1,1,77,0,0.922922," ","integrate((e*x^2+d*x+c)/(b*x+a)^(1/2),x, algorithm=""maxima"")","\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
2,1,237,0,0.900451," ","integrate((e*x^2+d*x+c)^2/(b*x+a)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(315 \, \sqrt{b x + a} c^{2} + 42 \, c {\left(\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)} + \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{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 + 42*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) + 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 + 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
3,1,525,0,0.977543," ","integrate((e*x^2+d*x+c)^3/(b*x+a)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(15015 \, \sqrt{b x + a} c^{3} + 3003 \, c^{2} {\left(\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)} + 143 \, c {\left(\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{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)} + \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{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{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 + 3003*c^2*(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) + 143*c*(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 + 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) + 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 + 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 + 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
4,1,128,0,0.833104," ","integrate((f*x^3+e*x^2+d*x+c)/(b*x+a)^(1/2),x, algorithm=""maxima"")","\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
5,1,500,0,1.002134," ","integrate((f*x^3+e*x^2+d*x+c)^2/(b*x+a)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(45045 \, \sqrt{b x + a} c^{2} + 858 \, c {\left(\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)} + \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{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{286 \, {\left(35 \, {\left(b x + a\right)}^{\frac{9}{2}} f + 45 \, {\left(b e - 4 \, a f\right)} {\left(b x + a\right)}^{\frac{7}{2}} - 189 \, {\left(a b e - 2 \, a^{2} f\right)} {\left(b x + a\right)}^{\frac{5}{2}} + 105 \, {\left(3 \, a^{2} b e - 4 \, a^{3} f\right)} {\left(b x + a\right)}^{\frac{3}{2}} - 315 \, {\left(a^{3} b e - a^{4} f\right)} \sqrt{b x + a}\right)} d}{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)} e f}{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 + 858*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) + 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 + 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 + 286*(35*(b*x + a)^(9/2)*f + 45*(b*e - 4*a*f)*(b*x + a)^(7/2) - 189*(a*b*e - 2*a^2*f)*(b*x + a)^(5/2) + 105*(3*a^2*b*e - 4*a^3*f)*(b*x + a)^(3/2) - 315*(a^3*b*e - a^4*f)*sqrt(b*x + a))*d/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)*e*f/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
6,1,1360,0,1.094183," ","integrate((f*x^3+e*x^2+d*x+c)^3/(b*x+a)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(4849845 \, \sqrt{b x + a} c^{3} + 138567 \, c^{2} {\left(\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)} + 323 \, c {\left(\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{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{286 \, {\left(35 \, {\left(b x + a\right)}^{\frac{9}{2}} f + 45 \, {\left(b e - 4 \, a f\right)} {\left(b x + a\right)}^{\frac{7}{2}} - 189 \, {\left(a b e - 2 \, a^{2} f\right)} {\left(b x + a\right)}^{\frac{5}{2}} + 105 \, {\left(3 \, a^{2} b e - 4 \, a^{3} f\right)} {\left(b x + a\right)}^{\frac{3}{2}} - 315 \, {\left(a^{3} b e - a^{4} f\right)} \sqrt{b x + a}\right)} d}{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)} e f}{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)} + \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{4199 \, {\left(315 \, {\left(b x + a\right)}^{\frac{11}{2}} f + 385 \, {\left(b e - 5 \, a f\right)} {\left(b x + a\right)}^{\frac{9}{2}} - 990 \, {\left(2 \, a b e - 5 \, a^{2} f\right)} {\left(b x + a\right)}^{\frac{7}{2}} + 1386 \, {\left(3 \, a^{2} b e - 5 \, a^{3} f\right)} {\left(b x + a\right)}^{\frac{5}{2}} - 1155 \, {\left(4 \, a^{3} b e - 5 \, a^{4} f\right)} {\left(b x + a\right)}^{\frac{3}{2}} + 3465 \, {\left(a^{4} b e - a^{5} f\right)} \sqrt{b x + a}\right)} d^{2}}{b^{5}} + \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)} e^{2} f}{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)} e f^{2}}{b^{8}} + \frac{323 \, {\left(3003 \, {\left(b x + a\right)}^{\frac{15}{2}} f^{2} + 3465 \, {\left(2 \, b e f - 7 \, a f^{2}\right)} {\left(b x + a\right)}^{\frac{13}{2}} + 4095 \, {\left(b^{2} e^{2} - 12 \, a b e f + 21 \, a^{2} f^{2}\right)} {\left(b x + a\right)}^{\frac{11}{2}} - 25025 \, {\left(a b^{2} e^{2} - 6 \, a^{2} b e f + 7 \, a^{3} f^{2}\right)} {\left(b x + a\right)}^{\frac{9}{2}} + 32175 \, {\left(2 \, a^{2} b^{2} e^{2} - 8 \, a^{3} b e f + 7 \, a^{4} f^{2}\right)} {\left(b x + a\right)}^{\frac{7}{2}} - 9009 \, {\left(10 \, a^{3} b^{2} e^{2} - 30 \, a^{4} b e f + 21 \, a^{5} f^{2}\right)} {\left(b x + a\right)}^{\frac{5}{2}} + 15015 \, {\left(5 \, a^{4} b^{2} e^{2} - 12 \, a^{5} b e f + 7 \, a^{6} f^{2}\right)} {\left(b x + a\right)}^{\frac{3}{2}} - 45045 \, {\left(a^{5} b^{2} e^{2} - 2 \, a^{6} b e f + a^{7} f^{2}\right)} \sqrt{b x + a}\right)} d}{b^{7}} + \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 + 138567*c^2*(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) + 323*c*(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 + 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 + 286*(35*(b*x + a)^(9/2)*f + 45*(b*e - 4*a*f)*(b*x + a)^(7/2) - 189*(a*b*e - 2*a^2*f)*(b*x + a)^(5/2) + 105*(3*a^2*b*e - 4*a^3*f)*(b*x + a)^(3/2) - 315*(a^3*b*e - a^4*f)*sqrt(b*x + a))*d/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)*e*f/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) + 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 + 4199*(315*(b*x + a)^(11/2)*f + 385*(b*e - 5*a*f)*(b*x + a)^(9/2) - 990*(2*a*b*e - 5*a^2*f)*(b*x + a)^(7/2) + 1386*(3*a^2*b*e - 5*a^3*f)*(b*x + a)^(5/2) - 1155*(4*a^3*b*e - 5*a^4*f)*(b*x + a)^(3/2) + 3465*(a^4*b*e - a^5*f)*sqrt(b*x + a))*d^2/b^5 + 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)*e^2*f/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)*e*f^2/b^8 + 323*(3003*(b*x + a)^(15/2)*f^2 + 3465*(2*b*e*f - 7*a*f^2)*(b*x + a)^(13/2) + 4095*(b^2*e^2 - 12*a*b*e*f + 21*a^2*f^2)*(b*x + a)^(11/2) - 25025*(a*b^2*e^2 - 6*a^2*b*e*f + 7*a^3*f^2)*(b*x + a)^(9/2) + 32175*(2*a^2*b^2*e^2 - 8*a^3*b*e*f + 7*a^4*f^2)*(b*x + a)^(7/2) - 9009*(10*a^3*b^2*e^2 - 30*a^4*b*e*f + 21*a^5*f^2)*(b*x + a)^(5/2) + 15015*(5*a^4*b^2*e^2 - 12*a^5*b*e*f + 7*a^6*f^2)*(b*x + a)^(3/2) - 45045*(a^5*b^2*e^2 - 2*a^6*b*e*f + a^7*f^2)*sqrt(b*x + a))*d/b^7 + 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
7,1,135,0,1.912191," ","integrate((d*x+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{\sqrt{3} {\left(d \left(\frac{a}{b}\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 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(d \left(\frac{a}{b}\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 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(d \left(\frac{a}{b}\right)^{\frac{1}{3}} - c\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*sqrt(3)*(d*(a/b)^(1/3) + c)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b*(a/b)^(2/3)) + 1/6*(d*(a/b)^(1/3) - c)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) - 1/3*(d*(a/b)^(1/3) - c)*log(x + (a/b)^(1/3))/(b*(a/b)^(2/3))","A",0
8,1,169,0,1.999684," ","integrate((d*x+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{d x^{2} + c x}{3 \, {\left(a b x^{3} + a^{2}\right)}} + \frac{\sqrt{3} {\left(d \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, 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 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, 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 \, a b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, c\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*(d*x^2 + c*x)/(a*b*x^3 + a^2) + 1/9*sqrt(3)*(d*(a/b)^(1/3) + 2*c)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b*(a/b)^(2/3)) + 1/18*(d*(a/b)^(1/3) - 2*c)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b*(a/b)^(2/3)) - 1/9*(d*(a/b)^(1/3) - 2*c)*log(x + (a/b)^(1/3))/(a*b*(a/b)^(2/3))","A",0
9,1,203,0,1.964972," ","integrate((d*x+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{4 \, b d x^{5} + 5 \, b c x^{4} + 7 \, a d x^{2} + 8 \, a c x}{18 \, {\left(a^{2} b^{2} x^{6} + 2 \, a^{3} b x^{3} + a^{4}\right)}} + \frac{\sqrt{3} {\left(2 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, 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^{2} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(2 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, 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^{2} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(2 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, c\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{2} b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/18*(4*b*d*x^5 + 5*b*c*x^4 + 7*a*d*x^2 + 8*a*c*x)/(a^2*b^2*x^6 + 2*a^3*b*x^3 + a^4) + 1/27*sqrt(3)*(2*d*(a/b)^(1/3) + 5*c)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b*(a/b)^(2/3)) + 1/54*(2*d*(a/b)^(1/3) - 5*c)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b*(a/b)^(2/3)) - 1/27*(2*d*(a/b)^(1/3) - 5*c)*log(x + (a/b)^(1/3))/(a^2*b*(a/b)^(2/3))","A",0
10,1,238,0,2.616297," ","integrate((d*x+c)/(b*x^3+a)^4,x, algorithm=""maxima"")","\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(a^{3} b^{3} x^{9} + 3 \, a^{4} b^{2} x^{6} + 3 \, a^{5} b x^{3} + a^{6}\right)}} + \frac{2 \, \sqrt{3} {\left(7 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} + 20 \, 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^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(7 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 20 \, 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^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{2 \, {\left(7 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 20 \, c\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \, a^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"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)/(a^3*b^3*x^9 + 3*a^4*b^2*x^6 + 3*a^5*b*x^3 + a^6) + 2/243*sqrt(3)*(7*d*(a/b)^(1/3) + 20*c)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^3*b*(a/b)^(2/3)) + 1/243*(7*d*(a/b)^(1/3) - 20*c)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*b*(a/b)^(2/3)) - 2/243*(7*d*(a/b)^(1/3) - 20*c)*log(x + (a/b)^(1/3))/(a^3*b*(a/b)^(2/3))","A",0
11,1,135,0,2.508876," ","integrate((b*x+a)/(e*x^3+d),x, algorithm=""maxima"")","\frac{\sqrt{3} {\left(b \left(\frac{d}{e}\right)^{\frac{1}{3}} + a\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{d}{e}\right)^{\frac{1}{3}}}\right)}{3 \, e \left(\frac{d}{e}\right)^{\frac{2}{3}}} + \frac{{\left(b \left(\frac{d}{e}\right)^{\frac{1}{3}} - a\right)} \log\left(x^{2} - x \left(\frac{d}{e}\right)^{\frac{1}{3}} + \left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \, e \left(\frac{d}{e}\right)^{\frac{2}{3}}} - \frac{{\left(b \left(\frac{d}{e}\right)^{\frac{1}{3}} - a\right)} \log\left(x + \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \, e \left(\frac{d}{e}\right)^{\frac{2}{3}}}"," ",0,"1/3*sqrt(3)*(b*(d/e)^(1/3) + a)*arctan(1/3*sqrt(3)*(2*x - (d/e)^(1/3))/(d/e)^(1/3))/(e*(d/e)^(2/3)) + 1/6*(b*(d/e)^(1/3) - a)*log(x^2 - x*(d/e)^(1/3) + (d/e)^(2/3))/(e*(d/e)^(2/3)) - 1/3*(b*(d/e)^(1/3) - a)*log(x + (d/e)^(1/3))/(e*(d/e)^(2/3))","A",0
12,1,132,0,2.678033," ","integrate((b*x+a)/(-e*x^3+d),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left(b \left(\frac{d}{e}\right)^{\frac{1}{3}} - a\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{d}{e}\right)^{\frac{1}{3}}}\right)}{3 \, e \left(\frac{d}{e}\right)^{\frac{2}{3}}} + \frac{{\left(b \left(\frac{d}{e}\right)^{\frac{1}{3}} + a\right)} \log\left(x^{2} + x \left(\frac{d}{e}\right)^{\frac{1}{3}} + \left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \, e \left(\frac{d}{e}\right)^{\frac{2}{3}}} - \frac{{\left(b \left(\frac{d}{e}\right)^{\frac{1}{3}} + a\right)} \log\left(x - \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \, e \left(\frac{d}{e}\right)^{\frac{2}{3}}}"," ",0,"-1/3*sqrt(3)*(b*(d/e)^(1/3) - a)*arctan(1/3*sqrt(3)*(2*x + (d/e)^(1/3))/(d/e)^(1/3))/(e*(d/e)^(2/3)) + 1/6*(b*(d/e)^(1/3) + a)*log(x^2 + x*(d/e)^(1/3) + (d/e)^(2/3))/(e*(d/e)^(2/3)) - 1/3*(b*(d/e)^(1/3) + a)*log(x - (d/e)^(1/3))/(e*(d/e)^(2/3))","A",0
13,1,16,0,2.484981," ","integrate((1+x)/(x^3+1),x, algorithm=""maxima"")","\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
14,1,16,0,2.425517," ","integrate((1-x)/(-x^3+1),x, algorithm=""maxima"")","\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
15,1,16,0,2.440972," ","integrate((1+x)/(-x^3+1),x, algorithm=""maxima"")","\frac{1}{3} \, \log\left(x^{2} + x + 1\right) - \frac{2}{3} \, \log\left(x - 1\right)"," ",0,"1/3*log(x^2 + x + 1) - 2/3*log(x - 1)","A",0
16,1,18,0,2.468622," ","integrate((1-x)/(x^3+1),x, algorithm=""maxima"")","-\frac{1}{3} \, \log\left(x^{2} - x + 1\right) + \frac{2}{3} \, \log\left(x + 1\right)"," ",0,"-1/3*log(x^2 - x + 1) + 2/3*log(x + 1)","A",0
17,1,32,0,2.432512," ","integrate((3-x)/(-x^3+1),x, algorithm=""maxima"")","\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(x - 1\right)"," ",0,"4/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/3*log(x^2 + x + 1) - 2/3*log(x - 1)","A",0
18,1,34,0,2.900720," ","integrate((d*x+c)/(d^3*x^3+c^3),x, algorithm=""maxima"")","\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, d^{2} x - c d\right)}}{3 \, c d}\right)}{3 \, c d}"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*d^2*x - c*d)/(c*d))/(c*d)","A",0
19,1,33,0,2.979855," ","integrate((-d*x+c)/(-d^3*x^3+c^3),x, algorithm=""maxima"")","\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, d^{2} x + c d\right)}}{3 \, c d}\right)}{3 \, c d}"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*d^2*x + c*d)/(c*d))/(c*d)","A",0
20,1,163,0,2.976701," ","integrate((a^(1/3)*b^(1/3)*B+b^(2/3)*B*x)/(b*x^3+a),x, algorithm=""maxima"")","\frac{\sqrt{3} {\left(B b^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{1}{3}} + B a^{\frac{1}{3}} b^{\frac{1}{3}}\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 \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(B b^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{1}{3}} - B a^{\frac{1}{3}} b^{\frac{1}{3}}\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 \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(B b^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{1}{3}} - B a^{\frac{1}{3}} b^{\frac{1}{3}}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*sqrt(3)*(B*b^(2/3)*(a/b)^(1/3) + B*a^(1/3)*b^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b*(a/b)^(2/3)) + 1/6*(B*b^(2/3)*(a/b)^(1/3) - B*a^(1/3)*b^(1/3))*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) - 1/3*(B*b^(2/3)*(a/b)^(1/3) - B*a^(1/3)*b^(1/3))*log(x + (a/b)^(1/3))/(b*(a/b)^(2/3))","B",0
21,1,174,0,2.950344," ","integrate((a^(1/3)*(-b)^(1/3)*B-(-b)^(2/3)*B*x)/(b*x^3+a),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left(B \left(-b\right)^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{1}{3}} - B a^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}}\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 \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(B \left(-b\right)^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{1}{3}} + B a^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}}\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 \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(B \left(-b\right)^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{1}{3}} + B a^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/3*sqrt(3)*(B*(-b)^(2/3)*(a/b)^(1/3) - B*a^(1/3)*(-b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b*(a/b)^(2/3)) - 1/6*(B*(-b)^(2/3)*(a/b)^(1/3) + B*a^(1/3)*(-b)^(1/3))*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) + 1/3*(B*(-b)^(2/3)*(a/b)^(1/3) + B*a^(1/3)*(-b)^(1/3))*log(x + (a/b)^(1/3))/(b*(a/b)^(2/3))","B",0
22,1,159,0,3.027934," ","integrate(-C*x^2/(b*x^3+a)+(C*x^2+B*x)/(b*x^3+a),x, algorithm=""maxima"")","-\frac{C \log\left(b x^{3} + a\right)}{3 \, b} + \frac{{\left(2 \, C \left(\frac{a}{b}\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 \, b \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(C \left(\frac{a}{b}\right)^{\frac{1}{3}} - B\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{\sqrt{3} {\left(2 \, C a - {\left(3 \, B \left(\frac{a}{b}\right)^{\frac{2}{3}} + \frac{2 \, C a}{b}\right)} 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)}{9 \, a b}"," ",0,"-1/3*C*log(b*x^3 + a)/b + 1/6*(2*C*(a/b)^(1/3) + B)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(1/3)) + 1/3*(C*(a/b)^(1/3) - B)*log(x + (a/b)^(1/3))/(b*(a/b)^(1/3)) - 1/9*sqrt(3)*(2*C*a - (3*B*(a/b)^(2/3) + 2*C*a/b)*b)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b)","A",0
23,1,159,0,2.993700," ","integrate(-C*x^2/(b*x^3+a)+(C*x^2+A)/(b*x^3+a),x, algorithm=""maxima"")","-\frac{C \log\left(b x^{3} + a\right)}{3 \, b} - \frac{\sqrt{3} {\left(2 \, C a - {\left(3 \, A \left(\frac{a}{b}\right)^{\frac{1}{3}} + \frac{2 \, C a}{b}\right)} 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)}{9 \, a b} + \frac{{\left(2 \, C \left(\frac{a}{b}\right)^{\frac{2}{3}} - A\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 \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(C \left(\frac{a}{b}\right)^{\frac{2}{3}} + A\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/3*C*log(b*x^3 + a)/b - 1/9*sqrt(3)*(2*C*a - (3*A*(a/b)^(1/3) + 2*C*a/b)*b)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b) + 1/6*(2*C*(a/b)^(2/3) - A)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) + 1/3*(C*(a/b)^(2/3) + A)*log(x + (a/b)^(1/3))/(b*(a/b)^(2/3))","A",0
24,1,188,0,2.958164," ","integrate(-C*x^2/(b*x^3+a)+(C*x^2+B*x+A)/(b*x^3+a),x, algorithm=""maxima"")","-\frac{C \log\left(b x^{3} + a\right)}{3 \, b} - \frac{\sqrt{3} {\left(2 \, C a - {\left(3 \, B \left(\frac{a}{b}\right)^{\frac{2}{3}} + 3 \, A \left(\frac{a}{b}\right)^{\frac{1}{3}} + \frac{2 \, C a}{b}\right)} 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)}{9 \, a b} + \frac{{\left(2 \, C \left(\frac{a}{b}\right)^{\frac{2}{3}} + B \left(\frac{a}{b}\right)^{\frac{1}{3}} - A\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 \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(C \left(\frac{a}{b}\right)^{\frac{2}{3}} - B \left(\frac{a}{b}\right)^{\frac{1}{3}} + A\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/3*C*log(b*x^3 + a)/b - 1/9*sqrt(3)*(2*C*a - (3*B*(a/b)^(2/3) + 3*A*(a/b)^(1/3) + 2*C*a/b)*b)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b) + 1/6*(2*C*(a/b)^(2/3) + B*(a/b)^(1/3) - A)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) + 1/3*(C*(a/b)^(2/3) - B*(a/b)^(1/3) + A)*log(x + (a/b)^(1/3))/(b*(a/b)^(2/3))","A",0
25,1,145,0,2.923604," ","integrate((c*x^2+b*x)/(e*x^3+d),x, algorithm=""maxima"")","\frac{{\left(2 \, c \left(\frac{d}{e}\right)^{\frac{1}{3}} + b\right)} \log\left(x^{2} - x \left(\frac{d}{e}\right)^{\frac{1}{3}} + \left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \, e \left(\frac{d}{e}\right)^{\frac{1}{3}}} + \frac{{\left(c \left(\frac{d}{e}\right)^{\frac{1}{3}} - b\right)} \log\left(x + \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \, e \left(\frac{d}{e}\right)^{\frac{1}{3}}} - \frac{\sqrt{3} {\left(2 \, c d - {\left(3 \, b \left(\frac{d}{e}\right)^{\frac{2}{3}} + \frac{2 \, c d}{e}\right)} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{d}{e}\right)^{\frac{1}{3}}}\right)}{9 \, d e}"," ",0,"1/6*(2*c*(d/e)^(1/3) + b)*log(x^2 - x*(d/e)^(1/3) + (d/e)^(2/3))/(e*(d/e)^(1/3)) + 1/3*(c*(d/e)^(1/3) - b)*log(x + (d/e)^(1/3))/(e*(d/e)^(1/3)) - 1/9*sqrt(3)*(2*c*d - (3*b*(d/e)^(2/3) + 2*c*d/e)*e)*arctan(1/3*sqrt(3)*(2*x - (d/e)^(1/3))/(d/e)^(1/3))/(d*e)","A",0
26,1,144,0,3.045430," ","integrate((c*x^2+a)/(-e*x^3+d),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left(2 \, c d - {\left(3 \, a \left(\frac{d}{e}\right)^{\frac{1}{3}} + \frac{2 \, c d}{e}\right)} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{d}{e}\right)^{\frac{1}{3}}}\right)}{9 \, d e} - \frac{{\left(2 \, c \left(\frac{d}{e}\right)^{\frac{2}{3}} - a\right)} \log\left(x^{2} + x \left(\frac{d}{e}\right)^{\frac{1}{3}} + \left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \, e \left(\frac{d}{e}\right)^{\frac{2}{3}}} - \frac{{\left(c \left(\frac{d}{e}\right)^{\frac{2}{3}} + a\right)} \log\left(x - \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \, e \left(\frac{d}{e}\right)^{\frac{2}{3}}}"," ",0,"-1/9*sqrt(3)*(2*c*d - (3*a*(d/e)^(1/3) + 2*c*d/e)*e)*arctan(1/3*sqrt(3)*(2*x + (d/e)^(1/3))/(d/e)^(1/3))/(d*e) - 1/6*(2*c*(d/e)^(2/3) - a)*log(x^2 + x*(d/e)^(1/3) + (d/e)^(2/3))/(e*(d/e)^(2/3)) - 1/3*(c*(d/e)^(2/3) + a)*log(x - (d/e)^(1/3))/(e*(d/e)^(2/3))","A",0
27,1,42,0,2.991544," ","integrate((b^2*x^2+2*a^2)/(b^3*x^3+a^3),x, algorithm=""maxima"")","\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, b^{2} x - a b\right)}}{3 \, a b}\right)}{3 \, b} + \frac{\log\left(b x + a\right)}{b}"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*b^2*x - a*b)/(a*b))/b + log(b*x + a)/b","A",0
28,1,44,0,2.965530," ","integrate((b^2*x^2+2*a^2)/(-b^3*x^3+a^3),x, algorithm=""maxima"")","\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, b^{2} x + a b\right)}}{3 \, a b}\right)}{3 \, b} - \frac{\log\left(b x - a\right)}{b}"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*b^2*x + a*b)/(a*b))/b - log(b*x - a)/b","A",0
29,1,47,0,2.990565," ","integrate((8*C+b^(2/3)*C*x^2)/(b*x^3+8),x, algorithm=""maxima"")","\frac{2 \, \sqrt{3} C \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{2}{3}} x - b^{\frac{1}{3}}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{3 \, b^{\frac{1}{3}}} + \frac{C \log\left(\frac{b^{\frac{1}{3}} x + 2}{b^{\frac{1}{3}}}\right)}{b^{\frac{1}{3}}}"," ",0,"2/3*sqrt(3)*C*arctan(1/3*sqrt(3)*(b^(2/3)*x - b^(1/3))/b^(1/3))/b^(1/3) + C*log((b^(1/3)*x + 2)/b^(1/3))/b^(1/3)","A",0
30,1,36,0,3.003033," ","integrate((a^(2/3)*C+2*C*x^2)/(8*x^3+a),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{3} C \arctan\left(\frac{\sqrt{3} {\left(4 \, x - a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right) + \frac{1}{4} \, C \log\left(x + \frac{1}{2} \, a^{\frac{1}{3}}\right)"," ",0,"1/6*sqrt(3)*C*arctan(1/3*sqrt(3)*(4*x - a^(1/3))/a^(1/3)) + 1/4*C*log(x + 1/2*a^(1/3))","A",0
31,1,122,0,2.943244," ","integrate((8*C+(-b)^(2/3)*C*x^2)/(b*x^3-8),x, algorithm=""maxima"")","\frac{{\left(C \left(-b\right)^{\frac{2}{3}} - C b^{\frac{2}{3}}\right)} \log\left(b^{\frac{2}{3}} x^{2} + 2 \, b^{\frac{1}{3}} x + 4\right)}{3 \, b} + \frac{{\left(C \left(-b\right)^{\frac{2}{3}} + 2 \, C b^{\frac{2}{3}}\right)} \log\left(\frac{b^{\frac{1}{3}} x - 2}{b^{\frac{1}{3}}}\right)}{3 \, b} + \frac{2 \, \sqrt{3} {\left(C \left(-b\right)^{\frac{2}{3}} b^{\frac{4}{3}} - {\left(C \left(-b\right)^{\frac{2}{3}} b^{\frac{1}{3}} + 3 \, C b\right)} b\right)} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{2}{3}} x + b^{\frac{1}{3}}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{9 \, b^{\frac{7}{3}}}"," ",0,"1/3*(C*(-b)^(2/3) - C*b^(2/3))*log(b^(2/3)*x^2 + 2*b^(1/3)*x + 4)/b + 1/3*(C*(-b)^(2/3) + 2*C*b^(2/3))*log((b^(1/3)*x - 2)/b^(1/3))/b + 2/9*sqrt(3)*(C*(-b)^(2/3)*b^(4/3) - (C*(-b)^(2/3)*b^(1/3) + 3*C*b)*b)*arctan(1/3*sqrt(3)*(b^(2/3)*x + b^(1/3))/b^(1/3))/b^(7/3)","B",0
32,1,93,0,2.987576," ","integrate(((-a)^(2/3)*C+2*C*x^2)/(-8*x^3+a),x, algorithm=""maxima"")","\frac{\sqrt{3} C \left(-a\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(4 \, x + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right)}{6 \, a^{\frac{2}{3}}} + \frac{{\left(C \left(-a\right)^{\frac{2}{3}} - C a^{\frac{2}{3}}\right)} \log\left(4 \, x^{2} + 2 \, a^{\frac{1}{3}} x + a^{\frac{2}{3}}\right)}{12 \, a^{\frac{2}{3}}} - \frac{{\left(2 \, C \left(-a\right)^{\frac{2}{3}} + C a^{\frac{2}{3}}\right)} \log\left(x - \frac{1}{2} \, a^{\frac{1}{3}}\right)}{12 \, a^{\frac{2}{3}}}"," ",0,"1/6*sqrt(3)*C*(-a)^(2/3)*arctan(1/3*sqrt(3)*(4*x + a^(1/3))/a^(1/3))/a^(2/3) + 1/12*(C*(-a)^(2/3) - C*a^(2/3))*log(4*x^2 + 2*a^(1/3)*x + a^(2/3))/a^(2/3) - 1/12*(2*C*(-a)^(2/3) + C*a^(2/3))*log(x - 1/2*a^(1/3))/a^(2/3)","B",0
33,1,51,0,3.030137," ","integrate((2*(a/b)^(2/3)*C+C*x^2)/(b*x^3+a),x, algorithm=""maxima"")","\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{C \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b}"," ",0,"2/3*sqrt(3)*C*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/b + C*log(x + (a/b)^(1/3))/b","A",0
34,1,167,0,3.031024," ","integrate((2*(-a/b)^(2/3)*C+C*x^2)/(-b*x^3+a),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{3} {\left(C a - {\left(3 \, C \left(\frac{a}{b}\right)^{\frac{1}{3}} \left(-\frac{a}{b}\right)^{\frac{2}{3}} + \frac{C a}{b}\right)} 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)}{9 \, a b} - \frac{{\left(C \left(\frac{a}{b}\right)^{\frac{2}{3}} - C \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)} \log\left(x^{2} + x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(C \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, C \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)} \log\left(x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-2/9*sqrt(3)*(C*a - (3*C*(a/b)^(1/3)*(-a/b)^(2/3) + C*a/b)*b)*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/(a*b) - 1/3*(C*(a/b)^(2/3) - C*(-a/b)^(2/3))*log(x^2 + x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) - 1/3*(C*(a/b)^(2/3) + 2*C*(-a/b)^(2/3))*log(x - (a/b)^(1/3))/(b*(a/b)^(2/3))","B",0
35,1,168,0,3.148546," ","integrate((2*(-a/b)^(2/3)*C+C*x^2)/(b*x^3+a),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{3} {\left(C a - {\left(3 \, C \left(\frac{a}{b}\right)^{\frac{1}{3}} \left(-\frac{a}{b}\right)^{\frac{2}{3}} + \frac{C a}{b}\right)} 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)}{9 \, a b} + \frac{{\left(C \left(\frac{a}{b}\right)^{\frac{2}{3}} - C \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(C \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, C \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-2/9*sqrt(3)*(C*a - (3*C*(a/b)^(1/3)*(-a/b)^(2/3) + C*a/b)*b)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b) + 1/3*(C*(a/b)^(2/3) - C*(-a/b)^(2/3))*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) + 1/3*(C*(a/b)^(2/3) + 2*C*(-a/b)^(2/3))*log(x + (a/b)^(1/3))/(b*(a/b)^(2/3))","B",0
36,1,52,0,2.998766," ","integrate((2*(a/b)^(2/3)*C+C*x^2)/(-b*x^3+a),x, algorithm=""maxima"")","\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{C \log\left(x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b}"," ",0,"2/3*sqrt(3)*C*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/b - C*log(x - (a/b)^(1/3))/b","A",0
37,1,162,0,2.869145," ","integrate((2*a^(2/3)*C+b^(2/3)*C*x^2)/(b*x^3+a),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{3} {\left(C a b^{\frac{2}{3}} - {\left(3 \, C a^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{1}{3}} + \frac{C a}{b^{\frac{1}{3}}}\right)} 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)}{9 \, a b} + \frac{{\left(C b^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{2}{3}} - C a^{\frac{2}{3}}\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(C b^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, C a^{\frac{2}{3}}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-2/9*sqrt(3)*(C*a*b^(2/3) - (3*C*a^(2/3)*(a/b)^(1/3) + C*a/b^(1/3))*b)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b) + 1/3*(C*b^(2/3)*(a/b)^(2/3) - C*a^(2/3))*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) + 1/3*(C*b^(2/3)*(a/b)^(2/3) + 2*C*a^(2/3))*log(x + (a/b)^(1/3))/(b*(a/b)^(2/3))","B",0
38,1,173,0,3.021811," ","integrate((-2*a^(2/3)*C-(-b)^(2/3)*C*x^2)/(b*x^3+a),x, algorithm=""maxima"")","\frac{2 \, \sqrt{3} {\left(C a \left(-b\right)^{\frac{2}{3}} - {\left(3 \, C a^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{1}{3}} + \frac{C a \left(-b\right)^{\frac{2}{3}}}{b}\right)} 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)}{9 \, a b} - \frac{{\left(C \left(-b\right)^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{2}{3}} - C a^{\frac{2}{3}}\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(C \left(-b\right)^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, C a^{\frac{2}{3}}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"2/9*sqrt(3)*(C*a*(-b)^(2/3) - (3*C*a^(2/3)*(a/b)^(1/3) + C*a*(-b)^(2/3)/b)*b)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b) - 1/3*(C*(-b)^(2/3)*(a/b)^(2/3) - C*a^(2/3))*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) - 1/3*(C*(-b)^(2/3)*(a/b)^(2/3) + 2*C*a^(2/3))*log(x + (a/b)^(1/3))/(b*(a/b)^(2/3))","B",0
39,1,31,0,2.987893," ","integrate((x^2-3)/(x^3-1),x, algorithm=""maxima"")","\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(x - 1\right)"," ",0,"sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 5/6*log(x^2 + x + 1) - 2/3*log(x - 1)","A",0
40,1,236,0,3.119869," ","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=""maxima"")","-\frac{\sqrt{3} {\left(2 \, C a b^{\frac{2}{3}} - {\left(6 \, C a^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{1}{3}} + 3 \, B a^{\frac{1}{3}} b^{\frac{1}{3}} \left(\frac{a}{b}\right)^{\frac{1}{3}} + {\left(3 \, B \left(\frac{a}{b}\right)^{\frac{2}{3}} + \frac{2 \, C a}{b}\right)} b^{\frac{2}{3}}\right)} 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)}{9 \, a b} - \frac{{\left(2 \, C a^{\frac{2}{3}} + B a^{\frac{1}{3}} b^{\frac{1}{3}} - {\left(2 \, C \left(\frac{a}{b}\right)^{\frac{2}{3}} + B \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} b^{\frac{2}{3}}\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 \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(2 \, C a^{\frac{2}{3}} + B a^{\frac{1}{3}} b^{\frac{1}{3}} + {\left(C \left(\frac{a}{b}\right)^{\frac{2}{3}} - B \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} b^{\frac{2}{3}}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/9*sqrt(3)*(2*C*a*b^(2/3) - (6*C*a^(2/3)*(a/b)^(1/3) + 3*B*a^(1/3)*b^(1/3)*(a/b)^(1/3) + (3*B*(a/b)^(2/3) + 2*C*a/b)*b^(2/3))*b)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b) - 1/6*(2*C*a^(2/3) + B*a^(1/3)*b^(1/3) - (2*C*(a/b)^(2/3) + B*(a/b)^(1/3))*b^(2/3))*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) + 1/3*(2*C*a^(2/3) + B*a^(1/3)*b^(1/3) + (C*(a/b)^(2/3) - B*(a/b)^(1/3))*b^(2/3))*log(x + (a/b)^(1/3))/(b*(a/b)^(2/3))","B",0
41,1,252,0,3.041033," ","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=""maxima"")","\frac{\sqrt{3} {\left(2 \, C a \left(-b\right)^{\frac{2}{3}} - {\left(6 \, C a^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{1}{3}} - 3 \, B a^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} \left(\frac{a}{b}\right)^{\frac{1}{3}} + {\left(3 \, B \left(\frac{a}{b}\right)^{\frac{2}{3}} + \frac{2 \, C a}{b}\right)} \left(-b\right)^{\frac{2}{3}}\right)} 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)}{9 \, a b} + \frac{{\left(2 \, C a^{\frac{2}{3}} - B a^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} - {\left(2 \, C \left(\frac{a}{b}\right)^{\frac{2}{3}} + B \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \left(-b\right)^{\frac{2}{3}}\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 \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(2 \, C a^{\frac{2}{3}} - B a^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} + {\left(C \left(\frac{a}{b}\right)^{\frac{2}{3}} - B \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \left(-b\right)^{\frac{2}{3}}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/9*sqrt(3)*(2*C*a*(-b)^(2/3) - (6*C*a^(2/3)*(a/b)^(1/3) - 3*B*a^(1/3)*(-b)^(1/3)*(a/b)^(1/3) + (3*B*(a/b)^(2/3) + 2*C*a/b)*(-b)^(2/3))*b)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b) + 1/6*(2*C*a^(2/3) - B*a^(1/3)*(-b)^(1/3) - (2*C*(a/b)^(2/3) + B*(a/b)^(1/3))*(-b)^(2/3))*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) - 1/3*(2*C*a^(2/3) - B*a^(1/3)*(-b)^(1/3) + (C*(a/b)^(2/3) - B*(a/b)^(1/3))*(-b)^(2/3))*log(x + (a/b)^(1/3))/(b*(a/b)^(2/3))","B",0
42,1,12,0,1.358563," ","integrate((C^2*x^2+B*C*x+B^2)/(C^3*x^3-B^3),x, algorithm=""maxima"")","\frac{\log\left(C x - B\right)}{C}"," ",0,"log(C*x - B)/C","A",0
43,1,210,0,2.988696," ","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=""maxima"")","-\frac{\sqrt{3} {\left(2 \, C a b^{\frac{2}{3}} + {\left(3 \, C a^{\frac{1}{3}} b^{\frac{1}{3}} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 3 \, C a^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{1}{3}} - \frac{2 \, C a}{b^{\frac{1}{3}}}\right)} 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)}{9 \, a b} + \frac{{\left(2 \, C b^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{2}{3}} - C a^{\frac{1}{3}} b^{\frac{1}{3}} \left(\frac{a}{b}\right)^{\frac{1}{3}} - C a^{\frac{2}{3}}\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 \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(C b^{\frac{2}{3}} \left(\frac{a}{b}\right)^{\frac{2}{3}} + C a^{\frac{1}{3}} b^{\frac{1}{3}} \left(\frac{a}{b}\right)^{\frac{1}{3}} + C a^{\frac{2}{3}}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/9*sqrt(3)*(2*C*a*b^(2/3) + (3*C*a^(1/3)*b^(1/3)*(a/b)^(2/3) - 3*C*a^(2/3)*(a/b)^(1/3) - 2*C*a/b^(1/3))*b)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b) + 1/6*(2*C*b^(2/3)*(a/b)^(2/3) - C*a^(1/3)*b^(1/3)*(a/b)^(1/3) - C*a^(2/3))*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) + 1/3*(C*b^(2/3)*(a/b)^(2/3) + C*a^(1/3)*b^(1/3)*(a/b)^(1/3) + C*a^(2/3))*log(x + (a/b)^(1/3))/(b*(a/b)^(2/3))","B",0
44,1,78,0,2.949610," ","integrate(((a/b)^(1/3)*B+2*(a/b)^(2/3)*C+B*x+C*x^2)/(b*x^3+a),x, algorithm=""maxima"")","\frac{C \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b} - \frac{2 \, \sqrt{3} {\left(C a - {\left(3 \, B \left(\frac{a}{b}\right)^{\frac{2}{3}} + \frac{4 \, C a}{b}\right)} 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)}{9 \, a b}"," ",0,"C*log(x + (a/b)^(1/3))/b - 2/9*sqrt(3)*(C*a - (3*B*(a/b)^(2/3) + 4*C*a/b)*b)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b)","A",0
45,1,238,0,3.009617," ","integrate(((-a/b)^(1/3)*B+2*(-a/b)^(2/3)*C+B*x+C*x^2)/(-b*x^3+a),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left(2 \, C a - {\left(6 \, C \left(\frac{a}{b}\right)^{\frac{1}{3}} \left(-\frac{a}{b}\right)^{\frac{2}{3}} - 3 \, B \left(\frac{a}{b}\right)^{\frac{2}{3}} + 3 \, B \left(\frac{a}{b}\right)^{\frac{1}{3}} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \frac{2 \, C a}{b}\right)} 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)}{9 \, a b} - \frac{{\left(2 \, C \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, C \left(-\frac{a}{b}\right)^{\frac{2}{3}} - B \left(\frac{a}{b}\right)^{\frac{1}{3}} - B \left(-\frac{a}{b}\right)^{\frac{1}{3}}\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 \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(C \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, C \left(-\frac{a}{b}\right)^{\frac{2}{3}} + B \left(\frac{a}{b}\right)^{\frac{1}{3}} + B \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)} \log\left(x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/9*sqrt(3)*(2*C*a - (6*C*(a/b)^(1/3)*(-a/b)^(2/3) - 3*B*(a/b)^(2/3) + 3*B*(a/b)^(1/3)*(-a/b)^(1/3) + 2*C*a/b)*b)*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/(a*b) - 1/6*(2*C*(a/b)^(2/3) - 2*C*(-a/b)^(2/3) - B*(a/b)^(1/3) - B*(-a/b)^(1/3))*log(x^2 + x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) - 1/3*(C*(a/b)^(2/3) + 2*C*(-a/b)^(2/3) + B*(a/b)^(1/3) + B*(-a/b)^(1/3))*log(x - (a/b)^(1/3))/(b*(a/b)^(2/3))","B",0
46,1,239,0,3.030942," ","integrate((-(-a/b)^(1/3)*B+2*(-a/b)^(2/3)*C+B*x+C*x^2)/(b*x^3+a),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left(2 \, C a - {\left(6 \, C \left(\frac{a}{b}\right)^{\frac{1}{3}} \left(-\frac{a}{b}\right)^{\frac{2}{3}} + 3 \, B \left(\frac{a}{b}\right)^{\frac{2}{3}} - 3 \, B \left(\frac{a}{b}\right)^{\frac{1}{3}} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \frac{2 \, C a}{b}\right)} 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)}{9 \, a b} + \frac{{\left(2 \, C \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, C \left(-\frac{a}{b}\right)^{\frac{2}{3}} + B \left(\frac{a}{b}\right)^{\frac{1}{3}} + B \left(-\frac{a}{b}\right)^{\frac{1}{3}}\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 \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(C \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, C \left(-\frac{a}{b}\right)^{\frac{2}{3}} - B \left(\frac{a}{b}\right)^{\frac{1}{3}} - B \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/9*sqrt(3)*(2*C*a - (6*C*(a/b)^(1/3)*(-a/b)^(2/3) + 3*B*(a/b)^(2/3) - 3*B*(a/b)^(1/3)*(-a/b)^(1/3) + 2*C*a/b)*b)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b) + 1/6*(2*C*(a/b)^(2/3) - 2*C*(-a/b)^(2/3) + B*(a/b)^(1/3) + B*(-a/b)^(1/3))*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) + 1/3*(C*(a/b)^(2/3) + 2*C*(-a/b)^(2/3) - B*(a/b)^(1/3) - B*(-a/b)^(1/3))*log(x + (a/b)^(1/3))/(b*(a/b)^(2/3))","B",0
47,1,78,0,3.140464," ","integrate((-(a/b)^(1/3)*B+2*(a/b)^(2/3)*C+B*x+C*x^2)/(-b*x^3+a),x, algorithm=""maxima"")","-\frac{C \log\left(x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b} - \frac{2 \, \sqrt{3} {\left(C a + {\left(3 \, B \left(\frac{a}{b}\right)^{\frac{2}{3}} - \frac{4 \, C a}{b}\right)} 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)}{9 \, a b}"," ",0,"-C*log(x - (a/b)^(1/3))/b - 2/9*sqrt(3)*(C*a + (3*B*(a/b)^(2/3) - 4*C*a/b)*b)*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/(a*b)","A",0
48,1,26,0,2.971663," ","integrate((c*x^2+a*x+a)/(-x^3+1),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(a - c\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{3} \, {\left(2 \, a + c\right)} \log\left(x - 1\right)"," ",0,"1/3*(a - c)*log(x^2 + x + 1) - 1/3*(2*a + c)*log(x - 1)","A",0
49,1,47,0,2.991566," ","integrate((c*x^2+b*x+a)/(-x^3+1),x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{3} {\left(a - 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(x - 1\right)"," ",0,"1/3*sqrt(3)*(a - 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(x - 1)","A",0
50,1,6,0,1.269679," ","integrate((x^2+x+1)/(-x^3+1),x, algorithm=""maxima"")","-\log\left(x - 1\right)"," ",0,"-log(x - 1)","A",0
51,1,32,0,2.958221," ","integrate((3*x^2-x+1)/(-x^3+1),x, algorithm=""maxima"")","\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(x - 1\right)"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - log(x^2 + x + 1) - log(x - 1)","A",0
52,1,16,0,2.926263," ","integrate((4*x^2+x+1)/(-x^3+1),x, algorithm=""maxima"")","-\log\left(x^{2} + x + 1\right) - 2 \, \log\left(x - 1\right)"," ",0,"-log(x^2 + x + 1) - 2*log(x - 1)","A",0
53,1,97,0,1.385750," ","integrate((b*x^3+a)^3*(b*d*x^4+b*c*x^3+a*d*x+a*c),x, algorithm=""maxima"")","\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
54,1,74,0,1.387398," ","integrate((b*x^3+a)^2*(b*d*x^4+b*c*x^3+a*d*x+a*c),x, algorithm=""maxima"")","\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
55,1,50,0,1.402046," ","integrate((b*x^3+a)*(b*d*x^4+b*c*x^3+a*d*x+a*c),x, algorithm=""maxima"")","\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
56,1,10,0,1.322129," ","integrate((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{1}{2} \, d x^{2} + c x"," ",0,"1/2*d*x^2 + c*x","A",0
57,1,135,0,2.984541," ","integrate((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{\sqrt{3} {\left(d \left(\frac{a}{b}\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 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(d \left(\frac{a}{b}\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 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(d \left(\frac{a}{b}\right)^{\frac{1}{3}} - c\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*sqrt(3)*(d*(a/b)^(1/3) + c)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b*(a/b)^(2/3)) + 1/6*(d*(a/b)^(1/3) - c)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) - 1/3*(d*(a/b)^(1/3) - c)*log(x + (a/b)^(1/3))/(b*(a/b)^(2/3))","A",0
58,1,169,0,3.015985," ","integrate((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{d x^{2} + c x}{3 \, {\left(a b x^{3} + a^{2}\right)}} + \frac{\sqrt{3} {\left(d \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, 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 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, 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 \, a b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, c\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*(d*x^2 + c*x)/(a*b*x^3 + a^2) + 1/9*sqrt(3)*(d*(a/b)^(1/3) + 2*c)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b*(a/b)^(2/3)) + 1/18*(d*(a/b)^(1/3) - 2*c)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b*(a/b)^(2/3)) - 1/9*(d*(a/b)^(1/3) - 2*c)*log(x + (a/b)^(1/3))/(a*b*(a/b)^(2/3))","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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
70,1,192,0,2.924745," ","integrate((b*x+a)^2/(d*x^3+c),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left(2 \, b^{2} c - {\left(6 \, a b \left(\frac{c}{d}\right)^{\frac{2}{3}} + 3 \, a^{2} \left(\frac{c}{d}\right)^{\frac{1}{3}} + \frac{2 \, b^{2} c}{d}\right)} 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)}{9 \, c d} + \frac{{\left(2 \, b^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}} + 2 \, a b \left(\frac{c}{d}\right)^{\frac{1}{3}} - a^{2}\right)} \log\left(x^{2} - x \left(\frac{c}{d}\right)^{\frac{1}{3}} + \left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \, d \left(\frac{c}{d}\right)^{\frac{2}{3}}} + \frac{{\left(b^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}} - 2 \, a b \left(\frac{c}{d}\right)^{\frac{1}{3}} + a^{2}\right)} \log\left(x + \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \, d \left(\frac{c}{d}\right)^{\frac{2}{3}}}"," ",0,"-1/9*sqrt(3)*(2*b^2*c - (6*a*b*(c/d)^(2/3) + 3*a^2*(c/d)^(1/3) + 2*b^2*c/d)*d)*arctan(1/3*sqrt(3)*(2*x - (c/d)^(1/3))/(c/d)^(1/3))/(c*d) + 1/6*(2*b^2*(c/d)^(2/3) + 2*a*b*(c/d)^(1/3) - a^2)*log(x^2 - x*(c/d)^(1/3) + (c/d)^(2/3))/(d*(c/d)^(2/3)) + 1/3*(b^2*(c/d)^(2/3) - 2*a*b*(c/d)^(1/3) + a^2)*log(x + (c/d)^(1/3))/(d*(c/d)^(2/3))","A",0
71,1,240,0,2.959858," ","integrate((b*x+a)^3/(d*x^3+c),x, algorithm=""maxima"")","\frac{b^{3} x}{d} - \frac{\sqrt{3} {\left({\left(b^{3} \left(\frac{c}{d}\right)^{\frac{1}{3}} + 2 \, a b^{2}\right)} c - {\left(3 \, a^{2} b \left(\frac{c}{d}\right)^{\frac{2}{3}} + a^{3} \left(\frac{c}{d}\right)^{\frac{1}{3}} + \frac{2 \, a b^{2} c}{d}\right)} 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 \, c d} + \frac{{\left(b^{3} c + {\left(6 \, a b^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}} + 3 \, a^{2} b \left(\frac{c}{d}\right)^{\frac{1}{3}} - a^{3}\right)} 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 \, d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}} - \frac{{\left(b^{3} c - {\left(3 \, a b^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}} - 3 \, a^{2} b \left(\frac{c}{d}\right)^{\frac{1}{3}} + a^{3}\right)} d\right)} \log\left(x + \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \, d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}}"," ",0,"b^3*x/d - 1/3*sqrt(3)*((b^3*(c/d)^(1/3) + 2*a*b^2)*c - (3*a^2*b*(c/d)^(2/3) + a^3*(c/d)^(1/3) + 2*a*b^2*c/d)*d)*arctan(1/3*sqrt(3)*(2*x - (c/d)^(1/3))/(c/d)^(1/3))/(c*d) + 1/6*(b^3*c + (6*a*b^2*(c/d)^(2/3) + 3*a^2*b*(c/d)^(1/3) - a^3)*d)*log(x^2 - x*(c/d)^(1/3) + (c/d)^(2/3))/(d^2*(c/d)^(2/3)) - 1/3*(b^3*c - (3*a*b^2*(c/d)^(2/3) - 3*a^2*b*(c/d)^(1/3) + a^3)*d)*log(x + (c/d)^(1/3))/(d^2*(c/d)^(2/3))","A",0
72,1,303,0,3.043583," ","integrate((b*x+a)^4/(d*x^3+c),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left({\left(b^{4} \left(\frac{c}{d}\right)^{\frac{2}{3}} + 4 \, a b^{3} \left(\frac{c}{d}\right)^{\frac{1}{3}} + 4 \, a^{2} b^{2}\right)} c - {\left(4 \, a^{3} b \left(\frac{c}{d}\right)^{\frac{2}{3}} + a^{4} \left(\frac{c}{d}\right)^{\frac{1}{3}} + \frac{4 \, a^{2} b^{2} c}{d}\right)} 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 \, c d} + \frac{b^{4} x^{2} + 8 \, a b^{3} x}{2 \, d} - \frac{{\left({\left(b^{4} \left(\frac{c}{d}\right)^{\frac{1}{3}} - 4 \, a b^{3}\right)} c - {\left(12 \, a^{2} b^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}} + 4 \, a^{3} b \left(\frac{c}{d}\right)^{\frac{1}{3}} - a^{4}\right)} 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 \, d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}} + \frac{{\left({\left(b^{4} \left(\frac{c}{d}\right)^{\frac{1}{3}} - 4 \, a b^{3}\right)} c + {\left(6 \, a^{2} b^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}} - 4 \, a^{3} b \left(\frac{c}{d}\right)^{\frac{1}{3}} + a^{4}\right)} d\right)} \log\left(x + \left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \, d^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}}"," ",0,"-1/3*sqrt(3)*((b^4*(c/d)^(2/3) + 4*a*b^3*(c/d)^(1/3) + 4*a^2*b^2)*c - (4*a^3*b*(c/d)^(2/3) + a^4*(c/d)^(1/3) + 4*a^2*b^2*c/d)*d)*arctan(1/3*sqrt(3)*(2*x - (c/d)^(1/3))/(c/d)^(1/3))/(c*d) + 1/2*(b^4*x^2 + 8*a*b^3*x)/d - 1/6*((b^4*(c/d)^(1/3) - 4*a*b^3)*c - (12*a^2*b^2*(c/d)^(2/3) + 4*a^3*b*(c/d)^(1/3) - a^4)*d)*log(x^2 - x*(c/d)^(1/3) + (c/d)^(2/3))/(d^2*(c/d)^(2/3)) + 1/3*((b^4*(c/d)^(1/3) - 4*a*b^3)*c + (6*a^2*b^2*(c/d)^(2/3) - 4*a^3*b*(c/d)^(1/3) + a^4)*d)*log(x + (c/d)^(1/3))/(d^2*(c/d)^(2/3))","A",0
73,1,314,0,3.032944," ","integrate((c*x^2+b*x+a)^2/(e*x^3+d),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left({\left(3 \, c^{2} \left(\frac{d}{e}\right)^{\frac{2}{3}} + 2 \, b^{2} + 2 \, {\left(3 \, b \left(\frac{d}{e}\right)^{\frac{1}{3}} + 2 \, a\right)} c\right)} d - {\left(6 \, a b \left(\frac{d}{e}\right)^{\frac{2}{3}} + 3 \, a^{2} \left(\frac{d}{e}\right)^{\frac{1}{3}} + \frac{2 \, b^{2} d}{e} + \frac{4 \, a c d}{e}\right)} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{d}{e}\right)^{\frac{1}{3}}}\right)}{9 \, d e} + \frac{c^{2} x^{2} + 4 \, b c x}{2 \, e} - \frac{{\left({\left(c^{2} \left(\frac{d}{e}\right)^{\frac{1}{3}} - 2 \, b c\right)} d - {\left(2 \, b^{2} \left(\frac{d}{e}\right)^{\frac{2}{3}} + 4 \, a c \left(\frac{d}{e}\right)^{\frac{2}{3}} + 2 \, a b \left(\frac{d}{e}\right)^{\frac{1}{3}} - a^{2}\right)} e\right)} \log\left(x^{2} - x \left(\frac{d}{e}\right)^{\frac{1}{3}} + \left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \, e^{2} \left(\frac{d}{e}\right)^{\frac{2}{3}}} + \frac{{\left({\left(c^{2} \left(\frac{d}{e}\right)^{\frac{1}{3}} - 2 \, b c\right)} d + {\left(b^{2} \left(\frac{d}{e}\right)^{\frac{2}{3}} + 2 \, a c \left(\frac{d}{e}\right)^{\frac{2}{3}} - 2 \, a b \left(\frac{d}{e}\right)^{\frac{1}{3}} + a^{2}\right)} e\right)} \log\left(x + \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \, e^{2} \left(\frac{d}{e}\right)^{\frac{2}{3}}}"," ",0,"-1/9*sqrt(3)*((3*c^2*(d/e)^(2/3) + 2*b^2 + 2*(3*b*(d/e)^(1/3) + 2*a)*c)*d - (6*a*b*(d/e)^(2/3) + 3*a^2*(d/e)^(1/3) + 2*b^2*d/e + 4*a*c*d/e)*e)*arctan(1/3*sqrt(3)*(2*x - (d/e)^(1/3))/(d/e)^(1/3))/(d*e) + 1/2*(c^2*x^2 + 4*b*c*x)/e - 1/6*((c^2*(d/e)^(1/3) - 2*b*c)*d - (2*b^2*(d/e)^(2/3) + 4*a*c*(d/e)^(2/3) + 2*a*b*(d/e)^(1/3) - a^2)*e)*log(x^2 - x*(d/e)^(1/3) + (d/e)^(2/3))/(e^2*(d/e)^(2/3)) + 1/3*((c^2*(d/e)^(1/3) - 2*b*c)*d + (b^2*(d/e)^(2/3) + 2*a*c*(d/e)^(2/3) - 2*a*b*(d/e)^(1/3) + a^2)*e)*log(x + (d/e)^(1/3))/(e^2*(d/e)^(2/3))","A",0
74,1,520,0,3.049081," ","integrate((c*x^2+b*x+a)^3/(e*x^3+d),x, algorithm=""maxima"")","\frac{\sqrt{3} {\left({\left(c^{3} \left(\frac{d}{e}\right)^{\frac{1}{3}} + 2 \, b c^{2}\right)} d^{2} - {\left(b^{3} \left(\frac{d}{e}\right)^{\frac{1}{3}} + 2 \, a b^{2} + {\left(3 \, a \left(\frac{d}{e}\right)^{\frac{2}{3}} + \frac{2 \, b d}{e}\right)} c^{2} + {\left(3 \, b^{2} \left(\frac{d}{e}\right)^{\frac{2}{3}} + 6 \, a b \left(\frac{d}{e}\right)^{\frac{1}{3}} + 2 \, a^{2}\right)} c\right)} d e + {\left(3 \, a^{2} b \left(\frac{d}{e}\right)^{\frac{2}{3}} + a^{3} \left(\frac{d}{e}\right)^{\frac{1}{3}} + \frac{2 \, a b^{2} d}{e} + \frac{2 \, a^{2} c d}{e}\right)} e^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{d}{e}\right)^{\frac{1}{3}}}\right)}{3 \, d e^{2}} + \frac{c^{3} e x^{4} + 4 \, b c^{2} e x^{3} + 6 \, {\left(b^{2} c + a c^{2}\right)} e x^{2} - 4 \, {\left(c^{3} d - {\left(b^{3} + 6 \, a b c\right)} e\right)} x}{4 \, e^{2}} - \frac{{\left(c^{3} d^{2} - {\left(b^{3} - 3 \, {\left(2 \, b \left(\frac{d}{e}\right)^{\frac{2}{3}} + a \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)} c^{2} - 3 \, {\left(b^{2} \left(\frac{d}{e}\right)^{\frac{1}{3}} - 2 \, a b\right)} c\right)} d e - {\left(6 \, a b^{2} \left(\frac{d}{e}\right)^{\frac{2}{3}} + 6 \, a^{2} c \left(\frac{d}{e}\right)^{\frac{2}{3}} + 3 \, a^{2} b \left(\frac{d}{e}\right)^{\frac{1}{3}} - a^{3}\right)} e^{2}\right)} \log\left(x^{2} - x \left(\frac{d}{e}\right)^{\frac{1}{3}} + \left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \, e^{3} \left(\frac{d}{e}\right)^{\frac{2}{3}}} + \frac{{\left(c^{3} d^{2} - {\left(b^{3} + 3 \, {\left(b \left(\frac{d}{e}\right)^{\frac{2}{3}} - a \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)} c^{2} - 3 \, {\left(b^{2} \left(\frac{d}{e}\right)^{\frac{1}{3}} - 2 \, a b\right)} c\right)} d e + {\left(3 \, a b^{2} \left(\frac{d}{e}\right)^{\frac{2}{3}} + 3 \, a^{2} c \left(\frac{d}{e}\right)^{\frac{2}{3}} - 3 \, a^{2} b \left(\frac{d}{e}\right)^{\frac{1}{3}} + a^{3}\right)} e^{2}\right)} \log\left(x + \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \, e^{3} \left(\frac{d}{e}\right)^{\frac{2}{3}}}"," ",0,"1/3*sqrt(3)*((c^3*(d/e)^(1/3) + 2*b*c^2)*d^2 - (b^3*(d/e)^(1/3) + 2*a*b^2 + (3*a*(d/e)^(2/3) + 2*b*d/e)*c^2 + (3*b^2*(d/e)^(2/3) + 6*a*b*(d/e)^(1/3) + 2*a^2)*c)*d*e + (3*a^2*b*(d/e)^(2/3) + a^3*(d/e)^(1/3) + 2*a*b^2*d/e + 2*a^2*c*d/e)*e^2)*arctan(1/3*sqrt(3)*(2*x - (d/e)^(1/3))/(d/e)^(1/3))/(d*e^2) + 1/4*(c^3*e*x^4 + 4*b*c^2*e*x^3 + 6*(b^2*c + a*c^2)*e*x^2 - 4*(c^3*d - (b^3 + 6*a*b*c)*e)*x)/e^2 - 1/6*(c^3*d^2 - (b^3 - 3*(2*b*(d/e)^(2/3) + a*(d/e)^(1/3))*c^2 - 3*(b^2*(d/e)^(1/3) - 2*a*b)*c)*d*e - (6*a*b^2*(d/e)^(2/3) + 6*a^2*c*(d/e)^(2/3) + 3*a^2*b*(d/e)^(1/3) - a^3)*e^2)*log(x^2 - x*(d/e)^(1/3) + (d/e)^(2/3))/(e^3*(d/e)^(2/3)) + 1/3*(c^3*d^2 - (b^3 + 3*(b*(d/e)^(2/3) - a*(d/e)^(1/3))*c^2 - 3*(b^2*(d/e)^(1/3) - 2*a*b)*c)*d*e + (3*a*b^2*(d/e)^(2/3) + 3*a^2*c*(d/e)^(2/3) - 3*a^2*b*(d/e)^(1/3) + a^3)*e^2)*log(x + (d/e)^(1/3))/(e^3*(d/e)^(2/3))","A",0
75,1,833,0,3.126320," ","integrate((c*x^2+b*x+a)^4/(e*x^3+d),x, algorithm=""maxima"")","\frac{5 \, c^{4} e x^{6} + 24 \, b c^{3} e x^{5} + 15 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e x^{4} - 10 \, {\left(c^{4} d - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e\right)} x^{3} - 15 \, {\left(4 \, b c^{3} d - {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e\right)} x^{2} - 60 \, {\left({\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d - 2 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e\right)} x}{30 \, e^{2}} - \frac{\sqrt{3} {\left(2 \, c^{4} d^{3} - 2 \, {\left(4 \, b^{3} c + 6 \, {\left(b \left(\frac{d}{e}\right)^{\frac{2}{3}} + a \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)} c^{3} + \frac{c^{4} d}{e} + 3 \, {\left(3 \, b^{2} \left(\frac{d}{e}\right)^{\frac{1}{3}} + 4 \, a b\right)} c^{2}\right)} d^{2} e + {\left(3 \, b^{4} \left(\frac{d}{e}\right)^{\frac{2}{3}} + 12 \, a b^{3} \left(\frac{d}{e}\right)^{\frac{1}{3}} + 12 \, a^{2} b^{2} + 6 \, {\left(3 \, a^{2} \left(\frac{d}{e}\right)^{\frac{2}{3}} + \frac{4 \, a b d}{e}\right)} c^{2} + 4 \, {\left(9 \, a b^{2} \left(\frac{d}{e}\right)^{\frac{2}{3}} + 9 \, a^{2} b \left(\frac{d}{e}\right)^{\frac{1}{3}} + 2 \, a^{3} + \frac{2 \, b^{3} d}{e}\right)} c\right)} d e^{2} - {\left(12 \, a^{3} b \left(\frac{d}{e}\right)^{\frac{2}{3}} + 3 \, a^{4} \left(\frac{d}{e}\right)^{\frac{1}{3}} + \frac{12 \, a^{2} b^{2} d}{e} + \frac{8 \, a^{3} c d}{e}\right)} e^{3}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{d}{e}\right)^{\frac{1}{3}}}\right)}{9 \, d e^{3}} + \frac{{\left(2 \, {\left(c^{4} \left(\frac{d}{e}\right)^{\frac{2}{3}} - 3 \, b^{2} c^{2} + 2 \, {\left(b \left(\frac{d}{e}\right)^{\frac{1}{3}} - a\right)} c^{3}\right)} d^{2} - {\left(b^{4} \left(\frac{d}{e}\right)^{\frac{1}{3}} - 4 \, a b^{3} + 6 \, {\left(4 \, a b \left(\frac{d}{e}\right)^{\frac{2}{3}} + a^{2} \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)} c^{2} + 4 \, {\left(2 \, b^{3} \left(\frac{d}{e}\right)^{\frac{2}{3}} + 3 \, a b^{2} \left(\frac{d}{e}\right)^{\frac{1}{3}} - 3 \, a^{2} b\right)} c\right)} d e + {\left(12 \, a^{2} b^{2} \left(\frac{d}{e}\right)^{\frac{2}{3}} + 8 \, a^{3} c \left(\frac{d}{e}\right)^{\frac{2}{3}} + 4 \, a^{3} b \left(\frac{d}{e}\right)^{\frac{1}{3}} - a^{4}\right)} e^{2}\right)} \log\left(x^{2} - x \left(\frac{d}{e}\right)^{\frac{1}{3}} + \left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \, e^{3} \left(\frac{d}{e}\right)^{\frac{2}{3}}} + \frac{{\left({\left(c^{4} \left(\frac{d}{e}\right)^{\frac{2}{3}} + 6 \, b^{2} c^{2} - 4 \, {\left(b \left(\frac{d}{e}\right)^{\frac{1}{3}} - a\right)} c^{3}\right)} d^{2} + {\left(b^{4} \left(\frac{d}{e}\right)^{\frac{1}{3}} - 4 \, a b^{3} - 6 \, {\left(2 \, a b \left(\frac{d}{e}\right)^{\frac{2}{3}} - a^{2} \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)} c^{2} - 4 \, {\left(b^{3} \left(\frac{d}{e}\right)^{\frac{2}{3}} - 3 \, a b^{2} \left(\frac{d}{e}\right)^{\frac{1}{3}} + 3 \, a^{2} b\right)} c\right)} d e + {\left(6 \, a^{2} b^{2} \left(\frac{d}{e}\right)^{\frac{2}{3}} + 4 \, a^{3} c \left(\frac{d}{e}\right)^{\frac{2}{3}} - 4 \, a^{3} b \left(\frac{d}{e}\right)^{\frac{1}{3}} + a^{4}\right)} e^{2}\right)} \log\left(x + \left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \, e^{3} \left(\frac{d}{e}\right)^{\frac{2}{3}}}"," ",0,"1/30*(5*c^4*e*x^6 + 24*b*c^3*e*x^5 + 15*(3*b^2*c^2 + 2*a*c^3)*e*x^4 - 10*(c^4*d - 4*(b^3*c + 3*a*b*c^2)*e)*x^3 - 15*(4*b*c^3*d - (b^4 + 12*a*b^2*c + 6*a^2*c^2)*e)*x^2 - 60*((3*b^2*c^2 + 2*a*c^3)*d - 2*(a*b^3 + 3*a^2*b*c)*e)*x)/e^2 - 1/9*sqrt(3)*(2*c^4*d^3 - 2*(4*b^3*c + 6*(b*(d/e)^(2/3) + a*(d/e)^(1/3))*c^3 + c^4*d/e + 3*(3*b^2*(d/e)^(1/3) + 4*a*b)*c^2)*d^2*e + (3*b^4*(d/e)^(2/3) + 12*a*b^3*(d/e)^(1/3) + 12*a^2*b^2 + 6*(3*a^2*(d/e)^(2/3) + 4*a*b*d/e)*c^2 + 4*(9*a*b^2*(d/e)^(2/3) + 9*a^2*b*(d/e)^(1/3) + 2*a^3 + 2*b^3*d/e)*c)*d*e^2 - (12*a^3*b*(d/e)^(2/3) + 3*a^4*(d/e)^(1/3) + 12*a^2*b^2*d/e + 8*a^3*c*d/e)*e^3)*arctan(1/3*sqrt(3)*(2*x - (d/e)^(1/3))/(d/e)^(1/3))/(d*e^3) + 1/6*(2*(c^4*(d/e)^(2/3) - 3*b^2*c^2 + 2*(b*(d/e)^(1/3) - a)*c^3)*d^2 - (b^4*(d/e)^(1/3) - 4*a*b^3 + 6*(4*a*b*(d/e)^(2/3) + a^2*(d/e)^(1/3))*c^2 + 4*(2*b^3*(d/e)^(2/3) + 3*a*b^2*(d/e)^(1/3) - 3*a^2*b)*c)*d*e + (12*a^2*b^2*(d/e)^(2/3) + 8*a^3*c*(d/e)^(2/3) + 4*a^3*b*(d/e)^(1/3) - a^4)*e^2)*log(x^2 - x*(d/e)^(1/3) + (d/e)^(2/3))/(e^3*(d/e)^(2/3)) + 1/3*((c^4*(d/e)^(2/3) + 6*b^2*c^2 - 4*(b*(d/e)^(1/3) - a)*c^3)*d^2 + (b^4*(d/e)^(1/3) - 4*a*b^3 - 6*(2*a*b*(d/e)^(2/3) - a^2*(d/e)^(1/3))*c^2 - 4*(b^3*(d/e)^(2/3) - 3*a*b^2*(d/e)^(1/3) + 3*a^2*b)*c)*d*e + (6*a^2*b^2*(d/e)^(2/3) + 4*a^3*c*(d/e)^(2/3) - 4*a^3*b*(d/e)^(1/3) + a^4)*e^2)*log(x + (d/e)^(1/3))/(e^3*(d/e)^(2/3))","A",0
