1,1,78,0,0.156531," ","integrate((e*x^2+d*x+c)/(b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(15 \, \sqrt{b x + a} c + \frac{5 \, {\left({\left(b x + a\right)}^{\frac{3}{2}} - 3 \, \sqrt{b x + a} a\right)} d}{b} + \frac{{\left(3 \, {\left(b x + a\right)}^{\frac{5}{2}} - 10 \, {\left(b x + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{b x + a} a^{2}\right)} e}{b^{2}}\right)}}{15 \, b}"," ",0,"2/15*(15*sqrt(b*x + a)*c + 5*((b*x + a)^(3/2) - 3*sqrt(b*x + a)*a)*d/b + (3*(b*x + a)^(5/2) - 10*(b*x + a)^(3/2)*a + 15*sqrt(b*x + a)*a^2)*e/b^2)/b","A",0
2,1,237,0,0.167452," ","integrate((e*x^2+d*x+c)^2/(b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(315 \, \sqrt{b x + a} c^{2} + \frac{210 \, {\left({\left(b x + a\right)}^{\frac{3}{2}} - 3 \, \sqrt{b x + a} a\right)} c d}{b} + \frac{21 \, {\left(3 \, {\left(b x + a\right)}^{\frac{5}{2}} - 10 \, {\left(b x + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{b x + a} a^{2}\right)} d^{2}}{b^{2}} + \frac{42 \, {\left(3 \, {\left(b x + a\right)}^{\frac{5}{2}} - 10 \, {\left(b x + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{b x + a} a^{2}\right)} c e}{b^{2}} + \frac{18 \, {\left(5 \, {\left(b x + a\right)}^{\frac{7}{2}} - 21 \, {\left(b x + a\right)}^{\frac{5}{2}} a + 35 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{2} - 35 \, \sqrt{b x + a} a^{3}\right)} d e}{b^{3}} + \frac{{\left(35 \, {\left(b x + a\right)}^{\frac{9}{2}} - 180 \, {\left(b x + a\right)}^{\frac{7}{2}} a + 378 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{2} - 420 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{3} + 315 \, \sqrt{b x + a} a^{4}\right)} e^{2}}{b^{4}}\right)}}{315 \, b}"," ",0,"2/315*(315*sqrt(b*x + a)*c^2 + 210*((b*x + a)^(3/2) - 3*sqrt(b*x + a)*a)*c*d/b + 21*(3*(b*x + a)^(5/2) - 10*(b*x + a)^(3/2)*a + 15*sqrt(b*x + a)*a^2)*d^2/b^2 + 42*(3*(b*x + a)^(5/2) - 10*(b*x + a)^(3/2)*a + 15*sqrt(b*x + a)*a^2)*c*e/b^2 + 18*(5*(b*x + a)^(7/2) - 21*(b*x + a)^(5/2)*a + 35*(b*x + a)^(3/2)*a^2 - 35*sqrt(b*x + a)*a^3)*d*e/b^3 + (35*(b*x + a)^(9/2) - 180*(b*x + a)^(7/2)*a + 378*(b*x + a)^(5/2)*a^2 - 420*(b*x + a)^(3/2)*a^3 + 315*sqrt(b*x + a)*a^4)*e^2/b^4)/b","A",0
3,1,526,0,0.226156," ","integrate((e*x^2+d*x+c)^3/(b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(15015 \, \sqrt{b x + a} c^{3} + \frac{15015 \, {\left({\left(b x + a\right)}^{\frac{3}{2}} - 3 \, \sqrt{b x + a} a\right)} c^{2} d}{b} + \frac{3003 \, {\left(3 \, {\left(b x + a\right)}^{\frac{5}{2}} - 10 \, {\left(b x + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{b x + a} a^{2}\right)} c d^{2}}{b^{2}} + \frac{3003 \, {\left(3 \, {\left(b x + a\right)}^{\frac{5}{2}} - 10 \, {\left(b x + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{b x + a} a^{2}\right)} c^{2} e}{b^{2}} + \frac{429 \, {\left(5 \, {\left(b x + a\right)}^{\frac{7}{2}} - 21 \, {\left(b x + a\right)}^{\frac{5}{2}} a + 35 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{2} - 35 \, \sqrt{b x + a} a^{3}\right)} d^{3}}{b^{3}} + \frac{2574 \, {\left(5 \, {\left(b x + a\right)}^{\frac{7}{2}} - 21 \, {\left(b x + a\right)}^{\frac{5}{2}} a + 35 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{2} - 35 \, \sqrt{b x + a} a^{3}\right)} c d e}{b^{3}} + \frac{143 \, {\left(35 \, {\left(b x + a\right)}^{\frac{9}{2}} - 180 \, {\left(b x + a\right)}^{\frac{7}{2}} a + 378 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{2} - 420 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{3} + 315 \, \sqrt{b x + a} a^{4}\right)} d^{2} e}{b^{4}} + \frac{143 \, {\left(35 \, {\left(b x + a\right)}^{\frac{9}{2}} - 180 \, {\left(b x + a\right)}^{\frac{7}{2}} a + 378 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{2} - 420 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{3} + 315 \, \sqrt{b x + a} a^{4}\right)} c e^{2}}{b^{4}} + \frac{65 \, {\left(63 \, {\left(b x + a\right)}^{\frac{11}{2}} - 385 \, {\left(b x + a\right)}^{\frac{9}{2}} a + 990 \, {\left(b x + a\right)}^{\frac{7}{2}} a^{2} - 1386 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{3} + 1155 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{4} - 693 \, \sqrt{b x + a} a^{5}\right)} d e^{2}}{b^{5}} + \frac{5 \, {\left(231 \, {\left(b x + a\right)}^{\frac{13}{2}} - 1638 \, {\left(b x + a\right)}^{\frac{11}{2}} a + 5005 \, {\left(b x + a\right)}^{\frac{9}{2}} a^{2} - 8580 \, {\left(b x + a\right)}^{\frac{7}{2}} a^{3} + 9009 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{4} - 6006 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{5} + 3003 \, \sqrt{b x + a} a^{6}\right)} e^{3}}{b^{6}}\right)}}{15015 \, b}"," ",0,"2/15015*(15015*sqrt(b*x + a)*c^3 + 15015*((b*x + a)^(3/2) - 3*sqrt(b*x + a)*a)*c^2*d/b + 3003*(3*(b*x + a)^(5/2) - 10*(b*x + a)^(3/2)*a + 15*sqrt(b*x + a)*a^2)*c*d^2/b^2 + 3003*(3*(b*x + a)^(5/2) - 10*(b*x + a)^(3/2)*a + 15*sqrt(b*x + a)*a^2)*c^2*e/b^2 + 429*(5*(b*x + a)^(7/2) - 21*(b*x + a)^(5/2)*a + 35*(b*x + a)^(3/2)*a^2 - 35*sqrt(b*x + a)*a^3)*d^3/b^3 + 2574*(5*(b*x + a)^(7/2) - 21*(b*x + a)^(5/2)*a + 35*(b*x + a)^(3/2)*a^2 - 35*sqrt(b*x + a)*a^3)*c*d*e/b^3 + 143*(35*(b*x + a)^(9/2) - 180*(b*x + a)^(7/2)*a + 378*(b*x + a)^(5/2)*a^2 - 420*(b*x + a)^(3/2)*a^3 + 315*sqrt(b*x + a)*a^4)*d^2*e/b^4 + 143*(35*(b*x + a)^(9/2) - 180*(b*x + a)^(7/2)*a + 378*(b*x + a)^(5/2)*a^2 - 420*(b*x + a)^(3/2)*a^3 + 315*sqrt(b*x + a)*a^4)*c*e^2/b^4 + 65*(63*(b*x + a)^(11/2) - 385*(b*x + a)^(9/2)*a + 990*(b*x + a)^(7/2)*a^2 - 1386*(b*x + a)^(5/2)*a^3 + 1155*(b*x + a)^(3/2)*a^4 - 693*sqrt(b*x + a)*a^5)*d*e^2/b^5 + 5*(231*(b*x + a)^(13/2) - 1638*(b*x + a)^(11/2)*a + 5005*(b*x + a)^(9/2)*a^2 - 8580*(b*x + a)^(7/2)*a^3 + 9009*(b*x + a)^(5/2)*a^4 - 6006*(b*x + a)^(3/2)*a^5 + 3003*sqrt(b*x + a)*a^6)*e^3/b^6)/b","B",0
4,1,129,0,0.173606," ","integrate((f*x^3+e*x^2+d*x+c)/(b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(105 \, \sqrt{b x + a} c + \frac{35 \, {\left({\left(b x + a\right)}^{\frac{3}{2}} - 3 \, \sqrt{b x + a} a\right)} d}{b} + \frac{7 \, {\left(3 \, {\left(b x + a\right)}^{\frac{5}{2}} - 10 \, {\left(b x + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{b x + a} a^{2}\right)} e}{b^{2}} + \frac{3 \, {\left(5 \, {\left(b x + a\right)}^{\frac{7}{2}} - 21 \, {\left(b x + a\right)}^{\frac{5}{2}} a + 35 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{2} - 35 \, \sqrt{b x + a} a^{3}\right)} f}{b^{3}}\right)}}{105 \, b}"," ",0,"2/105*(105*sqrt(b*x + a)*c + 35*((b*x + a)^(3/2) - 3*sqrt(b*x + a)*a)*d/b + 7*(3*(b*x + a)^(5/2) - 10*(b*x + a)^(3/2)*a + 15*sqrt(b*x + a)*a^2)*e/b^2 + 3*(5*(b*x + a)^(7/2) - 21*(b*x + a)^(5/2)*a + 35*(b*x + a)^(3/2)*a^2 - 35*sqrt(b*x + a)*a^3)*f/b^3)/b","A",0
5,1,516,0,0.200008," ","integrate((f*x^3+e*x^2+d*x+c)^2/(b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(45045 \, \sqrt{b x + a} c^{2} + \frac{30030 \, {\left({\left(b x + a\right)}^{\frac{3}{2}} - 3 \, \sqrt{b x + a} a\right)} c d}{b} + \frac{3003 \, {\left(3 \, {\left(b x + a\right)}^{\frac{5}{2}} - 10 \, {\left(b x + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{b x + a} a^{2}\right)} d^{2}}{b^{2}} + \frac{6006 \, {\left(3 \, {\left(b x + a\right)}^{\frac{5}{2}} - 10 \, {\left(b x + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{b x + a} a^{2}\right)} c e}{b^{2}} + \frac{2574 \, {\left(5 \, {\left(b x + a\right)}^{\frac{7}{2}} - 21 \, {\left(b x + a\right)}^{\frac{5}{2}} a + 35 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{2} - 35 \, \sqrt{b x + a} a^{3}\right)} c f}{b^{3}} + \frac{2574 \, {\left(5 \, {\left(b x + a\right)}^{\frac{7}{2}} - 21 \, {\left(b x + a\right)}^{\frac{5}{2}} a + 35 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{2} - 35 \, \sqrt{b x + a} a^{3}\right)} d e}{b^{3}} + \frac{286 \, {\left(35 \, {\left(b x + a\right)}^{\frac{9}{2}} - 180 \, {\left(b x + a\right)}^{\frac{7}{2}} a + 378 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{2} - 420 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{3} + 315 \, \sqrt{b x + a} a^{4}\right)} d f}{b^{4}} + \frac{143 \, {\left(35 \, {\left(b x + a\right)}^{\frac{9}{2}} - 180 \, {\left(b x + a\right)}^{\frac{7}{2}} a + 378 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{2} - 420 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{3} + 315 \, \sqrt{b x + a} a^{4}\right)} e^{2}}{b^{4}} + \frac{130 \, {\left(63 \, {\left(b x + a\right)}^{\frac{11}{2}} - 385 \, {\left(b x + a\right)}^{\frac{9}{2}} a + 990 \, {\left(b x + a\right)}^{\frac{7}{2}} a^{2} - 1386 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{3} + 1155 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{4} - 693 \, \sqrt{b x + a} a^{5}\right)} f e}{b^{5}} + \frac{15 \, {\left(231 \, {\left(b x + a\right)}^{\frac{13}{2}} - 1638 \, {\left(b x + a\right)}^{\frac{11}{2}} a + 5005 \, {\left(b x + a\right)}^{\frac{9}{2}} a^{2} - 8580 \, {\left(b x + a\right)}^{\frac{7}{2}} a^{3} + 9009 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{4} - 6006 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{5} + 3003 \, \sqrt{b x + a} a^{6}\right)} f^{2}}{b^{6}}\right)}}{45045 \, b}"," ",0,"2/45045*(45045*sqrt(b*x + a)*c^2 + 30030*((b*x + a)^(3/2) - 3*sqrt(b*x + a)*a)*c*d/b + 3003*(3*(b*x + a)^(5/2) - 10*(b*x + a)^(3/2)*a + 15*sqrt(b*x + a)*a^2)*d^2/b^2 + 6006*(3*(b*x + a)^(5/2) - 10*(b*x + a)^(3/2)*a + 15*sqrt(b*x + a)*a^2)*c*e/b^2 + 2574*(5*(b*x + a)^(7/2) - 21*(b*x + a)^(5/2)*a + 35*(b*x + a)^(3/2)*a^2 - 35*sqrt(b*x + a)*a^3)*c*f/b^3 + 2574*(5*(b*x + a)^(7/2) - 21*(b*x + a)^(5/2)*a + 35*(b*x + a)^(3/2)*a^2 - 35*sqrt(b*x + a)*a^3)*d*e/b^3 + 286*(35*(b*x + a)^(9/2) - 180*(b*x + a)^(7/2)*a + 378*(b*x + a)^(5/2)*a^2 - 420*(b*x + a)^(3/2)*a^3 + 315*sqrt(b*x + a)*a^4)*d*f/b^4 + 143*(35*(b*x + a)^(9/2) - 180*(b*x + a)^(7/2)*a + 378*(b*x + a)^(5/2)*a^2 - 420*(b*x + a)^(3/2)*a^3 + 315*sqrt(b*x + a)*a^4)*e^2/b^4 + 130*(63*(b*x + a)^(11/2) - 385*(b*x + a)^(9/2)*a + 990*(b*x + a)^(7/2)*a^2 - 1386*(b*x + a)^(5/2)*a^3 + 1155*(b*x + a)^(3/2)*a^4 - 693*sqrt(b*x + a)*a^5)*f*e/b^5 + 15*(231*(b*x + a)^(13/2) - 1638*(b*x + a)^(11/2)*a + 5005*(b*x + a)^(9/2)*a^2 - 8580*(b*x + a)^(7/2)*a^3 + 9009*(b*x + a)^(5/2)*a^4 - 6006*(b*x + a)^(3/2)*a^5 + 3003*sqrt(b*x + a)*a^6)*f^2/b^6)/b","A",0
6,1,1414,0,0.286723," ","integrate((f*x^3+e*x^2+d*x+c)^3/(b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(4849845 \, \sqrt{b x + a} c^{3} + \frac{4849845 \, {\left({\left(b x + a\right)}^{\frac{3}{2}} - 3 \, \sqrt{b x + a} a\right)} c^{2} d}{b} + \frac{969969 \, {\left(3 \, {\left(b x + a\right)}^{\frac{5}{2}} - 10 \, {\left(b x + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{b x + a} a^{2}\right)} c d^{2}}{b^{2}} + \frac{969969 \, {\left(3 \, {\left(b x + a\right)}^{\frac{5}{2}} - 10 \, {\left(b x + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{b x + a} a^{2}\right)} c^{2} e}{b^{2}} + \frac{138567 \, {\left(5 \, {\left(b x + a\right)}^{\frac{7}{2}} - 21 \, {\left(b x + a\right)}^{\frac{5}{2}} a + 35 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{2} - 35 \, \sqrt{b x + a} a^{3}\right)} d^{3}}{b^{3}} + \frac{415701 \, {\left(5 \, {\left(b x + a\right)}^{\frac{7}{2}} - 21 \, {\left(b x + a\right)}^{\frac{5}{2}} a + 35 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{2} - 35 \, \sqrt{b x + a} a^{3}\right)} c^{2} f}{b^{3}} + \frac{831402 \, {\left(5 \, {\left(b x + a\right)}^{\frac{7}{2}} - 21 \, {\left(b x + a\right)}^{\frac{5}{2}} a + 35 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{2} - 35 \, \sqrt{b x + a} a^{3}\right)} c d e}{b^{3}} + \frac{92378 \, {\left(35 \, {\left(b x + a\right)}^{\frac{9}{2}} - 180 \, {\left(b x + a\right)}^{\frac{7}{2}} a + 378 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{2} - 420 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{3} + 315 \, \sqrt{b x + a} a^{4}\right)} c d f}{b^{4}} + \frac{46189 \, {\left(35 \, {\left(b x + a\right)}^{\frac{9}{2}} - 180 \, {\left(b x + a\right)}^{\frac{7}{2}} a + 378 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{2} - 420 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{3} + 315 \, \sqrt{b x + a} a^{4}\right)} d^{2} e}{b^{4}} + \frac{20995 \, {\left(63 \, {\left(b x + a\right)}^{\frac{11}{2}} - 385 \, {\left(b x + a\right)}^{\frac{9}{2}} a + 990 \, {\left(b x + a\right)}^{\frac{7}{2}} a^{2} - 1386 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{3} + 1155 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{4} - 693 \, \sqrt{b x + a} a^{5}\right)} d^{2} f}{b^{5}} + \frac{46189 \, {\left(35 \, {\left(b x + a\right)}^{\frac{9}{2}} - 180 \, {\left(b x + a\right)}^{\frac{7}{2}} a + 378 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{2} - 420 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{3} + 315 \, \sqrt{b x + a} a^{4}\right)} c e^{2}}{b^{4}} + \frac{41990 \, {\left(63 \, {\left(b x + a\right)}^{\frac{11}{2}} - 385 \, {\left(b x + a\right)}^{\frac{9}{2}} a + 990 \, {\left(b x + a\right)}^{\frac{7}{2}} a^{2} - 1386 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{3} + 1155 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{4} - 693 \, \sqrt{b x + a} a^{5}\right)} c f e}{b^{5}} + \frac{4845 \, {\left(231 \, {\left(b x + a\right)}^{\frac{13}{2}} - 1638 \, {\left(b x + a\right)}^{\frac{11}{2}} a + 5005 \, {\left(b x + a\right)}^{\frac{9}{2}} a^{2} - 8580 \, {\left(b x + a\right)}^{\frac{7}{2}} a^{3} + 9009 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{4} - 6006 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{5} + 3003 \, \sqrt{b x + a} a^{6}\right)} c f^{2}}{b^{6}} + \frac{20995 \, {\left(63 \, {\left(b x + a\right)}^{\frac{11}{2}} - 385 \, {\left(b x + a\right)}^{\frac{9}{2}} a + 990 \, {\left(b x + a\right)}^{\frac{7}{2}} a^{2} - 1386 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{3} + 1155 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{4} - 693 \, \sqrt{b x + a} a^{5}\right)} d e^{2}}{b^{5}} + \frac{9690 \, {\left(231 \, {\left(b x + a\right)}^{\frac{13}{2}} - 1638 \, {\left(b x + a\right)}^{\frac{11}{2}} a + 5005 \, {\left(b x + a\right)}^{\frac{9}{2}} a^{2} - 8580 \, {\left(b x + a\right)}^{\frac{7}{2}} a^{3} + 9009 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{4} - 6006 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{5} + 3003 \, \sqrt{b x + a} a^{6}\right)} d f e}{b^{6}} + \frac{2261 \, {\left(429 \, {\left(b x + a\right)}^{\frac{15}{2}} - 3465 \, {\left(b x + a\right)}^{\frac{13}{2}} a + 12285 \, {\left(b x + a\right)}^{\frac{11}{2}} a^{2} - 25025 \, {\left(b x + a\right)}^{\frac{9}{2}} a^{3} + 32175 \, {\left(b x + a\right)}^{\frac{7}{2}} a^{4} - 27027 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{5} + 15015 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{6} - 6435 \, \sqrt{b x + a} a^{7}\right)} d f^{2}}{b^{7}} + \frac{1615 \, {\left(231 \, {\left(b x + a\right)}^{\frac{13}{2}} - 1638 \, {\left(b x + a\right)}^{\frac{11}{2}} a + 5005 \, {\left(b x + a\right)}^{\frac{9}{2}} a^{2} - 8580 \, {\left(b x + a\right)}^{\frac{7}{2}} a^{3} + 9009 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{4} - 6006 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{5} + 3003 \, \sqrt{b x + a} a^{6}\right)} e^{3}}{b^{6}} + \frac{2261 \, {\left(429 \, {\left(b x + a\right)}^{\frac{15}{2}} - 3465 \, {\left(b x + a\right)}^{\frac{13}{2}} a + 12285 \, {\left(b x + a\right)}^{\frac{11}{2}} a^{2} - 25025 \, {\left(b x + a\right)}^{\frac{9}{2}} a^{3} + 32175 \, {\left(b x + a\right)}^{\frac{7}{2}} a^{4} - 27027 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{5} + 15015 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{6} - 6435 \, \sqrt{b x + a} a^{7}\right)} f e^{2}}{b^{7}} + \frac{133 \, {\left(6435 \, {\left(b x + a\right)}^{\frac{17}{2}} - 58344 \, {\left(b x + a\right)}^{\frac{15}{2}} a + 235620 \, {\left(b x + a\right)}^{\frac{13}{2}} a^{2} - 556920 \, {\left(b x + a\right)}^{\frac{11}{2}} a^{3} + 850850 \, {\left(b x + a\right)}^{\frac{9}{2}} a^{4} - 875160 \, {\left(b x + a\right)}^{\frac{7}{2}} a^{5} + 612612 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{6} - 291720 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{7} + 109395 \, \sqrt{b x + a} a^{8}\right)} f^{2} e}{b^{8}} + \frac{21 \, {\left(12155 \, {\left(b x + a\right)}^{\frac{19}{2}} - 122265 \, {\left(b x + a\right)}^{\frac{17}{2}} a + 554268 \, {\left(b x + a\right)}^{\frac{15}{2}} a^{2} - 1492260 \, {\left(b x + a\right)}^{\frac{13}{2}} a^{3} + 2645370 \, {\left(b x + a\right)}^{\frac{11}{2}} a^{4} - 3233230 \, {\left(b x + a\right)}^{\frac{9}{2}} a^{5} + 2771340 \, {\left(b x + a\right)}^{\frac{7}{2}} a^{6} - 1662804 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{7} + 692835 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{8} - 230945 \, \sqrt{b x + a} a^{9}\right)} f^{3}}{b^{9}}\right)}}{4849845 \, b}"," ",0,"2/4849845*(4849845*sqrt(b*x + a)*c^3 + 4849845*((b*x + a)^(3/2) - 3*sqrt(b*x + a)*a)*c^2*d/b + 969969*(3*(b*x + a)^(5/2) - 10*(b*x + a)^(3/2)*a + 15*sqrt(b*x + a)*a^2)*c*d^2/b^2 + 969969*(3*(b*x + a)^(5/2) - 10*(b*x + a)^(3/2)*a + 15*sqrt(b*x + a)*a^2)*c^2*e/b^2 + 138567*(5*(b*x + a)^(7/2) - 21*(b*x + a)^(5/2)*a + 35*(b*x + a)^(3/2)*a^2 - 35*sqrt(b*x + a)*a^3)*d^3/b^3 + 415701*(5*(b*x + a)^(7/2) - 21*(b*x + a)^(5/2)*a + 35*(b*x + a)^(3/2)*a^2 - 35*sqrt(b*x + a)*a^3)*c^2*f/b^3 + 831402*(5*(b*x + a)^(7/2) - 21*(b*x + a)^(5/2)*a + 35*(b*x + a)^(3/2)*a^2 - 35*sqrt(b*x + a)*a^3)*c*d*e/b^3 + 92378*(35*(b*x + a)^(9/2) - 180*(b*x + a)^(7/2)*a + 378*(b*x + a)^(5/2)*a^2 - 420*(b*x + a)^(3/2)*a^3 + 315*sqrt(b*x + a)*a^4)*c*d*f/b^4 + 46189*(35*(b*x + a)^(9/2) - 180*(b*x + a)^(7/2)*a + 378*(b*x + a)^(5/2)*a^2 - 420*(b*x + a)^(3/2)*a^3 + 315*sqrt(b*x + a)*a^4)*d^2*e/b^4 + 20995*(63*(b*x + a)^(11/2) - 385*(b*x + a)^(9/2)*a + 990*(b*x + a)^(7/2)*a^2 - 1386*(b*x + a)^(5/2)*a^3 + 1155*(b*x + a)^(3/2)*a^4 - 693*sqrt(b*x + a)*a^5)*d^2*f/b^5 + 46189*(35*(b*x + a)^(9/2) - 180*(b*x + a)^(7/2)*a + 378*(b*x + a)^(5/2)*a^2 - 420*(b*x + a)^(3/2)*a^3 + 315*sqrt(b*x + a)*a^4)*c*e^2/b^4 + 41990*(63*(b*x + a)^(11/2) - 385*(b*x + a)^(9/2)*a + 990*(b*x + a)^(7/2)*a^2 - 1386*(b*x + a)^(5/2)*a^3 + 1155*(b*x + a)^(3/2)*a^4 - 693*sqrt(b*x + a)*a^5)*c*f*e/b^5 + 4845*(231*(b*x + a)^(13/2) - 1638*(b*x + a)^(11/2)*a + 5005*(b*x + a)^(9/2)*a^2 - 8580*(b*x + a)^(7/2)*a^3 + 9009*(b*x + a)^(5/2)*a^4 - 6006*(b*x + a)^(3/2)*a^5 + 3003*sqrt(b*x + a)*a^6)*c*f^2/b^6 + 20995*(63*(b*x + a)^(11/2) - 385*(b*x + a)^(9/2)*a + 990*(b*x + a)^(7/2)*a^2 - 1386*(b*x + a)^(5/2)*a^3 + 1155*(b*x + a)^(3/2)*a^4 - 693*sqrt(b*x + a)*a^5)*d*e^2/b^5 + 9690*(231*(b*x + a)^(13/2) - 1638*(b*x + a)^(11/2)*a + 5005*(b*x + a)^(9/2)*a^2 - 8580*(b*x + a)^(7/2)*a^3 + 9009*(b*x + a)^(5/2)*a^4 - 6006*(b*x + a)^(3/2)*a^5 + 3003*sqrt(b*x + a)*a^6)*d*f*e/b^6 + 2261*(429*(b*x + a)^(15/2) - 3465*(b*x + a)^(13/2)*a + 12285*(b*x + a)^(11/2)*a^2 - 25025*(b*x + a)^(9/2)*a^3 + 32175*(b*x + a)^(7/2)*a^4 - 27027*(b*x + a)^(5/2)*a^5 + 15015*(b*x + a)^(3/2)*a^6 - 6435*sqrt(b*x + a)*a^7)*d*f^2/b^7 + 1615*(231*(b*x + a)^(13/2) - 1638*(b*x + a)^(11/2)*a + 5005*(b*x + a)^(9/2)*a^2 - 8580*(b*x + a)^(7/2)*a^3 + 9009*(b*x + a)^(5/2)*a^4 - 6006*(b*x + a)^(3/2)*a^5 + 3003*sqrt(b*x + a)*a^6)*e^3/b^6 + 2261*(429*(b*x + a)^(15/2) - 3465*(b*x + a)^(13/2)*a + 12285*(b*x + a)^(11/2)*a^2 - 25025*(b*x + a)^(9/2)*a^3 + 32175*(b*x + a)^(7/2)*a^4 - 27027*(b*x + a)^(5/2)*a^5 + 15015*(b*x + a)^(3/2)*a^6 - 6435*sqrt(b*x + a)*a^7)*f*e^2/b^7 + 133*(6435*(b*x + a)^(17/2) - 58344*(b*x + a)^(15/2)*a + 235620*(b*x + a)^(13/2)*a^2 - 556920*(b*x + a)^(11/2)*a^3 + 850850*(b*x + a)^(9/2)*a^4 - 875160*(b*x + a)^(7/2)*a^5 + 612612*(b*x + a)^(5/2)*a^6 - 291720*(b*x + a)^(3/2)*a^7 + 109395*sqrt(b*x + a)*a^8)*f^2*e/b^8 + 21*(12155*(b*x + a)^(19/2) - 122265*(b*x + a)^(17/2)*a + 554268*(b*x + a)^(15/2)*a^2 - 1492260*(b*x + a)^(13/2)*a^3 + 2645370*(b*x + a)^(11/2)*a^4 - 3233230*(b*x + a)^(9/2)*a^5 + 2771340*(b*x + a)^(7/2)*a^6 - 1662804*(b*x + a)^(5/2)*a^7 + 692835*(b*x + a)^(3/2)*a^8 - 230945*sqrt(b*x + a)*a^9)*f^3/b^9)/b","B",0
7,1,141,0,0.165594," ","integrate((d*x+c)/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b c - \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}}} - \frac{{\left(b c + \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}}} - \frac{{\left(d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a}"," ",0,"-1/3*sqrt(3)*(b*c - (-a*b^2)^(1/3)*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(-a*b^2)^(2/3) - 1/6*(b*c + (-a*b^2)^(1/3)*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(-a*b^2)^(2/3) - 1/3*(d*(-a/b)^(1/3) + c)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a","A",0
8,1,174,0,0.177865," ","integrate((d*x+c)/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(2 \, b c - \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} - \frac{{\left(2 \, b c + \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} - \frac{{\left(d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{2}} + \frac{d x^{2} + c x}{3 \, {\left(b x^{3} + a\right)} a}"," ",0,"-1/9*sqrt(3)*(2*b*c - (-a*b^2)^(1/3)*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a) - 1/18*(2*b*c + (-a*b^2)^(1/3)*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a) - 1/9*(d*(-a/b)^(1/3) + 2*c)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^2 + 1/3*(d*x^2 + c*x)/((b*x^3 + a)*a)","A",0
9,1,194,0,0.225888," ","integrate((d*x+c)/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(5 \, b c - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2}} - \frac{{\left(5 \, b c + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2}} - \frac{{\left(2 \, d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{3}} + \frac{4 \, b d x^{5} + 5 \, b c x^{4} + 7 \, a d x^{2} + 8 \, a c x}{18 \, {\left(b x^{3} + a\right)}^{2} a^{2}}"," ",0,"-1/27*sqrt(3)*(5*b*c - 2*(-a*b^2)^(1/3)*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^2) - 1/54*(5*b*c + 2*(-a*b^2)^(1/3)*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^2) - 1/27*(2*d*(-a/b)^(1/3) + 5*c)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^3 + 1/18*(4*b*d*x^5 + 5*b*c*x^4 + 7*a*d*x^2 + 8*a*c*x)/((b*x^3 + a)^2*a^2)","A",0
10,1,218,0,0.229763," ","integrate((d*x+c)/(b*x^3+a)^4,x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} {\left(20 \, b c - 7 \, \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{243 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3}} - \frac{{\left(20 \, b c + 7 \, \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3}} - \frac{2 \, {\left(7 \, d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 20 \, c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{243 \, a^{4}} + \frac{28 \, b^{2} d x^{8} + 40 \, b^{2} c x^{7} + 77 \, a b d x^{5} + 104 \, a b c x^{4} + 67 \, a^{2} d x^{2} + 82 \, a^{2} c x}{162 \, {\left(b x^{3} + a\right)}^{3} a^{3}}"," ",0,"-2/243*sqrt(3)*(20*b*c - 7*(-a*b^2)^(1/3)*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^3) - 1/243*(20*b*c + 7*(-a*b^2)^(1/3)*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^3) - 2/243*(7*d*(-a/b)^(1/3) + 20*c)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^4 + 1/162*(28*b^2*d*x^8 + 40*b^2*c*x^7 + 77*a*b*d*x^5 + 104*a*b*c*x^4 + 67*a^2*d*x^2 + 82*a^2*c*x)/((b*x^3 + a)^3*a^3)","A",0
11,1,132,0,0.174911," ","integrate((b*x+a)/(e*x^3+d),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(a e - \left(-d e^{2}\right)^{\frac{1}{3}} b\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)}{3 \, \left(-d e^{2}\right)^{\frac{2}{3}}} - \frac{{\left(a e + \left(-d e^{2}\right)^{\frac{1}{3}} b\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(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} {\left(\left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} b + a\right)} \log\left({\left| x - \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} \right|}\right)}{3 \, d}"," ",0,"-1/3*sqrt(3)*(a*e - (-d*e^2)^(1/3)*b)*arctan(1/3*sqrt(3)*(2*x + (-d*e^(-1))^(1/3))/(-d*e^(-1))^(1/3))/(-d*e^2)^(2/3) - 1/6*(a*e + (-d*e^2)^(1/3)*b)*log(x^2 + (-d*e^(-1))^(1/3)*x + (-d*e^(-1))^(2/3))/(-d*e^2)^(2/3) - 1/3*(-d*e^(-1))^(1/3)*((-d*e^(-1))^(1/3)*b + a)*log(abs(x - (-d*e^(-1))^(1/3)))/d","A",0
12,1,115,0,0.181261," ","integrate((b*x+a)/(-e*x^3+d),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b d^{\frac{2}{3}} e^{\frac{4}{3}} - a d^{\frac{1}{3}} e^{\frac{5}{3}}\right)} \arctan\left(\frac{\sqrt{3} {\left(d^{\frac{1}{3}} e^{\left(-\frac{1}{3}\right)} + 2 \, x\right)} e^{\frac{1}{3}}}{3 \, d^{\frac{1}{3}}}\right) e^{\left(-2\right)}}{3 \, d} - \frac{{\left(b d^{\frac{1}{3}} e^{\left(-\frac{1}{3}\right)} + a\right)} e^{\left(-\frac{1}{3}\right)} \log\left({\left| -d^{\frac{1}{3}} e^{\left(-\frac{1}{3}\right)} + x \right|}\right)}{3 \, d^{\frac{2}{3}}} + \frac{{\left(b d^{\frac{2}{3}} e^{\frac{4}{3}} + a d^{\frac{1}{3}} e^{\frac{5}{3}}\right)} e^{\left(-2\right)} \log\left(d^{\frac{1}{3}} x e^{\left(-\frac{1}{3}\right)} + x^{2} + d^{\frac{2}{3}} e^{\left(-\frac{2}{3}\right)}\right)}{6 \, d}"," ",0,"-1/3*sqrt(3)*(b*d^(2/3)*e^(4/3) - a*d^(1/3)*e^(5/3))*arctan(1/3*sqrt(3)*(d^(1/3)*e^(-1/3) + 2*x)*e^(1/3)/d^(1/3))*e^(-2)/d - 1/3*(b*d^(1/3)*e^(-1/3) + a)*e^(-1/3)*log(abs(-d^(1/3)*e^(-1/3) + x))/d^(2/3) + 1/6*(b*d^(2/3)*e^(4/3) + a*d^(1/3)*e^(5/3))*e^(-2)*log(d^(1/3)*x*e^(-1/3) + x^2 + d^(2/3)*e^(-2/3))/d","A",0
13,1,16,0,0.189108," ","integrate((1+x)/(x^3+1),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right)"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1))","A",0
14,1,16,0,0.172025," ","integrate((1-x)/(-x^3+1),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right)"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1))","A",0
15,1,17,0,0.163899," ","integrate((1+x)/(-x^3+1),x, algorithm=""giac"")","\frac{1}{3} \, \log\left(x^{2} + x + 1\right) - \frac{2}{3} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/3*log(x^2 + x + 1) - 2/3*log(abs(x - 1))","A",0
16,1,19,0,0.169864," ","integrate((1-x)/(x^3+1),x, algorithm=""giac"")","-\frac{1}{3} \, \log\left(x^{2} - x + 1\right) + \frac{2}{3} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/3*log(x^2 - x + 1) + 2/3*log(abs(x + 1))","A",0
17,1,33,0,0.147067," ","integrate((3-x)/(-x^3+1),x, algorithm=""giac"")","\frac{4}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{3} \, \log\left(x^{2} + x + 1\right) - \frac{2}{3} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"4/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/3*log(x^2 + x + 1) - 2/3*log(abs(x - 1))","A",0
18,1,28,0,0.205939," ","integrate((d*x+c)/(d^3*x^3+c^3),x, algorithm=""giac"")","\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, d x - c\right)}}{3 \, c}\right)}{3 \, c d}"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*d*x - c)/c)/(c*d)","A",0
19,1,26,0,0.165045," ","integrate((-d*x+c)/(-d^3*x^3+c^3),x, algorithm=""giac"")","\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, d x + c\right)}}{3 \, c}\right)}{3 \, c d}"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*d*x + c)/c)/(c*d)","A",0
20,1,48,0,0.222682," ","integrate((a^(1/3)*b^(1/3)*B+b^(2/3)*B*x)/(b*x^3+a),x, algorithm=""giac"")","\frac{2 \, \sqrt{3} B b^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, b^{\frac{2}{3}} x - a^{\frac{1}{3}} b^{\frac{1}{3}}\right)}}{3 \, \sqrt{a^{\frac{2}{3}} b^{\frac{2}{3}}}}\right)}{3 \, \sqrt{a^{\frac{2}{3}} b^{\frac{2}{3}}}}"," ",0,"2/3*sqrt(3)*B*b^(1/3)*arctan(1/3*sqrt(3)*(2*b^(2/3)*x - a^(1/3)*b^(1/3))/sqrt(a^(2/3)*b^(2/3)))/sqrt(a^(2/3)*b^(2/3))","A",0
21,1,58,0,0.214044," ","integrate((a^(1/3)*(-b)^(1/3)*B-(-b)^(2/3)*B*x)/(b*x^3+a),x, algorithm=""giac"")","\frac{2 \, \sqrt{3} B b \arctan\left(-\frac{\sqrt{3} {\left(2 \, \left(-b\right)^{\frac{2}{3}} x + a^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}}\right)}}{3 \, \sqrt{a^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}}}}\right)}{3 \, \sqrt{a^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}}} \left(-b\right)^{\frac{2}{3}}}"," ",0,"2/3*sqrt(3)*B*b*arctan(-1/3*sqrt(3)*(2*(-b)^(2/3)*x + a^(1/3)*(-b)^(1/3))/sqrt(a^(2/3)*(-b)^(2/3)))/(sqrt(a^(2/3)*(-b)^(2/3))*(-b)^(2/3))","A",0
22,1,103,0,0.185595," ","integrate(-C*x^2/(b*x^3+a)+(C*x^2+B*x)/(b*x^3+a),x, algorithm=""giac"")","\frac{\sqrt{3} B \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{1}{3}}} - \frac{B \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{1}{3}}} - \frac{B \left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a}"," ",0,"1/3*sqrt(3)*B*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(-a*b^2)^(1/3) - 1/6*B*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(-a*b^2)^(1/3) - 1/3*B*(-a/b)^(2/3)*log(abs(x - (-a/b)^(1/3)))/a","A",0
23,1,115,0,0.208602," ","integrate(-C*x^2/(b*x^3+a)+(C*x^2+A)/(b*x^3+a),x, algorithm=""giac"")","-\frac{A \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a} + \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} A \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a b} + \frac{\left(-a b^{2}\right)^{\frac{1}{3}} A \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a b}"," ",0,"-1/3*A*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a + 1/3*sqrt(3)*(-a*b^2)^(1/3)*A*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a*b) + 1/6*(-a*b^2)^(1/3)*A*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a*b)","A",0
24,1,147,0,0.197878," ","integrate(-C*x^2/(b*x^3+a)+(C*x^2+B*x+A)/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(A b - \left(-a b^{2}\right)^{\frac{1}{3}} B\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}}} - \frac{{\left(A b + \left(-a b^{2}\right)^{\frac{1}{3}} B\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}}} - \frac{{\left(B b \left(-\frac{a}{b}\right)^{\frac{1}{3}} + A b\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b}"," ",0,"-1/3*sqrt(3)*(A*b - (-a*b^2)^(1/3)*B)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(-a*b^2)^(2/3) - 1/6*(A*b + (-a*b^2)^(1/3)*B)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(-a*b^2)^(2/3) - 1/3*(B*b*(-a/b)^(1/3) + A*b)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b)","A",0
25,1,110,0,0.175522," ","integrate((c*x^2+b*x)/(e*x^3+d),x, algorithm=""giac"")","\frac{1}{3} \, c e^{\left(-1\right)} \log\left({\left| x^{3} e + d \right|}\right) + \frac{\sqrt{3} b \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)}{3 \, \left(-d e^{2}\right)^{\frac{1}{3}}} - \frac{b \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{1}{3}}} - \frac{\left(-d e^{\left(-1\right)}\right)^{\frac{2}{3}} b \log\left({\left| x - \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} \right|}\right)}{3 \, d}"," ",0,"1/3*c*e^(-1)*log(abs(x^3*e + d)) + 1/3*sqrt(3)*b*arctan(1/3*sqrt(3)*(2*x + (-d*e^(-1))^(1/3))/(-d*e^(-1))^(1/3))/(-d*e^2)^(1/3) - 1/6*b*log(x^2 + (-d*e^(-1))^(1/3)*x + (-d*e^(-1))^(2/3))/(-d*e^2)^(1/3) - 1/3*(-d*e^(-1))^(2/3)*b*log(abs(x - (-d*e^(-1))^(1/3)))/d","A",0
26,1,95,0,0.173002," ","integrate((c*x^2+a)/(-e*x^3+d),x, algorithm=""giac"")","-\frac{1}{3} \, c e^{\left(-1\right)} \log\left({\left| x^{3} e - d \right|}\right) + \frac{\sqrt{3} a \arctan\left(\frac{\sqrt{3} {\left(d^{\frac{1}{3}} e^{\left(-\frac{1}{3}\right)} + 2 \, x\right)} e^{\frac{1}{3}}}{3 \, d^{\frac{1}{3}}}\right) e^{\left(-\frac{1}{3}\right)}}{3 \, d^{\frac{2}{3}}} + \frac{a e^{\left(-\frac{1}{3}\right)} \log\left(d^{\frac{1}{3}} x e^{\left(-\frac{1}{3}\right)} + x^{2} + d^{\frac{2}{3}} e^{\left(-\frac{2}{3}\right)}\right)}{6 \, d^{\frac{2}{3}}} - \frac{a e^{\left(-\frac{1}{3}\right)} \log\left({\left| -d^{\frac{1}{3}} e^{\left(-\frac{1}{3}\right)} + x \right|}\right)}{3 \, d^{\frac{2}{3}}}"," ",0,"-1/3*c*e^(-1)*log(abs(x^3*e - d)) + 1/3*sqrt(3)*a*arctan(1/3*sqrt(3)*(d^(1/3)*e^(-1/3) + 2*x)*e^(1/3)/d^(1/3))*e^(-1/3)/d^(2/3) + 1/6*a*e^(-1/3)*log(d^(1/3)*x*e^(-1/3) + x^2 + d^(2/3)*e^(-2/3))/d^(2/3) - 1/3*a*e^(-1/3)*log(abs(-d^(1/3)*e^(-1/3) + x))/d^(2/3)","A",0
27,1,37,0,0.168559," ","integrate((b^2*x^2+2*a^2)/(b^3*x^3+a^3),x, algorithm=""giac"")","\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, b x - a\right)}}{3 \, a}\right)}{3 \, b} + \frac{\log\left({\left| b x + a \right|}\right)}{b}"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*b*x - a)/a)/b + log(abs(b*x + a))/b","A",0
28,1,38,0,0.153810," ","integrate((b^2*x^2+2*a^2)/(-b^3*x^3+a^3),x, algorithm=""giac"")","\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, b x + a\right)}}{3 \, a}\right)}{3 \, b} - \frac{\log\left({\left| b x - a \right|}\right)}{b}"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*b*x + a)/a)/b - log(abs(b*x - a))/b","A",0
29,1,115,0,0.415604," ","integrate((8*C+b^(2/3)*C*x^2)/(b*x^3+8),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{3} C \left(-\frac{1}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(x + \left(-\frac{1}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{1}{b}\right)^{\frac{1}{3}}}\right) - \frac{1}{3} \, {\left(C b^{\frac{2}{3}} \left(-\frac{1}{b}\right)^{\frac{2}{3}} + 2 \, C\right)} \left(-\frac{1}{b}\right)^{\frac{1}{3}} \log\left({\left| x - 2 \, \left(-\frac{1}{b}\right)^{\frac{1}{3}} \right|}\right) + \frac{1}{3} \, {\left(C \left(-\frac{1}{b}\right)^{\frac{1}{3}} + \frac{C}{b^{\frac{1}{3}}}\right)} \log\left(x^{2} + 2 \, x \left(-\frac{1}{b}\right)^{\frac{1}{3}} + 4 \, \left(-\frac{1}{b}\right)^{\frac{2}{3}}\right)"," ",0,"2/3*sqrt(3)*C*(-1/b)^(1/3)*arctan(1/3*sqrt(3)*(x + (-1/b)^(1/3))/(-1/b)^(1/3)) - 1/3*(C*b^(2/3)*(-1/b)^(2/3) + 2*C)*(-1/b)^(1/3)*log(abs(x - 2*(-1/b)^(1/3))) + 1/3*(C*(-1/b)^(1/3) + C/b^(1/3))*log(x^2 + 2*x*(-1/b)^(1/3) + 4*(-1/b)^(2/3))","B",0
30,1,111,0,0.203803," ","integrate((a^(2/3)*C+2*C*x^2)/(8*x^3+a),x, algorithm=""giac"")","\frac{\sqrt{3} {\left(\sqrt{3} i {\left| a \right|} + a\right)} C \arctan\left(\frac{\sqrt{3} {\left(4 \, x + \left(-a\right)^{\frac{1}{3}}\right)}}{3 \, \left(-a\right)^{\frac{1}{3}}}\right)}{12 \, a} + \frac{{\left(\sqrt{3} i {\left| a \right|} + 3 \, a\right)} C \log\left(x^{2} + \frac{1}{2} \, \left(-a\right)^{\frac{1}{3}} x + \frac{1}{4} \, \left(-a\right)^{\frac{2}{3}}\right)}{24 \, a} - \frac{{\left(C \left(-a\right)^{\frac{2}{3}} + 2 \, C a^{\frac{2}{3}}\right)} \left(-a\right)^{\frac{1}{3}} \log\left({\left| x - \frac{1}{2} \, \left(-a\right)^{\frac{1}{3}} \right|}\right)}{12 \, a}"," ",0,"1/12*sqrt(3)*(sqrt(3)*i*abs(a) + a)*C*arctan(1/3*sqrt(3)*(4*x + (-a)^(1/3))/(-a)^(1/3))/a + 1/24*(sqrt(3)*i*abs(a) + 3*a)*C*log(x^2 + 1/2*(-a)^(1/3)*x + 1/4*(-a)^(2/3))/a - 1/12*(C*(-a)^(2/3) + 2*C*a^(2/3))*(-a)^(1/3)*log(abs(x - 1/2*(-a)^(1/3)))/a","B",0
31,1,91,0,0.305800," ","integrate((8*C+(-b)^(2/3)*C*x^2)/(b*x^3-8),x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} C {\left| b \right|}^{\frac{2}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} b^{\frac{1}{3}} {\left(x + \frac{1}{b^{\frac{1}{3}}}\right)}\right)}{3 \, b} + \frac{1}{3} \, {\left(\frac{C \left(-b\right)^{\frac{2}{3}}}{b} - \frac{C}{b^{\frac{1}{3}}}\right)} \log\left(x^{2} + \frac{2 \, x}{b^{\frac{1}{3}}} + \frac{4}{b^{\frac{2}{3}}}\right) + \frac{{\left(2 \, C + \frac{C \left(-b\right)^{\frac{2}{3}}}{b^{\frac{2}{3}}}\right)} \log\left({\left| x - \frac{2}{b^{\frac{1}{3}}} \right|}\right)}{3 \, b^{\frac{1}{3}}}"," ",0,"-2/3*sqrt(3)*C*abs(b)^(2/3)*arctan(1/3*sqrt(3)*b^(1/3)*(x + 1/b^(1/3)))/b + 1/3*(C*(-b)^(2/3)/b - C/b^(1/3))*log(x^2 + 2*x/b^(1/3) + 4/b^(2/3)) + 1/3*(2*C + C*(-b)^(2/3)/b^(2/3))*log(abs(x - 2/b^(1/3)))/b^(1/3)","B",0
32,1,98,0,0.213644," ","integrate(((-a)^(2/3)*C+2*C*x^2)/(-8*x^3+a),x, algorithm=""giac"")","\frac{\sqrt{3} {\left(\sqrt{3} i {\left| a \right|} - a\right)} C \arctan\left(\frac{\sqrt{3} {\left(4 \, x + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right)}{12 \, a} + \frac{{\left(\sqrt{3} i {\left| a \right|} - 3 \, a\right)} C \log\left(x^{2} + \frac{1}{2} \, a^{\frac{1}{3}} x + \frac{1}{4} \, a^{\frac{2}{3}}\right)}{24 \, a} - \frac{{\left(2 \, C \left(-a\right)^{\frac{2}{3}} + C a^{\frac{2}{3}}\right)} \log\left({\left| x - \frac{1}{2} \, a^{\frac{1}{3}} \right|}\right)}{12 \, a^{\frac{2}{3}}}"," ",0,"1/12*sqrt(3)*(sqrt(3)*i*abs(a) - a)*C*arctan(1/3*sqrt(3)*(4*x + a^(1/3))/a^(1/3))/a + 1/24*(sqrt(3)*i*abs(a) - 3*a)*C*log(x^2 + 1/2*a^(1/3)*x + 1/4*a^(2/3))/a - 1/12*(2*C*(-a)^(2/3) + C*a^(2/3))*log(abs(x - 1/2*a^(1/3)))/a^(2/3)","B",0
33,1,166,0,0.223584," ","integrate((2*(a/b)^(2/3)*C+C*x^2)/(b*x^3+a),x, algorithm=""giac"")","\frac{\sqrt{3} {\left(a b^{2} + \sqrt{3} \sqrt{a^{2} b^{4}} i\right)} C \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a b^{3}} - \frac{{\left(C b^{2} \left(-\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, \left(a b^{2}\right)^{\frac{2}{3}} C\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{2}} + \frac{{\left(3 \, a b^{2} + \sqrt{3} \sqrt{a^{2} b^{4}} i\right)} C \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a b^{3}}"," ",0,"1/3*sqrt(3)*(a*b^2 + sqrt(3)*sqrt(a^2*b^4)*i)*C*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a*b^3) - 1/3*(C*b^2*(-a/b)^(2/3) + 2*(a*b^2)^(2/3)*C)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^2) + 1/6*(3*a*b^2 + sqrt(3)*sqrt(a^2*b^4)*i)*C*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a*b^3)","B",0
34,1,162,0,0.220753," ","integrate((2*(-a/b)^(2/3)*C+C*x^2)/(-b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(a b^{2} - \sqrt{3} \sqrt{a^{2} b^{4}} i\right)} C \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a b^{3}} - \frac{{\left(C b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} C\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{2}} - \frac{{\left(3 \, a b^{2} - \sqrt{3} \sqrt{a^{2} b^{4}} i\right)} C \log\left(x^{2} + x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a b^{3}}"," ",0,"-1/3*sqrt(3)*(a*b^2 - sqrt(3)*sqrt(a^2*b^4)*i)*C*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/(a*b^3) - 1/3*(C*b^2*(a/b)^(2/3) + 2*(-a*b^2)^(2/3)*C)*(a/b)^(1/3)*log(abs(x - (a/b)^(1/3)))/(a*b^2) - 1/6*(3*a*b^2 - sqrt(3)*sqrt(a^2*b^4)*i)*C*log(x^2 + x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^3)","B",0
35,1,91,0,0.175552," ","integrate((2*(-a/b)^(2/3)*C+C*x^2)/(b*x^3+a),x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} C \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b} - \frac{{\left(C b^{2} \left(-\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} C\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{2}}"," ",0,"-2/3*sqrt(3)*C*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b - 1/3*(C*b^2*(-a/b)^(2/3) + 2*(-a*b^2)^(2/3)*C)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^2)","A",0
36,1,85,0,0.214861," ","integrate((2*(a/b)^(2/3)*C+C*x^2)/(-b*x^3+a),x, algorithm=""giac"")","\frac{2 \, \sqrt{3} C \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b} - \frac{{\left(C b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, \left(a b^{2}\right)^{\frac{2}{3}} C\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{2}}"," ",0,"2/3*sqrt(3)*C*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/b - 1/3*(C*b^2*(a/b)^(2/3) + 2*(a*b^2)^(2/3)*C)*(a/b)^(1/3)*log(abs(x - (a/b)^(1/3)))/(a*b^2)","A",0
37,-1,0,0,0.000000," ","integrate((2*a^(2/3)*C+b^(2/3)*C*x^2)/(b*x^3+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
38,-1,0,0,0.000000," ","integrate((-2*a^(2/3)*C-(-b)^(2/3)*C*x^2)/(b*x^3+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
39,1,32,0,0.320551," ","integrate((x^2-3)/(x^3-1),x, algorithm=""giac"")","\sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{5}{6} \, \log\left(x^{2} + x + 1\right) - \frac{2}{3} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 5/6*log(x^2 + x + 1) - 2/3*log(abs(x - 1))","A",0
40,-1,0,0,0.000000," ","integrate((a^(1/3)*b^(1/3)*B+2*a^(2/3)*C+b^(2/3)*B*x+b^(2/3)*C*x^2)/(b*x^3+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
41,-1,0,0,0.000000," ","integrate((a^(1/3)*(-b)^(1/3)*B-2*a^(2/3)*C-(-b)^(2/3)*B*x-(-b)^(2/3)*C*x^2)/(b*x^3+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,1,13,0,0.361722," ","integrate((C^2*x^2+B*C*x+B^2)/(C^3*x^3-B^3),x, algorithm=""giac"")","\frac{\log\left({\left| C x - B \right|}\right)}{C}"," ",0,"log(abs(C*x - B))/C","A",0
43,1,16,0,0.311765," ","integrate((a^(2/3)*C-a^(1/3)*b^(1/3)*C*x+b^(2/3)*C*x^2)/(b*x^3+a),x, algorithm=""giac"")","\frac{C \log\left({\left| b^{\frac{1}{3}} x + a^{\frac{1}{3}} \right|}\right)}{b^{\frac{1}{3}}}"," ",0,"C*log(abs(b^(1/3)*x + a^(1/3)))/b^(1/3)","A",0
44,1,242,0,0.204124," ","integrate(((a/b)^(1/3)*B+2*(a/b)^(2/3)*C+B*x+C*x^2)/(b*x^3+a),x, algorithm=""giac"")","\frac{{\left(2 \, C a b + \left(-a^{2} b^{4}\right)^{\frac{1}{3}} B\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \, a b^{2} - \sqrt{3} \sqrt{a^{2} b^{4}} i} - \frac{{\left(C b^{2} \left(-\frac{a}{b}\right)^{\frac{2}{3}} + B b^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(a b^{2}\right)^{\frac{1}{3}} B b + 2 \, \left(a b^{2}\right)^{\frac{2}{3}} C\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{2}} + \frac{\sqrt{3} {\left({\left(9 \, \left(-a^{2} b^{4}\right)^{\frac{1}{3}} a b^{2} - 27^{\frac{5}{6}} \left(-a^{2} b^{4}\right)^{\frac{5}{6}}\right)} B + 18 \, {\left(a^{2} b^{3} - \sqrt{3} \sqrt{a^{4} b^{6}} i\right)} C\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{54 \, a^{2} b^{4}}"," ",0,"(2*C*a*b + (-a^2*b^4)^(1/3)*B)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(3*a*b^2 - sqrt(3)*sqrt(a^2*b^4)*i) - 1/3*(C*b^2*(-a/b)^(2/3) + B*b^2*(-a/b)^(1/3) + (a*b^2)^(1/3)*B*b + 2*(a*b^2)^(2/3)*C)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^2) + 1/54*sqrt(3)*((9*(-a^2*b^4)^(1/3)*a*b^2 - 27^(5/6)*(-a^2*b^4)^(5/6))*B + 18*(a^2*b^3 - sqrt(3)*sqrt(a^4*b^6)*i)*C)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^2*b^4)","B",0
45,1,235,0,0.213508," ","integrate(((-a/b)^(1/3)*B+2*(-a/b)^(2/3)*C+B*x+C*x^2)/(-b*x^3+a),x, algorithm=""giac"")","-\frac{{\left(2 \, C a b - \left(-a^{2} b^{4}\right)^{\frac{1}{3}} B\right)} \log\left(x^{2} + x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \, a b^{2} + \sqrt{3} \sqrt{a^{2} b^{4}} i} - \frac{{\left(C b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + B b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(-a b^{2}\right)^{\frac{1}{3}} B b + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} C\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{2}} + \frac{\sqrt{3} {\left({\left(9 \, \left(-a^{2} b^{4}\right)^{\frac{1}{3}} a b^{2} + 27^{\frac{5}{6}} \left(-a^{2} b^{4}\right)^{\frac{5}{6}}\right)} B - 18 \, {\left(a^{2} b^{3} + \sqrt{3} \sqrt{a^{4} b^{6}} i\right)} C\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{54 \, a^{2} b^{4}}"," ",0,"-(2*C*a*b - (-a^2*b^4)^(1/3)*B)*log(x^2 + x*(a/b)^(1/3) + (a/b)^(2/3))/(3*a*b^2 + sqrt(3)*sqrt(a^2*b^4)*i) - 1/3*(C*b^2*(a/b)^(2/3) + B*b^2*(a/b)^(1/3) + (-a*b^2)^(1/3)*B*b + 2*(-a*b^2)^(2/3)*C)*(a/b)^(1/3)*log(abs(x - (a/b)^(1/3)))/(a*b^2) + 1/54*sqrt(3)*((9*(-a^2*b^4)^(1/3)*a*b^2 + 27^(5/6)*(-a^2*b^4)^(5/6))*B - 18*(a^2*b^3 + sqrt(3)*sqrt(a^4*b^6)*i)*C)*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b^4)","B",0
46,1,133,0,0.192070," ","integrate((-(-a/b)^(1/3)*B+2*(-a/b)^(2/3)*C+B*x+C*x^2)/(b*x^3+a),x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} {\left(C a b + \left(-a b^{2}\right)^{\frac{2}{3}} B\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a b^{2}} - \frac{{\left(C b^{2} \left(-\frac{a}{b}\right)^{\frac{2}{3}} + B b^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} - \left(-a b^{2}\right)^{\frac{1}{3}} B b + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} C\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{2}}"," ",0,"-2/3*sqrt(3)*(C*a*b + (-a*b^2)^(2/3)*B)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a*b^2) - 1/3*(C*b^2*(-a/b)^(2/3) + B*b^2*(-a/b)^(1/3) - (-a*b^2)^(1/3)*B*b + 2*(-a*b^2)^(2/3)*C)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^2)","A",0
47,1,125,0,0.178795," ","integrate((-(a/b)^(1/3)*B+2*(a/b)^(2/3)*C+B*x+C*x^2)/(-b*x^3+a),x, algorithm=""giac"")","\frac{2 \, \sqrt{3} {\left(C a b - \left(a b^{2}\right)^{\frac{2}{3}} B\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a b^{2}} - \frac{{\left(C b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + B b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}} - \left(a b^{2}\right)^{\frac{1}{3}} B b + 2 \, \left(a b^{2}\right)^{\frac{2}{3}} C\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{2}}"," ",0,"2/3*sqrt(3)*(C*a*b - (a*b^2)^(2/3)*B)*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/(a*b^2) - 1/3*(C*b^2*(a/b)^(2/3) + B*b^2*(a/b)^(1/3) - (a*b^2)^(1/3)*B*b + 2*(a*b^2)^(2/3)*C)*(a/b)^(1/3)*log(abs(x - (a/b)^(1/3)))/(a*b^2)","A",0
48,1,27,0,0.154813," ","integrate((c*x^2+a*x+a)/(-x^3+1),x, algorithm=""giac"")","\frac{1}{3} \, {\left(a - c\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{3} \, {\left(2 \, a + c\right)} \log\left({\left| x - 1 \right|}\right)"," ",0,"1/3*(a - c)*log(x^2 + x + 1) - 1/3*(2*a + c)*log(abs(x - 1))","A",0
49,1,52,0,0.169062," ","integrate((c*x^2+b*x+a)/(-x^3+1),x, algorithm=""giac"")","\frac{1}{3} \, {\left(\sqrt{3} a - \sqrt{3} b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, {\left(a + b - 2 \, c\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{3} \, {\left(a + b + c\right)} \log\left({\left| x - 1 \right|}\right)"," ",0,"1/3*(sqrt(3)*a - sqrt(3)*b)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*(a + b - 2*c)*log(x^2 + x + 1) - 1/3*(a + b + c)*log(abs(x - 1))","A",0
50,1,7,0,0.154035," ","integrate((x^2+x+1)/(-x^3+1),x, algorithm=""giac"")","-\log\left({\left| x - 1 \right|}\right)"," ",0,"-log(abs(x - 1))","A",0
51,1,33,0,0.155982," ","integrate((3*x^2-x+1)/(-x^3+1),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \log\left(x^{2} + x + 1\right) - \log\left({\left| x - 1 \right|}\right)"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - log(x^2 + x + 1) - log(abs(x - 1))","A",0
52,1,17,0,0.148884," ","integrate((4*x^2+x+1)/(-x^3+1),x, algorithm=""giac"")","-\log\left(x^{2} + x + 1\right) - 2 \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-log(x^2 + x + 1) - 2*log(abs(x - 1))","A",0
53,1,97,0,0.164621," ","integrate((b*x^3+a)^3*(b*d*x^4+b*c*x^3+a*d*x+a*c),x, algorithm=""giac"")","\frac{1}{14} \, b^{4} d x^{14} + \frac{1}{13} \, b^{4} c x^{13} + \frac{4}{11} \, a b^{3} d x^{11} + \frac{2}{5} \, a b^{3} c x^{10} + \frac{3}{4} \, a^{2} b^{2} d x^{8} + \frac{6}{7} \, a^{2} b^{2} c x^{7} + \frac{4}{5} \, a^{3} b d x^{5} + a^{3} b c x^{4} + \frac{1}{2} \, a^{4} d x^{2} + a^{4} c x"," ",0,"1/14*b^4*d*x^14 + 1/13*b^4*c*x^13 + 4/11*a*b^3*d*x^11 + 2/5*a*b^3*c*x^10 + 3/4*a^2*b^2*d*x^8 + 6/7*a^2*b^2*c*x^7 + 4/5*a^3*b*d*x^5 + a^3*b*c*x^4 + 1/2*a^4*d*x^2 + a^4*c*x","A",0
54,1,74,0,0.155011," ","integrate((b*x^3+a)^2*(b*d*x^4+b*c*x^3+a*d*x+a*c),x, algorithm=""giac"")","\frac{1}{11} \, b^{3} d x^{11} + \frac{1}{10} \, b^{3} c x^{10} + \frac{3}{8} \, a b^{2} d x^{8} + \frac{3}{7} \, a b^{2} c x^{7} + \frac{3}{5} \, a^{2} b d x^{5} + \frac{3}{4} \, a^{2} b c x^{4} + \frac{1}{2} \, a^{3} d x^{2} + a^{3} c x"," ",0,"1/11*b^3*d*x^11 + 1/10*b^3*c*x^10 + 3/8*a*b^2*d*x^8 + 3/7*a*b^2*c*x^7 + 3/5*a^2*b*d*x^5 + 3/4*a^2*b*c*x^4 + 1/2*a^3*d*x^2 + a^3*c*x","A",0
55,1,50,0,0.165346," ","integrate((b*x^3+a)*(b*d*x^4+b*c*x^3+a*d*x+a*c),x, algorithm=""giac"")","\frac{1}{8} \, b^{2} d x^{8} + \frac{1}{7} \, b^{2} c x^{7} + \frac{2}{5} \, a b d x^{5} + \frac{1}{2} \, a b c x^{4} + \frac{1}{2} \, a^{2} d x^{2} + a^{2} c x"," ",0,"1/8*b^2*d*x^8 + 1/7*b^2*c*x^7 + 2/5*a*b*d*x^5 + 1/2*a*b*c*x^4 + 1/2*a^2*d*x^2 + a^2*c*x","A",0
56,1,10,0,0.197512," ","integrate((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a),x, algorithm=""giac"")","\frac{1}{2} \, d x^{2} + c x"," ",0,"1/2*d*x^2 + c*x","A",0
57,1,141,0,0.184122," ","integrate((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b c - \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}}} - \frac{{\left(b c + \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}}} - \frac{{\left(d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a}"," ",0,"-1/3*sqrt(3)*(b*c - (-a*b^2)^(1/3)*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(-a*b^2)^(2/3) - 1/6*(b*c + (-a*b^2)^(1/3)*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(-a*b^2)^(2/3) - 1/3*(d*(-a/b)^(1/3) + c)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a","A",0
58,1,174,0,0.213026," ","integrate((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(2 \, b c - \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} - \frac{{\left(2 \, b c + \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} - \frac{{\left(d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{2}} + \frac{d x^{2} + c x}{3 \, {\left(b x^{3} + a\right)} a}"," ",0,"-1/9*sqrt(3)*(2*b*c - (-a*b^2)^(1/3)*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a) - 1/18*(2*b*c + (-a*b^2)^(1/3)*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a) - 1/9*(d*(-a/b)^(1/3) + 2*c)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^2 + 1/3*(d*x^2 + c*x)/((b*x^3 + a)*a)","A",0
59,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)*(b*d*x^4+b*c*x^3+a*d*x+a*c),x, algorithm=""giac"")","\int {\left(b d x^{4} + b c x^{3} + a d x + a c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*d*x^4 + b*c*x^3 + a*d*x + a*c)*(b*x^3 + a)^(3/2), x)","F",0
60,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/2)*(b*d*x^4+b*c*x^3+a*d*x+a*c),x, algorithm=""giac"")","\int {\left(b d x^{4} + b c x^{3} + a d x + a c\right)} \sqrt{b x^{3} + a}\,{d x}"," ",0,"integrate((b*d*x^4 + b*c*x^3 + a*d*x + a*c)*sqrt(b*x^3 + a), x)","F",0
61,0,0,0,0.000000," ","integrate((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{b d x^{4} + b c x^{3} + a d x + a c}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate((b*d*x^4 + b*c*x^3 + a*d*x + a*c)/sqrt(b*x^3 + a), x)","F",0
62,0,0,0,0.000000," ","integrate((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{b d x^{4} + b c x^{3} + a d x + a c}{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*d*x^4 + b*c*x^3 + a*d*x + a*c)/(b*x^3 + a)^(3/2), x)","F",0
63,0,0,0,0.000000," ","integrate((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a)^(5/2),x, algorithm=""giac"")","\int \frac{b d x^{4} + b c x^{3} + a d x + a c}{{\left(b x^{3} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*d*x^4 + b*c*x^3 + a*d*x + a*c)/(b*x^3 + a)^(5/2), x)","F",0
64,0,0,0,0.000000," ","integrate((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a)^(7/2),x, algorithm=""giac"")","\int \frac{b d x^{4} + b c x^{3} + a d x + a c}{{\left(b x^{3} + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*d*x^4 + b*c*x^3 + a*d*x + a*c)/(b*x^3 + a)^(7/2), x)","F",0
65,0,0,0,0.000000," ","integrate((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a)^(9/2),x, algorithm=""giac"")","\int \frac{b d x^{4} + b c x^{3} + a d x + a c}{{\left(b x^{3} + a\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*d*x^4 + b*c*x^3 + a*d*x + a*c)/(b*x^3 + a)^(9/2), x)","F",0
66,0,0,0,0.000000," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{g x^{4} + f x^{3} + e x^{2} + d x + c}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)/sqrt(b*x^3 + a), x)","F",0
67,0,0,0,0.000000," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{g x^{4} + f x^{3} + e x^{2} + d x + c}{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)/(b*x^3 + a)^(3/2), x)","F",0
68,0,0,0,0.000000," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^(5/2),x, algorithm=""giac"")","\int \frac{g x^{4} + f x^{3} + e x^{2} + d x + c}{{\left(b x^{3} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)/(b*x^3 + a)^(5/2), x)","F",0
69,0,0,0,0.000000," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^(7/2),x, algorithm=""giac"")","\int \frac{g x^{4} + f x^{3} + e x^{2} + d x + c}{{\left(b x^{3} + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)/(b*x^3 + a)^(7/2), x)","F",0
70,1,175,0,0.175550," ","integrate((b*x+a)^2/(d*x^3+c),x, algorithm=""giac"")","\frac{b^{2} \log\left({\left| d x^{3} + c \right|}\right)}{3 \, d} - \frac{\sqrt{3} {\left(a^{2} d - 2 \, \left(-c d^{2}\right)^{\frac{1}{3}} a b\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-c d^{2}\right)^{\frac{2}{3}}} - \frac{{\left(a^{2} d + 2 \, \left(-c d^{2}\right)^{\frac{1}{3}} a b\right)} \log\left(x^{2} + x \left(-\frac{c}{d}\right)^{\frac{1}{3}} + \left(-\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \, \left(-c d^{2}\right)^{\frac{2}{3}}} - \frac{{\left(2 \, a b d \left(-\frac{c}{d}\right)^{\frac{1}{3}} + a^{2} d\right)} \left(-\frac{c}{d}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{c}{d}\right)^{\frac{1}{3}} \right|}\right)}{3 \, c d}"," ",0,"1/3*b^2*log(abs(d*x^3 + c))/d - 1/3*sqrt(3)*(a^2*d - 2*(-c*d^2)^(1/3)*a*b)*arctan(1/3*sqrt(3)*(2*x + (-c/d)^(1/3))/(-c/d)^(1/3))/(-c*d^2)^(2/3) - 1/6*(a^2*d + 2*(-c*d^2)^(1/3)*a*b)*log(x^2 + x*(-c/d)^(1/3) + (-c/d)^(2/3))/(-c*d^2)^(2/3) - 1/3*(2*a*b*d*(-c/d)^(1/3) + a^2*d)*(-c/d)^(1/3)*log(abs(x - (-c/d)^(1/3)))/(c*d)","A",0
71,1,214,0,0.185745," ","integrate((b*x+a)^3/(d*x^3+c),x, algorithm=""giac"")","\frac{b^{3} x}{d} + \frac{a b^{2} \log\left({\left| d x^{3} + c \right|}\right)}{d} + \frac{\sqrt{3} {\left(b^{3} c - a^{3} d + 3 \, \left(-c d^{2}\right)^{\frac{1}{3}} a^{2} b\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-c d^{2}\right)^{\frac{2}{3}}} + \frac{{\left(b^{3} c - a^{3} d - 3 \, \left(-c d^{2}\right)^{\frac{1}{3}} a^{2} b\right)} \log\left(x^{2} + x \left(-\frac{c}{d}\right)^{\frac{1}{3}} + \left(-\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \, \left(-c d^{2}\right)^{\frac{2}{3}}} - \frac{{\left(3 \, a^{2} b d^{3} \left(-\frac{c}{d}\right)^{\frac{1}{3}} - b^{3} c d^{2} + a^{3} d^{3}\right)} \left(-\frac{c}{d}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{c}{d}\right)^{\frac{1}{3}} \right|}\right)}{3 \, c d^{3}}"," ",0,"b^3*x/d + a*b^2*log(abs(d*x^3 + c))/d + 1/3*sqrt(3)*(b^3*c - a^3*d + 3*(-c*d^2)^(1/3)*a^2*b)*arctan(1/3*sqrt(3)*(2*x + (-c/d)^(1/3))/(-c/d)^(1/3))/(-c*d^2)^(2/3) + 1/6*(b^3*c - a^3*d - 3*(-c*d^2)^(1/3)*a^2*b)*log(x^2 + x*(-c/d)^(1/3) + (-c/d)^(2/3))/(-c*d^2)^(2/3) - 1/3*(3*a^2*b*d^3*(-c/d)^(1/3) - b^3*c*d^2 + a^3*d^3)*(-c/d)^(1/3)*log(abs(x - (-c/d)^(1/3)))/(c*d^3)","A",0
72,1,294,0,0.192638," ","integrate((b*x+a)^4/(d*x^3+c),x, algorithm=""giac"")","\frac{2 \, a^{2} b^{2} \log\left({\left| d x^{3} + c \right|}\right)}{d} + \frac{\sqrt{3} {\left(4 \, a b^{3} c d - a^{4} d^{2} - \left(-c d^{2}\right)^{\frac{1}{3}} b^{4} c + 4 \, \left(-c d^{2}\right)^{\frac{1}{3}} a^{3} b d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-c d^{2}\right)^{\frac{2}{3}} d} + \frac{{\left(4 \, a b^{3} c d - a^{4} d^{2} + \left(-c d^{2}\right)^{\frac{1}{3}} b^{4} c - 4 \, \left(-c d^{2}\right)^{\frac{1}{3}} a^{3} b d\right)} \log\left(x^{2} + x \left(-\frac{c}{d}\right)^{\frac{1}{3}} + \left(-\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \, \left(-c d^{2}\right)^{\frac{2}{3}} d} + \frac{b^{4} d x^{2} + 8 \, a b^{3} d x}{2 \, d^{2}} + \frac{{\left(b^{4} c d^{4} \left(-\frac{c}{d}\right)^{\frac{1}{3}} - 4 \, a^{3} b d^{5} \left(-\frac{c}{d}\right)^{\frac{1}{3}} + 4 \, a b^{3} c d^{4} - a^{4} d^{5}\right)} \left(-\frac{c}{d}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{c}{d}\right)^{\frac{1}{3}} \right|}\right)}{3 \, c d^{5}}"," ",0,"2*a^2*b^2*log(abs(d*x^3 + c))/d + 1/3*sqrt(3)*(4*a*b^3*c*d - a^4*d^2 - (-c*d^2)^(1/3)*b^4*c + 4*(-c*d^2)^(1/3)*a^3*b*d)*arctan(1/3*sqrt(3)*(2*x + (-c/d)^(1/3))/(-c/d)^(1/3))/((-c*d^2)^(2/3)*d) + 1/6*(4*a*b^3*c*d - a^4*d^2 + (-c*d^2)^(1/3)*b^4*c - 4*(-c*d^2)^(1/3)*a^3*b*d)*log(x^2 + x*(-c/d)^(1/3) + (-c/d)^(2/3))/((-c*d^2)^(2/3)*d) + 1/2*(b^4*d*x^2 + 8*a*b^3*d*x)/d^2 + 1/3*(b^4*c*d^4*(-c/d)^(1/3) - 4*a^3*b*d^5*(-c/d)^(1/3) + 4*a*b^3*c*d^4 - a^4*d^5)*(-c/d)^(1/3)*log(abs(x - (-c/d)^(1/3)))/(c*d^5)","A",0
73,1,264,0,0.211850," ","integrate((c*x^2+b*x+a)^2/(e*x^3+d),x, algorithm=""giac"")","\frac{1}{3} \, {\left(b^{2} + 2 \, a c\right)} e^{\left(-1\right)} \log\left({\left| x^{3} e + d \right|}\right) + \frac{\sqrt{3} {\left(2 \, b c d e - \left(-d e^{2}\right)^{\frac{1}{3}} c^{2} d + 2 \, \left(-d e^{2}\right)^{\frac{1}{3}} a b e - a^{2} 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(2 \, b c d e + \left(-d e^{2}\right)^{\frac{1}{3}} c^{2} d - 2 \, \left(-d e^{2}\right)^{\frac{1}{3}} a b e - a^{2} 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(\left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} c^{2} d e^{4} + 2 \, b c d e^{4} - 2 \, \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} a b e^{5} - a^{2} e^{5}\right)} \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} e^{\left(-5\right)} \log\left({\left| x - \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} \right|}\right)}{3 \, d} + \frac{1}{2} \, {\left(c^{2} x^{2} e + 4 \, b c x e\right)} e^{\left(-2\right)}"," ",0,"1/3*(b^2 + 2*a*c)*e^(-1)*log(abs(x^3*e + d)) + 1/3*sqrt(3)*(2*b*c*d*e - (-d*e^2)^(1/3)*c^2*d + 2*(-d*e^2)^(1/3)*a*b*e - a^2*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*(2*b*c*d*e + (-d*e^2)^(1/3)*c^2*d - 2*(-d*e^2)^(1/3)*a*b*e - a^2*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*((-d*e^(-1))^(1/3)*c^2*d*e^4 + 2*b*c*d*e^4 - 2*(-d*e^(-1))^(1/3)*a*b*e^5 - a^2*e^5)*(-d*e^(-1))^(1/3)*e^(-5)*log(abs(x - (-d*e^(-1))^(1/3)))/d + 1/2*(c^2*x^2*e + 4*b*c*x*e)*e^(-2)","A",0
74,1,432,0,0.232781," ","integrate((c*x^2+b*x+a)^3/(e*x^3+d),x, algorithm=""giac"")","-{\left(b c^{2} d - a b^{2} e - a^{2} c e\right)} e^{\left(-2\right)} \log\left({\left| x^{3} e + d \right|}\right) - \frac{\sqrt{3} {\left(c^{3} d^{2} - b^{3} d e - 6 \, a b c d e + 3 \, \left(-d e^{2}\right)^{\frac{1}{3}} b^{2} c d + 3 \, \left(-d e^{2}\right)^{\frac{1}{3}} a c^{2} d - 3 \, \left(-d e^{2}\right)^{\frac{1}{3}} a^{2} b e + a^{3} 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^{3} d^{2} - b^{3} d e - 6 \, a b c d e - 3 \, \left(-d e^{2}\right)^{\frac{1}{3}} b^{2} c d - 3 \, \left(-d e^{2}\right)^{\frac{1}{3}} a c^{2} d + 3 \, \left(-d e^{2}\right)^{\frac{1}{3}} a^{2} b e + a^{3} 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^{3} d^{2} e^{7} - 3 \, \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} b^{2} c d e^{8} - 3 \, \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} a c^{2} d e^{8} - b^{3} d e^{8} - 6 \, a b c d e^{8} + 3 \, \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} a^{2} b e^{9} + a^{3} e^{9}\right)} \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} e^{\left(-9\right)} \log\left({\left| x - \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} \right|}\right)}{3 \, d} + \frac{1}{4} \, {\left(c^{3} x^{4} e^{3} + 4 \, b c^{2} x^{3} e^{3} + 6 \, b^{2} c x^{2} e^{3} + 6 \, a c^{2} x^{2} e^{3} - 4 \, c^{3} d x e^{2} + 4 \, b^{3} x e^{3} + 24 \, a b c x e^{3}\right)} e^{\left(-4\right)}"," ",0,"-(b*c^2*d - a*b^2*e - a^2*c*e)*e^(-2)*log(abs(x^3*e + d)) - 1/3*sqrt(3)*(c^3*d^2 - b^3*d*e - 6*a*b*c*d*e + 3*(-d*e^2)^(1/3)*b^2*c*d + 3*(-d*e^2)^(1/3)*a*c^2*d - 3*(-d*e^2)^(1/3)*a^2*b*e + a^3*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^3*d^2 - b^3*d*e - 6*a*b*c*d*e - 3*(-d*e^2)^(1/3)*b^2*c*d - 3*(-d*e^2)^(1/3)*a*c^2*d + 3*(-d*e^2)^(1/3)*a^2*b*e + a^3*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^3*d^2*e^7 - 3*(-d*e^(-1))^(1/3)*b^2*c*d*e^8 - 3*(-d*e^(-1))^(1/3)*a*c^2*d*e^8 - b^3*d*e^8 - 6*a*b*c*d*e^8 + 3*(-d*e^(-1))^(1/3)*a^2*b*e^9 + a^3*e^9)*(-d*e^(-1))^(1/3)*e^(-9)*log(abs(x - (-d*e^(-1))^(1/3)))/d + 1/4*(c^3*x^4*e^3 + 4*b*c^2*x^3*e^3 + 6*b^2*c*x^2*e^3 + 6*a*c^2*x^2*e^3 - 4*c^3*d*x*e^2 + 4*b^3*x*e^3 + 24*a*b*c*x*e^3)*e^(-4)","A",0
