{{\left(x e + d\right)}^{4}}\right)}^{2}} - \frac{e^{\left(-1\right)}}{{\left(x e + d\right)} a^{3}}"," ",0,"3/64*(2*(5*a^4*b^6*c - 57*a^5*b^4*c^2 + 208*a^6*b^2*c^3 - 240*a^7*c^4)*sqrt(2*a*b + 2*sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*abs(a^3*b^4*e^2 - 8*a^4*b^2*c*e^2 + 16*a^5*c^2*e^2)*e^2 - (a^3*b^4*e^2 - 8*a^4*b^2*c*e^2 + 16*a^5*c^2*e^2)^2*(5*b^5 - 42*a*b^3*c + 92*a^2*b*c^2)*sqrt(2*a*b + 2*sqrt(b^2 - 4*a*c)*a) + (5*a^6*b^13 - 112*a^7*b^11*c + 1030*a^8*b^9*c^2 - 4928*a^9*b^7*c^3 + 12736*a^10*b^5*c^4 - 16384*a^11*b^3*c^5 + 7680*a^12*b*c^6)*sqrt(2*a*b + 2*sqrt(b^2 - 4*a*c)*a)*e^4)*arctan(2*sqrt(1/2)*e^(-1)/((x*e + d)*sqrt((a^3*b^5*e^2 - 8*a^4*b^3*c*e^2 + 16*a^5*b*c^2*e^2 + sqrt((a^3*b^5*e^2 - 8*a^4*b^3*c*e^2 + 16*a^5*b*c^2*e^2)^2 - 4*(a^4*b^4*e^4 - 8*a^5*b^2*c*e^4 + 16*a^6*c^2*e^4)*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/(a^4*b^4*e^4 - 8*a^5*b^2*c*e^4 + 16*a^6*c^2*e^4))))*e^(-3)/((a^7*b^6*c - 12*a^8*b^4*c^2 + 48*a^9*b^2*c^3 - 64*a^10*c^4)*sqrt(b^2 - 4*a*c)*abs(a^3*b^4*e^2 - 8*a^4*b^2*c*e^2 + 16*a^5*c^2*e^2)*abs(a)) + 3/64*(2*(5*a^4*b^6*c - 57*a^5*b^4*c^2 + 208*a^6*b^2*c^3 - 240*a^7*c^4)*sqrt(2*a*b - 2*sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*abs(a^3*b^4*e^2 - 8*a^4*b^2*c*e^2 + 16*a^5*c^2*e^2)*e^2 + (a^3*b^4*e^2 - 8*a^4*b^2*c*e^2 + 16*a^5*c^2*e^2)^2*(5*b^5 - 42*a*b^3*c + 92*a^2*b*c^2)*sqrt(2*a*b - 2*sqrt(b^2 - 4*a*c)*a) - (5*a^6*b^13 - 112*a^7*b^11*c + 1030*a^8*b^9*c^2 - 4928*a^9*b^7*c^3 + 12736*a^10*b^5*c^4 - 16384*a^11*b^3*c^5 + 7680*a^12*b*c^6)*sqrt(2*a*b - 2*sqrt(b^2 - 4*a*c)*a)*e^4)*arctan(2*sqrt(1/2)*e^(-1)/((x*e + d)*sqrt((a^3*b^5*e^2 - 8*a^4*b^3*c*e^2 + 16*a^5*b*c^2*e^2 - sqrt((a^3*b^5*e^2 - 8*a^4*b^3*c*e^2 + 16*a^5*b*c^2*e^2)^2 - 4*(a^4*b^4*e^4 - 8*a^5*b^2*c*e^4 + 16*a^6*c^2*e^4)*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/(a^4*b^4*e^4 - 8*a^5*b^2*c*e^4 + 16*a^6*c^2*e^4))))*e^(-3)/((a^7*b^6*c - 12*a^8*b^4*c^2 + 48*a^9*b^2*c^3 - 64*a^10*c^4)*sqrt(b^2 - 4*a*c)*abs(a^3*b^4*e^2 - 8*a^4*b^2*c*e^2 + 16*a^5*c^2*e^2)*abs(a)) - 1/8*(7*b^4*c^2*e^(-1)/(x*e + d) - 47*a*b^2*c^3*e^(-1)/(x*e + d) + 52*a^2*c^4*e^(-1)/(x*e + d) + 14*b^5*c*e^(-1)/(x*e + d)^3 - 99*a*b^3*c^2*e^(-1)/(x*e + d)^3 + 136*a^2*b*c^3*e^(-1)/(x*e + d)^3 + 7*b^6*e^(-1)/(x*e + d)^5 - 43*a*b^4*c*e^(-1)/(x*e + d)^5 + 25*a^2*b^2*c^2*e^(-1)/(x*e + d)^5 + 68*a^3*c^3*e^(-1)/(x*e + d)^5 + 9*a*b^5*e^(-1)/(x*e + d)^7 - 66*a^2*b^3*c*e^(-1)/(x*e + d)^7 + 108*a^3*b*c^2*e^(-1)/(x*e + d)^7)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*(c + b/(x*e + d)^2 + a/(x*e + d)^4)^2) - e^(-1)/((x*e + d)*a^3)","B",0
637,1,377,0,0.639179," ","integrate(1/(e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","\frac{3 \, {\left(b^{6} - 10 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2} - 20 \, a^{3} c^{3}\right)} \arctan\left(-\frac{b + \frac{2 \, a}{{\left(x e + d\right)}^{2}}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-1\right)}}{2 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{3 \, b e^{\left(-1\right)} \log\left(c + \frac{b}{{\left(x e + d\right)}^{2}} + \frac{a}{{\left(x e + d\right)}^{4}}\right)}{4 \, a^{4}} - \frac{e^{\left(-1\right)}}{2 \, {\left(x e + d\right)}^{2} a^{3}} + \frac{{\left(5 \, b^{5} c^{2} - 36 \, a b^{3} c^{3} + 58 \, a^{2} b c^{4} + \frac{2 \, {\left(5 \, b^{6} c e - 38 \, a b^{4} c^{2} e + 71 \, a^{2} b^{2} c^{3} e - 14 \, a^{3} c^{4} e\right)} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}} + \frac{{\left(5 \, b^{7} e^{2} - 34 \, a b^{5} c e^{2} + 41 \, a^{2} b^{3} c^{2} e^{2} + 42 \, a^{3} b c^{3} e^{2}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{4}} + \frac{6 \, {\left(a b^{6} e^{3} - 8 \, a^{2} b^{4} c e^{3} + 17 \, a^{3} b^{2} c^{2} e^{3} - 6 \, a^{4} c^{3} e^{3}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{6}}\right)} e^{\left(-1\right)}}{4 \, {\left(b^{2} - 4 \, a c\right)}^{2} a^{4} {\left(c + \frac{b}{{\left(x e + d\right)}^{2}} + \frac{a}{{\left(x e + d\right)}^{4}}\right)}^{2}}"," ",0,"3/2*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3)*arctan(-(b + 2*a/(x*e + d)^2)/sqrt(-b^2 + 4*a*c))*e^(-1)/((a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*sqrt(-b^2 + 4*a*c)) + 3/4*b*e^(-1)*log(c + b/(x*e + d)^2 + a/(x*e + d)^4)/a^4 - 1/2*e^(-1)/((x*e + d)^2*a^3) + 1/4*(5*b^5*c^2 - 36*a*b^3*c^3 + 58*a^2*b*c^4 + 2*(5*b^6*c*e - 38*a*b^4*c^2*e + 71*a^2*b^2*c^3*e - 14*a^3*c^4*e)*e^(-1)/(x*e + d)^2 + (5*b^7*e^2 - 34*a*b^5*c*e^2 + 41*a^2*b^3*c^2*e^2 + 42*a^3*b*c^3*e^2)*e^(-2)/(x*e + d)^4 + 6*(a*b^6*e^3 - 8*a^2*b^4*c*e^3 + 17*a^3*b^2*c^2*e^3 - 6*a^4*c^3*e^3)*e^(-3)/(x*e + d)^6)*e^(-1)/((b^2 - 4*a*c)^2*a^4*(c + b/(x*e + d)^2 + a/(x*e + d)^4)^2)","A",0
638,1,1245,0,0.536407," ","integrate((e*f*x+d*f)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","\frac{f^{4} x}{c} + \frac{{\left(\frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b f^{4} e^{6} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b d f^{4} e^{5} + b d^{2} f^{4} e^{4} + a f^{4} e^{4}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b f^{4} e^{6} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b d f^{4} e^{5} + b d^{2} f^{4} e^{4} + a f^{4} e^{4}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b f^{4} e^{6} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b d f^{4} e^{5} + b d^{2} f^{4} e^{4} + a f^{4} e^{4}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b f^{4} e^{6} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b d f^{4} e^{5} + b d^{2} f^{4} e^{4} + a f^{4} e^{4}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}}\right)} e^{\left(-4\right)}}{2 \, c}"," ",0,"f^4*x/c + 1/2*(((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*f^4*e^6 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*d*f^4*e^5 + b*d^2*f^4*e^4 + a*f^4*e^4)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*f^4*e^6 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*d*f^4*e^5 + b*d^2*f^4*e^4 + a*f^4*e^4)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*f^4*e^6 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*d*f^4*e^5 + b*d^2*f^4*e^4 + a*f^4*e^4)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*f^4*e^6 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*d*f^4*e^5 + b*d^2*f^4*e^4 + a*f^4*e^4)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))))*e^(-4)/c","B",0
639,1,162,0,0.428842," ","integrate((e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","-\frac{b f^{3} \arctan\left(\frac{2 \, c d^{2} f + 2 \, {\left(f x^{2} e + 2 \, d f x\right)} c e + b f}{\sqrt{-b^{2} + 4 \, a c} f}\right) e^{\left(-1\right)}}{2 \, \sqrt{-b^{2} + 4 \, a c} c} + \frac{f^{3} e^{\left(-1\right)} \log\left(c d^{4} f^{2} + 2 \, {\left(f x^{2} e + 2 \, d f x\right)} c d^{2} f e + b d^{2} f^{2} + {\left(f x^{2} e + 2 \, d f x\right)}^{2} c e^{2} + {\left(f x^{2} e + 2 \, d f x\right)} b f e + a f^{2}\right)}{4 \, c}"," ",0,"-1/2*b*f^3*arctan((2*c*d^2*f + 2*(f*x^2*e + 2*d*f*x)*c*e + b*f)/(sqrt(-b^2 + 4*a*c)*f))*e^(-1)/(sqrt(-b^2 + 4*a*c)*c) + 1/4*f^3*e^(-1)*log(c*d^4*f^2 + 2*(f*x^2*e + 2*d*f*x)*c*d^2*f*e + b*d^2*f^2 + (f*x^2*e + 2*d*f*x)^2*c*e^2 + (f*x^2*e + 2*d*f*x)*b*f*e + a*f^2)/c","B",0
640,1,1325,0,0.466022," ","integrate((e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","-\frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} f^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} d f^{2} e + d^{2} f^{2}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} + 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} c d^{2} e^{2} - 2 \, c d^{3} e + {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b e^{2} - b d e\right)}} - \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} f^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} d f^{2} e + d^{2} f^{2}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} + 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} c d^{2} e^{2} - 2 \, c d^{3} e + {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b e^{2} - b d e\right)}} - \frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} f^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} d f^{2} e + d^{2} f^{2}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} + 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} c d^{2} e^{2} - 2 \, c d^{3} e + {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b e^{2} - b d e\right)}} - \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} f^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} d f^{2} e + d^{2} f^{2}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} + 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} c d^{2} e^{2} - 2 \, c d^{3} e + {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b e^{2} - b d e\right)}}"," ",0,"-1/2*((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*f^2*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*d*f^2*e + d^2*f^2)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 + 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*c*d^2*e^2 - 2*c*d^3*e + (d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*e^2 - b*d*e) - 1/2*((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*f^2*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*d*f^2*e + d^2*f^2)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 + 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*c*d^2*e^2 - 2*c*d^3*e + (d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*e^2 - b*d*e) - 1/2*((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*f^2*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*d*f^2*e + d^2*f^2)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 + 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*c*d^2*e^2 - 2*c*d^3*e + (d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*e^2 - b*d*e) - 1/2*((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*f^2*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*d*f^2*e + d^2*f^2)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 + 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*c*d^2*e^2 - 2*c*d^3*e + (d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*e^2 - b*d*e)","B",0