76,1,37,0,2.857759," ","integrate((x^4+2*x^2)/(x^3+1),x, algorithm=""maxima"")","\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(x + 1\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(x + 1)","A",0
77,1,37,0,2.900295," ","integrate((x^4+2*x^2)/(-x^3+1),x, algorithm=""maxima"")","-\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(x - 1\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(x - 1)","A",0
78,1,37,0,2.808537," ","integrate((4*x^3-x+1)/(x^3+1),x, algorithm=""maxima"")","-\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(x + 1\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(x + 1)","A",0
79,0,0,0,0.000000," ","integrate((1+x+3^(1/2))/(x^3+1)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","-\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=""maxima"")","-\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","-\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=""maxima"")","-\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=""maxima"")","\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
87,0,0,0,0.000000," ","integrate((1+(b/a)^(1/3)*x+3^(1/2))/(b*x^3+a)^(1/2),x, algorithm=""maxima"")","\int \frac{x \left(\frac{b}{a}\right)^{\frac{1}{3}} + \sqrt{3} + 1}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate((x*(b/a)^(1/3) + sqrt(3) + 1)/sqrt(b*x^3 + a), x)","F",0
88,0,0,0,0.000000," ","integrate((1-(b/a)^(1/3)*x+3^(1/2))/(-b*x^3+a)^(1/2),x, algorithm=""maxima"")","-\int \frac{x \left(\frac{b}{a}\right)^{\frac{1}{3}} - \sqrt{3} - 1}{\sqrt{-b x^{3} + a}}\,{d x}"," ",0,"-integrate((x*(b/a)^(1/3) - sqrt(3) - 1)/sqrt(-b*x^3 + a), x)","F",0
89,0,0,0,0.000000," ","integrate((1-(b/a)^(1/3)*x+3^(1/2))/(b*x^3-a)^(1/2),x, algorithm=""maxima"")","-\int \frac{x \left(\frac{b}{a}\right)^{\frac{1}{3}} - \sqrt{3} - 1}{\sqrt{b x^{3} - a}}\,{d x}"," ",0,"-integrate((x*(b/a)^(1/3) - sqrt(3) - 1)/sqrt(b*x^3 - a), x)","F",0
90,0,0,0,0.000000," ","integrate((1+(b/a)^(1/3)*x+3^(1/2))/(-b*x^3-a)^(1/2),x, algorithm=""maxima"")","\int \frac{x \left(\frac{b}{a}\right)^{\frac{1}{3}} + \sqrt{3} + 1}{\sqrt{-b x^{3} - a}}\,{d x}"," ",0,"integrate((x*(b/a)^(1/3) + sqrt(3) + 1)/sqrt(-b*x^3 - a), x)","F",0
91,0,0,0,0.000000," ","integrate((1+x-3^(1/2))/(x^3+1)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","-\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=""maxima"")","-\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=""maxima"")","\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=""maxima"")","-\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","-\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=""maxima"")","\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=""maxima"")","-\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=""maxima"")","-\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=""maxima"")","\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
103,0,0,0,0.000000," ","integrate((1+(b/a)^(1/3)*x-3^(1/2))/(b*x^3+a)^(1/2),x, algorithm=""maxima"")","\int \frac{x \left(\frac{b}{a}\right)^{\frac{1}{3}} - \sqrt{3} + 1}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate((x*(b/a)^(1/3) - sqrt(3) + 1)/sqrt(b*x^3 + a), x)","F",0
104,0,0,0,0.000000," ","integrate((1-(b/a)^(1/3)*x-3^(1/2))/(-b*x^3+a)^(1/2),x, algorithm=""maxima"")","-\int \frac{x \left(\frac{b}{a}\right)^{\frac{1}{3}} + \sqrt{3} - 1}{\sqrt{-b x^{3} + a}}\,{d x}"," ",0,"-integrate((x*(b/a)^(1/3) + sqrt(3) - 1)/sqrt(-b*x^3 + a), x)","F",0
105,0,0,0,0.000000," ","integrate((1-(b/a)^(1/3)*x-3^(1/2))/(b*x^3-a)^(1/2),x, algorithm=""maxima"")","-\int \frac{x \left(\frac{b}{a}\right)^{\frac{1}{3}} + \sqrt{3} - 1}{\sqrt{b x^{3} - a}}\,{d x}"," ",0,"-integrate((x*(b/a)^(1/3) + sqrt(3) - 1)/sqrt(b*x^3 - a), x)","F",0
106,0,0,0,0.000000," ","integrate((1+(b/a)^(1/3)*x-3^(1/2))/(-b*x^3-a)^(1/2),x, algorithm=""maxima"")","\int \frac{x \left(\frac{b}{a}\right)^{\frac{1}{3}} - \sqrt{3} + 1}{\sqrt{-b x^{3} - a}}\,{d x}"," ",0,"integrate((x*(b/a)^(1/3) - sqrt(3) + 1)/sqrt(-b*x^3 - a), x)","F",0
107,0,0,0,0.000000," ","integrate((d*x+c)/(b*x^3+a)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\int \frac{d x + c}{\sqrt{-x^{3} - 1}}\,{d x}"," ",0,"integrate((d*x + c)/sqrt(-x^3 - 1), x)","F",0
115,1,126,0,2.881508," ","integrate((d*x+c)/(-b*x^4+a),x, algorithm=""maxima"")","\frac{c \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{2 \, \sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{d \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{4 \, \sqrt{a} \sqrt{b}} - \frac{d \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{4 \, \sqrt{a} \sqrt{b}} - \frac{c \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{4 \, \sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}}"," ",0,"1/2*c*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 1/4*d*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 1/4*d*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) - 1/4*c*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b)))","B",0
116,1,207,0,3.042457," ","integrate((d*x+c)/(b*x^4+a),x, algorithm=""maxima"")","\frac{\sqrt{2} c \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{8 \, a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} c \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{8 \, a^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{{\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} c - 2 \, \sqrt{a} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{4 \, a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{1}{4}}} + \frac{{\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} c + 2 \, \sqrt{a} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{4 \, a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{1}{4}}}"," ",0,"1/8*sqrt(2)*c*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - 1/8*sqrt(2)*c*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) + 1/4*(sqrt(2)*a^(1/4)*b^(1/4)*c - 2*sqrt(a)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(1/4)) + 1/4*(sqrt(2)*a^(1/4)*b^(1/4)*c + 2*sqrt(a)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(1/4))","A",0
117,1,157,0,3.038224," ","integrate((d*x+c)/(-b*x^4+a)^2,x, algorithm=""maxima"")","-\frac{d x^{2} + c x}{4 \, {\left(a b x^{4} - a^{2}\right)}} + \frac{\frac{6 \, c \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, d \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{2 \, d \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{3 \, c \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}}}{16 \, a}"," ",0,"-1/4*(d*x^2 + c*x)/(a*b*x^4 - a^2) + 1/16*(6*c*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*d*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 2*d*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) - 3*c*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))))/a","A",0
118,1,238,0,2.932087," ","integrate((d*x+c)/(b*x^4+a)^2,x, algorithm=""maxima"")","\frac{d x^{2} + c x}{4 \, {\left(a b x^{4} + a^{2}\right)}} + \frac{\frac{3 \, \sqrt{2} c \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{3 \, \sqrt{2} c \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} c - 4 \, \sqrt{a} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{1}{4}}} + \frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} c + 4 \, \sqrt{a} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{1}{4}}}}{32 \, a}"," ",0,"1/4*(d*x^2 + c*x)/(a*b*x^4 + a^2) + 1/32*(3*sqrt(2)*c*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - 3*sqrt(2)*c*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) + 2*(3*sqrt(2)*a^(1/4)*b^(1/4)*c - 4*sqrt(a)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(1/4)) + 2*(3*sqrt(2)*a^(1/4)*b^(1/4)*c + 4*sqrt(a)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(1/4)))/a","A",0
119,1,186,0,3.014556," ","integrate((d*x+c)/(-b*x^4+a)^3,x, algorithm=""maxima"")","-\frac{6 \, b d x^{6} + 7 \, b c x^{5} - 10 \, a d x^{2} - 11 \, a c x}{32 \, {\left(a^{2} b^{2} x^{8} - 2 \, a^{3} b x^{4} + a^{4}\right)}} + \frac{3 \, {\left(\frac{14 \, c \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{4 \, d \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{4 \, d \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{7 \, c \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}}\right)}}{128 \, a^{2}}"," ",0,"-1/32*(6*b*d*x^6 + 7*b*c*x^5 - 10*a*d*x^2 - 11*a*c*x)/(a^2*b^2*x^8 - 2*a^3*b*x^4 + a^4) + 3/128*(14*c*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 4*d*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 4*d*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) - 7*c*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))))/a^2","A",0
120,1,269,0,3.061316," ","integrate((d*x+c)/(b*x^4+a)^3,x, algorithm=""maxima"")","\frac{6 \, b d x^{6} + 7 \, b c x^{5} + 10 \, a d x^{2} + 11 \, a c x}{32 \, {\left(a^{2} b^{2} x^{8} + 2 \, a^{3} b x^{4} + a^{4}\right)}} + \frac{3 \, {\left(\frac{7 \, \sqrt{2} c \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{7 \, \sqrt{2} c \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, {\left(7 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} c - 8 \, \sqrt{a} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{1}{4}}} + \frac{2 \, {\left(7 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} c + 8 \, \sqrt{a} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{1}{4}}}\right)}}{256 \, a^{2}}"," ",0,"1/32*(6*b*d*x^6 + 7*b*c*x^5 + 10*a*d*x^2 + 11*a*c*x)/(a^2*b^2*x^8 + 2*a^3*b*x^4 + a^4) + 3/256*(7*sqrt(2)*c*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - 7*sqrt(2)*c*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) + 2*(7*sqrt(2)*a^(1/4)*b^(1/4)*c - 8*sqrt(a)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(1/4)) + 2*(7*sqrt(2)*a^(1/4)*b^(1/4)*c + 8*sqrt(a)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(1/4)))/a^2","A",0
121,1,223,0,2.974164," ","integrate((d*x+c)/(-b*x^4+a)^4,x, algorithm=""maxima"")","-\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(a^{3} b^{3} x^{12} - 3 \, a^{4} b^{2} x^{8} + 3 \, a^{5} b x^{4} - a^{6}\right)}} + \frac{\frac{154 \, c \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{40 \, d \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{40 \, d \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{77 \, c \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}}}{512 \, a^{3}}"," ",0,"-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)/(a^3*b^3*x^12 - 3*a^4*b^2*x^8 + 3*a^5*b*x^4 - a^6) + 1/512*(154*c*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 40*d*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 40*d*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) - 77*c*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))))/a^3","A",0
122,1,304,0,3.197606," ","integrate((d*x+c)/(b*x^4+a)^4,x, algorithm=""maxima"")","\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(a^{3} b^{3} x^{12} + 3 \, a^{4} b^{2} x^{8} + 3 \, a^{5} b x^{4} + a^{6}\right)}} + \frac{\frac{77 \, \sqrt{2} c \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{77 \, \sqrt{2} c \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, {\left(77 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} c - 80 \, \sqrt{a} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{1}{4}}} + \frac{2 \, {\left(77 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} c + 80 \, \sqrt{a} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{1}{4}}}}{1024 \, a^{3}}"," ",0,"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)/(a^3*b^3*x^12 + 3*a^4*b^2*x^8 + 3*a^5*b*x^4 + a^6) + 1/1024*(77*sqrt(2)*c*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - 77*sqrt(2)*c*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(1/4)) + 2*(77*sqrt(2)*a^(1/4)*b^(1/4)*c - 80*sqrt(a)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(1/4)) + 2*(77*sqrt(2)*a^(1/4)*b^(1/4)*c + 80*sqrt(a)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(1/4)))/a^3","A",0
123,1,35,0,3.041563," ","integrate((d*x+c)/(-x^4+1),x, algorithm=""maxima"")","\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(x + 1\right) - \frac{1}{4} \, {\left(c + d\right)} \log\left(x - 1\right)"," ",0,"1/2*c*arctan(x) + 1/4*d*log(x^2 + 1) + 1/4*(c - d)*log(x + 1) - 1/4*(c + d)*log(x - 1)","A",0
124,1,86,0,2.998036," ","integrate((d*x+c)/(x^4+1),x, algorithm=""maxima"")","\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
125,1,153,0,2.911393," ","integrate((e*x^2+d*x+c)/(-b*x^4+a),x, algorithm=""maxima"")","\frac{d \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{4 \, \sqrt{a} \sqrt{b}} - \frac{d \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{4 \, \sqrt{a} \sqrt{b}} + \frac{{\left(\sqrt{b} c - \sqrt{a} e\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{2 \, \sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(\sqrt{b} c + \sqrt{a} e\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{4 \, \sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}"," ",0,"1/4*d*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 1/4*d*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) + 1/2*(sqrt(b)*c - sqrt(a)*e)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - 1/4*(sqrt(b)*c + sqrt(a)*e)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b))","A",0
126,1,257,0,3.041925," ","integrate((e*x^2+d*x+c)/(b*x^4+a),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\sqrt{b} c - \sqrt{a} e\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{8 \, a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(\sqrt{b} c - \sqrt{a} e\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{8 \, a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{{\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} e - 2 \, \sqrt{a} \sqrt{b} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{4 \, a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{{\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} e + 2 \, \sqrt{a} \sqrt{b} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{4 \, a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}"," ",0,"1/8*sqrt(2)*(sqrt(b)*c - sqrt(a)*e)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - 1/8*sqrt(2)*(sqrt(b)*c - sqrt(a)*e)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 1/4*(sqrt(2)*a^(1/4)*b^(3/4)*c + sqrt(2)*a^(3/4)*b^(1/4)*e - 2*sqrt(a)*sqrt(b)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 1/4*(sqrt(2)*a^(1/4)*b^(3/4)*c + sqrt(2)*a^(3/4)*b^(1/4)*e + 2*sqrt(a)*sqrt(b)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4))","A",0
127,1,191,0,2.936237," ","integrate((e*x^2+d*x+c)/(-b*x^4+a)^2,x, algorithm=""maxima"")","-\frac{e x^{3} + d x^{2} + c x}{4 \, {\left(a b x^{4} - a^{2}\right)}} + \frac{\frac{2 \, d \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{2 \, d \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} + \frac{2 \, {\left(3 \, \sqrt{b} c - \sqrt{a} e\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(3 \, \sqrt{b} c + \sqrt{a} e\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{16 \, a}"," ",0,"-1/4*(e*x^3 + d*x^2 + c*x)/(a*b*x^4 - a^2) + 1/16*(2*d*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 2*d*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) + 2*(3*sqrt(b)*c - sqrt(a)*e)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (3*sqrt(b)*c + sqrt(a)*e)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/a","A",0
128,1,294,0,3.102105," ","integrate((e*x^2+d*x+c)/(b*x^4+a)^2,x, algorithm=""maxima"")","\frac{e x^{3} + d x^{2} + c x}{4 \, {\left(a b x^{4} + a^{2}\right)}} + \frac{\frac{\sqrt{2} {\left(3 \, \sqrt{b} c - \sqrt{a} e\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(3 \, \sqrt{b} c - \sqrt{a} e\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} e - 4 \, \sqrt{a} \sqrt{b} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} e + 4 \, \sqrt{a} \sqrt{b} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{32 \, a}"," ",0,"1/4*(e*x^3 + d*x^2 + c*x)/(a*b*x^4 + a^2) + 1/32*(sqrt(2)*(3*sqrt(b)*c - sqrt(a)*e)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(3*sqrt(b)*c - sqrt(a)*e)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(3*sqrt(2)*a^(1/4)*b^(3/4)*c + sqrt(2)*a^(3/4)*b^(1/4)*e - 4*sqrt(a)*sqrt(b)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(3*sqrt(2)*a^(1/4)*b^(3/4)*c + sqrt(2)*a^(3/4)*b^(1/4)*e + 4*sqrt(a)*sqrt(b)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/a","A",0
129,1,230,0,3.124087," ","integrate((e*x^2+d*x+c)/(-b*x^4+a)^3,x, algorithm=""maxima"")","-\frac{5 \, b e x^{7} + 6 \, b d x^{6} + 7 \, b c x^{5} - 9 \, a e x^{3} - 10 \, a d x^{2} - 11 \, a c x}{32 \, {\left(a^{2} b^{2} x^{8} - 2 \, a^{3} b x^{4} + a^{4}\right)}} + \frac{\frac{12 \, d \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{12 \, d \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} + \frac{2 \, {\left(21 \, \sqrt{b} c - 5 \, \sqrt{a} e\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(21 \, \sqrt{b} c + 5 \, \sqrt{a} e\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{128 \, a^{2}}"," ",0,"-1/32*(5*b*e*x^7 + 6*b*d*x^6 + 7*b*c*x^5 - 9*a*e*x^3 - 10*a*d*x^2 - 11*a*c*x)/(a^2*b^2*x^8 - 2*a^3*b*x^4 + a^4) + 1/128*(12*d*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 12*d*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) + 2*(21*sqrt(b)*c - 5*sqrt(a)*e)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (21*sqrt(b)*c + 5*sqrt(a)*e)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/a^2","A",0
130,1,336,0,3.088542," ","integrate((e*x^2+d*x+c)/(b*x^4+a)^3,x, algorithm=""maxima"")","\frac{5 \, b e x^{7} + 6 \, b d x^{6} + 7 \, b c x^{5} + 9 \, a e x^{3} + 10 \, a d x^{2} + 11 \, a c x}{32 \, {\left(a^{2} b^{2} x^{8} + 2 \, a^{3} b x^{4} + a^{4}\right)}} + \frac{\frac{\sqrt{2} {\left(21 \, \sqrt{b} c - 5 \, \sqrt{a} e\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(21 \, \sqrt{b} c - 5 \, \sqrt{a} e\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(21 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} c + 5 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} e - 24 \, \sqrt{a} \sqrt{b} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(21 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} c + 5 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} e + 24 \, \sqrt{a} \sqrt{b} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{256 \, a^{2}}"," ",0,"1/32*(5*b*e*x^7 + 6*b*d*x^6 + 7*b*c*x^5 + 9*a*e*x^3 + 10*a*d*x^2 + 11*a*c*x)/(a^2*b^2*x^8 + 2*a^3*b*x^4 + a^4) + 1/256*(sqrt(2)*(21*sqrt(b)*c - 5*sqrt(a)*e)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(21*sqrt(b)*c - 5*sqrt(a)*e)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(21*sqrt(2)*a^(1/4)*b^(3/4)*c + 5*sqrt(2)*a^(3/4)*b^(1/4)*e - 24*sqrt(a)*sqrt(b)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(21*sqrt(2)*a^(1/4)*b^(3/4)*c + 5*sqrt(2)*a^(3/4)*b^(1/4)*e + 24*sqrt(a)*sqrt(b)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/a^2","A",0
131,1,279,0,3.018842," ","integrate((e*x^2+d*x+c)/(-b*x^4+a)^4,x, algorithm=""maxima"")","-\frac{45 \, b^{2} e x^{11} + 60 \, b^{2} d x^{10} + 77 \, b^{2} c x^{9} - 126 \, a b e x^{7} - 160 \, a b d x^{6} - 198 \, a b c x^{5} + 113 \, a^{2} e x^{3} + 132 \, a^{2} d x^{2} + 153 \, a^{2} c x}{384 \, {\left(a^{3} b^{3} x^{12} - 3 \, a^{4} b^{2} x^{8} + 3 \, a^{5} b x^{4} - a^{6}\right)}} + \frac{\frac{40 \, d \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{40 \, d \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} + \frac{2 \, {\left(77 \, \sqrt{b} c - 15 \, \sqrt{a} e\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(77 \, \sqrt{b} c + 15 \, \sqrt{a} e\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{512 \, a^{3}}"," ",0,"-1/384*(45*b^2*e*x^11 + 60*b^2*d*x^10 + 77*b^2*c*x^9 - 126*a*b*e*x^7 - 160*a*b*d*x^6 - 198*a*b*c*x^5 + 113*a^2*e*x^3 + 132*a^2*d*x^2 + 153*a^2*c*x)/(a^3*b^3*x^12 - 3*a^4*b^2*x^8 + 3*a^5*b*x^4 - a^6) + 1/512*(40*d*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 40*d*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) + 2*(77*sqrt(b)*c - 15*sqrt(a)*e)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (77*sqrt(b)*c + 15*sqrt(a)*e)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/a^3","A",0
132,1,383,0,3.107897," ","integrate((e*x^2+d*x+c)/(b*x^4+a)^4,x, algorithm=""maxima"")","\frac{45 \, b^{2} e x^{11} + 60 \, b^{2} d x^{10} + 77 \, b^{2} c x^{9} + 126 \, a b e x^{7} + 160 \, a b d x^{6} + 198 \, a b c x^{5} + 113 \, a^{2} e x^{3} + 132 \, a^{2} d x^{2} + 153 \, a^{2} c x}{384 \, {\left(a^{3} b^{3} x^{12} + 3 \, a^{4} b^{2} x^{8} + 3 \, a^{5} b x^{4} + a^{6}\right)}} + \frac{\frac{\sqrt{2} {\left(77 \, \sqrt{b} c - 15 \, \sqrt{a} e\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(77 \, \sqrt{b} c - 15 \, \sqrt{a} e\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(77 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} c + 15 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} e - 80 \, \sqrt{a} \sqrt{b} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(77 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} c + 15 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} e + 80 \, \sqrt{a} \sqrt{b} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{1024 \, a^{3}}"," ",0,"1/384*(45*b^2*e*x^11 + 60*b^2*d*x^10 + 77*b^2*c*x^9 + 126*a*b*e*x^7 + 160*a*b*d*x^6 + 198*a*b*c*x^5 + 113*a^2*e*x^3 + 132*a^2*d*x^2 + 153*a^2*c*x)/(a^3*b^3*x^12 + 3*a^4*b^2*x^8 + 3*a^5*b*x^4 + a^6) + 1/1024*(sqrt(2)*(77*sqrt(b)*c - 15*sqrt(a)*e)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(77*sqrt(b)*c - 15*sqrt(a)*e)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(77*sqrt(2)*a^(1/4)*b^(3/4)*c + 15*sqrt(2)*a^(3/4)*b^(1/4)*e - 80*sqrt(a)*sqrt(b)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(77*sqrt(2)*a^(1/4)*b^(3/4)*c + 15*sqrt(2)*a^(3/4)*b^(1/4)*e + 80*sqrt(a)*sqrt(b)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/a^3","A",0
133,1,25,0,1.372087," ","integrate(a*(f*x^4+e)^2,x, algorithm=""maxima"")","\frac{1}{45} \, {\left(5 \, f^{2} x^{9} + 18 \, e f x^{5} + 45 \, e^{2} x\right)} a"," ",0,"1/45*(5*f^2*x^9 + 18*e*f*x^5 + 45*e^2*x)*a","A",0
134,1,27,0,1.395838," ","integrate(b*x*(f*x^4+e)^2,x, algorithm=""maxima"")","\frac{1}{30} \, {\left(3 \, f^{2} x^{10} + 10 \, e f x^{6} + 15 \, e^{2} x^{2}\right)} b"," ",0,"1/30*(3*f^2*x^10 + 10*e*f*x^6 + 15*e^2*x^2)*b","A",0
135,1,50,0,1.356280," ","integrate((b*x+a)*(f*x^4+e)^2,x, algorithm=""maxima"")","\frac{1}{10} \, b f^{2} x^{10} + \frac{1}{9} \, a f^{2} x^{9} + \frac{1}{3} \, b e f x^{6} + \frac{2}{5} \, a e f x^{5} + \frac{1}{2} \, b e^{2} x^{2} + a e^{2} x"," ",0,"1/10*b*f^2*x^10 + 1/9*a*f^2*x^9 + 1/3*b*e*f*x^6 + 2/5*a*e*f*x^5 + 1/2*b*e^2*x^2 + a*e^2*x","A",0
136,1,27,0,1.357227," ","integrate(c*x^2*(f*x^4+e)^2,x, algorithm=""maxima"")","\frac{1}{231} \, {\left(21 \, f^{2} x^{11} + 66 \, e f x^{7} + 77 \, e^{2} x^{3}\right)} c"," ",0,"1/231*(21*f^2*x^11 + 66*e*f*x^7 + 77*e^2*x^3)*c","A",0
137,1,50,0,1.317299," ","integrate((c*x^2+a)*(f*x^4+e)^2,x, algorithm=""maxima"")","\frac{1}{11} \, c f^{2} x^{11} + \frac{1}{9} \, a f^{2} x^{9} + \frac{2}{7} \, c e f x^{7} + \frac{2}{5} \, a e f x^{5} + \frac{1}{3} \, c e^{2} x^{3} + a e^{2} x"," ",0,"1/11*c*f^2*x^11 + 1/9*a*f^2*x^9 + 2/7*c*e*f*x^7 + 2/5*a*e*f*x^5 + 1/3*c*e^2*x^3 + a*e^2*x","A",0
138,1,53,0,1.349174," ","integrate((c*x^2+b*x)*(f*x^4+e)^2,x, algorithm=""maxima"")","\frac{1}{11} \, c f^{2} x^{11} + \frac{1}{10} \, b f^{2} x^{10} + \frac{2}{7} \, c e f x^{7} + \frac{1}{3} \, b e f x^{6} + \frac{1}{3} \, c e^{2} x^{3} + \frac{1}{2} \, b e^{2} x^{2}"," ",0,"1/11*c*f^2*x^11 + 1/10*b*f^2*x^10 + 2/7*c*e*f*x^7 + 1/3*b*e*f*x^6 + 1/3*c*e^2*x^3 + 1/2*b*e^2*x^2","A",0
139,1,76,0,1.429607," ","integrate((c*x^2+b*x+a)*(f*x^4+e)^2,x, algorithm=""maxima"")","\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 e f x^{7} + \frac{1}{3} \, b e f x^{6} + \frac{2}{5} \, a e f x^{5} + \frac{1}{3} \, c e^{2} x^{3} + \frac{1}{2} \, b e^{2} x^{2} + a e^{2} x"," ",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*e*f*x^7 + 1/3*b*e*f*x^6 + 2/5*a*e*f*x^5 + 1/3*c*e^2*x^3 + 1/2*b*e^2*x^2 + a*e^2*x","A",0
140,1,15,0,1.386055," ","integrate(d*x^3*(f*x^4+e)^2,x, algorithm=""maxima"")","\frac{{\left(f x^{4} + e\right)}^{3} d}{12 \, f}"," ",0,"1/12*(f*x^4 + e)^3*d/f","A",0
141,1,50,0,1.314396," ","integrate((d*x^3+a)*(f*x^4+e)^2,x, algorithm=""maxima"")","\frac{1}{12} \, d f^{2} x^{12} + \frac{1}{9} \, a f^{2} x^{9} + \frac{1}{4} \, d e f x^{8} + \frac{2}{5} \, a e f x^{5} + \frac{1}{4} \, d e^{2} x^{4} + a e^{2} x"," ",0,"1/12*d*f^2*x^12 + 1/9*a*f^2*x^9 + 1/4*d*e*f*x^8 + 2/5*a*e*f*x^5 + 1/4*d*e^2*x^4 + a*e^2*x","A",0
142,1,53,0,1.319796," ","integrate((d*x^3+b*x)*(f*x^4+e)^2,x, algorithm=""maxima"")","\frac{1}{12} \, d f^{2} x^{12} + \frac{1}{10} \, b f^{2} x^{10} + \frac{1}{4} \, d e f x^{8} + \frac{1}{3} \, b e f x^{6} + \frac{1}{4} \, d e^{2} x^{4} + \frac{1}{2} \, b e^{2} x^{2}"," ",0,"1/12*d*f^2*x^12 + 1/10*b*f^2*x^10 + 1/4*d*e*f*x^8 + 1/3*b*e*f*x^6 + 1/4*d*e^2*x^4 + 1/2*b*e^2*x^2","A",0
143,1,76,0,1.362557," ","integrate((d*x^3+b*x+a)*(f*x^4+e)^2,x, algorithm=""maxima"")","\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 e f x^{8} + \frac{1}{3} \, b e f x^{6} + \frac{2}{5} \, a e f x^{5} + \frac{1}{4} \, d e^{2} x^{4} + \frac{1}{2} \, b e^{2} x^{2} + a e^{2} x"," ",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*e*f*x^8 + 1/3*b*e*f*x^6 + 2/5*a*e*f*x^5 + 1/4*d*e^2*x^4 + 1/2*b*e^2*x^2 + a*e^2*x","A",0
144,1,53,0,1.360464," ","integrate((d*x^3+c*x^2)*(f*x^4+e)^2,x, algorithm=""maxima"")","\frac{1}{12} \, d f^{2} x^{12} + \frac{1}{11} \, c f^{2} x^{11} + \frac{1}{4} \, d e f x^{8} + \frac{2}{7} \, c e f x^{7} + \frac{1}{4} \, d e^{2} x^{4} + \frac{1}{3} \, c e^{2} x^{3}"," ",0,"1/12*d*f^2*x^12 + 1/11*c*f^2*x^11 + 1/4*d*e*f*x^8 + 2/7*c*e*f*x^7 + 1/4*d*e^2*x^4 + 1/3*c*e^2*x^3","A",0
145,1,76,0,1.336803," ","integrate((d*x^3+c*x^2+a)*(f*x^4+e)^2,x, algorithm=""maxima"")","\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 e f x^{8} + \frac{2}{7} \, c e f x^{7} + \frac{2}{5} \, a e f x^{5} + \frac{1}{4} \, d e^{2} x^{4} + \frac{1}{3} \, c e^{2} x^{3} + a e^{2} x"," ",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*e*f*x^8 + 2/7*c*e*f*x^7 + 2/5*a*e*f*x^5 + 1/4*d*e^2*x^4 + 1/3*c*e^2*x^3 + a*e^2*x","A",0
146,1,79,0,1.417163," ","integrate((d*x^3+c*x^2+b*x)*(f*x^4+e)^2,x, algorithm=""maxima"")","\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 e f x^{8} + \frac{2}{7} \, c e f x^{7} + \frac{1}{3} \, b e f x^{6} + \frac{1}{4} \, d e^{2} x^{4} + \frac{1}{3} \, c e^{2} x^{3} + \frac{1}{2} \, b e^{2} x^{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*e*f*x^8 + 2/7*c*e*f*x^7 + 1/3*b*e*f*x^6 + 1/4*d*e^2*x^4 + 1/3*c*e^2*x^3 + 1/2*b*e^2*x^2","A",0
147,1,102,0,1.393469," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^2,x, algorithm=""maxima"")","\frac{1}{12} \, b^{2} f x^{12} + \frac{1}{11} \, b^{2} e x^{11} + \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 e x^{7} + \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} e x^{3} + \frac{1}{2} \, a^{2} d x^{2} + a^{2} c x"," ",0,"1/12*b^2*f*x^12 + 1/11*b^2*e*x^11 + 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*e*x^7 + 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*e*x^3 + 1/2*a^2*d*x^2 + a^2*c*x","A",0
148,1,150,0,1.339127," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^3,x, algorithm=""maxima"")","\frac{1}{16} \, b^{3} f x^{16} + \frac{1}{15} \, b^{3} e x^{15} + \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} e x^{11} + \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 e x^{7} + \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} e x^{3} + \frac{1}{2} \, a^{3} d x^{2} + a^{3} c x"," ",0,"1/16*b^3*f*x^16 + 1/15*b^3*e*x^15 + 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*e*x^11 + 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*e*x^7 + 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*e*x^3 + 1/2*a^3*d*x^2 + a^3*c*x","A",0
149,1,200,0,3.002108," ","integrate((f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^2,x, algorithm=""maxima"")","-\frac{b e x^{3} + b d x^{2} + b c x + a f}{4 \, {\left(a b^{2} x^{4} - a^{2} b\right)}} + \frac{\frac{2 \, d \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{2 \, d \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} + \frac{2 \, {\left(3 \, \sqrt{b} c - \sqrt{a} e\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(3 \, \sqrt{b} c + \sqrt{a} e\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{16 \, a}"," ",0,"-1/4*(b*e*x^3 + b*d*x^2 + b*c*x + a*f)/(a*b^2*x^4 - a^2*b) + 1/16*(2*d*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 2*d*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) + 2*(3*sqrt(b)*c - sqrt(a)*e)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (3*sqrt(b)*c + sqrt(a)*e)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/a","A",0
150,1,249,0,2.963835," ","integrate((f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^3,x, algorithm=""maxima"")","-\frac{5 \, b^{2} e x^{7} + 6 \, b^{2} d x^{6} + 7 \, b^{2} c x^{5} - 9 \, a b e x^{3} - 10 \, a b d x^{2} - 11 \, a b c x - 4 \, a^{2} f}{32 \, {\left(a^{2} b^{3} x^{8} - 2 \, a^{3} b^{2} x^{4} + a^{4} b\right)}} + \frac{\frac{12 \, d \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{12 \, d \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} + \frac{2 \, {\left(21 \, \sqrt{b} c - 5 \, \sqrt{a} e\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(21 \, \sqrt{b} c + 5 \, \sqrt{a} e\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{128 \, a^{2}}"," ",0,"-1/32*(5*b^2*e*x^7 + 6*b^2*d*x^6 + 7*b^2*c*x^5 - 9*a*b*e*x^3 - 10*a*b*d*x^2 - 11*a*b*c*x - 4*a^2*f)/(a^2*b^3*x^8 - 2*a^3*b^2*x^4 + a^4*b) + 1/128*(12*d*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 12*d*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) + 2*(21*sqrt(b)*c - 5*sqrt(a)*e)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (21*sqrt(b)*c + 5*sqrt(a)*e)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/a^2","A",0
151,1,297,0,3.060660," ","integrate((f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^4,x, algorithm=""maxima"")","-\frac{45 \, b^{3} e x^{11} + 60 \, b^{3} d x^{10} + 77 \, b^{3} c x^{9} - 126 \, a b^{2} e x^{7} - 160 \, a b^{2} d x^{6} - 198 \, a b^{2} c x^{5} + 113 \, a^{2} b e x^{3} + 132 \, a^{2} b d x^{2} + 153 \, a^{2} b c x + 32 \, a^{3} f}{384 \, {\left(a^{3} b^{4} x^{12} - 3 \, a^{4} b^{3} x^{8} + 3 \, a^{5} b^{2} x^{4} - a^{6} b\right)}} + \frac{\frac{40 \, d \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{40 \, d \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} + \frac{2 \, {\left(77 \, \sqrt{b} c - 15 \, \sqrt{a} e\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(77 \, \sqrt{b} c + 15 \, \sqrt{a} e\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{512 \, a^{3}}"," ",0,"-1/384*(45*b^3*e*x^11 + 60*b^3*d*x^10 + 77*b^3*c*x^9 - 126*a*b^2*e*x^7 - 160*a*b^2*d*x^6 - 198*a*b^2*c*x^5 + 113*a^2*b*e*x^3 + 132*a^2*b*d*x^2 + 153*a^2*b*c*x + 32*a^3*f)/(a^3*b^4*x^12 - 3*a^4*b^3*x^8 + 3*a^5*b^2*x^4 - a^6*b) + 1/512*(40*d*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 40*d*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) + 2*(77*sqrt(b)*c - 15*sqrt(a)*e)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (77*sqrt(b)*c + 15*sqrt(a)*e)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/a^3","A",0
152,1,123,0,2.936652," ","integrate(a/(3*x^4+2),x, algorithm=""maxima"")","\frac{1}{48} \, {\left(2 \cdot 3^{\frac{3}{4}} 2^{\frac{3}{4}} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x + 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + 2 \cdot 3^{\frac{3}{4}} 2^{\frac{3}{4}} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x - 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + 3^{\frac{3}{4}} 2^{\frac{3}{4}} \log\left(\sqrt{3} x^{2} + 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) - 3^{\frac{3}{4}} 2^{\frac{3}{4}} \log\left(\sqrt{3} x^{2} - 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right)\right)} a"," ",0,"1/48*(2*3^(3/4)*2^(3/4)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x + 3^(1/4)*2^(3/4))) + 2*3^(3/4)*2^(3/4)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x - 3^(1/4)*2^(3/4))) + 3^(3/4)*2^(3/4)*log(sqrt(3)*x^2 + 3^(1/4)*2^(3/4)*x + sqrt(2)) - 3^(3/4)*2^(3/4)*log(sqrt(3)*x^2 - 3^(1/4)*2^(3/4)*x + sqrt(2)))*a","A",0
153,1,15,0,2.875347," ","integrate(b*x/(3*x^4+2),x, algorithm=""maxima"")","\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
154,1,147,0,2.907226," ","integrate((b*x+a)/(3*x^4+2),x, algorithm=""maxima"")","\frac{1}{48} \cdot 3^{\frac{3}{4}} 2^{\frac{3}{4}} a \log\left(\sqrt{3} x^{2} + 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) - \frac{1}{48} \cdot 3^{\frac{3}{4}} 2^{\frac{3}{4}} a \log\left(\sqrt{3} x^{2} - 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) + \frac{1}{24} \, \sqrt{3} {\left(3^{\frac{1}{4}} 2^{\frac{3}{4}} a - 2 \, \sqrt{2} b\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x + 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + \frac{1}{24} \, \sqrt{3} {\left(3^{\frac{1}{4}} 2^{\frac{3}{4}} a + 2 \, \sqrt{2} b\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x - 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right)"," ",0,"1/48*3^(3/4)*2^(3/4)*a*log(sqrt(3)*x^2 + 3^(1/4)*2^(3/4)*x + sqrt(2)) - 1/48*3^(3/4)*2^(3/4)*a*log(sqrt(3)*x^2 - 3^(1/4)*2^(3/4)*x + sqrt(2)) + 1/24*sqrt(3)*(3^(1/4)*2^(3/4)*a - 2*sqrt(2)*b)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x + 3^(1/4)*2^(3/4))) + 1/24*sqrt(3)*(3^(1/4)*2^(3/4)*a + 2*sqrt(2)*b)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x - 3^(1/4)*2^(3/4)))","A",0
155,1,123,0,3.038068," ","integrate(c*x^2/(3*x^4+2),x, algorithm=""maxima"")","\frac{1}{24} \, {\left(2 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x + 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + 2 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x - 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) - 3^{\frac{1}{4}} 2^{\frac{1}{4}} \log\left(\sqrt{3} x^{2} + 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) + 3^{\frac{1}{4}} 2^{\frac{1}{4}} \log\left(\sqrt{3} x^{2} - 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right)\right)} c"," ",0,"1/24*(2*3^(1/4)*2^(1/4)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x + 3^(1/4)*2^(3/4))) + 2*3^(1/4)*2^(1/4)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x - 3^(1/4)*2^(3/4))) - 3^(1/4)*2^(1/4)*log(sqrt(3)*x^2 + 3^(1/4)*2^(3/4)*x + sqrt(2)) + 3^(1/4)*2^(1/4)*log(sqrt(3)*x^2 - 3^(1/4)*2^(3/4)*x + sqrt(2)))*c","A",0
156,1,167,0,3.038455," ","integrate((c*x^2+a)/(3*x^4+2),x, algorithm=""maxima"")","\frac{1}{24} \cdot 3^{\frac{1}{4}} 2^{\frac{3}{4}} {\left(\sqrt{3} a + \sqrt{2} c\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x + 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + \frac{1}{24} \cdot 3^{\frac{1}{4}} 2^{\frac{3}{4}} {\left(\sqrt{3} a + \sqrt{2} c\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x - 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + \frac{1}{48} \cdot 3^{\frac{1}{4}} 2^{\frac{3}{4}} {\left(\sqrt{3} a - \sqrt{2} c\right)} \log\left(\sqrt{3} x^{2} + 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) - \frac{1}{48} \cdot 3^{\frac{1}{4}} 2^{\frac{3}{4}} {\left(\sqrt{3} a - \sqrt{2} c\right)} \log\left(\sqrt{3} x^{2} - 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right)"," ",0,"1/24*3^(1/4)*2^(3/4)*(sqrt(3)*a + sqrt(2)*c)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x + 3^(1/4)*2^(3/4))) + 1/24*3^(1/4)*2^(3/4)*(sqrt(3)*a + sqrt(2)*c)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x - 3^(1/4)*2^(3/4))) + 1/48*3^(1/4)*2^(3/4)*(sqrt(3)*a - sqrt(2)*c)*log(sqrt(3)*x^2 + 3^(1/4)*2^(3/4)*x + sqrt(2)) - 1/48*3^(1/4)*2^(3/4)*(sqrt(3)*a - sqrt(2)*c)*log(sqrt(3)*x^2 - 3^(1/4)*2^(3/4)*x + sqrt(2))","A",0
157,1,147,0,3.089711," ","integrate((c*x^2+b*x)/(3*x^4+2),x, algorithm=""maxima"")","\frac{1}{24} \, \sqrt{2} {\left(3^{\frac{1}{4}} 2^{\frac{3}{4}} c - 2 \, \sqrt{3} b\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x + 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + \frac{1}{24} \, \sqrt{2} {\left(3^{\frac{1}{4}} 2^{\frac{3}{4}} c + 2 \, \sqrt{3} b\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x - 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) - \frac{1}{24} \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} c \log\left(\sqrt{3} x^{2} + 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) + \frac{1}{24} \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} c \log\left(\sqrt{3} x^{2} - 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right)"," ",0,"1/24*sqrt(2)*(3^(1/4)*2^(3/4)*c - 2*sqrt(3)*b)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x + 3^(1/4)*2^(3/4))) + 1/24*sqrt(2)*(3^(1/4)*2^(3/4)*c + 2*sqrt(3)*b)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x - 3^(1/4)*2^(3/4))) - 1/24*3^(1/4)*2^(1/4)*c*log(sqrt(3)*x^2 + 3^(1/4)*2^(3/4)*x + sqrt(2)) + 1/24*3^(1/4)*2^(1/4)*c*log(sqrt(3)*x^2 - 3^(1/4)*2^(3/4)*x + sqrt(2))","A",0
158,1,187,0,3.061737," ","integrate((c*x^2+b*x+a)/(3*x^4+2),x, algorithm=""maxima"")","\frac{1}{48} \cdot 3^{\frac{1}{4}} 2^{\frac{3}{4}} {\left(\sqrt{3} a - \sqrt{2} c\right)} \log\left(\sqrt{3} x^{2} + 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) - \frac{1}{48} \cdot 3^{\frac{1}{4}} 2^{\frac{3}{4}} {\left(\sqrt{3} a - \sqrt{2} c\right)} \log\left(\sqrt{3} x^{2} - 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) + \frac{1}{24} \, {\left(3^{\frac{3}{4}} 2^{\frac{3}{4}} a - 2 \, \sqrt{3} \sqrt{2} b + 2 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} c\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x + 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + \frac{1}{24} \, {\left(3^{\frac{3}{4}} 2^{\frac{3}{4}} a + 2 \, \sqrt{3} \sqrt{2} b + 2 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} c\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x - 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right)"," ",0,"1/48*3^(1/4)*2^(3/4)*(sqrt(3)*a - sqrt(2)*c)*log(sqrt(3)*x^2 + 3^(1/4)*2^(3/4)*x + sqrt(2)) - 1/48*3^(1/4)*2^(3/4)*(sqrt(3)*a - sqrt(2)*c)*log(sqrt(3)*x^2 - 3^(1/4)*2^(3/4)*x + sqrt(2)) + 1/24*(3^(3/4)*2^(3/4)*a - 2*sqrt(3)*sqrt(2)*b + 2*3^(1/4)*2^(1/4)*c)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x + 3^(1/4)*2^(3/4))) + 1/24*(3^(3/4)*2^(3/4)*a + 2*sqrt(3)*sqrt(2)*b + 2*3^(1/4)*2^(1/4)*c)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x - 3^(1/4)*2^(3/4)))","A",0
159,1,11,0,1.323296," ","integrate(d*x^3/(3*x^4+2),x, algorithm=""maxima"")","\frac{1}{12} \, d \log\left(3 \, x^{4} + 2\right)"," ",0,"1/12*d*log(3*x^4 + 2)","A",0
160,1,149,0,3.056403," ","integrate((d*x^3+a)/(3*x^4+2),x, algorithm=""maxima"")","\frac{1}{24} \cdot 3^{\frac{3}{4}} 2^{\frac{3}{4}} a \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x + 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + \frac{1}{24} \cdot 3^{\frac{3}{4}} 2^{\frac{3}{4}} a \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x - 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + \frac{1}{144} \cdot 3^{\frac{3}{4}} 2^{\frac{3}{4}} {\left(2 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} d + 3 \, a\right)} \log\left(\sqrt{3} x^{2} + 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) + \frac{1}{144} \cdot 3^{\frac{3}{4}} 2^{\frac{3}{4}} {\left(2 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} d - 3 \, a\right)} \log\left(\sqrt{3} x^{2} - 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right)"," ",0,"1/24*3^(3/4)*2^(3/4)*a*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x + 3^(1/4)*2^(3/4))) + 1/24*3^(3/4)*2^(3/4)*a*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x - 3^(1/4)*2^(3/4))) + 1/144*3^(3/4)*2^(3/4)*(2*3^(1/4)*2^(1/4)*d + 3*a)*log(sqrt(3)*x^2 + 3^(1/4)*2^(3/4)*x + sqrt(2)) + 1/144*3^(3/4)*2^(3/4)*(2*3^(1/4)*2^(1/4)*d - 3*a)*log(sqrt(3)*x^2 - 3^(1/4)*2^(3/4)*x + sqrt(2))","A",0
161,1,113,0,3.062433," ","integrate((d*x^3+b*x)/(3*x^4+2),x, algorithm=""maxima"")","-\frac{1}{12} \, \sqrt{3} \sqrt{2} b \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x + 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + \frac{1}{12} \, \sqrt{3} \sqrt{2} b \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x - 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + \frac{1}{12} \, d \log\left(\sqrt{3} x^{2} + 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) + \frac{1}{12} \, d \log\left(\sqrt{3} x^{2} - 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right)"," ",0,"-1/12*sqrt(3)*sqrt(2)*b*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x + 3^(1/4)*2^(3/4))) + 1/12*sqrt(3)*sqrt(2)*b*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x - 3^(1/4)*2^(3/4))) + 1/12*d*log(sqrt(3)*x^2 + 3^(1/4)*2^(3/4)*x + sqrt(2)) + 1/12*d*log(sqrt(3)*x^2 - 3^(1/4)*2^(3/4)*x + sqrt(2))","B",0
162,1,171,0,3.052658," ","integrate((d*x^3+b*x+a)/(3*x^4+2),x, algorithm=""maxima"")","\frac{1}{144} \cdot 3^{\frac{3}{4}} 2^{\frac{3}{4}} {\left(2 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} d + 3 \, a\right)} \log\left(\sqrt{3} x^{2} + 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) + \frac{1}{144} \cdot 3^{\frac{3}{4}} 2^{\frac{3}{4}} {\left(2 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} d - 3 \, a\right)} \log\left(\sqrt{3} x^{2} - 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) + \frac{1}{24} \, \sqrt{3} {\left(3^{\frac{1}{4}} 2^{\frac{3}{4}} a - 2 \, \sqrt{2} b\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x + 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + \frac{1}{24} \, \sqrt{3} {\left(3^{\frac{1}{4}} 2^{\frac{3}{4}} a + 2 \, \sqrt{2} b\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x - 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right)"," ",0,"1/144*3^(3/4)*2^(3/4)*(2*3^(1/4)*2^(1/4)*d + 3*a)*log(sqrt(3)*x^2 + 3^(1/4)*2^(3/4)*x + sqrt(2)) + 1/144*3^(3/4)*2^(3/4)*(2*3^(1/4)*2^(1/4)*d - 3*a)*log(sqrt(3)*x^2 - 3^(1/4)*2^(3/4)*x + sqrt(2)) + 1/24*sqrt(3)*(3^(1/4)*2^(3/4)*a - 2*sqrt(2)*b)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x + 3^(1/4)*2^(3/4))) + 1/24*sqrt(3)*(3^(1/4)*2^(3/4)*a + 2*sqrt(2)*b)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x - 3^(1/4)*2^(3/4)))","A",0
163,1,152,0,3.025604," ","integrate((d*x^3+c*x^2)/(3*x^4+2),x, algorithm=""maxima"")","\frac{1}{72} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(3^{\frac{1}{4}} 2^{\frac{3}{4}} d - \sqrt{3} c\right)} \log\left(\sqrt{3} x^{2} + 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) + \frac{1}{72} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(3^{\frac{1}{4}} 2^{\frac{3}{4}} d + \sqrt{3} c\right)} \log\left(\sqrt{3} x^{2} - 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) + \frac{1}{12} \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} c \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x + 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + \frac{1}{12} \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} c \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x - 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right)"," ",0,"1/72*3^(3/4)*2^(1/4)*(3^(1/4)*2^(3/4)*d - sqrt(3)*c)*log(sqrt(3)*x^2 + 3^(1/4)*2^(3/4)*x + sqrt(2)) + 1/72*3^(3/4)*2^(1/4)*(3^(1/4)*2^(3/4)*d + sqrt(3)*c)*log(sqrt(3)*x^2 - 3^(1/4)*2^(3/4)*x + sqrt(2)) + 1/12*3^(1/4)*2^(1/4)*c*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x + 3^(1/4)*2^(3/4))) + 1/12*3^(1/4)*2^(1/4)*c*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x - 3^(1/4)*2^(3/4)))","A",0
164,1,195,0,2.993009," ","integrate((d*x^3+c*x^2+a)/(3*x^4+2),x, algorithm=""maxima"")","-\frac{1}{144} \cdot 3^{\frac{3}{4}} 2^{\frac{3}{4}} {\left(\sqrt{3} \sqrt{2} c - 2 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} d - 3 \, a\right)} \log\left(\sqrt{3} x^{2} + 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) + \frac{1}{144} \cdot 3^{\frac{3}{4}} 2^{\frac{3}{4}} {\left(\sqrt{3} \sqrt{2} c + 2 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} d - 3 \, a\right)} \log\left(\sqrt{3} x^{2} - 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) + \frac{1}{72} \, \sqrt{3} {\left(3 \cdot 3^{\frac{1}{4}} 2^{\frac{3}{4}} a + 2 \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} c\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x + 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + \frac{1}{72} \, \sqrt{3} {\left(3 \cdot 3^{\frac{1}{4}} 2^{\frac{3}{4}} a + 2 \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} c\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x - 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right)"," ",0,"-1/144*3^(3/4)*2^(3/4)*(sqrt(3)*sqrt(2)*c - 2*3^(1/4)*2^(1/4)*d - 3*a)*log(sqrt(3)*x^2 + 3^(1/4)*2^(3/4)*x + sqrt(2)) + 1/144*3^(3/4)*2^(3/4)*(sqrt(3)*sqrt(2)*c + 2*3^(1/4)*2^(1/4)*d - 3*a)*log(sqrt(3)*x^2 - 3^(1/4)*2^(3/4)*x + sqrt(2)) + 1/72*sqrt(3)*(3*3^(1/4)*2^(3/4)*a + 2*3^(3/4)*2^(1/4)*c)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x + 3^(1/4)*2^(3/4))) + 1/72*sqrt(3)*(3*3^(1/4)*2^(3/4)*a + 2*3^(3/4)*2^(1/4)*c)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x - 3^(1/4)*2^(3/4)))","A",0
165,1,174,0,3.017049," ","integrate((d*x^3+c*x^2+b*x)/(3*x^4+2),x, algorithm=""maxima"")","\frac{1}{72} \, \sqrt{3} \sqrt{2} {\left(3^{\frac{3}{4}} 2^{\frac{3}{4}} c - 6 \, b\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x + 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + \frac{1}{72} \, \sqrt{3} \sqrt{2} {\left(3^{\frac{3}{4}} 2^{\frac{3}{4}} c + 6 \, b\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x - 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + \frac{1}{72} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(3^{\frac{1}{4}} 2^{\frac{3}{4}} d - \sqrt{3} c\right)} \log\left(\sqrt{3} x^{2} + 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) + \frac{1}{72} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(3^{\frac{1}{4}} 2^{\frac{3}{4}} d + \sqrt{3} c\right)} \log\left(\sqrt{3} x^{2} - 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right)"," ",0,"1/72*sqrt(3)*sqrt(2)*(3^(3/4)*2^(3/4)*c - 6*b)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x + 3^(1/4)*2^(3/4))) + 1/72*sqrt(3)*sqrt(2)*(3^(3/4)*2^(3/4)*c + 6*b)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x - 3^(1/4)*2^(3/4))) + 1/72*3^(3/4)*2^(1/4)*(3^(1/4)*2^(3/4)*d - sqrt(3)*c)*log(sqrt(3)*x^2 + 3^(1/4)*2^(3/4)*x + sqrt(2)) + 1/72*3^(3/4)*2^(1/4)*(3^(1/4)*2^(3/4)*d + sqrt(3)*c)*log(sqrt(3)*x^2 - 3^(1/4)*2^(3/4)*x + sqrt(2))","A",0
166,1,207,0,2.992972," ","integrate((d*x^3+c*x^2+b*x+a)/(3*x^4+2),x, algorithm=""maxima"")","-\frac{1}{144} \cdot 3^{\frac{3}{4}} 2^{\frac{3}{4}} {\left(\sqrt{3} \sqrt{2} c - 2 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} d - 3 \, a\right)} \log\left(\sqrt{3} x^{2} + 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) + \frac{1}{144} \cdot 3^{\frac{3}{4}} 2^{\frac{3}{4}} {\left(\sqrt{3} \sqrt{2} c + 2 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} d - 3 \, a\right)} \log\left(\sqrt{3} x^{2} - 3^{\frac{1}{4}} 2^{\frac{3}{4}} x + \sqrt{2}\right) + \frac{1}{72} \, \sqrt{3} {\left(3 \cdot 3^{\frac{1}{4}} 2^{\frac{3}{4}} a + 2 \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} c - 6 \, \sqrt{2} b\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x + 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right) + \frac{1}{72} \, \sqrt{3} {\left(3 \cdot 3^{\frac{1}{4}} 2^{\frac{3}{4}} a + 2 \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} c + 6 \, \sqrt{2} b\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} {\left(2 \, \sqrt{3} x - 3^{\frac{1}{4}} 2^{\frac{3}{4}}\right)}\right)"," ",0,"-1/144*3^(3/4)*2^(3/4)*(sqrt(3)*sqrt(2)*c - 2*3^(1/4)*2^(1/4)*d - 3*a)*log(sqrt(3)*x^2 + 3^(1/4)*2^(3/4)*x + sqrt(2)) + 1/144*3^(3/4)*2^(3/4)*(sqrt(3)*sqrt(2)*c + 2*3^(1/4)*2^(1/4)*d - 3*a)*log(sqrt(3)*x^2 - 3^(1/4)*2^(3/4)*x + sqrt(2)) + 1/72*sqrt(3)*(3*3^(1/4)*2^(3/4)*a + 2*3^(3/4)*2^(1/4)*c - 6*sqrt(2)*b)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x + 3^(1/4)*2^(3/4))) + 1/72*sqrt(3)*(3*3^(1/4)*2^(3/4)*a + 2*3^(3/4)*2^(1/4)*c + 6*sqrt(2)*b)*arctan(1/6*3^(3/4)*2^(1/4)*(2*sqrt(3)*x - 3^(1/4)*2^(3/4)))","A",0
167,1,6,0,1.346742," ","integrate((x^3+x^2+x+1)/(-x^4+1),x, algorithm=""maxima"")","-\log\left(x - 1\right)"," ",0,"-log(x - 1)","A",0
168,1,76,0,3.003684," ","integrate((x^3+x^2+x+1)/(x^4+1),x, algorithm=""maxima"")","-\frac{1}{4} \, \sqrt{2} {\left(\sqrt{2} - 2\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{1}{4} \, \sqrt{2} {\left(\sqrt{2} + 2\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,"-1/4*sqrt(2)*(sqrt(2) - 2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 1/4*sqrt(2)*(sqrt(2) + 2)*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
169,1,160,0,3.024179," ","integrate((x^3+x^2+x+1)/(-b*x^4+a),x, algorithm=""maxima"")","-\frac{{\left(\sqrt{a} - \sqrt{b}\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{2 \, \sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(\sqrt{a} - \sqrt{b}\right)} \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{4 \, \sqrt{a} b} - \frac{{\left(\sqrt{a} + \sqrt{b}\right)} \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{4 \, \sqrt{a} b} - \frac{{\left(\sqrt{a} + \sqrt{b}\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{4 \, \sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}"," ",0,"-1/2*(sqrt(a) - sqrt(b))*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - 1/4*(sqrt(a) - sqrt(b))*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*b) - 1/4*(sqrt(a) + sqrt(b))*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*b) - 1/4*(sqrt(a) + sqrt(b))*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b))","A",0
170,1,296,0,2.975053," ","integrate((x^3+x^2+x+1)/(b*x^4+a),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} - \sqrt{a} \sqrt{b} + b\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{8 \, a^{\frac{3}{4}} b^{\frac{5}{4}}} + \frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} + \sqrt{a} \sqrt{b} - b\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{8 \, a^{\frac{3}{4}} b^{\frac{5}{4}}} + \frac{{\left({\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{a}\right)} b + {\left(\sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} + 2 \, a\right)} \sqrt{b} - 2 \, a \sqrt{b}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{4 \, a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{5}{4}}} + \frac{{\left({\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{a}\right)} b + {\left(\sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} - 2 \, a\right)} \sqrt{b} + 2 \, a \sqrt{b}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{4 \, a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{5}{4}}}"," ",0,"1/8*sqrt(2)*(sqrt(2)*a^(3/4)*b^(1/4) - sqrt(a)*sqrt(b) + b)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(5/4)) + 1/8*sqrt(2)*(sqrt(2)*a^(3/4)*b^(1/4) + sqrt(a)*sqrt(b) - b)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(5/4)) + 1/4*((sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(a))*b + (sqrt(2)*a^(3/4)*b^(1/4) + 2*a)*sqrt(b) - 2*a*sqrt(b))*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(5/4)) + 1/4*((sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(a))*b + (sqrt(2)*a^(3/4)*b^(1/4) - 2*a)*sqrt(b) + 2*a*sqrt(b))*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(5/4))","A",0
171,1,202,0,3.103573," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x, algorithm=""maxima"")","-\frac{g x}{b} + \frac{\frac{2 \, {\left(b^{\frac{3}{2}} c - \sqrt{a} b e + a \sqrt{b} g\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{{\left(b^{\frac{3}{2}} d - \sqrt{a} b f\right)} \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} b} - \frac{{\left(b^{\frac{3}{2}} d + \sqrt{a} b f\right)} \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} b} - \frac{{\left(b^{\frac{3}{2}} c + \sqrt{a} b e + a \sqrt{b} g\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{4 \, b}"," ",0,"-g*x/b + 1/4*(2*(b^(3/2)*c - sqrt(a)*b*e + a*sqrt(b)*g)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + (b^(3/2)*d - sqrt(a)*b*f)*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*b) - (b^(3/2)*d + sqrt(a)*b*f)*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*b) - (b^(3/2)*c + sqrt(a)*b*e + a*sqrt(b)*g)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/b","A",0
172,1,224,0,3.113876," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^2,x, algorithm=""maxima"")","-\frac{b e x^{3} + b d x^{2} + a f + {\left(b c + a g\right)} x}{4 \, {\left(a b^{2} x^{4} - a^{2} b\right)}} + \frac{\frac{2 \, \sqrt{b} d \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a}} - \frac{2 \, \sqrt{b} d \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a}} + \frac{2 \, {\left(3 \, b^{\frac{3}{2}} c - \sqrt{a} b e - a \sqrt{b} g\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(3 \, b^{\frac{3}{2}} c + \sqrt{a} b e - a \sqrt{b} g\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{16 \, a b}"," ",0,"-1/4*(b*e*x^3 + b*d*x^2 + a*f + (b*c + a*g)*x)/(a*b^2*x^4 - a^2*b) + 1/16*(2*sqrt(b)*d*log(sqrt(b)*x^2 + sqrt(a))/sqrt(a) - 2*sqrt(b)*d*log(sqrt(b)*x^2 - sqrt(a))/sqrt(a) + 2*(3*b^(3/2)*c - sqrt(a)*b*e - a*sqrt(b)*g)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (3*b^(3/2)*c + sqrt(a)*b*e - a*sqrt(b)*g)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/(a*b)","A",0
173,1,284,0,3.003736," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^3,x, algorithm=""maxima"")","-\frac{5 \, b^{2} e x^{7} + 6 \, b^{2} d x^{6} - 9 \, a b e x^{3} + {\left(7 \, b^{2} c - a b g\right)} x^{5} - 10 \, a b d x^{2} - 4 \, a^{2} f - {\left(11 \, a b c + 3 \, a^{2} g\right)} x}{32 \, {\left(a^{2} b^{3} x^{8} - 2 \, a^{3} b^{2} x^{4} + a^{4} b\right)}} + \frac{\frac{12 \, \sqrt{b} d \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a}} - \frac{12 \, \sqrt{b} d \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a}} + \frac{2 \, {\left(21 \, b^{\frac{3}{2}} c - 5 \, \sqrt{a} b e - 3 \, a \sqrt{b} g\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(21 \, b^{\frac{3}{2}} c + 5 \, \sqrt{a} b e - 3 \, a \sqrt{b} g\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{128 \, a^{2} b}"," ",0,"-1/32*(5*b^2*e*x^7 + 6*b^2*d*x^6 - 9*a*b*e*x^3 + (7*b^2*c - a*b*g)*x^5 - 10*a*b*d*x^2 - 4*a^2*f - (11*a*b*c + 3*a^2*g)*x)/(a^2*b^3*x^8 - 2*a^3*b^2*x^4 + a^4*b) + 1/128*(12*sqrt(b)*d*log(sqrt(b)*x^2 + sqrt(a))/sqrt(a) - 12*sqrt(b)*d*log(sqrt(b)*x^2 - sqrt(a))/sqrt(a) + 2*(21*b^(3/2)*c - 5*sqrt(a)*b*e - 3*a*sqrt(b)*g)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (21*b^(3/2)*c + 5*sqrt(a)*b*e - 3*a*sqrt(b)*g)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/(a^2*b)","A",0