75,1,723,0,0.209874," ","integrate((c*x^2+b*x+a)^4/(e*x^3+d),x, algorithm=""giac"")","\frac{1}{3} \, {\left(c^{4} d^{2} - 4 \, b^{3} c d e - 12 \, a b c^{2} d e + 6 \, a^{2} b^{2} e^{2} + 4 \, a^{3} c e^{2}\right)} e^{\left(-3\right)} \log\left({\left| x^{3} e + d \right|}\right) - \frac{\sqrt{3} {\left(6 \, b^{2} c^{2} d^{2} e + 4 \, a c^{3} d^{2} e - 4 \, \left(-d e^{2}\right)^{\frac{1}{3}} b c^{3} d^{2} + \left(-d e^{2}\right)^{\frac{1}{3}} b^{4} d e + 12 \, \left(-d e^{2}\right)^{\frac{1}{3}} a b^{2} c d e + 6 \, \left(-d e^{2}\right)^{\frac{1}{3}} a^{2} c^{2} d e - 4 \, a b^{3} d e^{2} - 12 \, a^{2} b c d e^{2} - 4 \, \left(-d e^{2}\right)^{\frac{1}{3}} a^{3} b e^{2} + a^{4} e^{3}\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(-2\right)}}{3 \, \left(-d e^{2}\right)^{\frac{2}{3}}} - \frac{{\left(6 \, b^{2} c^{2} d^{2} e + 4 \, a c^{3} d^{2} e + 4 \, \left(-d e^{2}\right)^{\frac{1}{3}} b c^{3} d^{2} - \left(-d e^{2}\right)^{\frac{1}{3}} b^{4} d e - 12 \, \left(-d e^{2}\right)^{\frac{1}{3}} a b^{2} c d e - 6 \, \left(-d e^{2}\right)^{\frac{1}{3}} a^{2} c^{2} d e - 4 \, a b^{3} d e^{2} - 12 \, a^{2} b c d e^{2} + 4 \, \left(-d e^{2}\right)^{\frac{1}{3}} a^{3} b e^{2} + a^{4} e^{3}\right)} e^{\left(-2\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(4 \, \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} b c^{3} d^{2} e^{11} + 6 \, b^{2} c^{2} d^{2} e^{11} + 4 \, a c^{3} d^{2} e^{11} - \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} b^{4} d e^{12} - 12 \, \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} a b^{2} c d e^{12} - 6 \, \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} a^{2} c^{2} d e^{12} - 4 \, a b^{3} d e^{12} - 12 \, a^{2} b c d e^{12} + 4 \, \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} a^{3} b e^{13} + a^{4} e^{13}\right)} \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} e^{\left(-13\right)} \log\left({\left| x - \left(-d e^{\left(-1\right)}\right)^{\frac{1}{3}} \right|}\right)}{3 \, d} + \frac{1}{30} \, {\left(5 \, c^{4} x^{6} e^{5} + 24 \, b c^{3} x^{5} e^{5} + 45 \, b^{2} c^{2} x^{4} e^{5} + 30 \, a c^{3} x^{4} e^{5} - 10 \, c^{4} d x^{3} e^{4} + 40 \, b^{3} c x^{3} e^{5} + 120 \, a b c^{2} x^{3} e^{5} - 60 \, b c^{3} d x^{2} e^{4} + 15 \, b^{4} x^{2} e^{5} + 180 \, a b^{2} c x^{2} e^{5} + 90 \, a^{2} c^{2} x^{2} e^{5} - 180 \, b^{2} c^{2} d x e^{4} - 120 \, a c^{3} d x e^{4} + 120 \, a b^{3} x e^{5} + 360 \, a^{2} b c x e^{5}\right)} e^{\left(-6\right)}"," ",0,"1/3*(c^4*d^2 - 4*b^3*c*d*e - 12*a*b*c^2*d*e + 6*a^2*b^2*e^2 + 4*a^3*c*e^2)*e^(-3)*log(abs(x^3*e + d)) - 1/3*sqrt(3)*(6*b^2*c^2*d^2*e + 4*a*c^3*d^2*e - 4*(-d*e^2)^(1/3)*b*c^3*d^2 + (-d*e^2)^(1/3)*b^4*d*e + 12*(-d*e^2)^(1/3)*a*b^2*c*d*e + 6*(-d*e^2)^(1/3)*a^2*c^2*d*e - 4*a*b^3*d*e^2 - 12*a^2*b*c*d*e^2 - 4*(-d*e^2)^(1/3)*a^3*b*e^2 + a^4*e^3)*arctan(1/3*sqrt(3)*(2*x + (-d*e^(-1))^(1/3))/(-d*e^(-1))^(1/3))*e^(-2)/(-d*e^2)^(2/3) - 1/6*(6*b^2*c^2*d^2*e + 4*a*c^3*d^2*e + 4*(-d*e^2)^(1/3)*b*c^3*d^2 - (-d*e^2)^(1/3)*b^4*d*e - 12*(-d*e^2)^(1/3)*a*b^2*c*d*e - 6*(-d*e^2)^(1/3)*a^2*c^2*d*e - 4*a*b^3*d*e^2 - 12*a^2*b*c*d*e^2 + 4*(-d*e^2)^(1/3)*a^3*b*e^2 + a^4*e^3)*e^(-2)*log(x^2 + (-d*e^(-1))^(1/3)*x + (-d*e^(-1))^(2/3))/(-d*e^2)^(2/3) - 1/3*(4*(-d*e^(-1))^(1/3)*b*c^3*d^2*e^11 + 6*b^2*c^2*d^2*e^11 + 4*a*c^3*d^2*e^11 - (-d*e^(-1))^(1/3)*b^4*d*e^12 - 12*(-d*e^(-1))^(1/3)*a*b^2*c*d*e^12 - 6*(-d*e^(-1))^(1/3)*a^2*c^2*d*e^12 - 4*a*b^3*d*e^12 - 12*a^2*b*c*d*e^12 + 4*(-d*e^(-1))^(1/3)*a^3*b*e^13 + a^4*e^13)*(-d*e^(-1))^(1/3)*e^(-13)*log(abs(x - (-d*e^(-1))^(1/3)))/d + 1/30*(5*c^4*x^6*e^5 + 24*b*c^3*x^5*e^5 + 45*b^2*c^2*x^4*e^5 + 30*a*c^3*x^4*e^5 - 10*c^4*d*x^3*e^4 + 40*b^3*c*x^3*e^5 + 120*a*b*c^2*x^3*e^5 - 60*b*c^3*d*x^2*e^4 + 15*b^4*x^2*e^5 + 180*a*b^2*c*x^2*e^5 + 90*a^2*c^2*x^2*e^5 - 180*b^2*c^2*d*x*e^4 - 120*a*c^3*d*x*e^4 + 120*a*b^3*x*e^5 + 360*a^2*b*c*x*e^5)*e^(-6)","A",0
76,1,38,0,0.151486," ","integrate((x^4+2*x^2)/(x^3+1),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{2} \, \log\left(x^{2} - x + 1\right) + \log\left({\left| x + 1 \right|}\right)"," ",0,"1/2*x^2 - 1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/2*log(x^2 - x + 1) + log(abs(x + 1))","A",0
77,1,38,0,0.156670," ","integrate((x^4+2*x^2)/(-x^3+1),x, algorithm=""giac"")","-\frac{1}{2} \, x^{2} - \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{1}{2} \, \log\left(x^{2} + x + 1\right) - \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/2*x^2 - 1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/2*log(x^2 + x + 1) - log(abs(x - 1))","A",0
78,1,38,0,0.152891," ","integrate((4*x^3-x+1)/(x^3+1),x, algorithm=""giac"")","-\frac{4}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + 4 \, x + \frac{1}{3} \, \log\left(x^{2} - x + 1\right) - \frac{2}{3} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-4/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 4*x + 1/3*log(x^2 - x + 1) - 2/3*log(abs(x + 1))","A",0
79,0,0,0,0.000000," ","integrate((1+x+3^(1/2))/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x + \sqrt{3} + 1}{\sqrt{x^{3} + 1}}\,{d x}"," ",0,"integrate((x + sqrt(3) + 1)/sqrt(x^3 + 1), x)","F",0
80,0,0,0,0.000000," ","integrate((1-x+3^(1/2))/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x - \sqrt{3} - 1}{\sqrt{-x^{3} + 1}}\,{d x}"," ",0,"integrate(-(x - sqrt(3) - 1)/sqrt(-x^3 + 1), x)","F",0
81,0,0,0,0.000000," ","integrate((1-x+3^(1/2))/(x^3-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x - \sqrt{3} - 1}{\sqrt{x^{3} - 1}}\,{d x}"," ",0,"integrate(-(x - sqrt(3) - 1)/sqrt(x^3 - 1), x)","F",0
82,0,0,0,0.000000," ","integrate((1+x+3^(1/2))/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x + \sqrt{3} + 1}{\sqrt{-x^{3} - 1}}\,{d x}"," ",0,"integrate((x + sqrt(3) + 1)/sqrt(-x^3 - 1), x)","F",0
83,0,0,0,0.000000," ","integrate((b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{b^{\frac{1}{3}} x + a^{\frac{1}{3}} {\left(\sqrt{3} + 1\right)}}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate((b^(1/3)*x + a^(1/3)*(sqrt(3) + 1))/sqrt(b*x^3 + a), x)","F",0
84,0,0,0,0.000000," ","integrate((-b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\int -\frac{b^{\frac{1}{3}} x - a^{\frac{1}{3}} {\left(\sqrt{3} + 1\right)}}{\sqrt{-b x^{3} + a}}\,{d x}"," ",0,"integrate(-(b^(1/3)*x - a^(1/3)*(sqrt(3) + 1))/sqrt(-b*x^3 + a), x)","F",0
85,0,0,0,0.000000," ","integrate((-b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\int -\frac{b^{\frac{1}{3}} x - a^{\frac{1}{3}} {\left(\sqrt{3} + 1\right)}}{\sqrt{b x^{3} - a}}\,{d x}"," ",0,"integrate(-(b^(1/3)*x - a^(1/3)*(sqrt(3) + 1))/sqrt(b*x^3 - a), x)","F",0
86,0,0,0,0.000000," ","integrate((b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\int \frac{b^{\frac{1}{3}} x + a^{\frac{1}{3}} {\left(\sqrt{3} + 1\right)}}{\sqrt{-b x^{3} - a}}\,{d x}"," ",0,"integrate((b^(1/3)*x + a^(1/3)*(sqrt(3) + 1))/sqrt(-b*x^3 - a), x)","F",0
87,-2,0,0,0.000000," ","integrate((1+(b/a)^(1/3)*x+3^(1/2))/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueDone","F(-2)",0
88,-2,0,0,0.000000," ","integrate((1-(b/a)^(1/3)*x+3^(1/2))/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueDone","F(-2)",0
89,-2,0,0,0.000000," ","integrate((1-(b/a)^(1/3)*x+3^(1/2))/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueDone","F(-2)",0
90,-2,0,0,0.000000," ","integrate((1+(b/a)^(1/3)*x+3^(1/2))/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueDone","F(-2)",0
91,0,0,0,0.000000," ","integrate((1+x-3^(1/2))/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x - \sqrt{3} + 1}{\sqrt{x^{3} + 1}}\,{d x}"," ",0,"integrate((x - sqrt(3) + 1)/sqrt(x^3 + 1), x)","F",0
92,0,0,0,0.000000," ","integrate((1-x-3^(1/2))/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x + \sqrt{3} - 1}{\sqrt{-x^{3} + 1}}\,{d x}"," ",0,"integrate(-(x + sqrt(3) - 1)/sqrt(-x^3 + 1), x)","F",0
93,0,0,0,0.000000," ","integrate((1-x-3^(1/2))/(x^3-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x + \sqrt{3} - 1}{\sqrt{x^{3} - 1}}\,{d x}"," ",0,"integrate(-(x + sqrt(3) - 1)/sqrt(x^3 - 1), x)","F",0
94,0,0,0,0.000000," ","integrate((1+x-3^(1/2))/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x - \sqrt{3} + 1}{\sqrt{-x^{3} - 1}}\,{d x}"," ",0,"integrate((x - sqrt(3) + 1)/sqrt(-x^3 - 1), x)","F",0
95,0,0,0,0.000000," ","integrate((-1-x+3^(1/2))/(x^3+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x - \sqrt{3} + 1}{\sqrt{x^{3} + 1}}\,{d x}"," ",0,"integrate(-(x - sqrt(3) + 1)/sqrt(x^3 + 1), x)","F",0
96,0,0,0,0.000000," ","integrate((-1+x+3^(1/2))/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x + \sqrt{3} - 1}{\sqrt{-x^{3} + 1}}\,{d x}"," ",0,"integrate((x + sqrt(3) - 1)/sqrt(-x^3 + 1), x)","F",0
97,0,0,0,0.000000," ","integrate((-1+x+3^(1/2))/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x + \sqrt{3} - 1}{\sqrt{x^{3} - 1}}\,{d x}"," ",0,"integrate((x + sqrt(3) - 1)/sqrt(x^3 - 1), x)","F",0
98,0,0,0,0.000000," ","integrate((-1-x+3^(1/2))/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x - \sqrt{3} + 1}{\sqrt{-x^{3} - 1}}\,{d x}"," ",0,"integrate(-(x - sqrt(3) + 1)/sqrt(-x^3 - 1), x)","F",0
99,0,0,0,0.000000," ","integrate((b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{b^{\frac{1}{3}} x - a^{\frac{1}{3}} {\left(\sqrt{3} - 1\right)}}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate((b^(1/3)*x - a^(1/3)*(sqrt(3) - 1))/sqrt(b*x^3 + a), x)","F",0
100,0,0,0,0.000000," ","integrate((-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\int -\frac{b^{\frac{1}{3}} x + a^{\frac{1}{3}} {\left(\sqrt{3} - 1\right)}}{\sqrt{-b x^{3} + a}}\,{d x}"," ",0,"integrate(-(b^(1/3)*x + a^(1/3)*(sqrt(3) - 1))/sqrt(-b*x^3 + a), x)","F",0
101,0,0,0,0.000000," ","integrate((-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\int -\frac{b^{\frac{1}{3}} x + a^{\frac{1}{3}} {\left(\sqrt{3} - 1\right)}}{\sqrt{b x^{3} - a}}\,{d x}"," ",0,"integrate(-(b^(1/3)*x + a^(1/3)*(sqrt(3) - 1))/sqrt(b*x^3 - a), x)","F",0
102,0,0,0,0.000000," ","integrate((b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\int \frac{b^{\frac{1}{3}} x - a^{\frac{1}{3}} {\left(\sqrt{3} - 1\right)}}{\sqrt{-b x^{3} - a}}\,{d x}"," ",0,"integrate((b^(1/3)*x - a^(1/3)*(sqrt(3) - 1))/sqrt(-b*x^3 - a), x)","F",0
103,-2,0,0,0.000000," ","integrate((1+(b/a)^(1/3)*x-3^(1/2))/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueDone","F(-2)",0
104,-2,0,0,0.000000," ","integrate((1-(b/a)^(1/3)*x-3^(1/2))/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueDone","F(-2)",0
105,-2,0,0,0.000000," ","integrate((1-(b/a)^(1/3)*x-3^(1/2))/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueDone","F(-2)",0
106,-2,0,0,0.000000," ","integrate((1+(b/a)^(1/3)*x-3^(1/2))/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueDone","F(-2)",0
107,0,0,0,0.000000," ","integrate((d*x+c)/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{d x + c}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate((d*x + c)/sqrt(b*x^3 + a), x)","F",0
108,0,0,0,0.000000," ","integrate((d*x+c)/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{d x + c}{\sqrt{-b x^{3} + a}}\,{d x}"," ",0,"integrate((d*x + c)/sqrt(-b*x^3 + a), x)","F",0
109,0,0,0,0.000000," ","integrate((d*x+c)/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\int \frac{d x + c}{\sqrt{b x^{3} - a}}\,{d x}"," ",0,"integrate((d*x + c)/sqrt(b*x^3 - a), x)","F",0
110,0,0,0,0.000000," ","integrate((d*x+c)/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\int \frac{d x + c}{\sqrt{-b x^{3} - a}}\,{d x}"," ",0,"integrate((d*x + c)/sqrt(-b*x^3 - a), x)","F",0
111,0,0,0,0.000000," ","integrate((d*x+c)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{d x + c}{\sqrt{x^{3} + 1}}\,{d x}"," ",0,"integrate((d*x + c)/sqrt(x^3 + 1), x)","F",0
112,0,0,0,0.000000," ","integrate((d*x+c)/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{d x + c}{\sqrt{-x^{3} + 1}}\,{d x}"," ",0,"integrate((d*x + c)/sqrt(-x^3 + 1), x)","F",0
113,0,0,0,0.000000," ","integrate((d*x+c)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{d x + c}{\sqrt{x^{3} - 1}}\,{d x}"," ",0,"integrate((d*x + c)/sqrt(x^3 - 1), x)","F",0
114,0,0,0,0.000000," ","integrate((d*x+c)/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{d x + c}{\sqrt{-x^{3} - 1}}\,{d x}"," ",0,"integrate((d*x + c)/sqrt(-x^3 - 1), x)","F",0
115,1,225,0,0.180713," ","integrate((d*x+c)/(-b*x^4+a),x, algorithm=""giac"")","\frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} c \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, a b} - \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} c \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, a b} + \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{-a b} b d + \left(-a b^{3}\right)^{\frac{1}{4}} b c\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{2}} + \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{-a b} b d + \left(-a b^{3}\right)^{\frac{1}{4}} b c\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{2}}"," ",0,"1/8*sqrt(2)*(-a*b^3)^(1/4)*c*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a*b) - 1/8*sqrt(2)*(-a*b^3)^(1/4)*c*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a*b) + 1/4*sqrt(2)*(sqrt(2)*sqrt(-a*b)*b*d + (-a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a*b^2) + 1/4*sqrt(2)*(sqrt(2)*sqrt(-a*b)*b*d + (-a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a*b^2)","B",0
116,1,213,0,0.186117," ","integrate((d*x+c)/(b*x^4+a),x, algorithm=""giac"")","\frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} c \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} c \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b} - \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a b} b d - \left(a b^{3}\right)^{\frac{1}{4}} b c\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{2}} - \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a b} b d - \left(a b^{3}\right)^{\frac{1}{4}} b c\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{2}}"," ",0,"1/8*sqrt(2)*(a*b^3)^(1/4)*c*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b) - 1/8*sqrt(2)*(a*b^3)^(1/4)*c*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b) - 1/4*sqrt(2)*(sqrt(2)*sqrt(a*b)*b*d - (a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^2) - 1/4*sqrt(2)*(sqrt(2)*sqrt(a*b)*b*d - (a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^2)","A",0
117,1,254,0,0.173420," ","integrate((d*x+c)/(-b*x^4+a)^2,x, algorithm=""giac"")","\frac{3 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} c \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{32 \, a^{2} b} - \frac{3 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} c \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{32 \, a^{2} b} - \frac{d x^{2} + c x}{4 \, {\left(b x^{4} - a\right)} a} - \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{-a b} b d - 3 \, \left(-a b^{3}\right)^{\frac{1}{4}} b c\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{2}} - \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{-a b} b d - 3 \, \left(-a b^{3}\right)^{\frac{1}{4}} b c\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{2}}"," ",0,"3/32*sqrt(2)*(-a*b^3)^(1/4)*c*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a^2*b) - 3/32*sqrt(2)*(-a*b^3)^(1/4)*c*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a^2*b) - 1/4*(d*x^2 + c*x)/((b*x^4 - a)*a) - 1/16*sqrt(2)*(2*sqrt(2)*sqrt(-a*b)*b*d - 3*(-a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a^2*b^2) - 1/16*sqrt(2)*(2*sqrt(2)*sqrt(-a*b)*b*d - 3*(-a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a^2*b^2)","B",0
118,1,238,0,0.170292," ","integrate((d*x+c)/(b*x^4+a)^2,x, algorithm=""giac"")","\frac{3 \, \sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} c \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b} - \frac{3 \, \sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} c \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b} + \frac{d x^{2} + c x}{4 \, {\left(b x^{4} + a\right)} a} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a b} b d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} b c\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{2}} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a b} b d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} b c\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{2}}"," ",0,"3/32*sqrt(2)*(a*b^3)^(1/4)*c*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b) - 3/32*sqrt(2)*(a*b^3)^(1/4)*c*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b) + 1/4*(d*x^2 + c*x)/((b*x^4 + a)*a) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*b)*b*d + 3*(a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^2) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*b)*b*d + 3*(a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^2)","A",0
119,1,272,0,0.187721," ","integrate((d*x+c)/(-b*x^4+a)^3,x, algorithm=""giac"")","\frac{21 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} c \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{256 \, a^{3} b} - \frac{21 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} c \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{256 \, a^{3} b} + \frac{3 \, \sqrt{2} {\left(4 \, \sqrt{2} \sqrt{-a b} b d + 7 \, \left(-a b^{3}\right)^{\frac{1}{4}} b c\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} b^{2}} + \frac{3 \, \sqrt{2} {\left(4 \, \sqrt{2} \sqrt{-a b} b d + 7 \, \left(-a b^{3}\right)^{\frac{1}{4}} b c\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} b^{2}} - \frac{6 \, b d x^{6} + 7 \, b c x^{5} - 10 \, a d x^{2} - 11 \, a c x}{32 \, {\left(b x^{4} - a\right)}^{2} a^{2}}"," ",0,"21/256*sqrt(2)*(-a*b^3)^(1/4)*c*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a^3*b) - 21/256*sqrt(2)*(-a*b^3)^(1/4)*c*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a^3*b) + 3/128*sqrt(2)*(4*sqrt(2)*sqrt(-a*b)*b*d + 7*(-a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a^3*b^2) + 3/128*sqrt(2)*(4*sqrt(2)*sqrt(-a*b)*b*d + 7*(-a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a^3*b^2) - 1/32*(6*b*d*x^6 + 7*b*c*x^5 - 10*a*d*x^2 - 11*a*c*x)/((b*x^4 - a)^2*a^2)","B",0
120,1,256,0,0.180836," ","integrate((d*x+c)/(b*x^4+a)^3,x, algorithm=""giac"")","\frac{21 \, \sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} c \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{256 \, a^{3} b} - \frac{21 \, \sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} c \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{256 \, a^{3} b} + \frac{3 \, \sqrt{2} {\left(4 \, \sqrt{2} \sqrt{a b} b d + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} b c\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} b^{2}} + \frac{3 \, \sqrt{2} {\left(4 \, \sqrt{2} \sqrt{a b} b d + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} b c\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} b^{2}} + \frac{6 \, b d x^{6} + 7 \, b c x^{5} + 10 \, a d x^{2} + 11 \, a c x}{32 \, {\left(b x^{4} + a\right)}^{2} a^{2}}"," ",0,"21/256*sqrt(2)*(a*b^3)^(1/4)*c*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b) - 21/256*sqrt(2)*(a*b^3)^(1/4)*c*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b) + 3/128*sqrt(2)*(4*sqrt(2)*sqrt(a*b)*b*d + 7*(a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^2) + 3/128*sqrt(2)*(4*sqrt(2)*sqrt(a*b)*b*d + 7*(a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^2) + 1/32*(6*b*d*x^6 + 7*b*c*x^5 + 10*a*d*x^2 + 11*a*c*x)/((b*x^4 + a)^2*a^2)","A",0
121,1,296,0,0.277948," ","integrate((d*x+c)/(-b*x^4+a)^4,x, algorithm=""giac"")","\frac{77 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} c \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{1024 \, a^{4} b} - \frac{77 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} c \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{1024 \, a^{4} b} - \frac{\sqrt{2} {\left(40 \, \sqrt{2} \sqrt{-a b} b d - 77 \, \left(-a b^{3}\right)^{\frac{1}{4}} b c\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{4} b^{2}} - \frac{\sqrt{2} {\left(40 \, \sqrt{2} \sqrt{-a b} b d - 77 \, \left(-a b^{3}\right)^{\frac{1}{4}} b c\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{4} b^{2}} - \frac{60 \, b^{2} d x^{10} + 77 \, b^{2} c x^{9} - 160 \, a b d x^{6} - 198 \, a b c x^{5} + 132 \, a^{2} d x^{2} + 153 \, a^{2} c x}{384 \, {\left(b x^{4} - a\right)}^{3} a^{3}}"," ",0,"77/1024*sqrt(2)*(-a*b^3)^(1/4)*c*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a^4*b) - 77/1024*sqrt(2)*(-a*b^3)^(1/4)*c*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a^4*b) - 1/512*sqrt(2)*(40*sqrt(2)*sqrt(-a*b)*b*d - 77*(-a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a^4*b^2) - 1/512*sqrt(2)*(40*sqrt(2)*sqrt(-a*b)*b*d - 77*(-a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a^4*b^2) - 1/384*(60*b^2*d*x^10 + 77*b^2*c*x^9 - 160*a*b*d*x^6 - 198*a*b*c*x^5 + 132*a^2*d*x^2 + 153*a^2*c*x)/((b*x^4 - a)^3*a^3)","B",0
122,1,280,0,0.180057," ","integrate((d*x+c)/(b*x^4+a)^4,x, algorithm=""giac"")","\frac{77 \, \sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} c \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{1024 \, a^{4} b} - \frac{77 \, \sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} c \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{1024 \, a^{4} b} + \frac{\sqrt{2} {\left(40 \, \sqrt{2} \sqrt{a b} b d + 77 \, \left(a b^{3}\right)^{\frac{1}{4}} b c\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{4} b^{2}} + \frac{\sqrt{2} {\left(40 \, \sqrt{2} \sqrt{a b} b d + 77 \, \left(a b^{3}\right)^{\frac{1}{4}} b c\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{4} b^{2}} + \frac{60 \, b^{2} d x^{10} + 77 \, b^{2} c x^{9} + 160 \, a b d x^{6} + 198 \, a b c x^{5} + 132 \, a^{2} d x^{2} + 153 \, a^{2} c x}{384 \, {\left(b x^{4} + a\right)}^{3} a^{3}}"," ",0,"77/1024*sqrt(2)*(a*b^3)^(1/4)*c*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^4*b) - 77/1024*sqrt(2)*(a*b^3)^(1/4)*c*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^4*b) + 1/512*sqrt(2)*(40*sqrt(2)*sqrt(a*b)*b*d + 77*(a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^4*b^2) + 1/512*sqrt(2)*(40*sqrt(2)*sqrt(a*b)*b*d + 77*(a*b^3)^(1/4)*b*c)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^4*b^2) + 1/384*(60*b^2*d*x^10 + 77*b^2*c*x^9 + 160*a*b*d*x^6 + 198*a*b*c*x^5 + 132*a^2*d*x^2 + 153*a^2*c*x)/((b*x^4 + a)^3*a^3)","A",0
123,1,37,0,0.146661," ","integrate((d*x+c)/(-x^4+1),x, algorithm=""giac"")","\frac{1}{2} \, c \arctan\left(x\right) + \frac{1}{4} \, d \log\left(x^{2} + 1\right) + \frac{1}{4} \, {\left(c - d\right)} \log\left({\left| x + 1 \right|}\right) - \frac{1}{4} \, {\left(c + d\right)} \log\left({\left| x - 1 \right|}\right)"," ",0,"1/2*c*arctan(x) + 1/4*d*log(x^2 + 1) + 1/4*(c - d)*log(abs(x + 1)) - 1/4*(c + d)*log(abs(x - 1))","B",0
124,1,86,0,0.172205," ","integrate((d*x+c)/(x^4+1),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2} c \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{1}{8} \, \sqrt{2} c \log\left(x^{2} - \sqrt{2} x + 1\right) + \frac{1}{4} \, {\left(\sqrt{2} c - 2 \, d\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{1}{4} \, {\left(\sqrt{2} c + 2 \, d\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right)"," ",0,"1/8*sqrt(2)*c*log(x^2 + sqrt(2)*x + 1) - 1/8*sqrt(2)*c*log(x^2 - sqrt(2)*x + 1) + 1/4*(sqrt(2)*c - 2*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 1/4*(sqrt(2)*c + 2*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)))","A",0
125,1,263,0,0.179377," ","integrate((e*x^2+d*x+c)/(-b*x^4+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(b^{2} c - \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c + \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c - \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, \left(-a b^{3}\right)^{\frac{3}{4}}} + \frac{\sqrt{2} {\left(b^{2} c - \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, \left(-a b^{3}\right)^{\frac{3}{4}}}"," ",0,"-1/4*sqrt(2)*(b^2*c - sqrt(2)*(-a*b^3)^(1/4)*b*d + sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(-a*b^3)^(3/4) - 1/4*sqrt(2)*(b^2*c + sqrt(2)*(-a*b^3)^(1/4)*b*d - sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(-a*b^3)^(3/4) - 1/8*sqrt(2)*(b^2*c - sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(-a*b^3)^(3/4) + 1/8*sqrt(2)*(b^2*c - sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(-a*b^3)^(3/4)","B",0
126,1,275,0,0.173921," ","integrate((e*x^2+d*x+c)/(b*x^4+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a b} b^{2} d - \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} - \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a b} b^{2} d - \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}}"," ",0,"-1/4*sqrt(2)*(sqrt(2)*sqrt(a*b)*b^2*d - (a*b^3)^(1/4)*b^2*c - (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) - 1/4*sqrt(2)*(sqrt(2)*sqrt(a*b)*b^2*d - (a*b^3)^(1/4)*b^2*c - (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c - (a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3) - 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c - (a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3)","A",0
127,1,311,0,0.181673," ","integrate((e*x^2+d*x+c)/(-b*x^4+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(3 \, b^{2} c - 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{\sqrt{2} {\left(3 \, b^{2} c + 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{\sqrt{2} {\left(3 \, b^{2} c - \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{32 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} + \frac{\sqrt{2} {\left(3 \, b^{2} c - \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{32 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{x^{3} e + d x^{2} + c x}{4 \, {\left(b x^{4} - a\right)} a}"," ",0,"-1/16*sqrt(2)*(3*b^2*c - 2*sqrt(2)*(-a*b^3)^(1/4)*b*d + sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a) - 1/16*sqrt(2)*(3*b^2*c + 2*sqrt(2)*(-a*b^3)^(1/4)*b*d - sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a) - 1/32*sqrt(2)*(3*b^2*c - sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a) + 1/32*sqrt(2)*(3*b^2*c - sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a) - 1/4*(x^3*e + d*x^2 + c*x)/((b*x^4 - a)*a)","B",0
128,1,306,0,0.177349," ","integrate((e*x^2+d*x+c)/(b*x^4+a)^2,x, algorithm=""giac"")","\frac{x^{3} e + d x^{2} + c x}{4 \, {\left(b x^{4} + a\right)} a} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a b} b^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a b} b^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{3}} - \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{3}}"," ",0,"1/4*(x^3*e + d*x^2 + c*x)/((b*x^4 + a)*a) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*b)*b^2*d + 3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^3) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*b)*b^2*d + 3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^3) + 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^2*c - (a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^3) - 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^2*c - (a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^3)","A",0
129,1,340,0,0.234552," ","integrate((e*x^2+d*x+c)/(-b*x^4+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(21 \, b^{2} c - 12 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + 5 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} - \frac{\sqrt{2} {\left(21 \, b^{2} c + 12 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - 5 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} - \frac{\sqrt{2} {\left(21 \, b^{2} c - 5 \, \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{256 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} + \frac{\sqrt{2} {\left(21 \, b^{2} c - 5 \, \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{256 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} - \frac{5 \, b x^{7} e + 6 \, b d x^{6} + 7 \, b c x^{5} - 9 \, a x^{3} e - 10 \, a d x^{2} - 11 \, a c x}{32 \, {\left(b x^{4} - a\right)}^{2} a^{2}}"," ",0,"-1/128*sqrt(2)*(21*b^2*c - 12*sqrt(2)*(-a*b^3)^(1/4)*b*d + 5*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^2) - 1/128*sqrt(2)*(21*b^2*c + 12*sqrt(2)*(-a*b^3)^(1/4)*b*d - 5*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^2) - 1/256*sqrt(2)*(21*b^2*c - 5*sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^2) + 1/256*sqrt(2)*(21*b^2*c - 5*sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^2) - 1/32*(5*b*x^7*e + 6*b*d*x^6 + 7*b*c*x^5 - 9*a*x^3*e - 10*a*d*x^2 - 11*a*c*x)/((b*x^4 - a)^2*a^2)","B",0
130,1,336,0,0.190787," ","integrate((e*x^2+d*x+c)/(b*x^4+a)^3,x, algorithm=""giac"")","\frac{5 \, b x^{7} e + 6 \, b d x^{6} + 7 \, b c x^{5} + 9 \, a x^{3} e + 10 \, a d x^{2} + 11 \, a c x}{32 \, {\left(b x^{4} + a\right)}^{2} a^{2}} + \frac{\sqrt{2} {\left(12 \, \sqrt{2} \sqrt{a b} b^{2} d + 21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} b^{3}} + \frac{\sqrt{2} {\left(12 \, \sqrt{2} \sqrt{a b} b^{2} d + 21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} b^{3}} + \frac{\sqrt{2} {\left(21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{256 \, a^{3} b^{3}} - \frac{\sqrt{2} {\left(21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{256 \, a^{3} b^{3}}"," ",0,"1/32*(5*b*x^7*e + 6*b*d*x^6 + 7*b*c*x^5 + 9*a*x^3*e + 10*a*d*x^2 + 11*a*c*x)/((b*x^4 + a)^2*a^2) + 1/128*sqrt(2)*(12*sqrt(2)*sqrt(a*b)*b^2*d + 21*(a*b^3)^(1/4)*b^2*c + 5*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^3) + 1/128*sqrt(2)*(12*sqrt(2)*sqrt(a*b)*b^2*d + 21*(a*b^3)^(1/4)*b^2*c + 5*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^3) + 1/256*sqrt(2)*(21*(a*b^3)^(1/4)*b^2*c - 5*(a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^3) - 1/256*sqrt(2)*(21*(a*b^3)^(1/4)*b^2*c - 5*(a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^3)","A",0
131,1,377,0,0.223106," ","integrate((e*x^2+d*x+c)/(-b*x^4+a)^4,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(77 \, b^{2} c - 40 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + 15 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} - \frac{\sqrt{2} {\left(77 \, b^{2} c + 40 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - 15 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} - \frac{\sqrt{2} {\left(77 \, b^{2} c - 15 \, \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{1024 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} + \frac{\sqrt{2} {\left(77 \, b^{2} c - 15 \, \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{1024 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} - \frac{45 \, b^{2} x^{11} e + 60 \, b^{2} d x^{10} + 77 \, b^{2} c x^{9} - 126 \, a b x^{7} e - 160 \, a b d x^{6} - 198 \, a b c x^{5} + 113 \, a^{2} x^{3} e + 132 \, a^{2} d x^{2} + 153 \, a^{2} c x}{384 \, {\left(b x^{4} - a\right)}^{3} a^{3}}"," ",0,"-1/512*sqrt(2)*(77*b^2*c - 40*sqrt(2)*(-a*b^3)^(1/4)*b*d + 15*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^3) - 1/512*sqrt(2)*(77*b^2*c + 40*sqrt(2)*(-a*b^3)^(1/4)*b*d - 15*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^3) - 1/1024*sqrt(2)*(77*b^2*c - 15*sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^3) + 1/1024*sqrt(2)*(77*b^2*c - 15*sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^3) - 1/384*(45*b^2*x^11*e + 60*b^2*d*x^10 + 77*b^2*c*x^9 - 126*a*b*x^7*e - 160*a*b*d*x^6 - 198*a*b*c*x^5 + 113*a^2*x^3*e + 132*a^2*d*x^2 + 153*a^2*c*x)/((b*x^4 - a)^3*a^3)","B",0
132,1,373,0,0.190556," ","integrate((e*x^2+d*x+c)/(b*x^4+a)^4,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(40 \, \sqrt{2} \sqrt{a b} b^{2} d + 77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{4} b^{3}} + \frac{\sqrt{2} {\left(40 \, \sqrt{2} \sqrt{a b} b^{2} d + 77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{4} b^{3}} + \frac{\sqrt{2} {\left(77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{1024 \, a^{4} b^{3}} - \frac{\sqrt{2} {\left(77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{1024 \, a^{4} b^{3}} + \frac{45 \, b^{2} x^{11} e + 60 \, b^{2} d x^{10} + 77 \, b^{2} c x^{9} + 126 \, a b x^{7} e + 160 \, a b d x^{6} + 198 \, a b c x^{5} + 113 \, a^{2} x^{3} e + 132 \, a^{2} d x^{2} + 153 \, a^{2} c x}{384 \, {\left(b x^{4} + a\right)}^{3} a^{3}}"," ",0,"1/512*sqrt(2)*(40*sqrt(2)*sqrt(a*b)*b^2*d + 77*(a*b^3)^(1/4)*b^2*c + 15*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^4*b^3) + 1/512*sqrt(2)*(40*sqrt(2)*sqrt(a*b)*b^2*d + 77*(a*b^3)^(1/4)*b^2*c + 15*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^4*b^3) + 1/1024*sqrt(2)*(77*(a*b^3)^(1/4)*b^2*c - 15*(a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^4*b^3) - 1/1024*sqrt(2)*(77*(a*b^3)^(1/4)*b^2*c - 15*(a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^4*b^3) + 1/384*(45*b^2*x^11*e + 60*b^2*d*x^10 + 77*b^2*c*x^9 + 126*a*b*x^7*e + 160*a*b*d*x^6 + 198*a*b*c*x^5 + 113*a^2*x^3*e + 132*a^2*d*x^2 + 153*a^2*c*x)/((b*x^4 + a)^3*a^3)","A",0
133,1,25,0,0.144945," ","integrate(a*(f*x^4+e)^2,x, algorithm=""giac"")","\frac{1}{45} \, {\left(5 \, f^{2} x^{9} + 18 \, f x^{5} e + 45 \, x e^{2}\right)} a"," ",0,"1/45*(5*f^2*x^9 + 18*f*x^5*e + 45*x*e^2)*a","A",0
134,1,27,0,0.169083," ","integrate(b*x*(f*x^4+e)^2,x, algorithm=""giac"")","\frac{1}{30} \, {\left(3 \, f^{2} x^{10} + 10 \, f x^{6} e + 15 \, x^{2} e^{2}\right)} b"," ",0,"1/30*(3*f^2*x^10 + 10*f*x^6*e + 15*x^2*e^2)*b","A",0
135,1,50,0,0.149592," ","integrate((b*x+a)*(f*x^4+e)^2,x, algorithm=""giac"")","\frac{1}{10} \, b f^{2} x^{10} + \frac{1}{9} \, a f^{2} x^{9} + \frac{1}{3} \, b f x^{6} e + \frac{2}{5} \, a f x^{5} e + \frac{1}{2} \, b x^{2} e^{2} + a x e^{2}"," ",0,"1/10*b*f^2*x^10 + 1/9*a*f^2*x^9 + 1/3*b*f*x^6*e + 2/5*a*f*x^5*e + 1/2*b*x^2*e^2 + a*x*e^2","A",0
136,1,27,0,0.195447," ","integrate(c*x^2*(f*x^4+e)^2,x, algorithm=""giac"")","\frac{1}{231} \, {\left(21 \, f^{2} x^{11} + 66 \, f x^{7} e + 77 \, x^{3} e^{2}\right)} c"," ",0,"1/231*(21*f^2*x^11 + 66*f*x^7*e + 77*x^3*e^2)*c","A",0
137,1,50,0,0.151086," ","integrate((c*x^2+a)*(f*x^4+e)^2,x, algorithm=""giac"")","\frac{1}{11} \, c f^{2} x^{11} + \frac{1}{9} \, a f^{2} x^{9} + \frac{2}{7} \, c f x^{7} e + \frac{2}{5} \, a f x^{5} e + \frac{1}{3} \, c x^{3} e^{2} + a x e^{2}"," ",0,"1/11*c*f^2*x^11 + 1/9*a*f^2*x^9 + 2/7*c*f*x^7*e + 2/5*a*f*x^5*e + 1/3*c*x^3*e^2 + a*x*e^2","A",0
138,1,53,0,0.149300," ","integrate((c*x^2+b*x)*(f*x^4+e)^2,x, algorithm=""giac"")","\frac{1}{11} \, c f^{2} x^{11} + \frac{1}{10} \, b f^{2} x^{10} + \frac{2}{7} \, c f x^{7} e + \frac{1}{3} \, b f x^{6} e + \frac{1}{3} \, c x^{3} e^{2} + \frac{1}{2} \, b x^{2} e^{2}"," ",0,"1/11*c*f^2*x^11 + 1/10*b*f^2*x^10 + 2/7*c*f*x^7*e + 1/3*b*f*x^6*e + 1/3*c*x^3*e^2 + 1/2*b*x^2*e^2","A",0
139,1,76,0,0.149998," ","integrate((c*x^2+b*x+a)*(f*x^4+e)^2,x, algorithm=""giac"")","\frac{1}{11} \, c f^{2} x^{11} + \frac{1}{10} \, b f^{2} x^{10} + \frac{1}{9} \, a f^{2} x^{9} + \frac{2}{7} \, c f x^{7} e + \frac{1}{3} \, b f x^{6} e + \frac{2}{5} \, a f x^{5} e + \frac{1}{3} \, c x^{3} e^{2} + \frac{1}{2} \, b x^{2} e^{2} + a x e^{2}"," ",0,"1/11*c*f^2*x^11 + 1/10*b*f^2*x^10 + 1/9*a*f^2*x^9 + 2/7*c*f*x^7*e + 1/3*b*f*x^6*e + 2/5*a*f*x^5*e + 1/3*c*x^3*e^2 + 1/2*b*x^2*e^2 + a*x*e^2","A",0
140,1,16,0,0.142551," ","integrate(d*x^3*(f*x^4+e)^2,x, algorithm=""giac"")","\frac{{\left(f x^{4} + e\right)}^{3} d}{12 \, f}"," ",0,"1/12*(f*x^4 + e)^3*d/f","A",0
141,1,50,0,0.201113," ","integrate((d*x^3+a)*(f*x^4+e)^2,x, algorithm=""giac"")","\frac{1}{12} \, d f^{2} x^{12} + \frac{1}{9} \, a f^{2} x^{9} + \frac{1}{4} \, d f x^{8} e + \frac{2}{5} \, a f x^{5} e + \frac{1}{4} \, d x^{4} e^{2} + a x e^{2}"," ",0,"1/12*d*f^2*x^12 + 1/9*a*f^2*x^9 + 1/4*d*f*x^8*e + 2/5*a*f*x^5*e + 1/4*d*x^4*e^2 + a*x*e^2","A",0
142,1,53,0,0.163159," ","integrate((d*x^3+b*x)*(f*x^4+e)^2,x, algorithm=""giac"")","\frac{1}{12} \, d f^{2} x^{12} + \frac{1}{10} \, b f^{2} x^{10} + \frac{1}{4} \, d f x^{8} e + \frac{1}{3} \, b f x^{6} e + \frac{1}{4} \, d x^{4} e^{2} + \frac{1}{2} \, b x^{2} e^{2}"," ",0,"1/12*d*f^2*x^12 + 1/10*b*f^2*x^10 + 1/4*d*f*x^8*e + 1/3*b*f*x^6*e + 1/4*d*x^4*e^2 + 1/2*b*x^2*e^2","A",0
143,1,76,0,0.150356," ","integrate((d*x^3+b*x+a)*(f*x^4+e)^2,x, algorithm=""giac"")","\frac{1}{12} \, d f^{2} x^{12} + \frac{1}{10} \, b f^{2} x^{10} + \frac{1}{9} \, a f^{2} x^{9} + \frac{1}{4} \, d f x^{8} e + \frac{1}{3} \, b f x^{6} e + \frac{2}{5} \, a f x^{5} e + \frac{1}{4} \, d x^{4} e^{2} + \frac{1}{2} \, b x^{2} e^{2} + a x e^{2}"," ",0,"1/12*d*f^2*x^12 + 1/10*b*f^2*x^10 + 1/9*a*f^2*x^9 + 1/4*d*f*x^8*e + 1/3*b*f*x^6*e + 2/5*a*f*x^5*e + 1/4*d*x^4*e^2 + 1/2*b*x^2*e^2 + a*x*e^2","A",0
144,1,53,0,0.146285," ","integrate((d*x^3+c*x^2)*(f*x^4+e)^2,x, algorithm=""giac"")","\frac{1}{12} \, d f^{2} x^{12} + \frac{1}{11} \, c f^{2} x^{11} + \frac{1}{4} \, d f x^{8} e + \frac{2}{7} \, c f x^{7} e + \frac{1}{4} \, d x^{4} e^{2} + \frac{1}{3} \, c x^{3} e^{2}"," ",0,"1/12*d*f^2*x^12 + 1/11*c*f^2*x^11 + 1/4*d*f*x^8*e + 2/7*c*f*x^7*e + 1/4*d*x^4*e^2 + 1/3*c*x^3*e^2","A",0
145,1,76,0,0.200605," ","integrate((d*x^3+c*x^2+a)*(f*x^4+e)^2,x, algorithm=""giac"")","\frac{1}{12} \, d f^{2} x^{12} + \frac{1}{11} \, c f^{2} x^{11} + \frac{1}{9} \, a f^{2} x^{9} + \frac{1}{4} \, d f x^{8} e + \frac{2}{7} \, c f x^{7} e + \frac{2}{5} \, a f x^{5} e + \frac{1}{4} \, d x^{4} e^{2} + \frac{1}{3} \, c x^{3} e^{2} + a x e^{2}"," ",0,"1/12*d*f^2*x^12 + 1/11*c*f^2*x^11 + 1/9*a*f^2*x^9 + 1/4*d*f*x^8*e + 2/7*c*f*x^7*e + 2/5*a*f*x^5*e + 1/4*d*x^4*e^2 + 1/3*c*x^3*e^2 + a*x*e^2","A",0
146,1,79,0,0.160946," ","integrate((d*x^3+c*x^2+b*x)*(f*x^4+e)^2,x, algorithm=""giac"")","\frac{1}{12} \, d f^{2} x^{12} + \frac{1}{11} \, c f^{2} x^{11} + \frac{1}{10} \, b f^{2} x^{10} + \frac{1}{4} \, d f x^{8} e + \frac{2}{7} \, c f x^{7} e + \frac{1}{3} \, b f x^{6} e + \frac{1}{4} \, d x^{4} e^{2} + \frac{1}{3} \, c x^{3} e^{2} + \frac{1}{2} \, b x^{2} e^{2}"," ",0,"1/12*d*f^2*x^12 + 1/11*c*f^2*x^11 + 1/10*b*f^2*x^10 + 1/4*d*f*x^8*e + 2/7*c*f*x^7*e + 1/3*b*f*x^6*e + 1/4*d*x^4*e^2 + 1/3*c*x^3*e^2 + 1/2*b*x^2*e^2","A",0
147,1,105,0,0.166821," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^2,x, algorithm=""giac"")","\frac{1}{12} \, b^{2} f x^{12} + \frac{1}{11} \, b^{2} x^{11} e + \frac{1}{10} \, b^{2} d x^{10} + \frac{1}{9} \, b^{2} c x^{9} + \frac{1}{4} \, a b f x^{8} + \frac{2}{7} \, a b x^{7} e + \frac{1}{3} \, a b d x^{6} + \frac{2}{5} \, a b c x^{5} + \frac{1}{4} \, a^{2} f x^{4} + \frac{1}{3} \, a^{2} x^{3} e + \frac{1}{2} \, a^{2} d x^{2} + a^{2} c x"," ",0,"1/12*b^2*f*x^12 + 1/11*b^2*x^11*e + 1/10*b^2*d*x^10 + 1/9*b^2*c*x^9 + 1/4*a*b*f*x^8 + 2/7*a*b*x^7*e + 1/3*a*b*d*x^6 + 2/5*a*b*c*x^5 + 1/4*a^2*f*x^4 + 1/3*a^2*x^3*e + 1/2*a^2*d*x^2 + a^2*c*x","A",0
148,1,154,0,0.168234," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^3,x, algorithm=""giac"")","\frac{1}{16} \, b^{3} f x^{16} + \frac{1}{15} \, b^{3} x^{15} e + \frac{1}{14} \, b^{3} d x^{14} + \frac{1}{13} \, b^{3} c x^{13} + \frac{1}{4} \, a b^{2} f x^{12} + \frac{3}{11} \, a b^{2} x^{11} e + \frac{3}{10} \, a b^{2} d x^{10} + \frac{1}{3} \, a b^{2} c x^{9} + \frac{3}{8} \, a^{2} b f x^{8} + \frac{3}{7} \, a^{2} b x^{7} e + \frac{1}{2} \, a^{2} b d x^{6} + \frac{3}{5} \, a^{2} b c x^{5} + \frac{1}{4} \, a^{3} f x^{4} + \frac{1}{3} \, a^{3} x^{3} e + \frac{1}{2} \, a^{3} d x^{2} + a^{3} c x"," ",0,"1/16*b^3*f*x^16 + 1/15*b^3*x^15*e + 1/14*b^3*d*x^14 + 1/13*b^3*c*x^13 + 1/4*a*b^2*f*x^12 + 3/11*a*b^2*x^11*e + 3/10*a*b^2*d*x^10 + 1/3*a*b^2*c*x^9 + 3/8*a^2*b*f*x^8 + 3/7*a^2*b*x^7*e + 1/2*a^2*b*d*x^6 + 3/5*a^2*b*c*x^5 + 1/4*a^3*f*x^4 + 1/3*a^3*x^3*e + 1/2*a^3*d*x^2 + a^3*c*x","A",0
149,1,320,0,0.231166," ","integrate((f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(3 \, b^{2} c - 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{\sqrt{2} {\left(3 \, b^{2} c + 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{\sqrt{2} {\left(3 \, b^{2} c - \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{32 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} + \frac{\sqrt{2} {\left(3 \, b^{2} c - \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{32 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{b x^{3} e + b d x^{2} + b c x + a f}{4 \, {\left(b x^{4} - a\right)} a b}"," ",0,"-1/16*sqrt(2)*(3*b^2*c - 2*sqrt(2)*(-a*b^3)^(1/4)*b*d + sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a) - 1/16*sqrt(2)*(3*b^2*c + 2*sqrt(2)*(-a*b^3)^(1/4)*b*d - sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a) - 1/32*sqrt(2)*(3*b^2*c - sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a) + 1/32*sqrt(2)*(3*b^2*c - sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a) - 1/4*(b*x^3*e + b*d*x^2 + b*c*x + a*f)/((b*x^4 - a)*a*b)","B",0
150,1,358,0,0.203686," ","integrate((f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(21 \, b^{2} c - 12 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + 5 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} - \frac{\sqrt{2} {\left(21 \, b^{2} c + 12 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - 5 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} - \frac{\sqrt{2} {\left(21 \, b^{2} c - 5 \, \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{256 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} + \frac{\sqrt{2} {\left(21 \, b^{2} c - 5 \, \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{256 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} - \frac{5 \, b^{2} x^{7} e + 6 \, b^{2} d x^{6} + 7 \, b^{2} c x^{5} - 9 \, a b x^{3} e - 10 \, a b d x^{2} - 11 \, a b c x - 4 \, a^{2} f}{32 \, {\left(b x^{4} - a\right)}^{2} a^{2} b}"," ",0,"-1/128*sqrt(2)*(21*b^2*c - 12*sqrt(2)*(-a*b^3)^(1/4)*b*d + 5*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^2) - 1/128*sqrt(2)*(21*b^2*c + 12*sqrt(2)*(-a*b^3)^(1/4)*b*d - 5*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^2) - 1/256*sqrt(2)*(21*b^2*c - 5*sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^2) + 1/256*sqrt(2)*(21*b^2*c - 5*sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^2) - 1/32*(5*b^2*x^7*e + 6*b^2*d*x^6 + 7*b^2*c*x^5 - 9*a*b*x^3*e - 10*a*b*d*x^2 - 11*a*b*c*x - 4*a^2*f)/((b*x^4 - a)^2*a^2*b)","B",0
151,1,395,0,0.186793," ","integrate((f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^4,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(77 \, b^{2} c - 40 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + 15 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} - \frac{\sqrt{2} {\left(77 \, b^{2} c + 40 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - 15 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} - \frac{\sqrt{2} {\left(77 \, b^{2} c - 15 \, \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{1024 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} + \frac{\sqrt{2} {\left(77 \, b^{2} c - 15 \, \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{1024 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} - \frac{45 \, b^{3} x^{11} e + 60 \, b^{3} d x^{10} + 77 \, b^{3} c x^{9} - 126 \, a b^{2} x^{7} e - 160 \, a b^{2} d x^{6} - 198 \, a b^{2} c x^{5} + 113 \, a^{2} b x^{3} e + 132 \, a^{2} b d x^{2} + 153 \, a^{2} b c x + 32 \, a^{3} f}{384 \, {\left(b x^{4} - a\right)}^{3} a^{3} b}"," ",0,"-1/512*sqrt(2)*(77*b^2*c - 40*sqrt(2)*(-a*b^3)^(1/4)*b*d + 15*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^3) - 1/512*sqrt(2)*(77*b^2*c + 40*sqrt(2)*(-a*b^3)^(1/4)*b*d - 15*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^3) - 1/1024*sqrt(2)*(77*b^2*c - 15*sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^3) + 1/1024*sqrt(2)*(77*b^2*c - 15*sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^3) - 1/384*(45*b^3*x^11*e + 60*b^3*d*x^10 + 77*b^3*c*x^9 - 126*a*b^2*x^7*e - 160*a*b^2*d*x^6 - 198*a*b^2*c*x^5 + 113*a^2*b*x^3*e + 132*a^2*b*d*x^2 + 153*a^2*b*c*x + 32*a^3*f)/((b*x^4 - a)^3*a^3*b)","B",0
152,1,97,0,0.196253," ","integrate(a/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \cdot 6^{\frac{3}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + 2 \cdot 6^{\frac{3}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + 6^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - 6^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right)\right)} a"," ",0,"1/48*(2*6^(3/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 2*6^(3/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) + 6^(3/4)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 6^(3/4)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)))*a","A",0
153,1,15,0,0.165976," ","integrate(b*x/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{6} b \arctan\left(\frac{1}{2} \, \sqrt{6} x^{2}\right)"," ",0,"1/12*sqrt(6)*b*arctan(1/2*sqrt(6)*x^2)","A",0
154,1,115,0,0.190881," ","integrate((b*x+a)/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{48} \cdot 6^{\frac{3}{4}} a \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{1}{48} \cdot 6^{\frac{3}{4}} a \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) + \frac{1}{24} \, {\left(6^{\frac{3}{4}} a - 2 \, \sqrt{6} b\right)} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{24} \, {\left(6^{\frac{3}{4}} a + 2 \, \sqrt{6} b\right)} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right)"," ",0,"1/48*6^(3/4)*a*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 1/48*6^(3/4)*a*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) + 1/24*(6^(3/4)*a - 2*sqrt(6)*b)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 1/24*(6^(3/4)*a + 2*sqrt(6)*b)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4)))","A",0
155,1,97,0,0.201854," ","integrate(c*x^2/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{24} \, {\left(2 \cdot 6^{\frac{1}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + 2 \cdot 6^{\frac{1}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) - 6^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) + 6^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right)\right)} c"," ",0,"1/24*(2*6^(1/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 2*6^(1/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) - 6^(1/4)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) + 6^(1/4)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)))*c","A",0
156,1,131,0,0.203504," ","integrate((c*x^2+a)/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{24} \, {\left(6^{\frac{3}{4}} a + 2 \cdot 6^{\frac{1}{4}} c\right)} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{24} \, {\left(6^{\frac{3}{4}} a + 2 \cdot 6^{\frac{1}{4}} c\right)} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{48} \, {\left(6^{\frac{3}{4}} a - 2 \cdot 6^{\frac{1}{4}} c\right)} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{1}{48} \, {\left(6^{\frac{3}{4}} a - 2 \cdot 6^{\frac{1}{4}} c\right)} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right)"," ",0,"1/24*(6^(3/4)*a + 2*6^(1/4)*c)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 1/24*(6^(3/4)*a + 2*6^(1/4)*c)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) + 1/48*(6^(3/4)*a - 2*6^(1/4)*c)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 1/48*(6^(3/4)*a - 2*6^(1/4)*c)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3))","A",0
157,1,114,0,0.194690," ","integrate((c*x^2+b*x)/(3*x^4+2),x, algorithm=""giac"")","-\frac{1}{24} \cdot 6^{\frac{1}{4}} c \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) + \frac{1}{24} \cdot 6^{\frac{1}{4}} c \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{1}{12} \, {\left(\sqrt{6} b - 6^{\frac{1}{4}} c\right)} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{12} \, {\left(\sqrt{6} b + 6^{\frac{1}{4}} c\right)} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right)"," ",0,"-1/24*6^(1/4)*c*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) + 1/24*6^(1/4)*c*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 1/12*(sqrt(6)*b - 6^(1/4)*c)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 1/12*(sqrt(6)*b + 6^(1/4)*c)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4)))","A",0
158,1,143,0,0.215638," ","integrate((c*x^2+b*x+a)/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{24} \, {\left(6^{\frac{3}{4}} a - 2 \, \sqrt{6} b + 2 \cdot 6^{\frac{1}{4}} c\right)} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{24} \, {\left(6^{\frac{3}{4}} a + 2 \, \sqrt{6} b + 2 \cdot 6^{\frac{1}{4}} c\right)} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{48} \, {\left(6^{\frac{3}{4}} a - 2 \cdot 6^{\frac{1}{4}} c\right)} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{1}{48} \, {\left(6^{\frac{3}{4}} a - 2 \cdot 6^{\frac{1}{4}} c\right)} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right)"," ",0,"1/24*(6^(3/4)*a - 2*sqrt(6)*b + 2*6^(1/4)*c)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 1/24*(6^(3/4)*a + 2*sqrt(6)*b + 2*6^(1/4)*c)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) + 1/48*(6^(3/4)*a - 2*6^(1/4)*c)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 1/48*(6^(3/4)*a - 2*6^(1/4)*c)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3))","A",0
159,1,11,0,0.164283," ","integrate(d*x^3/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{12} \, d \log\left(3 \, x^{4} + 2\right)"," ",0,"1/12*d*log(3*x^4 + 2)","A",0
160,1,109,0,0.195982," ","integrate((d*x^3+a)/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{24} \cdot 6^{\frac{3}{4}} a \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{24} \cdot 6^{\frac{3}{4}} a \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{48} \, {\left(6^{\frac{3}{4}} a + 4 \, d\right)} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{1}{48} \, {\left(6^{\frac{3}{4}} a - 4 \, d\right)} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right)"," ",0,"1/24*6^(3/4)*a*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 1/24*6^(3/4)*a*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) + 1/48*(6^(3/4)*a + 4*d)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 1/48*(6^(3/4)*a - 4*d)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3))","A",0
161,1,93,0,0.180541," ","integrate((d*x^3+b*x)/(3*x^4+2),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{6} b \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{12} \, \sqrt{6} b \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{12} \, d \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) + \frac{1}{12} \, d \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right)"," ",0,"-1/12*sqrt(6)*b*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 1/12*sqrt(6)*b*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) + 1/12*d*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) + 1/12*d*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3))","B",0
162,1,125,0,0.196687," ","integrate((d*x^3+b*x+a)/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{24} \, {\left(6^{\frac{3}{4}} a - 2 \, \sqrt{6} b\right)} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{24} \, {\left(6^{\frac{3}{4}} a + 2 \, \sqrt{6} b\right)} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{48} \, {\left(6^{\frac{3}{4}} a + 4 \, d\right)} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{1}{48} \, {\left(6^{\frac{3}{4}} a - 4 \, d\right)} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right)"," ",0,"1/24*(6^(3/4)*a - 2*sqrt(6)*b)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 1/24*(6^(3/4)*a + 2*sqrt(6)*b)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) + 1/48*(6^(3/4)*a + 4*d)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 1/48*(6^(3/4)*a - 4*d)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3))","A",0
163,1,109,0,0.275968," ","integrate((d*x^3+c*x^2)/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{12} \cdot 6^{\frac{1}{4}} c \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{12} \cdot 6^{\frac{1}{4}} c \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) - \frac{1}{24} \, {\left(6^{\frac{1}{4}} c - 2 \, d\right)} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) + \frac{1}{24} \, {\left(6^{\frac{1}{4}} c + 2 \, d\right)} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right)"," ",0,"1/12*6^(1/4)*c*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 1/12*6^(1/4)*c*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) - 1/24*(6^(1/4)*c - 2*d)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) + 1/24*(6^(1/4)*c + 2*d)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3))","A",0
164,1,137,0,0.208537," ","integrate((d*x^3+c*x^2+a)/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{24} \, {\left(6^{\frac{3}{4}} a + 2 \cdot 6^{\frac{1}{4}} c\right)} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{24} \, {\left(6^{\frac{3}{4}} a + 2 \cdot 6^{\frac{1}{4}} c\right)} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{48} \, {\left(6^{\frac{3}{4}} a - 2 \cdot 6^{\frac{1}{4}} c + 4 \, d\right)} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{1}{48} \, {\left(6^{\frac{3}{4}} a - 2 \cdot 6^{\frac{1}{4}} c - 4 \, d\right)} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right)"," ",0,"1/24*(6^(3/4)*a + 2*6^(1/4)*c)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 1/24*(6^(3/4)*a + 2*6^(1/4)*c)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) + 1/48*(6^(3/4)*a - 2*6^(1/4)*c + 4*d)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 1/48*(6^(3/4)*a - 2*6^(1/4)*c - 4*d)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3))","A",0
165,1,124,0,0.196950," ","integrate((d*x^3+c*x^2+b*x)/(3*x^4+2),x, algorithm=""giac"")","-\frac{1}{12} \, {\left(\sqrt{6} b - 6^{\frac{1}{4}} c\right)} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{12} \, {\left(\sqrt{6} b + 6^{\frac{1}{4}} c\right)} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) - \frac{1}{24} \, {\left(6^{\frac{1}{4}} c - 2 \, d\right)} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) + \frac{1}{24} \, {\left(6^{\frac{1}{4}} c + 2 \, d\right)} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right)"," ",0,"-1/12*(sqrt(6)*b - 6^(1/4)*c)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 1/12*(sqrt(6)*b + 6^(1/4)*c)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) - 1/24*(6^(1/4)*c - 2*d)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) + 1/24*(6^(1/4)*c + 2*d)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3))","A",0
166,1,149,0,0.216045," ","integrate((d*x^3+c*x^2+b*x+a)/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{24} \, {\left(6^{\frac{3}{4}} a - 2 \, \sqrt{6} b + 2 \cdot 6^{\frac{1}{4}} c\right)} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{24} \, {\left(6^{\frac{3}{4}} a + 2 \, \sqrt{6} b + 2 \cdot 6^{\frac{1}{4}} c\right)} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{48} \, {\left(6^{\frac{3}{4}} a - 2 \cdot 6^{\frac{1}{4}} c + 4 \, d\right)} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{1}{48} \, {\left(6^{\frac{3}{4}} a - 2 \cdot 6^{\frac{1}{4}} c - 4 \, d\right)} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right)"," ",0,"1/24*(6^(3/4)*a - 2*sqrt(6)*b + 2*6^(1/4)*c)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 1/24*(6^(3/4)*a + 2*sqrt(6)*b + 2*6^(1/4)*c)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) + 1/48*(6^(3/4)*a - 2*6^(1/4)*c + 4*d)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 1/48*(6^(3/4)*a - 2*6^(1/4)*c - 4*d)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3))","A",0
167,1,7,0,0.150152," ","integrate((x^3+x^2+x+1)/(-x^4+1),x, algorithm=""giac"")","-\log\left({\left| x - 1 \right|}\right)"," ",0,"-log(abs(x - 1))","A",0
168,1,70,0,0.152019," ","integrate((x^3+x^2+x+1)/(x^4+1),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\sqrt{2} - 1\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{1}{2} \, {\left(\sqrt{2} + 1\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) + \frac{1}{4} \, \log\left(x^{2} + \sqrt{2} x + 1\right) + \frac{1}{4} \, \log\left(x^{2} - \sqrt{2} x + 1\right)"," ",0,"1/2*(sqrt(2) - 1)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 1/2*(sqrt(2) + 1)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) + 1/4*log(x^2 + sqrt(2)*x + 1) + 1/4*log(x^2 - sqrt(2)*x + 1)","A",0
169,1,290,0,0.173296," ","integrate((x^3+x^2+x+1)/(-b*x^4+a),x, algorithm=""giac"")","-\frac{\log\left({\left| b x^{4} - a \right|}\right)}{4 \, b} + \frac{\sqrt{2} {\left(\left(-a b^{3}\right)^{\frac{1}{4}} b^{2} - \sqrt{2} \sqrt{-a b^{3}} b + \left(-a b^{3}\right)^{\frac{3}{4}}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\left(-a b^{3}\right)^{\frac{1}{4}} b^{2} + \sqrt{2} \sqrt{-a b^{3}} b + \left(-a b^{3}\right)^{\frac{3}{4}}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\left(-a b^{3}\right)^{\frac{1}{4}} b^{2} - \left(-a b^{3}\right)^{\frac{3}{4}}\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, a b^{3}} - \frac{\sqrt{2} {\left(\left(-a b^{3}\right)^{\frac{1}{4}} b^{2} - \left(-a b^{3}\right)^{\frac{3}{4}}\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, a b^{3}}"," ",0,"-1/4*log(abs(b*x^4 - a))/b + 1/4*sqrt(2)*((-a*b^3)^(1/4)*b^2 - sqrt(2)*sqrt(-a*b^3)*b + (-a*b^3)^(3/4))*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a*b^3) + 1/4*sqrt(2)*((-a*b^3)^(1/4)*b^2 + sqrt(2)*sqrt(-a*b^3)*b + (-a*b^3)^(3/4))*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a*b^3) + 1/8*sqrt(2)*((-a*b^3)^(1/4)*b^2 - (-a*b^3)^(3/4))*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a*b^3) - 1/8*sqrt(2)*((-a*b^3)^(1/4)*b^2 - (-a*b^3)^(3/4))*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a*b^3)","B",0
170,1,270,0,0.208792," ","integrate((x^3+x^2+x+1)/(b*x^4+a),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{4} + a \right|}\right)}{4 \, b} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} - \sqrt{2} \sqrt{a b^{3}} b + \left(a b^{3}\right)^{\frac{3}{4}}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} + \sqrt{2} \sqrt{a b^{3}} b + \left(a b^{3}\right)^{\frac{3}{4}}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} - \left(a b^{3}\right)^{\frac{3}{4}}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} - \left(a b^{3}\right)^{\frac{3}{4}}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}}"," ",0,"1/4*log(abs(b*x^4 + a))/b + 1/4*sqrt(2)*((a*b^3)^(1/4)*b^2 - sqrt(2)*sqrt(a*b^3)*b + (a*b^3)^(3/4))*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/4*sqrt(2)*((a*b^3)^(1/4)*b^2 + sqrt(2)*sqrt(a*b^3)*b + (a*b^3)^(3/4))*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2 - (a*b^3)^(3/4))*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3) - 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2 - (a*b^3)^(3/4))*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3)","A",0
171,1,303,0,0.193674," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(b^{2} c + a b g - \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c + a b g + \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c + a b g - \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, \left(-a b^{3}\right)^{\frac{3}{4}}} + \frac{\sqrt{2} {\left(b^{2} c + a b g - \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{g x}{b} - \frac{f \log\left({\left| b x^{4} - a \right|}\right)}{4 \, b}"," ",0,"-1/4*sqrt(2)*(b^2*c + a*b*g - sqrt(2)*(-a*b^3)^(1/4)*b*d + sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(-a*b^3)^(3/4) - 1/4*sqrt(2)*(b^2*c + a*b*g + sqrt(2)*(-a*b^3)^(1/4)*b*d - sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(-a*b^3)^(3/4) - 1/8*sqrt(2)*(b^2*c + a*b*g - sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(-a*b^3)^(3/4) + 1/8*sqrt(2)*(b^2*c + a*b*g - sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(-a*b^3)^(3/4) - g*x/b - 1/4*f*log(abs(b*x^4 - a))/b","B",0
172,1,344,0,0.183675," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(3 \, b^{2} c - a b g - 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{\sqrt{2} {\left(3 \, b^{2} c - a b g + 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{\sqrt{2} {\left(3 \, b^{2} c - a b g - \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{32 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} + \frac{\sqrt{2} {\left(3 \, b^{2} c - a b g - \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{32 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{b x^{3} e + b d x^{2} + b c x + a g x + a f}{4 \, {\left(b x^{4} - a\right)} a b}"," ",0,"-1/16*sqrt(2)*(3*b^2*c - a*b*g - 2*sqrt(2)*(-a*b^3)^(1/4)*b*d + sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a) - 1/16*sqrt(2)*(3*b^2*c - a*b*g + 2*sqrt(2)*(-a*b^3)^(1/4)*b*d - sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a) - 1/32*sqrt(2)*(3*b^2*c - a*b*g - sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a) + 1/32*sqrt(2)*(3*b^2*c - a*b*g - sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a) - 1/4*(b*x^3*e + b*d*x^2 + b*c*x + a*g*x + a*f)/((b*x^4 - a)*a*b)","B",0
