1,1,854,0,1.304501," ","integrate((b*x+a)^3*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(45045 \, \sqrt{d x + c} A a^{3} + \frac{15015 \, {\left({\left(d x + c\right)}^{\frac{3}{2}} - 3 \, \sqrt{d x + c} c\right)} B a^{3}}{d} + \frac{45045 \, {\left({\left(d x + c\right)}^{\frac{3}{2}} - 3 \, \sqrt{d x + c} c\right)} A a^{2} b}{d} + \frac{3003 \, {\left(3 \, {\left(d x + c\right)}^{\frac{5}{2}} - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} c + 15 \, \sqrt{d x + c} c^{2}\right)} C a^{3}}{d^{2}} + \frac{9009 \, {\left(3 \, {\left(d x + c\right)}^{\frac{5}{2}} - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} c + 15 \, \sqrt{d x + c} c^{2}\right)} B a^{2} b}{d^{2}} + \frac{9009 \, {\left(3 \, {\left(d x + c\right)}^{\frac{5}{2}} - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} c + 15 \, \sqrt{d x + c} c^{2}\right)} A a b^{2}}{d^{2}} + \frac{1287 \, {\left(5 \, {\left(d x + c\right)}^{\frac{7}{2}} - 21 \, {\left(d x + c\right)}^{\frac{5}{2}} c + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{2} - 35 \, \sqrt{d x + c} c^{3}\right)} D a^{3}}{d^{3}} + \frac{3861 \, {\left(5 \, {\left(d x + c\right)}^{\frac{7}{2}} - 21 \, {\left(d x + c\right)}^{\frac{5}{2}} c + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{2} - 35 \, \sqrt{d x + c} c^{3}\right)} C a^{2} b}{d^{3}} + \frac{3861 \, {\left(5 \, {\left(d x + c\right)}^{\frac{7}{2}} - 21 \, {\left(d x + c\right)}^{\frac{5}{2}} c + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{2} - 35 \, \sqrt{d x + c} c^{3}\right)} B a b^{2}}{d^{3}} + \frac{1287 \, {\left(5 \, {\left(d x + c\right)}^{\frac{7}{2}} - 21 \, {\left(d x + c\right)}^{\frac{5}{2}} c + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{2} - 35 \, \sqrt{d x + c} c^{3}\right)} A b^{3}}{d^{3}} + \frac{429 \, {\left(35 \, {\left(d x + c\right)}^{\frac{9}{2}} - 180 \, {\left(d x + c\right)}^{\frac{7}{2}} c + 378 \, {\left(d x + c\right)}^{\frac{5}{2}} c^{2} - 420 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{3} + 315 \, \sqrt{d x + c} c^{4}\right)} D a^{2} b}{d^{4}} + \frac{429 \, {\left(35 \, {\left(d x + c\right)}^{\frac{9}{2}} - 180 \, {\left(d x + c\right)}^{\frac{7}{2}} c + 378 \, {\left(d x + c\right)}^{\frac{5}{2}} c^{2} - 420 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{3} + 315 \, \sqrt{d x + c} c^{4}\right)} C a b^{2}}{d^{4}} + \frac{143 \, {\left(35 \, {\left(d x + c\right)}^{\frac{9}{2}} - 180 \, {\left(d x + c\right)}^{\frac{7}{2}} c + 378 \, {\left(d x + c\right)}^{\frac{5}{2}} c^{2} - 420 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{3} + 315 \, \sqrt{d x + c} c^{4}\right)} B b^{3}}{d^{4}} + \frac{195 \, {\left(63 \, {\left(d x + c\right)}^{\frac{11}{2}} - 385 \, {\left(d x + c\right)}^{\frac{9}{2}} c + 990 \, {\left(d x + c\right)}^{\frac{7}{2}} c^{2} - 1386 \, {\left(d x + c\right)}^{\frac{5}{2}} c^{3} + 1155 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{4} - 693 \, \sqrt{d x + c} c^{5}\right)} D a b^{2}}{d^{5}} + \frac{65 \, {\left(63 \, {\left(d x + c\right)}^{\frac{11}{2}} - 385 \, {\left(d x + c\right)}^{\frac{9}{2}} c + 990 \, {\left(d x + c\right)}^{\frac{7}{2}} c^{2} - 1386 \, {\left(d x + c\right)}^{\frac{5}{2}} c^{3} + 1155 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{4} - 693 \, \sqrt{d x + c} c^{5}\right)} C b^{3}}{d^{5}} + \frac{15 \, {\left(231 \, {\left(d x + c\right)}^{\frac{13}{2}} - 1638 \, {\left(d x + c\right)}^{\frac{11}{2}} c + 5005 \, {\left(d x + c\right)}^{\frac{9}{2}} c^{2} - 8580 \, {\left(d x + c\right)}^{\frac{7}{2}} c^{3} + 9009 \, {\left(d x + c\right)}^{\frac{5}{2}} c^{4} - 6006 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{5} + 3003 \, \sqrt{d x + c} c^{6}\right)} D b^{3}}{d^{6}}\right)}}{45045 \, d}"," ",0,"2/45045*(45045*sqrt(d*x + c)*A*a^3 + 15015*((d*x + c)^(3/2) - 3*sqrt(d*x + c)*c)*B*a^3/d + 45045*((d*x + c)^(3/2) - 3*sqrt(d*x + c)*c)*A*a^2*b/d + 3003*(3*(d*x + c)^(5/2) - 10*(d*x + c)^(3/2)*c + 15*sqrt(d*x + c)*c^2)*C*a^3/d^2 + 9009*(3*(d*x + c)^(5/2) - 10*(d*x + c)^(3/2)*c + 15*sqrt(d*x + c)*c^2)*B*a^2*b/d^2 + 9009*(3*(d*x + c)^(5/2) - 10*(d*x + c)^(3/2)*c + 15*sqrt(d*x + c)*c^2)*A*a*b^2/d^2 + 1287*(5*(d*x + c)^(7/2) - 21*(d*x + c)^(5/2)*c + 35*(d*x + c)^(3/2)*c^2 - 35*sqrt(d*x + c)*c^3)*D*a^3/d^3 + 3861*(5*(d*x + c)^(7/2) - 21*(d*x + c)^(5/2)*c + 35*(d*x + c)^(3/2)*c^2 - 35*sqrt(d*x + c)*c^3)*C*a^2*b/d^3 + 3861*(5*(d*x + c)^(7/2) - 21*(d*x + c)^(5/2)*c + 35*(d*x + c)^(3/2)*c^2 - 35*sqrt(d*x + c)*c^3)*B*a*b^2/d^3 + 1287*(5*(d*x + c)^(7/2) - 21*(d*x + c)^(5/2)*c + 35*(d*x + c)^(3/2)*c^2 - 35*sqrt(d*x + c)*c^3)*A*b^3/d^3 + 429*(35*(d*x + c)^(9/2) - 180*(d*x + c)^(7/2)*c + 378*(d*x + c)^(5/2)*c^2 - 420*(d*x + c)^(3/2)*c^3 + 315*sqrt(d*x + c)*c^4)*D*a^2*b/d^4 + 429*(35*(d*x + c)^(9/2) - 180*(d*x + c)^(7/2)*c + 378*(d*x + c)^(5/2)*c^2 - 420*(d*x + c)^(3/2)*c^3 + 315*sqrt(d*x + c)*c^4)*C*a*b^2/d^4 + 143*(35*(d*x + c)^(9/2) - 180*(d*x + c)^(7/2)*c + 378*(d*x + c)^(5/2)*c^2 - 420*(d*x + c)^(3/2)*c^3 + 315*sqrt(d*x + c)*c^4)*B*b^3/d^4 + 195*(63*(d*x + c)^(11/2) - 385*(d*x + c)^(9/2)*c + 990*(d*x + c)^(7/2)*c^2 - 1386*(d*x + c)^(5/2)*c^3 + 1155*(d*x + c)^(3/2)*c^4 - 693*sqrt(d*x + c)*c^5)*D*a*b^2/d^5 + 65*(63*(d*x + c)^(11/2) - 385*(d*x + c)^(9/2)*c + 990*(d*x + c)^(7/2)*c^2 - 1386*(d*x + c)^(5/2)*c^3 + 1155*(d*x + c)^(3/2)*c^4 - 693*sqrt(d*x + c)*c^5)*C*b^3/d^5 + 15*(231*(d*x + c)^(13/2) - 1638*(d*x + c)^(11/2)*c + 5005*(d*x + c)^(9/2)*c^2 - 8580*(d*x + c)^(7/2)*c^3 + 9009*(d*x + c)^(5/2)*c^4 - 6006*(d*x + c)^(3/2)*c^5 + 3003*sqrt(d*x + c)*c^6)*D*b^3/d^6)/d","B",0
2,1,558,0,1.281296," ","integrate((b*x+a)^2*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(3465 \, \sqrt{d x + c} A a^{2} + \frac{1155 \, {\left({\left(d x + c\right)}^{\frac{3}{2}} - 3 \, \sqrt{d x + c} c\right)} B a^{2}}{d} + \frac{2310 \, {\left({\left(d x + c\right)}^{\frac{3}{2}} - 3 \, \sqrt{d x + c} c\right)} A a b}{d} + \frac{231 \, {\left(3 \, {\left(d x + c\right)}^{\frac{5}{2}} - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} c + 15 \, \sqrt{d x + c} c^{2}\right)} C a^{2}}{d^{2}} + \frac{462 \, {\left(3 \, {\left(d x + c\right)}^{\frac{5}{2}} - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} c + 15 \, \sqrt{d x + c} c^{2}\right)} B a b}{d^{2}} + \frac{231 \, {\left(3 \, {\left(d x + c\right)}^{\frac{5}{2}} - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} c + 15 \, \sqrt{d x + c} c^{2}\right)} A b^{2}}{d^{2}} + \frac{99 \, {\left(5 \, {\left(d x + c\right)}^{\frac{7}{2}} - 21 \, {\left(d x + c\right)}^{\frac{5}{2}} c + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{2} - 35 \, \sqrt{d x + c} c^{3}\right)} D a^{2}}{d^{3}} + \frac{198 \, {\left(5 \, {\left(d x + c\right)}^{\frac{7}{2}} - 21 \, {\left(d x + c\right)}^{\frac{5}{2}} c + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{2} - 35 \, \sqrt{d x + c} c^{3}\right)} C a b}{d^{3}} + \frac{99 \, {\left(5 \, {\left(d x + c\right)}^{\frac{7}{2}} - 21 \, {\left(d x + c\right)}^{\frac{5}{2}} c + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{2} - 35 \, \sqrt{d x + c} c^{3}\right)} B b^{2}}{d^{3}} + \frac{22 \, {\left(35 \, {\left(d x + c\right)}^{\frac{9}{2}} - 180 \, {\left(d x + c\right)}^{\frac{7}{2}} c + 378 \, {\left(d x + c\right)}^{\frac{5}{2}} c^{2} - 420 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{3} + 315 \, \sqrt{d x + c} c^{4}\right)} D a b}{d^{4}} + \frac{11 \, {\left(35 \, {\left(d x + c\right)}^{\frac{9}{2}} - 180 \, {\left(d x + c\right)}^{\frac{7}{2}} c + 378 \, {\left(d x + c\right)}^{\frac{5}{2}} c^{2} - 420 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{3} + 315 \, \sqrt{d x + c} c^{4}\right)} C b^{2}}{d^{4}} + \frac{5 \, {\left(63 \, {\left(d x + c\right)}^{\frac{11}{2}} - 385 \, {\left(d x + c\right)}^{\frac{9}{2}} c + 990 \, {\left(d x + c\right)}^{\frac{7}{2}} c^{2} - 1386 \, {\left(d x + c\right)}^{\frac{5}{2}} c^{3} + 1155 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{4} - 693 \, \sqrt{d x + c} c^{5}\right)} D b^{2}}{d^{5}}\right)}}{3465 \, d}"," ",0,"2/3465*(3465*sqrt(d*x + c)*A*a^2 + 1155*((d*x + c)^(3/2) - 3*sqrt(d*x + c)*c)*B*a^2/d + 2310*((d*x + c)^(3/2) - 3*sqrt(d*x + c)*c)*A*a*b/d + 231*(3*(d*x + c)^(5/2) - 10*(d*x + c)^(3/2)*c + 15*sqrt(d*x + c)*c^2)*C*a^2/d^2 + 462*(3*(d*x + c)^(5/2) - 10*(d*x + c)^(3/2)*c + 15*sqrt(d*x + c)*c^2)*B*a*b/d^2 + 231*(3*(d*x + c)^(5/2) - 10*(d*x + c)^(3/2)*c + 15*sqrt(d*x + c)*c^2)*A*b^2/d^2 + 99*(5*(d*x + c)^(7/2) - 21*(d*x + c)^(5/2)*c + 35*(d*x + c)^(3/2)*c^2 - 35*sqrt(d*x + c)*c^3)*D*a^2/d^3 + 198*(5*(d*x + c)^(7/2) - 21*(d*x + c)^(5/2)*c + 35*(d*x + c)^(3/2)*c^2 - 35*sqrt(d*x + c)*c^3)*C*a*b/d^3 + 99*(5*(d*x + c)^(7/2) - 21*(d*x + c)^(5/2)*c + 35*(d*x + c)^(3/2)*c^2 - 35*sqrt(d*x + c)*c^3)*B*b^2/d^3 + 22*(35*(d*x + c)^(9/2) - 180*(d*x + c)^(7/2)*c + 378*(d*x + c)^(5/2)*c^2 - 420*(d*x + c)^(3/2)*c^3 + 315*sqrt(d*x + c)*c^4)*D*a*b/d^4 + 11*(35*(d*x + c)^(9/2) - 180*(d*x + c)^(7/2)*c + 378*(d*x + c)^(5/2)*c^2 - 420*(d*x + c)^(3/2)*c^3 + 315*sqrt(d*x + c)*c^4)*C*b^2/d^4 + 5*(63*(d*x + c)^(11/2) - 385*(d*x + c)^(9/2)*c + 990*(d*x + c)^(7/2)*c^2 - 1386*(d*x + c)^(5/2)*c^3 + 1155*(d*x + c)^(3/2)*c^4 - 693*sqrt(d*x + c)*c^5)*D*b^2/d^5)/d","A",0