174,1,345,0,3.179169," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^4,x, algorithm=""maxima"")","-\frac{45 \, b^{3} e x^{11} + 60 \, b^{3} d x^{10} - 126 \, a b^{2} e x^{7} - 160 \, a b^{2} d x^{6} + 7 \, {\left(11 \, b^{3} c - a b^{2} g\right)} x^{9} + 113 \, a^{2} b e x^{3} + 132 \, a^{2} b d x^{2} - 18 \, {\left(11 \, a b^{2} c - a^{2} b g\right)} x^{5} + 32 \, a^{3} f + 3 \, {\left(51 \, a^{2} b c + 7 \, a^{3} g\right)} x}{384 \, {\left(a^{3} b^{4} x^{12} - 3 \, a^{4} b^{3} x^{8} + 3 \, a^{5} b^{2} x^{4} - a^{6} b\right)}} + \frac{\frac{40 \, \sqrt{b} d \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a}} - \frac{40 \, \sqrt{b} d \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a}} + \frac{2 \, {\left(77 \, b^{\frac{3}{2}} c - 15 \, \sqrt{a} b e - 7 \, a \sqrt{b} g\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(77 \, b^{\frac{3}{2}} c + 15 \, \sqrt{a} b e - 7 \, a \sqrt{b} g\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{512 \, a^{3} b}"," ",0,"-1/384*(45*b^3*e*x^11 + 60*b^3*d*x^10 - 126*a*b^2*e*x^7 - 160*a*b^2*d*x^6 + 7*(11*b^3*c - a*b^2*g)*x^9 + 113*a^2*b*e*x^3 + 132*a^2*b*d*x^2 - 18*(11*a*b^2*c - a^2*b*g)*x^5 + 32*a^3*f + 3*(51*a^2*b*c + 7*a^3*g)*x)/(a^3*b^4*x^12 - 3*a^4*b^3*x^8 + 3*a^5*b^2*x^4 - a^6*b) + 1/512*(40*sqrt(b)*d*log(sqrt(b)*x^2 + sqrt(a))/sqrt(a) - 40*sqrt(b)*d*log(sqrt(b)*x^2 - sqrt(a))/sqrt(a) + 2*(77*b^(3/2)*c - 15*sqrt(a)*b*e - 7*a*sqrt(b)*g)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (77*b^(3/2)*c + 15*sqrt(a)*b*e - 7*a*sqrt(b)*g)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/(a^3*b)","A",0
175,1,328,0,3.027992," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a),x, algorithm=""maxima"")","\frac{g x}{b} + \frac{\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} f + b^{2} c - \sqrt{a} b^{\frac{3}{2}} e - a b g\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{5}{4}}} + \frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} f - b^{2} c + \sqrt{a} b^{\frac{3}{2}} e + a b g\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{5}{4}}} + \frac{2 \, {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{9}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{7}{4}} e - \sqrt{2} a^{\frac{5}{4}} b^{\frac{5}{4}} g - 2 \, \sqrt{a} b^{2} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{5}{4}}} + \frac{2 \, {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{9}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{7}{4}} e - \sqrt{2} a^{\frac{5}{4}} b^{\frac{5}{4}} g + 2 \, \sqrt{a} b^{2} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{5}{4}}}}{8 \, b}"," ",0,"g*x/b + 1/8*(sqrt(2)*(sqrt(2)*a^(3/4)*b^(5/4)*f + b^2*c - sqrt(a)*b^(3/2)*e - a*b*g)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(5/4)) + sqrt(2)*(sqrt(2)*a^(3/4)*b^(5/4)*f - b^2*c + sqrt(a)*b^(3/2)*e + a*b*g)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(5/4)) + 2*(sqrt(2)*a^(1/4)*b^(9/4)*c + sqrt(2)*a^(3/4)*b^(7/4)*e - sqrt(2)*a^(5/4)*b^(5/4)*g - 2*sqrt(a)*b^2*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(5/4)) + 2*(sqrt(2)*a^(1/4)*b^(9/4)*c + sqrt(2)*a^(3/4)*b^(7/4)*e - sqrt(2)*a^(5/4)*b^(5/4)*g + 2*sqrt(a)*b^2*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(5/4)))/b","A",0
176,1,350,0,3.003313," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x, algorithm=""maxima"")","\frac{b e x^{3} + b d x^{2} - a f + {\left(b c - a g\right)} x}{4 \, {\left(a b^{2} x^{4} + a^{2} b\right)}} + \frac{\frac{\sqrt{2} {\left(3 \, b^{\frac{3}{2}} c - \sqrt{a} b e + a \sqrt{b} g\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(3 \, b^{\frac{3}{2}} c - \sqrt{a} b e + a \sqrt{b} g\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g - 4 \, \sqrt{a} b^{\frac{3}{2}} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g + 4 \, \sqrt{a} b^{\frac{3}{2}} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{32 \, a b}"," ",0,"1/4*(b*e*x^3 + b*d*x^2 - a*f + (b*c - a*g)*x)/(a*b^2*x^4 + a^2*b) + 1/32*(sqrt(2)*(3*b^(3/2)*c - sqrt(a)*b*e + a*sqrt(b)*g)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(3*b^(3/2)*c - sqrt(a)*b*e + a*sqrt(b)*g)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(3*sqrt(2)*a^(1/4)*b^(7/4)*c + sqrt(2)*a^(3/4)*b^(5/4)*e + sqrt(2)*a^(5/4)*b^(3/4)*g - 4*sqrt(a)*b^(3/2)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(3*sqrt(2)*a^(1/4)*b^(7/4)*c + sqrt(2)*a^(3/4)*b^(5/4)*e + sqrt(2)*a^(5/4)*b^(3/4)*g + 4*sqrt(a)*b^(3/2)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/(a*b)","A",0
177,1,412,0,3.029439," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x, algorithm=""maxima"")","\frac{5 \, b^{2} e x^{7} + 6 \, b^{2} d x^{6} + 9 \, a b e x^{3} + {\left(7 \, b^{2} c + a b g\right)} x^{5} + 10 \, a b d x^{2} - 4 \, a^{2} f + {\left(11 \, a b c - 3 \, a^{2} g\right)} x}{32 \, {\left(a^{2} b^{3} x^{8} + 2 \, a^{3} b^{2} x^{4} + a^{4} b\right)}} + \frac{\frac{\sqrt{2} {\left(21 \, b^{\frac{3}{2}} c - 5 \, \sqrt{a} b e + 3 \, a \sqrt{b} g\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(21 \, b^{\frac{3}{2}} c - 5 \, \sqrt{a} b e + 3 \, a \sqrt{b} g\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(21 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + 5 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + 3 \, \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g - 24 \, \sqrt{a} b^{\frac{3}{2}} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(21 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + 5 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + 3 \, \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g + 24 \, \sqrt{a} b^{\frac{3}{2}} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{256 \, a^{2} b}"," ",0,"1/32*(5*b^2*e*x^7 + 6*b^2*d*x^6 + 9*a*b*e*x^3 + (7*b^2*c + a*b*g)*x^5 + 10*a*b*d*x^2 - 4*a^2*f + (11*a*b*c - 3*a^2*g)*x)/(a^2*b^3*x^8 + 2*a^3*b^2*x^4 + a^4*b) + 1/256*(sqrt(2)*(21*b^(3/2)*c - 5*sqrt(a)*b*e + 3*a*sqrt(b)*g)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(21*b^(3/2)*c - 5*sqrt(a)*b*e + 3*a*sqrt(b)*g)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(21*sqrt(2)*a^(1/4)*b^(7/4)*c + 5*sqrt(2)*a^(3/4)*b^(5/4)*e + 3*sqrt(2)*a^(5/4)*b^(3/4)*g - 24*sqrt(a)*b^(3/2)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(21*sqrt(2)*a^(1/4)*b^(7/4)*c + 5*sqrt(2)*a^(3/4)*b^(5/4)*e + 3*sqrt(2)*a^(5/4)*b^(3/4)*g + 24*sqrt(a)*b^(3/2)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/(a^2*b)","A",0
178,1,472,0,3.120170," ","integrate((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x, algorithm=""maxima"")","\frac{45 \, b^{3} e x^{11} + 60 \, b^{3} d x^{10} + 126 \, a b^{2} e x^{7} + 160 \, a b^{2} d x^{6} + 7 \, {\left(11 \, b^{3} c + a b^{2} g\right)} x^{9} + 113 \, a^{2} b e x^{3} + 132 \, a^{2} b d x^{2} + 18 \, {\left(11 \, a b^{2} c + a^{2} b g\right)} x^{5} - 32 \, a^{3} f + 3 \, {\left(51 \, a^{2} b c - 7 \, a^{3} g\right)} x}{384 \, {\left(a^{3} b^{4} x^{12} + 3 \, a^{4} b^{3} x^{8} + 3 \, a^{5} b^{2} x^{4} + a^{6} b\right)}} + \frac{\frac{\sqrt{2} {\left(77 \, b^{\frac{3}{2}} c - 15 \, \sqrt{a} b e + 7 \, a \sqrt{b} g\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(77 \, b^{\frac{3}{2}} c - 15 \, \sqrt{a} b e + 7 \, a \sqrt{b} g\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(77 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + 15 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + 7 \, \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g - 80 \, \sqrt{a} b^{\frac{3}{2}} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(77 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + 15 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + 7 \, \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g + 80 \, \sqrt{a} b^{\frac{3}{2}} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{1024 \, a^{3} b}"," ",0,"1/384*(45*b^3*e*x^11 + 60*b^3*d*x^10 + 126*a*b^2*e*x^7 + 160*a*b^2*d*x^6 + 7*(11*b^3*c + a*b^2*g)*x^9 + 113*a^2*b*e*x^3 + 132*a^2*b*d*x^2 + 18*(11*a*b^2*c + a^2*b*g)*x^5 - 32*a^3*f + 3*(51*a^2*b*c - 7*a^3*g)*x)/(a^3*b^4*x^12 + 3*a^4*b^3*x^8 + 3*a^5*b^2*x^4 + a^6*b) + 1/1024*(sqrt(2)*(77*b^(3/2)*c - 15*sqrt(a)*b*e + 7*a*sqrt(b)*g)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(77*b^(3/2)*c - 15*sqrt(a)*b*e + 7*a*sqrt(b)*g)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(77*sqrt(2)*a^(1/4)*b^(7/4)*c + 15*sqrt(2)*a^(3/4)*b^(5/4)*e + 7*sqrt(2)*a^(5/4)*b^(3/4)*g - 80*sqrt(a)*b^(3/2)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(77*sqrt(2)*a^(1/4)*b^(7/4)*c + 15*sqrt(2)*a^(3/4)*b^(5/4)*e + 7*sqrt(2)*a^(5/4)*b^(3/4)*g + 80*sqrt(a)*b^(3/2)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/(a^3*b)","A",0
179,1,15,0,1.294917," ","integrate((-x^4+1)^3/(x^3+x^2+x+1)^3,x, algorithm=""maxima"")","-\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
180,1,12,0,1.291708," ","integrate((-x^4+1)^2/(x^3+x^2+x+1)^2,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} - x^{2} + x"," ",0,"1/3*x^3 - x^2 + x","A",0
181,1,7,0,1.294629," ","integrate((-x^4+1)/(x^3+x^2+x+1),x, algorithm=""maxima"")","-\frac{1}{2} \, x^{2} + x"," ",0,"-1/2*x^2 + x","A",0
182,1,6,0,1.371868," ","integrate((x^3+x^2+x+1)/(-x^4+1),x, algorithm=""maxima"")","-\log\left(x - 1\right)"," ",0,"-log(x - 1)","A",0
183,1,7,0,1.295630," ","integrate((x^3+x^2+x+1)^2/(-x^4+1)^2,x, algorithm=""maxima"")","-\frac{1}{x - 1}"," ",0,"-1/(x - 1)","A",0
184,1,12,0,1.301517," ","integrate((x^3+x^2+x+1)^3/(-x^4+1)^3,x, algorithm=""maxima"")","\frac{1}{2 \, {\left(x^{2} - 2 \, x + 1\right)}}"," ",0,"1/2/(x^2 - 2*x + 1)","A",0
185,1,17,0,1.324950," ","integrate((x^3+x^2+x+1)^4/(-x^4+1)^4,x, algorithm=""maxima"")","-\frac{1}{3 \, {\left(x^{3} - 3 \, x^{2} + 3 \, x - 1\right)}}"," ",0,"-1/3/(x^3 - 3*x^2 + 3*x - 1)","B",0
186,1,222,0,3.039469," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x, algorithm=""maxima"")","-\frac{h x^{2} + 2 \, g x}{2 \, b} + \frac{\frac{2 \, {\left(b^{\frac{3}{2}} c - \sqrt{a} b e + a \sqrt{b} g\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{{\left(b^{\frac{3}{2}} d - \sqrt{a} b f + a \sqrt{b} h\right)} \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} b} - \frac{{\left(b^{\frac{3}{2}} d + \sqrt{a} b f + a \sqrt{b} h\right)} \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} b} - \frac{{\left(b^{\frac{3}{2}} c + \sqrt{a} b e + a \sqrt{b} g\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{4 \, b}"," ",0,"-1/2*(h*x^2 + 2*g*x)/b + 1/4*(2*(b^(3/2)*c - sqrt(a)*b*e + a*sqrt(b)*g)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + (b^(3/2)*d - sqrt(a)*b*f + a*sqrt(b)*h)*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*b) - (b^(3/2)*d + sqrt(a)*b*f + a*sqrt(b)*h)*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*b) - (b^(3/2)*c + sqrt(a)*b*e + a*sqrt(b)*g)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/b","A",0
187,1,240,0,3.025330," ","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=""maxima"")","-\frac{2 \, i x^{3} + 3 \, h x^{2} + 6 \, g x}{6 \, b} + \frac{\frac{2 \, {\left(b^{\frac{3}{2}} c - \sqrt{a} b e + a \sqrt{b} g - a^{\frac{3}{2}} i\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{{\left(b^{\frac{3}{2}} d - \sqrt{a} b f + a \sqrt{b} h\right)} \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} b} - \frac{{\left(b^{\frac{3}{2}} d + \sqrt{a} b f + a \sqrt{b} h\right)} \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} b} - \frac{{\left(b^{\frac{3}{2}} c + \sqrt{a} b e + a \sqrt{b} g + a^{\frac{3}{2}} i\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{4 \, b}"," ",0,"-1/6*(2*i*x^3 + 3*h*x^2 + 6*g*x)/b + 1/4*(2*(b^(3/2)*c - sqrt(a)*b*e + a*sqrt(b)*g - a^(3/2)*i)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + (b^(3/2)*d - sqrt(a)*b*f + a*sqrt(b)*h)*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*b) - (b^(3/2)*d + sqrt(a)*b*f + a*sqrt(b)*h)*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*b) - (b^(3/2)*c + sqrt(a)*b*e + a*sqrt(b)*g + a^(3/2)*i)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/b","A",0
188,1,257,0,3.073822," ","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=""maxima"")","-\frac{3 \, j x^{4} + 4 \, i x^{3} + 6 \, h x^{2} + 12 \, g x}{12 \, b} + \frac{\frac{2 \, {\left(b^{\frac{3}{2}} c - \sqrt{a} b e + a \sqrt{b} g - a^{\frac{3}{2}} i\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{{\left(b^{\frac{3}{2}} d - \sqrt{a} b f + a \sqrt{b} h - a^{\frac{3}{2}} j\right)} \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} b} - \frac{{\left(b^{\frac{3}{2}} d + \sqrt{a} b f + a \sqrt{b} h + a^{\frac{3}{2}} j\right)} \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} b} - \frac{{\left(b^{\frac{3}{2}} c + \sqrt{a} b e + a \sqrt{b} g + a^{\frac{3}{2}} i\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{4 \, b}"," ",0,"-1/12*(3*j*x^4 + 4*i*x^3 + 6*h*x^2 + 12*g*x)/b + 1/4*(2*(b^(3/2)*c - sqrt(a)*b*e + a*sqrt(b)*g - a^(3/2)*i)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + (b^(3/2)*d - sqrt(a)*b*f + a*sqrt(b)*h - a^(3/2)*j)*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*b) - (b^(3/2)*d + sqrt(a)*b*f + a*sqrt(b)*h + a^(3/2)*j)*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*b) - (b^(3/2)*c + sqrt(a)*b*e + a*sqrt(b)*g + a^(3/2)*i)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/b","A",0
189,1,351,0,3.046651," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a),x, algorithm=""maxima"")","\frac{h x^{2} + 2 \, g x}{2 \, b} + \frac{\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} f + b^{2} c - \sqrt{a} b^{\frac{3}{2}} e - a b g\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{5}{4}}} + \frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} f - b^{2} c + \sqrt{a} b^{\frac{3}{2}} e + a b g\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{5}{4}}} + \frac{2 \, {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{9}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{7}{4}} e - \sqrt{2} a^{\frac{5}{4}} b^{\frac{5}{4}} g - 2 \, \sqrt{a} b^{2} d + 2 \, a^{\frac{3}{2}} b h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{5}{4}}} + \frac{2 \, {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{9}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{7}{4}} e - \sqrt{2} a^{\frac{5}{4}} b^{\frac{5}{4}} g + 2 \, \sqrt{a} b^{2} d - 2 \, a^{\frac{3}{2}} b h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{5}{4}}}}{8 \, b}"," ",0,"1/2*(h*x^2 + 2*g*x)/b + 1/8*(sqrt(2)*(sqrt(2)*a^(3/4)*b^(5/4)*f + b^2*c - sqrt(a)*b^(3/2)*e - a*b*g)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(5/4)) + sqrt(2)*(sqrt(2)*a^(3/4)*b^(5/4)*f - b^2*c + sqrt(a)*b^(3/2)*e + a*b*g)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(5/4)) + 2*(sqrt(2)*a^(1/4)*b^(9/4)*c + sqrt(2)*a^(3/4)*b^(7/4)*e - sqrt(2)*a^(5/4)*b^(5/4)*g - 2*sqrt(a)*b^2*d + 2*a^(3/2)*b*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(5/4)) + 2*(sqrt(2)*a^(1/4)*b^(9/4)*c + sqrt(2)*a^(3/4)*b^(7/4)*e - sqrt(2)*a^(5/4)*b^(5/4)*g + 2*sqrt(a)*b^2*d - 2*a^(3/2)*b*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(5/4)))/b","A",0
190,1,399,0,3.076994," ","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=""maxima"")","\frac{2 \, i x^{3} + 3 \, h x^{2} + 6 \, g x}{6 \, b} + \frac{\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} f + b^{2} c - \sqrt{a} b^{\frac{3}{2}} e - a b g + a^{\frac{3}{2}} \sqrt{b} i\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{5}{4}}} + \frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} f - b^{2} c + \sqrt{a} b^{\frac{3}{2}} e + a b g - a^{\frac{3}{2}} \sqrt{b} i\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{5}{4}}} + \frac{2 \, {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{9}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{7}{4}} e - \sqrt{2} a^{\frac{5}{4}} b^{\frac{5}{4}} g - \sqrt{2} a^{\frac{7}{4}} b^{\frac{3}{4}} i - 2 \, \sqrt{a} b^{2} d + 2 \, a^{\frac{3}{2}} b h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{5}{4}}} + \frac{2 \, {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{9}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{7}{4}} e - \sqrt{2} a^{\frac{5}{4}} b^{\frac{5}{4}} g - \sqrt{2} a^{\frac{7}{4}} b^{\frac{3}{4}} i + 2 \, \sqrt{a} b^{2} d - 2 \, a^{\frac{3}{2}} b h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{5}{4}}}}{8 \, b}"," ",0,"1/6*(2*i*x^3 + 3*h*x^2 + 6*g*x)/b + 1/8*(sqrt(2)*(sqrt(2)*a^(3/4)*b^(5/4)*f + b^2*c - sqrt(a)*b^(3/2)*e - a*b*g + a^(3/2)*sqrt(b)*i)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(5/4)) + sqrt(2)*(sqrt(2)*a^(3/4)*b^(5/4)*f - b^2*c + sqrt(a)*b^(3/2)*e + a*b*g - a^(3/2)*sqrt(b)*i)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(5/4)) + 2*(sqrt(2)*a^(1/4)*b^(9/4)*c + sqrt(2)*a^(3/4)*b^(7/4)*e - sqrt(2)*a^(5/4)*b^(5/4)*g - sqrt(2)*a^(7/4)*b^(3/4)*i - 2*sqrt(a)*b^2*d + 2*a^(3/2)*b*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(5/4)) + 2*(sqrt(2)*a^(1/4)*b^(9/4)*c + sqrt(2)*a^(3/4)*b^(7/4)*e - sqrt(2)*a^(5/4)*b^(5/4)*g - sqrt(2)*a^(7/4)*b^(3/4)*i + 2*sqrt(a)*b^2*d - 2*a^(3/2)*b*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(5/4)))/b","A",0
191,1,429,0,3.155771," ","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=""maxima"")","\frac{3 \, j x^{4} + 4 \, i x^{3} + 6 \, h x^{2} + 12 \, g x}{12 \, b} + \frac{\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} f - \sqrt{2} a^{\frac{7}{4}} b^{\frac{1}{4}} j + b^{2} c - \sqrt{a} b^{\frac{3}{2}} e - a b g + a^{\frac{3}{2}} \sqrt{b} i\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{5}{4}}} + \frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} f - \sqrt{2} a^{\frac{7}{4}} b^{\frac{1}{4}} j - b^{2} c + \sqrt{a} b^{\frac{3}{2}} e + a b g - a^{\frac{3}{2}} \sqrt{b} i\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{5}{4}}} + \frac{2 \, {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{9}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{7}{4}} e - \sqrt{2} a^{\frac{5}{4}} b^{\frac{5}{4}} g - \sqrt{2} a^{\frac{7}{4}} b^{\frac{3}{4}} i - 2 \, \sqrt{a} b^{2} d + 2 \, a^{\frac{3}{2}} b h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{5}{4}}} + \frac{2 \, {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{9}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{7}{4}} e - \sqrt{2} a^{\frac{5}{4}} b^{\frac{5}{4}} g - \sqrt{2} a^{\frac{7}{4}} b^{\frac{3}{4}} i + 2 \, \sqrt{a} b^{2} d - 2 \, a^{\frac{3}{2}} b h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{5}{4}}}}{8 \, b}"," ",0,"1/12*(3*j*x^4 + 4*i*x^3 + 6*h*x^2 + 12*g*x)/b + 1/8*(sqrt(2)*(sqrt(2)*a^(3/4)*b^(5/4)*f - sqrt(2)*a^(7/4)*b^(1/4)*j + b^2*c - sqrt(a)*b^(3/2)*e - a*b*g + a^(3/2)*sqrt(b)*i)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(5/4)) + sqrt(2)*(sqrt(2)*a^(3/4)*b^(5/4)*f - sqrt(2)*a^(7/4)*b^(1/4)*j - b^2*c + sqrt(a)*b^(3/2)*e + a*b*g - a^(3/2)*sqrt(b)*i)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(5/4)) + 2*(sqrt(2)*a^(1/4)*b^(9/4)*c + sqrt(2)*a^(3/4)*b^(7/4)*e - sqrt(2)*a^(5/4)*b^(5/4)*g - sqrt(2)*a^(7/4)*b^(3/4)*i - 2*sqrt(a)*b^2*d + 2*a^(3/2)*b*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(5/4)) + 2*(sqrt(2)*a^(1/4)*b^(9/4)*c + sqrt(2)*a^(3/4)*b^(7/4)*e - sqrt(2)*a^(5/4)*b^(5/4)*g - sqrt(2)*a^(7/4)*b^(3/4)*i + 2*sqrt(a)*b^2*d - 2*a^(3/2)*b*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(5/4)))/b","A",0
192,1,243,0,3.077423," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^2,x, algorithm=""maxima"")","-\frac{b e x^{3} + {\left(b d + a h\right)} x^{2} + a f + {\left(b c + a g\right)} x}{4 \, {\left(a b^{2} x^{4} - a^{2} b\right)}} + \frac{\frac{2 \, {\left(b d - a h\right)} \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{2 \, {\left(b d - a h\right)} \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} + \frac{2 \, {\left(3 \, b^{\frac{3}{2}} c - \sqrt{a} b e - a \sqrt{b} g\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(3 \, b^{\frac{3}{2}} c + \sqrt{a} b e - a \sqrt{b} g\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{16 \, a b}"," ",0,"-1/4*(b*e*x^3 + (b*d + a*h)*x^2 + a*f + (b*c + a*g)*x)/(a*b^2*x^4 - a^2*b) + 1/16*(2*(b*d - a*h)*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 2*(b*d - a*h)*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) + 2*(3*b^(3/2)*c - sqrt(a)*b*e - a*sqrt(b)*g)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (3*b^(3/2)*c + sqrt(a)*b*e - a*sqrt(b)*g)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/(a*b)","A",0
193,1,260,0,3.064043," ","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=""maxima"")","-\frac{{\left(b e + a i\right)} x^{3} + {\left(b d + a h\right)} x^{2} + a f + {\left(b c + a g\right)} x}{4 \, {\left(a b^{2} x^{4} - a^{2} b\right)}} + \frac{\frac{2 \, {\left(b d - a h\right)} \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{2 \, {\left(b d - a h\right)} \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} + \frac{2 \, {\left(3 \, b^{\frac{3}{2}} c - \sqrt{a} b e - a \sqrt{b} g + 3 \, a^{\frac{3}{2}} i\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(3 \, b^{\frac{3}{2}} c + \sqrt{a} b e - a \sqrt{b} g - 3 \, a^{\frac{3}{2}} i\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{16 \, a b}"," ",0,"-1/4*((b*e + a*i)*x^3 + (b*d + a*h)*x^2 + a*f + (b*c + a*g)*x)/(a*b^2*x^4 - a^2*b) + 1/16*(2*(b*d - a*h)*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 2*(b*d - a*h)*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) + 2*(3*b^(3/2)*c - sqrt(a)*b*e - a*sqrt(b)*g + 3*a^(3/2)*i)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (3*b^(3/2)*c + sqrt(a)*b*e - a*sqrt(b)*g - 3*a^(3/2)*i)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/(a*b)","A",0
194,1,299,0,3.149345," ","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=""maxima"")","-\frac{{\left(b^{2} e + a b i\right)} x^{3} + a b f + a^{2} j + {\left(b^{2} d + a b h\right)} x^{2} + {\left(b^{2} c + a b g\right)} x}{4 \, {\left(a b^{3} x^{4} - a^{2} b^{2}\right)}} + \frac{\frac{2 \, {\left(3 \, b^{\frac{3}{2}} c - \sqrt{a} b e - a \sqrt{b} g + 3 \, a^{\frac{3}{2}} i\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, {\left(b^{\frac{3}{2}} d - a \sqrt{b} h + 2 \, a^{\frac{3}{2}} j\right)} \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} b} - \frac{2 \, {\left(b^{\frac{3}{2}} d - a \sqrt{b} h - 2 \, a^{\frac{3}{2}} j\right)} \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} b} - \frac{{\left(3 \, b^{\frac{3}{2}} c + \sqrt{a} b e - a \sqrt{b} g - 3 \, a^{\frac{3}{2}} i\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{16 \, a b}"," ",0,"-1/4*((b^2*e + a*b*i)*x^3 + a*b*f + a^2*j + (b^2*d + a*b*h)*x^2 + (b^2*c + a*b*g)*x)/(a*b^3*x^4 - a^2*b^2) + 1/16*(2*(3*b^(3/2)*c - sqrt(a)*b*e - a*sqrt(b)*g + 3*a^(3/2)*i)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*(b^(3/2)*d - a*sqrt(b)*h + 2*a^(3/2)*j)*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*b) - 2*(b^(3/2)*d - a*sqrt(b)*h - 2*a^(3/2)*j)*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*b) - (3*b^(3/2)*c + sqrt(a)*b*e - a*sqrt(b)*g - 3*a^(3/2)*i)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/(a*b)","A",0
195,1,374,0,3.193546," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x, algorithm=""maxima"")","\frac{b e x^{3} + {\left(b d - a h\right)} x^{2} - a f + {\left(b c - a g\right)} x}{4 \, {\left(a b^{2} x^{4} + a^{2} b\right)}} + \frac{\frac{\sqrt{2} {\left(3 \, b^{\frac{3}{2}} c - \sqrt{a} b e + a \sqrt{b} g\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(3 \, b^{\frac{3}{2}} c - \sqrt{a} b e + a \sqrt{b} g\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g - 4 \, \sqrt{a} b^{\frac{3}{2}} d - 4 \, a^{\frac{3}{2}} \sqrt{b} h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g + 4 \, \sqrt{a} b^{\frac{3}{2}} d + 4 \, a^{\frac{3}{2}} \sqrt{b} h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{32 \, a b}"," ",0,"1/4*(b*e*x^3 + (b*d - a*h)*x^2 - a*f + (b*c - a*g)*x)/(a*b^2*x^4 + a^2*b) + 1/32*(sqrt(2)*(3*b^(3/2)*c - sqrt(a)*b*e + a*sqrt(b)*g)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(3*b^(3/2)*c - sqrt(a)*b*e + a*sqrt(b)*g)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(3*sqrt(2)*a^(1/4)*b^(7/4)*c + sqrt(2)*a^(3/4)*b^(5/4)*e + sqrt(2)*a^(5/4)*b^(3/4)*g - 4*sqrt(a)*b^(3/2)*d - 4*a^(3/2)*sqrt(b)*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(3*sqrt(2)*a^(1/4)*b^(7/4)*c + sqrt(2)*a^(3/4)*b^(5/4)*e + sqrt(2)*a^(5/4)*b^(3/4)*g + 4*sqrt(a)*b^(3/2)*d + 4*a^(3/2)*sqrt(b)*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/(a*b)","A",0
196,1,416,0,3.193900," ","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=""maxima"")","\frac{{\left(b e - a i\right)} x^{3} + {\left(b d - a h\right)} x^{2} - a f + {\left(b c - a g\right)} x}{4 \, {\left(a b^{2} x^{4} + a^{2} b\right)}} + \frac{\frac{\sqrt{2} {\left(3 \, b^{\frac{3}{2}} c - \sqrt{a} b e + a \sqrt{b} g - 3 \, a^{\frac{3}{2}} i\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(3 \, b^{\frac{3}{2}} c - \sqrt{a} b e + a \sqrt{b} g - 3 \, a^{\frac{3}{2}} i\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g + 3 \, \sqrt{2} a^{\frac{7}{4}} b^{\frac{1}{4}} i - 4 \, \sqrt{a} b^{\frac{3}{2}} d - 4 \, a^{\frac{3}{2}} \sqrt{b} h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g + 3 \, \sqrt{2} a^{\frac{7}{4}} b^{\frac{1}{4}} i + 4 \, \sqrt{a} b^{\frac{3}{2}} d + 4 \, a^{\frac{3}{2}} \sqrt{b} h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{32 \, a b}"," ",0,"1/4*((b*e - a*i)*x^3 + (b*d - a*h)*x^2 - a*f + (b*c - a*g)*x)/(a*b^2*x^4 + a^2*b) + 1/32*(sqrt(2)*(3*b^(3/2)*c - sqrt(a)*b*e + a*sqrt(b)*g - 3*a^(3/2)*i)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(3*b^(3/2)*c - sqrt(a)*b*e + a*sqrt(b)*g - 3*a^(3/2)*i)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(3*sqrt(2)*a^(1/4)*b^(7/4)*c + sqrt(2)*a^(3/4)*b^(5/4)*e + sqrt(2)*a^(5/4)*b^(3/4)*g + 3*sqrt(2)*a^(7/4)*b^(1/4)*i - 4*sqrt(a)*b^(3/2)*d - 4*a^(3/2)*sqrt(b)*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(3*sqrt(2)*a^(1/4)*b^(7/4)*c + sqrt(2)*a^(3/4)*b^(5/4)*e + sqrt(2)*a^(5/4)*b^(3/4)*g + 3*sqrt(2)*a^(7/4)*b^(1/4)*i + 4*sqrt(a)*b^(3/2)*d + 4*a^(3/2)*sqrt(b)*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/(a*b)","A",0
197,1,458,0,3.213865," ","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=""maxima"")","\frac{{\left(b^{2} e - a b i\right)} x^{3} - a b f + a^{2} j + {\left(b^{2} d - a b h\right)} x^{2} + {\left(b^{2} c - a b g\right)} x}{4 \, {\left(a b^{3} x^{4} + a^{2} b^{2}\right)}} + \frac{\frac{\sqrt{2} {\left(4 \, \sqrt{2} a^{\frac{7}{4}} b^{\frac{1}{4}} j + 3 \, b^{2} c - \sqrt{a} b^{\frac{3}{2}} e + a b g - 3 \, a^{\frac{3}{2}} \sqrt{b} i\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{5}{4}}} + \frac{\sqrt{2} {\left(4 \, \sqrt{2} a^{\frac{7}{4}} b^{\frac{1}{4}} j - 3 \, b^{2} c + \sqrt{a} b^{\frac{3}{2}} e - a b g + 3 \, a^{\frac{3}{2}} \sqrt{b} i\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{5}{4}}} + \frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{9}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{7}{4}} e + \sqrt{2} a^{\frac{5}{4}} b^{\frac{5}{4}} g + 3 \, \sqrt{2} a^{\frac{7}{4}} b^{\frac{3}{4}} i - 4 \, \sqrt{a} b^{2} d - 4 \, a^{\frac{3}{2}} b h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{5}{4}}} + \frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{9}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{7}{4}} e + \sqrt{2} a^{\frac{5}{4}} b^{\frac{5}{4}} g + 3 \, \sqrt{2} a^{\frac{7}{4}} b^{\frac{3}{4}} i + 4 \, \sqrt{a} b^{2} d + 4 \, a^{\frac{3}{2}} b h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{5}{4}}}}{32 \, a b}"," ",0,"1/4*((b^2*e - a*b*i)*x^3 - a*b*f + a^2*j + (b^2*d - a*b*h)*x^2 + (b^2*c - a*b*g)*x)/(a*b^3*x^4 + a^2*b^2) + 1/32*(sqrt(2)*(4*sqrt(2)*a^(7/4)*b^(1/4)*j + 3*b^2*c - sqrt(a)*b^(3/2)*e + a*b*g - 3*a^(3/2)*sqrt(b)*i)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(5/4)) + sqrt(2)*(4*sqrt(2)*a^(7/4)*b^(1/4)*j - 3*b^2*c + sqrt(a)*b^(3/2)*e - a*b*g + 3*a^(3/2)*sqrt(b)*i)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(5/4)) + 2*(3*sqrt(2)*a^(1/4)*b^(9/4)*c + sqrt(2)*a^(3/4)*b^(7/4)*e + sqrt(2)*a^(5/4)*b^(5/4)*g + 3*sqrt(2)*a^(7/4)*b^(3/4)*i - 4*sqrt(a)*b^2*d - 4*a^(3/2)*b*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(5/4)) + 2*(3*sqrt(2)*a^(1/4)*b^(9/4)*c + sqrt(2)*a^(3/4)*b^(7/4)*e + sqrt(2)*a^(5/4)*b^(5/4)*g + 3*sqrt(2)*a^(7/4)*b^(3/4)*i + 4*sqrt(a)*b^2*d + 4*a^(3/2)*b*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(5/4)))/(a*b)","A",0
198,1,316,0,2.963035," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^3,x, algorithm=""maxima"")","-\frac{5 \, b^{2} e x^{7} + 2 \, {\left(3 \, b^{2} d - a b h\right)} x^{6} - 9 \, a b e x^{3} + {\left(7 \, b^{2} c - a b g\right)} x^{5} - 4 \, a^{2} f - 2 \, {\left(5 \, a b d + a^{2} h\right)} x^{2} - {\left(11 \, a b c + 3 \, a^{2} g\right)} x}{32 \, {\left(a^{2} b^{3} x^{8} - 2 \, a^{3} b^{2} x^{4} + a^{4} b\right)}} + \frac{\frac{4 \, {\left(3 \, b d - a h\right)} \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{4 \, {\left(3 \, b d - a h\right)} \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} + \frac{2 \, {\left(21 \, b^{\frac{3}{2}} c - 5 \, \sqrt{a} b e - 3 \, a \sqrt{b} g\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(21 \, b^{\frac{3}{2}} c + 5 \, \sqrt{a} b e - 3 \, a \sqrt{b} g\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{128 \, a^{2} b}"," ",0,"-1/32*(5*b^2*e*x^7 + 2*(3*b^2*d - a*b*h)*x^6 - 9*a*b*e*x^3 + (7*b^2*c - a*b*g)*x^5 - 4*a^2*f - 2*(5*a*b*d + a^2*h)*x^2 - (11*a*b*c + 3*a^2*g)*x)/(a^2*b^3*x^8 - 2*a^3*b^2*x^4 + a^4*b) + 1/128*(4*(3*b*d - a*h)*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 4*(3*b*d - a*h)*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) + 2*(21*b^(3/2)*c - 5*sqrt(a)*b*e - 3*a*sqrt(b)*g)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (21*b^(3/2)*c + 5*sqrt(a)*b*e - 3*a*sqrt(b)*g)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/(a^2*b)","A",0
199,1,343,0,3.082618," ","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=""maxima"")","-\frac{{\left(5 \, b^{2} e - 3 \, a b i\right)} x^{7} + 2 \, {\left(3 \, b^{2} d - a b h\right)} x^{6} + {\left(7 \, b^{2} c - a b g\right)} x^{5} - {\left(9 \, a b e + a^{2} i\right)} x^{3} - 4 \, a^{2} f - 2 \, {\left(5 \, a b d + a^{2} h\right)} x^{2} - {\left(11 \, a b c + 3 \, a^{2} g\right)} x}{32 \, {\left(a^{2} b^{3} x^{8} - 2 \, a^{3} b^{2} x^{4} + a^{4} b\right)}} + \frac{\frac{4 \, {\left(3 \, b d - a h\right)} \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{4 \, {\left(3 \, b d - a h\right)} \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} + \frac{2 \, {\left(21 \, b^{\frac{3}{2}} c - 5 \, \sqrt{a} b e - 3 \, a \sqrt{b} g + 3 \, a^{\frac{3}{2}} i\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(21 \, b^{\frac{3}{2}} c + 5 \, \sqrt{a} b e - 3 \, a \sqrt{b} g - 3 \, a^{\frac{3}{2}} i\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{128 \, a^{2} b}"," ",0,"-1/32*((5*b^2*e - 3*a*b*i)*x^7 + 2*(3*b^2*d - a*b*h)*x^6 + (7*b^2*c - a*b*g)*x^5 - (9*a*b*e + a^2*i)*x^3 - 4*a^2*f - 2*(5*a*b*d + a^2*h)*x^2 - (11*a*b*c + 3*a^2*g)*x)/(a^2*b^3*x^8 - 2*a^3*b^2*x^4 + a^4*b) + 1/128*(4*(3*b*d - a*h)*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 4*(3*b*d - a*h)*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) + 2*(21*b^(3/2)*c - 5*sqrt(a)*b*e - 3*a*sqrt(b)*g + 3*a^(3/2)*i)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (21*b^(3/2)*c + 5*sqrt(a)*b*e - 3*a*sqrt(b)*g - 3*a^(3/2)*i)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/(a^2*b)","A",0
200,1,377,0,3.128591," ","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=""maxima"")","\frac{8 \, a^{2} b j x^{4} - {\left(5 \, b^{3} e - 3 \, a b^{2} i\right)} x^{7} - 2 \, {\left(3 \, b^{3} d - a b^{2} h\right)} x^{6} - {\left(7 \, b^{3} c - a b^{2} g\right)} x^{5} + 4 \, a^{2} b f - 4 \, a^{3} j + {\left(9 \, a b^{2} e + a^{2} b i\right)} x^{3} + 2 \, {\left(5 \, a b^{2} d + a^{2} b h\right)} x^{2} + {\left(11 \, a b^{2} c + 3 \, a^{2} b g\right)} x}{32 \, {\left(a^{2} b^{4} x^{8} - 2 \, a^{3} b^{3} x^{4} + a^{4} b^{2}\right)}} + \frac{\frac{4 \, {\left(3 \, b d - a h\right)} \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{4 \, {\left(3 \, b d - a h\right)} \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} + \frac{2 \, {\left(21 \, b^{\frac{3}{2}} c - 5 \, \sqrt{a} b e - 3 \, a \sqrt{b} g + 3 \, a^{\frac{3}{2}} i\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(21 \, b^{\frac{3}{2}} c + 5 \, \sqrt{a} b e - 3 \, a \sqrt{b} g - 3 \, a^{\frac{3}{2}} i\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{128 \, a^{2} b}"," ",0,"1/32*(8*a^2*b*j*x^4 - (5*b^3*e - 3*a*b^2*i)*x^7 - 2*(3*b^3*d - a*b^2*h)*x^6 - (7*b^3*c - a*b^2*g)*x^5 + 4*a^2*b*f - 4*a^3*j + (9*a*b^2*e + a^2*b*i)*x^3 + 2*(5*a*b^2*d + a^2*b*h)*x^2 + (11*a*b^2*c + 3*a^2*b*g)*x)/(a^2*b^4*x^8 - 2*a^3*b^3*x^4 + a^4*b^2) + 1/128*(4*(3*b*d - a*h)*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 4*(3*b*d - a*h)*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) + 2*(21*b^(3/2)*c - 5*sqrt(a)*b*e - 3*a*sqrt(b)*g + 3*a^(3/2)*i)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (21*b^(3/2)*c + 5*sqrt(a)*b*e - 3*a*sqrt(b)*g - 3*a^(3/2)*i)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/(a^2*b)","A",0
201,1,446,0,3.067672," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x, algorithm=""maxima"")","\frac{5 \, b^{2} e x^{7} + 2 \, {\left(3 \, b^{2} d + a b h\right)} x^{6} + 9 \, a b e x^{3} + {\left(7 \, b^{2} c + a b g\right)} x^{5} - 4 \, a^{2} f + 2 \, {\left(5 \, a b d - a^{2} h\right)} x^{2} + {\left(11 \, a b c - 3 \, a^{2} g\right)} x}{32 \, {\left(a^{2} b^{3} x^{8} + 2 \, a^{3} b^{2} x^{4} + a^{4} b\right)}} + \frac{\frac{\sqrt{2} {\left(21 \, b^{\frac{3}{2}} c - 5 \, \sqrt{a} b e + 3 \, a \sqrt{b} g\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(21 \, b^{\frac{3}{2}} c - 5 \, \sqrt{a} b e + 3 \, a \sqrt{b} g\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(21 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + 5 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + 3 \, \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g - 24 \, \sqrt{a} b^{\frac{3}{2}} d - 8 \, a^{\frac{3}{2}} \sqrt{b} h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(21 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + 5 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + 3 \, \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g + 24 \, \sqrt{a} b^{\frac{3}{2}} d + 8 \, a^{\frac{3}{2}} \sqrt{b} h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{256 \, a^{2} b}"," ",0,"1/32*(5*b^2*e*x^7 + 2*(3*b^2*d + a*b*h)*x^6 + 9*a*b*e*x^3 + (7*b^2*c + a*b*g)*x^5 - 4*a^2*f + 2*(5*a*b*d - a^2*h)*x^2 + (11*a*b*c - 3*a^2*g)*x)/(a^2*b^3*x^8 + 2*a^3*b^2*x^4 + a^4*b) + 1/256*(sqrt(2)*(21*b^(3/2)*c - 5*sqrt(a)*b*e + 3*a*sqrt(b)*g)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(21*b^(3/2)*c - 5*sqrt(a)*b*e + 3*a*sqrt(b)*g)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(21*sqrt(2)*a^(1/4)*b^(7/4)*c + 5*sqrt(2)*a^(3/4)*b^(5/4)*e + 3*sqrt(2)*a^(5/4)*b^(3/4)*g - 24*sqrt(a)*b^(3/2)*d - 8*a^(3/2)*sqrt(b)*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(21*sqrt(2)*a^(1/4)*b^(7/4)*c + 5*sqrt(2)*a^(3/4)*b^(5/4)*e + 3*sqrt(2)*a^(5/4)*b^(3/4)*g + 24*sqrt(a)*b^(3/2)*d + 8*a^(3/2)*sqrt(b)*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/(a^2*b)","A",0
202,1,497,0,3.174807," ","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=""maxima"")","\frac{{\left(5 \, b^{2} e + 3 \, a b i\right)} x^{7} + 2 \, {\left(3 \, b^{2} d + a b h\right)} x^{6} + {\left(7 \, b^{2} c + a b g\right)} x^{5} + {\left(9 \, a b e - a^{2} i\right)} x^{3} - 4 \, a^{2} f + 2 \, {\left(5 \, a b d - a^{2} h\right)} x^{2} + {\left(11 \, a b c - 3 \, a^{2} g\right)} x}{32 \, {\left(a^{2} b^{3} x^{8} + 2 \, a^{3} b^{2} x^{4} + a^{4} b\right)}} + \frac{\frac{\sqrt{2} {\left(21 \, b^{\frac{3}{2}} c - 5 \, \sqrt{a} b e + 3 \, a \sqrt{b} g - 3 \, a^{\frac{3}{2}} i\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(21 \, b^{\frac{3}{2}} c - 5 \, \sqrt{a} b e + 3 \, a \sqrt{b} g - 3 \, a^{\frac{3}{2}} i\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(21 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + 5 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + 3 \, \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g + 3 \, \sqrt{2} a^{\frac{7}{4}} b^{\frac{1}{4}} i - 24 \, \sqrt{a} b^{\frac{3}{2}} d - 8 \, a^{\frac{3}{2}} \sqrt{b} h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(21 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + 5 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + 3 \, \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g + 3 \, \sqrt{2} a^{\frac{7}{4}} b^{\frac{1}{4}} i + 24 \, \sqrt{a} b^{\frac{3}{2}} d + 8 \, a^{\frac{3}{2}} \sqrt{b} h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{256 \, a^{2} b}"," ",0,"1/32*((5*b^2*e + 3*a*b*i)*x^7 + 2*(3*b^2*d + a*b*h)*x^6 + (7*b^2*c + a*b*g)*x^5 + (9*a*b*e - a^2*i)*x^3 - 4*a^2*f + 2*(5*a*b*d - a^2*h)*x^2 + (11*a*b*c - 3*a^2*g)*x)/(a^2*b^3*x^8 + 2*a^3*b^2*x^4 + a^4*b) + 1/256*(sqrt(2)*(21*b^(3/2)*c - 5*sqrt(a)*b*e + 3*a*sqrt(b)*g - 3*a^(3/2)*i)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(21*b^(3/2)*c - 5*sqrt(a)*b*e + 3*a*sqrt(b)*g - 3*a^(3/2)*i)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(21*sqrt(2)*a^(1/4)*b^(7/4)*c + 5*sqrt(2)*a^(3/4)*b^(5/4)*e + 3*sqrt(2)*a^(5/4)*b^(3/4)*g + 3*sqrt(2)*a^(7/4)*b^(1/4)*i - 24*sqrt(a)*b^(3/2)*d - 8*a^(3/2)*sqrt(b)*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(21*sqrt(2)*a^(1/4)*b^(7/4)*c + 5*sqrt(2)*a^(3/4)*b^(5/4)*e + 3*sqrt(2)*a^(5/4)*b^(3/4)*g + 3*sqrt(2)*a^(7/4)*b^(1/4)*i + 24*sqrt(a)*b^(3/2)*d + 8*a^(3/2)*sqrt(b)*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/(a^2*b)","A",0
203,1,535,0,3.093404," ","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=""maxima"")","-\frac{8 \, a^{2} b j x^{4} - {\left(5 \, b^{3} e + 3 \, a b^{2} i\right)} x^{7} - 2 \, {\left(3 \, b^{3} d + a b^{2} h\right)} x^{6} - {\left(7 \, b^{3} c + a b^{2} g\right)} x^{5} + 4 \, a^{2} b f + 4 \, a^{3} j - {\left(9 \, a b^{2} e - a^{2} b i\right)} x^{3} - 2 \, {\left(5 \, a b^{2} d - a^{2} b h\right)} x^{2} - {\left(11 \, a b^{2} c - 3 \, a^{2} b g\right)} x}{32 \, {\left(a^{2} b^{4} x^{8} + 2 \, a^{3} b^{3} x^{4} + a^{4} b^{2}\right)}} + \frac{\frac{\sqrt{2} {\left(21 \, b^{\frac{3}{2}} c - 5 \, \sqrt{a} b e + 3 \, a \sqrt{b} g - 3 \, a^{\frac{3}{2}} i\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(21 \, b^{\frac{3}{2}} c - 5 \, \sqrt{a} b e + 3 \, a \sqrt{b} g - 3 \, a^{\frac{3}{2}} i\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(21 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + 5 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + 3 \, \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g + 3 \, \sqrt{2} a^{\frac{7}{4}} b^{\frac{1}{4}} i - 24 \, \sqrt{a} b^{\frac{3}{2}} d - 8 \, a^{\frac{3}{2}} \sqrt{b} h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(21 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + 5 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + 3 \, \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g + 3 \, \sqrt{2} a^{\frac{7}{4}} b^{\frac{1}{4}} i + 24 \, \sqrt{a} b^{\frac{3}{2}} d + 8 \, a^{\frac{3}{2}} \sqrt{b} h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{256 \, a^{2} b}"," ",0,"-1/32*(8*a^2*b*j*x^4 - (5*b^3*e + 3*a*b^2*i)*x^7 - 2*(3*b^3*d + a*b^2*h)*x^6 - (7*b^3*c + a*b^2*g)*x^5 + 4*a^2*b*f + 4*a^3*j - (9*a*b^2*e - a^2*b*i)*x^3 - 2*(5*a*b^2*d - a^2*b*h)*x^2 - (11*a*b^2*c - 3*a^2*b*g)*x)/(a^2*b^4*x^8 + 2*a^3*b^3*x^4 + a^4*b^2) + 1/256*(sqrt(2)*(21*b^(3/2)*c - 5*sqrt(a)*b*e + 3*a*sqrt(b)*g - 3*a^(3/2)*i)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(21*b^(3/2)*c - 5*sqrt(a)*b*e + 3*a*sqrt(b)*g - 3*a^(3/2)*i)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(21*sqrt(2)*a^(1/4)*b^(7/4)*c + 5*sqrt(2)*a^(3/4)*b^(5/4)*e + 3*sqrt(2)*a^(5/4)*b^(3/4)*g + 3*sqrt(2)*a^(7/4)*b^(1/4)*i - 24*sqrt(a)*b^(3/2)*d - 8*a^(3/2)*sqrt(b)*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(21*sqrt(2)*a^(1/4)*b^(7/4)*c + 5*sqrt(2)*a^(3/4)*b^(5/4)*e + 3*sqrt(2)*a^(5/4)*b^(3/4)*g + 3*sqrt(2)*a^(7/4)*b^(1/4)*i + 24*sqrt(a)*b^(3/2)*d + 8*a^(3/2)*sqrt(b)*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/(a^2*b)","A",0
204,1,389,0,3.177693," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^4,x, algorithm=""maxima"")","-\frac{45 \, b^{3} e x^{11} - 126 \, a b^{2} e x^{7} + 12 \, {\left(5 \, b^{3} d - a b^{2} h\right)} x^{10} + 7 \, {\left(11 \, b^{3} c - a b^{2} g\right)} x^{9} + 113 \, a^{2} b e x^{3} - 32 \, {\left(5 \, a b^{2} d - a^{2} b h\right)} x^{6} - 18 \, {\left(11 \, a b^{2} c - a^{2} b g\right)} x^{5} + 32 \, a^{3} f + 12 \, {\left(11 \, a^{2} b d + a^{3} h\right)} x^{2} + 3 \, {\left(51 \, a^{2} b c + 7 \, a^{3} g\right)} x}{384 \, {\left(a^{3} b^{4} x^{12} - 3 \, a^{4} b^{3} x^{8} + 3 \, a^{5} b^{2} x^{4} - a^{6} b\right)}} + \frac{\frac{8 \, {\left(5 \, b d - a h\right)} \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{8 \, {\left(5 \, b d - a h\right)} \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} + \frac{2 \, {\left(77 \, b^{\frac{3}{2}} c - 15 \, \sqrt{a} b e - 7 \, a \sqrt{b} g\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(77 \, b^{\frac{3}{2}} c + 15 \, \sqrt{a} b e - 7 \, a \sqrt{b} g\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{512 \, a^{3} b}"," ",0,"-1/384*(45*b^3*e*x^11 - 126*a*b^2*e*x^7 + 12*(5*b^3*d - a*b^2*h)*x^10 + 7*(11*b^3*c - a*b^2*g)*x^9 + 113*a^2*b*e*x^3 - 32*(5*a*b^2*d - a^2*b*h)*x^6 - 18*(11*a*b^2*c - a^2*b*g)*x^5 + 32*a^3*f + 12*(11*a^2*b*d + a^3*h)*x^2 + 3*(51*a^2*b*c + 7*a^3*g)*x)/(a^3*b^4*x^12 - 3*a^4*b^3*x^8 + 3*a^5*b^2*x^4 - a^6*b) + 1/512*(8*(5*b*d - a*h)*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 8*(5*b*d - a*h)*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) + 2*(77*b^(3/2)*c - 15*sqrt(a)*b*e - 7*a*sqrt(b)*g)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (77*b^(3/2)*c + 15*sqrt(a)*b*e - 7*a*sqrt(b)*g)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/(a^3*b)","A",0
205,1,429,0,3.163242," ","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=""maxima"")","-\frac{15 \, {\left(3 \, b^{3} e - a b^{2} i\right)} x^{11} + 12 \, {\left(5 \, b^{3} d - a b^{2} h\right)} x^{10} + 7 \, {\left(11 \, b^{3} c - a b^{2} g\right)} x^{9} - 42 \, {\left(3 \, a b^{2} e - a^{2} b i\right)} x^{7} - 32 \, {\left(5 \, a b^{2} d - a^{2} b h\right)} x^{6} - 18 \, {\left(11 \, a b^{2} c - a^{2} b g\right)} x^{5} + 32 \, a^{3} f + {\left(113 \, a^{2} b e + 5 \, a^{3} i\right)} x^{3} + 12 \, {\left(11 \, a^{2} b d + a^{3} h\right)} x^{2} + 3 \, {\left(51 \, a^{2} b c + 7 \, a^{3} g\right)} x}{384 \, {\left(a^{3} b^{4} x^{12} - 3 \, a^{4} b^{3} x^{8} + 3 \, a^{5} b^{2} x^{4} - a^{6} b\right)}} + \frac{\frac{8 \, {\left(5 \, b d - a h\right)} \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{8 \, {\left(5 \, b d - a h\right)} \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} + \frac{2 \, {\left(77 \, b^{\frac{3}{2}} c - 15 \, \sqrt{a} b e - 7 \, a \sqrt{b} g + 5 \, a^{\frac{3}{2}} i\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(77 \, b^{\frac{3}{2}} c + 15 \, \sqrt{a} b e - 7 \, a \sqrt{b} g - 5 \, a^{\frac{3}{2}} i\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{512 \, a^{3} b}"," ",0,"-1/384*(15*(3*b^3*e - a*b^2*i)*x^11 + 12*(5*b^3*d - a*b^2*h)*x^10 + 7*(11*b^3*c - a*b^2*g)*x^9 - 42*(3*a*b^2*e - a^2*b*i)*x^7 - 32*(5*a*b^2*d - a^2*b*h)*x^6 - 18*(11*a*b^2*c - a^2*b*g)*x^5 + 32*a^3*f + (113*a^2*b*e + 5*a^3*i)*x^3 + 12*(11*a^2*b*d + a^3*h)*x^2 + 3*(51*a^2*b*c + 7*a^3*g)*x)/(a^3*b^4*x^12 - 3*a^4*b^3*x^8 + 3*a^5*b^2*x^4 - a^6*b) + 1/512*(8*(5*b*d - a*h)*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 8*(5*b*d - a*h)*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) + 2*(77*b^(3/2)*c - 15*sqrt(a)*b*e - 7*a*sqrt(b)*g + 5*a^(3/2)*i)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (77*b^(3/2)*c + 15*sqrt(a)*b*e - 7*a*sqrt(b)*g - 5*a^(3/2)*i)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/(a^3*b)","A",0
206,1,463,0,3.084555," ","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=""maxima"")","-\frac{15 \, {\left(3 \, b^{4} e - a b^{3} i\right)} x^{11} + 12 \, {\left(5 \, b^{4} d - a b^{3} h\right)} x^{10} + 7 \, {\left(11 \, b^{4} c - a b^{3} g\right)} x^{9} + 48 \, a^{3} b j x^{4} - 42 \, {\left(3 \, a b^{3} e - a^{2} b^{2} i\right)} x^{7} - 32 \, {\left(5 \, a b^{3} d - a^{2} b^{2} h\right)} x^{6} - 18 \, {\left(11 \, a b^{3} c - a^{2} b^{2} g\right)} x^{5} + 32 \, a^{3} b f - 16 \, a^{4} j + {\left(113 \, a^{2} b^{2} e + 5 \, a^{3} b i\right)} x^{3} + 12 \, {\left(11 \, a^{2} b^{2} d + a^{3} b h\right)} x^{2} + 3 \, {\left(51 \, a^{2} b^{2} c + 7 \, a^{3} b g\right)} x}{384 \, {\left(a^{3} b^{5} x^{12} - 3 \, a^{4} b^{4} x^{8} + 3 \, a^{5} b^{3} x^{4} - a^{6} b^{2}\right)}} + \frac{\frac{8 \, {\left(5 \, b d - a h\right)} \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} - \frac{8 \, {\left(5 \, b d - a h\right)} \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} \sqrt{b}} + \frac{2 \, {\left(77 \, b^{\frac{3}{2}} c - 15 \, \sqrt{a} b e - 7 \, a \sqrt{b} g + 5 \, a^{\frac{3}{2}} i\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(77 \, b^{\frac{3}{2}} c + 15 \, \sqrt{a} b e - 7 \, a \sqrt{b} g - 5 \, a^{\frac{3}{2}} i\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{512 \, a^{3} b}"," ",0,"-1/384*(15*(3*b^4*e - a*b^3*i)*x^11 + 12*(5*b^4*d - a*b^3*h)*x^10 + 7*(11*b^4*c - a*b^3*g)*x^9 + 48*a^3*b*j*x^4 - 42*(3*a*b^3*e - a^2*b^2*i)*x^7 - 32*(5*a*b^3*d - a^2*b^2*h)*x^6 - 18*(11*a*b^3*c - a^2*b^2*g)*x^5 + 32*a^3*b*f - 16*a^4*j + (113*a^2*b^2*e + 5*a^3*b*i)*x^3 + 12*(11*a^2*b^2*d + a^3*b*h)*x^2 + 3*(51*a^2*b^2*c + 7*a^3*b*g)*x)/(a^3*b^5*x^12 - 3*a^4*b^4*x^8 + 3*a^5*b^3*x^4 - a^6*b^2) + 1/512*(8*(5*b*d - a*h)*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*sqrt(b)) - 8*(5*b*d - a*h)*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*sqrt(b)) + 2*(77*b^(3/2)*c - 15*sqrt(a)*b*e - 7*a*sqrt(b)*g + 5*a^(3/2)*i)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (77*b^(3/2)*c + 15*sqrt(a)*b*e - 7*a*sqrt(b)*g - 5*a^(3/2)*i)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/(a^3*b)","A",0
207,1,517,0,3.126190," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x, algorithm=""maxima"")","\frac{45 \, b^{3} e x^{11} + 126 \, a b^{2} e x^{7} + 12 \, {\left(5 \, b^{3} d + a b^{2} h\right)} x^{10} + 7 \, {\left(11 \, b^{3} c + a b^{2} g\right)} x^{9} + 113 \, a^{2} b e x^{3} + 32 \, {\left(5 \, a b^{2} d + a^{2} b h\right)} x^{6} + 18 \, {\left(11 \, a b^{2} c + a^{2} b g\right)} x^{5} - 32 \, a^{3} f + 12 \, {\left(11 \, a^{2} b d - a^{3} h\right)} x^{2} + 3 \, {\left(51 \, a^{2} b c - 7 \, a^{3} g\right)} x}{384 \, {\left(a^{3} b^{4} x^{12} + 3 \, a^{4} b^{3} x^{8} + 3 \, a^{5} b^{2} x^{4} + a^{6} b\right)}} + \frac{\frac{\sqrt{2} {\left(77 \, b^{\frac{3}{2}} c - 15 \, \sqrt{a} b e + 7 \, a \sqrt{b} g\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(77 \, b^{\frac{3}{2}} c - 15 \, \sqrt{a} b e + 7 \, a \sqrt{b} g\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(77 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + 15 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + 7 \, \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g - 80 \, \sqrt{a} b^{\frac{3}{2}} d - 16 \, a^{\frac{3}{2}} \sqrt{b} h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(77 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + 15 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + 7 \, \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g + 80 \, \sqrt{a} b^{\frac{3}{2}} d + 16 \, a^{\frac{3}{2}} \sqrt{b} h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{1024 \, a^{3} b}"," ",0,"1/384*(45*b^3*e*x^11 + 126*a*b^2*e*x^7 + 12*(5*b^3*d + a*b^2*h)*x^10 + 7*(11*b^3*c + a*b^2*g)*x^9 + 113*a^2*b*e*x^3 + 32*(5*a*b^2*d + a^2*b*h)*x^6 + 18*(11*a*b^2*c + a^2*b*g)*x^5 - 32*a^3*f + 12*(11*a^2*b*d - a^3*h)*x^2 + 3*(51*a^2*b*c - 7*a^3*g)*x)/(a^3*b^4*x^12 + 3*a^4*b^3*x^8 + 3*a^5*b^2*x^4 + a^6*b) + 1/1024*(sqrt(2)*(77*b^(3/2)*c - 15*sqrt(a)*b*e + 7*a*sqrt(b)*g)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(77*b^(3/2)*c - 15*sqrt(a)*b*e + 7*a*sqrt(b)*g)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(77*sqrt(2)*a^(1/4)*b^(7/4)*c + 15*sqrt(2)*a^(3/4)*b^(5/4)*e + 7*sqrt(2)*a^(5/4)*b^(3/4)*g - 80*sqrt(a)*b^(3/2)*d - 16*a^(3/2)*sqrt(b)*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(77*sqrt(2)*a^(1/4)*b^(7/4)*c + 15*sqrt(2)*a^(3/4)*b^(5/4)*e + 7*sqrt(2)*a^(5/4)*b^(3/4)*g + 80*sqrt(a)*b^(3/2)*d + 16*a^(3/2)*sqrt(b)*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/(a^3*b)","A",0
208,1,579,0,3.160211," ","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=""maxima"")","\frac{15 \, {\left(3 \, b^{3} e + a b^{2} i\right)} x^{11} + 12 \, {\left(5 \, b^{3} d + a b^{2} h\right)} x^{10} + 7 \, {\left(11 \, b^{3} c + a b^{2} g\right)} x^{9} + 42 \, {\left(3 \, a b^{2} e + a^{2} b i\right)} x^{7} + 32 \, {\left(5 \, a b^{2} d + a^{2} b h\right)} x^{6} + 18 \, {\left(11 \, a b^{2} c + a^{2} b g\right)} x^{5} - 32 \, a^{3} f + {\left(113 \, a^{2} b e - 5 \, a^{3} i\right)} x^{3} + 12 \, {\left(11 \, a^{2} b d - a^{3} h\right)} x^{2} + 3 \, {\left(51 \, a^{2} b c - 7 \, a^{3} g\right)} x}{384 \, {\left(a^{3} b^{4} x^{12} + 3 \, a^{4} b^{3} x^{8} + 3 \, a^{5} b^{2} x^{4} + a^{6} b\right)}} + \frac{\frac{\sqrt{2} {\left(77 \, b^{\frac{3}{2}} c - 15 \, \sqrt{a} b e + 7 \, a \sqrt{b} g - 5 \, a^{\frac{3}{2}} i\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(77 \, b^{\frac{3}{2}} c - 15 \, \sqrt{a} b e + 7 \, a \sqrt{b} g - 5 \, a^{\frac{3}{2}} i\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(77 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + 15 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + 7 \, \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g + 5 \, \sqrt{2} a^{\frac{7}{4}} b^{\frac{1}{4}} i - 80 \, \sqrt{a} b^{\frac{3}{2}} d - 16 \, a^{\frac{3}{2}} \sqrt{b} h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(77 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + 15 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + 7 \, \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g + 5 \, \sqrt{2} a^{\frac{7}{4}} b^{\frac{1}{4}} i + 80 \, \sqrt{a} b^{\frac{3}{2}} d + 16 \, a^{\frac{3}{2}} \sqrt{b} h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{1024 \, a^{3} b}"," ",0,"1/384*(15*(3*b^3*e + a*b^2*i)*x^11 + 12*(5*b^3*d + a*b^2*h)*x^10 + 7*(11*b^3*c + a*b^2*g)*x^9 + 42*(3*a*b^2*e + a^2*b*i)*x^7 + 32*(5*a*b^2*d + a^2*b*h)*x^6 + 18*(11*a*b^2*c + a^2*b*g)*x^5 - 32*a^3*f + (113*a^2*b*e - 5*a^3*i)*x^3 + 12*(11*a^2*b*d - a^3*h)*x^2 + 3*(51*a^2*b*c - 7*a^3*g)*x)/(a^3*b^4*x^12 + 3*a^4*b^3*x^8 + 3*a^5*b^2*x^4 + a^6*b) + 1/1024*(sqrt(2)*(77*b^(3/2)*c - 15*sqrt(a)*b*e + 7*a*sqrt(b)*g - 5*a^(3/2)*i)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(77*b^(3/2)*c - 15*sqrt(a)*b*e + 7*a*sqrt(b)*g - 5*a^(3/2)*i)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(77*sqrt(2)*a^(1/4)*b^(7/4)*c + 15*sqrt(2)*a^(3/4)*b^(5/4)*e + 7*sqrt(2)*a^(5/4)*b^(3/4)*g + 5*sqrt(2)*a^(7/4)*b^(1/4)*i - 80*sqrt(a)*b^(3/2)*d - 16*a^(3/2)*sqrt(b)*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(77*sqrt(2)*a^(1/4)*b^(7/4)*c + 15*sqrt(2)*a^(3/4)*b^(5/4)*e + 7*sqrt(2)*a^(5/4)*b^(3/4)*g + 5*sqrt(2)*a^(7/4)*b^(1/4)*i + 80*sqrt(a)*b^(3/2)*d + 16*a^(3/2)*sqrt(b)*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/(a^3*b)","A",0
209,1,613,0,3.227771," ","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=""maxima"")","\frac{15 \, {\left(3 \, b^{4} e + a b^{3} i\right)} x^{11} + 12 \, {\left(5 \, b^{4} d + a b^{3} h\right)} x^{10} + 7 \, {\left(11 \, b^{4} c + a b^{3} g\right)} x^{9} - 48 \, a^{3} b j x^{4} + 42 \, {\left(3 \, a b^{3} e + a^{2} b^{2} i\right)} x^{7} + 32 \, {\left(5 \, a b^{3} d + a^{2} b^{2} h\right)} x^{6} + 18 \, {\left(11 \, a b^{3} c + a^{2} b^{2} g\right)} x^{5} - 32 \, a^{3} b f - 16 \, a^{4} j + {\left(113 \, a^{2} b^{2} e - 5 \, a^{3} b i\right)} x^{3} + 12 \, {\left(11 \, a^{2} b^{2} d - a^{3} b h\right)} x^{2} + 3 \, {\left(51 \, a^{2} b^{2} c - 7 \, a^{3} b g\right)} x}{384 \, {\left(a^{3} b^{5} x^{12} + 3 \, a^{4} b^{4} x^{8} + 3 \, a^{5} b^{3} x^{4} + a^{6} b^{2}\right)}} + \frac{\frac{\sqrt{2} {\left(77 \, b^{\frac{3}{2}} c - 15 \, \sqrt{a} b e + 7 \, a \sqrt{b} g - 5 \, a^{\frac{3}{2}} i\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(77 \, b^{\frac{3}{2}} c - 15 \, \sqrt{a} b e + 7 \, a \sqrt{b} g - 5 \, a^{\frac{3}{2}} i\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(77 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + 15 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + 7 \, \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g + 5 \, \sqrt{2} a^{\frac{7}{4}} b^{\frac{1}{4}} i - 80 \, \sqrt{a} b^{\frac{3}{2}} d - 16 \, a^{\frac{3}{2}} \sqrt{b} h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(77 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{7}{4}} c + 15 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} e + 7 \, \sqrt{2} a^{\frac{5}{4}} b^{\frac{3}{4}} g + 5 \, \sqrt{2} a^{\frac{7}{4}} b^{\frac{1}{4}} i + 80 \, \sqrt{a} b^{\frac{3}{2}} d + 16 \, a^{\frac{3}{2}} \sqrt{b} h\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{1024 \, a^{3} b}"," ",0,"1/384*(15*(3*b^4*e + a*b^3*i)*x^11 + 12*(5*b^4*d + a*b^3*h)*x^10 + 7*(11*b^4*c + a*b^3*g)*x^9 - 48*a^3*b*j*x^4 + 42*(3*a*b^3*e + a^2*b^2*i)*x^7 + 32*(5*a*b^3*d + a^2*b^2*h)*x^6 + 18*(11*a*b^3*c + a^2*b^2*g)*x^5 - 32*a^3*b*f - 16*a^4*j + (113*a^2*b^2*e - 5*a^3*b*i)*x^3 + 12*(11*a^2*b^2*d - a^3*b*h)*x^2 + 3*(51*a^2*b^2*c - 7*a^3*b*g)*x)/(a^3*b^5*x^12 + 3*a^4*b^4*x^8 + 3*a^5*b^3*x^4 + a^6*b^2) + 1/1024*(sqrt(2)*(77*b^(3/2)*c - 15*sqrt(a)*b*e + 7*a*sqrt(b)*g - 5*a^(3/2)*i)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(77*b^(3/2)*c - 15*sqrt(a)*b*e + 7*a*sqrt(b)*g - 5*a^(3/2)*i)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(77*sqrt(2)*a^(1/4)*b^(7/4)*c + 15*sqrt(2)*a^(3/4)*b^(5/4)*e + 7*sqrt(2)*a^(5/4)*b^(3/4)*g + 5*sqrt(2)*a^(7/4)*b^(1/4)*i - 80*sqrt(a)*b^(3/2)*d - 16*a^(3/2)*sqrt(b)*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(77*sqrt(2)*a^(1/4)*b^(7/4)*c + 15*sqrt(2)*a^(3/4)*b^(5/4)*e + 7*sqrt(2)*a^(5/4)*b^(3/4)*g + 5*sqrt(2)*a^(7/4)*b^(1/4)*i + 80*sqrt(a)*b^(3/2)*d + 16*a^(3/2)*sqrt(b)*h)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/(a^3*b)","A",0
210,0,0,0,0.000000," ","integrate((d*x+c)/(b*x^4+a)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
215,1,12,0,1.764045," ","integrate((-b*g*x^4+a*g)/(b*x^4+a)^(3/2),x, algorithm=""maxima"")","\frac{g x}{\sqrt{b x^{4} + a}}"," ",0,"g*x/sqrt(b*x^4 + a)","A",0
216,1,25,0,1.767064," ","integrate((-b*g*x^4+a*g+e*x)/(b*x^4+a)^(3/2),x, algorithm=""maxima"")","\frac{2 \, a g x + e x^{2}}{2 \, \sqrt{b x^{4} + a} a}"," ",0,"1/2*(2*a*g*x + e*x^2)/(sqrt(b*x^4 + a)*a)","A",0
217,1,23,0,1.828187," ","integrate((-b*g*x^4+f*x^3+a*g)/(b*x^4+a)^(3/2),x, algorithm=""maxima"")","\frac{2 \, b g x - f}{2 \, \sqrt{b x^{4} + a} b}"," ",0,"1/2*(2*b*g*x - f)/(sqrt(b*x^4 + a)*b)","A",0
218,1,44,0,1.849713," ","integrate((-b*g*x^4+f*x^3+a*g+e*x)/(b*x^4+a)^(3/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{4} + a} {\left(2 \, a b g x + b e x^{2} - a f\right)}}{2 \, {\left(a b^{2} x^{4} + a^{2} b\right)}}"," ",0,"1/2*sqrt(b*x^4 + a)*(2*a*b*g*x + b*e*x^2 - a*f)/(a*b^2*x^4 + a^2*b)","A",0
219,1,10,0,3.243534," ","integrate((x^4-1)/(x^4+1)^(3/2),x, algorithm=""maxima"")","-\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=""maxima"")","\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
221,0,0,0,0.000000," ","integrate((1+x)/(x^5+1),x, algorithm=""maxima"")","\int \frac{x + 1}{x^{5} + 1}\,{d x}"," ",0,"integrate((x + 1)/(x^5 + 1), x)","F",0
222,0,0,0,0.000000," ","integrate((1-x)/(-x^5+1),x, algorithm=""maxima"")","\int \frac{x - 1}{x^{5} - 1}\,{d x}"," ",0,"integrate((x - 1)/(x^5 - 1), x)","F",0
