1,1,173,0,0.340026," ","integrate((e*x^3+d)^5*(c*x^6+b*x^3+a),x, algorithm=""giac"")","\frac{1}{22} \, c x^{22} e^{5} + \frac{5}{19} \, c d x^{19} e^{4} + \frac{1}{19} \, b x^{19} e^{5} + \frac{5}{8} \, c d^{2} x^{16} e^{3} + \frac{5}{16} \, b d x^{16} e^{4} + \frac{1}{16} \, a x^{16} e^{5} + \frac{10}{13} \, c d^{3} x^{13} e^{2} + \frac{10}{13} \, b d^{2} x^{13} e^{3} + \frac{5}{13} \, a d x^{13} e^{4} + \frac{1}{2} \, c d^{4} x^{10} e + b d^{3} x^{10} e^{2} + a d^{2} x^{10} e^{3} + \frac{1}{7} \, c d^{5} x^{7} + \frac{5}{7} \, b d^{4} x^{7} e + \frac{10}{7} \, a d^{3} x^{7} e^{2} + \frac{1}{4} \, b d^{5} x^{4} + \frac{5}{4} \, a d^{4} x^{4} e + a d^{5} x"," ",0,"1/22*c*x^22*e^5 + 5/19*c*d*x^19*e^4 + 1/19*b*x^19*e^5 + 5/8*c*d^2*x^16*e^3 + 5/16*b*d*x^16*e^4 + 1/16*a*x^16*e^5 + 10/13*c*d^3*x^13*e^2 + 10/13*b*d^2*x^13*e^3 + 5/13*a*d*x^13*e^4 + 1/2*c*d^4*x^10*e + b*d^3*x^10*e^2 + a*d^2*x^10*e^3 + 1/7*c*d^5*x^7 + 5/7*b*d^4*x^7*e + 10/7*a*d^3*x^7*e^2 + 1/4*b*d^5*x^4 + 5/4*a*d^4*x^4*e + a*d^5*x","A",0
2,1,141,0,0.340884," ","integrate((e*x^3+d)^4*(c*x^6+b*x^3+a),x, algorithm=""giac"")","\frac{1}{19} \, c x^{19} e^{4} + \frac{1}{4} \, c d x^{16} e^{3} + \frac{1}{16} \, b x^{16} e^{4} + \frac{6}{13} \, c d^{2} x^{13} e^{2} + \frac{4}{13} \, b d x^{13} e^{3} + \frac{1}{13} \, a x^{13} e^{4} + \frac{2}{5} \, c d^{3} x^{10} e + \frac{3}{5} \, b d^{2} x^{10} e^{2} + \frac{2}{5} \, a d x^{10} e^{3} + \frac{1}{7} \, c d^{4} x^{7} + \frac{4}{7} \, b d^{3} x^{7} e + \frac{6}{7} \, a d^{2} x^{7} e^{2} + \frac{1}{4} \, b d^{4} x^{4} + a d^{3} x^{4} e + a d^{4} x"," ",0,"1/19*c*x^19*e^4 + 1/4*c*d*x^16*e^3 + 1/16*b*x^16*e^4 + 6/13*c*d^2*x^13*e^2 + 4/13*b*d*x^13*e^3 + 1/13*a*x^13*e^4 + 2/5*c*d^3*x^10*e + 3/5*b*d^2*x^10*e^2 + 2/5*a*d*x^10*e^3 + 1/7*c*d^4*x^7 + 4/7*b*d^3*x^7*e + 6/7*a*d^2*x^7*e^2 + 1/4*b*d^4*x^4 + a*d^3*x^4*e + a*d^4*x","A",0
3,1,109,0,0.303669," ","integrate((e*x^3+d)^3*(c*x^6+b*x^3+a),x, algorithm=""giac"")","\frac{1}{16} \, c x^{16} e^{3} + \frac{3}{13} \, c d x^{13} e^{2} + \frac{1}{13} \, b x^{13} e^{3} + \frac{3}{10} \, c d^{2} x^{10} e + \frac{3}{10} \, b d x^{10} e^{2} + \frac{1}{10} \, a x^{10} e^{3} + \frac{1}{7} \, c d^{3} x^{7} + \frac{3}{7} \, b d^{2} x^{7} e + \frac{3}{7} \, a d x^{7} e^{2} + \frac{1}{4} \, b d^{3} x^{4} + \frac{3}{4} \, a d^{2} x^{4} e + a d^{3} x"," ",0,"1/16*c*x^16*e^3 + 3/13*c*d*x^13*e^2 + 1/13*b*x^13*e^3 + 3/10*c*d^2*x^10*e + 3/10*b*d*x^10*e^2 + 1/10*a*x^10*e^3 + 1/7*c*d^3*x^7 + 3/7*b*d^2*x^7*e + 3/7*a*d*x^7*e^2 + 1/4*b*d^3*x^4 + 3/4*a*d^2*x^4*e + a*d^3*x","A",0
4,1,76,0,0.332293," ","integrate((e*x^3+d)^2*(c*x^6+b*x^3+a),x, algorithm=""giac"")","\frac{1}{13} \, c x^{13} e^{2} + \frac{1}{5} \, c d x^{10} e + \frac{1}{10} \, b x^{10} e^{2} + \frac{1}{7} \, c d^{2} x^{7} + \frac{2}{7} \, b d x^{7} e + \frac{1}{7} \, a x^{7} e^{2} + \frac{1}{4} \, b d^{2} x^{4} + \frac{1}{2} \, a d x^{4} e + a d^{2} x"," ",0,"1/13*c*x^13*e^2 + 1/5*c*d*x^10*e + 1/10*b*x^10*e^2 + 1/7*c*d^2*x^7 + 2/7*b*d*x^7*e + 1/7*a*x^7*e^2 + 1/4*b*d^2*x^4 + 1/2*a*d*x^4*e + a*d^2*x","A",0
5,1,43,0,0.325374," ","integrate((e*x^3+d)*(c*x^6+b*x^3+a),x, algorithm=""giac"")","\frac{1}{10} \, c x^{10} e + \frac{1}{7} \, c d x^{7} + \frac{1}{7} \, b x^{7} e + \frac{1}{4} \, b d x^{4} + \frac{1}{4} \, a x^{4} e + a d x"," ",0,"1/10*c*x^10*e + 1/7*c*d*x^7 + 1/7*b*x^7*e + 1/4*b*d*x^4 + 1/4*a*x^4*e + a*d*x","A",0
6,1,173,0,0.371983," ","integrate((c*x^6+b*x^3+a)/(e*x^3+d),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(c d^{2} - b d e + a e^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}}}\right) e^{\left(-1\right)}}{3 \, \left(-d e^{2}\right)^{\frac{2}{3}}} - \frac{{\left(c d^{2} - b d e + a e^{2}\right)} e^{\left(-1\right)} \log\left(x^{2} + \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} x + \left(-d e^{\left(-1\right)}\right)^{\frac{2}{3}}\right)}{6 \, \left(-d e^{2}\right)^{\frac{2}{3}}} - \frac{{\left(c d^{2} e^{2} - b d e^{3} + a e^{4}\right)} \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} e^{\left(-4\right)} \log\left({\left| x - \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} \right|}\right)}{3 \, d} + \frac{1}{4} \, {\left(c x^{4} e^{3} - 4 \, c d x e^{2} + 4 \, b x e^{3}\right)} e^{\left(-4\right)}"," ",0,"-1/3*sqrt(3)*(c*d^2 - b*d*e + a*e^2)*arctan(1/3*sqrt(3)*(2*x + (-d*e^(-1))^(1/3))/(-d*e^(-1))^(1/3))*e^(-1)/(-d*e^2)^(2/3) - 1/6*(c*d^2 - b*d*e + a*e^2)*e^(-1)*log(x^2 + (-d*e^(-1))^(1/3)*x + (-d*e^(-1))^(2/3))/(-d*e^2)^(2/3) - 1/3*(c*d^2*e^2 - b*d*e^3 + a*e^4)*(-d*e^(-1))^(1/3)*e^(-4)*log(abs(x - (-d*e^(-1))^(1/3)))/d + 1/4*(c*x^4*e^3 - 4*c*d*x*e^2 + 4*b*x*e^3)*e^(-4)","A",0
7,1,199,0,0.379742," ","integrate((c*x^6+b*x^3+a)/(e*x^3+d)^2,x, algorithm=""giac"")","c x e^{\left(-2\right)} + \frac{\sqrt{3} {\left(4 \, c d^{2} - b d e - 2 \, a e^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}}}\right) e^{\left(-1\right)}}{9 \, \left(-d e^{2}\right)^{\frac{2}{3}} d} + \frac{{\left(4 \, c d^{2} - b d e - 2 \, a e^{2}\right)} e^{\left(-1\right)} \log\left(x^{2} + \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} x + \left(-d e^{\left(-1\right)}\right)^{\frac{2}{3}}\right)}{18 \, \left(-d e^{2}\right)^{\frac{2}{3}} d} + \frac{{\left(4 \, c d^{2} - b d e - 2 \, a e^{2}\right)} \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} e^{\left(-2\right)} \log\left({\left| x - \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} \right|}\right)}{9 \, d^{2}} + \frac{{\left(c d^{2} x - b d x e + a x e^{2}\right)} e^{\left(-2\right)}}{3 \, {\left(x^{3} e + d\right)} d}"," ",0,"c*x*e^(-2) + 1/9*sqrt(3)*(4*c*d^2 - b*d*e - 2*a*e^2)*arctan(1/3*sqrt(3)*(2*x + (-d*e^(-1))^(1/3))/(-d*e^(-1))^(1/3))*e^(-1)/((-d*e^2)^(2/3)*d) + 1/18*(4*c*d^2 - b*d*e - 2*a*e^2)*e^(-1)*log(x^2 + (-d*e^(-1))^(1/3)*x + (-d*e^(-1))^(2/3))/((-d*e^2)^(2/3)*d) + 1/9*(4*c*d^2 - b*d*e - 2*a*e^2)*(-d*e^(-1))^(1/3)*e^(-2)*log(abs(x - (-d*e^(-1))^(1/3)))/d^2 + 1/3*(c*d^2*x - b*d*x*e + a*x*e^2)*e^(-2)/((x^3*e + d)*d)","A",0
8,1,224,0,0.400903," ","integrate((c*x^6+b*x^3+a)/(e*x^3+d)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(2 \, c d^{2} + b d e + 5 \, a e^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}}}\right) e^{\left(-1\right)}}{27 \, \left(-d e^{2}\right)^{\frac{2}{3}} d^{2}} - \frac{{\left(2 \, c d^{2} + b d e + 5 \, a e^{2}\right)} e^{\left(-1\right)} \log\left(x^{2} + \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} x + \left(-d e^{\left(-1\right)}\right)^{\frac{2}{3}}\right)}{54 \, \left(-d e^{2}\right)^{\frac{2}{3}} d^{2}} - \frac{{\left(2 \, c d^{2} + b d e + 5 \, a e^{2}\right)} \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} e^{\left(-2\right)} \log\left({\left| x - \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} \right|}\right)}{27 \, d^{3}} - \frac{{\left(7 \, c d^{2} x^{4} e - b d x^{4} e^{2} - 5 \, a x^{4} e^{3} + 4 \, c d^{3} x + 2 \, b d^{2} x e - 8 \, a d x e^{2}\right)} e^{\left(-2\right)}}{18 \, {\left(x^{3} e + d\right)}^{2} d^{2}}"," ",0,"-1/27*sqrt(3)*(2*c*d^2 + b*d*e + 5*a*e^2)*arctan(1/3*sqrt(3)*(2*x + (-d*e^(-1))^(1/3))/(-d*e^(-1))^(1/3))*e^(-1)/((-d*e^2)^(2/3)*d^2) - 1/54*(2*c*d^2 + b*d*e + 5*a*e^2)*e^(-1)*log(x^2 + (-d*e^(-1))^(1/3)*x + (-d*e^(-1))^(2/3))/((-d*e^2)^(2/3)*d^2) - 1/27*(2*c*d^2 + b*d*e + 5*a*e^2)*(-d*e^(-1))^(1/3)*e^(-2)*log(abs(x - (-d*e^(-1))^(1/3)))/d^3 - 1/18*(7*c*d^2*x^4*e - b*d*x^4*e^2 - 5*a*x^4*e^3 + 4*c*d^3*x + 2*b*d^2*x*e - 8*a*d*x*e^2)*e^(-2)/((x^3*e + d)^2*d^2)","A",0
9,1,131,0,0.999059," ","integrate(x^8*(e*x^3+d)/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\frac{c x^{6} e + 2 \, c d x^{3} - 2 \, b x^{3} e}{6 \, c^{2}} - \frac{{\left(b c d - b^{2} e + a c e\right)} \log\left(c x^{6} + b x^{3} + a\right)}{6 \, c^{3}} + \frac{{\left(b^{2} c d - 2 \, a c^{2} d - b^{3} e + 3 \, a b c e\right)} \arctan\left(\frac{2 \, c x^{3} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{3 \, \sqrt{-b^{2} + 4 \, a c} c^{3}}"," ",0,"1/6*(c*x^6*e + 2*c*d*x^3 - 2*b*x^3*e)/c^2 - 1/6*(b*c*d - b^2*e + a*c*e)*log(c*x^6 + b*x^3 + a)/c^3 + 1/3*(b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)*arctan((2*c*x^3 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^3)","A",0
10,1,95,0,1.065388," ","integrate(x^5*(e*x^3+d)/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\frac{x^{3} e}{3 \, c} + \frac{{\left(c d - b e\right)} \log\left(c x^{6} + b x^{3} + a\right)}{6 \, c^{2}} - \frac{{\left(b c d - b^{2} e + 2 \, a c e\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*e/c + 1/6*(c*d - b*e)*log(c*x^6 + b*x^3 + a)/c^2 - 1/3*(b*c*d - b^2*e + 2*a*c*e)*arctan((2*c*x^3 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2)","A",0
11,1,70,0,1.205889," ","integrate(x^2*(e*x^3+d)/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\frac{e \log\left(c x^{6} + b x^{3} + a\right)}{6 \, c} + \frac{{\left(2 \, c d - b e\right)} \arctan\left(\frac{2 \, c x^{3} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{3 \, \sqrt{-b^{2} + 4 \, a c} c}"," ",0,"1/6*e*log(c*x^6 + b*x^3 + a)/c + 1/3*(2*c*d - b*e)*arctan((2*c*x^3 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c)","A",0
12,1,76,0,1.045571," ","integrate((e*x^3+d)/x/(c*x^6+b*x^3+a),x, algorithm=""giac"")","-\frac{d \log\left(c x^{6} + b x^{3} + a\right)}{6 \, a} + \frac{d \log\left({\left| x \right|}\right)}{a} - \frac{{\left(b d - 2 \, a e\right)} \arctan\left(\frac{2 \, c x^{3} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{3 \, \sqrt{-b^{2} + 4 \, a c} a}"," ",0,"-1/6*d*log(c*x^6 + b*x^3 + a)/a + d*log(abs(x))/a - 1/3*(b*d - 2*a*e)*arctan((2*c*x^3 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a)","A",0
13,1,128,0,1.070626," ","integrate((e*x^3+d)/x^4/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\frac{{\left(b d - a e\right)} \log\left(c x^{6} + b x^{3} + a\right)}{6 \, a^{2}} - \frac{{\left(b d - a e\right)} \log\left({\left| x \right|}\right)}{a^{2}} + \frac{{\left(b^{2} d - 2 \, a c d - a b e\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 d x^{3} - a x^{3} e - a d}{3 \, a^{2} x^{3}}"," ",0,"1/6*(b*d - a*e)*log(c*x^6 + b*x^3 + a)/a^2 - (b*d - a*e)*log(abs(x))/a^2 + 1/3*(b^2*d - 2*a*c*d - a*b*e)*arctan((2*c*x^3 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a^2) + 1/3*(b*d*x^3 - a*x^3*e - a*d)/(a^2*x^3)","A",0
14,-1,0,0,0.000000," ","integrate(x^4*(e*x^3+d)/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,0,0,0,0.000000," ","integrate(x^3*(e*x^3+d)/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int \frac{{\left(e x^{3} + d\right)} x^{3}}{c x^{6} + b x^{3} + a}\,{d x}"," ",0,"integrate((e*x^3 + d)*x^3/(c*x^6 + b*x^3 + a), x)","F",0
16,0,0,0,0.000000," ","integrate(x*(e*x^3+d)/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int \frac{{\left(e x^{3} + d\right)} x}{c x^{6} + b x^{3} + a}\,{d x}"," ",0,"integrate((e*x^3 + d)*x/(c*x^6 + b*x^3 + a), x)","F",0
17,0,0,0,0.000000," ","integrate((e*x^3+d)/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int \frac{e x^{3} + d}{c x^{6} + b x^{3} + a}\,{d x}"," ",0,"integrate((e*x^3 + d)/(c*x^6 + b*x^3 + a), x)","F",0
18,0,0,0,0.000000," ","integrate((e*x^3+d)/x^2/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int \frac{e x^{3} + d}{{\left(c x^{6} + b x^{3} + a\right)} x^{2}}\,{d x}"," ",0,"integrate((e*x^3 + d)/((c*x^6 + b*x^3 + a)*x^2), x)","F",0
19,0,0,0,0.000000," ","integrate((e*x^3+d)/x^3/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int \frac{e x^{3} + d}{{\left(c x^{6} + b x^{3} + a\right)} x^{3}}\,{d x}"," ",0,"integrate((e*x^3 + d)/((c*x^6 + b*x^3 + a)*x^3), x)","F",0
20,1,37,0,0.417847," ","integrate(x^8*(-x^3+1)/(x^6-x^3+1),x, algorithm=""giac"")","-\frac{1}{6} \, x^{6} + \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,"-1/6*x^6 + 1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1)) + 1/6*log(x^6 - x^3 + 1)","A",0
21,1,24,0,0.576617," ","integrate(x^5*(-x^3+1)/(x^6-x^3+1),x, algorithm=""giac"")","-\frac{1}{3} \, x^{3} + \frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{3} - 1\right)}\right)"," ",0,"-1/3*x^3 + 2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1))","A",0