641,1,62,0,0.397449," ","integrate((e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","\frac{f \arctan\left(\frac{2 \, c d^{2} f + 2 \, {\left(f x^{2} e + 2 \, d f x\right)} c e + b f}{\sqrt{-b^{2} + 4 \, a c} f}\right) e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}"," ",0,"f*arctan((2*c*d^2*f + 2*(f*x^2*e + 2*d*f*x)*c*e + b*f)/(sqrt(-b^2 + 4*a*c)*f))*e^(-1)/sqrt(-b^2 + 4*a*c)","A",0
642,1,285,0,1.192934," ","integrate(1/(e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","-\frac{e^{\left(-1\right)} \log\left({\left| c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a \right|}\right)}{4 \, a f} + \frac{e^{\left(-1\right)} \log\left({\left| x e + d \right|}\right)}{a f} - \frac{{\left(\frac{a b c f e^{3} \log\left({\left| b x^{2} e^{2} + 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e + b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} + 2 \, a \right|}\right)}{\sqrt{b^{2} - 4 \, a c}} - \frac{a b c f e^{3} \log\left({\left| -b x^{2} e^{2} - 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e - b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} - 2 \, a \right|}\right)}{\sqrt{b^{2} - 4 \, a c}}\right)} e^{\left(-4\right)}}{4 \, a^{2} c f^{2}}"," ",0,"-1/4*e^(-1)*log(abs(c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a))/(a*f) + e^(-1)*log(abs(x*e + d))/(a*f) - 1/4*(a*b*c*f*e^3*log(abs(b*x^2*e^2 + 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e + b*d^2 + sqrt(b^2 - 4*a*c)*d^2 + 2*a))/sqrt(b^2 - 4*a*c) - a*b*c*f*e^3*log(abs(-b*x^2*e^2 - 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e - b*d^2 + sqrt(b^2 - 4*a*c)*d^2 - 2*a))/sqrt(b^2 - 4*a*c))*e^(-4)/(a^2*c*f^2)","B",0
643,-2,0,0,0.000000," ","integrate(1/(e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument ValueDone","F(-2)",0
644,1,348,0,1.106366," ","integrate(1/(e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","\frac{b e^{\left(-1\right)} \log\left({\left| c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a \right|}\right)}{4 \, a^{2} f^{3}} - \frac{b e^{\left(-1\right)} \log\left({\left| x e + d \right|}\right)}{a^{2} f^{3}} - \frac{e^{\left(-1\right)}}{2 \, {\left(x e + d\right)}^{2} a f^{3}} + \frac{{\left(\frac{{\left(a^{2} b^{2} c f^{3} e^{3} - 2 \, a^{3} c^{2} f^{3} e^{3}\right)} \log\left({\left| b x^{2} e^{2} + 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e + b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} + 2 \, a \right|}\right)}{\sqrt{b^{2} - 4 \, a c}} - \frac{{\left(a^{2} b^{2} c f^{3} e^{3} - 2 \, a^{3} c^{2} f^{3} e^{3}\right)} \log\left({\left| -b x^{2} e^{2} - 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e - b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} - 2 \, a \right|}\right)}{\sqrt{b^{2} - 4 \, a c}}\right)} e^{\left(-4\right)}}{4 \, a^{4} c f^{6}}"," ",0,"1/4*b*e^(-1)*log(abs(c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a))/(a^2*f^3) - b*e^(-1)*log(abs(x*e + d))/(a^2*f^3) - 1/2*e^(-1)/((x*e + d)^2*a*f^3) + 1/4*((a^2*b^2*c*f^3*e^3 - 2*a^3*c^2*f^3*e^3)*log(abs(b*x^2*e^2 + 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e + b*d^2 + sqrt(b^2 - 4*a*c)*d^2 + 2*a))/sqrt(b^2 - 4*a*c) - (a^2*b^2*c*f^3*e^3 - 2*a^3*c^2*f^3*e^3)*log(abs(-b*x^2*e^2 - 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e - b*d^2 + sqrt(b^2 - 4*a*c)*d^2 - 2*a))/sqrt(b^2 - 4*a*c))*e^(-4)/(a^4*c*f^6)","B",0
645,1,1249,0,0.569643," ","integrate(1/(e*f*x+d*f)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""giac"")","-\frac{\frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d e + b c d^{2} + b^{2} - a c\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d e + b c d^{2} + b^{2} - a c\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d e + b c d^{2} + b^{2} - a c\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d e + b c d^{2} + b^{2} - a c\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}}}{2 \, a^{2} f^{4}} + \frac{{\left(3 \, b x^{2} e^{2} + 6 \, b d x e + 3 \, b d^{2} - a\right)} e^{\left(-1\right)}}{3 \, {\left(x e + d\right)}^{3} a^{2} f^{4}}"," ",0,"-1/2*(((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*e + b*c*d^2 + b^2 - a*c)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*e + b*c*d^2 + b^2 - a*c)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*e + b*c*d^2 + b^2 - a*c)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*e + b*c*d^2 + b^2 - a*c)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))))/(a^2*f^4) + 1/3*(3*b*x^2*e^2 + 6*b*d*x*e + 3*b*d^2 - a)*e^(-1)/((x*e + d)^3*a^2*f^4)","B",0
646,1,1370,0,0.602569," ","integrate((e*f*x+d*f)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","-\frac{\frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b f^{4} e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b d f^{4} e + b d^{2} f^{4} - 2 \, a f^{4}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b f^{4} e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b d f^{4} e + b d^{2} f^{4} - 2 \, a f^{4}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b f^{4} e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b d f^{4} e + b d^{2} f^{4} - 2 \, a f^{4}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b f^{4} e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b d f^{4} e + b d^{2} f^{4} - 2 \, a f^{4}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}}}{4 \, {\left(b^{2} - 4 \, a c\right)}} + \frac{b f^{4} x^{3} e^{3} + 3 \, b d f^{4} x^{2} e^{2} + 3 \, b d^{2} f^{4} x e + b d^{3} f^{4} + 2 \, a f^{4} x e + 2 \, a d f^{4}}{2 \, {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)} {\left(b^{2} e - 4 \, a c e\right)}}"," ",0,"-1/4*(((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*f^4*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*d*f^4*e + b*d^2*f^4 - 2*a*f^4)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*f^4*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*d*f^4*e + b*d^2*f^4 - 2*a*f^4)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*f^4*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*d*f^4*e + b*d^2*f^4 - 2*a*f^4)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*f^4*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*d*f^4*e + b*d^2*f^4 - 2*a*f^4)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))))/(b^2 - 4*a*c) + 1/2*(b*f^4*x^3*e^3 + 3*b*d*f^4*x^2*e^2 + 3*b*d^2*f^4*x*e + b*d^3*f^4 + 2*a*f^4*x*e + 2*a*d*f^4)/((c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)*(b^2*e - 4*a*c*e))","B",0
647,1,211,0,0.515473," ","integrate((e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","\frac{b f^{3} \arctan\left(\frac{2 \, c d^{2} f + 2 \, {\left(f x^{2} e + 2 \, d f x\right)} c e + b f}{\sqrt{-b^{2} + 4 \, a c} f}\right) e^{\left(-1\right)}}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{b d^{2} f^{5} + {\left(f x^{2} e + 2 \, d f x\right)} b f^{4} e + 2 \, a f^{5}}{2 \, {\left(c d^{4} f^{2} + 2 \, {\left(f x^{2} e + 2 \, d f x\right)} c d^{2} f e + b d^{2} f^{2} + {\left(f x^{2} e + 2 \, d f x\right)}^{2} c e^{2} + {\left(f x^{2} e + 2 \, d f x\right)} b f e + a f^{2}\right)} {\left(b^{2} e - 4 \, a c e\right)}}"," ",0,"b*f^3*arctan((2*c*d^2*f + 2*(f*x^2*e + 2*d*f*x)*c*e + b*f)/(sqrt(-b^2 + 4*a*c)*f))*e^(-1)/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) + 1/2*(b*d^2*f^5 + (f*x^2*e + 2*d*f*x)*b*f^4*e + 2*a*f^5)/((c*d^4*f^2 + 2*(f*x^2*e + 2*d*f*x)*c*d^2*f*e + b*d^2*f^2 + (f*x^2*e + 2*d*f*x)^2*c*e^2 + (f*x^2*e + 2*d*f*x)*b*f*e + a*f^2)*(b^2*e - 4*a*c*e))","B",0