3,1,309,0,1.247317," ","integrate((b*x+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(315 \, \sqrt{d x + c} A a + \frac{105 \, {\left({\left(d x + c\right)}^{\frac{3}{2}} - 3 \, \sqrt{d x + c} c\right)} B a}{d} + \frac{105 \, {\left({\left(d x + c\right)}^{\frac{3}{2}} - 3 \, \sqrt{d x + c} c\right)} A b}{d} + \frac{21 \, {\left(3 \, {\left(d x + c\right)}^{\frac{5}{2}} - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} c + 15 \, \sqrt{d x + c} c^{2}\right)} C a}{d^{2}} + \frac{21 \, {\left(3 \, {\left(d x + c\right)}^{\frac{5}{2}} - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} c + 15 \, \sqrt{d x + c} c^{2}\right)} B b}{d^{2}} + \frac{9 \, {\left(5 \, {\left(d x + c\right)}^{\frac{7}{2}} - 21 \, {\left(d x + c\right)}^{\frac{5}{2}} c + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{2} - 35 \, \sqrt{d x + c} c^{3}\right)} D a}{d^{3}} + \frac{9 \, {\left(5 \, {\left(d x + c\right)}^{\frac{7}{2}} - 21 \, {\left(d x + c\right)}^{\frac{5}{2}} c + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{2} - 35 \, \sqrt{d x + c} c^{3}\right)} C b}{d^{3}} + \frac{{\left(35 \, {\left(d x + c\right)}^{\frac{9}{2}} - 180 \, {\left(d x + c\right)}^{\frac{7}{2}} c + 378 \, {\left(d x + c\right)}^{\frac{5}{2}} c^{2} - 420 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{3} + 315 \, \sqrt{d x + c} c^{4}\right)} D b}{d^{4}}\right)}}{315 \, d}"," ",0,"2/315*(315*sqrt(d*x + c)*A*a + 105*((d*x + c)^(3/2) - 3*sqrt(d*x + c)*c)*B*a/d + 105*((d*x + c)^(3/2) - 3*sqrt(d*x + c)*c)*A*b/d + 21*(3*(d*x + c)^(5/2) - 10*(d*x + c)^(3/2)*c + 15*sqrt(d*x + c)*c^2)*C*a/d^2 + 21*(3*(d*x + c)^(5/2) - 10*(d*x + c)^(3/2)*c + 15*sqrt(d*x + c)*c^2)*B*b/d^2 + 9*(5*(d*x + c)^(7/2) - 21*(d*x + c)^(5/2)*c + 35*(d*x + c)^(3/2)*c^2 - 35*sqrt(d*x + c)*c^3)*D*a/d^3 + 9*(5*(d*x + c)^(7/2) - 21*(d*x + c)^(5/2)*c + 35*(d*x + c)^(3/2)*c^2 - 35*sqrt(d*x + c)*c^3)*C*b/d^3 + (35*(d*x + c)^(9/2) - 180*(d*x + c)^(7/2)*c + 378*(d*x + c)^(5/2)*c^2 - 420*(d*x + c)^(3/2)*c^3 + 315*sqrt(d*x + c)*c^4)*D*b/d^4)/d","A",0
4,1,128,0,1.208505," ","integrate((D*x^3+C*x^2+B*x+A)/(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(105 \, \sqrt{d x + c} A + \frac{35 \, {\left({\left(d x + c\right)}^{\frac{3}{2}} - 3 \, \sqrt{d x + c} c\right)} B}{d} + \frac{7 \, {\left(3 \, {\left(d x + c\right)}^{\frac{5}{2}} - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} c + 15 \, \sqrt{d x + c} c^{2}\right)} C}{d^{2}} + \frac{3 \, {\left(5 \, {\left(d x + c\right)}^{\frac{7}{2}} - 21 \, {\left(d x + c\right)}^{\frac{5}{2}} c + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{2} - 35 \, \sqrt{d x + c} c^{3}\right)} D}{d^{3}}\right)}}{105 \, d}"," ",0,"2/105*(105*sqrt(d*x + c)*A + 35*((d*x + c)^(3/2) - 3*sqrt(d*x + c)*c)*B/d + 7*(3*(d*x + c)^(5/2) - 10*(d*x + c)^(3/2)*c + 15*sqrt(d*x + c)*c^2)*C/d^2 + 3*(5*(d*x + c)^(7/2) - 21*(d*x + c)^(5/2)*c + 35*(d*x + c)^(3/2)*c^2 - 35*sqrt(d*x + c)*c^3)*D/d^3)/d","A",0
5,1,248,0,1.260566," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)/(d*x+c)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(D a^{3} - C a^{2} b + B a b^{2} - A b^{3}\right)} \arctan\left(\frac{\sqrt{d x + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} b^{3}} + \frac{2 \, {\left(3 \, {\left(d x + c\right)}^{\frac{5}{2}} D b^{4} d^{12} - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} D b^{4} c d^{12} + 15 \, \sqrt{d x + c} D b^{4} c^{2} d^{12} - 5 \, {\left(d x + c\right)}^{\frac{3}{2}} D a b^{3} d^{13} + 5 \, {\left(d x + c\right)}^{\frac{3}{2}} C b^{4} d^{13} + 15 \, \sqrt{d x + c} D a b^{3} c d^{13} - 15 \, \sqrt{d x + c} C b^{4} c d^{13} + 15 \, \sqrt{d x + c} D a^{2} b^{2} d^{14} - 15 \, \sqrt{d x + c} C a b^{3} d^{14} + 15 \, \sqrt{d x + c} B b^{4} d^{14}\right)}}{15 \, b^{5} d^{15}}"," ",0,"-2*(D*a^3 - C*a^2*b + B*a*b^2 - A*b^3)*arctan(sqrt(d*x + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*b^3) + 2/15*(3*(d*x + c)^(5/2)*D*b^4*d^12 - 10*(d*x + c)^(3/2)*D*b^4*c*d^12 + 15*sqrt(d*x + c)*D*b^4*c^2*d^12 - 5*(d*x + c)^(3/2)*D*a*b^3*d^13 + 5*(d*x + c)^(3/2)*C*b^4*d^13 + 15*sqrt(d*x + c)*D*a*b^3*c*d^13 - 15*sqrt(d*x + c)*C*b^4*c*d^13 + 15*sqrt(d*x + c)*D*a^2*b^2*d^14 - 15*sqrt(d*x + c)*C*a*b^3*d^14 + 15*sqrt(d*x + c)*B*b^4*d^14)/(b^5*d^15)","A",0
6,1,271,0,1.320592," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^2/(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{{\left(6 \, D a^{2} b c - 4 \, C a b^{2} c + 2 \, B b^{3} c - 5 \, D a^{3} d + 3 \, C a^{2} b d - B a b^{2} d - A b^{3} d\right)} \arctan\left(\frac{\sqrt{d x + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{{\left(b^{4} c - a b^{3} d\right)} \sqrt{-b^{2} c + a b d}} + \frac{\sqrt{d x + c} D a^{3} d - \sqrt{d x + c} C a^{2} b d + \sqrt{d x + c} B a b^{2} d - \sqrt{d x + c} A b^{3} d}{{\left(b^{4} c - a b^{3} d\right)} {\left({\left(d x + c\right)} b - b c + a d\right)}} + \frac{2 \, {\left({\left(d x + c\right)}^{\frac{3}{2}} D b^{4} d^{4} - 3 \, \sqrt{d x + c} D b^{4} c d^{4} - 6 \, \sqrt{d x + c} D a b^{3} d^{5} + 3 \, \sqrt{d x + c} C b^{4} d^{5}\right)}}{3 \, b^{6} d^{6}}"," ",0,"(6*D*a^2*b*c - 4*C*a*b^2*c + 2*B*b^3*c - 5*D*a^3*d + 3*C*a^2*b*d - B*a*b^2*d - A*b^3*d)*arctan(sqrt(d*x + c)*b/sqrt(-b^2*c + a*b*d))/((b^4*c - a*b^3*d)*sqrt(-b^2*c + a*b*d)) + (sqrt(d*x + c)*D*a^3*d - sqrt(d*x + c)*C*a^2*b*d + sqrt(d*x + c)*B*a*b^2*d - sqrt(d*x + c)*A*b^3*d)/((b^4*c - a*b^3*d)*((d*x + c)*b - b*c + a*d)) + 2/3*((d*x + c)^(3/2)*D*b^4*d^4 - 3*sqrt(d*x + c)*D*b^4*c*d^4 - 6*sqrt(d*x + c)*D*a*b^3*d^5 + 3*sqrt(d*x + c)*C*b^4*d^5)/(b^6*d^6)","A",0
7,1,529,0,1.238829," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^3/(d*x+c)^(1/2),x, algorithm=""giac"")","-\frac{{\left(24 \, D a b^{2} c^{2} - 8 \, C b^{3} c^{2} - 36 \, D a^{2} b c d + 8 \, C a b^{2} c d + 4 \, B b^{3} c d + 15 \, D a^{3} d^{2} - 3 \, C a^{2} b d^{2} - B a b^{2} d^{2} - 3 \, A b^{3} d^{2}\right)} \arctan\left(\frac{\sqrt{d x + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{4 \, {\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} \sqrt{-b^{2} c + a b d}} - \frac{12 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{2} b^{2} c d - 8 \, {\left(d x + c\right)}^{\frac{3}{2}} C a b^{3} c d + 4 \, {\left(d x + c\right)}^{\frac{3}{2}} B b^{4} c d - 12 \, \sqrt{d x + c} D a^{2} b^{2} c^{2} d + 8 \, \sqrt{d x + c} C a b^{3} c^{2} d - 4 \, \sqrt{d x + c} B b^{4} c^{2} d - 9 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{3} b d^{2} + 5 \, {\left(d x + c\right)}^{\frac{3}{2}} C a^{2} b^{2} d^{2} - {\left(d x + c\right)}^{\frac{3}{2}} B a b^{3} d^{2} - 3 \, {\left(d x + c\right)}^{\frac{3}{2}} A b^{4} d^{2} + 19 \, \sqrt{d x + c} D a^{3} b c d^{2} - 11 \, \sqrt{d x + c} C a^{2} b^{2} c d^{2} + 3 \, \sqrt{d x + c} B a b^{3} c d^{2} + 5 \, \sqrt{d x + c} A b^{4} c d^{2} - 7 \, \sqrt{d x + c} D a^{4} d^{3} + 3 \, \sqrt{d x + c} C a^{3} b d^{3} + \sqrt{d x + c} B a^{2} b^{2} d^{3} - 5 \, \sqrt{d x + c} A a b^{3} d^{3}}{4 \, {\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} {\left({\left(d x + c\right)} b - b c + a d\right)}^{2}} + \frac{2 \, \sqrt{d x + c} D}{b^{3} d}"," ",0,"-1/4*(24*D*a*b^2*c^2 - 8*C*b^3*c^2 - 36*D*a^2*b*c*d + 8*C*a*b^2*c*d + 4*B*b^3*c*d + 15*D*a^3*d^2 - 3*C*a^2*b*d^2 - B*a*b^2*d^2 - 3*A*b^3*d^2)*arctan(sqrt(d*x + c)*b/sqrt(-b^2*c + a*b*d))/((b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*sqrt(-b^2*c + a*b*d)) - 1/4*(12*(d*x + c)^(3/2)*D*a^2*b^2*c*d - 8*(d*x + c)^(3/2)*C*a*b^3*c*d + 4*(d*x + c)^(3/2)*B*b^4*c*d - 12*sqrt(d*x + c)*D*a^2*b^2*c^2*d + 8*sqrt(d*x + c)*C*a*b^3*c^2*d - 4*sqrt(d*x + c)*B*b^4*c^2*d - 9*(d*x + c)^(3/2)*D*a^3*b*d^2 + 5*(d*x + c)^(3/2)*C*a^2*b^2*d^2 - (d*x + c)^(3/2)*B*a*b^3*d^2 - 3*(d*x + c)^(3/2)*A*b^4*d^2 + 19*sqrt(d*x + c)*D*a^3*b*c*d^2 - 11*sqrt(d*x + c)*C*a^2*b^2*c*d^2 + 3*sqrt(d*x + c)*B*a*b^3*c*d^2 + 5*sqrt(d*x + c)*A*b^4*c*d^2 - 7*sqrt(d*x + c)*D*a^4*d^3 + 3*sqrt(d*x + c)*C*a^3*b*d^3 + sqrt(d*x + c)*B*a^2*b^2*d^3 - 5*sqrt(d*x + c)*A*a*b^3*d^3)/((b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*((d*x + c)*b - b*c + a*d)^2) + 2*sqrt(d*x + c)*D/(b^3*d)","B",0