22,1,32,0,0.568389," ","integrate(x^2*(-x^3+1)/(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
23,1,35,0,0.591526," ","integrate((-x^3+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
24,1,24,0,0.449091," ","integrate((-x^3+1)/x^4/(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) - \frac{1}{3 \, x^{3}}"," ",0,"-2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1)) - 1/3/x^3","A",0
25,1,642,0,0.575609," ","integrate(x^6*(-x^3+1)/(x^6-x^3+1),x, algorithm=""giac"")","-\frac{1}{4} \, x^{4} - \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,"-1/4*x^4 - 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
26,1,817,0,0.692165," ","integrate(x^4*(-x^3+1)/(x^6-x^3+1),x, algorithm=""giac"")","-\frac{1}{2} \, x^{2} - \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,"-1/2*x^2 - 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
27,1,632,0,0.625692," ","integrate(x^3*(-x^3+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) - 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 - 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) - x","B",0
28,1,821,0,0.582281," ","integrate(x*(-x^3+1)/(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)"," ",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)","B",0
29,1,637,0,0.721678," ","integrate((-x^3+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} + 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)"," ",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)","B",0
30,1,829,0,0.708339," ","integrate((-x^3+1)/x^2/(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{1}{x}"," ",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/x","B",0
31,1,642,0,0.641749," ","integrate((-x^3+1)/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) - \frac{1}{2 \, x^{2}}"," ",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) - 1/2/x^2","B",0
32,1,32,0,0.461980," ","integrate(x^2*(x^3-2)/(x^6-x^3+1),x, algorithm=""giac"")","-\frac{1}{3} \, \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,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1)) + 1/6*log(x^6 - x^3 + 1)","A",0
33,1,35,0,0.539707," ","integrate((x^3+1)/x/(x^6-x^3+1),x, algorithm=""giac"")","\frac{1}{3} \, \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,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1)) - 1/6*log(x^6 - x^3 + 1) + log(abs(x))","A",0
34,1,35,0,0.410303," ","integrate((x^3+1)/(x^7-x^4+x),x, algorithm=""giac"")","\frac{1}{3} \, \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,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1)) - 1/6*log(x^6 - x^3 + 1) + log(abs(x))","A",0
35,0,0,0,0.000000," ","integrate((e*x^3+d)^(5/2)*(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)} {\left(e x^{3} + d\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)*(e*x^3 + d)^(5/2), x)","F",0
36,0,0,0,0.000000," ","integrate((e*x^3+d)^(3/2)*(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)} {\left(e x^{3} + d\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)*(e*x^3 + d)^(3/2), x)","F",0
37,0,0,0,0.000000," ","integrate((e*x^3+d)^(1/2)*(c*x^6+b*x^3+a),x, algorithm=""giac"")","\int {\left(c x^{6} + b x^{3} + a\right)} \sqrt{e x^{3} + d}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)*sqrt(e*x^3 + d), x)","F",0
38,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)/(e*x^3+d)^(1/2),x, algorithm=""giac"")","\int \frac{c x^{6} + b x^{3} + a}{\sqrt{e x^{3} + d}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)/sqrt(e*x^3 + d), x)","F",0
39,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)/(e*x^3+d)^(3/2),x, algorithm=""giac"")","\int \frac{c x^{6} + b x^{3} + a}{{\left(e x^{3} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)/(e*x^3 + d)^(3/2), x)","F",0
40,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)/(e*x^3+d)^(5/2),x, algorithm=""giac"")","\int \frac{c x^{6} + b x^{3} + a}{{\left(e x^{3} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)/(e*x^3 + d)^(5/2), x)","F",0
41,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)/(e*x^3+d)^(7/2),x, algorithm=""giac"")","\int \frac{c x^{6} + b x^{3} + a}{{\left(e x^{3} + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)/(e*x^3 + d)^(7/2), x)","F",0
42,0,0,0,0.000000," ","integrate((c*x^6+b*x^3+a)/(e*x^3+d)^(9/2),x, algorithm=""giac"")","\int \frac{c x^{6} + b x^{3} + a}{{\left(e x^{3} + d\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((c*x^6 + b*x^3 + a)/(e*x^3 + d)^(9/2), x)","F",0
43,-1,0,0,0.000000," ","integrate(x^4*(e*x^4+d)/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,1,70,0,20.738058," ","integrate(x^3*(e*x^4+d)/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\frac{e \log\left(c x^{8} + b x^{4} + a\right)}{8 \, c} + \frac{{\left(2 \, c d - b e\right)} \arctan\left(\frac{2 \, c x^{4} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{4 \, \sqrt{-b^{2} + 4 \, a c} c}"," ",0,"1/8*e*log(c*x^8 + b*x^4 + a)/c + 1/4*(2*c*d - b*e)*arctan((2*c*x^4 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c)","A",0
45,-2,0,0,0.000000," ","integrate(x^2*(e*x^4+d)/(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: 8.38Unable to divide, perhaps due to rounding error%%%{-512,[0,10,0,3,5,2,7]%%%}+%%%{1152,[0,10,0,3,4,4,6]%%%}+%%%{-512,[0,10,0,3,3,6,5]%%%}+%%%{64,[0,10,0,3,2,8,4]%%%}+%%%{1024,[0,9,1,3,6,1,7]%%%}+%%%{-4352,[0,9,1,3,5,3,6]%%%}+%%%{512,[0,9,1,3,4,5,5]%%%}+%%%{640,[0,9,1,3,3,7,4]%%%}+%%%{-128,[0,9,1,3,2,9,3]%%%}+%%%{-512,[0,8,2,3,7,0,7]%%%}+%%%{7296,[0,8,2,3,6,2,6]%%%}+%%%{6144,[0,8,2,3,5,4,5]%%%}+%%%{-4544,[0,8,2,3,4,6,4]%%%}+%%%{384,[0,8,2,3,3,8,3]%%%}+%%%{64,[0,8,2,3,2,10,2]%%%}+%%%{-6144,[0,7,3,3,7,1,6]%%%}+%%%{-22016,[0,7,3,3,6,3,5]%%%}+%%%{9472,[0,7,3,3,5,5,4]%%%}+%%%{1152,[0,7,3,3,4,7,3]%%%}+%%%{-512,[0,7,3,3,3,9,2]%%%}+%%%{2048,[0,6,4,3,8,0,6]%%%}+%%%{31232,[0,6,4,3,7,2,5]%%%}+%%%{-4352,[0,6,4,3,6,4,4]%%%}+%%%{-8064,[0,6,4,3,5,6,3]%%%}+%%%{1792,[0,6,4,3,4,8,2]%%%}+%%%{1048576,[0,6,0,7,9,1,8]%%%}+%%%{-3670016,[0,6,0,7,8,3,7]%%%}+%%%{2424832,[0,6,0,7,7,5,6]%%%}+%%%{-589824,[0,6,0,7,6,7,5]%%%}+%%%{49152,[0,6,0,7,5,9,4]%%%}+%%%{-20480,[0,5,5,3,8,1,5]%%%}+%%%{-11264,[0,5,5,3,7,3,4]%%%}+%%%{18432,[0,5,5,3,6,5,3]%%%}+%%%{-3584,[0,5,5,3,5,7,2]%%%}+%%%{7340032,[0,5,1,7,9,2,7]%%%}+%%%{-2097152,[0,5,1,7,8,4,6]%%%}+%%%{-1376256,[0,5,1,7,7,6,5]%%%}+%%%{622592,[0,5,1,7,6,8,4]%%%}+%%%{-65536,[0,5,1,7,5,10,3]%%%}+%%%{5120,[0,4,6,3,9,0,5]%%%}+%%%{18176,[0,4,6,3,8,2,4]%%%}+%%%{-23040,[0,4,6,3,7,4,3]%%%}+%%%{4544,[0,4,6,3,6,6,2]%%%}+%%%{-8388608,[0,4,2,7,10,1,7]%%%}+%%%{-2359296,[0,4,2,7,9,3,6]%%%}+%%%{3801088,[0,4,2,7,8,5,5]%%%}+%%%{-409600,[0,4,2,7,7,7,4]%%%}+%%%{-196608,[0,4,2,7,6,9,3]%%%}+%%%{32768,[0,4,2,7,5,11,2]%%%}+%%%{-10240,[0,3,7,3,9,1,4]%%%}+%%%{17920,[0,3,7,3,8,3,3]%%%}+%%%{-3840,[0,3,7,3,7,5,2]%%%}+%%%{4194304,[0,3,3,7,10,2,6]%%%}+%%%{2621440,[0,3,3,7,9,4,5]%%%}+%%%{-4194304,[0,3,3,7,8,6,4]%%%}+%%%{1343488,[0,3,3,7,7,8,3]%%%}+%%%{-131072,[0,3,3,7,6,10,2]%%%}+%%%{2048,[0,2,8,3,10,0,4]%%%}+%%%{-9216,[0,2,8,3,9,2,3]%%%}+%%%{2176,[0,2,8,3,8,4,2]%%%}+%%%{5242880,[0,2,4,7,11,1,6]%%%}+%%%{-12582912,[0,2,4,7,10,3,5]%%%}+%%%{8454144,[0,2,4,7,9,5,4]%%%}+%%%{-2195456,[0,2,4,7,8,7,3]%%%}+%%%{196608,[0,2,4,7,7,9,2]%%%}+%%%{2147483648,[0,2,0,11,12,2,8]%%%}+%%%{-2147483648,[0,2,0,11,11,4,7]%%%}+%%%{805306368,[0,2,0,11,10,6,6]%%%}+%%%{-134217728,[0,2,0,11,9,8,5]%%%}+%%%{8388608,[0,2,0,11,8,10,4]%%%}+%%%{3072,[0,1,9,3,10,1,3]%%%}+%%%{-768,[0,1,9,3,9,3,2]%%%}+%%%{5242880,[0,1,5,7,11,2,5]%%%}+%%%{-4718592,[0,1,5,7,10,4,4]%%%}+%%%{1376256,[0,1,5,7,9,6,3]%%%}+%%%{-131072,[0,1,5,7,8,8,2]%%%}+%%%{-2147483648,[0,1,1,11,12,3,7]%%%}+%%%{2147483648,[0,1,1,11,11,5,6]%%%}+%%%{-805306368,[0,1,1,11,10,7,5]%%%}+%%%{134217728,[0,1,1,11,9,9,4]%%%}+%%%{-8388608,[0,1,1,11,8,11,3]%%%}+%%%{-512,[0,0,10,3,11,0,3]%%%}+%%%{128,[0,0,10,3,10,2,2]%%%}+%%%{-2097152,[0,0,6,7,12,1,5]%%%}+%%%{1835008,[0,0,6,7,11,3,4]%%%}+%%%{-524288,[0,0,6,7,10,5,3]%%%}+%%%{49152,[0,0,6,7,9,7,2]%%%}+%%%{-2147483648,[0,0,2,11,13,2,7]%%%}+%%%{3221225472,[0,0,2,11,12,4,6]%%%}+%%%{-1879048192,[0,0,2,11,11,6,5]%%%}+%%%{536870912,[0,0,2,11,10,8,4]%%%}+%%%{-75497472,[0,0,2,11,9,10,3]%%%}+%%%{4194304,[0,0,2,11,8,12,2]%%%} / %%%{1,[0,6,0,0,1,2,2]%%%}+%%%{-2,[0,5,1,0,2,1,2]%%%}+%%%{-2,[0,5,1,0,1,3,1]%%%}+%%%{1,[0,4,2,0,3,0,2]%%%}+%%%{6,[0,4,2,0,2,2,1]%%%}+%%%{1,[0,4,2,0,1,4,0]%%%}+%%%{-6,[0,3,3,0,3,1,1]%%%}+%%%{-4,[0,3,3,0,2,3,0]%%%}+%%%{2,[0,2,4,0,4,0,1]%%%}+%%%{6,[0,2,4,0,3,2,0]%%%}+%%%{-2048,[0,2,0,4,5,1,3]%%%}+%%%{512,[0,2,0,4,4,3,2]%%%}+%%%{-4,[0,1,5,0,4,1,0]%%%}+%%%{2048,[0,1,1,4,5,2,2]%%%}+%%%{-512,[0,1,1,4,4,4,1]%%%}+%%%{1,[0,0,6,0,5,0,0]%%%}+%%%{2048,[0,0,2,4,6,1,2]%%%}+%%%{-1536,[0,0,2,4,5,3,1]%%%}+%%%{256,[0,0,2,4,4,5,0]%%%} Error: Bad Argument Value","F(-2)",0
46,1,1406,0,20.308511," ","integrate(x*(e*x^4+d)/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\frac{{\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 16 \, a b^{2} c^{2} + 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 32 \, a^{2} c^{3} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} d - 2 \, {\left(2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} e\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({\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)} d + 2 \, {\left(2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} e\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)*d - 2*(2*a*b^2*c^2 - 8*a^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^2 - 2*(b^2 - 4*a*c)*a*c^2)*e)*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)*d + 2*(2*a*b^2*c^2 - 8*a^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^2 - 2*(b^2 - 4*a*c)*a*c^2)*e)*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
47,-1,0,0,0.000000," ","integrate((e*x^4+d)/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,1,78,0,20.627977," ","integrate((e*x^4+d)/x/(c*x^8+b*x^4+a),x, algorithm=""giac"")","-\frac{d \log\left(c x^{8} + b x^{4} + a\right)}{8 \, a} + \frac{d \log\left(x^{4}\right)}{4 \, a} - \frac{{\left(b d - 2 \, a e\right)} \arctan\left(\frac{2 \, c x^{4} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{4 \, \sqrt{-b^{2} + 4 \, a c} a}"," ",0,"-1/8*d*log(c*x^8 + b*x^4 + a)/a + 1/4*d*log(x^4)/a - 1/4*(b*d - 2*a*e)*arctan((2*c*x^4 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a)","A",0
49,-1,0,0,0.000000," ","integrate((e*x^4+d)/x^2/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,1,3006,0,22.518802," ","integrate((e*x^4+d)/x^3/(c*x^8+b*x^4+a),x, algorithm=""giac"")","-\frac{{\left({\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)} d 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)} d 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)} d {\left| a \right|} - {\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| a \right|} e + {\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}\right)} d - {\left(2 \, a^{2} b^{3} c^{2} - 8 \, a^{3} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2}\right)} e\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({\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)} d 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)} d 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)} d {\left| a \right|} - {\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| a \right|} e - {\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}\right)} d + {\left(2 \, a^{2} b^{3} c^{2} - 8 \, a^{3} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2}\right)} e\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{d}{2 \, a x^{2}}"," ",0,"-1/8*((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)*d*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)*d*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)*d*abs(a) - (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(a)*e + (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)*d - (2*a^2*b^3*c^2 - 8*a^3*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 2*(b^2 - 4*a*c)*a^2*b*c^2)*e)*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*((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)*d*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)*d*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)*d*abs(a) - (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(a)*e - (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)*d + (2*a^2*b^3*c^2 - 8*a^3*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 2*(b^2 - 4*a*c)*a^2*b*c^2)*e)*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*d/(a*x^2)","B",0