173,1,393,0,0.195208," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(21 \, b^{2} c - 3 \, a b g - 12 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + 5 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} - \frac{\sqrt{2} {\left(21 \, b^{2} c - 3 \, a b g + 12 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - 5 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} - \frac{\sqrt{2} {\left(21 \, b^{2} c - 3 \, a b g - 5 \, \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{256 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} + \frac{\sqrt{2} {\left(21 \, b^{2} c - 3 \, a b g - 5 \, \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{256 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} - \frac{5 \, b^{2} x^{7} e + 6 \, b^{2} d x^{6} + 7 \, b^{2} c x^{5} - a b g x^{5} - 9 \, a b x^{3} e - 10 \, a b d x^{2} - 11 \, a b c x - 3 \, a^{2} g x - 4 \, a^{2} f}{32 \, {\left(b x^{4} - a\right)}^{2} a^{2} b}"," ",0,"-1/128*sqrt(2)*(21*b^2*c - 3*a*b*g - 12*sqrt(2)*(-a*b^3)^(1/4)*b*d + 5*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^2) - 1/128*sqrt(2)*(21*b^2*c - 3*a*b*g + 12*sqrt(2)*(-a*b^3)^(1/4)*b*d - 5*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^2) - 1/256*sqrt(2)*(21*b^2*c - 3*a*b*g - 5*sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^2) + 1/256*sqrt(2)*(21*b^2*c - 3*a*b*g - 5*sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^2) - 1/32*(5*b^2*x^7*e + 6*b^2*d*x^6 + 7*b^2*c*x^5 - a*b*g*x^5 - 9*a*b*x^3*e - 10*a*b*d*x^2 - 11*a*b*c*x - 3*a^2*g*x - 4*a^2*f)/((b*x^4 - a)^2*a^2*b)","B",0
174,1,442,0,0.188601," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^4,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(77 \, b^{2} c - 7 \, a b g - 40 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + 15 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} - \frac{\sqrt{2} {\left(77 \, b^{2} c - 7 \, a b g + 40 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - 15 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} - \frac{\sqrt{2} {\left(77 \, b^{2} c - 7 \, a b g - 15 \, \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{1024 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} + \frac{\sqrt{2} {\left(77 \, b^{2} c - 7 \, a b g - 15 \, \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{1024 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} - \frac{45 \, b^{3} x^{11} e + 60 \, b^{3} d x^{10} + 77 \, b^{3} c x^{9} - 7 \, a b^{2} g x^{9} - 126 \, a b^{2} x^{7} e - 160 \, a b^{2} d x^{6} - 198 \, a b^{2} c x^{5} + 18 \, a^{2} b g x^{5} + 113 \, a^{2} b x^{3} e + 132 \, a^{2} b d x^{2} + 153 \, a^{2} b c x + 21 \, a^{3} g x + 32 \, a^{3} f}{384 \, {\left(b x^{4} - a\right)}^{3} a^{3} b}"," ",0,"-1/512*sqrt(2)*(77*b^2*c - 7*a*b*g - 40*sqrt(2)*(-a*b^3)^(1/4)*b*d + 15*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^3) - 1/512*sqrt(2)*(77*b^2*c - 7*a*b*g + 40*sqrt(2)*(-a*b^3)^(1/4)*b*d - 15*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^3) - 1/1024*sqrt(2)*(77*b^2*c - 7*a*b*g - 15*sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^3) + 1/1024*sqrt(2)*(77*b^2*c - 7*a*b*g - 15*sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^3) - 1/384*(45*b^3*x^11*e + 60*b^3*d*x^10 + 77*b^3*c*x^9 - 7*a*b^2*g*x^9 - 126*a*b^2*x^7*e - 160*a*b^2*d*x^6 - 198*a*b^2*c*x^5 + 18*a^2*b*g*x^5 + 113*a^2*b*x^3*e + 132*a^2*b*d*x^2 + 153*a^2*b*c*x + 21*a^3*g*x + 32*a^3*f)/((b*x^4 - a)^3*a^3*b)","A",0
175,1,340,0,0.272795," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a),x, algorithm=""giac"")","\frac{g x}{b} + \frac{f \log\left({\left| b x^{4} + a \right|}\right)}{4 \, b} + \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a b} b^{2} d + \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{1}{4}} a b g + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a b} b^{2} d + \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{1}{4}} a b g + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{1}{4}} a b g - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{1}{4}} a b g - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}}"," ",0,"g*x/b + 1/4*f*log(abs(b*x^4 + a))/b + 1/4*sqrt(2)*(sqrt(2)*sqrt(a*b)*b^2*d + (a*b^3)^(1/4)*b^2*c - (a*b^3)^(1/4)*a*b*g + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/4*sqrt(2)*(sqrt(2)*sqrt(a*b)*b^2*d + (a*b^3)^(1/4)*b^2*c - (a*b^3)^(1/4)*a*b*g + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c - (a*b^3)^(1/4)*a*b*g - (a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3) - 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c - (a*b^3)^(1/4)*a*b*g - (a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3)","A",0
176,1,365,0,0.202663," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x, algorithm=""giac"")","\frac{b x^{3} e + b d x^{2} + b c x - a g x - a f}{4 \, {\left(b x^{4} + a\right)} a b} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a b} b^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{1}{4}} a b g + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a b} b^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{1}{4}} a b g + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{1}{4}} a b g - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{3}} - \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{1}{4}} a b g - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{3}}"," ",0,"1/4*(b*x^3*e + b*d*x^2 + b*c*x - a*g*x - a*f)/((b*x^4 + a)*a*b) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*b)*b^2*d + 3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(1/4)*a*b*g + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^3) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*b)*b^2*d + 3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(1/4)*a*b*g + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^3) + 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(1/4)*a*b*g - (a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^3) - 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(1/4)*a*b*g - (a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^3)","A",0
177,1,416,0,0.196803," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(12 \, \sqrt{2} \sqrt{a b} b^{2} d + 21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} b^{3}} + \frac{\sqrt{2} {\left(12 \, \sqrt{2} \sqrt{a b} b^{2} d + 21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} b^{3}} + \frac{\sqrt{2} {\left(21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{256 \, a^{3} b^{3}} - \frac{\sqrt{2} {\left(21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{256 \, a^{3} b^{3}} + \frac{5 \, b^{2} x^{7} e + 6 \, b^{2} d x^{6} + 7 \, b^{2} c x^{5} + a b g x^{5} + 9 \, a b x^{3} e + 10 \, a b d x^{2} + 11 \, a b c x - 3 \, a^{2} g x - 4 \, a^{2} f}{32 \, {\left(b x^{4} + a\right)}^{2} a^{2} b}"," ",0,"1/128*sqrt(2)*(12*sqrt(2)*sqrt(a*b)*b^2*d + 21*(a*b^3)^(1/4)*b^2*c + 3*(a*b^3)^(1/4)*a*b*g + 5*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^3) + 1/128*sqrt(2)*(12*sqrt(2)*sqrt(a*b)*b^2*d + 21*(a*b^3)^(1/4)*b^2*c + 3*(a*b^3)^(1/4)*a*b*g + 5*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^3) + 1/256*sqrt(2)*(21*(a*b^3)^(1/4)*b^2*c + 3*(a*b^3)^(1/4)*a*b*g - 5*(a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^3) - 1/256*sqrt(2)*(21*(a*b^3)^(1/4)*b^2*c + 3*(a*b^3)^(1/4)*a*b*g - 5*(a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^3) + 1/32*(5*b^2*x^7*e + 6*b^2*d*x^6 + 7*b^2*c*x^5 + a*b*g*x^5 + 9*a*b*x^3*e + 10*a*b*d*x^2 + 11*a*b*c*x - 3*a^2*g*x - 4*a^2*f)/((b*x^4 + a)^2*a^2*b)","A",0
178,1,466,0,0.187847," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(40 \, \sqrt{2} \sqrt{a b} b^{2} d + 77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g + 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{4} b^{3}} + \frac{\sqrt{2} {\left(40 \, \sqrt{2} \sqrt{a b} b^{2} d + 77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g + 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{4} b^{3}} + \frac{\sqrt{2} {\left(77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g - 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{1024 \, a^{4} b^{3}} - \frac{\sqrt{2} {\left(77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g - 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{1024 \, a^{4} b^{3}} + \frac{45 \, b^{3} x^{11} e + 60 \, b^{3} d x^{10} + 77 \, b^{3} c x^{9} + 7 \, a b^{2} g x^{9} + 126 \, a b^{2} x^{7} e + 160 \, a b^{2} d x^{6} + 198 \, a b^{2} c x^{5} + 18 \, a^{2} b g x^{5} + 113 \, a^{2} b x^{3} e + 132 \, a^{2} b d x^{2} + 153 \, a^{2} b c x - 21 \, a^{3} g x - 32 \, a^{3} f}{384 \, {\left(b x^{4} + a\right)}^{3} a^{3} b}"," ",0,"1/512*sqrt(2)*(40*sqrt(2)*sqrt(a*b)*b^2*d + 77*(a*b^3)^(1/4)*b^2*c + 7*(a*b^3)^(1/4)*a*b*g + 15*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^4*b^3) + 1/512*sqrt(2)*(40*sqrt(2)*sqrt(a*b)*b^2*d + 77*(a*b^3)^(1/4)*b^2*c + 7*(a*b^3)^(1/4)*a*b*g + 15*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^4*b^3) + 1/1024*sqrt(2)*(77*(a*b^3)^(1/4)*b^2*c + 7*(a*b^3)^(1/4)*a*b*g - 15*(a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^4*b^3) - 1/1024*sqrt(2)*(77*(a*b^3)^(1/4)*b^2*c + 7*(a*b^3)^(1/4)*a*b*g - 15*(a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^4*b^3) + 1/384*(45*b^3*x^11*e + 60*b^3*d*x^10 + 77*b^3*c*x^9 + 7*a*b^2*g*x^9 + 126*a*b^2*x^7*e + 160*a*b^2*d*x^6 + 198*a*b^2*c*x^5 + 18*a^2*b*g*x^5 + 113*a^2*b*x^3*e + 132*a^2*b*d*x^2 + 153*a^2*b*c*x - 21*a^3*g*x - 32*a^3*f)/((b*x^4 + a)^3*a^3*b)","A",0
179,1,15,0,0.241893," ","integrate((-x^4+1)^3/(x^3+x^2+x+1)^3,x, algorithm=""giac"")","-\frac{1}{4} \, x^{4} + x^{3} - \frac{3}{2} \, x^{2} + x"," ",0,"-1/4*x^4 + x^3 - 3/2*x^2 + x","B",0
180,1,12,0,0.159261," ","integrate((-x^4+1)^2/(x^3+x^2+x+1)^2,x, algorithm=""giac"")","\frac{1}{3} \, x^{3} - x^{2} + x"," ",0,"1/3*x^3 - x^2 + x","A",0
181,1,7,0,0.154298," ","integrate((-x^4+1)/(x^3+x^2+x+1),x, algorithm=""giac"")","-\frac{1}{2} \, x^{2} + x"," ",0,"-1/2*x^2 + x","A",0
182,1,7,0,0.166034," ","integrate((x^3+x^2+x+1)/(-x^4+1),x, algorithm=""giac"")","-\log\left({\left| x - 1 \right|}\right)"," ",0,"-log(abs(x - 1))","A",0
183,1,7,0,0.213497," ","integrate((x^3+x^2+x+1)^2/(-x^4+1)^2,x, algorithm=""giac"")","-\frac{1}{x - 1}"," ",0,"-1/(x - 1)","A",0
184,1,7,0,0.156810," ","integrate((x^3+x^2+x+1)^3/(-x^4+1)^3,x, algorithm=""giac"")","\frac{1}{2 \, {\left(x - 1\right)}^{2}}"," ",0,"1/2/(x - 1)^2","A",0
185,1,7,0,0.156204," ","integrate((x^3+x^2+x+1)^4/(-x^4+1)^4,x, algorithm=""giac"")","-\frac{1}{3 \, {\left(x - 1\right)}^{3}}"," ",0,"-1/3/(x - 1)^3","A",0
186,1,342,0,0.197266," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(b^{2} c + a b g - \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h + \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c + a b g + \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h - \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c + a b g - \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, \left(-a b^{3}\right)^{\frac{3}{4}}} + \frac{\sqrt{2} {\left(b^{2} c + a b g - \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{f \log\left({\left| b x^{4} - a \right|}\right)}{4 \, b} - \frac{b h x^{2} + 2 \, b g x}{2 \, b^{2}}"," ",0,"-1/4*sqrt(2)*(b^2*c + a*b*g - sqrt(2)*(-a*b^3)^(1/4)*b*d - sqrt(2)*(-a*b^3)^(1/4)*a*h + sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(-a*b^3)^(3/4) - 1/4*sqrt(2)*(b^2*c + a*b*g + sqrt(2)*(-a*b^3)^(1/4)*b*d + sqrt(2)*(-a*b^3)^(1/4)*a*h - sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(-a*b^3)^(3/4) - 1/8*sqrt(2)*(b^2*c + a*b*g - sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(-a*b^3)^(3/4) + 1/8*sqrt(2)*(b^2*c + a*b*g - sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(-a*b^3)^(3/4) - 1/4*f*log(abs(b*x^4 - a))/b - 1/2*(b*h*x^2 + 2*b*g*x)/b^2","B",0
187,1,541,0,0.212812," ","integrate((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x, algorithm=""giac"")","\frac{1}{8} \, i {\left(\frac{2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{b^{4}} - \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{b^{4}}\right)} + \frac{1}{8} \, i {\left(\frac{2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{b^{4}} + \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{b^{4}}\right)} - \frac{\sqrt{2} {\left(b^{2} c + a b g - \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h + \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c + a b g + \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h - \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c + a b g - \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, \left(-a b^{3}\right)^{\frac{3}{4}}} + \frac{\sqrt{2} {\left(b^{2} c + a b g - \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{f \log\left({\left| b x^{4} - a \right|}\right)}{4 \, b} - \frac{2 \, b^{2} i x^{3} + 3 \, b^{2} h x^{2} + 6 \, b^{2} g x}{6 \, b^{3}}"," ",0,"1/8*i*(2*sqrt(2)*(-a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/b^4 - sqrt(2)*(-a*b^3)^(3/4)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/b^4) + 1/8*i*(2*sqrt(2)*(-a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/b^4 + sqrt(2)*(-a*b^3)^(3/4)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/b^4) - 1/4*sqrt(2)*(b^2*c + a*b*g - sqrt(2)*(-a*b^3)^(1/4)*b*d - sqrt(2)*(-a*b^3)^(1/4)*a*h + sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(-a*b^3)^(3/4) - 1/4*sqrt(2)*(b^2*c + a*b*g + sqrt(2)*(-a*b^3)^(1/4)*b*d + sqrt(2)*(-a*b^3)^(1/4)*a*h - sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(-a*b^3)^(3/4) - 1/8*sqrt(2)*(b^2*c + a*b*g - sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(-a*b^3)^(3/4) + 1/8*sqrt(2)*(b^2*c + a*b*g - sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(-a*b^3)^(3/4) - 1/4*f*log(abs(b*x^4 - a))/b - 1/6*(2*b^2*i*x^3 + 3*b^2*h*x^2 + 6*b^2*g*x)/b^3","B",0
188,1,556,0,0.214542," ","integrate((j*x^7+i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x, algorithm=""giac"")","\frac{1}{8} \, i {\left(\frac{2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{b^{4}} - \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{b^{4}}\right)} + \frac{1}{8} \, i {\left(\frac{2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{b^{4}} + \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{b^{4}}\right)} - \frac{\sqrt{2} {\left(b^{2} c + a b g - \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h + \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c + a b g + \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h - \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c + a b g - \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, \left(-a b^{3}\right)^{\frac{3}{4}}} + \frac{\sqrt{2} {\left(b^{2} c + a b g - \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{{\left(b f + a j\right)} \log\left({\left| b x^{4} - a \right|}\right)}{4 \, b^{2}} - \frac{3 \, b^{3} j x^{4} + 4 \, b^{3} i x^{3} + 6 \, b^{3} h x^{2} + 12 \, b^{3} g x}{12 \, b^{4}}"," ",0,"1/8*i*(2*sqrt(2)*(-a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/b^4 - sqrt(2)*(-a*b^3)^(3/4)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/b^4) + 1/8*i*(2*sqrt(2)*(-a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/b^4 + sqrt(2)*(-a*b^3)^(3/4)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/b^4) - 1/4*sqrt(2)*(b^2*c + a*b*g - sqrt(2)*(-a*b^3)^(1/4)*b*d - sqrt(2)*(-a*b^3)^(1/4)*a*h + sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(-a*b^3)^(3/4) - 1/4*sqrt(2)*(b^2*c + a*b*g + sqrt(2)*(-a*b^3)^(1/4)*b*d + sqrt(2)*(-a*b^3)^(1/4)*a*h - sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(-a*b^3)^(3/4) - 1/8*sqrt(2)*(b^2*c + a*b*g - sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(-a*b^3)^(3/4) + 1/8*sqrt(2)*(b^2*c + a*b*g - sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(-a*b^3)^(3/4) - 1/4*(b*f + a*j)*log(abs(b*x^4 - a))/b^2 - 1/12*(3*b^3*j*x^4 + 4*b^3*i*x^3 + 6*b^3*h*x^2 + 12*b^3*g*x)/b^4","B",0
189,1,375,0,0.188571," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a),x, algorithm=""giac"")","\frac{f \log\left({\left| b x^{4} + a \right|}\right)}{4 \, b} + \frac{b h x^{2} + 2 \, b g x}{2 \, b^{2}} + \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a b} b^{2} d + \sqrt{2} \sqrt{a b} a b h + \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{1}{4}} a b g + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a b} b^{2} d + \sqrt{2} \sqrt{a b} a b h + \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{1}{4}} a b g + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{1}{4}} a b g - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{1}{4}} a b g - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}}"," ",0,"1/4*f*log(abs(b*x^4 + a))/b + 1/2*(b*h*x^2 + 2*b*g*x)/b^2 + 1/4*sqrt(2)*(sqrt(2)*sqrt(a*b)*b^2*d + sqrt(2)*sqrt(a*b)*a*b*h + (a*b^3)^(1/4)*b^2*c - (a*b^3)^(1/4)*a*b*g + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/4*sqrt(2)*(sqrt(2)*sqrt(a*b)*b^2*d + sqrt(2)*sqrt(a*b)*a*b*h + (a*b^3)^(1/4)*b^2*c - (a*b^3)^(1/4)*a*b*g + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c - (a*b^3)^(1/4)*a*b*g - (a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3) - 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c - (a*b^3)^(1/4)*a*b*g - (a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3)","A",0
190,1,562,0,0.209101," ","integrate((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a),x, algorithm=""giac"")","-\frac{1}{8} \, i {\left(\frac{2 \, \sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{b^{4}} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{b^{4}}\right)} - \frac{1}{8} \, i {\left(\frac{2 \, \sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{b^{4}} + \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{b^{4}}\right)} + \frac{f \log\left({\left| b x^{4} + a \right|}\right)}{4 \, b} + \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a b} b^{2} d + \sqrt{2} \sqrt{a b} a b h + \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{1}{4}} a b g + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a b} b^{2} d + \sqrt{2} \sqrt{a b} a b h + \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{1}{4}} a b g + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{1}{4}} a b g - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{1}{4}} a b g - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}} + \frac{2 \, b^{2} i x^{3} + 3 \, b^{2} h x^{2} + 6 \, b^{2} g x}{6 \, b^{3}}"," ",0,"-1/8*i*(2*sqrt(2)*(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/b^4 - sqrt(2)*(a*b^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/b^4) - 1/8*i*(2*sqrt(2)*(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/b^4 + sqrt(2)*(a*b^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/b^4) + 1/4*f*log(abs(b*x^4 + a))/b + 1/4*sqrt(2)*(sqrt(2)*sqrt(a*b)*b^2*d + sqrt(2)*sqrt(a*b)*a*b*h + (a*b^3)^(1/4)*b^2*c - (a*b^3)^(1/4)*a*b*g + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/4*sqrt(2)*(sqrt(2)*sqrt(a*b)*b^2*d + sqrt(2)*sqrt(a*b)*a*b*h + (a*b^3)^(1/4)*b^2*c - (a*b^3)^(1/4)*a*b*g + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c - (a*b^3)^(1/4)*a*b*g - (a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3) - 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c - (a*b^3)^(1/4)*a*b*g - (a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3) + 1/6*(2*b^2*i*x^3 + 3*b^2*h*x^2 + 6*b^2*g*x)/b^3","A",0
191,1,578,0,0.203859," ","integrate((j*x^7+i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a),x, algorithm=""giac"")","-\frac{1}{8} \, i {\left(\frac{2 \, \sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{b^{4}} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{b^{4}}\right)} - \frac{1}{8} \, i {\left(\frac{2 \, \sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{b^{4}} + \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{b^{4}}\right)} + \frac{{\left(b f - a j\right)} \log\left({\left| b x^{4} + a \right|}\right)}{4 \, b^{2}} + \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a b} b^{2} d + \sqrt{2} \sqrt{a b} a b h + \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{1}{4}} a b g + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a b} b^{2} d + \sqrt{2} \sqrt{a b} a b h + \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{1}{4}} a b g + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{1}{4}} a b g - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{1}{4}} a b g - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}} + \frac{3 \, b^{3} j x^{4} + 4 \, b^{3} i x^{3} + 6 \, b^{3} h x^{2} + 12 \, b^{3} g x}{12 \, b^{4}}"," ",0,"-1/8*i*(2*sqrt(2)*(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/b^4 - sqrt(2)*(a*b^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/b^4) - 1/8*i*(2*sqrt(2)*(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/b^4 + sqrt(2)*(a*b^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/b^4) + 1/4*(b*f - a*j)*log(abs(b*x^4 + a))/b^2 + 1/4*sqrt(2)*(sqrt(2)*sqrt(a*b)*b^2*d + sqrt(2)*sqrt(a*b)*a*b*h + (a*b^3)^(1/4)*b^2*c - (a*b^3)^(1/4)*a*b*g + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/4*sqrt(2)*(sqrt(2)*sqrt(a*b)*b^2*d + sqrt(2)*sqrt(a*b)*a*b*h + (a*b^3)^(1/4)*b^2*c - (a*b^3)^(1/4)*a*b*g + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c - (a*b^3)^(1/4)*a*b*g - (a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3) - 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c - (a*b^3)^(1/4)*a*b*g - (a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3) + 1/12*(3*b^3*j*x^4 + 4*b^3*i*x^3 + 6*b^3*h*x^2 + 12*b^3*g*x)/b^4","A",0
192,1,380,0,0.193053," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(3 \, b^{2} c - a b g - 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h + \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{\sqrt{2} {\left(3 \, b^{2} c - a b g + 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h - \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{\sqrt{2} {\left(3 \, b^{2} c - a b g - \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{32 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} + \frac{\sqrt{2} {\left(3 \, b^{2} c - a b g - \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{32 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{b x^{3} e + b d x^{2} + a h x^{2} + b c x + a g x + a f}{4 \, {\left(b x^{4} - a\right)} a b}"," ",0,"-1/16*sqrt(2)*(3*b^2*c - a*b*g - 2*sqrt(2)*(-a*b^3)^(1/4)*b*d + 2*sqrt(2)*(-a*b^3)^(1/4)*a*h + sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a) - 1/16*sqrt(2)*(3*b^2*c - a*b*g + 2*sqrt(2)*(-a*b^3)^(1/4)*b*d - 2*sqrt(2)*(-a*b^3)^(1/4)*a*h - sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a) - 1/32*sqrt(2)*(3*b^2*c - a*b*g - sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a) + 1/32*sqrt(2)*(3*b^2*c - a*b*g - sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a) - 1/4*(b*x^3*e + b*d*x^2 + a*h*x^2 + b*c*x + a*g*x + a*f)/((b*x^4 - a)*a*b)","B",0
193,1,583,0,0.200011," ","integrate((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^2,x, algorithm=""giac"")","-\frac{3}{32} \, i {\left(\frac{2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a b^{4}} - \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{a b^{4}}\right)} - \frac{3}{32} \, i {\left(\frac{2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a b^{4}} + \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{a b^{4}}\right)} - \frac{\sqrt{2} {\left(3 \, b^{2} c - a b g - 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h + \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{\sqrt{2} {\left(3 \, b^{2} c - a b g + 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h - \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{\sqrt{2} {\left(3 \, b^{2} c - a b g - \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{32 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} + \frac{\sqrt{2} {\left(3 \, b^{2} c - a b g - \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{32 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{a i x^{3} + b x^{3} e + b d x^{2} + a h x^{2} + b c x + a g x + a f}{4 \, {\left(b x^{4} - a\right)} a b}"," ",0,"-3/32*i*(2*sqrt(2)*(-a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a*b^4) - sqrt(2)*(-a*b^3)^(3/4)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a*b^4)) - 3/32*i*(2*sqrt(2)*(-a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a*b^4) + sqrt(2)*(-a*b^3)^(3/4)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a*b^4)) - 1/16*sqrt(2)*(3*b^2*c - a*b*g - 2*sqrt(2)*(-a*b^3)^(1/4)*b*d + 2*sqrt(2)*(-a*b^3)^(1/4)*a*h + sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a) - 1/16*sqrt(2)*(3*b^2*c - a*b*g + 2*sqrt(2)*(-a*b^3)^(1/4)*b*d - 2*sqrt(2)*(-a*b^3)^(1/4)*a*h - sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a) - 1/32*sqrt(2)*(3*b^2*c - a*b*g - sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a) + 1/32*sqrt(2)*(3*b^2*c - a*b*g - sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a) - 1/4*(a*i*x^3 + b*x^3*e + b*d*x^2 + a*h*x^2 + b*c*x + a*g*x + a*f)/((b*x^4 - a)*a*b)","B",0
194,1,610,0,0.225039," ","integrate((j*x^7+i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^2,x, algorithm=""giac"")","-\frac{3}{32} \, i {\left(\frac{2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a b^{4}} - \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{a b^{4}}\right)} - \frac{3}{32} \, i {\left(\frac{2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a b^{4}} + \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{a b^{4}}\right)} - \frac{\sqrt{2} {\left(3 \, b^{2} c - a b g - 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h + \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{\sqrt{2} {\left(3 \, b^{2} c - a b g + 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - 2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h - \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} - \frac{\sqrt{2} {\left(3 \, b^{2} c - a b g - \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{32 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} + \frac{\sqrt{2} {\left(3 \, b^{2} c - a b g - \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{32 \, \left(-a b^{3}\right)^{\frac{3}{4}} a} + \frac{j \log\left({\left| b x^{4} - a \right|}\right)}{4 \, b^{2}} - \frac{{\left(a i + b e\right)} x^{3} + {\left(b d + a h\right)} x^{2} + {\left(b c + a g\right)} x + \frac{a b f + a^{2} j}{b}}{4 \, {\left(b x^{4} - a\right)} a b}"," ",0,"-3/32*i*(2*sqrt(2)*(-a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a*b^4) - sqrt(2)*(-a*b^3)^(3/4)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a*b^4)) - 3/32*i*(2*sqrt(2)*(-a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a*b^4) + sqrt(2)*(-a*b^3)^(3/4)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a*b^4)) - 1/16*sqrt(2)*(3*b^2*c - a*b*g - 2*sqrt(2)*(-a*b^3)^(1/4)*b*d + 2*sqrt(2)*(-a*b^3)^(1/4)*a*h + sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a) - 1/16*sqrt(2)*(3*b^2*c - a*b*g + 2*sqrt(2)*(-a*b^3)^(1/4)*b*d - 2*sqrt(2)*(-a*b^3)^(1/4)*a*h - sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a) - 1/32*sqrt(2)*(3*b^2*c - a*b*g - sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a) + 1/32*sqrt(2)*(3*b^2*c - a*b*g - sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a) + 1/4*j*log(abs(b*x^4 - a))/b^2 - 1/4*((a*i + b*e)*x^3 + (b*d + a*h)*x^2 + (b*c + a*g)*x + (a*b*f + a^2*j)/b)/((b*x^4 - a)*a*b)","B",0
195,1,398,0,0.186101," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x, algorithm=""giac"")","\frac{b x^{3} e + b d x^{2} - a h x^{2} + b c x - a g x - a f}{4 \, {\left(b x^{4} + a\right)} a b} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a b} b^{2} d + 2 \, \sqrt{2} \sqrt{a b} a b h + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{1}{4}} a b g + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a b} b^{2} d + 2 \, \sqrt{2} \sqrt{a b} a b h + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{1}{4}} a b g + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{1}{4}} a b g - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{3}} - \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{1}{4}} a b g - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{3}}"," ",0,"1/4*(b*x^3*e + b*d*x^2 - a*h*x^2 + b*c*x - a*g*x - a*f)/((b*x^4 + a)*a*b) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*b)*b^2*d + 2*sqrt(2)*sqrt(a*b)*a*b*h + 3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(1/4)*a*b*g + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^3) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*b)*b^2*d + 2*sqrt(2)*sqrt(a*b)*a*b*h + 3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(1/4)*a*b*g + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^3) + 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(1/4)*a*b*g - (a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^3) - 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(1/4)*a*b*g - (a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^3)","A",0
196,1,589,0,0.597859," ","integrate((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x, algorithm=""giac"")","\frac{3}{32} \, i {\left(\frac{2 \, \sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a b^{4}} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{a b^{4}}\right)} + \frac{3}{32} \, i {\left(\frac{2 \, \sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a b^{4}} + \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{a b^{4}}\right)} - \frac{a i x^{3} - b x^{3} e - b d x^{2} + a h x^{2} - b c x + a g x + a f}{4 \, {\left(b x^{4} + a\right)} a b} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a b} b^{2} d + 2 \, \sqrt{2} \sqrt{a b} a b h + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{1}{4}} a b g + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a b} b^{2} d + 2 \, \sqrt{2} \sqrt{a b} a b h + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{1}{4}} a b g + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{1}{4}} a b g - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{3}} - \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{1}{4}} a b g - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{3}}"," ",0,"3/32*i*(2*sqrt(2)*(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^4) - sqrt(2)*(a*b^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^4)) + 3/32*i*(2*sqrt(2)*(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^4) + sqrt(2)*(a*b^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^4)) - 1/4*(a*i*x^3 - b*x^3*e - b*d*x^2 + a*h*x^2 - b*c*x + a*g*x + a*f)/((b*x^4 + a)*a*b) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*b)*b^2*d + 2*sqrt(2)*sqrt(a*b)*a*b*h + 3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(1/4)*a*b*g + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^3) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*b)*b^2*d + 2*sqrt(2)*sqrt(a*b)*a*b*h + 3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(1/4)*a*b*g + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^3) + 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(1/4)*a*b*g - (a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^3) - 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(1/4)*a*b*g - (a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^3)","A",0
197,1,617,0,0.218945," ","integrate((j*x^7+i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x, algorithm=""giac"")","\frac{3}{32} \, i {\left(\frac{2 \, \sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a b^{4}} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{a b^{4}}\right)} + \frac{3}{32} \, i {\left(\frac{2 \, \sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a b^{4}} + \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{a b^{4}}\right)} + \frac{j \log\left({\left| b x^{4} + a \right|}\right)}{4 \, b^{2}} - \frac{{\left(a i - b e\right)} x^{3} - {\left(b d - a h\right)} x^{2} - {\left(b c - a g\right)} x + \frac{a b f - a^{2} j}{b}}{4 \, {\left(b x^{4} + a\right)} a b} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a b} b^{2} d + 2 \, \sqrt{2} \sqrt{a b} a b h + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{1}{4}} a b g + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a b} b^{2} d + 2 \, \sqrt{2} \sqrt{a b} a b h + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{1}{4}} a b g + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{1}{4}} a b g - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{3}} - \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{1}{4}} a b g - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{3}}"," ",0,"3/32*i*(2*sqrt(2)*(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^4) - sqrt(2)*(a*b^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^4)) + 3/32*i*(2*sqrt(2)*(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^4) + sqrt(2)*(a*b^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^4)) + 1/4*j*log(abs(b*x^4 + a))/b^2 - 1/4*((a*i - b*e)*x^3 - (b*d - a*h)*x^2 - (b*c - a*g)*x + (a*b*f - a^2*j)/b)/((b*x^4 + a)*a*b) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*b)*b^2*d + 2*sqrt(2)*sqrt(a*b)*a*b*h + 3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(1/4)*a*b*g + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^3) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*b)*b^2*d + 2*sqrt(2)*sqrt(a*b)*a*b*h + 3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(1/4)*a*b*g + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^3) + 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(1/4)*a*b*g - (a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^3) - 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(1/4)*a*b*g - (a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^3)","A",0
198,1,440,0,0.208491," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(21 \, b^{2} c - 3 \, a b g - 12 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + 4 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h + 5 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} - \frac{\sqrt{2} {\left(21 \, b^{2} c - 3 \, a b g + 12 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - 4 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h - 5 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} - \frac{\sqrt{2} {\left(21 \, b^{2} c - 3 \, a b g - 5 \, \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{256 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} + \frac{\sqrt{2} {\left(21 \, b^{2} c - 3 \, a b g - 5 \, \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{256 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} - \frac{5 \, b^{2} x^{7} e + 6 \, b^{2} d x^{6} - 2 \, a b h x^{6} + 7 \, b^{2} c x^{5} - a b g x^{5} - 9 \, a b x^{3} e - 10 \, a b d x^{2} - 2 \, a^{2} h x^{2} - 11 \, a b c x - 3 \, a^{2} g x - 4 \, a^{2} f}{32 \, {\left(b x^{4} - a\right)}^{2} a^{2} b}"," ",0,"-1/128*sqrt(2)*(21*b^2*c - 3*a*b*g - 12*sqrt(2)*(-a*b^3)^(1/4)*b*d + 4*sqrt(2)*(-a*b^3)^(1/4)*a*h + 5*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^2) - 1/128*sqrt(2)*(21*b^2*c - 3*a*b*g + 12*sqrt(2)*(-a*b^3)^(1/4)*b*d - 4*sqrt(2)*(-a*b^3)^(1/4)*a*h - 5*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^2) - 1/256*sqrt(2)*(21*b^2*c - 3*a*b*g - 5*sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^2) + 1/256*sqrt(2)*(21*b^2*c - 3*a*b*g - 5*sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^2) - 1/32*(5*b^2*x^7*e + 6*b^2*d*x^6 - 2*a*b*h*x^6 + 7*b^2*c*x^5 - a*b*g*x^5 - 9*a*b*x^3*e - 10*a*b*d*x^2 - 2*a^2*h*x^2 - 11*a*b*c*x - 3*a^2*g*x - 4*a^2*f)/((b*x^4 - a)^2*a^2*b)","B",0
199,1,652,0,0.280379," ","integrate((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^3,x, algorithm=""giac"")","-\frac{3}{256} \, i {\left(\frac{2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{4}} - \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{a^{2} b^{4}}\right)} - \frac{3}{256} \, i {\left(\frac{2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{4}} + \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{a^{2} b^{4}}\right)} - \frac{\sqrt{2} {\left(21 \, b^{2} c - 3 \, a b g - 12 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + 4 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h + 5 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} - \frac{\sqrt{2} {\left(21 \, b^{2} c - 3 \, a b g + 12 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - 4 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h - 5 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} - \frac{\sqrt{2} {\left(21 \, b^{2} c - 3 \, a b g - 5 \, \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{256 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} + \frac{\sqrt{2} {\left(21 \, b^{2} c - 3 \, a b g - 5 \, \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{256 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} + \frac{3 \, a b i x^{7} - 5 \, b^{2} x^{7} e - 6 \, b^{2} d x^{6} + 2 \, a b h x^{6} - 7 \, b^{2} c x^{5} + a b g x^{5} + a^{2} i x^{3} + 9 \, a b x^{3} e + 10 \, a b d x^{2} + 2 \, a^{2} h x^{2} + 11 \, a b c x + 3 \, a^{2} g x + 4 \, a^{2} f}{32 \, {\left(b x^{4} - a\right)}^{2} a^{2} b}"," ",0,"-3/256*i*(2*sqrt(2)*(-a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a^2*b^4) - sqrt(2)*(-a*b^3)^(3/4)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a^2*b^4)) - 3/256*i*(2*sqrt(2)*(-a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a^2*b^4) + sqrt(2)*(-a*b^3)^(3/4)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a^2*b^4)) - 1/128*sqrt(2)*(21*b^2*c - 3*a*b*g - 12*sqrt(2)*(-a*b^3)^(1/4)*b*d + 4*sqrt(2)*(-a*b^3)^(1/4)*a*h + 5*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^2) - 1/128*sqrt(2)*(21*b^2*c - 3*a*b*g + 12*sqrt(2)*(-a*b^3)^(1/4)*b*d - 4*sqrt(2)*(-a*b^3)^(1/4)*a*h - 5*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^2) - 1/256*sqrt(2)*(21*b^2*c - 3*a*b*g - 5*sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^2) + 1/256*sqrt(2)*(21*b^2*c - 3*a*b*g - 5*sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^2) + 1/32*(3*a*b*i*x^7 - 5*b^2*x^7*e - 6*b^2*d*x^6 + 2*a*b*h*x^6 - 7*b^2*c*x^5 + a*b*g*x^5 + a^2*i*x^3 + 9*a*b*x^3*e + 10*a*b*d*x^2 + 2*a^2*h*x^2 + 11*a*b*c*x + 3*a^2*g*x + 4*a^2*f)/((b*x^4 - a)^2*a^2*b)","B",0
200,1,684,0,0.213208," ","integrate((j*x^7+i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^3,x, algorithm=""giac"")","-\frac{3}{256} \, i {\left(\frac{2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{4}} - \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{a^{2} b^{4}}\right)} - \frac{3}{256} \, i {\left(\frac{2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{4}} + \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{a^{2} b^{4}}\right)} - \frac{\sqrt{2} {\left(21 \, b^{2} c - 3 \, a b g - 12 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + 4 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h + 5 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} - \frac{\sqrt{2} {\left(21 \, b^{2} c - 3 \, a b g + 12 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - 4 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h - 5 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} - \frac{\sqrt{2} {\left(21 \, b^{2} c - 3 \, a b g - 5 \, \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{256 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} + \frac{\sqrt{2} {\left(21 \, b^{2} c - 3 \, a b g - 5 \, \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{256 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{2}} + \frac{3 \, a b^{2} i x^{7} - 5 \, b^{3} x^{7} e - 6 \, b^{3} d x^{6} + 2 \, a b^{2} h x^{6} - 7 \, b^{3} c x^{5} + a b^{2} g x^{5} + 8 \, a^{2} b j x^{4} + a^{2} b i x^{3} + 9 \, a b^{2} x^{3} e + 10 \, a b^{2} d x^{2} + 2 \, a^{2} b h x^{2} + 11 \, a b^{2} c x + 3 \, a^{2} b g x + 4 \, a^{2} b f - 4 \, a^{3} j}{32 \, {\left(b x^{4} - a\right)}^{2} a^{2} b^{2}}"," ",0,"-3/256*i*(2*sqrt(2)*(-a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a^2*b^4) - sqrt(2)*(-a*b^3)^(3/4)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a^2*b^4)) - 3/256*i*(2*sqrt(2)*(-a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a^2*b^4) + sqrt(2)*(-a*b^3)^(3/4)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a^2*b^4)) - 1/128*sqrt(2)*(21*b^2*c - 3*a*b*g - 12*sqrt(2)*(-a*b^3)^(1/4)*b*d + 4*sqrt(2)*(-a*b^3)^(1/4)*a*h + 5*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^2) - 1/128*sqrt(2)*(21*b^2*c - 3*a*b*g + 12*sqrt(2)*(-a*b^3)^(1/4)*b*d - 4*sqrt(2)*(-a*b^3)^(1/4)*a*h - 5*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^2) - 1/256*sqrt(2)*(21*b^2*c - 3*a*b*g - 5*sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^2) + 1/256*sqrt(2)*(21*b^2*c - 3*a*b*g - 5*sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^2) + 1/32*(3*a*b^2*i*x^7 - 5*b^3*x^7*e - 6*b^3*d*x^6 + 2*a*b^2*h*x^6 - 7*b^3*c*x^5 + a*b^2*g*x^5 + 8*a^2*b*j*x^4 + a^2*b*i*x^3 + 9*a*b^2*x^3*e + 10*a*b^2*d*x^2 + 2*a^2*b*h*x^2 + 11*a*b^2*c*x + 3*a^2*b*g*x + 4*a^2*b*f - 4*a^3*j)/((b*x^4 - a)^2*a^2*b^2)","B",0
201,1,459,0,0.204249," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(12 \, \sqrt{2} \sqrt{a b} b^{2} d + 4 \, \sqrt{2} \sqrt{a b} a b h + 21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} b^{3}} + \frac{\sqrt{2} {\left(12 \, \sqrt{2} \sqrt{a b} b^{2} d + 4 \, \sqrt{2} \sqrt{a b} a b h + 21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} b^{3}} + \frac{\sqrt{2} {\left(21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{256 \, a^{3} b^{3}} - \frac{\sqrt{2} {\left(21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{256 \, a^{3} b^{3}} + \frac{5 \, b^{2} x^{7} e + 6 \, b^{2} d x^{6} + 2 \, a b h x^{6} + 7 \, b^{2} c x^{5} + a b g x^{5} + 9 \, a b x^{3} e + 10 \, a b d x^{2} - 2 \, a^{2} h x^{2} + 11 \, a b c x - 3 \, a^{2} g x - 4 \, a^{2} f}{32 \, {\left(b x^{4} + a\right)}^{2} a^{2} b}"," ",0,"1/128*sqrt(2)*(12*sqrt(2)*sqrt(a*b)*b^2*d + 4*sqrt(2)*sqrt(a*b)*a*b*h + 21*(a*b^3)^(1/4)*b^2*c + 3*(a*b^3)^(1/4)*a*b*g + 5*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^3) + 1/128*sqrt(2)*(12*sqrt(2)*sqrt(a*b)*b^2*d + 4*sqrt(2)*sqrt(a*b)*a*b*h + 21*(a*b^3)^(1/4)*b^2*c + 3*(a*b^3)^(1/4)*a*b*g + 5*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^3) + 1/256*sqrt(2)*(21*(a*b^3)^(1/4)*b^2*c + 3*(a*b^3)^(1/4)*a*b*g - 5*(a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^3) - 1/256*sqrt(2)*(21*(a*b^3)^(1/4)*b^2*c + 3*(a*b^3)^(1/4)*a*b*g - 5*(a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^3) + 1/32*(5*b^2*x^7*e + 6*b^2*d*x^6 + 2*a*b*h*x^6 + 7*b^2*c*x^5 + a*b*g*x^5 + 9*a*b*x^3*e + 10*a*b*d*x^2 - 2*a^2*h*x^2 + 11*a*b*c*x - 3*a^2*g*x - 4*a^2*f)/((b*x^4 + a)^2*a^2*b)","A",0
202,1,661,0,0.226384," ","integrate((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x, algorithm=""giac"")","\frac{3}{256} \, i {\left(\frac{2 \, \sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{4}} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{a^{2} b^{4}}\right)} + \frac{3}{256} \, i {\left(\frac{2 \, \sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{4}} + \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{a^{2} b^{4}}\right)} + \frac{\sqrt{2} {\left(12 \, \sqrt{2} \sqrt{a b} b^{2} d + 4 \, \sqrt{2} \sqrt{a b} a b h + 21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} b^{3}} + \frac{\sqrt{2} {\left(12 \, \sqrt{2} \sqrt{a b} b^{2} d + 4 \, \sqrt{2} \sqrt{a b} a b h + 21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} b^{3}} + \frac{\sqrt{2} {\left(21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{256 \, a^{3} b^{3}} - \frac{\sqrt{2} {\left(21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{256 \, a^{3} b^{3}} + \frac{3 \, a b i x^{7} + 5 \, b^{2} x^{7} e + 6 \, b^{2} d x^{6} + 2 \, a b h x^{6} + 7 \, b^{2} c x^{5} + a b g x^{5} - a^{2} i x^{3} + 9 \, a b x^{3} e + 10 \, a b d x^{2} - 2 \, a^{2} h x^{2} + 11 \, a b c x - 3 \, a^{2} g x - 4 \, a^{2} f}{32 \, {\left(b x^{4} + a\right)}^{2} a^{2} b}"," ",0,"3/256*i*(2*sqrt(2)*(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^4) - sqrt(2)*(a*b^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^4)) + 3/256*i*(2*sqrt(2)*(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^4) + sqrt(2)*(a*b^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^4)) + 1/128*sqrt(2)*(12*sqrt(2)*sqrt(a*b)*b^2*d + 4*sqrt(2)*sqrt(a*b)*a*b*h + 21*(a*b^3)^(1/4)*b^2*c + 3*(a*b^3)^(1/4)*a*b*g + 5*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^3) + 1/128*sqrt(2)*(12*sqrt(2)*sqrt(a*b)*b^2*d + 4*sqrt(2)*sqrt(a*b)*a*b*h + 21*(a*b^3)^(1/4)*b^2*c + 3*(a*b^3)^(1/4)*a*b*g + 5*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^3) + 1/256*sqrt(2)*(21*(a*b^3)^(1/4)*b^2*c + 3*(a*b^3)^(1/4)*a*b*g - 5*(a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^3) - 1/256*sqrt(2)*(21*(a*b^3)^(1/4)*b^2*c + 3*(a*b^3)^(1/4)*a*b*g - 5*(a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^3) + 1/32*(3*a*b*i*x^7 + 5*b^2*x^7*e + 6*b^2*d*x^6 + 2*a*b*h*x^6 + 7*b^2*c*x^5 + a*b*g*x^5 - a^2*i*x^3 + 9*a*b*x^3*e + 10*a*b*d*x^2 - 2*a^2*h*x^2 + 11*a*b*c*x - 3*a^2*g*x - 4*a^2*f)/((b*x^4 + a)^2*a^2*b)","A",0
203,1,693,0,0.221051," ","integrate((j*x^7+i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x, algorithm=""giac"")","\frac{3}{256} \, i {\left(\frac{2 \, \sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{4}} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{a^{2} b^{4}}\right)} + \frac{3}{256} \, i {\left(\frac{2 \, \sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{4}} + \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{a^{2} b^{4}}\right)} + \frac{\sqrt{2} {\left(12 \, \sqrt{2} \sqrt{a b} b^{2} d + 4 \, \sqrt{2} \sqrt{a b} a b h + 21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} b^{3}} + \frac{\sqrt{2} {\left(12 \, \sqrt{2} \sqrt{a b} b^{2} d + 4 \, \sqrt{2} \sqrt{a b} a b h + 21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} b^{3}} + \frac{\sqrt{2} {\left(21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{256 \, a^{3} b^{3}} - \frac{\sqrt{2} {\left(21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{256 \, a^{3} b^{3}} + \frac{3 \, a b^{2} i x^{7} + 5 \, b^{3} x^{7} e + 6 \, b^{3} d x^{6} + 2 \, a b^{2} h x^{6} + 7 \, b^{3} c x^{5} + a b^{2} g x^{5} - 8 \, a^{2} b j x^{4} - a^{2} b i x^{3} + 9 \, a b^{2} x^{3} e + 10 \, a b^{2} d x^{2} - 2 \, a^{2} b h x^{2} + 11 \, a b^{2} c x - 3 \, a^{2} b g x - 4 \, a^{2} b f - 4 \, a^{3} j}{32 \, {\left(b x^{4} + a\right)}^{2} a^{2} b^{2}}"," ",0,"3/256*i*(2*sqrt(2)*(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^4) - sqrt(2)*(a*b^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^4)) + 3/256*i*(2*sqrt(2)*(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^4) + sqrt(2)*(a*b^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^4)) + 1/128*sqrt(2)*(12*sqrt(2)*sqrt(a*b)*b^2*d + 4*sqrt(2)*sqrt(a*b)*a*b*h + 21*(a*b^3)^(1/4)*b^2*c + 3*(a*b^3)^(1/4)*a*b*g + 5*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^3) + 1/128*sqrt(2)*(12*sqrt(2)*sqrt(a*b)*b^2*d + 4*sqrt(2)*sqrt(a*b)*a*b*h + 21*(a*b^3)^(1/4)*b^2*c + 3*(a*b^3)^(1/4)*a*b*g + 5*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^3) + 1/256*sqrt(2)*(21*(a*b^3)^(1/4)*b^2*c + 3*(a*b^3)^(1/4)*a*b*g - 5*(a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^3) - 1/256*sqrt(2)*(21*(a*b^3)^(1/4)*b^2*c + 3*(a*b^3)^(1/4)*a*b*g - 5*(a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^3) + 1/32*(3*a*b^2*i*x^7 + 5*b^3*x^7*e + 6*b^3*d*x^6 + 2*a*b^2*h*x^6 + 7*b^3*c*x^5 + a*b^2*g*x^5 - 8*a^2*b*j*x^4 - a^2*b*i*x^3 + 9*a*b^2*x^3*e + 10*a*b^2*d*x^2 - 2*a^2*b*h*x^2 + 11*a*b^2*c*x - 3*a^2*b*g*x - 4*a^2*b*f - 4*a^3*j)/((b*x^4 + a)^2*a^2*b^2)","A",0
204,1,501,0,0.262549," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^4,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(77 \, b^{2} c - 7 \, a b g - 40 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + 8 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h + 15 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} - \frac{\sqrt{2} {\left(77 \, b^{2} c - 7 \, a b g + 40 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - 8 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h - 15 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} - \frac{\sqrt{2} {\left(77 \, b^{2} c - 7 \, a b g - 15 \, \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{1024 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} + \frac{\sqrt{2} {\left(77 \, b^{2} c - 7 \, a b g - 15 \, \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{1024 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} - \frac{45 \, b^{3} x^{11} e + 60 \, b^{3} d x^{10} - 12 \, a b^{2} h x^{10} + 77 \, b^{3} c x^{9} - 7 \, a b^{2} g x^{9} - 126 \, a b^{2} x^{7} e - 160 \, a b^{2} d x^{6} + 32 \, a^{2} b h x^{6} - 198 \, a b^{2} c x^{5} + 18 \, a^{2} b g x^{5} + 113 \, a^{2} b x^{3} e + 132 \, a^{2} b d x^{2} + 12 \, a^{3} h x^{2} + 153 \, a^{2} b c x + 21 \, a^{3} g x + 32 \, a^{3} f}{384 \, {\left(b x^{4} - a\right)}^{3} a^{3} b}"," ",0,"-1/512*sqrt(2)*(77*b^2*c - 7*a*b*g - 40*sqrt(2)*(-a*b^3)^(1/4)*b*d + 8*sqrt(2)*(-a*b^3)^(1/4)*a*h + 15*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^3) - 1/512*sqrt(2)*(77*b^2*c - 7*a*b*g + 40*sqrt(2)*(-a*b^3)^(1/4)*b*d - 8*sqrt(2)*(-a*b^3)^(1/4)*a*h - 15*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^3) - 1/1024*sqrt(2)*(77*b^2*c - 7*a*b*g - 15*sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^3) + 1/1024*sqrt(2)*(77*b^2*c - 7*a*b*g - 15*sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^3) - 1/384*(45*b^3*x^11*e + 60*b^3*d*x^10 - 12*a*b^2*h*x^10 + 77*b^3*c*x^9 - 7*a*b^2*g*x^9 - 126*a*b^2*x^7*e - 160*a*b^2*d*x^6 + 32*a^2*b*h*x^6 - 198*a*b^2*c*x^5 + 18*a^2*b*g*x^5 + 113*a^2*b*x^3*e + 132*a^2*b*d*x^2 + 12*a^3*h*x^2 + 153*a^2*b*c*x + 21*a^3*g*x + 32*a^3*f)/((b*x^4 - a)^3*a^3*b)","B",0
205,1,727,0,0.209423," ","integrate((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^4,x, algorithm=""giac"")","-\frac{5}{1024} \, i {\left(\frac{2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{4}} - \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{a^{3} b^{4}}\right)} - \frac{5}{1024} \, i {\left(\frac{2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{4}} + \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{a^{3} b^{4}}\right)} - \frac{\sqrt{2} {\left(77 \, b^{2} c - 7 \, a b g - 40 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + 8 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h + 15 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} - \frac{\sqrt{2} {\left(77 \, b^{2} c - 7 \, a b g + 40 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - 8 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h - 15 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} - \frac{\sqrt{2} {\left(77 \, b^{2} c - 7 \, a b g - 15 \, \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{1024 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} + \frac{\sqrt{2} {\left(77 \, b^{2} c - 7 \, a b g - 15 \, \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{1024 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} + \frac{15 \, a b^{2} i x^{11} - 45 \, b^{3} x^{11} e - 60 \, b^{3} d x^{10} + 12 \, a b^{2} h x^{10} - 77 \, b^{3} c x^{9} + 7 \, a b^{2} g x^{9} - 42 \, a^{2} b i x^{7} + 126 \, a b^{2} x^{7} e + 160 \, a b^{2} d x^{6} - 32 \, a^{2} b h x^{6} + 198 \, a b^{2} c x^{5} - 18 \, a^{2} b g x^{5} - 5 \, a^{3} i x^{3} - 113 \, a^{2} b x^{3} e - 132 \, a^{2} b d x^{2} - 12 \, a^{3} h x^{2} - 153 \, a^{2} b c x - 21 \, a^{3} g x - 32 \, a^{3} f}{384 \, {\left(b x^{4} - a\right)}^{3} a^{3} b}"," ",0,"-5/1024*i*(2*sqrt(2)*(-a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a^3*b^4) - sqrt(2)*(-a*b^3)^(3/4)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a^3*b^4)) - 5/1024*i*(2*sqrt(2)*(-a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a^3*b^4) + sqrt(2)*(-a*b^3)^(3/4)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a^3*b^4)) - 1/512*sqrt(2)*(77*b^2*c - 7*a*b*g - 40*sqrt(2)*(-a*b^3)^(1/4)*b*d + 8*sqrt(2)*(-a*b^3)^(1/4)*a*h + 15*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^3) - 1/512*sqrt(2)*(77*b^2*c - 7*a*b*g + 40*sqrt(2)*(-a*b^3)^(1/4)*b*d - 8*sqrt(2)*(-a*b^3)^(1/4)*a*h - 15*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^3) - 1/1024*sqrt(2)*(77*b^2*c - 7*a*b*g - 15*sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^3) + 1/1024*sqrt(2)*(77*b^2*c - 7*a*b*g - 15*sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^3) + 1/384*(15*a*b^2*i*x^11 - 45*b^3*x^11*e - 60*b^3*d*x^10 + 12*a*b^2*h*x^10 - 77*b^3*c*x^9 + 7*a*b^2*g*x^9 - 42*a^2*b*i*x^7 + 126*a*b^2*x^7*e + 160*a*b^2*d*x^6 - 32*a^2*b*h*x^6 + 198*a*b^2*c*x^5 - 18*a^2*b*g*x^5 - 5*a^3*i*x^3 - 113*a^2*b*x^3*e - 132*a^2*b*d*x^2 - 12*a^3*h*x^2 - 153*a^2*b*c*x - 21*a^3*g*x - 32*a^3*f)/((b*x^4 - a)^3*a^3*b)","B",0
206,1,759,0,0.207474," ","integrate((j*x^7+i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^4,x, algorithm=""giac"")","-\frac{5}{1024} \, i {\left(\frac{2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{4}} - \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{a^{3} b^{4}}\right)} - \frac{5}{1024} \, i {\left(\frac{2 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{4}} + \frac{\sqrt{2} \left(-a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{a^{3} b^{4}}\right)} - \frac{\sqrt{2} {\left(77 \, b^{2} c - 7 \, a b g - 40 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + 8 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h + 15 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} - \frac{\sqrt{2} {\left(77 \, b^{2} c - 7 \, a b g + 40 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - 8 \, \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} a h - 15 \, \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} - \frac{\sqrt{2} {\left(77 \, b^{2} c - 7 \, a b g - 15 \, \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{1024 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} + \frac{\sqrt{2} {\left(77 \, b^{2} c - 7 \, a b g - 15 \, \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{1024 \, \left(-a b^{3}\right)^{\frac{3}{4}} a^{3}} + \frac{15 \, a b^{3} i x^{11} - 45 \, b^{4} x^{11} e - 60 \, b^{4} d x^{10} + 12 \, a b^{3} h x^{10} - 77 \, b^{4} c x^{9} + 7 \, a b^{3} g x^{9} - 42 \, a^{2} b^{2} i x^{7} + 126 \, a b^{3} x^{7} e + 160 \, a b^{3} d x^{6} - 32 \, a^{2} b^{2} h x^{6} + 198 \, a b^{3} c x^{5} - 18 \, a^{2} b^{2} g x^{5} - 48 \, a^{3} b j x^{4} - 5 \, a^{3} b i x^{3} - 113 \, a^{2} b^{2} x^{3} e - 132 \, a^{2} b^{2} d x^{2} - 12 \, a^{3} b h x^{2} - 153 \, a^{2} b^{2} c x - 21 \, a^{3} b g x - 32 \, a^{3} b f + 16 \, a^{4} j}{384 \, {\left(b x^{4} - a\right)}^{3} a^{3} b^{2}}"," ",0,"-5/1024*i*(2*sqrt(2)*(-a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a^3*b^4) - sqrt(2)*(-a*b^3)^(3/4)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a^3*b^4)) - 5/1024*i*(2*sqrt(2)*(-a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(a^3*b^4) + sqrt(2)*(-a*b^3)^(3/4)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(a^3*b^4)) - 1/512*sqrt(2)*(77*b^2*c - 7*a*b*g - 40*sqrt(2)*(-a*b^3)^(1/4)*b*d + 8*sqrt(2)*(-a*b^3)^(1/4)*a*h + 15*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^3) - 1/512*sqrt(2)*(77*b^2*c - 7*a*b*g + 40*sqrt(2)*(-a*b^3)^(1/4)*b*d - 8*sqrt(2)*(-a*b^3)^(1/4)*a*h - 15*sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/((-a*b^3)^(3/4)*a^3) - 1/1024*sqrt(2)*(77*b^2*c - 7*a*b*g - 15*sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^3) + 1/1024*sqrt(2)*(77*b^2*c - 7*a*b*g - 15*sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/((-a*b^3)^(3/4)*a^3) + 1/384*(15*a*b^3*i*x^11 - 45*b^4*x^11*e - 60*b^4*d*x^10 + 12*a*b^3*h*x^10 - 77*b^4*c*x^9 + 7*a*b^3*g*x^9 - 42*a^2*b^2*i*x^7 + 126*a*b^3*x^7*e + 160*a*b^3*d*x^6 - 32*a^2*b^2*h*x^6 + 198*a*b^3*c*x^5 - 18*a^2*b^2*g*x^5 - 48*a^3*b*j*x^4 - 5*a^3*b*i*x^3 - 113*a^2*b^2*x^3*e - 132*a^2*b^2*d*x^2 - 12*a^3*b*h*x^2 - 153*a^2*b^2*c*x - 21*a^3*b*g*x - 32*a^3*b*f + 16*a^4*j)/((b*x^4 - a)^3*a^3*b^2)","B",0
207,1,521,0,0.203856," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(40 \, \sqrt{2} \sqrt{a b} b^{2} d + 8 \, \sqrt{2} \sqrt{a b} a b h + 77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g + 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{4} b^{3}} + \frac{\sqrt{2} {\left(40 \, \sqrt{2} \sqrt{a b} b^{2} d + 8 \, \sqrt{2} \sqrt{a b} a b h + 77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g + 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{4} b^{3}} + \frac{\sqrt{2} {\left(77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g - 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{1024 \, a^{4} b^{3}} - \frac{\sqrt{2} {\left(77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g - 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{1024 \, a^{4} b^{3}} + \frac{45 \, b^{3} x^{11} e + 60 \, b^{3} d x^{10} + 12 \, a b^{2} h x^{10} + 77 \, b^{3} c x^{9} + 7 \, a b^{2} g x^{9} + 126 \, a b^{2} x^{7} e + 160 \, a b^{2} d x^{6} + 32 \, a^{2} b h x^{6} + 198 \, a b^{2} c x^{5} + 18 \, a^{2} b g x^{5} + 113 \, a^{2} b x^{3} e + 132 \, a^{2} b d x^{2} - 12 \, a^{3} h x^{2} + 153 \, a^{2} b c x - 21 \, a^{3} g x - 32 \, a^{3} f}{384 \, {\left(b x^{4} + a\right)}^{3} a^{3} b}"," ",0,"1/512*sqrt(2)*(40*sqrt(2)*sqrt(a*b)*b^2*d + 8*sqrt(2)*sqrt(a*b)*a*b*h + 77*(a*b^3)^(1/4)*b^2*c + 7*(a*b^3)^(1/4)*a*b*g + 15*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^4*b^3) + 1/512*sqrt(2)*(40*sqrt(2)*sqrt(a*b)*b^2*d + 8*sqrt(2)*sqrt(a*b)*a*b*h + 77*(a*b^3)^(1/4)*b^2*c + 7*(a*b^3)^(1/4)*a*b*g + 15*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^4*b^3) + 1/1024*sqrt(2)*(77*(a*b^3)^(1/4)*b^2*c + 7*(a*b^3)^(1/4)*a*b*g - 15*(a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^4*b^3) - 1/1024*sqrt(2)*(77*(a*b^3)^(1/4)*b^2*c + 7*(a*b^3)^(1/4)*a*b*g - 15*(a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^4*b^3) + 1/384*(45*b^3*x^11*e + 60*b^3*d*x^10 + 12*a*b^2*h*x^10 + 77*b^3*c*x^9 + 7*a*b^2*g*x^9 + 126*a*b^2*x^7*e + 160*a*b^2*d*x^6 + 32*a^2*b*h*x^6 + 198*a*b^2*c*x^5 + 18*a^2*b*g*x^5 + 113*a^2*b*x^3*e + 132*a^2*b*d*x^2 - 12*a^3*h*x^2 + 153*a^2*b*c*x - 21*a^3*g*x - 32*a^3*f)/((b*x^4 + a)^3*a^3*b)","A",0
208,1,735,0,0.206638," ","integrate((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x, algorithm=""giac"")","\frac{5}{1024} \, i {\left(\frac{2 \, \sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{4}} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{a^{3} b^{4}}\right)} + \frac{5}{1024} \, i {\left(\frac{2 \, \sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{4}} + \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{a^{3} b^{4}}\right)} + \frac{\sqrt{2} {\left(40 \, \sqrt{2} \sqrt{a b} b^{2} d + 8 \, \sqrt{2} \sqrt{a b} a b h + 77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g + 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{4} b^{3}} + \frac{\sqrt{2} {\left(40 \, \sqrt{2} \sqrt{a b} b^{2} d + 8 \, \sqrt{2} \sqrt{a b} a b h + 77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g + 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{4} b^{3}} + \frac{\sqrt{2} {\left(77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g - 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{1024 \, a^{4} b^{3}} - \frac{\sqrt{2} {\left(77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g - 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{1024 \, a^{4} b^{3}} + \frac{15 \, a b^{2} i x^{11} + 45 \, b^{3} x^{11} e + 60 \, b^{3} d x^{10} + 12 \, a b^{2} h x^{10} + 77 \, b^{3} c x^{9} + 7 \, a b^{2} g x^{9} + 42 \, a^{2} b i x^{7} + 126 \, a b^{2} x^{7} e + 160 \, a b^{2} d x^{6} + 32 \, a^{2} b h x^{6} + 198 \, a b^{2} c x^{5} + 18 \, a^{2} b g x^{5} - 5 \, a^{3} i x^{3} + 113 \, a^{2} b x^{3} e + 132 \, a^{2} b d x^{2} - 12 \, a^{3} h x^{2} + 153 \, a^{2} b c x - 21 \, a^{3} g x - 32 \, a^{3} f}{384 \, {\left(b x^{4} + a\right)}^{3} a^{3} b}"," ",0,"5/1024*i*(2*sqrt(2)*(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^4) - sqrt(2)*(a*b^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^4)) + 5/1024*i*(2*sqrt(2)*(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^4) + sqrt(2)*(a*b^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^4)) + 1/512*sqrt(2)*(40*sqrt(2)*sqrt(a*b)*b^2*d + 8*sqrt(2)*sqrt(a*b)*a*b*h + 77*(a*b^3)^(1/4)*b^2*c + 7*(a*b^3)^(1/4)*a*b*g + 15*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^4*b^3) + 1/512*sqrt(2)*(40*sqrt(2)*sqrt(a*b)*b^2*d + 8*sqrt(2)*sqrt(a*b)*a*b*h + 77*(a*b^3)^(1/4)*b^2*c + 7*(a*b^3)^(1/4)*a*b*g + 15*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^4*b^3) + 1/1024*sqrt(2)*(77*(a*b^3)^(1/4)*b^2*c + 7*(a*b^3)^(1/4)*a*b*g - 15*(a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^4*b^3) - 1/1024*sqrt(2)*(77*(a*b^3)^(1/4)*b^2*c + 7*(a*b^3)^(1/4)*a*b*g - 15*(a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^4*b^3) + 1/384*(15*a*b^2*i*x^11 + 45*b^3*x^11*e + 60*b^3*d*x^10 + 12*a*b^2*h*x^10 + 77*b^3*c*x^9 + 7*a*b^2*g*x^9 + 42*a^2*b*i*x^7 + 126*a*b^2*x^7*e + 160*a*b^2*d*x^6 + 32*a^2*b*h*x^6 + 198*a*b^2*c*x^5 + 18*a^2*b*g*x^5 - 5*a^3*i*x^3 + 113*a^2*b*x^3*e + 132*a^2*b*d*x^2 - 12*a^3*h*x^2 + 153*a^2*b*c*x - 21*a^3*g*x - 32*a^3*f)/((b*x^4 + a)^3*a^3*b)","A",0