8,1,976,0,1.564330," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^4/(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{{\left(16 \, D b^{3} c^{3} - 24 \, D a b^{2} c^{2} d - 8 \, C b^{3} c^{2} d + 18 \, D a^{2} b c d^{2} + 4 \, C a b^{2} c d^{2} + 6 \, B b^{3} c d^{2} - 5 \, D a^{3} d^{3} - C a^{2} b d^{3} - B a b^{2} d^{3} - 5 \, A b^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{d x + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{8 \, {\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} \sqrt{-b^{2} c + a b d}} + \frac{72 \, {\left(d x + c\right)}^{\frac{5}{2}} D a b^{4} c^{2} d - 24 \, {\left(d x + c\right)}^{\frac{5}{2}} C b^{5} c^{2} d - 144 \, {\left(d x + c\right)}^{\frac{3}{2}} D a b^{4} c^{3} d + 48 \, {\left(d x + c\right)}^{\frac{3}{2}} C b^{5} c^{3} d + 72 \, \sqrt{d x + c} D a b^{4} c^{4} d - 24 \, \sqrt{d x + c} C b^{5} c^{4} d - 90 \, {\left(d x + c\right)}^{\frac{5}{2}} D a^{2} b^{3} c d^{2} + 12 \, {\left(d x + c\right)}^{\frac{5}{2}} C a b^{4} c d^{2} + 18 \, {\left(d x + c\right)}^{\frac{5}{2}} B b^{5} c d^{2} + 288 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{2} b^{3} c^{2} d^{2} - 48 \, {\left(d x + c\right)}^{\frac{3}{2}} C a b^{4} c^{2} d^{2} - 48 \, {\left(d x + c\right)}^{\frac{3}{2}} B b^{5} c^{2} d^{2} - 198 \, \sqrt{d x + c} D a^{2} b^{3} c^{3} d^{2} + 36 \, \sqrt{d x + c} C a b^{4} c^{3} d^{2} + 30 \, \sqrt{d x + c} B b^{5} c^{3} d^{2} + 33 \, {\left(d x + c\right)}^{\frac{5}{2}} D a^{3} b^{2} d^{3} - 3 \, {\left(d x + c\right)}^{\frac{5}{2}} C a^{2} b^{3} d^{3} - 3 \, {\left(d x + c\right)}^{\frac{5}{2}} B a b^{4} d^{3} - 15 \, {\left(d x + c\right)}^{\frac{5}{2}} A b^{5} d^{3} - 184 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{3} b^{2} c d^{3} - 8 \, {\left(d x + c\right)}^{\frac{3}{2}} C a^{2} b^{3} c d^{3} + 56 \, {\left(d x + c\right)}^{\frac{3}{2}} B a b^{4} c d^{3} + 40 \, {\left(d x + c\right)}^{\frac{3}{2}} A b^{5} c d^{3} + 195 \, \sqrt{d x + c} D a^{3} b^{2} c^{2} d^{3} + 3 \, \sqrt{d x + c} C a^{2} b^{3} c^{2} d^{3} - 57 \, \sqrt{d x + c} B a b^{4} c^{2} d^{3} - 33 \, \sqrt{d x + c} A b^{5} c^{2} d^{3} + 40 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{4} b d^{4} + 8 \, {\left(d x + c\right)}^{\frac{3}{2}} C a^{3} b^{2} d^{4} - 8 \, {\left(d x + c\right)}^{\frac{3}{2}} B a^{2} b^{3} d^{4} - 40 \, {\left(d x + c\right)}^{\frac{3}{2}} A a b^{4} d^{4} - 84 \, \sqrt{d x + c} D a^{4} b c d^{4} - 18 \, \sqrt{d x + c} C a^{3} b^{2} c d^{4} + 24 \, \sqrt{d x + c} B a^{2} b^{3} c d^{4} + 66 \, \sqrt{d x + c} A a b^{4} c d^{4} + 15 \, \sqrt{d x + c} D a^{5} d^{5} + 3 \, \sqrt{d x + c} C a^{4} b d^{5} + 3 \, \sqrt{d x + c} B a^{3} b^{2} d^{5} - 33 \, \sqrt{d x + c} A a^{2} b^{3} d^{5}}{24 \, {\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} {\left({\left(d x + c\right)} b - b c + a d\right)}^{3}}"," ",0,"1/8*(16*D*b^3*c^3 - 24*D*a*b^2*c^2*d - 8*C*b^3*c^2*d + 18*D*a^2*b*c*d^2 + 4*C*a*b^2*c*d^2 + 6*B*b^3*c*d^2 - 5*D*a^3*d^3 - C*a^2*b*d^3 - B*a*b^2*d^3 - 5*A*b^3*d^3)*arctan(sqrt(d*x + c)*b/sqrt(-b^2*c + a*b*d))/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*sqrt(-b^2*c + a*b*d)) + 1/24*(72*(d*x + c)^(5/2)*D*a*b^4*c^2*d - 24*(d*x + c)^(5/2)*C*b^5*c^2*d - 144*(d*x + c)^(3/2)*D*a*b^4*c^3*d + 48*(d*x + c)^(3/2)*C*b^5*c^3*d + 72*sqrt(d*x + c)*D*a*b^4*c^4*d - 24*sqrt(d*x + c)*C*b^5*c^4*d - 90*(d*x + c)^(5/2)*D*a^2*b^3*c*d^2 + 12*(d*x + c)^(5/2)*C*a*b^4*c*d^2 + 18*(d*x + c)^(5/2)*B*b^5*c*d^2 + 288*(d*x + c)^(3/2)*D*a^2*b^3*c^2*d^2 - 48*(d*x + c)^(3/2)*C*a*b^4*c^2*d^2 - 48*(d*x + c)^(3/2)*B*b^5*c^2*d^2 - 198*sqrt(d*x + c)*D*a^2*b^3*c^3*d^2 + 36*sqrt(d*x + c)*C*a*b^4*c^3*d^2 + 30*sqrt(d*x + c)*B*b^5*c^3*d^2 + 33*(d*x + c)^(5/2)*D*a^3*b^2*d^3 - 3*(d*x + c)^(5/2)*C*a^2*b^3*d^3 - 3*(d*x + c)^(5/2)*B*a*b^4*d^3 - 15*(d*x + c)^(5/2)*A*b^5*d^3 - 184*(d*x + c)^(3/2)*D*a^3*b^2*c*d^3 - 8*(d*x + c)^(3/2)*C*a^2*b^3*c*d^3 + 56*(d*x + c)^(3/2)*B*a*b^4*c*d^3 + 40*(d*x + c)^(3/2)*A*b^5*c*d^3 + 195*sqrt(d*x + c)*D*a^3*b^2*c^2*d^3 + 3*sqrt(d*x + c)*C*a^2*b^3*c^2*d^3 - 57*sqrt(d*x + c)*B*a*b^4*c^2*d^3 - 33*sqrt(d*x + c)*A*b^5*c^2*d^3 + 40*(d*x + c)^(3/2)*D*a^4*b*d^4 + 8*(d*x + c)^(3/2)*C*a^3*b^2*d^4 - 8*(d*x + c)^(3/2)*B*a^2*b^3*d^4 - 40*(d*x + c)^(3/2)*A*a*b^4*d^4 - 84*sqrt(d*x + c)*D*a^4*b*c*d^4 - 18*sqrt(d*x + c)*C*a^3*b^2*c*d^4 + 24*sqrt(d*x + c)*B*a^2*b^3*c*d^4 + 66*sqrt(d*x + c)*A*a*b^4*c*d^4 + 15*sqrt(d*x + c)*D*a^5*d^5 + 3*sqrt(d*x + c)*C*a^4*b*d^5 + 3*sqrt(d*x + c)*B*a^3*b^2*d^5 - 33*sqrt(d*x + c)*A*a^2*b^3*d^5)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*((d*x + c)*b - b*c + a*d)^3)","B",0
9,1,1512,0,1.653956," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^5/(d*x+c)^(1/2),x, algorithm=""giac"")","-\frac{{\left(64 \, D b^{3} c^{3} d - 48 \, D a b^{2} c^{2} d^{2} - 48 \, C b^{3} c^{2} d^{2} + 24 \, D a^{2} b c d^{3} + 16 \, C a b^{2} c d^{3} + 40 \, B b^{3} c d^{3} - 5 \, D a^{3} d^{4} - 3 \, C a^{2} b d^{4} - 5 \, B a b^{2} d^{4} - 35 \, A b^{3} d^{4}\right)} \arctan\left(\frac{\sqrt{d x + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{64 \, {\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} \sqrt{-b^{2} c + a b d}} - \frac{192 \, {\left(d x + c\right)}^{\frac{7}{2}} D b^{6} c^{3} d - 576 \, {\left(d x + c\right)}^{\frac{5}{2}} D b^{6} c^{4} d + 576 \, {\left(d x + c\right)}^{\frac{3}{2}} D b^{6} c^{5} d - 192 \, \sqrt{d x + c} D b^{6} c^{6} d - 144 \, {\left(d x + c\right)}^{\frac{7}{2}} D a b^{5} c^{2} d^{2} - 144 \, {\left(d x + c\right)}^{\frac{7}{2}} C b^{6} c^{2} d^{2} + 720 \, {\left(d x + c\right)}^{\frac{5}{2}} D a b^{5} c^{3} d^{2} + 528 \, {\left(d x + c\right)}^{\frac{5}{2}} C b^{6} c^{3} d^{2} - 1008 \, {\left(d x + c\right)}^{\frac{3}{2}} D a b^{5} c^{4} d^{2} - 624 \, {\left(d x + c\right)}^{\frac{3}{2}} C b^{6} c^{4} d^{2} + 432 \, \sqrt{d x + c} D a b^{5} c^{5} d^{2} + 240 \, \sqrt{d x + c} C b^{6} c^{5} d^{2} + 72 \, {\left(d x + c\right)}^{\frac{7}{2}} D a^{2} b^{4} c d^{3} + 48 \, {\left(d x + c\right)}^{\frac{7}{2}} C a b^{5} c d^{3} + 120 \, {\left(d x + c\right)}^{\frac{7}{2}} B b^{6} c d^{3} - 24 \, {\left(d x + c\right)}^{\frac{5}{2}} D a^{2} b^{4} c^{2} d^{3} - 704 \, {\left(d x + c\right)}^{\frac{5}{2}} C a b^{5} c^{2} d^{3} - 440 \, {\left(d x + c\right)}^{\frac{5}{2}} B b^{6} c^{2} d^{3} + 24 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{2} b^{4} c^{3} d^{3} + 1328 \, {\left(d x + c\right)}^{\frac{3}{2}} C a b^{5} c^{3} d^{3} + 584 \, {\left(d x + c\right)}^{\frac{3}{2}} B b^{6} c^{3} d^{3} - 72 \, \sqrt{d x + c} D a^{2} b^{4} c^{4} d^{3} - 672 \, \sqrt{d x + c} C a b^{5} c^{4} d^{3} - 264 \, \sqrt{d x + c} B b^{6} c^{4} d^{3} - 15 \, {\left(d x + c\right)}^{\frac{7}{2}} D a^{3} b^{3} d^{4} - 9 \, {\left(d x + c\right)}^{\frac{7}{2}} C a^{2} b^{4} d^{4} - 15 \, {\left(d x + c\right)}^{\frac{7}{2}} B a b^{5} d^{4} - 105 \, {\left(d x + c\right)}^{\frac{7}{2}} A b^{6} d^{4} - 193 \, {\left(d x + c\right)}^{\frac{5}{2}} D a^{3} b^{3} c d^{4} + 209 \, {\left(d x + c\right)}^{\frac{5}{2}} C a^{2} b^{4} c d^{4} + 495 \, {\left(d x + c\right)}^{\frac{5}{2}} B a b^{5} c d^{4} + 385 \, {\left(d x + c\right)}^{\frac{5}{2}} A b^{6} c d^{4} + 727 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{3} b^{3} c^{2} d^{4} - 751 \, {\left(d x + c\right)}^{\frac{3}{2}} C a^{2} b^{4} c^{2} d^{4} - 1241 \, {\left(d x + c\right)}^{\frac{3}{2}} B a b^{5} c^{2} d^{4} - 511 \, {\left(d x + c\right)}^{\frac{3}{2}} A b^{6} c^{2} d^{4} - 471 \, \sqrt{d x + c} D a^{3} b^{3} c^{3} d^{4} + 567 \, \sqrt{d x + c} C a^{2} b^{4} c^{3} d^{4} + 777 \, \sqrt{d x + c} B a b^{5} c^{3} d^{4} + 279 \, \sqrt{d x + c} A b^{6} c^{3} d^{4} + 73 \, {\left(d x + c\right)}^{\frac{5}{2}} D a^{4} b^{2} d^{5} - 33 \, {\left(d x + c\right)}^{\frac{5}{2}} C a^{3} b^{3} d^{5} - 55 \, {\left(d x + c\right)}^{\frac{5}{2}} B a^{2} b^{4} d^{5} - 385 \, {\left(d x + c\right)}^{\frac{5}{2}} A a b^{5} d^{5} - 374 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{4} b^{2} c d^{5} + 14 \, {\left(d x + c\right)}^{\frac{3}{2}} C a^{3} b^{3} c d^{5} + 730 \, {\left(d x + c\right)}^{\frac{3}{2}} B a^{2} b^{4} c d^{5} + 1022 \, {\left(d x + c\right)}^{\frac{3}{2}} A a b^{5} c d^{5} + 405 \, \sqrt{d x + c} D a^{4} b^{2} c^{2} d^{5} - 69 \, \sqrt{d x + c} C a^{3} b^{3} c^{2} d^{5} - 747 \, \sqrt{d x + c} B a^{2} b^{4} c^{2} d^{5} - 837 \, \sqrt{d x + c} A a b^{5} c^{2} d^{5} + 55 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{5} b d^{6} + 33 \, {\left(d x + c\right)}^{\frac{3}{2}} C a^{4} b^{2} d^{6} - 73 \, {\left(d x + c\right)}^{\frac{3}{2}} B a^{3} b^{3} d^{6} - 511 \, {\left(d x + c\right)}^{\frac{3}{2}} A a^{2} b^{4} d^{6} - 117 \, \sqrt{d x + c} D a^{5} b c d^{6} - 75 \, \sqrt{d x + c} C a^{4} b^{2} c d^{6} + 219 \, \sqrt{d x + c} B a^{3} b^{3} c d^{6} + 837 \, \sqrt{d x + c} A a^{2} b^{4} c d^{6} + 15 \, \sqrt{d x + c} D a^{6} d^{7} + 9 \, \sqrt{d x + c} C a^{5} b d^{7} + 15 \, \sqrt{d x + c} B a^{4} b^{2} d^{7} - 279 \, \sqrt{d x + c} A a^{3} b^{3} d^{7}}{192 \, {\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} {\left({\left(d x + c\right)} b - b c + a d\right)}^{4}}"," ",0,"-1/64*(64*D*b^3*c^3*d - 48*D*a*b^2*c^2*d^2 - 48*C*b^3*c^2*d^2 + 24*D*a^2*b*c*d^3 + 16*C*a*b^2*c*d^3 + 40*B*b^3*c*d^3 - 5*D*a^3*d^4 - 3*C*a^2*b*d^4 - 5*B*a*b^2*d^4 - 35*A*b^3*d^4)*arctan(sqrt(d*x + c)*b/sqrt(-b^2*c + a*b*d))/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*sqrt(-b^2*c + a*b*d)) - 1/192*(192*(d*x + c)^(7/2)*D*b^6*c^3*d - 576*(d*x + c)^(5/2)*D*b^6*c^4*d + 576*(d*x + c)^(3/2)*D*b^6*c^5*d - 192*sqrt(d*x + c)*D*b^6*c^6*d - 144*(d*x + c)^(7/2)*D*a*b^5*c^2*d^2 - 144*(d*x + c)^(7/2)*C*b^6*c^2*d^2 + 720*(d*x + c)^(5/2)*D*a*b^5*c^3*d^2 + 528*(d*x + c)^(5/2)*C*b^6*c^3*d^2 - 1008*(d*x + c)^(3/2)*D*a*b^5*c^4*d^2 - 624*(d*x + c)^(3/2)*C*b^6*c^4*d^2 + 432*sqrt(d*x + c)*D*a*b^5*c^5*d^2 + 240*sqrt(d*x + c)*C*b^6*c^5*d^2 + 72*(d*x + c)^(7/2)*D*a^2*b^4*c*d^3 + 48*(d*x + c)^(7/2)*C*a*b^5*c*d^3 + 120*(d*x + c)^(7/2)*B*b^6*c*d^3 - 24*(d*x + c)^(5/2)*D*a^2*b^4*c^2*d^3 - 704*(d*x + c)^(5/2)*C*a*b^5*c^2*d^3 - 440*(d*x + c)^(5/2)*B*b^6*c^2*d^3 + 24*(d*x + c)^(3/2)*D*a^2*b^4*c^3*d^3 + 1328*(d*x + c)^(3/2)*C*a*b^5*c^3*d^3 + 584*(d*x + c)^(3/2)*B*b^6*c^3*d^3 - 72*sqrt(d*x + c)*D*a^2*b^4*c^4*d^3 - 672*sqrt(d*x + c)*C*a*b^5*c^4*d^3 - 264*sqrt(d*x + c)*B*b^6*c^4*d^3 - 15*(d*x + c)^(7/2)*D*a^3*b^3*d^4 - 9*(d*x + c)^(7/2)*C*a^2*b^4*d^4 - 15*(d*x + c)^(7/2)*B*a*b^5*d^4 - 105*(d*x + c)^(7/2)*A*b^6*d^4 - 193*(d*x + c)^(5/2)*D*a^3*b^3*c*d^4 + 209*(d*x + c)^(5/2)*C*a^2*b^4*c*d^4 + 495*(d*x + c)^(5/2)*B*a*b^5*c*d^4 + 385*(d*x + c)^(5/2)*A*b^6*c*d^4 + 727*(d*x + c)^(3/2)*D*a^3*b^3*c^2*d^4 - 751*(d*x + c)^(3/2)*C*a^2*b^4*c^2*d^4 - 1241*(d*x + c)^(3/2)*B*a*b^5*c^2*d^4 - 511*(d*x + c)^(3/2)*A*b^6*c^2*d^4 - 471*sqrt(d*x + c)*D*a^3*b^3*c^3*d^4 + 567*sqrt(d*x + c)*C*a^2*b^4*c^3*d^4 + 777*sqrt(d*x + c)*B*a*b^5*c^3*d^4 + 279*sqrt(d*x + c)*A*b^6*c^3*d^4 + 73*(d*x + c)^(5/2)*D*a^4*b^2*d^5 - 33*(d*x + c)^(5/2)*C*a^3*b^3*d^5 - 55*(d*x + c)^(5/2)*B*a^2*b^4*d^5 - 385*(d*x + c)^(5/2)*A*a*b^5*d^5 - 374*(d*x + c)^(3/2)*D*a^4*b^2*c*d^5 + 14*(d*x + c)^(3/2)*C*a^3*b^3*c*d^5 + 730*(d*x + c)^(3/2)*B*a^2*b^4*c*d^5 + 1022*(d*x + c)^(3/2)*A*a*b^5*c*d^5 + 405*sqrt(d*x + c)*D*a^4*b^2*c^2*d^5 - 69*sqrt(d*x + c)*C*a^3*b^3*c^2*d^5 - 747*sqrt(d*x + c)*B*a^2*b^4*c^2*d^5 - 837*sqrt(d*x + c)*A*a*b^5*c^2*d^5 + 55*(d*x + c)^(3/2)*D*a^5*b*d^6 + 33*(d*x + c)^(3/2)*C*a^4*b^2*d^6 - 73*(d*x + c)^(3/2)*B*a^3*b^3*d^6 - 511*(d*x + c)^(3/2)*A*a^2*b^4*d^6 - 117*sqrt(d*x + c)*D*a^5*b*c*d^6 - 75*sqrt(d*x + c)*C*a^4*b^2*c*d^6 + 219*sqrt(d*x + c)*B*a^3*b^3*c*d^6 + 837*sqrt(d*x + c)*A*a^2*b^4*c*d^6 + 15*sqrt(d*x + c)*D*a^6*d^7 + 9*sqrt(d*x + c)*C*a^5*b*d^7 + 15*sqrt(d*x + c)*B*a^4*b^2*d^7 - 279*sqrt(d*x + c)*A*a^3*b^3*d^7)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*((d*x + c)*b - b*c + a*d)^4)","B",0