51,-1,0,0,0.000000," ","integrate((e*x^4+d)/x^4/(c*x^8+b*x^4+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,1,208,0,0.452432," ","integrate(x^4*(-x^4+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) - x"," ",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) - x","A",0
53,1,32,0,0.627908," ","integrate(x^3*(-x^4+1)/(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
54,1,253,0,0.481266," ","integrate(x^2*(-x^4+1)/(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
55,1,31,0,0.440026," ","integrate(x*(-x^4+1)/(x^8-x^4+1),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{3} \log\left(\frac{x^{2} - \sqrt{3} + \frac{1}{x^{2}}}{x^{2} + \sqrt{3} + \frac{1}{x^{2}}}\right)"," ",0,"-1/12*sqrt(3)*log((x^2 - sqrt(3) + 1/x^2)/(x^2 + sqrt(3) + 1/x^2))","A",0
56,1,253,0,0.535656," ","integrate((-x^4+1)/(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
57,1,38,0,0.452639," ","integrate((-x^4+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
58,1,210,0,0.582159," ","integrate((-x^4+1)/x^2/(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{1}{x}"," ",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/x","A",0
59,1,81,0,0.528016," ","integrate((-x^4+1)/x^3/(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) - \frac{1}{2 \, x^{2}}"," ",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)) - 1/2/x^2","A",0
60,1,258,0,0.443611," ","integrate((-x^4+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
61,1,295,0,0.375627," ","integrate(x^3/(a+c/x^2+b/x)/(e*x+d),x, algorithm=""giac"")","-\frac{d^{5} \log\left({\left| x e + d \right|}\right)}{a d^{2} e^{4} - b d e^{5} + c e^{6}} + \frac{{\left(b^{4} d - 3 \, a b^{2} c d + a^{2} c^{2} d - b^{3} c e + 2 \, a b c^{2} e\right)} \log\left(a x^{2} + b x + c\right)}{2 \, {\left(a^{5} d^{2} - a^{4} b d e + a^{4} c e^{2}\right)}} - \frac{{\left(b^{5} d - 5 \, a b^{3} c d + 5 \, a^{2} b c^{2} d - b^{4} c e + 4 \, a b^{2} c^{2} e - 2 \, a^{2} c^{3} e\right)} \arctan\left(\frac{2 \, a x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{5} d^{2} - a^{4} b d e + a^{4} c e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(2 \, a^{2} x^{3} e^{2} - 3 \, a^{2} d x^{2} e + 6 \, a^{2} d^{2} x - 3 \, a b x^{2} e^{2} + 6 \, a b d x e + 6 \, b^{2} x e^{2} - 6 \, a c x e^{2}\right)} e^{\left(-3\right)}}{6 \, a^{3}}"," ",0,"-d^5*log(abs(x*e + d))/(a*d^2*e^4 - b*d*e^5 + c*e^6) + 1/2*(b^4*d - 3*a*b^2*c*d + a^2*c^2*d - b^3*c*e + 2*a*b*c^2*e)*log(a*x^2 + b*x + c)/(a^5*d^2 - a^4*b*d*e + a^4*c*e^2) - (b^5*d - 5*a*b^3*c*d + 5*a^2*b*c^2*d - b^4*c*e + 4*a*b^2*c^2*e - 2*a^2*c^3*e)*arctan((2*a*x + b)/sqrt(-b^2 + 4*a*c))/((a^5*d^2 - a^4*b*d*e + a^4*c*e^2)*sqrt(-b^2 + 4*a*c)) + 1/6*(2*a^2*x^3*e^2 - 3*a^2*d*x^2*e + 6*a^2*d^2*x - 3*a*b*x^2*e^2 + 6*a*b*d*x*e + 6*b^2*x*e^2 - 6*a*c*x*e^2)*e^(-3)/a^3","A",0
62,1,224,0,0.367536," ","integrate(x^2/(a+c/x^2+b/x)/(e*x+d),x, algorithm=""giac"")","\frac{d^{4} \log\left({\left| x e + d \right|}\right)}{a d^{2} e^{3} - b d e^{4} + c e^{5}} - \frac{{\left(b^{3} d - 2 \, a b c d - b^{2} c e + a c^{2} e\right)} \log\left(a x^{2} + b x + c\right)}{2 \, {\left(a^{4} d^{2} - a^{3} b d e + a^{3} c e^{2}\right)}} + \frac{{\left(b^{4} d - 4 \, a b^{2} c d + 2 \, a^{2} c^{2} d - b^{3} c e + 3 \, a b c^{2} e\right)} \arctan\left(\frac{2 \, a x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{4} d^{2} - a^{3} b d e + a^{3} c e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(a x^{2} e - 2 \, a d x - 2 \, b x e\right)} e^{\left(-2\right)}}{2 \, a^{2}}"," ",0,"d^4*log(abs(x*e + d))/(a*d^2*e^3 - b*d*e^4 + c*e^5) - 1/2*(b^3*d - 2*a*b*c*d - b^2*c*e + a*c^2*e)*log(a*x^2 + b*x + c)/(a^4*d^2 - a^3*b*d*e + a^3*c*e^2) + (b^4*d - 4*a*b^2*c*d + 2*a^2*c^2*d - b^3*c*e + 3*a*b*c^2*e)*arctan((2*a*x + b)/sqrt(-b^2 + 4*a*c))/((a^4*d^2 - a^3*b*d*e + a^3*c*e^2)*sqrt(-b^2 + 4*a*c)) + 1/2*(a*x^2*e - 2*a*d*x - 2*b*x*e)*e^(-2)/a^2","A",0
63,1,185,0,0.400877," ","integrate(x/(a+c/x^2+b/x)/(e*x+d),x, algorithm=""giac"")","-\frac{d^{3} \log\left({\left| x e + d \right|}\right)}{a d^{2} e^{2} - b d e^{3} + c e^{4}} + \frac{x e^{\left(-1\right)}}{a} + \frac{{\left(b^{2} d - a c d - b c e\right)} \log\left(a x^{2} + b x + c\right)}{2 \, {\left(a^{3} d^{2} - a^{2} b d e + a^{2} c e^{2}\right)}} - \frac{{\left(b^{3} d - 3 \, a b c d - b^{2} c e + 2 \, a c^{2} e\right)} \arctan\left(\frac{2 \, a x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{3} d^{2} - a^{2} b d e + a^{2} c e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}}"," ",0,"-d^3*log(abs(x*e + d))/(a*d^2*e^2 - b*d*e^3 + c*e^4) + x*e^(-1)/a + 1/2*(b^2*d - a*c*d - b*c*e)*log(a*x^2 + b*x + c)/(a^3*d^2 - a^2*b*d*e + a^2*c*e^2) - (b^3*d - 3*a*b*c*d - b^2*c*e + 2*a*c^2*e)*arctan((2*a*x + b)/sqrt(-b^2 + 4*a*c))/((a^3*d^2 - a^2*b*d*e + a^2*c*e^2)*sqrt(-b^2 + 4*a*c))","A",0
64,1,149,0,0.366361," ","integrate(1/(a+c/x^2+b/x)/(e*x+d),x, algorithm=""giac"")","\frac{d^{2} \log\left({\left| x e + d \right|}\right)}{a d^{2} e - b d e^{2} + c e^{3}} - \frac{{\left(b d - c e\right)} \log\left(a x^{2} + b x + c\right)}{2 \, {\left(a^{2} d^{2} - a b d e + a c e^{2}\right)}} + \frac{{\left(b^{2} d - 2 \, a c d - b c e\right)} \arctan\left(\frac{2 \, a x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{2} d^{2} - a b d e + a c e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}}"," ",0,"d^2*log(abs(x*e + d))/(a*d^2*e - b*d*e^2 + c*e^3) - 1/2*(b*d - c*e)*log(a*x^2 + b*x + c)/(a^2*d^2 - a*b*d*e + a*c*e^2) + (b^2*d - 2*a*c*d - b*c*e)*arctan((2*a*x + b)/sqrt(-b^2 + 4*a*c))/((a^2*d^2 - a*b*d*e + a*c*e^2)*sqrt(-b^2 + 4*a*c))","A",0
65,1,127,0,0.392124," ","integrate(1/(a+c/x^2+b/x)/x/(e*x+d),x, algorithm=""giac"")","-\frac{d e \log\left({\left| x e + d \right|}\right)}{a d^{2} e - b d e^{2} + c e^{3}} + \frac{d \log\left(a x^{2} + b x + c\right)}{2 \, {\left(a d^{2} - b d e + c e^{2}\right)}} - \frac{{\left(b d - 2 \, c e\right)} \arctan\left(\frac{2 \, a x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a d^{2} - b d e + c e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}}"," ",0,"-d*e*log(abs(x*e + d))/(a*d^2*e - b*d*e^2 + c*e^3) + 1/2*d*log(a*x^2 + b*x + c)/(a*d^2 - b*d*e + c*e^2) - (b*d - 2*c*e)*arctan((2*a*x + b)/sqrt(-b^2 + 4*a*c))/((a*d^2 - b*d*e + c*e^2)*sqrt(-b^2 + 4*a*c))","A",0
66,1,126,0,0.340891," ","integrate(1/(a+c/x^2+b/x)/x^2/(e*x+d),x, algorithm=""giac"")","-\frac{e \log\left(a x^{2} + b x + c\right)}{2 \, {\left(a d^{2} - b d e + c e^{2}\right)}} + \frac{e^{2} \log\left({\left| x e + d \right|}\right)}{a d^{2} e - b d e^{2} + c e^{3}} + \frac{{\left(2 \, a d - b e\right)} \arctan\left(\frac{2 \, a x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a d^{2} - b d e + c e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}}"," ",0,"-1/2*e*log(a*x^2 + b*x + c)/(a*d^2 - b*d*e + c*e^2) + e^2*log(abs(x*e + d))/(a*d^2*e - b*d*e^2 + c*e^3) + (2*a*d - b*e)*arctan((2*a*x + b)/sqrt(-b^2 + 4*a*c))/((a*d^2 - b*d*e + c*e^2)*sqrt(-b^2 + 4*a*c))","A",0
67,1,164,0,0.350974," ","integrate(1/(a+c/x^2+b/x)/x^3/(e*x+d),x, algorithm=""giac"")","-\frac{{\left(a d - b e\right)} \log\left(a x^{2} + b x + c\right)}{2 \, {\left(a c d^{2} - b c d e + c^{2} e^{2}\right)}} - \frac{e^{3} \log\left({\left| x e + d \right|}\right)}{a d^{3} e - b d^{2} e^{2} + c d e^{3}} - \frac{{\left(a b d - b^{2} e + 2 \, a c e\right)} \arctan\left(\frac{2 \, a x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a c d^{2} - b c d e + c^{2} e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{\log\left({\left| x \right|}\right)}{c d}"," ",0,"-1/2*(a*d - b*e)*log(a*x^2 + b*x + c)/(a*c*d^2 - b*c*d*e + c^2*e^2) - e^3*log(abs(x*e + d))/(a*d^3*e - b*d^2*e^2 + c*d*e^3) - (a*b*d - b^2*e + 2*a*c*e)*arctan((2*a*x + b)/sqrt(-b^2 + 4*a*c))/((a*c*d^2 - b*c*d*e + c^2*e^2)*sqrt(-b^2 + 4*a*c)) + log(abs(x))/(c*d)","A",0
68,1,210,0,0.341586," ","integrate(1/(a+c/x^2+b/x)/x^4/(e*x+d),x, algorithm=""giac"")","\frac{{\left(a b d - b^{2} e + a c e\right)} \log\left(a x^{2} + b x + c\right)}{2 \, {\left(a c^{2} d^{2} - b c^{2} d e + c^{3} e^{2}\right)}} + \frac{e^{4} \log\left({\left| x e + d \right|}\right)}{a d^{4} e - b d^{3} e^{2} + c d^{2} e^{3}} + \frac{{\left(a b^{2} d - 2 \, a^{2} c d - b^{3} e + 3 \, a b c e\right)} \arctan\left(\frac{2 \, a x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a c^{2} d^{2} - b c^{2} d e + c^{3} e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{{\left(b d + c e\right)} \log\left({\left| x \right|}\right)}{c^{2} d^{2}} - \frac{1}{c d x}"," ",0,"1/2*(a*b*d - b^2*e + a*c*e)*log(a*x^2 + b*x + c)/(a*c^2*d^2 - b*c^2*d*e + c^3*e^2) + e^4*log(abs(x*e + d))/(a*d^4*e - b*d^3*e^2 + c*d^2*e^3) + (a*b^2*d - 2*a^2*c*d - b^3*e + 3*a*b*c*e)*arctan((2*a*x + b)/sqrt(-b^2 + 4*a*c))/((a*c^2*d^2 - b*c^2*d*e + c^3*e^2)*sqrt(-b^2 + 4*a*c)) - (b*d + c*e)*log(abs(x))/(c^2*d^2) - 1/(c*d*x)","A",0
69,1,279,0,0.347968," ","integrate(1/(a+c/x^2+b/x)/x^5/(e*x+d),x, algorithm=""giac"")","-\frac{{\left(a b^{2} d - a^{2} c d - b^{3} e + 2 \, a b c e\right)} \log\left(a x^{2} + b x + c\right)}{2 \, {\left(a c^{3} d^{2} - b c^{3} d e + c^{4} e^{2}\right)}} - \frac{e^{5} \log\left({\left| x e + d \right|}\right)}{a d^{5} e - b d^{4} e^{2} + c d^{3} e^{3}} - \frac{{\left(a b^{3} d - 3 \, a^{2} b c d - b^{4} e + 4 \, a b^{2} c e - 2 \, a^{2} c^{2} e\right)} \arctan\left(\frac{2 \, a x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a c^{3} d^{2} - b c^{3} d e + c^{4} e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(b^{2} d^{2} - a c d^{2} + b c d e + c^{2} e^{2}\right)} \log\left({\left| x \right|}\right)}{c^{3} d^{3}} - \frac{c^{2} d^{2} - 2 \, {\left(b c d^{2} + c^{2} d e\right)} x}{2 \, c^{3} d^{3} x^{2}}"," ",0,"-1/2*(a*b^2*d - a^2*c*d - b^3*e + 2*a*b*c*e)*log(a*x^2 + b*x + c)/(a*c^3*d^2 - b*c^3*d*e + c^4*e^2) - e^5*log(abs(x*e + d))/(a*d^5*e - b*d^4*e^2 + c*d^3*e^3) - (a*b^3*d - 3*a^2*b*c*d - b^4*e + 4*a*b^2*c*e - 2*a^2*c^2*e)*arctan((2*a*x + b)/sqrt(-b^2 + 4*a*c))/((a*c^3*d^2 - b*c^3*d*e + c^4*e^2)*sqrt(-b^2 + 4*a*c)) + (b^2*d^2 - a*c*d^2 + b*c*d*e + c^2*e^2)*log(abs(x))/(c^3*d^3) - 1/2*(c^2*d^2 - 2*(b*c*d^2 + c^2*d*e)*x)/(c^3*d^3*x^2)","A",0
70,1,565,0,0.420068," ","integrate(x^3/(a+c/x^2+b/x)/(e*x+d)^2,x, algorithm=""giac"")","\frac{d^{5} e^{4}}{{\left(a d^{2} e^{8} - b d e^{9} + c e^{10}\right)} {\left(x e + d\right)}} + \frac{{\left(b^{5} d^{2} e^{2} - 5 \, a b^{3} c d^{2} e^{2} + 5 \, a^{2} b c^{2} d^{2} e^{2} - 2 \, b^{4} c d e^{3} + 8 \, a b^{2} c^{2} d e^{3} - 4 \, a^{2} c^{3} d e^{3} + b^{3} c^{2} e^{4} - 3 \, a b c^{3} e^{4}\right)} \arctan\left(-\frac{{\left(2 \, a d - \frac{2 \, a d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, c e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(a^{5} d^{4} - 2 \, a^{4} b d^{3} e + a^{3} b^{2} d^{2} e^{2} + 2 \, a^{4} c d^{2} e^{2} - 2 \, a^{3} b c d e^{3} + a^{3} c^{2} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(a^{2} - \frac{2 \, {\left(3 \, a^{2} d e + a b e^{2}\right)} e^{\left(-1\right)}}{x e + d}\right)} {\left(x e + d\right)}^{2} e^{\left(-4\right)}}{2 \, a^{3}} + \frac{{\left(b^{4} d^{2} - 3 \, a b^{2} c d^{2} + a^{2} c^{2} d^{2} - 2 \, b^{3} c d e + 4 \, a b c^{2} d e + b^{2} c^{2} e^{2} - a c^{3} e^{2}\right)} \log\left(-a + \frac{2 \, a d}{x e + d} - \frac{a d^{2}}{{\left(x e + d\right)}^{2}} - \frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{c e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(a^{5} d^{4} - 2 \, a^{4} b d^{3} e + a^{3} b^{2} d^{2} e^{2} + 2 \, a^{4} c d^{2} e^{2} - 2 \, a^{3} b c d e^{3} + a^{3} c^{2} e^{4}\right)}} - \frac{{\left(3 \, a^{2} d^{2} + 2 \, a b d e + b^{2} e^{2} - a c e^{2}\right)} e^{\left(-4\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right)}{a^{3}}"," ",0,"d^5*e^4/((a*d^2*e^8 - b*d*e^9 + c*e^10)*(x*e + d)) + (b^5*d^2*e^2 - 5*a*b^3*c*d^2*e^2 + 5*a^2*b*c^2*d^2*e^2 - 2*b^4*c*d*e^3 + 8*a*b^2*c^2*d*e^3 - 4*a^2*c^3*d*e^3 + b^3*c^2*e^4 - 3*a*b*c^3*e^4)*arctan(-(2*a*d - 2*a*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*c*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((a^5*d^4 - 2*a^4*b*d^3*e + a^3*b^2*d^2*e^2 + 2*a^4*c*d^2*e^2 - 2*a^3*b*c*d*e^3 + a^3*c^2*e^4)*sqrt(-b^2 + 4*a*c)) + 1/2*(a^2 - 2*(3*a^2*d*e + a*b*e^2)*e^(-1)/(x*e + d))*(x*e + d)^2*e^(-4)/a^3 + 1/2*(b^4*d^2 - 3*a*b^2*c*d^2 + a^2*c^2*d^2 - 2*b^3*c*d*e + 4*a*b*c^2*d*e + b^2*c^2*e^2 - a*c^3*e^2)*log(-a + 2*a*d/(x*e + d) - a*d^2/(x*e + d)^2 - b*e/(x*e + d) + b*d*e/(x*e + d)^2 - c*e^2/(x*e + d)^2)/(a^5*d^4 - 2*a^4*b*d^3*e + a^3*b^2*d^2*e^2 + 2*a^4*c*d^2*e^2 - 2*a^3*b*c*d*e^3 + a^3*c^2*e^4) - (3*a^2*d^2 + 2*a*b*d*e + b^2*e^2 - a*c*e^2)*e^(-4)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2)/a^3","A",0