223,1,209,0,1.374154," ","integrate(x^11*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{10 \, b^{5} f x^{18} + 12 \, {\left(b^{5} e - a b^{4} f\right)} x^{15} + 15 \, {\left(b^{5} d - a b^{4} e + a^{2} b^{3} f\right)} x^{12} + 20 \, {\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} f\right)} x^{9} - 30 \, {\left(a b^{4} c - a^{2} b^{3} d + a^{3} b^{2} e - a^{4} b f\right)} x^{6} + 60 \, {\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} x^{3}}{180 \, b^{6}} - \frac{{\left(a^{3} b^{3} c - a^{4} b^{2} d + a^{5} b e - a^{6} f\right)} \log\left(b x^{3} + a\right)}{3 \, b^{7}}"," ",0,"1/180*(10*b^5*f*x^18 + 12*(b^5*e - a*b^4*f)*x^15 + 15*(b^5*d - a*b^4*e + a^2*b^3*f)*x^12 + 20*(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*x^9 - 30*(a*b^4*c - a^2*b^3*d + a^3*b^2*e - a^4*b*f)*x^6 + 60*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*x^3)/b^6 - 1/3*(a^3*b^3*c - a^4*b^2*d + a^5*b*e - a^6*f)*log(b*x^3 + a)/b^7","A",0
224,1,169,0,1.383326," ","integrate(x^8*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{12 \, b^{4} f x^{15} + 15 \, {\left(b^{4} e - a b^{3} f\right)} x^{12} + 20 \, {\left(b^{4} d - a b^{3} e + a^{2} b^{2} f\right)} x^{9} + 30 \, {\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} x^{6} - 60 \, {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} x^{3}}{180 \, b^{5}} + \frac{{\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} \log\left(b x^{3} + a\right)}{3 \, b^{6}}"," ",0,"1/180*(12*b^4*f*x^15 + 15*(b^4*e - a*b^3*f)*x^12 + 20*(b^4*d - a*b^3*e + a^2*b^2*f)*x^9 + 30*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*x^6 - 60*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*x^3)/b^5 + 1/3*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*log(b*x^3 + a)/b^6","A",0
225,1,129,0,1.374021," ","integrate(x^5*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{3 \, b^{3} f x^{12} + 4 \, {\left(b^{3} e - a b^{2} f\right)} x^{9} + 6 \, {\left(b^{3} d - a b^{2} e + a^{2} b f\right)} x^{6} + 12 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x^{3}}{36 \, b^{4}} - \frac{{\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} \log\left(b x^{3} + a\right)}{3 \, b^{5}}"," ",0,"1/36*(3*b^3*f*x^12 + 4*(b^3*e - a*b^2*f)*x^9 + 6*(b^3*d - a*b^2*e + a^2*b*f)*x^6 + 12*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^3)/b^4 - 1/3*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*log(b*x^3 + a)/b^5","A",0
226,1,91,0,1.388536," ","integrate(x^2*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{2 \, b^{2} f x^{9} + 3 \, {\left(b^{2} e - a b f\right)} x^{6} + 6 \, {\left(b^{2} d - a b e + a^{2} f\right)} x^{3}}{18 \, b^{3}} + \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \log\left(b x^{3} + a\right)}{3 \, b^{4}}"," ",0,"1/18*(2*b^2*f*x^9 + 3*(b^2*e - a*b*f)*x^6 + 6*(b^2*d - a*b*e + a^2*f)*x^3)/b^3 + 1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(b*x^3 + a)/b^4","A",0
227,1,77,0,1.382728," ","integrate((f*x^9+e*x^6+d*x^3+c)/x/(b*x^3+a),x, algorithm=""maxima"")","\frac{c \log\left(x^{3}\right)}{3 \, a} + \frac{b f x^{6} + 2 \, {\left(b e - a f\right)} x^{3}}{6 \, b^{2}} - \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \log\left(b x^{3} + a\right)}{3 \, a b^{3}}"," ",0,"1/3*c*log(x^3)/a + 1/6*(b*f*x^6 + 2*(b*e - a*f)*x^3)/b^2 - 1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(b*x^3 + a)/(a*b^3)","A",0
228,1,77,0,1.334668," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^4/(b*x^3+a),x, algorithm=""maxima"")","\frac{f x^{3}}{3 \, b} - \frac{{\left(b c - a d\right)} \log\left(x^{3}\right)}{3 \, a^{2}} + \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \log\left(b x^{3} + a\right)}{3 \, a^{2} b^{2}} - \frac{c}{3 \, a x^{3}}"," ",0,"1/3*f*x^3/b - 1/3*(b*c - a*d)*log(x^3)/a^2 + 1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(b*x^3 + a)/(a^2*b^2) - 1/3*c/(a*x^3)","A",0
229,1,93,0,1.356223," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^7/(b*x^3+a),x, algorithm=""maxima"")","\frac{{\left(b^{2} c - a b d + a^{2} e\right)} \log\left(x^{3}\right)}{3 \, a^{3}} - \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \log\left(b x^{3} + a\right)}{3 \, a^{3} b} + \frac{2 \, {\left(b c - a d\right)} x^{3} - a c}{6 \, a^{2} x^{6}}"," ",0,"1/3*(b^2*c - a*b*d + a^2*e)*log(x^3)/a^3 - 1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(b*x^3 + a)/(a^3*b) + 1/6*(2*(b*c - a*d)*x^3 - a*c)/(a^2*x^6)","A",0
230,1,125,0,1.358104," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^10/(b*x^3+a),x, algorithm=""maxima"")","\frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \log\left(b x^{3} + a\right)}{3 \, a^{4}} - \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \log\left(x^{3}\right)}{3 \, a^{4}} - \frac{6 \, {\left(b^{2} c - a b d + a^{2} e\right)} x^{6} - 3 \, {\left(a b c - a^{2} d\right)} x^{3} + 2 \, a^{2} c}{18 \, a^{3} x^{9}}"," ",0,"1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(b*x^3 + a)/a^4 - 1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x^3)/a^4 - 1/18*(6*(b^2*c - a*b*d + a^2*e)*x^6 - 3*(a*b*c - a^2*d)*x^3 + 2*a^2*c)/(a^3*x^9)","A",0
231,1,166,0,1.359023," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^13/(b*x^3+a),x, algorithm=""maxima"")","-\frac{{\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} \log\left(b x^{3} + a\right)}{3 \, a^{5}} + \frac{{\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} \log\left(x^{3}\right)}{3 \, a^{5}} + \frac{12 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x^{9} - 6 \, {\left(a b^{2} c - a^{2} b d + a^{3} e\right)} x^{6} - 3 \, a^{3} c + 4 \, {\left(a^{2} b c - a^{3} d\right)} x^{3}}{36 \, a^{4} x^{12}}"," ",0,"-1/3*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*log(b*x^3 + a)/a^5 + 1/3*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*log(x^3)/a^5 + 1/36*(12*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^9 - 6*(a*b^2*c - a^2*b*d + a^3*e)*x^6 - 3*a^3*c + 4*(a^2*b*c - a^3*d)*x^3)/(a^4*x^12)","A",0
232,1,208,0,1.414760," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^16/(b*x^3+a),x, algorithm=""maxima"")","\frac{{\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} f\right)} \log\left(b x^{3} + a\right)}{3 \, a^{6}} - \frac{{\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} f\right)} \log\left(x^{3}\right)}{3 \, a^{6}} - \frac{60 \, {\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} x^{12} - 30 \, {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} x^{9} + 20 \, {\left(a^{2} b^{2} c - a^{3} b d + a^{4} e\right)} x^{6} + 12 \, a^{4} c - 15 \, {\left(a^{3} b c - a^{4} d\right)} x^{3}}{180 \, a^{5} x^{15}}"," ",0,"1/3*(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*log(b*x^3 + a)/a^6 - 1/3*(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*log(x^3)/a^6 - 1/180*(60*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*x^12 - 30*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*x^9 + 20*(a^2*b^2*c - a^3*b*d + a^4*e)*x^6 + 12*a^4*c - 15*(a^3*b*c - a^4*d)*x^3)/(a^5*x^15)","A",0
233,1,351,0,3.014813," ","integrate(x^9*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{455 \, b^{5} f x^{16} + 560 \, {\left(b^{5} e - a b^{4} f\right)} x^{13} + 728 \, {\left(b^{5} d - a b^{4} e + a^{2} b^{3} f\right)} x^{10} + 1040 \, {\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} f\right)} x^{7} - 1820 \, {\left(a b^{4} c - a^{2} b^{3} d + a^{3} b^{2} e - a^{4} b f\right)} x^{4} + 7280 \, {\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} x}{7280 \, b^{6}} - \frac{\sqrt{3} {\left(a^{3} b^{3} c - a^{4} b^{2} d + a^{5} b e - a^{6} 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^{7} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(a^{3} b^{3} c - a^{4} b^{2} d + a^{5} b e - a^{6} 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^{7} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(a^{3} b^{3} c - a^{4} b^{2} d + a^{5} b e - a^{6} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{7} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/7280*(455*b^5*f*x^16 + 560*(b^5*e - a*b^4*f)*x^13 + 728*(b^5*d - a*b^4*e + a^2*b^3*f)*x^10 + 1040*(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*x^7 - 1820*(a*b^4*c - a^2*b^3*d + a^3*b^2*e - a^4*b*f)*x^4 + 7280*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*x)/b^6 - 1/3*sqrt(3)*(a^3*b^3*c - a^4*b^2*d + a^5*b*e - a^6*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^7*(a/b)^(2/3)) + 1/6*(a^3*b^3*c - a^4*b^2*d + a^5*b*e - a^6*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^7*(a/b)^(2/3)) - 1/3*(a^3*b^3*c - a^4*b^2*d + a^5*b*e - a^6*f)*log(x + (a/b)^(1/3))/(b^7*(a/b)^(2/3))","A",0
234,1,313,0,2.945698," ","integrate(x^7*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{\sqrt{3} {\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} 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^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{220 \, b^{4} f x^{14} + 280 \, {\left(b^{4} e - a b^{3} f\right)} x^{11} + 385 \, {\left(b^{4} d - a b^{3} e + a^{2} b^{2} f\right)} x^{8} + 616 \, {\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} x^{5} - 1540 \, {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} x^{2}}{3080 \, b^{5}} + \frac{{\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} 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^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"1/3*sqrt(3)*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^6*(a/b)^(1/3)) + 1/3080*(220*b^4*f*x^14 + 280*(b^4*e - a*b^3*f)*x^11 + 385*(b^4*d - a*b^3*e + a^2*b^2*f)*x^8 + 616*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*x^5 - 1540*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*x^2)/b^5 + 1/6*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^6*(a/b)^(1/3)) - 1/3*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*log(x + (a/b)^(1/3))/(b^6*(a/b)^(1/3))","A",0
235,1,311,0,2.968382," ","integrate(x^6*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{140 \, b^{4} f x^{13} + 182 \, {\left(b^{4} e - a b^{3} f\right)} x^{10} + 260 \, {\left(b^{4} d - a b^{3} e + a^{2} b^{2} f\right)} x^{7} + 455 \, {\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} x^{4} - 1820 \, {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} x}{1820 \, b^{5}} + \frac{\sqrt{3} {\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} 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^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} 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^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/1820*(140*b^4*f*x^13 + 182*(b^4*e - a*b^3*f)*x^10 + 260*(b^4*d - a*b^3*e + a^2*b^2*f)*x^7 + 455*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*x^4 - 1820*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*x)/b^5 + 1/3*sqrt(3)*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^6*(a/b)^(2/3)) - 1/6*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^6*(a/b)^(2/3)) + 1/3*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*log(x + (a/b)^(1/3))/(b^6*(a/b)^(2/3))","A",0
236,1,269,0,3.024771," ","integrate(x^4*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} 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^{5} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{40 \, b^{3} f x^{11} + 55 \, {\left(b^{3} e - a b^{2} f\right)} x^{8} + 88 \, {\left(b^{3} d - a b^{2} e + a^{2} b f\right)} x^{5} + 220 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x^{2}}{440 \, b^{4}} - \frac{{\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} 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^{5} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{5} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"-1/3*sqrt(3)*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^5*(a/b)^(1/3)) + 1/440*(40*b^3*f*x^11 + 55*(b^3*e - a*b^2*f)*x^8 + 88*(b^3*d - a*b^2*e + a^2*b*f)*x^5 + 220*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/b^4 - 1/6*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^5*(a/b)^(1/3)) + 1/3*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*log(x + (a/b)^(1/3))/(b^5*(a/b)^(1/3))","A",0
237,1,267,0,2.929402," ","integrate(x^3*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{14 \, b^{3} f x^{10} + 20 \, {\left(b^{3} e - a b^{2} f\right)} x^{7} + 35 \, {\left(b^{3} d - a b^{2} e + a^{2} b f\right)} x^{4} + 140 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x}{140 \, b^{4}} - \frac{\sqrt{3} {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} 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^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} 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^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/140*(14*b^3*f*x^10 + 20*(b^3*e - a*b^2*f)*x^7 + 35*(b^3*d - a*b^2*e + a^2*b*f)*x^4 + 140*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/b^4 - 1/3*sqrt(3)*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^5*(a/b)^(2/3)) + 1/6*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^5*(a/b)^(2/3)) - 1/3*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*log(x + (a/b)^(1/3))/(b^5*(a/b)^(2/3))","A",0
238,1,225,0,3.013837," ","integrate(x*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{\sqrt{3} {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{5 \, b^{2} f x^{8} + 8 \, {\left(b^{2} e - a b f\right)} x^{5} + 20 \, {\left(b^{2} d - a b e + a^{2} f\right)} x^{2}}{40 \, b^{3}} + \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{4} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"1/3*sqrt(3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^4*(a/b)^(1/3)) + 1/40*(5*b^2*f*x^8 + 8*(b^2*e - a*b*f)*x^5 + 20*(b^2*d - a*b*e + a^2*f)*x^2)/b^3 + 1/6*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^4*(a/b)^(1/3)) - 1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x + (a/b)^(1/3))/(b^4*(a/b)^(1/3))","A",0
239,1,223,0,3.013700," ","integrate((f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{4 \, b^{2} f x^{7} + 7 \, {\left(b^{2} e - a b f\right)} x^{4} + 28 \, {\left(b^{2} d - a b e + a^{2} f\right)} x}{28 \, b^{3}} + \frac{\sqrt{3} {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/28*(4*b^2*f*x^7 + 7*(b^2*e - a*b*f)*x^4 + 28*(b^2*d - a*b*e + a^2*f)*x)/b^3 + 1/3*sqrt(3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^4*(a/b)^(2/3)) - 1/6*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^4*(a/b)^(2/3)) + 1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x + (a/b)^(1/3))/(b^4*(a/b)^(2/3))","A",0
240,1,217,0,2.962134," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^2/(b*x^3+a),x, algorithm=""maxima"")","\frac{2 \, b f x^{5} + 5 \, {\left(b e - a f\right)} x^{2}}{10 \, b^{2}} - \frac{c}{a x} - \frac{\sqrt{3} {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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 \, a b^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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 \, a b^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a b^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"1/10*(2*b*f*x^5 + 5*(b*e - a*f)*x^2)/b^2 - c/(a*x) - 1/3*sqrt(3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^3*(a/b)^(1/3)) - 1/6*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^3*(a/b)^(1/3)) + 1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x + (a/b)^(1/3))/(a*b^3*(a/b)^(1/3))","A",0
241,1,214,0,2.981774," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^3/(b*x^3+a),x, algorithm=""maxima"")","\frac{b f x^{4} + 4 \, {\left(b e - a f\right)} x}{4 \, b^{2}} - \frac{c}{2 \, a x^{2}} - \frac{\sqrt{3} {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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 \, a b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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 \, a b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/4*(b*f*x^4 + 4*(b*e - a*f)*x)/b^2 - 1/2*c/(a*x^2) - 1/3*sqrt(3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^3*(a/b)^(2/3)) + 1/6*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^3*(a/b)^(2/3)) - 1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x + (a/b)^(1/3))/(a*b^3*(a/b)^(2/3))","A",0
242,1,217,0,3.037254," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^5/(b*x^3+a),x, algorithm=""maxima"")","\frac{f x^{2}}{2 \, b} + \frac{\sqrt{3} {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{4 \, {\left(b c - a d\right)} 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^2*b*e - a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b^2*(a/b)^(1/3)) + 1/6*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b^2*(a/b)^(1/3)) - 1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x + (a/b)^(1/3))/(a^2*b^2*(a/b)^(1/3)) + 1/4*(4*(b*c - a*d)*x^3 - a*c)/(a^2*x^4)","A",0
243,1,214,0,3.080189," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^6/(b*x^3+a),x, algorithm=""maxima"")","\frac{f x}{b} + \frac{\sqrt{3} {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{5 \, {\left(b c - a d\right)} 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^2*b*e - a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b^2*(a/b)^(2/3)) - 1/6*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b^2*(a/b)^(2/3)) + 1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x + (a/b)^(1/3))/(a^2*b^2*(a/b)^(2/3)) + 1/10*(5*(b*c - a*d)*x^3 - 2*a*c)/(a^2*x^5)","A",0
244,1,234,0,3.066603," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^8/(b*x^3+a),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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 \, a^{3} b \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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 \, a^{3} b \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a^{3} b \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{28 \, {\left(b^{2} c - a b d + a^{2} e\right)} x^{6} - 7 \, {\left(a b c - a^{2} d\right)} x^{3} + 4 \, a^{2} c}{28 \, a^{3} x^{7}}"," ",0,"-1/3*sqrt(3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^3*b*(a/b)^(1/3)) - 1/6*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*b*(a/b)^(1/3)) + 1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x + (a/b)^(1/3))/(a^3*b*(a/b)^(1/3)) - 1/28*(28*(b^2*c - a*b*d + a^2*e)*x^6 - 7*(a*b*c - a^2*d)*x^3 + 4*a^2*c)/(a^3*x^7)","A",0
245,1,234,0,3.008823," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^9/(b*x^3+a),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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 \, a^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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 \, a^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{20 \, {\left(b^{2} c - a b d + a^{2} e\right)} x^{6} - 8 \, {\left(a b c - a^{2} d\right)} x^{3} + 5 \, a^{2} c}{40 \, a^{3} x^{8}}"," ",0,"-1/3*sqrt(3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^3*b*(a/b)^(2/3)) + 1/6*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*b*(a/b)^(2/3)) - 1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x + (a/b)^(1/3))/(a^3*b*(a/b)^(2/3)) - 1/40*(20*(b^2*c - a*b*d + a^2*e)*x^6 - 8*(a*b*c - a^2*d)*x^3 + 5*a^2*c)/(a^3*x^8)","A",0
246,1,260,0,3.054004," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^11/(b*x^3+a),x, algorithm=""maxima"")","\frac{\sqrt{3} {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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 \, a^{4} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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 \, a^{4} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a^{4} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{140 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x^{9} - 35 \, {\left(a b^{2} c - a^{2} b d + a^{3} e\right)} x^{6} - 14 \, a^{3} c + 20 \, {\left(a^{2} b c - a^{3} d\right)} x^{3}}{140 \, a^{4} x^{10}}"," ",0,"1/3*sqrt(3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^4*(a/b)^(1/3)) + 1/6*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^4*(a/b)^(1/3)) - 1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x + (a/b)^(1/3))/(a^4*(a/b)^(1/3)) + 1/140*(140*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^9 - 35*(a*b^2*c - a^2*b*d + a^3*e)*x^6 - 14*a^3*c + 20*(a^2*b*c - a^3*d)*x^3)/(a^4*x^10)","A",0
247,1,260,0,2.974332," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^12/(b*x^3+a),x, algorithm=""maxima"")","\frac{\sqrt{3} {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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 \, a^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} 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 \, a^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{220 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x^{9} - 88 \, {\left(a b^{2} c - a^{2} b d + a^{3} e\right)} x^{6} - 40 \, a^{3} c + 55 \, {\left(a^{2} b c - a^{3} d\right)} x^{3}}{440 \, a^{4} x^{11}}"," ",0,"1/3*sqrt(3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^4*(a/b)^(2/3)) - 1/6*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^4*(a/b)^(2/3)) + 1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x + (a/b)^(1/3))/(a^4*(a/b)^(2/3)) + 1/440*(220*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^9 - 88*(a*b^2*c - a^2*b*d + a^3*e)*x^6 - 40*a^3*c + 55*(a^2*b*c - a^3*d)*x^3)/(a^4*x^11)","A",0
248,1,307,0,2.987929," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^14/(b*x^3+a),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b 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 \, a^{5} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b 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 \, a^{5} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a^{5} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{1820 \, {\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} x^{12} - 455 \, {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} x^{9} + 260 \, {\left(a^{2} b^{2} c - a^{3} b d + a^{4} e\right)} x^{6} + 140 \, a^{4} c - 182 \, {\left(a^{3} b c - a^{4} d\right)} x^{3}}{1820 \, a^{5} x^{13}}"," ",0,"-1/3*sqrt(3)*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^5*(a/b)^(1/3)) - 1/6*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^5*(a/b)^(1/3)) + 1/3*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*log(x + (a/b)^(1/3))/(a^5*(a/b)^(1/3)) - 1/1820*(1820*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*x^12 - 455*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*x^9 + 260*(a^2*b^2*c - a^3*b*d + a^4*e)*x^6 + 140*a^4*c - 182*(a^3*b*c - a^4*d)*x^3)/(a^5*x^13)","A",0
249,1,307,0,3.114447," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^15/(b*x^3+a),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b 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 \, a^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b 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 \, a^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{1540 \, {\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} x^{12} - 616 \, {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} x^{9} + 385 \, {\left(a^{2} b^{2} c - a^{3} b d + a^{4} e\right)} x^{6} + 220 \, a^{4} c - 280 \, {\left(a^{3} b c - a^{4} d\right)} x^{3}}{3080 \, a^{5} x^{14}}"," ",0,"-1/3*sqrt(3)*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^5*(a/b)^(2/3)) + 1/6*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^5*(a/b)^(2/3)) - 1/3*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*log(x + (a/b)^(1/3))/(a^5*(a/b)^(2/3)) - 1/3080*(1540*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*x^12 - 616*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*x^9 + 385*(a^2*b^2*c - a^3*b*d + a^4*e)*x^6 + 220*a^4*c - 280*(a^3*b*c - a^4*d)*x^3)/(a^5*x^14)","A",0
250,1,353,0,3.029354," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^17/(b*x^3+a),x, algorithm=""maxima"")","\frac{\sqrt{3} {\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} 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 \, a^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} 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 \, a^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{7280 \, {\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} f\right)} x^{15} - 1820 \, {\left(a b^{4} c - a^{2} b^{3} d + a^{3} b^{2} e - a^{4} b f\right)} x^{12} + 1040 \, {\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} x^{9} - 728 \, {\left(a^{3} b^{2} c - a^{4} b d + a^{5} e\right)} x^{6} - 455 \, a^{5} c + 560 \, {\left(a^{4} b c - a^{5} d\right)} x^{3}}{7280 \, a^{6} x^{16}}"," ",0,"1/3*sqrt(3)*(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^6*(a/b)^(1/3)) + 1/6*(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^6*(a/b)^(1/3)) - 1/3*(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*log(x + (a/b)^(1/3))/(a^6*(a/b)^(1/3)) + 1/7280*(7280*(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*x^15 - 1820*(a*b^4*c - a^2*b^3*d + a^3*b^2*e - a^4*b*f)*x^12 + 1040*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*x^9 - 728*(a^3*b^2*c - a^4*b*d + a^5*e)*x^6 - 455*a^5*c + 560*(a^4*b*c - a^5*d)*x^3)/(a^6*x^16)","A",0
251,1,222,0,1.303446," ","integrate(x^11*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{a^{3} b^{3} c - a^{4} b^{2} d + a^{5} b e - a^{6} f}{3 \, {\left(b^{8} x^{3} + a b^{7}\right)}} + \frac{12 \, b^{4} f x^{15} + 15 \, {\left(b^{4} e - 2 \, a b^{3} f\right)} x^{12} + 20 \, {\left(b^{4} d - 2 \, a b^{3} e + 3 \, a^{2} b^{2} f\right)} x^{9} + 30 \, {\left(b^{4} c - 2 \, a b^{3} d + 3 \, a^{2} b^{2} e - 4 \, a^{3} b f\right)} x^{6} - 60 \, {\left(2 \, a b^{3} c - 3 \, a^{2} b^{2} d + 4 \, a^{3} b e - 5 \, a^{4} f\right)} x^{3}}{180 \, b^{6}} + \frac{{\left(3 \, a^{2} b^{3} c - 4 \, a^{3} b^{2} d + 5 \, a^{4} b e - 6 \, a^{5} f\right)} \log\left(b x^{3} + a\right)}{3 \, b^{7}}"," ",0,"1/3*(a^3*b^3*c - a^4*b^2*d + a^5*b*e - a^6*f)/(b^8*x^3 + a*b^7) + 1/180*(12*b^4*f*x^15 + 15*(b^4*e - 2*a*b^3*f)*x^12 + 20*(b^4*d - 2*a*b^3*e + 3*a^2*b^2*f)*x^9 + 30*(b^4*c - 2*a*b^3*d + 3*a^2*b^2*e - 4*a^3*b*f)*x^6 - 60*(2*a*b^3*c - 3*a^2*b^2*d + 4*a^3*b*e - 5*a^4*f)*x^3)/b^6 + 1/3*(3*a^2*b^3*c - 4*a^3*b^2*d + 5*a^4*b*e - 6*a^5*f)*log(b*x^3 + a)/b^7","A",0
252,1,180,0,1.381186," ","integrate(x^8*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f}{3 \, {\left(b^{7} x^{3} + a b^{6}\right)}} + \frac{3 \, b^{3} f x^{12} + 4 \, {\left(b^{3} e - 2 \, a b^{2} f\right)} x^{9} + 6 \, {\left(b^{3} d - 2 \, a b^{2} e + 3 \, a^{2} b f\right)} x^{6} + 12 \, {\left(b^{3} c - 2 \, a b^{2} d + 3 \, a^{2} b e - 4 \, a^{3} f\right)} x^{3}}{36 \, b^{5}} - \frac{{\left(2 \, a b^{3} c - 3 \, a^{2} b^{2} d + 4 \, a^{3} b e - 5 \, a^{4} f\right)} \log\left(b x^{3} + a\right)}{3 \, b^{6}}"," ",0,"-1/3*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)/(b^7*x^3 + a*b^6) + 1/36*(3*b^3*f*x^12 + 4*(b^3*e - 2*a*b^2*f)*x^9 + 6*(b^3*d - 2*a*b^2*e + 3*a^2*b*f)*x^6 + 12*(b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*x^3)/b^5 - 1/3*(2*a*b^3*c - 3*a^2*b^2*d + 4*a^3*b*e - 5*a^4*f)*log(b*x^3 + a)/b^6","A",0
253,1,138,0,1.396560," ","integrate(x^5*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f}{3 \, {\left(b^{6} x^{3} + a b^{5}\right)}} + \frac{2 \, b^{2} f x^{9} + 3 \, {\left(b^{2} e - 2 \, a b f\right)} x^{6} + 6 \, {\left(b^{2} d - 2 \, a b e + 3 \, a^{2} f\right)} x^{3}}{18 \, b^{4}} + \frac{{\left(b^{3} c - 2 \, a b^{2} d + 3 \, a^{2} b e - 4 \, a^{3} f\right)} \log\left(b x^{3} + a\right)}{3 \, b^{5}}"," ",0,"1/3*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)/(b^6*x^3 + a*b^5) + 1/18*(2*b^2*f*x^9 + 3*(b^2*e - 2*a*b*f)*x^6 + 6*(b^2*d - 2*a*b*e + 3*a^2*f)*x^3)/b^4 + 1/3*(b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*log(b*x^3 + a)/b^5","A",0
254,1,98,0,1.352223," ","integrate(x^2*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{b^{3} c - a b^{2} d + a^{2} b e - a^{3} f}{3 \, {\left(b^{5} x^{3} + a b^{4}\right)}} + \frac{b f x^{6} + 2 \, {\left(b e - 2 \, a f\right)} x^{3}}{6 \, b^{3}} + \frac{{\left(b^{2} d - 2 \, a b e + 3 \, a^{2} f\right)} \log\left(b x^{3} + a\right)}{3 \, b^{4}}"," ",0,"-1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(b^5*x^3 + a*b^4) + 1/6*(b*f*x^6 + 2*(b*e - 2*a*f)*x^3)/b^3 + 1/3*(b^2*d - 2*a*b*e + 3*a^2*f)*log(b*x^3 + a)/b^4","A",0
255,1,100,0,1.318832," ","integrate((f*x^9+e*x^6+d*x^3+c)/x/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{f x^{3}}{3 \, b^{2}} + \frac{b^{3} c - a b^{2} d + a^{2} b e - a^{3} f}{3 \, {\left(a b^{4} x^{3} + a^{2} b^{3}\right)}} + \frac{c \log\left(x^{3}\right)}{3 \, a^{2}} - \frac{{\left(b^{3} c - a^{2} b e + 2 \, a^{3} f\right)} \log\left(b x^{3} + a\right)}{3 \, a^{2} b^{3}}"," ",0,"1/3*f*x^3/b^2 + 1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(a*b^4*x^3 + a^2*b^3) + 1/3*c*log(x^3)/a^2 - 1/3*(b^3*c - a^2*b*e + 2*a^3*f)*log(b*x^3 + a)/(a^2*b^3)","A",0
256,1,116,0,1.433911," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^4/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{a b^{2} c + {\left(2 \, b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x^{3}}{3 \, {\left(a^{2} b^{3} x^{6} + a^{3} b^{2} x^{3}\right)}} - \frac{{\left(2 \, b c - a d\right)} \log\left(x^{3}\right)}{3 \, a^{3}} + \frac{{\left(2 \, b^{3} c - a b^{2} d + a^{3} f\right)} \log\left(b x^{3} + a\right)}{3 \, a^{3} b^{2}}"," ",0,"-1/3*(a*b^2*c + (2*b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^3)/(a^2*b^3*x^6 + a^3*b^2*x^3) - 1/3*(2*b*c - a*d)*log(x^3)/a^3 + 1/3*(2*b^3*c - a*b^2*d + a^3*f)*log(b*x^3 + a)/(a^3*b^2)","A",0
257,1,138,0,1.353124," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^7/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, b^{3} c - 2 \, a b^{2} d + a^{2} b e - a^{3} f\right)} x^{6} - a^{2} b c + {\left(3 \, a b^{2} c - 2 \, a^{2} b d\right)} x^{3}}{6 \, {\left(a^{3} b^{2} x^{9} + a^{4} b x^{6}\right)}} - \frac{{\left(3 \, b^{2} c - 2 \, a b d + a^{2} e\right)} \log\left(b x^{3} + a\right)}{3 \, a^{4}} + \frac{{\left(3 \, b^{2} c - 2 \, a b d + a^{2} e\right)} \log\left(x^{3}\right)}{3 \, a^{4}}"," ",0,"1/6*(2*(3*b^3*c - 2*a*b^2*d + a^2*b*e - a^3*f)*x^6 - a^2*b*c + (3*a*b^2*c - 2*a^2*b*d)*x^3)/(a^3*b^2*x^9 + a^4*b*x^6) - 1/3*(3*b^2*c - 2*a*b*d + a^2*e)*log(b*x^3 + a)/a^4 + 1/3*(3*b^2*c - 2*a*b*d + a^2*e)*log(x^3)/a^4","A",0
258,1,181,0,1.432781," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^10/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{6 \, {\left(4 \, b^{3} c - 3 \, a b^{2} d + 2 \, a^{2} b e - a^{3} f\right)} x^{9} + 3 \, {\left(4 \, a b^{2} c - 3 \, a^{2} b d + 2 \, a^{3} e\right)} x^{6} + 2 \, a^{3} c - {\left(4 \, a^{2} b c - 3 \, a^{3} d\right)} x^{3}}{18 \, {\left(a^{4} b x^{12} + a^{5} x^{9}\right)}} + \frac{{\left(4 \, b^{3} c - 3 \, a b^{2} d + 2 \, a^{2} b e - a^{3} f\right)} \log\left(b x^{3} + a\right)}{3 \, a^{5}} - \frac{{\left(4 \, b^{3} c - 3 \, a b^{2} d + 2 \, a^{2} b e - a^{3} f\right)} \log\left(x^{3}\right)}{3 \, a^{5}}"," ",0,"-1/18*(6*(4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)*x^9 + 3*(4*a*b^2*c - 3*a^2*b*d + 2*a^3*e)*x^6 + 2*a^3*c - (4*a^2*b*c - 3*a^3*d)*x^3)/(a^4*b*x^12 + a^5*x^9) + 1/3*(4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)*log(b*x^3 + a)/a^5 - 1/3*(4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)*log(x^3)/a^5","A",0
259,1,226,0,1.438172," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^13/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{12 \, {\left(5 \, b^{4} c - 4 \, a b^{3} d + 3 \, a^{2} b^{2} e - 2 \, a^{3} b f\right)} x^{12} + 6 \, {\left(5 \, a b^{3} c - 4 \, a^{2} b^{2} d + 3 \, a^{3} b e - 2 \, a^{4} f\right)} x^{9} - 2 \, {\left(5 \, a^{2} b^{2} c - 4 \, a^{3} b d + 3 \, a^{4} e\right)} x^{6} - 3 \, a^{4} c + {\left(5 \, a^{3} b c - 4 \, a^{4} d\right)} x^{3}}{36 \, {\left(a^{5} b x^{15} + a^{6} x^{12}\right)}} - \frac{{\left(5 \, b^{4} c - 4 \, a b^{3} d + 3 \, a^{2} b^{2} e - 2 \, a^{3} b f\right)} \log\left(b x^{3} + a\right)}{3 \, a^{6}} + \frac{{\left(5 \, b^{4} c - 4 \, a b^{3} d + 3 \, a^{2} b^{2} e - 2 \, a^{3} b f\right)} \log\left(x^{3}\right)}{3 \, a^{6}}"," ",0,"1/36*(12*(5*b^4*c - 4*a*b^3*d + 3*a^2*b^2*e - 2*a^3*b*f)*x^12 + 6*(5*a*b^3*c - 4*a^2*b^2*d + 3*a^3*b*e - 2*a^4*f)*x^9 - 2*(5*a^2*b^2*c - 4*a^3*b*d + 3*a^4*e)*x^6 - 3*a^4*c + (5*a^3*b*c - 4*a^4*d)*x^3)/(a^5*b*x^15 + a^6*x^12) - 1/3*(5*b^4*c - 4*a*b^3*d + 3*a^2*b^2*e - 2*a^3*b*f)*log(b*x^3 + a)/a^6 + 1/3*(5*b^4*c - 4*a*b^3*d + 3*a^2*b^2*e - 2*a^3*b*f)*log(x^3)/a^6","A",0
260,1,369,0,2.981766," ","integrate(x^9*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} x}{3 \, {\left(b^{7} x^{3} + a b^{6}\right)}} + \frac{140 \, b^{4} f x^{13} + 182 \, {\left(b^{4} e - 2 \, a b^{3} f\right)} x^{10} + 260 \, {\left(b^{4} d - 2 \, a b^{3} e + 3 \, a^{2} b^{2} f\right)} x^{7} + 455 \, {\left(b^{4} c - 2 \, a b^{3} d + 3 \, a^{2} b^{2} e - 4 \, a^{3} b f\right)} x^{4} - 1820 \, {\left(2 \, a b^{3} c - 3 \, a^{2} b^{2} d + 4 \, a^{3} b e - 5 \, a^{4} f\right)} x}{1820 \, b^{6}} + \frac{\sqrt{3} {\left(7 \, a^{2} b^{3} c - 10 \, a^{3} b^{2} d + 13 \, a^{4} b e - 16 \, a^{5} 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 \, b^{7} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(7 \, a^{2} b^{3} c - 10 \, a^{3} b^{2} d + 13 \, a^{4} b e - 16 \, a^{5} 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 \, b^{7} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(7 \, a^{2} b^{3} c - 10 \, a^{3} b^{2} d + 13 \, a^{4} b e - 16 \, a^{5} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, b^{7} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/3*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*x/(b^7*x^3 + a*b^6) + 1/1820*(140*b^4*f*x^13 + 182*(b^4*e - 2*a*b^3*f)*x^10 + 260*(b^4*d - 2*a*b^3*e + 3*a^2*b^2*f)*x^7 + 455*(b^4*c - 2*a*b^3*d + 3*a^2*b^2*e - 4*a^3*b*f)*x^4 - 1820*(2*a*b^3*c - 3*a^2*b^2*d + 4*a^3*b*e - 5*a^4*f)*x)/b^6 + 1/9*sqrt(3)*(7*a^2*b^3*c - 10*a^3*b^2*d + 13*a^4*b*e - 16*a^5*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^7*(a/b)^(2/3)) - 1/18*(7*a^2*b^3*c - 10*a^3*b^2*d + 13*a^4*b*e - 16*a^5*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^7*(a/b)^(2/3)) + 1/9*(7*a^2*b^3*c - 10*a^3*b^2*d + 13*a^4*b*e - 16*a^5*f)*log(x + (a/b)^(1/3))/(b^7*(a/b)^(2/3))","A",0
261,1,325,0,3.021255," ","integrate(x^7*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{{\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} x^{2}}{3 \, {\left(b^{6} x^{3} + a b^{5}\right)}} - \frac{\sqrt{3} {\left(5 \, a b^{3} c - 8 \, a^{2} b^{2} d + 11 \, a^{3} b e - 14 \, a^{4} 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 \, b^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{40 \, b^{3} f x^{11} + 55 \, {\left(b^{3} e - 2 \, a b^{2} f\right)} x^{8} + 88 \, {\left(b^{3} d - 2 \, a b^{2} e + 3 \, a^{2} b f\right)} x^{5} + 220 \, {\left(b^{3} c - 2 \, a b^{2} d + 3 \, a^{2} b e - 4 \, a^{3} f\right)} x^{2}}{440 \, b^{5}} - \frac{{\left(5 \, a b^{3} c - 8 \, a^{2} b^{2} d + 11 \, a^{3} b e - 14 \, a^{4} 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 \, b^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(5 \, a b^{3} c - 8 \, a^{2} b^{2} d + 11 \, a^{3} b e - 14 \, a^{4} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, b^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"1/3*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*x^2/(b^6*x^3 + a*b^5) - 1/9*sqrt(3)*(5*a*b^3*c - 8*a^2*b^2*d + 11*a^3*b*e - 14*a^4*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^6*(a/b)^(1/3)) + 1/440*(40*b^3*f*x^11 + 55*(b^3*e - 2*a*b^2*f)*x^8 + 88*(b^3*d - 2*a*b^2*e + 3*a^2*b*f)*x^5 + 220*(b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*x^2)/b^5 - 1/18*(5*a*b^3*c - 8*a^2*b^2*d + 11*a^3*b*e - 14*a^4*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^6*(a/b)^(1/3)) + 1/9*(5*a*b^3*c - 8*a^2*b^2*d + 11*a^3*b*e - 14*a^4*f)*log(x + (a/b)^(1/3))/(b^6*(a/b)^(1/3))","A",0
262,1,321,0,3.016113," ","integrate(x^6*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{{\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} x}{3 \, {\left(b^{6} x^{3} + a b^{5}\right)}} + \frac{14 \, b^{3} f x^{10} + 20 \, {\left(b^{3} e - 2 \, a b^{2} f\right)} x^{7} + 35 \, {\left(b^{3} d - 2 \, a b^{2} e + 3 \, a^{2} b f\right)} x^{4} + 140 \, {\left(b^{3} c - 2 \, a b^{2} d + 3 \, a^{2} b e - 4 \, a^{3} f\right)} x}{140 \, b^{5}} - \frac{\sqrt{3} {\left(4 \, a b^{3} c - 7 \, a^{2} b^{2} d + 10 \, a^{3} b e - 13 \, a^{4} 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 \, b^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(4 \, a b^{3} c - 7 \, a^{2} b^{2} d + 10 \, a^{3} b e - 13 \, a^{4} 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 \, b^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(4 \, a b^{3} c - 7 \, a^{2} b^{2} d + 10 \, a^{3} b e - 13 \, a^{4} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, b^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*x/(b^6*x^3 + a*b^5) + 1/140*(14*b^3*f*x^10 + 20*(b^3*e - 2*a*b^2*f)*x^7 + 35*(b^3*d - 2*a*b^2*e + 3*a^2*b*f)*x^4 + 140*(b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*x)/b^5 - 1/9*sqrt(3)*(4*a*b^3*c - 7*a^2*b^2*d + 10*a^3*b*e - 13*a^4*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^6*(a/b)^(2/3)) + 1/18*(4*a*b^3*c - 7*a^2*b^2*d + 10*a^3*b*e - 13*a^4*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^6*(a/b)^(2/3)) - 1/9*(4*a*b^3*c - 7*a^2*b^2*d + 10*a^3*b*e - 13*a^4*f)*log(x + (a/b)^(1/3))/(b^6*(a/b)^(2/3))","A",0
263,1,277,0,3.077893," ","integrate(x^4*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x^{2}}{3 \, {\left(b^{5} x^{3} + a b^{4}\right)}} + \frac{\sqrt{3} {\left(2 \, b^{3} c - 5 \, a b^{2} d + 8 \, a^{2} b e - 11 \, a^{3} 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 \, b^{5} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{5 \, b^{2} f x^{8} + 8 \, {\left(b^{2} e - 2 \, a b f\right)} x^{5} + 20 \, {\left(b^{2} d - 2 \, a b e + 3 \, a^{2} f\right)} x^{2}}{40 \, b^{4}} + \frac{{\left(2 \, b^{3} c - 5 \, a b^{2} d + 8 \, a^{2} b e - 11 \, a^{3} 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 \, b^{5} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(2 \, b^{3} c - 5 \, a b^{2} d + 8 \, a^{2} b e - 11 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, b^{5} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"-1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2/(b^5*x^3 + a*b^4) + 1/9*sqrt(3)*(2*b^3*c - 5*a*b^2*d + 8*a^2*b*e - 11*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^5*(a/b)^(1/3)) + 1/40*(5*b^2*f*x^8 + 8*(b^2*e - 2*a*b*f)*x^5 + 20*(b^2*d - 2*a*b*e + 3*a^2*f)*x^2)/b^4 + 1/18*(2*b^3*c - 5*a*b^2*d + 8*a^2*b*e - 11*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^5*(a/b)^(1/3)) - 1/9*(2*b^3*c - 5*a*b^2*d + 8*a^2*b*e - 11*a^3*f)*log(x + (a/b)^(1/3))/(b^5*(a/b)^(1/3))","A",0
264,1,270,0,2.984903," ","integrate(x^3*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x}{3 \, {\left(b^{5} x^{3} + a b^{4}\right)}} + \frac{4 \, b^{2} f x^{7} + 7 \, {\left(b^{2} e - 2 \, a b f\right)} x^{4} + 28 \, {\left(b^{2} d - 2 \, a b e + 3 \, a^{2} f\right)} x}{28 \, b^{4}} + \frac{\sqrt{3} {\left(b^{3} c - 4 \, a b^{2} d + 7 \, a^{2} b e - 10 \, a^{3} 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 \, b^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b^{3} c - 4 \, a b^{2} d + 7 \, a^{2} b e - 10 \, a^{3} 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 \, b^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b^{3} c - 4 \, a b^{2} d + 7 \, a^{2} b e - 10 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, b^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x/(b^5*x^3 + a*b^4) + 1/28*(4*b^2*f*x^7 + 7*(b^2*e - 2*a*b*f)*x^4 + 28*(b^2*d - 2*a*b*e + 3*a^2*f)*x)/b^4 + 1/9*sqrt(3)*(b^3*c - 4*a*b^2*d + 7*a^2*b*e - 10*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^5*(a/b)^(2/3)) - 1/18*(b^3*c - 4*a*b^2*d + 7*a^2*b*e - 10*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^5*(a/b)^(2/3)) + 1/9*(b^3*c - 4*a*b^2*d + 7*a^2*b*e - 10*a^3*f)*log(x + (a/b)^(1/3))/(b^5*(a/b)^(2/3))","A",0
265,1,259,0,3.121906," ","integrate(x*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x^{2}}{3 \, {\left(a b^{4} x^{3} + a^{2} b^{3}\right)}} + \frac{2 \, b f x^{5} + 5 \, {\left(b e - 2 \, a f\right)} x^{2}}{10 \, b^{3}} + \frac{\sqrt{3} {\left(b^{3} c + 2 \, a b^{2} d - 5 \, a^{2} b e + 8 \, a^{3} 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 \, a b^{4} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(b^{3} c + 2 \, a b^{2} d - 5 \, a^{2} b e + 8 \, a^{3} 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 \, a b^{4} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(b^{3} c + 2 \, a b^{2} d - 5 \, a^{2} b e + 8 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a b^{4} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2/(a*b^4*x^3 + a^2*b^3) + 1/10*(2*b*f*x^5 + 5*(b*e - 2*a*f)*x^2)/b^3 + 1/9*sqrt(3)*(b^3*c + 2*a*b^2*d - 5*a^2*b*e + 8*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^4*(a/b)^(1/3)) + 1/18*(b^3*c + 2*a*b^2*d - 5*a^2*b*e + 8*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^4*(a/b)^(1/3)) - 1/9*(b^3*c + 2*a*b^2*d - 5*a^2*b*e + 8*a^3*f)*log(x + (a/b)^(1/3))/(a*b^4*(a/b)^(1/3))","A",0
266,1,254,0,3.045303," ","integrate((f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x}{3 \, {\left(a b^{4} x^{3} + a^{2} b^{3}\right)}} + \frac{b f x^{4} + 4 \, {\left(b e - 2 \, a f\right)} x}{4 \, b^{3}} + \frac{\sqrt{3} {\left(2 \, b^{3} c + a b^{2} d - 4 \, a^{2} b e + 7 \, a^{3} 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 \, a b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(2 \, b^{3} c + a b^{2} d - 4 \, a^{2} b e + 7 \, a^{3} 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 \, a b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(2 \, b^{3} c + a b^{2} d - 4 \, a^{2} b e + 7 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x/(a*b^4*x^3 + a^2*b^3) + 1/4*(b*f*x^4 + 4*(b*e - 2*a*f)*x)/b^3 + 1/9*sqrt(3)*(2*b^3*c + a*b^2*d - 4*a^2*b*e + 7*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^4*(a/b)^(2/3)) - 1/18*(2*b^3*c + a*b^2*d - 4*a^2*b*e + 7*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^4*(a/b)^(2/3)) + 1/9*(2*b^3*c + a*b^2*d - 4*a^2*b*e + 7*a^3*f)*log(x + (a/b)^(1/3))/(a*b^4*(a/b)^(2/3))","A",0
267,1,258,0,3.014993," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^2/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{f x^{2}}{2 \, b^{2}} - \frac{3 \, a b^{2} c + {\left(4 \, b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x^{3}}{3 \, {\left(a^{2} b^{3} x^{4} + a^{3} b^{2} x\right)}} - \frac{\sqrt{3} {\left(4 \, b^{3} c - a b^{2} d - 2 \, a^{2} b e + 5 \, a^{3} 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 \, a^{2} b^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(4 \, b^{3} c - a b^{2} d - 2 \, a^{2} b e + 5 \, a^{3} 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 \, a^{2} b^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(4 \, b^{3} c - a b^{2} d - 2 \, a^{2} b e + 5 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{2} b^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"1/2*f*x^2/b^2 - 1/3*(3*a*b^2*c + (4*b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^3)/(a^2*b^3*x^4 + a^3*b^2*x) - 1/9*sqrt(3)*(4*b^3*c - a*b^2*d - 2*a^2*b*e + 5*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b^3*(a/b)^(1/3)) - 1/18*(4*b^3*c - a*b^2*d - 2*a^2*b*e + 5*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b^3*(a/b)^(1/3)) + 1/9*(4*b^3*c - a*b^2*d - 2*a^2*b*e + 5*a^3*f)*log(x + (a/b)^(1/3))/(a^2*b^3*(a/b)^(1/3))","A",0
268,1,258,0,2.971057," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^3/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{3 \, a b^{2} c + {\left(5 \, b^{3} c - 2 \, a b^{2} d + 2 \, a^{2} b e - 2 \, a^{3} f\right)} x^{3}}{6 \, {\left(a^{2} b^{3} x^{5} + a^{3} b^{2} x^{2}\right)}} + \frac{f x}{b^{2}} - \frac{\sqrt{3} {\left(5 \, b^{3} c - 2 \, a b^{2} d - a^{2} b e + 4 \, a^{3} 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 \, a^{2} b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(5 \, b^{3} c - 2 \, a b^{2} d - a^{2} b e + 4 \, a^{3} 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 \, a^{2} b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(5 \, b^{3} c - 2 \, a b^{2} d - a^{2} b e + 4 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{2} b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/6*(3*a*b^2*c + (5*b^3*c - 2*a*b^2*d + 2*a^2*b*e - 2*a^3*f)*x^3)/(a^2*b^3*x^5 + a^3*b^2*x^2) + f*x/b^2 - 1/9*sqrt(3)*(5*b^3*c - 2*a*b^2*d - a^2*b*e + 4*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b^3*(a/b)^(2/3)) + 1/18*(5*b^3*c - 2*a*b^2*d - a^2*b*e + 4*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b^3*(a/b)^(2/3)) - 1/9*(5*b^3*c - 2*a*b^2*d - a^2*b*e + 4*a^3*f)*log(x + (a/b)^(1/3))/(a^2*b^3*(a/b)^(2/3))","A",0
269,1,267,0,2.929995," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^5/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(7 \, b^{3} c - 4 \, a b^{2} d + a^{2} b e - a^{3} f\right)} x^{6} - 3 \, a^{2} b c + 3 \, {\left(7 \, a b^{2} c - 4 \, a^{2} b d\right)} x^{3}}{12 \, {\left(a^{3} b^{2} x^{7} + a^{4} b x^{4}\right)}} + \frac{\sqrt{3} {\left(7 \, b^{3} c - 4 \, a b^{2} d + a^{2} b e + 2 \, a^{3} 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 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(7 \, b^{3} c - 4 \, a b^{2} d + a^{2} b e + 2 \, a^{3} 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 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(7 \, b^{3} c - 4 \, a b^{2} d + a^{2} b e + 2 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"1/12*(4*(7*b^3*c - 4*a*b^2*d + a^2*b*e - a^3*f)*x^6 - 3*a^2*b*c + 3*(7*a*b^2*c - 4*a^2*b*d)*x^3)/(a^3*b^2*x^7 + a^4*b*x^4) + 1/9*sqrt(3)*(7*b^3*c - 4*a*b^2*d + a^2*b*e + 2*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^3*b^2*(a/b)^(1/3)) + 1/18*(7*b^3*c - 4*a*b^2*d + a^2*b*e + 2*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*b^2*(a/b)^(1/3)) - 1/9*(7*b^3*c - 4*a*b^2*d + a^2*b*e + 2*a^3*f)*log(x + (a/b)^(1/3))/(a^3*b^2*(a/b)^(1/3))","A",0
270,1,268,0,2.927283," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^6/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{5 \, {\left(8 \, b^{3} c - 5 \, a b^{2} d + 2 \, a^{2} b e - 2 \, a^{3} f\right)} x^{6} - 6 \, a^{2} b c + 3 \, {\left(8 \, a b^{2} c - 5 \, a^{2} b d\right)} x^{3}}{30 \, {\left(a^{3} b^{2} x^{8} + a^{4} b x^{5}\right)}} + \frac{\sqrt{3} {\left(8 \, b^{3} c - 5 \, a b^{2} d + 2 \, a^{2} b e + a^{3} 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 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(8 \, b^{3} c - 5 \, a b^{2} d + 2 \, a^{2} b e + a^{3} 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 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(8 \, b^{3} c - 5 \, a b^{2} d + 2 \, a^{2} b e + a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/30*(5*(8*b^3*c - 5*a*b^2*d + 2*a^2*b*e - 2*a^3*f)*x^6 - 6*a^2*b*c + 3*(8*a*b^2*c - 5*a^2*b*d)*x^3)/(a^3*b^2*x^8 + a^4*b*x^5) + 1/9*sqrt(3)*(8*b^3*c - 5*a*b^2*d + 2*a^2*b*e + a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^3*b^2*(a/b)^(2/3)) - 1/18*(8*b^3*c - 5*a*b^2*d + 2*a^2*b*e + a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*b^2*(a/b)^(2/3)) + 1/9*(8*b^3*c - 5*a*b^2*d + 2*a^2*b*e + a^3*f)*log(x + (a/b)^(1/3))/(a^3*b^2*(a/b)^(2/3))","A",0
271,1,292,0,3.053138," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^8/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{28 \, {\left(10 \, b^{3} c - 7 \, a b^{2} d + 4 \, a^{2} b e - a^{3} f\right)} x^{9} + 21 \, {\left(10 \, a b^{2} c - 7 \, a^{2} b d + 4 \, a^{3} e\right)} x^{6} + 12 \, a^{3} c - 3 \, {\left(10 \, a^{2} b c - 7 \, a^{3} d\right)} x^{3}}{84 \, {\left(a^{4} b x^{10} + a^{5} x^{7}\right)}} - \frac{\sqrt{3} {\left(10 \, b^{3} c - 7 \, a b^{2} d + 4 \, a^{2} b e - a^{3} 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 \, a^{4} b \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(10 \, b^{3} c - 7 \, a b^{2} d + 4 \, a^{2} b e - a^{3} 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 \, a^{4} b \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(10 \, b^{3} c - 7 \, a b^{2} d + 4 \, a^{2} b e - a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{4} b \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"-1/84*(28*(10*b^3*c - 7*a*b^2*d + 4*a^2*b*e - a^3*f)*x^9 + 21*(10*a*b^2*c - 7*a^2*b*d + 4*a^3*e)*x^6 + 12*a^3*c - 3*(10*a^2*b*c - 7*a^3*d)*x^3)/(a^4*b*x^10 + a^5*x^7) - 1/9*sqrt(3)*(10*b^3*c - 7*a*b^2*d + 4*a^2*b*e - a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^4*b*(a/b)^(1/3)) - 1/18*(10*b^3*c - 7*a*b^2*d + 4*a^2*b*e - a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^4*b*(a/b)^(1/3)) + 1/9*(10*b^3*c - 7*a*b^2*d + 4*a^2*b*e - a^3*f)*log(x + (a/b)^(1/3))/(a^4*b*(a/b)^(1/3))","A",0
272,1,292,0,3.031112," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^9/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{20 \, {\left(11 \, b^{3} c - 8 \, a b^{2} d + 5 \, a^{2} b e - 2 \, a^{3} f\right)} x^{9} + 12 \, {\left(11 \, a b^{2} c - 8 \, a^{2} b d + 5 \, a^{3} e\right)} x^{6} + 15 \, a^{3} c - 3 \, {\left(11 \, a^{2} b c - 8 \, a^{3} d\right)} x^{3}}{120 \, {\left(a^{4} b x^{11} + a^{5} x^{8}\right)}} - \frac{\sqrt{3} {\left(11 \, b^{3} c - 8 \, a b^{2} d + 5 \, a^{2} b e - 2 \, a^{3} 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 \, a^{4} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(11 \, b^{3} c - 8 \, a b^{2} d + 5 \, a^{2} b e - 2 \, a^{3} 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 \, a^{4} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(11 \, b^{3} c - 8 \, a b^{2} d + 5 \, a^{2} b e - 2 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{4} b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/120*(20*(11*b^3*c - 8*a*b^2*d + 5*a^2*b*e - 2*a^3*f)*x^9 + 12*(11*a*b^2*c - 8*a^2*b*d + 5*a^3*e)*x^6 + 15*a^3*c - 3*(11*a^2*b*c - 8*a^3*d)*x^3)/(a^4*b*x^11 + a^5*x^8) - 1/9*sqrt(3)*(11*b^3*c - 8*a*b^2*d + 5*a^2*b*e - 2*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^4*b*(a/b)^(2/3)) + 1/18*(11*b^3*c - 8*a*b^2*d + 5*a^2*b*e - 2*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^4*b*(a/b)^(2/3)) - 1/9*(11*b^3*c - 8*a*b^2*d + 5*a^2*b*e - 2*a^3*f)*log(x + (a/b)^(1/3))/(a^4*b*(a/b)^(2/3))","A",0
273,1,323,0,3.133154," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^11/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{140 \, {\left(13 \, b^{4} c - 10 \, a b^{3} d + 7 \, a^{2} b^{2} e - 4 \, a^{3} b f\right)} x^{12} + 105 \, {\left(13 \, a b^{3} c - 10 \, a^{2} b^{2} d + 7 \, a^{3} b e - 4 \, a^{4} f\right)} x^{9} - 15 \, {\left(13 \, a^{2} b^{2} c - 10 \, a^{3} b d + 7 \, a^{4} e\right)} x^{6} - 42 \, a^{4} c + 6 \, {\left(13 \, a^{3} b c - 10 \, a^{4} d\right)} x^{3}}{420 \, {\left(a^{5} b x^{13} + a^{6} x^{10}\right)}} + \frac{\sqrt{3} {\left(13 \, b^{3} c - 10 \, a b^{2} d + 7 \, a^{2} b e - 4 \, a^{3} 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 \, a^{5} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(13 \, b^{3} c - 10 \, a b^{2} d + 7 \, a^{2} b e - 4 \, a^{3} 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 \, a^{5} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(13 \, b^{3} c - 10 \, a b^{2} d + 7 \, a^{2} b e - 4 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{5} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"1/420*(140*(13*b^4*c - 10*a*b^3*d + 7*a^2*b^2*e - 4*a^3*b*f)*x^12 + 105*(13*a*b^3*c - 10*a^2*b^2*d + 7*a^3*b*e - 4*a^4*f)*x^9 - 15*(13*a^2*b^2*c - 10*a^3*b*d + 7*a^4*e)*x^6 - 42*a^4*c + 6*(13*a^3*b*c - 10*a^4*d)*x^3)/(a^5*b*x^13 + a^6*x^10) + 1/9*sqrt(3)*(13*b^3*c - 10*a*b^2*d + 7*a^2*b*e - 4*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^5*(a/b)^(1/3)) + 1/18*(13*b^3*c - 10*a*b^2*d + 7*a^2*b*e - 4*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^5*(a/b)^(1/3)) - 1/9*(13*b^3*c - 10*a*b^2*d + 7*a^2*b*e - 4*a^3*f)*log(x + (a/b)^(1/3))/(a^5*(a/b)^(1/3))","A",0
274,1,323,0,3.065401," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^12/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{220 \, {\left(14 \, b^{4} c - 11 \, a b^{3} d + 8 \, a^{2} b^{2} e - 5 \, a^{3} b f\right)} x^{12} + 132 \, {\left(14 \, a b^{3} c - 11 \, a^{2} b^{2} d + 8 \, a^{3} b e - 5 \, a^{4} f\right)} x^{9} - 33 \, {\left(14 \, a^{2} b^{2} c - 11 \, a^{3} b d + 8 \, a^{4} e\right)} x^{6} - 120 \, a^{4} c + 15 \, {\left(14 \, a^{3} b c - 11 \, a^{4} d\right)} x^{3}}{1320 \, {\left(a^{5} b x^{14} + a^{6} x^{11}\right)}} + \frac{\sqrt{3} {\left(14 \, b^{3} c - 11 \, a b^{2} d + 8 \, a^{2} b e - 5 \, a^{3} 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 \, a^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(14 \, b^{3} c - 11 \, a b^{2} d + 8 \, a^{2} b e - 5 \, a^{3} 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 \, a^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(14 \, b^{3} c - 11 \, a b^{2} d + 8 \, a^{2} b e - 5 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/1320*(220*(14*b^4*c - 11*a*b^3*d + 8*a^2*b^2*e - 5*a^3*b*f)*x^12 + 132*(14*a*b^3*c - 11*a^2*b^2*d + 8*a^3*b*e - 5*a^4*f)*x^9 - 33*(14*a^2*b^2*c - 11*a^3*b*d + 8*a^4*e)*x^6 - 120*a^4*c + 15*(14*a^3*b*c - 11*a^4*d)*x^3)/(a^5*b*x^14 + a^6*x^11) + 1/9*sqrt(3)*(14*b^3*c - 11*a*b^2*d + 8*a^2*b*e - 5*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^5*(a/b)^(2/3)) - 1/18*(14*b^3*c - 11*a*b^2*d + 8*a^2*b*e - 5*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^5*(a/b)^(2/3)) + 1/9*(14*b^3*c - 11*a*b^2*d + 8*a^2*b*e - 5*a^3*f)*log(x + (a/b)^(1/3))/(a^5*(a/b)^(2/3))","A",0
275,1,374,0,2.974384," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^14/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{1820 \, {\left(16 \, b^{5} c - 13 \, a b^{4} d + 10 \, a^{2} b^{3} e - 7 \, a^{3} b^{2} f\right)} x^{15} + 1365 \, {\left(16 \, a b^{4} c - 13 \, a^{2} b^{3} d + 10 \, a^{3} b^{2} e - 7 \, a^{4} b f\right)} x^{12} - 195 \, {\left(16 \, a^{2} b^{3} c - 13 \, a^{3} b^{2} d + 10 \, a^{4} b e - 7 \, a^{5} f\right)} x^{9} + 78 \, {\left(16 \, a^{3} b^{2} c - 13 \, a^{4} b d + 10 \, a^{5} e\right)} x^{6} + 420 \, a^{5} c - 42 \, {\left(16 \, a^{4} b c - 13 \, a^{5} d\right)} x^{3}}{5460 \, {\left(a^{6} b x^{16} + a^{7} x^{13}\right)}} - \frac{\sqrt{3} {\left(16 \, b^{4} c - 13 \, a b^{3} d + 10 \, a^{2} b^{2} e - 7 \, a^{3} b 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 \, a^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(16 \, b^{4} c - 13 \, a b^{3} d + 10 \, a^{2} b^{2} e - 7 \, a^{3} b 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 \, a^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(16 \, b^{4} c - 13 \, a b^{3} d + 10 \, a^{2} b^{2} e - 7 \, a^{3} b f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"-1/5460*(1820*(16*b^5*c - 13*a*b^4*d + 10*a^2*b^3*e - 7*a^3*b^2*f)*x^15 + 1365*(16*a*b^4*c - 13*a^2*b^3*d + 10*a^3*b^2*e - 7*a^4*b*f)*x^12 - 195*(16*a^2*b^3*c - 13*a^3*b^2*d + 10*a^4*b*e - 7*a^5*f)*x^9 + 78*(16*a^3*b^2*c - 13*a^4*b*d + 10*a^5*e)*x^6 + 420*a^5*c - 42*(16*a^4*b*c - 13*a^5*d)*x^3)/(a^6*b*x^16 + a^7*x^13) - 1/9*sqrt(3)*(16*b^4*c - 13*a*b^3*d + 10*a^2*b^2*e - 7*a^3*b*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^6*(a/b)^(1/3)) - 1/18*(16*b^4*c - 13*a*b^3*d + 10*a^2*b^2*e - 7*a^3*b*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^6*(a/b)^(1/3)) + 1/9*(16*b^4*c - 13*a*b^3*d + 10*a^2*b^2*e - 7*a^3*b*f)*log(x + (a/b)^(1/3))/(a^6*(a/b)^(1/3))","A",0