209,1,767,0,0.205966," ","integrate((j*x^7+i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x, algorithm=""giac"")","\frac{5}{1024} \, i {\left(\frac{2 \, \sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{4}} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{a^{3} b^{4}}\right)} + \frac{5}{1024} \, i {\left(\frac{2 \, \sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{4}} + \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{a^{3} b^{4}}\right)} + \frac{\sqrt{2} {\left(40 \, \sqrt{2} \sqrt{a b} b^{2} d + 8 \, \sqrt{2} \sqrt{a b} a b h + 77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g + 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{4} b^{3}} + \frac{\sqrt{2} {\left(40 \, \sqrt{2} \sqrt{a b} b^{2} d + 8 \, \sqrt{2} \sqrt{a b} a b h + 77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g + 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{4} b^{3}} + \frac{\sqrt{2} {\left(77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g - 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{1024 \, a^{4} b^{3}} - \frac{\sqrt{2} {\left(77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a b g - 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{1024 \, a^{4} b^{3}} + \frac{15 \, a b^{3} i x^{11} + 45 \, b^{4} x^{11} e + 60 \, b^{4} d x^{10} + 12 \, a b^{3} h x^{10} + 77 \, b^{4} c x^{9} + 7 \, a b^{3} g x^{9} + 42 \, a^{2} b^{2} i x^{7} + 126 \, a b^{3} x^{7} e + 160 \, a b^{3} d x^{6} + 32 \, a^{2} b^{2} h x^{6} + 198 \, a b^{3} c x^{5} + 18 \, a^{2} b^{2} g x^{5} - 48 \, a^{3} b j x^{4} - 5 \, a^{3} b i x^{3} + 113 \, a^{2} b^{2} x^{3} e + 132 \, a^{2} b^{2} d x^{2} - 12 \, a^{3} b h x^{2} + 153 \, a^{2} b^{2} c x - 21 \, a^{3} b g x - 32 \, a^{3} b f - 16 \, a^{4} j}{384 \, {\left(b x^{4} + a\right)}^{3} a^{3} b^{2}}"," ",0,"5/1024*i*(2*sqrt(2)*(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^4) - sqrt(2)*(a*b^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^4)) + 5/1024*i*(2*sqrt(2)*(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^4) + sqrt(2)*(a*b^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^4)) + 1/512*sqrt(2)*(40*sqrt(2)*sqrt(a*b)*b^2*d + 8*sqrt(2)*sqrt(a*b)*a*b*h + 77*(a*b^3)^(1/4)*b^2*c + 7*(a*b^3)^(1/4)*a*b*g + 15*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^4*b^3) + 1/512*sqrt(2)*(40*sqrt(2)*sqrt(a*b)*b^2*d + 8*sqrt(2)*sqrt(a*b)*a*b*h + 77*(a*b^3)^(1/4)*b^2*c + 7*(a*b^3)^(1/4)*a*b*g + 15*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^4*b^3) + 1/1024*sqrt(2)*(77*(a*b^3)^(1/4)*b^2*c + 7*(a*b^3)^(1/4)*a*b*g - 15*(a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^4*b^3) - 1/1024*sqrt(2)*(77*(a*b^3)^(1/4)*b^2*c + 7*(a*b^3)^(1/4)*a*b*g - 15*(a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^4*b^3) + 1/384*(15*a*b^3*i*x^11 + 45*b^4*x^11*e + 60*b^4*d*x^10 + 12*a*b^3*h*x^10 + 77*b^4*c*x^9 + 7*a*b^3*g*x^9 + 42*a^2*b^2*i*x^7 + 126*a*b^3*x^7*e + 160*a*b^3*d*x^6 + 32*a^2*b^2*h*x^6 + 198*a*b^3*c*x^5 + 18*a^2*b^2*g*x^5 - 48*a^3*b*j*x^4 - 5*a^3*b*i*x^3 + 113*a^2*b^2*x^3*e + 132*a^2*b^2*d*x^2 - 12*a^3*b*h*x^2 + 153*a^2*b^2*c*x - 21*a^3*b*g*x - 32*a^3*b*f - 16*a^4*j)/((b*x^4 + a)^3*a^3*b^2)","A",0
210,0,0,0,0.000000," ","integrate((d*x+c)/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{d x + c}{\sqrt{b x^{4} + a}}\,{d x}"," ",0,"integrate((d*x + c)/sqrt(b*x^4 + a), x)","F",0
211,0,0,0,0.000000," ","integrate((d*x+c)/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{d x + c}{\sqrt{-b x^{4} + a}}\,{d x}"," ",0,"integrate((d*x + c)/sqrt(-b*x^4 + a), x)","F",0
212,0,0,0,0.000000," ","integrate((d*x+c)/(b*x^4-a)^(1/2),x, algorithm=""giac"")","\int \frac{d x + c}{\sqrt{b x^{4} - a}}\,{d x}"," ",0,"integrate((d*x + c)/sqrt(b*x^4 - a), x)","F",0
213,0,0,0,0.000000," ","integrate((d*x+c)/(-b*x^4-a)^(1/2),x, algorithm=""giac"")","\int \frac{d x + c}{\sqrt{-b x^{4} - a}}\,{d x}"," ",0,"integrate((d*x + c)/sqrt(-b*x^4 - a), x)","F",0
214,0,0,0,0.000000," ","integrate((e*x^2+d*x+c)/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d x + c}{\sqrt{b x^{4} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)/sqrt(b*x^4 + a), x)","F",0
215,1,12,0,0.198143," ","integrate((-b*g*x^4+a*g)/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\frac{g x}{\sqrt{b x^{4} + a}}"," ",0,"g*x/sqrt(b*x^4 + a)","A",0
216,1,23,0,0.244514," ","integrate((-b*g*x^4+a*g+e*x)/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(2 \, g + \frac{x e}{a}\right)} x}{2 \, \sqrt{b x^{4} + a}}"," ",0,"1/2*(2*g + x*e/a)*x/sqrt(b*x^4 + a)","A",0
217,1,22,0,0.200838," ","integrate((-b*g*x^4+f*x^3+a*g)/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, g x - \frac{f}{b}}{2 \, \sqrt{b x^{4} + a}}"," ",0,"1/2*(2*g*x - f/b)/sqrt(b*x^4 + a)","A",0
218,1,31,0,0.223541," ","integrate((-b*g*x^4+f*x^3+a*g+e*x)/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(2 \, g + \frac{x e}{a}\right)} x - \frac{f}{b}}{2 \, \sqrt{b x^{4} + a}}"," ",0,"1/2*((2*g + x*e/a)*x - f/b)/sqrt(b*x^4 + a)","A",0
219,1,10,0,0.181382," ","integrate((x^4-1)/(x^4+1)^(3/2),x, algorithm=""giac"")","-\frac{x}{\sqrt{x^{4} + 1}}"," ",0,"-x/sqrt(x^4 + 1)","A",0
220,0,0,0,0.000000," ","integrate((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{i x^{6} + h x^{5} + g x^{4} + f x^{3} + e x^{2} + d x + c}{\sqrt{b x^{4} + a}}\,{d x}"," ",0,"integrate((i*x^6 + h*x^5 + g*x^4 + f*x^3 + e*x^2 + d*x + c)/sqrt(b*x^4 + a), x)","F",0
221,1,101,0,0.220844," ","integrate((1+x)/(x^5+1),x, algorithm=""giac"")","\frac{1}{5} \, \sqrt{-2 \, \sqrt{5} + 5} \arctan\left(\frac{4 \, x + \sqrt{5} - 1}{\sqrt{2 \, \sqrt{5} + 10}}\right) + \frac{1}{5} \, \sqrt{2 \, \sqrt{5} + 5} \arctan\left(\frac{4 \, x - \sqrt{5} - 1}{\sqrt{-2 \, \sqrt{5} + 10}}\right) - \frac{1}{10} \, \sqrt{5} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{5} + 1\right)} + 1\right) + \frac{1}{10} \, \sqrt{5} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{5} - 1\right)} + 1\right)"," ",0,"1/5*sqrt(-2*sqrt(5) + 5)*arctan((4*x + sqrt(5) - 1)/sqrt(2*sqrt(5) + 10)) + 1/5*sqrt(2*sqrt(5) + 5)*arctan((4*x - sqrt(5) - 1)/sqrt(-2*sqrt(5) + 10)) - 1/10*sqrt(5)*log(x^2 - 1/2*x*(sqrt(5) + 1) + 1) + 1/10*sqrt(5)*log(x^2 + 1/2*x*(sqrt(5) - 1) + 1)","A",0
222,1,101,0,0.184854," ","integrate((1-x)/(-x^5+1),x, algorithm=""giac"")","\frac{1}{5} \, \sqrt{-2 \, \sqrt{5} + 5} \arctan\left(\frac{4 \, x - \sqrt{5} + 1}{\sqrt{2 \, \sqrt{5} + 10}}\right) + \frac{1}{5} \, \sqrt{2 \, \sqrt{5} + 5} \arctan\left(\frac{4 \, x + \sqrt{5} + 1}{\sqrt{-2 \, \sqrt{5} + 10}}\right) + \frac{1}{10} \, \sqrt{5} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{5} + 1\right)} + 1\right) - \frac{1}{10} \, \sqrt{5} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{5} - 1\right)} + 1\right)"," ",0,"1/5*sqrt(-2*sqrt(5) + 5)*arctan((4*x - sqrt(5) + 1)/sqrt(2*sqrt(5) + 10)) + 1/5*sqrt(2*sqrt(5) + 5)*arctan((4*x + sqrt(5) + 1)/sqrt(-2*sqrt(5) + 10)) + 1/10*sqrt(5)*log(x^2 + 1/2*x*(sqrt(5) + 1) + 1) - 1/10*sqrt(5)*log(x^2 - 1/2*x*(sqrt(5) - 1) + 1)","A",0
223,1,246,0,0.173162," ","integrate(x^11*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""giac"")","\frac{10 \, b^{5} f x^{18} - 12 \, a b^{4} f x^{15} + 12 \, b^{5} x^{15} e + 15 \, b^{5} d x^{12} + 15 \, a^{2} b^{3} f x^{12} - 15 \, a b^{4} x^{12} e + 20 \, b^{5} c x^{9} - 20 \, a b^{4} d x^{9} - 20 \, a^{3} b^{2} f x^{9} + 20 \, a^{2} b^{3} x^{9} e - 30 \, a b^{4} c x^{6} + 30 \, a^{2} b^{3} d x^{6} + 30 \, a^{4} b f x^{6} - 30 \, a^{3} b^{2} x^{6} e + 60 \, a^{2} b^{3} c x^{3} - 60 \, a^{3} b^{2} d x^{3} - 60 \, a^{5} f x^{3} + 60 \, a^{4} b x^{3} e}{180 \, b^{6}} - \frac{{\left(a^{3} b^{3} c - a^{4} b^{2} d - a^{6} f + a^{5} b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{7}}"," ",0,"1/180*(10*b^5*f*x^18 - 12*a*b^4*f*x^15 + 12*b^5*x^15*e + 15*b^5*d*x^12 + 15*a^2*b^3*f*x^12 - 15*a*b^4*x^12*e + 20*b^5*c*x^9 - 20*a*b^4*d*x^9 - 20*a^3*b^2*f*x^9 + 20*a^2*b^3*x^9*e - 30*a*b^4*c*x^6 + 30*a^2*b^3*d*x^6 + 30*a^4*b*f*x^6 - 30*a^3*b^2*x^6*e + 60*a^2*b^3*c*x^3 - 60*a^3*b^2*d*x^3 - 60*a^5*f*x^3 + 60*a^4*b*x^3*e)/b^6 - 1/3*(a^3*b^3*c - a^4*b^2*d - a^6*f + a^5*b*e)*log(abs(b*x^3 + a))/b^7","A",0
224,1,197,0,0.185578," ","integrate(x^8*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""giac"")","\frac{12 \, b^{4} f x^{15} - 15 \, a b^{3} f x^{12} + 15 \, b^{4} x^{12} e + 20 \, b^{4} d x^{9} + 20 \, a^{2} b^{2} f x^{9} - 20 \, a b^{3} x^{9} e + 30 \, b^{4} c x^{6} - 30 \, a b^{3} d x^{6} - 30 \, a^{3} b f x^{6} + 30 \, a^{2} b^{2} x^{6} e - 60 \, a b^{3} c x^{3} + 60 \, a^{2} b^{2} d x^{3} + 60 \, a^{4} f x^{3} - 60 \, a^{3} b x^{3} e}{180 \, b^{5}} + \frac{{\left(a^{2} b^{3} c - a^{3} b^{2} d - a^{5} f + a^{4} b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{6}}"," ",0,"1/180*(12*b^4*f*x^15 - 15*a*b^3*f*x^12 + 15*b^4*x^12*e + 20*b^4*d*x^9 + 20*a^2*b^2*f*x^9 - 20*a*b^3*x^9*e + 30*b^4*c*x^6 - 30*a*b^3*d*x^6 - 30*a^3*b*f*x^6 + 30*a^2*b^2*x^6*e - 60*a*b^3*c*x^3 + 60*a^2*b^2*d*x^3 + 60*a^4*f*x^3 - 60*a^3*b*x^3*e)/b^5 + 1/3*(a^2*b^3*c - a^3*b^2*d - a^5*f + a^4*b*e)*log(abs(b*x^3 + a))/b^6","A",0
225,1,148,0,0.167882," ","integrate(x^5*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""giac"")","\frac{3 \, b^{3} f x^{12} - 4 \, a b^{2} f x^{9} + 4 \, b^{3} x^{9} e + 6 \, b^{3} d x^{6} + 6 \, a^{2} b f x^{6} - 6 \, a b^{2} x^{6} e + 12 \, b^{3} c x^{3} - 12 \, a b^{2} d x^{3} - 12 \, a^{3} f x^{3} + 12 \, a^{2} b x^{3} e}{36 \, b^{4}} - \frac{{\left(a b^{3} c - a^{2} b^{2} d - a^{4} f + a^{3} b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{5}}"," ",0,"1/36*(3*b^3*f*x^12 - 4*a*b^2*f*x^9 + 4*b^3*x^9*e + 6*b^3*d*x^6 + 6*a^2*b*f*x^6 - 6*a*b^2*x^6*e + 12*b^3*c*x^3 - 12*a*b^2*d*x^3 - 12*a^3*f*x^3 + 12*a^2*b*x^3*e)/b^4 - 1/3*(a*b^3*c - a^2*b^2*d - a^4*f + a^3*b*e)*log(abs(b*x^3 + a))/b^5","A",0
226,1,101,0,0.204850," ","integrate(x^2*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""giac"")","\frac{2 \, b^{2} f x^{9} - 3 \, a b f x^{6} + 3 \, b^{2} x^{6} e + 6 \, b^{2} d x^{3} + 6 \, a^{2} f x^{3} - 6 \, a b x^{3} e}{18 \, b^{3}} + \frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{4}}"," ",0,"1/18*(2*b^2*f*x^9 - 3*a*b*f*x^6 + 3*b^2*x^6*e + 6*b^2*d*x^3 + 6*a^2*f*x^3 - 6*a*b*x^3*e)/b^3 + 1/3*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*log(abs(b*x^3 + a))/b^4","A",0
227,1,79,0,0.205124," ","integrate((f*x^9+e*x^6+d*x^3+c)/x/(b*x^3+a),x, algorithm=""giac"")","\frac{c \log\left({\left| x \right|}\right)}{a} + \frac{b f x^{6} - 2 \, a f x^{3} + 2 \, b x^{3} e}{6 \, b^{2}} - \frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a b^{3}}"," ",0,"c*log(abs(x))/a + 1/6*(b*f*x^6 - 2*a*f*x^3 + 2*b*x^3*e)/b^2 - 1/3*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*log(abs(b*x^3 + a))/(a*b^3)","A",0
228,1,95,0,0.176546," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^4/(b*x^3+a),x, algorithm=""giac"")","\frac{f x^{3}}{3 \, b} - \frac{{\left(b c - a d\right)} \log\left({\left| x \right|}\right)}{a^{2}} + \frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{2} b^{2}} + \frac{b c x^{3} - a d x^{3} - a c}{3 \, a^{2} x^{3}}"," ",0,"1/3*f*x^3/b - (b*c - a*d)*log(abs(x))/a^2 + 1/3*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*log(abs(b*x^3 + a))/(a^2*b^2) + 1/3*(b*c*x^3 - a*d*x^3 - a*c)/(a^2*x^3)","A",0
229,1,126,0,0.162742," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^7/(b*x^3+a),x, algorithm=""giac"")","\frac{{\left(b^{2} c - a b d + a^{2} e\right)} \log\left({\left| x \right|}\right)}{a^{3}} - \frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{3} b} - \frac{3 \, b^{2} c x^{6} - 3 \, a b d x^{6} + 3 \, a^{2} x^{6} e - 2 \, a b c x^{3} + 2 \, a^{2} d x^{3} + a^{2} c}{6 \, a^{3} x^{6}}"," ",0,"(b^2*c - a*b*d + a^2*e)*log(abs(x))/a^3 - 1/3*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*log(abs(b*x^3 + a))/(a^3*b) - 1/6*(3*b^2*c*x^6 - 3*a*b*d*x^6 + 3*a^2*x^6*e - 2*a*b*c*x^3 + 2*a^2*d*x^3 + a^2*c)/(a^3*x^6)","A",0
230,1,184,0,0.178076," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^10/(b*x^3+a),x, algorithm=""giac"")","-\frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \log\left({\left| x \right|}\right)}{a^{4}} + \frac{{\left(b^{4} c - a b^{3} d - a^{3} b f + a^{2} b^{2} e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{4} b} + \frac{11 \, b^{3} c x^{9} - 11 \, a b^{2} d x^{9} - 11 \, a^{3} f x^{9} + 11 \, a^{2} b x^{9} e - 6 \, a b^{2} c x^{6} + 6 \, a^{2} b d x^{6} - 6 \, a^{3} x^{6} e + 3 \, a^{2} b c x^{3} - 3 \, a^{3} d x^{3} - 2 \, a^{3} c}{18 \, a^{4} x^{9}}"," ",0,"-(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*log(abs(x))/a^4 + 1/3*(b^4*c - a*b^3*d - a^3*b*f + a^2*b^2*e)*log(abs(b*x^3 + a))/(a^4*b) + 1/18*(11*b^3*c*x^9 - 11*a*b^2*d*x^9 - 11*a^3*f*x^9 + 11*a^2*b*x^9*e - 6*a*b^2*c*x^6 + 6*a^2*b*d*x^6 - 6*a^3*x^6*e + 3*a^2*b*c*x^3 - 3*a^3*d*x^3 - 2*a^3*c)/(a^4*x^9)","A",0
231,1,235,0,0.167839," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^13/(b*x^3+a),x, algorithm=""giac"")","\frac{{\left(b^{4} c - a b^{3} d - a^{3} b f + a^{2} b^{2} e\right)} \log\left({\left| x \right|}\right)}{a^{5}} - \frac{{\left(b^{5} c - a b^{4} d - a^{3} b^{2} f + a^{2} b^{3} e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{5} b} - \frac{25 \, b^{4} c x^{12} - 25 \, a b^{3} d x^{12} - 25 \, a^{3} b f x^{12} + 25 \, a^{2} b^{2} x^{12} e - 12 \, a b^{3} c x^{9} + 12 \, a^{2} b^{2} d x^{9} + 12 \, a^{4} f x^{9} - 12 \, a^{3} b x^{9} e + 6 \, a^{2} b^{2} c x^{6} - 6 \, a^{3} b d x^{6} + 6 \, a^{4} x^{6} e - 4 \, a^{3} b c x^{3} + 4 \, a^{4} d x^{3} + 3 \, a^{4} c}{36 \, a^{5} x^{12}}"," ",0,"(b^4*c - a*b^3*d - a^3*b*f + a^2*b^2*e)*log(abs(x))/a^5 - 1/3*(b^5*c - a*b^4*d - a^3*b^2*f + a^2*b^3*e)*log(abs(b*x^3 + a))/(a^5*b) - 1/36*(25*b^4*c*x^12 - 25*a*b^3*d*x^12 - 25*a^3*b*f*x^12 + 25*a^2*b^2*x^12*e - 12*a*b^3*c*x^9 + 12*a^2*b^2*d*x^9 + 12*a^4*f*x^9 - 12*a^3*b*x^9*e + 6*a^2*b^2*c*x^6 - 6*a^3*b*d*x^6 + 6*a^4*x^6*e - 4*a^3*b*c*x^3 + 4*a^4*d*x^3 + 3*a^4*c)/(a^5*x^12)","A",0
232,1,287,0,0.169683," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^16/(b*x^3+a),x, algorithm=""giac"")","-\frac{{\left(b^{5} c - a b^{4} d - a^{3} b^{2} f + a^{2} b^{3} e\right)} \log\left({\left| x \right|}\right)}{a^{6}} + \frac{{\left(b^{6} c - a b^{5} d - a^{3} b^{3} f + a^{2} b^{4} e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{6} b} + \frac{137 \, b^{5} c x^{15} - 137 \, a b^{4} d x^{15} - 137 \, a^{3} b^{2} f x^{15} + 137 \, a^{2} b^{3} x^{15} e - 60 \, a b^{4} c x^{12} + 60 \, a^{2} b^{3} d x^{12} + 60 \, a^{4} b f x^{12} - 60 \, a^{3} b^{2} x^{12} e + 30 \, a^{2} b^{3} c x^{9} - 30 \, a^{3} b^{2} d x^{9} - 30 \, a^{5} f x^{9} + 30 \, a^{4} b x^{9} e - 20 \, a^{3} b^{2} c x^{6} + 20 \, a^{4} b d x^{6} - 20 \, a^{5} x^{6} e + 15 \, a^{4} b c x^{3} - 15 \, a^{5} d x^{3} - 12 \, a^{5} c}{180 \, a^{6} x^{15}}"," ",0,"-(b^5*c - a*b^4*d - a^3*b^2*f + a^2*b^3*e)*log(abs(x))/a^6 + 1/3*(b^6*c - a*b^5*d - a^3*b^3*f + a^2*b^4*e)*log(abs(b*x^3 + a))/(a^6*b) + 1/180*(137*b^5*c*x^15 - 137*a*b^4*d*x^15 - 137*a^3*b^2*f*x^15 + 137*a^2*b^3*x^15*e - 60*a*b^4*c*x^12 + 60*a^2*b^3*d*x^12 + 60*a^4*b*f*x^12 - 60*a^3*b^2*x^12*e + 30*a^2*b^3*c*x^9 - 30*a^3*b^2*d*x^9 - 30*a^5*f*x^9 + 30*a^4*b*x^9*e - 20*a^3*b^2*c*x^6 + 20*a^4*b*d*x^6 - 20*a^5*x^6*e + 15*a^4*b*c*x^3 - 15*a^5*d*x^3 - 12*a^5*c)/(a^6*x^15)","A",0
233,1,454,0,0.181682," ","integrate(x^9*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b^{3} c - \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} b^{2} d - \left(-a b^{2}\right)^{\frac{1}{3}} a^{5} f + \left(-a b^{2}\right)^{\frac{1}{3}} a^{4} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{7}} - \frac{{\left(\left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b^{3} c - \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} b^{2} d - \left(-a b^{2}\right)^{\frac{1}{3}} a^{5} f + \left(-a b^{2}\right)^{\frac{1}{3}} a^{4} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{7}} + \frac{{\left(a^{3} b^{13} c - a^{4} b^{12} d - a^{6} b^{10} f + a^{5} b^{11} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{16}} + \frac{455 \, b^{15} f x^{16} - 560 \, a b^{14} f x^{13} + 560 \, b^{15} x^{13} e + 728 \, b^{15} d x^{10} + 728 \, a^{2} b^{13} f x^{10} - 728 \, a b^{14} x^{10} e + 1040 \, b^{15} c x^{7} - 1040 \, a b^{14} d x^{7} - 1040 \, a^{3} b^{12} f x^{7} + 1040 \, a^{2} b^{13} x^{7} e - 1820 \, a b^{14} c x^{4} + 1820 \, a^{2} b^{13} d x^{4} + 1820 \, a^{4} b^{11} f x^{4} - 1820 \, a^{3} b^{12} x^{4} e + 7280 \, a^{2} b^{13} c x - 7280 \, a^{3} b^{12} d x - 7280 \, a^{5} b^{10} f x + 7280 \, a^{4} b^{11} x e}{7280 \, b^{16}}"," ",0,"-1/3*sqrt(3)*((-a*b^2)^(1/3)*a^2*b^3*c - (-a*b^2)^(1/3)*a^3*b^2*d - (-a*b^2)^(1/3)*a^5*f + (-a*b^2)^(1/3)*a^4*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^7 - 1/6*((-a*b^2)^(1/3)*a^2*b^3*c - (-a*b^2)^(1/3)*a^3*b^2*d - (-a*b^2)^(1/3)*a^5*f + (-a*b^2)^(1/3)*a^4*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^7 + 1/3*(a^3*b^13*c - a^4*b^12*d - a^6*b^10*f + a^5*b^11*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^16) + 1/7280*(455*b^15*f*x^16 - 560*a*b^14*f*x^13 + 560*b^15*x^13*e + 728*b^15*d*x^10 + 728*a^2*b^13*f*x^10 - 728*a*b^14*x^10*e + 1040*b^15*c*x^7 - 1040*a*b^14*d*x^7 - 1040*a^3*b^12*f*x^7 + 1040*a^2*b^13*x^7*e - 1820*a*b^14*c*x^4 + 1820*a^2*b^13*d*x^4 + 1820*a^4*b^11*f*x^4 - 1820*a^3*b^12*x^4*e + 7280*a^2*b^13*c*x - 7280*a^3*b^12*d*x - 7280*a^5*b^10*f*x + 7280*a^4*b^11*x*e)/b^16","A",0
234,1,441,0,0.184552," ","integrate(x^7*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{2}{3}} a b^{3} c - \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b^{2} d - \left(-a b^{2}\right)^{\frac{2}{3}} a^{4} f + \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{7}} + \frac{{\left(\left(-a b^{2}\right)^{\frac{2}{3}} a b^{3} c - \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b^{2} d - \left(-a b^{2}\right)^{\frac{2}{3}} a^{4} f + \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{7}} - \frac{{\left(a^{2} b^{12} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{3} b^{11} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{5} b^{9} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a^{4} b^{10} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{14}} + \frac{220 \, b^{13} f x^{14} - 280 \, a b^{12} f x^{11} + 280 \, b^{13} x^{11} e + 385 \, b^{13} d x^{8} + 385 \, a^{2} b^{11} f x^{8} - 385 \, a b^{12} x^{8} e + 616 \, b^{13} c x^{5} - 616 \, a b^{12} d x^{5} - 616 \, a^{3} b^{10} f x^{5} + 616 \, a^{2} b^{11} x^{5} e - 1540 \, a b^{12} c x^{2} + 1540 \, a^{2} b^{11} d x^{2} + 1540 \, a^{4} b^{9} f x^{2} - 1540 \, a^{3} b^{10} x^{2} e}{3080 \, b^{14}}"," ",0,"-1/3*sqrt(3)*((-a*b^2)^(2/3)*a*b^3*c - (-a*b^2)^(2/3)*a^2*b^2*d - (-a*b^2)^(2/3)*a^4*f + (-a*b^2)^(2/3)*a^3*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^7 + 1/6*((-a*b^2)^(2/3)*a*b^3*c - (-a*b^2)^(2/3)*a^2*b^2*d - (-a*b^2)^(2/3)*a^4*f + (-a*b^2)^(2/3)*a^3*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^7 - 1/3*(a^2*b^12*c*(-a/b)^(1/3) - a^3*b^11*d*(-a/b)^(1/3) - a^5*b^9*f*(-a/b)^(1/3) + a^4*b^10*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^14) + 1/3080*(220*b^13*f*x^14 - 280*a*b^12*f*x^11 + 280*b^13*x^11*e + 385*b^13*d*x^8 + 385*a^2*b^11*f*x^8 - 385*a*b^12*x^8*e + 616*b^13*c*x^5 - 616*a*b^12*d*x^5 - 616*a^3*b^10*f*x^5 + 616*a^2*b^11*x^5*e - 1540*a*b^12*c*x^2 + 1540*a^2*b^11*d*x^2 + 1540*a^4*b^9*f*x^2 - 1540*a^3*b^10*x^2*e)/b^14","A",0
235,1,401,0,0.178598," ","integrate(x^6*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""giac"")","\frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{1}{3}} a b^{3} c - \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b^{2} d - \left(-a b^{2}\right)^{\frac{1}{3}} a^{4} f + \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{6}} + \frac{{\left(\left(-a b^{2}\right)^{\frac{1}{3}} a b^{3} c - \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b^{2} d - \left(-a b^{2}\right)^{\frac{1}{3}} a^{4} f + \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{6}} - \frac{{\left(a^{2} b^{11} c - a^{3} b^{10} d - a^{5} b^{8} f + a^{4} b^{9} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{13}} + \frac{140 \, b^{12} f x^{13} - 182 \, a b^{11} f x^{10} + 182 \, b^{12} x^{10} e + 260 \, b^{12} d x^{7} + 260 \, a^{2} b^{10} f x^{7} - 260 \, a b^{11} x^{7} e + 455 \, b^{12} c x^{4} - 455 \, a b^{11} d x^{4} - 455 \, a^{3} b^{9} f x^{4} + 455 \, a^{2} b^{10} x^{4} e - 1820 \, a b^{11} c x + 1820 \, a^{2} b^{10} d x + 1820 \, a^{4} b^{8} f x - 1820 \, a^{3} b^{9} x e}{1820 \, b^{13}}"," ",0,"1/3*sqrt(3)*((-a*b^2)^(1/3)*a*b^3*c - (-a*b^2)^(1/3)*a^2*b^2*d - (-a*b^2)^(1/3)*a^4*f + (-a*b^2)^(1/3)*a^3*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^6 + 1/6*((-a*b^2)^(1/3)*a*b^3*c - (-a*b^2)^(1/3)*a^2*b^2*d - (-a*b^2)^(1/3)*a^4*f + (-a*b^2)^(1/3)*a^3*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^6 - 1/3*(a^2*b^11*c - a^3*b^10*d - a^5*b^8*f + a^4*b^9*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^13) + 1/1820*(140*b^12*f*x^13 - 182*a*b^11*f*x^10 + 182*b^12*x^10*e + 260*b^12*d*x^7 + 260*a^2*b^10*f*x^7 - 260*a*b^11*x^7*e + 455*b^12*c*x^4 - 455*a*b^11*d*x^4 - 455*a^3*b^9*f*x^4 + 455*a^2*b^10*x^4*e - 1820*a*b^11*c*x + 1820*a^2*b^10*d*x + 1820*a^4*b^8*f*x - 1820*a^3*b^9*x*e)/b^13","A",0
236,1,386,0,0.181505," ","integrate(x^4*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""giac"")","\frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{6}} - \frac{{\left(\left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{6}} + \frac{{\left(a b^{10} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} b^{9} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{4} b^{7} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a^{3} b^{8} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{11}} + \frac{40 \, b^{10} f x^{11} - 55 \, a b^{9} f x^{8} + 55 \, b^{10} x^{8} e + 88 \, b^{10} d x^{5} + 88 \, a^{2} b^{8} f x^{5} - 88 \, a b^{9} x^{5} e + 220 \, b^{10} c x^{2} - 220 \, a b^{9} d x^{2} - 220 \, a^{3} b^{7} f x^{2} + 220 \, a^{2} b^{8} x^{2} e}{440 \, b^{11}}"," ",0,"1/3*sqrt(3)*((-a*b^2)^(2/3)*b^3*c - (-a*b^2)^(2/3)*a*b^2*d - (-a*b^2)^(2/3)*a^3*f + (-a*b^2)^(2/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^6 - 1/6*((-a*b^2)^(2/3)*b^3*c - (-a*b^2)^(2/3)*a*b^2*d - (-a*b^2)^(2/3)*a^3*f + (-a*b^2)^(2/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^6 + 1/3*(a*b^10*c*(-a/b)^(1/3) - a^2*b^9*d*(-a/b)^(1/3) - a^4*b^7*f*(-a/b)^(1/3) + a^3*b^8*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^11) + 1/440*(40*b^10*f*x^11 - 55*a*b^9*f*x^8 + 55*b^10*x^8*e + 88*b^10*d*x^5 + 88*a^2*b^8*f*x^5 - 88*a*b^9*x^5*e + 220*b^10*c*x^2 - 220*a*b^9*d*x^2 - 220*a^3*b^7*f*x^2 + 220*a^2*b^8*x^2*e)/b^11","A",0
237,1,346,0,0.185091," ","integrate(x^3*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{5}} - \frac{{\left(\left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{5}} + \frac{{\left(a b^{9} c - a^{2} b^{8} d - a^{4} b^{6} f + a^{3} b^{7} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{10}} + \frac{14 \, b^{9} f x^{10} - 20 \, a b^{8} f x^{7} + 20 \, b^{9} x^{7} e + 35 \, b^{9} d x^{4} + 35 \, a^{2} b^{7} f x^{4} - 35 \, a b^{8} x^{4} e + 140 \, b^{9} c x - 140 \, a b^{8} d x - 140 \, a^{3} b^{6} f x + 140 \, a^{2} b^{7} x e}{140 \, b^{10}}"," ",0,"-1/3*sqrt(3)*((-a*b^2)^(1/3)*b^3*c - (-a*b^2)^(1/3)*a*b^2*d - (-a*b^2)^(1/3)*a^3*f + (-a*b^2)^(1/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^5 - 1/6*((-a*b^2)^(1/3)*b^3*c - (-a*b^2)^(1/3)*a*b^2*d - (-a*b^2)^(1/3)*a^3*f + (-a*b^2)^(1/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^5 + 1/3*(a*b^9*c - a^2*b^8*d - a^4*b^6*f + a^3*b^7*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^10) + 1/140*(14*b^9*f*x^10 - 20*a*b^8*f*x^7 + 20*b^9*x^7*e + 35*b^9*d*x^4 + 35*a^2*b^7*f*x^4 - 35*a*b^8*x^4*e + 140*b^9*c*x - 140*a*b^8*d*x - 140*a^3*b^6*f*x + 140*a^2*b^7*x*e)/b^10","A",0
238,1,291,0,0.196215," ","integrate(x*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""giac"")","\frac{\sqrt{3} {\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{3}} - \frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{3}} - \frac{{\left(b^{8} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a b^{7} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{3} b^{5} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} b^{6} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{8}} + \frac{5 \, b^{7} f x^{8} - 8 \, a b^{6} f x^{5} + 8 \, b^{7} x^{5} e + 20 \, b^{7} d x^{2} + 20 \, a^{2} b^{5} f x^{2} - 20 \, a b^{6} x^{2} e}{40 \, b^{8}}"," ",0,"1/3*sqrt(3)*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(1/3)*b^3) - 1/6*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(1/3)*b^3) - 1/3*(b^8*c*(-a/b)^(1/3) - a*b^7*d*(-a/b)^(1/3) - a^3*b^5*f*(-a/b)^(1/3) + a^2*b^6*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^8) + 1/40*(5*b^7*f*x^8 - 8*a*b^6*f*x^5 + 8*b^7*x^5*e + 20*b^7*d*x^2 + 20*a^2*b^5*f*x^2 - 20*a*b^6*x^2*e)/b^8","A",0
239,1,253,0,0.187034," ","integrate((f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{2}} - \frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{2}} - \frac{{\left(b^{7} c - a b^{6} d - a^{3} b^{4} f + a^{2} b^{5} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{7}} + \frac{4 \, b^{6} f x^{7} - 7 \, a b^{5} f x^{4} + 7 \, b^{6} x^{4} e + 28 \, b^{6} d x + 28 \, a^{2} b^{4} f x - 28 \, a b^{5} x e}{28 \, b^{7}}"," ",0,"-1/3*sqrt(3)*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*b^2) - 1/6*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*b^2) - 1/3*(b^7*c - a*b^6*d - a^3*b^4*f + a^2*b^5*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^7) + 1/28*(4*b^6*f*x^7 - 7*a*b^5*f*x^4 + 7*b^6*x^4*e + 28*b^6*d*x + 28*a^2*b^4*f*x - 28*a*b^5*x*e)/b^7","A",0
240,1,269,0,0.180897," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^2/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2}} - \frac{c}{a x} + \frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2}} + \frac{{\left(b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{2} b^{2}} + \frac{2 \, b^{4} f x^{5} - 5 \, a b^{3} f x^{2} + 5 \, b^{4} x^{2} e}{10 \, b^{5}}"," ",0,"-1/3*sqrt(3)*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(1/3)*a*b^2) - c/(a*x) + 1/6*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(1/3)*a*b^2) + 1/3*(b^3*c*(-a/b)^(1/3) - a*b^2*d*(-a/b)^(1/3) - a^3*f*(-a/b)^(1/3) + a^2*b*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b^2) + 1/10*(2*b^4*f*x^5 - 5*a*b^3*f*x^2 + 5*b^4*x^2*e)/b^5","A",0
241,1,232,0,0.216723," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^3/(b*x^3+a),x, algorithm=""giac"")","\frac{\sqrt{3} {\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b} + \frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b} + \frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{2} b^{2}} - \frac{c}{2 \, a x^{2}} + \frac{b^{3} f x^{4} - 4 \, a b^{2} f x + 4 \, b^{3} x e}{4 \, b^{4}}"," ",0,"1/3*sqrt(3)*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a*b) + 1/6*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a*b) + 1/3*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b^2) - 1/2*c/(a*x^2) + 1/4*(b^3*f*x^4 - 4*a*b^2*f*x + 4*b^3*x*e)/b^4","A",0
242,1,261,0,0.183608," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^5/(b*x^3+a),x, algorithm=""giac"")","\frac{f x^{2}}{2 \, b} + \frac{\sqrt{3} {\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b} - \frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b} - \frac{{\left(b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{3} b} + \frac{4 \, b c x^{3} - 4 \, a d x^{3} - a c}{4 \, a^{2} x^{4}}"," ",0,"1/2*f*x^2/b + 1/3*sqrt(3)*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(1/3)*a^2*b) - 1/6*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(1/3)*a^2*b) - 1/3*(b^3*c*(-a/b)^(1/3) - a*b^2*d*(-a/b)^(1/3) - a^3*f*(-a/b)^(1/3) + a^2*b*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b) + 1/4*(4*b*c*x^3 - 4*a*d*x^3 - a*c)/(a^2*x^4)","A",0
243,1,220,0,0.482863," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^6/(b*x^3+a),x, algorithm=""giac"")","\frac{f x}{b} - \frac{\sqrt{3} {\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2}} - \frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2}} - \frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{3} b} + \frac{5 \, b c x^{3} - 5 \, a d x^{3} - 2 \, a c}{10 \, a^{2} x^{5}}"," ",0,"f*x/b - 1/3*sqrt(3)*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^2) - 1/6*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^2) - 1/3*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b) + 1/10*(5*b*c*x^3 - 5*a*d*x^3 - 2*a*c)/(a^2*x^5)","A",0
244,1,275,0,0.212909," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^8/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3}} + \frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3}} + \frac{{\left(b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{4}} - \frac{28 \, b^{2} c x^{6} - 28 \, a b d x^{6} + 28 \, a^{2} x^{6} e - 7 \, a b c x^{3} + 7 \, a^{2} d x^{3} + 4 \, a^{2} c}{28 \, a^{3} x^{7}}"," ",0,"-1/3*sqrt(3)*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(1/3)*a^3) + 1/6*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(1/3)*a^3) + 1/3*(b^3*c*(-a/b)^(1/3) - a*b^2*d*(-a/b)^(1/3) - a^3*f*(-a/b)^(1/3) + a^2*b*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^4 - 1/28*(28*b^2*c*x^6 - 28*a*b*d*x^6 + 28*a^2*x^6*e - 7*a*b*c*x^3 + 7*a^2*d*x^3 + 4*a^2*c)/(a^3*x^7)","A",0
245,1,297,0,0.195947," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^9/(b*x^3+a),x, algorithm=""giac"")","\frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{4}} - \frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a^{4} b} - \frac{{\left(\left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a^{4} b} - \frac{20 \, b^{2} c x^{6} - 20 \, a b d x^{6} + 20 \, a^{2} x^{6} e - 8 \, a b c x^{3} + 8 \, a^{2} d x^{3} + 5 \, a^{2} c}{40 \, a^{3} x^{8}}"," ",0,"1/3*(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^4 - 1/3*sqrt(3)*((-a*b^2)^(1/3)*b^3*c - (-a*b^2)^(1/3)*a*b^2*d - (-a*b^2)^(1/3)*a^3*f + (-a*b^2)^(1/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^4*b) - 1/6*((-a*b^2)^(1/3)*b^3*c - (-a*b^2)^(1/3)*a*b^2*d - (-a*b^2)^(1/3)*a^3*f + (-a*b^2)^(1/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^4*b) - 1/40*(20*b^2*c*x^6 - 20*a*b*d*x^6 + 20*a^2*x^6*e - 8*a*b*c*x^3 + 8*a^2*d*x^3 + 5*a^2*c)/(a^3*x^8)","A",0
246,1,376,0,0.193776," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^11/(b*x^3+a),x, algorithm=""giac"")","-\frac{{\left(b^{4} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a b^{3} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{3} b f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} b^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{5}} - \frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a^{5} b} + \frac{{\left(\left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a^{5} b} + \frac{140 \, b^{3} c x^{9} - 140 \, a b^{2} d x^{9} - 140 \, a^{3} f x^{9} + 140 \, a^{2} b x^{9} e - 35 \, a b^{2} c x^{6} + 35 \, a^{2} b d x^{6} - 35 \, a^{3} x^{6} e + 20 \, a^{2} b c x^{3} - 20 \, a^{3} d x^{3} - 14 \, a^{3} c}{140 \, a^{4} x^{10}}"," ",0,"-1/3*(b^4*c*(-a/b)^(1/3) - a*b^3*d*(-a/b)^(1/3) - a^3*b*f*(-a/b)^(1/3) + a^2*b^2*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^5 - 1/3*sqrt(3)*((-a*b^2)^(2/3)*b^3*c - (-a*b^2)^(2/3)*a*b^2*d - (-a*b^2)^(2/3)*a^3*f + (-a*b^2)^(2/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^5*b) + 1/6*((-a*b^2)^(2/3)*b^3*c - (-a*b^2)^(2/3)*a*b^2*d - (-a*b^2)^(2/3)*a^3*f + (-a*b^2)^(2/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^5*b) + 1/140*(140*b^3*c*x^9 - 140*a*b^2*d*x^9 - 140*a^3*f*x^9 + 140*a^2*b*x^9*e - 35*a*b^2*c*x^6 + 35*a^2*b*d*x^6 - 35*a^3*x^6*e + 20*a^2*b*c*x^3 - 20*a^3*d*x^3 - 14*a^3*c)/(a^4*x^10)","A",0
247,1,338,0,0.185366," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^12/(b*x^3+a),x, algorithm=""giac"")","\frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a^{5}} - \frac{{\left(b^{4} c - a b^{3} d - a^{3} b f + a^{2} b^{2} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{5}} + \frac{{\left(\left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a^{5}} + \frac{220 \, b^{3} c x^{9} - 220 \, a b^{2} d x^{9} - 220 \, a^{3} f x^{9} + 220 \, a^{2} b x^{9} e - 88 \, a b^{2} c x^{6} + 88 \, a^{2} b d x^{6} - 88 \, a^{3} x^{6} e + 55 \, a^{2} b c x^{3} - 55 \, a^{3} d x^{3} - 40 \, a^{3} c}{440 \, a^{4} x^{11}}"," ",0,"1/3*sqrt(3)*((-a*b^2)^(1/3)*b^3*c - (-a*b^2)^(1/3)*a*b^2*d - (-a*b^2)^(1/3)*a^3*f + (-a*b^2)^(1/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/a^5 - 1/3*(b^4*c - a*b^3*d - a^3*b*f + a^2*b^2*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^5 + 1/6*((-a*b^2)^(1/3)*b^3*c - (-a*b^2)^(1/3)*a*b^2*d - (-a*b^2)^(1/3)*a^3*f + (-a*b^2)^(1/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/a^5 + 1/440*(220*b^3*c*x^9 - 220*a*b^2*d*x^9 - 220*a^3*f*x^9 + 220*a^2*b*x^9*e - 88*a*b^2*c*x^6 + 88*a^2*b*d*x^6 - 88*a^3*x^6*e + 55*a^2*b*c*x^3 - 55*a^3*d*x^3 - 40*a^3*c)/(a^4*x^11)","A",0
248,1,419,0,0.183283," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^14/(b*x^3+a),x, algorithm=""giac"")","\frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a^{6}} + \frac{{\left(b^{5} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a b^{4} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{3} b^{2} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} b^{3} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{6}} - \frac{{\left(\left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a^{6}} - \frac{1820 \, b^{4} c x^{12} - 1820 \, a b^{3} d x^{12} - 1820 \, a^{3} b f x^{12} + 1820 \, a^{2} b^{2} x^{12} e - 455 \, a b^{3} c x^{9} + 455 \, a^{2} b^{2} d x^{9} + 455 \, a^{4} f x^{9} - 455 \, a^{3} b x^{9} e + 260 \, a^{2} b^{2} c x^{6} - 260 \, a^{3} b d x^{6} + 260 \, a^{4} x^{6} e - 182 \, a^{3} b c x^{3} + 182 \, a^{4} d x^{3} + 140 \, a^{4} c}{1820 \, a^{5} x^{13}}"," ",0,"1/3*sqrt(3)*((-a*b^2)^(2/3)*b^3*c - (-a*b^2)^(2/3)*a*b^2*d - (-a*b^2)^(2/3)*a^3*f + (-a*b^2)^(2/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/a^6 + 1/3*(b^5*c*(-a/b)^(1/3) - a*b^4*d*(-a/b)^(1/3) - a^3*b^2*f*(-a/b)^(1/3) + a^2*b^3*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^6 - 1/6*((-a*b^2)^(2/3)*b^3*c - (-a*b^2)^(2/3)*a*b^2*d - (-a*b^2)^(2/3)*a^3*f + (-a*b^2)^(2/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/a^6 - 1/1820*(1820*b^4*c*x^12 - 1820*a*b^3*d*x^12 - 1820*a^3*b*f*x^12 + 1820*a^2*b^2*x^12*e - 455*a*b^3*c*x^9 + 455*a^2*b^2*d*x^9 + 455*a^4*f*x^9 - 455*a^3*b*x^9*e + 260*a^2*b^2*c*x^6 - 260*a^3*b*d*x^6 + 260*a^4*x^6*e - 182*a^3*b*c*x^3 + 182*a^4*d*x^3 + 140*a^4*c)/(a^5*x^13)","A",0
249,1,393,0,0.194827," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^15/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{1}{3}} b^{4} c - \left(-a b^{2}\right)^{\frac{1}{3}} a b^{3} d - \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} b f + \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b^{2} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a^{6}} + \frac{{\left(b^{5} c - a b^{4} d - a^{3} b^{2} f + a^{2} b^{3} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{6}} - \frac{{\left(\left(-a b^{2}\right)^{\frac{1}{3}} b^{4} c - \left(-a b^{2}\right)^{\frac{1}{3}} a b^{3} d - \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} b f + \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b^{2} e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a^{6}} - \frac{1540 \, b^{4} c x^{12} - 1540 \, a b^{3} d x^{12} - 1540 \, a^{3} b f x^{12} + 1540 \, a^{2} b^{2} x^{12} e - 616 \, a b^{3} c x^{9} + 616 \, a^{2} b^{2} d x^{9} + 616 \, a^{4} f x^{9} - 616 \, a^{3} b x^{9} e + 385 \, a^{2} b^{2} c x^{6} - 385 \, a^{3} b d x^{6} + 385 \, a^{4} x^{6} e - 280 \, a^{3} b c x^{3} + 280 \, a^{4} d x^{3} + 220 \, a^{4} c}{3080 \, a^{5} x^{14}}"," ",0,"-1/3*sqrt(3)*((-a*b^2)^(1/3)*b^4*c - (-a*b^2)^(1/3)*a*b^3*d - (-a*b^2)^(1/3)*a^3*b*f + (-a*b^2)^(1/3)*a^2*b^2*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/a^6 + 1/3*(b^5*c - a*b^4*d - a^3*b^2*f + a^2*b^3*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^6 - 1/6*((-a*b^2)^(1/3)*b^4*c - (-a*b^2)^(1/3)*a*b^3*d - (-a*b^2)^(1/3)*a^3*b*f + (-a*b^2)^(1/3)*a^2*b^2*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/a^6 - 1/3080*(1540*b^4*c*x^12 - 1540*a*b^3*d*x^12 - 1540*a^3*b*f*x^12 + 1540*a^2*b^2*x^12*e - 616*a*b^3*c*x^9 + 616*a^2*b^2*d*x^9 + 616*a^4*f*x^9 - 616*a^3*b*x^9*e + 385*a^2*b^2*c*x^6 - 385*a^3*b*d*x^6 + 385*a^4*x^6*e - 280*a^3*b*c*x^3 + 280*a^4*d*x^3 + 220*a^4*c)/(a^5*x^14)","A",0
250,1,474,0,0.190027," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^17/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{2}{3}} b^{4} c - \left(-a b^{2}\right)^{\frac{2}{3}} a b^{3} d - \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} b f + \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b^{2} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a^{7}} - \frac{{\left(b^{6} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a b^{5} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{3} b^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} b^{4} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{7}} + \frac{{\left(\left(-a b^{2}\right)^{\frac{2}{3}} b^{4} c - \left(-a b^{2}\right)^{\frac{2}{3}} a b^{3} d - \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} b f + \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b^{2} e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a^{7}} + \frac{7280 \, b^{5} c x^{15} - 7280 \, a b^{4} d x^{15} - 7280 \, a^{3} b^{2} f x^{15} + 7280 \, a^{2} b^{3} x^{15} e - 1820 \, a b^{4} c x^{12} + 1820 \, a^{2} b^{3} d x^{12} + 1820 \, a^{4} b f x^{12} - 1820 \, a^{3} b^{2} x^{12} e + 1040 \, a^{2} b^{3} c x^{9} - 1040 \, a^{3} b^{2} d x^{9} - 1040 \, a^{5} f x^{9} + 1040 \, a^{4} b x^{9} e - 728 \, a^{3} b^{2} c x^{6} + 728 \, a^{4} b d x^{6} - 728 \, a^{5} x^{6} e + 560 \, a^{4} b c x^{3} - 560 \, a^{5} d x^{3} - 455 \, a^{5} c}{7280 \, a^{6} x^{16}}"," ",0,"-1/3*sqrt(3)*((-a*b^2)^(2/3)*b^4*c - (-a*b^2)^(2/3)*a*b^3*d - (-a*b^2)^(2/3)*a^3*b*f + (-a*b^2)^(2/3)*a^2*b^2*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/a^7 - 1/3*(b^6*c*(-a/b)^(1/3) - a*b^5*d*(-a/b)^(1/3) - a^3*b^3*f*(-a/b)^(1/3) + a^2*b^4*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^7 + 1/6*((-a*b^2)^(2/3)*b^4*c - (-a*b^2)^(2/3)*a*b^3*d - (-a*b^2)^(2/3)*a^3*b*f + (-a*b^2)^(2/3)*a^2*b^2*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/a^7 + 1/7280*(7280*b^5*c*x^15 - 7280*a*b^4*d*x^15 - 7280*a^3*b^2*f*x^15 + 7280*a^2*b^3*x^15*e - 1820*a*b^4*c*x^12 + 1820*a^2*b^3*d*x^12 + 1820*a^4*b*f*x^12 - 1820*a^3*b^2*x^12*e + 1040*a^2*b^3*c*x^9 - 1040*a^3*b^2*d*x^9 - 1040*a^5*f*x^9 + 1040*a^4*b*x^9*e - 728*a^3*b^2*c*x^6 + 728*a^4*b*d*x^6 - 728*a^5*x^6*e + 560*a^4*b*c*x^3 - 560*a^5*d*x^3 - 455*a^5*c)/(a^6*x^16)","A",0
251,1,300,0,0.248628," ","integrate(x^11*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{{\left(3 \, a^{2} b^{3} c - 4 \, a^{3} b^{2} d - 6 \, a^{5} f + 5 \, a^{4} b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{7}} - \frac{3 \, a^{2} b^{4} c x^{3} - 4 \, a^{3} b^{3} d x^{3} - 6 \, a^{5} b f x^{3} + 5 \, a^{4} b^{2} x^{3} e + 2 \, a^{3} b^{3} c - 3 \, a^{4} b^{2} d - 5 \, a^{6} f + 4 \, a^{5} b e}{3 \, {\left(b x^{3} + a\right)} b^{7}} + \frac{12 \, b^{8} f x^{15} - 30 \, a b^{7} f x^{12} + 15 \, b^{8} x^{12} e + 20 \, b^{8} d x^{9} + 60 \, a^{2} b^{6} f x^{9} - 40 \, a b^{7} x^{9} e + 30 \, b^{8} c x^{6} - 60 \, a b^{7} d x^{6} - 120 \, a^{3} b^{5} f x^{6} + 90 \, a^{2} b^{6} x^{6} e - 120 \, a b^{7} c x^{3} + 180 \, a^{2} b^{6} d x^{3} + 300 \, a^{4} b^{4} f x^{3} - 240 \, a^{3} b^{5} x^{3} e}{180 \, b^{10}}"," ",0,"1/3*(3*a^2*b^3*c - 4*a^3*b^2*d - 6*a^5*f + 5*a^4*b*e)*log(abs(b*x^3 + a))/b^7 - 1/3*(3*a^2*b^4*c*x^3 - 4*a^3*b^3*d*x^3 - 6*a^5*b*f*x^3 + 5*a^4*b^2*x^3*e + 2*a^3*b^3*c - 3*a^4*b^2*d - 5*a^6*f + 4*a^5*b*e)/((b*x^3 + a)*b^7) + 1/180*(12*b^8*f*x^15 - 30*a*b^7*f*x^12 + 15*b^8*x^12*e + 20*b^8*d*x^9 + 60*a^2*b^6*f*x^9 - 40*a*b^7*x^9*e + 30*b^8*c*x^6 - 60*a*b^7*d*x^6 - 120*a^3*b^5*f*x^6 + 90*a^2*b^6*x^6*e - 120*a*b^7*c*x^3 + 180*a^2*b^6*d*x^3 + 300*a^4*b^4*f*x^3 - 240*a^3*b^5*x^3*e)/b^10","A",0
252,1,248,0,0.183383," ","integrate(x^8*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, a b^{3} c - 3 \, a^{2} b^{2} d - 5 \, a^{4} f + 4 \, a^{3} b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{6}} + \frac{2 \, a b^{4} c x^{3} - 3 \, a^{2} b^{3} d x^{3} - 5 \, a^{4} b f x^{3} + 4 \, a^{3} b^{2} x^{3} e + a^{2} b^{3} c - 2 \, a^{3} b^{2} d - 4 \, a^{5} f + 3 \, a^{4} b e}{3 \, {\left(b x^{3} + a\right)} b^{6}} + \frac{3 \, b^{6} f x^{12} - 8 \, a b^{5} f x^{9} + 4 \, b^{6} x^{9} e + 6 \, b^{6} d x^{6} + 18 \, a^{2} b^{4} f x^{6} - 12 \, a b^{5} x^{6} e + 12 \, b^{6} c x^{3} - 24 \, a b^{5} d x^{3} - 48 \, a^{3} b^{3} f x^{3} + 36 \, a^{2} b^{4} x^{3} e}{36 \, b^{8}}"," ",0,"-1/3*(2*a*b^3*c - 3*a^2*b^2*d - 5*a^4*f + 4*a^3*b*e)*log(abs(b*x^3 + a))/b^6 + 1/3*(2*a*b^4*c*x^3 - 3*a^2*b^3*d*x^3 - 5*a^4*b*f*x^3 + 4*a^3*b^2*x^3*e + a^2*b^3*c - 2*a^3*b^2*d - 4*a^5*f + 3*a^4*b*e)/((b*x^3 + a)*b^6) + 1/36*(3*b^6*f*x^12 - 8*a*b^5*f*x^9 + 4*b^6*x^9*e + 6*b^6*d*x^6 + 18*a^2*b^4*f*x^6 - 12*a*b^5*x^6*e + 12*b^6*c*x^3 - 24*a*b^5*d*x^3 - 48*a^3*b^3*f*x^3 + 36*a^2*b^4*x^3*e)/b^8","A",0
253,1,217,0,0.197223," ","integrate(x^5*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{\frac{{\left(b x^{3} + a\right)}^{3} {\left(2 \, f - \frac{3 \, {\left(4 \, a b f - b^{2} e\right)}}{{\left(b x^{3} + a\right)} b} + \frac{6 \, {\left(b^{4} d + 6 \, a^{2} b^{2} f - 3 \, a b^{3} e\right)}}{{\left(b x^{3} + a\right)}^{2} b^{2}}\right)}}{b^{4}} - \frac{6 \, {\left(b^{3} c - 2 \, a b^{2} d - 4 \, a^{3} f + 3 \, a^{2} b e\right)} \log\left(\frac{{\left| b x^{3} + a \right|}}{{\left(b x^{3} + a\right)}^{2} {\left| b \right|}}\right)}{b^{4}} + \frac{6 \, {\left(\frac{a b^{6} c}{b x^{3} + a} - \frac{a^{2} b^{5} d}{b x^{3} + a} - \frac{a^{4} b^{3} f}{b x^{3} + a} + \frac{a^{3} b^{4} e}{b x^{3} + a}\right)}}{b^{7}}}{18 \, b}"," ",0,"1/18*((b*x^3 + a)^3*(2*f - 3*(4*a*b*f - b^2*e)/((b*x^3 + a)*b) + 6*(b^4*d + 6*a^2*b^2*f - 3*a*b^3*e)/((b*x^3 + a)^2*b^2))/b^4 - 6*(b^3*c - 2*a*b^2*d - 4*a^3*f + 3*a^2*b*e)*log(abs(b*x^3 + a)/((b*x^3 + a)^2*abs(b)))/b^4 + 6*(a*b^6*c/(b*x^3 + a) - a^2*b^5*d/(b*x^3 + a) - a^4*b^3*f/(b*x^3 + a) + a^3*b^4*e/(b*x^3 + a))/b^7)/b","A",0
254,1,206,0,0.188720," ","integrate(x^2*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{1}{6} \, f {\left(\frac{{\left(b x^{3} + a\right)}^{2} {\left(\frac{6 \, a}{b x^{3} + a} - 1\right)}}{b^{4}} + \frac{6 \, a^{2} \log\left(\frac{{\left| b x^{3} + a \right|}}{{\left(b x^{3} + a\right)}^{2} {\left| b \right|}}\right)}{b^{4}} - \frac{2 \, a^{3}}{{\left(b x^{3} + a\right)} b^{4}}\right)} + \frac{1}{3} \, {\left(\frac{2 \, a \log\left(\frac{{\left| b x^{3} + a \right|}}{{\left(b x^{3} + a\right)}^{2} {\left| b \right|}}\right)}{b^{3}} + \frac{b x^{3} + a}{b^{3}} - \frac{a^{2}}{{\left(b x^{3} + a\right)} b^{3}}\right)} e - \frac{d {\left(\frac{\log\left(\frac{{\left| b x^{3} + a \right|}}{{\left(b x^{3} + a\right)}^{2} {\left| b \right|}}\right)}{b} - \frac{a}{{\left(b x^{3} + a\right)} b}\right)}}{3 \, b} - \frac{c}{3 \, {\left(b x^{3} + a\right)} b}"," ",0,"-1/6*f*((b*x^3 + a)^2*(6*a/(b*x^3 + a) - 1)/b^4 + 6*a^2*log(abs(b*x^3 + a)/((b*x^3 + a)^2*abs(b)))/b^4 - 2*a^3/((b*x^3 + a)*b^4)) + 1/3*(2*a*log(abs(b*x^3 + a)/((b*x^3 + a)^2*abs(b)))/b^3 + (b*x^3 + a)/b^3 - a^2/((b*x^3 + a)*b^3))*e - 1/3*d*(log(abs(b*x^3 + a)/((b*x^3 + a)^2*abs(b)))/b - a/((b*x^3 + a)*b))/b - 1/3*c/((b*x^3 + a)*b)","B",0
255,1,125,0,0.168072," ","integrate((f*x^9+e*x^6+d*x^3+c)/x/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{f x^{3}}{3 \, b^{2}} + \frac{c \log\left({\left| x \right|}\right)}{a^{2}} - \frac{{\left(b^{3} c + 2 \, a^{3} f - a^{2} b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{2} b^{3}} + \frac{b^{4} c x^{3} + 2 \, a^{3} b f x^{3} - a^{2} b^{2} x^{3} e + 2 \, a b^{3} c - a^{2} b^{2} d + a^{4} f}{3 \, {\left(b x^{3} + a\right)} a^{2} b^{3}}"," ",0,"1/3*f*x^3/b^2 + c*log(abs(x))/a^2 - 1/3*(b^3*c + 2*a^3*f - a^2*b*e)*log(abs(b*x^3 + a))/(a^2*b^3) + 1/3*(b^4*c*x^3 + 2*a^3*b*f*x^3 - a^2*b^2*x^3*e + 2*a*b^3*c - a^2*b^2*d + a^4*f)/((b*x^3 + a)*a^2*b^3)","A",0
256,1,131,0,0.212701," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^4/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, b c - a d\right)} \log\left({\left| x \right|}\right)}{a^{3}} + \frac{{\left(2 \, b^{3} c - a b^{2} d + a^{3} f\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{3} b^{2}} - \frac{a^{2} b f x^{6} + 4 \, b^{3} c x^{3} - 2 \, a b^{2} d x^{3} - a^{3} f x^{3} + 2 \, a^{2} b x^{3} e + 2 \, a b^{2} c}{6 \, {\left(b x^{6} + a x^{3}\right)} a^{2} b^{2}}"," ",0,"-(2*b*c - a*d)*log(abs(x))/a^3 + 1/3*(2*b^3*c - a*b^2*d + a^3*f)*log(abs(b*x^3 + a))/(a^3*b^2) - 1/6*(a^2*b*f*x^6 + 4*b^3*c*x^3 - 2*a*b^2*d*x^3 - a^3*f*x^3 + 2*a^2*b*x^3*e + 2*a*b^2*c)/((b*x^6 + a*x^3)*a^2*b^2)","A",0
257,1,201,0,0.168255," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^7/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{{\left(3 \, b^{2} c - 2 \, a b d + a^{2} e\right)} \log\left({\left| x \right|}\right)}{a^{4}} - \frac{{\left(3 \, b^{3} c - 2 \, a b^{2} d + a^{2} b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{4} b} + \frac{3 \, b^{4} c x^{3} - 2 \, a b^{3} d x^{3} + a^{2} b^{2} x^{3} e + 4 \, a b^{3} c - 3 \, a^{2} b^{2} d - a^{4} f + 2 \, a^{3} b e}{3 \, {\left(b x^{3} + a\right)} a^{4} b} - \frac{9 \, b^{2} c x^{6} - 6 \, a b d x^{6} + 3 \, a^{2} x^{6} e - 4 \, a b c x^{3} + 2 \, a^{2} d x^{3} + a^{2} c}{6 \, a^{4} x^{6}}"," ",0,"(3*b^2*c - 2*a*b*d + a^2*e)*log(abs(x))/a^4 - 1/3*(3*b^3*c - 2*a*b^2*d + a^2*b*e)*log(abs(b*x^3 + a))/(a^4*b) + 1/3*(3*b^4*c*x^3 - 2*a*b^3*d*x^3 + a^2*b^2*x^3*e + 4*a*b^3*c - 3*a^2*b^2*d - a^4*f + 2*a^3*b*e)/((b*x^3 + a)*a^4*b) - 1/6*(9*b^2*c*x^6 - 6*a*b*d*x^6 + 3*a^2*x^6*e - 4*a*b*c*x^3 + 2*a^2*d*x^3 + a^2*c)/(a^4*x^6)","A",0
258,1,275,0,0.196147," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^10/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{{\left(4 \, b^{3} c - 3 \, a b^{2} d - a^{3} f + 2 \, a^{2} b e\right)} \log\left({\left| x \right|}\right)}{a^{5}} + \frac{{\left(4 \, b^{4} c - 3 \, a b^{3} d - a^{3} b f + 2 \, a^{2} b^{2} e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{5} b} - \frac{4 \, b^{4} c x^{3} - 3 \, a b^{3} d x^{3} - a^{3} b f x^{3} + 2 \, a^{2} b^{2} x^{3} e + 5 \, a b^{3} c - 4 \, a^{2} b^{2} d - 2 \, a^{4} f + 3 \, a^{3} b e}{3 \, {\left(b x^{3} + a\right)} a^{5}} + \frac{44 \, b^{3} c x^{9} - 33 \, a b^{2} d x^{9} - 11 \, a^{3} f x^{9} + 22 \, a^{2} b x^{9} e - 18 \, a b^{2} c x^{6} + 12 \, a^{2} b d x^{6} - 6 \, a^{3} x^{6} e + 6 \, a^{2} b c x^{3} - 3 \, a^{3} d x^{3} - 2 \, a^{3} c}{18 \, a^{5} x^{9}}"," ",0,"-(4*b^3*c - 3*a*b^2*d - a^3*f + 2*a^2*b*e)*log(abs(x))/a^5 + 1/3*(4*b^4*c - 3*a*b^3*d - a^3*b*f + 2*a^2*b^2*e)*log(abs(b*x^3 + a))/(a^5*b) - 1/3*(4*b^4*c*x^3 - 3*a*b^3*d*x^3 - a^3*b*f*x^3 + 2*a^2*b^2*x^3*e + 5*a*b^3*c - 4*a^2*b^2*d - 2*a^4*f + 3*a^3*b*e)/((b*x^3 + a)*a^5) + 1/18*(44*b^3*c*x^9 - 33*a*b^2*d*x^9 - 11*a^3*f*x^9 + 22*a^2*b*x^9*e - 18*a*b^2*c*x^6 + 12*a^2*b*d*x^6 - 6*a^3*x^6*e + 6*a^2*b*c*x^3 - 3*a^3*d*x^3 - 2*a^3*c)/(a^5*x^9)","A",0
259,1,331,0,0.170775," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^13/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{{\left(5 \, b^{4} c - 4 \, a b^{3} d - 2 \, a^{3} b f + 3 \, a^{2} b^{2} e\right)} \log\left({\left| x \right|}\right)}{a^{6}} - \frac{{\left(5 \, b^{5} c - 4 \, a b^{4} d - 2 \, a^{3} b^{2} f + 3 \, a^{2} b^{3} e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{6} b} + \frac{5 \, b^{5} c x^{3} - 4 \, a b^{4} d x^{3} - 2 \, a^{3} b^{2} f x^{3} + 3 \, a^{2} b^{3} x^{3} e + 6 \, a b^{4} c - 5 \, a^{2} b^{3} d - 3 \, a^{4} b f + 4 \, a^{3} b^{2} e}{3 \, {\left(b x^{3} + a\right)} a^{6}} - \frac{125 \, b^{4} c x^{12} - 100 \, a b^{3} d x^{12} - 50 \, a^{3} b f x^{12} + 75 \, a^{2} b^{2} x^{12} e - 48 \, a b^{3} c x^{9} + 36 \, a^{2} b^{2} d x^{9} + 12 \, a^{4} f x^{9} - 24 \, a^{3} b x^{9} e + 18 \, a^{2} b^{2} c x^{6} - 12 \, a^{3} b d x^{6} + 6 \, a^{4} x^{6} e - 8 \, a^{3} b c x^{3} + 4 \, a^{4} d x^{3} + 3 \, a^{4} c}{36 \, a^{6} x^{12}}"," ",0,"(5*b^4*c - 4*a*b^3*d - 2*a^3*b*f + 3*a^2*b^2*e)*log(abs(x))/a^6 - 1/3*(5*b^5*c - 4*a*b^4*d - 2*a^3*b^2*f + 3*a^2*b^3*e)*log(abs(b*x^3 + a))/(a^6*b) + 1/3*(5*b^5*c*x^3 - 4*a*b^4*d*x^3 - 2*a^3*b^2*f*x^3 + 3*a^2*b^3*x^3*e + 6*a*b^4*c - 5*a^2*b^3*d - 3*a^4*b*f + 4*a^3*b^2*e)/((b*x^3 + a)*a^6) - 1/36*(125*b^4*c*x^12 - 100*a*b^3*d*x^12 - 50*a^3*b*f*x^12 + 75*a^2*b^2*x^12*e - 48*a*b^3*c*x^9 + 36*a^2*b^2*d*x^9 + 12*a^4*f*x^9 - 24*a^3*b*x^9*e + 18*a^2*b^2*c*x^6 - 12*a^3*b*d*x^6 + 6*a^4*x^6*e - 8*a^3*b*c*x^3 + 4*a^4*d*x^3 + 3*a^4*c)/(a^6*x^12)","A",0
260,1,451,0,0.199178," ","integrate(x^9*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{\sqrt{3} {\left(7 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{3} c - 10 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b^{2} d - 16 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{4} f + 13 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, b^{7}} - \frac{{\left(7 \, a^{2} b^{3} c - 10 \, a^{3} b^{2} d - 16 \, a^{5} f + 13 \, a^{4} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a b^{6}} + \frac{{\left(7 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{3} c - 10 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b^{2} d - 16 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{4} f + 13 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, b^{7}} - \frac{a^{2} b^{3} c x - a^{3} b^{2} d x - a^{5} f x + a^{4} b x e}{3 \, {\left(b x^{3} + a\right)} b^{6}} + \frac{140 \, b^{24} f x^{13} - 364 \, a b^{23} f x^{10} + 182 \, b^{24} x^{10} e + 260 \, b^{24} d x^{7} + 780 \, a^{2} b^{22} f x^{7} - 520 \, a b^{23} x^{7} e + 455 \, b^{24} c x^{4} - 910 \, a b^{23} d x^{4} - 1820 \, a^{3} b^{21} f x^{4} + 1365 \, a^{2} b^{22} x^{4} e - 3640 \, a b^{23} c x + 5460 \, a^{2} b^{22} d x + 9100 \, a^{4} b^{20} f x - 7280 \, a^{3} b^{21} x e}{1820 \, b^{26}}"," ",0,"1/9*sqrt(3)*(7*(-a*b^2)^(1/3)*a*b^3*c - 10*(-a*b^2)^(1/3)*a^2*b^2*d - 16*(-a*b^2)^(1/3)*a^4*f + 13*(-a*b^2)^(1/3)*a^3*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^7 - 1/9*(7*a^2*b^3*c - 10*a^3*b^2*d - 16*a^5*f + 13*a^4*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^6) + 1/18*(7*(-a*b^2)^(1/3)*a*b^3*c - 10*(-a*b^2)^(1/3)*a^2*b^2*d - 16*(-a*b^2)^(1/3)*a^4*f + 13*(-a*b^2)^(1/3)*a^3*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^7 - 1/3*(a^2*b^3*c*x - a^3*b^2*d*x - a^5*f*x + a^4*b*x*e)/((b*x^3 + a)*b^6) + 1/1820*(140*b^24*f*x^13 - 364*a*b^23*f*x^10 + 182*b^24*x^10*e + 260*b^24*d*x^7 + 780*a^2*b^22*f*x^7 - 520*a*b^23*x^7*e + 455*b^24*c*x^4 - 910*a*b^23*d*x^4 - 1820*a^3*b^21*f*x^4 + 1365*a^2*b^22*x^4*e - 3640*a*b^23*c*x + 5460*a^2*b^22*d*x + 9100*a^4*b^20*f*x - 7280*a^3*b^21*x*e)/b^26","A",0
261,1,442,0,0.200451," ","integrate(x^7*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{{\left(5 \, a b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 8 \, a^{2} b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 14 \, a^{4} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 11 \, a^{3} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a b^{5}} + \frac{\sqrt{3} {\left(5 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - 8 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - 14 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + 11 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, b^{7}} + \frac{a b^{3} c x^{2} - a^{2} b^{2} d x^{2} - a^{4} f x^{2} + a^{3} b x^{2} e}{3 \, {\left(b x^{3} + a\right)} b^{5}} - \frac{{\left(5 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - 8 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - 14 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + 11 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, b^{7}} + \frac{40 \, b^{20} f x^{11} - 110 \, a b^{19} f x^{8} + 55 \, b^{20} x^{8} e + 88 \, b^{20} d x^{5} + 264 \, a^{2} b^{18} f x^{5} - 176 \, a b^{19} x^{5} e + 220 \, b^{20} c x^{2} - 440 \, a b^{19} d x^{2} - 880 \, a^{3} b^{17} f x^{2} + 660 \, a^{2} b^{18} x^{2} e}{440 \, b^{22}}"," ",0,"1/9*(5*a*b^3*c*(-a/b)^(1/3) - 8*a^2*b^2*d*(-a/b)^(1/3) - 14*a^4*f*(-a/b)^(1/3) + 11*a^3*b*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^5) + 1/9*sqrt(3)*(5*(-a*b^2)^(2/3)*b^3*c - 8*(-a*b^2)^(2/3)*a*b^2*d - 14*(-a*b^2)^(2/3)*a^3*f + 11*(-a*b^2)^(2/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^7 + 1/3*(a*b^3*c*x^2 - a^2*b^2*d*x^2 - a^4*f*x^2 + a^3*b*x^2*e)/((b*x^3 + a)*b^5) - 1/18*(5*(-a*b^2)^(2/3)*b^3*c - 8*(-a*b^2)^(2/3)*a*b^2*d - 14*(-a*b^2)^(2/3)*a^3*f + 11*(-a*b^2)^(2/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^7 + 1/440*(40*b^20*f*x^11 - 110*a*b^19*f*x^8 + 55*b^20*x^8*e + 88*b^20*d*x^5 + 264*a^2*b^18*f*x^5 - 176*a*b^19*x^5*e + 220*b^20*c*x^2 - 440*a*b^19*d*x^2 - 880*a^3*b^17*f*x^2 + 660*a^2*b^18*x^2*e)/b^22","A",0
262,1,394,0,0.182710," ","integrate(x^6*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(4 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - 7 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - 13 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + 10 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, b^{6}} + \frac{{\left(4 \, a b^{3} c - 7 \, a^{2} b^{2} d - 13 \, a^{4} f + 10 \, a^{3} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a b^{5}} - \frac{{\left(4 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - 7 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - 13 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + 10 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, b^{6}} + \frac{a b^{3} c x - a^{2} b^{2} d x - a^{4} f x + a^{3} b x e}{3 \, {\left(b x^{3} + a\right)} b^{5}} + \frac{14 \, b^{18} f x^{10} - 40 \, a b^{17} f x^{7} + 20 \, b^{18} x^{7} e + 35 \, b^{18} d x^{4} + 105 \, a^{2} b^{16} f x^{4} - 70 \, a b^{17} x^{4} e + 140 \, b^{18} c x - 280 \, a b^{17} d x - 560 \, a^{3} b^{15} f x + 420 \, a^{2} b^{16} x e}{140 \, b^{20}}"," ",0,"-1/9*sqrt(3)*(4*(-a*b^2)^(1/3)*b^3*c - 7*(-a*b^2)^(1/3)*a*b^2*d - 13*(-a*b^2)^(1/3)*a^3*f + 10*(-a*b^2)^(1/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^6 + 1/9*(4*a*b^3*c - 7*a^2*b^2*d - 13*a^4*f + 10*a^3*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^5) - 1/18*(4*(-a*b^2)^(1/3)*b^3*c - 7*(-a*b^2)^(1/3)*a*b^2*d - 13*(-a*b^2)^(1/3)*a^3*f + 10*(-a*b^2)^(1/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^6 + 1/3*(a*b^3*c*x - a^2*b^2*d*x - a^4*f*x + a^3*b*x*e)/((b*x^3 + a)*b^5) + 1/140*(14*b^18*f*x^10 - 40*a*b^17*f*x^7 + 20*b^18*x^7*e + 35*b^18*d*x^4 + 105*a^2*b^16*f*x^4 - 70*a*b^17*x^4*e + 140*b^18*c*x - 280*a*b^17*d*x - 560*a^3*b^15*f*x + 420*a^2*b^16*x*e)/b^20","A",0
263,1,344,0,0.186624," ","integrate(x^4*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{\sqrt{3} {\left(2 \, b^{3} c - 5 \, a b^{2} d - 11 \, a^{3} f + 8 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{4}} - \frac{{\left(2 \, b^{3} c - 5 \, a b^{2} d - 11 \, a^{3} f + 8 \, a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{4}} - \frac{{\left(2 \, b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 11 \, a^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 8 \, a^{2} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a b^{4}} - \frac{b^{3} c x^{2} - a b^{2} d x^{2} - a^{3} f x^{2} + a^{2} b x^{2} e}{3 \, {\left(b x^{3} + a\right)} b^{4}} + \frac{5 \, b^{14} f x^{8} - 16 \, a b^{13} f x^{5} + 8 \, b^{14} x^{5} e + 20 \, b^{14} d x^{2} + 60 \, a^{2} b^{12} f x^{2} - 40 \, a b^{13} x^{2} e}{40 \, b^{16}}"," ",0,"1/9*sqrt(3)*(2*b^3*c - 5*a*b^2*d - 11*a^3*f + 8*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(1/3)*b^4) - 1/18*(2*b^3*c - 5*a*b^2*d - 11*a^3*f + 8*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(1/3)*b^4) - 1/9*(2*b^3*c*(-a/b)^(1/3) - 5*a*b^2*d*(-a/b)^(1/3) - 11*a^3*f*(-a/b)^(1/3) + 8*a^2*b*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^4) - 1/3*(b^3*c*x^2 - a*b^2*d*x^2 - a^3*f*x^2 + a^2*b*x^2*e)/((b*x^3 + a)*b^4) + 1/40*(5*b^14*f*x^8 - 16*a*b^13*f*x^5 + 8*b^14*x^5*e + 20*b^14*d*x^2 + 60*a^2*b^12*f*x^2 - 40*a*b^13*x^2*e)/b^16","A",0
264,1,295,0,0.179460," ","integrate(x^3*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b^{3} c - 4 \, a b^{2} d - 10 \, a^{3} f + 7 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{3}} - \frac{{\left(b^{3} c - 4 \, a b^{2} d - 10 \, a^{3} f + 7 \, a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{3}} - \frac{{\left(b^{3} c - 4 \, a b^{2} d - 10 \, a^{3} f + 7 \, a^{2} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a b^{4}} - \frac{b^{3} c x - a b^{2} d x - a^{3} f x + a^{2} b x e}{3 \, {\left(b x^{3} + a\right)} b^{4}} + \frac{4 \, b^{12} f x^{7} - 14 \, a b^{11} f x^{4} + 7 \, b^{12} x^{4} e + 28 \, b^{12} d x + 84 \, a^{2} b^{10} f x - 56 \, a b^{11} x e}{28 \, b^{14}}"," ",0,"-1/9*sqrt(3)*(b^3*c - 4*a*b^2*d - 10*a^3*f + 7*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*b^3) - 1/18*(b^3*c - 4*a*b^2*d - 10*a^3*f + 7*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*b^3) - 1/9*(b^3*c - 4*a*b^2*d - 10*a^3*f + 7*a^2*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^4) - 1/3*(b^3*c*x - a*b^2*d*x - a^3*f*x + a^2*b*x*e)/((b*x^3 + a)*b^4) + 1/28*(4*b^12*f*x^7 - 14*a*b^11*f*x^4 + 7*b^12*x^4*e + 28*b^12*d*x + 84*a^2*b^10*f*x - 56*a*b^11*x*e)/b^14","A",0
265,1,318,0,0.220299," ","integrate(x*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{\sqrt{3} {\left(b^{3} c + 2 \, a b^{2} d + 8 \, a^{3} f - 5 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{3}} - \frac{{\left(b^{3} c + 2 \, a b^{2} d + 8 \, a^{3} f - 5 \, a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{3}} - \frac{{\left(b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 8 \, a^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a^{2} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{2} b^{3}} + \frac{b^{3} c x^{2} - a b^{2} d x^{2} - a^{3} f x^{2} + a^{2} b x^{2} e}{3 \, {\left(b x^{3} + a\right)} a b^{3}} + \frac{2 \, b^{8} f x^{5} - 10 \, a b^{7} f x^{2} + 5 \, b^{8} x^{2} e}{10 \, b^{10}}"," ",0,"1/9*sqrt(3)*(b^3*c + 2*a*b^2*d + 8*a^3*f - 5*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(1/3)*a*b^3) - 1/18*(b^3*c + 2*a*b^2*d + 8*a^3*f - 5*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(1/3)*a*b^3) - 1/9*(b^3*c*(-a/b)^(1/3) + 2*a*b^2*d*(-a/b)^(1/3) + 8*a^3*f*(-a/b)^(1/3) - 5*a^2*b*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b^3) + 1/3*(b^3*c*x^2 - a*b^2*d*x^2 - a^3*f*x^2 + a^2*b*x^2*e)/((b*x^3 + a)*a*b^3) + 1/10*(2*b^8*f*x^5 - 10*a*b^7*f*x^2 + 5*b^8*x^2*e)/b^10","A",0
266,1,273,0,0.207820," ","integrate((f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(2 \, b^{3} c + a b^{2} d + 7 \, a^{3} f - 4 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2}} - \frac{{\left(2 \, b^{3} c + a b^{2} d + 7 \, a^{3} f - 4 \, a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2}} - \frac{{\left(2 \, b^{3} c + a b^{2} d + 7 \, a^{3} f - 4 \, a^{2} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{2} b^{3}} + \frac{b^{3} c x - a b^{2} d x - a^{3} f x + a^{2} b x e}{3 \, {\left(b x^{3} + a\right)} a b^{3}} + \frac{b^{6} f x^{4} - 8 \, a b^{5} f x + 4 \, b^{6} x e}{4 \, b^{8}}"," ",0,"-1/9*sqrt(3)*(2*b^3*c + a*b^2*d + 7*a^3*f - 4*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a*b^2) - 1/18*(2*b^3*c + a*b^2*d + 7*a^3*f - 4*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a*b^2) - 1/9*(2*b^3*c + a*b^2*d + 7*a^3*f - 4*a^2*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b^3) + 1/3*(b^3*c*x - a*b^2*d*x - a^3*f*x + a^2*b*x*e)/((b*x^3 + a)*a*b^3) + 1/4*(b^6*f*x^4 - 8*a*b^5*f*x + 4*b^6*x*e)/b^8","A",0