71,1,476,0,0.401317," ","integrate(x^2/(a+c/x^2+b/x)/(e*x+d)^2,x, algorithm=""giac"")","-\frac{d^{4} e^{3}}{{\left(a d^{2} e^{6} - b d e^{7} + c e^{8}\right)} {\left(x e + d\right)}} - \frac{{\left(b^{4} d^{2} e^{2} - 4 \, a b^{2} c d^{2} e^{2} + 2 \, a^{2} c^{2} d^{2} e^{2} - 2 \, b^{3} c d e^{3} + 6 \, a b c^{2} d e^{3} + b^{2} c^{2} e^{4} - 2 \, a c^{3} e^{4}\right)} \arctan\left(-\frac{{\left(2 \, a d - \frac{2 \, a d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, c e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(a^{4} d^{4} - 2 \, a^{3} b d^{3} e + a^{2} b^{2} d^{2} e^{2} + 2 \, a^{3} c d^{2} e^{2} - 2 \, a^{2} b c d e^{3} + a^{2} c^{2} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(x e + d\right)} e^{\left(-3\right)}}{a} - \frac{{\left(b^{3} d^{2} - 2 \, a b c d^{2} - 2 \, b^{2} c d e + 2 \, a c^{2} d e + b c^{2} e^{2}\right)} \log\left(-a + \frac{2 \, a d}{x e + d} - \frac{a d^{2}}{{\left(x e + d\right)}^{2}} - \frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{c e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(a^{4} d^{4} - 2 \, a^{3} b d^{3} e + a^{2} b^{2} d^{2} e^{2} + 2 \, a^{3} c d^{2} e^{2} - 2 \, a^{2} b c d e^{3} + a^{2} c^{2} e^{4}\right)}} + \frac{{\left(2 \, a d + b e\right)} e^{\left(-3\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right)}{a^{2}}"," ",0,"-d^4*e^3/((a*d^2*e^6 - b*d*e^7 + c*e^8)*(x*e + d)) - (b^4*d^2*e^2 - 4*a*b^2*c*d^2*e^2 + 2*a^2*c^2*d^2*e^2 - 2*b^3*c*d*e^3 + 6*a*b*c^2*d*e^3 + b^2*c^2*e^4 - 2*a*c^3*e^4)*arctan(-(2*a*d - 2*a*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*c*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((a^4*d^4 - 2*a^3*b*d^3*e + a^2*b^2*d^2*e^2 + 2*a^3*c*d^2*e^2 - 2*a^2*b*c*d*e^3 + a^2*c^2*e^4)*sqrt(-b^2 + 4*a*c)) + (x*e + d)*e^(-3)/a - 1/2*(b^3*d^2 - 2*a*b*c*d^2 - 2*b^2*c*d*e + 2*a*c^2*d*e + b*c^2*e^2)*log(-a + 2*a*d/(x*e + d) - a*d^2/(x*e + d)^2 - b*e/(x*e + d) + b*d*e/(x*e + d)^2 - c*e^2/(x*e + d)^2)/(a^4*d^4 - 2*a^3*b*d^3*e + a^2*b^2*d^2*e^2 + 2*a^3*c*d^2*e^2 - 2*a^2*b*c*d*e^3 + a^2*c^2*e^4) + (2*a*d + b*e)*e^(-3)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2)/a^2","A",0
72,1,412,0,0.422260," ","integrate(x/(a+c/x^2+b/x)/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{2 \, d^{3} e^{2}}{{\left(a d^{2} e^{3} - b d e^{4} + c e^{5}\right)} {\left(x e + d\right)}} + \frac{2 \, {\left(b^{3} d^{2} e^{3} - 3 \, a b c d^{2} e^{3} - 2 \, b^{2} c d e^{4} + 4 \, a c^{2} d e^{4} + b c^{2} e^{5}\right)} \arctan\left(-\frac{{\left(2 \, a d - \frac{2 \, a d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, c e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(a^{3} d^{4} - 2 \, a^{2} b d^{3} e + a b^{2} d^{2} e^{2} + 2 \, a^{2} c d^{2} e^{2} - 2 \, a b c d e^{3} + a c^{2} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(b^{2} d^{2} e - a c d^{2} e - 2 \, b c d e^{2} + c^{2} e^{3}\right)} \log\left(-a + \frac{2 \, a d}{x e + d} - \frac{a d^{2}}{{\left(x e + d\right)}^{2}} - \frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{c e^{2}}{{\left(x e + d\right)}^{2}}\right)}{a^{3} d^{4} - 2 \, a^{2} b d^{3} e + a b^{2} d^{2} e^{2} + 2 \, a^{2} c d^{2} e^{2} - 2 \, a b c d e^{3} + a c^{2} e^{4}} - \frac{2 \, e^{\left(-1\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right)}{a}\right)} e^{\left(-1\right)}"," ",0,"1/2*(2*d^3*e^2/((a*d^2*e^3 - b*d*e^4 + c*e^5)*(x*e + d)) + 2*(b^3*d^2*e^3 - 3*a*b*c*d^2*e^3 - 2*b^2*c*d*e^4 + 4*a*c^2*d*e^4 + b*c^2*e^5)*arctan(-(2*a*d - 2*a*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*c*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((a^3*d^4 - 2*a^2*b*d^3*e + a*b^2*d^2*e^2 + 2*a^2*c*d^2*e^2 - 2*a*b*c*d*e^3 + a*c^2*e^4)*sqrt(-b^2 + 4*a*c)) + (b^2*d^2*e - a*c*d^2*e - 2*b*c*d*e^2 + c^2*e^3)*log(-a + 2*a*d/(x*e + d) - a*d^2/(x*e + d)^2 - b*e/(x*e + d) + b*d*e/(x*e + d)^2 - c*e^2/(x*e + d)^2)/(a^3*d^4 - 2*a^2*b*d^3*e + a*b^2*d^2*e^2 + 2*a^2*c*d^2*e^2 - 2*a*b*c*d*e^3 + a*c^2*e^4) - 2*e^(-1)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2)/a)*e^(-1)","A",0
73,1,331,0,0.347286," ","integrate(1/(a+c/x^2+b/x)/(e*x+d)^2,x, algorithm=""giac"")","\frac{{\left(b^{2} d^{2} e^{2} - 2 \, a c d^{2} e^{2} - 2 \, b c d e^{3} + 2 \, c^{2} e^{4}\right)} \arctan\left(\frac{{\left(2 \, a d - \frac{2 \, a d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, c e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(a^{2} d^{4} - 2 \, a b d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, b c d e^{3} + c^{2} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{d^{2} e}{{\left(a d^{2} e^{2} - b d e^{3} + c e^{4}\right)} {\left(x e + d\right)}} - \frac{{\left(b d^{2} - 2 \, c d e\right)} \log\left(a - \frac{2 \, a d}{x e + d} + \frac{a d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{c e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(a^{2} d^{4} - 2 \, a b d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, b c d e^{3} + c^{2} e^{4}\right)}}"," ",0,"(b^2*d^2*e^2 - 2*a*c*d^2*e^2 - 2*b*c*d*e^3 + 2*c^2*e^4)*arctan((2*a*d - 2*a*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*c*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((a^2*d^4 - 2*a*b*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*b*c*d*e^3 + c^2*e^4)*sqrt(-b^2 + 4*a*c)) - d^2*e/((a*d^2*e^2 - b*d*e^3 + c*e^4)*(x*e + d)) - 1/2*(b*d^2 - 2*c*d*e)*log(a - 2*a*d/(x*e + d) + a*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + c*e^2/(x*e + d)^2)/(a^2*d^4 - 2*a*b*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*b*c*d*e^3 + c^2*e^4)","A",0
74,1,323,0,0.366001," ","integrate(1/(a+c/x^2+b/x)/x/(e*x+d)^2,x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\frac{2 \, {\left(a b d^{2} e - 4 \, a c d e^{2} + b c e^{3}\right)} \arctan\left(\frac{{\left(2 \, a d - \frac{2 \, a d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, c e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(a^{2} d^{4} - 2 \, a b d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, b c d e^{3} + c^{2} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{{\left(a d^{2} - c e^{2}\right)} \log\left(a - \frac{2 \, a d}{x e + d} + \frac{a d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{c e^{2}}{{\left(x e + d\right)}^{2}}\right)}{a^{2} d^{4} e - 2 \, a b d^{3} e^{2} + b^{2} d^{2} e^{3} + 2 \, a c d^{2} e^{3} - 2 \, b c d e^{4} + c^{2} e^{5}} - \frac{2 \, d e}{{\left(a d^{2} e^{2} - b d e^{3} + c e^{4}\right)} {\left(x e + d\right)}}\right)} e"," ",0,"-1/2*(2*(a*b*d^2*e - 4*a*c*d*e^2 + b*c*e^3)*arctan((2*a*d - 2*a*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*c*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((a^2*d^4 - 2*a*b*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*b*c*d*e^3 + c^2*e^4)*sqrt(-b^2 + 4*a*c)) - (a*d^2 - c*e^2)*log(a - 2*a*d/(x*e + d) + a*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + c*e^2/(x*e + d)^2)/(a^2*d^4*e - 2*a*b*d^3*e^2 + b^2*d^2*e^3 + 2*a*c*d^2*e^3 - 2*b*c*d*e^4 + c^2*e^5) - 2*d*e/((a*d^2*e^2 - b*d*e^3 + c*e^4)*(x*e + d)))*e","A",0
75,1,331,0,0.354024," ","integrate(1/(a+c/x^2+b/x)/x^2/(e*x+d)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, a^{2} d^{2} e^{2} - 2 \, a b d e^{3} + b^{2} e^{4} - 2 \, a c e^{4}\right)} \arctan\left(-\frac{{\left(2 \, a d - \frac{2 \, a d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, c e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(a^{2} d^{4} - 2 \, a b d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, b c d e^{3} + c^{2} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{{\left(2 \, a d e - b e^{2}\right)} \log\left(-a + \frac{2 \, a d}{x e + d} - \frac{a d^{2}}{{\left(x e + d\right)}^{2}} - \frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{c e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(a^{2} d^{4} - 2 \, a b d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, b c d e^{3} + c^{2} e^{4}\right)}} - \frac{e^{3}}{{\left(a d^{2} e^{2} - b d e^{3} + c e^{4}\right)} {\left(x e + d\right)}}"," ",0,"-(2*a^2*d^2*e^2 - 2*a*b*d*e^3 + b^2*e^4 - 2*a*c*e^4)*arctan(-(2*a*d - 2*a*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*c*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((a^2*d^4 - 2*a*b*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*b*c*d*e^3 + c^2*e^4)*sqrt(-b^2 + 4*a*c)) - 1/2*(2*a*d*e - b*e^2)*log(-a + 2*a*d/(x*e + d) - a*d^2/(x*e + d)^2 - b*e/(x*e + d) + b*d*e/(x*e + d)^2 - c*e^2/(x*e + d)^2)/(a^2*d^4 - 2*a*b*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*b*c*d*e^3 + c^2*e^4) - e^3/((a*d^2*e^2 - b*d*e^3 + c*e^4)*(x*e + d))","A",0
76,1,391,0,0.408079," ","integrate(1/(a+c/x^2+b/x)/x^3/(e*x+d)^2,x, algorithm=""giac"")","-\frac{{\left(a^{2} b d^{2} e^{2} - 2 \, a b^{2} d e^{3} + 4 \, a^{2} c d e^{3} + b^{3} e^{4} - 3 \, a b c e^{4}\right)} \arctan\left(\frac{{\left(2 \, a d - \frac{2 \, a d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, c e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(a^{2} c d^{4} - 2 \, a b c d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, b c^{2} d e^{3} + c^{3} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{{\left(a^{2} d^{2} - 2 \, a b d e + b^{2} e^{2} - a c e^{2}\right)} \log\left(a - \frac{2 \, a d}{x e + d} + \frac{a d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{c e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(a^{2} c d^{4} - 2 \, a b c d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, b c^{2} d e^{3} + c^{3} e^{4}\right)}} + \frac{e^{5}}{{\left(a d^{3} e^{3} - b d^{2} e^{4} + c d e^{5}\right)} {\left(x e + d\right)}} + \frac{\log\left({\left| -\frac{d}{x e + d} + 1 \right|}\right)}{c d^{2}}"," ",0,"-(a^2*b*d^2*e^2 - 2*a*b^2*d*e^3 + 4*a^2*c*d*e^3 + b^3*e^4 - 3*a*b*c*e^4)*arctan((2*a*d - 2*a*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*c*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((a^2*c*d^4 - 2*a*b*c*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*b*c^2*d*e^3 + c^3*e^4)*sqrt(-b^2 + 4*a*c)) - 1/2*(a^2*d^2 - 2*a*b*d*e + b^2*e^2 - a*c*e^2)*log(a - 2*a*d/(x*e + d) + a*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + c*e^2/(x*e + d)^2)/(a^2*c*d^4 - 2*a*b*c*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*b*c^2*d*e^3 + c^3*e^4) + e^5/((a*d^3*e^3 - b*d^2*e^4 + c*d*e^5)*(x*e + d)) + log(abs(-d/(x*e + d) + 1))/(c*d^2)","A",0