276,1,275,0,1.541860," ","integrate(x^14*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{7 \, a^{4} b^{3} c - 9 \, a^{5} b^{2} d + 11 \, a^{6} b e - 13 \, a^{7} f + 2 \, {\left(4 \, a^{3} b^{4} c - 5 \, a^{4} b^{3} d + 6 \, a^{5} b^{2} e - 7 \, a^{6} b f\right)} x^{3}}{6 \, {\left(b^{10} x^{6} + 2 \, a b^{9} x^{3} + a^{2} b^{8}\right)}} + \frac{12 \, b^{4} f x^{15} + 15 \, {\left(b^{4} e - 3 \, a b^{3} f\right)} x^{12} + 20 \, {\left(b^{4} d - 3 \, a b^{3} e + 6 \, a^{2} b^{2} f\right)} x^{9} + 30 \, {\left(b^{4} c - 3 \, a b^{3} d + 6 \, a^{2} b^{2} e - 10 \, a^{3} b f\right)} x^{6} - 60 \, {\left(3 \, a b^{3} c - 6 \, a^{2} b^{2} d + 10 \, a^{3} b e - 15 \, a^{4} f\right)} x^{3}}{180 \, b^{7}} + \frac{{\left(6 \, a^{2} b^{3} c - 10 \, a^{3} b^{2} d + 15 \, a^{4} b e - 21 \, a^{5} f\right)} \log\left(b x^{3} + a\right)}{3 \, b^{8}}"," ",0,"1/6*(7*a^4*b^3*c - 9*a^5*b^2*d + 11*a^6*b*e - 13*a^7*f + 2*(4*a^3*b^4*c - 5*a^4*b^3*d + 6*a^5*b^2*e - 7*a^6*b*f)*x^3)/(b^10*x^6 + 2*a*b^9*x^3 + a^2*b^8) + 1/180*(12*b^4*f*x^15 + 15*(b^4*e - 3*a*b^3*f)*x^12 + 20*(b^4*d - 3*a*b^3*e + 6*a^2*b^2*f)*x^9 + 30*(b^4*c - 3*a*b^3*d + 6*a^2*b^2*e - 10*a^3*b*f)*x^6 - 60*(3*a*b^3*c - 6*a^2*b^2*d + 10*a^3*b*e - 15*a^4*f)*x^3)/b^7 + 1/3*(6*a^2*b^3*c - 10*a^3*b^2*d + 15*a^4*b*e - 21*a^5*f)*log(b*x^3 + a)/b^8","A",0
277,1,233,0,1.422940," ","integrate(x^11*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{5 \, a^{3} b^{3} c - 7 \, a^{4} b^{2} d + 9 \, a^{5} b e - 11 \, a^{6} f + 2 \, {\left(3 \, a^{2} b^{4} c - 4 \, a^{3} b^{3} d + 5 \, a^{4} b^{2} e - 6 \, a^{5} b f\right)} x^{3}}{6 \, {\left(b^{9} x^{6} + 2 \, a b^{8} x^{3} + a^{2} b^{7}\right)}} + \frac{3 \, b^{3} f x^{12} + 4 \, {\left(b^{3} e - 3 \, a b^{2} f\right)} x^{9} + 6 \, {\left(b^{3} d - 3 \, a b^{2} e + 6 \, a^{2} b f\right)} x^{6} + 12 \, {\left(b^{3} c - 3 \, a b^{2} d + 6 \, a^{2} b e - 10 \, a^{3} f\right)} x^{3}}{36 \, b^{6}} - \frac{{\left(3 \, a b^{3} c - 6 \, a^{2} b^{2} d + 10 \, a^{3} b e - 15 \, a^{4} f\right)} \log\left(b x^{3} + a\right)}{3 \, b^{7}}"," ",0,"-1/6*(5*a^3*b^3*c - 7*a^4*b^2*d + 9*a^5*b*e - 11*a^6*f + 2*(3*a^2*b^4*c - 4*a^3*b^3*d + 5*a^4*b^2*e - 6*a^5*b*f)*x^3)/(b^9*x^6 + 2*a*b^8*x^3 + a^2*b^7) + 1/36*(3*b^3*f*x^12 + 4*(b^3*e - 3*a*b^2*f)*x^9 + 6*(b^3*d - 3*a*b^2*e + 6*a^2*b*f)*x^6 + 12*(b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*x^3)/b^6 - 1/3*(3*a*b^3*c - 6*a^2*b^2*d + 10*a^3*b*e - 15*a^4*f)*log(b*x^3 + a)/b^7","A",0
278,1,191,0,1.351548," ","integrate(x^8*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{3 \, a^{2} b^{3} c - 5 \, a^{3} b^{2} d + 7 \, a^{4} b e - 9 \, a^{5} f + 2 \, {\left(2 \, a b^{4} c - 3 \, a^{2} b^{3} d + 4 \, a^{3} b^{2} e - 5 \, a^{4} b f\right)} x^{3}}{6 \, {\left(b^{8} x^{6} + 2 \, a b^{7} x^{3} + a^{2} b^{6}\right)}} + \frac{2 \, b^{2} f x^{9} + 3 \, {\left(b^{2} e - 3 \, a b f\right)} x^{6} + 6 \, {\left(b^{2} d - 3 \, a b e + 6 \, a^{2} f\right)} x^{3}}{18 \, b^{5}} + \frac{{\left(b^{3} c - 3 \, a b^{2} d + 6 \, a^{2} b e - 10 \, a^{3} f\right)} \log\left(b x^{3} + a\right)}{3 \, b^{6}}"," ",0,"1/6*(3*a^2*b^3*c - 5*a^3*b^2*d + 7*a^4*b*e - 9*a^5*f + 2*(2*a*b^4*c - 3*a^2*b^3*d + 4*a^3*b^2*e - 5*a^4*b*f)*x^3)/(b^8*x^6 + 2*a*b^7*x^3 + a^2*b^6) + 1/18*(2*b^2*f*x^9 + 3*(b^2*e - 3*a*b*f)*x^6 + 6*(b^2*d - 3*a*b*e + 6*a^2*f)*x^3)/b^5 + 1/3*(b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*log(b*x^3 + a)/b^6","A",0
279,1,147,0,1.394583," ","integrate(x^5*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{a b^{3} c - 3 \, a^{2} b^{2} d + 5 \, a^{3} b e - 7 \, a^{4} f + 2 \, {\left(b^{4} c - 2 \, a b^{3} d + 3 \, a^{2} b^{2} e - 4 \, a^{3} b f\right)} x^{3}}{6 \, {\left(b^{7} x^{6} + 2 \, a b^{6} x^{3} + a^{2} b^{5}\right)}} + \frac{b f x^{6} + 2 \, {\left(b e - 3 \, a f\right)} x^{3}}{6 \, b^{4}} + \frac{{\left(b^{2} d - 3 \, a b e + 6 \, a^{2} f\right)} \log\left(b x^{3} + a\right)}{3 \, b^{5}}"," ",0,"-1/6*(a*b^3*c - 3*a^2*b^2*d + 5*a^3*b*e - 7*a^4*f + 2*(b^4*c - 2*a*b^3*d + 3*a^2*b^2*e - 4*a^3*b*f)*x^3)/(b^7*x^6 + 2*a*b^6*x^3 + a^2*b^5) + 1/6*(b*f*x^6 + 2*(b*e - 3*a*f)*x^3)/b^4 + 1/3*(b^2*d - 3*a*b*e + 6*a^2*f)*log(b*x^3 + a)/b^5","A",0
280,1,109,0,1.383867," ","integrate(x^2*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{f x^{3}}{3 \, b^{3}} - \frac{b^{3} c + a b^{2} d - 3 \, a^{2} b e + 5 \, a^{3} f + 2 \, {\left(b^{3} d - 2 \, a b^{2} e + 3 \, a^{2} b f\right)} x^{3}}{6 \, {\left(b^{6} x^{6} + 2 \, a b^{5} x^{3} + a^{2} b^{4}\right)}} + \frac{{\left(b e - 3 \, a f\right)} \log\left(b x^{3} + a\right)}{3 \, b^{4}}"," ",0,"1/3*f*x^3/b^3 - 1/6*(b^3*c + a*b^2*d - 3*a^2*b*e + 5*a^3*f + 2*(b^3*d - 2*a*b^2*e + 3*a^2*b*f)*x^3)/(b^6*x^6 + 2*a*b^5*x^3 + a^2*b^4) + 1/3*(b*e - 3*a*f)*log(b*x^3 + a)/b^4","A",0
281,1,129,0,1.369317," ","integrate((f*x^9+e*x^6+d*x^3+c)/x/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{3 \, a b^{3} c - a^{2} b^{2} d - a^{3} b e + 3 \, a^{4} f + 2 \, {\left(b^{4} c - a^{2} b^{2} e + 2 \, a^{3} b f\right)} x^{3}}{6 \, {\left(a^{2} b^{5} x^{6} + 2 \, a^{3} b^{4} x^{3} + a^{4} b^{3}\right)}} + \frac{c \log\left(x^{3}\right)}{3 \, a^{3}} - \frac{{\left(b^{3} c - a^{3} f\right)} \log\left(b x^{3} + a\right)}{3 \, a^{3} b^{3}}"," ",0,"1/6*(3*a*b^3*c - a^2*b^2*d - a^3*b*e + 3*a^4*f + 2*(b^4*c - a^2*b^2*e + 2*a^3*b*f)*x^3)/(a^2*b^5*x^6 + 2*a^3*b^4*x^3 + a^4*b^3) + 1/3*c*log(x^3)/a^3 - 1/3*(b^3*c - a^3*f)*log(b*x^3 + a)/(a^3*b^3)","A",0
282,1,144,0,1.355085," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^4/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, b^{4} c - a b^{3} d + a^{3} b f\right)} x^{6} + 2 \, a^{2} b^{2} c + {\left(9 \, a b^{3} c - 3 \, a^{2} b^{2} d + a^{3} b e + a^{4} f\right)} x^{3}}{6 \, {\left(a^{3} b^{4} x^{9} + 2 \, a^{4} b^{3} x^{6} + a^{5} b^{2} x^{3}\right)}} + \frac{{\left(3 \, b c - a d\right)} \log\left(b x^{3} + a\right)}{3 \, a^{4}} - \frac{{\left(3 \, b c - a d\right)} \log\left(x^{3}\right)}{3 \, a^{4}}"," ",0,"-1/6*(2*(3*b^4*c - a*b^3*d + a^3*b*f)*x^6 + 2*a^2*b^2*c + (9*a*b^3*c - 3*a^2*b^2*d + a^3*b*e + a^4*f)*x^3)/(a^3*b^4*x^9 + 2*a^4*b^3*x^6 + a^5*b^2*x^3) + 1/3*(3*b*c - a*d)*log(b*x^3 + a)/a^4 - 1/3*(3*b*c - a*d)*log(x^3)/a^4","A",0
283,1,182,0,1.398474," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^7/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(6 \, b^{4} c - 3 \, a b^{3} d + a^{2} b^{2} e\right)} x^{9} + {\left(18 \, a b^{3} c - 9 \, a^{2} b^{2} d + 3 \, a^{3} b e - a^{4} f\right)} x^{6} - a^{3} b c + 2 \, {\left(2 \, a^{2} b^{2} c - a^{3} b d\right)} x^{3}}{6 \, {\left(a^{4} b^{3} x^{12} + 2 \, a^{5} b^{2} x^{9} + a^{6} b x^{6}\right)}} - \frac{{\left(6 \, b^{2} c - 3 \, a b d + a^{2} e\right)} \log\left(b x^{3} + a\right)}{3 \, a^{5}} + \frac{{\left(6 \, b^{2} c - 3 \, a b d + a^{2} e\right)} \log\left(x^{3}\right)}{3 \, a^{5}}"," ",0,"1/6*(2*(6*b^4*c - 3*a*b^3*d + a^2*b^2*e)*x^9 + (18*a*b^3*c - 9*a^2*b^2*d + 3*a^3*b*e - a^4*f)*x^6 - a^3*b*c + 2*(2*a^2*b^2*c - a^3*b*d)*x^3)/(a^4*b^3*x^12 + 2*a^5*b^2*x^9 + a^6*b*x^6) - 1/3*(6*b^2*c - 3*a*b*d + a^2*e)*log(b*x^3 + a)/a^5 + 1/3*(6*b^2*c - 3*a*b*d + a^2*e)*log(x^3)/a^5","A",0
284,1,232,0,1.459221," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^10/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{6 \, {\left(10 \, b^{4} c - 6 \, a b^{3} d + 3 \, a^{2} b^{2} e - a^{3} b f\right)} x^{12} + 9 \, {\left(10 \, a b^{3} c - 6 \, a^{2} b^{2} d + 3 \, a^{3} b e - a^{4} f\right)} x^{9} + 2 \, {\left(10 \, a^{2} b^{2} c - 6 \, a^{3} b d + 3 \, a^{4} e\right)} x^{6} + 2 \, a^{4} c - {\left(5 \, a^{3} b c - 3 \, a^{4} d\right)} x^{3}}{18 \, {\left(a^{5} b^{2} x^{15} + 2 \, a^{6} b x^{12} + a^{7} x^{9}\right)}} + \frac{{\left(10 \, b^{3} c - 6 \, a b^{2} d + 3 \, a^{2} b e - a^{3} f\right)} \log\left(b x^{3} + a\right)}{3 \, a^{6}} - \frac{{\left(10 \, b^{3} c - 6 \, a b^{2} d + 3 \, a^{2} b e - a^{3} f\right)} \log\left(x^{3}\right)}{3 \, a^{6}}"," ",0,"-1/18*(6*(10*b^4*c - 6*a*b^3*d + 3*a^2*b^2*e - a^3*b*f)*x^12 + 9*(10*a*b^3*c - 6*a^2*b^2*d + 3*a^3*b*e - a^4*f)*x^9 + 2*(10*a^2*b^2*c - 6*a^3*b*d + 3*a^4*e)*x^6 + 2*a^4*c - (5*a^3*b*c - 3*a^4*d)*x^3)/(a^5*b^2*x^15 + 2*a^6*b*x^12 + a^7*x^9) + 1/3*(10*b^3*c - 6*a*b^2*d + 3*a^2*b*e - a^3*f)*log(b*x^3 + a)/a^6 - 1/3*(10*b^3*c - 6*a*b^2*d + 3*a^2*b*e - a^3*f)*log(x^3)/a^6","A",0
285,1,280,0,1.465466," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^13/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{12 \, {\left(15 \, b^{5} c - 10 \, a b^{4} d + 6 \, a^{2} b^{3} e - 3 \, a^{3} b^{2} f\right)} x^{15} + 18 \, {\left(15 \, a b^{4} c - 10 \, a^{2} b^{3} d + 6 \, a^{3} b^{2} e - 3 \, a^{4} b f\right)} x^{12} + 4 \, {\left(15 \, a^{2} b^{3} c - 10 \, a^{3} b^{2} d + 6 \, a^{4} b e - 3 \, a^{5} f\right)} x^{9} - {\left(15 \, a^{3} b^{2} c - 10 \, a^{4} b d + 6 \, a^{5} e\right)} x^{6} - 3 \, a^{5} c + 2 \, {\left(3 \, a^{4} b c - 2 \, a^{5} d\right)} x^{3}}{36 \, {\left(a^{6} b^{2} x^{18} + 2 \, a^{7} b x^{15} + a^{8} x^{12}\right)}} - \frac{{\left(15 \, b^{4} c - 10 \, a b^{3} d + 6 \, a^{2} b^{2} e - 3 \, a^{3} b f\right)} \log\left(b x^{3} + a\right)}{3 \, a^{7}} + \frac{{\left(15 \, b^{4} c - 10 \, a b^{3} d + 6 \, a^{2} b^{2} e - 3 \, a^{3} b f\right)} \log\left(x^{3}\right)}{3 \, a^{7}}"," ",0,"1/36*(12*(15*b^5*c - 10*a*b^4*d + 6*a^2*b^3*e - 3*a^3*b^2*f)*x^15 + 18*(15*a*b^4*c - 10*a^2*b^3*d + 6*a^3*b^2*e - 3*a^4*b*f)*x^12 + 4*(15*a^2*b^3*c - 10*a^3*b^2*d + 6*a^4*b*e - 3*a^5*f)*x^9 - (15*a^3*b^2*c - 10*a^4*b*d + 6*a^5*e)*x^6 - 3*a^5*c + 2*(3*a^4*b*c - 2*a^5*d)*x^3)/(a^6*b^2*x^18 + 2*a^7*b*x^15 + a^8*x^12) - 1/3*(15*b^4*c - 10*a*b^3*d + 6*a^2*b^2*e - 3*a^3*b*f)*log(b*x^3 + a)/a^7 + 1/3*(15*b^4*c - 10*a*b^3*d + 6*a^2*b^2*e - 3*a^3*b*f)*log(x^3)/a^7","A",0
286,1,424,0,3.055547," ","integrate(x^12*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{{\left(19 \, a^{2} b^{4} c - 25 \, a^{3} b^{3} d + 31 \, a^{4} b^{2} e - 37 \, a^{5} b f\right)} x^{4} + 2 \, {\left(8 \, a^{3} b^{3} c - 11 \, a^{4} b^{2} d + 14 \, a^{5} b e - 17 \, a^{6} f\right)} x}{18 \, {\left(b^{9} x^{6} + 2 \, a b^{8} x^{3} + a^{2} b^{7}\right)}} + \frac{140 \, b^{4} f x^{13} + 182 \, {\left(b^{4} e - 3 \, a b^{3} f\right)} x^{10} + 260 \, {\left(b^{4} d - 3 \, a b^{3} e + 6 \, a^{2} b^{2} f\right)} x^{7} + 455 \, {\left(b^{4} c - 3 \, a b^{3} d + 6 \, a^{2} b^{2} e - 10 \, a^{3} b f\right)} x^{4} - 1820 \, {\left(3 \, a b^{3} c - 6 \, a^{2} b^{2} d + 10 \, a^{3} b e - 15 \, a^{4} f\right)} x}{1820 \, b^{7}} + \frac{\sqrt{3} {\left(35 \, a^{2} b^{3} c - 65 \, a^{3} b^{2} d + 104 \, a^{4} b e - 152 \, a^{5} 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 \, b^{8} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(35 \, a^{2} b^{3} c - 65 \, a^{3} b^{2} d + 104 \, a^{4} b e - 152 \, a^{5} 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 \, b^{8} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(35 \, a^{2} b^{3} c - 65 \, a^{3} b^{2} d + 104 \, a^{4} b e - 152 \, a^{5} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, b^{8} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/18*((19*a^2*b^4*c - 25*a^3*b^3*d + 31*a^4*b^2*e - 37*a^5*b*f)*x^4 + 2*(8*a^3*b^3*c - 11*a^4*b^2*d + 14*a^5*b*e - 17*a^6*f)*x)/(b^9*x^6 + 2*a*b^8*x^3 + a^2*b^7) + 1/1820*(140*b^4*f*x^13 + 182*(b^4*e - 3*a*b^3*f)*x^10 + 260*(b^4*d - 3*a*b^3*e + 6*a^2*b^2*f)*x^7 + 455*(b^4*c - 3*a*b^3*d + 6*a^2*b^2*e - 10*a^3*b*f)*x^4 - 1820*(3*a*b^3*c - 6*a^2*b^2*d + 10*a^3*b*e - 15*a^4*f)*x)/b^7 + 1/27*sqrt(3)*(35*a^2*b^3*c - 65*a^3*b^2*d + 104*a^4*b*e - 152*a^5*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^8*(a/b)^(2/3)) - 1/54*(35*a^2*b^3*c - 65*a^3*b^2*d + 104*a^4*b*e - 152*a^5*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^8*(a/b)^(2/3)) + 1/27*(35*a^2*b^3*c - 65*a^3*b^2*d + 104*a^4*b*e - 152*a^5*f)*log(x + (a/b)^(1/3))/(b^8*(a/b)^(2/3))","A",0
287,1,380,0,3.004375," ","integrate(x^10*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(7 \, a b^{4} c - 10 \, a^{2} b^{3} d + 13 \, a^{3} b^{2} e - 16 \, a^{4} b f\right)} x^{5} + {\left(11 \, a^{2} b^{3} c - 17 \, a^{3} b^{2} d + 23 \, a^{4} b e - 29 \, a^{5} f\right)} x^{2}}{18 \, {\left(b^{8} x^{6} + 2 \, a b^{7} x^{3} + a^{2} b^{6}\right)}} - \frac{\sqrt{3} {\left(20 \, a b^{3} c - 44 \, a^{2} b^{2} d + 77 \, a^{3} b e - 119 \, a^{4} 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 \, b^{7} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{40 \, b^{3} f x^{11} + 55 \, {\left(b^{3} e - 3 \, a b^{2} f\right)} x^{8} + 88 \, {\left(b^{3} d - 3 \, a b^{2} e + 6 \, a^{2} b f\right)} x^{5} + 220 \, {\left(b^{3} c - 3 \, a b^{2} d + 6 \, a^{2} b e - 10 \, a^{3} f\right)} x^{2}}{440 \, b^{6}} - \frac{{\left(20 \, a b^{3} c - 44 \, a^{2} b^{2} d + 77 \, a^{3} b e - 119 \, a^{4} 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 \, b^{7} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(20 \, a b^{3} c - 44 \, a^{2} b^{2} d + 77 \, a^{3} b e - 119 \, a^{4} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, b^{7} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"1/18*(2*(7*a*b^4*c - 10*a^2*b^3*d + 13*a^3*b^2*e - 16*a^4*b*f)*x^5 + (11*a^2*b^3*c - 17*a^3*b^2*d + 23*a^4*b*e - 29*a^5*f)*x^2)/(b^8*x^6 + 2*a*b^7*x^3 + a^2*b^6) - 1/27*sqrt(3)*(20*a*b^3*c - 44*a^2*b^2*d + 77*a^3*b*e - 119*a^4*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^7*(a/b)^(1/3)) + 1/440*(40*b^3*f*x^11 + 55*(b^3*e - 3*a*b^2*f)*x^8 + 88*(b^3*d - 3*a*b^2*e + 6*a^2*b*f)*x^5 + 220*(b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*x^2)/b^6 - 1/54*(20*a*b^3*c - 44*a^2*b^2*d + 77*a^3*b*e - 119*a^4*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^7*(a/b)^(1/3)) + 1/27*(20*a*b^3*c - 44*a^2*b^2*d + 77*a^3*b*e - 119*a^4*f)*log(x + (a/b)^(1/3))/(b^7*(a/b)^(1/3))","A",0
288,1,376,0,3.033084," ","integrate(x^9*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{{\left(13 \, a b^{4} c - 19 \, a^{2} b^{3} d + 25 \, a^{3} b^{2} e - 31 \, a^{4} b f\right)} x^{4} + 2 \, {\left(5 \, a^{2} b^{3} c - 8 \, a^{3} b^{2} d + 11 \, a^{4} b e - 14 \, a^{5} f\right)} x}{18 \, {\left(b^{8} x^{6} + 2 \, a b^{7} x^{3} + a^{2} b^{6}\right)}} + \frac{14 \, b^{3} f x^{10} + 20 \, {\left(b^{3} e - 3 \, a b^{2} f\right)} x^{7} + 35 \, {\left(b^{3} d - 3 \, a b^{2} e + 6 \, a^{2} b f\right)} x^{4} + 140 \, {\left(b^{3} c - 3 \, a b^{2} d + 6 \, a^{2} b e - 10 \, a^{3} f\right)} x}{140 \, b^{6}} - \frac{\sqrt{3} {\left(14 \, a b^{3} c - 35 \, a^{2} b^{2} d + 65 \, a^{3} b e - 104 \, a^{4} 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 \, b^{7} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(14 \, a b^{3} c - 35 \, a^{2} b^{2} d + 65 \, a^{3} b e - 104 \, a^{4} 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 \, b^{7} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(14 \, a b^{3} c - 35 \, a^{2} b^{2} d + 65 \, a^{3} b e - 104 \, a^{4} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, b^{7} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/18*((13*a*b^4*c - 19*a^2*b^3*d + 25*a^3*b^2*e - 31*a^4*b*f)*x^4 + 2*(5*a^2*b^3*c - 8*a^3*b^2*d + 11*a^4*b*e - 14*a^5*f)*x)/(b^8*x^6 + 2*a*b^7*x^3 + a^2*b^6) + 1/140*(14*b^3*f*x^10 + 20*(b^3*e - 3*a*b^2*f)*x^7 + 35*(b^3*d - 3*a*b^2*e + 6*a^2*b*f)*x^4 + 140*(b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*x)/b^6 - 1/27*sqrt(3)*(14*a*b^3*c - 35*a^2*b^2*d + 65*a^3*b*e - 104*a^4*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^7*(a/b)^(2/3)) + 1/54*(14*a*b^3*c - 35*a^2*b^2*d + 65*a^3*b*e - 104*a^4*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^7*(a/b)^(2/3)) - 1/27*(14*a*b^3*c - 35*a^2*b^2*d + 65*a^3*b*e - 104*a^4*f)*log(x + (a/b)^(1/3))/(b^7*(a/b)^(2/3))","A",0
289,1,330,0,3.075097," ","integrate(x^7*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(4 \, b^{4} c - 7 \, a b^{3} d + 10 \, a^{2} b^{2} e - 13 \, a^{3} b f\right)} x^{5} + {\left(5 \, a b^{3} c - 11 \, a^{2} b^{2} d + 17 \, a^{3} b e - 23 \, a^{4} f\right)} x^{2}}{18 \, {\left(b^{7} x^{6} + 2 \, a b^{6} x^{3} + a^{2} b^{5}\right)}} + \frac{\sqrt{3} {\left(5 \, b^{3} c - 20 \, a b^{2} d + 44 \, a^{2} b e - 77 \, a^{3} 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 \, b^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{5 \, b^{2} f x^{8} + 8 \, {\left(b^{2} e - 3 \, a b f\right)} x^{5} + 20 \, {\left(b^{2} d - 3 \, a b e + 6 \, a^{2} f\right)} x^{2}}{40 \, b^{5}} + \frac{{\left(5 \, b^{3} c - 20 \, a b^{2} d + 44 \, a^{2} b e - 77 \, a^{3} 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 \, b^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(5 \, b^{3} c - 20 \, a b^{2} d + 44 \, a^{2} b e - 77 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, b^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"-1/18*(2*(4*b^4*c - 7*a*b^3*d + 10*a^2*b^2*e - 13*a^3*b*f)*x^5 + (5*a*b^3*c - 11*a^2*b^2*d + 17*a^3*b*e - 23*a^4*f)*x^2)/(b^7*x^6 + 2*a*b^6*x^3 + a^2*b^5) + 1/27*sqrt(3)*(5*b^3*c - 20*a*b^2*d + 44*a^2*b*e - 77*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^6*(a/b)^(1/3)) + 1/40*(5*b^2*f*x^8 + 8*(b^2*e - 3*a*b*f)*x^5 + 20*(b^2*d - 3*a*b*e + 6*a^2*f)*x^2)/b^5 + 1/54*(5*b^3*c - 20*a*b^2*d + 44*a^2*b*e - 77*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^6*(a/b)^(1/3)) - 1/27*(5*b^3*c - 20*a*b^2*d + 44*a^2*b*e - 77*a^3*f)*log(x + (a/b)^(1/3))/(b^6*(a/b)^(1/3))","A",0
290,1,326,0,3.035376," ","integrate(x^6*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{{\left(7 \, b^{4} c - 13 \, a b^{3} d + 19 \, a^{2} b^{2} e - 25 \, a^{3} b f\right)} x^{4} + 2 \, {\left(2 \, a b^{3} c - 5 \, a^{2} b^{2} d + 8 \, a^{3} b e - 11 \, a^{4} f\right)} x}{18 \, {\left(b^{7} x^{6} + 2 \, a b^{6} x^{3} + a^{2} b^{5}\right)}} + \frac{4 \, b^{2} f x^{7} + 7 \, {\left(b^{2} e - 3 \, a b f\right)} x^{4} + 28 \, {\left(b^{2} d - 3 \, a b e + 6 \, a^{2} f\right)} x}{28 \, b^{5}} + \frac{\sqrt{3} {\left(2 \, b^{3} c - 14 \, a b^{2} d + 35 \, a^{2} b e - 65 \, a^{3} 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 \, b^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(2 \, b^{3} c - 14 \, a b^{2} d + 35 \, a^{2} b e - 65 \, a^{3} 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 \, b^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(2 \, b^{3} c - 14 \, a b^{2} d + 35 \, a^{2} b e - 65 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, b^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/18*((7*b^4*c - 13*a*b^3*d + 19*a^2*b^2*e - 25*a^3*b*f)*x^4 + 2*(2*a*b^3*c - 5*a^2*b^2*d + 8*a^3*b*e - 11*a^4*f)*x)/(b^7*x^6 + 2*a*b^6*x^3 + a^2*b^5) + 1/28*(4*b^2*f*x^7 + 7*(b^2*e - 3*a*b*f)*x^4 + 28*(b^2*d - 3*a*b*e + 6*a^2*f)*x)/b^5 + 1/27*sqrt(3)*(2*b^3*c - 14*a*b^2*d + 35*a^2*b*e - 65*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^6*(a/b)^(2/3)) - 1/54*(2*b^3*c - 14*a*b^2*d + 35*a^2*b*e - 65*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^6*(a/b)^(2/3)) + 1/27*(2*b^3*c - 14*a*b^2*d + 35*a^2*b*e - 65*a^3*f)*log(x + (a/b)^(1/3))/(b^6*(a/b)^(2/3))","A",0
291,1,311,0,3.095888," ","integrate(x^4*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(b^{4} c - 4 \, a b^{3} d + 7 \, a^{2} b^{2} e - 10 \, a^{3} b f\right)} x^{5} - {\left(a b^{3} c + 5 \, a^{2} b^{2} d - 11 \, a^{3} b e + 17 \, a^{4} f\right)} x^{2}}{18 \, {\left(a b^{6} x^{6} + 2 \, a^{2} b^{5} x^{3} + a^{3} b^{4}\right)}} + \frac{2 \, b f x^{5} + 5 \, {\left(b e - 3 \, a f\right)} x^{2}}{10 \, b^{4}} + \frac{\sqrt{3} {\left(b^{3} c + 5 \, a b^{2} d - 20 \, a^{2} b e + 44 \, a^{3} 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 \, a b^{5} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(b^{3} c + 5 \, a b^{2} d - 20 \, a^{2} b e + 44 \, a^{3} 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 \, a b^{5} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(b^{3} c + 5 \, a b^{2} d - 20 \, a^{2} b e + 44 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a b^{5} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"1/18*(2*(b^4*c - 4*a*b^3*d + 7*a^2*b^2*e - 10*a^3*b*f)*x^5 - (a*b^3*c + 5*a^2*b^2*d - 11*a^3*b*e + 17*a^4*f)*x^2)/(a*b^6*x^6 + 2*a^2*b^5*x^3 + a^3*b^4) + 1/10*(2*b*f*x^5 + 5*(b*e - 3*a*f)*x^2)/b^4 + 1/27*sqrt(3)*(b^3*c + 5*a*b^2*d - 20*a^2*b*e + 44*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^5*(a/b)^(1/3)) + 1/54*(b^3*c + 5*a*b^2*d - 20*a^2*b*e + 44*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^5*(a/b)^(1/3)) - 1/27*(b^3*c + 5*a*b^2*d - 20*a^2*b*e + 44*a^3*f)*log(x + (a/b)^(1/3))/(a*b^5*(a/b)^(1/3))","A",0
292,1,305,0,3.061116," ","integrate(x^3*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{{\left(b^{4} c - 7 \, a b^{3} d + 13 \, a^{2} b^{2} e - 19 \, a^{3} b f\right)} x^{4} - 2 \, {\left(a b^{3} c + 2 \, a^{2} b^{2} d - 5 \, a^{3} b e + 8 \, a^{4} f\right)} x}{18 \, {\left(a b^{6} x^{6} + 2 \, a^{2} b^{5} x^{3} + a^{3} b^{4}\right)}} + \frac{b f x^{4} + 4 \, {\left(b e - 3 \, a f\right)} x}{4 \, b^{4}} + \frac{\sqrt{3} {\left(b^{3} c + 2 \, a b^{2} d - 14 \, a^{2} b e + 35 \, a^{3} 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 \, a b^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b^{3} c + 2 \, a b^{2} d - 14 \, a^{2} b e + 35 \, a^{3} 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 \, a b^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b^{3} c + 2 \, a b^{2} d - 14 \, a^{2} b e + 35 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a b^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/18*((b^4*c - 7*a*b^3*d + 13*a^2*b^2*e - 19*a^3*b*f)*x^4 - 2*(a*b^3*c + 2*a^2*b^2*d - 5*a^3*b*e + 8*a^4*f)*x)/(a*b^6*x^6 + 2*a^2*b^5*x^3 + a^3*b^4) + 1/4*(b*f*x^4 + 4*(b*e - 3*a*f)*x)/b^4 + 1/27*sqrt(3)*(b^3*c + 2*a*b^2*d - 14*a^2*b*e + 35*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^5*(a/b)^(2/3)) - 1/54*(b^3*c + 2*a*b^2*d - 14*a^2*b*e + 35*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^5*(a/b)^(2/3)) + 1/27*(b^3*c + 2*a*b^2*d - 14*a^2*b*e + 35*a^3*f)*log(x + (a/b)^(1/3))/(a*b^5*(a/b)^(2/3))","A",0
293,1,296,0,2.942264," ","integrate(x*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, b^{4} c + a b^{3} d - 4 \, a^{2} b^{2} e + 7 \, a^{3} b f\right)} x^{5} + {\left(7 \, a b^{3} c - a^{2} b^{2} d - 5 \, a^{3} b e + 11 \, a^{4} f\right)} x^{2}}{18 \, {\left(a^{2} b^{5} x^{6} + 2 \, a^{3} b^{4} x^{3} + a^{4} b^{3}\right)}} + \frac{f x^{2}}{2 \, b^{3}} + \frac{\sqrt{3} {\left(2 \, b^{3} c + a b^{2} d + 5 \, a^{2} b e - 20 \, a^{3} 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 \, a^{2} b^{4} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(2 \, b^{3} c + a b^{2} d + 5 \, a^{2} b e - 20 \, a^{3} 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 \, a^{2} b^{4} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(2 \, b^{3} c + a b^{2} d + 5 \, a^{2} b e - 20 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{2} b^{4} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"1/18*(2*(2*b^4*c + a*b^3*d - 4*a^2*b^2*e + 7*a^3*b*f)*x^5 + (7*a*b^3*c - a^2*b^2*d - 5*a^3*b*e + 11*a^4*f)*x^2)/(a^2*b^5*x^6 + 2*a^3*b^4*x^3 + a^4*b^3) + 1/2*f*x^2/b^3 + 1/27*sqrt(3)*(2*b^3*c + a*b^2*d + 5*a^2*b*e - 20*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b^4*(a/b)^(1/3)) + 1/54*(2*b^3*c + a*b^2*d + 5*a^2*b*e - 20*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b^4*(a/b)^(1/3)) - 1/27*(2*b^3*c + a*b^2*d + 5*a^2*b*e - 20*a^3*f)*log(x + (a/b)^(1/3))/(a^2*b^4*(a/b)^(1/3))","A",0
294,1,291,0,3.067694," ","integrate((f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{{\left(5 \, b^{4} c + a b^{3} d - 7 \, a^{2} b^{2} e + 13 \, a^{3} b f\right)} x^{4} + 2 \, {\left(4 \, a b^{3} c - a^{2} b^{2} d - 2 \, a^{3} b e + 5 \, a^{4} f\right)} x}{18 \, {\left(a^{2} b^{5} x^{6} + 2 \, a^{3} b^{4} x^{3} + a^{4} b^{3}\right)}} + \frac{f x}{b^{3}} + \frac{\sqrt{3} {\left(5 \, b^{3} c + a b^{2} d + 2 \, a^{2} b e - 14 \, a^{3} 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 \, a^{2} b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(5 \, b^{3} c + a b^{2} d + 2 \, a^{2} b e - 14 \, a^{3} 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 \, a^{2} b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(5 \, b^{3} c + a b^{2} d + 2 \, a^{2} b e - 14 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{2} b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/18*((5*b^4*c + a*b^3*d - 7*a^2*b^2*e + 13*a^3*b*f)*x^4 + 2*(4*a*b^3*c - a^2*b^2*d - 2*a^3*b*e + 5*a^4*f)*x)/(a^2*b^5*x^6 + 2*a^3*b^4*x^3 + a^4*b^3) + f*x/b^3 + 1/27*sqrt(3)*(5*b^3*c + a*b^2*d + 2*a^2*b*e - 14*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b^4*(a/b)^(2/3)) - 1/54*(5*b^3*c + a*b^2*d + 2*a^2*b*e - 14*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b^4*(a/b)^(2/3)) + 1/27*(5*b^3*c + a*b^2*d + 2*a^2*b*e - 14*a^3*f)*log(x + (a/b)^(1/3))/(a^2*b^4*(a/b)^(2/3))","A",0
295,1,300,0,2.960613," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^2/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(14 \, b^{4} c - 2 \, a b^{3} d - a^{2} b^{2} e + 4 \, a^{3} b f\right)} x^{6} + 18 \, a^{2} b^{2} c + {\left(49 \, a b^{3} c - 7 \, a^{2} b^{2} d + a^{3} b e + 5 \, a^{4} f\right)} x^{3}}{18 \, {\left(a^{3} b^{4} x^{7} + 2 \, a^{4} b^{3} x^{4} + a^{5} b^{2} x\right)}} - \frac{\sqrt{3} {\left(14 \, b^{3} c - 2 \, a b^{2} d - a^{2} b e - 5 \, a^{3} 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 \, a^{3} b^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(14 \, b^{3} c - 2 \, a b^{2} d - a^{2} b e - 5 \, a^{3} 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 \, a^{3} b^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(14 \, b^{3} c - 2 \, a b^{2} d - a^{2} b e - 5 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{3} b^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"-1/18*(2*(14*b^4*c - 2*a*b^3*d - a^2*b^2*e + 4*a^3*b*f)*x^6 + 18*a^2*b^2*c + (49*a*b^3*c - 7*a^2*b^2*d + a^3*b*e + 5*a^4*f)*x^3)/(a^3*b^4*x^7 + 2*a^4*b^3*x^4 + a^5*b^2*x) - 1/27*sqrt(3)*(14*b^3*c - 2*a*b^2*d - a^2*b*e - 5*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^3*b^3*(a/b)^(1/3)) - 1/54*(14*b^3*c - 2*a*b^2*d - a^2*b*e - 5*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*b^3*(a/b)^(1/3)) + 1/27*(14*b^3*c - 2*a*b^2*d - a^2*b*e - 5*a^3*f)*log(x + (a/b)^(1/3))/(a^3*b^3*(a/b)^(1/3))","A",0
296,1,302,0,3.073168," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^3/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{{\left(20 \, b^{4} c - 5 \, a b^{3} d - a^{2} b^{2} e + 7 \, a^{3} b f\right)} x^{6} + 9 \, a^{2} b^{2} c + 2 \, {\left(16 \, a b^{3} c - 4 \, a^{2} b^{2} d + a^{3} b e + 2 \, a^{4} f\right)} x^{3}}{18 \, {\left(a^{3} b^{4} x^{8} + 2 \, a^{4} b^{3} x^{5} + a^{5} b^{2} x^{2}\right)}} - \frac{\sqrt{3} {\left(20 \, b^{3} c - 5 \, a b^{2} d - a^{2} b e - 2 \, a^{3} 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 \, a^{3} b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(20 \, b^{3} c - 5 \, a b^{2} d - a^{2} b e - 2 \, a^{3} 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 \, a^{3} b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(20 \, b^{3} c - 5 \, a b^{2} d - a^{2} b e - 2 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{3} b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/18*((20*b^4*c - 5*a*b^3*d - a^2*b^2*e + 7*a^3*b*f)*x^6 + 9*a^2*b^2*c + 2*(16*a*b^3*c - 4*a^2*b^2*d + a^3*b*e + 2*a^4*f)*x^3)/(a^3*b^4*x^8 + 2*a^4*b^3*x^5 + a^5*b^2*x^2) - 1/27*sqrt(3)*(20*b^3*c - 5*a*b^2*d - a^2*b*e - 2*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^3*b^3*(a/b)^(2/3)) + 1/54*(20*b^3*c - 5*a*b^2*d - a^2*b*e - 2*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*b^3*(a/b)^(2/3)) - 1/27*(20*b^3*c - 5*a*b^2*d - a^2*b*e - 2*a^3*f)*log(x + (a/b)^(1/3))/(a^3*b^3*(a/b)^(2/3))","A",0
297,1,317,0,3.030792," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^5/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(35 \, b^{4} c - 14 \, a b^{3} d + 2 \, a^{2} b^{2} e + a^{3} b f\right)} x^{9} + {\left(245 \, a b^{3} c - 98 \, a^{2} b^{2} d + 14 \, a^{3} b e - 2 \, a^{4} f\right)} x^{6} - 9 \, a^{3} b c + 18 \, {\left(5 \, a^{2} b^{2} c - 2 \, a^{3} b d\right)} x^{3}}{36 \, {\left(a^{4} b^{3} x^{10} + 2 \, a^{5} b^{2} x^{7} + a^{6} b x^{4}\right)}} + \frac{\sqrt{3} {\left(35 \, b^{3} c - 14 \, a b^{2} d + 2 \, a^{2} b e + a^{3} 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 \, a^{4} b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(35 \, b^{3} c - 14 \, a b^{2} d + 2 \, a^{2} b e + a^{3} 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 \, a^{4} b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(35 \, b^{3} c - 14 \, a b^{2} d + 2 \, a^{2} b e + a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{4} b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"1/36*(4*(35*b^4*c - 14*a*b^3*d + 2*a^2*b^2*e + a^3*b*f)*x^9 + (245*a*b^3*c - 98*a^2*b^2*d + 14*a^3*b*e - 2*a^4*f)*x^6 - 9*a^3*b*c + 18*(5*a^2*b^2*c - 2*a^3*b*d)*x^3)/(a^4*b^3*x^10 + 2*a^5*b^2*x^7 + a^6*b*x^4) + 1/27*sqrt(3)*(35*b^3*c - 14*a*b^2*d + 2*a^2*b*e + a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^4*b^2*(a/b)^(1/3)) + 1/54*(35*b^3*c - 14*a*b^2*d + 2*a^2*b*e + a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^4*b^2*(a/b)^(1/3)) - 1/27*(35*b^3*c - 14*a*b^2*d + 2*a^2*b*e + a^3*f)*log(x + (a/b)^(1/3))/(a^4*b^2*(a/b)^(1/3))","A",0
298,1,318,0,3.051202," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^6/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{5 \, {\left(44 \, b^{4} c - 20 \, a b^{3} d + 5 \, a^{2} b^{2} e + a^{3} b f\right)} x^{9} + 2 \, {\left(176 \, a b^{3} c - 80 \, a^{2} b^{2} d + 20 \, a^{3} b e - 5 \, a^{4} f\right)} x^{6} - 18 \, a^{3} b c + 9 \, {\left(11 \, a^{2} b^{2} c - 5 \, a^{3} b d\right)} x^{3}}{90 \, {\left(a^{4} b^{3} x^{11} + 2 \, a^{5} b^{2} x^{8} + a^{6} b x^{5}\right)}} + \frac{\sqrt{3} {\left(44 \, b^{3} c - 20 \, a b^{2} d + 5 \, a^{2} b e + a^{3} 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 \, a^{4} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(44 \, b^{3} c - 20 \, a b^{2} d + 5 \, a^{2} b e + a^{3} 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 \, a^{4} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(44 \, b^{3} c - 20 \, a b^{2} d + 5 \, a^{2} b e + a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{4} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/90*(5*(44*b^4*c - 20*a*b^3*d + 5*a^2*b^2*e + a^3*b*f)*x^9 + 2*(176*a*b^3*c - 80*a^2*b^2*d + 20*a^3*b*e - 5*a^4*f)*x^6 - 18*a^3*b*c + 9*(11*a^2*b^2*c - 5*a^3*b*d)*x^3)/(a^4*b^3*x^11 + 2*a^5*b^2*x^8 + a^6*b*x^5) + 1/27*sqrt(3)*(44*b^3*c - 20*a*b^2*d + 5*a^2*b*e + a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^4*b^2*(a/b)^(2/3)) - 1/54*(44*b^3*c - 20*a*b^2*d + 5*a^2*b*e + a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^4*b^2*(a/b)^(2/3)) + 1/27*(44*b^3*c - 20*a*b^2*d + 5*a^2*b*e + a^3*f)*log(x + (a/b)^(1/3))/(a^4*b^2*(a/b)^(2/3))","A",0
299,1,343,0,3.046216," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^8/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{28 \, {\left(65 \, b^{4} c - 35 \, a b^{3} d + 14 \, a^{2} b^{2} e - 2 \, a^{3} b f\right)} x^{12} + 49 \, {\left(65 \, a b^{3} c - 35 \, a^{2} b^{2} d + 14 \, a^{3} b e - 2 \, a^{4} f\right)} x^{9} + 18 \, {\left(65 \, a^{2} b^{2} c - 35 \, a^{3} b d + 14 \, a^{4} e\right)} x^{6} + 36 \, a^{4} c - 9 \, {\left(13 \, a^{3} b c - 7 \, a^{4} d\right)} x^{3}}{252 \, {\left(a^{5} b^{2} x^{13} + 2 \, a^{6} b x^{10} + a^{7} x^{7}\right)}} - \frac{\sqrt{3} {\left(65 \, b^{3} c - 35 \, a b^{2} d + 14 \, a^{2} b e - 2 \, a^{3} 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 \, a^{5} b \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(65 \, b^{3} c - 35 \, a b^{2} d + 14 \, a^{2} b e - 2 \, a^{3} 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 \, a^{5} b \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(65 \, b^{3} c - 35 \, a b^{2} d + 14 \, a^{2} b e - 2 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{5} b \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"-1/252*(28*(65*b^4*c - 35*a*b^3*d + 14*a^2*b^2*e - 2*a^3*b*f)*x^12 + 49*(65*a*b^3*c - 35*a^2*b^2*d + 14*a^3*b*e - 2*a^4*f)*x^9 + 18*(65*a^2*b^2*c - 35*a^3*b*d + 14*a^4*e)*x^6 + 36*a^4*c - 9*(13*a^3*b*c - 7*a^4*d)*x^3)/(a^5*b^2*x^13 + 2*a^6*b*x^10 + a^7*x^7) - 1/27*sqrt(3)*(65*b^3*c - 35*a*b^2*d + 14*a^2*b*e - 2*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^5*b*(a/b)^(1/3)) - 1/54*(65*b^3*c - 35*a*b^2*d + 14*a^2*b*e - 2*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^5*b*(a/b)^(1/3)) + 1/27*(65*b^3*c - 35*a*b^2*d + 14*a^2*b*e - 2*a^3*f)*log(x + (a/b)^(1/3))/(a^5*b*(a/b)^(1/3))","A",0
300,1,343,0,2.949487," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^9/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{20 \, {\left(77 \, b^{4} c - 44 \, a b^{3} d + 20 \, a^{2} b^{2} e - 5 \, a^{3} b f\right)} x^{12} + 32 \, {\left(77 \, a b^{3} c - 44 \, a^{2} b^{2} d + 20 \, a^{3} b e - 5 \, a^{4} f\right)} x^{9} + 9 \, {\left(77 \, a^{2} b^{2} c - 44 \, a^{3} b d + 20 \, a^{4} e\right)} x^{6} + 45 \, a^{4} c - 18 \, {\left(7 \, a^{3} b c - 4 \, a^{4} d\right)} x^{3}}{360 \, {\left(a^{5} b^{2} x^{14} + 2 \, a^{6} b x^{11} + a^{7} x^{8}\right)}} - \frac{\sqrt{3} {\left(77 \, b^{3} c - 44 \, a b^{2} d + 20 \, a^{2} b e - 5 \, a^{3} 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 \, a^{5} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(77 \, b^{3} c - 44 \, a b^{2} d + 20 \, a^{2} b e - 5 \, a^{3} 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 \, a^{5} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(77 \, b^{3} c - 44 \, a b^{2} d + 20 \, a^{2} b e - 5 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{5} b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/360*(20*(77*b^4*c - 44*a*b^3*d + 20*a^2*b^2*e - 5*a^3*b*f)*x^12 + 32*(77*a*b^3*c - 44*a^2*b^2*d + 20*a^3*b*e - 5*a^4*f)*x^9 + 9*(77*a^2*b^2*c - 44*a^3*b*d + 20*a^4*e)*x^6 + 45*a^4*c - 18*(7*a^3*b*c - 4*a^4*d)*x^3)/(a^5*b^2*x^14 + 2*a^6*b*x^11 + a^7*x^8) - 1/27*sqrt(3)*(77*b^3*c - 44*a*b^2*d + 20*a^2*b*e - 5*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^5*b*(a/b)^(2/3)) + 1/54*(77*b^3*c - 44*a*b^2*d + 20*a^2*b*e - 5*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^5*b*(a/b)^(2/3)) - 1/27*(77*b^3*c - 44*a*b^2*d + 20*a^2*b*e - 5*a^3*f)*log(x + (a/b)^(1/3))/(a^5*b*(a/b)^(2/3))","A",0
301,1,376,0,3.199429," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^11/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{140 \, {\left(104 \, b^{5} c - 65 \, a b^{4} d + 35 \, a^{2} b^{3} e - 14 \, a^{3} b^{2} f\right)} x^{15} + 245 \, {\left(104 \, a b^{4} c - 65 \, a^{2} b^{3} d + 35 \, a^{3} b^{2} e - 14 \, a^{4} b f\right)} x^{12} + 90 \, {\left(104 \, a^{2} b^{3} c - 65 \, a^{3} b^{2} d + 35 \, a^{4} b e - 14 \, a^{5} f\right)} x^{9} - 9 \, {\left(104 \, a^{3} b^{2} c - 65 \, a^{4} b d + 35 \, a^{5} e\right)} x^{6} - 126 \, a^{5} c + 36 \, {\left(8 \, a^{4} b c - 5 \, a^{5} d\right)} x^{3}}{1260 \, {\left(a^{6} b^{2} x^{16} + 2 \, a^{7} b x^{13} + a^{8} x^{10}\right)}} + \frac{\sqrt{3} {\left(104 \, b^{3} c - 65 \, a b^{2} d + 35 \, a^{2} b e - 14 \, a^{3} 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 \, a^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(104 \, b^{3} c - 65 \, a b^{2} d + 35 \, a^{2} b e - 14 \, a^{3} 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 \, a^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(104 \, b^{3} c - 65 \, a b^{2} d + 35 \, a^{2} b e - 14 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{6} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"1/1260*(140*(104*b^5*c - 65*a*b^4*d + 35*a^2*b^3*e - 14*a^3*b^2*f)*x^15 + 245*(104*a*b^4*c - 65*a^2*b^3*d + 35*a^3*b^2*e - 14*a^4*b*f)*x^12 + 90*(104*a^2*b^3*c - 65*a^3*b^2*d + 35*a^4*b*e - 14*a^5*f)*x^9 - 9*(104*a^3*b^2*c - 65*a^4*b*d + 35*a^5*e)*x^6 - 126*a^5*c + 36*(8*a^4*b*c - 5*a^5*d)*x^3)/(a^6*b^2*x^16 + 2*a^7*b*x^13 + a^8*x^10) + 1/27*sqrt(3)*(104*b^3*c - 65*a*b^2*d + 35*a^2*b*e - 14*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^6*(a/b)^(1/3)) + 1/54*(104*b^3*c - 65*a*b^2*d + 35*a^2*b*e - 14*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^6*(a/b)^(1/3)) - 1/27*(104*b^3*c - 65*a*b^2*d + 35*a^2*b*e - 14*a^3*f)*log(x + (a/b)^(1/3))/(a^6*(a/b)^(1/3))","A",0
302,1,376,0,3.285581," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^12/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{220 \, {\left(119 \, b^{5} c - 77 \, a b^{4} d + 44 \, a^{2} b^{3} e - 20 \, a^{3} b^{2} f\right)} x^{15} + 352 \, {\left(119 \, a b^{4} c - 77 \, a^{2} b^{3} d + 44 \, a^{3} b^{2} e - 20 \, a^{4} b f\right)} x^{12} + 99 \, {\left(119 \, a^{2} b^{3} c - 77 \, a^{3} b^{2} d + 44 \, a^{4} b e - 20 \, a^{5} f\right)} x^{9} - 18 \, {\left(119 \, a^{3} b^{2} c - 77 \, a^{4} b d + 44 \, a^{5} e\right)} x^{6} - 360 \, a^{5} c + 45 \, {\left(17 \, a^{4} b c - 11 \, a^{5} d\right)} x^{3}}{3960 \, {\left(a^{6} b^{2} x^{17} + 2 \, a^{7} b x^{14} + a^{8} x^{11}\right)}} + \frac{\sqrt{3} {\left(119 \, b^{3} c - 77 \, a b^{2} d + 44 \, a^{2} b e - 20 \, a^{3} 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 \, a^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(119 \, b^{3} c - 77 \, a b^{2} d + 44 \, a^{2} b e - 20 \, a^{3} 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 \, a^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(119 \, b^{3} c - 77 \, a b^{2} d + 44 \, a^{2} b e - 20 \, a^{3} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3960*(220*(119*b^5*c - 77*a*b^4*d + 44*a^2*b^3*e - 20*a^3*b^2*f)*x^15 + 352*(119*a*b^4*c - 77*a^2*b^3*d + 44*a^3*b^2*e - 20*a^4*b*f)*x^12 + 99*(119*a^2*b^3*c - 77*a^3*b^2*d + 44*a^4*b*e - 20*a^5*f)*x^9 - 18*(119*a^3*b^2*c - 77*a^4*b*d + 44*a^5*e)*x^6 - 360*a^5*c + 45*(17*a^4*b*c - 11*a^5*d)*x^3)/(a^6*b^2*x^17 + 2*a^7*b*x^14 + a^8*x^11) + 1/27*sqrt(3)*(119*b^3*c - 77*a*b^2*d + 44*a^2*b*e - 20*a^3*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^6*(a/b)^(2/3)) - 1/54*(119*b^3*c - 77*a*b^2*d + 44*a^2*b*e - 20*a^3*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^6*(a/b)^(2/3)) + 1/27*(119*b^3*c - 77*a*b^2*d + 44*a^2*b*e - 20*a^3*f)*log(x + (a/b)^(1/3))/(a^6*(a/b)^(2/3))","A",0
303,1,427,0,3.054717," ","integrate((f*x^9+e*x^6+d*x^3+c)/x^14/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{1820 \, {\left(152 \, b^{6} c - 104 \, a b^{5} d + 65 \, a^{2} b^{4} e - 35 \, a^{3} b^{3} f\right)} x^{18} + 3185 \, {\left(152 \, a b^{5} c - 104 \, a^{2} b^{4} d + 65 \, a^{3} b^{3} e - 35 \, a^{4} b^{2} f\right)} x^{15} + 1170 \, {\left(152 \, a^{2} b^{4} c - 104 \, a^{3} b^{3} d + 65 \, a^{4} b^{2} e - 35 \, a^{5} b f\right)} x^{12} - 117 \, {\left(152 \, a^{3} b^{3} c - 104 \, a^{4} b^{2} d + 65 \, a^{5} b e - 35 \, a^{6} f\right)} x^{9} + 1260 \, a^{6} c + 36 \, {\left(152 \, a^{4} b^{2} c - 104 \, a^{5} b d + 65 \, a^{6} e\right)} x^{6} - 126 \, {\left(19 \, a^{5} b c - 13 \, a^{6} d\right)} x^{3}}{16380 \, {\left(a^{7} b^{2} x^{19} + 2 \, a^{8} b x^{16} + a^{9} x^{13}\right)}} - \frac{\sqrt{3} {\left(152 \, b^{4} c - 104 \, a b^{3} d + 65 \, a^{2} b^{2} e - 35 \, a^{3} b 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 \, a^{7} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(152 \, b^{4} c - 104 \, a b^{3} d + 65 \, a^{2} b^{2} e - 35 \, a^{3} b 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 \, a^{7} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(152 \, b^{4} c - 104 \, a b^{3} d + 65 \, a^{2} b^{2} e - 35 \, a^{3} b f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{7} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"-1/16380*(1820*(152*b^6*c - 104*a*b^5*d + 65*a^2*b^4*e - 35*a^3*b^3*f)*x^18 + 3185*(152*a*b^5*c - 104*a^2*b^4*d + 65*a^3*b^3*e - 35*a^4*b^2*f)*x^15 + 1170*(152*a^2*b^4*c - 104*a^3*b^3*d + 65*a^4*b^2*e - 35*a^5*b*f)*x^12 - 117*(152*a^3*b^3*c - 104*a^4*b^2*d + 65*a^5*b*e - 35*a^6*f)*x^9 + 1260*a^6*c + 36*(152*a^4*b^2*c - 104*a^5*b*d + 65*a^6*e)*x^6 - 126*(19*a^5*b*c - 13*a^6*d)*x^3)/(a^7*b^2*x^19 + 2*a^8*b*x^16 + a^9*x^13) - 1/27*sqrt(3)*(152*b^4*c - 104*a*b^3*d + 65*a^2*b^2*e - 35*a^3*b*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^7*(a/b)^(1/3)) - 1/54*(152*b^4*c - 104*a*b^3*d + 65*a^2*b^2*e - 35*a^3*b*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^7*(a/b)^(1/3)) + 1/27*(152*b^4*c - 104*a*b^3*d + 65*a^2*b^2*e - 35*a^3*b*f)*log(x + (a/b)^(1/3))/(a^7*(a/b)^(1/3))","A",0
304,1,44,0,2.897122," ","integrate((1-x)*x^4/(x^3+1),x, algorithm=""maxima"")","-\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(x + 1\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(x + 1)","A",0
305,1,24,0,3.005759," ","integrate((1-x)*x^3/(x^3+1),x, algorithm=""maxima"")","-\frac{1}{2} \, x^{2} + x + \frac{1}{3} \, \log\left(x^{2} - x + 1\right) - \frac{2}{3} \, \log\left(x + 1\right)"," ",0,"-1/2*x^2 + x + 1/3*log(x^2 - x + 1) - 2/3*log(x + 1)","A",0
306,1,37,0,2.962400," ","integrate((1-x)*x^2/(x^3+1),x, algorithm=""maxima"")","\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(x + 1\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(x + 1)","A",0
307,1,34,0,2.867907," ","integrate((1-x)*x/(x^3+1),x, algorithm=""maxima"")","\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(x + 1\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/6*log(x^2 - x + 1) - 2/3*log(x + 1)","A",0
308,1,36,0,2.879319," ","integrate((1-x)/x/(x^3+1),x, algorithm=""maxima"")","-\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(x + 1\right) + \log\left(x\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/6*log(x^2 - x + 1) - 2/3*log(x + 1) + log(x)","A",0
309,1,43,0,3.033822," ","integrate((1-x)/x^2/(x^3+1),x, algorithm=""maxima"")","-\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(x + 1\right) - \log\left(x\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(x + 1) - log(x)","A",0
310,1,28,0,2.995718," ","integrate((1-x)/x^3/(x^3+1),x, algorithm=""maxima"")","\frac{2 \, x - 1}{2 \, x^{2}} + \frac{1}{3} \, \log\left(x^{2} - x + 1\right) - \frac{2}{3} \, \log\left(x + 1\right)"," ",0,"1/2*(2*x - 1)/x^2 + 1/3*log(x^2 - x + 1) - 2/3*log(x + 1)","A",0
311,1,34,0,2.990523," ","integrate(x*(1+2*x)/(x^3+1),x, algorithm=""maxima"")","\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(x + 1\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 5/6*log(x^2 - x + 1) + 1/3*log(x + 1)","A",0
312,1,32,0,2.987687," ","integrate(x*(1+2*x)/(-x^3+1),x, algorithm=""maxima"")","-\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(x - 1\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/2*log(x^2 + x + 1) - log(x - 1)","A",0
313,1,43,0,1.334099," ","integrate(x^2*(e*x^2+d*x+c)*(b*x^3+a),x, algorithm=""maxima"")","\frac{1}{8} \, b e x^{8} + \frac{1}{7} \, b d x^{7} + \frac{1}{6} \, b c x^{6} + \frac{1}{5} \, a e x^{5} + \frac{1}{4} \, a d x^{4} + \frac{1}{3} \, a c x^{3}"," ",0,"1/8*b*e*x^8 + 1/7*b*d*x^7 + 1/6*b*c*x^6 + 1/5*a*e*x^5 + 1/4*a*d*x^4 + 1/3*a*c*x^3","A",0
314,1,43,0,1.358761," ","integrate(x*(e*x^2+d*x+c)*(b*x^3+a),x, algorithm=""maxima"")","\frac{1}{7} \, b e x^{7} + \frac{1}{6} \, b d x^{6} + \frac{1}{5} \, b c x^{5} + \frac{1}{4} \, a e x^{4} + \frac{1}{3} \, a d x^{3} + \frac{1}{2} \, a c x^{2}"," ",0,"1/7*b*e*x^7 + 1/6*b*d*x^6 + 1/5*b*c*x^5 + 1/4*a*e*x^4 + 1/3*a*d*x^3 + 1/2*a*c*x^2","A",0
315,1,40,0,1.344843," ","integrate((e*x^2+d*x+c)*(b*x^3+a),x, algorithm=""maxima"")","\frac{1}{6} \, b e x^{6} + \frac{1}{5} \, b d x^{5} + \frac{1}{4} \, b c x^{4} + \frac{1}{3} \, a e x^{3} + \frac{1}{2} \, a d x^{2} + a c x"," ",0,"1/6*b*e*x^6 + 1/5*b*d*x^5 + 1/4*b*c*x^4 + 1/3*a*e*x^3 + 1/2*a*d*x^2 + a*c*x","A",0
316,1,38,0,1.326149," ","integrate((e*x^2+d*x+c)*(b*x^3+a)/x,x, algorithm=""maxima"")","\frac{1}{5} \, b e x^{5} + \frac{1}{4} \, b d x^{4} + \frac{1}{3} \, b c x^{3} + \frac{1}{2} \, a e x^{2} + a d x + a c \log\left(x\right)"," ",0,"1/5*b*e*x^5 + 1/4*b*d*x^4 + 1/3*b*c*x^3 + 1/2*a*e*x^2 + a*d*x + a*c*log(x)","A",0
317,1,38,0,1.335459," ","integrate((e*x^2+d*x+c)*(b*x^3+a)/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, b e x^{4} + \frac{1}{3} \, b d x^{3} + \frac{1}{2} \, b c x^{2} + a e x + a d \log\left(x\right) - \frac{a c}{x}"," ",0,"1/4*b*e*x^4 + 1/3*b*d*x^3 + 1/2*b*c*x^2 + a*e*x + a*d*log(x) - a*c/x","A",0
318,1,38,0,1.350565," ","integrate((e*x^2+d*x+c)*(b*x^3+a)/x^3,x, algorithm=""maxima"")","\frac{1}{3} \, b e x^{3} + \frac{1}{2} \, b d x^{2} + b c x + a e \log\left(x\right) - \frac{2 \, a d x + a c}{2 \, x^{2}}"," ",0,"1/3*b*e*x^3 + 1/2*b*d*x^2 + b*c*x + a*e*log(x) - 1/2*(2*a*d*x + a*c)/x^2","A",0
319,1,79,0,1.352291," ","integrate(x^2*(e*x^2+d*x+c)*(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{1}{11} \, b^{2} e x^{11} + \frac{1}{10} \, b^{2} d x^{10} + \frac{1}{9} \, b^{2} c x^{9} + \frac{1}{4} \, a b e x^{8} + \frac{2}{7} \, a b d x^{7} + \frac{1}{3} \, a b c x^{6} + \frac{1}{5} \, a^{2} e x^{5} + \frac{1}{4} \, a^{2} d x^{4} + \frac{1}{3} \, a^{2} c x^{3}"," ",0,"1/11*b^2*e*x^11 + 1/10*b^2*d*x^10 + 1/9*b^2*c*x^9 + 1/4*a*b*e*x^8 + 2/7*a*b*d*x^7 + 1/3*a*b*c*x^6 + 1/5*a^2*e*x^5 + 1/4*a^2*d*x^4 + 1/3*a^2*c*x^3","A",0
320,1,79,0,1.292376," ","integrate(x*(e*x^2+d*x+c)*(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{1}{10} \, b^{2} e x^{10} + \frac{1}{9} \, b^{2} d x^{9} + \frac{1}{8} \, b^{2} c x^{8} + \frac{2}{7} \, a b e x^{7} + \frac{1}{3} \, a b d x^{6} + \frac{2}{5} \, a b c x^{5} + \frac{1}{4} \, a^{2} e x^{4} + \frac{1}{3} \, a^{2} d x^{3} + \frac{1}{2} \, a^{2} c x^{2}"," ",0,"1/10*b^2*e*x^10 + 1/9*b^2*d*x^9 + 1/8*b^2*c*x^8 + 2/7*a*b*e*x^7 + 1/3*a*b*d*x^6 + 2/5*a*b*c*x^5 + 1/4*a^2*e*x^4 + 1/3*a^2*d*x^3 + 1/2*a^2*c*x^2","A",0
321,1,76,0,1.403691," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{1}{9} \, b^{2} e x^{9} + \frac{1}{8} \, b^{2} d x^{8} + \frac{1}{7} \, b^{2} c x^{7} + \frac{1}{3} \, a b e x^{6} + \frac{2}{5} \, a b d x^{5} + \frac{1}{2} \, a b c x^{4} + \frac{1}{3} \, a^{2} e x^{3} + \frac{1}{2} \, a^{2} d x^{2} + a^{2} c x"," ",0,"1/9*b^2*e*x^9 + 1/8*b^2*d*x^8 + 1/7*b^2*c*x^7 + 1/3*a*b*e*x^6 + 2/5*a*b*d*x^5 + 1/2*a*b*c*x^4 + 1/3*a^2*e*x^3 + 1/2*a^2*d*x^2 + a^2*c*x","A",0
322,1,74,0,1.371273," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^2/x,x, algorithm=""maxima"")","\frac{1}{8} \, b^{2} e x^{8} + \frac{1}{7} \, b^{2} d x^{7} + \frac{1}{6} \, b^{2} c x^{6} + \frac{2}{5} \, a b e x^{5} + \frac{1}{2} \, a b d x^{4} + \frac{2}{3} \, a b c x^{3} + \frac{1}{2} \, a^{2} e x^{2} + a^{2} d x + a^{2} c \log\left(x\right)"," ",0,"1/8*b^2*e*x^8 + 1/7*b^2*d*x^7 + 1/6*b^2*c*x^6 + 2/5*a*b*e*x^5 + 1/2*a*b*d*x^4 + 2/3*a*b*c*x^3 + 1/2*a^2*e*x^2 + a^2*d*x + a^2*c*log(x)","A",0
323,1,73,0,1.297231," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^2/x^2,x, algorithm=""maxima"")","\frac{1}{7} \, b^{2} e x^{7} + \frac{1}{6} \, b^{2} d x^{6} + \frac{1}{5} \, b^{2} c x^{5} + \frac{1}{2} \, a b e x^{4} + \frac{2}{3} \, a b d x^{3} + a b c x^{2} + a^{2} e x + a^{2} d \log\left(x\right) - \frac{a^{2} c}{x}"," ",0,"1/7*b^2*e*x^7 + 1/6*b^2*d*x^6 + 1/5*b^2*c*x^5 + 1/2*a*b*e*x^4 + 2/3*a*b*d*x^3 + a*b*c*x^2 + a^2*e*x + a^2*d*log(x) - a^2*c/x","A",0
324,1,74,0,1.311165," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^2/x^3,x, algorithm=""maxima"")","\frac{1}{6} \, b^{2} e x^{6} + \frac{1}{5} \, b^{2} d x^{5} + \frac{1}{4} \, b^{2} c x^{4} + \frac{2}{3} \, a b e x^{3} + a b d x^{2} + 2 \, a b c x + a^{2} e \log\left(x\right) - \frac{2 \, a^{2} d x + a^{2} c}{2 \, x^{2}}"," ",0,"1/6*b^2*e*x^6 + 1/5*b^2*d*x^5 + 1/4*b^2*c*x^4 + 2/3*a*b*e*x^3 + a*b*d*x^2 + 2*a*b*c*x + a^2*e*log(x) - 1/2*(2*a^2*d*x + a^2*c)/x^2","A",0
325,1,115,0,1.332442," ","integrate(x^2*(e*x^2+d*x+c)*(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{1}{14} \, b^{3} e x^{14} + \frac{1}{13} \, b^{3} d x^{13} + \frac{1}{12} \, b^{3} c x^{12} + \frac{3}{11} \, a b^{2} e x^{11} + \frac{3}{10} \, a b^{2} d x^{10} + \frac{1}{3} \, a b^{2} c x^{9} + \frac{3}{8} \, a^{2} b e x^{8} + \frac{3}{7} \, a^{2} b d x^{7} + \frac{1}{2} \, a^{2} b c x^{6} + \frac{1}{5} \, a^{3} e x^{5} + \frac{1}{4} \, a^{3} d x^{4} + \frac{1}{3} \, a^{3} c x^{3}"," ",0,"1/14*b^3*e*x^14 + 1/13*b^3*d*x^13 + 1/12*b^3*c*x^12 + 3/11*a*b^2*e*x^11 + 3/10*a*b^2*d*x^10 + 1/3*a*b^2*c*x^9 + 3/8*a^2*b*e*x^8 + 3/7*a^2*b*d*x^7 + 1/2*a^2*b*c*x^6 + 1/5*a^3*e*x^5 + 1/4*a^3*d*x^4 + 1/3*a^3*c*x^3","A",0
326,1,115,0,1.371029," ","integrate(x*(e*x^2+d*x+c)*(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{1}{13} \, b^{3} e x^{13} + \frac{1}{12} \, b^{3} d x^{12} + \frac{1}{11} \, b^{3} c x^{11} + \frac{3}{10} \, a b^{2} e x^{10} + \frac{1}{3} \, a b^{2} d x^{9} + \frac{3}{8} \, a b^{2} c x^{8} + \frac{3}{7} \, a^{2} b e x^{7} + \frac{1}{2} \, a^{2} b d x^{6} + \frac{3}{5} \, a^{2} b c x^{5} + \frac{1}{4} \, a^{3} e x^{4} + \frac{1}{3} \, a^{3} d x^{3} + \frac{1}{2} \, a^{3} c x^{2}"," ",0,"1/13*b^3*e*x^13 + 1/12*b^3*d*x^12 + 1/11*b^3*c*x^11 + 3/10*a*b^2*e*x^10 + 1/3*a*b^2*d*x^9 + 3/8*a*b^2*c*x^8 + 3/7*a^2*b*e*x^7 + 1/2*a^2*b*d*x^6 + 3/5*a^2*b*c*x^5 + 1/4*a^3*e*x^4 + 1/3*a^3*d*x^3 + 1/2*a^3*c*x^2","A",0
327,1,112,0,1.329088," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{1}{12} \, b^{3} e x^{12} + \frac{1}{11} \, b^{3} d x^{11} + \frac{1}{10} \, b^{3} c x^{10} + \frac{1}{3} \, a b^{2} e x^{9} + \frac{3}{8} \, a b^{2} d x^{8} + \frac{3}{7} \, a b^{2} c x^{7} + \frac{1}{2} \, a^{2} b e x^{6} + \frac{3}{5} \, a^{2} b d x^{5} + \frac{3}{4} \, a^{2} b c x^{4} + \frac{1}{3} \, a^{3} e x^{3} + \frac{1}{2} \, a^{3} d x^{2} + a^{3} c x"," ",0,"1/12*b^3*e*x^12 + 1/11*b^3*d*x^11 + 1/10*b^3*c*x^10 + 1/3*a*b^2*e*x^9 + 3/8*a*b^2*d*x^8 + 3/7*a*b^2*c*x^7 + 1/2*a^2*b*e*x^6 + 3/5*a^2*b*d*x^5 + 3/4*a^2*b*c*x^4 + 1/3*a^3*e*x^3 + 1/2*a^3*d*x^2 + a^3*c*x","A",0
328,1,109,0,1.286480," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^3/x,x, algorithm=""maxima"")","\frac{1}{11} \, b^{3} e x^{11} + \frac{1}{10} \, b^{3} d x^{10} + \frac{1}{9} \, b^{3} c x^{9} + \frac{3}{8} \, a b^{2} e x^{8} + \frac{3}{7} \, a b^{2} d x^{7} + \frac{1}{2} \, a b^{2} c x^{6} + \frac{3}{5} \, a^{2} b e x^{5} + \frac{3}{4} \, a^{2} b d x^{4} + a^{2} b c x^{3} + \frac{1}{2} \, a^{3} e x^{2} + a^{3} d x + a^{3} c \log\left(x\right)"," ",0,"1/11*b^3*e*x^11 + 1/10*b^3*d*x^10 + 1/9*b^3*c*x^9 + 3/8*a*b^2*e*x^8 + 3/7*a*b^2*d*x^7 + 1/2*a*b^2*c*x^6 + 3/5*a^2*b*e*x^5 + 3/4*a^2*b*d*x^4 + a^2*b*c*x^3 + 1/2*a^3*e*x^2 + a^3*d*x + a^3*c*log(x)","A",0
329,1,109,0,1.349774," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^3/x^2,x, algorithm=""maxima"")","\frac{1}{10} \, b^{3} e x^{10} + \frac{1}{9} \, b^{3} d x^{9} + \frac{1}{8} \, b^{3} c x^{8} + \frac{3}{7} \, a b^{2} e x^{7} + \frac{1}{2} \, a b^{2} d x^{6} + \frac{3}{5} \, a b^{2} c x^{5} + \frac{3}{4} \, a^{2} b e x^{4} + a^{2} b d x^{3} + \frac{3}{2} \, a^{2} b c x^{2} + a^{3} e x + a^{3} d \log\left(x\right) - \frac{a^{3} c}{x}"," ",0,"1/10*b^3*e*x^10 + 1/9*b^3*d*x^9 + 1/8*b^3*c*x^8 + 3/7*a*b^2*e*x^7 + 1/2*a*b^2*d*x^6 + 3/5*a*b^2*c*x^5 + 3/4*a^2*b*e*x^4 + a^2*b*d*x^3 + 3/2*a^2*b*c*x^2 + a^3*e*x + a^3*d*log(x) - a^3*c/x","A",0
330,1,110,0,1.324537," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^3/x^3,x, algorithm=""maxima"")","\frac{1}{9} \, b^{3} e x^{9} + \frac{1}{8} \, b^{3} d x^{8} + \frac{1}{7} \, b^{3} c x^{7} + \frac{1}{2} \, a b^{2} e x^{6} + \frac{3}{5} \, a b^{2} d x^{5} + \frac{3}{4} \, a b^{2} c x^{4} + a^{2} b e x^{3} + \frac{3}{2} \, a^{2} b d x^{2} + 3 \, a^{2} b c x + a^{3} e \log\left(x\right) - \frac{2 \, a^{3} d x + a^{3} c}{2 \, x^{2}}"," ",0,"1/9*b^3*e*x^9 + 1/8*b^3*d*x^8 + 1/7*b^3*c*x^7 + 1/2*a*b^2*e*x^6 + 3/5*a*b^2*d*x^5 + 3/4*a*b^2*c*x^4 + a^2*b*e*x^3 + 3/2*a^2*b*d*x^2 + 3*a^2*b*c*x + a^3*e*log(x) - 1/2*(2*a^3*d*x + a^3*c)/x^2","A",0
331,1,151,0,1.309531," ","integrate(x^2*(e*x^2+d*x+c)*(b*x^3+a)^4,x, algorithm=""maxima"")","\frac{1}{17} \, b^{4} e x^{17} + \frac{1}{16} \, b^{4} d x^{16} + \frac{1}{15} \, b^{4} c x^{15} + \frac{2}{7} \, a b^{3} e x^{14} + \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} e x^{11} + \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 e x^{8} + \frac{4}{7} \, a^{3} b d x^{7} + \frac{2}{3} \, a^{3} b c x^{6} + \frac{1}{5} \, a^{4} e x^{5} + \frac{1}{4} \, a^{4} d x^{4} + \frac{1}{3} \, a^{4} c x^{3}"," ",0,"1/17*b^4*e*x^17 + 1/16*b^4*d*x^16 + 1/15*b^4*c*x^15 + 2/7*a*b^3*e*x^14 + 4/13*a*b^3*d*x^13 + 1/3*a*b^3*c*x^12 + 6/11*a^2*b^2*e*x^11 + 3/5*a^2*b^2*d*x^10 + 2/3*a^2*b^2*c*x^9 + 1/2*a^3*b*e*x^8 + 4/7*a^3*b*d*x^7 + 2/3*a^3*b*c*x^6 + 1/5*a^4*e*x^5 + 1/4*a^4*d*x^4 + 1/3*a^4*c*x^3","A",0
332,1,151,0,1.336484," ","integrate(x*(e*x^2+d*x+c)*(b*x^3+a)^4,x, algorithm=""maxima"")","\frac{1}{16} \, b^{4} e x^{16} + \frac{1}{15} \, b^{4} d x^{15} + \frac{1}{14} \, b^{4} c x^{14} + \frac{4}{13} \, a b^{3} e x^{13} + \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} e x^{10} + \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 e x^{7} + \frac{2}{3} \, a^{3} b d x^{6} + \frac{4}{5} \, a^{3} b c x^{5} + \frac{1}{4} \, a^{4} e x^{4} + \frac{1}{3} \, a^{4} d x^{3} + \frac{1}{2} \, a^{4} c x^{2}"," ",0,"1/16*b^4*e*x^16 + 1/15*b^4*d*x^15 + 1/14*b^4*c*x^14 + 4/13*a*b^3*e*x^13 + 1/3*a*b^3*d*x^12 + 4/11*a*b^3*c*x^11 + 3/5*a^2*b^2*e*x^10 + 2/3*a^2*b^2*d*x^9 + 3/4*a^2*b^2*c*x^8 + 4/7*a^3*b*e*x^7 + 2/3*a^3*b*d*x^6 + 4/5*a^3*b*c*x^5 + 1/4*a^4*e*x^4 + 1/3*a^4*d*x^3 + 1/2*a^4*c*x^2","A",0
333,1,147,0,1.314276," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^4,x, algorithm=""maxima"")","\frac{1}{15} \, b^{4} e x^{15} + \frac{1}{14} \, b^{4} d x^{14} + \frac{1}{13} \, b^{4} c x^{13} + \frac{1}{3} \, a b^{3} e x^{12} + \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} e x^{9} + \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 e x^{6} + \frac{4}{5} \, a^{3} b d x^{5} + a^{3} b c x^{4} + \frac{1}{3} \, a^{4} e x^{3} + \frac{1}{2} \, a^{4} d x^{2} + a^{4} c x"," ",0,"1/15*b^4*e*x^15 + 1/14*b^4*d*x^14 + 1/13*b^4*c*x^13 + 1/3*a*b^3*e*x^12 + 4/11*a*b^3*d*x^11 + 2/5*a*b^3*c*x^10 + 2/3*a^2*b^2*e*x^9 + 3/4*a^2*b^2*d*x^8 + 6/7*a^2*b^2*c*x^7 + 2/3*a^3*b*e*x^6 + 4/5*a^3*b*d*x^5 + a^3*b*c*x^4 + 1/3*a^4*e*x^3 + 1/2*a^4*d*x^2 + a^4*c*x","A",0
334,1,144,0,1.300867," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^4/x,x, algorithm=""maxima"")","\frac{1}{14} \, b^{4} e x^{14} + \frac{1}{13} \, b^{4} d x^{13} + \frac{1}{12} \, b^{4} c x^{12} + \frac{4}{11} \, a b^{3} e x^{11} + \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} e x^{8} + \frac{6}{7} \, a^{2} b^{2} d x^{7} + a^{2} b^{2} c x^{6} + \frac{4}{5} \, a^{3} b e x^{5} + a^{3} b d x^{4} + \frac{4}{3} \, a^{3} b c x^{3} + \frac{1}{2} \, a^{4} e x^{2} + a^{4} d x + a^{4} c \log\left(x\right)"," ",0,"1/14*b^4*e*x^14 + 1/13*b^4*d*x^13 + 1/12*b^4*c*x^12 + 4/11*a*b^3*e*x^11 + 2/5*a*b^3*d*x^10 + 4/9*a*b^3*c*x^9 + 3/4*a^2*b^2*e*x^8 + 6/7*a^2*b^2*d*x^7 + a^2*b^2*c*x^6 + 4/5*a^3*b*e*x^5 + a^3*b*d*x^4 + 4/3*a^3*b*c*x^3 + 1/2*a^4*e*x^2 + a^4*d*x + a^4*c*log(x)","A",0
335,1,144,0,1.311155," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^4/x^2,x, algorithm=""maxima"")","\frac{1}{13} \, b^{4} e x^{13} + \frac{1}{12} \, b^{4} d x^{12} + \frac{1}{11} \, b^{4} c x^{11} + \frac{2}{5} \, a b^{3} e x^{10} + \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} e x^{7} + a^{2} b^{2} d x^{6} + \frac{6}{5} \, a^{2} b^{2} c x^{5} + a^{3} b e x^{4} + \frac{4}{3} \, a^{3} b d x^{3} + 2 \, a^{3} b c x^{2} + a^{4} e x + a^{4} d \log\left(x\right) - \frac{a^{4} c}{x}"," ",0,"1/13*b^4*e*x^13 + 1/12*b^4*d*x^12 + 1/11*b^4*c*x^11 + 2/5*a*b^3*e*x^10 + 4/9*a*b^3*d*x^9 + 1/2*a*b^3*c*x^8 + 6/7*a^2*b^2*e*x^7 + a^2*b^2*d*x^6 + 6/5*a^2*b^2*c*x^5 + a^3*b*e*x^4 + 4/3*a^3*b*d*x^3 + 2*a^3*b*c*x^2 + a^4*e*x + a^4*d*log(x) - a^4*c/x","A",0