648,1,1378,0,0.674817," ","integrate((e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c f^{2} e^{2} - 4 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} c d f^{2} e + 2 \, c d^{2} f^{2} - b f^{2}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c f^{2} e^{2} - 4 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} c d f^{2} e + 2 \, c d^{2} f^{2} - b f^{2}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c f^{2} e^{2} - 4 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} c d f^{2} e + 2 \, c d^{2} f^{2} - b f^{2}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c f^{2} e^{2} - 4 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} c d f^{2} e + 2 \, c d^{2} f^{2} - b f^{2}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}}}{4 \, {\left(b^{2} - 4 \, a c\right)}} - \frac{2 \, c f^{2} x^{3} e^{3} + 6 \, c d f^{2} x^{2} e^{2} + 6 \, c d^{2} f^{2} x e + 2 \, c d^{3} f^{2} + b f^{2} x e + b d f^{2}}{2 \, {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)} {\left(b^{2} e - 4 \, a c e\right)}}"," ",0,"1/4*((2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*f^2*e^2 - 4*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*c*d*f^2*e + 2*c*d^2*f^2 - b*f^2)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*f^2*e^2 - 4*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*c*d*f^2*e + 2*c*d^2*f^2 - b*f^2)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*f^2*e^2 - 4*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*c*d*f^2*e + 2*c*d^2*f^2 - b*f^2)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*f^2*e^2 - 4*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*c*d*f^2*e + 2*c*d^2*f^2 - b*f^2)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))))/(b^2 - 4*a*c) - 1/2*(2*c*f^2*x^3*e^3 + 6*c*d*f^2*x^2*e^2 + 6*c*d^2*f^2*x*e + 2*c*d^3*f^2 + b*f^2*x*e + b*d*f^2)/((c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)*(b^2*e - 4*a*c*e))","B",0
649,1,211,0,0.444894," ","integrate((e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","-\frac{2 \, c f \arctan\left(\frac{2 \, c d^{2} f + 2 \, {\left(f x^{2} e + 2 \, d f x\right)} c e + b f}{\sqrt{-b^{2} + 4 \, a c} f}\right) e^{\left(-1\right)}}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, c d^{2} f^{3} + 2 \, {\left(f x^{2} e + 2 \, d f x\right)} c f^{2} e + b f^{3}}{2 \, {\left(c d^{4} f^{2} + 2 \, {\left(f x^{2} e + 2 \, d f x\right)} c d^{2} f e + b d^{2} f^{2} + {\left(f x^{2} e + 2 \, d f x\right)}^{2} c e^{2} + {\left(f x^{2} e + 2 \, d f x\right)} b f e + a f^{2}\right)} {\left(b^{2} e - 4 \, a c e\right)}}"," ",0,"-2*c*f*arctan((2*c*d^2*f + 2*(f*x^2*e + 2*d*f*x)*c*e + b*f)/(sqrt(-b^2 + 4*a*c)*f))*e^(-1)/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - 1/2*(2*c*d^2*f^3 + 2*(f*x^2*e + 2*d*f*x)*c*f^2*e + b*f^3)/((c*d^4*f^2 + 2*(f*x^2*e + 2*d*f*x)*c*d^2*f*e + b*d^2*f^2 + (f*x^2*e + 2*d*f*x)^2*c*e^2 + (f*x^2*e + 2*d*f*x)*b*f*e + a*f^2)*(b^2*e - 4*a*c*e))","B",0
650,1,476,0,1.431865," ","integrate(1/(e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","-\frac{{\left(a^{2} b^{3} c f e^{3} - 6 \, a^{3} b c^{2} f e^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left({\left| b x^{2} e^{2} + 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e + b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} + 2 \, a \right|}\right) - {\left(a^{2} b^{3} c f e^{3} - 6 \, a^{3} b c^{2} f e^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left({\left| -b x^{2} e^{2} - 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e - b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} - 2 \, a \right|}\right)}{4 \, {\left(a^{4} b^{4} c f^{2} e^{4} - 8 \, a^{5} b^{2} c^{2} f^{2} e^{4} + 16 \, a^{6} c^{3} f^{2} e^{4}\right)}} - \frac{e^{\left(-1\right)} \log\left({\left| c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a \right|}\right)}{4 \, a^{2} f} + \frac{e^{\left(-1\right)} \log\left({\left| x e + d \right|}\right)}{a^{2} f} + \frac{{\left(a b c x^{2} e^{2} + 2 \, a b c d x e + a b c d^{2} + a b^{2} - 2 \, a^{2} c\right)} e^{\left(-1\right)}}{2 \, {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)} a^{2} f}"," ",0,"-1/4*((a^2*b^3*c*f*e^3 - 6*a^3*b*c^2*f*e^3)*sqrt(b^2 - 4*a*c)*log(abs(b*x^2*e^2 + 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e + b*d^2 + sqrt(b^2 - 4*a*c)*d^2 + 2*a)) - (a^2*b^3*c*f*e^3 - 6*a^3*b*c^2*f*e^3)*sqrt(b^2 - 4*a*c)*log(abs(-b*x^2*e^2 - 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e - b*d^2 + sqrt(b^2 - 4*a*c)*d^2 - 2*a)))/(a^4*b^4*c*f^2*e^4 - 8*a^5*b^2*c^2*f^2*e^4 + 16*a^6*c^3*f^2*e^4) - 1/4*e^(-1)*log(abs(c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a))/(a^2*f) + e^(-1)*log(abs(x*e + d))/(a^2*f) + 1/2*(a*b*c*x^2*e^2 + 2*a*b*c*d*x*e + a*b*c*d^2 + a*b^2 - 2*a^2*c)*e^(-1)/((c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)*(b^2 - 4*a*c)*a^2*f)","B",0
651,1,999,0,1.020638," ","integrate(1/(e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","-\frac{\frac{b^{2} c e^{\left(-1\right)}}{{\left(f x e + d f\right)} f} - \frac{2 \, a c^{2} e^{\left(-1\right)}}{{\left(f x e + d f\right)} f} + \frac{b^{3} f e^{\left(-1\right)}}{{\left(f x e + d f\right)}^{3}} - \frac{3 \, a b c f e^{\left(-1\right)}}{{\left(f x e + d f\right)}^{3}}}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(c + \frac{b f^{2}}{{\left(f x e + d f\right)}^{2}} + \frac{a f^{4}}{{\left(f x e + d f\right)}^{4}}\right)}} - \frac{e^{\left(-1\right)}}{{\left(f x e + d f\right)} a^{2} f} + \frac{{\left({\left(3 \, a^{4} b^{7} - 31 \, a^{5} b^{5} c + 96 \, a^{6} b^{3} c^{2} - 80 \, a^{7} b c^{3}\right)} \sqrt{2 \, a b + 2 \, \sqrt{b^{2} - 4 \, a c} a} f^{8} e^{4} + 2 \, {\left(3 \, a^{3} b^{2} c - 10 \, a^{4} c^{2}\right)} \sqrt{2 \, a b + 2 \, \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} f^{4} {\left| a^{2} b^{2} f^{4} e^{2} - 4 \, a^{3} c f^{4} e^{2} \right|} e^{2} - {\left(a^{2} b^{2} f^{4} e^{2} - 4 \, a^{3} c f^{4} e^{2}\right)}^{2} {\left(3 \, b^{3} - 13 \, a b c\right)} \sqrt{2 \, a b + 2 \, \sqrt{b^{2} - 4 \, a c} a}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} e^{\left(-1\right)}}{{\left(f x e + d f\right)} f \sqrt{\frac{a^{2} b^{3} f^{4} e^{2} - 4 \, a^{3} b c f^{4} e^{2} + \sqrt{{\left(a^{2} b^{3} f^{4} e^{2} - 4 \, a^{3} b c f^{4} e^{2}\right)}^{2} - 4 \, {\left(a^{3} b^{2} f^{8} e^{4} - 4 \, a^{4} c f^{8} e^{4}\right)} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)}}}{a^{3} b^{2} f^{8} e^{4} - 4 \, a^{4} c f^{8} e^{4}}}}\right) e^{\left(-3\right)}}{16 \, {\left(a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} f^{6} {\left| a^{2} b^{2} f^{4} e^{2} - 4 \, a^{3} c f^{4} e^{2} \right|} {\left| a \right|}} - \frac{{\left({\left(3 \, a^{4} b^{7} - 31 \, a^{5} b^{5} c + 96 \, a^{6} b^{3} c^{2} - 80 \, a^{7} b c^{3}\right)} \sqrt{2 \, a b - 2 \, \sqrt{b^{2} - 4 \, a c} a} f^{8} e^{4} - 2 \, {\left(3 \, a^{3} b^{2} c - 10 \, a^{4} c^{2}\right)} \sqrt{2 \, a b - 2 \, \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} f^{4} {\left| a^{2} b^{2} f^{4} e^{2} - 4 \, a^{3} c f^{4} e^{2} \right|} e^{2} - {\left(a^{2} b^{2} f^{4} e^{2} - 4 \, a^{3} c f^{4} e^{2}\right)}^{2} {\left(3 \, b^{3} - 13 \, a b c\right)} \sqrt{2 \, a b - 2 \, \sqrt{b^{2} - 4 \, a c} a}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} e^{\left(-1\right)}}{{\left(f x e + d f\right)} f \sqrt{\frac{a^{2} b^{3} f^{4} e^{2} - 4 \, a^{3} b c f^{4} e^{2} - \sqrt{{\left(a^{2} b^{3} f^{4} e^{2} - 4 \, a^{3} b c f^{4} e^{2}\right)}^{2} - 4 \, {\left(a^{3} b^{2} f^{8} e^{4} - 4 \, a^{4} c f^{8} e^{4}\right)} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)}}}{a^{3} b^{2} f^{8} e^{4} - 4 \, a^{4} c f^{8} e^{4}}}}\right) e^{\left(-3\right)}}{16 \, {\left(a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} f^{6} {\left| a^{2} b^{2} f^{4} e^{2} - 4 \, a^{3} c f^{4} e^{2} \right|} {\left| a \right|}}"," ",0,"-1/2*(b^2*c*e^(-1)/((f*x*e + d*f)*f) - 2*a*c^2*e^(-1)/((f*x*e + d*f)*f) + b^3*f*e^(-1)/(f*x*e + d*f)^3 - 3*a*b*c*f*e^(-1)/(f*x*e + d*f)^3)/((a^2*b^2 - 4*a^3*c)*(c + b*f^2/(f*x*e + d*f)^2 + a*f^4/(f*x*e + d*f)^4)) - e^(-1)/((f*x*e + d*f)*a^2*f) + 1/16*((3*a^4*b^7 - 31*a^5*b^5*c + 96*a^6*b^3*c^2 - 80*a^7*b*c^3)*sqrt(2*a*b + 2*sqrt(b^2 - 4*a*c)*a)*f^8*e^4 + 2*(3*a^3*b^2*c - 10*a^4*c^2)*sqrt(2*a*b + 2*sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*f^4*abs(a^2*b^2*f^4*e^2 - 4*a^3*c*f^4*e^2)*e^2 - (a^2*b^2*f^4*e^2 - 4*a^3*c*f^4*e^2)^2*(3*b^3 - 13*a*b*c)*sqrt(2*a*b + 2*sqrt(b^2 - 4*a*c)*a))*arctan(2*sqrt(1/2)*e^(-1)/((f*x*e + d*f)*f*sqrt((a^2*b^3*f^4*e^2 - 4*a^3*b*c*f^4*e^2 + sqrt((a^2*b^3*f^4*e^2 - 4*a^3*b*c*f^4*e^2)^2 - 4*(a^3*b^2*f^8*e^4 - 4*a^4*c*f^8*e^4)*(a^2*b^2*c - 4*a^3*c^2)))/(a^3*b^2*f^8*e^4 - 4*a^4*c*f^8*e^4))))*e^(-3)/((a^5*b^2*c - 4*a^6*c^2)*sqrt(b^2 - 4*a*c)*f^6*abs(a^2*b^2*f^4*e^2 - 4*a^3*c*f^4*e^2)*abs(a)) - 1/16*((3*a^4*b^7 - 31*a^5*b^5*c + 96*a^6*b^3*c^2 - 80*a^7*b*c^3)*sqrt(2*a*b - 2*sqrt(b^2 - 4*a*c)*a)*f^8*e^4 - 2*(3*a^3*b^2*c - 10*a^4*c^2)*sqrt(2*a*b - 2*sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*f^4*abs(a^2*b^2*f^4*e^2 - 4*a^3*c*f^4*e^2)*e^2 - (a^2*b^2*f^4*e^2 - 4*a^3*c*f^4*e^2)^2*(3*b^3 - 13*a*b*c)*sqrt(2*a*b - 2*sqrt(b^2 - 4*a*c)*a))*arctan(2*sqrt(1/2)*e^(-1)/((f*x*e + d*f)*f*sqrt((a^2*b^3*f^4*e^2 - 4*a^3*b*c*f^4*e^2 - sqrt((a^2*b^3*f^4*e^2 - 4*a^3*b*c*f^4*e^2)^2 - 4*(a^3*b^2*f^8*e^4 - 4*a^4*c*f^8*e^4)*(a^2*b^2*c - 4*a^3*c^2)))/(a^3*b^2*f^8*e^4 - 4*a^4*c*f^8*e^4))))*e^(-3)/((a^5*b^2*c - 4*a^6*c^2)*sqrt(b^2 - 4*a*c)*f^6*abs(a^2*b^2*f^4*e^2 - 4*a^3*c*f^4*e^2)*abs(a))","B",0