10,1,1067,0,1.489371," ","integrate((b*x+a)^3*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(D b^{3} c^{6} - 3 \, D a b^{2} c^{5} d - C b^{3} c^{5} d + 3 \, D a^{2} b c^{4} d^{2} + 3 \, C a b^{2} c^{4} d^{2} + B b^{3} c^{4} d^{2} - D a^{3} c^{3} d^{3} - 3 \, C a^{2} b c^{3} d^{3} - 3 \, B a b^{2} c^{3} d^{3} - A b^{3} c^{3} d^{3} + C a^{3} c^{2} d^{4} + 3 \, B a^{2} b c^{2} d^{4} + 3 \, A a b^{2} c^{2} d^{4} - B a^{3} c d^{5} - 3 \, A a^{2} b c d^{5} + A a^{3} d^{6}\right)}}{\sqrt{d x + c} d^{7}} + \frac{2 \, {\left(315 \, {\left(d x + c\right)}^{\frac{11}{2}} D b^{3} d^{70} - 2310 \, {\left(d x + c\right)}^{\frac{9}{2}} D b^{3} c d^{70} + 7425 \, {\left(d x + c\right)}^{\frac{7}{2}} D b^{3} c^{2} d^{70} - 13860 \, {\left(d x + c\right)}^{\frac{5}{2}} D b^{3} c^{3} d^{70} + 17325 \, {\left(d x + c\right)}^{\frac{3}{2}} D b^{3} c^{4} d^{70} - 20790 \, \sqrt{d x + c} D b^{3} c^{5} d^{70} + 1155 \, {\left(d x + c\right)}^{\frac{9}{2}} D a b^{2} d^{71} + 385 \, {\left(d x + c\right)}^{\frac{9}{2}} C b^{3} d^{71} - 7425 \, {\left(d x + c\right)}^{\frac{7}{2}} D a b^{2} c d^{71} - 2475 \, {\left(d x + c\right)}^{\frac{7}{2}} C b^{3} c d^{71} + 20790 \, {\left(d x + c\right)}^{\frac{5}{2}} D a b^{2} c^{2} d^{71} + 6930 \, {\left(d x + c\right)}^{\frac{5}{2}} C b^{3} c^{2} d^{71} - 34650 \, {\left(d x + c\right)}^{\frac{3}{2}} D a b^{2} c^{3} d^{71} - 11550 \, {\left(d x + c\right)}^{\frac{3}{2}} C b^{3} c^{3} d^{71} + 51975 \, \sqrt{d x + c} D a b^{2} c^{4} d^{71} + 17325 \, \sqrt{d x + c} C b^{3} c^{4} d^{71} + 1485 \, {\left(d x + c\right)}^{\frac{7}{2}} D a^{2} b d^{72} + 1485 \, {\left(d x + c\right)}^{\frac{7}{2}} C a b^{2} d^{72} + 495 \, {\left(d x + c\right)}^{\frac{7}{2}} B b^{3} d^{72} - 8316 \, {\left(d x + c\right)}^{\frac{5}{2}} D a^{2} b c d^{72} - 8316 \, {\left(d x + c\right)}^{\frac{5}{2}} C a b^{2} c d^{72} - 2772 \, {\left(d x + c\right)}^{\frac{5}{2}} B b^{3} c d^{72} + 20790 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{2} b c^{2} d^{72} + 20790 \, {\left(d x + c\right)}^{\frac{3}{2}} C a b^{2} c^{2} d^{72} + 6930 \, {\left(d x + c\right)}^{\frac{3}{2}} B b^{3} c^{2} d^{72} - 41580 \, \sqrt{d x + c} D a^{2} b c^{3} d^{72} - 41580 \, \sqrt{d x + c} C a b^{2} c^{3} d^{72} - 13860 \, \sqrt{d x + c} B b^{3} c^{3} d^{72} + 693 \, {\left(d x + c\right)}^{\frac{5}{2}} D a^{3} d^{73} + 2079 \, {\left(d x + c\right)}^{\frac{5}{2}} C a^{2} b d^{73} + 2079 \, {\left(d x + c\right)}^{\frac{5}{2}} B a b^{2} d^{73} + 693 \, {\left(d x + c\right)}^{\frac{5}{2}} A b^{3} d^{73} - 3465 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{3} c d^{73} - 10395 \, {\left(d x + c\right)}^{\frac{3}{2}} C a^{2} b c d^{73} - 10395 \, {\left(d x + c\right)}^{\frac{3}{2}} B a b^{2} c d^{73} - 3465 \, {\left(d x + c\right)}^{\frac{3}{2}} A b^{3} c d^{73} + 10395 \, \sqrt{d x + c} D a^{3} c^{2} d^{73} + 31185 \, \sqrt{d x + c} C a^{2} b c^{2} d^{73} + 31185 \, \sqrt{d x + c} B a b^{2} c^{2} d^{73} + 10395 \, \sqrt{d x + c} A b^{3} c^{2} d^{73} + 1155 \, {\left(d x + c\right)}^{\frac{3}{2}} C a^{3} d^{74} + 3465 \, {\left(d x + c\right)}^{\frac{3}{2}} B a^{2} b d^{74} + 3465 \, {\left(d x + c\right)}^{\frac{3}{2}} A a b^{2} d^{74} - 6930 \, \sqrt{d x + c} C a^{3} c d^{74} - 20790 \, \sqrt{d x + c} B a^{2} b c d^{74} - 20790 \, \sqrt{d x + c} A a b^{2} c d^{74} + 3465 \, \sqrt{d x + c} B a^{3} d^{75} + 10395 \, \sqrt{d x + c} A a^{2} b d^{75}\right)}}{3465 \, d^{77}}"," ",0,"-2*(D*b^3*c^6 - 3*D*a*b^2*c^5*d - C*b^3*c^5*d + 3*D*a^2*b*c^4*d^2 + 3*C*a*b^2*c^4*d^2 + B*b^3*c^4*d^2 - D*a^3*c^3*d^3 - 3*C*a^2*b*c^3*d^3 - 3*B*a*b^2*c^3*d^3 - A*b^3*c^3*d^3 + C*a^3*c^2*d^4 + 3*B*a^2*b*c^2*d^4 + 3*A*a*b^2*c^2*d^4 - B*a^3*c*d^5 - 3*A*a^2*b*c*d^5 + A*a^3*d^6)/(sqrt(d*x + c)*d^7) + 2/3465*(315*(d*x + c)^(11/2)*D*b^3*d^70 - 2310*(d*x + c)^(9/2)*D*b^3*c*d^70 + 7425*(d*x + c)^(7/2)*D*b^3*c^2*d^70 - 13860*(d*x + c)^(5/2)*D*b^3*c^3*d^70 + 17325*(d*x + c)^(3/2)*D*b^3*c^4*d^70 - 20790*sqrt(d*x + c)*D*b^3*c^5*d^70 + 1155*(d*x + c)^(9/2)*D*a*b^2*d^71 + 385*(d*x + c)^(9/2)*C*b^3*d^71 - 7425*(d*x + c)^(7/2)*D*a*b^2*c*d^71 - 2475*(d*x + c)^(7/2)*C*b^3*c*d^71 + 20790*(d*x + c)^(5/2)*D*a*b^2*c^2*d^71 + 6930*(d*x + c)^(5/2)*C*b^3*c^2*d^71 - 34650*(d*x + c)^(3/2)*D*a*b^2*c^3*d^71 - 11550*(d*x + c)^(3/2)*C*b^3*c^3*d^71 + 51975*sqrt(d*x + c)*D*a*b^2*c^4*d^71 + 17325*sqrt(d*x + c)*C*b^3*c^4*d^71 + 1485*(d*x + c)^(7/2)*D*a^2*b*d^72 + 1485*(d*x + c)^(7/2)*C*a*b^2*d^72 + 495*(d*x + c)^(7/2)*B*b^3*d^72 - 8316*(d*x + c)^(5/2)*D*a^2*b*c*d^72 - 8316*(d*x + c)^(5/2)*C*a*b^2*c*d^72 - 2772*(d*x + c)^(5/2)*B*b^3*c*d^72 + 20790*(d*x + c)^(3/2)*D*a^2*b*c^2*d^72 + 20790*(d*x + c)^(3/2)*C*a*b^2*c^2*d^72 + 6930*(d*x + c)^(3/2)*B*b^3*c^2*d^72 - 41580*sqrt(d*x + c)*D*a^2*b*c^3*d^72 - 41580*sqrt(d*x + c)*C*a*b^2*c^3*d^72 - 13860*sqrt(d*x + c)*B*b^3*c^3*d^72 + 693*(d*x + c)^(5/2)*D*a^3*d^73 + 2079*(d*x + c)^(5/2)*C*a^2*b*d^73 + 2079*(d*x + c)^(5/2)*B*a*b^2*d^73 + 693*(d*x + c)^(5/2)*A*b^3*d^73 - 3465*(d*x + c)^(3/2)*D*a^3*c*d^73 - 10395*(d*x + c)^(3/2)*C*a^2*b*c*d^73 - 10395*(d*x + c)^(3/2)*B*a*b^2*c*d^73 - 3465*(d*x + c)^(3/2)*A*b^3*c*d^73 + 10395*sqrt(d*x + c)*D*a^3*c^2*d^73 + 31185*sqrt(d*x + c)*C*a^2*b*c^2*d^73 + 31185*sqrt(d*x + c)*B*a*b^2*c^2*d^73 + 10395*sqrt(d*x + c)*A*b^3*c^2*d^73 + 1155*(d*x + c)^(3/2)*C*a^3*d^74 + 3465*(d*x + c)^(3/2)*B*a^2*b*d^74 + 3465*(d*x + c)^(3/2)*A*a*b^2*d^74 - 6930*sqrt(d*x + c)*C*a^3*c*d^74 - 20790*sqrt(d*x + c)*B*a^2*b*c*d^74 - 20790*sqrt(d*x + c)*A*a*b^2*c*d^74 + 3465*sqrt(d*x + c)*B*a^3*d^75 + 10395*sqrt(d*x + c)*A*a^2*b*d^75)/d^77","B",0
11,1,651,0,1.372815," ","integrate((b*x+a)^2*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(D b^{2} c^{5} - 2 \, D a b c^{4} d - C b^{2} c^{4} d + D a^{2} c^{3} d^{2} + 2 \, C a b c^{3} d^{2} + B b^{2} c^{3} d^{2} - C a^{2} c^{2} d^{3} - 2 \, B a b c^{2} d^{3} - A b^{2} c^{2} d^{3} + B a^{2} c d^{4} + 2 \, A a b c d^{4} - A a^{2} d^{5}\right)}}{\sqrt{d x + c} d^{6}} + \frac{2 \, {\left(35 \, {\left(d x + c\right)}^{\frac{9}{2}} D b^{2} d^{48} - 225 \, {\left(d x + c\right)}^{\frac{7}{2}} D b^{2} c d^{48} + 630 \, {\left(d x + c\right)}^{\frac{5}{2}} D b^{2} c^{2} d^{48} - 1050 \, {\left(d x + c\right)}^{\frac{3}{2}} D b^{2} c^{3} d^{48} + 1575 \, \sqrt{d x + c} D b^{2} c^{4} d^{48} + 90 \, {\left(d x + c\right)}^{\frac{7}{2}} D a b d^{49} + 45 \, {\left(d x + c\right)}^{\frac{7}{2}} C b^{2} d^{49} - 504 \, {\left(d x + c\right)}^{\frac{5}{2}} D a b c d^{49} - 252 \, {\left(d x + c\right)}^{\frac{5}{2}} C b^{2} c d^{49} + 1260 \, {\left(d x + c\right)}^{\frac{3}{2}} D a b c^{2} d^{49} + 630 \, {\left(d x + c\right)}^{\frac{3}{2}} C b^{2} c^{2} d^{49} - 2520 \, \sqrt{d x + c} D a b c^{3} d^{49} - 1260 \, \sqrt{d x + c} C b^{2} c^{3} d^{49} + 63 \, {\left(d x + c\right)}^{\frac{5}{2}} D a^{2} d^{50} + 126 \, {\left(d x + c\right)}^{\frac{5}{2}} C a b d^{50} + 63 \, {\left(d x + c\right)}^{\frac{5}{2}} B b^{2} d^{50} - 315 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{2} c d^{50} - 630 \, {\left(d x + c\right)}^{\frac{3}{2}} C a b c d^{50} - 315 \, {\left(d x + c\right)}^{\frac{3}{2}} B b^{2} c d^{50} + 945 \, \sqrt{d x + c} D a^{2} c^{2} d^{50} + 1890 \, \sqrt{d x + c} C a b c^{2} d^{50} + 945 \, \sqrt{d x + c} B b^{2} c^{2} d^{50} + 105 \, {\left(d x + c\right)}^{\frac{3}{2}} C a^{2} d^{51} + 210 \, {\left(d x + c\right)}^{\frac{3}{2}} B a b d^{51} + 105 \, {\left(d x + c\right)}^{\frac{3}{2}} A b^{2} d^{51} - 630 \, \sqrt{d x + c} C a^{2} c d^{51} - 1260 \, \sqrt{d x + c} B a b c d^{51} - 630 \, \sqrt{d x + c} A b^{2} c d^{51} + 315 \, \sqrt{d x + c} B a^{2} d^{52} + 630 \, \sqrt{d x + c} A a b d^{52}\right)}}{315 \, d^{54}}"," ",0,"2*(D*b^2*c^5 - 2*D*a*b*c^4*d - C*b^2*c^4*d + D*a^2*c^3*d^2 + 2*C*a*b*c^3*d^2 + B*b^2*c^3*d^2 - C*a^2*c^2*d^3 - 2*B*a*b*c^2*d^3 - A*b^2*c^2*d^3 + B*a^2*c*d^4 + 2*A*a*b*c*d^4 - A*a^2*d^5)/(sqrt(d*x + c)*d^6) + 2/315*(35*(d*x + c)^(9/2)*D*b^2*d^48 - 225*(d*x + c)^(7/2)*D*b^2*c*d^48 + 630*(d*x + c)^(5/2)*D*b^2*c^2*d^48 - 1050*(d*x + c)^(3/2)*D*b^2*c^3*d^48 + 1575*sqrt(d*x + c)*D*b^2*c^4*d^48 + 90*(d*x + c)^(7/2)*D*a*b*d^49 + 45*(d*x + c)^(7/2)*C*b^2*d^49 - 504*(d*x + c)^(5/2)*D*a*b*c*d^49 - 252*(d*x + c)^(5/2)*C*b^2*c*d^49 + 1260*(d*x + c)^(3/2)*D*a*b*c^2*d^49 + 630*(d*x + c)^(3/2)*C*b^2*c^2*d^49 - 2520*sqrt(d*x + c)*D*a*b*c^3*d^49 - 1260*sqrt(d*x + c)*C*b^2*c^3*d^49 + 63*(d*x + c)^(5/2)*D*a^2*d^50 + 126*(d*x + c)^(5/2)*C*a*b*d^50 + 63*(d*x + c)^(5/2)*B*b^2*d^50 - 315*(d*x + c)^(3/2)*D*a^2*c*d^50 - 630*(d*x + c)^(3/2)*C*a*b*c*d^50 - 315*(d*x + c)^(3/2)*B*b^2*c*d^50 + 945*sqrt(d*x + c)*D*a^2*c^2*d^50 + 1890*sqrt(d*x + c)*C*a*b*c^2*d^50 + 945*sqrt(d*x + c)*B*b^2*c^2*d^50 + 105*(d*x + c)^(3/2)*C*a^2*d^51 + 210*(d*x + c)^(3/2)*B*a*b*d^51 + 105*(d*x + c)^(3/2)*A*b^2*d^51 - 630*sqrt(d*x + c)*C*a^2*c*d^51 - 1260*sqrt(d*x + c)*B*a*b*c*d^51 - 630*sqrt(d*x + c)*A*b^2*c*d^51 + 315*sqrt(d*x + c)*B*a^2*d^52 + 630*sqrt(d*x + c)*A*a*b*d^52)/d^54","B",0