77,1,487,0,0.360867," ","integrate(1/(a+c/x^2+b/x)/x^4/(e*x+d)^2,x, algorithm=""giac"")","-\frac{{\left(a^{2} b^{2} d^{2} e^{2} - 2 \, a^{3} c d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 6 \, a^{2} b c d e^{3} + b^{4} e^{4} - 4 \, a b^{2} c e^{4} + 2 \, a^{2} c^{2} e^{4}\right)} \arctan\left(-\frac{{\left(2 \, a d - \frac{2 \, a d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, c e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(a^{2} c^{2} d^{4} - 2 \, a b c^{2} d^{3} e + b^{2} c^{2} d^{2} e^{2} + 2 \, a c^{3} d^{2} e^{2} - 2 \, b c^{3} d e^{3} + c^{4} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(a^{2} b d^{2} - 2 \, a b^{2} d e + 2 \, a^{2} c d e + b^{3} e^{2} - 2 \, a b c e^{2}\right)} \log\left(-a + \frac{2 \, a d}{x e + d} - \frac{a d^{2}}{{\left(x e + d\right)}^{2}} - \frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{c e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(a^{2} c^{2} d^{4} - 2 \, a b c^{2} d^{3} e + b^{2} c^{2} d^{2} e^{2} + 2 \, a c^{3} d^{2} e^{2} - 2 \, b c^{3} d e^{3} + c^{4} e^{4}\right)}} - \frac{e^{7}}{{\left(a d^{4} e^{4} - b d^{3} e^{5} + c d^{2} e^{6}\right)} {\left(x e + d\right)}} - \frac{{\left(b d e + 2 \, c e^{2}\right)} e^{\left(-1\right)} \log\left({\left| -\frac{d}{x e + d} + 1 \right|}\right)}{c^{2} d^{3}} + \frac{e}{c d^{3} {\left(\frac{d}{x e + d} - 1\right)}}"," ",0,"-(a^2*b^2*d^2*e^2 - 2*a^3*c*d^2*e^2 - 2*a*b^3*d*e^3 + 6*a^2*b*c*d*e^3 + b^4*e^4 - 4*a*b^2*c*e^4 + 2*a^2*c^2*e^4)*arctan(-(2*a*d - 2*a*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*c*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((a^2*c^2*d^4 - 2*a*b*c^2*d^3*e + b^2*c^2*d^2*e^2 + 2*a*c^3*d^2*e^2 - 2*b*c^3*d*e^3 + c^4*e^4)*sqrt(-b^2 + 4*a*c)) + 1/2*(a^2*b*d^2 - 2*a*b^2*d*e + 2*a^2*c*d*e + b^3*e^2 - 2*a*b*c*e^2)*log(-a + 2*a*d/(x*e + d) - a*d^2/(x*e + d)^2 - b*e/(x*e + d) + b*d*e/(x*e + d)^2 - c*e^2/(x*e + d)^2)/(a^2*c^2*d^4 - 2*a*b*c^2*d^3*e + b^2*c^2*d^2*e^2 + 2*a*c^3*d^2*e^2 - 2*b*c^3*d*e^3 + c^4*e^4) - e^7/((a*d^4*e^4 - b*d^3*e^5 + c*d^2*e^6)*(x*e + d)) - (b*d*e + 2*c*e^2)*e^(-1)*log(abs(-d/(x*e + d) + 1))/(c^2*d^3) + e/(c*d^3*(d/(x*e + d) - 1))","A",0
78,1,587,0,0.488230," ","integrate(1/(a+c/x^2+b/x)/x^5/(e*x+d)^2,x, algorithm=""giac"")","\frac{{\left(a^{2} b^{3} d^{2} e^{2} - 3 \, a^{3} b c d^{2} e^{2} - 2 \, a b^{4} d e^{3} + 8 \, a^{2} b^{2} c d e^{3} - 4 \, a^{3} c^{2} d e^{3} + b^{5} e^{4} - 5 \, a b^{3} c e^{4} + 5 \, a^{2} b c^{2} e^{4}\right)} \arctan\left(-\frac{{\left(2 \, a d - \frac{2 \, a d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, c e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(a^{2} c^{3} d^{4} - 2 \, a b c^{3} d^{3} e + b^{2} c^{3} d^{2} e^{2} + 2 \, a c^{4} d^{2} e^{2} - 2 \, b c^{4} d e^{3} + c^{5} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{{\left(a^{2} b^{2} d^{2} - a^{3} c d^{2} - 2 \, a b^{3} d e + 4 \, a^{2} b c d e + b^{4} e^{2} - 3 \, a b^{2} c e^{2} + a^{2} c^{2} e^{2}\right)} \log\left(-a + \frac{2 \, a d}{x e + d} - \frac{a d^{2}}{{\left(x e + d\right)}^{2}} - \frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{c e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(a^{2} c^{3} d^{4} - 2 \, a b c^{3} d^{3} e + b^{2} c^{3} d^{2} e^{2} + 2 \, a c^{4} d^{2} e^{2} - 2 \, b c^{4} d e^{3} + c^{5} e^{4}\right)}} + \frac{e^{9}}{{\left(a d^{5} e^{5} - b d^{4} e^{6} + c d^{3} e^{7}\right)} {\left(x e + d\right)}} + \frac{{\left(b^{2} d^{2} e - a c d^{2} e + 2 \, b c d e^{2} + 3 \, c^{2} e^{3}\right)} e^{\left(-1\right)} \log\left({\left| -\frac{d}{x e + d} + 1 \right|}\right)}{c^{3} d^{4}} + \frac{2 \, b c d e + 5 \, c^{2} e^{2} - \frac{2 \, {\left(b c d^{2} e^{2} + 3 \, c^{2} d e^{3}\right)} e^{\left(-1\right)}}{x e + d}}{2 \, c^{3} d^{4} {\left(\frac{d}{x e + d} - 1\right)}^{2}}"," ",0,"(a^2*b^3*d^2*e^2 - 3*a^3*b*c*d^2*e^2 - 2*a*b^4*d*e^3 + 8*a^2*b^2*c*d*e^3 - 4*a^3*c^2*d*e^3 + b^5*e^4 - 5*a*b^3*c*e^4 + 5*a^2*b*c^2*e^4)*arctan(-(2*a*d - 2*a*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*c*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((a^2*c^3*d^4 - 2*a*b*c^3*d^3*e + b^2*c^3*d^2*e^2 + 2*a*c^4*d^2*e^2 - 2*b*c^4*d*e^3 + c^5*e^4)*sqrt(-b^2 + 4*a*c)) - 1/2*(a^2*b^2*d^2 - a^3*c*d^2 - 2*a*b^3*d*e + 4*a^2*b*c*d*e + b^4*e^2 - 3*a*b^2*c*e^2 + a^2*c^2*e^2)*log(-a + 2*a*d/(x*e + d) - a*d^2/(x*e + d)^2 - b*e/(x*e + d) + b*d*e/(x*e + d)^2 - c*e^2/(x*e + d)^2)/(a^2*c^3*d^4 - 2*a*b*c^3*d^3*e + b^2*c^3*d^2*e^2 + 2*a*c^4*d^2*e^2 - 2*b*c^4*d*e^3 + c^5*e^4) + e^9/((a*d^5*e^5 - b*d^4*e^6 + c*d^3*e^7)*(x*e + d)) + (b^2*d^2*e - a*c*d^2*e + 2*b*c*d*e^2 + 3*c^2*e^3)*e^(-1)*log(abs(-d/(x*e + d) + 1))/(c^3*d^4) + 1/2*(2*b*c*d*e + 5*c^2*e^2 - 2*(b*c*d^2*e^2 + 3*c^2*d*e^3)*e^(-1)/(x*e + d))/(c^3*d^4*(d/(x*e + d) - 1)^2)","A",0
79,0,0,0,0.000000," ","integrate(x^4*(a+c/x^2+b/x)^(1/2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x + d} \sqrt{a + \frac{b}{x} + \frac{c}{x^{2}}} x^{4}\,{d x}"," ",0,"integrate(sqrt(e*x + d)*sqrt(a + b/x + c/x^2)*x^4, x)","F",0
80,0,0,0,0.000000," ","integrate(x^3*(a+c/x^2+b/x)^(1/2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x + d} \sqrt{a + \frac{b}{x} + \frac{c}{x^{2}}} x^{3}\,{d x}"," ",0,"integrate(sqrt(e*x + d)*sqrt(a + b/x + c/x^2)*x^3, x)","F",0
81,0,0,0,0.000000," ","integrate(x^2*(a+c/x^2+b/x)^(1/2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x + d} \sqrt{a + \frac{b}{x} + \frac{c}{x^{2}}} x^{2}\,{d x}"," ",0,"integrate(sqrt(e*x + d)*sqrt(a + b/x + c/x^2)*x^2, x)","F",0
82,0,0,0,0.000000," ","integrate(x*(a+c/x^2+b/x)^(1/2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x + d} \sqrt{a + \frac{b}{x} + \frac{c}{x^{2}}} x\,{d x}"," ",0,"integrate(sqrt(e*x + d)*sqrt(a + b/x + c/x^2)*x, x)","F",0
83,0,0,0,0.000000," ","integrate((a+c/x^2+b/x)^(1/2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x + d} \sqrt{a + \frac{b}{x} + \frac{c}{x^{2}}}\,{d x}"," ",0,"integrate(sqrt(e*x + d)*sqrt(a + b/x + c/x^2), x)","F",0
84,0,0,0,0.000000," ","integrate((a+c/x^2+b/x)^(1/2)*(e*x+d)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{e x + d} \sqrt{a + \frac{b}{x} + \frac{c}{x^{2}}}}{x}\,{d x}"," ",0,"integrate(sqrt(e*x + d)*sqrt(a + b/x + c/x^2)/x, x)","F",0
85,0,0,0,0.000000," ","integrate((a+c/x^2+b/x)^(1/2)*(e*x+d)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{e x + d} \sqrt{a + \frac{b}{x} + \frac{c}{x^{2}}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(e*x + d)*sqrt(a + b/x + c/x^2)/x^2, x)","F",0
86,0,0,0,0.000000," ","integrate((f*x)^m*(d+e*x^n)^q*(a+c*x^(2*n))^p,x, algorithm=""giac"")","\int {\left(c x^{2 \, n} + a\right)}^{p} {\left(e x^{n} + d\right)}^{q} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((c*x^(2*n) + a)^p*(e*x^n + d)^q*(f*x)^m, x)","F",0
87,-2,0,0,0.000000," ","integrate((f*x)^m*(d+e*x^n)^3*(a+c*x^(2*n))^p,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming x near 0Simplification assuming f near 0Simplification assuming x near 0Simplification assuming f near 0Unable to divide, perhaps due to rounding error%%%{-16,[1,0,6,3,1,2,4,4,1]%%%}+%%%{-64,[1,0,6,3,1,2,3,4,1]%%%}+%%%{-96,[1,0,6,3,1,2,2,4,1]%%%}+%%%{-64,[1,0,6,3,1,2,1,4,1]%%%}+%%%{-16,[1,0,6,3,1,2,0,4,1]%%%}+%%%{-16,[1,0,6,3,0,2,4,4,1]%%%}+%%%{-64,[1,0,6,3,0,2,3,4,1]%%%}+%%%{-96,[1,0,6,3,0,2,2,4,1]%%%}+%%%{-64,[1,0,6,3,0,2,1,4,1]%%%}+%%%{-16,[1,0,6,3,0,2,0,4,1]%%%} / %%%{16,[0,0,6,4,0,2,4,4,0]%%%}+%%%{64,[0,0,6,4,0,2,3,4,0]%%%}+%%%{96,[0,0,6,4,0,2,2,4,0]%%%}+%%%{64,[0,0,6,4,0,2,1,4,0]%%%}+%%%{16,[0,0,6,4,0,2,0,4,0]%%%} Error: Bad Argument Value","F(-2)",0
88,-2,0,0,0.000000," ","integrate((f*x)^m*(d+e*x^n)^2*(a+c*x^(2*n))^p,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming x near 0Simplification assuming f near 0Simplification assuming x near 0Simplification assuming f near 0Unable to divide, perhaps due to rounding error%%%{4,[0,0,3,2,1,0,2,3,1]%%%}+%%%{8,[0,0,3,2,1,0,1,3,1]%%%}+%%%{4,[0,0,3,2,1,0,0,3,1]%%%}+%%%{4,[0,0,3,2,0,0,2,3,1]%%%}+%%%{8,[0,0,3,2,0,0,1,3,1]%%%}+%%%{4,[0,0,3,2,0,0,0,3,1]%%%} / %%%{-8,[0,0,4,3,0,1,3,3,0]%%%}+%%%{-24,[0,0,4,3,0,1,2,3,0]%%%}+%%%{-24,[0,0,4,3,0,1,1,3,0]%%%}+%%%{-8,[0,0,4,3,0,1,0,3,0]%%%} Error: Bad Argument Value","F(-2)",0
89,0,0,0,0.000000," ","integrate((f*x)^m*(d+e*x^n)*(a+c*x^(2*n))^p,x, algorithm=""giac"")","\int {\left(e x^{n} + d\right)} {\left(c x^{2 \, n} + a\right)}^{p} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((e*x^n + d)*(c*x^(2*n) + a)^p*(f*x)^m, x)","F",0
90,0,0,0,0.000000," ","integrate((f*x)^m*(a+c*x^(2*n))^p/(d+e*x^n),x, algorithm=""giac"")","\int \frac{{\left(c x^{2 \, n} + a\right)}^{p} \left(f x\right)^{m}}{e x^{n} + d}\,{d x}"," ",0,"integrate((c*x^(2*n) + a)^p*(f*x)^m/(e*x^n + d), x)","F",0
91,0,0,0,0.000000," ","integrate((f*x)^m*(a+c*x^(2*n))^p/(d+e*x^n)^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{2 \, n} + a\right)}^{p} \left(f x\right)^{m}}{{\left(e x^{n} + d\right)}^{2}}\,{d x}"," ",0,"integrate((c*x^(2*n) + a)^p*(f*x)^m/(e*x^n + d)^2, x)","F",0
92,0,0,0,0.000000," ","integrate((f*x)^m*(a+c*x^(2*n))^p/(d+e*x^n)^3,x, algorithm=""giac"")","\int \frac{{\left(c x^{2 \, n} + a\right)}^{p} \left(f x\right)^{m}}{{\left(e x^{n} + d\right)}^{3}}\,{d x}"," ",0,"integrate((c*x^(2*n) + a)^p*(f*x)^m/(e*x^n + d)^3, x)","F",0
93,1,216,0,0.433587," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^13,x, algorithm=""giac"")","\frac{1}{14} \, {\left(c x^{2} + b x\right)}^{14} + {\left(c x^{2} + b x\right)}^{13} a + \frac{13}{2} \, {\left(c x^{2} + b x\right)}^{12} a^{2} + 26 \, {\left(c x^{2} + b x\right)}^{11} a^{3} + \frac{143}{2} \, {\left(c x^{2} + b x\right)}^{10} a^{4} + 143 \, {\left(c x^{2} + b x\right)}^{9} a^{5} + \frac{429}{2} \, {\left(c x^{2} + b x\right)}^{8} a^{6} + \frac{1716}{7} \, {\left(c x^{2} + b x\right)}^{7} a^{7} + \frac{429}{2} \, {\left(c x^{2} + b x\right)}^{6} a^{8} + 143 \, {\left(c x^{2} + b x\right)}^{5} a^{9} + \frac{143}{2} \, {\left(c x^{2} + b x\right)}^{4} a^{10} + 26 \, {\left(c x^{2} + b x\right)}^{3} a^{11} + \frac{13}{2} \, {\left(c x^{2} + b x\right)}^{2} a^{12} + {\left(c x^{2} + b x\right)} a^{13}"," ",0,"1/14*(c*x^2 + b*x)^14 + (c*x^2 + b*x)^13*a + 13/2*(c*x^2 + b*x)^12*a^2 + 26*(c*x^2 + b*x)^11*a^3 + 143/2*(c*x^2 + b*x)^10*a^4 + 143*(c*x^2 + b*x)^9*a^5 + 429/2*(c*x^2 + b*x)^8*a^6 + 1716/7*(c*x^2 + b*x)^7*a^7 + 429/2*(c*x^2 + b*x)^6*a^8 + 143*(c*x^2 + b*x)^5*a^9 + 143/2*(c*x^2 + b*x)^4*a^10 + 26*(c*x^2 + b*x)^3*a^11 + 13/2*(c*x^2 + b*x)^2*a^12 + (c*x^2 + b*x)*a^13","B",0
94,1,246,0,0.660818," ","integrate(x*(2*c*x^2+b)*(c*x^4+b*x^2+a)^13,x, algorithm=""giac"")","\frac{1}{28} \, {\left(c x^{4} + b x^{2}\right)}^{14} + \frac{1}{2} \, {\left(c x^{4} + b x^{2}\right)}^{13} a + \frac{13}{4} \, {\left(c x^{4} + b x^{2}\right)}^{12} a^{2} + 13 \, {\left(c x^{4} + b x^{2}\right)}^{11} a^{3} + \frac{143}{4} \, {\left(c x^{4} + b x^{2}\right)}^{10} a^{4} + \frac{143}{2} \, {\left(c x^{4} + b x^{2}\right)}^{9} a^{5} + \frac{429}{4} \, {\left(c x^{4} + b x^{2}\right)}^{8} a^{6} + \frac{858}{7} \, {\left(c x^{4} + b x^{2}\right)}^{7} a^{7} + \frac{429}{4} \, {\left(c x^{4} + b x^{2}\right)}^{6} a^{8} + \frac{143}{2} \, {\left(c x^{4} + b x^{2}\right)}^{5} a^{9} + \frac{143}{4} \, {\left(c x^{4} + b x^{2}\right)}^{4} a^{10} + 13 \, {\left(c x^{4} + b x^{2}\right)}^{3} a^{11} + \frac{13}{4} \, {\left(c x^{4} + b x^{2}\right)}^{2} a^{12} + \frac{1}{2} \, {\left(c x^{4} + b x^{2}\right)} a^{13}"," ",0,"1/28*(c*x^4 + b*x^2)^14 + 1/2*(c*x^4 + b*x^2)^13*a + 13/4*(c*x^4 + b*x^2)^12*a^2 + 13*(c*x^4 + b*x^2)^11*a^3 + 143/4*(c*x^4 + b*x^2)^10*a^4 + 143/2*(c*x^4 + b*x^2)^9*a^5 + 429/4*(c*x^4 + b*x^2)^8*a^6 + 858/7*(c*x^4 + b*x^2)^7*a^7 + 429/4*(c*x^4 + b*x^2)^6*a^8 + 143/2*(c*x^4 + b*x^2)^5*a^9 + 143/4*(c*x^4 + b*x^2)^4*a^10 + 13*(c*x^4 + b*x^2)^3*a^11 + 13/4*(c*x^4 + b*x^2)^2*a^12 + 1/2*(c*x^4 + b*x^2)*a^13","B",0
95,1,246,0,0.608573," ","integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3+a)^13,x, algorithm=""giac"")","\frac{1}{42} \, {\left(c x^{6} + b x^{3}\right)}^{14} + \frac{1}{3} \, {\left(c x^{6} + b x^{3}\right)}^{13} a + \frac{13}{6} \, {\left(c x^{6} + b x^{3}\right)}^{12} a^{2} + \frac{26}{3} \, {\left(c x^{6} + b x^{3}\right)}^{11} a^{3} + \frac{143}{6} \, {\left(c x^{6} + b x^{3}\right)}^{10} a^{4} + \frac{143}{3} \, {\left(c x^{6} + b x^{3}\right)}^{9} a^{5} + \frac{143}{2} \, {\left(c x^{6} + b x^{3}\right)}^{8} a^{6} + \frac{572}{7} \, {\left(c x^{6} + b x^{3}\right)}^{7} a^{7} + \frac{143}{2} \, {\left(c x^{6} + b x^{3}\right)}^{6} a^{8} + \frac{143}{3} \, {\left(c x^{6} + b x^{3}\right)}^{5} a^{9} + \frac{143}{6} \, {\left(c x^{6} + b x^{3}\right)}^{4} a^{10} + \frac{26}{3} \, {\left(c x^{6} + b x^{3}\right)}^{3} a^{11} + \frac{13}{6} \, {\left(c x^{6} + b x^{3}\right)}^{2} a^{12} + \frac{1}{3} \, {\left(c x^{6} + b x^{3}\right)} a^{13}"," ",0,"1/42*(c*x^6 + b*x^3)^14 + 1/3*(c*x^6 + b*x^3)^13*a + 13/6*(c*x^6 + b*x^3)^12*a^2 + 26/3*(c*x^6 + b*x^3)^11*a^3 + 143/6*(c*x^6 + b*x^3)^10*a^4 + 143/3*(c*x^6 + b*x^3)^9*a^5 + 143/2*(c*x^6 + b*x^3)^8*a^6 + 572/7*(c*x^6 + b*x^3)^7*a^7 + 143/2*(c*x^6 + b*x^3)^6*a^8 + 143/3*(c*x^6 + b*x^3)^5*a^9 + 143/6*(c*x^6 + b*x^3)^4*a^10 + 26/3*(c*x^6 + b*x^3)^3*a^11 + 13/6*(c*x^6 + b*x^3)^2*a^12 + 1/3*(c*x^6 + b*x^3)*a^13","B",0