336,1,146,0,1.334403," ","integrate((e*x^2+d*x+c)*(b*x^3+a)^4/x^3,x, algorithm=""maxima"")","\frac{1}{12} \, b^{4} e x^{12} + \frac{1}{11} \, b^{4} d x^{11} + \frac{1}{10} \, b^{4} c x^{10} + \frac{4}{9} \, a b^{3} e x^{9} + \frac{1}{2} \, a b^{3} d x^{8} + \frac{4}{7} \, a b^{3} c x^{7} + a^{2} b^{2} e x^{6} + \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 e x^{3} + 2 \, a^{3} b d x^{2} + 4 \, a^{3} b c x + a^{4} e \log\left(x\right) - \frac{2 \, a^{4} d x + a^{4} c}{2 \, x^{2}}"," ",0,"1/12*b^4*e*x^12 + 1/11*b^4*d*x^11 + 1/10*b^4*c*x^10 + 4/9*a*b^3*e*x^9 + 1/2*a*b^3*d*x^8 + 4/7*a*b^3*c*x^7 + a^2*b^2*e*x^6 + 6/5*a^2*b^2*d*x^5 + 3/2*a^2*b^2*c*x^4 + 4/3*a^3*b*e*x^3 + 2*a^3*b*d*x^2 + 4*a^3*b*c*x + a^4*e*log(x) - 1/2*(2*a^4*d*x + a^4*c)/x^2","A",0
337,1,190,0,2.942157," ","integrate(x^3*(e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{2 \, e x^{3} + 3 \, d x^{2} + 6 \, c x}{6 \, b} - \frac{\sqrt{3} {\left(a b d \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b c \left(\frac{a}{b}\right)^{\frac{1}{3}}\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(2 \, a e \left(\frac{a}{b}\right)^{\frac{2}{3}} + a d \left(\frac{a}{b}\right)^{\frac{1}{3}} - a 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 \, b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(a e \left(\frac{a}{b}\right)^{\frac{2}{3}} - a d \left(\frac{a}{b}\right)^{\frac{1}{3}} + a c\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/6*(2*e*x^3 + 3*d*x^2 + 6*c*x)/b - 1/3*sqrt(3)*(a*b*d*(a/b)^(2/3) + a*b*c*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^2) - 1/6*(2*a*e*(a/b)^(2/3) + a*d*(a/b)^(1/3) - a*c)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^2*(a/b)^(2/3)) - 1/3*(a*e*(a/b)^(2/3) - a*d*(a/b)^(1/3) + a*c)*log(x + (a/b)^(1/3))/(b^2*(a/b)^(2/3))","A",0
338,1,181,0,2.935646," ","integrate(x^2*(e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left(a e \left(\frac{a}{b}\right)^{\frac{2}{3}} + a d \left(\frac{a}{b}\right)^{\frac{1}{3}}\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} + \frac{e x^{2} + 2 \, d x}{2 \, b} + \frac{{\left(2 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} - a e \left(\frac{a}{b}\right)^{\frac{1}{3}} + a 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^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b c \left(\frac{a}{b}\right)^{\frac{2}{3}} + a e \left(\frac{a}{b}\right)^{\frac{1}{3}} - a d\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/3*sqrt(3)*(a*e*(a/b)^(2/3) + a*d*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b) + 1/2*(e*x^2 + 2*d*x)/b + 1/6*(2*b*c*(a/b)^(2/3) - a*e*(a/b)^(1/3) + a*d)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^2*(a/b)^(2/3)) + 1/3*(b*c*(a/b)^(2/3) + a*e*(a/b)^(1/3) - a*d)*log(x + (a/b)^(1/3))/(b^2*(a/b)^(2/3))","A",0
339,1,173,0,2.943484," ","integrate(x*(e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{e x}{b} + \frac{\sqrt{3} {\left(b c \left(\frac{a}{b}\right)^{\frac{2}{3}} - a e \left(\frac{a}{b}\right)^{\frac{1}{3}}\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} + \frac{{\left(2 \, b d \left(\frac{a}{b}\right)^{\frac{2}{3}} + b c \left(\frac{a}{b}\right)^{\frac{1}{3}} + a 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^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b d \left(\frac{a}{b}\right)^{\frac{2}{3}} - b c \left(\frac{a}{b}\right)^{\frac{1}{3}} - a e\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"e*x/b + 1/3*sqrt(3)*(b*c*(a/b)^(2/3) - a*e*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b) + 1/6*(2*b*d*(a/b)^(2/3) + b*c*(a/b)^(1/3) + a*e)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^2*(a/b)^(2/3)) + 1/3*(b*d*(a/b)^(2/3) - b*c*(a/b)^(1/3) - a*e)*log(x + (a/b)^(1/3))/(b^2*(a/b)^(2/3))","A",0
340,1,159,0,3.012638," ","integrate((e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{\sqrt{3} {\left(b d \left(\frac{a}{b}\right)^{\frac{2}{3}} + b c \left(\frac{a}{b}\right)^{\frac{1}{3}}\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} + \frac{{\left(2 \, e \left(\frac{a}{b}\right)^{\frac{2}{3}} + d \left(\frac{a}{b}\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 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(e \left(\frac{a}{b}\right)^{\frac{2}{3}} - d \left(\frac{a}{b}\right)^{\frac{1}{3}} + c\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*sqrt(3)*(b*d*(a/b)^(2/3) + b*c*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b) + 1/6*(2*e*(a/b)^(2/3) + d*(a/b)^(1/3) - c)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) + 1/3*(e*(a/b)^(2/3) - d*(a/b)^(1/3) + c)*log(x + (a/b)^(1/3))/(b*(a/b)^(2/3))","A",0
341,1,176,0,3.018413," ","integrate((e*x^2+d*x+c)/x/(b*x^3+a),x, algorithm=""maxima"")","\frac{c \log\left(x\right)}{a} + \frac{\sqrt{3} {\left(a e \left(\frac{a}{b}\right)^{\frac{2}{3}} + a d \left(\frac{a}{b}\right)^{\frac{1}{3}}\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}} - \frac{{\left(2 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} - a e \left(\frac{a}{b}\right)^{\frac{1}{3}} + a 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 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b c \left(\frac{a}{b}\right)^{\frac{2}{3}} + a e \left(\frac{a}{b}\right)^{\frac{1}{3}} - a d\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"c*log(x)/a + 1/3*sqrt(3)*(a*e*(a/b)^(2/3) + a*d*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^2 - 1/6*(2*b*c*(a/b)^(2/3) - a*e*(a/b)^(1/3) + a*d)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b*(a/b)^(2/3)) - 1/3*(b*c*(a/b)^(2/3) + a*e*(a/b)^(1/3) - a*d)*log(x + (a/b)^(1/3))/(a*b*(a/b)^(2/3))","A",0
342,1,186,0,2.980654," ","integrate((e*x^2+d*x+c)/x^2/(b*x^3+a),x, algorithm=""maxima"")","\frac{d \log\left(x\right)}{a} - \frac{\sqrt{3} {\left(b c \left(\frac{a}{b}\right)^{\frac{2}{3}} - a e \left(\frac{a}{b}\right)^{\frac{1}{3}}\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}} - \frac{{\left(2 \, b d \left(\frac{a}{b}\right)^{\frac{2}{3}} + b c \left(\frac{a}{b}\right)^{\frac{1}{3}} + a 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 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b d \left(\frac{a}{b}\right)^{\frac{2}{3}} - b c \left(\frac{a}{b}\right)^{\frac{1}{3}} - a e\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{c}{a x}"," ",0,"d*log(x)/a - 1/3*sqrt(3)*(b*c*(a/b)^(2/3) - a*e*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^2 - 1/6*(2*b*d*(a/b)^(2/3) + b*c*(a/b)^(1/3) + a*e)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b*(a/b)^(2/3)) - 1/3*(b*d*(a/b)^(2/3) - b*c*(a/b)^(1/3) - a*e)*log(x + (a/b)^(1/3))/(a*b*(a/b)^(2/3)) - c/(a*x)","A",0
343,1,177,0,3.032359," ","integrate((e*x^2+d*x+c)/x^3/(b*x^3+a),x, algorithm=""maxima"")","\frac{e \log\left(x\right)}{a} - \frac{\sqrt{3} {\left(b d \left(\frac{a}{b}\right)^{\frac{2}{3}} + b c \left(\frac{a}{b}\right)^{\frac{1}{3}}\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}} - \frac{{\left(2 \, e \left(\frac{a}{b}\right)^{\frac{2}{3}} + d \left(\frac{a}{b}\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 \, a \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(e \left(\frac{a}{b}\right)^{\frac{2}{3}} - d \left(\frac{a}{b}\right)^{\frac{1}{3}} + c\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{2 \, d x + c}{2 \, a x^{2}}"," ",0,"e*log(x)/a - 1/3*sqrt(3)*(b*d*(a/b)^(2/3) + b*c*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^2 - 1/6*(2*e*(a/b)^(2/3) + d*(a/b)^(1/3) - c)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*(a/b)^(2/3)) - 1/3*(e*(a/b)^(2/3) - d*(a/b)^(1/3) + c)*log(x + (a/b)^(1/3))/(a*(a/b)^(2/3)) - 1/2*(2*d*x + c)/(a*x^2)","A",0
344,1,163,0,3.033367," ","integrate(x^2*(e*x^2+d*x+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{e x^{2} + d x + c}{3 \, {\left(b^{2} x^{3} + a b\right)}} + \frac{\sqrt{3} {\left(2 \, e \left(\frac{a}{b}\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 \, b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(2 \, e \left(\frac{a}{b}\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 \, b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(2 \, e \left(\frac{a}{b}\right)^{\frac{1}{3}} - d\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/3*(e*x^2 + d*x + c)/(b^2*x^3 + a*b) + 1/9*sqrt(3)*(2*e*(a/b)^(1/3) + d)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^2*(a/b)^(2/3)) + 1/18*(2*e*(a/b)^(1/3) - d)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^2*(a/b)^(2/3)) - 1/9*(2*e*(a/b)^(1/3) - d)*log(x + (a/b)^(1/3))/(b^2*(a/b)^(2/3))","A",0
345,1,185,0,2.840237," ","integrate(x*(e*x^2+d*x+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{b c x^{2} - a e x - a d}{3 \, {\left(a b^{2} x^{3} + a^{2} b\right)}} + \frac{\sqrt{3} {\left(b c \left(\frac{a}{b}\right)^{\frac{1}{3}} + a 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 b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b c \left(\frac{a}{b}\right)^{\frac{1}{3}} - a 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 b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b c \left(\frac{a}{b}\right)^{\frac{1}{3}} - a e\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*(b*c*x^2 - a*e*x - a*d)/(a*b^2*x^3 + a^2*b) + 1/9*sqrt(3)*(b*c*(a/b)^(1/3) + a*e)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^2*(a/b)^(2/3)) + 1/18*(b*c*(a/b)^(1/3) - a*e)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^2*(a/b)^(2/3)) - 1/9*(b*c*(a/b)^(1/3) - a*e)*log(x + (a/b)^(1/3))/(a*b^2*(a/b)^(2/3))","A",0
346,1,179,0,3.024567," ","integrate((e*x^2+d*x+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{b d x^{2} + b c x - a e}{3 \, {\left(a b^{2} x^{3} + a^{2} b\right)}} + \frac{\sqrt{3} {\left(d \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, 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 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, 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 \, a b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, c\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*(b*d*x^2 + b*c*x - a*e)/(a*b^2*x^3 + a^2*b) + 1/9*sqrt(3)*(d*(a/b)^(1/3) + 2*c)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b*(a/b)^(2/3)) + 1/18*(d*(a/b)^(1/3) - 2*c)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b*(a/b)^(2/3)) - 1/9*(d*(a/b)^(1/3) - 2*c)*log(x + (a/b)^(1/3))/(a*b*(a/b)^(2/3))","A",0
347,1,203,0,2.938419," ","integrate((e*x^2+d*x+c)/x/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{e x^{2} + d x + c}{3 \, {\left(a b x^{3} + a^{2}\right)}} + \frac{c \log\left(x\right)}{a^{2}} + \frac{\sqrt{3} {\left(a e \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, a d \left(\frac{a}{b}\right)^{\frac{1}{3}}\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}} - \frac{{\left(6 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} - a e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a 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^{2} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(3 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} + a e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a d\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{2} b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*(e*x^2 + d*x + c)/(a*b*x^3 + a^2) + c*log(x)/a^2 + 1/9*sqrt(3)*(a*e*(a/b)^(2/3) + 2*a*d*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^3 - 1/18*(6*b*c*(a/b)^(2/3) - a*e*(a/b)^(1/3) + 2*a*d)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b*(a/b)^(2/3)) - 1/9*(3*b*c*(a/b)^(2/3) + a*e*(a/b)^(1/3) - 2*a*d)*log(x + (a/b)^(1/3))/(a^2*b*(a/b)^(2/3))","A",0
348,1,222,0,3.098851," ","integrate((e*x^2+d*x+c)/x^2/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{4 \, b c x^{3} - a e x^{2} - a d x + 3 \, a c}{3 \, {\left(a^{2} b x^{4} + a^{3} x\right)}} + \frac{d \log\left(x\right)}{a^{2}} - \frac{2 \, \sqrt{3} {\left(2 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} - a e \left(\frac{a}{b}\right)^{\frac{1}{3}}\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}} - \frac{{\left(3 \, b d \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}} + a e\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^{2} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(3 \, b d \left(\frac{a}{b}\right)^{\frac{2}{3}} - 4 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a e\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{2} b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/3*(4*b*c*x^3 - a*e*x^2 - a*d*x + 3*a*c)/(a^2*b*x^4 + a^3*x) + d*log(x)/a^2 - 2/9*sqrt(3)*(2*b*c*(a/b)^(2/3) - a*e*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^3 - 1/9*(3*b*d*(a/b)^(2/3) + 2*b*c*(a/b)^(1/3) + a*e)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b*(a/b)^(2/3)) - 1/9*(3*b*d*(a/b)^(2/3) - 4*b*c*(a/b)^(1/3) - 2*a*e)*log(x + (a/b)^(1/3))/(a^2*b*(a/b)^(2/3))","A",0
349,1,220,0,2.862392," ","integrate((e*x^2+d*x+c)/x^3/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{8 \, b d x^{4} + 5 \, b c x^{3} - 2 \, a e x^{2} + 6 \, a d x + 3 \, a c}{6 \, {\left(a^{2} b x^{5} + a^{3} x^{2}\right)}} + \frac{e \log\left(x\right)}{a^{2}} - \frac{\sqrt{3} {\left(4 \, b d \left(\frac{a}{b}\right)^{\frac{2}{3}} + 5 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}}\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}} - \frac{{\left(6 \, e \left(\frac{a}{b}\right)^{\frac{2}{3}} + 4 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, 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 \, a^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(3 \, e \left(\frac{a}{b}\right)^{\frac{2}{3}} - 4 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, c\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/6*(8*b*d*x^4 + 5*b*c*x^3 - 2*a*e*x^2 + 6*a*d*x + 3*a*c)/(a^2*b*x^5 + a^3*x^2) + e*log(x)/a^2 - 1/9*sqrt(3)*(4*b*d*(a/b)^(2/3) + 5*b*c*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^3 - 1/18*(6*e*(a/b)^(2/3) + 4*d*(a/b)^(1/3) - 5*c)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*(a/b)^(2/3)) - 1/9*(3*e*(a/b)^(2/3) - 4*d*(a/b)^(1/3) + 5*c)*log(x + (a/b)^(1/3))/(a^2*(a/b)^(2/3))","A",0
350,1,236,0,3.066485," ","integrate((e*x^2+d*x+c)/x^4/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{8 \, b e x^{5} + 5 \, b d x^{4} + 4 \, b c x^{3} + 6 \, a e x^{2} + 3 \, a d x + 2 \, a c}{6 \, {\left(a^{2} b x^{6} + a^{3} x^{3}\right)}} - \frac{2 \, b c \log\left(x\right)}{a^{3}} - \frac{\sqrt{3} {\left(4 \, a e \left(\frac{a}{b}\right)^{\frac{2}{3}} + 5 \, a d \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} 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)}{9 \, a^{4}} + \frac{{\left(12 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 4 \, a e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a 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} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(6 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} + 4 \, a e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a d\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/6*(8*b*e*x^5 + 5*b*d*x^4 + 4*b*c*x^3 + 6*a*e*x^2 + 3*a*d*x + 2*a*c)/(a^2*b*x^6 + a^3*x^3) - 2*b*c*log(x)/a^3 - 1/9*sqrt(3)*(4*a*e*(a/b)^(2/3) + 5*a*d*(a/b)^(1/3))*b*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^4 + 1/18*(12*b*c*(a/b)^(2/3) - 4*a*e*(a/b)^(1/3) + 5*a*d)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*(a/b)^(2/3)) + 1/9*(6*b*c*(a/b)^(2/3) + 4*a*e*(a/b)^(1/3) - 5*a*d)*log(x + (a/b)^(1/3))/(a^3*(a/b)^(2/3))","A",0
351,1,203,0,3.019913," ","integrate(x^2*(e*x^2+d*x+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{2 \, b e x^{5} + b d x^{4} - a e x^{2} - 2 \, a d x - 3 \, a c}{18 \, {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)}} + \frac{\sqrt{3} {\left(e \left(\frac{a}{b}\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 \, a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(e \left(\frac{a}{b}\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 \, a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(e \left(\frac{a}{b}\right)^{\frac{1}{3}} - d\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/18*(2*b*e*x^5 + b*d*x^4 - a*e*x^2 - 2*a*d*x - 3*a*c)/(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b) + 1/27*sqrt(3)*(e*(a/b)^(1/3) + d)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^2*(a/b)^(2/3)) + 1/54*(e*(a/b)^(1/3) - d)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^2*(a/b)^(2/3)) - 1/27*(e*(a/b)^(1/3) - d)*log(x + (a/b)^(1/3))/(a*b^2*(a/b)^(2/3))","A",0
352,1,223,0,3.055341," ","integrate(x*(e*x^2+d*x+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{4 \, b^{2} c x^{5} + a b e x^{4} + 7 \, a b c x^{2} - 2 \, a^{2} e x - 3 \, a^{2} d}{18 \, {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)}} + \frac{\sqrt{3} {\left(2 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}} + a 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^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(2 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}} - a 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^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(2 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}} - a e\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/18*(4*b^2*c*x^5 + a*b*e*x^4 + 7*a*b*c*x^2 - 2*a^2*e*x - 3*a^2*d)/(a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b) + 1/27*sqrt(3)*(2*b*c*(a/b)^(1/3) + a*e)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b^2*(a/b)^(2/3)) + 1/54*(2*b*c*(a/b)^(1/3) - a*e)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b^2*(a/b)^(2/3)) - 1/27*(2*b*c*(a/b)^(1/3) - a*e)*log(x + (a/b)^(1/3))/(a^2*b^2*(a/b)^(2/3))","A",0
353,1,219,0,2.991570," ","integrate((e*x^2+d*x+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","\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(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)}} + \frac{\sqrt{3} {\left(2 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, 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^{2} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(2 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, 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^{2} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(2 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, c\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{2} b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"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)/(a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b) + 1/27*sqrt(3)*(2*d*(a/b)^(1/3) + 5*c)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b*(a/b)^(2/3)) + 1/54*(2*d*(a/b)^(1/3) - 5*c)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b*(a/b)^(2/3)) - 1/27*(2*d*(a/b)^(1/3) - 5*c)*log(x + (a/b)^(1/3))/(a^2*b*(a/b)^(2/3))","A",0
354,1,246,0,3.004102," ","integrate((e*x^2+d*x+c)/x/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{4 \, b e x^{5} + 5 \, b d x^{4} + 6 \, b c x^{3} + 7 \, a e x^{2} + 8 \, a d x + 9 \, a c}{18 \, {\left(a^{2} b^{2} x^{6} + 2 \, a^{3} b x^{3} + a^{4}\right)}} + \frac{c \log\left(x\right)}{a^{3}} + \frac{\sqrt{3} {\left(2 \, a e \left(\frac{a}{b}\right)^{\frac{2}{3}} + 5 \, a d \left(\frac{a}{b}\right)^{\frac{1}{3}}\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}} - \frac{{\left(18 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a 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 \, a^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(9 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, a e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a d\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/18*(4*b*e*x^5 + 5*b*d*x^4 + 6*b*c*x^3 + 7*a*e*x^2 + 8*a*d*x + 9*a*c)/(a^2*b^2*x^6 + 2*a^3*b*x^3 + a^4) + c*log(x)/a^3 + 1/27*sqrt(3)*(2*a*e*(a/b)^(2/3) + 5*a*d*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^4 - 1/54*(18*b*c*(a/b)^(2/3) - 2*a*e*(a/b)^(1/3) + 5*a*d)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*b*(a/b)^(2/3)) - 1/27*(9*b*c*(a/b)^(2/3) + 2*a*e*(a/b)^(1/3) - 5*a*d)*log(x + (a/b)^(1/3))/(a^3*b*(a/b)^(2/3))","A",0
355,1,266,0,3.093903," ","integrate((e*x^2+d*x+c)/x^2/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{28 \, b^{2} c x^{6} - 5 \, a b e x^{5} - 6 \, a b d x^{4} + 49 \, a b c x^{3} - 8 \, a^{2} e x^{2} - 9 \, a^{2} d x + 18 \, a^{2} c}{18 \, {\left(a^{3} b^{2} x^{7} + 2 \, a^{4} b x^{4} + a^{5} x\right)}} + \frac{d \log\left(x\right)}{a^{3}} - \frac{\sqrt{3} {\left(14 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 5 \, a e \left(\frac{a}{b}\right)^{\frac{1}{3}}\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}} - \frac{{\left(18 \, b d \left(\frac{a}{b}\right)^{\frac{2}{3}} + 14 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a 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^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(9 \, b d \left(\frac{a}{b}\right)^{\frac{2}{3}} - 14 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a e\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/18*(28*b^2*c*x^6 - 5*a*b*e*x^5 - 6*a*b*d*x^4 + 49*a*b*c*x^3 - 8*a^2*e*x^2 - 9*a^2*d*x + 18*a^2*c)/(a^3*b^2*x^7 + 2*a^4*b*x^4 + a^5*x) + d*log(x)/a^3 - 1/27*sqrt(3)*(14*b*c*(a/b)^(2/3) - 5*a*e*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^4 - 1/54*(18*b*d*(a/b)^(2/3) + 14*b*c*(a/b)^(1/3) + 5*a*e)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*b*(a/b)^(2/3)) - 1/27*(9*b*d*(a/b)^(2/3) - 14*b*c*(a/b)^(1/3) - 5*a*e)*log(x + (a/b)^(1/3))/(a^3*b*(a/b)^(2/3))","A",0
356,1,265,0,3.106089," ","integrate((e*x^2+d*x+c)/x^3/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{28 \, b^{2} d x^{7} + 20 \, b^{2} c x^{6} - 6 \, a b e x^{5} + 49 \, a b d x^{4} + 32 \, a b c x^{3} - 9 \, a^{2} e x^{2} + 18 \, a^{2} d x + 9 \, a^{2} c}{18 \, {\left(a^{3} b^{2} x^{8} + 2 \, a^{4} b x^{5} + a^{5} x^{2}\right)}} + \frac{e \log\left(x\right)}{a^{3}} - \frac{2 \, \sqrt{3} {\left(7 \, b d \left(\frac{a}{b}\right)^{\frac{2}{3}} + 10 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}}\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}} - \frac{{\left(9 \, e \left(\frac{a}{b}\right)^{\frac{2}{3}} + 7 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 10 \, c\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^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(9 \, e \left(\frac{a}{b}\right)^{\frac{2}{3}} - 14 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} + 20 \, c\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/18*(28*b^2*d*x^7 + 20*b^2*c*x^6 - 6*a*b*e*x^5 + 49*a*b*d*x^4 + 32*a*b*c*x^3 - 9*a^2*e*x^2 + 18*a^2*d*x + 9*a^2*c)/(a^3*b^2*x^8 + 2*a^4*b*x^5 + a^5*x^2) + e*log(x)/a^3 - 2/27*sqrt(3)*(7*b*d*(a/b)^(2/3) + 10*b*c*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^4 - 1/27*(9*e*(a/b)^(2/3) + 7*d*(a/b)^(1/3) - 10*c)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*(a/b)^(2/3)) - 1/27*(9*e*(a/b)^(2/3) - 14*d*(a/b)^(1/3) + 20*c)*log(x + (a/b)^(1/3))/(a^3*(a/b)^(2/3))","A",0
357,1,283,0,3.027421," ","integrate((e*x^2+d*x+c)/x^4/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{28 \, b^{2} e x^{8} + 20 \, b^{2} d x^{7} + 18 \, b^{2} c x^{6} + 49 \, a b e x^{5} + 32 \, a b d x^{4} + 27 \, a b c x^{3} + 18 \, a^{2} e x^{2} + 9 \, a^{2} d x + 6 \, a^{2} c}{18 \, {\left(a^{3} b^{2} x^{9} + 2 \, a^{4} b x^{6} + a^{5} x^{3}\right)}} - \frac{3 \, b c \log\left(x\right)}{a^{4}} - \frac{2 \, \sqrt{3} {\left(7 \, a e \left(\frac{a}{b}\right)^{\frac{2}{3}} + 10 \, a d \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} 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)}{27 \, a^{5}} + \frac{{\left(27 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 7 \, a e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 10 \, a 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} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(27 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} + 14 \, a e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 20 \, a d\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/18*(28*b^2*e*x^8 + 20*b^2*d*x^7 + 18*b^2*c*x^6 + 49*a*b*e*x^5 + 32*a*b*d*x^4 + 27*a*b*c*x^3 + 18*a^2*e*x^2 + 9*a^2*d*x + 6*a^2*c)/(a^3*b^2*x^9 + 2*a^4*b*x^6 + a^5*x^3) - 3*b*c*log(x)/a^4 - 2/27*sqrt(3)*(7*a*e*(a/b)^(2/3) + 10*a*d*(a/b)^(1/3))*b*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^5 + 1/27*(27*b*c*(a/b)^(2/3) - 7*a*e*(a/b)^(1/3) + 10*a*d)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^4*(a/b)^(2/3)) + 1/27*(27*b*c*(a/b)^(2/3) + 14*a*e*(a/b)^(1/3) - 20*a*d)*log(x + (a/b)^(1/3))/(a^4*(a/b)^(2/3))","A",0
358,1,248,0,3.006028," ","integrate(x^2*(e*x^2+d*x+c)/(b*x^3+a)^4,x, algorithm=""maxima"")","\frac{8 \, b^{2} e x^{8} + 5 \, b^{2} d x^{7} + 22 \, a b e x^{5} + 13 \, a b d x^{4} - 4 \, a^{2} e x^{2} - 10 \, a^{2} d x - 18 \, a^{2} c}{162 \, {\left(a^{2} b^{4} x^{9} + 3 \, a^{3} b^{3} x^{6} + 3 \, a^{4} b^{2} x^{3} + a^{5} b\right)}} + \frac{\sqrt{3} {\left(4 \, e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, 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^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(4 \, e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, d\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{486 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(4 \, e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, d\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/162*(8*b^2*e*x^8 + 5*b^2*d*x^7 + 22*a*b*e*x^5 + 13*a*b*d*x^4 - 4*a^2*e*x^2 - 10*a^2*d*x - 18*a^2*c)/(a^2*b^4*x^9 + 3*a^3*b^3*x^6 + 3*a^4*b^2*x^3 + a^5*b) + 1/243*sqrt(3)*(4*e*(a/b)^(1/3) + 5*d)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b^2*(a/b)^(2/3)) + 1/486*(4*e*(a/b)^(1/3) - 5*d)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b^2*(a/b)^(2/3)) - 1/243*(4*e*(a/b)^(1/3) - 5*d)*log(x + (a/b)^(1/3))/(a^2*b^2*(a/b)^(2/3))","A",0
359,1,260,0,3.029244," ","integrate(x*(e*x^2+d*x+c)/(b*x^3+a)^4,x, algorithm=""maxima"")","\frac{28 \, b^{3} c x^{8} + 5 \, a b^{2} e x^{7} + 77 \, a b^{2} c x^{5} + 13 \, a^{2} b e x^{4} + 67 \, a^{2} b c x^{2} - 10 \, a^{3} e x - 18 \, a^{3} d}{162 \, {\left(a^{3} b^{4} x^{9} + 3 \, a^{4} b^{3} x^{6} + 3 \, a^{5} b^{2} x^{3} + a^{6} b\right)}} + \frac{\sqrt{3} {\left(14 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a 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^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(14 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a 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 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(14 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a e\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/162*(28*b^3*c*x^8 + 5*a*b^2*e*x^7 + 77*a*b^2*c*x^5 + 13*a^2*b*e*x^4 + 67*a^2*b*c*x^2 - 10*a^3*e*x - 18*a^3*d)/(a^3*b^4*x^9 + 3*a^4*b^3*x^6 + 3*a^5*b^2*x^3 + a^6*b) + 1/243*sqrt(3)*(14*b*c*(a/b)^(1/3) + 5*a*e)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^3*b^2*(a/b)^(2/3)) + 1/486*(14*b*c*(a/b)^(1/3) - 5*a*e)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*b^2*(a/b)^(2/3)) - 1/243*(14*b*c*(a/b)^(1/3) - 5*a*e)*log(x + (a/b)^(1/3))/(a^3*b^2*(a/b)^(2/3))","A",0
360,1,254,0,2.991269," ","integrate((e*x^2+d*x+c)/(b*x^3+a)^4,x, algorithm=""maxima"")","\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(a^{3} b^{4} x^{9} + 3 \, a^{4} b^{3} x^{6} + 3 \, a^{5} b^{2} x^{3} + a^{6} b\right)}} + \frac{2 \, \sqrt{3} {\left(7 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} + 20 \, 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^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(7 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 20 \, 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^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{2 \, {\left(7 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 20 \, c\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \, a^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"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)/(a^3*b^4*x^9 + 3*a^4*b^3*x^6 + 3*a^5*b^2*x^3 + a^6*b) + 2/243*sqrt(3)*(7*d*(a/b)^(1/3) + 20*c)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^3*b*(a/b)^(2/3)) + 1/243*(7*d*(a/b)^(1/3) - 20*c)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*b*(a/b)^(2/3)) - 2/243*(7*d*(a/b)^(1/3) - 20*c)*log(x + (a/b)^(1/3))/(a^3*b*(a/b)^(2/3))","A",0
361,1,293,0,3.036613," ","integrate((e*x^2+d*x+c)/x/(b*x^3+a)^4,x, algorithm=""maxima"")","\frac{28 \, b^{2} e x^{8} + 40 \, b^{2} d x^{7} + 54 \, b^{2} c x^{6} + 77 \, a b e x^{5} + 104 \, a b d x^{4} + 135 \, a b c x^{3} + 67 \, a^{2} e x^{2} + 82 \, a^{2} d x + 99 \, a^{2} c}{162 \, {\left(a^{3} b^{3} x^{9} + 3 \, a^{4} b^{2} x^{6} + 3 \, a^{5} b x^{3} + a^{6}\right)}} + \frac{c \log\left(x\right)}{a^{4}} + \frac{2 \, \sqrt{3} {\left(7 \, a e \left(\frac{a}{b}\right)^{\frac{2}{3}} + 20 \, a d \left(\frac{a}{b}\right)^{\frac{1}{3}}\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}} - \frac{{\left(81 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 7 \, a e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 20 \, a 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^{4} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(81 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} + 14 \, a e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 40 \, a d\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \, a^{4} b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/162*(28*b^2*e*x^8 + 40*b^2*d*x^7 + 54*b^2*c*x^6 + 77*a*b*e*x^5 + 104*a*b*d*x^4 + 135*a*b*c*x^3 + 67*a^2*e*x^2 + 82*a^2*d*x + 99*a^2*c)/(a^3*b^3*x^9 + 3*a^4*b^2*x^6 + 3*a^5*b*x^3 + a^6) + c*log(x)/a^4 + 2/243*sqrt(3)*(7*a*e*(a/b)^(2/3) + 20*a*d*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^5 - 1/243*(81*b*c*(a/b)^(2/3) - 7*a*e*(a/b)^(1/3) + 20*a*d)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^4*b*(a/b)^(2/3)) - 1/243*(81*b*c*(a/b)^(2/3) + 14*a*e*(a/b)^(1/3) - 40*a*d)*log(x + (a/b)^(1/3))/(a^4*b*(a/b)^(2/3))","A",0
362,1,313,0,2.995234," ","integrate((e*x^2+d*x+c)/x^2/(b*x^3+a)^4,x, algorithm=""maxima"")","-\frac{280 \, b^{3} c x^{9} - 40 \, a b^{2} e x^{8} - 54 \, a b^{2} d x^{7} + 770 \, a b^{2} c x^{6} - 104 \, a^{2} b e x^{5} - 135 \, a^{2} b d x^{4} + 670 \, a^{2} b c x^{3} - 82 \, a^{3} e x^{2} - 99 \, a^{3} d x + 162 \, a^{3} c}{162 \, {\left(a^{4} b^{3} x^{10} + 3 \, a^{5} b^{2} x^{7} + 3 \, a^{6} b x^{4} + a^{7} x\right)}} + \frac{d \log\left(x\right)}{a^{4}} - \frac{20 \, \sqrt{3} {\left(7 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a e \left(\frac{a}{b}\right)^{\frac{1}{3}}\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}} - \frac{{\left(81 \, b d \left(\frac{a}{b}\right)^{\frac{2}{3}} + 70 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}} + 20 \, a 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^{4} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(81 \, b d \left(\frac{a}{b}\right)^{\frac{2}{3}} - 140 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}} - 40 \, a e\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \, a^{4} b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/162*(280*b^3*c*x^9 - 40*a*b^2*e*x^8 - 54*a*b^2*d*x^7 + 770*a*b^2*c*x^6 - 104*a^2*b*e*x^5 - 135*a^2*b*d*x^4 + 670*a^2*b*c*x^3 - 82*a^3*e*x^2 - 99*a^3*d*x + 162*a^3*c)/(a^4*b^3*x^10 + 3*a^5*b^2*x^7 + 3*a^6*b*x^4 + a^7*x) + d*log(x)/a^4 - 20/243*sqrt(3)*(7*b*c*(a/b)^(2/3) - 2*a*e*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^5 - 1/243*(81*b*d*(a/b)^(2/3) + 70*b*c*(a/b)^(1/3) + 20*a*e)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^4*b*(a/b)^(2/3)) - 1/243*(81*b*d*(a/b)^(2/3) - 140*b*c*(a/b)^(1/3) - 40*a*e)*log(x + (a/b)^(1/3))/(a^4*b*(a/b)^(2/3))","A",0
363,1,312,0,3.104036," ","integrate((e*x^2+d*x+c)/x^3/(b*x^3+a)^4,x, algorithm=""maxima"")","-\frac{280 \, b^{3} d x^{10} + 220 \, b^{3} c x^{9} - 54 \, a b^{2} e x^{8} + 770 \, a b^{2} d x^{7} + 572 \, a b^{2} c x^{6} - 135 \, a^{2} b e x^{5} + 670 \, a^{2} b d x^{4} + 451 \, a^{2} b c x^{3} - 99 \, a^{3} e x^{2} + 162 \, a^{3} d x + 81 \, a^{3} c}{162 \, {\left(a^{4} b^{3} x^{11} + 3 \, a^{5} b^{2} x^{8} + 3 \, a^{6} b x^{5} + a^{7} x^{2}\right)}} + \frac{e \log\left(x\right)}{a^{4}} - \frac{20 \, \sqrt{3} {\left(7 \, b d \left(\frac{a}{b}\right)^{\frac{2}{3}} + 11 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}}\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}} - \frac{{\left(81 \, e \left(\frac{a}{b}\right)^{\frac{2}{3}} + 70 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 110 \, 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^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(81 \, e \left(\frac{a}{b}\right)^{\frac{2}{3}} - 140 \, d \left(\frac{a}{b}\right)^{\frac{1}{3}} + 220 \, c\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \, a^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/162*(280*b^3*d*x^10 + 220*b^3*c*x^9 - 54*a*b^2*e*x^8 + 770*a*b^2*d*x^7 + 572*a*b^2*c*x^6 - 135*a^2*b*e*x^5 + 670*a^2*b*d*x^4 + 451*a^2*b*c*x^3 - 99*a^3*e*x^2 + 162*a^3*d*x + 81*a^3*c)/(a^4*b^3*x^11 + 3*a^5*b^2*x^8 + 3*a^6*b*x^5 + a^7*x^2) + e*log(x)/a^4 - 20/243*sqrt(3)*(7*b*d*(a/b)^(2/3) + 11*b*c*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^5 - 1/243*(81*e*(a/b)^(2/3) + 70*d*(a/b)^(1/3) - 110*c)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^4*(a/b)^(2/3)) - 1/243*(81*e*(a/b)^(2/3) - 140*d*(a/b)^(1/3) + 220*c)*log(x + (a/b)^(1/3))/(a^4*(a/b)^(2/3))","A",0
364,1,330,0,3.080877," ","integrate((e*x^2+d*x+c)/x^4/(b*x^3+a)^4,x, algorithm=""maxima"")","-\frac{280 \, b^{3} e x^{11} + 220 \, b^{3} d x^{10} + 216 \, b^{3} c x^{9} + 770 \, a b^{2} e x^{8} + 572 \, a b^{2} d x^{7} + 540 \, a b^{2} c x^{6} + 670 \, a^{2} b e x^{5} + 451 \, a^{2} b d x^{4} + 396 \, a^{2} b c x^{3} + 162 \, a^{3} e x^{2} + 81 \, a^{3} d x + 54 \, a^{3} c}{162 \, {\left(a^{4} b^{3} x^{12} + 3 \, a^{5} b^{2} x^{9} + 3 \, a^{6} b x^{6} + a^{7} x^{3}\right)}} - \frac{4 \, b c \log\left(x\right)}{a^{5}} - \frac{20 \, \sqrt{3} {\left(7 \, a e \left(\frac{a}{b}\right)^{\frac{2}{3}} + 11 \, a d \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} 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)}{243 \, a^{6}} + \frac{2 \, {\left(162 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 35 \, a e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 55 \, a 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} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{4 \, {\left(81 \, b c \left(\frac{a}{b}\right)^{\frac{2}{3}} + 35 \, a e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 55 \, a d\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \, a^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/162*(280*b^3*e*x^11 + 220*b^3*d*x^10 + 216*b^3*c*x^9 + 770*a*b^2*e*x^8 + 572*a*b^2*d*x^7 + 540*a*b^2*c*x^6 + 670*a^2*b*e*x^5 + 451*a^2*b*d*x^4 + 396*a^2*b*c*x^3 + 162*a^3*e*x^2 + 81*a^3*d*x + 54*a^3*c)/(a^4*b^3*x^12 + 3*a^5*b^2*x^9 + 3*a^6*b*x^6 + a^7*x^3) - 4*b*c*log(x)/a^5 - 20/243*sqrt(3)*(7*a*e*(a/b)^(2/3) + 11*a*d*(a/b)^(1/3))*b*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^6 + 2/243*(162*b*c*(a/b)^(2/3) - 35*a*e*(a/b)^(1/3) + 55*a*d)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^5*(a/b)^(2/3)) + 4/243*(81*b*c*(a/b)^(2/3) + 35*a*e*(a/b)^(1/3) - 55*a*d)*log(x + (a/b)^(1/3))/(a^5*(a/b)^(2/3))","A",0
365,1,26,0,2.892460," ","integrate((2*a*x-x^2)/(a^3+x^3),x, algorithm=""maxima"")","\frac{2}{3} \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} {\left(a - 2 \, x\right)}}{3 \, a}\right) - \log\left(a + x\right)"," ",0,"2/3*sqrt(3)*arctan(-1/3*sqrt(3)*(a - 2*x)/a) - log(a + x)","A",0
366,1,26,0,2.967456," ","integrate((2*a-x)*x/(a^3+x^3),x, algorithm=""maxima"")","\frac{2}{3} \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} {\left(a - 2 \, x\right)}}{3 \, a}\right) - \log\left(a + x\right)"," ",0,"2/3*sqrt(3)*arctan(-1/3*sqrt(3)*(a - 2*x)/a) - log(a + x)","A",0
367,1,28,0,2.923301," ","integrate((2*a*x+x^2)/(a^3-x^3),x, algorithm=""maxima"")","-\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(a + 2 \, x\right)}}{3 \, a}\right) - \log\left(-a + x\right)"," ",0,"-2/3*sqrt(3)*arctan(1/3*sqrt(3)*(a + 2*x)/a) - log(-a + x)","A",0
368,1,28,0,2.838345," ","integrate(x*(2*a+x)/(a^3-x^3),x, algorithm=""maxima"")","-\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(a + 2 \, x\right)}}{3 \, a}\right) - \log\left(-a + x\right)"," ",0,"-2/3*sqrt(3)*arctan(1/3*sqrt(3)*(a + 2*x)/a) - log(-a + x)","A",0
369,1,51,0,3.067753," ","integrate(x*(-2*(a/b)^(1/3)*C+C*x)/(b*x^3+a),x, algorithm=""maxima"")","-\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{C \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b}"," ",0,"-2/3*sqrt(3)*C*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/b + C*log(x + (a/b)^(1/3))/b","A",0
370,1,166,0,3.020813," ","integrate(x*(-2*(-a/b)^(1/3)*C+C*x)/(-b*x^3+a),x, algorithm=""maxima"")","-\frac{{\left(C \left(\frac{a}{b}\right)^{\frac{1}{3}} + C \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)} \log\left(x^{2} + x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(C \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, C \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)} \log\left(x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{2 \, \sqrt{3} {\left(C a - {\left(3 \, C \left(\frac{a}{b}\right)^{\frac{2}{3}} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \frac{C a}{b}\right)} 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)}{9 \, a b}"," ",0,"-1/3*(C*(a/b)^(1/3) + C*(-a/b)^(1/3))*log(x^2 + x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(1/3)) - 1/3*(C*(a/b)^(1/3) - 2*C*(-a/b)^(1/3))*log(x - (a/b)^(1/3))/(b*(a/b)^(1/3)) - 2/9*sqrt(3)*(C*a - (3*C*(a/b)^(2/3)*(-a/b)^(1/3) + C*a/b)*b)*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/(a*b)","B",0
371,1,167,0,2.994378," ","integrate(x*(2*(-a/b)^(1/3)*C+C*x)/(b*x^3+a),x, algorithm=""maxima"")","\frac{{\left(C \left(\frac{a}{b}\right)^{\frac{1}{3}} + C \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{{\left(C \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, C \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{2 \, \sqrt{3} {\left(C a - {\left(3 \, C \left(\frac{a}{b}\right)^{\frac{2}{3}} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \frac{C a}{b}\right)} 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)}{9 \, a b}"," ",0,"1/3*(C*(a/b)^(1/3) + C*(-a/b)^(1/3))*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(1/3)) + 1/3*(C*(a/b)^(1/3) - 2*C*(-a/b)^(1/3))*log(x + (a/b)^(1/3))/(b*(a/b)^(1/3)) - 2/9*sqrt(3)*(C*a - (3*C*(a/b)^(2/3)*(-a/b)^(1/3) + C*a/b)*b)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b)","B",0
372,1,52,0,3.017641," ","integrate(x*(2*(a/b)^(1/3)*C+C*x)/(-b*x^3+a),x, algorithm=""maxima"")","-\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{C \log\left(x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b}"," ",0,"-2/3*sqrt(3)*C*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/b - C*log(x - (a/b)^(1/3))/b","A",0
373,1,79,0,1.352995," ","integrate(x^4*(b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""maxima"")","\frac{1}{13} \, b h x^{13} + \frac{1}{12} \, b g x^{12} + \frac{1}{11} \, b f x^{11} + \frac{1}{10} \, {\left(b e + a h\right)} x^{10} + \frac{1}{9} \, {\left(b d + a g\right)} x^{9} + \frac{1}{7} \, a e x^{7} + \frac{1}{8} \, {\left(b c + a f\right)} x^{8} + \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*(b*e + a*h)*x^10 + 1/9*(b*d + a*g)*x^9 + 1/7*a*e*x^7 + 1/8*(b*c + a*f)*x^8 + 1/6*a*d*x^6 + 1/5*a*c*x^5","A",0
374,1,79,0,1.345538," ","integrate(x^3*(b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""maxima"")","\frac{1}{12} \, b h x^{12} + \frac{1}{11} \, b g x^{11} + \frac{1}{10} \, b f x^{10} + \frac{1}{9} \, {\left(b e + a h\right)} x^{9} + \frac{1}{8} \, {\left(b d + a g\right)} x^{8} + \frac{1}{6} \, a e x^{6} + \frac{1}{7} \, {\left(b c + a f\right)} x^{7} + \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*(b*e + a*h)*x^9 + 1/8*(b*d + a*g)*x^8 + 1/6*a*e*x^6 + 1/7*(b*c + a*f)*x^7 + 1/5*a*d*x^5 + 1/4*a*c*x^4","A",0
375,1,79,0,1.337416," ","integrate(x^2*(b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""maxima"")","\frac{1}{11} \, b h x^{11} + \frac{1}{10} \, b g x^{10} + \frac{1}{9} \, b f x^{9} + \frac{1}{8} \, {\left(b e + a h\right)} x^{8} + \frac{1}{7} \, {\left(b d + a g\right)} x^{7} + \frac{1}{5} \, a e x^{5} + \frac{1}{6} \, {\left(b c + a f\right)} x^{6} + \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*(b*e + a*h)*x^8 + 1/7*(b*d + a*g)*x^7 + 1/5*a*e*x^5 + 1/6*(b*c + a*f)*x^6 + 1/4*a*d*x^4 + 1/3*a*c*x^3","A",0
376,1,79,0,1.373662," ","integrate(x*(b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""maxima"")","\frac{1}{10} \, b h x^{10} + \frac{1}{9} \, b g x^{9} + \frac{1}{8} \, b f x^{8} + \frac{1}{7} \, {\left(b e + a h\right)} x^{7} + \frac{1}{6} \, {\left(b d + a g\right)} x^{6} + \frac{1}{4} \, a e x^{4} + \frac{1}{5} \, {\left(b c + a f\right)} x^{5} + \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*(b*e + a*h)*x^7 + 1/6*(b*d + a*g)*x^6 + 1/4*a*e*x^4 + 1/5*(b*c + a*f)*x^5 + 1/3*a*d*x^3 + 1/2*a*c*x^2","A",0
377,1,76,0,1.404848," ","integrate((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""maxima"")","\frac{1}{9} \, b h x^{9} + \frac{1}{8} \, b g x^{8} + \frac{1}{7} \, b f x^{7} + \frac{1}{6} \, {\left(b e + a h\right)} x^{6} + \frac{1}{5} \, {\left(b d + a g\right)} x^{5} + \frac{1}{3} \, a e x^{3} + \frac{1}{4} \, {\left(b c + a f\right)} x^{4} + \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*(b*e + a*h)*x^6 + 1/5*(b*d + a*g)*x^5 + 1/3*a*e*x^3 + 1/4*(b*c + a*f)*x^4 + 1/2*a*d*x^2 + a*c*x","A",0
378,1,74,0,1.344373," ","integrate((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x,x, algorithm=""maxima"")","\frac{1}{8} \, b h x^{8} + \frac{1}{7} \, b g x^{7} + \frac{1}{6} \, b f x^{6} + \frac{1}{5} \, {\left(b e + a h\right)} x^{5} + \frac{1}{4} \, {\left(b d + a g\right)} x^{4} + \frac{1}{2} \, a e x^{2} + \frac{1}{3} \, {\left(b c + a f\right)} x^{3} + a d x + a c \log\left(x\right)"," ",0,"1/8*b*h*x^8 + 1/7*b*g*x^7 + 1/6*b*f*x^6 + 1/5*(b*e + a*h)*x^5 + 1/4*(b*d + a*g)*x^4 + 1/2*a*e*x^2 + 1/3*(b*c + a*f)*x^3 + a*d*x + a*c*log(x)","A",0
379,1,74,0,1.351939," ","integrate((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^2,x, algorithm=""maxima"")","\frac{1}{7} \, b h x^{7} + \frac{1}{6} \, b g x^{6} + \frac{1}{5} \, b f x^{5} + \frac{1}{4} \, {\left(b e + a h\right)} x^{4} + \frac{1}{3} \, {\left(b d + a g\right)} x^{3} + a e x + \frac{1}{2} \, {\left(b c + a f\right)} x^{2} + a d \log\left(x\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*(b*e + a*h)*x^4 + 1/3*(b*d + a*g)*x^3 + a*e*x + 1/2*(b*c + a*f)*x^2 + a*d*log(x) - a*c/x","A",0
380,1,74,0,1.341783," ","integrate((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^3,x, algorithm=""maxima"")","\frac{1}{6} \, b h x^{6} + \frac{1}{5} \, b g x^{5} + \frac{1}{4} \, b f x^{4} + \frac{1}{3} \, {\left(b e + a h\right)} x^{3} + \frac{1}{2} \, {\left(b d + a g\right)} x^{2} + a e \log\left(x\right) + {\left(b c + a f\right)} x - \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*(b*e + a*h)*x^3 + 1/2*(b*d + a*g)*x^2 + a*e*log(x) + (b*c + a*f)*x - 1/2*(2*a*d*x + a*c)/x^2","A",0
381,1,75,0,1.363241," ","integrate((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^4,x, algorithm=""maxima"")","\frac{1}{5} \, b h x^{5} + \frac{1}{4} \, b g x^{4} + \frac{1}{3} \, b f x^{3} + \frac{1}{2} \, {\left(b e + a h\right)} x^{2} + {\left(b d + a g\right)} x + {\left(b c + a f\right)} \log\left(x\right) - \frac{6 \, a e x^{2} + 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*(b*e + a*h)*x^2 + (b*d + a*g)*x + (b*c + a*f)*log(x) - 1/6*(6*a*e*x^2 + 3*a*d*x + 2*a*c)/x^3","A",0
382,1,75,0,1.340846," ","integrate((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^5,x, algorithm=""maxima"")","\frac{1}{4} \, b h x^{4} + \frac{1}{3} \, b g x^{3} + \frac{1}{2} \, b f x^{2} + {\left(b e + a h\right)} x + {\left(b d + a g\right)} \log\left(x\right) - \frac{6 \, a e x^{2} + 12 \, {\left(b c + a f\right)} x^{3} + 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 + (b*e + a*h)*x + (b*d + a*g)*log(x) - 1/12*(6*a*e*x^2 + 12*(b*c + a*f)*x^3 + 4*a*d*x + 3*a*c)/x^4","A",0
383,1,151,0,1.373965," ","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=""maxima"")","\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{1}{13} \, {\left(b^{2} e + 2 \, a b h\right)} x^{13} + \frac{1}{12} \, {\left(b^{2} d + 2 \, a b g\right)} x^{12} + \frac{1}{11} \, {\left(b^{2} c + 2 \, a b f\right)} x^{11} + \frac{1}{10} \, {\left(2 \, a b e + a^{2} h\right)} x^{10} + \frac{1}{7} \, a^{2} e x^{7} + \frac{1}{9} \, {\left(2 \, a b d + a^{2} g\right)} x^{9} + \frac{1}{6} \, a^{2} d x^{6} + \frac{1}{8} \, {\left(2 \, a b c + a^{2} f\right)} x^{8} + \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 + 1/13*(b^2*e + 2*a*b*h)*x^13 + 1/12*(b^2*d + 2*a*b*g)*x^12 + 1/11*(b^2*c + 2*a*b*f)*x^11 + 1/10*(2*a*b*e + a^2*h)*x^10 + 1/7*a^2*e*x^7 + 1/9*(2*a*b*d + a^2*g)*x^9 + 1/6*a^2*d*x^6 + 1/8*(2*a*b*c + a^2*f)*x^8 + 1/5*a^2*c*x^5","A",0
384,1,151,0,1.348752," ","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=""maxima"")","\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}{12} \, {\left(b^{2} e + 2 \, a b h\right)} x^{12} + \frac{1}{11} \, {\left(b^{2} d + 2 \, a b g\right)} x^{11} + \frac{1}{10} \, {\left(b^{2} c + 2 \, a b f\right)} x^{10} + \frac{1}{9} \, {\left(2 \, a b e + a^{2} h\right)} x^{9} + \frac{1}{6} \, a^{2} e x^{6} + \frac{1}{8} \, {\left(2 \, a b d + a^{2} g\right)} x^{8} + \frac{1}{5} \, a^{2} d x^{5} + \frac{1}{7} \, {\left(2 \, a b c + a^{2} f\right)} x^{7} + \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 + 1/12*(b^2*e + 2*a*b*h)*x^12 + 1/11*(b^2*d + 2*a*b*g)*x^11 + 1/10*(b^2*c + 2*a*b*f)*x^10 + 1/9*(2*a*b*e + a^2*h)*x^9 + 1/6*a^2*e*x^6 + 1/8*(2*a*b*d + a^2*g)*x^8 + 1/5*a^2*d*x^5 + 1/7*(2*a*b*c + a^2*f)*x^7 + 1/4*a^2*c*x^4","A",0
385,1,151,0,1.376368," ","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=""maxima"")","\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{1}{11} \, {\left(b^{2} e + 2 \, a b h\right)} x^{11} + \frac{1}{10} \, {\left(b^{2} d + 2 \, a b g\right)} x^{10} + \frac{1}{9} \, {\left(b^{2} c + 2 \, a b f\right)} x^{9} + \frac{1}{8} \, {\left(2 \, a b e + a^{2} h\right)} x^{8} + \frac{1}{5} \, a^{2} e x^{5} + \frac{1}{7} \, {\left(2 \, a b d + a^{2} g\right)} x^{7} + \frac{1}{4} \, a^{2} d x^{4} + \frac{1}{6} \, {\left(2 \, a b c + a^{2} f\right)} x^{6} + \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 + 1/11*(b^2*e + 2*a*b*h)*x^11 + 1/10*(b^2*d + 2*a*b*g)*x^10 + 1/9*(b^2*c + 2*a*b*f)*x^9 + 1/8*(2*a*b*e + a^2*h)*x^8 + 1/5*a^2*e*x^5 + 1/7*(2*a*b*d + a^2*g)*x^7 + 1/4*a^2*d*x^4 + 1/6*(2*a*b*c + a^2*f)*x^6 + 1/3*a^2*c*x^3","A",0
386,1,151,0,1.277451," ","integrate(x*(b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""maxima"")","\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}{10} \, {\left(b^{2} e + 2 \, a b h\right)} x^{10} + \frac{1}{9} \, {\left(b^{2} d + 2 \, a b g\right)} x^{9} + \frac{1}{8} \, {\left(b^{2} c + 2 \, a b f\right)} x^{8} + \frac{1}{7} \, {\left(2 \, a b e + a^{2} h\right)} x^{7} + \frac{1}{4} \, a^{2} e x^{4} + \frac{1}{6} \, {\left(2 \, a b d + a^{2} g\right)} x^{6} + \frac{1}{3} \, a^{2} d x^{3} + \frac{1}{5} \, {\left(2 \, a b c + a^{2} f\right)} x^{5} + \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 + 1/10*(b^2*e + 2*a*b*h)*x^10 + 1/9*(b^2*d + 2*a*b*g)*x^9 + 1/8*(b^2*c + 2*a*b*f)*x^8 + 1/7*(2*a*b*e + a^2*h)*x^7 + 1/4*a^2*e*x^4 + 1/6*(2*a*b*d + a^2*g)*x^6 + 1/3*a^2*d*x^3 + 1/5*(2*a*b*c + a^2*f)*x^5 + 1/2*a^2*c*x^2","A",0
387,1,148,0,1.318148," ","integrate((b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""maxima"")","\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{1}{9} \, {\left(b^{2} e + 2 \, a b h\right)} x^{9} + \frac{1}{8} \, {\left(b^{2} d + 2 \, a b g\right)} x^{8} + \frac{1}{7} \, {\left(b^{2} c + 2 \, a b f\right)} x^{7} + \frac{1}{6} \, {\left(2 \, a b e + a^{2} h\right)} x^{6} + \frac{1}{3} \, a^{2} e x^{3} + \frac{1}{5} \, {\left(2 \, a b d + a^{2} g\right)} x^{5} + \frac{1}{2} \, a^{2} d x^{2} + \frac{1}{4} \, {\left(2 \, a b c + a^{2} f\right)} x^{4} + 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 + 1/9*(b^2*e + 2*a*b*h)*x^9 + 1/8*(b^2*d + 2*a*b*g)*x^8 + 1/7*(b^2*c + 2*a*b*f)*x^7 + 1/6*(2*a*b*e + a^2*h)*x^6 + 1/3*a^2*e*x^3 + 1/5*(2*a*b*d + a^2*g)*x^5 + 1/2*a^2*d*x^2 + 1/4*(2*a*b*c + a^2*f)*x^4 + a^2*c*x","A",0
388,1,146,0,1.314353," ","integrate((b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x,x, algorithm=""maxima"")","\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}{8} \, {\left(b^{2} e + 2 \, a b h\right)} x^{8} + \frac{1}{7} \, {\left(b^{2} d + 2 \, a b g\right)} x^{7} + \frac{1}{6} \, {\left(b^{2} c + 2 \, a b f\right)} x^{6} + \frac{1}{5} \, {\left(2 \, a b e + a^{2} h\right)} x^{5} + \frac{1}{2} \, a^{2} e x^{2} + \frac{1}{4} \, {\left(2 \, a b d + a^{2} g\right)} x^{4} + a^{2} d x + \frac{1}{3} \, {\left(2 \, a b c + a^{2} f\right)} x^{3} + a^{2} c \log\left(x\right)"," ",0,"1/11*b^2*h*x^11 + 1/10*b^2*g*x^10 + 1/9*b^2*f*x^9 + 1/8*(b^2*e + 2*a*b*h)*x^8 + 1/7*(b^2*d + 2*a*b*g)*x^7 + 1/6*(b^2*c + 2*a*b*f)*x^6 + 1/5*(2*a*b*e + a^2*h)*x^5 + 1/2*a^2*e*x^2 + 1/4*(2*a*b*d + a^2*g)*x^4 + a^2*d*x + 1/3*(2*a*b*c + a^2*f)*x^3 + a^2*c*log(x)","A",0
389,1,146,0,1.398440," ","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=""maxima"")","\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{1}{7} \, {\left(b^{2} e + 2 \, a b h\right)} x^{7} + \frac{1}{6} \, {\left(b^{2} d + 2 \, a b g\right)} x^{6} + \frac{1}{5} \, {\left(b^{2} c + 2 \, a b f\right)} x^{5} + \frac{1}{4} \, {\left(2 \, a b e + a^{2} h\right)} x^{4} + a^{2} e x + \frac{1}{3} \, {\left(2 \, a b d + a^{2} g\right)} x^{3} + a^{2} d \log\left(x\right) + \frac{1}{2} \, {\left(2 \, a b c + a^{2} f\right)} x^{2} - \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 + 1/7*(b^2*e + 2*a*b*h)*x^7 + 1/6*(b^2*d + 2*a*b*g)*x^6 + 1/5*(b^2*c + 2*a*b*f)*x^5 + 1/4*(2*a*b*e + a^2*h)*x^4 + a^2*e*x + 1/3*(2*a*b*d + a^2*g)*x^3 + a^2*d*log(x) + 1/2*(2*a*b*c + a^2*f)*x^2 - a^2*c/x","A",0
390,1,146,0,1.346992," ","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=""maxima"")","\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}{6} \, {\left(b^{2} e + 2 \, a b h\right)} x^{6} + \frac{1}{5} \, {\left(b^{2} d + 2 \, a b g\right)} x^{5} + \frac{1}{4} \, {\left(b^{2} c + 2 \, a b f\right)} x^{4} + \frac{1}{3} \, {\left(2 \, a b e + a^{2} h\right)} x^{3} + a^{2} e \log\left(x\right) + \frac{1}{2} \, {\left(2 \, a b d + a^{2} g\right)} x^{2} + {\left(2 \, a b c + a^{2} f\right)} x - \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 + 1/6*(b^2*e + 2*a*b*h)*x^6 + 1/5*(b^2*d + 2*a*b*g)*x^5 + 1/4*(b^2*c + 2*a*b*f)*x^4 + 1/3*(2*a*b*e + a^2*h)*x^3 + a^2*e*log(x) + 1/2*(2*a*b*d + a^2*g)*x^2 + (2*a*b*c + a^2*f)*x - 1/2*(2*a^2*d*x + a^2*c)/x^2","A",0
391,1,147,0,1.321726," ","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=""maxima"")","\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{1}{5} \, {\left(b^{2} e + 2 \, a b h\right)} x^{5} + \frac{1}{4} \, {\left(b^{2} d + 2 \, a b g\right)} x^{4} + \frac{1}{3} \, {\left(b^{2} c + 2 \, a b f\right)} x^{3} + \frac{1}{2} \, {\left(2 \, a b e + a^{2} h\right)} x^{2} + {\left(2 \, a b d + a^{2} g\right)} x + {\left(2 \, a b c + a^{2} f\right)} \log\left(x\right) - \frac{6 \, a^{2} e x^{2} + 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 + 1/5*(b^2*e + 2*a*b*h)*x^5 + 1/4*(b^2*d + 2*a*b*g)*x^4 + 1/3*(b^2*c + 2*a*b*f)*x^3 + 1/2*(2*a*b*e + a^2*h)*x^2 + (2*a*b*d + a^2*g)*x + (2*a*b*c + a^2*f)*log(x) - 1/6*(6*a^2*e*x^2 + 3*a^2*d*x + 2*a^2*c)/x^3","A",0
392,1,147,0,1.366422," ","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=""maxima"")","\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}{4} \, {\left(b^{2} e + 2 \, a b h\right)} x^{4} + \frac{1}{3} \, {\left(b^{2} d + 2 \, a b g\right)} x^{3} + \frac{1}{2} \, {\left(b^{2} c + 2 \, a b f\right)} x^{2} + {\left(2 \, a b e + a^{2} h\right)} x + {\left(2 \, a b d + a^{2} g\right)} \log\left(x\right) - \frac{6 \, a^{2} e x^{2} + 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 + 1/4*(b^2*e + 2*a*b*h)*x^4 + 1/3*(b^2*d + 2*a*b*g)*x^3 + 1/2*(b^2*c + 2*a*b*f)*x^2 + (2*a*b*e + a^2*h)*x + (2*a*b*d + a^2*g)*log(x) - 1/12*(6*a^2*e*x^2 + 4*a^2*d*x + 12*(2*a*b*c + a^2*f)*x^3 + 3*a^2*c)/x^4","A",0
393,1,217,0,1.373423," ","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=""maxima"")","\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{1}{16} \, {\left(b^{3} e + 3 \, a b^{2} h\right)} x^{16} + \frac{1}{15} \, {\left(b^{3} d + 3 \, a b^{2} g\right)} x^{15} + \frac{1}{14} \, {\left(b^{3} c + 3 \, a b^{2} f\right)} x^{14} + \frac{3}{13} \, {\left(a b^{2} e + a^{2} b h\right)} x^{13} + \frac{1}{4} \, {\left(a b^{2} d + a^{2} b g\right)} x^{12} + \frac{3}{11} \, {\left(a b^{2} c + a^{2} b f\right)} x^{11} + \frac{1}{7} \, a^{3} e x^{7} + \frac{1}{10} \, {\left(3 \, a^{2} b e + a^{3} h\right)} x^{10} + \frac{1}{6} \, a^{3} d x^{6} + \frac{1}{9} \, {\left(3 \, a^{2} b d + a^{3} g\right)} x^{9} + \frac{1}{5} \, a^{3} c x^{5} + \frac{1}{8} \, {\left(3 \, a^{2} b c + a^{3} f\right)} x^{8}"," ",0,"1/19*b^3*h*x^19 + 1/18*b^3*g*x^18 + 1/17*b^3*f*x^17 + 1/16*(b^3*e + 3*a*b^2*h)*x^16 + 1/15*(b^3*d + 3*a*b^2*g)*x^15 + 1/14*(b^3*c + 3*a*b^2*f)*x^14 + 3/13*(a*b^2*e + a^2*b*h)*x^13 + 1/4*(a*b^2*d + a^2*b*g)*x^12 + 3/11*(a*b^2*c + a^2*b*f)*x^11 + 1/7*a^3*e*x^7 + 1/10*(3*a^2*b*e + a^3*h)*x^10 + 1/6*a^3*d*x^6 + 1/9*(3*a^2*b*d + a^3*g)*x^9 + 1/5*a^3*c*x^5 + 1/8*(3*a^2*b*c + a^3*f)*x^8","A",0
394,1,217,0,1.374570," ","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=""maxima"")","\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}{15} \, {\left(b^{3} e + 3 \, a b^{2} h\right)} x^{15} + \frac{1}{14} \, {\left(b^{3} d + 3 \, a b^{2} g\right)} x^{14} + \frac{1}{13} \, {\left(b^{3} c + 3 \, a b^{2} f\right)} x^{13} + \frac{1}{4} \, {\left(a b^{2} e + a^{2} b h\right)} x^{12} + \frac{3}{11} \, {\left(a b^{2} d + a^{2} b g\right)} x^{11} + \frac{3}{10} \, {\left(a b^{2} c + a^{2} b f\right)} x^{10} + \frac{1}{6} \, a^{3} e x^{6} + \frac{1}{9} \, {\left(3 \, a^{2} b e + a^{3} h\right)} x^{9} + \frac{1}{5} \, a^{3} d x^{5} + \frac{1}{8} \, {\left(3 \, a^{2} b d + a^{3} g\right)} x^{8} + \frac{1}{4} \, a^{3} c x^{4} + \frac{1}{7} \, {\left(3 \, a^{2} b c + a^{3} f\right)} x^{7}"," ",0,"1/18*b^3*h*x^18 + 1/17*b^3*g*x^17 + 1/16*b^3*f*x^16 + 1/15*(b^3*e + 3*a*b^2*h)*x^15 + 1/14*(b^3*d + 3*a*b^2*g)*x^14 + 1/13*(b^3*c + 3*a*b^2*f)*x^13 + 1/4*(a*b^2*e + a^2*b*h)*x^12 + 3/11*(a*b^2*d + a^2*b*g)*x^11 + 3/10*(a*b^2*c + a^2*b*f)*x^10 + 1/6*a^3*e*x^6 + 1/9*(3*a^2*b*e + a^3*h)*x^9 + 1/5*a^3*d*x^5 + 1/8*(3*a^2*b*d + a^3*g)*x^8 + 1/4*a^3*c*x^4 + 1/7*(3*a^2*b*c + a^3*f)*x^7","A",0
395,1,217,0,1.355593," ","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=""maxima"")","\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{1}{14} \, {\left(b^{3} e + 3 \, a b^{2} h\right)} x^{14} + \frac{1}{13} \, {\left(b^{3} d + 3 \, a b^{2} g\right)} x^{13} + \frac{1}{12} \, {\left(b^{3} c + 3 \, a b^{2} f\right)} x^{12} + \frac{3}{11} \, {\left(a b^{2} e + a^{2} b h\right)} x^{11} + \frac{3}{10} \, {\left(a b^{2} d + a^{2} b g\right)} x^{10} + \frac{1}{3} \, {\left(a b^{2} c + a^{2} b f\right)} x^{9} + \frac{1}{5} \, a^{3} e x^{5} + \frac{1}{8} \, {\left(3 \, a^{2} b e + a^{3} h\right)} x^{8} + \frac{1}{4} \, a^{3} d x^{4} + \frac{1}{7} \, {\left(3 \, a^{2} b d + a^{3} g\right)} x^{7} + \frac{1}{3} \, a^{3} c x^{3} + \frac{1}{6} \, {\left(3 \, a^{2} b c + a^{3} f\right)} x^{6}"," ",0,"1/17*b^3*h*x^17 + 1/16*b^3*g*x^16 + 1/15*b^3*f*x^15 + 1/14*(b^3*e + 3*a*b^2*h)*x^14 + 1/13*(b^3*d + 3*a*b^2*g)*x^13 + 1/12*(b^3*c + 3*a*b^2*f)*x^12 + 3/11*(a*b^2*e + a^2*b*h)*x^11 + 3/10*(a*b^2*d + a^2*b*g)*x^10 + 1/3*(a*b^2*c + a^2*b*f)*x^9 + 1/5*a^3*e*x^5 + 1/8*(3*a^2*b*e + a^3*h)*x^8 + 1/4*a^3*d*x^4 + 1/7*(3*a^2*b*d + a^3*g)*x^7 + 1/3*a^3*c*x^3 + 1/6*(3*a^2*b*c + a^3*f)*x^6","A",0