652,1,687,0,1.296140," ","integrate(1/(e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","\frac{{\left(a^{3} b^{4} c f^{3} e^{3} - 6 \, a^{4} b^{2} c^{2} f^{3} e^{3} + 6 \, a^{5} c^{3} f^{3} e^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left({\left| b x^{2} e^{2} + 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e + b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} + 2 \, a \right|}\right) - {\left(a^{3} b^{4} c f^{3} e^{3} - 6 \, a^{4} b^{2} c^{2} f^{3} e^{3} + 6 \, a^{5} c^{3} f^{3} e^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left({\left| -b x^{2} e^{2} - 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e - b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} - 2 \, a \right|}\right)}{2 \, {\left(a^{6} b^{4} c f^{6} e^{4} - 8 \, a^{7} b^{2} c^{2} f^{6} e^{4} + 16 \, a^{8} c^{3} f^{6} e^{4}\right)}} + \frac{b e^{\left(-1\right)} \log\left({\left| c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a \right|}\right)}{2 \, a^{3} f^{3}} - \frac{2 \, b e^{\left(-1\right)} \log\left({\left| x e + d \right|}\right)}{a^{3} f^{3}} - \frac{{\left(2 \, a b^{2} c d^{4} - 6 \, a^{2} c^{2} d^{4} + 2 \, a b^{3} d^{2} - 7 \, a^{2} b c d^{2} + 2 \, {\left(a b^{2} c e^{4} - 3 \, a^{2} c^{2} e^{4}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 8 \, {\left(a b^{2} c d e^{3} - 3 \, a^{2} c^{2} d e^{3}\right)} x^{3} + {\left(12 \, a b^{2} c d^{2} e^{2} - 36 \, a^{2} c^{2} d^{2} e^{2} + 2 \, a b^{3} e^{2} - 7 \, a^{2} b c e^{2}\right)} x^{2} + 2 \, {\left(4 \, a b^{2} c d^{3} e - 12 \, a^{2} c^{2} d^{3} e + 2 \, a b^{3} d e - 7 \, a^{2} b c d e\right)} x\right)} e^{\left(-1\right)}}{2 \, {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)} {\left(x e + d\right)}^{2} a^{3} f^{3}}"," ",0,"1/2*((a^3*b^4*c*f^3*e^3 - 6*a^4*b^2*c^2*f^3*e^3 + 6*a^5*c^3*f^3*e^3)*sqrt(b^2 - 4*a*c)*log(abs(b*x^2*e^2 + 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e + b*d^2 + sqrt(b^2 - 4*a*c)*d^2 + 2*a)) - (a^3*b^4*c*f^3*e^3 - 6*a^4*b^2*c^2*f^3*e^3 + 6*a^5*c^3*f^3*e^3)*sqrt(b^2 - 4*a*c)*log(abs(-b*x^2*e^2 - 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e - b*d^2 + sqrt(b^2 - 4*a*c)*d^2 - 2*a)))/(a^6*b^4*c*f^6*e^4 - 8*a^7*b^2*c^2*f^6*e^4 + 16*a^8*c^3*f^6*e^4) + 1/2*b*e^(-1)*log(abs(c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a))/(a^3*f^3) - 2*b*e^(-1)*log(abs(x*e + d))/(a^3*f^3) - 1/2*(2*a*b^2*c*d^4 - 6*a^2*c^2*d^4 + 2*a*b^3*d^2 - 7*a^2*b*c*d^2 + 2*(a*b^2*c*e^4 - 3*a^2*c^2*e^4)*x^4 + a^2*b^2 - 4*a^3*c + 8*(a*b^2*c*d*e^3 - 3*a^2*c^2*d*e^3)*x^3 + (12*a*b^2*c*d^2*e^2 - 36*a^2*c^2*d^2*e^2 + 2*a*b^3*e^2 - 7*a^2*b*c*e^2)*x^2 + 2*(4*a*b^2*c*d^3*e - 12*a^2*c^2*d^3*e + 2*a*b^3*d*e - 7*a^2*b*c*d*e)*x)*e^(-1)/((c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)*(b^2 - 4*a*c)*(x*e + d)^2*a^3*f^3)","B",0
653,1,2002,0,0.713874," ","integrate(1/(e*f*x+d*f)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(5 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{3} c e^{2} - 19 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a b c^{2} e^{2} - 10 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{3} c d e + 38 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a b c^{2} d e + 5 \, b^{3} c d^{2} - 19 \, a b c^{2} d^{2} + 5 \, b^{4} - 24 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(5 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{3} c e^{2} - 19 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a b c^{2} e^{2} - 10 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{3} c d e + 38 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a b c^{2} d e + 5 \, b^{3} c d^{2} - 19 \, a b c^{2} d^{2} + 5 \, b^{4} - 24 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(5 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{3} c e^{2} - 19 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a b c^{2} e^{2} - 10 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{3} c d e + 38 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a b c^{2} d e + 5 \, b^{3} c d^{2} - 19 \, a b c^{2} d^{2} + 5 \, b^{4} - 24 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(5 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{3} c e^{2} - 19 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a b c^{2} e^{2} - 10 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{3} c d e + 38 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a b c^{2} d e + 5 \, b^{3} c d^{2} - 19 \, a b c^{2} d^{2} + 5 \, b^{4} - 24 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}}}{4 \, {\left(a^{3} b^{2} f^{4} - 4 \, a^{4} c f^{4}\right)}} + \frac{b^{3} c x^{3} e^{3} - 3 \, a b c^{2} x^{3} e^{3} + 3 \, b^{3} c d x^{2} e^{2} - 9 \, a b c^{2} d x^{2} e^{2} + 3 \, b^{3} c d^{2} x e - 9 \, a b c^{2} d^{2} x e + b^{3} c d^{3} - 3 \, a b c^{2} d^{3} + b^{4} x e - 4 \, a b^{2} c x e + 2 \, a^{2} c^{2} x e + b^{4} d - 4 \, a b^{2} c d + 2 \, a^{2} c^{2} d}{2 \, {\left(a^{3} b^{2} f^{4} e - 4 \, a^{4} c f^{4} e\right)} {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)}} + \frac{{\left(6 \, b x^{2} e^{2} + 12 \, b d x e + 6 \, b d^{2} - a\right)} e^{\left(-1\right)}}{3 \, {\left(x e + d\right)}^{3} a^{3} f^{4}}"," ",0,"-1/4*((5*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^3*c*e^2 - 19*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*b*c^2*e^2 - 10*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^3*c*d*e + 38*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*b*c^2*d*e + 5*b^3*c*d^2 - 19*a*b*c^2*d^2 + 5*b^4 - 24*a*b^2*c + 14*a^2*c^2)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (5*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^3*c*e^2 - 19*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*b*c^2*e^2 - 10*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^3*c*d*e + 38*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*b*c^2*d*e + 5*b^3*c*d^2 - 19*a*b*c^2*d^2 + 5*b^4 - 24*a*b^2*c + 14*a^2*c^2)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (5*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^3*c*e^2 - 19*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*b*c^2*e^2 - 10*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^3*c*d*e + 38*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*b*c^2*d*e + 5*b^3*c*d^2 - 19*a*b*c^2*d^2 + 5*b^4 - 24*a*b^2*c + 14*a^2*c^2)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (5*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^3*c*e^2 - 19*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*b*c^2*e^2 - 10*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^3*c*d*e + 38*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*b*c^2*d*e + 5*b^3*c*d^2 - 19*a*b*c^2*d^2 + 5*b^4 - 24*a*b^2*c + 14*a^2*c^2)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))))/(a^3*b^2*f^4 - 4*a^4*c*f^4) + 1/2*(b^3*c*x^3*e^3 - 3*a*b*c^2*x^3*e^3 + 3*b^3*c*d*x^2*e^2 - 9*a*b*c^2*d*x^2*e^2 + 3*b^3*c*d^2*x*e - 9*a*b*c^2*d^2*x*e + b^3*c*d^3 - 3*a*b*c^2*d^3 + b^4*x*e - 4*a*b^2*c*x*e + 2*a^2*c^2*x*e + b^4*d - 4*a*b^2*c*d + 2*a^2*c^2*d)/((a^3*b^2*f^4*e - 4*a^4*c*f^4*e)*(c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)) + 1/3*(6*b*x^2*e^2 + 12*b*d*x*e + 6*b*d^2 - a)*e^(-1)/((x*e + d)^3*a^3*f^4)","B",0