267,1,305,0,0.185371," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^2/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{f x^{2}}{2 \, b^{2}} - \frac{\sqrt{3} {\left(4 \, b^{3} c - a b^{2} d + 5 \, a^{3} f - 2 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b^{2}} + \frac{{\left(4 \, b^{3} c - a b^{2} d + 5 \, a^{3} f - 2 \, a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b^{2}} + \frac{{\left(4 \, b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a^{2} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{3} b^{2}} - \frac{4 \, b^{3} c x^{3} - a b^{2} d x^{3} - a^{3} f x^{3} + a^{2} b x^{3} e + 3 \, a b^{2} c}{3 \, {\left(b x^{4} + a x\right)} a^{2} b^{2}}"," ",0,"1/2*f*x^2/b^2 - 1/9*sqrt(3)*(4*b^3*c - a*b^2*d + 5*a^3*f - 2*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(1/3)*a^2*b^2) + 1/18*(4*b^3*c - a*b^2*d + 5*a^3*f - 2*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(1/3)*a^2*b^2) + 1/9*(4*b^3*c*(-a/b)^(1/3) - a*b^2*d*(-a/b)^(1/3) + 5*a^3*f*(-a/b)^(1/3) - 2*a^2*b*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b^2) - 1/3*(4*b^3*c*x^3 - a*b^2*d*x^3 - a^3*f*x^3 + a^2*b*x^3*e + 3*a*b^2*c)/((b*x^4 + a*x)*a^2*b^2)","A",0
268,1,261,0,0.178005," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^3/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{f x}{b^{2}} + \frac{\sqrt{3} {\left(5 \, b^{3} c - 2 \, a b^{2} d + 4 \, a^{3} f - a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b} + \frac{{\left(5 \, b^{3} c - 2 \, a b^{2} d + 4 \, a^{3} f - a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b} + \frac{{\left(5 \, b^{3} c - 2 \, a b^{2} d + 4 \, a^{3} f - a^{2} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{3} b^{2}} - \frac{c}{2 \, a^{2} x^{2}} - \frac{b^{3} c x - a b^{2} d x - a^{3} f x + a^{2} b x e}{3 \, {\left(b x^{3} + a\right)} a^{2} b^{2}}"," ",0,"f*x/b^2 + 1/9*sqrt(3)*(5*b^3*c - 2*a*b^2*d + 4*a^3*f - a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^2*b) + 1/18*(5*b^3*c - 2*a*b^2*d + 4*a^3*f - a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^2*b) + 1/9*(5*b^3*c - 2*a*b^2*d + 4*a^3*f - a^2*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b^2) - 1/2*c/(a^2*x^2) - 1/3*(b^3*c*x - a*b^2*d*x - a^3*f*x + a^2*b*x*e)/((b*x^3 + a)*a^2*b^2)","A",0
269,1,310,0,0.196507," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^5/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{\sqrt{3} {\left(7 \, b^{3} c - 4 \, a b^{2} d + 2 \, a^{3} f + a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} b} - \frac{{\left(7 \, b^{3} c - 4 \, a b^{2} d + 2 \, a^{3} f + a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} b} - \frac{{\left(7 \, b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 4 \, a b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{4} b} + \frac{b^{3} c x^{2} - a b^{2} d x^{2} - a^{3} f x^{2} + a^{2} b x^{2} e}{3 \, {\left(b x^{3} + a\right)} a^{3} b} + \frac{8 \, b c x^{3} - 4 \, a d x^{3} - a c}{4 \, a^{3} x^{4}}"," ",0,"1/9*sqrt(3)*(7*b^3*c - 4*a*b^2*d + 2*a^3*f + a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(1/3)*a^3*b) - 1/18*(7*b^3*c - 4*a*b^2*d + 2*a^3*f + a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(1/3)*a^3*b) - 1/9*(7*b^3*c*(-a/b)^(1/3) - 4*a*b^2*d*(-a/b)^(1/3) + 2*a^3*f*(-a/b)^(1/3) + a^2*b*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^4*b) + 1/3*(b^3*c*x^2 - a*b^2*d*x^2 - a^3*f*x^2 + a^2*b*x^2*e)/((b*x^3 + a)*a^3*b) + 1/4*(8*b*c*x^3 - 4*a*d*x^3 - a*c)/(a^3*x^4)","A",0
270,1,264,0,0.177395," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^6/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(8 \, b^{3} c - 5 \, a b^{2} d + a^{3} f + 2 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3}} - \frac{{\left(8 \, b^{3} c - 5 \, a b^{2} d + a^{3} f + 2 \, a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3}} - \frac{{\left(8 \, b^{3} c - 5 \, a b^{2} d + a^{3} f + 2 \, a^{2} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{4} b} + \frac{b^{3} c x - a b^{2} d x - a^{3} f x + a^{2} b x e}{3 \, {\left(b x^{3} + a\right)} a^{3} b} + \frac{10 \, b c x^{3} - 5 \, a d x^{3} - 2 \, a c}{10 \, a^{3} x^{5}}"," ",0,"-1/9*sqrt(3)*(8*b^3*c - 5*a*b^2*d + a^3*f + 2*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^3) - 1/18*(8*b^3*c - 5*a*b^2*d + a^3*f + 2*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^3) - 1/9*(8*b^3*c - 5*a*b^2*d + a^3*f + 2*a^2*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^4*b) + 1/3*(b^3*c*x - a*b^2*d*x - a^3*f*x + a^2*b*x*e)/((b*x^3 + a)*a^3*b) + 1/10*(10*b*c*x^3 - 5*a*d*x^3 - 2*a*c)/(a^3*x^5)","A",0
271,1,333,0,0.231422," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^8/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(10 \, b^{3} c - 7 \, a b^{2} d - a^{3} f + 4 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{4}} + \frac{{\left(10 \, b^{3} c - 7 \, a b^{2} d - a^{3} f + 4 \, a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{4}} + \frac{{\left(10 \, b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 7 \, a b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 4 \, a^{2} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{5}} - \frac{b^{3} c x^{2} - a b^{2} d x^{2} - a^{3} f x^{2} + a^{2} b x^{2} e}{3 \, {\left(b x^{3} + a\right)} a^{4}} - \frac{84 \, b^{2} c x^{6} - 56 \, a b d x^{6} + 28 \, a^{2} x^{6} e - 14 \, a b c x^{3} + 7 \, a^{2} d x^{3} + 4 \, a^{2} c}{28 \, a^{4} x^{7}}"," ",0,"-1/9*sqrt(3)*(10*b^3*c - 7*a*b^2*d - a^3*f + 4*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(1/3)*a^4) + 1/18*(10*b^3*c - 7*a*b^2*d - a^3*f + 4*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(1/3)*a^4) + 1/9*(10*b^3*c*(-a/b)^(1/3) - 7*a*b^2*d*(-a/b)^(1/3) - a^3*f*(-a/b)^(1/3) + 4*a^2*b*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^5 - 1/3*(b^3*c*x^2 - a*b^2*d*x^2 - a^3*f*x^2 + a^2*b*x^2*e)/((b*x^3 + a)*a^4) - 1/28*(84*b^2*c*x^6 - 56*a*b*d*x^6 + 28*a^2*x^6*e - 14*a*b*c*x^3 + 7*a^2*d*x^3 + 4*a^2*c)/(a^4*x^7)","A",0
272,1,347,0,0.199037," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^9/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{{\left(11 \, b^{3} c - 8 \, a b^{2} d - 2 \, a^{3} f + 5 \, a^{2} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{5}} - \frac{\sqrt{3} {\left(11 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - 8 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a^{5} b} - \frac{b^{3} c x - a b^{2} d x - a^{3} f x + a^{2} b x e}{3 \, {\left(b x^{3} + a\right)} a^{4}} - \frac{{\left(11 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - 8 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, a^{5} b} - \frac{60 \, b^{2} c x^{6} - 40 \, a b d x^{6} + 20 \, a^{2} x^{6} e - 16 \, a b c x^{3} + 8 \, a^{2} d x^{3} + 5 \, a^{2} c}{40 \, a^{4} x^{8}}"," ",0,"1/9*(11*b^3*c - 8*a*b^2*d - 2*a^3*f + 5*a^2*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^5 - 1/9*sqrt(3)*(11*(-a*b^2)^(1/3)*b^3*c - 8*(-a*b^2)^(1/3)*a*b^2*d - 2*(-a*b^2)^(1/3)*a^3*f + 5*(-a*b^2)^(1/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^5*b) - 1/3*(b^3*c*x - a*b^2*d*x - a^3*f*x + a^2*b*x*e)/((b*x^3 + a)*a^4) - 1/18*(11*(-a*b^2)^(1/3)*b^3*c - 8*(-a*b^2)^(1/3)*a*b^2*d - 2*(-a*b^2)^(1/3)*a^3*f + 5*(-a*b^2)^(1/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^5*b) - 1/40*(60*b^2*c*x^6 - 40*a*b*d*x^6 + 20*a^2*x^6*e - 16*a*b*c*x^3 + 8*a^2*d*x^3 + 5*a^2*c)/(a^4*x^8)","A",0
273,1,437,0,0.370650," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^11/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{{\left(13 \, b^{4} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 10 \, a b^{3} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 4 \, a^{3} b f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 7 \, a^{2} b^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{6}} - \frac{\sqrt{3} {\left(13 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - 10 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - 4 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + 7 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a^{6} b} + \frac{b^{4} c x^{2} - a b^{3} d x^{2} - a^{3} b f x^{2} + a^{2} b^{2} x^{2} e}{3 \, {\left(b x^{3} + a\right)} a^{5}} + \frac{{\left(13 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - 10 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - 4 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + 7 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, a^{6} b} + \frac{560 \, b^{3} c x^{9} - 420 \, a b^{2} d x^{9} - 140 \, a^{3} f x^{9} + 280 \, a^{2} b x^{9} e - 105 \, a b^{2} c x^{6} + 70 \, a^{2} b d x^{6} - 35 \, a^{3} x^{6} e + 40 \, a^{2} b c x^{3} - 20 \, a^{3} d x^{3} - 14 \, a^{3} c}{140 \, a^{5} x^{10}}"," ",0,"-1/9*(13*b^4*c*(-a/b)^(1/3) - 10*a*b^3*d*(-a/b)^(1/3) - 4*a^3*b*f*(-a/b)^(1/3) + 7*a^2*b^2*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^6 - 1/9*sqrt(3)*(13*(-a*b^2)^(2/3)*b^3*c - 10*(-a*b^2)^(2/3)*a*b^2*d - 4*(-a*b^2)^(2/3)*a^3*f + 7*(-a*b^2)^(2/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^6*b) + 1/3*(b^4*c*x^2 - a*b^3*d*x^2 - a^3*b*f*x^2 + a^2*b^2*x^2*e)/((b*x^3 + a)*a^5) + 1/18*(13*(-a*b^2)^(2/3)*b^3*c - 10*(-a*b^2)^(2/3)*a*b^2*d - 4*(-a*b^2)^(2/3)*a^3*f + 7*(-a*b^2)^(2/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^6*b) + 1/140*(560*b^3*c*x^9 - 420*a*b^2*d*x^9 - 140*a^3*f*x^9 + 280*a^2*b*x^9*e - 105*a*b^2*c*x^6 + 70*a^2*b*d*x^6 - 35*a^3*x^6*e + 40*a^2*b*c*x^3 - 20*a^3*d*x^3 - 14*a^3*c)/(a^5*x^10)","A",0
274,1,391,0,0.179783," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^12/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{\sqrt{3} {\left(14 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - 11 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + 8 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a^{6}} - \frac{{\left(14 \, b^{4} c - 11 \, a b^{3} d - 5 \, a^{3} b f + 8 \, a^{2} b^{2} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{6}} + \frac{{\left(14 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - 11 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + 8 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, a^{6}} + \frac{b^{4} c x - a b^{3} d x - a^{3} b f x + a^{2} b^{2} x e}{3 \, {\left(b x^{3} + a\right)} a^{5}} + \frac{880 \, b^{3} c x^{9} - 660 \, a b^{2} d x^{9} - 220 \, a^{3} f x^{9} + 440 \, a^{2} b x^{9} e - 264 \, a b^{2} c x^{6} + 176 \, a^{2} b d x^{6} - 88 \, a^{3} x^{6} e + 110 \, a^{2} b c x^{3} - 55 \, a^{3} d x^{3} - 40 \, a^{3} c}{440 \, a^{5} x^{11}}"," ",0,"1/9*sqrt(3)*(14*(-a*b^2)^(1/3)*b^3*c - 11*(-a*b^2)^(1/3)*a*b^2*d - 5*(-a*b^2)^(1/3)*a^3*f + 8*(-a*b^2)^(1/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/a^6 - 1/9*(14*b^4*c - 11*a*b^3*d - 5*a^3*b*f + 8*a^2*b^2*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^6 + 1/18*(14*(-a*b^2)^(1/3)*b^3*c - 11*(-a*b^2)^(1/3)*a*b^2*d - 5*(-a*b^2)^(1/3)*a^3*f + 8*(-a*b^2)^(1/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/a^6 + 1/3*(b^4*c*x - a*b^3*d*x - a^3*b*f*x + a^2*b^2*x*e)/((b*x^3 + a)*a^5) + 1/440*(880*b^3*c*x^9 - 660*a*b^2*d*x^9 - 220*a^3*f*x^9 + 440*a^2*b*x^9*e - 264*a*b^2*c*x^6 + 176*a^2*b*d*x^6 - 88*a^3*x^6*e + 110*a^2*b*c*x^3 - 55*a^3*d*x^3 - 40*a^3*c)/(a^5*x^11)","A",0
275,1,482,0,0.207220," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^14/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{\sqrt{3} {\left(16 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - 13 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - 7 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + 10 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a^{7}} + \frac{{\left(16 \, b^{5} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 13 \, a b^{4} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 7 \, a^{3} b^{2} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 10 \, a^{2} b^{3} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{7}} - \frac{{\left(16 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - 13 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - 7 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + 10 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, a^{7}} - \frac{b^{5} c x^{2} - a b^{4} d x^{2} - a^{3} b^{2} f x^{2} + a^{2} b^{3} x^{2} e}{3 \, {\left(b x^{3} + a\right)} a^{6}} - \frac{9100 \, b^{4} c x^{12} - 7280 \, a b^{3} d x^{12} - 3640 \, a^{3} b f x^{12} + 5460 \, a^{2} b^{2} x^{12} e - 1820 \, a b^{3} c x^{9} + 1365 \, a^{2} b^{2} d x^{9} + 455 \, a^{4} f x^{9} - 910 \, a^{3} b x^{9} e + 780 \, a^{2} b^{2} c x^{6} - 520 \, a^{3} b d x^{6} + 260 \, a^{4} x^{6} e - 364 \, a^{3} b c x^{3} + 182 \, a^{4} d x^{3} + 140 \, a^{4} c}{1820 \, a^{6} x^{13}}"," ",0,"1/9*sqrt(3)*(16*(-a*b^2)^(2/3)*b^3*c - 13*(-a*b^2)^(2/3)*a*b^2*d - 7*(-a*b^2)^(2/3)*a^3*f + 10*(-a*b^2)^(2/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/a^7 + 1/9*(16*b^5*c*(-a/b)^(1/3) - 13*a*b^4*d*(-a/b)^(1/3) - 7*a^3*b^2*f*(-a/b)^(1/3) + 10*a^2*b^3*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^7 - 1/18*(16*(-a*b^2)^(2/3)*b^3*c - 13*(-a*b^2)^(2/3)*a*b^2*d - 7*(-a*b^2)^(2/3)*a^3*f + 10*(-a*b^2)^(2/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/a^7 - 1/3*(b^5*c*x^2 - a*b^4*d*x^2 - a^3*b^2*f*x^2 + a^2*b^3*x^2*e)/((b*x^3 + a)*a^6) - 1/1820*(9100*b^4*c*x^12 - 7280*a*b^3*d*x^12 - 3640*a^3*b*f*x^12 + 5460*a^2*b^2*x^12*e - 1820*a*b^3*c*x^9 + 1365*a^2*b^2*d*x^9 + 455*a^4*f*x^9 - 910*a^3*b*x^9*e + 780*a^2*b^2*c*x^6 - 520*a^3*b*d*x^6 + 260*a^4*x^6*e - 364*a^3*b*c*x^3 + 182*a^4*d*x^3 + 140*a^4*c)/(a^6*x^13)","A",0
276,1,349,0,0.183695," ","integrate(x^14*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{{\left(6 \, a^{2} b^{3} c - 10 \, a^{3} b^{2} d - 21 \, a^{5} f + 15 \, a^{4} b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{8}} - \frac{18 \, a^{2} b^{5} c x^{6} - 30 \, a^{3} b^{4} d x^{6} - 63 \, a^{5} b^{2} f x^{6} + 45 \, a^{4} b^{3} x^{6} e + 28 \, a^{3} b^{4} c x^{3} - 50 \, a^{4} b^{3} d x^{3} - 112 \, a^{6} b f x^{3} + 78 \, a^{5} b^{2} x^{3} e + 11 \, a^{4} b^{3} c - 21 \, a^{5} b^{2} d - 50 \, a^{7} f + 34 \, a^{6} b e}{6 \, {\left(b x^{3} + a\right)}^{2} b^{8}} + \frac{12 \, b^{12} f x^{15} - 45 \, a b^{11} f x^{12} + 15 \, b^{12} x^{12} e + 20 \, b^{12} d x^{9} + 120 \, a^{2} b^{10} f x^{9} - 60 \, a b^{11} x^{9} e + 30 \, b^{12} c x^{6} - 90 \, a b^{11} d x^{6} - 300 \, a^{3} b^{9} f x^{6} + 180 \, a^{2} b^{10} x^{6} e - 180 \, a b^{11} c x^{3} + 360 \, a^{2} b^{10} d x^{3} + 900 \, a^{4} b^{8} f x^{3} - 600 \, a^{3} b^{9} x^{3} e}{180 \, b^{15}}"," ",0,"1/3*(6*a^2*b^3*c - 10*a^3*b^2*d - 21*a^5*f + 15*a^4*b*e)*log(abs(b*x^3 + a))/b^8 - 1/6*(18*a^2*b^5*c*x^6 - 30*a^3*b^4*d*x^6 - 63*a^5*b^2*f*x^6 + 45*a^4*b^3*x^6*e + 28*a^3*b^4*c*x^3 - 50*a^4*b^3*d*x^3 - 112*a^6*b*f*x^3 + 78*a^5*b^2*x^3*e + 11*a^4*b^3*c - 21*a^5*b^2*d - 50*a^7*f + 34*a^6*b*e)/((b*x^3 + a)^2*b^8) + 1/180*(12*b^12*f*x^15 - 45*a*b^11*f*x^12 + 15*b^12*x^12*e + 20*b^12*d*x^9 + 120*a^2*b^10*f*x^9 - 60*a*b^11*x^9*e + 30*b^12*c*x^6 - 90*a*b^11*d*x^6 - 300*a^3*b^9*f*x^6 + 180*a^2*b^10*x^6*e - 180*a*b^11*c*x^3 + 360*a^2*b^10*d*x^3 + 900*a^4*b^8*f*x^3 - 600*a^3*b^9*x^3*e)/b^15","A",0
277,1,298,0,0.245766," ","integrate(x^11*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{{\left(3 \, a b^{3} c - 6 \, a^{2} b^{2} d - 15 \, a^{4} f + 10 \, a^{3} b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{7}} + \frac{9 \, a b^{5} c x^{6} - 18 \, a^{2} b^{4} d x^{6} - 45 \, a^{4} b^{2} f x^{6} + 30 \, a^{3} b^{3} x^{6} e + 12 \, a^{2} b^{4} c x^{3} - 28 \, a^{3} b^{3} d x^{3} - 78 \, a^{5} b f x^{3} + 50 \, a^{4} b^{2} x^{3} e + 4 \, a^{3} b^{3} c - 11 \, a^{4} b^{2} d - 34 \, a^{6} f + 21 \, a^{5} b e}{6 \, {\left(b x^{3} + a\right)}^{2} b^{7}} + \frac{3 \, b^{9} f x^{12} - 12 \, a b^{8} f x^{9} + 4 \, b^{9} x^{9} e + 6 \, b^{9} d x^{6} + 36 \, a^{2} b^{7} f x^{6} - 18 \, a b^{8} x^{6} e + 12 \, b^{9} c x^{3} - 36 \, a b^{8} d x^{3} - 120 \, a^{3} b^{6} f x^{3} + 72 \, a^{2} b^{7} x^{3} e}{36 \, b^{12}}"," ",0,"-1/3*(3*a*b^3*c - 6*a^2*b^2*d - 15*a^4*f + 10*a^3*b*e)*log(abs(b*x^3 + a))/b^7 + 1/6*(9*a*b^5*c*x^6 - 18*a^2*b^4*d*x^6 - 45*a^4*b^2*f*x^6 + 30*a^3*b^3*x^6*e + 12*a^2*b^4*c*x^3 - 28*a^3*b^3*d*x^3 - 78*a^5*b*f*x^3 + 50*a^4*b^2*x^3*e + 4*a^3*b^3*c - 11*a^4*b^2*d - 34*a^6*f + 21*a^5*b*e)/((b*x^3 + a)^2*b^7) + 1/36*(3*b^9*f*x^12 - 12*a*b^8*f*x^9 + 4*b^9*x^9*e + 6*b^9*d*x^6 + 36*a^2*b^7*f*x^6 - 18*a*b^8*x^6*e + 12*b^9*c*x^3 - 36*a*b^8*d*x^3 - 120*a^3*b^6*f*x^3 + 72*a^2*b^7*x^3*e)/b^12","A",0
278,1,236,0,0.215655," ","integrate(x^8*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{{\left(b^{3} c - 3 \, a b^{2} d - 10 \, a^{3} f + 6 \, a^{2} b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{6}} - \frac{3 \, b^{5} c x^{6} - 9 \, a b^{4} d x^{6} - 30 \, a^{3} b^{2} f x^{6} + 18 \, a^{2} b^{3} x^{6} e + 2 \, a b^{4} c x^{3} - 12 \, a^{2} b^{3} d x^{3} - 50 \, a^{4} b f x^{3} + 28 \, a^{3} b^{2} x^{3} e - 4 \, a^{3} b^{2} d - 21 \, a^{5} f + 11 \, a^{4} b e}{6 \, {\left(b x^{3} + a\right)}^{2} b^{6}} + \frac{2 \, b^{6} f x^{9} - 9 \, a b^{5} f x^{6} + 3 \, b^{6} x^{6} e + 6 \, b^{6} d x^{3} + 36 \, a^{2} b^{4} f x^{3} - 18 \, a b^{5} x^{3} e}{18 \, b^{9}}"," ",0,"1/3*(b^3*c - 3*a*b^2*d - 10*a^3*f + 6*a^2*b*e)*log(abs(b*x^3 + a))/b^6 - 1/6*(3*b^5*c*x^6 - 9*a*b^4*d*x^6 - 30*a^3*b^2*f*x^6 + 18*a^2*b^3*x^6*e + 2*a*b^4*c*x^3 - 12*a^2*b^3*d*x^3 - 50*a^4*b*f*x^3 + 28*a^3*b^2*x^3*e - 4*a^3*b^2*d - 21*a^5*f + 11*a^4*b*e)/((b*x^3 + a)^2*b^6) + 1/18*(2*b^6*f*x^9 - 9*a*b^5*f*x^6 + 3*b^6*x^6*e + 6*b^6*d*x^3 + 36*a^2*b^4*f*x^3 - 18*a*b^5*x^3*e)/b^9","A",0
279,1,146,0,0.184006," ","integrate(x^5*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{{\left(b^{2} d + 6 \, a^{2} f - 3 \, a b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{5}} + \frac{b^{3} f x^{6} - 6 \, a b^{2} f x^{3} + 2 \, b^{3} x^{3} e}{6 \, b^{6}} - \frac{a b^{3} c - 3 \, a^{2} b^{2} d - 7 \, a^{4} f + 5 \, a^{3} b e + 2 \, {\left(b^{4} c - 2 \, a b^{3} d - 4 \, a^{3} b f + 3 \, a^{2} b^{2} e\right)} x^{3}}{6 \, {\left(b x^{3} + a\right)}^{2} b^{5}}"," ",0,"1/3*(b^2*d + 6*a^2*f - 3*a*b*e)*log(abs(b*x^3 + a))/b^5 + 1/6*(b^3*f*x^6 - 6*a*b^2*f*x^3 + 2*b^3*x^3*e)/b^6 - 1/6*(a*b^3*c - 3*a^2*b^2*d - 7*a^4*f + 5*a^3*b*e + 2*(b^4*c - 2*a*b^3*d - 4*a^3*b*f + 3*a^2*b^2*e)*x^3)/((b*x^3 + a)^2*b^5)","A",0
280,1,100,0,0.196395," ","integrate(x^2*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{f x^{3}}{3 \, b^{3}} - \frac{{\left(3 \, a f - b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{4}} - \frac{b^{3} c + a b^{2} d + 5 \, a^{3} f + 2 \, {\left(b^{3} d + 3 \, a^{2} b f - 2 \, a b^{2} e\right)} x^{3} - 3 \, a^{2} b e}{6 \, {\left(b x^{3} + a\right)}^{2} b^{4}}"," ",0,"1/3*f*x^3/b^3 - 1/3*(3*a*f - b*e)*log(abs(b*x^3 + a))/b^4 - 1/6*(b^3*c + a*b^2*d + 5*a^3*f + 2*(b^3*d + 3*a^2*b*f - 2*a*b^2*e)*x^3 - 3*a^2*b*e)/((b*x^3 + a)^2*b^4)","A",0
281,1,128,0,0.240575," ","integrate((f*x^9+e*x^6+d*x^3+c)/x/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{c \log\left({\left| x \right|}\right)}{a^{3}} - \frac{{\left(b^{3} c - a^{3} f\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{3} b^{3}} + \frac{3 \, b^{4} c x^{6} - 3 \, a^{3} b f x^{6} + 8 \, a b^{3} c x^{3} - 2 \, a^{4} f x^{3} - 2 \, a^{3} b x^{3} e + 6 \, a^{2} b^{2} c - a^{3} b d - a^{4} e}{6 \, {\left(b x^{3} + a\right)}^{2} a^{3} b^{2}}"," ",0,"c*log(abs(x))/a^3 - 1/3*(b^3*c - a^3*f)*log(abs(b*x^3 + a))/(a^3*b^3) + 1/6*(3*b^4*c*x^6 - 3*a^3*b*f*x^6 + 8*a*b^3*c*x^3 - 2*a^4*f*x^3 - 2*a^3*b*x^3*e + 6*a^2*b^2*c - a^3*b*d - a^4*e)/((b*x^3 + a)^2*a^3*b^2)","A",0
282,1,173,0,0.182864," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^4/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{{\left(3 \, b c - a d\right)} \log\left({\left| x \right|}\right)}{a^{4}} + \frac{{\left(3 \, b^{2} c - a b d\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{4} b} + \frac{3 \, b c x^{3} - a d x^{3} - a c}{3 \, a^{4} x^{3}} - \frac{9 \, b^{5} c x^{6} - 3 \, a b^{4} d x^{6} + 22 \, a b^{4} c x^{3} - 8 \, a^{2} b^{3} d x^{3} + 2 \, a^{4} b f x^{3} + 14 \, a^{2} b^{3} c - 6 \, a^{3} b^{2} d + a^{5} f + a^{4} b e}{6 \, {\left(b x^{3} + a\right)}^{2} a^{4} b^{2}}"," ",0,"-(3*b*c - a*d)*log(abs(x))/a^4 + 1/3*(3*b^2*c - a*b*d)*log(abs(b*x^3 + a))/(a^4*b) + 1/3*(3*b*c*x^3 - a*d*x^3 - a*c)/(a^4*x^3) - 1/6*(9*b^5*c*x^6 - 3*a*b^4*d*x^6 + 22*a*b^4*c*x^3 - 8*a^2*b^3*d*x^3 + 2*a^4*b*f*x^3 + 14*a^2*b^3*c - 6*a^3*b^2*d + a^5*f + a^4*b*e)/((b*x^3 + a)^2*a^4*b^2)","A",0
283,1,189,0,0.193587," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^7/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{{\left(6 \, b^{2} c - 3 \, a b d + a^{2} e\right)} \log\left({\left| x \right|}\right)}{a^{5}} - \frac{{\left(6 \, b^{3} c - 3 \, a b^{2} d + a^{2} b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{5} b} + \frac{12 \, b^{4} c x^{9} - 6 \, a b^{3} d x^{9} + 2 \, a^{2} b^{2} x^{9} e + 18 \, a b^{3} c x^{6} - 9 \, a^{2} b^{2} d x^{6} - a^{4} f x^{6} + 3 \, a^{3} b x^{6} e + 4 \, a^{2} b^{2} c x^{3} - 2 \, a^{3} b d x^{3} - a^{3} b c}{6 \, {\left(b x^{6} + a x^{3}\right)}^{2} a^{4} b}"," ",0,"(6*b^2*c - 3*a*b*d + a^2*e)*log(abs(x))/a^5 - 1/3*(6*b^3*c - 3*a*b^2*d + a^2*b*e)*log(abs(b*x^3 + a))/(a^5*b) + 1/6*(12*b^4*c*x^9 - 6*a*b^3*d*x^9 + 2*a^2*b^2*x^9*e + 18*a*b^3*c*x^6 - 9*a^2*b^2*d*x^6 - a^4*f*x^6 + 3*a^3*b*x^6*e + 4*a^2*b^2*c*x^3 - 2*a^3*b*d*x^3 - a^3*b*c)/((b*x^6 + a*x^3)^2*a^4*b)","A",0
284,1,324,0,0.188304," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^10/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{{\left(10 \, b^{3} c - 6 \, a b^{2} d - a^{3} f + 3 \, a^{2} b e\right)} \log\left({\left| x \right|}\right)}{a^{6}} + \frac{{\left(10 \, b^{4} c - 6 \, a b^{3} d - a^{3} b f + 3 \, a^{2} b^{2} e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{6} b} - \frac{30 \, b^{5} c x^{6} - 18 \, a b^{4} d x^{6} - 3 \, a^{3} b^{2} f x^{6} + 9 \, a^{2} b^{3} x^{6} e + 68 \, a b^{4} c x^{3} - 42 \, a^{2} b^{3} d x^{3} - 8 \, a^{4} b f x^{3} + 22 \, a^{3} b^{2} x^{3} e + 39 \, a^{2} b^{3} c - 25 \, a^{3} b^{2} d - 6 \, a^{5} f + 14 \, a^{4} b e}{6 \, {\left(b x^{3} + a\right)}^{2} a^{6}} + \frac{110 \, b^{3} c x^{9} - 66 \, a b^{2} d x^{9} - 11 \, a^{3} f x^{9} + 33 \, a^{2} b x^{9} e - 36 \, a b^{2} c x^{6} + 18 \, a^{2} b d x^{6} - 6 \, a^{3} x^{6} e + 9 \, a^{2} b c x^{3} - 3 \, a^{3} d x^{3} - 2 \, a^{3} c}{18 \, a^{6} x^{9}}"," ",0,"-(10*b^3*c - 6*a*b^2*d - a^3*f + 3*a^2*b*e)*log(abs(x))/a^6 + 1/3*(10*b^4*c - 6*a*b^3*d - a^3*b*f + 3*a^2*b^2*e)*log(abs(b*x^3 + a))/(a^6*b) - 1/6*(30*b^5*c*x^6 - 18*a*b^4*d*x^6 - 3*a^3*b^2*f*x^6 + 9*a^2*b^3*x^6*e + 68*a*b^4*c*x^3 - 42*a^2*b^3*d*x^3 - 8*a^4*b*f*x^3 + 22*a^3*b^2*x^3*e + 39*a^2*b^3*c - 25*a^3*b^2*d - 6*a^5*f + 14*a^4*b*e)/((b*x^3 + a)^2*a^6) + 1/18*(110*b^3*c*x^9 - 66*a*b^2*d*x^9 - 11*a^3*f*x^9 + 33*a^2*b*x^9*e - 36*a*b^2*c*x^6 + 18*a^2*b*d*x^6 - 6*a^3*x^6*e + 9*a^2*b*c*x^3 - 3*a^3*d*x^3 - 2*a^3*c)/(a^6*x^9)","A",0
285,1,380,0,0.201241," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^13/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{{\left(15 \, b^{4} c - 10 \, a b^{3} d - 3 \, a^{3} b f + 6 \, a^{2} b^{2} e\right)} \log\left({\left| x \right|}\right)}{a^{7}} - \frac{{\left(15 \, b^{5} c - 10 \, a b^{4} d - 3 \, a^{3} b^{2} f + 6 \, a^{2} b^{3} e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{7} b} + \frac{45 \, b^{6} c x^{6} - 30 \, a b^{5} d x^{6} - 9 \, a^{3} b^{3} f x^{6} + 18 \, a^{2} b^{4} x^{6} e + 100 \, a b^{5} c x^{3} - 68 \, a^{2} b^{4} d x^{3} - 22 \, a^{4} b^{2} f x^{3} + 42 \, a^{3} b^{3} x^{3} e + 56 \, a^{2} b^{4} c - 39 \, a^{3} b^{3} d - 14 \, a^{5} b f + 25 \, a^{4} b^{2} e}{6 \, {\left(b x^{3} + a\right)}^{2} a^{7}} - \frac{375 \, b^{4} c x^{12} - 250 \, a b^{3} d x^{12} - 75 \, a^{3} b f x^{12} + 150 \, a^{2} b^{2} x^{12} e - 120 \, a b^{3} c x^{9} + 72 \, a^{2} b^{2} d x^{9} + 12 \, a^{4} f x^{9} - 36 \, a^{3} b x^{9} e + 36 \, a^{2} b^{2} c x^{6} - 18 \, a^{3} b d x^{6} + 6 \, a^{4} x^{6} e - 12 \, a^{3} b c x^{3} + 4 \, a^{4} d x^{3} + 3 \, a^{4} c}{36 \, a^{7} x^{12}}"," ",0,"(15*b^4*c - 10*a*b^3*d - 3*a^3*b*f + 6*a^2*b^2*e)*log(abs(x))/a^7 - 1/3*(15*b^5*c - 10*a*b^4*d - 3*a^3*b^2*f + 6*a^2*b^3*e)*log(abs(b*x^3 + a))/(a^7*b) + 1/6*(45*b^6*c*x^6 - 30*a*b^5*d*x^6 - 9*a^3*b^3*f*x^6 + 18*a^2*b^4*x^6*e + 100*a*b^5*c*x^3 - 68*a^2*b^4*d*x^3 - 22*a^4*b^2*f*x^3 + 42*a^3*b^3*x^3*e + 56*a^2*b^4*c - 39*a^3*b^3*d - 14*a^5*b*f + 25*a^4*b^2*e)/((b*x^3 + a)^2*a^7) - 1/36*(375*b^4*c*x^12 - 250*a*b^3*d*x^12 - 75*a^3*b*f*x^12 + 150*a^2*b^2*x^12*e - 120*a*b^3*c*x^9 + 72*a^2*b^2*d*x^9 + 12*a^4*f*x^9 - 36*a^3*b*x^9*e + 36*a^2*b^2*c*x^6 - 18*a^3*b*d*x^6 + 6*a^4*x^6*e - 12*a^3*b*c*x^3 + 4*a^4*d*x^3 + 3*a^4*c)/(a^7*x^12)","A",0
286,1,500,0,0.202568," ","integrate(x^12*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{\sqrt{3} {\left(35 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{3} c - 65 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b^{2} d - 152 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{4} f + 104 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, b^{8}} - \frac{{\left(35 \, a^{2} b^{3} c - 65 \, a^{3} b^{2} d - 152 \, a^{5} f + 104 \, a^{4} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a b^{7}} + \frac{{\left(35 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{3} c - 65 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b^{2} d - 152 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{4} f + 104 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, b^{8}} - \frac{19 \, a^{2} b^{4} c x^{4} - 25 \, a^{3} b^{3} d x^{4} - 37 \, a^{5} b f x^{4} + 31 \, a^{4} b^{2} x^{4} e + 16 \, a^{3} b^{3} c x - 22 \, a^{4} b^{2} d x - 34 \, a^{6} f x + 28 \, a^{5} b x e}{18 \, {\left(b x^{3} + a\right)}^{2} b^{7}} + \frac{140 \, b^{36} f x^{13} - 546 \, a b^{35} f x^{10} + 182 \, b^{36} x^{10} e + 260 \, b^{36} d x^{7} + 1560 \, a^{2} b^{34} f x^{7} - 780 \, a b^{35} x^{7} e + 455 \, b^{36} c x^{4} - 1365 \, a b^{35} d x^{4} - 4550 \, a^{3} b^{33} f x^{4} + 2730 \, a^{2} b^{34} x^{4} e - 5460 \, a b^{35} c x + 10920 \, a^{2} b^{34} d x + 27300 \, a^{4} b^{32} f x - 18200 \, a^{3} b^{33} x e}{1820 \, b^{39}}"," ",0,"1/27*sqrt(3)*(35*(-a*b^2)^(1/3)*a*b^3*c - 65*(-a*b^2)^(1/3)*a^2*b^2*d - 152*(-a*b^2)^(1/3)*a^4*f + 104*(-a*b^2)^(1/3)*a^3*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^8 - 1/27*(35*a^2*b^3*c - 65*a^3*b^2*d - 152*a^5*f + 104*a^4*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^7) + 1/54*(35*(-a*b^2)^(1/3)*a*b^3*c - 65*(-a*b^2)^(1/3)*a^2*b^2*d - 152*(-a*b^2)^(1/3)*a^4*f + 104*(-a*b^2)^(1/3)*a^3*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^8 - 1/18*(19*a^2*b^4*c*x^4 - 25*a^3*b^3*d*x^4 - 37*a^5*b*f*x^4 + 31*a^4*b^2*x^4*e + 16*a^3*b^3*c*x - 22*a^4*b^2*d*x - 34*a^6*f*x + 28*a^5*b*x*e)/((b*x^3 + a)^2*b^7) + 1/1820*(140*b^36*f*x^13 - 546*a*b^35*f*x^10 + 182*b^36*x^10*e + 260*b^36*d*x^7 + 1560*a^2*b^34*f*x^7 - 780*a*b^35*x^7*e + 455*b^36*c*x^4 - 1365*a*b^35*d*x^4 - 4550*a^3*b^33*f*x^4 + 2730*a^2*b^34*x^4*e - 5460*a*b^35*c*x + 10920*a^2*b^34*d*x + 27300*a^4*b^32*f*x - 18200*a^3*b^33*x*e)/b^39","A",0
287,1,491,0,0.202296," ","integrate(x^10*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{{\left(20 \, a b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 44 \, a^{2} b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 119 \, a^{4} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 77 \, a^{3} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a b^{6}} + \frac{\sqrt{3} {\left(20 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - 44 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - 119 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + 77 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, b^{8}} - \frac{{\left(20 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - 44 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - 119 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + 77 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, b^{8}} + \frac{14 \, a b^{4} c x^{5} - 20 \, a^{2} b^{3} d x^{5} - 32 \, a^{4} b f x^{5} + 26 \, a^{3} b^{2} x^{5} e + 11 \, a^{2} b^{3} c x^{2} - 17 \, a^{3} b^{2} d x^{2} - 29 \, a^{5} f x^{2} + 23 \, a^{4} b x^{2} e}{18 \, {\left(b x^{3} + a\right)}^{2} b^{6}} + \frac{40 \, b^{30} f x^{11} - 165 \, a b^{29} f x^{8} + 55 \, b^{30} x^{8} e + 88 \, b^{30} d x^{5} + 528 \, a^{2} b^{28} f x^{5} - 264 \, a b^{29} x^{5} e + 220 \, b^{30} c x^{2} - 660 \, a b^{29} d x^{2} - 2200 \, a^{3} b^{27} f x^{2} + 1320 \, a^{2} b^{28} x^{2} e}{440 \, b^{33}}"," ",0,"1/27*(20*a*b^3*c*(-a/b)^(1/3) - 44*a^2*b^2*d*(-a/b)^(1/3) - 119*a^4*f*(-a/b)^(1/3) + 77*a^3*b*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^6) + 1/27*sqrt(3)*(20*(-a*b^2)^(2/3)*b^3*c - 44*(-a*b^2)^(2/3)*a*b^2*d - 119*(-a*b^2)^(2/3)*a^3*f + 77*(-a*b^2)^(2/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^8 - 1/54*(20*(-a*b^2)^(2/3)*b^3*c - 44*(-a*b^2)^(2/3)*a*b^2*d - 119*(-a*b^2)^(2/3)*a^3*f + 77*(-a*b^2)^(2/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^8 + 1/18*(14*a*b^4*c*x^5 - 20*a^2*b^3*d*x^5 - 32*a^4*b*f*x^5 + 26*a^3*b^2*x^5*e + 11*a^2*b^3*c*x^2 - 17*a^3*b^2*d*x^2 - 29*a^5*f*x^2 + 23*a^4*b*x^2*e)/((b*x^3 + a)^2*b^6) + 1/440*(40*b^30*f*x^11 - 165*a*b^29*f*x^8 + 55*b^30*x^8*e + 88*b^30*d*x^5 + 528*a^2*b^28*f*x^5 - 264*a*b^29*x^5*e + 220*b^30*c*x^2 - 660*a*b^29*d*x^2 - 2200*a^3*b^27*f*x^2 + 1320*a^2*b^28*x^2*e)/b^33","A",0
288,1,443,0,0.196816," ","integrate(x^9*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(14 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - 35 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - 104 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + 65 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, b^{7}} + \frac{{\left(14 \, a b^{3} c - 35 \, a^{2} b^{2} d - 104 \, a^{4} f + 65 \, a^{3} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a b^{6}} - \frac{{\left(14 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - 35 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - 104 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + 65 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, b^{7}} + \frac{13 \, a b^{4} c x^{4} - 19 \, a^{2} b^{3} d x^{4} - 31 \, a^{4} b f x^{4} + 25 \, a^{3} b^{2} x^{4} e + 10 \, a^{2} b^{3} c x - 16 \, a^{3} b^{2} d x - 28 \, a^{5} f x + 22 \, a^{4} b x e}{18 \, {\left(b x^{3} + a\right)}^{2} b^{6}} + \frac{14 \, b^{27} f x^{10} - 60 \, a b^{26} f x^{7} + 20 \, b^{27} x^{7} e + 35 \, b^{27} d x^{4} + 210 \, a^{2} b^{25} f x^{4} - 105 \, a b^{26} x^{4} e + 140 \, b^{27} c x - 420 \, a b^{26} d x - 1400 \, a^{3} b^{24} f x + 840 \, a^{2} b^{25} x e}{140 \, b^{30}}"," ",0,"-1/27*sqrt(3)*(14*(-a*b^2)^(1/3)*b^3*c - 35*(-a*b^2)^(1/3)*a*b^2*d - 104*(-a*b^2)^(1/3)*a^3*f + 65*(-a*b^2)^(1/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^7 + 1/27*(14*a*b^3*c - 35*a^2*b^2*d - 104*a^4*f + 65*a^3*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^6) - 1/54*(14*(-a*b^2)^(1/3)*b^3*c - 35*(-a*b^2)^(1/3)*a*b^2*d - 104*(-a*b^2)^(1/3)*a^3*f + 65*(-a*b^2)^(1/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^7 + 1/18*(13*a*b^4*c*x^4 - 19*a^2*b^3*d*x^4 - 31*a^4*b*f*x^4 + 25*a^3*b^2*x^4*e + 10*a^2*b^3*c*x - 16*a^3*b^2*d*x - 28*a^5*f*x + 22*a^4*b*x*e)/((b*x^3 + a)^2*b^6) + 1/140*(14*b^27*f*x^10 - 60*a*b^26*f*x^7 + 20*b^27*x^7*e + 35*b^27*d*x^4 + 210*a^2*b^25*f*x^4 - 105*a*b^26*x^4*e + 140*b^27*c*x - 420*a*b^26*d*x - 1400*a^3*b^24*f*x + 840*a^2*b^25*x*e)/b^30","A",0
289,1,391,0,0.203313," ","integrate(x^7*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{\sqrt{3} {\left(5 \, b^{3} c - 20 \, a b^{2} d - 77 \, a^{3} f + 44 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{5}} - \frac{{\left(5 \, b^{3} c - 20 \, a b^{2} d - 77 \, a^{3} f + 44 \, a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{5}} - \frac{{\left(5 \, b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 20 \, a b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 77 \, a^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 44 \, a^{2} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a b^{5}} - \frac{8 \, b^{4} c x^{5} - 14 \, a b^{3} d x^{5} - 26 \, a^{3} b f x^{5} + 20 \, a^{2} b^{2} x^{5} e + 5 \, a b^{3} c x^{2} - 11 \, a^{2} b^{2} d x^{2} - 23 \, a^{4} f x^{2} + 17 \, a^{3} b x^{2} e}{18 \, {\left(b x^{3} + a\right)}^{2} b^{5}} + \frac{5 \, b^{21} f x^{8} - 24 \, a b^{20} f x^{5} + 8 \, b^{21} x^{5} e + 20 \, b^{21} d x^{2} + 120 \, a^{2} b^{19} f x^{2} - 60 \, a b^{20} x^{2} e}{40 \, b^{24}}"," ",0,"1/27*sqrt(3)*(5*b^3*c - 20*a*b^2*d - 77*a^3*f + 44*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(1/3)*b^5) - 1/54*(5*b^3*c - 20*a*b^2*d - 77*a^3*f + 44*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(1/3)*b^5) - 1/27*(5*b^3*c*(-a/b)^(1/3) - 20*a*b^2*d*(-a/b)^(1/3) - 77*a^3*f*(-a/b)^(1/3) + 44*a^2*b*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^5) - 1/18*(8*b^4*c*x^5 - 14*a*b^3*d*x^5 - 26*a^3*b*f*x^5 + 20*a^2*b^2*x^5*e + 5*a*b^3*c*x^2 - 11*a^2*b^2*d*x^2 - 23*a^4*f*x^2 + 17*a^3*b*x^2*e)/((b*x^3 + a)^2*b^5) + 1/40*(5*b^21*f*x^8 - 24*a*b^20*f*x^5 + 8*b^21*x^5*e + 20*b^21*d*x^2 + 120*a^2*b^19*f*x^2 - 60*a*b^20*x^2*e)/b^24","A",0
290,1,345,0,0.197393," ","integrate(x^6*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(2 \, b^{3} c - 14 \, a b^{2} d - 65 \, a^{3} f + 35 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{4}} - \frac{{\left(2 \, b^{3} c - 14 \, a b^{2} d - 65 \, a^{3} f + 35 \, a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{4}} - \frac{{\left(2 \, b^{3} c - 14 \, a b^{2} d - 65 \, a^{3} f + 35 \, a^{2} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a b^{5}} - \frac{7 \, b^{4} c x^{4} - 13 \, a b^{3} d x^{4} - 25 \, a^{3} b f x^{4} + 19 \, a^{2} b^{2} x^{4} e + 4 \, a b^{3} c x - 10 \, a^{2} b^{2} d x - 22 \, a^{4} f x + 16 \, a^{3} b x e}{18 \, {\left(b x^{3} + a\right)}^{2} b^{5}} + \frac{4 \, b^{18} f x^{7} - 21 \, a b^{17} f x^{4} + 7 \, b^{18} x^{4} e + 28 \, b^{18} d x + 168 \, a^{2} b^{16} f x - 84 \, a b^{17} x e}{28 \, b^{21}}"," ",0,"-1/27*sqrt(3)*(2*b^3*c - 14*a*b^2*d - 65*a^3*f + 35*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*b^4) - 1/54*(2*b^3*c - 14*a*b^2*d - 65*a^3*f + 35*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*b^4) - 1/27*(2*b^3*c - 14*a*b^2*d - 65*a^3*f + 35*a^2*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^5) - 1/18*(7*b^4*c*x^4 - 13*a*b^3*d*x^4 - 25*a^3*b*f*x^4 + 19*a^2*b^2*x^4*e + 4*a*b^3*c*x - 10*a^2*b^2*d*x - 22*a^4*f*x + 16*a^3*b*x*e)/((b*x^3 + a)^2*b^5) + 1/28*(4*b^18*f*x^7 - 21*a*b^17*f*x^4 + 7*b^18*x^4*e + 28*b^18*d*x + 168*a^2*b^16*f*x - 84*a*b^17*x*e)/b^21","A",0
291,1,365,0,0.200572," ","integrate(x^4*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{\sqrt{3} {\left(b^{3} c + 5 \, a b^{2} d + 44 \, a^{3} f - 20 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{4}} - \frac{{\left(b^{3} c + 5 \, a b^{2} d + 44 \, a^{3} f - 20 \, a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{4}} - \frac{{\left(b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 44 \, a^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 20 \, a^{2} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{2} b^{4}} + \frac{2 \, b^{4} c x^{5} - 8 \, a b^{3} d x^{5} - 20 \, a^{3} b f x^{5} + 14 \, a^{2} b^{2} x^{5} e - a b^{3} c x^{2} - 5 \, a^{2} b^{2} d x^{2} - 17 \, a^{4} f x^{2} + 11 \, a^{3} b x^{2} e}{18 \, {\left(b x^{3} + a\right)}^{2} a b^{4}} + \frac{2 \, b^{12} f x^{5} - 15 \, a b^{11} f x^{2} + 5 \, b^{12} x^{2} e}{10 \, b^{15}}"," ",0,"1/27*sqrt(3)*(b^3*c + 5*a*b^2*d + 44*a^3*f - 20*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(1/3)*a*b^4) - 1/54*(b^3*c + 5*a*b^2*d + 44*a^3*f - 20*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(1/3)*a*b^4) - 1/27*(b^3*c*(-a/b)^(1/3) + 5*a*b^2*d*(-a/b)^(1/3) + 44*a^3*f*(-a/b)^(1/3) - 20*a^2*b*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b^4) + 1/18*(2*b^4*c*x^5 - 8*a*b^3*d*x^5 - 20*a^3*b*f*x^5 + 14*a^2*b^2*x^5*e - a*b^3*c*x^2 - 5*a^2*b^2*d*x^2 - 17*a^4*f*x^2 + 11*a^3*b*x^2*e)/((b*x^3 + a)^2*a*b^4) + 1/10*(2*b^12*f*x^5 - 15*a*b^11*f*x^2 + 5*b^12*x^2*e)/b^15","A",0
292,1,319,0,0.216199," ","integrate(x^3*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b^{3} c + 2 \, a b^{2} d + 35 \, a^{3} f - 14 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{3}} - \frac{{\left(b^{3} c + 2 \, a b^{2} d + 35 \, a^{3} f - 14 \, a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{3}} - \frac{{\left(b^{3} c + 2 \, a b^{2} d + 35 \, a^{3} f - 14 \, a^{2} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{2} b^{4}} + \frac{b^{4} c x^{4} - 7 \, a b^{3} d x^{4} - 19 \, a^{3} b f x^{4} + 13 \, a^{2} b^{2} x^{4} e - 2 \, a b^{3} c x - 4 \, a^{2} b^{2} d x - 16 \, a^{4} f x + 10 \, a^{3} b x e}{18 \, {\left(b x^{3} + a\right)}^{2} a b^{4}} + \frac{b^{9} f x^{4} - 12 \, a b^{8} f x + 4 \, b^{9} x e}{4 \, b^{12}}"," ",0,"-1/27*sqrt(3)*(b^3*c + 2*a*b^2*d + 35*a^3*f - 14*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a*b^3) - 1/54*(b^3*c + 2*a*b^2*d + 35*a^3*f - 14*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a*b^3) - 1/27*(b^3*c + 2*a*b^2*d + 35*a^3*f - 14*a^2*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b^4) + 1/18*(b^4*c*x^4 - 7*a*b^3*d*x^4 - 19*a^3*b*f*x^4 + 13*a^2*b^2*x^4*e - 2*a*b^3*c*x - 4*a^2*b^2*d*x - 16*a^4*f*x + 10*a^3*b*x*e)/((b*x^3 + a)^2*a*b^4) + 1/4*(b^9*f*x^4 - 12*a*b^8*f*x + 4*b^9*x*e)/b^12","A",0
293,1,339,0,0.206064," ","integrate(x*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{f x^{2}}{2 \, b^{3}} + \frac{\sqrt{3} {\left(2 \, b^{3} c + a b^{2} d - 20 \, a^{3} f + 5 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b^{3}} - \frac{{\left(2 \, b^{3} c + a b^{2} d - 20 \, a^{3} f + 5 \, a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b^{3}} - \frac{{\left(2 \, b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 20 \, a^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a^{2} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{3} b^{3}} + \frac{4 \, b^{4} c x^{5} + 2 \, a b^{3} d x^{5} + 14 \, a^{3} b f x^{5} - 8 \, a^{2} b^{2} x^{5} e + 7 \, a b^{3} c x^{2} - a^{2} b^{2} d x^{2} + 11 \, a^{4} f x^{2} - 5 \, a^{3} b x^{2} e}{18 \, {\left(b x^{3} + a\right)}^{2} a^{2} b^{3}}"," ",0,"1/2*f*x^2/b^3 + 1/27*sqrt(3)*(2*b^3*c + a*b^2*d - 20*a^3*f + 5*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(1/3)*a^2*b^3) - 1/54*(2*b^3*c + a*b^2*d - 20*a^3*f + 5*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(1/3)*a^2*b^3) - 1/27*(2*b^3*c*(-a/b)^(1/3) + a*b^2*d*(-a/b)^(1/3) - 20*a^3*f*(-a/b)^(1/3) + 5*a^2*b*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b^3) + 1/18*(4*b^4*c*x^5 + 2*a*b^3*d*x^5 + 14*a^3*b*f*x^5 - 8*a^2*b^2*x^5*e + 7*a*b^3*c*x^2 - a^2*b^2*d*x^2 + 11*a^4*f*x^2 - 5*a^3*b*x^2*e)/((b*x^3 + a)^2*a^2*b^3)","A",0
294,1,295,0,0.197758," ","integrate((f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{f x}{b^{3}} - \frac{\sqrt{3} {\left(5 \, b^{3} c + a b^{2} d - 14 \, a^{3} f + 2 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b^{2}} - \frac{{\left(5 \, b^{3} c + a b^{2} d - 14 \, a^{3} f + 2 \, a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b^{2}} - \frac{{\left(5 \, b^{3} c + a b^{2} d - 14 \, a^{3} f + 2 \, a^{2} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{3} b^{3}} + \frac{5 \, b^{4} c x^{4} + a b^{3} d x^{4} + 13 \, a^{3} b f x^{4} - 7 \, a^{2} b^{2} x^{4} e + 8 \, a b^{3} c x - 2 \, a^{2} b^{2} d x + 10 \, a^{4} f x - 4 \, a^{3} b x e}{18 \, {\left(b x^{3} + a\right)}^{2} a^{2} b^{3}}"," ",0,"f*x/b^3 - 1/27*sqrt(3)*(5*b^3*c + a*b^2*d - 14*a^3*f + 2*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^2*b^2) - 1/54*(5*b^3*c + a*b^2*d - 14*a^3*f + 2*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^2*b^2) - 1/27*(5*b^3*c + a*b^2*d - 14*a^3*f + 2*a^2*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b^3) + 1/18*(5*b^4*c*x^4 + a*b^3*d*x^4 + 13*a^3*b*f*x^4 - 7*a^2*b^2*x^4*e + 8*a*b^3*c*x - 2*a^2*b^2*d*x + 10*a^4*f*x - 4*a^3*b*x*e)/((b*x^3 + a)^2*a^2*b^3)","A",0
295,1,341,0,0.209542," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^2/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(14 \, b^{3} c - 2 \, a b^{2} d - 5 \, a^{3} f - a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} b^{2}} - \frac{c}{a^{3} x} + \frac{{\left(14 \, b^{3} c - 2 \, a b^{2} d - 5 \, a^{3} f - a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} b^{2}} + \frac{{\left(14 \, b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{4} b^{2}} - \frac{10 \, b^{4} c x^{5} - 4 \, a b^{3} d x^{5} + 8 \, a^{3} b f x^{5} - 2 \, a^{2} b^{2} x^{5} e + 13 \, a b^{3} c x^{2} - 7 \, a^{2} b^{2} d x^{2} + 5 \, a^{4} f x^{2} + a^{3} b x^{2} e}{18 \, {\left(b x^{3} + a\right)}^{2} a^{3} b^{2}}"," ",0,"-1/27*sqrt(3)*(14*b^3*c - 2*a*b^2*d - 5*a^3*f - a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(1/3)*a^3*b^2) - c/(a^3*x) + 1/54*(14*b^3*c - 2*a*b^2*d - 5*a^3*f - a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(1/3)*a^3*b^2) + 1/27*(14*b^3*c*(-a/b)^(1/3) - 2*a*b^2*d*(-a/b)^(1/3) - 5*a^3*f*(-a/b)^(1/3) - a^2*b*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^4*b^2) - 1/18*(10*b^4*c*x^5 - 4*a*b^3*d*x^5 + 8*a^3*b*f*x^5 - 2*a^2*b^2*x^5*e + 13*a*b^3*c*x^2 - 7*a^2*b^2*d*x^2 + 5*a^4*f*x^2 + a^3*b*x^2*e)/((b*x^3 + a)^2*a^3*b^2)","A",0
296,1,312,0,0.214653," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^3/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{\sqrt{3} {\left(20 \, b^{3} c - 5 \, a b^{2} d - 2 \, a^{3} f - a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} b} + \frac{{\left(20 \, b^{3} c - 5 \, a b^{2} d - 2 \, a^{3} f - a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} b} + \frac{{\left(20 \, b^{3} c - 5 \, a b^{2} d - 2 \, a^{3} f - a^{2} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{4} b^{2}} - \frac{20 \, b^{4} c x^{6} - 5 \, a b^{3} d x^{6} + 7 \, a^{3} b f x^{6} - a^{2} b^{2} x^{6} e + 32 \, a b^{3} c x^{3} - 8 \, a^{2} b^{2} d x^{3} + 4 \, a^{4} f x^{3} + 2 \, a^{3} b x^{3} e + 9 \, a^{2} b^{2} c}{18 \, {\left(b x^{4} + a x\right)}^{2} a^{3} b^{2}}"," ",0,"1/27*sqrt(3)*(20*b^3*c - 5*a*b^2*d - 2*a^3*f - a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^3*b) + 1/54*(20*b^3*c - 5*a*b^2*d - 2*a^3*f - a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^3*b) + 1/27*(20*b^3*c - 5*a*b^2*d - 2*a^3*f - a^2*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^4*b^2) - 1/18*(20*b^4*c*x^6 - 5*a*b^3*d*x^6 + 7*a^3*b*f*x^6 - a^2*b^2*x^6*e + 32*a*b^3*c*x^3 - 8*a^2*b^2*d*x^3 + 4*a^4*f*x^3 + 2*a^3*b*x^3*e + 9*a^2*b^2*c)/((b*x^4 + a*x)^2*a^3*b^2)","A",0
297,1,357,0,0.243690," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^5/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{\sqrt{3} {\left(35 \, b^{3} c - 14 \, a b^{2} d + a^{3} f + 2 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{4} b} - \frac{{\left(35 \, b^{3} c - 14 \, a b^{2} d + a^{3} f + 2 \, a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{4} b} - \frac{{\left(35 \, b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 14 \, a b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a^{2} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{5} b} + \frac{16 \, b^{4} c x^{5} - 10 \, a b^{3} d x^{5} + 2 \, a^{3} b f x^{5} + 4 \, a^{2} b^{2} x^{5} e + 19 \, a b^{3} c x^{2} - 13 \, a^{2} b^{2} d x^{2} - a^{4} f x^{2} + 7 \, a^{3} b x^{2} e}{18 \, {\left(b x^{3} + a\right)}^{2} a^{4} b} + \frac{12 \, b c x^{3} - 4 \, a d x^{3} - a c}{4 \, a^{4} x^{4}}"," ",0,"1/27*sqrt(3)*(35*b^3*c - 14*a*b^2*d + a^3*f + 2*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(1/3)*a^4*b) - 1/54*(35*b^3*c - 14*a*b^2*d + a^3*f + 2*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(1/3)*a^4*b) - 1/27*(35*b^3*c*(-a/b)^(1/3) - 14*a*b^2*d*(-a/b)^(1/3) + a^3*f*(-a/b)^(1/3) + 2*a^2*b*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^5*b) + 1/18*(16*b^4*c*x^5 - 10*a*b^3*d*x^5 + 2*a^3*b*f*x^5 + 4*a^2*b^2*x^5*e + 19*a*b^3*c*x^2 - 13*a^2*b^2*d*x^2 - a^4*f*x^2 + 7*a^3*b*x^2*e)/((b*x^3 + a)^2*a^4*b) + 1/4*(12*b*c*x^3 - 4*a*d*x^3 - a*c)/(a^4*x^4)","A",0
298,1,310,0,0.230514," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^6/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(44 \, b^{3} c - 20 \, a b^{2} d + a^{3} f + 5 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{4}} - \frac{{\left(44 \, b^{3} c - 20 \, a b^{2} d + a^{3} f + 5 \, a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{4}} - \frac{{\left(44 \, b^{3} c - 20 \, a b^{2} d + a^{3} f + 5 \, a^{2} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{5} b} + \frac{17 \, b^{4} c x^{4} - 11 \, a b^{3} d x^{4} + a^{3} b f x^{4} + 5 \, a^{2} b^{2} x^{4} e + 20 \, a b^{3} c x - 14 \, a^{2} b^{2} d x - 2 \, a^{4} f x + 8 \, a^{3} b x e}{18 \, {\left(b x^{3} + a\right)}^{2} a^{4} b} + \frac{15 \, b c x^{3} - 5 \, a d x^{3} - 2 \, a c}{10 \, a^{4} x^{5}}"," ",0,"-1/27*sqrt(3)*(44*b^3*c - 20*a*b^2*d + a^3*f + 5*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^4) - 1/54*(44*b^3*c - 20*a*b^2*d + a^3*f + 5*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^4) - 1/27*(44*b^3*c - 20*a*b^2*d + a^3*f + 5*a^2*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^5*b) + 1/18*(17*b^4*c*x^4 - 11*a*b^3*d*x^4 + a^3*b*f*x^4 + 5*a^2*b^2*x^4*e + 20*a*b^3*c*x - 14*a^2*b^2*d*x - 2*a^4*f*x + 8*a^3*b*x*e)/((b*x^3 + a)^2*a^4*b) + 1/10*(15*b*c*x^3 - 5*a*d*x^3 - 2*a*c)/(a^4*x^5)","A",0
299,1,380,0,0.314921," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^8/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(65 \, b^{3} c - 35 \, a b^{2} d - 2 \, a^{3} f + 14 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{5}} + \frac{{\left(65 \, b^{3} c - 35 \, a b^{2} d - 2 \, a^{3} f + 14 \, a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{5}} + \frac{{\left(65 \, b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 35 \, a b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 14 \, a^{2} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{6}} - \frac{22 \, b^{4} c x^{5} - 16 \, a b^{3} d x^{5} - 4 \, a^{3} b f x^{5} + 10 \, a^{2} b^{2} x^{5} e + 25 \, a b^{3} c x^{2} - 19 \, a^{2} b^{2} d x^{2} - 7 \, a^{4} f x^{2} + 13 \, a^{3} b x^{2} e}{18 \, {\left(b x^{3} + a\right)}^{2} a^{5}} - \frac{168 \, b^{2} c x^{6} - 84 \, a b d x^{6} + 28 \, a^{2} x^{6} e - 21 \, a b c x^{3} + 7 \, a^{2} d x^{3} + 4 \, a^{2} c}{28 \, a^{5} x^{7}}"," ",0,"-1/27*sqrt(3)*(65*b^3*c - 35*a*b^2*d - 2*a^3*f + 14*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(1/3)*a^5) + 1/54*(65*b^3*c - 35*a*b^2*d - 2*a^3*f + 14*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(1/3)*a^5) + 1/27*(65*b^3*c*(-a/b)^(1/3) - 35*a*b^2*d*(-a/b)^(1/3) - 2*a^3*f*(-a/b)^(1/3) + 14*a^2*b*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^6 - 1/18*(22*b^4*c*x^5 - 16*a*b^3*d*x^5 - 4*a^3*b*f*x^5 + 10*a^2*b^2*x^5*e + 25*a*b^3*c*x^2 - 19*a^2*b^2*d*x^2 - 7*a^4*f*x^2 + 13*a^3*b*x^2*e)/((b*x^3 + a)^2*a^5) - 1/28*(168*b^2*c*x^6 - 84*a*b*d*x^6 + 28*a^2*x^6*e - 21*a*b*c*x^3 + 7*a^2*d*x^3 + 4*a^2*c)/(a^5*x^7)","A",0
300,1,394,0,0.231572," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^9/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{{\left(77 \, b^{3} c - 44 \, a b^{2} d - 5 \, a^{3} f + 20 \, a^{2} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{6}} - \frac{\sqrt{3} {\left(77 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - 44 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + 20 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, a^{6} b} - \frac{{\left(77 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - 44 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + 20 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, a^{6} b} - \frac{23 \, b^{4} c x^{4} - 17 \, a b^{3} d x^{4} - 5 \, a^{3} b f x^{4} + 11 \, a^{2} b^{2} x^{4} e + 26 \, a b^{3} c x - 20 \, a^{2} b^{2} d x - 8 \, a^{4} f x + 14 \, a^{3} b x e}{18 \, {\left(b x^{3} + a\right)}^{2} a^{5}} - \frac{120 \, b^{2} c x^{6} - 60 \, a b d x^{6} + 20 \, a^{2} x^{6} e - 24 \, a b c x^{3} + 8 \, a^{2} d x^{3} + 5 \, a^{2} c}{40 \, a^{5} x^{8}}"," ",0,"1/27*(77*b^3*c - 44*a*b^2*d - 5*a^3*f + 20*a^2*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^6 - 1/27*sqrt(3)*(77*(-a*b^2)^(1/3)*b^3*c - 44*(-a*b^2)^(1/3)*a*b^2*d - 5*(-a*b^2)^(1/3)*a^3*f + 20*(-a*b^2)^(1/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^6*b) - 1/54*(77*(-a*b^2)^(1/3)*b^3*c - 44*(-a*b^2)^(1/3)*a*b^2*d - 5*(-a*b^2)^(1/3)*a^3*f + 20*(-a*b^2)^(1/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^6*b) - 1/18*(23*b^4*c*x^4 - 17*a*b^3*d*x^4 - 5*a^3*b*f*x^4 + 11*a^2*b^2*x^4*e + 26*a*b^3*c*x - 20*a^2*b^2*d*x - 8*a^4*f*x + 14*a^3*b*x*e)/((b*x^3 + a)^2*a^5) - 1/40*(120*b^2*c*x^6 - 60*a*b*d*x^6 + 20*a^2*x^6*e - 24*a*b*c*x^3 + 8*a^2*d*x^3 + 5*a^2*c)/(a^5*x^8)","A",0
301,1,486,0,0.202270," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^11/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{{\left(104 \, b^{4} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 65 \, a b^{3} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 14 \, a^{3} b f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 35 \, a^{2} b^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{7}} - \frac{\sqrt{3} {\left(104 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - 65 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - 14 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + 35 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, a^{7} b} + \frac{{\left(104 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - 65 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - 14 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + 35 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, a^{7} b} + \frac{28 \, b^{5} c x^{5} - 22 \, a b^{4} d x^{5} - 10 \, a^{3} b^{2} f x^{5} + 16 \, a^{2} b^{3} x^{5} e + 31 \, a b^{4} c x^{2} - 25 \, a^{2} b^{3} d x^{2} - 13 \, a^{4} b f x^{2} + 19 \, a^{3} b^{2} x^{2} e}{18 \, {\left(b x^{3} + a\right)}^{2} a^{6}} + \frac{1400 \, b^{3} c x^{9} - 840 \, a b^{2} d x^{9} - 140 \, a^{3} f x^{9} + 420 \, a^{2} b x^{9} e - 210 \, a b^{2} c x^{6} + 105 \, a^{2} b d x^{6} - 35 \, a^{3} x^{6} e + 60 \, a^{2} b c x^{3} - 20 \, a^{3} d x^{3} - 14 \, a^{3} c}{140 \, a^{6} x^{10}}"," ",0,"-1/27*(104*b^4*c*(-a/b)^(1/3) - 65*a*b^3*d*(-a/b)^(1/3) - 14*a^3*b*f*(-a/b)^(1/3) + 35*a^2*b^2*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^7 - 1/27*sqrt(3)*(104*(-a*b^2)^(2/3)*b^3*c - 65*(-a*b^2)^(2/3)*a*b^2*d - 14*(-a*b^2)^(2/3)*a^3*f + 35*(-a*b^2)^(2/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^7*b) + 1/54*(104*(-a*b^2)^(2/3)*b^3*c - 65*(-a*b^2)^(2/3)*a*b^2*d - 14*(-a*b^2)^(2/3)*a^3*f + 35*(-a*b^2)^(2/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^7*b) + 1/18*(28*b^5*c*x^5 - 22*a*b^4*d*x^5 - 10*a^3*b^2*f*x^5 + 16*a^2*b^3*x^5*e + 31*a*b^4*c*x^2 - 25*a^2*b^3*d*x^2 - 13*a^4*b*f*x^2 + 19*a^3*b^2*x^2*e)/((b*x^3 + a)^2*a^6) + 1/140*(1400*b^3*c*x^9 - 840*a*b^2*d*x^9 - 140*a^3*f*x^9 + 420*a^2*b*x^9*e - 210*a*b^2*c*x^6 + 105*a^2*b*d*x^6 - 35*a^3*x^6*e + 60*a^2*b*c*x^3 - 20*a^3*d*x^3 - 14*a^3*c)/(a^6*x^10)","A",0
302,1,440,0,0.350055," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^12/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{\sqrt{3} {\left(119 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - 77 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - 20 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + 44 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, a^{7}} - \frac{{\left(119 \, b^{4} c - 77 \, a b^{3} d - 20 \, a^{3} b f + 44 \, a^{2} b^{2} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{7}} + \frac{{\left(119 \, \left(-a b^{2}\right)^{\frac{1}{3}} b^{3} c - 77 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b^{2} d - 20 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{3} f + 44 \, \left(-a b^{2}\right)^{\frac{1}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, a^{7}} + \frac{29 \, b^{5} c x^{4} - 23 \, a b^{4} d x^{4} - 11 \, a^{3} b^{2} f x^{4} + 17 \, a^{2} b^{3} x^{4} e + 32 \, a b^{4} c x - 26 \, a^{2} b^{3} d x - 14 \, a^{4} b f x + 20 \, a^{3} b^{2} x e}{18 \, {\left(b x^{3} + a\right)}^{2} a^{6}} + \frac{2200 \, b^{3} c x^{9} - 1320 \, a b^{2} d x^{9} - 220 \, a^{3} f x^{9} + 660 \, a^{2} b x^{9} e - 528 \, a b^{2} c x^{6} + 264 \, a^{2} b d x^{6} - 88 \, a^{3} x^{6} e + 165 \, a^{2} b c x^{3} - 55 \, a^{3} d x^{3} - 40 \, a^{3} c}{440 \, a^{6} x^{11}}"," ",0,"1/27*sqrt(3)*(119*(-a*b^2)^(1/3)*b^3*c - 77*(-a*b^2)^(1/3)*a*b^2*d - 20*(-a*b^2)^(1/3)*a^3*f + 44*(-a*b^2)^(1/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/a^7 - 1/27*(119*b^4*c - 77*a*b^3*d - 20*a^3*b*f + 44*a^2*b^2*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^7 + 1/54*(119*(-a*b^2)^(1/3)*b^3*c - 77*(-a*b^2)^(1/3)*a*b^2*d - 20*(-a*b^2)^(1/3)*a^3*f + 44*(-a*b^2)^(1/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/a^7 + 1/18*(29*b^5*c*x^4 - 23*a*b^4*d*x^4 - 11*a^3*b^2*f*x^4 + 17*a^2*b^3*x^4*e + 32*a*b^4*c*x - 26*a^2*b^3*d*x - 14*a^4*b*f*x + 20*a^3*b^2*x*e)/((b*x^3 + a)^2*a^6) + 1/440*(2200*b^3*c*x^9 - 1320*a*b^2*d*x^9 - 220*a^3*f*x^9 + 660*a^2*b*x^9*e - 528*a*b^2*c*x^6 + 264*a^2*b*d*x^6 - 88*a^3*x^6*e + 165*a^2*b*c*x^3 - 55*a^3*d*x^3 - 40*a^3*c)/(a^6*x^11)","A",0
303,1,531,0,0.220283," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^14/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{\sqrt{3} {\left(152 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - 104 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - 35 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + 65 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, a^{8}} + \frac{{\left(152 \, b^{5} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 104 \, a b^{4} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 35 \, a^{3} b^{2} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 65 \, a^{2} b^{3} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{8}} - \frac{{\left(152 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{3} c - 104 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2} d - 35 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3} f + 65 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, a^{8}} - \frac{34 \, b^{6} c x^{5} - 28 \, a b^{5} d x^{5} - 16 \, a^{3} b^{3} f x^{5} + 22 \, a^{2} b^{4} x^{5} e + 37 \, a b^{5} c x^{2} - 31 \, a^{2} b^{4} d x^{2} - 19 \, a^{4} b^{2} f x^{2} + 25 \, a^{3} b^{3} x^{2} e}{18 \, {\left(b x^{3} + a\right)}^{2} a^{7}} - \frac{27300 \, b^{4} c x^{12} - 18200 \, a b^{3} d x^{12} - 5460 \, a^{3} b f x^{12} + 10920 \, a^{2} b^{2} x^{12} e - 4550 \, a b^{3} c x^{9} + 2730 \, a^{2} b^{2} d x^{9} + 455 \, a^{4} f x^{9} - 1365 \, a^{3} b x^{9} e + 1560 \, a^{2} b^{2} c x^{6} - 780 \, a^{3} b d x^{6} + 260 \, a^{4} x^{6} e - 546 \, a^{3} b c x^{3} + 182 \, a^{4} d x^{3} + 140 \, a^{4} c}{1820 \, a^{7} x^{13}}"," ",0,"1/27*sqrt(3)*(152*(-a*b^2)^(2/3)*b^3*c - 104*(-a*b^2)^(2/3)*a*b^2*d - 35*(-a*b^2)^(2/3)*a^3*f + 65*(-a*b^2)^(2/3)*a^2*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/a^8 + 1/27*(152*b^5*c*(-a/b)^(1/3) - 104*a*b^4*d*(-a/b)^(1/3) - 35*a^3*b^2*f*(-a/b)^(1/3) + 65*a^2*b^3*(-a/b)^(1/3)*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^8 - 1/54*(152*(-a*b^2)^(2/3)*b^3*c - 104*(-a*b^2)^(2/3)*a*b^2*d - 35*(-a*b^2)^(2/3)*a^3*f + 65*(-a*b^2)^(2/3)*a^2*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/a^8 - 1/18*(34*b^6*c*x^5 - 28*a*b^5*d*x^5 - 16*a^3*b^3*f*x^5 + 22*a^2*b^4*x^5*e + 37*a*b^5*c*x^2 - 31*a^2*b^4*d*x^2 - 19*a^4*b^2*f*x^2 + 25*a^3*b^3*x^2*e)/((b*x^3 + a)^2*a^7) - 1/1820*(27300*b^4*c*x^12 - 18200*a*b^3*d*x^12 - 5460*a^3*b*f*x^12 + 10920*a^2*b^2*x^12*e - 4550*a*b^3*c*x^9 + 2730*a^2*b^2*d*x^9 + 455*a^4*f*x^9 - 1365*a^3*b*x^9*e + 1560*a^2*b^2*c*x^6 - 780*a^3*b*d*x^6 + 260*a^4*x^6*e - 546*a^3*b*c*x^3 + 182*a^4*d*x^3 + 140*a^4*c)/(a^7*x^13)","A",0
304,1,45,0,0.162469," ","integrate((1-x)*x^4/(x^3+1),x, algorithm=""giac"")","-\frac{1}{3} \, x^{3} + \frac{1}{2} \, x^{2} - \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{6} \, \log\left(x^{2} - x + 1\right) + \frac{2}{3} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/3*x^3 + 1/2*x^2 - 1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/6*log(x^2 - x + 1) + 2/3*log(abs(x + 1))","A",0
305,1,25,0,0.162611," ","integrate((1-x)*x^3/(x^3+1),x, algorithm=""giac"")","-\frac{1}{2} \, x^{2} + x + \frac{1}{3} \, \log\left(x^{2} - x + 1\right) - \frac{2}{3} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/2*x^2 + x + 1/3*log(x^2 - x + 1) - 2/3*log(abs(x + 1))","A",0
306,1,38,0,0.152029," ","integrate((1-x)*x^2/(x^3+1),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - x + \frac{1}{6} \, \log\left(x^{2} - x + 1\right) + \frac{2}{3} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - x + 1/6*log(x^2 - x + 1) + 2/3*log(abs(x + 1))","A",0
307,1,35,0,0.148022," ","integrate((1-x)*x/(x^3+1),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{6} \, \log\left(x^{2} - x + 1\right) - \frac{2}{3} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/6*log(x^2 - x + 1) - 2/3*log(abs(x + 1))","A",0
308,1,38,0,0.164208," ","integrate((1-x)/x/(x^3+1),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{6} \, \log\left(x^{2} - x + 1\right) - \frac{2}{3} \, \log\left({\left| x + 1 \right|}\right) + \log\left({\left| x \right|}\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/6*log(x^2 - x + 1) - 2/3*log(abs(x + 1)) + log(abs(x))","A",0
309,1,45,0,0.162620," ","integrate((1-x)/x^2/(x^3+1),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{x} + \frac{1}{6} \, \log\left(x^{2} - x + 1\right) + \frac{2}{3} \, \log\left({\left| x + 1 \right|}\right) - \log\left({\left| x \right|}\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/x + 1/6*log(x^2 - x + 1) + 2/3*log(abs(x + 1)) - log(abs(x))","A",0
310,1,29,0,0.146782," ","integrate((1-x)/x^3/(x^3+1),x, algorithm=""giac"")","\frac{2 \, x - 1}{2 \, x^{2}} + \frac{1}{3} \, \log\left(x^{2} - x + 1\right) - \frac{2}{3} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/2*(2*x - 1)/x^2 + 1/3*log(x^2 - x + 1) - 2/3*log(abs(x + 1))","A",0
311,1,35,0,0.151120," ","integrate(x*(1+2*x)/(x^3+1),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{5}{6} \, \log\left(x^{2} - x + 1\right) + \frac{1}{3} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 5/6*log(x^2 - x + 1) + 1/3*log(abs(x + 1))","A",0
312,1,33,0,0.152043," ","integrate(x*(1+2*x)/(-x^3+1),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{1}{2} \, \log\left(x^{2} + x + 1\right) - \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/2*log(x^2 + x + 1) - log(abs(x - 1))","A",0
313,1,45,0,0.198688," ","integrate(x^2*(e*x^2+d*x+c)*(b*x^3+a),x, algorithm=""giac"")","\frac{1}{8} \, b x^{8} e + \frac{1}{7} \, b d x^{7} + \frac{1}{6} \, b c x^{6} + \frac{1}{5} \, a x^{5} e + \frac{1}{4} \, a d x^{4} + \frac{1}{3} \, a c x^{3}"," ",0,"1/8*b*x^8*e + 1/7*b*d*x^7 + 1/6*b*c*x^6 + 1/5*a*x^5*e + 1/4*a*d*x^4 + 1/3*a*c*x^3","A",0
314,1,45,0,0.177410," ","integrate(x*(e*x^2+d*x+c)*(b*x^3+a),x, algorithm=""giac"")","\frac{1}{7} \, b x^{7} e + \frac{1}{6} \, b d x^{6} + \frac{1}{5} \, b c x^{5} + \frac{1}{4} \, a x^{4} e + \frac{1}{3} \, a d x^{3} + \frac{1}{2} \, a c x^{2}"," ",0,"1/7*b*x^7*e + 1/6*b*d*x^6 + 1/5*b*c*x^5 + 1/4*a*x^4*e + 1/3*a*d*x^3 + 1/2*a*c*x^2","A",0
315,1,42,0,0.146982," ","integrate((e*x^2+d*x+c)*(b*x^3+a),x, algorithm=""giac"")","\frac{1}{6} \, b x^{6} e + \frac{1}{5} \, b d x^{5} + \frac{1}{4} \, b c x^{4} + \frac{1}{3} \, a x^{3} e + \frac{1}{2} \, a d x^{2} + a c x"," ",0,"1/6*b*x^6*e + 1/5*b*d*x^5 + 1/4*b*c*x^4 + 1/3*a*x^3*e + 1/2*a*d*x^2 + a*c*x","A",0
316,1,41,0,0.152501," ","integrate((e*x^2+d*x+c)*(b*x^3+a)/x,x, algorithm=""giac"")","\frac{1}{5} \, b x^{5} e + \frac{1}{4} \, b d x^{4} + \frac{1}{3} \, b c x^{3} + \frac{1}{2} \, a x^{2} e + a d x + a c \log\left({\left| x \right|}\right)"," ",0,"1/5*b*x^5*e + 1/4*b*d*x^4 + 1/3*b*c*x^3 + 1/2*a*x^2*e + a*d*x + a*c*log(abs(x))","A",0
317,1,41,0,0.148927," ","integrate((e*x^2+d*x+c)*(b*x^3+a)/x^2,x, algorithm=""giac"")","\frac{1}{4} \, b x^{4} e + \frac{1}{3} \, b d x^{3} + \frac{1}{2} \, b c x^{2} + a x e + a d \log\left({\left| x \right|}\right) - \frac{a c}{x}"," ",0,"1/4*b*x^4*e + 1/3*b*d*x^3 + 1/2*b*c*x^2 + a*x*e + a*d*log(abs(x)) - a*c/x","A",0
318,1,41,0,0.162705," ","integrate((e*x^2+d*x+c)*(b*x^3+a)/x^3,x, algorithm=""giac"")","\frac{1}{3} \, b x^{3} e + \frac{1}{2} \, b d x^{2} + b c x + a e \log\left({\left| x \right|}\right) - \frac{2 \, a d x + a c}{2 \, x^{2}}"," ",0,"1/3*b*x^3*e + 1/2*b*d*x^2 + b*c*x + a*e*log(abs(x)) - 1/2*(2*a*d*x + a*c)/x^2","A",0