396,1,217,0,1.345117," ","integrate(x*(b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""maxima"")","\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{1}{13} \, {\left(b^{3} e + 3 \, a b^{2} h\right)} x^{13} + \frac{1}{12} \, {\left(b^{3} d + 3 \, a b^{2} g\right)} x^{12} + \frac{1}{11} \, {\left(b^{3} c + 3 \, a b^{2} f\right)} x^{11} + \frac{3}{10} \, {\left(a b^{2} e + a^{2} b h\right)} x^{10} + \frac{1}{3} \, {\left(a b^{2} d + a^{2} b g\right)} x^{9} + \frac{3}{8} \, {\left(a b^{2} c + a^{2} b f\right)} x^{8} + \frac{1}{4} \, a^{3} e x^{4} + \frac{1}{7} \, {\left(3 \, a^{2} b e + a^{3} h\right)} x^{7} + \frac{1}{3} \, a^{3} d x^{3} + \frac{1}{6} \, {\left(3 \, a^{2} b d + a^{3} g\right)} x^{6} + \frac{1}{2} \, a^{3} c x^{2} + \frac{1}{5} \, {\left(3 \, a^{2} b c + a^{3} f\right)} x^{5}"," ",0,"1/16*b^3*h*x^16 + 1/15*b^3*g*x^15 + 1/14*b^3*f*x^14 + 1/13*(b^3*e + 3*a*b^2*h)*x^13 + 1/12*(b^3*d + 3*a*b^2*g)*x^12 + 1/11*(b^3*c + 3*a*b^2*f)*x^11 + 3/10*(a*b^2*e + a^2*b*h)*x^10 + 1/3*(a*b^2*d + a^2*b*g)*x^9 + 3/8*(a*b^2*c + a^2*b*f)*x^8 + 1/4*a^3*e*x^4 + 1/7*(3*a^2*b*e + a^3*h)*x^7 + 1/3*a^3*d*x^3 + 1/6*(3*a^2*b*d + a^3*g)*x^6 + 1/2*a^3*c*x^2 + 1/5*(3*a^2*b*c + a^3*f)*x^5","A",0
397,1,214,0,1.337786," ","integrate((b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x, algorithm=""maxima"")","\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}{12} \, {\left(b^{3} e + 3 \, a b^{2} h\right)} x^{12} + \frac{1}{11} \, {\left(b^{3} d + 3 \, a b^{2} g\right)} x^{11} + \frac{1}{10} \, {\left(b^{3} c + 3 \, a b^{2} f\right)} x^{10} + \frac{1}{3} \, {\left(a b^{2} e + a^{2} b h\right)} x^{9} + \frac{3}{8} \, {\left(a b^{2} d + a^{2} b g\right)} x^{8} + \frac{3}{7} \, {\left(a b^{2} c + a^{2} b f\right)} x^{7} + \frac{1}{3} \, a^{3} e x^{3} + \frac{1}{6} \, {\left(3 \, a^{2} b e + a^{3} h\right)} x^{6} + \frac{1}{2} \, a^{3} d x^{2} + \frac{1}{5} \, {\left(3 \, a^{2} b d + a^{3} g\right)} x^{5} + a^{3} c x + \frac{1}{4} \, {\left(3 \, a^{2} b c + a^{3} f\right)} x^{4}"," ",0,"1/15*b^3*h*x^15 + 1/14*b^3*g*x^14 + 1/13*b^3*f*x^13 + 1/12*(b^3*e + 3*a*b^2*h)*x^12 + 1/11*(b^3*d + 3*a*b^2*g)*x^11 + 1/10*(b^3*c + 3*a*b^2*f)*x^10 + 1/3*(a*b^2*e + a^2*b*h)*x^9 + 3/8*(a*b^2*d + a^2*b*g)*x^8 + 3/7*(a*b^2*c + a^2*b*f)*x^7 + 1/3*a^3*e*x^3 + 1/6*(3*a^2*b*e + a^3*h)*x^6 + 1/2*a^3*d*x^2 + 1/5*(3*a^2*b*d + a^3*g)*x^5 + a^3*c*x + 1/4*(3*a^2*b*c + a^3*f)*x^4","A",0
398,1,212,0,1.424291," ","integrate((b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x,x, algorithm=""maxima"")","\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{1}{11} \, {\left(b^{3} e + 3 \, a b^{2} h\right)} x^{11} + \frac{1}{10} \, {\left(b^{3} d + 3 \, a b^{2} g\right)} x^{10} + \frac{1}{9} \, {\left(b^{3} c + 3 \, a b^{2} f\right)} x^{9} + \frac{3}{8} \, {\left(a b^{2} e + a^{2} b h\right)} x^{8} + \frac{3}{7} \, {\left(a b^{2} d + a^{2} b g\right)} x^{7} + \frac{1}{2} \, {\left(a b^{2} c + a^{2} b f\right)} x^{6} + \frac{1}{2} \, a^{3} e x^{2} + \frac{1}{5} \, {\left(3 \, a^{2} b e + a^{3} h\right)} x^{5} + a^{3} d x + \frac{1}{4} \, {\left(3 \, a^{2} b d + a^{3} g\right)} x^{4} + a^{3} c \log\left(x\right) + \frac{1}{3} \, {\left(3 \, a^{2} b c + a^{3} f\right)} x^{3}"," ",0,"1/14*b^3*h*x^14 + 1/13*b^3*g*x^13 + 1/12*b^3*f*x^12 + 1/11*(b^3*e + 3*a*b^2*h)*x^11 + 1/10*(b^3*d + 3*a*b^2*g)*x^10 + 1/9*(b^3*c + 3*a*b^2*f)*x^9 + 3/8*(a*b^2*e + a^2*b*h)*x^8 + 3/7*(a*b^2*d + a^2*b*g)*x^7 + 1/2*(a*b^2*c + a^2*b*f)*x^6 + 1/2*a^3*e*x^2 + 1/5*(3*a^2*b*e + a^3*h)*x^5 + a^3*d*x + 1/4*(3*a^2*b*d + a^3*g)*x^4 + a^3*c*log(x) + 1/3*(3*a^2*b*c + a^3*f)*x^3","A",0
399,1,212,0,1.291890," ","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=""maxima"")","\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{1}{10} \, {\left(b^{3} e + 3 \, a b^{2} h\right)} x^{10} + \frac{1}{9} \, {\left(b^{3} d + 3 \, a b^{2} g\right)} x^{9} + \frac{1}{8} \, {\left(b^{3} c + 3 \, a b^{2} f\right)} x^{8} + \frac{3}{7} \, {\left(a b^{2} e + a^{2} b h\right)} x^{7} + \frac{1}{2} \, {\left(a b^{2} d + a^{2} b g\right)} x^{6} + \frac{3}{5} \, {\left(a b^{2} c + a^{2} b f\right)} x^{5} + a^{3} e x + \frac{1}{4} \, {\left(3 \, a^{2} b e + a^{3} h\right)} x^{4} + a^{3} d \log\left(x\right) + \frac{1}{3} \, {\left(3 \, a^{2} b d + a^{3} g\right)} x^{3} - \frac{a^{3} c}{x} + \frac{1}{2} \, {\left(3 \, a^{2} b c + a^{3} f\right)} x^{2}"," ",0,"1/13*b^3*h*x^13 + 1/12*b^3*g*x^12 + 1/11*b^3*f*x^11 + 1/10*(b^3*e + 3*a*b^2*h)*x^10 + 1/9*(b^3*d + 3*a*b^2*g)*x^9 + 1/8*(b^3*c + 3*a*b^2*f)*x^8 + 3/7*(a*b^2*e + a^2*b*h)*x^7 + 1/2*(a*b^2*d + a^2*b*g)*x^6 + 3/5*(a*b^2*c + a^2*b*f)*x^5 + a^3*e*x + 1/4*(3*a^2*b*e + a^3*h)*x^4 + a^3*d*log(x) + 1/3*(3*a^2*b*d + a^3*g)*x^3 - a^3*c/x + 1/2*(3*a^2*b*c + a^3*f)*x^2","A",0
400,1,212,0,1.382548," ","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=""maxima"")","\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}{9} \, {\left(b^{3} e + 3 \, a b^{2} h\right)} x^{9} + \frac{1}{8} \, {\left(b^{3} d + 3 \, a b^{2} g\right)} x^{8} + \frac{1}{7} \, {\left(b^{3} c + 3 \, a b^{2} f\right)} x^{7} + \frac{1}{2} \, {\left(a b^{2} e + a^{2} b h\right)} x^{6} + \frac{3}{5} \, {\left(a b^{2} d + a^{2} b g\right)} x^{5} + \frac{3}{4} \, {\left(a b^{2} c + a^{2} b f\right)} x^{4} + a^{3} e \log\left(x\right) + \frac{1}{3} \, {\left(3 \, a^{2} b e + a^{3} h\right)} x^{3} + \frac{1}{2} \, {\left(3 \, a^{2} b d + a^{3} g\right)} x^{2} + {\left(3 \, a^{2} b c + a^{3} f\right)} x - \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 + 1/9*(b^3*e + 3*a*b^2*h)*x^9 + 1/8*(b^3*d + 3*a*b^2*g)*x^8 + 1/7*(b^3*c + 3*a*b^2*f)*x^7 + 1/2*(a*b^2*e + a^2*b*h)*x^6 + 3/5*(a*b^2*d + a^2*b*g)*x^5 + 3/4*(a*b^2*c + a^2*b*f)*x^4 + a^3*e*log(x) + 1/3*(3*a^2*b*e + a^3*h)*x^3 + 1/2*(3*a^2*b*d + a^3*g)*x^2 + (3*a^2*b*c + a^3*f)*x - 1/2*(2*a^3*d*x + a^3*c)/x^2","A",0
401,1,212,0,1.359594," ","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=""maxima"")","\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{1}{8} \, {\left(b^{3} e + 3 \, a b^{2} h\right)} x^{8} + \frac{1}{7} \, {\left(b^{3} d + 3 \, a b^{2} g\right)} x^{7} + \frac{1}{6} \, {\left(b^{3} c + 3 \, a b^{2} f\right)} x^{6} + \frac{3}{5} \, {\left(a b^{2} e + a^{2} b h\right)} x^{5} + \frac{3}{4} \, {\left(a b^{2} d + a^{2} b g\right)} x^{4} + {\left(a b^{2} c + a^{2} b f\right)} x^{3} + \frac{1}{2} \, {\left(3 \, a^{2} b e + a^{3} h\right)} x^{2} + {\left(3 \, a^{2} b d + a^{3} g\right)} x + {\left(3 \, a^{2} b c + a^{3} f\right)} \log\left(x\right) - \frac{6 \, a^{3} e x^{2} + 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 + 1/8*(b^3*e + 3*a*b^2*h)*x^8 + 1/7*(b^3*d + 3*a*b^2*g)*x^7 + 1/6*(b^3*c + 3*a*b^2*f)*x^6 + 3/5*(a*b^2*e + a^2*b*h)*x^5 + 3/4*(a*b^2*d + a^2*b*g)*x^4 + (a*b^2*c + a^2*b*f)*x^3 + 1/2*(3*a^2*b*e + a^3*h)*x^2 + (3*a^2*b*d + a^3*g)*x + (3*a^2*b*c + a^3*f)*log(x) - 1/6*(6*a^3*e*x^2 + 3*a^3*d*x + 2*a^3*c)/x^3","A",0
402,1,212,0,1.393842," ","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=""maxima"")","\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{1}{7} \, {\left(b^{3} e + 3 \, a b^{2} h\right)} x^{7} + \frac{1}{6} \, {\left(b^{3} d + 3 \, a b^{2} g\right)} x^{6} + \frac{1}{5} \, {\left(b^{3} c + 3 \, a b^{2} f\right)} x^{5} + \frac{3}{4} \, {\left(a b^{2} e + a^{2} b h\right)} x^{4} + {\left(a b^{2} d + a^{2} b g\right)} x^{3} + \frac{3}{2} \, {\left(a b^{2} c + a^{2} b f\right)} x^{2} + {\left(3 \, a^{2} b e + a^{3} h\right)} x + {\left(3 \, a^{2} b d + a^{3} g\right)} \log\left(x\right) - \frac{6 \, a^{3} e x^{2} + 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 + 1/7*(b^3*e + 3*a*b^2*h)*x^7 + 1/6*(b^3*d + 3*a*b^2*g)*x^6 + 1/5*(b^3*c + 3*a*b^2*f)*x^5 + 3/4*(a*b^2*e + a^2*b*h)*x^4 + (a*b^2*d + a^2*b*g)*x^3 + 3/2*(a*b^2*c + a^2*b*f)*x^2 + (3*a^2*b*e + a^3*h)*x + (3*a^2*b*d + a^3*g)*log(x) - 1/12*(6*a^3*e*x^2 + 4*a^3*d*x + 3*a^3*c + 12*(3*a^2*b*c + a^3*f)*x^3)/x^4","A",0
403,1,378,0,2.978496," ","integrate(x^4*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left(a b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - a^{2} b f \left(\frac{a}{b}\right)^{\frac{2}{3}} - a^{2} b e \left(\frac{a}{b}\right)^{\frac{1}{3}} + a^{3} h \left(\frac{a}{b}\right)^{\frac{1}{3}}\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^{3}} + \frac{60 \, b^{2} h x^{7} + 70 \, b^{2} g x^{6} + 84 \, b^{2} f x^{5} + 105 \, {\left(b^{2} e - a b h\right)} x^{4} + 140 \, {\left(b^{2} d - a b g\right)} x^{3} + 210 \, {\left(b^{2} c - a b f\right)} x^{2} - 420 \, {\left(a b e - a^{2} h\right)} x}{420 \, b^{3}} - \frac{{\left(2 \, a b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a^{2} b g \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} b f \left(\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} b e - a^{3} h\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} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(a b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} - a^{2} b g \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} b f \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} b e + a^{3} h\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/3*sqrt(3)*(a*b^2*c*(a/b)^(2/3) - a^2*b*f*(a/b)^(2/3) - a^2*b*e*(a/b)^(1/3) + a^3*h*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^3) + 1/420*(60*b^2*h*x^7 + 70*b^2*g*x^6 + 84*b^2*f*x^5 + 105*(b^2*e - a*b*h)*x^4 + 140*(b^2*d - a*b*g)*x^3 + 210*(b^2*c - a*b*f)*x^2 - 420*(a*b*e - a^2*h)*x)/b^3 - 1/6*(2*a*b^2*d*(a/b)^(2/3) - 2*a^2*b*g*(a/b)^(2/3) + a*b^2*c*(a/b)^(1/3) - a^2*b*f*(a/b)^(1/3) + a^2*b*e - a^3*h)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^4*(a/b)^(2/3)) - 1/3*(a*b^2*d*(a/b)^(2/3) - a^2*b*g*(a/b)^(2/3) - a*b^2*c*(a/b)^(1/3) + a^2*b*f*(a/b)^(1/3) - a^2*b*e + a^3*h)*log(x + (a/b)^(1/3))/(b^4*(a/b)^(2/3))","A",0
404,1,332,0,2.895642," ","integrate(x^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{10 \, b h x^{6} + 12 \, b g x^{5} + 15 \, b f x^{4} + 20 \, {\left(b e - a h\right)} x^{3} + 30 \, {\left(b d - a g\right)} x^{2} + 60 \, {\left(b c - a f\right)} x}{60 \, b^{2}} - \frac{\sqrt{3} {\left(a b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} - a^{2} b g \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} b f \left(\frac{a}{b}\right)^{\frac{1}{3}}\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^{3}} - \frac{{\left(2 \, a b e \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a^{2} h \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b d \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} g \left(\frac{a}{b}\right)^{\frac{1}{3}} - a b c + a^{2} 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^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(a b e \left(\frac{a}{b}\right)^{\frac{2}{3}} - a^{2} h \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b d \left(\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} g \left(\frac{a}{b}\right)^{\frac{1}{3}} + a b c - a^{2} f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/60*(10*b*h*x^6 + 12*b*g*x^5 + 15*b*f*x^4 + 20*(b*e - a*h)*x^3 + 30*(b*d - a*g)*x^2 + 60*(b*c - a*f)*x)/b^2 - 1/3*sqrt(3)*(a*b^2*d*(a/b)^(2/3) - a^2*b*g*(a/b)^(2/3) + a*b^2*c*(a/b)^(1/3) - a^2*b*f*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^3) - 1/6*(2*a*b*e*(a/b)^(2/3) - 2*a^2*h*(a/b)^(2/3) + a*b*d*(a/b)^(1/3) - a^2*g*(a/b)^(1/3) - a*b*c + a^2*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^3*(a/b)^(2/3)) - 1/3*(a*b*e*(a/b)^(2/3) - a^2*h*(a/b)^(2/3) - a*b*d*(a/b)^(1/3) + a^2*g*(a/b)^(1/3) + a*b*c - a^2*f)*log(x + (a/b)^(1/3))/(b^3*(a/b)^(2/3))","A",0
405,1,313,0,2.996725," ","integrate(x^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left(a b e \left(\frac{a}{b}\right)^{\frac{2}{3}} - a^{2} h \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b d \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} g \left(\frac{a}{b}\right)^{\frac{1}{3}}\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{12 \, b h x^{5} + 15 \, b g x^{4} + 20 \, b f x^{3} + 30 \, {\left(b e - a h\right)} x^{2} + 60 \, {\left(b d - a g\right)} x}{60 \, b^{2}} + \frac{{\left(2 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}} + a b d - a^{2} 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^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}} - a b d + a^{2} g\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/3*sqrt(3)*(a*b*e*(a/b)^(2/3) - a^2*h*(a/b)^(2/3) + a*b*d*(a/b)^(1/3) - a^2*g*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^2) + 1/60*(12*b*h*x^5 + 15*b*g*x^4 + 20*b*f*x^3 + 30*(b*e - a*h)*x^2 + 60*(b*d - a*g)*x)/b^2 + 1/6*(2*b^2*c*(a/b)^(2/3) - 2*a*b*f*(a/b)^(2/3) - a*b*e*(a/b)^(1/3) + a^2*h*(a/b)^(1/3) + a*b*d - a^2*g)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^3*(a/b)^(2/3)) + 1/3*(b^2*c*(a/b)^(2/3) - a*b*f*(a/b)^(2/3) + a*b*e*(a/b)^(1/3) - a^2*h*(a/b)^(1/3) - a*b*d + a^2*g)*log(x + (a/b)^(1/3))/(b^3*(a/b)^(2/3))","A",0
406,1,300,0,3.028633," ","integrate(x*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{\sqrt{3} {\left(b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}}\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{3 \, b h x^{4} + 4 \, b g x^{3} + 6 \, b f x^{2} + 12 \, {\left(b e - a h\right)} x}{12 \, b^{2}} + \frac{{\left(2 \, b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a b g \left(\frac{a}{b}\right)^{\frac{2}{3}} + b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} - a b f \left(\frac{a}{b}\right)^{\frac{1}{3}} + a b e - a^{2} h\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} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b g \left(\frac{a}{b}\right)^{\frac{2}{3}} - b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} + a b f \left(\frac{a}{b}\right)^{\frac{1}{3}} - a b e + a^{2} h\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*sqrt(3)*(b^2*c*(a/b)^(2/3) - a*b*f*(a/b)^(2/3) - a*b*e*(a/b)^(1/3) + a^2*h*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^2) + 1/12*(3*b*h*x^4 + 4*b*g*x^3 + 6*b*f*x^2 + 12*(b*e - a*h)*x)/b^2 + 1/6*(2*b^2*d*(a/b)^(2/3) - 2*a*b*g*(a/b)^(2/3) + b^2*c*(a/b)^(1/3) - a*b*f*(a/b)^(1/3) + a*b*e - a^2*h)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^3*(a/b)^(2/3)) + 1/3*(b^2*d*(a/b)^(2/3) - a*b*g*(a/b)^(2/3) - b^2*c*(a/b)^(1/3) + a*b*f*(a/b)^(1/3) - a*b*e + a^2*h)*log(x + (a/b)^(1/3))/(b^3*(a/b)^(2/3))","A",0
407,1,266,0,3.036891," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a),x, algorithm=""maxima"")","\frac{2 \, h x^{3} + 3 \, g x^{2} + 6 \, f x}{6 \, b} + \frac{\sqrt{3} {\left(b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b g \left(\frac{a}{b}\right)^{\frac{2}{3}} + b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} - a b f \left(\frac{a}{b}\right)^{\frac{1}{3}}\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(2 \, b e \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a h \left(\frac{a}{b}\right)^{\frac{2}{3}} + b d \left(\frac{a}{b}\right)^{\frac{1}{3}} - a g \left(\frac{a}{b}\right)^{\frac{1}{3}} - b c + 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^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b e \left(\frac{a}{b}\right)^{\frac{2}{3}} - a h \left(\frac{a}{b}\right)^{\frac{2}{3}} - b d \left(\frac{a}{b}\right)^{\frac{1}{3}} + a g \left(\frac{a}{b}\right)^{\frac{1}{3}} + b c - a f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/6*(2*h*x^3 + 3*g*x^2 + 6*f*x)/b + 1/3*sqrt(3)*(b^2*d*(a/b)^(2/3) - a*b*g*(a/b)^(2/3) + b^2*c*(a/b)^(1/3) - a*b*f*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^2) + 1/6*(2*b*e*(a/b)^(2/3) - 2*a*h*(a/b)^(2/3) + b*d*(a/b)^(1/3) - a*g*(a/b)^(1/3) - b*c + a*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^2*(a/b)^(2/3)) + 1/3*(b*e*(a/b)^(2/3) - a*h*(a/b)^(2/3) - b*d*(a/b)^(1/3) + a*g*(a/b)^(1/3) + b*c - a*f)*log(x + (a/b)^(1/3))/(b^2*(a/b)^(2/3))","A",0
408,1,290,0,3.018842," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x/(b*x^3+a),x, algorithm=""maxima"")","\frac{c \log\left(x\right)}{a} + \frac{h x^{2} + 2 \, g x}{2 \, b} + \frac{\sqrt{3} {\left(a b e \left(\frac{a}{b}\right)^{\frac{2}{3}} - a^{2} h \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b d \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} g \left(\frac{a}{b}\right)^{\frac{1}{3}}\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(2 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}} + a b d - a^{2} 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 \, a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}} - a b d + a^{2} g\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"c*log(x)/a + 1/2*(h*x^2 + 2*g*x)/b + 1/3*sqrt(3)*(a*b*e*(a/b)^(2/3) - a^2*h*(a/b)^(2/3) + a*b*d*(a/b)^(1/3) - a^2*g*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b) - 1/6*(2*b^2*c*(a/b)^(2/3) - 2*a*b*f*(a/b)^(2/3) - a*b*e*(a/b)^(1/3) + a^2*h*(a/b)^(1/3) + a*b*d - a^2*g)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^2*(a/b)^(2/3)) - 1/3*(b^2*c*(a/b)^(2/3) - a*b*f*(a/b)^(2/3) + a*b*e*(a/b)^(1/3) - a^2*h*(a/b)^(1/3) - a*b*d + a^2*g)*log(x + (a/b)^(1/3))/(a*b^2*(a/b)^(2/3))","A",0
409,1,290,0,3.024869," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^2/(b*x^3+a),x, algorithm=""maxima"")","\frac{h x}{b} + \frac{d \log\left(x\right)}{a} - \frac{\sqrt{3} {\left(b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}}\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(2 \, b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a b g \left(\frac{a}{b}\right)^{\frac{2}{3}} + b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} - a b f \left(\frac{a}{b}\right)^{\frac{1}{3}} + a b e - a^{2} h\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 b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b g \left(\frac{a}{b}\right)^{\frac{2}{3}} - b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} + a b f \left(\frac{a}{b}\right)^{\frac{1}{3}} - a b e + a^{2} h\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"h*x/b + d*log(x)/a - 1/3*sqrt(3)*(b^2*c*(a/b)^(2/3) - a*b*f*(a/b)^(2/3) - a*b*e*(a/b)^(1/3) + a^2*h*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b) - c/(a*x) - 1/6*(2*b^2*d*(a/b)^(2/3) - 2*a*b*g*(a/b)^(2/3) + b^2*c*(a/b)^(1/3) - a*b*f*(a/b)^(1/3) + a*b*e - a^2*h)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^2*(a/b)^(2/3)) - 1/3*(b^2*d*(a/b)^(2/3) - a*b*g*(a/b)^(2/3) - b^2*c*(a/b)^(1/3) + a*b*f*(a/b)^(1/3) - a*b*e + a^2*h)*log(x + (a/b)^(1/3))/(a*b^2*(a/b)^(2/3))","A",0
410,1,271,0,2.996431," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^3/(b*x^3+a),x, algorithm=""maxima"")","\frac{e \log\left(x\right)}{a} - \frac{\sqrt{3} {\left(b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b g \left(\frac{a}{b}\right)^{\frac{2}{3}} + b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} - a b f \left(\frac{a}{b}\right)^{\frac{1}{3}}\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(2 \, b e \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a h \left(\frac{a}{b}\right)^{\frac{2}{3}} + b d \left(\frac{a}{b}\right)^{\frac{1}{3}} - a g \left(\frac{a}{b}\right)^{\frac{1}{3}} - b c + 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 \, a b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b e \left(\frac{a}{b}\right)^{\frac{2}{3}} - a h \left(\frac{a}{b}\right)^{\frac{2}{3}} - b d \left(\frac{a}{b}\right)^{\frac{1}{3}} + a g \left(\frac{a}{b}\right)^{\frac{1}{3}} + b c - a f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{2 \, d x + c}{2 \, a x^{2}}"," ",0,"e*log(x)/a - 1/3*sqrt(3)*(b^2*d*(a/b)^(2/3) - a*b*g*(a/b)^(2/3) + b^2*c*(a/b)^(1/3) - a*b*f*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b) - 1/6*(2*b*e*(a/b)^(2/3) - 2*a*h*(a/b)^(2/3) + b*d*(a/b)^(1/3) - a*g*(a/b)^(1/3) - b*c + a*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b*(a/b)^(2/3)) - 1/3*(b*e*(a/b)^(2/3) - a*h*(a/b)^(2/3) - b*d*(a/b)^(1/3) + a*g*(a/b)^(1/3) + b*c - a*f)*log(x + (a/b)^(1/3))/(a*b*(a/b)^(2/3)) - 1/2*(2*d*x + c)/(a*x^2)","A",0
411,1,302,0,3.078668," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^4/(b*x^3+a),x, algorithm=""maxima"")","-\frac{{\left(b c - a f\right)} \log\left(x\right)}{a^{2}} - \frac{\sqrt{3} {\left(a b e \left(\frac{a}{b}\right)^{\frac{2}{3}} - a^{2} h \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b d \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} g \left(\frac{a}{b}\right)^{\frac{1}{3}}\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^{3}} + \frac{{\left(2 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}} + a b d - a^{2} 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 \, a^{2} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}} - a b d + a^{2} g\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \, a^{2} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{6 \, e x^{2} + 3 \, d x + 2 \, c}{6 \, a x^{3}}"," ",0,"-(b*c - a*f)*log(x)/a^2 - 1/3*sqrt(3)*(a*b*e*(a/b)^(2/3) - a^2*h*(a/b)^(2/3) + a*b*d*(a/b)^(1/3) - a^2*g*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^3 + 1/6*(2*b^2*c*(a/b)^(2/3) - 2*a*b*f*(a/b)^(2/3) - a*b*e*(a/b)^(1/3) + a^2*h*(a/b)^(1/3) + a*b*d - a^2*g)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b*(a/b)^(2/3)) + 1/3*(b^2*c*(a/b)^(2/3) - a*b*f*(a/b)^(2/3) + a*b*e*(a/b)^(1/3) - a^2*h*(a/b)^(1/3) - a*b*d + a^2*g)*log(x + (a/b)^(1/3))/(a^2*b*(a/b)^(2/3)) - 1/6*(6*e*x^2 + 3*d*x + 2*c)/(a*x^3)","A",0
412,1,364,0,3.053909," ","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=""maxima"")","\frac{a b d - a^{2} g - {\left(b^{2} c - a b f\right)} x^{2} + {\left(a b e - a^{2} h\right)} x}{3 \, {\left(b^{4} x^{3} + a b^{3}\right)}} + \frac{\sqrt{3} {\left(2 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 5 \, a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} - 4 \, a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 7 \, a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}}\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 b^{3}} + \frac{3 \, b h x^{4} + 4 \, b g x^{3} + 6 \, b f x^{2} + 12 \, {\left(b e - 2 \, a h\right)} x}{12 \, b^{3}} + \frac{{\left(6 \, b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} - 12 \, a b g \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a b f \left(\frac{a}{b}\right)^{\frac{1}{3}} + 4 \, a b e - 7 \, a^{2} h\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^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(3 \, b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} - 6 \, a b g \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a b f \left(\frac{a}{b}\right)^{\frac{1}{3}} - 4 \, a b e + 7 \, a^{2} h\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*(a*b*d - a^2*g - (b^2*c - a*b*f)*x^2 + (a*b*e - a^2*h)*x)/(b^4*x^3 + a*b^3) + 1/9*sqrt(3)*(2*b^2*c*(a/b)^(2/3) - 5*a*b*f*(a/b)^(2/3) - 4*a*b*e*(a/b)^(1/3) + 7*a^2*h*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^3) + 1/12*(3*b*h*x^4 + 4*b*g*x^3 + 6*b*f*x^2 + 12*(b*e - 2*a*h)*x)/b^3 + 1/18*(6*b^2*d*(a/b)^(2/3) - 12*a*b*g*(a/b)^(2/3) + 2*b^2*c*(a/b)^(1/3) - 5*a*b*f*(a/b)^(1/3) + 4*a*b*e - 7*a^2*h)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^4*(a/b)^(2/3)) + 1/9*(3*b^2*d*(a/b)^(2/3) - 6*a*b*g*(a/b)^(2/3) - 2*b^2*c*(a/b)^(1/3) + 5*a*b*f*(a/b)^(1/3) - 4*a*b*e + 7*a^2*h)*log(x + (a/b)^(1/3))/(b^4*(a/b)^(2/3))","A",0
413,1,329,0,3.135609," ","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=""maxima"")","\frac{a b e - a^{2} h - {\left(b^{2} d - a b g\right)} x^{2} - {\left(b^{2} c - a b f\right)} x}{3 \, {\left(b^{4} x^{3} + a b^{3}\right)}} + \frac{2 \, h x^{3} + 3 \, g x^{2} + 6 \, f x}{6 \, b^{2}} + \frac{\sqrt{3} {\left(2 \, b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} - 5 \, a b g \left(\frac{a}{b}\right)^{\frac{2}{3}} + b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} - 4 \, a b f \left(\frac{a}{b}\right)^{\frac{1}{3}}\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 b^{3}} + \frac{{\left(6 \, b e \left(\frac{a}{b}\right)^{\frac{2}{3}} - 12 \, a h \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, b d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a g \left(\frac{a}{b}\right)^{\frac{1}{3}} - b c + 4 \, 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 \, b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(3 \, b e \left(\frac{a}{b}\right)^{\frac{2}{3}} - 6 \, a h \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, b d \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a g \left(\frac{a}{b}\right)^{\frac{1}{3}} + b c - 4 \, a f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*(a*b*e - a^2*h - (b^2*d - a*b*g)*x^2 - (b^2*c - a*b*f)*x)/(b^4*x^3 + a*b^3) + 1/6*(2*h*x^3 + 3*g*x^2 + 6*f*x)/b^2 + 1/9*sqrt(3)*(2*b^2*d*(a/b)^(2/3) - 5*a*b*g*(a/b)^(2/3) + b^2*c*(a/b)^(1/3) - 4*a*b*f*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^3) + 1/18*(6*b*e*(a/b)^(2/3) - 12*a*h*(a/b)^(2/3) + 2*b*d*(a/b)^(1/3) - 5*a*g*(a/b)^(1/3) - b*c + 4*a*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^3*(a/b)^(2/3)) + 1/9*(3*b*e*(a/b)^(2/3) - 6*a*h*(a/b)^(2/3) - 2*b*d*(a/b)^(1/3) + 5*a*g*(a/b)^(1/3) + b*c - 4*a*f)*log(x + (a/b)^(1/3))/(b^3*(a/b)^(2/3))","A",0
414,1,283,0,3.027439," ","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=""maxima"")","-\frac{{\left(b e - a h\right)} x^{2} + b c - a f + {\left(b d - a g\right)} x}{3 \, {\left(b^{3} x^{3} + a b^{2}\right)}} + \frac{\sqrt{3} {\left(2 \, b e \left(\frac{a}{b}\right)^{\frac{2}{3}} - 5 \, a h \left(\frac{a}{b}\right)^{\frac{2}{3}} + b d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 4 \, a g \left(\frac{a}{b}\right)^{\frac{1}{3}}\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 b^{2}} + \frac{h x^{2} + 2 \, g x}{2 \, b^{2}} + \frac{{\left(6 \, b f \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, b e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a h \left(\frac{a}{b}\right)^{\frac{1}{3}} - b d + 4 \, 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 \, b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(3 \, b f \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, b e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a h \left(\frac{a}{b}\right)^{\frac{1}{3}} + b d - 4 \, a g\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/3*((b*e - a*h)*x^2 + b*c - a*f + (b*d - a*g)*x)/(b^3*x^3 + a*b^2) + 1/9*sqrt(3)*(2*b*e*(a/b)^(2/3) - 5*a*h*(a/b)^(2/3) + b*d*(a/b)^(1/3) - 4*a*g*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^2) + 1/2*(h*x^2 + 2*g*x)/b^2 + 1/18*(6*b*f*(a/b)^(2/3) + 2*b*e*(a/b)^(1/3) - 5*a*h*(a/b)^(1/3) - b*d + 4*a*g)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^3*(a/b)^(2/3)) + 1/9*(3*b*f*(a/b)^(2/3) - 2*b*e*(a/b)^(1/3) + 5*a*h*(a/b)^(1/3) + b*d - 4*a*g)*log(x + (a/b)^(1/3))/(b^3*(a/b)^(2/3))","A",0
415,1,311,0,2.962890," ","integrate(x*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{a b d - a^{2} g - {\left(b^{2} c - a b f\right)} x^{2} + {\left(a b e - a^{2} h\right)} x}{3 \, {\left(a b^{3} x^{3} + a^{2} b^{2}\right)}} + \frac{h x}{b^{2}} + \frac{\sqrt{3} {\left(b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 4 \, a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}}\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^{2} b^{2}} + \frac{{\left(6 \, a b g \left(\frac{a}{b}\right)^{\frac{2}{3}} + b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a b f \left(\frac{a}{b}\right)^{\frac{1}{3}} - a b e + 4 \, a^{2} h\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 b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(3 \, a b g \left(\frac{a}{b}\right)^{\frac{2}{3}} - b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a b f \left(\frac{a}{b}\right)^{\frac{1}{3}} + a b e - 4 \, a^{2} h\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/3*(a*b*d - a^2*g - (b^2*c - a*b*f)*x^2 + (a*b*e - a^2*h)*x)/(a*b^3*x^3 + a^2*b^2) + h*x/b^2 + 1/9*sqrt(3)*(b^2*c*(a/b)^(2/3) + 2*a*b*f*(a/b)^(2/3) + a*b*e*(a/b)^(1/3) - 4*a^2*h*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b^2) + 1/18*(6*a*b*g*(a/b)^(2/3) + b^2*c*(a/b)^(1/3) + 2*a*b*f*(a/b)^(1/3) - a*b*e + 4*a^2*h)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^3*(a/b)^(2/3)) + 1/9*(3*a*b*g*(a/b)^(2/3) - b^2*c*(a/b)^(1/3) - 2*a*b*f*(a/b)^(1/3) + a*b*e - 4*a^2*h)*log(x + (a/b)^(1/3))/(a*b^3*(a/b)^(2/3))","A",0
416,1,292,0,2.953419," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^2,x, algorithm=""maxima"")","-\frac{a b e - a^{2} h - {\left(b^{2} d - a b g\right)} x^{2} - {\left(b^{2} c - a b f\right)} x}{3 \, {\left(a b^{3} x^{3} + a^{2} b^{2}\right)}} + \frac{\sqrt{3} {\left(b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, a b g \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} + a b f \left(\frac{a}{b}\right)^{\frac{1}{3}}\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^{2} b^{2}} + \frac{{\left(6 \, a h \left(\frac{a}{b}\right)^{\frac{2}{3}} + b d \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a g \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, b c - 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 \, a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(3 \, a h \left(\frac{a}{b}\right)^{\frac{2}{3}} - b d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a g \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, b c + a f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/3*(a*b*e - a^2*h - (b^2*d - a*b*g)*x^2 - (b^2*c - a*b*f)*x)/(a*b^3*x^3 + a^2*b^2) + 1/9*sqrt(3)*(b^2*d*(a/b)^(2/3) + 2*a*b*g*(a/b)^(2/3) + 2*b^2*c*(a/b)^(1/3) + a*b*f*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b^2) + 1/18*(6*a*h*(a/b)^(2/3) + b*d*(a/b)^(1/3) + 2*a*g*(a/b)^(1/3) - 2*b*c - a*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^2*(a/b)^(2/3)) + 1/9*(3*a*h*(a/b)^(2/3) - b*d*(a/b)^(1/3) - 2*a*g*(a/b)^(1/3) + 2*b*c + a*f)*log(x + (a/b)^(1/3))/(a*b^2*(a/b)^(2/3))","A",0
417,1,302,0,3.044537," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x/(b*x^3+a)^2,x, algorithm=""maxima"")","\frac{{\left(b e - a h\right)} x^{2} + b c - a f + {\left(b d - a g\right)} x}{3 \, {\left(a b^{2} x^{3} + a^{2} b\right)}} + \frac{c \log\left(x\right)}{a^{2}} + \frac{\sqrt{3} {\left(a b e \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, a^{2} h \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, a b d \left(\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} g \left(\frac{a}{b}\right)^{\frac{1}{3}}\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(6 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a b d + a^{2} 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 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(3 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a b d - a^{2} g\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*((b*e - a*h)*x^2 + b*c - a*f + (b*d - a*g)*x)/(a*b^2*x^3 + a^2*b) + c*log(x)/a^2 + 1/9*sqrt(3)*(a*b*e*(a/b)^(2/3) + 2*a^2*h*(a/b)^(2/3) + 2*a*b*d*(a/b)^(1/3) + a^2*g*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^3*b) - 1/18*(6*b^2*c*(a/b)^(2/3) - a*b*e*(a/b)^(1/3) - 2*a^2*h*(a/b)^(1/3) + 2*a*b*d + a^2*g)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b^2*(a/b)^(2/3)) - 1/9*(3*b^2*c*(a/b)^(2/3) + a*b*e*(a/b)^(1/3) + 2*a^2*h*(a/b)^(1/3) - 2*a*b*d - a^2*g)*log(x + (a/b)^(1/3))/(a^2*b^2*(a/b)^(2/3))","A",0
418,1,329,0,3.134515," ","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=""maxima"")","-\frac{{\left(4 \, b^{2} c - a b f\right)} x^{3} + 3 \, a b c - {\left(a b e - a^{2} h\right)} x^{2} - {\left(a b d - a^{2} g\right)} x}{3 \, {\left(a^{2} b^{2} x^{4} + a^{3} b x\right)}} + \frac{d \log\left(x\right)}{a^{2}} - \frac{\sqrt{3} {\left(4 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}}\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(6 \, b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} + 4 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} - a b f \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a b e + a^{2} h\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^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(3 \, b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} - 4 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} + a b f \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a b e - a^{2} h\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/3*((4*b^2*c - a*b*f)*x^3 + 3*a*b*c - (a*b*e - a^2*h)*x^2 - (a*b*d - a^2*g)*x)/(a^2*b^2*x^4 + a^3*b*x) + d*log(x)/a^2 - 1/9*sqrt(3)*(4*b^2*c*(a/b)^(2/3) - a*b*f*(a/b)^(2/3) - 2*a*b*e*(a/b)^(1/3) - a^2*h*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^3*b) - 1/18*(6*b^2*d*(a/b)^(2/3) + 4*b^2*c*(a/b)^(1/3) - a*b*f*(a/b)^(1/3) + 2*a*b*e + a^2*h)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b^2*(a/b)^(2/3)) - 1/9*(3*b^2*d*(a/b)^(2/3) - 4*b^2*c*(a/b)^(1/3) + a*b*f*(a/b)^(1/3) - 2*a*b*e - a^2*h)*log(x + (a/b)^(1/3))/(a^2*b^2*(a/b)^(2/3))","A",0
419,1,316,0,3.063179," ","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=""maxima"")","-\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 b e - a^{2} h\right)} x^{2}}{6 \, {\left(a^{2} b^{2} x^{5} + a^{3} b x^{2}\right)}} + \frac{e \log\left(x\right)}{a^{2}} - \frac{\sqrt{3} {\left(4 \, b d \left(\frac{a}{b}\right)^{\frac{2}{3}} - a g \left(\frac{a}{b}\right)^{\frac{2}{3}} + 5 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a f \left(\frac{a}{b}\right)^{\frac{1}{3}}\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}} - \frac{{\left(6 \, b e \left(\frac{a}{b}\right)^{\frac{2}{3}} + 4 \, b d \left(\frac{a}{b}\right)^{\frac{1}{3}} - a g \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, b c + 2 \, 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 \, a^{2} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(3 \, b e \left(\frac{a}{b}\right)^{\frac{2}{3}} - 4 \, b d \left(\frac{a}{b}\right)^{\frac{1}{3}} + a g \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, b c - 2 \, a f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{2} b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-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*b*e - a^2*h)*x^2)/(a^2*b^2*x^5 + a^3*b*x^2) + e*log(x)/a^2 - 1/9*sqrt(3)*(4*b*d*(a/b)^(2/3) - a*g*(a/b)^(2/3) + 5*b*c*(a/b)^(1/3) - 2*a*f*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^3 - 1/18*(6*b*e*(a/b)^(2/3) + 4*b*d*(a/b)^(1/3) - a*g*(a/b)^(1/3) - 5*b*c + 2*a*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b*(a/b)^(2/3)) - 1/9*(3*b*e*(a/b)^(2/3) - 4*b*d*(a/b)^(1/3) + a*g*(a/b)^(1/3) + 5*b*c - 2*a*f)*log(x + (a/b)^(1/3))/(a^2*b*(a/b)^(2/3))","A",0
420,1,365,0,3.078887," ","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=""maxima"")","-\frac{2 \, {\left(4 \, b e - a h\right)} x^{5} + {\left(5 \, b d - 2 \, a g\right)} x^{4} + 6 \, a e x^{2} + 2 \, {\left(2 \, b c - a f\right)} x^{3} + 3 \, a d x + 2 \, a c}{6 \, {\left(a^{2} b x^{6} + a^{3} x^{3}\right)}} - \frac{{\left(2 \, b c - a f\right)} \log\left(x\right)}{a^{3}} - \frac{\sqrt{3} {\left(4 \, a b e \left(\frac{a}{b}\right)^{\frac{2}{3}} - a^{2} h \left(\frac{a}{b}\right)^{\frac{2}{3}} + 5 \, a b d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a^{2} g \left(\frac{a}{b}\right)^{\frac{1}{3}}\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^{4}} + \frac{{\left(12 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 6 \, a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} - 4 \, a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a b d - 2 \, a^{2} 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 \, a^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(6 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 3 \, a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} + 4 \, a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a b d + 2 \, a^{2} g\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \, a^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/6*(2*(4*b*e - a*h)*x^5 + (5*b*d - 2*a*g)*x^4 + 6*a*e*x^2 + 2*(2*b*c - a*f)*x^3 + 3*a*d*x + 2*a*c)/(a^2*b*x^6 + a^3*x^3) - (2*b*c - a*f)*log(x)/a^3 - 1/9*sqrt(3)*(4*a*b*e*(a/b)^(2/3) - a^2*h*(a/b)^(2/3) + 5*a*b*d*(a/b)^(1/3) - 2*a^2*g*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^4 + 1/18*(12*b^2*c*(a/b)^(2/3) - 6*a*b*f*(a/b)^(2/3) - 4*a*b*e*(a/b)^(1/3) + a^2*h*(a/b)^(1/3) + 5*a*b*d - 2*a^2*g)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*b*(a/b)^(2/3)) + 1/9*(6*b^2*c*(a/b)^(2/3) - 3*a*b*f*(a/b)^(2/3) + 4*a*b*e*(a/b)^(1/3) - a^2*h*(a/b)^(1/3) - 5*a*b*d + 2*a^2*g)*log(x + (a/b)^(1/3))/(a^3*b*(a/b)^(2/3))","A",0
421,1,391,0,3.128865," ","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=""maxima"")","\frac{2 \, {\left(b^{3} c - 4 \, a b^{2} f\right)} x^{5} - {\left(7 \, a b^{2} e - 13 \, a^{2} b h\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(2 \, a^{2} b e - 5 \, a^{3} h\right)} x}{18 \, {\left(a b^{5} x^{6} + 2 \, a^{2} b^{4} x^{3} + a^{3} b^{3}\right)}} + \frac{h x}{b^{3}} + \frac{\sqrt{3} {\left(b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} + 5 \, a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 14 \, a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}}\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^{2} b^{3}} + \frac{{\left(18 \, a b g \left(\frac{a}{b}\right)^{\frac{2}{3}} + b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a b f \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a b e + 14 \, a^{2} h\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 b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(9 \, a b g \left(\frac{a}{b}\right)^{\frac{2}{3}} - b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a b f \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a b e - 14 \, a^{2} h\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/18*(2*(b^3*c - 4*a*b^2*f)*x^5 - (7*a*b^2*e - 13*a^2*b*h)*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*(2*a^2*b*e - 5*a^3*h)*x)/(a*b^5*x^6 + 2*a^2*b^4*x^3 + a^3*b^3) + h*x/b^3 + 1/27*sqrt(3)*(b^2*c*(a/b)^(2/3) + 5*a*b*f*(a/b)^(2/3) + 2*a*b*e*(a/b)^(1/3) - 14*a^2*h*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b^3) + 1/54*(18*a*b*g*(a/b)^(2/3) + b^2*c*(a/b)^(1/3) + 5*a*b*f*(a/b)^(1/3) - 2*a*b*e + 14*a^2*h)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^4*(a/b)^(2/3)) + 1/27*(9*a*b*g*(a/b)^(2/3) - b^2*c*(a/b)^(1/3) - 5*a*b*f*(a/b)^(1/3) + 2*a*b*e - 14*a^2*h)*log(x + (a/b)^(1/3))/(a*b^4*(a/b)^(2/3))","A",0
422,1,366,0,3.119033," ","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=""maxima"")","\frac{2 \, {\left(b^{3} d - 4 \, a b^{2} g\right)} x^{5} + {\left(b^{3} c - 7 \, a b^{2} f\right)} x^{4} - 3 \, a^{2} b e + 9 \, a^{3} h - 6 \, {\left(a b^{2} e - 2 \, a^{2} b h\right)} x^{3} - {\left(a b^{2} d + 5 \, a^{2} b g\right)} x^{2} - 2 \, {\left(a b^{2} c + 2 \, a^{2} b f\right)} x}{18 \, {\left(a b^{5} x^{6} + 2 \, a^{2} b^{4} x^{3} + a^{3} b^{3}\right)}} + \frac{\sqrt{3} {\left(b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} + 5 \, a b g \left(\frac{a}{b}\right)^{\frac{2}{3}} + b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a b f \left(\frac{a}{b}\right)^{\frac{1}{3}}\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^{2} b^{3}} + \frac{{\left(18 \, a h \left(\frac{a}{b}\right)^{\frac{2}{3}} + b d \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a g \left(\frac{a}{b}\right)^{\frac{1}{3}} - b c - 2 \, 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 \, a b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(9 \, a h \left(\frac{a}{b}\right)^{\frac{2}{3}} - b d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a g \left(\frac{a}{b}\right)^{\frac{1}{3}} + b c + 2 \, a f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/18*(2*(b^3*d - 4*a*b^2*g)*x^5 + (b^3*c - 7*a*b^2*f)*x^4 - 3*a^2*b*e + 9*a^3*h - 6*(a*b^2*e - 2*a^2*b*h)*x^3 - (a*b^2*d + 5*a^2*b*g)*x^2 - 2*(a*b^2*c + 2*a^2*b*f)*x)/(a*b^5*x^6 + 2*a^2*b^4*x^3 + a^3*b^3) + 1/27*sqrt(3)*(b^2*d*(a/b)^(2/3) + 5*a*b*g*(a/b)^(2/3) + b^2*c*(a/b)^(1/3) + 2*a*b*f*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b^3) + 1/54*(18*a*h*(a/b)^(2/3) + b*d*(a/b)^(1/3) + 5*a*g*(a/b)^(1/3) - b*c - 2*a*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^3*(a/b)^(2/3)) + 1/27*(9*a*h*(a/b)^(2/3) - b*d*(a/b)^(1/3) - 5*a*g*(a/b)^(1/3) + b*c + 2*a*f)*log(x + (a/b)^(1/3))/(a*b^3*(a/b)^(2/3))","A",0
423,1,308,0,3.051327," ","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=""maxima"")","-\frac{6 \, a b f x^{3} - 2 \, {\left(b^{2} e - 4 \, a b h\right)} x^{5} - {\left(b^{2} d - 7 \, a b g\right)} x^{4} + 3 \, a b c + 3 \, a^{2} f + {\left(a b e + 5 \, a^{2} h\right)} x^{2} + 2 \, {\left(a b d + 2 \, a^{2} g\right)} x}{18 \, {\left(a b^{4} x^{6} + 2 \, a^{2} b^{3} x^{3} + a^{3} b^{2}\right)}} + \frac{\sqrt{3} {\left(b e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a h \left(\frac{a}{b}\right)^{\frac{1}{3}} + b d + 2 \, 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 \, a b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(b e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a h \left(\frac{a}{b}\right)^{\frac{1}{3}} - b d - 2 \, 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 \, a b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(b e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a h \left(\frac{a}{b}\right)^{\frac{1}{3}} - b d - 2 \, a g\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/18*(6*a*b*f*x^3 - 2*(b^2*e - 4*a*b*h)*x^5 - (b^2*d - 7*a*b*g)*x^4 + 3*a*b*c + 3*a^2*f + (a*b*e + 5*a^2*h)*x^2 + 2*(a*b*d + 2*a^2*g)*x)/(a*b^4*x^6 + 2*a^2*b^3*x^3 + a^3*b^2) + 1/27*sqrt(3)*(b*e*(a/b)^(1/3) + 5*a*h*(a/b)^(1/3) + b*d + 2*a*g)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^3*(a/b)^(2/3)) + 1/54*(b*e*(a/b)^(1/3) + 5*a*h*(a/b)^(1/3) - b*d - 2*a*g)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^3*(a/b)^(2/3)) - 1/27*(b*e*(a/b)^(1/3) + 5*a*h*(a/b)^(1/3) - b*d - 2*a*g)*log(x + (a/b)^(1/3))/(a*b^3*(a/b)^(2/3))","A",0
424,1,344,0,3.067443," ","integrate(x*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{6 \, a^{2} b g x^{3} - 2 \, {\left(2 \, b^{3} c + a b^{2} f\right)} x^{5} - {\left(a b^{2} e - 7 \, a^{2} b h\right)} x^{4} + 3 \, a^{2} b d + 3 \, a^{3} g - {\left(7 \, a b^{2} c - a^{2} b f\right)} x^{2} + 2 \, {\left(a^{2} b e + 2 \, a^{3} h\right)} x}{18 \, {\left(a^{2} b^{4} x^{6} + 2 \, a^{3} b^{3} x^{3} + a^{4} b^{2}\right)}} + \frac{\sqrt{3} {\left(2 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} + a b f \left(\frac{a}{b}\right)^{\frac{1}{3}} + a b e + 2 \, a^{2} h\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^{2} b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \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}} - a b e - 2 \, a^{2} h\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^{2} b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \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}} - a b e - 2 \, a^{2} h\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{2} b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/18*(6*a^2*b*g*x^3 - 2*(2*b^3*c + a*b^2*f)*x^5 - (a*b^2*e - 7*a^2*b*h)*x^4 + 3*a^2*b*d + 3*a^3*g - (7*a*b^2*c - a^2*b*f)*x^2 + 2*(a^2*b*e + 2*a^3*h)*x)/(a^2*b^4*x^6 + 2*a^3*b^3*x^3 + a^4*b^2) + 1/27*sqrt(3)*(2*b^2*c*(a/b)^(1/3) + a*b*f*(a/b)^(1/3) + a*b*e + 2*a^2*h)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b^3*(a/b)^(2/3)) + 1/54*(2*b^2*c*(a/b)^(1/3) + a*b*f*(a/b)^(1/3) - a*b*e - 2*a^2*h)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b^3*(a/b)^(2/3)) - 1/27*(2*b^2*c*(a/b)^(1/3) + a*b*f*(a/b)^(1/3) - a*b*e - 2*a^2*h)*log(x + (a/b)^(1/3))/(a^2*b^3*(a/b)^(2/3))","A",0
425,1,327,0,3.106778," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^3,x, algorithm=""maxima"")","-\frac{6 \, a^{2} b h x^{3} - 2 \, {\left(2 \, b^{3} d + a b^{2} g\right)} x^{5} - {\left(5 \, b^{3} c + a b^{2} f\right)} x^{4} + 3 \, a^{2} b e + 3 \, a^{3} h - {\left(7 \, a b^{2} d - a^{2} b g\right)} x^{2} - 2 \, {\left(4 \, a b^{2} c - a^{2} b f\right)} x}{18 \, {\left(a^{2} b^{4} x^{6} + 2 \, a^{3} b^{3} x^{3} + a^{4} b^{2}\right)}} + \frac{\sqrt{3} {\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)} \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^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \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)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \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)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/18*(6*a^2*b*h*x^3 - 2*(2*b^3*d + a*b^2*g)*x^5 - (5*b^3*c + a*b^2*f)*x^4 + 3*a^2*b*e + 3*a^3*h - (7*a*b^2*d - a^2*b*g)*x^2 - 2*(4*a*b^2*c - a^2*b*f)*x)/(a^2*b^4*x^6 + 2*a^3*b^3*x^3 + a^4*b^2) + 1/27*sqrt(3)*(2*b*d*(a/b)^(1/3) + a*g*(a/b)^(1/3) + 5*b*c + a*f)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b^2*(a/b)^(2/3)) + 1/54*(2*b*d*(a/b)^(1/3) + a*g*(a/b)^(1/3) - 5*b*c - a*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b^2*(a/b)^(2/3)) - 1/27*(2*b*d*(a/b)^(1/3) + a*g*(a/b)^(1/3) - 5*b*c - a*f)*log(x + (a/b)^(1/3))/(a^2*b^2*(a/b)^(2/3))","A",0
426,1,368,0,3.112181," ","integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x/(b*x^3+a)^3,x, algorithm=""maxima"")","\frac{6 \, b^{2} c x^{3} + 2 \, {\left(2 \, b^{2} e + a b h\right)} x^{5} + {\left(5 \, b^{2} d + a b g\right)} x^{4} + 9 \, a b c - 3 \, a^{2} f + {\left(7 \, a b e - a^{2} h\right)} x^{2} + 2 \, {\left(4 \, a b d - a^{2} g\right)} x}{18 \, {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)}} + \frac{c \log\left(x\right)}{a^{3}} + \frac{\sqrt{3} {\left(2 \, a b e \left(\frac{a}{b}\right)^{\frac{2}{3}} + a^{2} h \left(\frac{a}{b}\right)^{\frac{2}{3}} + 5 \, a b d \left(\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} g \left(\frac{a}{b}\right)^{\frac{1}{3}}\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(18 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a b d + a^{2} 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 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(9 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} + a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a b d - a^{2} g\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/18*(6*b^2*c*x^3 + 2*(2*b^2*e + a*b*h)*x^5 + (5*b^2*d + a*b*g)*x^4 + 9*a*b*c - 3*a^2*f + (7*a*b*e - a^2*h)*x^2 + 2*(4*a*b*d - a^2*g)*x)/(a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b) + c*log(x)/a^3 + 1/27*sqrt(3)*(2*a*b*e*(a/b)^(2/3) + a^2*h*(a/b)^(2/3) + 5*a*b*d*(a/b)^(1/3) + a^2*g*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^4*b) - 1/54*(18*b^2*c*(a/b)^(2/3) - 2*a*b*e*(a/b)^(1/3) - a^2*h*(a/b)^(1/3) + 5*a*b*d + a^2*g)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*b^2*(a/b)^(2/3)) - 1/27*(9*b^2*c*(a/b)^(2/3) + 2*a*b*e*(a/b)^(1/3) + a^2*h*(a/b)^(1/3) - 5*a*b*d - a^2*g)*log(x + (a/b)^(1/3))/(a^3*b^2*(a/b)^(2/3))","A",0
427,1,400,0,3.073680," ","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=""maxima"")","\frac{6 \, a b^{2} d x^{4} - 4 \, {\left(7 \, b^{3} c - a b^{2} f\right)} x^{6} + {\left(5 \, a b^{2} e + a^{2} b h\right)} x^{5} - 18 \, a^{2} b c - 7 \, {\left(7 \, a b^{2} c - a^{2} b f\right)} x^{3} + 2 \, {\left(4 \, a^{2} b e - a^{3} h\right)} x^{2} + 3 \, {\left(3 \, a^{2} b d - a^{3} g\right)} x}{18 \, {\left(a^{3} b^{3} x^{7} + 2 \, a^{4} b^{2} x^{4} + a^{5} b x\right)}} + \frac{d \log\left(x\right)}{a^{3}} - \frac{\sqrt{3} {\left(14 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} - 5 \, a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}}\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(18 \, b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} + 14 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a b f \left(\frac{a}{b}\right)^{\frac{1}{3}} + 5 \, a b e + a^{2} h\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^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(9 \, b^{2} d \left(\frac{a}{b}\right)^{\frac{2}{3}} - 14 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a b f \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a b e - a^{2} h\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/18*(6*a*b^2*d*x^4 - 4*(7*b^3*c - a*b^2*f)*x^6 + (5*a*b^2*e + a^2*b*h)*x^5 - 18*a^2*b*c - 7*(7*a*b^2*c - a^2*b*f)*x^3 + 2*(4*a^2*b*e - a^3*h)*x^2 + 3*(3*a^2*b*d - a^3*g)*x)/(a^3*b^3*x^7 + 2*a^4*b^2*x^4 + a^5*b*x) + d*log(x)/a^3 - 1/27*sqrt(3)*(14*b^2*c*(a/b)^(2/3) - 2*a*b*f*(a/b)^(2/3) - 5*a*b*e*(a/b)^(1/3) - a^2*h*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a^4*b) - 1/54*(18*b^2*d*(a/b)^(2/3) + 14*b^2*c*(a/b)^(1/3) - 2*a*b*f*(a/b)^(1/3) + 5*a*b*e + a^2*h)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*b^2*(a/b)^(2/3)) - 1/27*(9*b^2*d*(a/b)^(2/3) - 14*b^2*c*(a/b)^(1/3) + 2*a*b*f*(a/b)^(1/3) - 5*a*b*e - a^2*h)*log(x + (a/b)^(1/3))/(a^3*b^2*(a/b)^(2/3))","A",0
428,1,390,0,3.101971," ","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=""maxima"")","\frac{6 \, a b^{2} e x^{5} - 4 \, {\left(7 \, b^{3} d - a b^{2} g\right)} x^{7} - 5 \, {\left(4 \, b^{3} c - a b^{2} f\right)} x^{6} - 18 \, a^{2} b d x - 7 \, {\left(7 \, a b^{2} d - a^{2} b g\right)} x^{4} - 9 \, a^{2} b c - 8 \, {\left(4 \, a b^{2} c - a^{2} b f\right)} x^{3} + 3 \, {\left(3 \, a^{2} b e - a^{3} h\right)} x^{2}}{18 \, {\left(a^{3} b^{3} x^{8} + 2 \, a^{4} b^{2} x^{5} + a^{5} b x^{2}\right)}} + \frac{e \log\left(x\right)}{a^{3}} - \frac{\sqrt{3} {\left(14 \, b d \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a g \left(\frac{a}{b}\right)^{\frac{2}{3}} + 20 \, b c \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a f \left(\frac{a}{b}\right)^{\frac{1}{3}}\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}} - \frac{{\left(18 \, b e \left(\frac{a}{b}\right)^{\frac{2}{3}} + 14 \, b d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a g \left(\frac{a}{b}\right)^{\frac{1}{3}} - 20 \, b c + 5 \, 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 \, a^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(9 \, b e \left(\frac{a}{b}\right)^{\frac{2}{3}} - 14 \, b d \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a g \left(\frac{a}{b}\right)^{\frac{1}{3}} + 20 \, b c - 5 \, a f\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{3} b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/18*(6*a*b^2*e*x^5 - 4*(7*b^3*d - a*b^2*g)*x^7 - 5*(4*b^3*c - a*b^2*f)*x^6 - 18*a^2*b*d*x - 7*(7*a*b^2*d - a^2*b*g)*x^4 - 9*a^2*b*c - 8*(4*a*b^2*c - a^2*b*f)*x^3 + 3*(3*a^2*b*e - a^3*h)*x^2)/(a^3*b^3*x^8 + 2*a^4*b^2*x^5 + a^5*b*x^2) + e*log(x)/a^3 - 1/27*sqrt(3)*(14*b*d*(a/b)^(2/3) - 2*a*g*(a/b)^(2/3) + 20*b*c*(a/b)^(1/3) - 5*a*f*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^4 - 1/54*(18*b*e*(a/b)^(2/3) + 14*b*d*(a/b)^(1/3) - 2*a*g*(a/b)^(1/3) - 20*b*c + 5*a*f)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^3*b*(a/b)^(2/3)) - 1/27*(9*b*e*(a/b)^(2/3) - 14*b*d*(a/b)^(1/3) + 2*a*g*(a/b)^(1/3) + 20*b*c - 5*a*f)*log(x + (a/b)^(1/3))/(a^3*b*(a/b)^(2/3))","A",0
429,1,444,0,3.088995," ","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=""maxima"")","-\frac{4 \, {\left(7 \, b^{2} e - a b h\right)} x^{8} + 5 \, {\left(4 \, b^{2} d - a b g\right)} x^{7} + 6 \, {\left(3 \, b^{2} c - a b f\right)} x^{6} + 7 \, {\left(7 \, a b e - a^{2} h\right)} x^{5} + 18 \, a^{2} e x^{2} + 8 \, {\left(4 \, a b d - a^{2} g\right)} x^{4} + 9 \, a^{2} d x + 9 \, {\left(3 \, a b c - a^{2} f\right)} x^{3} + 6 \, a^{2} c}{18 \, {\left(a^{3} b^{2} x^{9} + 2 \, a^{4} b x^{6} + a^{5} x^{3}\right)}} - \frac{{\left(3 \, b c - a f\right)} \log\left(x\right)}{a^{4}} - \frac{\sqrt{3} {\left(14 \, a b e \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a^{2} h \left(\frac{a}{b}\right)^{\frac{2}{3}} + 20 \, a b d \left(\frac{a}{b}\right)^{\frac{1}{3}} - 5 \, a^{2} g \left(\frac{a}{b}\right)^{\frac{1}{3}}\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^{5}} + \frac{{\left(54 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 18 \, a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} - 14 \, a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}} + 20 \, a b d - 5 \, a^{2} 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 \, a^{4} b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(27 \, b^{2} c \left(\frac{a}{b}\right)^{\frac{2}{3}} - 9 \, a b f \left(\frac{a}{b}\right)^{\frac{2}{3}} + 14 \, a b e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a^{2} h \left(\frac{a}{b}\right)^{\frac{1}{3}} - 20 \, a b d + 5 \, a^{2} g\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \, a^{4} b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"-1/18*(4*(7*b^2*e - a*b*h)*x^8 + 5*(4*b^2*d - a*b*g)*x^7 + 6*(3*b^2*c - a*b*f)*x^6 + 7*(7*a*b*e - a^2*h)*x^5 + 18*a^2*e*x^2 + 8*(4*a*b*d - a^2*g)*x^4 + 9*a^2*d*x + 9*(3*a*b*c - a^2*f)*x^3 + 6*a^2*c)/(a^3*b^2*x^9 + 2*a^4*b*x^6 + a^5*x^3) - (3*b*c - a*f)*log(x)/a^4 - 1/27*sqrt(3)*(14*a*b*e*(a/b)^(2/3) - 2*a^2*h*(a/b)^(2/3) + 20*a*b*d*(a/b)^(1/3) - 5*a^2*g*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/a^5 + 1/54*(54*b^2*c*(a/b)^(2/3) - 18*a*b*f*(a/b)^(2/3) - 14*a*b*e*(a/b)^(1/3) + 2*a^2*h*(a/b)^(1/3) + 20*a*b*d - 5*a^2*g)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a^4*b*(a/b)^(2/3)) + 1/27*(27*b^2*c*(a/b)^(2/3) - 9*a*b*f*(a/b)^(2/3) + 14*a*b*e*(a/b)^(1/3) - 2*a^2*h*(a/b)^(1/3) - 20*a*b*d + 5*a^2*g)*log(x + (a/b)^(1/3))/(a^4*b*(a/b)^(2/3))","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=""maxima"")","\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=""maxima"")","\frac{2 \, \sqrt{b x^{3} + a} c}{3 \, b} + \int \frac{e x^{4} + d x^{3}}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"2/3*sqrt(b*x^3 + a)*c/b + integrate((e*x^4 + d*x^3)/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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\frac{2}{3} \, c {\left(\frac{\sqrt{b x^{3} + a}}{b^{2}} + \frac{a}{\sqrt{b x^{3} + a} b^{2}}\right)} + \int \frac{{\left(e x^{7} + d x^{6}\right)} \sqrt{b x^{3} + a}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}\,{d x}"," ",0,"2/3*c*(sqrt(b*x^3 + a)/b^2 + a/(sqrt(b*x^3 + a)*b^2)) + integrate((e*x^7 + d*x^6)*sqrt(b*x^3 + a)/(b^2*x^6 + 2*a*b*x^3 + a^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=""maxima"")","\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=""maxima"")","\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=""maxima"")","-\frac{2 \, c}{3 \, \sqrt{b x^{3} + a} b} + \int \frac{{\left(e x^{4} + d x^{3}\right)} \sqrt{b x^{3} + a}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}\,{d x}"," ",0,"-2/3*c/(sqrt(b*x^3 + a)*b) + integrate((e*x^4 + d*x^3)*sqrt(b*x^3 + a)/(b^2*x^6 + 2*a*b*x^3 + a^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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\frac{2 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}} c}{9 \, b} + \int {\left(g x^{6} + f x^{5} + e x^{4} + d x^{3}\right)} \sqrt{b x^{3} + a}\,{d x}"," ",0,"2/9*(b*x^3 + a)^(3/2)*c/b + integrate((g*x^6 + f*x^5 + e*x^4 + d*x^3)*sqrt(b*x^3 + a), 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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","-\frac{1}{24} \, {\left(\frac{b^{2} \log\left(\frac{\sqrt{b x^{3} + a} - \sqrt{a}}{\sqrt{b x^{3} + a} + \sqrt{a}}\right)}{a^{\frac{3}{2}}} + \frac{2 \, {\left({\left(b x^{3} + a\right)}^{\frac{3}{2}} b^{2} + \sqrt{b x^{3} + a} a b^{2}\right)}}{{\left(b x^{3} + a\right)}^{2} a - 2 \, {\left(b x^{3} + a\right)} a^{2} + a^{3}}\right)} c + \int \frac{\sqrt{b x^{3} + a} {\left(g x^{3} + f x^{2} + e x + d\right)}}{x^{6}}\,{d x}"," ",0,"-1/24*(b^2*log((sqrt(b*x^3 + a) - sqrt(a))/(sqrt(b*x^3 + a) + sqrt(a)))/a^(3/2) + 2*((b*x^3 + a)^(3/2)*b^2 + sqrt(b*x^3 + a)*a*b^2)/((b*x^3 + a)^2*a - 2*(b*x^3 + a)*a^2 + a^3))*c + integrate(sqrt(b*x^3 + a)*(g*x^3 + f*x^2 + e*x + d)/x^6, 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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\frac{2 \, {\left(b x^{3} + a\right)}^{\frac{5}{2}} c}{15 \, b} + \int {\left(b g x^{9} + b f x^{8} + b e x^{7} + a f x^{5} + {\left(b d + a g\right)} x^{6} + a e x^{4} + a d x^{3}\right)} \sqrt{b x^{3} + a}\,{d x}"," ",0,"2/15*(b*x^3 + a)^(5/2)*c/b + integrate((b*g*x^9 + b*f*x^8 + b*e*x^7 + a*f*x^5 + (b*d + a*g)*x^6 + a*e*x^4 + a*d*x^3)*sqrt(b*x^3 + a), 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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\frac{1}{24} \, {\left(\frac{3 \, b^{2} \log\left(\frac{\sqrt{b x^{3} + a} - \sqrt{a}}{\sqrt{b x^{3} + a} + \sqrt{a}}\right)}{\sqrt{a}} - \frac{2 \, {\left(5 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}} b^{2} - 3 \, \sqrt{b x^{3} + a} a b^{2}\right)}}{{\left(b x^{3} + a\right)}^{2} - 2 \, {\left(b x^{3} + a\right)} a + a^{2}}\right)} c + \int \frac{{\left(b g x^{6} + b f x^{5} + b e x^{4} + a f x^{2} + {\left(b d + a g\right)} x^{3} + a e x + a d\right)} \sqrt{b x^{3} + a}}{x^{6}}\,{d x}"," ",0,"1/24*(3*b^2*log((sqrt(b*x^3 + a) - sqrt(a))/(sqrt(b*x^3 + a) + sqrt(a)))/sqrt(a) - 2*(5*(b*x^3 + a)^(3/2)*b^2 - 3*sqrt(b*x^3 + a)*a*b^2)/((b*x^3 + a)^2 - 2*(b*x^3 + a)*a + a^2))*c + integrate((b*g*x^6 + b*f*x^5 + b*e*x^4 + a*f*x^2 + (b*d + a*g)*x^3 + a*e*x + a*d)*sqrt(b*x^3 + a)/x^6, 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=""maxima"")","\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=""maxima"")","\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=""maxima"")","-\frac{1}{144} \, {\left(\frac{3 \, b^{3} \log\left(\frac{\sqrt{b x^{3} + a} - \sqrt{a}}{\sqrt{b x^{3} + a} + \sqrt{a}}\right)}{a^{\frac{3}{2}}} + \frac{2 \, {\left(3 \, {\left(b x^{3} + a\right)}^{\frac{5}{2}} b^{3} + 8 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}} a b^{3} - 3 \, \sqrt{b x^{3} + a} a^{2} b^{3}\right)}}{{\left(b x^{3} + a\right)}^{3} a - 3 \, {\left(b x^{3} + a\right)}^{2} a^{2} + 3 \, {\left(b x^{3} + a\right)} a^{3} - a^{4}}\right)} c + \int \frac{{\left(b g x^{6} + b f x^{5} + b e x^{4} + a f x^{2} + {\left(b d + a g\right)} x^{3} + a e x + a d\right)} \sqrt{b x^{3} + a}}{x^{9}}\,{d x}"," ",0,"-1/144*(3*b^3*log((sqrt(b*x^3 + a) - sqrt(a))/(sqrt(b*x^3 + a) + sqrt(a)))/a^(3/2) + 2*(3*(b*x^3 + a)^(5/2)*b^3 + 8*(b*x^3 + a)^(3/2)*a*b^3 - 3*sqrt(b*x^3 + a)*a^2*b^3)/((b*x^3 + a)^3*a - 3*(b*x^3 + a)^2*a^2 + 3*(b*x^3 + a)*a^3 - a^4))*c + integrate((b*g*x^6 + b*f*x^5 + b*e*x^4 + a*f*x^2 + (b*d + a*g)*x^3 + a*e*x + a*d)*sqrt(b*x^3 + a)/x^9, 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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\frac{{\left(b x^{3} + a\right)}^{p + 1} c}{3 \, b {\left(p + 1\right)}} + \int {\left(e x^{4} + d x^{3}\right)} {\left(b x^{3} + a\right)}^{p}\,{d x}"," ",0,"1/3*(b*x^3 + a)^(p + 1)*c/(b*(p + 1)) + integrate((e*x^4 + d*x^3)*(b*x^3 + a)^p, x)","F",0