12,1,323,0,1.269271," ","integrate((b*x+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(D b c^{4} - D a c^{3} d - C b c^{3} d + C a c^{2} d^{2} + B b c^{2} d^{2} - B a c d^{3} - A b c d^{3} + A a d^{4}\right)}}{\sqrt{d x + c} d^{5}} + \frac{2 \, {\left(15 \, {\left(d x + c\right)}^{\frac{7}{2}} D b d^{30} - 84 \, {\left(d x + c\right)}^{\frac{5}{2}} D b c d^{30} + 210 \, {\left(d x + c\right)}^{\frac{3}{2}} D b c^{2} d^{30} - 420 \, \sqrt{d x + c} D b c^{3} d^{30} + 21 \, {\left(d x + c\right)}^{\frac{5}{2}} D a d^{31} + 21 \, {\left(d x + c\right)}^{\frac{5}{2}} C b d^{31} - 105 \, {\left(d x + c\right)}^{\frac{3}{2}} D a c d^{31} - 105 \, {\left(d x + c\right)}^{\frac{3}{2}} C b c d^{31} + 315 \, \sqrt{d x + c} D a c^{2} d^{31} + 315 \, \sqrt{d x + c} C b c^{2} d^{31} + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} C a d^{32} + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} B b d^{32} - 210 \, \sqrt{d x + c} C a c d^{32} - 210 \, \sqrt{d x + c} B b c d^{32} + 105 \, \sqrt{d x + c} B a d^{33} + 105 \, \sqrt{d x + c} A b d^{33}\right)}}{105 \, d^{35}}"," ",0,"-2*(D*b*c^4 - D*a*c^3*d - C*b*c^3*d + C*a*c^2*d^2 + B*b*c^2*d^2 - B*a*c*d^3 - A*b*c*d^3 + A*a*d^4)/(sqrt(d*x + c)*d^5) + 2/105*(15*(d*x + c)^(7/2)*D*b*d^30 - 84*(d*x + c)^(5/2)*D*b*c*d^30 + 210*(d*x + c)^(3/2)*D*b*c^2*d^30 - 420*sqrt(d*x + c)*D*b*c^3*d^30 + 21*(d*x + c)^(5/2)*D*a*d^31 + 21*(d*x + c)^(5/2)*C*b*d^31 - 105*(d*x + c)^(3/2)*D*a*c*d^31 - 105*(d*x + c)^(3/2)*C*b*c*d^31 + 315*sqrt(d*x + c)*D*a*c^2*d^31 + 315*sqrt(d*x + c)*C*b*c^2*d^31 + 35*(d*x + c)^(3/2)*C*a*d^32 + 35*(d*x + c)^(3/2)*B*b*d^32 - 210*sqrt(d*x + c)*C*a*c*d^32 - 210*sqrt(d*x + c)*B*b*c*d^32 + 105*sqrt(d*x + c)*B*a*d^33 + 105*sqrt(d*x + c)*A*b*d^33)/d^35","A",0
13,1,127,0,1.287971," ","integrate((D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(D c^{3} - C c^{2} d + B c d^{2} - A d^{3}\right)}}{\sqrt{d x + c} d^{4}} + \frac{2 \, {\left(3 \, {\left(d x + c\right)}^{\frac{5}{2}} D d^{16} - 15 \, {\left(d x + c\right)}^{\frac{3}{2}} D c d^{16} + 45 \, \sqrt{d x + c} D c^{2} d^{16} + 5 \, {\left(d x + c\right)}^{\frac{3}{2}} C d^{17} - 30 \, \sqrt{d x + c} C c d^{17} + 15 \, \sqrt{d x + c} B d^{18}\right)}}{15 \, d^{20}}"," ",0,"2*(D*c^3 - C*c^2*d + B*c*d^2 - A*d^3)/(sqrt(d*x + c)*d^4) + 2/15*(3*(d*x + c)^(5/2)*D*d^16 - 15*(d*x + c)^(3/2)*D*c*d^16 + 45*sqrt(d*x + c)*D*c^2*d^16 + 5*(d*x + c)^(3/2)*C*d^17 - 30*sqrt(d*x + c)*C*c*d^17 + 15*sqrt(d*x + c)*B*d^18)/d^20","A",0
14,1,200,0,1.332029," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)/(d*x+c)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(D a^{3} - C a^{2} b + B a b^{2} - A b^{3}\right)} \arctan\left(\frac{\sqrt{d x + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{{\left(b^{3} c - a b^{2} d\right)} \sqrt{-b^{2} c + a b d}} - \frac{2 \, {\left(D c^{3} - C c^{2} d + B c d^{2} - A d^{3}\right)}}{{\left(b c d^{3} - a d^{4}\right)} \sqrt{d x + c}} + \frac{2 \, {\left({\left(d x + c\right)}^{\frac{3}{2}} D b^{2} d^{6} - 6 \, \sqrt{d x + c} D b^{2} c d^{6} - 3 \, \sqrt{d x + c} D a b d^{7} + 3 \, \sqrt{d x + c} C b^{2} d^{7}\right)}}{3 \, b^{3} d^{9}}"," ",0,"-2*(D*a^3 - C*a^2*b + B*a*b^2 - A*b^3)*arctan(sqrt(d*x + c)*b/sqrt(-b^2*c + a*b*d))/((b^3*c - a*b^2*d)*sqrt(-b^2*c + a*b*d)) - 2*(D*c^3 - C*c^2*d + B*c*d^2 - A*d^3)/((b*c*d^3 - a*d^4)*sqrt(d*x + c)) + 2/3*((d*x + c)^(3/2)*D*b^2*d^6 - 6*sqrt(d*x + c)*D*b^2*c*d^6 - 3*sqrt(d*x + c)*D*a*b*d^7 + 3*sqrt(d*x + c)*C*b^2*d^7)/(b^3*d^9)","A",0
15,1,388,0,1.327956," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^2/(d*x+c)^(3/2),x, algorithm=""giac"")","\frac{{\left(6 \, D a^{2} b c - 4 \, C a b^{2} c + 2 \, B b^{3} c - 3 \, D a^{3} d + C a^{2} b d + B a b^{2} d - 3 \, A b^{3} d\right)} \arctan\left(\frac{\sqrt{d x + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} \sqrt{-b^{2} c + a b d}} + \frac{2 \, {\left(d x + c\right)} D b^{3} c^{3} - 2 \, D b^{3} c^{4} - 2 \, {\left(d x + c\right)} C b^{3} c^{2} d + 2 \, D a b^{2} c^{3} d + 2 \, C b^{3} c^{3} d + 2 \, {\left(d x + c\right)} B b^{3} c d^{2} - 2 \, C a b^{2} c^{2} d^{2} - 2 \, B b^{3} c^{2} d^{2} + {\left(d x + c\right)} D a^{3} d^{3} - {\left(d x + c\right)} C a^{2} b d^{3} + {\left(d x + c\right)} B a b^{2} d^{3} - 3 \, {\left(d x + c\right)} A b^{3} d^{3} + 2 \, B a b^{2} c d^{3} + 2 \, A b^{3} c d^{3} - 2 \, A a b^{2} d^{4}}{{\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} {\left({\left(d x + c\right)}^{\frac{3}{2}} b - \sqrt{d x + c} b c + \sqrt{d x + c} a d\right)}} + \frac{2 \, \sqrt{d x + c} D}{b^{2} d^{2}}"," ",0,"(6*D*a^2*b*c - 4*C*a*b^2*c + 2*B*b^3*c - 3*D*a^3*d + C*a^2*b*d + B*a*b^2*d - 3*A*b^3*d)*arctan(sqrt(d*x + c)*b/sqrt(-b^2*c + a*b*d))/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*sqrt(-b^2*c + a*b*d)) + (2*(d*x + c)*D*b^3*c^3 - 2*D*b^3*c^4 - 2*(d*x + c)*C*b^3*c^2*d + 2*D*a*b^2*c^3*d + 2*C*b^3*c^3*d + 2*(d*x + c)*B*b^3*c*d^2 - 2*C*a*b^2*c^2*d^2 - 2*B*b^3*c^2*d^2 + (d*x + c)*D*a^3*d^3 - (d*x + c)*C*a^2*b*d^3 + (d*x + c)*B*a*b^2*d^3 - 3*(d*x + c)*A*b^3*d^3 + 2*B*a*b^2*c*d^3 + 2*A*b^3*c*d^3 - 2*A*a*b^2*d^4)/((b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*((d*x + c)^(3/2)*b - sqrt(d*x + c)*b*c + sqrt(d*x + c)*a*d)) + 2*sqrt(d*x + c)*D/(b^2*d^2)","A",0
16,1,617,0,1.412833," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^3/(d*x+c)^(3/2),x, algorithm=""giac"")","-\frac{{\left(24 \, D a b^{2} c^{2} - 8 \, C b^{3} c^{2} - 12 \, D a^{2} b c d - 8 \, C a b^{2} c d + 12 \, B b^{3} c d + 3 \, D a^{3} d^{2} + C a^{2} b d^{2} + 3 \, B a b^{2} d^{2} - 15 \, A b^{3} d^{2}\right)} \arctan\left(\frac{\sqrt{d x + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{4 \, {\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} \sqrt{-b^{2} c + a b d}} - \frac{2 \, {\left(D c^{3} - C c^{2} d + B c d^{2} - A d^{3}\right)}}{{\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \sqrt{d x + c}} - \frac{12 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{2} b^{2} c d - 8 \, {\left(d x + c\right)}^{\frac{3}{2}} C a b^{3} c d + 4 \, {\left(d x + c\right)}^{\frac{3}{2}} B b^{4} c d - 12 \, \sqrt{d x + c} D a^{2} b^{2} c^{2} d + 8 \, \sqrt{d x + c} C a b^{3} c^{2} d - 4 \, \sqrt{d x + c} B b^{4} c^{2} d - 5 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{3} b d^{2} + {\left(d x + c\right)}^{\frac{3}{2}} C a^{2} b^{2} d^{2} + 3 \, {\left(d x + c\right)}^{\frac{3}{2}} B a b^{3} d^{2} - 7 \, {\left(d x + c\right)}^{\frac{3}{2}} A b^{4} d^{2} + 15 \, \sqrt{d x + c} D a^{3} b c d^{2} - 7 \, \sqrt{d x + c} C a^{2} b^{2} c d^{2} - \sqrt{d x + c} B a b^{3} c d^{2} + 9 \, \sqrt{d x + c} A b^{4} c d^{2} - 3 \, \sqrt{d x + c} D a^{4} d^{3} - \sqrt{d x + c} C a^{3} b d^{3} + 5 \, \sqrt{d x + c} B a^{2} b^{2} d^{3} - 9 \, \sqrt{d x + c} A a b^{3} d^{3}}{4 \, {\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} {\left({\left(d x + c\right)} b - b c + a d\right)}^{2}}"," ",0,"-1/4*(24*D*a*b^2*c^2 - 8*C*b^3*c^2 - 12*D*a^2*b*c*d - 8*C*a*b^2*c*d + 12*B*b^3*c*d + 3*D*a^3*d^2 + C*a^2*b*d^2 + 3*B*a*b^2*d^2 - 15*A*b^3*d^2)*arctan(sqrt(d*x + c)*b/sqrt(-b^2*c + a*b*d))/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*sqrt(-b^2*c + a*b*d)) - 2*(D*c^3 - C*c^2*d + B*c*d^2 - A*d^3)/((b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*sqrt(d*x + c)) - 1/4*(12*(d*x + c)^(3/2)*D*a^2*b^2*c*d - 8*(d*x + c)^(3/2)*C*a*b^3*c*d + 4*(d*x + c)^(3/2)*B*b^4*c*d - 12*sqrt(d*x + c)*D*a^2*b^2*c^2*d + 8*sqrt(d*x + c)*C*a*b^3*c^2*d - 4*sqrt(d*x + c)*B*b^4*c^2*d - 5*(d*x + c)^(3/2)*D*a^3*b*d^2 + (d*x + c)^(3/2)*C*a^2*b^2*d^2 + 3*(d*x + c)^(3/2)*B*a*b^3*d^2 - 7*(d*x + c)^(3/2)*A*b^4*d^2 + 15*sqrt(d*x + c)*D*a^3*b*c*d^2 - 7*sqrt(d*x + c)*C*a^2*b^2*c*d^2 - sqrt(d*x + c)*B*a*b^3*c*d^2 + 9*sqrt(d*x + c)*A*b^4*c*d^2 - 3*sqrt(d*x + c)*D*a^4*d^3 - sqrt(d*x + c)*C*a^3*b*d^3 + 5*sqrt(d*x + c)*B*a^2*b^2*d^3 - 9*sqrt(d*x + c)*A*a*b^3*d^3)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*((d*x + c)*b - b*c + a*d)^2)","A",0