319,1,82,0,0.162779," ","integrate(x^2*(e*x^2+d*x+c)*(b*x^3+a)^2,x, algorithm=""giac"")","\frac{1}{11} \, b^{2} x^{11} e + \frac{1}{10} \, b^{2} d x^{10} + \frac{1}{9} \, b^{2} c x^{9} + \frac{1}{4} \, a b x^{8} e + \frac{2}{7} \, a b d x^{7} + \frac{1}{3} \, a b c x^{6} + \frac{1}{5} \, a^{2} x^{5} e + \frac{1}{4} \, a^{2} d x^{4} + \frac{1}{3} \, a^{2} c x^{3}"," ",0,"1/11*b^2*x^11*e + 1/10*b^2*d*x^10 + 1/9*b^2*c*x^9 + 1/4*a*b*x^8*e + 2/7*a*b*d*x^7 + 1/3*a*b*c*x^6 + 1/5*a^2*x^5*e + 1/4*a^2*d*x^4 + 1/3*a^2*c*x^3","A",0
320,1,82,0,0.150287," ","integrate(x*(e*x^2+d*x+c)*(b*x^3+a)^2,x, algorithm=""giac"")","\frac{1}{10} \, b^{2} x^{10} e + \frac{1}{9} \, b^{2} d x^{9} + \frac{1}{8} \, b^{2} c x^{8} + \frac{2}{7} \, a b x^{7} e + \frac{1}{3} \, a b d x^{6} + \frac{2}{5} \, a b c x^{5} + \frac{1}{4} \, a^{2} x^{4} e + \frac{1}{3} \, a^{2} d x^{3} + \frac{1}{2} \, a^{2} c x^{2}"," ",0,"1/10*b^2*x^10*e + 1/9*b^2*d*x^9 + 1/8*b^2*c*x^8 + 2/7*a*b*x^7*e + 1/3*a*b*d*x^6 + 2/5*a*b*c*x^5 + 1/4*a^2*x^4*e + 1/3*a^2*d*x^3 + 1/2*a^2*c*x^2","A",0
321,1,79,0,0.178188," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^2,x, algorithm=""giac"")","\frac{1}{9} \, b^{2} x^{9} e + \frac{1}{8} \, b^{2} d x^{8} + \frac{1}{7} \, b^{2} c x^{7} + \frac{1}{3} \, a b x^{6} e + \frac{2}{5} \, a b d x^{5} + \frac{1}{2} \, a b c x^{4} + \frac{1}{3} \, a^{2} x^{3} e + \frac{1}{2} \, a^{2} d x^{2} + a^{2} c x"," ",0,"1/9*b^2*x^9*e + 1/8*b^2*d*x^8 + 1/7*b^2*c*x^7 + 1/3*a*b*x^6*e + 2/5*a*b*d*x^5 + 1/2*a*b*c*x^4 + 1/3*a^2*x^3*e + 1/2*a^2*d*x^2 + a^2*c*x","A",0
322,1,78,0,0.150828," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^2/x,x, algorithm=""giac"")","\frac{1}{8} \, b^{2} x^{8} e + \frac{1}{7} \, b^{2} d x^{7} + \frac{1}{6} \, b^{2} c x^{6} + \frac{2}{5} \, a b x^{5} e + \frac{1}{2} \, a b d x^{4} + \frac{2}{3} \, a b c x^{3} + \frac{1}{2} \, a^{2} x^{2} e + a^{2} d x + a^{2} c \log\left({\left| x \right|}\right)"," ",0,"1/8*b^2*x^8*e + 1/7*b^2*d*x^7 + 1/6*b^2*c*x^6 + 2/5*a*b*x^5*e + 1/2*a*b*d*x^4 + 2/3*a*b*c*x^3 + 1/2*a^2*x^2*e + a^2*d*x + a^2*c*log(abs(x))","A",0
323,1,77,0,0.149964," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^2/x^2,x, algorithm=""giac"")","\frac{1}{7} \, b^{2} x^{7} e + \frac{1}{6} \, b^{2} d x^{6} + \frac{1}{5} \, b^{2} c x^{5} + \frac{1}{2} \, a b x^{4} e + \frac{2}{3} \, a b d x^{3} + a b c x^{2} + a^{2} x e + a^{2} d \log\left({\left| x \right|}\right) - \frac{a^{2} c}{x}"," ",0,"1/7*b^2*x^7*e + 1/6*b^2*d*x^6 + 1/5*b^2*c*x^5 + 1/2*a*b*x^4*e + 2/3*a*b*d*x^3 + a*b*c*x^2 + a^2*x*e + a^2*d*log(abs(x)) - a^2*c/x","A",0
324,1,78,0,0.164512," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^2/x^3,x, algorithm=""giac"")","\frac{1}{6} \, b^{2} x^{6} e + \frac{1}{5} \, b^{2} d x^{5} + \frac{1}{4} \, b^{2} c x^{4} + \frac{2}{3} \, a b x^{3} e + a b d x^{2} + 2 \, a b c x + a^{2} e \log\left({\left| x \right|}\right) - \frac{2 \, a^{2} d x + a^{2} c}{2 \, x^{2}}"," ",0,"1/6*b^2*x^6*e + 1/5*b^2*d*x^5 + 1/4*b^2*c*x^4 + 2/3*a*b*x^3*e + a*b*d*x^2 + 2*a*b*c*x + a^2*e*log(abs(x)) - 1/2*(2*a^2*d*x + a^2*c)/x^2","A",0
325,1,119,0,0.156752," ","integrate(x^2*(e*x^2+d*x+c)*(b*x^3+a)^3,x, algorithm=""giac"")","\frac{1}{14} \, b^{3} x^{14} e + \frac{1}{13} \, b^{3} d x^{13} + \frac{1}{12} \, b^{3} c x^{12} + \frac{3}{11} \, a b^{2} x^{11} e + \frac{3}{10} \, a b^{2} d x^{10} + \frac{1}{3} \, a b^{2} c x^{9} + \frac{3}{8} \, a^{2} b x^{8} e + \frac{3}{7} \, a^{2} b d x^{7} + \frac{1}{2} \, a^{2} b c x^{6} + \frac{1}{5} \, a^{3} x^{5} e + \frac{1}{4} \, a^{3} d x^{4} + \frac{1}{3} \, a^{3} c x^{3}"," ",0,"1/14*b^3*x^14*e + 1/13*b^3*d*x^13 + 1/12*b^3*c*x^12 + 3/11*a*b^2*x^11*e + 3/10*a*b^2*d*x^10 + 1/3*a*b^2*c*x^9 + 3/8*a^2*b*x^8*e + 3/7*a^2*b*d*x^7 + 1/2*a^2*b*c*x^6 + 1/5*a^3*x^5*e + 1/4*a^3*d*x^4 + 1/3*a^3*c*x^3","A",0
326,1,119,0,0.169382," ","integrate(x*(e*x^2+d*x+c)*(b*x^3+a)^3,x, algorithm=""giac"")","\frac{1}{13} \, b^{3} x^{13} e + \frac{1}{12} \, b^{3} d x^{12} + \frac{1}{11} \, b^{3} c x^{11} + \frac{3}{10} \, a b^{2} x^{10} e + \frac{1}{3} \, a b^{2} d x^{9} + \frac{3}{8} \, a b^{2} c x^{8} + \frac{3}{7} \, a^{2} b x^{7} e + \frac{1}{2} \, a^{2} b d x^{6} + \frac{3}{5} \, a^{2} b c x^{5} + \frac{1}{4} \, a^{3} x^{4} e + \frac{1}{3} \, a^{3} d x^{3} + \frac{1}{2} \, a^{3} c x^{2}"," ",0,"1/13*b^3*x^13*e + 1/12*b^3*d*x^12 + 1/11*b^3*c*x^11 + 3/10*a*b^2*x^10*e + 1/3*a*b^2*d*x^9 + 3/8*a*b^2*c*x^8 + 3/7*a^2*b*x^7*e + 1/2*a^2*b*d*x^6 + 3/5*a^2*b*c*x^5 + 1/4*a^3*x^4*e + 1/3*a^3*d*x^3 + 1/2*a^3*c*x^2","A",0
327,1,116,0,0.149100," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^3,x, algorithm=""giac"")","\frac{1}{12} \, b^{3} x^{12} e + \frac{1}{11} \, b^{3} d x^{11} + \frac{1}{10} \, b^{3} c x^{10} + \frac{1}{3} \, a b^{2} x^{9} e + \frac{3}{8} \, a b^{2} d x^{8} + \frac{3}{7} \, a b^{2} c x^{7} + \frac{1}{2} \, a^{2} b x^{6} e + \frac{3}{5} \, a^{2} b d x^{5} + \frac{3}{4} \, a^{2} b c x^{4} + \frac{1}{3} \, a^{3} x^{3} e + \frac{1}{2} \, a^{3} d x^{2} + a^{3} c x"," ",0,"1/12*b^3*x^12*e + 1/11*b^3*d*x^11 + 1/10*b^3*c*x^10 + 1/3*a*b^2*x^9*e + 3/8*a*b^2*d*x^8 + 3/7*a*b^2*c*x^7 + 1/2*a^2*b*x^6*e + 3/5*a^2*b*d*x^5 + 3/4*a^2*b*c*x^4 + 1/3*a^3*x^3*e + 1/2*a^3*d*x^2 + a^3*c*x","A",0
328,1,114,0,0.152287," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^3/x,x, algorithm=""giac"")","\frac{1}{11} \, b^{3} x^{11} e + \frac{1}{10} \, b^{3} d x^{10} + \frac{1}{9} \, b^{3} c x^{9} + \frac{3}{8} \, a b^{2} x^{8} e + \frac{3}{7} \, a b^{2} d x^{7} + \frac{1}{2} \, a b^{2} c x^{6} + \frac{3}{5} \, a^{2} b x^{5} e + \frac{3}{4} \, a^{2} b d x^{4} + a^{2} b c x^{3} + \frac{1}{2} \, a^{3} x^{2} e + a^{3} d x + a^{3} c \log\left({\left| x \right|}\right)"," ",0,"1/11*b^3*x^11*e + 1/10*b^3*d*x^10 + 1/9*b^3*c*x^9 + 3/8*a*b^2*x^8*e + 3/7*a*b^2*d*x^7 + 1/2*a*b^2*c*x^6 + 3/5*a^2*b*x^5*e + 3/4*a^2*b*d*x^4 + a^2*b*c*x^3 + 1/2*a^3*x^2*e + a^3*d*x + a^3*c*log(abs(x))","A",0
329,1,114,0,0.180527," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^3/x^2,x, algorithm=""giac"")","\frac{1}{10} \, b^{3} x^{10} e + \frac{1}{9} \, b^{3} d x^{9} + \frac{1}{8} \, b^{3} c x^{8} + \frac{3}{7} \, a b^{2} x^{7} e + \frac{1}{2} \, a b^{2} d x^{6} + \frac{3}{5} \, a b^{2} c x^{5} + \frac{3}{4} \, a^{2} b x^{4} e + a^{2} b d x^{3} + \frac{3}{2} \, a^{2} b c x^{2} + a^{3} x e + a^{3} d \log\left({\left| x \right|}\right) - \frac{a^{3} c}{x}"," ",0,"1/10*b^3*x^10*e + 1/9*b^3*d*x^9 + 1/8*b^3*c*x^8 + 3/7*a*b^2*x^7*e + 1/2*a*b^2*d*x^6 + 3/5*a*b^2*c*x^5 + 3/4*a^2*b*x^4*e + a^2*b*d*x^3 + 3/2*a^2*b*c*x^2 + a^3*x*e + a^3*d*log(abs(x)) - a^3*c/x","A",0
330,1,115,0,0.153385," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^3/x^3,x, algorithm=""giac"")","\frac{1}{9} \, b^{3} x^{9} e + \frac{1}{8} \, b^{3} d x^{8} + \frac{1}{7} \, b^{3} c x^{7} + \frac{1}{2} \, a b^{2} x^{6} e + \frac{3}{5} \, a b^{2} d x^{5} + \frac{3}{4} \, a b^{2} c x^{4} + a^{2} b x^{3} e + \frac{3}{2} \, a^{2} b d x^{2} + 3 \, a^{2} b c x + a^{3} e \log\left({\left| x \right|}\right) - \frac{2 \, a^{3} d x + a^{3} c}{2 \, x^{2}}"," ",0,"1/9*b^3*x^9*e + 1/8*b^3*d*x^8 + 1/7*b^3*c*x^7 + 1/2*a*b^2*x^6*e + 3/5*a*b^2*d*x^5 + 3/4*a*b^2*c*x^4 + a^2*b*x^3*e + 3/2*a^2*b*d*x^2 + 3*a^2*b*c*x + a^3*e*log(abs(x)) - 1/2*(2*a^3*d*x + a^3*c)/x^2","A",0
331,1,156,0,0.164617," ","integrate(x^2*(e*x^2+d*x+c)*(b*x^3+a)^4,x, algorithm=""giac"")","\frac{1}{17} \, b^{4} x^{17} e + \frac{1}{16} \, b^{4} d x^{16} + \frac{1}{15} \, b^{4} c x^{15} + \frac{2}{7} \, a b^{3} x^{14} e + \frac{4}{13} \, a b^{3} d x^{13} + \frac{1}{3} \, a b^{3} c x^{12} + \frac{6}{11} \, a^{2} b^{2} x^{11} e + \frac{3}{5} \, a^{2} b^{2} d x^{10} + \frac{2}{3} \, a^{2} b^{2} c x^{9} + \frac{1}{2} \, a^{3} b x^{8} e + \frac{4}{7} \, a^{3} b d x^{7} + \frac{2}{3} \, a^{3} b c x^{6} + \frac{1}{5} \, a^{4} x^{5} e + \frac{1}{4} \, a^{4} d x^{4} + \frac{1}{3} \, a^{4} c x^{3}"," ",0,"1/17*b^4*x^17*e + 1/16*b^4*d*x^16 + 1/15*b^4*c*x^15 + 2/7*a*b^3*x^14*e + 4/13*a*b^3*d*x^13 + 1/3*a*b^3*c*x^12 + 6/11*a^2*b^2*x^11*e + 3/5*a^2*b^2*d*x^10 + 2/3*a^2*b^2*c*x^9 + 1/2*a^3*b*x^8*e + 4/7*a^3*b*d*x^7 + 2/3*a^3*b*c*x^6 + 1/5*a^4*x^5*e + 1/4*a^4*d*x^4 + 1/3*a^4*c*x^3","A",0
332,1,156,0,0.158164," ","integrate(x*(e*x^2+d*x+c)*(b*x^3+a)^4,x, algorithm=""giac"")","\frac{1}{16} \, b^{4} x^{16} e + \frac{1}{15} \, b^{4} d x^{15} + \frac{1}{14} \, b^{4} c x^{14} + \frac{4}{13} \, a b^{3} x^{13} e + \frac{1}{3} \, a b^{3} d x^{12} + \frac{4}{11} \, a b^{3} c x^{11} + \frac{3}{5} \, a^{2} b^{2} x^{10} e + \frac{2}{3} \, a^{2} b^{2} d x^{9} + \frac{3}{4} \, a^{2} b^{2} c x^{8} + \frac{4}{7} \, a^{3} b x^{7} e + \frac{2}{3} \, a^{3} b d x^{6} + \frac{4}{5} \, a^{3} b c x^{5} + \frac{1}{4} \, a^{4} x^{4} e + \frac{1}{3} \, a^{4} d x^{3} + \frac{1}{2} \, a^{4} c x^{2}"," ",0,"1/16*b^4*x^16*e + 1/15*b^4*d*x^15 + 1/14*b^4*c*x^14 + 4/13*a*b^3*x^13*e + 1/3*a*b^3*d*x^12 + 4/11*a*b^3*c*x^11 + 3/5*a^2*b^2*x^10*e + 2/3*a^2*b^2*d*x^9 + 3/4*a^2*b^2*c*x^8 + 4/7*a^3*b*x^7*e + 2/3*a^3*b*d*x^6 + 4/5*a^3*b*c*x^5 + 1/4*a^4*x^4*e + 1/3*a^4*d*x^3 + 1/2*a^4*c*x^2","A",0
333,1,152,0,0.167410," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^4,x, algorithm=""giac"")","\frac{1}{15} \, b^{4} x^{15} e + \frac{1}{14} \, b^{4} d x^{14} + \frac{1}{13} \, b^{4} c x^{13} + \frac{1}{3} \, a b^{3} x^{12} e + \frac{4}{11} \, a b^{3} d x^{11} + \frac{2}{5} \, a b^{3} c x^{10} + \frac{2}{3} \, a^{2} b^{2} x^{9} e + \frac{3}{4} \, a^{2} b^{2} d x^{8} + \frac{6}{7} \, a^{2} b^{2} c x^{7} + \frac{2}{3} \, a^{3} b x^{6} e + \frac{4}{5} \, a^{3} b d x^{5} + a^{3} b c x^{4} + \frac{1}{3} \, a^{4} x^{3} e + \frac{1}{2} \, a^{4} d x^{2} + a^{4} c x"," ",0,"1/15*b^4*x^15*e + 1/14*b^4*d*x^14 + 1/13*b^4*c*x^13 + 1/3*a*b^3*x^12*e + 4/11*a*b^3*d*x^11 + 2/5*a*b^3*c*x^10 + 2/3*a^2*b^2*x^9*e + 3/4*a^2*b^2*d*x^8 + 6/7*a^2*b^2*c*x^7 + 2/3*a^3*b*x^6*e + 4/5*a^3*b*d*x^5 + a^3*b*c*x^4 + 1/3*a^4*x^3*e + 1/2*a^4*d*x^2 + a^4*c*x","A",0
334,1,150,0,0.153351," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^4/x,x, algorithm=""giac"")","\frac{1}{14} \, b^{4} x^{14} e + \frac{1}{13} \, b^{4} d x^{13} + \frac{1}{12} \, b^{4} c x^{12} + \frac{4}{11} \, a b^{3} x^{11} e + \frac{2}{5} \, a b^{3} d x^{10} + \frac{4}{9} \, a b^{3} c x^{9} + \frac{3}{4} \, a^{2} b^{2} x^{8} e + \frac{6}{7} \, a^{2} b^{2} d x^{7} + a^{2} b^{2} c x^{6} + \frac{4}{5} \, a^{3} b x^{5} e + a^{3} b d x^{4} + \frac{4}{3} \, a^{3} b c x^{3} + \frac{1}{2} \, a^{4} x^{2} e + a^{4} d x + a^{4} c \log\left({\left| x \right|}\right)"," ",0,"1/14*b^4*x^14*e + 1/13*b^4*d*x^13 + 1/12*b^4*c*x^12 + 4/11*a*b^3*x^11*e + 2/5*a*b^3*d*x^10 + 4/9*a*b^3*c*x^9 + 3/4*a^2*b^2*x^8*e + 6/7*a^2*b^2*d*x^7 + a^2*b^2*c*x^6 + 4/5*a^3*b*x^5*e + a^3*b*d*x^4 + 4/3*a^3*b*c*x^3 + 1/2*a^4*x^2*e + a^4*d*x + a^4*c*log(abs(x))","A",0
335,1,150,0,0.158971," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^4/x^2,x, algorithm=""giac"")","\frac{1}{13} \, b^{4} x^{13} e + \frac{1}{12} \, b^{4} d x^{12} + \frac{1}{11} \, b^{4} c x^{11} + \frac{2}{5} \, a b^{3} x^{10} e + \frac{4}{9} \, a b^{3} d x^{9} + \frac{1}{2} \, a b^{3} c x^{8} + \frac{6}{7} \, a^{2} b^{2} x^{7} e + a^{2} b^{2} d x^{6} + \frac{6}{5} \, a^{2} b^{2} c x^{5} + a^{3} b x^{4} e + \frac{4}{3} \, a^{3} b d x^{3} + 2 \, a^{3} b c x^{2} + a^{4} x e + a^{4} d \log\left({\left| x \right|}\right) - \frac{a^{4} c}{x}"," ",0,"1/13*b^4*x^13*e + 1/12*b^4*d*x^12 + 1/11*b^4*c*x^11 + 2/5*a*b^3*x^10*e + 4/9*a*b^3*d*x^9 + 1/2*a*b^3*c*x^8 + 6/7*a^2*b^2*x^7*e + a^2*b^2*d*x^6 + 6/5*a^2*b^2*c*x^5 + a^3*b*x^4*e + 4/3*a^3*b*d*x^3 + 2*a^3*b*c*x^2 + a^4*x*e + a^4*d*log(abs(x)) - a^4*c/x","A",0
336,1,152,0,0.166491," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^4/x^3,x, algorithm=""giac"")","\frac{1}{12} \, b^{4} x^{12} e + \frac{1}{11} \, b^{4} d x^{11} + \frac{1}{10} \, b^{4} c x^{10} + \frac{4}{9} \, a b^{3} x^{9} e + \frac{1}{2} \, a b^{3} d x^{8} + \frac{4}{7} \, a b^{3} c x^{7} + a^{2} b^{2} x^{6} e + \frac{6}{5} \, a^{2} b^{2} d x^{5} + \frac{3}{2} \, a^{2} b^{2} c x^{4} + \frac{4}{3} \, a^{3} b x^{3} e + 2 \, a^{3} b d x^{2} + 4 \, a^{3} b c x + a^{4} e \log\left({\left| x \right|}\right) - \frac{2 \, a^{4} d x + a^{4} c}{2 \, x^{2}}"," ",0,"1/12*b^4*x^12*e + 1/11*b^4*d*x^11 + 1/10*b^4*c*x^10 + 4/9*a*b^3*x^9*e + 1/2*a*b^3*d*x^8 + 4/7*a*b^3*c*x^7 + a^2*b^2*x^6*e + 6/5*a^2*b^2*d*x^5 + 3/2*a^2*b^2*c*x^4 + 4/3*a^3*b*x^3*e + 2*a^3*b*d*x^2 + 4*a^3*b*c*x + a^4*e*log(abs(x)) - 1/2*(2*a^4*d*x + a^4*c)/x^2","A",0
337,1,208,0,0.180108," ","integrate(x^3*(e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""giac"")","-\frac{a e \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{2}} - \frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{1}{3}} b c - \left(-a b^{2}\right)^{\frac{2}{3}} d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{3}} - \frac{{\left(\left(-a b^{2}\right)^{\frac{1}{3}} b c + \left(-a b^{2}\right)^{\frac{2}{3}} d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{3}} + \frac{2 \, b^{2} x^{3} e + 3 \, b^{2} d x^{2} + 6 \, b^{2} c x}{6 \, b^{3}} + \frac{{\left(a b^{6} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a b^{6} c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{7}}"," ",0,"-1/3*a*e*log(abs(b*x^3 + a))/b^2 - 1/3*sqrt(3)*((-a*b^2)^(1/3)*b*c - (-a*b^2)^(2/3)*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^3 - 1/6*((-a*b^2)^(1/3)*b*c + (-a*b^2)^(2/3)*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^3 + 1/6*(2*b^2*x^3*e + 3*b^2*d*x^2 + 6*b^2*c*x)/b^3 + 1/3*(a*b^6*d*(-a/b)^(1/3) + a*b^6*c)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^7)","A",0
338,1,195,0,0.211242," ","integrate(x^2*(e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""giac"")","\frac{c \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b} - \frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{1}{3}} b d - \left(-a b^{2}\right)^{\frac{2}{3}} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{3}} + \frac{b x^{2} e + 2 \, b d x}{2 \, b^{2}} - \frac{{\left(\left(-a b^{2}\right)^{\frac{1}{3}} b d + \left(-a b^{2}\right)^{\frac{2}{3}} e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{3}} + \frac{{\left(a b^{4} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e + a b^{4} d\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{5}}"," ",0,"1/3*c*log(abs(b*x^3 + a))/b - 1/3*sqrt(3)*((-a*b^2)^(1/3)*b*d - (-a*b^2)^(2/3)*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^3 + 1/2*(b*x^2*e + 2*b*d*x)/b^2 - 1/6*((-a*b^2)^(1/3)*b*d + (-a*b^2)^(2/3)*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^3 + 1/3*(a*b^4*(-a/b)^(1/3)*e + a*b^4*d)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^5)","A",0
339,1,178,0,0.207964," ","integrate(x*(e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""giac"")","\frac{\sqrt{3} {\left(a e + \left(-a b^{2}\right)^{\frac{1}{3}} c\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}}} + \frac{{\left(a e - \left(-a b^{2}\right)^{\frac{1}{3}} c\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}}} + \frac{x e}{b} + \frac{d \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b} - \frac{{\left(b^{3} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a b^{2} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{3}}"," ",0,"1/3*sqrt(3)*(a*e + (-a*b^2)^(1/3)*c)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(-a*b^2)^(2/3) + 1/6*(a*e - (-a*b^2)^(1/3)*c)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(-a*b^2)^(2/3) + x*e/b + 1/3*d*log(abs(b*x^3 + a))/b - 1/3*(b^3*c*(-a/b)^(1/3) - a*b^2*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^3)","A",0
340,1,163,0,0.179986," ","integrate((e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b c - \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}}} - \frac{{\left(b c + \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}}} + \frac{e \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b} - \frac{{\left(b d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + b c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b}"," ",0,"-1/3*sqrt(3)*(b*c - (-a*b^2)^(1/3)*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(-a*b^2)^(2/3) - 1/6*(b*c + (-a*b^2)^(1/3)*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(-a*b^2)^(2/3) + 1/3*e*log(abs(b*x^3 + a))/b - 1/3*(b*d*(-a/b)^(1/3) + b*c)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b)","A",0
341,1,179,0,0.184089," ","integrate((e*x^2+d*x+c)/x/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b d - \left(-a b^{2}\right)^{\frac{1}{3}} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}}} - \frac{{\left(b d + \left(-a b^{2}\right)^{\frac{1}{3}} e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}}} - \frac{c \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a} + \frac{c \log\left({\left| x \right|}\right)}{a} - \frac{{\left(a^{2} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e + a^{2} b d\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{3} b}"," ",0,"-1/3*sqrt(3)*(b*d - (-a*b^2)^(1/3)*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(-a*b^2)^(2/3) - 1/6*(b*d + (-a*b^2)^(1/3)*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(-a*b^2)^(2/3) - 1/3*c*log(abs(b*x^3 + a))/a + c*log(abs(x))/a - 1/3*(a^2*b*(-a/b)^(1/3)*e + a^2*b*d)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b)","A",0
342,1,201,0,0.229841," ","integrate((e*x^2+d*x+c)/x^2/(b*x^3+a),x, algorithm=""giac"")","-\frac{d \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a} + \frac{d \log\left({\left| x \right|}\right)}{a} + \frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{1}{3}} a e + \left(-a b^{2}\right)^{\frac{2}{3}} c\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a^{2} b} - \frac{c}{a x} + \frac{{\left(\left(-a b^{2}\right)^{\frac{1}{3}} a e - \left(-a b^{2}\right)^{\frac{2}{3}} c\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b} + \frac{{\left(a b^{2} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{3} b}"," ",0,"-1/3*d*log(abs(b*x^3 + a))/a + d*log(abs(x))/a + 1/3*sqrt(3)*((-a*b^2)^(1/3)*a*e + (-a*b^2)^(2/3)*c)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^2*b) - c/(a*x) + 1/6*((-a*b^2)^(1/3)*a*e - (-a*b^2)^(2/3)*c)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^2*b) + 1/3*(a*b^2*c*(-a/b)^(1/3) - a^2*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b)","A",0
343,1,204,0,0.183371," ","integrate((e*x^2+d*x+c)/x^3/(b*x^3+a),x, algorithm=""giac"")","-\frac{e \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a} + \frac{e \log\left({\left| x \right|}\right)}{a} - \frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{1}{3}} b c - \left(-a b^{2}\right)^{\frac{2}{3}} d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a^{2} b} - \frac{{\left(\left(-a b^{2}\right)^{\frac{1}{3}} b c + \left(-a b^{2}\right)^{\frac{2}{3}} d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b} + \frac{{\left(a b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a b^{2} c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{3} b} - \frac{2 \, d x + c}{2 \, a x^{2}}"," ",0,"-1/3*e*log(abs(b*x^3 + a))/a + e*log(abs(x))/a - 1/3*sqrt(3)*((-a*b^2)^(1/3)*b*c - (-a*b^2)^(2/3)*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^2*b) - 1/6*((-a*b^2)^(1/3)*b*c + (-a*b^2)^(2/3)*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^2*b) + 1/3*(a*b^2*d*(-a/b)^(1/3) + a*b^2*c)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b) - 1/2*(2*d*x + c)/(a*x^2)","A",0
344,1,180,0,0.204464," ","integrate(x^2*(e*x^2+d*x+c)/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b d - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} b} - \frac{{\left(b d + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} b} - \frac{{\left(2 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}} e + d\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a b} - \frac{x^{2} e + d x + c}{3 \, {\left(b x^{3} + a\right)} b}"," ",0,"-1/9*sqrt(3)*(b*d - 2*(-a*b^2)^(1/3)*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*b) - 1/18*(b*d + 2*(-a*b^2)^(1/3)*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*b) - 1/9*(2*(-a/b)^(1/3)*e + d)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b) - 1/3*(x^2*e + d*x + c)/((b*x^3 + a)*b)","A",0
345,1,190,0,0.182115," ","integrate(x*(e*x^2+d*x+c)/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(a e - \left(-a b^{2}\right)^{\frac{1}{3}} c\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} - \frac{{\left(a e + \left(-a b^{2}\right)^{\frac{1}{3}} c\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} - \frac{{\left(b c \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{2} b} + \frac{b c x^{2} - a x e - a d}{3 \, {\left(b x^{3} + a\right)} a b}"," ",0,"-1/9*sqrt(3)*(a*e - (-a*b^2)^(1/3)*c)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a) - 1/18*(a*e + (-a*b^2)^(1/3)*c)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a) - 1/9*(b*c*(-a/b)^(1/3) + a*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b) + 1/3*(b*c*x^2 - a*x*e - a*d)/((b*x^3 + a)*a*b)","A",0
346,1,184,0,0.183214," ","integrate((e*x^2+d*x+c)/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(2 \, b c - \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} - \frac{{\left(2 \, b c + \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} - \frac{{\left(d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{2}} + \frac{b d x^{2} + b c x - a e}{3 \, {\left(b x^{3} + a\right)} a b}"," ",0,"-1/9*sqrt(3)*(2*b*c - (-a*b^2)^(1/3)*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a) - 1/18*(2*b*c + (-a*b^2)^(1/3)*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a) - 1/9*(d*(-a/b)^(1/3) + 2*c)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^2 + 1/3*(b*d*x^2 + b*c*x - a*e)/((b*x^3 + a)*a*b)","A",0
347,1,217,0,0.182789," ","integrate((e*x^2+d*x+c)/x/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(2 \, b d - \left(-a b^{2}\right)^{\frac{1}{3}} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} - \frac{{\left(2 \, b d + \left(-a b^{2}\right)^{\frac{1}{3}} e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} - \frac{c \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{2}} + \frac{c \log\left({\left| x \right|}\right)}{a^{2}} + \frac{a x^{2} e + a d x + a c}{3 \, {\left(b x^{3} + a\right)} a^{2}} - \frac{{\left(a^{3} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e + 2 \, a^{3} b d\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{5} b}"," ",0,"-1/9*sqrt(3)*(2*b*d - (-a*b^2)^(1/3)*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a) - 1/18*(2*b*d + (-a*b^2)^(1/3)*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a) - 1/3*c*log(abs(b*x^3 + a))/a^2 + c*log(abs(x))/a^2 + 1/3*(a*x^2*e + a*d*x + a*c)/((b*x^3 + a)*a^2) - 1/9*(a^3*b*(-a/b)^(1/3)*e + 2*a^3*b*d)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^5*b)","A",0
348,1,237,0,0.179553," ","integrate((e*x^2+d*x+c)/x^2/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{d \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{2}} + \frac{d \log\left({\left| x \right|}\right)}{a^{2}} + \frac{2 \, \sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{1}{3}} a e + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} c\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a^{3} b} - \frac{4 \, b c x^{3} - a x^{2} e - a d x + 3 \, a c}{3 \, {\left(b x^{4} + a x\right)} a^{2}} + \frac{{\left(\left(-a b^{2}\right)^{\frac{1}{3}} a e - 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} c\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \, a^{3} b} + \frac{2 \, {\left(2 \, a^{2} b^{2} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{3} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{5} b}"," ",0,"-1/3*d*log(abs(b*x^3 + a))/a^2 + d*log(abs(x))/a^2 + 2/9*sqrt(3)*((-a*b^2)^(1/3)*a*e + 2*(-a*b^2)^(2/3)*c)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^3*b) - 1/3*(4*b*c*x^3 - a*x^2*e - a*d*x + 3*a*c)/((b*x^4 + a*x)*a^2) + 1/9*((-a*b^2)^(1/3)*a*e - 2*(-a*b^2)^(2/3)*c)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^3*b) + 2/9*(2*a^2*b^2*c*(-a/b)^(1/3) - a^3*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^5*b)","A",0
349,1,248,0,0.197037," ","integrate((e*x^2+d*x+c)/x^3/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{e \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{2}} + \frac{e \log\left({\left| x \right|}\right)}{a^{2}} - \frac{\sqrt{3} {\left(5 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c - 4 \, \left(-a b^{2}\right)^{\frac{2}{3}} d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a^{3} b} - \frac{{\left(5 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c + 4 \, \left(-a b^{2}\right)^{\frac{2}{3}} d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, a^{3} b} + \frac{{\left(4 \, a^{2} b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a^{2} b^{2} c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{5} b} - \frac{8 \, b d x^{4} + 5 \, b c x^{3} - 2 \, a x^{2} e + 6 \, a d x + 3 \, a c}{6 \, {\left(b x^{3} + a\right)} a^{2} x^{2}}"," ",0,"-1/3*e*log(abs(b*x^3 + a))/a^2 + e*log(abs(x))/a^2 - 1/9*sqrt(3)*(5*(-a*b^2)^(1/3)*b*c - 4*(-a*b^2)^(2/3)*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^3*b) - 1/18*(5*(-a*b^2)^(1/3)*b*c + 4*(-a*b^2)^(2/3)*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^3*b) + 1/9*(4*a^2*b^2*d*(-a/b)^(1/3) + 5*a^2*b^2*c)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^5*b) - 1/6*(8*b*d*x^4 + 5*b*c*x^3 - 2*a*x^2*e + 6*a*d*x + 3*a*c)/((b*x^3 + a)*a^2*x^2)","A",0
350,1,269,0,0.181062," ","integrate((e*x^2+d*x+c)/x^4/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{2 \, b c \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{3}} - \frac{2 \, b c \log\left({\left| x \right|}\right)}{a^{3}} - \frac{\sqrt{3} {\left(5 \, \left(-a b^{2}\right)^{\frac{1}{3}} b d - 4 \, \left(-a b^{2}\right)^{\frac{2}{3}} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a^{3} b} - \frac{{\left(5 \, \left(-a b^{2}\right)^{\frac{1}{3}} b d + 4 \, \left(-a b^{2}\right)^{\frac{2}{3}} e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, a^{3} b} + \frac{{\left(4 \, a^{4} b^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e + 5 \, a^{4} b^{2} d\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{7} b} - \frac{8 \, a b x^{5} e + 5 \, a b d x^{4} + 4 \, a b c x^{3} + 6 \, a^{2} x^{2} e + 3 \, a^{2} d x + 2 \, a^{2} c}{6 \, {\left(b x^{3} + a\right)} a^{3} x^{3}}"," ",0,"2/3*b*c*log(abs(b*x^3 + a))/a^3 - 2*b*c*log(abs(x))/a^3 - 1/9*sqrt(3)*(5*(-a*b^2)^(1/3)*b*d - 4*(-a*b^2)^(2/3)*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^3*b) - 1/18*(5*(-a*b^2)^(1/3)*b*d + 4*(-a*b^2)^(2/3)*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^3*b) + 1/9*(4*a^4*b^2*(-a/b)^(1/3)*e + 5*a^4*b^2*d)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^7*b) - 1/6*(8*a*b*x^5*e + 5*a*b*d*x^4 + 4*a*b*c*x^3 + 6*a^2*x^2*e + 3*a^2*d*x + 2*a^2*c)/((b*x^3 + a)*a^3*x^3)","A",0
351,1,208,0,0.205345," ","integrate(x^2*(e*x^2+d*x+c)/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b d - \left(-a b^{2}\right)^{\frac{1}{3}} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b} - \frac{{\left(b d + \left(-a b^{2}\right)^{\frac{1}{3}} e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b} - \frac{{\left(\left(-\frac{a}{b}\right)^{\frac{1}{3}} e + d\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{2} b} + \frac{2 \, b x^{5} e + b d x^{4} - a x^{2} e - 2 \, a d x - 3 \, a c}{18 \, {\left(b x^{3} + a\right)}^{2} a b}"," ",0,"-1/27*sqrt(3)*(b*d - (-a*b^2)^(1/3)*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a*b) - 1/54*(b*d + (-a*b^2)^(1/3)*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a*b) - 1/27*((-a/b)^(1/3)*e + d)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b) + 1/18*(2*b*x^5*e + b*d*x^4 - a*x^2*e - 2*a*d*x - 3*a*c)/((b*x^3 + a)^2*a*b)","A",0
352,1,215,0,0.197169," ","integrate(x*(e*x^2+d*x+c)/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(a e - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} c\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2}} - \frac{{\left(a e + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} c\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2}} - \frac{{\left(2 \, b c \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{3} b} + \frac{4 \, b^{2} c x^{5} + a b x^{4} e + 7 \, a b c x^{2} - 2 \, a^{2} x e - 3 \, a^{2} d}{18 \, {\left(b x^{3} + a\right)}^{2} a^{2} b}"," ",0,"-1/27*sqrt(3)*(a*e - 2*(-a*b^2)^(1/3)*c)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^2) - 1/54*(a*e + 2*(-a*b^2)^(1/3)*c)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^2) - 1/27*(2*b*c*(-a/b)^(1/3) + a*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b) + 1/18*(4*b^2*c*x^5 + a*b*x^4*e + 7*a*b*c*x^2 - 2*a^2*x*e - 3*a^2*d)/((b*x^3 + a)^2*a^2*b)","A",0
353,1,210,0,0.213396," ","integrate((e*x^2+d*x+c)/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(5 \, b c - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2}} - \frac{{\left(5 \, b c + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2}} - \frac{{\left(2 \, d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{3}} + \frac{4 \, b^{2} d x^{5} + 5 \, b^{2} c x^{4} + 7 \, a b d x^{2} + 8 \, a b c x - 3 \, a^{2} e}{18 \, {\left(b x^{3} + a\right)}^{2} a^{2} b}"," ",0,"-1/27*sqrt(3)*(5*b*c - 2*(-a*b^2)^(1/3)*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^2) - 1/54*(5*b*c + 2*(-a*b^2)^(1/3)*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^2) - 1/27*(2*d*(-a/b)^(1/3) + 5*c)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^3 + 1/18*(4*b^2*d*x^5 + 5*b^2*c*x^4 + 7*a*b*d*x^2 + 8*a*b*c*x - 3*a^2*e)/((b*x^3 + a)^2*a^2*b)","A",0
354,1,253,0,0.244400," ","integrate((e*x^2+d*x+c)/x/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(5 \, b d - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2}} - \frac{{\left(5 \, b d + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2}} - \frac{c \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{3}} + \frac{c \log\left({\left| x \right|}\right)}{a^{3}} + \frac{4 \, a b x^{5} e + 5 \, a b d x^{4} + 6 \, a b c x^{3} + 7 \, a^{2} x^{2} e + 8 \, a^{2} d x + 9 \, a^{2} c}{18 \, {\left(b x^{3} + a\right)}^{2} a^{3}} - \frac{{\left(2 \, a^{4} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e + 5 \, a^{4} b d\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{7} b}"," ",0,"-1/27*sqrt(3)*(5*b*d - 2*(-a*b^2)^(1/3)*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^2) - 1/54*(5*b*d + 2*(-a*b^2)^(1/3)*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^2) - 1/3*c*log(abs(b*x^3 + a))/a^3 + c*log(abs(x))/a^3 + 1/18*(4*a*b*x^5*e + 5*a*b*d*x^4 + 6*a*b*c*x^3 + 7*a^2*x^2*e + 8*a^2*d*x + 9*a^2*c)/((b*x^3 + a)^2*a^3) - 1/27*(2*a^4*b*(-a/b)^(1/3)*e + 5*a^4*b*d)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^7*b)","A",0
355,1,273,0,0.207023," ","integrate((e*x^2+d*x+c)/x^2/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{d \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{3}} + \frac{d \log\left({\left| x \right|}\right)}{a^{3}} + \frac{\sqrt{3} {\left(5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a e + 14 \, \left(-a b^{2}\right)^{\frac{2}{3}} c\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, a^{4} b} + \frac{{\left(5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a e - 14 \, \left(-a b^{2}\right)^{\frac{2}{3}} c\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, a^{4} b} - \frac{28 \, b^{2} c x^{6} - 5 \, a b x^{5} e - 6 \, a b d x^{4} + 49 \, a b c x^{3} - 8 \, a^{2} x^{2} e - 9 \, a^{2} d x + 18 \, a^{2} c}{18 \, {\left(b x^{3} + a\right)}^{2} a^{3} x} + \frac{{\left(14 \, a^{3} b^{2} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a^{4} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{7} b}"," ",0,"-1/3*d*log(abs(b*x^3 + a))/a^3 + d*log(abs(x))/a^3 + 1/27*sqrt(3)*(5*(-a*b^2)^(1/3)*a*e + 14*(-a*b^2)^(2/3)*c)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^4*b) + 1/54*(5*(-a*b^2)^(1/3)*a*e - 14*(-a*b^2)^(2/3)*c)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^4*b) - 1/18*(28*b^2*c*x^6 - 5*a*b*x^5*e - 6*a*b*d*x^4 + 49*a*b*c*x^3 - 8*a^2*x^2*e - 9*a^2*d*x + 18*a^2*c)/((b*x^3 + a)^2*a^3*x) + 1/27*(14*a^3*b^2*c*(-a/b)^(1/3) - 5*a^4*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^7*b)","A",0
356,1,282,0,0.192799," ","integrate((e*x^2+d*x+c)/x^3/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{e \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{3}} + \frac{e \log\left({\left| x \right|}\right)}{a^{3}} - \frac{2 \, \sqrt{3} {\left(10 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c - 7 \, \left(-a b^{2}\right)^{\frac{2}{3}} d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, a^{4} b} - \frac{{\left(10 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c + 7 \, \left(-a b^{2}\right)^{\frac{2}{3}} d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \, a^{4} b} - \frac{28 \, b^{2} d x^{7} + 20 \, b^{2} c x^{6} - 6 \, a b x^{5} e + 49 \, a b d x^{4} + 32 \, a b c x^{3} - 9 \, a^{2} x^{2} e + 18 \, a^{2} d x + 9 \, a^{2} c}{18 \, {\left(b x^{4} + a x\right)}^{2} a^{3}} + \frac{2 \, {\left(7 \, a^{3} b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 10 \, a^{3} b^{2} c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{7} b}"," ",0,"-1/3*e*log(abs(b*x^3 + a))/a^3 + e*log(abs(x))/a^3 - 2/27*sqrt(3)*(10*(-a*b^2)^(1/3)*b*c - 7*(-a*b^2)^(2/3)*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^4*b) - 1/27*(10*(-a*b^2)^(1/3)*b*c + 7*(-a*b^2)^(2/3)*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^4*b) - 1/18*(28*b^2*d*x^7 + 20*b^2*c*x^6 - 6*a*b*x^5*e + 49*a*b*d*x^4 + 32*a*b*c*x^3 - 9*a^2*x^2*e + 18*a^2*d*x + 9*a^2*c)/((b*x^4 + a*x)^2*a^3) + 2/27*(7*a^3*b^2*d*(-a/b)^(1/3) + 10*a^3*b^2*c)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^7*b)","A",0
357,1,305,0,0.259163," ","integrate((e*x^2+d*x+c)/x^4/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{b c \log\left({\left| b x^{3} + a \right|}\right)}{a^{4}} - \frac{3 \, b c \log\left({\left| x \right|}\right)}{a^{4}} - \frac{2 \, \sqrt{3} {\left(10 \, \left(-a b^{2}\right)^{\frac{1}{3}} b d - 7 \, \left(-a b^{2}\right)^{\frac{2}{3}} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, a^{4} b} - \frac{{\left(10 \, \left(-a b^{2}\right)^{\frac{1}{3}} b d + 7 \, \left(-a b^{2}\right)^{\frac{2}{3}} e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \, a^{4} b} + \frac{2 \, {\left(7 \, a^{5} b^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e + 10 \, a^{5} b^{2} d\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{9} b} - \frac{28 \, a b^{2} x^{8} e + 20 \, a b^{2} d x^{7} + 18 \, a b^{2} c x^{6} + 49 \, a^{2} b x^{5} e + 32 \, a^{2} b d x^{4} + 27 \, a^{2} b c x^{3} + 18 \, a^{3} x^{2} e + 9 \, a^{3} d x + 6 \, a^{3} c}{18 \, {\left(b x^{3} + a\right)}^{2} a^{4} x^{3}}"," ",0,"b*c*log(abs(b*x^3 + a))/a^4 - 3*b*c*log(abs(x))/a^4 - 2/27*sqrt(3)*(10*(-a*b^2)^(1/3)*b*d - 7*(-a*b^2)^(2/3)*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^4*b) - 1/27*(10*(-a*b^2)^(1/3)*b*d + 7*(-a*b^2)^(2/3)*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^4*b) + 2/27*(7*a^5*b^2*(-a/b)^(1/3)*e + 10*a^5*b^2*d)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^9*b) - 1/18*(28*a*b^2*x^8*e + 20*a*b^2*d*x^7 + 18*a*b^2*c*x^6 + 49*a^2*b*x^5*e + 32*a^2*b*d*x^4 + 27*a^2*b*c*x^3 + 18*a^3*x^2*e + 9*a^3*d*x + 6*a^3*c)/((b*x^3 + a)^2*a^4*x^3)","A",0
358,1,242,0,0.212077," ","integrate(x^2*(e*x^2+d*x+c)/(b*x^3+a)^4,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(5 \, b d - 4 \, \left(-a b^{2}\right)^{\frac{1}{3}} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{243 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b} - \frac{{\left(5 \, b d + 4 \, \left(-a b^{2}\right)^{\frac{1}{3}} e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{486 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b} - \frac{{\left(4 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}} e + 5 \, d\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{243 \, a^{3} b} + \frac{8 \, b^{2} x^{8} e + 5 \, b^{2} d x^{7} + 22 \, a b x^{5} e + 13 \, a b d x^{4} - 4 \, a^{2} x^{2} e - 10 \, a^{2} d x - 18 \, a^{2} c}{162 \, {\left(b x^{3} + a\right)}^{3} a^{2} b}"," ",0,"-1/243*sqrt(3)*(5*b*d - 4*(-a*b^2)^(1/3)*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^2*b) - 1/486*(5*b*d + 4*(-a*b^2)^(1/3)*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^2*b) - 1/243*(4*(-a/b)^(1/3)*e + 5*d)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b) + 1/162*(8*b^2*x^8*e + 5*b^2*d*x^7 + 22*a*b*x^5*e + 13*a*b*d*x^4 - 4*a^2*x^2*e - 10*a^2*d*x - 18*a^2*c)/((b*x^3 + a)^3*a^2*b)","A",0
359,1,244,0,0.237952," ","integrate(x*(e*x^2+d*x+c)/(b*x^3+a)^4,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(5 \, a e - 14 \, \left(-a b^{2}\right)^{\frac{1}{3}} c\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{243 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3}} - \frac{{\left(5 \, a e + 14 \, \left(-a b^{2}\right)^{\frac{1}{3}} c\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{486 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3}} - \frac{{\left(14 \, b c \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{243 \, a^{4} b} + \frac{28 \, b^{3} c x^{8} + 5 \, a b^{2} x^{7} e + 77 \, a b^{2} c x^{5} + 13 \, a^{2} b x^{4} e + 67 \, a^{2} b c x^{2} - 10 \, a^{3} x e - 18 \, a^{3} d}{162 \, {\left(b x^{3} + a\right)}^{3} a^{3} b}"," ",0,"-1/243*sqrt(3)*(5*a*e - 14*(-a*b^2)^(1/3)*c)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^3) - 1/486*(5*a*e + 14*(-a*b^2)^(1/3)*c)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^3) - 1/243*(14*b*c*(-a/b)^(1/3) + 5*a*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^4*b) + 1/162*(28*b^3*c*x^8 + 5*a*b^2*x^7*e + 77*a*b^2*c*x^5 + 13*a^2*b*x^4*e + 67*a^2*b*c*x^2 - 10*a^3*x*e - 18*a^3*d)/((b*x^3 + a)^3*a^3*b)","A",0
360,1,234,0,0.205181," ","integrate((e*x^2+d*x+c)/(b*x^3+a)^4,x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} {\left(20 \, b c - 7 \, \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{243 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3}} - \frac{{\left(20 \, b c + 7 \, \left(-a b^{2}\right)^{\frac{1}{3}} d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3}} - \frac{2 \, {\left(7 \, d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 20 \, c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{243 \, a^{4}} + \frac{28 \, b^{3} d x^{8} + 40 \, b^{3} c x^{7} + 77 \, a b^{2} d x^{5} + 104 \, a b^{2} c x^{4} + 67 \, a^{2} b d x^{2} + 82 \, a^{2} b c x - 18 \, a^{3} e}{162 \, {\left(b x^{3} + a\right)}^{3} a^{3} b}"," ",0,"-2/243*sqrt(3)*(20*b*c - 7*(-a*b^2)^(1/3)*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^3) - 1/243*(20*b*c + 7*(-a*b^2)^(1/3)*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^3) - 2/243*(7*d*(-a/b)^(1/3) + 20*c)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^4 + 1/162*(28*b^3*d*x^8 + 40*b^3*c*x^7 + 77*a*b^2*d*x^5 + 104*a*b^2*c*x^4 + 67*a^2*b*d*x^2 + 82*a^2*b*c*x - 18*a^3*e)/((b*x^3 + a)^3*a^3*b)","A",0
361,1,290,0,0.238294," ","integrate((e*x^2+d*x+c)/x/(b*x^3+a)^4,x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} {\left(20 \, b d - 7 \, \left(-a b^{2}\right)^{\frac{1}{3}} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{243 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3}} - \frac{{\left(20 \, b d + 7 \, \left(-a b^{2}\right)^{\frac{1}{3}} e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3}} - \frac{c \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{4}} + \frac{c \log\left({\left| x \right|}\right)}{a^{4}} + \frac{28 \, a b^{2} x^{8} e + 40 \, a b^{2} d x^{7} + 54 \, a b^{2} c x^{6} + 77 \, a^{2} b x^{5} e + 104 \, a^{2} b d x^{4} + 135 \, a^{2} b c x^{3} + 67 \, a^{3} x^{2} e + 82 \, a^{3} d x + 99 \, a^{3} c}{162 \, {\left(b x^{3} + a\right)}^{3} a^{4}} - \frac{2 \, {\left(7 \, a^{5} b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e + 20 \, a^{5} b d\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{243 \, a^{9} b}"," ",0,"-2/243*sqrt(3)*(20*b*d - 7*(-a*b^2)^(1/3)*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^3) - 1/243*(20*b*d + 7*(-a*b^2)^(1/3)*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^3) - 1/3*c*log(abs(b*x^3 + a))/a^4 + c*log(abs(x))/a^4 + 1/162*(28*a*b^2*x^8*e + 40*a*b^2*d*x^7 + 54*a*b^2*c*x^6 + 77*a^2*b*x^5*e + 104*a^2*b*d*x^4 + 135*a^2*b*c*x^3 + 67*a^3*x^2*e + 82*a^3*d*x + 99*a^3*c)/((b*x^3 + a)^3*a^4) - 2/243*(7*a^5*b*(-a/b)^(1/3)*e + 20*a^5*b*d)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^9*b)","A",0
362,1,310,0,0.183774," ","integrate((e*x^2+d*x+c)/x^2/(b*x^3+a)^4,x, algorithm=""giac"")","-\frac{d \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{4}} + \frac{d \log\left({\left| x \right|}\right)}{a^{4}} + \frac{20 \, \sqrt{3} {\left(2 \, \left(-a b^{2}\right)^{\frac{1}{3}} a e + 7 \, \left(-a b^{2}\right)^{\frac{2}{3}} c\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{243 \, a^{5} b} + \frac{10 \, {\left(2 \, \left(-a b^{2}\right)^{\frac{1}{3}} a e - 7 \, \left(-a b^{2}\right)^{\frac{2}{3}} c\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \, a^{5} b} - \frac{280 \, b^{3} c x^{9} - 40 \, a b^{2} x^{8} e - 54 \, a b^{2} d x^{7} + 770 \, a b^{2} c x^{6} - 104 \, a^{2} b x^{5} e - 135 \, a^{2} b d x^{4} + 670 \, a^{2} b c x^{3} - 82 \, a^{3} x^{2} e - 99 \, a^{3} d x + 162 \, a^{3} c}{162 \, {\left(b x^{3} + a\right)}^{3} a^{4} x} + \frac{20 \, {\left(7 \, a^{4} b^{2} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a^{5} b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{243 \, a^{9} b}"," ",0,"-1/3*d*log(abs(b*x^3 + a))/a^4 + d*log(abs(x))/a^4 + 20/243*sqrt(3)*(2*(-a*b^2)^(1/3)*a*e + 7*(-a*b^2)^(2/3)*c)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^5*b) + 10/243*(2*(-a*b^2)^(1/3)*a*e - 7*(-a*b^2)^(2/3)*c)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^5*b) - 1/162*(280*b^3*c*x^9 - 40*a*b^2*x^8*e - 54*a*b^2*d*x^7 + 770*a*b^2*c*x^6 - 104*a^2*b*x^5*e - 135*a^2*b*d*x^4 + 670*a^2*b*c*x^3 - 82*a^3*x^2*e - 99*a^3*d*x + 162*a^3*c)/((b*x^3 + a)^3*a^4*x) + 20/243*(7*a^4*b^2*c*(-a/b)^(1/3) - 2*a^5*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^9*b)","A",0
363,1,320,0,0.184913," ","integrate((e*x^2+d*x+c)/x^3/(b*x^3+a)^4,x, algorithm=""giac"")","-\frac{e \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{4}} + \frac{e \log\left({\left| x \right|}\right)}{a^{4}} - \frac{20 \, \sqrt{3} {\left(11 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c - 7 \, \left(-a b^{2}\right)^{\frac{2}{3}} d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{243 \, a^{5} b} - \frac{10 \, {\left(11 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c + 7 \, \left(-a b^{2}\right)^{\frac{2}{3}} d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \, a^{5} b} + \frac{20 \, {\left(7 \, a^{4} b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 11 \, a^{4} b^{2} c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{243 \, a^{9} b} - \frac{280 \, b^{3} d x^{10} + 220 \, b^{3} c x^{9} - 54 \, a b^{2} x^{8} e + 770 \, a b^{2} d x^{7} + 572 \, a b^{2} c x^{6} - 135 \, a^{2} b x^{5} e + 670 \, a^{2} b d x^{4} + 451 \, a^{2} b c x^{3} - 99 \, a^{3} x^{2} e + 162 \, a^{3} d x + 81 \, a^{3} c}{162 \, {\left(b x^{3} + a\right)}^{3} a^{4} x^{2}}"," ",0,"-1/3*e*log(abs(b*x^3 + a))/a^4 + e*log(abs(x))/a^4 - 20/243*sqrt(3)*(11*(-a*b^2)^(1/3)*b*c - 7*(-a*b^2)^(2/3)*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^5*b) - 10/243*(11*(-a*b^2)^(1/3)*b*c + 7*(-a*b^2)^(2/3)*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^5*b) + 20/243*(7*a^4*b^2*d*(-a/b)^(1/3) + 11*a^4*b^2*c)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^9*b) - 1/162*(280*b^3*d*x^10 + 220*b^3*c*x^9 - 54*a*b^2*x^8*e + 770*a*b^2*d*x^7 + 572*a*b^2*c*x^6 - 135*a^2*b*x^5*e + 670*a^2*b*d*x^4 + 451*a^2*b*c*x^3 - 99*a^3*x^2*e + 162*a^3*d*x + 81*a^3*c)/((b*x^3 + a)^3*a^4*x^2)","A",0
364,1,333,0,0.196633," ","integrate((e*x^2+d*x+c)/x^4/(b*x^3+a)^4,x, algorithm=""giac"")","\frac{4 \, b c \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{5}} - \frac{4 \, b c \log\left({\left| x \right|}\right)}{a^{5}} - \frac{20 \, \sqrt{3} {\left(11 \, \left(-a b^{2}\right)^{\frac{1}{3}} b d - 7 \, \left(-a b^{2}\right)^{\frac{2}{3}} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{243 \, a^{5} b} - \frac{10 \, {\left(11 \, \left(-a b^{2}\right)^{\frac{1}{3}} b d + 7 \, \left(-a b^{2}\right)^{\frac{2}{3}} e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \, a^{5} b} - \frac{280 \, b^{3} x^{11} e + 220 \, b^{3} d x^{10} + 216 \, b^{3} c x^{9} + 770 \, a b^{2} x^{8} e + 572 \, a b^{2} d x^{7} + 540 \, a b^{2} c x^{6} + 670 \, a^{2} b x^{5} e + 451 \, a^{2} b d x^{4} + 396 \, a^{2} b c x^{3} + 162 \, a^{3} x^{2} e + 81 \, a^{3} d x + 54 \, a^{3} c}{162 \, {\left(b x^{4} + a x\right)}^{3} a^{4}} + \frac{20 \, {\left(7 \, a^{6} b^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e + 11 \, a^{6} b^{2} d\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{243 \, a^{11} b}"," ",0,"4/3*b*c*log(abs(b*x^3 + a))/a^5 - 4*b*c*log(abs(x))/a^5 - 20/243*sqrt(3)*(11*(-a*b^2)^(1/3)*b*d - 7*(-a*b^2)^(2/3)*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^5*b) - 10/243*(11*(-a*b^2)^(1/3)*b*d + 7*(-a*b^2)^(2/3)*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^5*b) - 1/162*(280*b^3*x^11*e + 220*b^3*d*x^10 + 216*b^3*c*x^9 + 770*a*b^2*x^8*e + 572*a*b^2*d*x^7 + 540*a*b^2*c*x^6 + 670*a^2*b*x^5*e + 451*a^2*b*d*x^4 + 396*a^2*b*c*x^3 + 162*a^3*x^2*e + 81*a^3*d*x + 54*a^3*c)/((b*x^4 + a*x)^3*a^4) + 20/243*(7*a^6*b^2*(-a/b)^(1/3)*e + 11*a^6*b^2*d)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^11*b)","A",0
365,1,27,0,0.154582," ","integrate((2*a*x-x^2)/(a^3+x^3),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} {\left(a - 2 \, x\right)}}{3 \, a}\right) - \log\left({\left| a + x \right|}\right)"," ",0,"2/3*sqrt(3)*arctan(-1/3*sqrt(3)*(a - 2*x)/a) - log(abs(a + x))","A",0
366,1,27,0,0.153553," ","integrate((2*a-x)*x/(a^3+x^3),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} {\left(a - 2 \, x\right)}}{3 \, a}\right) - \log\left({\left| a + x \right|}\right)"," ",0,"2/3*sqrt(3)*arctan(-1/3*sqrt(3)*(a - 2*x)/a) - log(abs(a + x))","A",0
367,1,29,0,0.153909," ","integrate((2*a*x+x^2)/(a^3-x^3),x, algorithm=""giac"")","-\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(a + 2 \, x\right)}}{3 \, a}\right) - \log\left({\left| -a + x \right|}\right)"," ",0,"-2/3*sqrt(3)*arctan(1/3*sqrt(3)*(a + 2*x)/a) - log(abs(-a + x))","A",0
368,1,29,0,0.150652," ","integrate(x*(2*a+x)/(a^3-x^3),x, algorithm=""giac"")","-\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(a + 2 \, x\right)}}{3 \, a}\right) - \log\left({\left| -a + x \right|}\right)"," ",0,"-2/3*sqrt(3)*arctan(1/3*sqrt(3)*(a + 2*x)/a) - log(abs(-a + x))","A",0
369,1,174,0,0.480455," ","integrate(x*(-2*(a/b)^(1/3)*C+C*x)/(b*x^3+a),x, algorithm=""giac"")","-\frac{{\left(C b \left(-\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, \left(a b^{2}\right)^{\frac{1}{3}} C \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b} - \frac{\sqrt{3} {\left(a b^{2} - \sqrt{3} \sqrt{a^{2} b^{4}} i\right)} C \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a b^{3}} + \frac{{\left(3 \, a b^{2} - \sqrt{3} \sqrt{a^{2} b^{4}} i\right)} C \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a b^{3}}"," ",0,"-1/3*(C*b*(-a/b)^(2/3) - 2*(a*b^2)^(1/3)*C*(-a/b)^(1/3))*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b) - 1/3*sqrt(3)*(a*b^2 - sqrt(3)*sqrt(a^2*b^4)*i)*C*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a*b^3) + 1/6*(3*a*b^2 - sqrt(3)*sqrt(a^2*b^4)*i)*C*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a*b^3)","B",0
370,1,165,0,0.205433," ","integrate(x*(-2*(-a/b)^(1/3)*C+C*x)/(-b*x^3+a),x, algorithm=""giac"")","-\frac{{\left(C b \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} C \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b} + \frac{\sqrt{3} {\left(a b^{2} + \sqrt{3} \sqrt{a^{2} b^{4}} i\right)} C \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a b^{3}} - \frac{{\left(3 \, a b^{2} + \sqrt{3} \sqrt{a^{2} b^{4}} i\right)} C \log\left(x^{2} + x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a b^{3}}"," ",0,"-1/3*(C*b*(a/b)^(2/3) - 2*(-a*b^2)^(1/3)*C*(a/b)^(1/3))*(a/b)^(1/3)*log(abs(x - (a/b)^(1/3)))/(a*b) + 1/3*sqrt(3)*(a*b^2 + sqrt(3)*sqrt(a^2*b^4)*i)*C*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/(a*b^3) - 1/6*(3*a*b^2 + sqrt(3)*sqrt(a^2*b^4)*i)*C*log(x^2 + x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^3)","B",0
371,1,97,0,0.190226," ","integrate(x*(2*(-a/b)^(1/3)*C+C*x)/(b*x^3+a),x, algorithm=""giac"")","\frac{2 \, \sqrt{3} C \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b} - \frac{{\left(C b \left(-\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} C \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b}"," ",0,"2/3*sqrt(3)*C*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b - 1/3*(C*b*(-a/b)^(2/3) + 2*(-a*b^2)^(1/3)*C*(-a/b)^(1/3))*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b)","B",0
372,1,90,0,0.196391," ","integrate(x*(2*(a/b)^(1/3)*C+C*x)/(-b*x^3+a),x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} C \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b} - \frac{{\left(C b \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, \left(a b^{2}\right)^{\frac{1}{3}} C \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b}"," ",0,"-2/3*sqrt(3)*C*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/b - 1/3*(C*b*(a/b)^(2/3) + 2*(a*b^2)^(1/3)*C*(a/b)^(1/3))*(a/b)^(1/3)*log(abs(x - (a/b)^(1/3)))/(a*b)","A",0
373,1,87,0,0.154600," ","integrate(x^4*(b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\frac{1}{13} \, b h x^{13} + \frac{1}{12} \, b g x^{12} + \frac{1}{11} \, b f x^{11} + \frac{1}{10} \, a h x^{10} + \frac{1}{10} \, b x^{10} e + \frac{1}{9} \, b d x^{9} + \frac{1}{9} \, a g x^{9} + \frac{1}{8} \, b c x^{8} + \frac{1}{8} \, a f x^{8} + \frac{1}{7} \, a x^{7} e + \frac{1}{6} \, a d x^{6} + \frac{1}{5} \, a c x^{5}"," ",0,"1/13*b*h*x^13 + 1/12*b*g*x^12 + 1/11*b*f*x^11 + 1/10*a*h*x^10 + 1/10*b*x^10*e + 1/9*b*d*x^9 + 1/9*a*g*x^9 + 1/8*b*c*x^8 + 1/8*a*f*x^8 + 1/7*a*x^7*e + 1/6*a*d*x^6 + 1/5*a*c*x^5","A",0
374,1,87,0,0.161154," ","integrate(x^3*(b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\frac{1}{12} \, b h x^{12} + \frac{1}{11} \, b g x^{11} + \frac{1}{10} \, b f x^{10} + \frac{1}{9} \, a h x^{9} + \frac{1}{9} \, b x^{9} e + \frac{1}{8} \, b d x^{8} + \frac{1}{8} \, a g x^{8} + \frac{1}{7} \, b c x^{7} + \frac{1}{7} \, a f x^{7} + \frac{1}{6} \, a x^{6} e + \frac{1}{5} \, a d x^{5} + \frac{1}{4} \, a c x^{4}"," ",0,"1/12*b*h*x^12 + 1/11*b*g*x^11 + 1/10*b*f*x^10 + 1/9*a*h*x^9 + 1/9*b*x^9*e + 1/8*b*d*x^8 + 1/8*a*g*x^8 + 1/7*b*c*x^7 + 1/7*a*f*x^7 + 1/6*a*x^6*e + 1/5*a*d*x^5 + 1/4*a*c*x^4","A",0
375,1,87,0,0.164128," ","integrate(x^2*(b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\frac{1}{11} \, b h x^{11} + \frac{1}{10} \, b g x^{10} + \frac{1}{9} \, b f x^{9} + \frac{1}{8} \, a h x^{8} + \frac{1}{8} \, b x^{8} e + \frac{1}{7} \, b d x^{7} + \frac{1}{7} \, a g x^{7} + \frac{1}{6} \, b c x^{6} + \frac{1}{6} \, a f x^{6} + \frac{1}{5} \, a x^{5} e + \frac{1}{4} \, a d x^{4} + \frac{1}{3} \, a c x^{3}"," ",0,"1/11*b*h*x^11 + 1/10*b*g*x^10 + 1/9*b*f*x^9 + 1/8*a*h*x^8 + 1/8*b*x^8*e + 1/7*b*d*x^7 + 1/7*a*g*x^7 + 1/6*b*c*x^6 + 1/6*a*f*x^6 + 1/5*a*x^5*e + 1/4*a*d*x^4 + 1/3*a*c*x^3","A",0
376,1,87,0,0.146987," ","integrate(x*(b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\frac{1}{10} \, b h x^{10} + \frac{1}{9} \, b g x^{9} + \frac{1}{8} \, b f x^{8} + \frac{1}{7} \, a h x^{7} + \frac{1}{7} \, b x^{7} e + \frac{1}{6} \, b d x^{6} + \frac{1}{6} \, a g x^{6} + \frac{1}{5} \, b c x^{5} + \frac{1}{5} \, a f x^{5} + \frac{1}{4} \, a x^{4} e + \frac{1}{3} \, a d x^{3} + \frac{1}{2} \, a c x^{2}"," ",0,"1/10*b*h*x^10 + 1/9*b*g*x^9 + 1/8*b*f*x^8 + 1/7*a*h*x^7 + 1/7*b*x^7*e + 1/6*b*d*x^6 + 1/6*a*g*x^6 + 1/5*b*c*x^5 + 1/5*a*f*x^5 + 1/4*a*x^4*e + 1/3*a*d*x^3 + 1/2*a*c*x^2","A",0
377,1,84,0,0.148436," ","integrate((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\frac{1}{9} \, b h x^{9} + \frac{1}{8} \, b g x^{8} + \frac{1}{7} \, b f x^{7} + \frac{1}{6} \, a h x^{6} + \frac{1}{6} \, b x^{6} e + \frac{1}{5} \, b d x^{5} + \frac{1}{5} \, a g x^{5} + \frac{1}{4} \, b c x^{4} + \frac{1}{4} \, a f x^{4} + \frac{1}{3} \, a x^{3} e + \frac{1}{2} \, a d x^{2} + a c x"," ",0,"1/9*b*h*x^9 + 1/8*b*g*x^8 + 1/7*b*f*x^7 + 1/6*a*h*x^6 + 1/6*b*x^6*e + 1/5*b*d*x^5 + 1/5*a*g*x^5 + 1/4*b*c*x^4 + 1/4*a*f*x^4 + 1/3*a*x^3*e + 1/2*a*d*x^2 + a*c*x","A",0
378,1,83,0,0.151904," ","integrate((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x,x, algorithm=""giac"")","\frac{1}{8} \, b h x^{8} + \frac{1}{7} \, b g x^{7} + \frac{1}{6} \, b f x^{6} + \frac{1}{5} \, a h x^{5} + \frac{1}{5} \, b x^{5} e + \frac{1}{4} \, b d x^{4} + \frac{1}{4} \, a g x^{4} + \frac{1}{3} \, b c x^{3} + \frac{1}{3} \, a f x^{3} + \frac{1}{2} \, a x^{2} e + a d x + a c \log\left({\left| x \right|}\right)"," ",0,"1/8*b*h*x^8 + 1/7*b*g*x^7 + 1/6*b*f*x^6 + 1/5*a*h*x^5 + 1/5*b*x^5*e + 1/4*b*d*x^4 + 1/4*a*g*x^4 + 1/3*b*c*x^3 + 1/3*a*f*x^3 + 1/2*a*x^2*e + a*d*x + a*c*log(abs(x))","A",0
379,1,83,0,0.162509," ","integrate((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^2,x, algorithm=""giac"")","\frac{1}{7} \, b h x^{7} + \frac{1}{6} \, b g x^{6} + \frac{1}{5} \, b f x^{5} + \frac{1}{4} \, a h x^{4} + \frac{1}{4} \, b x^{4} e + \frac{1}{3} \, b d x^{3} + \frac{1}{3} \, a g x^{3} + \frac{1}{2} \, b c x^{2} + \frac{1}{2} \, a f x^{2} + a x e + a d \log\left({\left| x \right|}\right) - \frac{a c}{x}"," ",0,"1/7*b*h*x^7 + 1/6*b*g*x^6 + 1/5*b*f*x^5 + 1/4*a*h*x^4 + 1/4*b*x^4*e + 1/3*b*d*x^3 + 1/3*a*g*x^3 + 1/2*b*c*x^2 + 1/2*a*f*x^2 + a*x*e + a*d*log(abs(x)) - a*c/x","A",0
380,1,80,0,0.161591," ","integrate((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^3,x, algorithm=""giac"")","\frac{1}{6} \, b h x^{6} + \frac{1}{5} \, b g x^{5} + \frac{1}{4} \, b f x^{4} + \frac{1}{3} \, a h x^{3} + \frac{1}{3} \, b x^{3} e + \frac{1}{2} \, b d x^{2} + \frac{1}{2} \, a g x^{2} + b c x + a f x + a e \log\left({\left| x \right|}\right) - \frac{2 \, a d x + a c}{2 \, x^{2}}"," ",0,"1/6*b*h*x^6 + 1/5*b*g*x^5 + 1/4*b*f*x^4 + 1/3*a*h*x^3 + 1/3*b*x^3*e + 1/2*b*d*x^2 + 1/2*a*g*x^2 + b*c*x + a*f*x + a*e*log(abs(x)) - 1/2*(2*a*d*x + a*c)/x^2","A",0
381,1,79,0,0.169012," ","integrate((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^4,x, algorithm=""giac"")","\frac{1}{5} \, b h x^{5} + \frac{1}{4} \, b g x^{4} + \frac{1}{3} \, b f x^{3} + \frac{1}{2} \, a h x^{2} + \frac{1}{2} \, b x^{2} e + b d x + a g x + {\left(b c + a f\right)} \log\left({\left| x \right|}\right) - \frac{6 \, a x^{2} e + 3 \, a d x + 2 \, a c}{6 \, x^{3}}"," ",0,"1/5*b*h*x^5 + 1/4*b*g*x^4 + 1/3*b*f*x^3 + 1/2*a*h*x^2 + 1/2*b*x^2*e + b*d*x + a*g*x + (b*c + a*f)*log(abs(x)) - 1/6*(6*a*x^2*e + 3*a*d*x + 2*a*c)/x^3","A",0
382,1,77,0,0.151750," ","integrate((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^5,x, algorithm=""giac"")","\frac{1}{4} \, b h x^{4} + \frac{1}{3} \, b g x^{3} + \frac{1}{2} \, b f x^{2} + a h x + b x e + {\left(b d + a g\right)} \log\left({\left| x \right|}\right) - \frac{12 \, {\left(b c + a f\right)} x^{3} + 6 \, a x^{2} e + 4 \, a d x + 3 \, a c}{12 \, x^{4}}"," ",0,"1/4*b*h*x^4 + 1/3*b*g*x^3 + 1/2*b*f*x^2 + a*h*x + b*x*e + (b*d + a*g)*log(abs(x)) - 1/12*(12*(b*c + a*f)*x^3 + 6*a*x^2*e + 4*a*d*x + 3*a*c)/x^4","A",0
383,1,160,0,0.154175," ","integrate(x^4*(b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\frac{1}{16} \, b^{2} h x^{16} + \frac{1}{15} \, b^{2} g x^{15} + \frac{1}{14} \, b^{2} f x^{14} + \frac{2}{13} \, a b h x^{13} + \frac{1}{13} \, b^{2} x^{13} e + \frac{1}{12} \, b^{2} d x^{12} + \frac{1}{6} \, a b g x^{12} + \frac{1}{11} \, b^{2} c x^{11} + \frac{2}{11} \, a b f x^{11} + \frac{1}{10} \, a^{2} h x^{10} + \frac{1}{5} \, a b x^{10} e + \frac{2}{9} \, a b d x^{9} + \frac{1}{9} \, a^{2} g x^{9} + \frac{1}{4} \, a b c x^{8} + \frac{1}{8} \, a^{2} f x^{8} + \frac{1}{7} \, a^{2} x^{7} e + \frac{1}{6} \, a^{2} d x^{6} + \frac{1}{5} \, a^{2} c x^{5}"," ",0,"1/16*b^2*h*x^16 + 1/15*b^2*g*x^15 + 1/14*b^2*f*x^14 + 2/13*a*b*h*x^13 + 1/13*b^2*x^13*e + 1/12*b^2*d*x^12 + 1/6*a*b*g*x^12 + 1/11*b^2*c*x^11 + 2/11*a*b*f*x^11 + 1/10*a^2*h*x^10 + 1/5*a*b*x^10*e + 2/9*a*b*d*x^9 + 1/9*a^2*g*x^9 + 1/4*a*b*c*x^8 + 1/8*a^2*f*x^8 + 1/7*a^2*x^7*e + 1/6*a^2*d*x^6 + 1/5*a^2*c*x^5","A",0
384,1,160,0,0.152900," ","integrate(x^3*(b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\frac{1}{15} \, b^{2} h x^{15} + \frac{1}{14} \, b^{2} g x^{14} + \frac{1}{13} \, b^{2} f x^{13} + \frac{1}{6} \, a b h x^{12} + \frac{1}{12} \, b^{2} x^{12} e + \frac{1}{11} \, b^{2} d x^{11} + \frac{2}{11} \, a b g x^{11} + \frac{1}{10} \, b^{2} c x^{10} + \frac{1}{5} \, a b f x^{10} + \frac{1}{9} \, a^{2} h x^{9} + \frac{2}{9} \, a b x^{9} e + \frac{1}{4} \, a b d x^{8} + \frac{1}{8} \, a^{2} g x^{8} + \frac{2}{7} \, a b c x^{7} + \frac{1}{7} \, a^{2} f x^{7} + \frac{1}{6} \, a^{2} x^{6} e + \frac{1}{5} \, a^{2} d x^{5} + \frac{1}{4} \, a^{2} c x^{4}"," ",0,"1/15*b^2*h*x^15 + 1/14*b^2*g*x^14 + 1/13*b^2*f*x^13 + 1/6*a*b*h*x^12 + 1/12*b^2*x^12*e + 1/11*b^2*d*x^11 + 2/11*a*b*g*x^11 + 1/10*b^2*c*x^10 + 1/5*a*b*f*x^10 + 1/9*a^2*h*x^9 + 2/9*a*b*x^9*e + 1/4*a*b*d*x^8 + 1/8*a^2*g*x^8 + 2/7*a*b*c*x^7 + 1/7*a^2*f*x^7 + 1/6*a^2*x^6*e + 1/5*a^2*d*x^5 + 1/4*a^2*c*x^4","A",0
385,1,160,0,0.182129," ","integrate(x^2*(b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\frac{1}{14} \, b^{2} h x^{14} + \frac{1}{13} \, b^{2} g x^{13} + \frac{1}{12} \, b^{2} f x^{12} + \frac{2}{11} \, a b h x^{11} + \frac{1}{11} \, b^{2} x^{11} e + \frac{1}{10} \, b^{2} d x^{10} + \frac{1}{5} \, a b g x^{10} + \frac{1}{9} \, b^{2} c x^{9} + \frac{2}{9} \, a b f x^{9} + \frac{1}{8} \, a^{2} h x^{8} + \frac{1}{4} \, a b x^{8} e + \frac{2}{7} \, a b d x^{7} + \frac{1}{7} \, a^{2} g x^{7} + \frac{1}{3} \, a b c x^{6} + \frac{1}{6} \, a^{2} f x^{6} + \frac{1}{5} \, a^{2} x^{5} e + \frac{1}{4} \, a^{2} d x^{4} + \frac{1}{3} \, a^{2} c x^{3}"," ",0,"1/14*b^2*h*x^14 + 1/13*b^2*g*x^13 + 1/12*b^2*f*x^12 + 2/11*a*b*h*x^11 + 1/11*b^2*x^11*e + 1/10*b^2*d*x^10 + 1/5*a*b*g*x^10 + 1/9*b^2*c*x^9 + 2/9*a*b*f*x^9 + 1/8*a^2*h*x^8 + 1/4*a*b*x^8*e + 2/7*a*b*d*x^7 + 1/7*a^2*g*x^7 + 1/3*a*b*c*x^6 + 1/6*a^2*f*x^6 + 1/5*a^2*x^5*e + 1/4*a^2*d*x^4 + 1/3*a^2*c*x^3","A",0
386,1,160,0,0.187558," ","integrate(x*(b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\frac{1}{13} \, b^{2} h x^{13} + \frac{1}{12} \, b^{2} g x^{12} + \frac{1}{11} \, b^{2} f x^{11} + \frac{1}{5} \, a b h x^{10} + \frac{1}{10} \, b^{2} x^{10} e + \frac{1}{9} \, b^{2} d x^{9} + \frac{2}{9} \, a b g x^{9} + \frac{1}{8} \, b^{2} c x^{8} + \frac{1}{4} \, a b f x^{8} + \frac{1}{7} \, a^{2} h x^{7} + \frac{2}{7} \, a b x^{7} e + \frac{1}{3} \, a b d x^{6} + \frac{1}{6} \, a^{2} g x^{6} + \frac{2}{5} \, a b c x^{5} + \frac{1}{5} \, a^{2} f x^{5} + \frac{1}{4} \, a^{2} x^{4} e + \frac{1}{3} \, a^{2} d x^{3} + \frac{1}{2} \, a^{2} c x^{2}"," ",0,"1/13*b^2*h*x^13 + 1/12*b^2*g*x^12 + 1/11*b^2*f*x^11 + 1/5*a*b*h*x^10 + 1/10*b^2*x^10*e + 1/9*b^2*d*x^9 + 2/9*a*b*g*x^9 + 1/8*b^2*c*x^8 + 1/4*a*b*f*x^8 + 1/7*a^2*h*x^7 + 2/7*a*b*x^7*e + 1/3*a*b*d*x^6 + 1/6*a^2*g*x^6 + 2/5*a*b*c*x^5 + 1/5*a^2*f*x^5 + 1/4*a^2*x^4*e + 1/3*a^2*d*x^3 + 1/2*a^2*c*x^2","A",0
387,1,157,0,0.163864," ","integrate((b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\frac{1}{12} \, b^{2} h x^{12} + \frac{1}{11} \, b^{2} g x^{11} + \frac{1}{10} \, b^{2} f x^{10} + \frac{2}{9} \, a b h x^{9} + \frac{1}{9} \, b^{2} x^{9} e + \frac{1}{8} \, b^{2} d x^{8} + \frac{1}{4} \, a b g x^{8} + \frac{1}{7} \, b^{2} c x^{7} + \frac{2}{7} \, a b f x^{7} + \frac{1}{6} \, a^{2} h x^{6} + \frac{1}{3} \, a b x^{6} e + \frac{2}{5} \, a b d x^{5} + \frac{1}{5} \, a^{2} g x^{5} + \frac{1}{2} \, a b c x^{4} + \frac{1}{4} \, a^{2} f x^{4} + \frac{1}{3} \, a^{2} x^{3} e + \frac{1}{2} \, a^{2} d x^{2} + a^{2} c x"," ",0,"1/12*b^2*h*x^12 + 1/11*b^2*g*x^11 + 1/10*b^2*f*x^10 + 2/9*a*b*h*x^9 + 1/9*b^2*x^9*e + 1/8*b^2*d*x^8 + 1/4*a*b*g*x^8 + 1/7*b^2*c*x^7 + 2/7*a*b*f*x^7 + 1/6*a^2*h*x^6 + 1/3*a*b*x^6*e + 2/5*a*b*d*x^5 + 1/5*a^2*g*x^5 + 1/2*a*b*c*x^4 + 1/4*a^2*f*x^4 + 1/3*a^2*x^3*e + 1/2*a^2*d*x^2 + a^2*c*x","A",0