96,1,1693,0,1.001596," ","integrate(x^(-1+n)*(b+2*c*x^n)*(a+b*x^n+c*x^(2*n))^13,x, algorithm=""giac"")","\frac{c^{14} x^{28 \, n} + 14 \, b c^{13} x^{27 \, n} + 91 \, b^{2} c^{12} x^{26 \, n} + 14 \, a c^{13} x^{26 \, n} + 364 \, b^{3} c^{11} x^{25 \, n} + 182 \, a b c^{12} x^{25 \, n} + 1001 \, b^{4} c^{10} x^{24 \, n} + 1092 \, a b^{2} c^{11} x^{24 \, n} + 91 \, a^{2} c^{12} x^{24 \, n} + 2002 \, b^{5} c^{9} x^{23 \, n} + 4004 \, a b^{3} c^{10} x^{23 \, n} + 1092 \, a^{2} b c^{11} x^{23 \, n} + 3003 \, b^{6} c^{8} x^{22 \, n} + 10010 \, a b^{4} c^{9} x^{22 \, n} + 6006 \, a^{2} b^{2} c^{10} x^{22 \, n} + 364 \, a^{3} c^{11} x^{22 \, n} + 3432 \, b^{7} c^{7} x^{21 \, n} + 18018 \, a b^{5} c^{8} x^{21 \, n} + 20020 \, a^{2} b^{3} c^{9} x^{21 \, n} + 4004 \, a^{3} b c^{10} x^{21 \, n} + 3003 \, b^{8} c^{6} x^{20 \, n} + 24024 \, a b^{6} c^{7} x^{20 \, n} + 45045 \, a^{2} b^{4} c^{8} x^{20 \, n} + 20020 \, a^{3} b^{2} c^{9} x^{20 \, n} + 1001 \, a^{4} c^{10} x^{20 \, n} + 2002 \, b^{9} c^{5} x^{19 \, n} + 24024 \, a b^{7} c^{6} x^{19 \, n} + 72072 \, a^{2} b^{5} c^{7} x^{19 \, n} + 60060 \, a^{3} b^{3} c^{8} x^{19 \, n} + 10010 \, a^{4} b c^{9} x^{19 \, n} + 1001 \, b^{10} c^{4} x^{18 \, n} + 18018 \, a b^{8} c^{5} x^{18 \, n} + 84084 \, a^{2} b^{6} c^{6} x^{18 \, n} + 120120 \, a^{3} b^{4} c^{7} x^{18 \, n} + 45045 \, a^{4} b^{2} c^{8} x^{18 \, n} + 2002 \, a^{5} c^{9} x^{18 \, n} + 364 \, b^{11} c^{3} x^{17 \, n} + 10010 \, a b^{9} c^{4} x^{17 \, n} + 72072 \, a^{2} b^{7} c^{5} x^{17 \, n} + 168168 \, a^{3} b^{5} c^{6} x^{17 \, n} + 120120 \, a^{4} b^{3} c^{7} x^{17 \, n} + 18018 \, a^{5} b c^{8} x^{17 \, n} + 91 \, b^{12} c^{2} x^{16 \, n} + 4004 \, a b^{10} c^{3} x^{16 \, n} + 45045 \, a^{2} b^{8} c^{4} x^{16 \, n} + 168168 \, a^{3} b^{6} c^{5} x^{16 \, n} + 210210 \, a^{4} b^{4} c^{6} x^{16 \, n} + 72072 \, a^{5} b^{2} c^{7} x^{16 \, n} + 3003 \, a^{6} c^{8} x^{16 \, n} + 14 \, b^{13} c x^{15 \, n} + 1092 \, a b^{11} c^{2} x^{15 \, n} + 20020 \, a^{2} b^{9} c^{3} x^{15 \, n} + 120120 \, a^{3} b^{7} c^{4} x^{15 \, n} + 252252 \, a^{4} b^{5} c^{5} x^{15 \, n} + 168168 \, a^{5} b^{3} c^{6} x^{15 \, n} + 24024 \, a^{6} b c^{7} x^{15 \, n} + b^{14} x^{14 \, n} + 182 \, a b^{12} c x^{14 \, n} + 6006 \, a^{2} b^{10} c^{2} x^{14 \, n} + 60060 \, a^{3} b^{8} c^{3} x^{14 \, n} + 210210 \, a^{4} b^{6} c^{4} x^{14 \, n} + 252252 \, a^{5} b^{4} c^{5} x^{14 \, n} + 84084 \, a^{6} b^{2} c^{6} x^{14 \, n} + 3432 \, a^{7} c^{7} x^{14 \, n} + 14 \, a b^{13} x^{13 \, n} + 1092 \, a^{2} b^{11} c x^{13 \, n} + 20020 \, a^{3} b^{9} c^{2} x^{13 \, n} + 120120 \, a^{4} b^{7} c^{3} x^{13 \, n} + 252252 \, a^{5} b^{5} c^{4} x^{13 \, n} + 168168 \, a^{6} b^{3} c^{5} x^{13 \, n} + 24024 \, a^{7} b c^{6} x^{13 \, n} + 91 \, a^{2} b^{12} x^{12 \, n} + 4004 \, a^{3} b^{10} c x^{12 \, n} + 45045 \, a^{4} b^{8} c^{2} x^{12 \, n} + 168168 \, a^{5} b^{6} c^{3} x^{12 \, n} + 210210 \, a^{6} b^{4} c^{4} x^{12 \, n} + 72072 \, a^{7} b^{2} c^{5} x^{12 \, n} + 3003 \, a^{8} c^{6} x^{12 \, n} + 364 \, a^{3} b^{11} x^{11 \, n} + 10010 \, a^{4} b^{9} c x^{11 \, n} + 72072 \, a^{5} b^{7} c^{2} x^{11 \, n} + 168168 \, a^{6} b^{5} c^{3} x^{11 \, n} + 120120 \, a^{7} b^{3} c^{4} x^{11 \, n} + 18018 \, a^{8} b c^{5} x^{11 \, n} + 1001 \, a^{4} b^{10} x^{10 \, n} + 18018 \, a^{5} b^{8} c x^{10 \, n} + 84084 \, a^{6} b^{6} c^{2} x^{10 \, n} + 120120 \, a^{7} b^{4} c^{3} x^{10 \, n} + 45045 \, a^{8} b^{2} c^{4} x^{10 \, n} + 2002 \, a^{9} c^{5} x^{10 \, n} + 2002 \, a^{5} b^{9} x^{9 \, n} + 24024 \, a^{6} b^{7} c x^{9 \, n} + 72072 \, a^{7} b^{5} c^{2} x^{9 \, n} + 60060 \, a^{8} b^{3} c^{3} x^{9 \, n} + 10010 \, a^{9} b c^{4} x^{9 \, n} + 3003 \, a^{6} b^{8} x^{8 \, n} + 24024 \, a^{7} b^{6} c x^{8 \, n} + 45045 \, a^{8} b^{4} c^{2} x^{8 \, n} + 20020 \, a^{9} b^{2} c^{3} x^{8 \, n} + 1001 \, a^{10} c^{4} x^{8 \, n} + 3432 \, a^{7} b^{7} x^{7 \, n} + 18018 \, a^{8} b^{5} c x^{7 \, n} + 20020 \, a^{9} b^{3} c^{2} x^{7 \, n} + 4004 \, a^{10} b c^{3} x^{7 \, n} + 3003 \, a^{8} b^{6} x^{6 \, n} + 10010 \, a^{9} b^{4} c x^{6 \, n} + 6006 \, a^{10} b^{2} c^{2} x^{6 \, n} + 364 \, a^{11} c^{3} x^{6 \, n} + 2002 \, a^{9} b^{5} x^{5 \, n} + 4004 \, a^{10} b^{3} c x^{5 \, n} + 1092 \, a^{11} b c^{2} x^{5 \, n} + 1001 \, a^{10} b^{4} x^{4 \, n} + 1092 \, a^{11} b^{2} c x^{4 \, n} + 91 \, a^{12} c^{2} x^{4 \, n} + 364 \, a^{11} b^{3} x^{3 \, n} + 182 \, a^{12} b c x^{3 \, n} + 91 \, a^{12} b^{2} x^{2 \, n} + 14 \, a^{13} c x^{2 \, n} + 14 \, a^{13} b x^{n}}{14 \, n}"," ",0,"1/14*(c^14*x^(28*n) + 14*b*c^13*x^(27*n) + 91*b^2*c^12*x^(26*n) + 14*a*c^13*x^(26*n) + 364*b^3*c^11*x^(25*n) + 182*a*b*c^12*x^(25*n) + 1001*b^4*c^10*x^(24*n) + 1092*a*b^2*c^11*x^(24*n) + 91*a^2*c^12*x^(24*n) + 2002*b^5*c^9*x^(23*n) + 4004*a*b^3*c^10*x^(23*n) + 1092*a^2*b*c^11*x^(23*n) + 3003*b^6*c^8*x^(22*n) + 10010*a*b^4*c^9*x^(22*n) + 6006*a^2*b^2*c^10*x^(22*n) + 364*a^3*c^11*x^(22*n) + 3432*b^7*c^7*x^(21*n) + 18018*a*b^5*c^8*x^(21*n) + 20020*a^2*b^3*c^9*x^(21*n) + 4004*a^3*b*c^10*x^(21*n) + 3003*b^8*c^6*x^(20*n) + 24024*a*b^6*c^7*x^(20*n) + 45045*a^2*b^4*c^8*x^(20*n) + 20020*a^3*b^2*c^9*x^(20*n) + 1001*a^4*c^10*x^(20*n) + 2002*b^9*c^5*x^(19*n) + 24024*a*b^7*c^6*x^(19*n) + 72072*a^2*b^5*c^7*x^(19*n) + 60060*a^3*b^3*c^8*x^(19*n) + 10010*a^4*b*c^9*x^(19*n) + 1001*b^10*c^4*x^(18*n) + 18018*a*b^8*c^5*x^(18*n) + 84084*a^2*b^6*c^6*x^(18*n) + 120120*a^3*b^4*c^7*x^(18*n) + 45045*a^4*b^2*c^8*x^(18*n) + 2002*a^5*c^9*x^(18*n) + 364*b^11*c^3*x^(17*n) + 10010*a*b^9*c^4*x^(17*n) + 72072*a^2*b^7*c^5*x^(17*n) + 168168*a^3*b^5*c^6*x^(17*n) + 120120*a^4*b^3*c^7*x^(17*n) + 18018*a^5*b*c^8*x^(17*n) + 91*b^12*c^2*x^(16*n) + 4004*a*b^10*c^3*x^(16*n) + 45045*a^2*b^8*c^4*x^(16*n) + 168168*a^3*b^6*c^5*x^(16*n) + 210210*a^4*b^4*c^6*x^(16*n) + 72072*a^5*b^2*c^7*x^(16*n) + 3003*a^6*c^8*x^(16*n) + 14*b^13*c*x^(15*n) + 1092*a*b^11*c^2*x^(15*n) + 20020*a^2*b^9*c^3*x^(15*n) + 120120*a^3*b^7*c^4*x^(15*n) + 252252*a^4*b^5*c^5*x^(15*n) + 168168*a^5*b^3*c^6*x^(15*n) + 24024*a^6*b*c^7*x^(15*n) + b^14*x^(14*n) + 182*a*b^12*c*x^(14*n) + 6006*a^2*b^10*c^2*x^(14*n) + 60060*a^3*b^8*c^3*x^(14*n) + 210210*a^4*b^6*c^4*x^(14*n) + 252252*a^5*b^4*c^5*x^(14*n) + 84084*a^6*b^2*c^6*x^(14*n) + 3432*a^7*c^7*x^(14*n) + 14*a*b^13*x^(13*n) + 1092*a^2*b^11*c*x^(13*n) + 20020*a^3*b^9*c^2*x^(13*n) + 120120*a^4*b^7*c^3*x^(13*n) + 252252*a^5*b^5*c^4*x^(13*n) + 168168*a^6*b^3*c^5*x^(13*n) + 24024*a^7*b*c^6*x^(13*n) + 91*a^2*b^12*x^(12*n) + 4004*a^3*b^10*c*x^(12*n) + 45045*a^4*b^8*c^2*x^(12*n) + 168168*a^5*b^6*c^3*x^(12*n) + 210210*a^6*b^4*c^4*x^(12*n) + 72072*a^7*b^2*c^5*x^(12*n) + 3003*a^8*c^6*x^(12*n) + 364*a^3*b^11*x^(11*n) + 10010*a^4*b^9*c*x^(11*n) + 72072*a^5*b^7*c^2*x^(11*n) + 168168*a^6*b^5*c^3*x^(11*n) + 120120*a^7*b^3*c^4*x^(11*n) + 18018*a^8*b*c^5*x^(11*n) + 1001*a^4*b^10*x^(10*n) + 18018*a^5*b^8*c*x^(10*n) + 84084*a^6*b^6*c^2*x^(10*n) + 120120*a^7*b^4*c^3*x^(10*n) + 45045*a^8*b^2*c^4*x^(10*n) + 2002*a^9*c^5*x^(10*n) + 2002*a^5*b^9*x^(9*n) + 24024*a^6*b^7*c*x^(9*n) + 72072*a^7*b^5*c^2*x^(9*n) + 60060*a^8*b^3*c^3*x^(9*n) + 10010*a^9*b*c^4*x^(9*n) + 3003*a^6*b^8*x^(8*n) + 24024*a^7*b^6*c*x^(8*n) + 45045*a^8*b^4*c^2*x^(8*n) + 20020*a^9*b^2*c^3*x^(8*n) + 1001*a^10*c^4*x^(8*n) + 3432*a^7*b^7*x^(7*n) + 18018*a^8*b^5*c*x^(7*n) + 20020*a^9*b^3*c^2*x^(7*n) + 4004*a^10*b*c^3*x^(7*n) + 3003*a^8*b^6*x^(6*n) + 10010*a^9*b^4*c*x^(6*n) + 6006*a^10*b^2*c^2*x^(6*n) + 364*a^11*c^3*x^(6*n) + 2002*a^9*b^5*x^(5*n) + 4004*a^10*b^3*c*x^(5*n) + 1092*a^11*b*c^2*x^(5*n) + 1001*a^10*b^4*x^(4*n) + 1092*a^11*b^2*c*x^(4*n) + 91*a^12*c^2*x^(4*n) + 364*a^11*b^3*x^(3*n) + 182*a^12*b*c*x^(3*n) + 91*a^12*b^2*x^(2*n) + 14*a^13*c*x^(2*n) + 14*a^13*b*x^n)/n","B",0
97,1,218,0,0.472809," ","integrate((2*c*x+b)*(c*x^2+b*x-a)^13,x, algorithm=""giac"")","\frac{1}{14} \, {\left(c x^{2} + b x\right)}^{14} - {\left(c x^{2} + b x\right)}^{13} a + \frac{13}{2} \, {\left(c x^{2} + b x\right)}^{12} a^{2} - 26 \, {\left(c x^{2} + b x\right)}^{11} a^{3} + \frac{143}{2} \, {\left(c x^{2} + b x\right)}^{10} a^{4} - 143 \, {\left(c x^{2} + b x\right)}^{9} a^{5} + \frac{429}{2} \, {\left(c x^{2} + b x\right)}^{8} a^{6} - \frac{1716}{7} \, {\left(c x^{2} + b x\right)}^{7} a^{7} + \frac{429}{2} \, {\left(c x^{2} + b x\right)}^{6} a^{8} - 143 \, {\left(c x^{2} + b x\right)}^{5} a^{9} + \frac{143}{2} \, {\left(c x^{2} + b x\right)}^{4} a^{10} - 26 \, {\left(c x^{2} + b x\right)}^{3} a^{11} + \frac{13}{2} \, {\left(c x^{2} + b x\right)}^{2} a^{12} - {\left(c x^{2} + b x\right)} a^{13}"," ",0,"1/14*(c*x^2 + b*x)^14 - (c*x^2 + b*x)^13*a + 13/2*(c*x^2 + b*x)^12*a^2 - 26*(c*x^2 + b*x)^11*a^3 + 143/2*(c*x^2 + b*x)^10*a^4 - 143*(c*x^2 + b*x)^9*a^5 + 429/2*(c*x^2 + b*x)^8*a^6 - 1716/7*(c*x^2 + b*x)^7*a^7 + 429/2*(c*x^2 + b*x)^6*a^8 - 143*(c*x^2 + b*x)^5*a^9 + 143/2*(c*x^2 + b*x)^4*a^10 - 26*(c*x^2 + b*x)^3*a^11 + 13/2*(c*x^2 + b*x)^2*a^12 - (c*x^2 + b*x)*a^13","B",0
98,1,246,0,0.571974," ","integrate(x*(2*c*x^2+b)*(c*x^4+b*x^2-a)^13,x, algorithm=""giac"")","\frac{1}{28} \, {\left(c x^{4} + b x^{2}\right)}^{14} - \frac{1}{2} \, {\left(c x^{4} + b x^{2}\right)}^{13} a + \frac{13}{4} \, {\left(c x^{4} + b x^{2}\right)}^{12} a^{2} - 13 \, {\left(c x^{4} + b x^{2}\right)}^{11} a^{3} + \frac{143}{4} \, {\left(c x^{4} + b x^{2}\right)}^{10} a^{4} - \frac{143}{2} \, {\left(c x^{4} + b x^{2}\right)}^{9} a^{5} + \frac{429}{4} \, {\left(c x^{4} + b x^{2}\right)}^{8} a^{6} - \frac{858}{7} \, {\left(c x^{4} + b x^{2}\right)}^{7} a^{7} + \frac{429}{4} \, {\left(c x^{4} + b x^{2}\right)}^{6} a^{8} - \frac{143}{2} \, {\left(c x^{4} + b x^{2}\right)}^{5} a^{9} + \frac{143}{4} \, {\left(c x^{4} + b x^{2}\right)}^{4} a^{10} - 13 \, {\left(c x^{4} + b x^{2}\right)}^{3} a^{11} + \frac{13}{4} \, {\left(c x^{4} + b x^{2}\right)}^{2} a^{12} - \frac{1}{2} \, {\left(c x^{4} + b x^{2}\right)} a^{13}"," ",0,"1/28*(c*x^4 + b*x^2)^14 - 1/2*(c*x^4 + b*x^2)^13*a + 13/4*(c*x^4 + b*x^2)^12*a^2 - 13*(c*x^4 + b*x^2)^11*a^3 + 143/4*(c*x^4 + b*x^2)^10*a^4 - 143/2*(c*x^4 + b*x^2)^9*a^5 + 429/4*(c*x^4 + b*x^2)^8*a^6 - 858/7*(c*x^4 + b*x^2)^7*a^7 + 429/4*(c*x^4 + b*x^2)^6*a^8 - 143/2*(c*x^4 + b*x^2)^5*a^9 + 143/4*(c*x^4 + b*x^2)^4*a^10 - 13*(c*x^4 + b*x^2)^3*a^11 + 13/4*(c*x^4 + b*x^2)^2*a^12 - 1/2*(c*x^4 + b*x^2)*a^13","B",0
99,1,246,0,0.682715," ","integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3-a)^13,x, algorithm=""giac"")","\frac{1}{42} \, {\left(c x^{6} + b x^{3}\right)}^{14} - \frac{1}{3} \, {\left(c x^{6} + b x^{3}\right)}^{13} a + \frac{13}{6} \, {\left(c x^{6} + b x^{3}\right)}^{12} a^{2} - \frac{26}{3} \, {\left(c x^{6} + b x^{3}\right)}^{11} a^{3} + \frac{143}{6} \, {\left(c x^{6} + b x^{3}\right)}^{10} a^{4} - \frac{143}{3} \, {\left(c x^{6} + b x^{3}\right)}^{9} a^{5} + \frac{143}{2} \, {\left(c x^{6} + b x^{3}\right)}^{8} a^{6} - \frac{572}{7} \, {\left(c x^{6} + b x^{3}\right)}^{7} a^{7} + \frac{143}{2} \, {\left(c x^{6} + b x^{3}\right)}^{6} a^{8} - \frac{143}{3} \, {\left(c x^{6} + b x^{3}\right)}^{5} a^{9} + \frac{143}{6} \, {\left(c x^{6} + b x^{3}\right)}^{4} a^{10} - \frac{26}{3} \, {\left(c x^{6} + b x^{3}\right)}^{3} a^{11} + \frac{13}{6} \, {\left(c x^{6} + b x^{3}\right)}^{2} a^{12} - \frac{1}{3} \, {\left(c x^{6} + b x^{3}\right)} a^{13}"," ",0,"1/42*(c*x^6 + b*x^3)^14 - 1/3*(c*x^6 + b*x^3)^13*a + 13/6*(c*x^6 + b*x^3)^12*a^2 - 26/3*(c*x^6 + b*x^3)^11*a^3 + 143/6*(c*x^6 + b*x^3)^10*a^4 - 143/3*(c*x^6 + b*x^3)^9*a^5 + 143/2*(c*x^6 + b*x^3)^8*a^6 - 572/7*(c*x^6 + b*x^3)^7*a^7 + 143/2*(c*x^6 + b*x^3)^6*a^8 - 143/3*(c*x^6 + b*x^3)^5*a^9 + 143/6*(c*x^6 + b*x^3)^4*a^10 - 26/3*(c*x^6 + b*x^3)^3*a^11 + 13/6*(c*x^6 + b*x^3)^2*a^12 - 1/3*(c*x^6 + b*x^3)*a^13","B",0