17,1,1085,0,1.557736," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^4/(d*x+c)^(3/2),x, algorithm=""giac"")","\frac{{\left(16 \, D b^{3} c^{3} + 24 \, D a b^{2} c^{2} d - 24 \, C b^{3} c^{2} d - 6 \, D a^{2} b c d^{2} - 12 \, C a b^{2} c d^{2} + 30 \, B b^{3} c d^{2} + D a^{3} d^{3} + C a^{2} b d^{3} + 5 \, B a b^{2} d^{3} - 35 \, A b^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{d x + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{8 \, {\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} \sqrt{-b^{2} c + a b d}} + \frac{2 \, {\left(D c^{3} - C c^{2} d + B c d^{2} - A d^{3}\right)}}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{d x + c}} + \frac{72 \, {\left(d x + c\right)}^{\frac{5}{2}} D a b^{4} c^{2} d - 24 \, {\left(d x + c\right)}^{\frac{5}{2}} C b^{5} c^{2} d - 144 \, {\left(d x + c\right)}^{\frac{3}{2}} D a b^{4} c^{3} d + 48 \, {\left(d x + c\right)}^{\frac{3}{2}} C b^{5} c^{3} d + 72 \, \sqrt{d x + c} D a b^{4} c^{4} d - 24 \, \sqrt{d x + c} C b^{5} c^{4} d - 18 \, {\left(d x + c\right)}^{\frac{5}{2}} D a^{2} b^{3} c d^{2} - 36 \, {\left(d x + c\right)}^{\frac{5}{2}} C a b^{4} c d^{2} + 42 \, {\left(d x + c\right)}^{\frac{5}{2}} B b^{5} c d^{2} + 144 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{2} b^{3} c^{2} d^{2} + 48 \, {\left(d x + c\right)}^{\frac{3}{2}} C a b^{4} c^{2} d^{2} - 96 \, {\left(d x + c\right)}^{\frac{3}{2}} B b^{5} c^{2} d^{2} - 126 \, \sqrt{d x + c} D a^{2} b^{3} c^{3} d^{2} - 12 \, \sqrt{d x + c} C a b^{4} c^{3} d^{2} + 54 \, \sqrt{d x + c} B b^{5} c^{3} d^{2} + 3 \, {\left(d x + c\right)}^{\frac{5}{2}} D a^{3} b^{2} d^{3} + 3 \, {\left(d x + c\right)}^{\frac{5}{2}} C a^{2} b^{3} d^{3} + 15 \, {\left(d x + c\right)}^{\frac{5}{2}} B a b^{4} d^{3} - 57 \, {\left(d x + c\right)}^{\frac{5}{2}} A b^{5} d^{3} + 8 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{3} b^{2} c d^{3} - 104 \, {\left(d x + c\right)}^{\frac{3}{2}} C a^{2} b^{3} c d^{3} + 56 \, {\left(d x + c\right)}^{\frac{3}{2}} B a b^{4} c d^{3} + 136 \, {\left(d x + c\right)}^{\frac{3}{2}} A b^{5} c d^{3} + 33 \, \sqrt{d x + c} D a^{3} b^{2} c^{2} d^{3} + 93 \, \sqrt{d x + c} C a^{2} b^{3} c^{2} d^{3} - 75 \, \sqrt{d x + c} B a b^{4} c^{2} d^{3} - 87 \, \sqrt{d x + c} A b^{5} c^{2} d^{3} - 8 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{4} b d^{4} + 8 \, {\left(d x + c\right)}^{\frac{3}{2}} C a^{3} b^{2} d^{4} + 40 \, {\left(d x + c\right)}^{\frac{3}{2}} B a^{2} b^{3} d^{4} - 136 \, {\left(d x + c\right)}^{\frac{3}{2}} A a b^{4} d^{4} + 24 \, \sqrt{d x + c} D a^{4} b c d^{4} - 54 \, \sqrt{d x + c} C a^{3} b^{2} c d^{4} - 12 \, \sqrt{d x + c} B a^{2} b^{3} c d^{4} + 174 \, \sqrt{d x + c} A a b^{4} c d^{4} - 3 \, \sqrt{d x + c} D a^{5} d^{5} - 3 \, \sqrt{d x + c} C a^{4} b d^{5} + 33 \, \sqrt{d x + c} B a^{3} b^{2} d^{5} - 87 \, \sqrt{d x + c} A a^{2} b^{3} d^{5}}{24 \, {\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} {\left({\left(d x + c\right)} b - b c + a d\right)}^{3}}"," ",0,"1/8*(16*D*b^3*c^3 + 24*D*a*b^2*c^2*d - 24*C*b^3*c^2*d - 6*D*a^2*b*c*d^2 - 12*C*a*b^2*c*d^2 + 30*B*b^3*c*d^2 + D*a^3*d^3 + C*a^2*b*d^3 + 5*B*a*b^2*d^3 - 35*A*b^3*d^3)*arctan(sqrt(d*x + c)*b/sqrt(-b^2*c + a*b*d))/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*sqrt(-b^2*c + a*b*d)) + 2*(D*c^3 - C*c^2*d + B*c*d^2 - A*d^3)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(d*x + c)) + 1/24*(72*(d*x + c)^(5/2)*D*a*b^4*c^2*d - 24*(d*x + c)^(5/2)*C*b^5*c^2*d - 144*(d*x + c)^(3/2)*D*a*b^4*c^3*d + 48*(d*x + c)^(3/2)*C*b^5*c^3*d + 72*sqrt(d*x + c)*D*a*b^4*c^4*d - 24*sqrt(d*x + c)*C*b^5*c^4*d - 18*(d*x + c)^(5/2)*D*a^2*b^3*c*d^2 - 36*(d*x + c)^(5/2)*C*a*b^4*c*d^2 + 42*(d*x + c)^(5/2)*B*b^5*c*d^2 + 144*(d*x + c)^(3/2)*D*a^2*b^3*c^2*d^2 + 48*(d*x + c)^(3/2)*C*a*b^4*c^2*d^2 - 96*(d*x + c)^(3/2)*B*b^5*c^2*d^2 - 126*sqrt(d*x + c)*D*a^2*b^3*c^3*d^2 - 12*sqrt(d*x + c)*C*a*b^4*c^3*d^2 + 54*sqrt(d*x + c)*B*b^5*c^3*d^2 + 3*(d*x + c)^(5/2)*D*a^3*b^2*d^3 + 3*(d*x + c)^(5/2)*C*a^2*b^3*d^3 + 15*(d*x + c)^(5/2)*B*a*b^4*d^3 - 57*(d*x + c)^(5/2)*A*b^5*d^3 + 8*(d*x + c)^(3/2)*D*a^3*b^2*c*d^3 - 104*(d*x + c)^(3/2)*C*a^2*b^3*c*d^3 + 56*(d*x + c)^(3/2)*B*a*b^4*c*d^3 + 136*(d*x + c)^(3/2)*A*b^5*c*d^3 + 33*sqrt(d*x + c)*D*a^3*b^2*c^2*d^3 + 93*sqrt(d*x + c)*C*a^2*b^3*c^2*d^3 - 75*sqrt(d*x + c)*B*a*b^4*c^2*d^3 - 87*sqrt(d*x + c)*A*b^5*c^2*d^3 - 8*(d*x + c)^(3/2)*D*a^4*b*d^4 + 8*(d*x + c)^(3/2)*C*a^3*b^2*d^4 + 40*(d*x + c)^(3/2)*B*a^2*b^3*d^4 - 136*(d*x + c)^(3/2)*A*a*b^4*d^4 + 24*sqrt(d*x + c)*D*a^4*b*c*d^4 - 54*sqrt(d*x + c)*C*a^3*b^2*c*d^4 - 12*sqrt(d*x + c)*B*a^2*b^3*c*d^4 + 174*sqrt(d*x + c)*A*a*b^4*c*d^4 - 3*sqrt(d*x + c)*D*a^5*d^5 - 3*sqrt(d*x + c)*C*a^4*b*d^5 + 33*sqrt(d*x + c)*B*a^3*b^2*d^5 - 87*sqrt(d*x + c)*A*a^2*b^3*d^5)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*((d*x + c)*b - b*c + a*d)^3)","B",0
18,1,1030,0,1.451276," ","integrate((b*x+a)^3*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(18 \, {\left(d x + c\right)} D b^{3} c^{5} - D b^{3} c^{6} - 45 \, {\left(d x + c\right)} D a b^{2} c^{4} d - 15 \, {\left(d x + c\right)} C b^{3} c^{4} d + 3 \, D a b^{2} c^{5} d + C b^{3} c^{5} d + 36 \, {\left(d x + c\right)} D a^{2} b c^{3} d^{2} + 36 \, {\left(d x + c\right)} C a b^{2} c^{3} d^{2} + 12 \, {\left(d x + c\right)} B b^{3} c^{3} d^{2} - 3 \, D a^{2} b c^{4} d^{2} - 3 \, C a b^{2} c^{4} d^{2} - B b^{3} c^{4} d^{2} - 9 \, {\left(d x + c\right)} D a^{3} c^{2} d^{3} - 27 \, {\left(d x + c\right)} C a^{2} b c^{2} d^{3} - 27 \, {\left(d x + c\right)} B a b^{2} c^{2} d^{3} - 9 \, {\left(d x + c\right)} A b^{3} c^{2} d^{3} + D a^{3} c^{3} d^{3} + 3 \, C a^{2} b c^{3} d^{3} + 3 \, B a b^{2} c^{3} d^{3} + A b^{3} c^{3} d^{3} + 6 \, {\left(d x + c\right)} C a^{3} c d^{4} + 18 \, {\left(d x + c\right)} B a^{2} b c d^{4} + 18 \, {\left(d x + c\right)} A a b^{2} c d^{4} - C a^{3} c^{2} d^{4} - 3 \, B a^{2} b c^{2} d^{4} - 3 \, A a b^{2} c^{2} d^{4} - 3 \, {\left(d x + c\right)} B a^{3} d^{5} - 9 \, {\left(d x + c\right)} A a^{2} b d^{5} + B a^{3} c d^{5} + 3 \, A a^{2} b c d^{5} - A a^{3} d^{6}\right)}}{3 \, {\left(d x + c\right)}^{\frac{3}{2}} d^{7}} + \frac{2 \, {\left(35 \, {\left(d x + c\right)}^{\frac{9}{2}} D b^{3} d^{56} - 270 \, {\left(d x + c\right)}^{\frac{7}{2}} D b^{3} c d^{56} + 945 \, {\left(d x + c\right)}^{\frac{5}{2}} D b^{3} c^{2} d^{56} - 2100 \, {\left(d x + c\right)}^{\frac{3}{2}} D b^{3} c^{3} d^{56} + 4725 \, \sqrt{d x + c} D b^{3} c^{4} d^{56} + 135 \, {\left(d x + c\right)}^{\frac{7}{2}} D a b^{2} d^{57} + 45 \, {\left(d x + c\right)}^{\frac{7}{2}} C b^{3} d^{57} - 945 \, {\left(d x + c\right)}^{\frac{5}{2}} D a b^{2} c d^{57} - 315 \, {\left(d x + c\right)}^{\frac{5}{2}} C b^{3} c d^{57} + 3150 \, {\left(d x + c\right)}^{\frac{3}{2}} D a b^{2} c^{2} d^{57} + 1050 \, {\left(d x + c\right)}^{\frac{3}{2}} C b^{3} c^{2} d^{57} - 9450 \, \sqrt{d x + c} D a b^{2} c^{3} d^{57} - 3150 \, \sqrt{d x + c} C b^{3} c^{3} d^{57} + 189 \, {\left(d x + c\right)}^{\frac{5}{2}} D a^{2} b d^{58} + 189 \, {\left(d x + c\right)}^{\frac{5}{2}} C a b^{2} d^{58} + 63 \, {\left(d x + c\right)}^{\frac{5}{2}} B b^{3} d^{58} - 1260 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{2} b c d^{58} - 1260 \, {\left(d x + c\right)}^{\frac{3}{2}} C a b^{2} c d^{58} - 420 \, {\left(d x + c\right)}^{\frac{3}{2}} B b^{3} c d^{58} + 5670 \, \sqrt{d x + c} D a^{2} b c^{2} d^{58} + 5670 \, \sqrt{d x + c} C a b^{2} c^{2} d^{58} + 1890 \, \sqrt{d x + c} B b^{3} c^{2} d^{58} + 105 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{3} d^{59} + 315 \, {\left(d x + c\right)}^{\frac{3}{2}} C a^{2} b d^{59} + 315 \, {\left(d x + c\right)}^{\frac{3}{2}} B a b^{2} d^{59} + 105 \, {\left(d x + c\right)}^{\frac{3}{2}} A b^{3} d^{59} - 945 \, \sqrt{d x + c} D a^{3} c d^{59} - 2835 \, \sqrt{d x + c} C a^{2} b c d^{59} - 2835 \, \sqrt{d x + c} B a b^{2} c d^{59} - 945 \, \sqrt{d x + c} A b^{3} c d^{59} + 315 \, \sqrt{d x + c} C a^{3} d^{60} + 945 \, \sqrt{d x + c} B a^{2} b d^{60} + 945 \, \sqrt{d x + c} A a b^{2} d^{60}\right)}}{315 \, d^{63}}"," ",0,"2/3*(18*(d*x + c)*D*b^3*c^5 - D*b^3*c^6 - 45*(d*x + c)*D*a*b^2*c^4*d - 15*(d*x + c)*C*b^3*c^4*d + 3*D*a*b^2*c^5*d + C*b^3*c^5*d + 36*(d*x + c)*D*a^2*b*c^3*d^2 + 36*(d*x + c)*C*a*b^2*c^3*d^2 + 12*(d*x + c)*B*b^3*c^3*d^2 - 3*D*a^2*b*c^4*d^2 - 3*C*a*b^2*c^4*d^2 - B*b^3*c^4*d^2 - 9*(d*x + c)*D*a^3*c^2*d^3 - 27*(d*x + c)*C*a^2*b*c^2*d^3 - 27*(d*x + c)*B*a*b^2*c^2*d^3 - 9*(d*x + c)*A*b^3*c^2*d^3 + D*a^3*c^3*d^3 + 3*C*a^2*b*c^3*d^3 + 3*B*a*b^2*c^3*d^3 + A*b^3*c^3*d^3 + 6*(d*x + c)*C*a^3*c*d^4 + 18*(d*x + c)*B*a^2*b*c*d^4 + 18*(d*x + c)*A*a*b^2*c*d^4 - C*a^3*c^2*d^4 - 3*B*a^2*b*c^2*d^4 - 3*A*a*b^2*c^2*d^4 - 3*(d*x + c)*B*a^3*d^5 - 9*(d*x + c)*A*a^2*b*d^5 + B*a^3*c*d^5 + 3*A*a^2*b*c*d^5 - A*a^3*d^6)/((d*x + c)^(3/2)*d^7) + 2/315*(35*(d*x + c)^(9/2)*D*b^3*d^56 - 270*(d*x + c)^(7/2)*D*b^3*c*d^56 + 945*(d*x + c)^(5/2)*D*b^3*c^2*d^56 - 2100*(d*x + c)^(3/2)*D*b^3*c^3*d^56 + 4725*sqrt(d*x + c)*D*b^3*c^4*d^56 + 135*(d*x + c)^(7/2)*D*a*b^2*d^57 + 45*(d*x + c)^(7/2)*C*b^3*d^57 - 945*(d*x + c)^(5/2)*D*a*b^2*c*d^57 - 315*(d*x + c)^(5/2)*C*b^3*c*d^57 + 3150*(d*x + c)^(3/2)*D*a*b^2*c^2*d^57 + 1050*(d*x + c)^(3/2)*C*b^3*c^2*d^57 - 9450*sqrt(d*x + c)*D*a*b^2*c^3*d^57 - 3150*sqrt(d*x + c)*C*b^3*c^3*d^57 + 189*(d*x + c)^(5/2)*D*a^2*b*d^58 + 189*(d*x + c)^(5/2)*C*a*b^2*d^58 + 63*(d*x + c)^(5/2)*B*b^3*d^58 - 1260*(d*x + c)^(3/2)*D*a^2*b*c*d^58 - 1260*(d*x + c)^(3/2)*C*a*b^2*c*d^58 - 420*(d*x + c)^(3/2)*B*b^3*c*d^58 + 5670*sqrt(d*x + c)*D*a^2*b*c^2*d^58 + 5670*sqrt(d*x + c)*C*a*b^2*c^2*d^58 + 1890*sqrt(d*x + c)*B*b^3*c^2*d^58 + 105*(d*x + c)^(3/2)*D*a^3*d^59 + 315*(d*x + c)^(3/2)*C*a^2*b*d^59 + 315*(d*x + c)^(3/2)*B*a*b^2*d^59 + 105*(d*x + c)^(3/2)*A*b^3*d^59 - 945*sqrt(d*x + c)*D*a^3*c*d^59 - 2835*sqrt(d*x + c)*C*a^2*b*c*d^59 - 2835*sqrt(d*x + c)*B*a*b^2*c*d^59 - 945*sqrt(d*x + c)*A*b^3*c*d^59 + 315*sqrt(d*x + c)*C*a^3*d^60 + 945*sqrt(d*x + c)*B*a^2*b*d^60 + 945*sqrt(d*x + c)*A*a*b^2*d^60)/d^63","B",0