654,1,1844,0,0.799006," ","integrate((e*f*x+d*f)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","\frac{3 \, {\left(\frac{{\left(4 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c f^{4} e^{2} - 8 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d f^{4} e + 4 \, b c d^{2} f^{4} - b^{2} f^{4} - 4 \, a c f^{4}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(4 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c f^{4} e^{2} - 8 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d f^{4} e + 4 \, b c d^{2} f^{4} - b^{2} f^{4} - 4 \, a c f^{4}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(4 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c f^{4} e^{2} - 8 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d f^{4} e + 4 \, b c d^{2} f^{4} - b^{2} f^{4} - 4 \, a c f^{4}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left(4 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b c f^{4} e^{2} - 8 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b c d f^{4} e + 4 \, b c d^{2} f^{4} - b^{2} f^{4} - 4 \, a c f^{4}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}}\right)}}{16 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}} - \frac{12 \, b c^{2} f^{4} x^{7} e^{7} + 84 \, b c^{2} d f^{4} x^{6} e^{6} + 252 \, b c^{2} d^{2} f^{4} x^{5} e^{5} + 420 \, b c^{2} d^{3} f^{4} x^{4} e^{4} + 420 \, b c^{2} d^{4} f^{4} x^{3} e^{3} + 252 \, b c^{2} d^{5} f^{4} x^{2} e^{2} + 84 \, b c^{2} d^{6} f^{4} x e + 12 \, b c^{2} d^{7} f^{4} + 19 \, b^{2} c f^{4} x^{5} e^{5} - 4 \, a c^{2} f^{4} x^{5} e^{5} + 95 \, b^{2} c d f^{4} x^{4} e^{4} - 20 \, a c^{2} d f^{4} x^{4} e^{4} + 190 \, b^{2} c d^{2} f^{4} x^{3} e^{3} - 40 \, a c^{2} d^{2} f^{4} x^{3} e^{3} + 190 \, b^{2} c d^{3} f^{4} x^{2} e^{2} - 40 \, a c^{2} d^{3} f^{4} x^{2} e^{2} + 95 \, b^{2} c d^{4} f^{4} x e - 20 \, a c^{2} d^{4} f^{4} x e + 19 \, b^{2} c d^{5} f^{4} - 4 \, a c^{2} d^{5} f^{4} + 5 \, b^{3} f^{4} x^{3} e^{3} + 16 \, a b c f^{4} x^{3} e^{3} + 15 \, b^{3} d f^{4} x^{2} e^{2} + 48 \, a b c d f^{4} x^{2} e^{2} + 15 \, b^{3} d^{2} f^{4} x e + 48 \, a b c d^{2} f^{4} x e + 5 \, b^{3} d^{3} f^{4} + 16 \, a b c d^{3} f^{4} + 3 \, a b^{2} f^{4} x e + 12 \, a^{2} c f^{4} x e + 3 \, a b^{2} d f^{4} + 12 \, a^{2} c d f^{4}}{8 \, {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)}^{2} {\left(b^{4} e - 8 \, a b^{2} c e + 16 \, a^{2} c^{2} e\right)}}"," ",0,"3/16*((4*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*f^4*e^2 - 8*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*f^4*e + 4*b*c*d^2*f^4 - b^2*f^4 - 4*a*c*f^4)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (4*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*f^4*e^2 - 8*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*f^4*e + 4*b*c*d^2*f^4 - b^2*f^4 - 4*a*c*f^4)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (4*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*f^4*e^2 - 8*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*f^4*e + 4*b*c*d^2*f^4 - b^2*f^4 - 4*a*c*f^4)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + (4*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b*c*f^4*e^2 - 8*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b*c*d*f^4*e + 4*b*c*d^2*f^4 - b^2*f^4 - 4*a*c*f^4)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))))/(b^4 - 8*a*b^2*c + 16*a^2*c^2) - 1/8*(12*b*c^2*f^4*x^7*e^7 + 84*b*c^2*d*f^4*x^6*e^6 + 252*b*c^2*d^2*f^4*x^5*e^5 + 420*b*c^2*d^3*f^4*x^4*e^4 + 420*b*c^2*d^4*f^4*x^3*e^3 + 252*b*c^2*d^5*f^4*x^2*e^2 + 84*b*c^2*d^6*f^4*x*e + 12*b*c^2*d^7*f^4 + 19*b^2*c*f^4*x^5*e^5 - 4*a*c^2*f^4*x^5*e^5 + 95*b^2*c*d*f^4*x^4*e^4 - 20*a*c^2*d*f^4*x^4*e^4 + 190*b^2*c*d^2*f^4*x^3*e^3 - 40*a*c^2*d^2*f^4*x^3*e^3 + 190*b^2*c*d^3*f^4*x^2*e^2 - 40*a*c^2*d^3*f^4*x^2*e^2 + 95*b^2*c*d^4*f^4*x*e - 20*a*c^2*d^4*f^4*x*e + 19*b^2*c*d^5*f^4 - 4*a*c^2*d^5*f^4 + 5*b^3*f^4*x^3*e^3 + 16*a*b*c*f^4*x^3*e^3 + 15*b^3*d*f^4*x^2*e^2 + 48*a*b*c*d*f^4*x^2*e^2 + 15*b^3*d^2*f^4*x*e + 48*a*b*c*d^2*f^4*x*e + 5*b^3*d^3*f^4 + 16*a*b*c*d^3*f^4 + 3*a*b^2*f^4*x*e + 12*a^2*c*f^4*x*e + 3*a*b^2*d*f^4 + 12*a^2*c*d*f^4)/((c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)^2*(b^4*e - 8*a*b^2*c*e + 16*a^2*c^2*e))","B",0
655,1,447,0,0.781051," ","integrate((e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","-\frac{3 \, b c f^{3} \arctan\left(\frac{2 \, c d^{2} f + 2 \, {\left(f x^{2} e + 2 \, d f x\right)} c e + b f}{\sqrt{-b^{2} + 4 \, a c} f}\right) e^{\left(-1\right)}}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{6 \, b c^{2} d^{6} f^{7} + 18 \, {\left(f x^{2} e + 2 \, d f x\right)} b c^{2} d^{4} f^{6} e + 9 \, b^{2} c d^{4} f^{7} + 18 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} b c^{2} d^{2} f^{5} e^{2} + 18 \, {\left(f x^{2} e + 2 \, d f x\right)} b^{2} c d^{2} f^{6} e + 2 \, b^{3} d^{2} f^{7} + 10 \, a b c d^{2} f^{7} + 6 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} b c^{2} f^{4} e^{3} + 9 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} b^{2} c f^{5} e^{2} + 2 \, {\left(f x^{2} e + 2 \, d f x\right)} b^{3} f^{6} e + 10 \, {\left(f x^{2} e + 2 \, d f x\right)} a b c f^{6} e + a b^{2} f^{7} + 8 \, a^{2} c f^{7}}{4 \, {\left(c d^{4} f^{2} + 2 \, {\left(f x^{2} e + 2 \, d f x\right)} c d^{2} f e + b d^{2} f^{2} + {\left(f x^{2} e + 2 \, d f x\right)}^{2} c e^{2} + {\left(f x^{2} e + 2 \, d f x\right)} b f e + a f^{2}\right)}^{2} {\left(b^{4} e - 8 \, a b^{2} c e + 16 \, a^{2} c^{2} e\right)}}"," ",0,"-3*b*c*f^3*arctan((2*c*d^2*f + 2*(f*x^2*e + 2*d*f*x)*c*e + b*f)/(sqrt(-b^2 + 4*a*c)*f))*e^(-1)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) - 1/4*(6*b*c^2*d^6*f^7 + 18*(f*x^2*e + 2*d*f*x)*b*c^2*d^4*f^6*e + 9*b^2*c*d^4*f^7 + 18*(f*x^2*e + 2*d*f*x)^2*b*c^2*d^2*f^5*e^2 + 18*(f*x^2*e + 2*d*f*x)*b^2*c*d^2*f^6*e + 2*b^3*d^2*f^7 + 10*a*b*c*d^2*f^7 + 6*(f*x^2*e + 2*d*f*x)^3*b*c^2*f^4*e^3 + 9*(f*x^2*e + 2*d*f*x)^2*b^2*c*f^5*e^2 + 2*(f*x^2*e + 2*d*f*x)*b^3*f^6*e + 10*(f*x^2*e + 2*d*f*x)*a*b*c*f^6*e + a*b^2*f^7 + 8*a^2*c*f^7)/((c*d^4*f^2 + 2*(f*x^2*e + 2*d*f*x)*c*d^2*f*e + b*d^2*f^2 + (f*x^2*e + 2*d*f*x)^2*c*e^2 + (f*x^2*e + 2*d*f*x)*b*f*e + a*f^2)^2*(b^4*e - 8*a*b^2*c*e + 16*a^2*c^2*e))","B",0
656,1,2527,0,0.794463," ","integrate((e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","-\frac{\frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{2} c f^{2} e^{2} + 20 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a c^{2} f^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{2} c d f^{2} e - 40 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a c^{2} d f^{2} e + b^{2} c d^{2} f^{2} + 20 \, a c^{2} d^{2} f^{2} + b^{3} f^{2} - 16 \, a b c f^{2}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{2} c f^{2} e^{2} + 20 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a c^{2} f^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{2} c d f^{2} e - 40 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a c^{2} d f^{2} e + b^{2} c d^{2} f^{2} + 20 \, a c^{2} d^{2} f^{2} + b^{3} f^{2} - 16 \, a b c f^{2}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} + \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{2} c f^{2} e^{2} + 20 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a c^{2} f^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{2} c d f^{2} e - 40 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a c^{2} d f^{2} e + b^{2} c d^{2} f^{2} + 20 \, a c^{2} d^{2} f^{2} + b^{3} f^{2} - 16 \, a b c f^{2}\right)} \log\left(d e^{\left(-1\right)} + x + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} + \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}} + \frac{{\left({\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} b^{2} c f^{2} e^{2} + 20 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} a c^{2} f^{2} e^{2} - 2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} b^{2} c d f^{2} e - 40 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)} a c^{2} d f^{2} e + b^{2} c d^{2} f^{2} + 20 \, a c^{2} d^{2} f^{2} + b^{3} f^{2} - 16 \, a b c f^{2}\right)} \log\left(d e^{\left(-1\right)} + x - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}{2 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{3} c e^{4} - 6 \, {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}^{2} c d e^{3} - 2 \, c d^{3} e - b d e + {\left(6 \, c d^{2} e^{2} + b e^{2}\right)} {\left(d e^{\left(-1\right)} - \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b e^{2} - \sqrt{b^{2} - 4 \, a c} e^{2}\right)} e^{\left(-4\right)}}{c}}\right)}}}{16 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)}} + \frac{b^{2} c^{2} f^{2} x^{7} e^{7} + 20 \, a c^{3} f^{2} x^{7} e^{7} + 7 \, b^{2} c^{2} d f^{2} x^{6} e^{6} + 140 \, a c^{3} d f^{2} x^{6} e^{6} + 21 \, b^{2} c^{2} d^{2} f^{2} x^{5} e^{5} + 420 \, a c^{3} d^{2} f^{2} x^{5} e^{5} + 35 \, b^{2} c^{2} d^{3} f^{2} x^{4} e^{4} + 700 \, a c^{3} d^{3} f^{2} x^{4} e^{4} + 35 \, b^{2} c^{2} d^{4} f^{2} x^{3} e^{3} + 700 \, a c^{3} d^{4} f^{2} x^{3} e^{3} + 21 \, b^{2} c^{2} d^{5} f^{2} x^{2} e^{2} + 420 \, a c^{3} d^{5} f^{2} x^{2} e^{2} + 7 \, b^{2} c^{2} d^{6} f^{2} x e + 140 \, a c^{3} d^{6} f^{2} x e + b^{2} c^{2} d^{7} f^{2} + 20 \, a c^{3} d^{7} f^{2} + 2 \, b^{3} c f^{2} x^{5} e^{5} + 28 \, a b c^{2} f^{2} x^{5} e^{5} + 10 \, b^{3} c d f^{2} x^{4} e^{4} + 140 \, a b c^{2} d f^{2} x^{4} e^{4} + 20 \, b^{3} c d^{2} f^{2} x^{3} e^{3} + 280 \, a b c^{2} d^{2} f^{2} x^{3} e^{3} + 20 \, b^{3} c d^{3} f^{2} x^{2} e^{2} + 280 \, a b c^{2} d^{3} f^{2} x^{2} e^{2} + 10 \, b^{3} c d^{4} f^{2} x e + 140 \, a b c^{2} d^{4} f^{2} x e + 2 \, b^{3} c d^{5} f^{2} + 28 \, a b