388,1,156,0,0.151417," ","integrate((b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x,x, algorithm=""giac"")","\frac{1}{11} \, b^{2} h x^{11} + \frac{1}{10} \, b^{2} g x^{10} + \frac{1}{9} \, b^{2} f x^{9} + \frac{1}{4} \, a b h x^{8} + \frac{1}{8} \, b^{2} x^{8} e + \frac{1}{7} \, b^{2} d x^{7} + \frac{2}{7} \, a b g x^{7} + \frac{1}{6} \, b^{2} c x^{6} + \frac{1}{3} \, a b f x^{6} + \frac{1}{5} \, a^{2} h x^{5} + \frac{2}{5} \, a b x^{5} e + \frac{1}{2} \, a b d x^{4} + \frac{1}{4} \, a^{2} g x^{4} + \frac{2}{3} \, a b c x^{3} + \frac{1}{3} \, a^{2} f x^{3} + \frac{1}{2} \, a^{2} x^{2} e + a^{2} d x + a^{2} c \log\left({\left| x \right|}\right)"," ",0,"1/11*b^2*h*x^11 + 1/10*b^2*g*x^10 + 1/9*b^2*f*x^9 + 1/4*a*b*h*x^8 + 1/8*b^2*x^8*e + 1/7*b^2*d*x^7 + 2/7*a*b*g*x^7 + 1/6*b^2*c*x^6 + 1/3*a*b*f*x^6 + 1/5*a^2*h*x^5 + 2/5*a*b*x^5*e + 1/2*a*b*d*x^4 + 1/4*a^2*g*x^4 + 2/3*a*b*c*x^3 + 1/3*a^2*f*x^3 + 1/2*a^2*x^2*e + a^2*d*x + a^2*c*log(abs(x))","A",0
389,1,155,0,0.151647," ","integrate((b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^2,x, algorithm=""giac"")","\frac{1}{10} \, b^{2} h x^{10} + \frac{1}{9} \, b^{2} g x^{9} + \frac{1}{8} \, b^{2} f x^{8} + \frac{2}{7} \, a b h x^{7} + \frac{1}{7} \, b^{2} x^{7} e + \frac{1}{6} \, b^{2} d x^{6} + \frac{1}{3} \, a b g x^{6} + \frac{1}{5} \, b^{2} c x^{5} + \frac{2}{5} \, a b f x^{5} + \frac{1}{4} \, a^{2} h x^{4} + \frac{1}{2} \, a b x^{4} e + \frac{2}{3} \, a b d x^{3} + \frac{1}{3} \, a^{2} g x^{3} + a b c x^{2} + \frac{1}{2} \, a^{2} f x^{2} + a^{2} x e + a^{2} d \log\left({\left| x \right|}\right) - \frac{a^{2} c}{x}"," ",0,"1/10*b^2*h*x^10 + 1/9*b^2*g*x^9 + 1/8*b^2*f*x^8 + 2/7*a*b*h*x^7 + 1/7*b^2*x^7*e + 1/6*b^2*d*x^6 + 1/3*a*b*g*x^6 + 1/5*b^2*c*x^5 + 2/5*a*b*f*x^5 + 1/4*a^2*h*x^4 + 1/2*a*b*x^4*e + 2/3*a*b*d*x^3 + 1/3*a^2*g*x^3 + a*b*c*x^2 + 1/2*a^2*f*x^2 + a^2*x*e + a^2*d*log(abs(x)) - a^2*c/x","A",0
390,1,153,0,0.153478," ","integrate((b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^3,x, algorithm=""giac"")","\frac{1}{9} \, b^{2} h x^{9} + \frac{1}{8} \, b^{2} g x^{8} + \frac{1}{7} \, b^{2} f x^{7} + \frac{1}{3} \, a b h x^{6} + \frac{1}{6} \, b^{2} x^{6} e + \frac{1}{5} \, b^{2} d x^{5} + \frac{2}{5} \, a b g x^{5} + \frac{1}{4} \, b^{2} c x^{4} + \frac{1}{2} \, a b f x^{4} + \frac{1}{3} \, a^{2} h x^{3} + \frac{2}{3} \, a b x^{3} e + a b d x^{2} + \frac{1}{2} \, a^{2} g x^{2} + 2 \, a b c x + a^{2} f x + a^{2} e \log\left({\left| x \right|}\right) - \frac{2 \, a^{2} d x + a^{2} c}{2 \, x^{2}}"," ",0,"1/9*b^2*h*x^9 + 1/8*b^2*g*x^8 + 1/7*b^2*f*x^7 + 1/3*a*b*h*x^6 + 1/6*b^2*x^6*e + 1/5*b^2*d*x^5 + 2/5*a*b*g*x^5 + 1/4*b^2*c*x^4 + 1/2*a*b*f*x^4 + 1/3*a^2*h*x^3 + 2/3*a*b*x^3*e + a*b*d*x^2 + 1/2*a^2*g*x^2 + 2*a*b*c*x + a^2*f*x + a^2*e*log(abs(x)) - 1/2*(2*a^2*d*x + a^2*c)/x^2","A",0
391,1,153,0,0.171859," ","integrate((b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^4,x, algorithm=""giac"")","\frac{1}{8} \, b^{2} h x^{8} + \frac{1}{7} \, b^{2} g x^{7} + \frac{1}{6} \, b^{2} f x^{6} + \frac{2}{5} \, a b h x^{5} + \frac{1}{5} \, b^{2} x^{5} e + \frac{1}{4} \, b^{2} d x^{4} + \frac{1}{2} \, a b g x^{4} + \frac{1}{3} \, b^{2} c x^{3} + \frac{2}{3} \, a b f x^{3} + \frac{1}{2} \, a^{2} h x^{2} + a b x^{2} e + 2 \, a b d x + a^{2} g x + {\left(2 \, a b c + a^{2} f\right)} \log\left({\left| x \right|}\right) - \frac{6 \, a^{2} x^{2} e + 3 \, a^{2} d x + 2 \, a^{2} c}{6 \, x^{3}}"," ",0,"1/8*b^2*h*x^8 + 1/7*b^2*g*x^7 + 1/6*b^2*f*x^6 + 2/5*a*b*h*x^5 + 1/5*b^2*x^5*e + 1/4*b^2*d*x^4 + 1/2*a*b*g*x^4 + 1/3*b^2*c*x^3 + 2/3*a*b*f*x^3 + 1/2*a^2*h*x^2 + a*b*x^2*e + 2*a*b*d*x + a^2*g*x + (2*a*b*c + a^2*f)*log(abs(x)) - 1/6*(6*a^2*x^2*e + 3*a^2*d*x + 2*a^2*c)/x^3","A",0
392,1,152,0,0.169558," ","integrate((b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^5,x, algorithm=""giac"")","\frac{1}{7} \, b^{2} h x^{7} + \frac{1}{6} \, b^{2} g x^{6} + \frac{1}{5} \, b^{2} f x^{5} + \frac{1}{2} \, a b h x^{4} + \frac{1}{4} \, b^{2} x^{4} e + \frac{1}{3} \, b^{2} d x^{3} + \frac{2}{3} \, a b g x^{3} + \frac{1}{2} \, b^{2} c x^{2} + a b f x^{2} + a^{2} h x + 2 \, a b x e + {\left(2 \, a b d + a^{2} g\right)} \log\left({\left| x \right|}\right) - \frac{6 \, a^{2} x^{2} e + 4 \, a^{2} d x + 12 \, {\left(2 \, a b c + a^{2} f\right)} x^{3} + 3 \, a^{2} c}{12 \, x^{4}}"," ",0,"1/7*b^2*h*x^7 + 1/6*b^2*g*x^6 + 1/5*b^2*f*x^5 + 1/2*a*b*h*x^4 + 1/4*b^2*x^4*e + 1/3*b^2*d*x^3 + 2/3*a*b*g*x^3 + 1/2*b^2*c*x^2 + a*b*f*x^2 + a^2*h*x + 2*a*b*x*e + (2*a*b*d + a^2*g)*log(abs(x)) - 1/12*(6*a^2*x^2*e + 4*a^2*d*x + 12*(2*a*b*c + a^2*f)*x^3 + 3*a^2*c)/x^4","A",0
393,1,233,0,0.151563," ","integrate(x^4*(b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\frac{1}{19} \, b^{3} h x^{19} + \frac{1}{18} \, b^{3} g x^{18} + \frac{1}{17} \, b^{3} f x^{17} + \frac{3}{16} \, a b^{2} h x^{16} + \frac{1}{16} \, b^{3} x^{16} e + \frac{1}{15} \, b^{3} d x^{15} + \frac{1}{5} \, a b^{2} g x^{15} + \frac{1}{14} \, b^{3} c x^{14} + \frac{3}{14} \, a b^{2} f x^{14} + \frac{3}{13} \, a^{2} b h x^{13} + \frac{3}{13} \, a b^{2} x^{13} e + \frac{1}{4} \, a b^{2} d x^{12} + \frac{1}{4} \, a^{2} b g x^{12} + \frac{3}{11} \, a b^{2} c x^{11} + \frac{3}{11} \, a^{2} b f x^{11} + \frac{1}{10} \, a^{3} h x^{10} + \frac{3}{10} \, a^{2} b x^{10} e + \frac{1}{3} \, a^{2} b d x^{9} + \frac{1}{9} \, a^{3} g x^{9} + \frac{3}{8} \, a^{2} b c x^{8} + \frac{1}{8} \, a^{3} f x^{8} + \frac{1}{7} \, a^{3} x^{7} e + \frac{1}{6} \, a^{3} d x^{6} + \frac{1}{5} \, a^{3} c x^{5}"," ",0,"1/19*b^3*h*x^19 + 1/18*b^3*g*x^18 + 1/17*b^3*f*x^17 + 3/16*a*b^2*h*x^16 + 1/16*b^3*x^16*e + 1/15*b^3*d*x^15 + 1/5*a*b^2*g*x^15 + 1/14*b^3*c*x^14 + 3/14*a*b^2*f*x^14 + 3/13*a^2*b*h*x^13 + 3/13*a*b^2*x^13*e + 1/4*a*b^2*d*x^12 + 1/4*a^2*b*g*x^12 + 3/11*a*b^2*c*x^11 + 3/11*a^2*b*f*x^11 + 1/10*a^3*h*x^10 + 3/10*a^2*b*x^10*e + 1/3*a^2*b*d*x^9 + 1/9*a^3*g*x^9 + 3/8*a^2*b*c*x^8 + 1/8*a^3*f*x^8 + 1/7*a^3*x^7*e + 1/6*a^3*d*x^6 + 1/5*a^3*c*x^5","A",0
394,1,233,0,0.169768," ","integrate(x^3*(b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\frac{1}{18} \, b^{3} h x^{18} + \frac{1}{17} \, b^{3} g x^{17} + \frac{1}{16} \, b^{3} f x^{16} + \frac{1}{5} \, a b^{2} h x^{15} + \frac{1}{15} \, b^{3} x^{15} e + \frac{1}{14} \, b^{3} d x^{14} + \frac{3}{14} \, a b^{2} g x^{14} + \frac{1}{13} \, b^{3} c x^{13} + \frac{3}{13} \, a b^{2} f x^{13} + \frac{1}{4} \, a^{2} b h x^{12} + \frac{1}{4} \, a b^{2} x^{12} e + \frac{3}{11} \, a b^{2} d x^{11} + \frac{3}{11} \, a^{2} b g x^{11} + \frac{3}{10} \, a b^{2} c x^{10} + \frac{3}{10} \, a^{2} b f x^{10} + \frac{1}{9} \, a^{3} h x^{9} + \frac{1}{3} \, a^{2} b x^{9} e + \frac{3}{8} \, a^{2} b d x^{8} + \frac{1}{8} \, a^{3} g x^{8} + \frac{3}{7} \, a^{2} b c x^{7} + \frac{1}{7} \, a^{3} f x^{7} + \frac{1}{6} \, a^{3} x^{6} e + \frac{1}{5} \, a^{3} d x^{5} + \frac{1}{4} \, a^{3} c x^{4}"," ",0,"1/18*b^3*h*x^18 + 1/17*b^3*g*x^17 + 1/16*b^3*f*x^16 + 1/5*a*b^2*h*x^15 + 1/15*b^3*x^15*e + 1/14*b^3*d*x^14 + 3/14*a*b^2*g*x^14 + 1/13*b^3*c*x^13 + 3/13*a*b^2*f*x^13 + 1/4*a^2*b*h*x^12 + 1/4*a*b^2*x^12*e + 3/11*a*b^2*d*x^11 + 3/11*a^2*b*g*x^11 + 3/10*a*b^2*c*x^10 + 3/10*a^2*b*f*x^10 + 1/9*a^3*h*x^9 + 1/3*a^2*b*x^9*e + 3/8*a^2*b*d*x^8 + 1/8*a^3*g*x^8 + 3/7*a^2*b*c*x^7 + 1/7*a^3*f*x^7 + 1/6*a^3*x^6*e + 1/5*a^3*d*x^5 + 1/4*a^3*c*x^4","A",0
395,1,233,0,0.175544," ","integrate(x^2*(b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\frac{1}{17} \, b^{3} h x^{17} + \frac{1}{16} \, b^{3} g x^{16} + \frac{1}{15} \, b^{3} f x^{15} + \frac{3}{14} \, a b^{2} h x^{14} + \frac{1}{14} \, b^{3} x^{14} e + \frac{1}{13} \, b^{3} d x^{13} + \frac{3}{13} \, a b^{2} g x^{13} + \frac{1}{12} \, b^{3} c x^{12} + \frac{1}{4} \, a b^{2} f x^{12} + \frac{3}{11} \, a^{2} b h x^{11} + \frac{3}{11} \, a b^{2} x^{11} e + \frac{3}{10} \, a b^{2} d x^{10} + \frac{3}{10} \, a^{2} b g x^{10} + \frac{1}{3} \, a b^{2} c x^{9} + \frac{1}{3} \, a^{2} b f x^{9} + \frac{1}{8} \, a^{3} h x^{8} + \frac{3}{8} \, a^{2} b x^{8} e + \frac{3}{7} \, a^{2} b d x^{7} + \frac{1}{7} \, a^{3} g x^{7} + \frac{1}{2} \, a^{2} b c x^{6} + \frac{1}{6} \, a^{3} f x^{6} + \frac{1}{5} \, a^{3} x^{5} e + \frac{1}{4} \, a^{3} d x^{4} + \frac{1}{3} \, a^{3} c x^{3}"," ",0,"1/17*b^3*h*x^17 + 1/16*b^3*g*x^16 + 1/15*b^3*f*x^15 + 3/14*a*b^2*h*x^14 + 1/14*b^3*x^14*e + 1/13*b^3*d*x^13 + 3/13*a*b^2*g*x^13 + 1/12*b^3*c*x^12 + 1/4*a*b^2*f*x^12 + 3/11*a^2*b*h*x^11 + 3/11*a*b^2*x^11*e + 3/10*a*b^2*d*x^10 + 3/10*a^2*b*g*x^10 + 1/3*a*b^2*c*x^9 + 1/3*a^2*b*f*x^9 + 1/8*a^3*h*x^8 + 3/8*a^2*b*x^8*e + 3/7*a^2*b*d*x^7 + 1/7*a^3*g*x^7 + 1/2*a^2*b*c*x^6 + 1/6*a^3*f*x^6 + 1/5*a^3*x^5*e + 1/4*a^3*d*x^4 + 1/3*a^3*c*x^3","A",0
396,1,233,0,0.166015," ","integrate(x*(b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\frac{1}{16} \, b^{3} h x^{16} + \frac{1}{15} \, b^{3} g x^{15} + \frac{1}{14} \, b^{3} f x^{14} + \frac{3}{13} \, a b^{2} h x^{13} + \frac{1}{13} \, b^{3} x^{13} e + \frac{1}{12} \, b^{3} d x^{12} + \frac{1}{4} \, a b^{2} g x^{12} + \frac{1}{11} \, b^{3} c x^{11} + \frac{3}{11} \, a b^{2} f x^{11} + \frac{3}{10} \, a^{2} b h x^{10} + \frac{3}{10} \, a b^{2} x^{10} e + \frac{1}{3} \, a b^{2} d x^{9} + \frac{1}{3} \, a^{2} b g x^{9} + \frac{3}{8} \, a b^{2} c x^{8} + \frac{3}{8} \, a^{2} b f x^{8} + \frac{1}{7} \, a^{3} h x^{7} + \frac{3}{7} \, a^{2} b x^{7} e + \frac{1}{2} \, a^{2} b d x^{6} + \frac{1}{6} \, a^{3} g x^{6} + \frac{3}{5} \, a^{2} b c x^{5} + \frac{1}{5} \, a^{3} f x^{5} + \frac{1}{4} \, a^{3} x^{4} e + \frac{1}{3} \, a^{3} d x^{3} + \frac{1}{2} \, a^{3} c x^{2}"," ",0,"1/16*b^3*h*x^16 + 1/15*b^3*g*x^15 + 1/14*b^3*f*x^14 + 3/13*a*b^2*h*x^13 + 1/13*b^3*x^13*e + 1/12*b^3*d*x^12 + 1/4*a*b^2*g*x^12 + 1/11*b^3*c*x^11 + 3/11*a*b^2*f*x^11 + 3/10*a^2*b*h*x^10 + 3/10*a*b^2*x^10*e + 1/3*a*b^2*d*x^9 + 1/3*a^2*b*g*x^9 + 3/8*a*b^2*c*x^8 + 3/8*a^2*b*f*x^8 + 1/7*a^3*h*x^7 + 3/7*a^2*b*x^7*e + 1/2*a^2*b*d*x^6 + 1/6*a^3*g*x^6 + 3/5*a^2*b*c*x^5 + 1/5*a^3*f*x^5 + 1/4*a^3*x^4*e + 1/3*a^3*d*x^3 + 1/2*a^3*c*x^2","A",0
397,1,230,0,0.152201," ","integrate((b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\frac{1}{15} \, b^{3} h x^{15} + \frac{1}{14} \, b^{3} g x^{14} + \frac{1}{13} \, b^{3} f x^{13} + \frac{1}{4} \, a b^{2} h x^{12} + \frac{1}{12} \, b^{3} x^{12} e + \frac{1}{11} \, b^{3} d x^{11} + \frac{3}{11} \, a b^{2} g x^{11} + \frac{1}{10} \, b^{3} c x^{10} + \frac{3}{10} \, a b^{2} f x^{10} + \frac{1}{3} \, a^{2} b h x^{9} + \frac{1}{3} \, a b^{2} x^{9} e + \frac{3}{8} \, a b^{2} d x^{8} + \frac{3}{8} \, a^{2} b g x^{8} + \frac{3}{7} \, a b^{2} c x^{7} + \frac{3}{7} \, a^{2} b f x^{7} + \frac{1}{6} \, a^{3} h x^{6} + \frac{1}{2} \, a^{2} b x^{6} e + \frac{3}{5} \, a^{2} b d x^{5} + \frac{1}{5} \, a^{3} g x^{5} + \frac{3}{4} \, a^{2} b c x^{4} + \frac{1}{4} \, a^{3} f x^{4} + \frac{1}{3} \, a^{3} x^{3} e + \frac{1}{2} \, a^{3} d x^{2} + a^{3} c x"," ",0,"1/15*b^3*h*x^15 + 1/14*b^3*g*x^14 + 1/13*b^3*f*x^13 + 1/4*a*b^2*h*x^12 + 1/12*b^3*x^12*e + 1/11*b^3*d*x^11 + 3/11*a*b^2*g*x^11 + 1/10*b^3*c*x^10 + 3/10*a*b^2*f*x^10 + 1/3*a^2*b*h*x^9 + 1/3*a*b^2*x^9*e + 3/8*a*b^2*d*x^8 + 3/8*a^2*b*g*x^8 + 3/7*a*b^2*c*x^7 + 3/7*a^2*b*f*x^7 + 1/6*a^3*h*x^6 + 1/2*a^2*b*x^6*e + 3/5*a^2*b*d*x^5 + 1/5*a^3*g*x^5 + 3/4*a^2*b*c*x^4 + 1/4*a^3*f*x^4 + 1/3*a^3*x^3*e + 1/2*a^3*d*x^2 + a^3*c*x","A",0
398,1,228,0,0.158950," ","integrate((b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x,x, algorithm=""giac"")","\frac{1}{14} \, b^{3} h x^{14} + \frac{1}{13} \, b^{3} g x^{13} + \frac{1}{12} \, b^{3} f x^{12} + \frac{3}{11} \, a b^{2} h x^{11} + \frac{1}{11} \, b^{3} x^{11} e + \frac{1}{10} \, b^{3} d x^{10} + \frac{3}{10} \, a b^{2} g x^{10} + \frac{1}{9} \, b^{3} c x^{9} + \frac{1}{3} \, a b^{2} f x^{9} + \frac{3}{8} \, a^{2} b h x^{8} + \frac{3}{8} \, a b^{2} x^{8} e + \frac{3}{7} \, a b^{2} d x^{7} + \frac{3}{7} \, a^{2} b g x^{7} + \frac{1}{2} \, a b^{2} c x^{6} + \frac{1}{2} \, a^{2} b f x^{6} + \frac{1}{5} \, a^{3} h x^{5} + \frac{3}{5} \, a^{2} b x^{5} e + \frac{3}{4} \, a^{2} b d x^{4} + \frac{1}{4} \, a^{3} g x^{4} + a^{2} b c x^{3} + \frac{1}{3} \, a^{3} f x^{3} + \frac{1}{2} \, a^{3} x^{2} e + a^{3} d x + a^{3} c \log\left({\left| x \right|}\right)"," ",0,"1/14*b^3*h*x^14 + 1/13*b^3*g*x^13 + 1/12*b^3*f*x^12 + 3/11*a*b^2*h*x^11 + 1/11*b^3*x^11*e + 1/10*b^3*d*x^10 + 3/10*a*b^2*g*x^10 + 1/9*b^3*c*x^9 + 1/3*a*b^2*f*x^9 + 3/8*a^2*b*h*x^8 + 3/8*a*b^2*x^8*e + 3/7*a*b^2*d*x^7 + 3/7*a^2*b*g*x^7 + 1/2*a*b^2*c*x^6 + 1/2*a^2*b*f*x^6 + 1/5*a^3*h*x^5 + 3/5*a^2*b*x^5*e + 3/4*a^2*b*d*x^4 + 1/4*a^3*g*x^4 + a^2*b*c*x^3 + 1/3*a^3*f*x^3 + 1/2*a^3*x^2*e + a^3*d*x + a^3*c*log(abs(x))","A",0
399,1,228,0,0.154965," ","integrate((b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^2,x, algorithm=""giac"")","\frac{1}{13} \, b^{3} h x^{13} + \frac{1}{12} \, b^{3} g x^{12} + \frac{1}{11} \, b^{3} f x^{11} + \frac{3}{10} \, a b^{2} h x^{10} + \frac{1}{10} \, b^{3} x^{10} e + \frac{1}{9} \, b^{3} d x^{9} + \frac{1}{3} \, a b^{2} g x^{9} + \frac{1}{8} \, b^{3} c x^{8} + \frac{3}{8} \, a b^{2} f x^{8} + \frac{3}{7} \, a^{2} b h x^{7} + \frac{3}{7} \, a b^{2} x^{7} e + \frac{1}{2} \, a b^{2} d x^{6} + \frac{1}{2} \, a^{2} b g x^{6} + \frac{3}{5} \, a b^{2} c x^{5} + \frac{3}{5} \, a^{2} b f x^{5} + \frac{1}{4} \, a^{3} h x^{4} + \frac{3}{4} \, a^{2} b x^{4} e + a^{2} b d x^{3} + \frac{1}{3} \, a^{3} g x^{3} + \frac{3}{2} \, a^{2} b c x^{2} + \frac{1}{2} \, a^{3} f x^{2} + a^{3} x e + a^{3} d \log\left({\left| x \right|}\right) - \frac{a^{3} c}{x}"," ",0,"1/13*b^3*h*x^13 + 1/12*b^3*g*x^12 + 1/11*b^3*f*x^11 + 3/10*a*b^2*h*x^10 + 1/10*b^3*x^10*e + 1/9*b^3*d*x^9 + 1/3*a*b^2*g*x^9 + 1/8*b^3*c*x^8 + 3/8*a*b^2*f*x^8 + 3/7*a^2*b*h*x^7 + 3/7*a*b^2*x^7*e + 1/2*a*b^2*d*x^6 + 1/2*a^2*b*g*x^6 + 3/5*a*b^2*c*x^5 + 3/5*a^2*b*f*x^5 + 1/4*a^3*h*x^4 + 3/4*a^2*b*x^4*e + a^2*b*d*x^3 + 1/3*a^3*g*x^3 + 3/2*a^2*b*c*x^2 + 1/2*a^3*f*x^2 + a^3*x*e + a^3*d*log(abs(x)) - a^3*c/x","A",0
400,1,226,0,0.158046," ","integrate((b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^3,x, algorithm=""giac"")","\frac{1}{12} \, b^{3} h x^{12} + \frac{1}{11} \, b^{3} g x^{11} + \frac{1}{10} \, b^{3} f x^{10} + \frac{1}{3} \, a b^{2} h x^{9} + \frac{1}{9} \, b^{3} x^{9} e + \frac{1}{8} \, b^{3} d x^{8} + \frac{3}{8} \, a b^{2} g x^{8} + \frac{1}{7} \, b^{3} c x^{7} + \frac{3}{7} \, a b^{2} f x^{7} + \frac{1}{2} \, a^{2} b h x^{6} + \frac{1}{2} \, a b^{2} x^{6} e + \frac{3}{5} \, a b^{2} d x^{5} + \frac{3}{5} \, a^{2} b g x^{5} + \frac{3}{4} \, a b^{2} c x^{4} + \frac{3}{4} \, a^{2} b f x^{4} + \frac{1}{3} \, a^{3} h x^{3} + a^{2} b x^{3} e + \frac{3}{2} \, a^{2} b d x^{2} + \frac{1}{2} \, a^{3} g x^{2} + 3 \, a^{2} b c x + a^{3} f x + a^{3} e \log\left({\left| x \right|}\right) - \frac{2 \, a^{3} d x + a^{3} c}{2 \, x^{2}}"," ",0,"1/12*b^3*h*x^12 + 1/11*b^3*g*x^11 + 1/10*b^3*f*x^10 + 1/3*a*b^2*h*x^9 + 1/9*b^3*x^9*e + 1/8*b^3*d*x^8 + 3/8*a*b^2*g*x^8 + 1/7*b^3*c*x^7 + 3/7*a*b^2*f*x^7 + 1/2*a^2*b*h*x^6 + 1/2*a*b^2*x^6*e + 3/5*a*b^2*d*x^5 + 3/5*a^2*b*g*x^5 + 3/4*a*b^2*c*x^4 + 3/4*a^2*b*f*x^4 + 1/3*a^3*h*x^3 + a^2*b*x^3*e + 3/2*a^2*b*d*x^2 + 1/2*a^3*g*x^2 + 3*a^2*b*c*x + a^3*f*x + a^3*e*log(abs(x)) - 1/2*(2*a^3*d*x + a^3*c)/x^2","A",0
401,1,225,0,0.185196," ","integrate((b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^4,x, algorithm=""giac"")","\frac{1}{11} \, b^{3} h x^{11} + \frac{1}{10} \, b^{3} g x^{10} + \frac{1}{9} \, b^{3} f x^{9} + \frac{3}{8} \, a b^{2} h x^{8} + \frac{1}{8} \, b^{3} x^{8} e + \frac{1}{7} \, b^{3} d x^{7} + \frac{3}{7} \, a b^{2} g x^{7} + \frac{1}{6} \, b^{3} c x^{6} + \frac{1}{2} \, a b^{2} f x^{6} + \frac{3}{5} \, a^{2} b h x^{5} + \frac{3}{5} \, a b^{2} x^{5} e + \frac{3}{4} \, a b^{2} d x^{4} + \frac{3}{4} \, a^{2} b g x^{4} + a b^{2} c x^{3} + a^{2} b f x^{3} + \frac{1}{2} \, a^{3} h x^{2} + \frac{3}{2} \, a^{2} b x^{2} e + 3 \, a^{2} b d x + a^{3} g x + {\left(3 \, a^{2} b c + a^{3} f\right)} \log\left({\left| x \right|}\right) - \frac{6 \, a^{3} x^{2} e + 3 \, a^{3} d x + 2 \, a^{3} c}{6 \, x^{3}}"," ",0,"1/11*b^3*h*x^11 + 1/10*b^3*g*x^10 + 1/9*b^3*f*x^9 + 3/8*a*b^2*h*x^8 + 1/8*b^3*x^8*e + 1/7*b^3*d*x^7 + 3/7*a*b^2*g*x^7 + 1/6*b^3*c*x^6 + 1/2*a*b^2*f*x^6 + 3/5*a^2*b*h*x^5 + 3/5*a*b^2*x^5*e + 3/4*a*b^2*d*x^4 + 3/4*a^2*b*g*x^4 + a*b^2*c*x^3 + a^2*b*f*x^3 + 1/2*a^3*h*x^2 + 3/2*a^2*b*x^2*e + 3*a^2*b*d*x + a^3*g*x + (3*a^2*b*c + a^3*f)*log(abs(x)) - 1/6*(6*a^3*x^2*e + 3*a^3*d*x + 2*a^3*c)/x^3","A",0
402,1,224,0,0.154874," ","integrate((b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^5,x, algorithm=""giac"")","\frac{1}{10} \, b^{3} h x^{10} + \frac{1}{9} \, b^{3} g x^{9} + \frac{1}{8} \, b^{3} f x^{8} + \frac{3}{7} \, a b^{2} h x^{7} + \frac{1}{7} \, b^{3} x^{7} e + \frac{1}{6} \, b^{3} d x^{6} + \frac{1}{2} \, a b^{2} g x^{6} + \frac{1}{5} \, b^{3} c x^{5} + \frac{3}{5} \, a b^{2} f x^{5} + \frac{3}{4} \, a^{2} b h x^{4} + \frac{3}{4} \, a b^{2} x^{4} e + a b^{2} d x^{3} + a^{2} b g x^{3} + \frac{3}{2} \, a b^{2} c x^{2} + \frac{3}{2} \, a^{2} b f x^{2} + a^{3} h x + 3 \, a^{2} b x e + {\left(3 \, a^{2} b d + a^{3} g\right)} \log\left({\left| x \right|}\right) - \frac{6 \, a^{3} x^{2} e + 4 \, a^{3} d x + 3 \, a^{3} c + 12 \, {\left(3 \, a^{2} b c + a^{3} f\right)} x^{3}}{12 \, x^{4}}"," ",0,"1/10*b^3*h*x^10 + 1/9*b^3*g*x^9 + 1/8*b^3*f*x^8 + 3/7*a*b^2*h*x^7 + 1/7*b^3*x^7*e + 1/6*b^3*d*x^6 + 1/2*a*b^2*g*x^6 + 1/5*b^3*c*x^5 + 3/5*a*b^2*f*x^5 + 3/4*a^2*b*h*x^4 + 3/4*a*b^2*x^4*e + a*b^2*d*x^3 + a^2*b*g*x^3 + 3/2*a*b^2*c*x^2 + 3/2*a^2*b*f*x^2 + a^3*h*x + 3*a^2*b*x*e + (3*a^2*b*d + a^3*g)*log(abs(x)) - 1/12*(6*a^3*x^2*e + 4*a^3*d*x + 3*a^3*c + 12*(3*a^2*b*c + a^3*f)*x^3)/x^4","A",0
403,1,380,0,0.200015," ","integrate(x^4*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""giac"")","-\frac{{\left(a b d - a^{2} g\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{3}} - \frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{1}{3}} a^{2} h - \left(-a b^{2}\right)^{\frac{1}{3}} a b e - \left(-a b^{2}\right)^{\frac{2}{3}} b c + \left(-a b^{2}\right)^{\frac{2}{3}} a f\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{4}} - \frac{{\left(\left(-a b^{2}\right)^{\frac{1}{3}} a^{2} h - \left(-a b^{2}\right)^{\frac{1}{3}} a b e + \left(-a b^{2}\right)^{\frac{2}{3}} b c - \left(-a b^{2}\right)^{\frac{2}{3}} a f\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{4}} + \frac{60 \, b^{6} h x^{7} + 70 \, b^{6} g x^{6} + 84 \, b^{6} f x^{5} - 105 \, a b^{5} h x^{4} + 105 \, b^{6} x^{4} e + 140 \, b^{6} d x^{3} - 140 \, a b^{5} g x^{3} + 210 \, b^{6} c x^{2} - 210 \, a b^{5} f x^{2} + 420 \, a^{2} b^{4} h x - 420 \, a b^{5} x e}{420 \, b^{7}} + \frac{{\left(a b^{14} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} b^{13} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a^{3} b^{12} h - a^{2} b^{13} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{15}}"," ",0,"-1/3*(a*b*d - a^2*g)*log(abs(b*x^3 + a))/b^3 - 1/3*sqrt(3)*((-a*b^2)^(1/3)*a^2*h - (-a*b^2)^(1/3)*a*b*e - (-a*b^2)^(2/3)*b*c + (-a*b^2)^(2/3)*a*f)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^4 - 1/6*((-a*b^2)^(1/3)*a^2*h - (-a*b^2)^(1/3)*a*b*e + (-a*b^2)^(2/3)*b*c - (-a*b^2)^(2/3)*a*f)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^4 + 1/420*(60*b^6*h*x^7 + 70*b^6*g*x^6 + 84*b^6*f*x^5 - 105*a*b^5*h*x^4 + 105*b^6*x^4*e + 140*b^6*d*x^3 - 140*a*b^5*g*x^3 + 210*b^6*c*x^2 - 210*a*b^5*f*x^2 + 420*a^2*b^4*h*x - 420*a*b^5*x*e)/b^7 + 1/3*(a*b^14*c*(-a/b)^(1/3) - a^2*b^13*f*(-a/b)^(1/3) + a^3*b^12*h - a^2*b^13*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^15)","A",0
404,1,353,0,0.184154," ","integrate(x^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""giac"")","\frac{{\left(a^{2} h - a b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{3}} - \frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{1}{3}} b^{2} c - \left(-a b^{2}\right)^{\frac{1}{3}} a b f - \left(-a b^{2}\right)^{\frac{2}{3}} b d + \left(-a b^{2}\right)^{\frac{2}{3}} a g\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{4}} - \frac{{\left(\left(-a b^{2}\right)^{\frac{1}{3}} b^{2} c - \left(-a b^{2}\right)^{\frac{1}{3}} a b f + \left(-a b^{2}\right)^{\frac{2}{3}} b d - \left(-a b^{2}\right)^{\frac{2}{3}} a g\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{4}} + \frac{10 \, b^{5} h x^{6} + 12 \, b^{5} g x^{5} + 15 \, b^{5} f x^{4} - 20 \, a b^{4} h x^{3} + 20 \, b^{5} x^{3} e + 30 \, b^{5} d x^{2} - 30 \, a b^{4} g x^{2} + 60 \, b^{5} c x - 60 \, a b^{4} f x}{60 \, b^{6}} + \frac{{\left(a b^{12} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} b^{11} g \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a b^{12} c - a^{2} b^{11} f\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{13}}"," ",0,"1/3*(a^2*h - a*b*e)*log(abs(b*x^3 + a))/b^3 - 1/3*sqrt(3)*((-a*b^2)^(1/3)*b^2*c - (-a*b^2)^(1/3)*a*b*f - (-a*b^2)^(2/3)*b*d + (-a*b^2)^(2/3)*a*g)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^4 - 1/6*((-a*b^2)^(1/3)*b^2*c - (-a*b^2)^(1/3)*a*b*f + (-a*b^2)^(2/3)*b*d - (-a*b^2)^(2/3)*a*g)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^4 + 1/60*(10*b^5*h*x^6 + 12*b^5*g*x^5 + 15*b^5*f*x^4 - 20*a*b^4*h*x^3 + 20*b^5*x^3*e + 30*b^5*d*x^2 - 30*a*b^4*g*x^2 + 60*b^5*c*x - 60*a*b^4*f*x)/b^6 + 1/3*(a*b^12*d*(-a/b)^(1/3) - a^2*b^11*g*(-a/b)^(1/3) + a*b^12*c - a^2*b^11*f)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^13)","A",0
405,1,333,0,0.243659," ","integrate(x^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""giac"")","\frac{{\left(b c - a f\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{2}} - \frac{\sqrt{3} {\left(\left(-a b^{2}\right)^{\frac{1}{3}} b^{2} d - \left(-a b^{2}\right)^{\frac{1}{3}} a b g + \left(-a b^{2}\right)^{\frac{2}{3}} a h - \left(-a b^{2}\right)^{\frac{2}{3}} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{4}} - \frac{{\left(\left(-a b^{2}\right)^{\frac{1}{3}} b^{2} d - \left(-a b^{2}\right)^{\frac{1}{3}} a b g - \left(-a b^{2}\right)^{\frac{2}{3}} a h + \left(-a b^{2}\right)^{\frac{2}{3}} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{4}} + \frac{12 \, b^{4} h x^{5} + 15 \, b^{4} g x^{4} + 20 \, b^{4} f x^{3} - 30 \, a b^{3} h x^{2} + 30 \, b^{4} x^{2} e + 60 \, b^{4} d x - 60 \, a b^{3} g x}{60 \, b^{5}} - \frac{{\left(a^{2} b^{9} h \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a b^{10} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e - a b^{10} d + a^{2} b^{9} g\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{11}}"," ",0,"1/3*(b*c - a*f)*log(abs(b*x^3 + a))/b^2 - 1/3*sqrt(3)*((-a*b^2)^(1/3)*b^2*d - (-a*b^2)^(1/3)*a*b*g + (-a*b^2)^(2/3)*a*h - (-a*b^2)^(2/3)*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^4 - 1/6*((-a*b^2)^(1/3)*b^2*d - (-a*b^2)^(1/3)*a*b*g - (-a*b^2)^(2/3)*a*h + (-a*b^2)^(2/3)*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^4 + 1/60*(12*b^4*h*x^5 + 15*b^4*g*x^4 + 20*b^4*f*x^3 - 30*a*b^3*h*x^2 + 30*b^4*x^2*e + 60*b^4*d*x - 60*a*b^3*g*x)/b^5 - 1/3*(a^2*b^9*h*(-a/b)^(1/3) - a*b^10*(-a/b)^(1/3)*e - a*b^10*d + a^2*b^9*g)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^11)","A",0
406,1,295,0,0.284144," ","integrate(x*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(a^{2} h - a b e - \left(-a b^{2}\right)^{\frac{1}{3}} b c + \left(-a b^{2}\right)^{\frac{1}{3}} a f\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}} b} - \frac{{\left(a^{2} h - a b e + \left(-a b^{2}\right)^{\frac{1}{3}} b c - \left(-a b^{2}\right)^{\frac{1}{3}} a f\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}} b} + \frac{{\left(b d - a g\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{2}} + \frac{3 \, b^{3} h x^{4} + 4 \, b^{3} g x^{3} + 6 \, b^{3} f x^{2} - 12 \, a b^{2} h x + 12 \, b^{3} x e}{12 \, b^{4}} - \frac{{\left(b^{9} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a b^{8} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} b^{7} h - a b^{8} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{9}}"," ",0,"-1/3*sqrt(3)*(a^2*h - a*b*e - (-a*b^2)^(1/3)*b*c + (-a*b^2)^(1/3)*a*f)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*b) - 1/6*(a^2*h - a*b*e + (-a*b^2)^(1/3)*b*c - (-a*b^2)^(1/3)*a*f)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*b) + 1/3*(b*d - a*g)*log(abs(b*x^3 + a))/b^2 + 1/12*(3*b^3*h*x^4 + 4*b^3*g*x^3 + 6*b^3*f*x^2 - 12*a*b^2*h*x + 12*b^3*x*e)/b^4 - 1/3*(b^9*c*(-a/b)^(1/3) - a*b^8*f*(-a/b)^(1/3) + a^2*b^7*h - a*b^8*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^9)","A",0
407,1,272,0,0.189560," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b^{2} c - a b f - \left(-a b^{2}\right)^{\frac{1}{3}} b d + \left(-a b^{2}\right)^{\frac{1}{3}} a g\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}} b} - \frac{{\left(b^{2} c - a b f + \left(-a b^{2}\right)^{\frac{1}{3}} b d - \left(-a b^{2}\right)^{\frac{1}{3}} a g\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}} b} - \frac{{\left(a h - b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{2}} + \frac{2 \, b^{2} h x^{3} + 3 \, b^{2} g x^{2} + 6 \, b^{2} f x}{6 \, b^{3}} - \frac{{\left(b^{7} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a b^{6} g \left(-\frac{a}{b}\right)^{\frac{1}{3}} + b^{7} c - a b^{6} f\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{7}}"," ",0,"-1/3*sqrt(3)*(b^2*c - a*b*f - (-a*b^2)^(1/3)*b*d + (-a*b^2)^(1/3)*a*g)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*b) - 1/6*(b^2*c - a*b*f + (-a*b^2)^(1/3)*b*d - (-a*b^2)^(1/3)*a*g)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*b) - 1/3*(a*h - b*e)*log(abs(b*x^3 + a))/b^2 + 1/6*(2*b^2*h*x^3 + 3*b^2*g*x^2 + 6*b^2*f*x)/b^3 - 1/3*(b^7*d*(-a/b)^(1/3) - a*b^6*g*(-a/b)^(1/3) + b^7*c - a*b^6*f)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^7)","A",0
408,1,281,0,0.189060," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x/(b*x^3+a),x, algorithm=""giac"")","\frac{c \log\left({\left| x \right|}\right)}{a} - \frac{\sqrt{3} {\left(b^{2} d - a b g + \left(-a b^{2}\right)^{\frac{1}{3}} a h - \left(-a b^{2}\right)^{\frac{1}{3}} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}} b} - \frac{{\left(b^{2} d - a b g - \left(-a b^{2}\right)^{\frac{1}{3}} a h + \left(-a b^{2}\right)^{\frac{1}{3}} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}} b} - \frac{{\left(b c - a f\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a b} + \frac{b h x^{2} + 2 \, b g x}{2 \, b^{2}} + \frac{{\left(a^{3} b^{2} h \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} b^{3} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e - a^{2} b^{3} d + a^{3} b^{2} g\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{3} b^{3}}"," ",0,"c*log(abs(x))/a - 1/3*sqrt(3)*(b^2*d - a*b*g + (-a*b^2)^(1/3)*a*h - (-a*b^2)^(1/3)*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*b) - 1/6*(b^2*d - a*b*g - (-a*b^2)^(1/3)*a*h + (-a*b^2)^(1/3)*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*b) - 1/3*(b*c - a*f)*log(abs(b*x^3 + a))/(a*b) + 1/2*(b*h*x^2 + 2*b*g*x)/b^2 + 1/3*(a^3*b^2*h*(-a/b)^(1/3) - a^2*b^3*(-a/b)^(1/3)*e - a^2*b^3*d + a^3*b^2*g)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b^3)","A",0
409,1,277,0,0.186599," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^2/(b*x^3+a),x, algorithm=""giac"")","\frac{h x}{b} + \frac{d \log\left({\left| x \right|}\right)}{a} + \frac{\sqrt{3} {\left(a^{2} h - a b e - \left(-a b^{2}\right)^{\frac{1}{3}} b c + \left(-a b^{2}\right)^{\frac{1}{3}} a f\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} + \frac{{\left(a^{2} h - a b e + \left(-a b^{2}\right)^{\frac{1}{3}} b c - \left(-a b^{2}\right)^{\frac{1}{3}} a f\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} - \frac{{\left(b d - a g\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a b} - \frac{c}{a x} + \frac{{\left(a b^{4} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} b^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a^{3} b^{2} h - a^{2} b^{3} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{3} b^{3}}"," ",0,"h*x/b + d*log(abs(x))/a + 1/3*sqrt(3)*(a^2*h - a*b*e - (-a*b^2)^(1/3)*b*c + (-a*b^2)^(1/3)*a*f)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a) + 1/6*(a^2*h - a*b*e + (-a*b^2)^(1/3)*b*c - (-a*b^2)^(1/3)*a*f)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a) - 1/3*(b*d - a*g)*log(abs(b*x^3 + a))/(a*b) - c/(a*x) + 1/3*(a*b^4*c*(-a/b)^(1/3) - a^2*b^3*f*(-a/b)^(1/3) + a^3*b^2*h - a^2*b^3*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b^3)","A",0
410,1,269,0,0.275055," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^3/(b*x^3+a),x, algorithm=""giac"")","\frac{e \log\left({\left| x \right|}\right)}{a} + \frac{\sqrt{3} {\left(b^{2} c - a b f - \left(-a b^{2}\right)^{\frac{1}{3}} b d + \left(-a b^{2}\right)^{\frac{1}{3}} a g\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} + \frac{{\left(b^{2} c - a b f + \left(-a b^{2}\right)^{\frac{1}{3}} b d - \left(-a b^{2}\right)^{\frac{1}{3}} a g\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} + \frac{{\left(a h - b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a b} + \frac{{\left(a b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} b g \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a b^{2} c - a^{2} b f\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{3} b} - \frac{2 \, d x + c}{2 \, a x^{2}}"," ",0,"e*log(abs(x))/a + 1/3*sqrt(3)*(b^2*c - a*b*f - (-a*b^2)^(1/3)*b*d + (-a*b^2)^(1/3)*a*g)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a) + 1/6*(b^2*c - a*b*f + (-a*b^2)^(1/3)*b*d - (-a*b^2)^(1/3)*a*g)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a) + 1/3*(a*h - b*e)*log(abs(b*x^3 + a))/(a*b) + 1/3*(a*b^2*d*(-a/b)^(1/3) - a^2*b*g*(-a/b)^(1/3) + a*b^2*c - a^2*b*f)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b) - 1/2*(2*d*x + c)/(a*x^2)","A",0
411,1,291,0,0.225742," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^4/(b*x^3+a),x, algorithm=""giac"")","\frac{\sqrt{3} {\left(b^{2} d - a b g + \left(-a b^{2}\right)^{\frac{1}{3}} a h - \left(-a b^{2}\right)^{\frac{1}{3}} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} + \frac{{\left(b^{2} d - a b g - \left(-a b^{2}\right)^{\frac{1}{3}} a h + \left(-a b^{2}\right)^{\frac{1}{3}} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} + \frac{{\left(b c - a f\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{2}} - \frac{{\left(b c - a f\right)} \log\left({\left| x \right|}\right)}{a^{2}} - \frac{{\left(a^{4} b h \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{3} b^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e - a^{3} b^{2} d + a^{4} b g\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{5} b} - \frac{6 \, a x^{2} e + 3 \, a d x + 2 \, a c}{6 \, a^{2} x^{3}}"," ",0,"1/3*sqrt(3)*(b^2*d - a*b*g + (-a*b^2)^(1/3)*a*h - (-a*b^2)^(1/3)*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a) + 1/6*(b^2*d - a*b*g - (-a*b^2)^(1/3)*a*h + (-a*b^2)^(1/3)*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a) + 1/3*(b*c - a*f)*log(abs(b*x^3 + a))/a^2 - (b*c - a*f)*log(abs(x))/a^2 - 1/3*(a^4*b*h*(-a/b)^(1/3) - a^3*b^2*(-a/b)^(1/3)*e - a^3*b^2*d + a^4*b*g)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^5*b) - 1/6*(6*a*x^2*e + 3*a*d*x + 2*a*c)/(a^2*x^3)","A",0
412,1,357,0,0.198570," ","integrate(x^4*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(7 \, a^{2} h - 4 \, a b e - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c + 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a f\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{2}} - \frac{{\left(7 \, a^{2} h - 4 \, a b e + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c - 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a f\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{2}} + \frac{{\left(b d - 2 \, a g\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{3}} + \frac{a b d - a^{2} g - {\left(b^{2} c - a b f\right)} x^{2} - {\left(a^{2} h - a b e\right)} x}{3 \, {\left(b x^{3} + a\right)} b^{3}} - \frac{{\left(2 \, b^{6} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a b^{5} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 7 \, a^{2} b^{4} h - 4 \, a b^{5} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a b^{7}} + \frac{3 \, b^{6} h x^{4} + 4 \, b^{6} g x^{3} + 6 \, b^{6} f x^{2} - 24 \, a b^{5} h x + 12 \, b^{6} x e}{12 \, b^{8}}"," ",0,"-1/9*sqrt(3)*(7*a^2*h - 4*a*b*e - 2*(-a*b^2)^(1/3)*b*c + 5*(-a*b^2)^(1/3)*a*f)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*b^2) - 1/18*(7*a^2*h - 4*a*b*e + 2*(-a*b^2)^(1/3)*b*c - 5*(-a*b^2)^(1/3)*a*f)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*b^2) + 1/3*(b*d - 2*a*g)*log(abs(b*x^3 + a))/b^3 + 1/3*(a*b*d - a^2*g - (b^2*c - a*b*f)*x^2 - (a^2*h - a*b*e)*x)/((b*x^3 + a)*b^3) - 1/9*(2*b^6*c*(-a/b)^(1/3) - 5*a*b^5*f*(-a/b)^(1/3) + 7*a^2*b^4*h - 4*a*b^5*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^7) + 1/12*(3*b^6*h*x^4 + 4*b^6*g*x^3 + 6*b^6*f*x^2 - 24*a*b^5*h*x + 12*b^6*x*e)/b^8","A",0
413,1,330,0,0.213979," ","integrate(x^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b^{2} c - 4 \, a b f - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} b d + 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a g\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{2}} - \frac{{\left(b^{2} c - 4 \, a b f + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} b d - 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a g\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{2}} - \frac{{\left(2 \, a h - b e\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{3}} - \frac{a^{2} h + {\left(b^{2} d - a b g\right)} x^{2} - a b e + {\left(b^{2} c - a b f\right)} x}{3 \, {\left(b x^{3} + a\right)} b^{3}} - \frac{{\left(2 \, b^{4} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a b^{3} g \left(-\frac{a}{b}\right)^{\frac{1}{3}} + b^{4} c - 4 \, a b^{3} f\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a b^{5}} + \frac{2 \, b^{4} h x^{3} + 3 \, b^{4} g x^{2} + 6 \, b^{4} f x}{6 \, b^{6}}"," ",0,"-1/9*sqrt(3)*(b^2*c - 4*a*b*f - 2*(-a*b^2)^(1/3)*b*d + 5*(-a*b^2)^(1/3)*a*g)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*b^2) - 1/18*(b^2*c - 4*a*b*f + 2*(-a*b^2)^(1/3)*b*d - 5*(-a*b^2)^(1/3)*a*g)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*b^2) - 1/3*(2*a*h - b*e)*log(abs(b*x^3 + a))/b^3 - 1/3*(a^2*h + (b^2*d - a*b*g)*x^2 - a*b*e + (b^2*c - a*b*f)*x)/((b*x^3 + a)*b^3) - 1/9*(2*b^4*d*(-a/b)^(1/3) - 5*a*b^3*g*(-a/b)^(1/3) + b^4*c - 4*a*b^3*f)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^5) + 1/6*(2*b^4*h*x^3 + 3*b^4*g*x^2 + 6*b^4*f*x)/b^6","A",0
414,1,307,0,0.190484," ","integrate(x^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{f \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{2}} - \frac{\sqrt{3} {\left(b^{2} d - 4 \, a b g + 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a h - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{2}} - \frac{{\left(b^{2} d - 4 \, a b g - 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a h + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{2}} + \frac{{\left(a h - b e\right)} x^{2} - b c + a f - {\left(b d - a g\right)} x}{3 \, {\left(b x^{3} + a\right)} b^{2}} + \frac{b^{2} h x^{2} + 2 \, b^{2} g x}{2 \, b^{4}} + \frac{{\left(5 \, a b^{3} h \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, b^{4} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e - b^{4} d + 4 \, a b^{3} g\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a b^{5}}"," ",0,"1/3*f*log(abs(b*x^3 + a))/b^2 - 1/9*sqrt(3)*(b^2*d - 4*a*b*g + 5*(-a*b^2)^(1/3)*a*h - 2*(-a*b^2)^(1/3)*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*b^2) - 1/18*(b^2*d - 4*a*b*g - 5*(-a*b^2)^(1/3)*a*h + 2*(-a*b^2)^(1/3)*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*b^2) + 1/3*((a*h - b*e)*x^2 - b*c + a*f - (b*d - a*g)*x)/((b*x^3 + a)*b^2) + 1/2*(b^2*h*x^2 + 2*b^2*g*x)/b^4 + 1/9*(5*a*b^3*h*(-a/b)^(1/3) - 2*b^4*(-a/b)^(1/3)*e - b^4*d + 4*a*b^3*g)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^5)","A",0
415,1,318,0,0.199238," ","integrate(x*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{h x}{b^{2}} + \frac{g \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{2}} + \frac{\sqrt{3} {\left(4 \, a^{2} h - a b e + \left(-a b^{2}\right)^{\frac{1}{3}} b c + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} a f\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b} + \frac{{\left(4 \, a^{2} h - a b e - \left(-a b^{2}\right)^{\frac{1}{3}} b c - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} a f\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b} - \frac{a b d - a^{2} g - {\left(b^{2} c - a b f\right)} x^{2} - {\left(a^{2} h - a b e\right)} x}{3 \, {\left(b x^{3} + a\right)} a b^{2}} - \frac{{\left(a b^{5} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a^{2} b^{4} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 4 \, a^{3} b^{3} h + a^{2} b^{4} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{3} b^{5}}"," ",0,"h*x/b^2 + 1/3*g*log(abs(b*x^3 + a))/b^2 + 1/9*sqrt(3)*(4*a^2*h - a*b*e + (-a*b^2)^(1/3)*b*c + 2*(-a*b^2)^(1/3)*a*f)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a*b) + 1/18*(4*a^2*h - a*b*e - (-a*b^2)^(1/3)*b*c - 2*(-a*b^2)^(1/3)*a*f)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a*b) - 1/3*(a*b*d - a^2*g - (b^2*c - a*b*f)*x^2 - (a^2*h - a*b*e)*x)/((b*x^3 + a)*a*b^2) - 1/9*(a*b^5*c*(-a/b)^(1/3) + 2*a^2*b^4*f*(-a/b)^(1/3) - 4*a^3*b^3*h + a^2*b^4*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b^5)","A",0
416,1,302,0,0.193612," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{h \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{2}} - \frac{\sqrt{3} {\left(2 \, b^{2} c + a b f - \left(-a b^{2}\right)^{\frac{1}{3}} b d - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} a g\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b} - \frac{{\left(2 \, b^{2} c + a b f + \left(-a b^{2}\right)^{\frac{1}{3}} b d + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} a g\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b} + \frac{{\left(b d - a g\right)} x^{2} + {\left(b c - a f\right)} x + \frac{a^{2} h - a b e}{b}}{3 \, {\left(b x^{3} + a\right)} a b} - \frac{{\left(a b^{3} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a^{2} b^{2} g \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a b^{3} c + a^{2} b^{2} f\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{3} b^{3}}"," ",0,"1/3*h*log(abs(b*x^3 + a))/b^2 - 1/9*sqrt(3)*(2*b^2*c + a*b*f - (-a*b^2)^(1/3)*b*d - 2*(-a*b^2)^(1/3)*a*g)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a*b) - 1/18*(2*b^2*c + a*b*f + (-a*b^2)^(1/3)*b*d + 2*(-a*b^2)^(1/3)*a*g)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a*b) + 1/3*((b*d - a*g)*x^2 + (b*c - a*f)*x + (a^2*h - a*b*e)/b)/((b*x^3 + a)*a*b) - 1/9*(a*b^3*d*(-a/b)^(1/3) + 2*a^2*b^2*g*(-a/b)^(1/3) + 2*a*b^3*c + a^2*b^2*f)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b^3)","A",0
417,1,319,0,0.202786," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{c \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{2}} + \frac{c \log\left({\left| x \right|}\right)}{a^{2}} - \frac{\sqrt{3} {\left(2 \, b^{2} d + a b g - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} a h - \left(-a b^{2}\right)^{\frac{1}{3}} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b} - \frac{{\left(2 \, b^{2} d + a b g + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} a h + \left(-a b^{2}\right)^{\frac{1}{3}} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b} + \frac{a b c - a^{2} f - {\left(a^{2} h - a b e\right)} x^{2} + {\left(a b d - a^{2} g\right)} x}{3 \, {\left(b x^{3} + a\right)} a^{2} b} - \frac{{\left(2 \, a^{4} b^{2} h \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a^{3} b^{3} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e + 2 \, a^{3} b^{3} d + a^{4} b^{2} g\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{5} b^{3}}"," ",0,"-1/3*c*log(abs(b*x^3 + a))/a^2 + c*log(abs(x))/a^2 - 1/9*sqrt(3)*(2*b^2*d + a*b*g - 2*(-a*b^2)^(1/3)*a*h - (-a*b^2)^(1/3)*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a*b) - 1/18*(2*b^2*d + a*b*g + 2*(-a*b^2)^(1/3)*a*h + (-a*b^2)^(1/3)*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a*b) + 1/3*(a*b*c - a^2*f - (a^2*h - a*b*e)*x^2 + (a*b*d - a^2*g)*x)/((b*x^3 + a)*a^2*b) - 1/9*(2*a^4*b^2*h*(-a/b)^(1/3) + a^3*b^3*(-a/b)^(1/3)*e + 2*a^3*b^3*d + a^4*b^2*g)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^5*b^3)","A",0
418,1,328,0,0.201401," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^2/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{d \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{2}} + \frac{d \log\left({\left| x \right|}\right)}{a^{2}} - \frac{\sqrt{3} {\left(a^{2} h + 2 \, a b e + 4 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c - \left(-a b^{2}\right)^{\frac{1}{3}} a f\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2}} - \frac{{\left(a^{2} h + 2 \, a b e - 4 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c + \left(-a b^{2}\right)^{\frac{1}{3}} a f\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2}} - \frac{4 \, b^{2} c x^{3} - a b f x^{3} + a^{2} h x^{2} - a b x^{2} e - a b d x + a^{2} g x + 3 \, a b c}{3 \, {\left(b x^{4} + a x\right)} a^{2} b} + \frac{{\left(4 \, a^{2} b^{4} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{3} b^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{4} b^{2} h - 2 \, a^{3} b^{3} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{5} b^{3}}"," ",0,"-1/3*d*log(abs(b*x^3 + a))/a^2 + d*log(abs(x))/a^2 - 1/9*sqrt(3)*(a^2*h + 2*a*b*e + 4*(-a*b^2)^(1/3)*b*c - (-a*b^2)^(1/3)*a*f)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^2) - 1/18*(a^2*h + 2*a*b*e - 4*(-a*b^2)^(1/3)*b*c + (-a*b^2)^(1/3)*a*f)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^2) - 1/3*(4*b^2*c*x^3 - a*b*f*x^3 + a^2*h*x^2 - a*b*x^2*e - a*b*d*x + a^2*g*x + 3*a*b*c)/((b*x^4 + a*x)*a^2*b) + 1/9*(4*a^2*b^4*c*(-a/b)^(1/3) - a^3*b^3*f*(-a/b)^(1/3) - a^4*b^2*h - 2*a^3*b^3*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^5*b^3)","A",0
419,1,336,0,0.190620," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^3/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{e \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{2}} + \frac{e \log\left({\left| x \right|}\right)}{a^{2}} + \frac{\sqrt{3} {\left(5 \, b^{2} c - 2 \, a b f - 4 \, \left(-a b^{2}\right)^{\frac{1}{3}} b d + \left(-a b^{2}\right)^{\frac{1}{3}} a g\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2}} + \frac{{\left(5 \, b^{2} c - 2 \, a b f + 4 \, \left(-a b^{2}\right)^{\frac{1}{3}} b d - \left(-a b^{2}\right)^{\frac{1}{3}} a g\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2}} + \frac{{\left(4 \, a^{2} b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{3} b g \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a^{2} b^{2} c - 2 \, a^{3} b f\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{5} b} - \frac{2 \, {\left(4 \, b^{2} d - a b g\right)} x^{4} + 6 \, a b d x + {\left(5 \, b^{2} c - 2 \, a b f\right)} x^{3} + 3 \, a b c + 2 \, {\left(a^{2} h - a b e\right)} x^{2}}{6 \, {\left(b x^{3} + a\right)} a^{2} b x^{2}}"," ",0,"-1/3*e*log(abs(b*x^3 + a))/a^2 + e*log(abs(x))/a^2 + 1/9*sqrt(3)*(5*b^2*c - 2*a*b*f - 4*(-a*b^2)^(1/3)*b*d + (-a*b^2)^(1/3)*a*g)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^2) + 1/18*(5*b^2*c - 2*a*b*f + 4*(-a*b^2)^(1/3)*b*d - (-a*b^2)^(1/3)*a*g)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^2) + 1/9*(4*a^2*b^2*d*(-a/b)^(1/3) - a^3*b*g*(-a/b)^(1/3) + 5*a^2*b^2*c - 2*a^3*b*f)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^5*b) - 1/6*(2*(4*b^2*d - a*b*g)*x^4 + 6*a*b*d*x + (5*b^2*c - 2*a*b*f)*x^3 + 3*a*b*c + 2*(a^2*h - a*b*e)*x^2)/((b*x^3 + a)*a^2*b*x^2)","A",0
420,1,363,0,0.228880," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^4/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{\sqrt{3} {\left(5 \, b^{2} d - 2 \, a b g + \left(-a b^{2}\right)^{\frac{1}{3}} a h - 4 \, \left(-a b^{2}\right)^{\frac{1}{3}} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2}} + \frac{{\left(5 \, b^{2} d - 2 \, a b g - \left(-a b^{2}\right)^{\frac{1}{3}} a h + 4 \, \left(-a b^{2}\right)^{\frac{1}{3}} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2}} + \frac{{\left(2 \, b c - a f\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{3}} - \frac{{\left(2 \, b c - a f\right)} \log\left({\left| x \right|}\right)}{a^{3}} - \frac{{\left(a^{5} b h \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 4 \, a^{4} b^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e - 5 \, a^{4} b^{2} d + 2 \, a^{5} b g\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{7} b} + \frac{2 \, {\left(a^{2} h - 4 \, a b e\right)} x^{5} - {\left(5 \, a b d - 2 \, a^{2} g\right)} x^{4} - 6 \, a^{2} x^{2} e - 3 \, a^{2} d x - 2 \, {\left(2 \, a b c - a^{2} f\right)} x^{3} - 2 \, a^{2} c}{6 \, {\left(b x^{3} + a\right)} a^{3} x^{3}}"," ",0,"1/9*sqrt(3)*(5*b^2*d - 2*a*b*g + (-a*b^2)^(1/3)*a*h - 4*(-a*b^2)^(1/3)*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^2) + 1/18*(5*b^2*d - 2*a*b*g - (-a*b^2)^(1/3)*a*h + 4*(-a*b^2)^(1/3)*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^2) + 1/3*(2*b*c - a*f)*log(abs(b*x^3 + a))/a^3 - (2*b*c - a*f)*log(abs(x))/a^3 - 1/9*(a^5*b*h*(-a/b)^(1/3) - 4*a^4*b^2*(-a/b)^(1/3)*e - 5*a^4*b^2*d + 2*a^5*b*g)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^7*b) + 1/6*(2*(a^2*h - 4*a*b*e)*x^5 - (5*a*b*d - 2*a^2*g)*x^4 - 6*a^2*x^2*e - 3*a^2*d*x - 2*(2*a*b*c - a^2*f)*x^3 - 2*a^2*c)/((b*x^3 + a)*a^3*x^3)","A",0
421,1,385,0,0.206815," ","integrate(x^4*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{h x}{b^{3}} + \frac{g \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{3}} + \frac{\sqrt{3} {\left(14 \, a^{2} h - 2 \, a b e + \left(-a b^{2}\right)^{\frac{1}{3}} b c + 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a f\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2}} + \frac{{\left(14 \, a^{2} h - 2 \, a b e - \left(-a b^{2}\right)^{\frac{1}{3}} b c - 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a f\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2}} + \frac{2 \, {\left(b^{3} c - 4 \, a b^{2} f\right)} x^{5} + {\left(13 \, a^{2} b h - 7 \, a b^{2} e\right)} x^{4} - 3 \, a^{2} b d + 9 \, a^{3} g - 6 \, {\left(a b^{2} d - 2 \, a^{2} b g\right)} x^{3} - {\left(a b^{2} c + 5 \, a^{2} b f\right)} x^{2} + 2 \, {\left(5 \, a^{3} h - 2 \, a^{2} b e\right)} x}{18 \, {\left(b x^{3} + a\right)}^{2} a b^{3}} - \frac{{\left(a b^{6} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a^{2} b^{5} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 14 \, a^{3} b^{4} h + 2 \, a^{2} b^{5} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{3} b^{7}}"," ",0,"h*x/b^3 + 1/3*g*log(abs(b*x^3 + a))/b^3 + 1/27*sqrt(3)*(14*a^2*h - 2*a*b*e + (-a*b^2)^(1/3)*b*c + 5*(-a*b^2)^(1/3)*a*f)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a*b^2) + 1/54*(14*a^2*h - 2*a*b*e - (-a*b^2)^(1/3)*b*c - 5*(-a*b^2)^(1/3)*a*f)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a*b^2) + 1/18*(2*(b^3*c - 4*a*b^2*f)*x^5 + (13*a^2*b*h - 7*a*b^2*e)*x^4 - 3*a^2*b*d + 9*a^3*g - 6*(a*b^2*d - 2*a^2*b*g)*x^3 - (a*b^2*c + 5*a^2*b*f)*x^2 + 2*(5*a^3*h - 2*a^2*b*e)*x)/((b*x^3 + a)^2*a*b^3) - 1/27*(a*b^6*c*(-a/b)^(1/3) + 5*a^2*b^5*f*(-a/b)^(1/3) - 14*a^3*b^4*h + 2*a^2*b^5*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b^7)","A",0
422,1,363,0,0.777210," ","integrate(x^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{h \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{3}} - \frac{\sqrt{3} {\left(b^{2} c + 2 \, a b f - \left(-a b^{2}\right)^{\frac{1}{3}} b d - 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a g\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2}} - \frac{{\left(b^{2} c + 2 \, a b f + \left(-a b^{2}\right)^{\frac{1}{3}} b d + 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a g\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2}} + \frac{2 \, {\left(b^{2} d - 4 \, a b g\right)} x^{5} + {\left(b^{2} c - 7 \, a b f\right)} x^{4} + 6 \, {\left(2 \, a^{2} h - a b e\right)} x^{3} - {\left(a b d + 5 \, a^{2} g\right)} x^{2} - 2 \, {\left(a b c + 2 \, a^{2} f\right)} x + \frac{3 \, {\left(3 \, a^{3} h - a^{2} b e\right)}}{b}}{18 \, {\left(b x^{3} + a\right)}^{2} a b^{2}} - \frac{{\left(a b^{4} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a^{2} b^{3} g \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a b^{4} c + 2 \, a^{2} b^{3} f\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{3} b^{5}}"," ",0,"1/3*h*log(abs(b*x^3 + a))/b^3 - 1/27*sqrt(3)*(b^2*c + 2*a*b*f - (-a*b^2)^(1/3)*b*d - 5*(-a*b^2)^(1/3)*a*g)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a*b^2) - 1/54*(b^2*c + 2*a*b*f + (-a*b^2)^(1/3)*b*d + 5*(-a*b^2)^(1/3)*a*g)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a*b^2) + 1/18*(2*(b^2*d - 4*a*b*g)*x^5 + (b^2*c - 7*a*b*f)*x^4 + 6*(2*a^2*h - a*b*e)*x^3 - (a*b*d + 5*a^2*g)*x^2 - 2*(a*b*c + 2*a^2*f)*x + 3*(3*a^3*h - a^2*b*e)/b)/((b*x^3 + a)^2*a*b^2) - 1/27*(a*b^4*d*(-a/b)^(1/3) + 5*a^2*b^3*g*(-a/b)^(1/3) + a*b^4*c + 2*a^2*b^3*f)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b^5)","A",0
423,1,320,0,0.230452," ","integrate(x^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b^{2} d + 2 \, a b g - 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a h - \left(-a b^{2}\right)^{\frac{1}{3}} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2}} - \frac{{\left(b^{2} d + 2 \, a b g + 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a h + \left(-a b^{2}\right)^{\frac{1}{3}} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2}} - \frac{{\left(5 \, a h \left(-\frac{a}{b}\right)^{\frac{1}{3}} + b \left(-\frac{a}{b}\right)^{\frac{1}{3}} e + b d + 2 \, a g\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{2} b^{2}} - \frac{8 \, a b h x^{5} - 2 \, b^{2} x^{5} e - b^{2} d x^{4} + 7 \, a b g x^{4} + 6 \, a b f x^{3} + 5 \, a^{2} h x^{2} + a b x^{2} e + 2 \, a b d x + 4 \, a^{2} g x + 3 \, a b c + 3 \, a^{2} f}{18 \, {\left(b x^{3} + a\right)}^{2} a b^{2}}"," ",0,"-1/27*sqrt(3)*(b^2*d + 2*a*b*g - 5*(-a*b^2)^(1/3)*a*h - (-a*b^2)^(1/3)*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a*b^2) - 1/54*(b^2*d + 2*a*b*g + 5*(-a*b^2)^(1/3)*a*h + (-a*b^2)^(1/3)*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a*b^2) - 1/27*(5*a*h*(-a/b)^(1/3) + b*(-a/b)^(1/3)*e + b*d + 2*a*g)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b^2) - 1/18*(8*a*b*h*x^5 - 2*b^2*x^5*e - b^2*d*x^4 + 7*a*b*g*x^4 + 6*a*b*f*x^3 + 5*a^2*h*x^2 + a*b*x^2*e + 2*a*b*d*x + 4*a^2*g*x + 3*a*b*c + 3*a^2*f)/((b*x^3 + a)^2*a*b^2)","A",0
424,1,340,0,0.207299," ","integrate(x*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(2 \, a^{2} h + a b e - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c - \left(-a b^{2}\right)^{\frac{1}{3}} a f\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b} - \frac{{\left(2 \, a^{2} h + a b e + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c + \left(-a b^{2}\right)^{\frac{1}{3}} a f\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b} - \frac{{\left(2 \, b^{2} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a b f \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a^{2} h + a b e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{3} b^{2}} + \frac{4 \, b^{3} c x^{5} + 2 \, a b^{2} f x^{5} - 7 \, a^{2} b h x^{4} + a b^{2} x^{4} e - 6 \, a^{2} b g x^{3} + 7 \, a b^{2} c x^{2} - a^{2} b f x^{2} - 4 \, a^{3} h x - 2 \, a^{2} b x e - 3 \, a^{2} b d - 3 \, a^{3} g}{18 \, {\left(b x^{3} + a\right)}^{2} a^{2} b^{2}}"," ",0,"-1/27*sqrt(3)*(2*a^2*h + a*b*e - 2*(-a*b^2)^(1/3)*b*c - (-a*b^2)^(1/3)*a*f)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^2*b) - 1/54*(2*a^2*h + a*b*e + 2*(-a*b^2)^(1/3)*b*c + (-a*b^2)^(1/3)*a*f)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^2*b) - 1/27*(2*b^2*c*(-a/b)^(1/3) + a*b*f*(-a/b)^(1/3) + 2*a^2*h + a*b*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b^2) + 1/18*(4*b^3*c*x^5 + 2*a*b^2*f*x^5 - 7*a^2*b*h*x^4 + a*b^2*x^4*e - 6*a^2*b*g*x^3 + 7*a*b^2*c*x^2 - a^2*b*f*x^2 - 4*a^3*h*x - 2*a^2*b*x*e - 3*a^2*b*d - 3*a^3*g)/((b*x^3 + a)^2*a^2*b^2)","A",0
425,1,330,0,0.218109," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(5 \, b^{2} c + a b f - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} b d - \left(-a b^{2}\right)^{\frac{1}{3}} a g\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b} - \frac{{\left(5 \, b^{2} c + a b f + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} b d + \left(-a b^{2}\right)^{\frac{1}{3}} a g\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b} - \frac{{\left(2 \, b d \left(-\frac{a}{b}\right)^{\frac{1}{3}} + a g \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, b c + a f\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{3} b} + \frac{4 \, b^{3} d x^{5} + 2 \, a b^{2} g x^{5} + 5 \, b^{3} c x^{4} + a b^{2} f x^{4} - 6 \, a^{2} b h x^{3} + 7 \, a b^{2} d x^{2} - a^{2} b g x^{2} + 8 \, a b^{2} c x - 2 \, a^{2} b f x - 3 \, a^{3} h - 3 \, a^{2} b e}{18 \, {\left(b x^{3} + a\right)}^{2} a^{2} b^{2}}"," ",0,"-1/27*sqrt(3)*(5*b^2*c + a*b*f - 2*(-a*b^2)^(1/3)*b*d - (-a*b^2)^(1/3)*a*g)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^2*b) - 1/54*(5*b^2*c + a*b*f + 2*(-a*b^2)^(1/3)*b*d + (-a*b^2)^(1/3)*a*g)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^2*b) - 1/27*(2*b*d*(-a/b)^(1/3) + a*g*(-a/b)^(1/3) + 5*b*c + a*f)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^3*b) + 1/18*(4*b^3*d*x^5 + 2*a*b^2*g*x^5 + 5*b^3*c*x^4 + a*b^2*f*x^4 - 6*a^2*b*h*x^3 + 7*a*b^2*d*x^2 - a^2*b*g*x^2 + 8*a*b^2*c*x - 2*a^2*b*f*x - 3*a^3*h - 3*a^2*b*e)/((b*x^3 + a)^2*a^2*b^2)","A",0
426,1,376,0,0.265359," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{c \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{3}} + \frac{c \log\left({\left| x \right|}\right)}{a^{3}} - \frac{\sqrt{3} {\left(5 \, b^{2} d + a b g - \left(-a b^{2}\right)^{\frac{1}{3}} a h - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b} - \frac{{\left(5 \, b^{2} d + a b g + \left(-a b^{2}\right)^{\frac{1}{3}} a h + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{2} b} + \frac{6 \, a b^{2} c x^{3} + 2 \, {\left(a^{2} b h + 2 \, a b^{2} e\right)} x^{5} + {\left(5 \, a b^{2} d + a^{2} b g\right)} x^{4} + 9 \, a^{2} b c - 3 \, a^{3} f - {\left(a^{3} h - 7 \, a^{2} b e\right)} x^{2} + 2 \, {\left(4 \, a^{2} b d - a^{3} g\right)} x}{18 \, {\left(b x^{3} + a\right)}^{2} a^{3} b} - \frac{{\left(a^{5} b^{2} h \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a^{4} b^{3} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e + 5 \, a^{4} b^{3} d + a^{5} b^{2} g\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{7} b^{3}}"," ",0,"-1/3*c*log(abs(b*x^3 + a))/a^3 + c*log(abs(x))/a^3 - 1/27*sqrt(3)*(5*b^2*d + a*b*g - (-a*b^2)^(1/3)*a*h - 2*(-a*b^2)^(1/3)*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^2*b) - 1/54*(5*b^2*d + a*b*g + (-a*b^2)^(1/3)*a*h + 2*(-a*b^2)^(1/3)*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^2*b) + 1/18*(6*a*b^2*c*x^3 + 2*(a^2*b*h + 2*a*b^2*e)*x^5 + (5*a*b^2*d + a^2*b*g)*x^4 + 9*a^2*b*c - 3*a^3*f - (a^3*h - 7*a^2*b*e)*x^2 + 2*(4*a^2*b*d - a^3*g)*x)/((b*x^3 + a)^2*a^3*b) - 1/27*(a^5*b^2*h*(-a/b)^(1/3) + 2*a^4*b^3*(-a/b)^(1/3)*e + 5*a^4*b^3*d + a^5*b^2*g)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^7*b^3)","A",0
427,1,390,0,0.219521," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^2/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{d \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{3}} + \frac{d \log\left({\left| x \right|}\right)}{a^{3}} - \frac{\sqrt{3} {\left(a^{2} h + 5 \, a b e + 14 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} a f\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3}} - \frac{{\left(a^{2} h + 5 \, a b e - 14 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} a f\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3}} + \frac{6 \, a b^{2} d x^{4} - 4 \, {\left(7 \, b^{3} c - a b^{2} f\right)} x^{6} + {\left(a^{2} b h + 5 \, a b^{2} e\right)} x^{5} - 18 \, a^{2} b c - 7 \, {\left(7 \, a b^{2} c - a^{2} b f\right)} x^{3} - 2 \, {\left(a^{3} h - 4 \, a^{2} b e\right)} x^{2} + 3 \, {\left(3 \, a^{2} b d - a^{3} g\right)} x}{18 \, {\left(b x^{3} + a\right)}^{2} a^{3} b x} + \frac{{\left(14 \, a^{3} b^{4} c \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a^{4} b^{3} f \left(-\frac{a}{b}\right)^{\frac{1}{3}} - a^{5} b^{2} h - 5 \, a^{4} b^{3} e\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{7} b^{3}}"," ",0,"-1/3*d*log(abs(b*x^3 + a))/a^3 + d*log(abs(x))/a^3 - 1/27*sqrt(3)*(a^2*h + 5*a*b*e + 14*(-a*b^2)^(1/3)*b*c - 2*(-a*b^2)^(1/3)*a*f)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^3) - 1/54*(a^2*h + 5*a*b*e - 14*(-a*b^2)^(1/3)*b*c + 2*(-a*b^2)^(1/3)*a*f)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^3) + 1/18*(6*a*b^2*d*x^4 - 4*(7*b^3*c - a*b^2*f)*x^6 + (a^2*b*h + 5*a*b^2*e)*x^5 - 18*a^2*b*c - 7*(7*a*b^2*c - a^2*b*f)*x^3 - 2*(a^3*h - 4*a^2*b*e)*x^2 + 3*(3*a^2*b*d - a^3*g)*x)/((b*x^3 + a)^2*a^3*b*x) + 1/27*(14*a^3*b^4*c*(-a/b)^(1/3) - 2*a^4*b^3*f*(-a/b)^(1/3) - a^5*b^2*h - 5*a^4*b^3*e)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^7*b^3)","A",0
428,1,399,0,0.225950," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^3/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{e \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{3}} + \frac{e \log\left({\left| x \right|}\right)}{a^{3}} + \frac{\sqrt{3} {\left(20 \, b^{2} c - 5 \, a b f - 14 \, \left(-a b^{2}\right)^{\frac{1}{3}} b d + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} a g\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3}} + \frac{{\left(20 \, b^{2} c - 5 \, a b f + 14 \, \left(-a b^{2}\right)^{\frac{1}{3}} b d - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} a g\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3}} - \frac{28 \, b^{3} d x^{7} - 4 \, a b^{2} g x^{7} + 20 \, b^{3} c x^{6} - 5 \, a b^{2} f x^{6} - 6 \, a b^{2} x^{5} e + 49 \, a b^{2} d x^{4} - 7 \, a^{2} b g x^{4} + 32 \, a b^{2} c x^{3} - 8 \, a^{2} b f x^{3} + 3 \, a^{3} h x^{2} - 9 \, a^{2} b x^{2} e + 18 \, a^{2} b d x + 9 \, a^{2} b c}{18 \, {\left(b x^{4} + a x\right)}^{2} a^{3} b} + \frac{{\left(14 \, a^{3} b^{2} d \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a^{4} b g \left(-\frac{a}{b}\right)^{\frac{1}{3}} + 20 \, a^{3} b^{2} c - 5 \, a^{4} b f\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{7} b}"," ",0,"-1/3*e*log(abs(b*x^3 + a))/a^3 + e*log(abs(x))/a^3 + 1/27*sqrt(3)*(20*b^2*c - 5*a*b*f - 14*(-a*b^2)^(1/3)*b*d + 2*(-a*b^2)^(1/3)*a*g)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^3) + 1/54*(20*b^2*c - 5*a*b*f + 14*(-a*b^2)^(1/3)*b*d - 2*(-a*b^2)^(1/3)*a*g)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^3) - 1/18*(28*b^3*d*x^7 - 4*a*b^2*g*x^7 + 20*b^3*c*x^6 - 5*a*b^2*f*x^6 - 6*a*b^2*x^5*e + 49*a*b^2*d*x^4 - 7*a^2*b*g*x^4 + 32*a*b^2*c*x^3 - 8*a^2*b*f*x^3 + 3*a^3*h*x^2 - 9*a^2*b*x^2*e + 18*a^2*b*d*x + 9*a^2*b*c)/((b*x^4 + a*x)^2*a^3*b) + 1/27*(14*a^3*b^2*d*(-a/b)^(1/3) - 2*a^4*b*g*(-a/b)^(1/3) + 20*a^3*b^2*c - 5*a^4*b*f)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^7*b)","A",0