19,1,622,0,1.392970," ","integrate((b*x+a)^2*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, {\left(d x + c\right)} D b^{2} c^{4} - D b^{2} c^{5} - 24 \, {\left(d x + c\right)} D a b c^{3} d - 12 \, {\left(d x + c\right)} C b^{2} c^{3} d + 2 \, D a b c^{4} d + C b^{2} c^{4} d + 9 \, {\left(d x + c\right)} D a^{2} c^{2} d^{2} + 18 \, {\left(d x + c\right)} C a b c^{2} d^{2} + 9 \, {\left(d x + c\right)} B b^{2} c^{2} d^{2} - D a^{2} c^{3} d^{2} - 2 \, C a b c^{3} d^{2} - B b^{2} c^{3} d^{2} - 6 \, {\left(d x + c\right)} C a^{2} c d^{3} - 12 \, {\left(d x + c\right)} B a b c d^{3} - 6 \, {\left(d x + c\right)} A b^{2} c d^{3} + C a^{2} c^{2} d^{3} + 2 \, B a b c^{2} d^{3} + A b^{2} c^{2} d^{3} + 3 \, {\left(d x + c\right)} B a^{2} d^{4} + 6 \, {\left(d x + c\right)} A a b d^{4} - B a^{2} c d^{4} - 2 \, A a b c d^{4} + A a^{2} d^{5}\right)}}{3 \, {\left(d x + c\right)}^{\frac{3}{2}} d^{6}} + \frac{2 \, {\left(15 \, {\left(d x + c\right)}^{\frac{7}{2}} D b^{2} d^{36} - 105 \, {\left(d x + c\right)}^{\frac{5}{2}} D b^{2} c d^{36} + 350 \, {\left(d x + c\right)}^{\frac{3}{2}} D b^{2} c^{2} d^{36} - 1050 \, \sqrt{d x + c} D b^{2} c^{3} d^{36} + 42 \, {\left(d x + c\right)}^{\frac{5}{2}} D a b d^{37} + 21 \, {\left(d x + c\right)}^{\frac{5}{2}} C b^{2} d^{37} - 280 \, {\left(d x + c\right)}^{\frac{3}{2}} D a b c d^{37} - 140 \, {\left(d x + c\right)}^{\frac{3}{2}} C b^{2} c d^{37} + 1260 \, \sqrt{d x + c} D a b c^{2} d^{37} + 630 \, \sqrt{d x + c} C b^{2} c^{2} d^{37} + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{2} d^{38} + 70 \, {\left(d x + c\right)}^{\frac{3}{2}} C a b d^{38} + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} B b^{2} d^{38} - 315 \, \sqrt{d x + c} D a^{2} c d^{38} - 630 \, \sqrt{d x + c} C a b c d^{38} - 315 \, \sqrt{d x + c} B b^{2} c d^{38} + 105 \, \sqrt{d x + c} C a^{2} d^{39} + 210 \, \sqrt{d x + c} B a b d^{39} + 105 \, \sqrt{d x + c} A b^{2} d^{39}\right)}}{105 \, d^{42}}"," ",0,"-2/3*(15*(d*x + c)*D*b^2*c^4 - D*b^2*c^5 - 24*(d*x + c)*D*a*b*c^3*d - 12*(d*x + c)*C*b^2*c^3*d + 2*D*a*b*c^4*d + C*b^2*c^4*d + 9*(d*x + c)*D*a^2*c^2*d^2 + 18*(d*x + c)*C*a*b*c^2*d^2 + 9*(d*x + c)*B*b^2*c^2*d^2 - D*a^2*c^3*d^2 - 2*C*a*b*c^3*d^2 - B*b^2*c^3*d^2 - 6*(d*x + c)*C*a^2*c*d^3 - 12*(d*x + c)*B*a*b*c*d^3 - 6*(d*x + c)*A*b^2*c*d^3 + C*a^2*c^2*d^3 + 2*B*a*b*c^2*d^3 + A*b^2*c^2*d^3 + 3*(d*x + c)*B*a^2*d^4 + 6*(d*x + c)*A*a*b*d^4 - B*a^2*c*d^4 - 2*A*a*b*c*d^4 + A*a^2*d^5)/((d*x + c)^(3/2)*d^6) + 2/105*(15*(d*x + c)^(7/2)*D*b^2*d^36 - 105*(d*x + c)^(5/2)*D*b^2*c*d^36 + 350*(d*x + c)^(3/2)*D*b^2*c^2*d^36 - 1050*sqrt(d*x + c)*D*b^2*c^3*d^36 + 42*(d*x + c)^(5/2)*D*a*b*d^37 + 21*(d*x + c)^(5/2)*C*b^2*d^37 - 280*(d*x + c)^(3/2)*D*a*b*c*d^37 - 140*(d*x + c)^(3/2)*C*b^2*c*d^37 + 1260*sqrt(d*x + c)*D*a*b*c^2*d^37 + 630*sqrt(d*x + c)*C*b^2*c^2*d^37 + 35*(d*x + c)^(3/2)*D*a^2*d^38 + 70*(d*x + c)^(3/2)*C*a*b*d^38 + 35*(d*x + c)^(3/2)*B*b^2*d^38 - 315*sqrt(d*x + c)*D*a^2*c*d^38 - 630*sqrt(d*x + c)*C*a*b*c*d^38 - 315*sqrt(d*x + c)*B*b^2*c*d^38 + 105*sqrt(d*x + c)*C*a^2*d^39 + 210*sqrt(d*x + c)*B*a*b*d^39 + 105*sqrt(d*x + c)*A*b^2*d^39)/d^42","B",0
20,1,302,0,1.217100," ","integrate((b*x+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(12 \, {\left(d x + c\right)} D b c^{3} - D b c^{4} - 9 \, {\left(d x + c\right)} D a c^{2} d - 9 \, {\left(d x + c\right)} C b c^{2} d + D a c^{3} d + C b c^{3} d + 6 \, {\left(d x + c\right)} C a c d^{2} + 6 \, {\left(d x + c\right)} B b c d^{2} - C a c^{2} d^{2} - B b c^{2} d^{2} - 3 \, {\left(d x + c\right)} B a d^{3} - 3 \, {\left(d x + c\right)} A b d^{3} + B a c d^{3} + A b c d^{3} - A a d^{4}\right)}}{3 \, {\left(d x + c\right)}^{\frac{3}{2}} d^{5}} + \frac{2 \, {\left(3 \, {\left(d x + c\right)}^{\frac{5}{2}} D b d^{20} - 20 \, {\left(d x + c\right)}^{\frac{3}{2}} D b c d^{20} + 90 \, \sqrt{d x + c} D b c^{2} d^{20} + 5 \, {\left(d x + c\right)}^{\frac{3}{2}} D a d^{21} + 5 \, {\left(d x + c\right)}^{\frac{3}{2}} C b d^{21} - 45 \, \sqrt{d x + c} D a c d^{21} - 45 \, \sqrt{d x + c} C b c d^{21} + 15 \, \sqrt{d x + c} C a d^{22} + 15 \, \sqrt{d x + c} B b d^{22}\right)}}{15 \, d^{25}}"," ",0,"2/3*(12*(d*x + c)*D*b*c^3 - D*b*c^4 - 9*(d*x + c)*D*a*c^2*d - 9*(d*x + c)*C*b*c^2*d + D*a*c^3*d + C*b*c^3*d + 6*(d*x + c)*C*a*c*d^2 + 6*(d*x + c)*B*b*c*d^2 - C*a*c^2*d^2 - B*b*c^2*d^2 - 3*(d*x + c)*B*a*d^3 - 3*(d*x + c)*A*b*d^3 + B*a*c*d^3 + A*b*c*d^3 - A*a*d^4)/((d*x + c)^(3/2)*d^5) + 2/15*(3*(d*x + c)^(5/2)*D*b*d^20 - 20*(d*x + c)^(3/2)*D*b*c*d^20 + 90*sqrt(d*x + c)*D*b*c^2*d^20 + 5*(d*x + c)^(3/2)*D*a*d^21 + 5*(d*x + c)^(3/2)*C*b*d^21 - 45*sqrt(d*x + c)*D*a*c*d^21 - 45*sqrt(d*x + c)*C*b*c*d^21 + 15*sqrt(d*x + c)*C*a*d^22 + 15*sqrt(d*x + c)*B*b*d^22)/d^25","A",0
21,1,115,0,1.228932," ","integrate((D*x^3+C*x^2+B*x+A)/(d*x+c)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(9 \, {\left(d x + c\right)} D c^{2} - D c^{3} - 6 \, {\left(d x + c\right)} C c d + C c^{2} d + 3 \, {\left(d x + c\right)} B d^{2} - B c d^{2} + A d^{3}\right)}}{3 \, {\left(d x + c\right)}^{\frac{3}{2}} d^{4}} + \frac{2 \, {\left({\left(d x + c\right)}^{\frac{3}{2}} D d^{8} - 9 \, \sqrt{d x + c} D c d^{8} + 3 \, \sqrt{d x + c} C d^{9}\right)}}{3 \, d^{12}}"," ",0,"-2/3*(9*(d*x + c)*D*c^2 - D*c^3 - 6*(d*x + c)*C*c*d + C*c^2*d + 3*(d*x + c)*B*d^2 - B*c*d^2 + A*d^3)/((d*x + c)^(3/2)*d^4) + 2/3*((d*x + c)^(3/2)*D*d^8 - 9*sqrt(d*x + c)*D*c*d^8 + 3*sqrt(d*x + c)*C*d^9)/d^12","A",0
22,1,281,0,1.312561," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)/(d*x+c)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(D a^{3} - C a^{2} b + B a b^{2} - A b^{3}\right)} \arctan\left(\frac{\sqrt{d x + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} \sqrt{-b^{2} c + a b d}} + \frac{2 \, {\left(6 \, {\left(d x + c\right)} D b c^{3} - D b c^{4} - 9 \, {\left(d x + c\right)} D a c^{2} d - 3 \, {\left(d x + c\right)} C b c^{2} d + D a c^{3} d + C b c^{3} d + 6 \, {\left(d x + c\right)} C a c d^{2} - C a c^{2} d^{2} - B b c^{2} d^{2} - 3 \, {\left(d x + c\right)} B a d^{3} + 3 \, {\left(d x + c\right)} A b d^{3} + B a c d^{3} + A b c d^{3} - A a d^{4}\right)}}{3 \, {\left(b^{2} c^{2} d^{3} - 2 \, a b c d^{4} + a^{2} d^{5}\right)} {\left(d x + c\right)}^{\frac{3}{2}}} + \frac{2 \, \sqrt{d x + c} D}{b d^{3}}"," ",0,"-2*(D*a^3 - C*a^2*b + B*a*b^2 - A*b^3)*arctan(sqrt(d*x + c)*b/sqrt(-b^2*c + a*b*d))/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*sqrt(-b^2*c + a*b*d)) + 2/3*(6*(d*x + c)*D*b*c^3 - D*b*c^4 - 9*(d*x + c)*D*a*c^2*d - 3*(d*x + c)*C*b*c^2*d + D*a*c^3*d + C*b*c^3*d + 6*(d*x + c)*C*a*c*d^2 - C*a*c^2*d^2 - B*b*c^2*d^2 - 3*(d*x + c)*B*a*d^3 + 3*(d*x + c)*A*b*d^3 + B*a*c*d^3 + A*b*c*d^3 - A*a*d^4)/((b^2*c^2*d^3 - 2*a*b*c*d^4 + a^2*d^5)*(d*x + c)^(3/2)) + 2*sqrt(d*x + c)*D/(b*d^3)","A",0
23,1,439,0,1.416586," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^2/(d*x+c)^(5/2),x, algorithm=""giac"")","\frac{{\left(6 \, D a^{2} b c - 4 \, C a b^{2} c + 2 \, B b^{3} c - D a^{3} d - C a^{2} b d + 3 \, B a b^{2} d - 5 \, A b^{3} d\right)} \arctan\left(\frac{\sqrt{d x + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} \sqrt{-b^{2} c + a b d}} + \frac{\sqrt{d x + c} D a^{3} d - \sqrt{d x + c} C a^{2} b d + \sqrt{d x + c} B a b^{2} d - \sqrt{d x + c} A b^{3} d}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} {\left({\left(d x + c\right)} b - b c + a d\right)}} - \frac{2 \, {\left(3 \, {\left(d x + c\right)} D b c^{3} - D b c^{4} - 9 \, {\left(d x + c\right)} D a c^{2} d + D a c^{3} d + C b c^{3} d + 6 \, {\left(d x + c\right)} C a c d^{2} - 3 \, {\left(d x + c\right)} B b c d^{2} - C a c^{2} d^{2} - B b c^{2} d^{2} - 3 \, {\left(d x + c\right)} B a d^{3} + 6 \, {\left(d x + c\right)} A b d^{3} + B a c d^{3} + A b c d^{3} - A a d^{4}\right)}}{3 \, {\left(b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} {\left(d x + c\right)}^{\frac{3}{2}}}"," ",0,"(6*D*a^2*b*c - 4*C*a*b^2*c + 2*B*b^3*c - D*a^3*d - C*a^2*b*d + 3*B*a*b^2*d - 5*A*b^3*d)*arctan(sqrt(d*x + c)*b/sqrt(-b^2*c + a*b*d))/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*sqrt(-b^2*c + a*b*d)) + (sqrt(d*x + c)*D*a^3*d - sqrt(d*x + c)*C*a^2*b*d + sqrt(d*x + c)*B*a*b^2*d - sqrt(d*x + c)*A*b^3*d)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*((d*x + c)*b - b*c + a*d)) - 2/3*(3*(d*x + c)*D*b*c^3 - D*b*c^4 - 9*(d*x + c)*D*a*c^2*d + D*a*c^3*d + C*b*c^3*d + 6*(d*x + c)*C*a*c*d^2 - 3*(d*x + c)*B*b*c*d^2 - C*a*c^2*d^2 - B*b*c^2*d^2 - 3*(d*x + c)*B*a*d^3 + 6*(d*x + c)*A*b*d^3 + B*a*c*d^3 + A*b*c*d^3 - A*a*d^4)/((b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4 - a^3*d^5)*(d*x + c)^(3/2))","A",0