c^{2} d^{5} f^{2} + b^{4} f^{2} x^{3} e^{3} + 5 \, a b^{2} c f^{2} x^{3} e^{3} + 36 \, a^{2} c^{2} f^{2} x^{3} e^{3} + 3 \, b^{4} d f^{2} x^{2} e^{2} + 15 \, a b^{2} c d f^{2} x^{2} e^{2} + 108 \, a^{2} c^{2} d f^{2} x^{2} e^{2} + 3 \, b^{4} d^{2} f^{2} x e + 15 \, a b^{2} c d^{2} f^{2} x e + 108 \, a^{2} c^{2} d^{2} f^{2} x e + b^{4} d^{3} f^{2} + 5 \, a b^{2} c d^{3} f^{2} + 36 \, a^{2} c^{2} d^{3} f^{2} - a b^{3} f^{2} x e + 16 \, a^{2} b c f^{2} x e - a b^{3} d f^{2} + 16 \, a^{2} b c d f^{2}}{8 \, {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)}^{2} {\left(a b^{4} e - 8 \, a^{2} b^{2} c e + 16 \, a^{3} c^{2} e\right)}}"," ",0,"-1/16*(((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^2*c*f^2*e^2 + 20*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*c^2*f^2*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^2*c*d*f^2*e - 40*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*c^2*d*f^2*e + b^2*c*d^2*f^2 + 20*a*c^2*d^2*f^2 + b^3*f^2 - 16*a*b*c*f^2)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^2*c*f^2*e^2 + 20*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*c^2*f^2*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^2*c*d*f^2*e - 40*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*c^2*d*f^2*e + b^2*c*d^2*f^2 + 20*a*c^2*d^2*f^2 + b^3*f^2 - 16*a*b*c*f^2)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 + sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^2*c*f^2*e^2 + 20*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*c^2*f^2*e^2 - 2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^2*c*d*f^2*e - 40*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*c^2*d*f^2*e + b^2*c*d^2*f^2 + 20*a*c^2*d^2*f^2 + b^3*f^2 - 16*a*b*c*f^2)*log(d*e^(-1) + x + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) + sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))) + ((d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*b^2*c*f^2*e^2 + 20*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*a*c^2*f^2*e^2 - 2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*b^2*c*d*f^2*e - 40*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))*a*c^2*d*f^2*e + b^2*c*d^2*f^2 + 20*a*c^2*d^2*f^2 + b^3*f^2 - 16*a*b*c*f^2)*log(d*e^(-1) + x - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))/(2*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^3*c*e^4 - 6*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))^2*c*d*e^3 - 2*c*d^3*e - b*d*e + (6*c*d^2*e^2 + b*e^2)*(d*e^(-1) - sqrt(1/2)*sqrt(-(b*e^2 - sqrt(b^2 - 4*a*c)*e^2)*e^(-4)/c))))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2) + 1/8*(b^2*c^2*f^2*x^7*e^7 + 20*a*c^3*f^2*x^7*e^7 + 7*b^2*c^2*d*f^2*x^6*e^6 + 140*a*c^3*d*f^2*x^6*e^6 + 21*b^2*c^2*d^2*f^2*x^5*e^5 + 420*a*c^3*d^2*f^2*x^5*e^5 + 35*b^2*c^2*d^3*f^2*x^4*e^4 + 700*a*c^3*d^3*f^2*x^4*e^4 + 35*b^2*c^2*d^4*f^2*x^3*e^3 + 700*a*c^3*d^4*f^2*x^3*e^3 + 21*b^2*c^2*d^5*f^2*x^2*e^2 + 420*a*c^3*d^5*f^2*x^2*e^2 + 7*b^2*c^2*d^6*f^2*x*e + 140*a*c^3*d^6*f^2*x*e + b^2*c^2*d^7*f^2 + 20*a*c^3*d^7*f^2 + 2*b^3*c*f^2*x^5*e^5 + 28*a*b*c^2*f^2*x^5*e^5 + 10*b^3*c*d*f^2*x^4*e^4 + 140*a*b*c^2*d*f^2*x^4*e^4 + 20*b^3*c*d^2*f^2*x^3*e^3 + 280*a*b*c^2*d^2*f^2*x^3*e^3 + 20*b^3*c*d^3*f^2*x^2*e^2 + 280*a*b*c^2*d^3*f^2*x^2*e^2 + 10*b^3*c*d^4*f^2*x*e + 140*a*b*c^2*d^4*f^2*x*e + 2*b^3*c*d^5*f^2 + 28*a*b*c^2*d^5*f^2 + b^4*f^2*x^3*e^3 + 5*a*b^2*c*f^2*x^3*e^3 + 36*a^2*c^2*f^2*x^3*e^3 + 3*b^4*d*f^2*x^2*e^2 + 15*a*b^2*c*d*f^2*x^2*e^2 + 108*a^2*c^2*d*f^2*x^2*e^2 + 3*b^4*d^2*f^2*x*e + 15*a*b^2*c*d^2*f^2*x*e + 108*a^2*c^2*d^2*f^2*x*e + b^4*d^3*f^2 + 5*a*b^2*c*d^3*f^2 + 36*a^2*c^2*d^3*f^2 - a*b^3*f^2*x*e + 16*a^2*b*c*f^2*x*e - a*b^3*d*f^2 + 16*a^2*b*c*d*f^2)/((c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)^2*(a*b^4*e - 8*a^2*b^2*c*e + 16*a^3*c^2*e))","B",0
657,1,445,0,0.690161," ","integrate((e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","\frac{6 \, c^{2} f \arctan\left(\frac{2 \, c d^{2} f + 2 \, {\left(f x^{2} e + 2 \, d f x\right)} c e + b f}{\sqrt{-b^{2} + 4 \, a c} f}\right) e^{\left(-1\right)}}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{12 \, c^{3} d^{6} f^{5} + 36 \, {\left(f x^{2} e + 2 \, d f x\right)} c^{3} d^{4} f^{4} e + 18 \, b c^{2} d^{4} f^{5} + 36 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} c^{3} d^{2} f^{3} e^{2} + 36 \, {\left(f x^{2} e + 2 \, d f x\right)} b c^{2} d^{2} f^{4} e + 4 \, b^{2} c d^{2} f^{5} + 20 \, a c^{2} d^{2} f^{5} + 12 \, {\left(f x^{2} e + 2 \, d f x\right)}^{3} c^{3} f^{2} e^{3} + 18 \, {\left(f x^{2} e + 2 \, d f x\right)}^{2} b c^{2} f^{3} e^{2} + 4 \, {\left(f x^{2} e + 2 \, d f x\right)} b^{2} c f^{4} e + 20 \, {\left(f x^{2} e + 2 \, d f x\right)} a c^{2} f^{4} e - b^{3} f^{5} + 10 \, a b c f^{5}}{4 \, {\left(c d^{4} f^{2} + 2 \, {\left(f x^{2} e + 2 \, d f x\right)} c d^{2} f e + b d^{2} f^{2} + {\left(f x^{2} e + 2 \, d f x\right)}^{2} c e^{2} + {\left(f x^{2} e + 2 \, d f x\right)} b f e + a f^{2}\right)}^{2} {\left(b^{4} e - 8 \, a b^{2} c e + 16 \, a^{2} c^{2} e\right)}}"," ",0,"6*c^2*f*arctan((2*c*d^2*f + 2*(f*x^2*e + 2*d*f*x)*c*e + b*f)/(sqrt(-b^2 + 4*a*c)*f))*e^(-1)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/4*(12*c^3*d^6*f^5 + 36*(f*x^2*e + 2*d*f*x)*c^3*d^4*f^4*e + 18*b*c^2*d^4*f^5 + 36*(f*x^2*e + 2*d*f*x)^2*c^3*d^2*f^3*e^2 + 36*(f*x^2*e + 2*d*f*x)*b*c^2*d^2*f^4*e + 4*b^2*c*d^2*f^5 + 20*a*c^2*d^2*f^5 + 12*(f*x^2*e + 2*d*f*x)^3*c^3*f^2*e^3 + 18*(f*x^2*e + 2*d*f*x)^2*b*c^2*f^3*e^2 + 4*(f*x^2*e + 2*d*f*x)*b^2*c*f^4*e + 20*(f*x^2*e + 2*d*f*x)*a*c^2*f^4*e - b^3*f^5 + 10*a*b*c*f^5)/((c*d^4*f^2 + 2*(f*x^2*e + 2*d*f*x)*c*d^2*f*e + b*d^2*f^2 + (f*x^2*e + 2*d*f*x)^2*c*e^2 + (f*x^2*e + 2*d*f*x)*b*f*e + a*f^2)^2*(b^4*e - 8*a*b^2*c*e + 16*a^2*c^2*e))","B",0
658,1,1044,0,1.699525," ","integrate(1/(e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","-\frac{{\left(a^{3} b^{7} c f e^{3} - 14 \, a^{4} b^{5} c^{2} f e^{3} + 70 \, a^{5} b^{3} c^{3} f e^{3} - 120 \, a^{6} b c^{4} f e^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left({\left| b x^{2} e^{2} + 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e + b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} + 2 \, a \right|}\right) - {\left(a^{3} b^{7} c f e^{3} - 14 \, a^{4} b^{5} c^{2} f e^{3} + 70 \, a^{5} b^{3} c^{3} f e^{3} - 120 \, a^{6} b c^{4} f e^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left({\left| -b x^{2} e^{2} - 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e - b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} - 2 \, a \right|}\right)}{4 \, {\left(a^{6} b^{8} c f^{2} e^{4} - 16 \, a^{7} b^{6} c^{2} f^{2} e^{4} + 96 \, a^{8} b^{4} c^{3} f^{2} e^{4} - 256 \, a^{9} b^{2} c^{4} f^{2} e^{4} + 256 \, a^{10} c^{5} f^{2} e^{4}\right)}} - \frac{e^{\left(-1\right)} \log\left({\left| c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a \right|}\right)}{4 \, a^{3} f} + \frac{e^{\left(-1\right)} \log\left({\left| x e + d \right|}\right)}{a^{3} f} + \frac{{\left(2 \, a b^{3} c^{2} d^{6} - 14 \, a^{2} b c^{3} d^{6} + 4 \, a b^{4} c d^{4} - 29 \, a^{2} b^{2} c^{2} d^{4} + 16 \, a^{3} c^{3} d^{4} + 2 \, a b^{5} d^{2} - 12 \, a^{2} b^{3} c d^{2} - 2 \, a^{3} b c^{2} d^{2} + 2 \, {\left(a b^{3} c^{2} e^{6} - 7 \, a^{2} b c^{3} e^{6}\right)} x^{6} + 3 \, a^{2} b^{4} - 21 \, a^{3} b^{2} c + 24 \, a^{4} c^{2} + 12 \, {\left(a b^{3} c^{2} d e^{5} - 7 \, a^{2} b c^{3} d e^{5}\right)} x^{5} + {\left(30 \, a b^{3} c^{2} d^{2} e^{4} - 210 \, a^{2} b c^{3} d^{2} e^{4} + 4 \, a b^{4} c e^{4} - 29 \, a^{2} b^{2} c^{2} e^{4} + 16 \, a^{3} c^{3} e^{4}\right)} x^{4} + 4 \, {\left(10 \, a b^{3} c^{2} d^{3} e^{3} - 70 \, a^{2} b c^{3} d^{3} e^{3} + 4 \, a b^{4} c d e^{3} - 29 \, a^{2} b^{2} c^{2} d e^{3} + 16 \, a^{3} c^{3} d e^{3}\right)} x^{3} + 2 \, {\left(15 \, a b^{3} c^{2} d^{4} e^{2} - 105 \, a^{2} b c^{3} d^{4} e^{2} + 12 \, a b^{4} c d^{2} e^{2} - 87 \, a^{2} b^{2} c^{2} d^{2} e^{2} + 48 \, a^{3} c^{3} d^{2} e^{2} + a b^{5} e^{2} - 6 \, a^{2} b^{3} c e^{2} - a^{3} b c^{2} e^{2}\right)} x^{2} + 4 \, {\left(3 \, a b^{3} c^{2} d^{5} e - 21 \, a^{2} b c^{3} d^{5} e + 4 \, a b^{4} c d^{3} e - 29 \, a^{2} b^{2} c^{2} d^{3} e + 16 \, a^{3} c^{3} d^{3} e + a b^{5} d e - 6 \, a^{2} b^{3} c d e - a^{3} b c^{2} d e\right)} x\right)} e^{\left(-1\right)}}{4 \, {\left(c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}^{2} a^{3} f}"," ",0,"-1/4*((a^3*b^7*c*f*e^3 - 14*a^4*b^5*c^2*f*e^3 + 70*a^5*b^3*c^3*f*e^3 - 120*a^6*b*c^4*f*e^3)*sqrt(b^2 - 4*a*c)*log(abs(b*x^2*e^2 + 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e + b*d^2 + sqrt(b^2 - 4*a*c)*d^2 + 2*a)) - (a^3*b^7*c*f*e^3 - 14*a^4*b^5*c^2*f*e^3 + 70*a^5*b^3*c^3*f*e^3 - 120*a^6*b*c^4*f*e^3)*sqrt(b^2 - 4*a*c)*log(abs(-b*x^2*e^2 - 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e - b*d^2 + sqrt(b^2 - 4*a*c)*d^2 - 2*a)))/(a^6*b^8*c*f^2*e^4 - 16*a^7*b^6*c^2*f^2*e^4 + 96*a^8*b^4*c^3*f^2*e^4 - 256*a^9*b^2*c^4*f^2*e^4 + 256*a^10*c^5*f^2*e^4) - 1/4*e^(-1)*log(abs(c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a))/(a^3*f) + e^(-1)*log(abs(x*e + d))/(a^3*f) + 1/4*(2*a*b^3*c^2*d^6 - 14*a^2*b*c^3*d^6 + 4*a*b^4*c*d^4 - 29*a^2*b^2*c^2*d^4 + 16*a^3*c^3*d^4 + 2*a*b^5*d^2 - 12*a^2*b^3*c*d^2 - 2*a^3*b*c^2*d^2 + 2*(a*b^3*c^2*e^6 - 7*a^2*b*c^3*e^6)*x^6 + 3*a^2*b^4 - 21*a^3*b^2*c + 24*a^4*c^2 + 12*(a*b^3*c^2*d*e^5 - 7*a^2*b*c^3*d*e^5)*x^5 + (30*a*b^3*c^2*d^2*e^4 - 210*a^2*b*c^3*d^2*e^4 + 4*a*b^4*c*e^4 - 29*a^2*b^2*c^2*e^4 + 16*a^3*c^3*e^4)*x^4 + 4*(10*a*b^3*c^2*d^3*e^3 - 70*a^2*b*c^3*d^3*e^3 + 4*a*b^4*c*d*e^3 - 29*a^2*b^2*c^2*d*e^3 + 16*a^3*c^3*d*e^3)*x^3 + 2*(15*a*b^3*c^2*d^4*e^2 - 105*a^2*b*c^3*d^4*e^2 + 12*a*b^4*c*d^2*e^2 - 87*a^2*b^2*c^2*d^2*e^2 + 48*a^3*c^3*d^2*e^2 + a*b^5*e^2 - 6*a^2*b^3*c*e^2 - a^3*b*c^2*e^2)*x^2 + 4*(3*a*b^3*c^2*d^5*e - 21*a^2*b*c^3*d^5*e + 4*a*b^4*c*d^3*e - 29*a^2*b^2*c^2*d^3*e + 16*a^3*c^3*d^3*e + a*b^5*d*e - 6*a^2*b^3*c*d*e - a^3*b*c^2*d*e)*x)*e^(-1)/((c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a)^2*(b^2 - 4*a*c)^2*a^3*f)","B",0