100,1,1693,0,1.088619," ","integrate(x^(-1+n)*(b+2*c*x^n)*(-a+b*x^n+c*x^(2*n))^13,x, algorithm=""giac"")","\frac{c^{14} x^{28 \, n} + 14 \, b c^{13} x^{27 \, n} + 91 \, b^{2} c^{12} x^{26 \, n} - 14 \, a c^{13} x^{26 \, n} + 364 \, b^{3} c^{11} x^{25 \, n} - 182 \, a b c^{12} x^{25 \, n} + 1001 \, b^{4} c^{10} x^{24 \, n} - 1092 \, a b^{2} c^{11} x^{24 \, n} + 91 \, a^{2} c^{12} x^{24 \, n} + 2002 \, b^{5} c^{9} x^{23 \, n} - 4004 \, a b^{3} c^{10} x^{23 \, n} + 1092 \, a^{2} b c^{11} x^{23 \, n} + 3003 \, b^{6} c^{8} x^{22 \, n} - 10010 \, a b^{4} c^{9} x^{22 \, n} + 6006 \, a^{2} b^{2} c^{10} x^{22 \, n} - 364 \, a^{3} c^{11} x^{22 \, n} + 3432 \, b^{7} c^{7} x^{21 \, n} - 18018 \, a b^{5} c^{8} x^{21 \, n} + 20020 \, a^{2} b^{3} c^{9} x^{21 \, n} - 4004 \, a^{3} b c^{10} x^{21 \, n} + 3003 \, b^{8} c^{6} x^{20 \, n} - 24024 \, a b^{6} c^{7} x^{20 \, n} + 45045 \, a^{2} b^{4} c^{8} x^{20 \, n} - 20020 \, a^{3} b^{2} c^{9} x^{20 \, n} + 1001 \, a^{4} c^{10} x^{20 \, n} + 2002 \, b^{9} c^{5} x^{19 \, n} - 24024 \, a b^{7} c^{6} x^{19 \, n} + 72072 \, a^{2} b^{5} c^{7} x^{19 \, n} - 60060 \, a^{3} b^{3} c^{8} x^{19 \, n} + 10010 \, a^{4} b c^{9} x^{19 \, n} + 1001 \, b^{10} c^{4} x^{18 \, n} - 18018 \, a b^{8} c^{5} x^{18 \, n} + 84084 \, a^{2} b^{6} c^{6} x^{18 \, n} - 120120 \, a^{3} b^{4} c^{7} x^{18 \, n} + 45045 \, a^{4} b^{2} c^{8} x^{18 \, n} - 2002 \, a^{5} c^{9} x^{18 \, n} + 364 \, b^{11} c^{3} x^{17 \, n} - 10010 \, a b^{9} c^{4} x^{17 \, n} + 72072 \, a^{2} b^{7} c^{5} x^{17 \, n} - 168168 \, a^{3} b^{5} c^{6} x^{17 \, n} + 120120 \, a^{4} b^{3} c^{7} x^{17 \, n} - 18018 \, a^{5} b c^{8} x^{17 \, n} + 91 \, b^{12} c^{2} x^{16 \, n} - 4004 \, a b^{10} c^{3} x^{16 \, n} + 45045 \, a^{2} b^{8} c^{4} x^{16 \, n} - 168168 \, a^{3} b^{6} c^{5} x^{16 \, n} + 210210 \, a^{4} b^{4} c^{6} x^{16 \, n} - 72072 \, a^{5} b^{2} c^{7} x^{16 \, n} + 3003 \, a^{6} c^{8} x^{16 \, n} + 14 \, b^{13} c x^{15 \, n} - 1092 \, a b^{11} c^{2} x^{15 \, n} + 20020 \, a^{2} b^{9} c^{3} x^{15 \, n} - 120120 \, a^{3} b^{7} c^{4} x^{15 \, n} + 252252 \, a^{4} b^{5} c^{5} x^{15 \, n} - 168168 \, a^{5} b^{3} c^{6} x^{15 \, n} + 24024 \, a^{6} b c^{7} x^{15 \, n} + b^{14} x^{14 \, n} - 182 \, a b^{12} c x^{14 \, n} + 6006 \, a^{2} b^{10} c^{2} x^{14 \, n} - 60060 \, a^{3} b^{8} c^{3} x^{14 \, n} + 210210 \, a^{4} b^{6} c^{4} x^{14 \, n} - 252252 \, a^{5} b^{4} c^{5} x^{14 \, n} + 84084 \, a^{6} b^{2} c^{6} x^{14 \, n} - 3432 \, a^{7} c^{7} x^{14 \, n} - 14 \, a b^{13} x^{13 \, n} + 1092 \, a^{2} b^{11} c x^{13 \, n} - 20020 \, a^{3} b^{9} c^{2} x^{13 \, n} + 120120 \, a^{4} b^{7} c^{3} x^{13 \, n} - 252252 \, a^{5} b^{5} c^{4} x^{13 \, n} + 168168 \, a^{6} b^{3} c^{5} x^{13 \, n} - 24024 \, a^{7} b c^{6} x^{13 \, n} + 91 \, a^{2} b^{12} x^{12 \, n} - 4004 \, a^{3} b^{10} c x^{12 \, n} + 45045 \, a^{4} b^{8} c^{2} x^{12 \, n} - 168168 \, a^{5} b^{6} c^{3} x^{12 \, n} + 210210 \, a^{6} b^{4} c^{4} x^{12 \, n} - 72072 \, a^{7} b^{2} c^{5} x^{12 \, n} + 3003 \, a^{8} c^{6} x^{12 \, n} - 364 \, a^{3} b^{11} x^{11 \, n} + 10010 \, a^{4} b^{9} c x^{11 \, n} - 72072 \, a^{5} b^{7} c^{2} x^{11 \, n} + 168168 \, a^{6} b^{5} c^{3} x^{11 \, n} - 120120 \, a^{7} b^{3} c^{4} x^{11 \, n} + 18018 \, a^{8} b c^{5} x^{11 \, n} + 1001 \, a^{4} b^{10} x^{10 \, n} - 18018 \, a^{5} b^{8} c x^{10 \, n} + 84084 \, a^{6} b^{6} c^{2} x^{10 \, n} - 120120 \, a^{7} b^{4} c^{3} x^{10 \, n} + 45045 \, a^{8} b^{2} c^{4} x^{10 \, n} - 2002 \, a^{9} c^{5} x^{10 \, n} - 2002 \, a^{5} b^{9} x^{9 \, n} + 24024 \, a^{6} b^{7} c x^{9 \, n} - 72072 \, a^{7} b^{5} c^{2} x^{9 \, n} + 60060 \, a^{8} b^{3} c^{3} x^{9 \, n} - 10010 \, a^{9} b c^{4} x^{9 \, n} + 3003 \, a^{6} b^{8} x^{8 \, n} - 24024 \, a^{7} b^{6} c x^{8 \, n} + 45045 \, a^{8} b^{4} c^{2} x^{8 \, n} - 20020 \, a^{9} b^{2} c^{3} x^{8 \, n} + 1001 \, a^{10} c^{4} x^{8 \, n} - 3432 \, a^{7} b^{7} x^{7 \, n} + 18018 \, a^{8} b^{5} c x^{7 \, n} - 20020 \, a^{9} b^{3} c^{2} x^{7 \, n} + 4004 \, a^{10} b c^{3} x^{7 \, n} + 3003 \, a^{8} b^{6} x^{6 \, n} - 10010 \, a^{9} b^{4} c x^{6 \, n} + 6006 \, a^{10} b^{2} c^{2} x^{6 \, n} - 364 \, a^{11} c^{3} x^{6 \, n} - 2002 \, a^{9} b^{5} x^{5 \, n} + 4004 \, a^{10} b^{3} c x^{5 \, n} - 1092 \, a^{11} b c^{2} x^{5 \, n} + 1001 \, a^{10} b^{4} x^{4 \, n} - 1092 \, a^{11} b^{2} c x^{4 \, n} + 91 \, a^{12} c^{2} x^{4 \, n} - 364 \, a^{11} b^{3} x^{3 \, n} + 182 \, a^{12} b c x^{3 \, n} + 91 \, a^{12} b^{2} x^{2 \, n} - 14 \, a^{13} c x^{2 \, n} - 14 \, a^{13} b x^{n}}{14 \, n}"," ",0,"1/14*(c^14*x^(28*n) + 14*b*c^13*x^(27*n) + 91*b^2*c^12*x^(26*n) - 14*a*c^13*x^(26*n) + 364*b^3*c^11*x^(25*n) - 182*a*b*c^12*x^(25*n) + 1001*b^4*c^10*x^(24*n) - 1092*a*b^2*c^11*x^(24*n) + 91*a^2*c^12*x^(24*n) + 2002*b^5*c^9*x^(23*n) - 4004*a*b^3*c^10*x^(23*n) + 1092*a^2*b*c^11*x^(23*n) + 3003*b^6*c^8*x^(22*n) - 10010*a*b^4*c^9*x^(22*n) + 6006*a^2*b^2*c^10*x^(22*n) - 364*a^3*c^11*x^(22*n) + 3432*b^7*c^7*x^(21*n) - 18018*a*b^5*c^8*x^(21*n) + 20020*a^2*b^3*c^9*x^(21*n) - 4004*a^3*b*c^10*x^(21*n) + 3003*b^8*c^6*x^(20*n) - 24024*a*b^6*c^7*x^(20*n) + 45045*a^2*b^4*c^8*x^(20*n) - 20020*a^3*b^2*c^9*x^(20*n) + 1001*a^4*c^10*x^(20*n) + 2002*b^9*c^5*x^(19*n) - 24024*a*b^7*c^6*x^(19*n) + 72072*a^2*b^5*c^7*x^(19*n) - 60060*a^3*b^3*c^8*x^(19*n) + 10010*a^4*b*c^9*x^(19*n) + 1001*b^10*c^4*x^(18*n) - 18018*a*b^8*c^5*x^(18*n) + 84084*a^2*b^6*c^6*x^(18*n) - 120120*a^3*b^4*c^7*x^(18*n) + 45045*a^4*b^2*c^8*x^(18*n) - 2002*a^5*c^9*x^(18*n) + 364*b^11*c^3*x^(17*n) - 10010*a*b^9*c^4*x^(17*n) + 72072*a^2*b^7*c^5*x^(17*n) - 168168*a^3*b^5*c^6*x^(17*n) + 120120*a^4*b^3*c^7*x^(17*n) - 18018*a^5*b*c^8*x^(17*n) + 91*b^12*c^2*x^(16*n) - 4004*a*b^10*c^3*x^(16*n) + 45045*a^2*b^8*c^4*x^(16*n) - 168168*a^3*b^6*c^5*x^(16*n) + 210210*a^4*b^4*c^6*x^(16*n) - 72072*a^5*b^2*c^7*x^(16*n) + 3003*a^6*c^8*x^(16*n) + 14*b^13*c*x^(15*n) - 1092*a*b^11*c^2*x^(15*n) + 20020*a^2*b^9*c^3*x^(15*n) - 120120*a^3*b^7*c^4*x^(15*n) + 252252*a^4*b^5*c^5*x^(15*n) - 168168*a^5*b^3*c^6*x^(15*n) + 24024*a^6*b*c^7*x^(15*n) + b^14*x^(14*n) - 182*a*b^12*c*x^(14*n) + 6006*a^2*b^10*c^2*x^(14*n) - 60060*a^3*b^8*c^3*x^(14*n) + 210210*a^4*b^6*c^4*x^(14*n) - 252252*a^5*b^4*c^5*x^(14*n) + 84084*a^6*b^2*c^6*x^(14*n) - 3432*a^7*c^7*x^(14*n) - 14*a*b^13*x^(13*n) + 1092*a^2*b^11*c*x^(13*n) - 20020*a^3*b^9*c^2*x^(13*n) + 120120*a^4*b^7*c^3*x^(13*n) - 252252*a^5*b^5*c^4*x^(13*n) + 168168*a^6*b^3*c^5*x^(13*n) - 24024*a^7*b*c^6*x^(13*n) + 91*a^2*b^12*x^(12*n) - 4004*a^3*b^10*c*x^(12*n) + 45045*a^4*b^8*c^2*x^(12*n) - 168168*a^5*b^6*c^3*x^(12*n) + 210210*a^6*b^4*c^4*x^(12*n) - 72072*a^7*b^2*c^5*x^(12*n) + 3003*a^8*c^6*x^(12*n) - 364*a^3*b^11*x^(11*n) + 10010*a^4*b^9*c*x^(11*n) - 72072*a^5*b^7*c^2*x^(11*n) + 168168*a^6*b^5*c^3*x^(11*n) - 120120*a^7*b^3*c^4*x^(11*n) + 18018*a^8*b*c^5*x^(11*n) + 1001*a^4*b^10*x^(10*n) - 18018*a^5*b^8*c*x^(10*n) + 84084*a^6*b^6*c^2*x^(10*n) - 120120*a^7*b^4*c^3*x^(10*n) + 45045*a^8*b^2*c^4*x^(10*n) - 2002*a^9*c^5*x^(10*n) - 2002*a^5*b^9*x^(9*n) + 24024*a^6*b^7*c*x^(9*n) - 72072*a^7*b^5*c^2*x^(9*n) + 60060*a^8*b^3*c^3*x^(9*n) - 10010*a^9*b*c^4*x^(9*n) + 3003*a^6*b^8*x^(8*n) - 24024*a^7*b^6*c*x^(8*n) + 45045*a^8*b^4*c^2*x^(8*n) - 20020*a^9*b^2*c^3*x^(8*n) + 1001*a^10*c^4*x^(8*n) - 3432*a^7*b^7*x^(7*n) + 18018*a^8*b^5*c*x^(7*n) - 20020*a^9*b^3*c^2*x^(7*n) + 4004*a^10*b*c^3*x^(7*n) + 3003*a^8*b^6*x^(6*n) - 10010*a^9*b^4*c*x^(6*n) + 6006*a^10*b^2*c^2*x^(6*n) - 364*a^11*c^3*x^(6*n) - 2002*a^9*b^5*x^(5*n) + 4004*a^10*b^3*c*x^(5*n) - 1092*a^11*b*c^2*x^(5*n) + 1001*a^10*b^4*x^(4*n) - 1092*a^11*b^2*c*x^(4*n) + 91*a^12*c^2*x^(4*n) - 364*a^11*b^3*x^(3*n) + 182*a^12*b*c*x^(3*n) + 91*a^12*b^2*x^(2*n) - 14*a^13*c*x^(2*n) - 14*a^13*b*x^n)/n","B",0
101,1,13,0,0.402154," ","integrate((2*c*x+b)*(c*x^2+b*x)^13,x, algorithm=""giac"")","\frac{1}{14} \, {\left(c x^{2} + b x\right)}^{14}"," ",0,"1/14*(c*x^2 + b*x)^14","A",0
102,1,15,0,0.382650," ","integrate(x*(2*c*x^2+b)*(c*x^4+b*x^2)^13,x, algorithm=""giac"")","\frac{1}{28} \, {\left(c x^{4} + b x^{2}\right)}^{14}"," ",0,"1/28*(c*x^4 + b*x^2)^14","A",0
103,1,15,0,0.507909," ","integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3)^13,x, algorithm=""giac"")","\frac{1}{42} \, {\left(c x^{6} + b x^{3}\right)}^{14}"," ",0,"1/42*(c*x^6 + b*x^3)^14","A",0
104,1,189,0,0.433350," ","integrate(x^(-1+n)*(b+2*c*x^n)*(b*x^n+c*x^(2*n))^13,x, algorithm=""giac"")","\frac{c^{14} x^{28 \, n} + 14 \, b c^{13} x^{27 \, n} + 91 \, b^{2} c^{12} x^{26 \, n} + 364 \, b^{3} c^{11} x^{25 \, n} + 1001 \, b^{4} c^{10} x^{24 \, n} + 2002 \, b^{5} c^{9} x^{23 \, n} + 3003 \, b^{6} c^{8} x^{22 \, n} + 3432 \, b^{7} c^{7} x^{21 \, n} + 3003 \, b^{8} c^{6} x^{20 \, n} + 2002 \, b^{9} c^{5} x^{19 \, n} + 1001 \, b^{10} c^{4} x^{18 \, n} + 364 \, b^{11} c^{3} x^{17 \, n} + 91 \, b^{12} c^{2} x^{16 \, n} + 14 \, b^{13} c x^{15 \, n} + b^{14} x^{14 \, n}}{14 \, n}"," ",0,"1/14*(c^14*x^(28*n) + 14*b*c^13*x^(27*n) + 91*b^2*c^12*x^(26*n) + 364*b^3*c^11*x^(25*n) + 1001*b^4*c^10*x^(24*n) + 2002*b^5*c^9*x^(23*n) + 3003*b^6*c^8*x^(22*n) + 3432*b^7*c^7*x^(21*n) + 3003*b^8*c^6*x^(20*n) + 2002*b^9*c^5*x^(19*n) + 1001*b^10*c^4*x^(18*n) + 364*b^11*c^3*x^(17*n) + 91*b^12*c^2*x^(16*n) + 14*b^13*c*x^(15*n) + b^14*x^(14*n))/n","B",0
105,1,12,0,0.346709," ","integrate((2*c*x+b)/(c*x^2+b*x+a),x, algorithm=""giac"")","\log\left({\left| c x^{2} + b x + a \right|}\right)"," ",0,"log(abs(c*x^2 + b*x + a))","A",0
106,1,16,0,1.733643," ","integrate(x*(2*c*x^2+b)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| c x^{4} + b x^{2} + a \right|}\right)"," ",0,"1/2*log(abs(c*x^4 + b*x^2 + a))","A",0
107,1,16,0,1.091765," ","integrate(x^2*(2*c*x^3+b)/(c*x^6+b*x^3+a),x, algorithm=""giac"")","\frac{1}{3} \, \log\left({\left| c x^{6} + b x^{3} + a \right|}\right)"," ",0,"1/3*log(abs(c*x^6 + b*x^3 + a))","A",0
108,1,19,0,0.464270," ","integrate(x^(-1+n)*(b+2*c*x^n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\frac{\log\left(c x^{2 \, n} + b x^{n} + a\right)}{n}"," ",0,"log(c*x^(2*n) + b*x^n + a)/n","A",0
109,1,14,0,0.395413," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^8,x, algorithm=""giac"")","-\frac{1}{7 \, {\left(c x^{2} + b x + a\right)}^{7}}"," ",0,"-1/7/(c*x^2 + b*x + a)^7","A",0
110,1,16,0,6.776119," ","integrate(x*(2*c*x^2+b)/(c*x^4+b*x^2+a)^8,x, algorithm=""giac"")","-\frac{1}{14 \, {\left(c x^{4} + b x^{2} + a\right)}^{7}}"," ",0,"-1/14/(c*x^4 + b*x^2 + a)^7","A",0
111,1,16,0,22.371063," ","integrate(x^2*(2*c*x^3+b)/(c*x^6+b*x^3+a)^8,x, algorithm=""giac"")","-\frac{1}{21 \, {\left(c x^{6} + b x^{3} + a\right)}^{7}}"," ",0,"-1/21/(c*x^6 + b*x^3 + a)^7","A",0
112,1,21,0,0.632881," ","integrate(x^(-1+n)*(b+2*c*x^n)/(a+b*x^n+c*x^(2*n))^8,x, algorithm=""giac"")","-\frac{1}{7 \, {\left(c x^{2 \, n} + b x^{n} + a\right)}^{7} n}"," ",0,"-1/7/((c*x^(2*n) + b*x^n + a)^7*n)","A",0
113,1,14,0,0.390056," ","integrate((2*c*x+b)/(c*x^2+b*x-a),x, algorithm=""giac"")","\log\left({\left| c x^{2} + b x - a \right|}\right)"," ",0,"log(abs(c*x^2 + b*x - a))","A",0
114,1,18,0,1.623825," ","integrate(x*(2*c*x^2+b)/(c*x^4+b*x^2-a),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| c x^{4} + b x^{2} - a \right|}\right)"," ",0,"1/2*log(abs(c*x^4 + b*x^2 - a))","A",0
115,1,18,0,1.039651," ","integrate(x^2*(2*c*x^3+b)/(c*x^6+b*x^3-a),x, algorithm=""giac"")","\frac{1}{3} \, \log\left({\left| c x^{6} + b x^{3} - a \right|}\right)"," ",0,"1/3*log(abs(c*x^6 + b*x^3 - a))","A",0
116,1,21,0,0.373801," ","integrate(x^(-1+n)*(b+2*c*x^n)/(-a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\frac{\log\left(c x^{2 \, n} + b x^{n} - a\right)}{n}"," ",0,"log(c*x^(2*n) + b*x^n - a)/n","A",0
117,1,16,0,0.427047," ","integrate((2*c*x+b)/(c*x^2+b*x-a)^8,x, algorithm=""giac"")","-\frac{1}{7 \, {\left(c x^{2} + b x - a\right)}^{7}}"," ",0,"-1/7/(c*x^2 + b*x - a)^7","A",0
118,1,18,0,7.187231," ","integrate(x*(2*c*x^2+b)/(c*x^4+b*x^2-a)^8,x, algorithm=""giac"")","-\frac{1}{14 \, {\left(c x^{4} + b x^{2} - a\right)}^{7}}"," ",0,"-1/14/(c*x^4 + b*x^2 - a)^7","A",0
119,1,18,0,22.350954," ","integrate(x^2*(2*c*x^3+b)/(c*x^6+b*x^3-a)^8,x, algorithm=""giac"")","-\frac{1}{21 \, {\left(c x^{6} + b x^{3} - a\right)}^{7}}"," ",0,"-1/21/(c*x^6 + b*x^3 - a)^7","A",0
120,1,23,0,0.789524," ","integrate(x^(-1+n)*(b+2*c*x^n)/(-a+b*x^n+c*x^(2*n))^8,x, algorithm=""giac"")","-\frac{1}{7 \, {\left(c x^{2 \, n} + b x^{n} - a\right)}^{7} n}"," ",0,"-1/7/((c*x^(2*n) + b*x^n - a)^7*n)","A",0