429,1,431,0,0.203136," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^4/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{\sqrt{3} {\left(20 \, b^{2} d - 5 \, a b g + 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} a h - 14 \, \left(-a b^{2}\right)^{\frac{1}{3}} b e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3}} + \frac{{\left(20 \, b^{2} d - 5 \, a b g - 2 \, \left(-a b^{2}\right)^{\frac{1}{3}} a h + 14 \, \left(-a b^{2}\right)^{\frac{1}{3}} b e\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, \left(-a b^{2}\right)^{\frac{2}{3}} a^{3}} + \frac{{\left(3 \, b c - a f\right)} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{4}} - \frac{{\left(3 \, b c - a f\right)} \log\left({\left| x \right|}\right)}{a^{4}} - \frac{{\left(2 \, a^{6} b h \left(-\frac{a}{b}\right)^{\frac{1}{3}} - 14 \, a^{5} b^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} e - 20 \, a^{5} b^{2} d + 5 \, a^{6} b g\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{9} b} + \frac{4 \, {\left(a^{2} b h - 7 \, a b^{2} e\right)} x^{8} - 5 \, {\left(4 \, a b^{2} d - a^{2} b g\right)} x^{7} - 6 \, {\left(3 \, a b^{2} c - a^{2} b f\right)} x^{6} + 7 \, {\left(a^{3} h - 7 \, a^{2} b e\right)} x^{5} - 18 \, a^{3} x^{2} e - 9 \, a^{3} d x - 8 \, {\left(4 \, a^{2} b d - a^{3} g\right)} x^{4} - 6 \, a^{3} c - 9 \, {\left(3 \, a^{2} b c - a^{3} f\right)} x^{3}}{18 \, {\left(b x^{3} + a\right)}^{2} a^{4} x^{3}}"," ",0,"1/27*sqrt(3)*(20*b^2*d - 5*a*b*g + 2*(-a*b^2)^(1/3)*a*h - 14*(-a*b^2)^(1/3)*b*e)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a^3) + 1/54*(20*b^2*d - 5*a*b*g - 2*(-a*b^2)^(1/3)*a*h + 14*(-a*b^2)^(1/3)*b*e)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a^3) + 1/3*(3*b*c - a*f)*log(abs(b*x^3 + a))/a^4 - (3*b*c - a*f)*log(abs(x))/a^4 - 1/27*(2*a^6*b*h*(-a/b)^(1/3) - 14*a^5*b^2*(-a/b)^(1/3)*e - 20*a^5*b^2*d + 5*a^6*b*g)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^9*b) + 1/18*(4*(a^2*b*h - 7*a*b^2*e)*x^8 - 5*(4*a*b^2*d - a^2*b*g)*x^7 - 6*(3*a*b^2*c - a^2*b*f)*x^6 + 7*(a^3*h - 7*a^2*b*e)*x^5 - 18*a^3*x^2*e - 9*a^3*d*x - 8*(4*a^2*b*d - a^3*g)*x^4 - 6*a^3*c - 9*(3*a^2*b*c - a^3*f)*x^3)/((b*x^3 + a)^2*a^4*x^3)","A",0
430,0,0,0,0.000000," ","integrate(x^3*(e*x^2+d*x+c)/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d x + c\right)} x^{3}}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)*x^3/sqrt(b*x^3 + a), x)","F",0
431,0,0,0,0.000000," ","integrate(x^2*(e*x^2+d*x+c)/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d x + c\right)} x^{2}}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)*x^2/sqrt(b*x^3 + a), x)","F",0
432,0,0,0,0.000000," ","integrate(x*(e*x^2+d*x+c)/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d x + c\right)} x}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)*x/sqrt(b*x^3 + a), x)","F",0
433,0,0,0,0.000000," ","integrate((e*x^2+d*x+c)/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d x + c}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)/sqrt(b*x^3 + a), x)","F",0
434,0,0,0,0.000000," ","integrate((e*x^2+d*x+c)/x/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d x + c}{\sqrt{b x^{3} + a} x}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)/(sqrt(b*x^3 + a)*x), x)","F",0
435,0,0,0,0.000000," ","integrate((e*x^2+d*x+c)/x^2/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d x + c}{\sqrt{b x^{3} + a} x^{2}}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)/(sqrt(b*x^3 + a)*x^2), x)","F",0
436,0,0,0,0.000000," ","integrate((e*x^2+d*x+c)/x^3/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d x + c}{\sqrt{b x^{3} + a} x^{3}}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)/(sqrt(b*x^3 + a)*x^3), x)","F",0
437,0,0,0,0.000000," ","integrate(x^5*(e*x^2+d*x+c)/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d x + c\right)} x^{5}}{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)*x^5/(b*x^3 + a)^(3/2), x)","F",0
438,0,0,0,0.000000," ","integrate(x^4*(e*x^2+d*x+c)/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d x + c\right)} x^{4}}{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)*x^4/(b*x^3 + a)^(3/2), x)","F",0
439,0,0,0,0.000000," ","integrate(x^3*(e*x^2+d*x+c)/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d x + c\right)} x^{3}}{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)*x^3/(b*x^3 + a)^(3/2), x)","F",0
440,0,0,0,0.000000," ","integrate(x^2*(e*x^2+d*x+c)/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d x + c\right)} x^{2}}{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)*x^2/(b*x^3 + a)^(3/2), x)","F",0
441,0,0,0,0.000000," ","integrate(x*(e*x^2+d*x+c)/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d x + c\right)} x}{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)*x/(b*x^3 + a)^(3/2), x)","F",0
442,0,0,0,0.000000," ","integrate((e*x^2+d*x+c)/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d x + c}{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)/(b*x^3 + a)^(3/2), x)","F",0
443,0,0,0,0.000000," ","integrate((e*x^2+d*x+c)/x/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d x + c}{{\left(b x^{3} + a\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)/((b*x^3 + a)^(3/2)*x), x)","F",0
444,0,0,0,0.000000," ","integrate((e*x^2+d*x+c)/x^2/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d x + c}{{\left(b x^{3} + a\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)/((b*x^3 + a)^(3/2)*x^2), x)","F",0
445,0,0,0,0.000000," ","integrate(x^3*(g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int {\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} \sqrt{b x^{3} + a} x^{3}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*sqrt(b*x^3 + a)*x^3, x)","F",0
446,0,0,0,0.000000," ","integrate(x^2*(g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int {\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} \sqrt{b x^{3} + a} x^{2}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*sqrt(b*x^3 + a)*x^2, x)","F",0
447,0,0,0,0.000000," ","integrate(x*(g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int {\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} \sqrt{b x^{3} + a} x\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*sqrt(b*x^3 + a)*x, x)","F",0
448,0,0,0,0.000000," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int {\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} \sqrt{b x^{3} + a}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*sqrt(b*x^3 + a), x)","F",0
449,0,0,0,0.000000," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} \sqrt{b x^{3} + a}}{x}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*sqrt(b*x^3 + a)/x, x)","F",0
450,0,0,0,0.000000," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} \sqrt{b x^{3} + a}}{x^{2}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*sqrt(b*x^3 + a)/x^2, x)","F",0
451,0,0,0,0.000000," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} \sqrt{b x^{3} + a}}{x^{3}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*sqrt(b*x^3 + a)/x^3, x)","F",0
452,0,0,0,0.000000," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} \sqrt{b x^{3} + a}}{x^{4}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*sqrt(b*x^3 + a)/x^4, x)","F",0
453,0,0,0,0.000000," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x^5,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} \sqrt{b x^{3} + a}}{x^{5}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*sqrt(b*x^3 + a)/x^5, x)","F",0
454,0,0,0,0.000000," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x^6,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} \sqrt{b x^{3} + a}}{x^{6}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*sqrt(b*x^3 + a)/x^6, x)","F",0
455,0,0,0,0.000000," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x^7,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} \sqrt{b x^{3} + a}}{x^{7}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*sqrt(b*x^3 + a)/x^7, x)","F",0
456,0,0,0,0.000000," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x^8,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} \sqrt{b x^{3} + a}}{x^{8}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*sqrt(b*x^3 + a)/x^8, x)","F",0
457,0,0,0,0.000000," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x^9,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} \sqrt{b x^{3} + a}}{x^{9}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*sqrt(b*x^3 + a)/x^9, x)","F",0
458,0,0,0,0.000000," ","integrate(x^3*(b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\int {\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}} x^{3}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)^(3/2)*x^3, x)","F",0
459,0,0,0,0.000000," ","integrate(x^2*(b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\int {\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}} x^{2}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)^(3/2)*x^2, x)","F",0
460,0,0,0,0.000000," ","integrate(x*(b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\int {\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}} x\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)^(3/2)*x, x)","F",0
461,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""giac"")","\int {\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)^(3/2), x)","F",0
462,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)^(3/2)/x, x)","F",0
463,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^2,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)^(3/2)/x^2, x)","F",0
464,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^3,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)^(3/2)/x^3, x)","F",0
465,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^4,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)^(3/2)/x^4, x)","F",0
466,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^5,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{5}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)^(3/2)/x^5, x)","F",0
467,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^6,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{6}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)^(3/2)/x^6, x)","F",0
468,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^7,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{7}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)^(3/2)/x^7, x)","F",0
469,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^8,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{8}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)^(3/2)/x^8, x)","F",0
470,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^9,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{9}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)^(3/2)/x^9, x)","F",0
471,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^10,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{10}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)^(3/2)/x^10, x)","F",0
472,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^11,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{11}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)^(3/2)/x^11, x)","F",0
473,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^12,x, algorithm=""giac"")","\int \frac{{\left(g x^{4} + f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{12}}\,{d x}"," ",0,"integrate((g*x^4 + f*x^3 + e*x^2 + d*x + c)*(b*x^3 + a)^(3/2)/x^12, x)","F",0
474,0,0,0,0.000000," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^p,x, algorithm=""giac"")","\int {\left(e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)*(b*x^3 + a)^p, x)","F",0
475,0,0,0,0.000000," ","integrate(x*(e*x^2+d*x+c)*(b*x^3+a)^p,x, algorithm=""giac"")","\int {\left(e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{p} x\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)*(b*x^3 + a)^p*x, x)","F",0
476,0,0,0,0.000000," ","integrate(x^2*(e*x^2+d*x+c)*(b*x^3+a)^p,x, algorithm=""giac"")","\int {\left(e x^{2} + d x + c\right)} {\left(b x^{3} + a\right)}^{p} x^{2}\,{d x}"," ",0,"integrate((e*x^2 + d*x + c)*(b*x^3 + a)^p*x^2, x)","F",0
477,1,56,0,0.150562," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a),x, algorithm=""giac"")","\frac{1}{8} \, b f x^{8} + \frac{1}{7} \, b x^{7} e + \frac{1}{6} \, b d x^{6} + \frac{1}{5} \, b c x^{5} + \frac{1}{4} \, a f x^{4} + \frac{1}{3} \, a x^{3} e + \frac{1}{2} \, a d x^{2} + a c x"," ",0,"1/8*b*f*x^8 + 1/7*b*x^7*e + 1/6*b*d*x^6 + 1/5*b*c*x^5 + 1/4*a*f*x^4 + 1/3*a*x^3*e + 1/2*a*d*x^2 + a*c*x","A",0
478,1,59,0,0.155856," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a),x, algorithm=""giac"")","\frac{1}{11} \, b f x^{11} + \frac{1}{10} \, b x^{10} e + \frac{1}{9} \, b d x^{9} + \frac{1}{8} \, b c x^{8} + \frac{1}{7} \, a f x^{7} + \frac{1}{6} \, a x^{6} e + \frac{1}{5} \, a d x^{5} + \frac{1}{4} \, a c x^{4}"," ",0,"1/11*b*f*x^11 + 1/10*b*x^10*e + 1/9*b*d*x^9 + 1/8*b*c*x^8 + 1/7*a*f*x^7 + 1/6*a*x^6*e + 1/5*a*d*x^5 + 1/4*a*c*x^4","A",0
479,1,105,0,0.160237," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^2,x, algorithm=""giac"")","\frac{1}{12} \, b^{2} f x^{12} + \frac{1}{11} \, b^{2} x^{11} e + \frac{1}{10} \, b^{2} d x^{10} + \frac{1}{9} \, b^{2} c x^{9} + \frac{1}{4} \, a b f x^{8} + \frac{2}{7} \, a b x^{7} e + \frac{1}{3} \, a b d x^{6} + \frac{2}{5} \, a b c x^{5} + \frac{1}{4} \, a^{2} f x^{4} + \frac{1}{3} \, a^{2} x^{3} e + \frac{1}{2} \, a^{2} d x^{2} + a^{2} c x"," ",0,"1/12*b^2*f*x^12 + 1/11*b^2*x^11*e + 1/10*b^2*d*x^10 + 1/9*b^2*c*x^9 + 1/4*a*b*f*x^8 + 2/7*a*b*x^7*e + 1/3*a*b*d*x^6 + 2/5*a*b*c*x^5 + 1/4*a^2*f*x^4 + 1/3*a^2*x^3*e + 1/2*a^2*d*x^2 + a^2*c*x","A",0
480,1,108,0,0.149271," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^2,x, algorithm=""giac"")","\frac{1}{15} \, b^{2} f x^{15} + \frac{1}{14} \, b^{2} x^{14} e + \frac{1}{13} \, b^{2} d x^{13} + \frac{1}{12} \, b^{2} c x^{12} + \frac{2}{11} \, a b f x^{11} + \frac{1}{5} \, a b x^{10} e + \frac{2}{9} \, a b d x^{9} + \frac{1}{4} \, a b c x^{8} + \frac{1}{7} \, a^{2} f x^{7} + \frac{1}{6} \, a^{2} x^{6} e + \frac{1}{5} \, a^{2} d x^{5} + \frac{1}{4} \, a^{2} c x^{4}"," ",0,"1/15*b^2*f*x^15 + 1/14*b^2*x^14*e + 1/13*b^2*d*x^13 + 1/12*b^2*c*x^12 + 2/11*a*b*f*x^11 + 1/5*a*b*x^10*e + 2/9*a*b*d*x^9 + 1/4*a*b*c*x^8 + 1/7*a^2*f*x^7 + 1/6*a^2*x^6*e + 1/5*a^2*d*x^5 + 1/4*a^2*c*x^4","A",0
481,1,154,0,0.156628," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^3,x, algorithm=""giac"")","\frac{1}{16} \, b^{3} f x^{16} + \frac{1}{15} \, b^{3} x^{15} e + \frac{1}{14} \, b^{3} d x^{14} + \frac{1}{13} \, b^{3} c x^{13} + \frac{1}{4} \, a b^{2} f x^{12} + \frac{3}{11} \, a b^{2} x^{11} e + \frac{3}{10} \, a b^{2} d x^{10} + \frac{1}{3} \, a b^{2} c x^{9} + \frac{3}{8} \, a^{2} b f x^{8} + \frac{3}{7} \, a^{2} b x^{7} e + \frac{1}{2} \, a^{2} b d x^{6} + \frac{3}{5} \, a^{2} b c x^{5} + \frac{1}{4} \, a^{3} f x^{4} + \frac{1}{3} \, a^{3} x^{3} e + \frac{1}{2} \, a^{3} d x^{2} + a^{3} c x"," ",0,"1/16*b^3*f*x^16 + 1/15*b^3*x^15*e + 1/14*b^3*d*x^14 + 1/13*b^3*c*x^13 + 1/4*a*b^2*f*x^12 + 3/11*a*b^2*x^11*e + 3/10*a*b^2*d*x^10 + 1/3*a*b^2*c*x^9 + 3/8*a^2*b*f*x^8 + 3/7*a^2*b*x^7*e + 1/2*a^2*b*d*x^6 + 3/5*a^2*b*c*x^5 + 1/4*a^3*f*x^4 + 1/3*a^3*x^3*e + 1/2*a^3*d*x^2 + a^3*c*x","A",0
482,1,157,0,0.164015," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^3,x, algorithm=""giac"")","\frac{1}{19} \, b^{3} f x^{19} + \frac{1}{18} \, b^{3} x^{18} e + \frac{1}{17} \, b^{3} d x^{17} + \frac{1}{16} \, b^{3} c x^{16} + \frac{1}{5} \, a b^{2} f x^{15} + \frac{3}{14} \, a b^{2} x^{14} e + \frac{3}{13} \, a b^{2} d x^{13} + \frac{1}{4} \, a b^{2} c x^{12} + \frac{3}{11} \, a^{2} b f x^{11} + \frac{3}{10} \, a^{2} b x^{10} e + \frac{1}{3} \, a^{2} b d x^{9} + \frac{3}{8} \, a^{2} b c x^{8} + \frac{1}{7} \, a^{3} f x^{7} + \frac{1}{6} \, a^{3} x^{6} e + \frac{1}{5} \, a^{3} d x^{5} + \frac{1}{4} \, a^{3} c x^{4}"," ",0,"1/19*b^3*f*x^19 + 1/18*b^3*x^18*e + 1/17*b^3*d*x^17 + 1/16*b^3*c*x^16 + 1/5*a*b^2*f*x^15 + 3/14*a*b^2*x^14*e + 3/13*a*b^2*d*x^13 + 1/4*a*b^2*c*x^12 + 3/11*a^2*b*f*x^11 + 3/10*a^2*b*x^10*e + 1/3*a^2*b*d*x^9 + 3/8*a^2*b*c*x^8 + 1/7*a^3*f*x^7 + 1/6*a^3*x^6*e + 1/5*a^3*d*x^5 + 1/4*a^3*c*x^4","A",0
483,1,203,0,0.172994," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^4,x, algorithm=""giac"")","\frac{1}{20} \, b^{4} f x^{20} + \frac{1}{19} \, b^{4} x^{19} e + \frac{1}{18} \, b^{4} d x^{18} + \frac{1}{17} \, b^{4} c x^{17} + \frac{1}{4} \, a b^{3} f x^{16} + \frac{4}{15} \, a b^{3} x^{15} e + \frac{2}{7} \, a b^{3} d x^{14} + \frac{4}{13} \, a b^{3} c x^{13} + \frac{1}{2} \, a^{2} b^{2} f x^{12} + \frac{6}{11} \, a^{2} b^{2} x^{11} e + \frac{3}{5} \, a^{2} b^{2} d x^{10} + \frac{2}{3} \, a^{2} b^{2} c x^{9} + \frac{1}{2} \, a^{3} b f x^{8} + \frac{4}{7} \, a^{3} b x^{7} e + \frac{2}{3} \, a^{3} b d x^{6} + \frac{4}{5} \, a^{3} b c x^{5} + \frac{1}{4} \, a^{4} f x^{4} + \frac{1}{3} \, a^{4} x^{3} e + \frac{1}{2} \, a^{4} d x^{2} + a^{4} c x"," ",0,"1/20*b^4*f*x^20 + 1/19*b^4*x^19*e + 1/18*b^4*d*x^18 + 1/17*b^4*c*x^17 + 1/4*a*b^3*f*x^16 + 4/15*a*b^3*x^15*e + 2/7*a*b^3*d*x^14 + 4/13*a*b^3*c*x^13 + 1/2*a^2*b^2*f*x^12 + 6/11*a^2*b^2*x^11*e + 3/5*a^2*b^2*d*x^10 + 2/3*a^2*b^2*c*x^9 + 1/2*a^3*b*f*x^8 + 4/7*a^3*b*x^7*e + 2/3*a^3*b*d*x^6 + 4/5*a^3*b*c*x^5 + 1/4*a^4*f*x^4 + 1/3*a^4*x^3*e + 1/2*a^4*d*x^2 + a^4*c*x","A",0
484,1,206,0,0.192634," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^4,x, algorithm=""giac"")","\frac{1}{23} \, b^{4} f x^{23} + \frac{1}{22} \, b^{4} x^{22} e + \frac{1}{21} \, b^{4} d x^{21} + \frac{1}{20} \, b^{4} c x^{20} + \frac{4}{19} \, a b^{3} f x^{19} + \frac{2}{9} \, a b^{3} x^{18} e + \frac{4}{17} \, a b^{3} d x^{17} + \frac{1}{4} \, a b^{3} c x^{16} + \frac{2}{5} \, a^{2} b^{2} f x^{15} + \frac{3}{7} \, a^{2} b^{2} x^{14} e + \frac{6}{13} \, a^{2} b^{2} d x^{13} + \frac{1}{2} \, a^{2} b^{2} c x^{12} + \frac{4}{11} \, a^{3} b f x^{11} + \frac{2}{5} \, a^{3} b x^{10} e + \frac{4}{9} \, a^{3} b d x^{9} + \frac{1}{2} \, a^{3} b c x^{8} + \frac{1}{7} \, a^{4} f x^{7} + \frac{1}{6} \, a^{4} x^{6} e + \frac{1}{5} \, a^{4} d x^{5} + \frac{1}{4} \, a^{4} c x^{4}"," ",0,"1/23*b^4*f*x^23 + 1/22*b^4*x^22*e + 1/21*b^4*d*x^21 + 1/20*b^4*c*x^20 + 4/19*a*b^3*f*x^19 + 2/9*a*b^3*x^18*e + 4/17*a*b^3*d*x^17 + 1/4*a*b^3*c*x^16 + 2/5*a^2*b^2*f*x^15 + 3/7*a^2*b^2*x^14*e + 6/13*a^2*b^2*d*x^13 + 1/2*a^2*b^2*c*x^12 + 4/11*a^3*b*f*x^11 + 2/5*a^3*b*x^10*e + 4/9*a^3*b*d*x^9 + 1/2*a^3*b*c*x^8 + 1/7*a^4*f*x^7 + 1/6*a^4*x^6*e + 1/5*a^4*d*x^5 + 1/4*a^4*c*x^4","A",0
485,1,280,0,0.186499," ","integrate((f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(b^{2} c - \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d + \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c + \sqrt{2} \left(-a b^{3}\right)^{\frac{1}{4}} b d - \sqrt{-a b} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c - \sqrt{-a b} b e\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, \left(-a b^{3}\right)^{\frac{3}{4}}} + \frac{\sqrt{2} {\left(b^{2} c - \sqrt{-a b} b e\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{f \log\left({\left| b x^{4} - a \right|}\right)}{4 \, b}"," ",0,"-1/4*sqrt(2)*(b^2*c - sqrt(2)*(-a*b^3)^(1/4)*b*d + sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(-a*b^3)^(3/4) - 1/4*sqrt(2)*(b^2*c + sqrt(2)*(-a*b^3)^(1/4)*b*d - sqrt(-a*b)*b*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(-a*b^3)^(3/4) - 1/8*sqrt(2)*(b^2*c - sqrt(-a*b)*b*e)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(-a*b^3)^(3/4) + 1/8*sqrt(2)*(b^2*c - sqrt(-a*b)*b*e)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(-a*b^3)^(3/4) - 1/4*f*log(abs(b*x^4 - a))/b","B",0
486,1,328,0,0.190350," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x, algorithm=""giac"")","-\frac{c \log\left({\left| b x^{4} - a \right|}\right)}{4 \, b} - \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{-a b} b^{2} e - \left(-a b^{3}\right)^{\frac{1}{4}} b^{2} d - \left(-a b^{3}\right)^{\frac{3}{4}} f\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, b^{4}} - \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{-a b} b^{2} e - \left(-a b^{3}\right)^{\frac{1}{4}} b^{2} d - \left(-a b^{3}\right)^{\frac{3}{4}} f\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, b^{4}} + \frac{\sqrt{2} {\left(\left(-a b^{3}\right)^{\frac{1}{4}} b^{2} d - \left(-a b^{3}\right)^{\frac{3}{4}} f\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, b^{4}} - \frac{\sqrt{2} {\left(\left(-a b^{3}\right)^{\frac{1}{4}} b^{2} d - \left(-a b^{3}\right)^{\frac{3}{4}} f\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, b^{4}} - \frac{2 \, b^{2} f x^{3} + 3 \, b^{2} x^{2} e + 6 \, b^{2} d x}{6 \, b^{3}}"," ",0,"-1/4*c*log(abs(b*x^4 - a))/b - 1/4*sqrt(2)*(sqrt(2)*sqrt(-a*b)*b^2*e - (-a*b^3)^(1/4)*b^2*d - (-a*b^3)^(3/4)*f)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/b^4 - 1/4*sqrt(2)*(sqrt(2)*sqrt(-a*b)*b^2*e - (-a*b^3)^(1/4)*b^2*d - (-a*b^3)^(3/4)*f)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/b^4 + 1/8*sqrt(2)*((-a*b^3)^(1/4)*b^2*d - (-a*b^3)^(3/4)*f)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/b^4 - 1/8*sqrt(2)*((-a*b^3)^(1/4)*b^2*d - (-a*b^3)^(3/4)*f)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/b^4 - 1/6*(2*b^2*f*x^3 + 3*b^2*x^2*e + 6*b^2*d*x)/b^3","B",0
487,1,290,0,0.183535," ","integrate((f*x^3+e*x^2+d*x+c)/(b*x^4+a),x, algorithm=""giac"")","\frac{f \log\left({\left| b x^{4} + a \right|}\right)}{4 \, b} - \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a b} b^{2} d - \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} - \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a b} b^{2} d - \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}}"," ",0,"1/4*f*log(abs(b*x^4 + a))/b - 1/4*sqrt(2)*(sqrt(2)*sqrt(a*b)*b^2*d - (a*b^3)^(1/4)*b^2*c - (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) - 1/4*sqrt(2)*(sqrt(2)*sqrt(a*b)*b^2*d - (a*b^3)^(1/4)*b^2*c - (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c - (a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3) - 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c - (a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3)","A",0
488,1,308,0,0.185076," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a),x, algorithm=""giac"")","\frac{c \log\left({\left| b x^{4} + a \right|}\right)}{4 \, b} + \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a b} b^{2} e - \left(a b^{3}\right)^{\frac{1}{4}} b^{2} d - \left(a b^{3}\right)^{\frac{3}{4}} f\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, b^{4}} + \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{a b} b^{2} e - \left(a b^{3}\right)^{\frac{1}{4}} b^{2} d - \left(a b^{3}\right)^{\frac{3}{4}} f\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, b^{4}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} d - \left(a b^{3}\right)^{\frac{3}{4}} f\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, b^{4}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} d - \left(a b^{3}\right)^{\frac{3}{4}} f\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, b^{4}} + \frac{2 \, b^{2} f x^{3} + 3 \, b^{2} x^{2} e + 6 \, b^{2} d x}{6 \, b^{3}}"," ",0,"1/4*c*log(abs(b*x^4 + a))/b + 1/4*sqrt(2)*(sqrt(2)*sqrt(a*b)*b^2*e - (a*b^3)^(1/4)*b^2*d - (a*b^3)^(3/4)*f)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/b^4 + 1/4*sqrt(2)*(sqrt(2)*sqrt(a*b)*b^2*e - (a*b^3)^(1/4)*b^2*d - (a*b^3)^(3/4)*f)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/b^4 - 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*d - (a*b^3)^(3/4)*f)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/b^4 + 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*d - (a*b^3)^(3/4)*f)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/b^4 + 1/6*(2*b^2*f*x^3 + 3*b^2*x^2*e + 6*b^2*d*x)/b^3","A",0
489,1,316,0,0.183972," ","integrate((f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x, algorithm=""giac"")","\frac{b x^{3} e + b d x^{2} + b c x - a f}{4 \, {\left(b x^{4} + a\right)} a b} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a b} b^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a b} b^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{3}} - \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{3}}"," ",0,"1/4*(b*x^3*e + b*d*x^2 + b*c*x - a*f)/((b*x^4 + a)*a*b) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*b)*b^2*d + 3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^3) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*b)*b^2*d + 3*(a*b^3)^(1/4)*b^2*c + (a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^3) + 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^2*c - (a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^3) - 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^2*c - (a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^3)","A",0
490,1,303,0,0.215453," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x, algorithm=""giac"")","-\frac{f x^{3} + x^{2} e + d x + c}{4 \, {\left(b x^{4} + a\right)} b} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a b} b^{2} e + \left(a b^{3}\right)^{\frac{1}{4}} b^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} f\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a b^{4}} + \frac{\sqrt{2} {\left(2 \, \sqrt{2} \sqrt{a b} b^{2} e + \left(a b^{3}\right)^{\frac{1}{4}} b^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} f\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a b^{4}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} d - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} f\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a b^{4}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} d - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} f\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a b^{4}}"," ",0,"-1/4*(f*x^3 + x^2*e + d*x + c)/((b*x^4 + a)*b) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*b)*b^2*e + (a*b^3)^(1/4)*b^2*d + 3*(a*b^3)^(3/4)*f)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^4) + 1/16*sqrt(2)*(2*sqrt(2)*sqrt(a*b)*b^2*e + (a*b^3)^(1/4)*b^2*d + 3*(a*b^3)^(3/4)*f)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^4) + 1/32*sqrt(2)*((a*b^3)^(1/4)*b^2*d - 3*(a*b^3)^(3/4)*f)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^4) - 1/32*sqrt(2)*((a*b^3)^(1/4)*b^2*d - 3*(a*b^3)^(3/4)*f)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^4)","A",0
491,1,354,0,0.191815," ","integrate((f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(12 \, \sqrt{2} \sqrt{a b} b^{2} d + 21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} b^{3}} + \frac{\sqrt{2} {\left(12 \, \sqrt{2} \sqrt{a b} b^{2} d + 21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} b^{3}} + \frac{\sqrt{2} {\left(21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{256 \, a^{3} b^{3}} - \frac{\sqrt{2} {\left(21 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{256 \, a^{3} b^{3}} + \frac{5 \, b^{2} x^{7} e + 6 \, b^{2} d x^{6} + 7 \, b^{2} c x^{5} + 9 \, a b x^{3} e + 10 \, a b d x^{2} + 11 \, a b c x - 4 \, a^{2} f}{32 \, {\left(b x^{4} + a\right)}^{2} a^{2} b}"," ",0,"1/128*sqrt(2)*(12*sqrt(2)*sqrt(a*b)*b^2*d + 21*(a*b^3)^(1/4)*b^2*c + 5*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^3) + 1/128*sqrt(2)*(12*sqrt(2)*sqrt(a*b)*b^2*d + 21*(a*b^3)^(1/4)*b^2*c + 5*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^3) + 1/256*sqrt(2)*(21*(a*b^3)^(1/4)*b^2*c - 5*(a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^3) - 1/256*sqrt(2)*(21*(a*b^3)^(1/4)*b^2*c - 5*(a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^3) + 1/32*(5*b^2*x^7*e + 6*b^2*d*x^6 + 7*b^2*c*x^5 + 9*a*b*x^3*e + 10*a*b*d*x^2 + 11*a*b*c*x - 4*a^2*f)/((b*x^4 + a)^2*a^2*b)","A",0
492,1,338,0,0.294067," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x, algorithm=""giac"")","\frac{3 \, b f x^{7} + 2 \, b x^{6} e + b d x^{5} - a f x^{3} - 2 \, a x^{2} e - 3 \, a d x - 4 \, a c}{32 \, {\left(b x^{4} + a\right)}^{2} a b} + \frac{\sqrt{2} {\left(4 \, \sqrt{2} \sqrt{a b} b^{2} e + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} f\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{2} b^{4}} + \frac{\sqrt{2} {\left(4 \, \sqrt{2} \sqrt{a b} b^{2} e + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} f\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \, a^{2} b^{4}} + \frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} d - \left(a b^{3}\right)^{\frac{3}{4}} f\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{256 \, a^{2} b^{4}} - \frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} d - \left(a b^{3}\right)^{\frac{3}{4}} f\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{256 \, a^{2} b^{4}}"," ",0,"1/32*(3*b*f*x^7 + 2*b*x^6*e + b*d*x^5 - a*f*x^3 - 2*a*x^2*e - 3*a*d*x - 4*a*c)/((b*x^4 + a)^2*a*b) + 1/128*sqrt(2)*(4*sqrt(2)*sqrt(a*b)*b^2*e + 3*(a*b^3)^(1/4)*b^2*d + 3*(a*b^3)^(3/4)*f)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^4) + 1/128*sqrt(2)*(4*sqrt(2)*sqrt(a*b)*b^2*e + 3*(a*b^3)^(1/4)*b^2*d + 3*(a*b^3)^(3/4)*f)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^4) + 3/256*sqrt(2)*((a*b^3)^(1/4)*b^2*d - (a*b^3)^(3/4)*f)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^4) - 3/256*sqrt(2)*((a*b^3)^(1/4)*b^2*d - (a*b^3)^(3/4)*f)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^4)","A",0
493,1,391,0,0.329290," ","integrate((f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(40 \, \sqrt{2} \sqrt{a b} b^{2} d + 77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{4} b^{3}} + \frac{\sqrt{2} {\left(40 \, \sqrt{2} \sqrt{a b} b^{2} d + 77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{4} b^{3}} + \frac{\sqrt{2} {\left(77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{1024 \, a^{4} b^{3}} - \frac{\sqrt{2} {\left(77 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - 15 \, \left(a b^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{1024 \, a^{4} b^{3}} + \frac{45 \, b^{3} x^{11} e + 60 \, b^{3} d x^{10} + 77 \, b^{3} c x^{9} + 126 \, a b^{2} x^{7} e + 160 \, a b^{2} d x^{6} + 198 \, a b^{2} c x^{5} + 113 \, a^{2} b x^{3} e + 132 \, a^{2} b d x^{2} + 153 \, a^{2} b c x - 32 \, a^{3} f}{384 \, {\left(b x^{4} + a\right)}^{3} a^{3} b}"," ",0,"1/512*sqrt(2)*(40*sqrt(2)*sqrt(a*b)*b^2*d + 77*(a*b^3)^(1/4)*b^2*c + 15*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^4*b^3) + 1/512*sqrt(2)*(40*sqrt(2)*sqrt(a*b)*b^2*d + 77*(a*b^3)^(1/4)*b^2*c + 15*(a*b^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^4*b^3) + 1/1024*sqrt(2)*(77*(a*b^3)^(1/4)*b^2*c - 15*(a*b^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^4*b^3) - 1/1024*sqrt(2)*(77*(a*b^3)^(1/4)*b^2*c - 15*(a*b^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^4*b^3) + 1/384*(45*b^3*x^11*e + 60*b^3*d*x^10 + 77*b^3*c*x^9 + 126*a*b^2*x^7*e + 160*a*b^2*d*x^6 + 198*a*b^2*c*x^5 + 113*a^2*b*x^3*e + 132*a^2*b*d*x^2 + 153*a^2*b*c*x - 32*a^3*f)/((b*x^4 + a)^3*a^3*b)","A",0
494,1,380,0,0.185019," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(8 \, \sqrt{2} \sqrt{a b} b^{2} e + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} d + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} f\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{3} b^{4}} + \frac{\sqrt{2} {\left(8 \, \sqrt{2} \sqrt{a b} b^{2} e + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} d + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} f\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \, a^{3} b^{4}} + \frac{\sqrt{2} {\left(7 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} d - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} f\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{1024 \, a^{3} b^{4}} - \frac{\sqrt{2} {\left(7 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} d - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} f\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{1024 \, a^{3} b^{4}} + \frac{15 \, b^{2} f x^{11} + 12 \, b^{2} x^{10} e + 7 \, b^{2} d x^{9} + 42 \, a b f x^{7} + 32 \, a b x^{6} e + 18 \, a b d x^{5} - 5 \, a^{2} f x^{3} - 12 \, a^{2} x^{2} e - 21 \, a^{2} d x - 32 \, a^{2} c}{384 \, {\left(b x^{4} + a\right)}^{3} a^{2} b}"," ",0,"1/512*sqrt(2)*(8*sqrt(2)*sqrt(a*b)*b^2*e + 7*(a*b^3)^(1/4)*b^2*d + 5*(a*b^3)^(3/4)*f)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^4) + 1/512*sqrt(2)*(8*sqrt(2)*sqrt(a*b)*b^2*e + 7*(a*b^3)^(1/4)*b^2*d + 5*(a*b^3)^(3/4)*f)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^3*b^4) + 1/1024*sqrt(2)*(7*(a*b^3)^(1/4)*b^2*d - 5*(a*b^3)^(3/4)*f)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^4) - 1/1024*sqrt(2)*(7*(a*b^3)^(1/4)*b^2*d - 5*(a*b^3)^(3/4)*f)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^3*b^4) + 1/384*(15*b^2*f*x^11 + 12*b^2*x^10*e + 7*b^2*d*x^9 + 42*a*b*f*x^7 + 32*a*b*x^6*e + 18*a*b*d*x^5 - 5*a^2*f*x^3 - 12*a^2*x^2*e - 21*a^2*d*x - 32*a^2*c)/((b*x^4 + a)^3*a^2*b)","A",0
495,0,0,0,0.000000," ","integrate(x^4*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{4} + a} {\left(f x^{3} + e x^{2} + d x + c\right)} x^{4}\,{d x}"," ",0,"integrate(sqrt(b*x^4 + a)*(f*x^3 + e*x^2 + d*x + c)*x^4, x)","F",0
496,0,0,0,0.000000," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{4} + a} {\left(f x^{3} + e x^{2} + d x + c\right)} x^{3}\,{d x}"," ",0,"integrate(sqrt(b*x^4 + a)*(f*x^3 + e*x^2 + d*x + c)*x^3, x)","F",0
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545,0,0,0,0.000000," ","integrate(x*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(f x^{3} + e x^{2} + d x + c\right)} x}{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)*x/(b*x^4 + a)^(3/2), x)","F",0
546,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{f x^{3} + e x^{2} + d x + c}{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)/(b*x^4 + a)^(3/2), x)","F",0
547,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)/x/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{f x^{3} + e x^{2} + d x + c}{{\left(b x^{4} + a\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)/((b*x^4 + a)^(3/2)*x), x)","F",0
548,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)/x^2/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{f x^{3} + e x^{2} + d x + c}{{\left(b x^{4} + a\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)/((b*x^4 + a)^(3/2)*x^2), x)","F",0
549,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)/x^3/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{f x^{3} + e x^{2} + d x + c}{{\left(b x^{4} + a\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)/((b*x^4 + a)^(3/2)*x^3), x)","F",0
550,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)/x^4/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{f x^{3} + e x^{2} + d x + c}{{\left(b x^{4} + a\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)/((b*x^4 + a)^(3/2)*x^4), x)","F",0
551,0,0,0,0.000000," ","integrate((g*x)^m*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^p,x, algorithm=""giac"")","\int {\left(f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{4} + a\right)}^{p} \left(g x\right)^{m}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)*(b*x^4 + a)^p*(g*x)^m, x)","F",0
552,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^p,x, algorithm=""giac"")","\int {\left(f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{4} + a\right)}^{p}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)*(b*x^4 + a)^p, x)","F",0
553,0,0,0,0.000000," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^p,x, algorithm=""giac"")","\int {\left(f x^{3} + e x^{2} + d x + c\right)} {\left(b x^{4} + a\right)}^{p} x^{3}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)*(b*x^4 + a)^p*x^3, x)","F",0
554,1,7,0,0.170344," ","integrate((x^4+x^3+x^2+x+1)/(-x^5+1),x, algorithm=""giac"")","-\log\left({\left| x - 1 \right|}\right)"," ",0,"-log(abs(x - 1))","A",0
555,1,9,0,0.191614," ","integrate((-32*x^5+48*x^4-72*x^3+108*x^2-162*x+243)/(-64*x^6+729),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| 2 \, x + 3 \right|}\right)"," ",0,"1/2*log(abs(2*x + 3))","A",0
556,1,9,0,0.182046," ","integrate((32*x^5+48*x^4+72*x^3+108*x^2+162*x+243)/(-64*x^6+729),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left({\left| 2 \, x - 3 \right|}\right)"," ",0,"-1/2*log(abs(2*x - 3))","A",0
557,1,15,0,0.196107," ","integrate((16*x^4+36*x^2+81)/(-64*x^6+729),x, algorithm=""giac"")","\frac{1}{12} \, \log\left({\left| x + \frac{3}{2} \right|}\right) - \frac{1}{12} \, \log\left({\left| x - \frac{3}{2} \right|}\right)"," ",0,"1/12*log(abs(x + 3/2)) - 1/12*log(abs(x - 3/2))","B",0
558,1,16,0,0.187578," ","integrate((-16*x^4-24*x^3+54*x+81)/(-64*x^6+729),x, algorithm=""giac"")","\frac{1}{9} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right)"," ",0,"1/9*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3))","A",0
559,1,39,0,0.201726," ","integrate((3-2*x)/(-64*x^6+729),x, algorithm=""giac"")","\frac{1}{486} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x + 3\right)}\right) - \frac{1}{972} \, \log\left(4 \, x^{2} - 6 \, x + 9\right) + \frac{1}{486} \, \log\left({\left| 2 \, x + 3 \right|}\right)"," ",0,"1/486*sqrt(3)*arctan(1/9*sqrt(3)*(4*x + 3)) - 1/972*log(4*x^2 - 6*x + 9) + 1/486*log(abs(2*x + 3))","A",0
560,1,39,0,0.182517," ","integrate((3+2*x)/(-64*x^6+729),x, algorithm=""giac"")","\frac{1}{486} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right) + \frac{1}{972} \, \log\left(4 \, x^{2} + 6 \, x + 9\right) - \frac{1}{486} \, \log\left({\left| 2 \, x - 3 \right|}\right)"," ",0,"1/486*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3)) + 1/972*log(4*x^2 + 6*x + 9) - 1/486*log(abs(2*x - 3))","A",0
561,1,48,0,0.188495," ","integrate((4*x^2-6*x+9)/(-64*x^6+729),x, algorithm=""giac"")","\frac{1}{162} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x + 3\right)}\right) - \frac{1}{324} \, \log\left(4 \, x^{2} + 6 \, x + 9\right) + \frac{1}{108} \, \log\left({\left| 2 \, x + 3 \right|}\right) - \frac{1}{324} \, \log\left({\left| 2 \, x - 3 \right|}\right)"," ",0,"1/162*sqrt(3)*arctan(1/9*sqrt(3)*(4*x + 3)) - 1/324*log(4*x^2 + 6*x + 9) + 1/108*log(abs(2*x + 3)) - 1/324*log(abs(2*x - 3))","A",0
562,1,48,0,0.180580," ","integrate((4*x^2+6*x+9)/(-64*x^6+729),x, algorithm=""giac"")","\frac{1}{162} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right) + \frac{1}{324} \, \log\left(4 \, x^{2} - 6 \, x + 9\right) + \frac{1}{324} \, \log\left({\left| 2 \, x + 3 \right|}\right) - \frac{1}{108} \, \log\left({\left| 2 \, x - 3 \right|}\right)"," ",0,"1/162*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3)) + 1/324*log(4*x^2 - 6*x + 9) + 1/324*log(abs(2*x + 3)) - 1/108*log(abs(2*x - 3))","A",0
563,1,35,0,0.172504," ","integrate((-8*x^3+27)/(-64*x^6+729),x, algorithm=""giac"")","\frac{1}{54} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right) - \frac{1}{108} \, \log\left(x^{2} - \frac{3}{2} \, x + \frac{9}{4}\right) + \frac{1}{54} \, \log\left({\left| x + \frac{3}{2} \right|}\right)"," ",0,"1/54*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3)) - 1/108*log(x^2 - 3/2*x + 9/4) + 1/54*log(abs(x + 3/2))","A",0
564,1,39,0,0.179145," ","integrate((8*x^3+24*x^2+36*x+27)/(-64*x^6+729),x, algorithm=""giac"")","\frac{1}{54} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right) + \frac{1}{36} \, \log\left(4 \, x^{2} - 6 \, x + 9\right) - \frac{1}{18} \, \log\left({\left| 2 \, x - 3 \right|}\right)"," ",0,"1/54*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3)) + 1/36*log(4*x^2 - 6*x + 9) - 1/18*log(abs(2*x - 3))","A",0
565,1,86,0,0.191809," ","integrate((-32*x^5+48*x^4-72*x^3+108*x^2-162*x+243)/(-64*x^6+729)^2,x, algorithm=""giac"")","\frac{1}{8748} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x + 3\right)}\right) + \frac{1}{26244} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right) - \frac{1}{2916 \, {\left(2 \, x + 3\right)}} - \frac{1}{17496} \, \log\left(4 \, x^{2} + 6 \, x + 9\right) - \frac{1}{17496} \, \log\left(4 \, x^{2} - 6 \, x + 9\right) + \frac{5}{17496} \, \log\left({\left| 2 \, x + 3 \right|}\right) - \frac{1}{17496} \, \log\left({\left| 2 \, x - 3 \right|}\right)"," ",0,"1/8748*sqrt(3)*arctan(1/9*sqrt(3)*(4*x + 3)) + 1/26244*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3)) - 1/2916/(2*x + 3) - 1/17496*log(4*x^2 + 6*x + 9) - 1/17496*log(4*x^2 - 6*x + 9) + 5/17496*log(abs(2*x + 3)) - 1/17496*log(abs(2*x - 3))","A",0
566,1,86,0,0.208044," ","integrate((32*x^5+48*x^4+72*x^3+108*x^2+162*x+243)/(-64*x^6+729)^2,x, algorithm=""giac"")","\frac{1}{26244} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x + 3\right)}\right) + \frac{1}{8748} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right) - \frac{1}{2916 \, {\left(2 \, x - 3\right)}} + \frac{1}{17496} \, \log\left(4 \, x^{2} + 6 \, x + 9\right) + \frac{1}{17496} \, \log\left(4 \, x^{2} - 6 \, x + 9\right) + \frac{1}{17496} \, \log\left({\left| 2 \, x + 3 \right|}\right) - \frac{5}{17496} \, \log\left({\left| 2 \, x - 3 \right|}\right)"," ",0,"1/26244*sqrt(3)*arctan(1/9*sqrt(3)*(4*x + 3)) + 1/8748*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3)) - 1/2916/(2*x - 3) + 1/17496*log(4*x^2 + 6*x + 9) + 1/17496*log(4*x^2 - 6*x + 9) + 1/17496*log(abs(2*x + 3)) - 5/17496*log(abs(2*x - 3))","A",0
567,1,63,0,0.169528," ","integrate((16*x^4+36*x^2+81)/(-64*x^6+729)^2,x, algorithm=""giac"")","\frac{1}{39366} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x + 3\right)}\right) + \frac{1}{39366} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right) - \frac{x}{4374 \, {\left(4 \, x^{2} - 9\right)}} + \frac{1}{17496} \, \log\left({\left| 2 \, x + 3 \right|}\right) - \frac{1}{17496} \, \log\left({\left| 2 \, x - 3 \right|}\right)"," ",0,"1/39366*sqrt(3)*arctan(1/9*sqrt(3)*(4*x + 3)) + 1/39366*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3)) - 1/4374*x/(4*x^2 - 9) + 1/17496*log(abs(2*x + 3)) - 1/17496*log(abs(2*x - 3))","A",0
568,1,76,0,0.188108," ","integrate((-16*x^4-24*x^3+54*x+81)/(-64*x^6+729)^2,x, algorithm=""giac"")","\frac{1}{13122} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right) + \frac{x}{4374 \, {\left(4 \, x^{2} - 6 \, x + 9\right)}} + \frac{1}{52488} \, \log\left(4 \, x^{2} + 6 \, x + 9\right) - \frac{1}{157464} \, \log\left(4 \, x^{2} - 6 \, x + 9\right) + \frac{1}{78732} \, \log\left({\left| 2 \, x + 3 \right|}\right) - \frac{1}{26244} \, \log\left({\left| 2 \, x - 3 \right|}\right)"," ",0,"1/13122*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3)) + 1/4374*x/(4*x^2 - 6*x + 9) + 1/52488*log(4*x^2 + 6*x + 9) - 1/157464*log(4*x^2 - 6*x + 9) + 1/78732*log(abs(2*x + 3)) - 1/26244*log(abs(2*x - 3))","A",0
569,1,111,0,0.203180," ","integrate((3-2*x)/(-64*x^6+729)^2,x, algorithm=""giac"")","\frac{1}{472392} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x + 3\right)}\right) + \frac{1}{4251528} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right) + \frac{x}{4374 \, {\left(4 \, x^{2} + 6 \, x + 9\right)} {\left(4 \, x^{2} - 6 \, x + 9\right)} {\left(2 \, x + 3\right)}} + \frac{1}{8503056} \, \log\left(4 \, x^{2} + 6 \, x + 9\right) - \frac{1}{944784} \, \log\left(4 \, x^{2} - 6 \, x + 9\right) + \frac{1}{472392} \, \log\left({\left| 2 \, x + 3 \right|}\right) - \frac{1}{4251528} \, \log\left({\left| 2 \, x - 3 \right|}\right)"," ",0,"1/472392*sqrt(3)*arctan(1/9*sqrt(3)*(4*x + 3)) + 1/4251528*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3)) + 1/4374*x/((4*x^2 + 6*x + 9)*(4*x^2 - 6*x + 9)*(2*x + 3)) + 1/8503056*log(4*x^2 + 6*x + 9) - 1/944784*log(4*x^2 - 6*x + 9) + 1/472392*log(abs(2*x + 3)) - 1/4251528*log(abs(2*x - 3))","A",0
570,1,111,0,0.177335," ","integrate((3+2*x)/(-64*x^6+729)^2,x, algorithm=""giac"")","\frac{1}{4251528} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x + 3\right)}\right) + \frac{1}{472392} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right) - \frac{x}{4374 \, {\left(4 \, x^{2} + 6 \, x + 9\right)} {\left(4 \, x^{2} - 6 \, x + 9\right)} {\left(2 \, x - 3\right)}} + \frac{1}{944784} \, \log\left(4 \, x^{2} + 6 \, x + 9\right) - \frac{1}{8503056} \, \log\left(4 \, x^{2} - 6 \, x + 9\right) + \frac{1}{4251528} \, \log\left({\left| 2 \, x + 3 \right|}\right) - \frac{1}{472392} \, \log\left({\left| 2 \, x - 3 \right|}\right)"," ",0,"1/4251528*sqrt(3)*arctan(1/9*sqrt(3)*(4*x + 3)) + 1/472392*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3)) - 1/4374*x/((4*x^2 + 6*x + 9)*(4*x^2 - 6*x + 9)*(2*x - 3)) + 1/944784*log(4*x^2 + 6*x + 9) - 1/8503056*log(4*x^2 - 6*x + 9) + 1/4251528*log(abs(2*x + 3)) - 1/472392*log(abs(2*x - 3))","A",0
571,1,106,0,0.180216," ","integrate((4*x^2-6*x+9)/(-64*x^6+729)^2,x, algorithm=""giac"")","\frac{1}{157464} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x + 3\right)}\right) + \frac{1}{1417176} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right) - \frac{x}{4374 \, {\left(4 \, x^{2} + 6 \, x + 9\right)} {\left(2 \, x + 3\right)} {\left(2 \, x - 3\right)}} - \frac{5}{2834352} \, \log\left(4 \, x^{2} + 6 \, x + 9\right) - \frac{1}{944784} \, \log\left(4 \, x^{2} - 6 \, x + 9\right) + \frac{1}{118098} \, \log\left({\left| 2 \, x + 3 \right|}\right) - \frac{1}{354294} \, \log\left({\left| 2 \, x - 3 \right|}\right)"," ",0,"1/157464*sqrt(3)*arctan(1/9*sqrt(3)*(4*x + 3)) + 1/1417176*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3)) - 1/4374*x/((4*x^2 + 6*x + 9)*(2*x + 3)*(2*x - 3)) - 5/2834352*log(4*x^2 + 6*x + 9) - 1/944784*log(4*x^2 - 6*x + 9) + 1/118098*log(abs(2*x + 3)) - 1/354294*log(abs(2*x - 3))","A",0
572,1,106,0,0.242747," ","integrate((4*x^2+6*x+9)/(-64*x^6+729)^2,x, algorithm=""giac"")","\frac{1}{1417176} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x + 3\right)}\right) + \frac{1}{157464} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right) - \frac{x}{4374 \, {\left(4 \, x^{2} - 6 \, x + 9\right)} {\left(2 \, x + 3\right)} {\left(2 \, x - 3\right)}} + \frac{1}{944784} \, \log\left(4 \, x^{2} + 6 \, x + 9\right) + \frac{5}{2834352} \, \log\left(4 \, x^{2} - 6 \, x + 9\right) + \frac{1}{354294} \, \log\left({\left| 2 \, x + 3 \right|}\right) - \frac{1}{118098} \, \log\left({\left| 2 \, x - 3 \right|}\right)"," ",0,"1/1417176*sqrt(3)*arctan(1/9*sqrt(3)*(4*x + 3)) + 1/157464*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3)) - 1/4374*x/((4*x^2 - 6*x + 9)*(2*x + 3)*(2*x - 3)) + 1/944784*log(4*x^2 + 6*x + 9) + 5/2834352*log(4*x^2 - 6*x + 9) + 1/354294*log(abs(2*x + 3)) - 1/118098*log(abs(2*x - 3))","A",0
573,1,89,0,0.174260," ","integrate((-8*x^3+27)/(-64*x^6+729)^2,x, algorithm=""giac"")","\frac{1}{157464} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x + 3\right)}\right) + \frac{7}{472392} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right) + \frac{x}{4374 \, {\left(8 \, x^{3} + 27\right)}} + \frac{1}{314928} \, \log\left(4 \, x^{2} + 6 \, x + 9\right) - \frac{7}{944784} \, \log\left(4 \, x^{2} - 6 \, x + 9\right) + \frac{7}{472392} \, \log\left({\left| 2 \, x + 3 \right|}\right) - \frac{1}{157464} \, \log\left({\left| 2 \, x - 3 \right|}\right)"," ",0,"1/157464*sqrt(3)*arctan(1/9*sqrt(3)*(4*x + 3)) + 7/472392*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3)) + 1/4374*x/(8*x^3 + 27) + 1/314928*log(4*x^2 + 6*x + 9) - 7/944784*log(4*x^2 - 6*x + 9) + 7/472392*log(abs(2*x + 3)) - 1/157464*log(abs(2*x - 3))","A",0
574,1,99,0,0.176969," ","integrate((8*x^3+24*x^2+36*x+27)/(-64*x^6+729)^2,x, algorithm=""giac"")","-\frac{1}{472392} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x + 3\right)}\right) + \frac{11}{472392} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right) - \frac{x}{4374 \, {\left(4 \, x^{2} - 6 \, x + 9\right)} {\left(2 \, x - 3\right)}} + \frac{1}{314928} \, \log\left(4 \, x^{2} + 6 \, x + 9\right) + \frac{17}{944784} \, \log\left(4 \, x^{2} - 6 \, x + 9\right) + \frac{1}{472392} \, \log\left({\left| 2 \, x + 3 \right|}\right) - \frac{7}{157464} \, \log\left({\left| 2 \, x - 3 \right|}\right)"," ",0,"-1/472392*sqrt(3)*arctan(1/9*sqrt(3)*(4*x + 3)) + 11/472392*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3)) - 1/4374*x/((4*x^2 - 6*x + 9)*(2*x - 3)) + 1/314928*log(4*x^2 + 6*x + 9) + 17/944784*log(4*x^2 - 6*x + 9) + 1/472392*log(abs(2*x + 3)) - 7/157464*log(abs(2*x - 3))","A",0
575,1,69,0,0.191967," ","integrate(x*(-2*x^3+27)/(-64*x^6+729),x, algorithm=""giac"")","-\frac{1}{96} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x + 3\right)}\right) + \frac{5}{288} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right) + \frac{1}{192} \, \log\left(x^{2} + \frac{3}{2} \, x + \frac{9}{4}\right) + \frac{5}{576} \, \log\left(x^{2} - \frac{3}{2} \, x + \frac{9}{4}\right) - \frac{5}{288} \, \log\left({\left| x + \frac{3}{2} \right|}\right) - \frac{1}{96} \, \log\left({\left| x - \frac{3}{2} \right|}\right)"," ",0,"-1/96*sqrt(3)*arctan(1/9*sqrt(3)*(4*x + 3)) + 5/288*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3)) + 1/192*log(x^2 + 3/2*x + 9/4) + 5/576*log(x^2 - 3/2*x + 9/4) - 5/288*log(abs(x + 3/2)) - 1/96*log(abs(x - 3/2))","A",0
576,0,0,0,0.000000," ","integrate((c*x)^m*(d+e*x^n+f*x^(2*n)+g*x^(3*n))/(a+b*x^n),x, algorithm=""giac"")","\int \frac{{\left(g x^{3 \, n} + f x^{2 \, n} + e x^{n} + d\right)} \left(c x\right)^{m}}{b x^{n} + a}\,{d x}"," ",0,"integrate((g*x^(3*n) + f*x^(2*n) + e*x^n + d)*(c*x)^m/(b*x^n + a), x)","F",0
577,1,392,0,0.261582," ","integrate((c+d*x^(-1+n))*(a+b*x^n)^3,x, algorithm=""giac"")","\frac{24 \, a^{3} c n^{4} x + 8 \, b^{3} c n^{3} x x^{3 \, n} + 36 \, a b^{2} c n^{3} x x^{2 \, n} + 72 \, a^{2} b c n^{3} x x^{n} + 44 \, a^{3} c n^{3} x + 6 \, b^{3} d n^{3} x^{4 \, n} + 24 \, a b^{2} d n^{3} x^{3 \, n} + 12 \, b^{3} c n^{2} x x^{3 \, n} + 36 \, a^{2} b d n^{3} x^{2 \, n} + 48 \, a b^{2} c n^{2} x x^{2 \, n} + 24 \, a^{3} d n^{3} x^{n} + 60 \, a^{2} b c n^{2} x x^{n} + 24 \, a^{3} c n^{2} x + 11 \, b^{3} d n^{2} x^{4 \, n} + 44 \, a b^{2} d n^{2} x^{3 \, n} + 4 \, b^{3} c n x x^{3 \, n} + 66 \, a^{2} b d n^{2} x^{2 \, n} + 12 \, a b^{2} c n x x^{2 \, n} + 44 \, a^{3} d n^{2} x^{n} + 12 \, a^{2} b c n x x^{n} + 4 \, a^{3} c n x + 6 \, b^{3} d n x^{4 \, n} + 24 \, a b^{2} d n x^{3 \, n} + 36 \, a^{2} b d n x^{2 \, n} + 24 \, a^{3} d n x^{n} + b^{3} d x^{4 \, n} + 4 \, a b^{2} d x^{3 \, n} + 6 \, a^{2} b d x^{2 \, n} + 4 \, a^{3} d x^{n}}{4 \, {\left(6 \, n^{4} + 11 \, n^{3} + 6 \, n^{2} + n\right)}}"," ",0,"1/4*(24*a^3*c*n^4*x + 8*b^3*c*n^3*x*x^(3*n) + 36*a*b^2*c*n^3*x*x^(2*n) + 72*a^2*b*c*n^3*x*x^n + 44*a^3*c*n^3*x + 6*b^3*d*n^3*x^(4*n) + 24*a*b^2*d*n^3*x^(3*n) + 12*b^3*c*n^2*x*x^(3*n) + 36*a^2*b*d*n^3*x^(2*n) + 48*a*b^2*c*n^2*x*x^(2*n) + 24*a^3*d*n^3*x^n + 60*a^2*b*c*n^2*x*x^n + 24*a^3*c*n^2*x + 11*b^3*d*n^2*x^(4*n) + 44*a*b^2*d*n^2*x^(3*n) + 4*b^3*c*n*x*x^(3*n) + 66*a^2*b*d*n^2*x^(2*n) + 12*a*b^2*c*n*x*x^(2*n) + 44*a^3*d*n^2*x^n + 12*a^2*b*c*n*x*x^n + 4*a^3*c*n*x + 6*b^3*d*n*x^(4*n) + 24*a*b^2*d*n*x^(3*n) + 36*a^2*b*d*n*x^(2*n) + 24*a^3*d*n*x^n + b^3*d*x^(4*n) + 4*a*b^2*d*x^(3*n) + 6*a^2*b*d*x^(2*n) + 4*a^3*d*x^n)/(6*n^4 + 11*n^3 + 6*n^2 + n)","B",0
578,1,196,0,0.219047," ","integrate((c+d*x^(-1+n))*(a+b*x^n)^2,x, algorithm=""giac"")","\frac{6 \, a^{2} c n^{3} x + 3 \, b^{2} c n^{2} x x^{2 \, n} + 12 \, a b c n^{2} x x^{n} + 9 \, a^{2} c n^{2} x + 2 \, b^{2} d n^{2} x^{3 \, n} + 6 \, a b d n^{2} x^{2 \, n} + 3 \, b^{2} c n x x^{2 \, n} + 6 \, a^{2} d n^{2} x^{n} + 6 \, a b c n x x^{n} + 3 \, a^{2} c n x + 3 \, b^{2} d n x^{3 \, n} + 9 \, a b d n x^{2 \, n} + 9 \, a^{2} d n x^{n} + b^{2} d x^{3 \, n} + 3 \, a b d x^{2 \, n} + 3 \, a^{2} d x^{n}}{3 \, {\left(2 \, n^{3} + 3 \, n^{2} + n\right)}}"," ",0,"1/3*(6*a^2*c*n^3*x + 3*b^2*c*n^2*x*x^(2*n) + 12*a*b*c*n^2*x*x^n + 9*a^2*c*n^2*x + 2*b^2*d*n^2*x^(3*n) + 6*a*b*d*n^2*x^(2*n) + 3*b^2*c*n*x*x^(2*n) + 6*a^2*d*n^2*x^n + 6*a*b*c*n*x*x^n + 3*a^2*c*n*x + 3*b^2*d*n*x^(3*n) + 9*a*b*d*n*x^(2*n) + 9*a^2*d*n*x^n + b^2*d*x^(3*n) + 3*a*b*d*x^(2*n) + 3*a^2*d*x^n)/(2*n^3 + 3*n^2 + n)","B",0
579,1,65,0,0.221803," ","integrate((c+d*x^(-1+n))*(a+b*x^n),x, algorithm=""giac"")","\frac{2 \, a c n^{2} x + 2 \, b c n x x^{n} + 2 \, a c n x + b d n x^{2 \, n} + 2 \, a d n x^{n} + b d x^{2 \, n} + 2 \, a d x^{n}}{2 \, {\left(n^{2} + n\right)}}"," ",0,"1/2*(2*a*c*n^2*x + 2*b*c*n*x*x^n + 2*a*c*n*x + b*d*n*x^(2*n) + 2*a*d*n*x^n + b*d*x^(2*n) + 2*a*d*x^n)/(n^2 + n)","A",0
580,1,12,0,0.166835," ","integrate(c+d*x^(-1+n),x, algorithm=""giac"")","c x + \frac{d x^{n}}{n}"," ",0,"c*x + d*x^n/n","A",0
581,0,0,0,0.000000," ","integrate((c+d*x^(-1+n))/(a+b*x^n),x, algorithm=""giac"")","\int \frac{d x^{n - 1} + c}{b x^{n} + a}\,{d x}"," ",0,"integrate((d*x^(n - 1) + c)/(b*x^n + a), x)","F",0
582,0,0,0,0.000000," ","integrate((c+d*x^(-1+n))/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{d x^{n - 1} + c}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^(n - 1) + c)/(b*x^n + a)^2, x)","F",0
583,0,0,0,0.000000," ","integrate((c+d*x^(-1+n))/(a+b*x^n)^3,x, algorithm=""giac"")","\int \frac{d x^{n - 1} + c}{{\left(b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*x^(n - 1) + c)/(b*x^n + a)^3, x)","F",0
584,0,0,0,0.000000," ","integrate((c*x)^m*(d+e*x^n+f*x^(2*n)+g*x^(3*n))/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(g x^{3 \, n} + f x^{2 \, n} + e x^{n} + d\right)} \left(c x\right)^{m}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate((g*x^(3*n) + f*x^(2*n) + e*x^n + d)*(c*x)^m/sqrt(b*x^n + a), x)","F",0
585,0,0,0,0.000000," ","integrate((-a*h*x^(-1+1/4*n)+b*f*x^(-1+1/2*n)+b*g*x^(-1+n)+b*h*x^(-1+5/4*n))/(a+b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{b h x^{\frac{5}{4} \, n - 1} + b g x^{n - 1} + b f x^{\frac{1}{2} \, n - 1} - a h x^{\frac{1}{4} \, n - 1}}{{\left(b x^{n} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*h*x^(5/4*n - 1) + b*g*x^(n - 1) + b*f*x^(1/2*n - 1) - a*h*x^(1/4*n - 1))/(b*x^n + a)^(3/2), x)","F",0
586,0,0,0,0.000000," ","integrate((c*x)^m*(g*x^3+f*x^2+e*x+d)*(a+b*x^n)^p,x, algorithm=""giac"")","\int {\left(g x^{3} + f x^{2} + e x + d\right)} {\left(b x^{n} + a\right)}^{p} \left(c x\right)^{m}\,{d x}"," ",0,"integrate((g*x^3 + f*x^2 + e*x + d)*(b*x^n + a)^p*(c*x)^m, x)","F",0
587,-2,0,0,0.000000," ","integrate((c*x)^m*(a+b*x^n)^p*(d+e*x^n+f*x^(2*n)+g*x^(3*n)),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 c near 0Simplification assuming x near 0Simplification assuming c near 0Unable to divide, perhaps due to rounding error%%%{1,[2,0,6,4,0,2,4,4,1,0,0]%%%}+%%%{4,[2,0,6,4,0,2,3,4,1,0,0]%%%}+%%%{6,[2,0,6,4,0,2,2,4,1,0,0]%%%}+%%%{4,[2,0,6,4,0,2,1,4,1,0,0]%%%}+%%%{1,[2,0,6,4,0,2,0,4,1,0,0]%%%}+%%%{1,[1,0,6,4,0,2,4,4,0,1,0]%%%}+%%%{4,[1,0,6,4,0,2,3,4,0,1,0]%%%}+%%%{6,[1,0,6,4,0,2,2,4,0,1,0]%%%}+%%%{4,[1,0,6,4,0,2,1,4,0,1,0]%%%}+%%%{1,[1,0,6,4,0,2,0,4,0,1,0]%%%}+%%%{-1,[1,0,6,4,0,1,4,5,1,0,0]%%%}+%%%{-4,[1,0,6,4,0,1,3,5,1,0,0]%%%}+%%%{-6,[1,0,6,4,0,1,2,5,1,0,0]%%%}+%%%{-4,[1,0,6,4,0,1,1,5,1,0,0]%%%}+%%%{-1,[1,0,6,4,0,1,0,5,1,0,0]%%%}+%%%{1,[0,0,6,4,0,3,4,3,0,0,1]%%%}+%%%{4,[0,0,6,4,0,3,3,3,0,0,1]%%%}+%%%{6,[0,0,6,4,0,3,2,3,0,0,1]%%%}+%%%{4,[0,0,6,4,0,3,1,3,0,0,1]%%%}+%%%{1,[0,0,6,4,0,3,0,3,0,0,1]%%%}+%%%{1,[0,0,6,3,1,3,3,3,0,0,1]%%%}+%%%{3,[0,0,6,3,1,3,2,3,0,0,1]%%%}+%%%{3,[0,0,6,3,1,3,1,3,0,0,1]%%%}+%%%{1,[0,0,6,3,1,3,0,3,0,0,1]%%%}+%%%{1,[0,0,6,3,1,1,3,5,0,1,0]%%%}+%%%{3,[0,0,6,3,1,1,2,5,0,1,0]%%%}+%%%{3,[0,0,6,3,1,1,1,5,0,1,0]%%%}+%%%{1,[0,0,6,3,1,1,0,5,0,1,0]%%%}+%%%{-1,[0,0,6,3,1,0,3,6,1,0,0]%%%}+%%%{-3,[0,0,6,3,1,0,2,6,1,0,0]%%%}+%%%{-3,[0,0,6,3,1,0,1,6,1,0,0]%%%}+%%%{-1,[0,0,6,3,1,0,0,6,1,0,0]%%%}+%%%{1,[0,0,6,3,0,3,3,3,0,0,1]%%%}+%%%{3,[0,0,6,3,0,3,2,3,0,0,1]%%%}+%%%{3,[0,0,6,3,0,3,1,3,0,0,1]%%%}+%%%{1,[0,0,6,3,0,3,0,3,0,0,1]%%%}+%%%{1,[0,0,6,3,0,1,3,5,0,1,0]%%%}+%%%{3,[0,0,6,3,0,1,2,5,0,1,0]%%%}+%%%{3,[0,0,6,3,0,1,1,5,0,1,0]%%%}+%%%{1,[0,0,6,3,0,1,0,5,0,1,0]%%%}+%%%{-1,[0,0,6,3,0,0,3,6,1,0,0]%%%}+%%%{-3,[0,0,6,3,0,0,2,6,1,0,0]%%%}+%%%{-3,[0,0,6,3,0,0,1,6,1,0,0]%%%}+%%%{-1,[0,0,6,3,0,0,0,6,1,0,0]%%%} / %%%{1,[0,0,7,4,0,3,4,4,0,0,0]%%%}+%%%{4,[0,0,7,4,0,3,3,4,0,0,0]%%%}+%%%{6,[0,0,7,4,0,3,2,4,0,0,0]%%%}+%%%{4,[0,0,7,4,0,3,1,4,0,0,0]%%%}+%%%{1,[0,0,7,4,0,3,0,4,0,0,0]%%%} Error: Bad Argument Value","F(-2)",0
588,0,0,0,0.000000," ","integrate((c+d*x^(1/2*n)+e*x^n+f*x^(3/2*n))/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{f x^{\frac{3}{2} \, n} + d x^{\frac{1}{2} \, n} + e x^{n} + c}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((f*x^(3/2*n) + d*x^(1/2*n) + e*x^n + c)/(b*x^n + a)^2, x)","F",0
589,0,0,0,0.000000," ","integrate((a*c+2*(a*d+b*c)*x^2+3*b*d*x^4)/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{3 \, b d x^{4} + 2 \, {\left(b c + a d\right)} x^{2} + a c}{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate((3*b*d*x^4 + 2*(b*c + a*d)*x^2 + a*c)/(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)), x)","F",0
590,0,0,0,0.000000," ","integrate((x^3+1)/(-x^4+1)/(x^4+1)^(1/4),x, algorithm=""giac"")","\int -\frac{x^{3} + 1}{{\left(x^{4} + 1\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate(-(x^3 + 1)/((x^4 + 1)^(1/4)*(x^4 - 1)), x)","F",0
591,1,228,0,0.422431," ","integrate((a+b*x^n)^((-1-n)/n)*(c+d*x^n)^((-1-n)/n)*(a*c-b*d*x^(2*n)),x, algorithm=""giac"")","b d x x^{2 \, n} e^{\left(-\frac{n \log\left(b x^{n} + a\right) + \log\left(b x^{n} + a\right)}{n} - \frac{n \log\left(d x^{n} + c\right) + \log\left(d x^{n} + c\right)}{n}\right)} + b c x x^{n} e^{\left(-\frac{n \log\left(b x^{n} + a\right) + \log\left(b x^{n} + a\right)}{n} - \frac{n \log\left(d x^{n} + c\right) + \log\left(d x^{n} + c\right)}{n}\right)} + a d x x^{n} e^{\left(-\frac{n \log\left(b x^{n} + a\right) + \log\left(b x^{n} + a\right)}{n} - \frac{n \log\left(d x^{n} + c\right) + \log\left(d x^{n} + c\right)}{n}\right)} + a c x e^{\left(-\frac{n \log\left(b x^{n} + a\right) + \log\left(b x^{n} + a\right)}{n} - \frac{n \log\left(d x^{n} + c\right) + \log\left(d x^{n} + c\right)}{n}\right)}"," ",0,"b*d*x*x^(2*n)*e^(-(n*log(b*x^n + a) + log(b*x^n + a))/n - (n*log(d*x^n + c) + log(d*x^n + c))/n) + b*c*x*x^n*e^(-(n*log(b*x^n + a) + log(b*x^n + a))/n - (n*log(d*x^n + c) + log(d*x^n + c))/n) + a*d*x*x^n*e^(-(n*log(b*x^n + a) + log(b*x^n + a))/n - (n*log(d*x^n + c) + log(d*x^n + c))/n) + a*c*x*e^(-(n*log(b*x^n + a) + log(b*x^n + a))/n - (n*log(d*x^n + c) + log(d*x^n + c))/n)","B",0
592,1,237,0,0.426437," ","integrate((h*x)^(-n*p-n-1)*(a+b*x^n)^p*(c+d*x^n)^p*(a*c-b*d*x^(2*n)),x, algorithm=""giac"")","-\frac{{\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{p} b d x x^{2 \, n} e^{\left(-n p \log\left(h\right) - n p \log\left(x\right) - n \log\left(h\right) - n \log\left(x\right) - \log\left(h\right) - \log\left(x\right)\right)} + {\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{p} b c x x^{n} e^{\left(-n p \log\left(h\right) - n p \log\left(x\right) - n \log\left(h\right) - n \log\left(x\right) - \log\left(h\right) - \log\left(x\right)\right)} + {\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{p} a d x x^{n} e^{\left(-n p \log\left(h\right) - n p \log\left(x\right) - n \log\left(h\right) - n \log\left(x\right) - \log\left(h\right) - \log\left(x\right)\right)} + {\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{p} a c x e^{\left(-n p \log\left(h\right) - n p \log\left(x\right) - n \log\left(h\right) - n \log\left(x\right) - \log\left(h\right) - \log\left(x\right)\right)}}{n p + n}"," ",0,"-((b*x^n + a)^p*(d*x^n + c)^p*b*d*x*x^(2*n)*e^(-n*p*log(h) - n*p*log(x) - n*log(h) - n*log(x) - log(h) - log(x)) + (b*x^n + a)^p*(d*x^n + c)^p*b*c*x*x^n*e^(-n*p*log(h) - n*p*log(x) - n*log(h) - n*log(x) - log(h) - log(x)) + (b*x^n + a)^p*(d*x^n + c)^p*a*d*x*x^n*e^(-n*p*log(h) - n*p*log(x) - n*log(h) - n*log(x) - log(h) - log(x)) + (b*x^n + a)^p*(d*x^n + c)^p*a*c*x*e^(-n*p*log(h) - n*p*log(x) - n*log(h) - n*log(x) - log(h) - log(x)))/(n*p + n)","B",0
593,1,115,0,0.555578," ","integrate((a+b*x^n)^p*(c+d*x^n)^p*(e+(a*d+b*c)*e*(n*p+n+1)*x^n/a/c+b*d*e*(2*n*p+2*n+1)*x^(2*n)/a/c),x, algorithm=""giac"")","\frac{{\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{p} b d x x^{2 \, n} e + {\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{p} b c x x^{n} e + {\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{p} a d x x^{n} e + {\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{p} a c x e}{a c}"," ",0,"((b*x^n + a)^p*(d*x^n + c)^p*b*d*x*x^(2*n)*e + (b*x^n + a)^p*(d*x^n + c)^p*b*c*x*x^n*e + (b*x^n + a)^p*(d*x^n + c)^p*a*d*x*x^n*e + (b*x^n + a)^p*(d*x^n + c)^p*a*c*x*e)/(a*c)","B",0
594,1,155,0,0.808506," ","integrate((h*x)^m*(a+b*x^n)^p*(c+d*x^n)^p*(e+(a*d+b*c)*e*(n*p+m+n+1)*x^n/a/c/(1+m)+b*d*e*(2*n*p+m+2*n+1)*x^(2*n)/a/c/(1+m)),x, algorithm=""giac"")","\frac{{\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{p} b d x x^{2 \, n} e^{\left(m \log\left(h\right) + m \log\left(x\right) + 1\right)} + {\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{p} b c x x^{n} e^{\left(m \log\left(h\right) + m \log\left(x\right) + 1\right)} + {\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{p} a d x x^{n} e^{\left(m \log\left(h\right) + m \log\left(x\right) + 1\right)} + {\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{p} a c x e^{\left(m \log\left(h\right) + m \log\left(x\right) + 1\right)}}{a c m + a c}"," ",0,"((b*x^n + a)^p*(d*x^n + c)^p*b*d*x*x^(2*n)*e^(m*log(h) + m*log(x) + 1) + (b*x^n + a)^p*(d*x^n + c)^p*b*c*x*x^n*e^(m*log(h) + m*log(x) + 1) + (b*x^n + a)^p*(d*x^n + c)^p*a*d*x*x^n*e^(m*log(h) + m*log(x) + 1) + (b*x^n + a)^p*(d*x^n + c)^p*a*c*x*e^(m*log(h) + m*log(x) + 1))/(a*c*m + a*c)","B",0