659,1,1658,0,1.419463," ","integrate(1/(e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","-\frac{\frac{7 \, b^{4} c^{2} e^{\left(-1\right)}}{{\left(f x e + d f\right)} f} - \frac{47 \, a b^{2} c^{3} e^{\left(-1\right)}}{{\left(f x e + d f\right)} f} + \frac{52 \, a^{2} c^{4} e^{\left(-1\right)}}{{\left(f x e + d f\right)} f} + \frac{14 \, b^{5} c f e^{\left(-1\right)}}{{\left(f x e + d f\right)}^{3}} - \frac{99 \, a b^{3} c^{2} f e^{\left(-1\right)}}{{\left(f x e + d f\right)}^{3}} + \frac{136 \, a^{2} b c^{3} f e^{\left(-1\right)}}{{\left(f x e + d f\right)}^{3}} + \frac{7 \, b^{6} f^{3} e^{\left(-1\right)}}{{\left(f x e + d f\right)}^{5}} - \frac{43 \, a b^{4} c f^{3} e^{\left(-1\right)}}{{\left(f x e + d f\right)}^{5}} + \frac{25 \, a^{2} b^{2} c^{2} f^{3} e^{\left(-1\right)}}{{\left(f x e + d f\right)}^{5}} + \frac{68 \, a^{3} c^{3} f^{3} e^{\left(-1\right)}}{{\left(f x e + d f\right)}^{5}} + \frac{9 \, a b^{5} f^{5} e^{\left(-1\right)}}{{\left(f x e + d f\right)}^{7}} - \frac{66 \, a^{2} b^{3} c f^{5} e^{\left(-1\right)}}{{\left(f x e + d f\right)}^{7}} + \frac{108 \, a^{3} b c^{2} f^{5} e^{\left(-1\right)}}{{\left(f x e + d f\right)}^{7}}}{8 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} {\left(c + \frac{b f^{2}}{{\left(f x e + d f\right)}^{2}} + \frac{a f^{4}}{{\left(f x e + d f\right)}^{4}}\right)}^{2}} - \frac{e^{\left(-1\right)}}{{\left(f x e + d f\right)} a^{3} f} + \frac{3 \, {\left({\left(5 \, a^{6} b^{13} - 112 \, a^{7} b^{11} c + 1030 \, a^{8} b^{9} c^{2} - 4928 \, a^{9} b^{7} c^{3} + 12736 \, a^{10} b^{5} c^{4} - 16384 \, a^{11} b^{3} c^{5} + 7680 \, a^{12} b c^{6}\right)} \sqrt{2 \, a b + 2 \, \sqrt{b^{2} - 4 \, a c} a} f^{8} e^{4} + 2 \, {\left(5 \, a^{4} b^{6} c - 57 \, a^{5} b^{4} c^{2} + 208 \, a^{6} b^{2} c^{3} - 240 \, a^{7} c^{4}\right)} \sqrt{2 \, a b + 2 \, \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} f^{4} {\left| a^{3} b^{4} f^{4} e^{2} - 8 \, a^{4} b^{2} c f^{4} e^{2} + 16 \, a^{5} c^{2} f^{4} e^{2} \right|} e^{2} - {\left(a^{3} b^{4} f^{4} e^{2} - 8 \, a^{4} b^{2} c f^{4} e^{2} + 16 \, a^{5} c^{2} f^{4} e^{2}\right)}^{2} {\left(5 \, b^{5} - 42 \, a b^{3} c + 92 \, a^{2} b c^{2}\right)} \sqrt{2 \, a b + 2 \, \sqrt{b^{2} - 4 \, a c} a}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} e^{\left(-1\right)}}{{\left(f x e + d f\right)} f \sqrt{\frac{a^{3} b^{5} f^{4} e^{2} - 8 \, a^{4} b^{3} c f^{4} e^{2} + 16 \, a^{5} b c^{2} f^{4} e^{2} + \sqrt{{\left(a^{3} b^{5} f^{4} e^{2} - 8 \, a^{4} b^{3} c f^{4} e^{2} + 16 \, a^{5} b c^{2} f^{4} e^{2}\right)}^{2} - 4 \, {\left(a^{4} b^{4} f^{8} e^{4} - 8 \, a^{5} b^{2} c f^{8} e^{4} + 16 \, a^{6} c^{2} f^{8} e^{4}\right)} {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)}}}{a^{4} b^{4} f^{8} e^{4} - 8 \, a^{5} b^{2} c f^{8} e^{4} + 16 \, a^{6} c^{2} f^{8} e^{4}}}}\right) e^{\left(-3\right)}}{64 \, {\left(a^{7} b^{6} c - 12 \, a^{8} b^{4} c^{2} + 48 \, a^{9} b^{2} c^{3} - 64 \, a^{10} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} f^{6} {\left| a^{3} b^{4} f^{4} e^{2} - 8 \, a^{4} b^{2} c f^{4} e^{2} + 16 \, a^{5} c^{2} f^{4} e^{2} \right|} {\left| a \right|}} - \frac{3 \, {\left({\left(5 \, a^{6} b^{13} - 112 \, a^{7} b^{11} c + 1030 \, a^{8} b^{9} c^{2} - 4928 \, a^{9} b^{7} c^{3} + 12736 \, a^{10} b^{5} c^{4} - 16384 \, a^{11} b^{3} c^{5} + 7680 \, a^{12} b c^{6}\right)} \sqrt{2 \, a b - 2 \, \sqrt{b^{2} - 4 \, a c} a} f^{8} e^{4} - 2 \, {\left(5 \, a^{4} b^{6} c - 57 \, a^{5} b^{4} c^{2} + 208 \, a^{6} b^{2} c^{3} - 240 \, a^{7} c^{4}\right)} \sqrt{2 \, a b - 2 \, \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} f^{4} {\left| a^{3} b^{4} f^{4} e^{2} - 8 \, a^{4} b^{2} c f^{4} e^{2} + 16 \, a^{5} c^{2} f^{4} e^{2} \right|} e^{2} - {\left(a^{3} b^{4} f^{4} e^{2} - 8 \, a^{4} b^{2} c f^{4} e^{2} + 16 \, a^{5} c^{2} f^{4} e^{2}\right)}^{2} {\left(5 \, b^{5} - 42 \, a b^{3} c + 92 \, a^{2} b c^{2}\right)} \sqrt{2 \, a b - 2 \, \sqrt{b^{2} - 4 \, a c} a}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} e^{\left(-1\right)}}{{\left(f x e + d f\right)} f \sqrt{\frac{a^{3} b^{5} f^{4} e^{2} - 8 \, a^{4} b^{3} c f^{4} e^{2} + 16 \, a^{5} b c^{2} f^{4} e^{2} - \sqrt{{\left(a^{3} b^{5} f^{4} e^{2} - 8 \, a^{4} b^{3} c f^{4} e^{2} + 16 \, a^{5} b c^{2} f^{4} e^{2}\right)}^{2} - 4 \, {\left(a^{4} b^{4} f^{8} e^{4} - 8 \, a^{5} b^{2} c f^{8} e^{4} + 16 \, a^{6} c^{2} f^{8} e^{4}\right)} {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)}}}{a^{4} b^{4} f^{8} e^{4} - 8 \, a^{5} b^{2} c f^{8} e^{4} + 16 \, a^{6} c^{2} f^{8} e^{4}}}}\right) e^{\left(-3\right)}}{64 \, {\left(a^{7} b^{6} c - 12 \, a^{8} b^{4} c^{2} + 48 \, a^{9} b^{2} c^{3} - 64 \, a^{10} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} f^{6} {\left| a^{3} b^{4} f^{4} e^{2} - 8 \, a^{4} b^{2} c f^{4} e^{2} + 16 \, a^{5} c^{2} f^{4} e^{2} \right|} {\left| a \right|}}"," ",0,"-1/8*(7*b^4*c^2*e^(-1)/((f*x*e + d*f)*f) - 47*a*b^2*c^3*e^(-1)/((f*x*e + d*f)*f) + 52*a^2*c^4*e^(-1)/((f*x*e + d*f)*f) + 14*b^5*c*f*e^(-1)/(f*x*e + d*f)^3 - 99*a*b^3*c^2*f*e^(-1)/(f*x*e + d*f)^3 + 136*a^2*b*c^3*f*e^(-1)/(f*x*e + d*f)^3 + 7*b^6*f^3*e^(-1)/(f*x*e + d*f)^5 - 43*a*b^4*c*f^3*e^(-1)/(f*x*e + d*f)^5 + 25*a^2*b^2*c^2*f^3*e^(-1)/(f*x*e + d*f)^5 + 68*a^3*c^3*f^3*e^(-1)/(f*x*e + d*f)^5 + 9*a*b^5*f^5*e^(-1)/(f*x*e + d*f)^7 - 66*a^2*b^3*c*f^5*e^(-1)/(f*x*e + d*f)^7 + 108*a^3*b*c^2*f^5*e^(-1)/(f*x*e + d*f)^7)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*(c + b*f^2/(f*x*e + d*f)^2 + a*f^4/(f*x*e + d*f)^4)^2) - e^(-1)/((f*x*e + d*f)*a^3*f) + 3/64*((5*a^6*b^13 - 112*a^7*b^11*c + 1030*a^8*b^9*c^2 - 4928*a^9*b^7*c^3 + 12736*a^10*b^5*c^4 - 16384*a^11*b^3*c^5 + 7680*a^12*b*c^6)*sqrt(2*a*b + 2*sqrt(b^2 - 4*a*c)*a)*f^8*e^4 + 2*(5*a^4*b^6*c - 57*a^5*b^4*c^2 + 208*a^6*b^2*c^3 - 240*a^7*c^4)*sqrt(2*a*b + 2*sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*f^4*abs(a^3*b^4*f^4*e^2 - 8*a^4*b^2*c*f^4*e^2 + 16*a^5*c^2*f^4*e^2)*e^2 - (a^3*b^4*f^4*e^2 - 8*a^4*b^2*c*f^4*e^2 + 16*a^5*c^2*f^4*e^2)^2*(5*b^5 - 42*a*b^3*c + 92*a^2*b*c^2)*sqrt(2*a*b + 2*sqrt(b^2 - 4*a*c)*a))*arctan(2*sqrt(1/2)*e^(-1)/((f*x*e + d*f)*f*sqrt((a^3*b^5*f^4*e^2 - 8*a^4*b^3*c*f^4*e^2 + 16*a^5*b*c^2*f^4*e^2 + sqrt((a^3*b^5*f^4*e^2 - 8*a^4*b^3*c*f^4*e^2 + 16*a^5*b*c^2*f^4*e^2)^2 - 4*(a^4*b^4*f^8*e^4 - 8*a^5*b^2*c*f^8*e^4 + 16*a^6*c^2*f^8*e^4)*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/(a^4*b^4*f^8*e^4 - 8*a^5*b^2*c*f^8*e^4 + 16*a^6*c^2*f^8*e^4))))*e^(-3)/((a^7*b^6*c - 12*a^8*b^4*c^2 + 48*a^9*b^2*c^3 - 64*a^10*c^4)*sqrt(b^2 - 4*a*c)*f^6*abs(a^3*b^4*f^4*e^2 - 8*a^4*b^2*c*f^4*e^2 + 16*a^5*c^2*f^4*e^2)*abs(a)) - 3/64*((5*a^6*b^13 - 112*a^7*b^11*c + 1030*a^8*b^9*c^2 - 4928*a^9*b^7*c^3 + 12736*a^10*b^5*c^4 - 16384*a^11*b^3*c^5 + 7680*a^12*b*c^6)*sqrt(2*a*b - 2*sqrt(b^2 - 4*a*c)*a)*f^8*e^4 - 2*(5*a^4*b^6*c - 57*a^5*b^4*c^2 + 208*a^6*b^2*c^3 - 240*a^7*c^4)*sqrt(2*a*b - 2*sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*f^4*abs(a^3*b^4*f^4*e^2 - 8*a^4*b^2*c*f^4*e^2 + 16*a^5*c^2*f^4*e^2)*e^2 - (a^3*b^4*f^4*e^2 - 8*a^4*b^2*c*f^4*e^2 + 16*a^5*c^2*f^4*e^2)^2*(5*b^5 - 42*a*b^3*c + 92*a^2*b*c^2)*sqrt(2*a*b - 2*sqrt(b^2 - 4*a*c)*a))*arctan(2*sqrt(1/2)*e^(-1)/((f*x*e + d*f)*f*sqrt((a^3*b^5*f^4*e^2 - 8*a^4*b^3*c*f^4*e^2 + 16*a^5*b*c^2*f^4*e^2 - sqrt((a^3*b^5*f^4*e^2 - 8*a^4*b^3*c*f^4*e^2 + 16*a^5*b*c^2*f^4*e^2)^2 - 4*(a^4*b^4*f^8*e^4 - 8*a^5*b^2*c*f^8*e^4 + 16*a^6*c^2*f^8*e^4)*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/(a^4*b^4*f^8*e^4 - 8*a^5*b^2*c*f^8*e^4 + 16*a^6*c^2*f^8*e^4))))*e^(-3)/((a^7*b^6*c - 12*a^8*b^4*c^2 + 48*a^9*b^2*c^3 - 64*a^10*c^4)*sqrt(b^2 - 4*a*c)*f^6*abs(a^3*b^4*f^4*e^2 - 8*a^4*b^2*c*f^4*e^2 + 16*a^5*c^2*f^4*e^2)*abs(a))","B",0