121,1,11,0,0.456015," ","integrate((2*c*x+b)/(c*x^2+b*x),x, algorithm=""giac"")","\log\left({\left| c x^{2} + b x \right|}\right)"," ",0,"log(abs(c*x^2 + b*x))","A",0
122,1,15,0,0.486046," ","integrate(x*(2*c*x^2+b)/(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| c x^{4} + b x^{2} \right|}\right)"," ",0,"1/2*log(abs(c*x^4 + b*x^2))","A",0
123,1,15,0,0.339933," ","integrate(x^2*(2*c*x^3+b)/(c*x^6+b*x^3),x, algorithm=""giac"")","\frac{1}{3} \, \log\left({\left| c x^{6} + b x^{3} \right|}\right)"," ",0,"1/3*log(abs(c*x^6 + b*x^3))","A",0
124,1,17,0,0.373538," ","integrate(x^(-1+n)*(b+2*c*x^n)/(b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\frac{\log\left({\left| c x^{n} + b \right|}\right)}{n} + \log\left({\left| x \right|}\right)"," ",0,"log(abs(c*x^n + b))/n + log(abs(x))","A",0
125,1,13,0,0.317715," ","integrate((2*c*x+b)/(c*x^2+b*x)^8,x, algorithm=""giac"")","-\frac{1}{7 \, {\left(c x^{2} + b x\right)}^{7}}"," ",0,"-1/7/(c*x^2 + b*x)^7","A",0
126,1,15,0,0.449797," ","integrate(x*(2*c*x^2+b)/(c*x^4+b*x^2)^8,x, algorithm=""giac"")","-\frac{1}{14 \, {\left(c x^{4} + b x^{2}\right)}^{7}}"," ",0,"-1/14/(c*x^4 + b*x^2)^7","A",0
127,1,15,0,0.606189," ","integrate(x^2*(2*c*x^3+b)/(c*x^6+b*x^3)^8,x, algorithm=""giac"")","-\frac{1}{21 \, {\left(c x^{6} + b x^{3}\right)}^{7}}"," ",0,"-1/21/(c*x^6 + b*x^3)^7","A",0
128,1,20,0,0.440207," ","integrate(x^(-1+n)*(b+2*c*x^n)/(b*x^n+c*x^(2*n))^8,x, algorithm=""giac"")","-\frac{1}{7 \, {\left(c x^{2 \, n} + b x^{n}\right)}^{7} n}"," ",0,"-1/7/((c*x^(2*n) + b*x^n)^7*n)","A",0
129,1,20,0,0.413996," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\frac{{\left(c x^{2} + b x + a\right)}^{p + 1}}{p + 1}"," ",0,"(c*x^2 + b*x + a)^(p + 1)/(p + 1)","A",0
130,1,23,0,0.459609," ","integrate(x*(2*c*x^2+b)*(c*x^4+b*x^2+a)^p,x, algorithm=""giac"")","\frac{{\left(c x^{4} + b x^{2} + a\right)}^{p + 1}}{2 \, {\left(p + 1\right)}}"," ",0,"1/2*(c*x^4 + b*x^2 + a)^(p + 1)/(p + 1)","A",0
131,1,23,0,0.318886," ","integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3+a)^p,x, algorithm=""giac"")","\frac{{\left(c x^{6} + b x^{3} + a\right)}^{p + 1}}{3 \, {\left(p + 1\right)}}"," ",0,"1/3*(c*x^6 + b*x^3 + a)^(p + 1)/(p + 1)","A",0
132,1,27,0,0.844999," ","integrate(x^(-1+n)*(b+2*c*x^n)*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""giac"")","\frac{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{p + 1}}{n {\left(p + 1\right)}}"," ",0,"(c*x^(2*n) + b*x^n + a)^(p + 1)/(n*(p + 1))","A",0
133,1,22,0,0.397346," ","integrate((2*c*x+b)*(c*x^2+b*x-a)^p,x, algorithm=""giac"")","\frac{{\left(c x^{2} + b x - a\right)}^{p + 1}}{p + 1}"," ",0,"(c*x^2 + b*x - a)^(p + 1)/(p + 1)","A",0
134,1,25,0,0.453658," ","integrate(x*(2*c*x^2+b)*(c*x^4+b*x^2-a)^p,x, algorithm=""giac"")","\frac{{\left(c x^{4} + b x^{2} - a\right)}^{p + 1}}{2 \, {\left(p + 1\right)}}"," ",0,"1/2*(c*x^4 + b*x^2 - a)^(p + 1)/(p + 1)","A",0
135,1,25,0,0.385449," ","integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3-a)^p,x, algorithm=""giac"")","\frac{{\left(c x^{6} + b x^{3} - a\right)}^{p + 1}}{3 \, {\left(p + 1\right)}}"," ",0,"1/3*(c*x^6 + b*x^3 - a)^(p + 1)/(p + 1)","A",0
136,1,29,0,0.820205," ","integrate(x^(-1+n)*(b+2*c*x^n)*(-a+b*x^n+c*x^(2*n))^p,x, algorithm=""giac"")","\frac{{\left(c x^{2 \, n} + b x^{n} - a\right)}^{p + 1}}{n {\left(p + 1\right)}}"," ",0,"(c*x^(2*n) + b*x^n - a)^(p + 1)/(n*(p + 1))","A",0
137,1,19,0,0.409562," ","integrate((2*c*x+b)*(c*x^2+b*x)^p,x, algorithm=""giac"")","\frac{{\left(c x^{2} + b x\right)}^{p + 1}}{p + 1}"," ",0,"(c*x^2 + b*x)^(p + 1)/(p + 1)","A",0
138,1,22,0,0.399951," ","integrate(x*(2*c*x^2+b)*(c*x^4+b*x^2)^p,x, algorithm=""giac"")","\frac{{\left(c x^{4} + b x^{2}\right)}^{p + 1}}{2 \, {\left(p + 1\right)}}"," ",0,"1/2*(c*x^4 + b*x^2)^(p + 1)/(p + 1)","A",0
139,1,22,0,0.671240," ","integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3)^p,x, algorithm=""giac"")","\frac{{\left(c x^{6} + b x^{3}\right)}^{p + 1}}{3 \, {\left(p + 1\right)}}"," ",0,"1/3*(c*x^6 + b*x^3)^(p + 1)/(p + 1)","A",0
140,1,26,0,0.834199," ","integrate(x^(-1+n)*(b+2*c*x^n)*(b*x^n+c*x^(2*n))^p,x, algorithm=""giac"")","\frac{{\left(c x^{2 \, n} + b x^{n}\right)}^{p + 1}}{n {\left(p + 1\right)}}"," ",0,"(c*x^(2*n) + b*x^n)^(p + 1)/(n*(p + 1))","A",0
141,0,0,0,0.000000," ","integrate((f*x)^m*(d+e*x^n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)} \left(f x\right)^{m}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate((e*x^n + d)*(f*x)^m/(c*x^(2*n) + b*x^n + a), x)","F",0
142,0,0,0,0.000000," ","integrate((f*x)^m*(d+e*x^n)/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)} \left(f x\right)^{m}}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*x^n + d)*(f*x)^m/(c*x^(2*n) + b*x^n + a)^2, x)","F",0
143,0,0,0,0.000000," ","integrate((f*x)^m*(d+e*x^n)/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)} \left(f x\right)^{m}}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*x^n + d)*(f*x)^m/(c*x^(2*n) + b*x^n + a)^3, x)","F",0
144,-2,0,0,0.000000," ","integrate((c^(1/3)-2*d^(1/3)*x^(1/3))/(c*d^(1/3)*x^(2/3)-c^(2/3)*d^(2/3)*x+c^(1/3)*d*x^(4/3)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{[%%%{%%{[%%%{1,[1]%%%},0]:[1,0,0,%%%{-1,[1]%%%}]%%},[1]%%%},0]:[1,0,0,%%%{-1,[1]%%%}]%%},[2]%%%}+%%%{%%%{%%{[%%%{-1,[1]%%%},0,0]:[1,0,0,%%%{-1,[1]%%%}]%%},[1]%%%},[1]%%%}+%%%{%%{[%%%{%%%{1,[2]%%%},[0]%%%},0,0]:[1,0,0,%%%{-1,[1]%%%}]%%},[0]%%%} / %%%{%%%{%%{[-1,0]:[1,0,0,%%%{-1,[1]%%%}]%%},[2]%%%},[2]%%%}+%%%{%%{[%%%{%%{[1,0,0]:[1,0,0,%%%{-1,[1]%%%}]%%},[1]%%%},0,0]:[1,0,0,%%%{-1,[1]%%%}]%%},[1]%%%}+%%%{%%{[%%%{%%%{-1,[1]%%%},[1]%%%},0]:[1,0,0,%%%{-1,[1]%%%}]%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
145,0,0,0,0.000000," ","integrate((f*x)^m*(d+e*x^n)^q/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{q} \left(f x\right)^{m}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate((e*x^n + d)^q*(f*x)^m/(c*x^(2*n) + b*x^n + a), x)","F",0
146,0,0,0,0.000000," ","integrate(x^2*(d+e*x^n)^q/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{q} x^{2}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate((e*x^n + d)^q*x^2/(c*x^(2*n) + b*x^n + a), x)","F",0
147,0,0,0,0.000000," ","integrate(x*(d+e*x^n)^q/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{q} x}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate((e*x^n + d)^q*x/(c*x^(2*n) + b*x^n + a), x)","F",0
148,0,0,0,0.000000," ","integrate((d+e*x^n)^q/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{q}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate((e*x^n + d)^q/(c*x^(2*n) + b*x^n + a), x)","F",0
149,0,0,0,0.000000," ","integrate((d+e*x^n)^q/x/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{q}}{{\left(c x^{2 \, n} + b x^{n} + a\right)} x}\,{d x}"," ",0,"integrate((e*x^n + d)^q/((c*x^(2*n) + b*x^n + a)*x), x)","F",0
150,0,0,0,0.000000," ","integrate((d+e*x^n)^q/x^2/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{q}}{{\left(c x^{2 \, n} + b x^{n} + a\right)} x^{2}}\,{d x}"," ",0,"integrate((e*x^n + d)^q/((c*x^(2*n) + b*x^n + a)*x^2), x)","F",0
151,0,0,0,0.000000," ","integrate((d+e*x^n)^q/x^3/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{q}}{{\left(c x^{2 \, n} + b x^{n} + a\right)} x^{3}}\,{d x}"," ",0,"integrate((e*x^n + d)^q/((c*x^(2*n) + b*x^n + a)*x^3), x)","F",0
152,-2,0,0,0.000000," ","integrate((f*x)^m*(d+e*x^n)^2*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming x near 0Simplification assuming f near 0Simplification assuming x near 0Simplification assuming f near 0Unable to divide, perhaps due to rounding error%%%{128,[1,0,5,3,0,5,4,1,6,1]%%%}+%%%{512,[1,0,5,3,0,5,3,1,6,1]%%%}+%%%{768,[1,0,5,3,0,5,2,1,6,1]%%%}+%%%{512,[1,0,5,3,0,5,1,1,6,1]%%%}+%%%{128,[1,0,5,3,0,5,0,1,6,1]%%%}+%%%{-96,[1,0,5,3,0,4,4,3,5,1]%%%}+%%%{-384,[1,0,5,3,0,4,3,3,5,1]%%%}+%%%{-576,[1,0,5,3,0,4,2,3,5,1]%%%}+%%%{-384,[1,0,5,3,0,4,1,3,5,1]%%%}+%%%{-96,[1,0,5,3,0,4,0,3,5,1]%%%}+%%%{24,[1,0,5,3,0,3,4,5,4,1]%%%}+%%%{96,[1,0,5,3,0,3,3,5,4,1]%%%}+%%%{144,[1,0,5,3,0,3,2,5,4,1]%%%}+%%%{96,[1,0,5,3,0,3,1,5,4,1]%%%}+%%%{24,[1,0,5,3,0,3,0,5,4,1]%%%}+%%%{-2,[1,0,5,3,0,2,4,7,3,1]%%%}+%%%{-8,[1,0,5,3,0,2,3,7,3,1]%%%}+%%%{-12,[1,0,5,3,0,2,2,7,3,1]%%%}+%%%{-8,[1,0,5,3,0,2,1,7,3,1]%%%}+%%%{-2,[1,0,5,3,0,2,0,7,3,1]%%%}+%%%{64,[1,0,5,2,1,5,3,1,6,1]%%%}+%%%{192,[1,0,5,2,1,5,2,1,6,1]%%%}+%%%{192,[1,0,5,2,1,5,1,1,6,1]%%%}+%%%{64,[1,0,5,2,1,5,0,1,6,1]%%%}+%%%{-48,[1,0,5,2,1,4,3,3,5,1]%%%}+%%%{-144,[1,0,5,2,1,4,2,3,5,1]%%%}+%%%{-144,[1,0,5,2,1,4,1,3,5,1]%%%}+%%%{-48,[1,0,5,2,1,4,0,3,5,1]%%%}+%%%{12,[1,0,5,2,1,3,3,5,4,1]%%%}+%%%{36,[1,0,5,2,1,3,2,5,4,1]%%%}+%%%{36,[1,0,5,2,1,3,1,5,4,1]%%%}+%%%{12,[1,0,5,2,1,3,0,5,4,1]%%%}+%%%{-1,[1,0,5,2,1,2,3,7,3,1]%%%}+%%%{-3,[1,0,5,2,1,2,2,7,3,1]%%%}+%%%{-3,[1,0,5,2,1,2,1,7,3,1]%%%}+%%%{-1,[1,0,5,2,1,2,0,7,3,1]%%%}+%%%{64,[1,0,5,2,0,5,3,1,6,1]%%%}+%%%{192,[1,0,5,2,0,5,2,1,6,1]%%%}+%%%{192,[1,0,5,2,0,5,1,1,6,1]%%%}+%%%{64,[1,0,5,2,0,5,0,1,6,1]%%%}+%%%{-48,[1,0,5,2,0,4,3,3,5,1]%%%}+%%%{-144,[1,0,5,2,0,4,2,3,5,1]%%%}+%%%{-144,[1,0,5,2,0,4,1,3,5,1]%%%}+%%%{-48,[1,0,5,2,0,4,0,3,5,1]%%%}+%%%{12,[1,0,5,2,0,3,3,5,4,1]%%%}+%%%{36,[1,0,5,2,0,3,2,5,4,1]%%%}+%%%{36,[1,0,5,2,0,3,1,5,4,1]%%%}+%%%{12,[1,0,5,2,0,3,0,5,4,1]%%%}+%%%{-1,[1,0,5,2,0,2,3,7,3,1]%%%}+%%%{-3,[1,0,5,2,0,2,2,7,3,1]%%%}+%%%{-3,[1,0,5,2,0,2,1,7,3,1]%%%}+%%%{-1,[1,0,5,2,0,2,0,7,3,1]%%%}+%%%{128,[0,0,5,2,1,5,3,0,7,1]%%%}+%%%{384,[0,0,5,2,1,5,2,0,7,1]%%%}+%%%{384,[0,0,5,2,1,5,1,0,7,1]%%%}+%%%{128,[0,0,5,2,1,5,0,0,7,1]%%%}+%%%{-96,[0,0,5,2,1,4,3,2,6,1]%%%}+%%%{-288,[0,0,5,2,1,4,2,2,6,1]%%%}+%%%{-288,[0,0,5,2,1,4,1,2,6,1]%%%}+%%%{-96,[0,0,5,2,1,4,0,2,6,1]%%%}+%%%{24,[0,0,5,2,1,3,3,4,5,1]%%%}+%%%{72,[0,0,5,2,1,3,2,4,5,1]%%%}+%%%{72,[0,0,5,2,1,3,1,4,5,1]%%%}+%%%{24,[0,0,5,2,1,3,0,4,5,1]%%%}+%%%{-2,[0,0,5,2,1,2,3,6,4,1]%%%}+%%%{-6,[0,0,5,2,1,2,2,6,4,1]%%%}+%%%{-6,[0,0,5,2,1,2,1,6,4,1]%%%}+%%%{-2,[0,0,5,2,1,2,0,6,4,1]%%%}+%%%{128,[0,0,5,2,0,5,3,0,7,1]%%%}+%%%{384,[0,0,5,2,0,5,2,0,7,1]%%%}+%%%{384,[0,0,5,2,0,5,1,0,7,1]%%%}+%%%{128,[0,0,5,2,0,5,0,0,7,1]%%%}+%%%{-96,[0,0,5,2,0,4,3,2,6,1]%%%}+%%%{-288,[0,0,5,2,0,4,2,2,6,1]%%%}+%%%{-288,[0,0,5,2,0,4,1,2,6,1]%%%}+%%%{-96,[0,0,5,2,0,4,0,2,6,1]%%%}+%%%{24,[0,0,5,2,0,3,3,4,5,1]%%%}+%%%{72,[0,0,5,2,0,3,2,4,5,1]%%%}+%%%{72,[0,0,5,2,0,3,1,4,5,1]%%%}+%%%{24,[0,0,5,2,0,3,0,4,5,1]%%%}+%%%{-2,[0,0,5,2,0,2,3,6,4,1]%%%}+%%%{-6,[0,0,5,2,0,2,2,6,4,1]%%%}+%%%{-6,[0,0,5,2,0,2,1,6,4,1]%%%}+%%%{-2,[0,0,5,2,0,2,0,6,4,1]%%%} / %%%{64,[0,0,5,3,0,5,3,0,6,0]%%%}+%%%{192,[0,0,5,3,0,5,2,0,6,0]%%%}+%%%{192,[0,0,5,3,0,5,1,0,6,0]%%%}+%%%{64,[0,0,5,3,0,5,0,0,6,0]%%%}+%%%{-48,[0,0,5,3,0,4,3,2,5,0]%%%}+%%%{-144,[0,0,5,3,0,4,2,2,5,0]%%%}+%%%{-144,[0,0,5,3,0,4,1,2,5,0]%%%}+%%%{-48,[0,0,5,3,0,4,0,2,5,0]%%%}+%%%{12,[0,0,5,3,0,3,3,4,4,0]%%%}+%%%{36,[0,0,5,3,0,3,2,4,4,0]%%%}+%%%{36,[0,0,5,3,0,3,1,4,4,0]%%%}+%%%{12,[0,0,5,3,0,3,0,4,4,0]%%%}+%%%{-1,[0,0,5,3,0,2,3,6,3,0]%%%}+%%%{-3,[0,0,5,3,0,2,2,6,3,0]%%%}+%%%{-3,[0,0,5,3,0,2,1,6,3,0]%%%}+%%%{-1,[0,0,5,3,0,2,0,6,3,0]%%%} Error: Bad Argument Value","F(-2)",0
153,0,0,0,0.000000," ","integrate((f*x)^m*(d+e*x^n)*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""giac"")","\int {\left(e x^{n} + d\right)} {\left(c x^{2 \, n} + b x^{n} + a\right)}^{p} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((e*x^n + d)*(c*x^(2*n) + b*x^n + a)^p*(f*x)^m, x)","F",0
154,0,0,0,0.000000," ","integrate((f*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(f x\right)^{m}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^p*(f*x)^m, x)","F",0
155,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*x^n+c*x^(2*n))^p/(d+e*x^n),x, algorithm=""giac"")","\int \frac{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{p} \left(f x\right)^{m}}{e x^{n} + d}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^p*(f*x)^m/(e*x^n + d), x)","F",0
156,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*x^n+c*x^(2*n))^p/(d+e*x^n)^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{p} \left(f x\right)^{m}}{{\left(e x^{n} + d\right)}^{2}}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^p*(f*x)^m/(e*x^n + d)^2, x)","F",0