477,1,54,0,1.319000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a),x, algorithm=""maxima"")","\frac{1}{8} \, b f x^{8} + \frac{1}{7} \, b e x^{7} + \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 e x^{3} + \frac{1}{2} \, a d x^{2} + a c x"," ",0,"1/8*b*f*x^8 + 1/7*b*e*x^7 + 1/6*b*d*x^6 + 1/5*b*c*x^5 + 1/4*a*f*x^4 + 1/3*a*e*x^3 + 1/2*a*d*x^2 + a*c*x","A",0
478,1,57,0,1.333633," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a),x, algorithm=""maxima"")","\frac{1}{11} \, b f x^{11} + \frac{1}{10} \, b e x^{10} + \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 e x^{6} + \frac{1}{5} \, a d x^{5} + \frac{1}{4} \, a c x^{4}"," ",0,"1/11*b*f*x^11 + 1/10*b*e*x^10 + 1/9*b*d*x^9 + 1/8*b*c*x^8 + 1/7*a*f*x^7 + 1/6*a*e*x^6 + 1/5*a*d*x^5 + 1/4*a*c*x^4","A",0
479,1,102,0,1.356225," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^2,x, algorithm=""maxima"")","\frac{1}{12} \, b^{2} f x^{12} + \frac{1}{11} \, b^{2} e x^{11} + \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 e x^{7} + \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} e x^{3} + \frac{1}{2} \, a^{2} d x^{2} + a^{2} c x"," ",0,"1/12*b^2*f*x^12 + 1/11*b^2*e*x^11 + 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*e*x^7 + 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*e*x^3 + 1/2*a^2*d*x^2 + a^2*c*x","A",0
480,1,105,0,1.329170," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^2,x, algorithm=""maxima"")","\frac{1}{15} \, b^{2} f x^{15} + \frac{1}{14} \, b^{2} e x^{14} + \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 e x^{10} + \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} e x^{6} + \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*e*x^14 + 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*e*x^10 + 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*e*x^6 + 1/5*a^2*d*x^5 + 1/4*a^2*c*x^4","A",0
481,1,150,0,1.369406," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^3,x, algorithm=""maxima"")","\frac{1}{16} \, b^{3} f x^{16} + \frac{1}{15} \, b^{3} e x^{15} + \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} e x^{11} + \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 e x^{7} + \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} e x^{3} + \frac{1}{2} \, a^{3} d x^{2} + a^{3} c x"," ",0,"1/16*b^3*f*x^16 + 1/15*b^3*e*x^15 + 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*e*x^11 + 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*e*x^7 + 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*e*x^3 + 1/2*a^3*d*x^2 + a^3*c*x","A",0
482,1,153,0,1.382032," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^3,x, algorithm=""maxima"")","\frac{1}{19} \, b^{3} f x^{19} + \frac{1}{18} \, b^{3} e x^{18} + \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} e x^{14} + \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 e x^{10} + \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} e x^{6} + \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*e*x^18 + 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*e*x^14 + 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*e*x^10 + 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*e*x^6 + 1/5*a^3*d*x^5 + 1/4*a^3*c*x^4","A",0
483,1,198,0,1.329910," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^4,x, algorithm=""maxima"")","\frac{1}{20} \, b^{4} f x^{20} + \frac{1}{19} \, b^{4} e x^{19} + \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} e x^{15} + \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} e x^{11} + \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 e x^{7} + \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} e x^{3} + \frac{1}{2} \, a^{4} d x^{2} + a^{4} c x"," ",0,"1/20*b^4*f*x^20 + 1/19*b^4*e*x^19 + 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*e*x^15 + 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*e*x^11 + 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*e*x^7 + 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*e*x^3 + 1/2*a^4*d*x^2 + a^4*c*x","A",0
484,1,201,0,1.370719," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^4,x, algorithm=""maxima"")","\frac{1}{23} \, b^{4} f x^{23} + \frac{1}{22} \, b^{4} e x^{22} + \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} e x^{18} + \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} e x^{14} + \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 e x^{10} + \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} e x^{6} + \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*e*x^22 + 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*e*x^18 + 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*e*x^14 + 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*e*x^10 + 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*e*x^6 + 1/5*a^4*d*x^5 + 1/4*a^4*c*x^4","A",0
485,1,174,0,3.031160," ","integrate((f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x, algorithm=""maxima"")","\frac{{\left(\sqrt{b} c - \sqrt{a} e\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{2 \, \sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{{\left(\sqrt{b} d - \sqrt{a} f\right)} \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{4 \, \sqrt{a} b} - \frac{{\left(\sqrt{b} d + \sqrt{a} f\right)} \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{4 \, \sqrt{a} b} - \frac{{\left(\sqrt{b} c + \sqrt{a} e\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{4 \, \sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}"," ",0,"1/2*(sqrt(b)*c - sqrt(a)*e)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 1/4*(sqrt(b)*d - sqrt(a)*f)*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*b) - 1/4*(sqrt(b)*d + sqrt(a)*f)*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*b) - 1/4*(sqrt(b)*c + sqrt(a)*e)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b))","A",0
486,1,208,0,2.976474," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x, algorithm=""maxima"")","-\frac{2 \, f x^{3} + 3 \, e x^{2} + 6 \, d x}{6 \, b} + \frac{\frac{2 \, {\left(a \sqrt{b} d - a^{\frac{3}{2}} f\right)} \arctan\left(\frac{\sqrt{b} x}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{{\left(\sqrt{a} b c - a \sqrt{b} e\right)} \log\left(\sqrt{b} x^{2} + \sqrt{a}\right)}{\sqrt{a} b} - \frac{{\left(\sqrt{a} b c + a \sqrt{b} e\right)} \log\left(\sqrt{b} x^{2} - \sqrt{a}\right)}{\sqrt{a} b} - \frac{{\left(a \sqrt{b} d + a^{\frac{3}{2}} f\right)} \log\left(\frac{\sqrt{b} x - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} x + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{4 \, b}"," ",0,"-1/6*(2*f*x^3 + 3*e*x^2 + 6*d*x)/b + 1/4*(2*(a*sqrt(b)*d - a^(3/2)*f)*arctan(sqrt(b)*x/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - (sqrt(a)*b*c - a*sqrt(b)*e)*log(sqrt(b)*x^2 + sqrt(a))/(sqrt(a)*b) - (sqrt(a)*b*c + a*sqrt(b)*e)*log(sqrt(b)*x^2 - sqrt(a))/(sqrt(a)*b) - (a*sqrt(b)*d + a^(3/2)*f)*log((sqrt(b)*x - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*x + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/b","A",0
487,1,277,0,3.029804," ","integrate((f*x^3+e*x^2+d*x+c)/(b*x^4+a),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} f + b c - \sqrt{a} \sqrt{b} e\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{8 \, a^{\frac{3}{4}} b^{\frac{5}{4}}} + \frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} f - b c + \sqrt{a} \sqrt{b} e\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{8 \, a^{\frac{3}{4}} b^{\frac{5}{4}}} + \frac{{\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{5}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{3}{4}} e - 2 \, \sqrt{a} b d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{4 \, a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{5}{4}}} + \frac{{\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{5}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{3}{4}} e + 2 \, \sqrt{a} b d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{4 \, a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{5}{4}}}"," ",0,"1/8*sqrt(2)*(sqrt(2)*a^(3/4)*b^(1/4)*f + b*c - sqrt(a)*sqrt(b)*e)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(5/4)) + 1/8*sqrt(2)*(sqrt(2)*a^(3/4)*b^(1/4)*f - b*c + sqrt(a)*sqrt(b)*e)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(5/4)) + 1/4*(sqrt(2)*a^(1/4)*b^(5/4)*c + sqrt(2)*a^(3/4)*b^(3/4)*e - 2*sqrt(a)*b*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(5/4)) + 1/4*(sqrt(2)*a^(1/4)*b^(5/4)*c + sqrt(2)*a^(3/4)*b^(3/4)*e + 2*sqrt(a)*b*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(5/4))","A",0
488,1,305,0,3.014578," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a),x, algorithm=""maxima"")","\frac{2 \, f x^{3} + 3 \, e x^{2} + 6 \, d x}{6 \, b} + \frac{\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} c - a b d + a^{\frac{3}{2}} \sqrt{b} f\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{5}{4}}} + \frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{3}{4}} b^{\frac{5}{4}} c + a b d - a^{\frac{3}{2}} \sqrt{b} f\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{5}{4}}} - \frac{2 \, {\left(\sqrt{2} a^{\frac{5}{4}} b^{\frac{5}{4}} d + \sqrt{2} a^{\frac{7}{4}} b^{\frac{3}{4}} f - 2 \, a^{\frac{3}{2}} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{5}{4}}} - \frac{2 \, {\left(\sqrt{2} a^{\frac{5}{4}} b^{\frac{5}{4}} d + \sqrt{2} a^{\frac{7}{4}} b^{\frac{3}{4}} f + 2 \, a^{\frac{3}{2}} b e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{5}{4}}}}{8 \, b}"," ",0,"1/6*(2*f*x^3 + 3*e*x^2 + 6*d*x)/b + 1/8*(sqrt(2)*(sqrt(2)*a^(3/4)*b^(5/4)*c - a*b*d + a^(3/2)*sqrt(b)*f)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(5/4)) + sqrt(2)*(sqrt(2)*a^(3/4)*b^(5/4)*c + a*b*d - a^(3/2)*sqrt(b)*f)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(5/4)) - 2*(sqrt(2)*a^(5/4)*b^(5/4)*d + sqrt(2)*a^(7/4)*b^(3/4)*f - 2*a^(3/2)*b*e)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(5/4)) - 2*(sqrt(2)*a^(5/4)*b^(5/4)*d + sqrt(2)*a^(7/4)*b^(3/4)*f + 2*a^(3/2)*b*e)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(5/4)))/b","A",0
489,1,305,0,3.057595," ","integrate((f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x, algorithm=""maxima"")","\frac{b e x^{3} + b d x^{2} + b c x - a f}{4 \, {\left(a b^{2} x^{4} + a^{2} b\right)}} + \frac{\frac{\sqrt{2} {\left(3 \, \sqrt{b} c - \sqrt{a} e\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(3 \, \sqrt{b} c - \sqrt{a} e\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} e - 4 \, \sqrt{a} \sqrt{b} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} c + \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} e + 4 \, \sqrt{a} \sqrt{b} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{32 \, a}"," ",0,"1/4*(b*e*x^3 + b*d*x^2 + b*c*x - a*f)/(a*b^2*x^4 + a^2*b) + 1/32*(sqrt(2)*(3*sqrt(b)*c - sqrt(a)*e)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(3*sqrt(b)*c - sqrt(a)*e)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(3*sqrt(2)*a^(1/4)*b^(3/4)*c + sqrt(2)*a^(3/4)*b^(1/4)*e - 4*sqrt(a)*sqrt(b)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(3*sqrt(2)*a^(1/4)*b^(3/4)*c + sqrt(2)*a^(3/4)*b^(1/4)*e + 4*sqrt(a)*sqrt(b)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/a","A",0
490,1,294,0,3.021802," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x, algorithm=""maxima"")","-\frac{f x^{3} + e x^{2} + d x + c}{4 \, {\left(b^{2} x^{4} + a b\right)}} + \frac{\frac{\sqrt{2} {\left(\sqrt{b} d - 3 \, \sqrt{a} f\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(\sqrt{b} d - 3 \, \sqrt{a} f\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} d + 3 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} f - 4 \, \sqrt{a} \sqrt{b} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} d + 3 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} f + 4 \, \sqrt{a} \sqrt{b} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{32 \, b}"," ",0,"-1/4*(f*x^3 + e*x^2 + d*x + c)/(b^2*x^4 + a*b) + 1/32*(sqrt(2)*(sqrt(b)*d - 3*sqrt(a)*f)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(sqrt(b)*d - 3*sqrt(a)*f)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(sqrt(2)*a^(1/4)*b^(3/4)*d + 3*sqrt(2)*a^(3/4)*b^(1/4)*f - 4*sqrt(a)*sqrt(b)*e)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(sqrt(2)*a^(1/4)*b^(3/4)*d + 3*sqrt(2)*a^(3/4)*b^(1/4)*f + 4*sqrt(a)*sqrt(b)*e)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/b","A",0
491,1,355,0,3.019428," ","integrate((f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x, algorithm=""maxima"")","\frac{5 \, b^{2} e x^{7} + 6 \, b^{2} d x^{6} + 7 \, b^{2} c x^{5} + 9 \, a b e x^{3} + 10 \, a b d x^{2} + 11 \, a b c x - 4 \, a^{2} f}{32 \, {\left(a^{2} b^{3} x^{8} + 2 \, a^{3} b^{2} x^{4} + a^{4} b\right)}} + \frac{\frac{\sqrt{2} {\left(21 \, \sqrt{b} c - 5 \, \sqrt{a} e\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(21 \, \sqrt{b} c - 5 \, \sqrt{a} e\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(21 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} c + 5 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} e - 24 \, \sqrt{a} \sqrt{b} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(21 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} c + 5 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} e + 24 \, \sqrt{a} \sqrt{b} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{256 \, a^{2}}"," ",0,"1/32*(5*b^2*e*x^7 + 6*b^2*d*x^6 + 7*b^2*c*x^5 + 9*a*b*e*x^3 + 10*a*b*d*x^2 + 11*a*b*c*x - 4*a^2*f)/(a^2*b^3*x^8 + 2*a^3*b^2*x^4 + a^4*b) + 1/256*(sqrt(2)*(21*sqrt(b)*c - 5*sqrt(a)*e)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(21*sqrt(b)*c - 5*sqrt(a)*e)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(21*sqrt(2)*a^(1/4)*b^(3/4)*c + 5*sqrt(2)*a^(3/4)*b^(1/4)*e - 24*sqrt(a)*sqrt(b)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(21*sqrt(2)*a^(1/4)*b^(3/4)*c + 5*sqrt(2)*a^(3/4)*b^(1/4)*e + 24*sqrt(a)*sqrt(b)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/a^2","A",0
492,1,343,0,3.084046," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x, algorithm=""maxima"")","\frac{3 \, b f x^{7} + 2 \, b e x^{6} + b d x^{5} - a f x^{3} - 2 \, a e x^{2} - 3 \, a d x - 4 \, a c}{32 \, {\left(a b^{3} x^{8} + 2 \, a^{2} b^{2} x^{4} + a^{3} b\right)}} + \frac{\frac{3 \, \sqrt{2} {\left(\sqrt{b} d - \sqrt{a} f\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{3 \, \sqrt{2} {\left(\sqrt{b} d - \sqrt{a} f\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} d + 3 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} f - 8 \, \sqrt{a} \sqrt{b} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} d + 3 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} f + 8 \, \sqrt{a} \sqrt{b} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{256 \, a b}"," ",0,"1/32*(3*b*f*x^7 + 2*b*e*x^6 + b*d*x^5 - a*f*x^3 - 2*a*e*x^2 - 3*a*d*x - 4*a*c)/(a*b^3*x^8 + 2*a^2*b^2*x^4 + a^3*b) + 1/256*(3*sqrt(2)*(sqrt(b)*d - sqrt(a)*f)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - 3*sqrt(2)*(sqrt(b)*d - sqrt(a)*f)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(3*sqrt(2)*a^(1/4)*b^(3/4)*d + 3*sqrt(2)*a^(3/4)*b^(1/4)*f - 8*sqrt(a)*sqrt(b)*e)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(3*sqrt(2)*a^(1/4)*b^(3/4)*d + 3*sqrt(2)*a^(3/4)*b^(1/4)*f + 8*sqrt(a)*sqrt(b)*e)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/(a*b)","A",0
493,1,402,0,3.088238," ","integrate((f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x, algorithm=""maxima"")","\frac{45 \, b^{3} e x^{11} + 60 \, b^{3} d x^{10} + 77 \, b^{3} c x^{9} + 126 \, a b^{2} e x^{7} + 160 \, a b^{2} d x^{6} + 198 \, a b^{2} c x^{5} + 113 \, a^{2} b e x^{3} + 132 \, a^{2} b d x^{2} + 153 \, a^{2} b c x - 32 \, a^{3} f}{384 \, {\left(a^{3} b^{4} x^{12} + 3 \, a^{4} b^{3} x^{8} + 3 \, a^{5} b^{2} x^{4} + a^{6} b\right)}} + \frac{\frac{\sqrt{2} {\left(77 \, \sqrt{b} c - 15 \, \sqrt{a} e\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(77 \, \sqrt{b} c - 15 \, \sqrt{a} e\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(77 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} c + 15 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} e - 80 \, \sqrt{a} \sqrt{b} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(77 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} c + 15 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} e + 80 \, \sqrt{a} \sqrt{b} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{1024 \, a^{3}}"," ",0,"1/384*(45*b^3*e*x^11 + 60*b^3*d*x^10 + 77*b^3*c*x^9 + 126*a*b^2*e*x^7 + 160*a*b^2*d*x^6 + 198*a*b^2*c*x^5 + 113*a^2*b*e*x^3 + 132*a^2*b*d*x^2 + 153*a^2*b*c*x - 32*a^3*f)/(a^3*b^4*x^12 + 3*a^4*b^3*x^8 + 3*a^5*b^2*x^4 + a^6*b) + 1/1024*(sqrt(2)*(77*sqrt(b)*c - 15*sqrt(a)*e)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(77*sqrt(b)*c - 15*sqrt(a)*e)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(77*sqrt(2)*a^(1/4)*b^(3/4)*c + 15*sqrt(2)*a^(3/4)*b^(1/4)*e - 80*sqrt(a)*sqrt(b)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(77*sqrt(2)*a^(1/4)*b^(3/4)*c + 15*sqrt(2)*a^(3/4)*b^(1/4)*e + 80*sqrt(a)*sqrt(b)*d)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/a^3","A",0
494,1,396,0,3.124630," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x, algorithm=""maxima"")","\frac{15 \, b^{2} f x^{11} + 12 \, b^{2} e x^{10} + 7 \, b^{2} d x^{9} + 42 \, a b f x^{7} + 32 \, a b e x^{6} + 18 \, a b d x^{5} - 5 \, a^{2} f x^{3} - 12 \, a^{2} e x^{2} - 21 \, a^{2} d x - 32 \, a^{2} c}{384 \, {\left(a^{2} b^{4} x^{12} + 3 \, a^{3} b^{3} x^{8} + 3 \, a^{4} b^{2} x^{4} + a^{5} b\right)}} + \frac{\frac{\sqrt{2} {\left(7 \, \sqrt{b} d - 5 \, \sqrt{a} f\right)} \log\left(\sqrt{b} x^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(7 \, \sqrt{b} d - 5 \, \sqrt{a} f\right)} \log\left(\sqrt{b} x^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{2 \, {\left(7 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} d + 5 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} f - 16 \, \sqrt{a} \sqrt{b} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}} + \frac{2 \, {\left(7 \, \sqrt{2} a^{\frac{1}{4}} b^{\frac{3}{4}} d + 5 \, \sqrt{2} a^{\frac{3}{4}} b^{\frac{1}{4}} f + 16 \, \sqrt{a} \sqrt{b} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} x - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{a^{\frac{3}{4}} \sqrt{\sqrt{a} \sqrt{b}} b^{\frac{3}{4}}}}{1024 \, a^{2} b}"," ",0,"1/384*(15*b^2*f*x^11 + 12*b^2*e*x^10 + 7*b^2*d*x^9 + 42*a*b*f*x^7 + 32*a*b*e*x^6 + 18*a*b*d*x^5 - 5*a^2*f*x^3 - 12*a^2*e*x^2 - 21*a^2*d*x - 32*a^2*c)/(a^2*b^4*x^12 + 3*a^3*b^3*x^8 + 3*a^4*b^2*x^4 + a^5*b) + 1/1024*(sqrt(2)*(7*sqrt(b)*d - 5*sqrt(a)*f)*log(sqrt(b)*x^2 + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) - sqrt(2)*(7*sqrt(b)*d - 5*sqrt(a)*f)*log(sqrt(b)*x^2 - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a))/(a^(3/4)*b^(3/4)) + 2*(7*sqrt(2)*a^(1/4)*b^(3/4)*d + 5*sqrt(2)*a^(3/4)*b^(1/4)*f - 16*sqrt(a)*sqrt(b)*e)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)) + 2*(7*sqrt(2)*a^(1/4)*b^(3/4)*d + 5*sqrt(2)*a^(3/4)*b^(1/4)*f + 16*sqrt(a)*sqrt(b)*e)*arctan(1/2*sqrt(2)*(2*sqrt(b)*x - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(a^(3/4)*sqrt(sqrt(a)*sqrt(b))*b^(3/4)))/(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=""maxima"")","\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=""maxima"")","\frac{{\left(b x^{4} + a\right)}^{\frac{3}{2}} c}{6 \, b} + \int {\left(f x^{6} + e x^{5} + d x^{4}\right)} \sqrt{b x^{4} + a}\,{d x}"," ",0,"1/6*(b*x^4 + a)^(3/2)*c/b + integrate((f*x^6 + e*x^5 + d*x^4)*sqrt(b*x^4 + a), x)","F",0
497,0,0,0,0.000000," ","integrate(x^2*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b x^{4} + a} {\left(f x^{3} + e x^{2} + d x + c\right)} x^{2}\,{d x}"," ",0,"integrate(sqrt(b*x^4 + a)*(f*x^3 + e*x^2 + d*x + c)*x^2, x)","F",0
498,0,0,0,0.000000," ","integrate(x*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2),x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(\frac{a \log\left(-\frac{\sqrt{b} - \frac{\sqrt{b x^{4} + a}}{x^{2}}}{\sqrt{b} + \frac{\sqrt{b x^{4} + a}}{x^{2}}}\right)}{\sqrt{b}} + \frac{2 \, \sqrt{b x^{4} + a} a}{{\left(b - \frac{b x^{4} + a}{x^{4}}\right)} x^{2}}\right)} c + \int \sqrt{b x^{4} + a} {\left(f x^{4} + e x^{3} + d x^{2}\right)}\,{d x}"," ",0,"-1/8*(a*log(-(sqrt(b) - sqrt(b*x^4 + a)/x^2)/(sqrt(b) + sqrt(b*x^4 + a)/x^2))/sqrt(b) + 2*sqrt(b*x^4 + a)*a/((b - (b*x^4 + a)/x^4)*x^2))*c + integrate(sqrt(b*x^4 + a)*(f*x^4 + e*x^3 + d*x^2), x)","F",0
499,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b x^{4} + a} {\left(f x^{3} + e x^{2} + d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(b*x^4 + a)*(f*x^3 + e*x^2 + d*x + c), x)","F",0
500,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{4} + a} {\left(f x^{3} + e x^{2} + d x + c\right)}}{x}\,{d x}"," ",0,"integrate(sqrt(b*x^4 + a)*(f*x^3 + e*x^2 + d*x + c)/x, x)","F",0
501,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{4} + a} {\left(f x^{3} + e x^{2} + d x + c\right)}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(b*x^4 + a)*(f*x^3 + e*x^2 + d*x + c)/x^2, x)","F",0
502,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\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
503,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\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
504,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^5,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(\frac{b \log\left(\frac{\sqrt{b x^{4} + a} - \sqrt{a}}{\sqrt{b x^{4} + a} + \sqrt{a}}\right)}{\sqrt{a}} - \frac{2 \, \sqrt{b x^{4} + a}}{x^{4}}\right)} c + \int \frac{\sqrt{b x^{4} + a} {\left(f x^{2} + e x + d\right)}}{x^{4}}\,{d x}"," ",0,"1/8*(b*log((sqrt(b*x^4 + a) - sqrt(a))/(sqrt(b*x^4 + a) + sqrt(a)))/sqrt(a) - 2*sqrt(b*x^4 + a)/x^4)*c + integrate(sqrt(b*x^4 + a)*(f*x^2 + e*x + d)/x^4, x)","F",0
505,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^6,x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{4} + a} {\left(f x^{3} + e x^{2} + d x + c\right)}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt(b*x^4 + a)*(f*x^3 + e*x^2 + d*x + c)/x^6, x)","F",0
506,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^7,x, algorithm=""maxima"")","-\frac{{\left(b x^{4} + a\right)}^{\frac{3}{2}} c}{6 \, a x^{6}} + \int \frac{\sqrt{b x^{4} + a} {\left(f x^{2} + e x + d\right)}}{x^{6}}\,{d x}"," ",0,"-1/6*(b*x^4 + a)^(3/2)*c/(a*x^6) + integrate(sqrt(b*x^4 + a)*(f*x^2 + e*x + d)/x^6, x)","F",0
507,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^8,x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{4} + a} {\left(f x^{3} + e x^{2} + d x + c\right)}}{x^{8}}\,{d x}"," ",0,"integrate(sqrt(b*x^4 + a)*(f*x^3 + e*x^2 + d*x + c)/x^8, x)","F",0
508,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^9,x, algorithm=""maxima"")","-\frac{1}{32} \, {\left(\frac{b^{2} \log\left(\frac{\sqrt{b x^{4} + a} - \sqrt{a}}{\sqrt{b x^{4} + a} + \sqrt{a}}\right)}{a^{\frac{3}{2}}} + \frac{2 \, {\left({\left(b x^{4} + a\right)}^{\frac{3}{2}} b^{2} + \sqrt{b x^{4} + a} a b^{2}\right)}}{{\left(b x^{4} + a\right)}^{2} a - 2 \, {\left(b x^{4} + a\right)} a^{2} + a^{3}}\right)} c + \int \frac{\sqrt{b x^{4} + a} {\left(f x^{2} + e x + d\right)}}{x^{8}}\,{d x}"," ",0,"-1/32*(b^2*log((sqrt(b*x^4 + a) - sqrt(a))/(sqrt(b*x^4 + a) + sqrt(a)))/a^(3/2) + 2*((b*x^4 + a)^(3/2)*b^2 + sqrt(b*x^4 + a)*a*b^2)/((b*x^4 + a)^2*a - 2*(b*x^4 + a)*a^2 + a^3))*c + integrate(sqrt(b*x^4 + a)*(f*x^2 + e*x + d)/x^8, x)","F",0
509,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^10,x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{4} + a} {\left(f x^{3} + e x^{2} + d x + c\right)}}{x^{10}}\,{d x}"," ",0,"integrate(sqrt(b*x^4 + a)*(f*x^3 + e*x^2 + d*x + c)/x^10, x)","F",0
510,0,0,0,0.000000," ","integrate(x^4*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2),x, algorithm=""maxima"")","\int {\left(b x^{4} + a\right)}^{\frac{3}{2}} {\left(f x^{3} + e x^{2} + d x + c\right)} x^{4}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/2)*(f*x^3 + e*x^2 + d*x + c)*x^4, x)","F",0
511,0,0,0,0.000000," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2),x, algorithm=""maxima"")","\frac{{\left(b x^{4} + a\right)}^{\frac{5}{2}} c}{10 \, b} + \int {\left(b f x^{10} + b e x^{9} + b d x^{8} + a f x^{6} + a e x^{5} + a d x^{4}\right)} \sqrt{b x^{4} + a}\,{d x}"," ",0,"1/10*(b*x^4 + a)^(5/2)*c/b + integrate((b*f*x^10 + b*e*x^9 + b*d*x^8 + a*f*x^6 + a*e*x^5 + a*d*x^4)*sqrt(b*x^4 + a), x)","F",0
512,0,0,0,0.000000," ","integrate(x^2*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2),x, algorithm=""maxima"")","\int {\left(b x^{4} + a\right)}^{\frac{3}{2}} {\left(f x^{3} + e x^{2} + d x + c\right)} x^{2}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/2)*(f*x^3 + e*x^2 + d*x + c)*x^2, x)","F",0
513,0,0,0,0.000000," ","integrate(x*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2),x, algorithm=""maxima"")","-\frac{1}{32} \, {\left(\frac{3 \, a^{2} \log\left(-\frac{\sqrt{b} - \frac{\sqrt{b x^{4} + a}}{x^{2}}}{\sqrt{b} + \frac{\sqrt{b x^{4} + a}}{x^{2}}}\right)}{\sqrt{b}} + \frac{2 \, {\left(\frac{3 \, \sqrt{b x^{4} + a} a^{2} b}{x^{2}} - \frac{5 \, {\left(b x^{4} + a\right)}^{\frac{3}{2}} a^{2}}{x^{6}}\right)}}{b^{2} - \frac{2 \, {\left(b x^{4} + a\right)} b}{x^{4}} + \frac{{\left(b x^{4} + a\right)}^{2}}{x^{8}}}\right)} c + \int {\left(b f x^{8} + b e x^{7} + b d x^{6} + a f x^{4} + a e x^{3} + a d x^{2}\right)} \sqrt{b x^{4} + a}\,{d x}"," ",0,"-1/32*(3*a^2*log(-(sqrt(b) - sqrt(b*x^4 + a)/x^2)/(sqrt(b) + sqrt(b*x^4 + a)/x^2))/sqrt(b) + 2*(3*sqrt(b*x^4 + a)*a^2*b/x^2 - 5*(b*x^4 + a)^(3/2)*a^2/x^6)/(b^2 - 2*(b*x^4 + a)*b/x^4 + (b*x^4 + a)^2/x^8))*c + integrate((b*f*x^8 + b*e*x^7 + b*d*x^6 + a*f*x^4 + a*e*x^3 + a*d*x^2)*sqrt(b*x^4 + a), x)","F",0
514,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2),x, algorithm=""maxima"")","\int {\left(b x^{4} + a\right)}^{\frac{3}{2}} {\left(f x^{3} + e x^{2} + d x + c\right)}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/2)*(f*x^3 + e*x^2 + d*x + c), x)","F",0
515,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x,x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{2}} {\left(f x^{3} + e x^{2} + d x + c\right)}}{x}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/2)*(f*x^3 + e*x^2 + d*x + c)/x, x)","F",0
516,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{2}} {\left(f x^{3} + e x^{2} + d x + c\right)}}{x^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/2)*(f*x^3 + e*x^2 + d*x + c)/x^2, x)","F",0
517,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{2}} {\left(f x^{3} + e x^{2} + d x + c\right)}}{x^{3}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/2)*(f*x^3 + e*x^2 + d*x + c)/x^3, x)","F",0
518,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{2}} {\left(f x^{3} + e x^{2} + d x + c\right)}}{x^{4}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/2)*(f*x^3 + e*x^2 + d*x + c)/x^4, x)","F",0
519,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^5,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(3 \, \sqrt{a} b \log\left(\frac{\sqrt{b x^{4} + a} - \sqrt{a}}{\sqrt{b x^{4} + a} + \sqrt{a}}\right) + 4 \, \sqrt{b x^{4} + a} b - \frac{2 \, \sqrt{b x^{4} + a} a}{x^{4}}\right)} c + \int \frac{{\left(b f x^{6} + b e x^{5} + b d x^{4} + a f x^{2} + a e x + a d\right)} \sqrt{b x^{4} + a}}{x^{4}}\,{d x}"," ",0,"1/8*(3*sqrt(a)*b*log((sqrt(b*x^4 + a) - sqrt(a))/(sqrt(b*x^4 + a) + sqrt(a))) + 4*sqrt(b*x^4 + a)*b - 2*sqrt(b*x^4 + a)*a/x^4)*c + integrate((b*f*x^6 + b*e*x^5 + b*d*x^4 + a*f*x^2 + a*e*x + a*d)*sqrt(b*x^4 + a)/x^4, x)","F",0
520,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^6,x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{2}} {\left(f x^{3} + e x^{2} + d x + c\right)}}{x^{6}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/2)*(f*x^3 + e*x^2 + d*x + c)/x^6, x)","F",0
521,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^7,x, algorithm=""maxima"")","-\frac{1}{12} \, {\left(3 \, b^{\frac{3}{2}} \log\left(-\frac{\sqrt{b} - \frac{\sqrt{b x^{4} + a}}{x^{2}}}{\sqrt{b} + \frac{\sqrt{b x^{4} + a}}{x^{2}}}\right) + \frac{6 \, \sqrt{b x^{4} + a} b}{x^{2}} + \frac{2 \, {\left(b x^{4} + a\right)}^{\frac{3}{2}}}{x^{6}}\right)} c + \int \frac{{\left(b f x^{6} + b e x^{5} + b d x^{4} + a f x^{2} + a e x + a d\right)} \sqrt{b x^{4} + a}}{x^{6}}\,{d x}"," ",0,"-1/12*(3*b^(3/2)*log(-(sqrt(b) - sqrt(b*x^4 + a)/x^2)/(sqrt(b) + sqrt(b*x^4 + a)/x^2)) + 6*sqrt(b*x^4 + a)*b/x^2 + 2*(b*x^4 + a)^(3/2)/x^6)*c + integrate((b*f*x^6 + b*e*x^5 + b*d*x^4 + a*f*x^2 + a*e*x + a*d)*sqrt(b*x^4 + a)/x^6, x)","F",0
522,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^8,x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{2}} {\left(f x^{3} + e x^{2} + d x + c\right)}}{x^{8}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/2)*(f*x^3 + e*x^2 + d*x + c)/x^8, x)","F",0
523,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^9,x, algorithm=""maxima"")","\frac{1}{32} \, {\left(\frac{3 \, b^{2} \log\left(\frac{\sqrt{b x^{4} + a} - \sqrt{a}}{\sqrt{b x^{4} + a} + \sqrt{a}}\right)}{\sqrt{a}} - \frac{2 \, {\left(5 \, {\left(b x^{4} + a\right)}^{\frac{3}{2}} b^{2} - 3 \, \sqrt{b x^{4} + a} a b^{2}\right)}}{{\left(b x^{4} + a\right)}^{2} - 2 \, {\left(b x^{4} + a\right)} a + a^{2}}\right)} c + \int \frac{{\left(b f x^{6} + b e x^{5} + b d x^{4} + a f x^{2} + a e x + a d\right)} \sqrt{b x^{4} + a}}{x^{8}}\,{d x}"," ",0,"1/32*(3*b^2*log((sqrt(b*x^4 + a) - sqrt(a))/(sqrt(b*x^4 + a) + sqrt(a)))/sqrt(a) - 2*(5*(b*x^4 + a)^(3/2)*b^2 - 3*sqrt(b*x^4 + a)*a*b^2)/((b*x^4 + a)^2 - 2*(b*x^4 + a)*a + a^2))*c + integrate((b*f*x^6 + b*e*x^5 + b*d*x^4 + a*f*x^2 + a*e*x + a*d)*sqrt(b*x^4 + a)/x^8, x)","F",0
524,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^10,x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{2}} {\left(f x^{3} + e x^{2} + d x + c\right)}}{x^{10}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/2)*(f*x^3 + e*x^2 + d*x + c)/x^10, x)","F",0
525,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^11,x, algorithm=""maxima"")","-\frac{{\left(b x^{4} + a\right)}^{\frac{5}{2}} c}{10 \, a x^{10}} + \int \frac{{\left(b f x^{6} + b e x^{5} + b d x^{4} + a f x^{2} + a e x + a d\right)} \sqrt{b x^{4} + a}}{x^{10}}\,{d x}"," ",0,"-1/10*(b*x^4 + a)^(5/2)*c/(a*x^10) + integrate((b*f*x^6 + b*e*x^5 + b*d*x^4 + a*f*x^2 + a*e*x + a*d)*sqrt(b*x^4 + a)/x^10, x)","F",0
526,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^12,x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{2}} {\left(f x^{3} + e x^{2} + d x + c\right)}}{x^{12}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/2)*(f*x^3 + e*x^2 + d*x + c)/x^12, x)","F",0
527,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^13,x, algorithm=""maxima"")","-\frac{1}{192} \, {\left(\frac{3 \, b^{3} \log\left(\frac{\sqrt{b x^{4} + a} - \sqrt{a}}{\sqrt{b x^{4} + a} + \sqrt{a}}\right)}{a^{\frac{3}{2}}} + \frac{2 \, {\left(3 \, {\left(b x^{4} + a\right)}^{\frac{5}{2}} b^{3} + 8 \, {\left(b x^{4} + a\right)}^{\frac{3}{2}} a b^{3} - 3 \, \sqrt{b x^{4} + a} a^{2} b^{3}\right)}}{{\left(b x^{4} + a\right)}^{3} a - 3 \, {\left(b x^{4} + a\right)}^{2} a^{2} + 3 \, {\left(b x^{4} + a\right)} a^{3} - a^{4}}\right)} c + \int \frac{{\left(b f x^{6} + b e x^{5} + b d x^{4} + a f x^{2} + a e x + a d\right)} \sqrt{b x^{4} + a}}{x^{12}}\,{d x}"," ",0,"-1/192*(3*b^3*log((sqrt(b*x^4 + a) - sqrt(a))/(sqrt(b*x^4 + a) + sqrt(a)))/a^(3/2) + 2*(3*(b*x^4 + a)^(5/2)*b^3 + 8*(b*x^4 + a)^(3/2)*a*b^3 - 3*sqrt(b*x^4 + a)*a^2*b^3)/((b*x^4 + a)^3*a - 3*(b*x^4 + a)^2*a^2 + 3*(b*x^4 + a)*a^3 - a^4))*c + integrate((b*f*x^6 + b*e*x^5 + b*d*x^4 + a*f*x^2 + a*e*x + a*d)*sqrt(b*x^4 + a)/x^12, x)","F",0
528,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^14,x, algorithm=""maxima"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{2}} {\left(f x^{3} + e x^{2} + d x + c\right)}}{x^{14}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/2)*(f*x^3 + e*x^2 + d*x + c)/x^14, x)","F",0
529,0,0,0,0.000000," ","integrate(x^4*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(f x^{3} + e x^{2} + d x + c\right)} x^{4}}{\sqrt{b x^{4} + a}}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)*x^4/sqrt(b*x^4 + a), x)","F",0
530,0,0,0,0.000000," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{4} + a} c}{2 \, b} + \int \frac{f x^{6} + e x^{5} + d x^{4}}{\sqrt{b x^{4} + a}}\,{d x}"," ",0,"1/2*sqrt(b*x^4 + a)*c/b + integrate((f*x^6 + e*x^5 + d*x^4)/sqrt(b*x^4 + a), x)","F",0
531,0,0,0,0.000000," ","integrate(x^2*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(f x^{3} + e x^{2} + d x + c\right)} x^{2}}{\sqrt{b x^{4} + a}}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)*x^2/sqrt(b*x^4 + a), x)","F",0
532,0,0,0,0.000000," ","integrate(x*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(1/2),x, algorithm=""maxima"")","-\frac{c \log\left(-\frac{\sqrt{b} - \frac{\sqrt{b x^{4} + a}}{x^{2}}}{\sqrt{b} + \frac{\sqrt{b x^{4} + a}}{x^{2}}}\right)}{4 \, \sqrt{b}} + \int \frac{f x^{4} + e x^{3} + d x^{2}}{\sqrt{b x^{4} + a}}\,{d x}"," ",0,"-1/4*c*log(-(sqrt(b) - sqrt(b*x^4 + a)/x^2)/(sqrt(b) + sqrt(b*x^4 + a)/x^2))/sqrt(b) + integrate((f*x^4 + e*x^3 + d*x^2)/sqrt(b*x^4 + a), x)","F",0
533,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(1/2),x, algorithm=""maxima"")","\int \frac{f x^{3} + e x^{2} + d x + c}{\sqrt{b x^{4} + a}}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)/sqrt(b*x^4 + a), x)","F",0
534,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)/x/(b*x^4+a)^(1/2),x, algorithm=""maxima"")","\int \frac{f x^{3} + e x^{2} + d x + c}{\sqrt{b x^{4} + a} x}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)/(sqrt(b*x^4 + a)*x), x)","F",0
535,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)/x^2/(b*x^4+a)^(1/2),x, algorithm=""maxima"")","\int \frac{f x^{3} + e x^{2} + d x + c}{\sqrt{b x^{4} + a} x^{2}}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)/(sqrt(b*x^4 + a)*x^2), x)","F",0
536,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)/x^3/(b*x^4+a)^(1/2),x, algorithm=""maxima"")","\int \frac{f x^{3} + e x^{2} + d x + c}{\sqrt{b x^{4} + a} x^{3}}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)/(sqrt(b*x^4 + a)*x^3), x)","F",0
537,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)/x^4/(b*x^4+a)^(1/2),x, algorithm=""maxima"")","\int \frac{f x^{3} + e x^{2} + d x + c}{\sqrt{b x^{4} + a} x^{4}}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)/(sqrt(b*x^4 + a)*x^4), x)","F",0
538,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)/x^5/(b*x^4+a)^(1/2),x, algorithm=""maxima"")","-\frac{1}{8} \, c {\left(\frac{2 \, \sqrt{b x^{4} + a} b}{{\left(b x^{4} + a\right)} a - a^{2}} + \frac{b \log\left(\frac{\sqrt{b x^{4} + a} - \sqrt{a}}{\sqrt{b x^{4} + a} + \sqrt{a}}\right)}{a^{\frac{3}{2}}}\right)} + \int \frac{f x^{2} + e x + d}{\sqrt{b x^{4} + a} x^{4}}\,{d x}"," ",0,"-1/8*c*(2*sqrt(b*x^4 + a)*b/((b*x^4 + a)*a - a^2) + b*log((sqrt(b*x^4 + a) - sqrt(a))/(sqrt(b*x^4 + a) + sqrt(a)))/a^(3/2)) + integrate((f*x^2 + e*x + d)/(sqrt(b*x^4 + a)*x^4), x)","F",0
539,0,0,0,0.000000," ","integrate((f*x^3+e*x^2+d*x+c)/x^6/(b*x^4+a)^(1/2),x, algorithm=""maxima"")","\int \frac{f x^{3} + e x^{2} + d x + c}{\sqrt{b x^{4} + a} x^{6}}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)/(sqrt(b*x^4 + a)*x^6), x)","F",0
540,0,0,0,0.000000," ","integrate(x^6*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(f x^{3} + e x^{2} + d x + c\right)} x^{6}}{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)*x^6/(b*x^4 + a)^(3/2), x)","F",0
541,0,0,0,0.000000," ","integrate(x^5*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x, algorithm=""maxima"")","-\frac{1}{4} \, c {\left(\frac{2 \, x^{2}}{\sqrt{b x^{4} + a} b} + \frac{\log\left(-\frac{\sqrt{b} - \frac{\sqrt{b x^{4} + a}}{x^{2}}}{\sqrt{b} + \frac{\sqrt{b x^{4} + a}}{x^{2}}}\right)}{b^{\frac{3}{2}}}\right)} + \int \frac{f x^{8} + e x^{7} + d x^{6}}{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-1/4*c*(2*x^2/(sqrt(b*x^4 + a)*b) + log(-(sqrt(b) - sqrt(b*x^4 + a)/x^2)/(sqrt(b) + sqrt(b*x^4 + a)/x^2))/b^(3/2)) + integrate((f*x^8 + e*x^7 + d*x^6)/(b*x^4 + a)^(3/2), x)","F",0
542,0,0,0,0.000000," ","integrate(x^4*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(f x^{3} + e x^{2} + d x + c\right)} x^{4}}{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)*x^4/(b*x^4 + a)^(3/2), x)","F",0
543,0,0,0,0.000000," ","integrate(x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x, algorithm=""maxima"")","-\frac{c}{2 \, \sqrt{b x^{4} + a} b} + \int \frac{f x^{6} + e x^{5} + d x^{4}}{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-1/2*c/(sqrt(b*x^4 + a)*b) + integrate((f*x^6 + e*x^5 + d*x^4)/(b*x^4 + a)^(3/2), x)","F",0
544,0,0,0,0.000000," ","integrate(x^2*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(f x^{3} + e x^{2} + d x + c\right)} x^{2}}{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((f*x^3 + e*x^2 + d*x + c)*x^2/(b*x^4 + a)^(3/2), x)","F",0
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=""maxima"")","\frac{c x^{2}}{2 \, \sqrt{b x^{4} + a} a} + \int \frac{f x^{4} + e x^{3} + d x^{2}}{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"1/2*c*x^2/(sqrt(b*x^4 + a)*a) + integrate((f*x^4 + e*x^3 + d*x^2)/(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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\frac{{\left(b x^{4} + a\right)}^{p + 1} c}{4 \, b {\left(p + 1\right)}} + \int {\left(f x^{6} + e x^{5} + d x^{4}\right)} {\left(b x^{4} + a\right)}^{p}\,{d x}"," ",0,"1/4*(b*x^4 + a)^(p + 1)*c/(b*(p + 1)) + integrate((f*x^6 + e*x^5 + d*x^4)*(b*x^4 + a)^p, x)","F",0
554,1,6,0,1.301780," ","integrate((x^4+x^3+x^2+x+1)/(-x^5+1),x, algorithm=""maxima"")","-\log\left(x - 1\right)"," ",0,"-log(x - 1)","A",0
555,1,8,0,1.334311," ","integrate((-32*x^5+48*x^4-72*x^3+108*x^2-162*x+243)/(-64*x^6+729),x, algorithm=""maxima"")","\frac{1}{2} \, \log\left(2 \, x + 3\right)"," ",0,"1/2*log(2*x + 3)","A",0
556,1,8,0,1.392265," ","integrate((32*x^5+48*x^4+72*x^3+108*x^2+162*x+243)/(-64*x^6+729),x, algorithm=""maxima"")","-\frac{1}{2} \, \log\left(2 \, x - 3\right)"," ",0,"-1/2*log(2*x - 3)","A",0
557,1,17,0,1.329177," ","integrate((16*x^4+36*x^2+81)/(-64*x^6+729),x, algorithm=""maxima"")","\frac{1}{12} \, \log\left(2 \, x + 3\right) - \frac{1}{12} \, \log\left(2 \, x - 3\right)"," ",0,"1/12*log(2*x + 3) - 1/12*log(2*x - 3)","B",0
558,1,16,0,2.928057," ","integrate((-16*x^4-24*x^3+54*x+81)/(-64*x^6+729),x, algorithm=""maxima"")","\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
559,1,38,0,2.887472," ","integrate((3-2*x)/(-64*x^6+729),x, algorithm=""maxima"")","\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(2 \, x + 3\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(2*x + 3)","A",0
560,1,38,0,2.954001," ","integrate((3+2*x)/(-64*x^6+729),x, algorithm=""maxima"")","\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(2 \, x - 3\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(2*x - 3)","A",0
561,1,46,0,2.943693," ","integrate((4*x^2-6*x+9)/(-64*x^6+729),x, algorithm=""maxima"")","\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(2 \, x + 3\right) - \frac{1}{324} \, \log\left(2 \, x - 3\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(2*x + 3) - 1/324*log(2*x - 3)","A",0
562,1,46,0,3.076255," ","integrate((4*x^2+6*x+9)/(-64*x^6+729),x, algorithm=""maxima"")","\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(2 \, x + 3\right) - \frac{1}{108} \, \log\left(2 \, x - 3\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(2*x + 3) - 1/108*log(2*x - 3)","A",0
563,1,38,0,2.926304," ","integrate((-8*x^3+27)/(-64*x^6+729),x, algorithm=""maxima"")","\frac{1}{54} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(4 \, x - 3\right)}\right) - \frac{1}{108} \, \log\left(4 \, x^{2} - 6 \, x + 9\right) + \frac{1}{54} \, \log\left(2 \, x + 3\right)"," ",0,"1/54*sqrt(3)*arctan(1/9*sqrt(3)*(4*x - 3)) - 1/108*log(4*x^2 - 6*x + 9) + 1/54*log(2*x + 3)","A",0
564,1,38,0,2.947596," ","integrate((8*x^3+24*x^2+36*x+27)/(-64*x^6+729),x, algorithm=""maxima"")","\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(2 \, x - 3\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(2*x - 3)","A",0
565,1,84,0,2.984496," ","integrate((-32*x^5+48*x^4-72*x^3+108*x^2-162*x+243)/(-64*x^6+729)^2,x, algorithm=""maxima"")","\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(2 \, x + 3\right) - \frac{1}{17496} \, \log\left(2 \, x - 3\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(2*x + 3) - 1/17496*log(2*x - 3)","A",0
566,1,84,0,2.942982," ","integrate((32*x^5+48*x^4+72*x^3+108*x^2+162*x+243)/(-64*x^6+729)^2,x, algorithm=""maxima"")","\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(2 \, x + 3\right) - \frac{5}{17496} \, \log\left(2 \, x - 3\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(2*x + 3) - 5/17496*log(2*x - 3)","A",0
567,1,61,0,3.063257," ","integrate((16*x^4+36*x^2+81)/(-64*x^6+729)^2,x, algorithm=""maxima"")","\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(2 \, x + 3\right) - \frac{1}{17496} \, \log\left(2 \, x - 3\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(2*x + 3) - 1/17496*log(2*x - 3)","A",0
568,1,74,0,2.966145," ","integrate((-16*x^4-24*x^3+54*x+81)/(-64*x^6+729)^2,x, algorithm=""maxima"")","\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(2 \, x + 3\right) - \frac{1}{26244} \, \log\left(2 \, x - 3\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(2*x + 3) - 1/26244*log(2*x - 3)","A",0
569,1,105,0,2.907830," ","integrate((3-2*x)/(-64*x^6+729)^2,x, algorithm=""maxima"")","\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(32 \, x^{5} + 48 \, x^{4} + 72 \, x^{3} + 108 \, x^{2} + 162 \, x + 243\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(2 \, x + 3\right) - \frac{1}{4251528} \, \log\left(2 \, x - 3\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/(32*x^5 + 48*x^4 + 72*x^3 + 108*x^2 + 162*x + 243) + 1/8503056*log(4*x^2 + 6*x + 9) - 1/944784*log(4*x^2 - 6*x + 9) + 1/472392*log(2*x + 3) - 1/4251528*log(2*x - 3)","A",0
570,1,105,0,2.896415," ","integrate((3+2*x)/(-64*x^6+729)^2,x, algorithm=""maxima"")","\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(32 \, x^{5} - 48 \, x^{4} + 72 \, x^{3} - 108 \, x^{2} + 162 \, x - 243\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(2 \, x + 3\right) - \frac{1}{472392} \, \log\left(2 \, x - 3\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/(32*x^5 - 48*x^4 + 72*x^3 - 108*x^2 + 162*x - 243) + 1/944784*log(4*x^2 + 6*x + 9) - 1/8503056*log(4*x^2 - 6*x + 9) + 1/4251528*log(2*x + 3) - 1/472392*log(2*x - 3)","A",0
571,1,95,0,2.983284," ","integrate((4*x^2-6*x+9)/(-64*x^6+729)^2,x, algorithm=""maxima"")","\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(16 \, x^{4} + 24 \, x^{3} - 54 \, x - 81\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(2 \, x + 3\right) - \frac{1}{354294} \, \log\left(2 \, x - 3\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/(16*x^4 + 24*x^3 - 54*x - 81) - 5/2834352*log(4*x^2 + 6*x + 9) - 1/944784*log(4*x^2 - 6*x + 9) + 1/118098*log(2*x + 3) - 1/354294*log(2*x - 3)","A",0
572,1,95,0,2.884317," ","integrate((4*x^2+6*x+9)/(-64*x^6+729)^2,x, algorithm=""maxima"")","\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(16 \, x^{4} - 24 \, x^{3} + 54 \, x - 81\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(2 \, x + 3\right) - \frac{1}{118098} \, \log\left(2 \, x - 3\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/(16*x^4 - 24*x^3 + 54*x - 81) + 1/944784*log(4*x^2 + 6*x + 9) + 5/2834352*log(4*x^2 - 6*x + 9) + 1/354294*log(2*x + 3) - 1/118098*log(2*x - 3)","A",0
573,1,87,0,2.936234," ","integrate((-8*x^3+27)/(-64*x^6+729)^2,x, algorithm=""maxima"")","\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(2 \, x + 3\right) - \frac{1}{157464} \, \log\left(2 \, x - 3\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(2*x + 3) - 1/157464*log(2*x - 3)","A",0
574,1,95,0,2.986041," ","integrate((8*x^3+24*x^2+36*x+27)/(-64*x^6+729)^2,x, algorithm=""maxima"")","-\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(8 \, x^{3} - 24 \, x^{2} + 36 \, x - 27\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(2 \, x + 3\right) - \frac{7}{157464} \, \log\left(2 \, x - 3\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/(8*x^3 - 24*x^2 + 36*x - 27) + 1/314928*log(4*x^2 + 6*x + 9) + 17/944784*log(4*x^2 - 6*x + 9) + 1/472392*log(2*x + 3) - 7/157464*log(2*x - 3)","A",0
575,1,75,0,2.987743," ","integrate(x*(-2*x^3+27)/(-64*x^6+729),x, algorithm=""maxima"")","-\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(4 \, x^{2} + 6 \, x + 9\right) + \frac{5}{576} \, \log\left(4 \, x^{2} - 6 \, x + 9\right) - \frac{5}{288} \, \log\left(2 \, x + 3\right) - \frac{1}{96} \, \log\left(2 \, x - 3\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(4*x^2 + 6*x + 9) + 5/576*log(4*x^2 - 6*x + 9) - 5/288*log(2*x + 3) - 1/96*log(2*x - 3)","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=""maxima"")","{\left(b^{3} c^{m} d - a b^{2} c^{m} e + a^{2} b c^{m} f - a^{3} c^{m} g\right)} \int \frac{x^{m}}{b^{4} x^{n} + a b^{3}}\,{d x} + \frac{{\left(m^{2} + m {\left(n + 2\right)} + n + 1\right)} b^{2} c^{m} g x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} + {\left({\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} b^{2} c^{m} e - {\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} a b c^{m} f + {\left(m^{2} + m {\left(3 \, n + 2\right)} + 2 \, n^{2} + 3 \, n + 1\right)} a^{2} c^{m} g\right)} x x^{m} + {\left({\left(m^{2} + 2 \, m {\left(n + 1\right)} + 2 \, n + 1\right)} b^{2} c^{m} f - {\left(m^{2} + 2 \, m {\left(n + 1\right)} + 2 \, n + 1\right)} a b c^{m} g\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{{\left(m^{3} + 3 \, m^{2} {\left(n + 1\right)} + {\left(2 \, n^{2} + 6 \, n + 3\right)} m + 2 \, n^{2} + 3 \, n + 1\right)} b^{3}}"," ",0,"(b^3*c^m*d - a*b^2*c^m*e + a^2*b*c^m*f - a^3*c^m*g)*integrate(x^m/(b^4*x^n + a*b^3), x) + ((m^2 + m*(n + 2) + n + 1)*b^2*c^m*g*x*e^(m*log(x) + 2*n*log(x)) + ((m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*b^2*c^m*e - (m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*a*b*c^m*f + (m^2 + m*(3*n + 2) + 2*n^2 + 3*n + 1)*a^2*c^m*g)*x*x^m + ((m^2 + 2*m*(n + 1) + 2*n + 1)*b^2*c^m*f - (m^2 + 2*m*(n + 1) + 2*n + 1)*a*b*c^m*g)*x*e^(m*log(x) + n*log(x)))/((m^3 + 3*m^2*(n + 1) + (2*n^2 + 6*n + 3)*m + 2*n^2 + 3*n + 1)*b^3)","F",0
577,1,118,0,1.355826," ","integrate((c+d*x^(-1+n))*(a+b*x^n)^3,x, algorithm=""maxima"")","a^{3} c x + \frac{b^{3} d x^{4 \, n}}{4 \, n} + \frac{a b^{2} d x^{3 \, n}}{n} + \frac{3 \, a^{2} b d x^{2 \, n}}{2 \, n} + \frac{b^{3} c x^{3 \, n + 1}}{3 \, n + 1} + \frac{3 \, a b^{2} c x^{2 \, n + 1}}{2 \, n + 1} + \frac{3 \, a^{2} b c x^{n + 1}}{n + 1} + \frac{a^{3} d x^{n}}{n}"," ",0,"a^3*c*x + 1/4*b^3*d*x^(4*n)/n + a*b^2*d*x^(3*n)/n + 3/2*a^2*b*d*x^(2*n)/n + b^3*c*x^(3*n + 1)/(3*n + 1) + 3*a*b^2*c*x^(2*n + 1)/(2*n + 1) + 3*a^2*b*c*x^(n + 1)/(n + 1) + a^3*d*x^n/n","A",0
578,1,78,0,1.397258," ","integrate((c+d*x^(-1+n))*(a+b*x^n)^2,x, algorithm=""maxima"")","a^{2} c x + \frac{b^{2} d x^{3 \, n}}{3 \, n} + \frac{a b d x^{2 \, n}}{n} + \frac{b^{2} c x^{2 \, n + 1}}{2 \, n + 1} + \frac{2 \, a b c x^{n + 1}}{n + 1} + \frac{a^{2} d x^{n}}{n}"," ",0,"a^2*c*x + 1/3*b^2*d*x^(3*n)/n + a*b*d*x^(2*n)/n + b^2*c*x^(2*n + 1)/(2*n + 1) + 2*a*b*c*x^(n + 1)/(n + 1) + a^2*d*x^n/n","A",0
579,1,39,0,1.292725," ","integrate((c+d*x^(-1+n))*(a+b*x^n),x, algorithm=""maxima"")","a c x + \frac{b d x^{2 \, n}}{2 \, n} + \frac{b c x^{n + 1}}{n + 1} + \frac{a d x^{n}}{n}"," ",0,"a*c*x + 1/2*b*d*x^(2*n)/n + b*c*x^(n + 1)/(n + 1) + a*d*x^n/n","A",0
580,1,12,0,1.319316," ","integrate(c+d*x^(-1+n),x, algorithm=""maxima"")","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=""maxima"")","\frac{d \log\left(x\right)}{b} + \int \frac{b c x - a d}{b^{2} x x^{n} + a b x}\,{d x}"," ",0,"d*log(x)/b + integrate((b*c*x - a*d)/(b^2*x*x^n + a*b*x), x)","F",0
582,0,0,0,0.000000," ","integrate((c+d*x^(-1+n))/(a+b*x^n)^2,x, algorithm=""maxima"")","c {\left(n - 1\right)} \int \frac{1}{a b n x^{n} + a^{2} n}\,{d x} + \frac{b c x - a d}{a b^{2} n x^{n} + a^{2} b n}"," ",0,"c*(n - 1)*integrate(1/(a*b*n*x^n + a^2*n), x) + (b*c*x - a*d)/(a*b^2*n*x^n + a^2*b*n)","F",0
583,0,0,0,0.000000," ","integrate((c+d*x^(-1+n))/(a+b*x^n)^3,x, algorithm=""maxima"")","{\left(2 \, n^{2} - 3 \, n + 1\right)} c \int \frac{1}{2 \, {\left(a^{2} b n^{2} x^{n} + a^{3} n^{2}\right)}}\,{d x} + \frac{b^{2} c {\left(2 \, n - 1\right)} x x^{n} + a b c {\left(3 \, n - 1\right)} x - a^{2} d n}{2 \, {\left(a^{2} b^{3} n^{2} x^{2 \, n} + 2 \, a^{3} b^{2} n^{2} x^{n} + a^{4} b n^{2}\right)}}"," ",0,"(2*n^2 - 3*n + 1)*c*integrate(1/2/(a^2*b*n^2*x^n + a^3*n^2), x) + 1/2*(b^2*c*(2*n - 1)*x*x^n + a*b*c*(3*n - 1)*x - a^2*d*n)/(a^2*b^3*n^2*x^(2*n) + 2*a^3*b^2*n^2*x^n + a^4*b*n^2)","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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
587,0,0,0,0.000000," ","integrate((c*x)^m*(a+b*x^n)^p*(d+e*x^n+f*x^(2*n)+g*x^(3*n)),x, algorithm=""maxima"")","\int {\left(g x^{3 \, n} + f x^{2 \, n} + e x^{n} + d\right)} {\left(b x^{n} + a\right)}^{p} \left(c x\right)^{m}\,{d x}"," ",0,"integrate((g*x^(3*n) + f*x^(2*n) + e*x^n + d)*(b*x^n + a)^p*(c*x)^m, x)","F",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=""maxima"")","\frac{{\left(b d - a f\right)} x x^{\frac{1}{2} \, n} + {\left(b c - a e\right)} x}{a b^{2} n x^{n} + a^{2} b n} + \int \frac{2 \, b c {\left(n - 1\right)} + 2 \, a e + {\left(a f {\left(n + 2\right)} + b d {\left(n - 2\right)}\right)} x^{\frac{1}{2} \, n}}{2 \, {\left(a b^{2} n x^{n} + a^{2} b n\right)}}\,{d x}"," ",0,"((b*d - a*f)*x*x^(1/2*n) + (b*c - a*e)*x)/(a*b^2*n*x^n + a^2*b*n) + integrate(1/2*(2*b*c*(n - 1) + 2*a*e + (a*f*(n + 2) + b*d*(n - 2))*x^(1/2*n))/(a*b^2*n*x^n + a^2*b*n), x)","F",0
589,1,20,0,2.125548," ","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=""maxima"")","\sqrt{b x^{2} + a} \sqrt{d x^{2} + c} x"," ",0,"sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*x","A",0
590,0,0,0,0.000000," ","integrate((x^3+1)/(-x^4+1)/(x^4+1)^(1/4),x, algorithm=""maxima"")","-\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
591,0,0,0,0.000000," ","integrate((a+b*x^n)^((-1-n)/n)*(c+d*x^n)^((-1-n)/n)*(a*c-b*d*x^(2*n)),x, algorithm=""maxima"")","-\int \frac{b d x^{2 \, n} - a c}{{\left(b x^{n} + a\right)}^{\frac{n + 1}{n}} {\left(d x^{n} + c\right)}^{\frac{n + 1}{n}}}\,{d x}"," ",0,"-integrate((b*d*x^(2*n) - a*c)/((b*x^n + a)^((n + 1)/n)*(d*x^n + c)^((n + 1)/n)), x)","F",0
592,1,77,0,3.039302," ","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=""maxima"")","-\frac{{\left(b d x^{2 \, n} + a c + {\left(b c + a d\right)} x^{n}\right)} h^{-n p - n - 1} e^{\left(-n p \log\left(x\right) + p \log\left(b x^{n} + a\right) + p \log\left(d x^{n} + c\right) - n \log\left(x\right)\right)}}{n {\left(p + 1\right)}}"," ",0,"-(b*d*x^(2*n) + a*c + (b*c + a*d)*x^n)*h^(-n*p - n - 1)*e^(-n*p*log(x) + p*log(b*x^n + a) + p*log(d*x^n + c) - n*log(x))/(n*(p + 1))","A",0
593,1,59,0,2.671621," ","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=""maxima"")","\frac{{\left(b d e x x^{2 \, n} + a c e x + {\left(b c e + a d e\right)} x x^{n}\right)} e^{\left(p \log\left(b x^{n} + a\right) + p \log\left(d x^{n} + c\right)\right)}}{a c}"," ",0,"(b*d*e*x*x^(2*n) + a*c*e*x + (b*c*e + a*d*e)*x*x^n)*e^(p*log(b*x^n + a) + p*log(d*x^n + c))/(a*c)","A",0
594,1,92,0,3.035453," ","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=""maxima"")","\frac{{\left(a c e h^{m} x x^{m} + b d e h^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} + {\left(b c e h^{m} + a d e h^{m}\right)} x e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}\right)} e^{\left(p \log\left(b x^{n} + a\right) + p \log\left(d x^{n} + c\right)\right)}}{a c {\left(m + 1\right)}}"," ",0,"(a*c*e*h^m*x*x^m + b*d*e*h^m*x*e^(m*log(x) + 2*n*log(x)) + (b*c*e*h^m + a*d*e*h^m)*x*e^(m*log(x) + n*log(x)))*e^(p*log(b*x^n + a) + p*log(d*x^n + c))/(a*c*(m + 1))","B",0