660,1,1735,0,1.627833," ","integrate(1/(e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""giac"")","\frac{3 \, {\left({\left(a^{4} b^{8} c f^{3} e^{3} - 14 \, a^{5} b^{6} c^{2} f^{3} e^{3} + 70 \, a^{6} b^{4} c^{3} f^{3} e^{3} - 140 \, a^{7} b^{2} c^{4} f^{3} e^{3} + 80 \, a^{8} c^{5} f^{3} e^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left({\left| b x^{2} e^{2} + 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e + b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} + 2 \, a \right|}\right) - {\left(a^{4} b^{8} c f^{3} e^{3} - 14 \, a^{5} b^{6} c^{2} f^{3} e^{3} + 70 \, a^{6} b^{4} c^{3} f^{3} e^{3} - 140 \, a^{7} b^{2} c^{4} f^{3} e^{3} + 80 \, a^{8} c^{5} f^{3} e^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left({\left| -b x^{2} e^{2} - 2 \, b d x e + \sqrt{b^{2} - 4 \, a c} x^{2} e^{2} + 2 \, \sqrt{b^{2} - 4 \, a c} d x e - b d^{2} + \sqrt{b^{2} - 4 \, a c} d^{2} - 2 \, a \right|}\right)\right)}}{4 \, {\left(a^{8} b^{8} c f^{6} e^{4} - 16 \, a^{9} b^{6} c^{2} f^{6} e^{4} + 96 \, a^{10} b^{4} c^{3} f^{6} e^{4} - 256 \, a^{11} b^{2} c^{4} f^{6} e^{4} + 256 \, a^{12} c^{5} f^{6} e^{4}\right)}} - \frac{6 \, b^{4} c^{2} x^{8} e^{8} - 42 \, a b^{2} c^{3} x^{8} e^{8} + 60 \, a^{2} c^{4} x^{8} e^{8} + 48 \, b^{4} c^{2} d x^{7} e^{7} - 336 \, a b^{2} c^{3} d x^{7} e^{7} + 480 \, a^{2} c^{4} d x^{7} e^{7} + 168 \, b^{4} c^{2} d^{2} x^{6} e^{6} - 1176 \, a b^{2} c^{3} d^{2} x^{6} e^{6} + 1680 \, a^{2} c^{4} d^{2} x^{6} e^{6} + 336 \, b^{4} c^{2} d^{3} x^{5} e^{5} - 2352 \, a b^{2} c^{3} d^{3} x^{5} e^{5} + 3360 \, a^{2} c^{4} d^{3} x^{5} e^{5} + 420 \, b^{4} c^{2} d^{4} x^{4} e^{4} - 2940 \, a b^{2} c^{3} d^{4} x^{4} e^{4} + 4200 \, a^{2} c^{4} d^{4} x^{4} e^{4} + 336 \, b^{4} c^{2} d^{5} x^{3} e^{3} - 2352 \, a b^{2} c^{3} d^{5} x^{3} e^{3} + 3360 \, a^{2} c^{4} d^{5} x^{3} e^{3} + 168 \, b^{4} c^{2} d^{6} x^{2} e^{2} - 1176 \, a b^{2} c^{3} d^{6} x^{2} e^{2} + 1680 \, a^{2} c^{4} d^{6} x^{2} e^{2} + 48 \, b^{4} c^{2} d^{7} x e - 336 \, a b^{2} c^{3} d^{7} x e + 480 \, a^{2} c^{4} d^{7} x e + 6 \, b^{4} c^{2} d^{8} - 42 \, a b^{2} c^{3} d^{8} + 60 \, a^{2} c^{4} d^{8} + 12 \, b^{5} c x^{6} e^{6} - 87 \, a b^{3} c^{2} x^{6} e^{6} + 138 \, a^{2} b c^{3} x^{6} e^{6} + 72 \, b^{5} c d x^{5} e^{5} - 522 \, a b^{3} c^{2} d x^{5} e^{5} + 828 \, a^{2} b c^{3} d x^{5} e^{5} + 180 \, b^{5} c d^{2} x^{4} e^{4} - 1305 \, a b^{3} c^{2} d^{2} x^{4} e^{4} + 2070 \, a^{2} b c^{3} d^{2} x^{4} e^{4} + 240 \, b^{5} c d^{3} x^{3} e^{3} - 1740 \, a b^{3} c^{2} d^{3} x^{3} e^{3} + 2760 \, a^{2} b c^{3} d^{3} x^{3} e^{3} + 180 \, b^{5} c d^{4} x^{2} e^{2} - 1305 \, a b^{3} c^{2} d^{4} x^{2} e^{2} + 2070 \, a^{2} b c^{3} d^{4} x^{2} e^{2} + 72 \, b^{5} c d^{5} x e - 522 \, a b^{3} c^{2} d^{5} x e + 828 \, a^{2} b c^{3} d^{5} x e + 12 \, b^{5} c d^{6} - 87 \, a b^{3} c^{2} d^{6} + 138 \, a^{2} b c^{3} d^{6} + 6 \, b^{6} x^{4} e^{4} - 36 \, a b^{4} c x^{4} e^{4} + 14 \, a^{2} b^{2} c^{2} x^{4} e^{4} + 100 \, a^{3} c^{3} x^{4} e^{4} + 24 \, b^{6} d x^{3} e^{3} - 144 \, a b^{4} c d x^{3} e^{3} + 56 \, a^{2} b^{2} c^{2} d x^{3} e^{3} + 400 \, a^{3} c^{3} d x^{3} e^{3} + 36 \, b^{6} d^{2} x^{2} e^{2} - 216 \, a b^{4} c d^{2} x^{2} e^{2} + 84 \, a^{2} b^{2} c^{2} d^{2} x^{2} e^{2} + 600 \, a^{3} c^{3} d^{2} x^{2} e^{2} + 24 \, b^{6} d^{3} x e - 144 \, a b^{4} c d^{3} x e + 56 \, a^{2} b^{2} c^{2} d^{3} x e + 400 \, a^{3} c^{3} d^{3} x e + 6 \, b^{6} d^{4} - 36 \, a b^{4} c d^{4} + 14 \, a^{2} b^{2} c^{2} d^{4} + 100 \, a^{3} c^{3} d^{4} + 9 \, a b^{5} x^{2} e^{2} - 68 \, a^{2} b^{3} c x^{2} e^{2} + 122 \, a^{3} b c^{2} x^{2} e^{2} + 18 \, a b^{5} d x e - 136 \, a^{2} b^{3} c d x e + 244 \, a^{3} b c^{2} d x e + 9 \, a b^{5} d^{2} - 68 \, a^{2} b^{3} c d^{2} + 122 \, a^{3} b c^{2} d^{2} + 2 \, a^{2} b^{4} - 16 \, a^{3} b^{2} c + 32 \, a^{4} c^{2}}{4 \, {\left(a^{3} b^{4} f^{3} e - 8 \, a^{4} b^{2} c f^{3} e + 16 \, a^{5} c^{2} f^{3} e\right)} {\left(c x^{5} e^{5} + 5 \, c d x^{4} e^{4} + 10 \, c d^{2} x^{3} e^{3} + 10 \, c d^{3} x^{2} e^{2} + 5 \, c d^{4} x e + c d^{5} + b x^{3} e^{3} + 3 \, b d x^{2} e^{2} + 3 \, b d^{2} x e + b d^{3} + a x e + a d\right)}^{2}} + \frac{3 \, b e^{\left(-1\right)} \log\left({\left| c x^{4} e^{4} + 4 \, c d x^{3} e^{3} + 6 \, c d^{2} x^{2} e^{2} + 4 \, c d^{3} x e + c d^{4} + b x^{2} e^{2} + 2 \, b d x e + b d^{2} + a \right|}\right)}{4 \, a^{4} f^{3}} - \frac{3 \, b e^{\left(-1\right)} \log\left({\left| x e + d \right|}\right)}{a^{4} f^{3}}"," ",0,"3/4*((a^4*b^8*c*f^3*e^3 - 14*a^5*b^6*c^2*f^3*e^3 + 70*a^6*b^4*c^3*f^3*e^3 - 140*a^7*b^2*c^4*f^3*e^3 + 80*a^8*c^5*f^3*e^3)*sqrt(b^2 - 4*a*c)*log(abs(b*x^2*e^2 + 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e + b*d^2 + sqrt(b^2 - 4*a*c)*d^2 + 2*a)) - (a^4*b^8*c*f^3*e^3 - 14*a^5*b^6*c^2*f^3*e^3 + 70*a^6*b^4*c^3*f^3*e^3 - 140*a^7*b^2*c^4*f^3*e^3 + 80*a^8*c^5*f^3*e^3)*sqrt(b^2 - 4*a*c)*log(abs(-b*x^2*e^2 - 2*b*d*x*e + sqrt(b^2 - 4*a*c)*x^2*e^2 + 2*sqrt(b^2 - 4*a*c)*d*x*e - b*d^2 + sqrt(b^2 - 4*a*c)*d^2 - 2*a)))/(a^8*b^8*c*f^6*e^4 - 16*a^9*b^6*c^2*f^6*e^4 + 96*a^10*b^4*c^3*f^6*e^4 - 256*a^11*b^2*c^4*f^6*e^4 + 256*a^12*c^5*f^6*e^4) - 1/4*(6*b^4*c^2*x^8*e^8 - 42*a*b^2*c^3*x^8*e^8 + 60*a^2*c^4*x^8*e^8 + 48*b^4*c^2*d*x^7*e^7 - 336*a*b^2*c^3*d*x^7*e^7 + 480*a^2*c^4*d*x^7*e^7 + 168*b^4*c^2*d^2*x^6*e^6 - 1176*a*b^2*c^3*d^2*x^6*e^6 + 1680*a^2*c^4*d^2*x^6*e^6 + 336*b^4*c^2*d^3*x^5*e^5 - 2352*a*b^2*c^3*d^3*x^5*e^5 + 3360*a^2*c^4*d^3*x^5*e^5 + 420*b^4*c^2*d^4*x^4*e^4 - 2940*a*b^2*c^3*d^4*x^4*e^4 + 4200*a^2*c^4*d^4*x^4*e^4 + 336*b^4*c^2*d^5*x^3*e^3 - 2352*a*b^2*c^3*d^5*x^3*e^3 + 3360*a^2*c^4*d^5*x^3*e^3 + 168*b^4*c^2*d^6*x^2*e^2 - 1176*a*b^2*c^3*d^6*x^2*e^2 + 1680*a^2*c^4*d^6*x^2*e^2 + 48*b^4*c^2*d^7*x*e - 336*a*b^2*c^3*d^7*x*e + 480*a^2*c^4*d^7*x*e + 6*b^4*c^2*d^8 - 42*a*b^2*c^3*d^8 + 60*a^2*c^4*d^8 + 12*b^5*c*x^6*e^6 - 87*a*b^3*c^2*x^6*e^6 + 138*a^2*b*c^3*x^6*e^6 + 72*b^5*c*d*x^5*e^5 - 522*a*b^3*c^2*d*x^5*e^5 + 828*a^2*b*c^3*d*x^5*e^5 + 180*b^5*c*d^2*x^4*e^4 - 1305*a*b^3*c^2*d^2*x^4*e^4 + 2070*a^2*b*c^3*d^2*x^4*e^4 + 240*b^5*c*d^3*x^3*e^3 - 1740*a*b^3*c^2*d^3*x^3*e^3 + 2760*a^2*b*c^3*d^3*x^3*e^3 + 180*b^5*c*d^4*x^2*e^2 - 1305*a*b^3*c^2*d^4*x^2*e^2 + 2070*a^2*b*c^3*d^4*x^2*e^2 + 72*b^5*c*d^5*x*e - 522*a*b^3*c^2*d^5*x*e + 828*a^2*b*c^3*d^5*x*e + 12*b^5*c*d^6 - 87*a*b^3*c^2*d^6 + 138*a^2*b*c^3*d^6 + 6*b^6*x^4*e^4 - 36*a*b^4*c*x^4*e^4 + 14*a^2*b^2*c^2*x^4*e^4 + 100*a^3*c^3*x^4*e^4 + 24*b^6*d*x^3*e^3 - 144*a*b^4*c*d*x^3*e^3 + 56*a^2*b^2*c^2*d*x^3*e^3 + 400*a^3*c^3*d*x^3*e^3 + 36*b^6*d^2*x^2*e^2 - 216*a*b^4*c*d^2*x^2*e^2 + 84*a^2*b^2*c^2*d^2*x^2*e^2 + 600*a^3*c^3*d^2*x^2*e^2 + 24*b^6*d^3*x*e - 144*a*b^4*c*d^3*x*e + 56*a^2*b^2*c^2*d^3*x*e + 400*a^3*c^3*d^3*x*e + 6*b^6*d^4 - 36*a*b^4*c*d^4 + 14*a^2*b^2*c^2*d^4 + 100*a^3*c^3*d^4 + 9*a*b^5*x^2*e^2 - 68*a^2*b^3*c*x^2*e^2 + 122*a^3*b*c^2*x^2*e^2 + 18*a*b^5*d*x*e - 136*a^2*b^3*c*d*x*e + 244*a^3*b*c^2*d*x*e + 9*a*b^5*d^2 - 68*a^2*b^3*c*d^2 + 122*a^3*b*c^2*d^2 + 2*a^2*b^4 - 16*a^3*b^2*c + 32*a^4*c^2)/((a^3*b^4*f^3*e - 8*a^4*b^2*c*f^3*e + 16*a^5*c^2*f^3*e)*(c*x^5*e^5 + 5*c*d*x^4*e^4 + 10*c*d^2*x^3*e^3 + 10*c*d^3*x^2*e^2 + 5*c*d^4*x*e + c*d^5 + b*x^3*e^3 + 3*b*d*x^2*e^2 + 3*b*d^2*x*e + b*d^3 + a*x*e + a*d)^2) + 3/4*b*e^(-1)*log(abs(c*x^4*e^4 + 4*c*d*x^3*e^3 + 6*c*d^2*x^2*e^2 + 4*c*d^3*x*e + c*d^4 + b*x^2*e^2 + 2*b*d*x*e + b*d^2 + a))/(a^4*f^3) - 3*b*e^(-1)*log(abs(x*e + d))/(a^4*f^3)","B",0
661,0,0,0,0.000000," ","integrate(x/(a+b*(e*x+d)^3+c*(e*x+d)^6)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{{\left(e x + d\right)}^{6} c + {\left(e x + d\right)}^{3} b + a}}\,{d x}"," ",0,"integrate(x/sqrt((e*x + d)^6*c + (e*x + d)^3*b + a), x)","F",0
662,0,0,0,0.000000," ","integrate(x^2/(a+b*(e*x+d)^3+c*(e*x+d)^6)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{{\left(e x + d\right)}^{6} c + {\left(e x + d\right)}^{3} b + a}}\,{d x}"," ",0,"integrate(x^2/sqrt((e*x + d)^6*c + (e*x + d)^3*b + a), x)","F",0
663,1,28,0,0.349067," ","integrate((2+3*x)^6*(1+(2+3*x)^7+(2+3*x)^14),x, algorithm=""giac"")","\frac{1}{63} \, {\left(3 \, x + 2\right)}^{21} + \frac{1}{42} \, {\left(3 \, x + 2\right)}^{14} + \frac{1}{21} \, {\left(3 \, x + 2\right)}^{7}"," ",0,"1/63*(3*x + 2)^21 + 1/42*(3*x + 2)^14 + 1/21*(3*x + 2)^7","A",0
664,1,46,0,0.415124," ","integrate((2+3*x)^6*(1+(2+3*x)^7+(2+3*x)^14)^2,x, algorithm=""giac"")","\frac{1}{105} \, {\left(3 \, x + 2\right)}^{35} + \frac{1}{42} \, {\left(3 \, x + 2\right)}^{28} + \frac{1}{21} \, {\left(3 \, x + 2\right)}^{21} + \frac{1}{21} \, {\left(3 \, x + 2\right)}^{14} + \frac{1}{21} \, {\left(3 \, x + 2\right)}^{7}"," ",0,"1/105*(3*x + 2)^35 + 1/42*(3*x + 2)^28 + 1/21*(3*x + 2)^21 + 1/21*(3*x + 2)^14 + 1/21*(3*x + 2)^7","A",0