24,1,767,0,1.450148," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^3/(d*x+c)^(5/2),x, algorithm=""giac"")","-\frac{{\left(24 \, D a b^{2} c^{2} - 8 \, C b^{3} c^{2} + 12 \, D a^{2} b c d - 24 \, C a b^{2} c d + 20 \, B b^{3} c d - D a^{3} d^{2} - 3 \, C a^{2} b d^{2} + 15 \, B a b^{2} d^{2} - 35 \, A b^{3} d^{2}\right)} \arctan\left(\frac{\sqrt{d x + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{4 \, {\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} \sqrt{-b^{2} c + a b d}} - \frac{2 \, {\left(D b c^{4} + 9 \, {\left(d x + c\right)} D a c^{2} d - 3 \, {\left(d x + c\right)} C b c^{2} d - D a c^{3} d - C b c^{3} d - 6 \, {\left(d x + c\right)} C a c d^{2} + 6 \, {\left(d x + c\right)} B b c d^{2} + C a c^{2} d^{2} + B b c^{2} d^{2} + 3 \, {\left(d x + c\right)} B a d^{3} - 9 \, {\left(d x + c\right)} A b d^{3} - B a c d^{3} - A b c d^{3} + A a d^{4}\right)}}{3 \, {\left(b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}\right)} {\left(d x + c\right)}^{\frac{3}{2}}} - \frac{12 \, {\left(d x + c\right)}^{\frac{3}{2}} D a^{2} b^{2} c d - 8 \, {\left(d x + c\right)}^{\frac{3}{2}} C a b^{3} c d + 4 \, {\left(d x + c\right)}^{\frac{3}{2}} B b^{4} c d - 12 \, \sqrt{d x + c} D a^{2} b^{2} c^{2} d + 8 \, \sqrt{d x + c} C a b^{3} c^{2} d - 4 \, \sqrt{d x + c} B b^{4} c^{2} d - {\left(d x + c\right)}^{\frac{3}{2}} D a^{3} b d^{2} - 3 \, {\left(d x + c\right)}^{\frac{3}{2}} C a^{2} b^{2} d^{2} + 7 \, {\left(d x + c\right)}^{\frac{3}{2}} B a b^{3} d^{2} - 11 \, {\left(d x + c\right)}^{\frac{3}{2}} A b^{4} d^{2} + 11 \, \sqrt{d x + c} D a^{3} b c d^{2} - 3 \, \sqrt{d x + c} C a^{2} b^{2} c d^{2} - 5 \, \sqrt{d x + c} B a b^{3} c d^{2} + 13 \, \sqrt{d x + c} A b^{4} c d^{2} + \sqrt{d x + c} D a^{4} d^{3} - 5 \, \sqrt{d x + c} C a^{3} b d^{3} + 9 \, \sqrt{d x + c} B a^{2} b^{2} d^{3} - 13 \, \sqrt{d x + c} A a b^{3} d^{3}}{4 \, {\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} {\left({\left(d x + c\right)} b - b c + a d\right)}^{2}}"," ",0,"-1/4*(24*D*a*b^2*c^2 - 8*C*b^3*c^2 + 12*D*a^2*b*c*d - 24*C*a*b^2*c*d + 20*B*b^3*c*d - D*a^3*d^2 - 3*C*a^2*b*d^2 + 15*B*a*b^2*d^2 - 35*A*b^3*d^2)*arctan(sqrt(d*x + c)*b/sqrt(-b^2*c + a*b*d))/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*sqrt(-b^2*c + a*b*d)) - 2/3*(D*b*c^4 + 9*(d*x + c)*D*a*c^2*d - 3*(d*x + c)*C*b*c^2*d - D*a*c^3*d - C*b*c^3*d - 6*(d*x + c)*C*a*c*d^2 + 6*(d*x + c)*B*b*c*d^2 + C*a*c^2*d^2 + B*b*c^2*d^2 + 3*(d*x + c)*B*a*d^3 - 9*(d*x + c)*A*b*d^3 - B*a*c*d^3 - A*b*c*d^3 + A*a*d^4)/((b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5)*(d*x + c)^(3/2)) - 1/4*(12*(d*x + c)^(3/2)*D*a^2*b^2*c*d - 8*(d*x + c)^(3/2)*C*a*b^3*c*d + 4*(d*x + c)^(3/2)*B*b^4*c*d - 12*sqrt(d*x + c)*D*a^2*b^2*c^2*d + 8*sqrt(d*x + c)*C*a*b^3*c^2*d - 4*sqrt(d*x + c)*B*b^4*c^2*d - (d*x + c)^(3/2)*D*a^3*b*d^2 - 3*(d*x + c)^(3/2)*C*a^2*b^2*d^2 + 7*(d*x + c)^(3/2)*B*a*b^3*d^2 - 11*(d*x + c)^(3/2)*A*b^4*d^2 + 11*sqrt(d*x + c)*D*a^3*b*c*d^2 - 3*sqrt(d*x + c)*C*a^2*b^2*c*d^2 - 5*sqrt(d*x + c)*B*a*b^3*c*d^2 + 13*sqrt(d*x + c)*A*b^4*c*d^2 + sqrt(d*x + c)*D*a^4*d^3 - 5*sqrt(d*x + c)*C*a^3*b*d^3 + 9*sqrt(d*x + c)*B*a^2*b^2*d^3 - 13*sqrt(d*x + c)*A*a*b^3*d^3)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*((d*x + c)*b - b*c + a*d)^2)","A",0
25,1,9032,0,1.864793," ","integrate((b*x+a)^3*(d*x+c)^n*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\frac{{\left(d x + c\right)}^{n} D b^{3} d^{7} n^{6} x^{7} + {\left(d x + c\right)}^{n} D b^{3} c d^{6} n^{6} x^{6} + 3 \, {\left(d x + c\right)}^{n} D a b^{2} d^{7} n^{6} x^{6} + {\left(d x + c\right)}^{n} C b^{3} d^{7} n^{6} x^{6} + 21 \, {\left(d x + c\right)}^{n} D b^{3} d^{7} n^{5} x^{7} + 3 \, {\left(d x + c\right)}^{n} D a b^{2} c d^{6} n^{6} x^{5} + {\left(d x + c\right)}^{n} C b^{3} c d^{6} n^{6} x^{5} + 3 \, {\left(d x + c\right)}^{n} D a^{2} b d^{7} n^{6} x^{5} + 3 \, {\left(d x + c\right)}^{n} C a b^{2} d^{7} n^{6} x^{5} + {\left(d x + c\right)}^{n} B b^{3} d^{7} n^{6} x^{5} + 15 \, {\left(d x + c\right)}^{n} D b^{3} c d^{6} n^{5} x^{6} + 66 \, {\left(d x + c\right)}^{n} D a b^{2} d^{7} n^{5} x^{6} + 22 \, {\left(d x + c\right)}^{n} C b^{3} d^{7} n^{5} x^{6} + 175 \, {\left(d x + c\right)}^{n} D b^{3} d^{7} n^{4} x^{7} + 3 \, {\left(d x + c\right)}^{n} D a^{2} b c d^{6} n^{6} x^{4} + 3 \, {\left(d x + c\right)}^{n} C a b^{2} c d^{6} n^{6} x^{4} + {\left(d x + c\right)}^{n} B b^{3} c d^{6} n^{6} x^{4} + {\left(d x + c\right)}^{n} D a^{3} d^{7} n^{6} x^{4} + 3 \, {\left(d x + c\right)}^{n} C a^{2} b d^{7} n^{6} x^{4} + 3 \, {\left(d x + c\right)}^{n} B a b^{2} d^{7} n^{6} x^{4} + {\left(d x + c\right)}^{n} A b^{3} d^{7} n^{6} x^{4} - 6 \, {\left(d x + c\right)}^{n} D b^{3} c^{2} d^{5} n^{5} x^{5} + 51 \, {\left(d x + c\right)}^{n} D a b^{2} c d^{6} n^{5} x^{5} + 17 \, {\left(d x + c\right)}^{n} C b^{3} c d^{6} n^{5} x^{5} + 69 \, {\left(d x + c\right)}^{n} D a^{2} b d^{7} n^{5} x^{5} + 69 \, {\left(d x + c\right)}^{n} C a b^{2} d^{7} n^{5} x^{5} + 23 \, {\left(d x + c\right)}^{n} B b^{3} d^{7} n^{5} x^{5} + 85 \, {\left(d x + c\right)}^{n} D b^{3} c d^{6} n^{4} x^{6} + 570 \, {\left(d x + c\right)}^{n} D a b^{2} d^{7} n^{4} x^{6} + 190 \, {\left(d x + c\right)}^{n} C b^{3} d^{7} n^{4} x^{6} + 735 \, {\left(d x + c\right)}^{n} D b^{3} d^{7} n^{3} x^{7} + {\left(d x + c\right)}^{n} D a^{3} c d^{6} n^{6} x^{3} + 3 \, {\left(d x + c\right)}^{n} C a^{2} b c d^{6} n^{6} x^{3} + 3 \, {\left(d x + c\right)}^{n} B a b^{2} c d^{6} n^{6} x^{3} + {\left(d x + c\right)}^{n} A b^{3} c d^{6} n^{6} x^{3} + {\left(d x + c\right)}^{n} C a^{3} d^{7} n^{6} x^{3} + 3 \, {\left(d x + c\right)}^{n} B a^{2} b d^{7} n^{6} x^{3} + 3 \, {\left(d x + c\right)}^{n} A a b^{2} d^{7} n^{6} x^{3} - 15 \, {\left(d x + c\right)}^{n} D a b^{2} c^{2} d^{5} n^{5} x^{4} - 5 \, {\left(d x + c\right)}^{n} C b^{3} c^{2} d^{5} n^{5} x^{4} + 57 \, {\left(d x + c\right)}^{n} D a^{2} b c d^{6} n^{5} x^{4} + 57 \, {\left(d x + c\right)}^{n} C a b^{2} c d^{6} n^{5} x^{4} + 19 \, {\left(d x + c\right)}^{n} B b^{3} c d^{6} n^{5} x^{4} + 24 \, {\left(d x + c\right)}^{n} D a^{3} d^{7} n^{5} x^{4} + 72 \, {\left(d x + c\right)}^{n} C a^{2} b d^{7} n^{5} x^{4} + 72 \, {\left(d x + c\right)}^{n} B a b^{2} d^{7} n^{5} x^{4} + 24 \, {\left(d x + c\right)}^{n} A b^{3} d^{7} n^{5} x^{4} - 60 \, {\left(d x + c\right)}^{n} D b^{3} c^{2} d^{5} n^{4} x^{5} + 315 \, {\left(d x + c\right)}^{n} D a b^{2} c d^{6} n^{4} x^{5} + 105 \, {\left(d x + c\right)}^{n} C b^{3} c d^{6} n^{4} x^{5} + 621 \, {\left(d x + c\right)}^{n} D a^{2} b d^{7} n^{4} x^{5} + 621 \, {\left(d x + c\right)}^{n} C a b^{2} d^{7} n^{4} x^{5} + 207 \, {\left(d x + c\right)}^{n} B b^{3} d^{7} n^{4} x^{5} + 225 \, {\left(d x + c\right)}^{n} D b^{3} c d^{6} n^{3} x^{6} + 2460 \, {\left(d x + c\right)}^{n} D a b^{2} d^{7} n^{3} x^{6} + 820 \, {\left(d x + c\right)}^{n} C b^{3} d^{7} n^{3} x^{6} + 1624 \, {\left(d x + c\right)}^{n} D b^{3} d^{7} n^{2} x^{7} + {\left(d x + c\right)}^{n} C a^{3} c d^{6} n^{6} x^{2} + 3 \, {\left(d x + c\right)}^{n} B a^{2} b c d^{6} n^{6} x^{2} + 3 \, {\left(d x + c\right)}^{n} A a b^{2} c d^{6} n^{6} x^{2} + {\left(d x + c\right)}^{n} B a^{3} d^{7} n^{6} x^{2} + 3 \, {\left(d x + c\right)}^{n} A a^{2} b d^{7} n^{6} x^{2} - 12 \, {\left(d x + c\right)}^{n} D a^{2} b c^{2} d^{5} n^{5} x^{3} - 12 \, {\left(d x + c\right)}^{n} C a b^{2} c^{2} d^{5} n^{5} x^{3} - 4 \, {\left(d x + c\right)}^{n} B b^{3} c^{2} d^{5} n^{5} x^{3} + 21 \, {\left(d x + c\right)}^{n} D a^{3} c d^{6} n^{5} x^{3} + 63 \, {\left(d x + c\right)}^{n} C a^{2} b c d^{6} n^{5} x^{3} + 63 \, {\left(d x + c\right)}^{n} B a b^{2} c d^{6} n^{5} x^{3} + 21 \, {\left(d x + c\right)}^{n} A b^{3} c d^{6} n^{5} x^{3} + 25 \, {\left(d x + c\right)}^{n} C a^{3} d^{7} n^{5} x^{3} + 75 \, {\left(d x + c\right)}^{n} B a^{2} b d^{7} n^{5} x^{3} + 75 \, {\left(d x + c\right)}^{n} A a b^{2} d^{7} n^{5} x^{3} + 30 \, {\left(d x + c\right)}^{n} D b^{3} c^{3} d^{4} n^{4} x^{4} - 195 \, {\left(d x + c\right)}^{n} D a b^{2} c^{2} d^{5} n^{4} x^{4} - 65 \, {\left(d x + c\right)}^{n} C b^{3} c^{2} d^{5} n^{4} x^{4} + 393 \, {\left(d x + c\right)}^{n} D a^{2} b c d^{6} n^{4} x^{4} + 393 \, {\left(d x + c\right)}^{n} C a b^{2} c d^{6} n^{4} x^{4} + 131 \, {\left(d x + c\right)}^{n} B b^{3} c d^{6} n^{4} x^{4} + 226 \, {\left(d x + c\right)}^{n} D a^{3} d^{7} n^{4} x^{4} + 678 \, {\left(d x + c\right)}^{n} C a^{2} b d^{7} n^{4} x^{4} + 678 \, {\left(d x + c\right)}^{n} B a b^{2} d^{7} n^{4} x^{4} + 226 \, {\left(d x + c\right)}^{n} A b^{3} d^{7} n^{4} x^{4} - 210 \, {\left(d x + c\right)}^{n} D b^{3} c^{2} d^{5} n^{3} x^{5} + 885 \, {\left(d x + c\right)}^{n} D a b^{2} c d^{6} n^{3} x^{5} + 295 \, {\left(d x + c\right)}^{n} C b^{3} c d^{6} n^{3} x^{5} + 2775 \, {\left(d x + c\right)}^{n} D a^{2} b d^{7} n^{3} x^{5} + 2775 \, {\left(d x + c\right)}^{n} C a b^{2} d^{7} n^{3} x^{5} + 925 \, {\left(d x + c\right)}^{n} B b^{3} d^{7} n^{3} x^{5} + 274 \, {\left(d x + c\right)}^{n} D b^{3} c d^{6} n^{2} x^{6} + 5547 \, {\left(d x + c\right)}^{n} D a b^{2} d^{7} n^{2} x^{6} + 1849 \, {\left(d x + c\right)}^{n} C b^{3} d^{7} n^{2} x^{6} + 1764 \, {\left(d x + c\right)}^{n} D b^{3} d^{7} n x^{7} + {\left(d x + c\right)}^{n} B a^{3} c d^{6} n^{6} x + 3 \, {\left(d x + c\right)}^{n} A a^{2} b c d^{6} n^{6} x + {\left(d x + c\right)}^{n} A a^{3} d^{7} n^{6} x - 3 \, {\left(d x + c\right)}^{n} D a^{3} c^{2} d^{5} n^{5} x^{2} - 9 \, {\left(d x + c\right)}^{n} C a^{2} b c^{2} d^{5} n^{5} x^{2} - 9 \, {\left(d x + c\right)}^{n} B a b^{2} c^{2} d^{5} n^{5} x^{2} - 3 \, {\left(d x + c\right)}^{n} A b^{3} c^{2} d^{5} n^{5} x^{2} + 23 \, {\left(d x + c\right)}^{n} C a^{3} c d^{6} n^{5} x^{2} + 69 \, {\left(d x + c\right)}^{n} B a^{2} b c d^{6} n^{5} x^{2} + 69 \, {\left(d x + c\right)}^{n} A a b^{2} c d^{6} n^{5} x^{2} + 26 \, {\left(d x + c\right)}^{n} B a^{3} d^{7} n^{5} x^{2} + 78 \, {\left(d x + c\right)}^{n} A a^{2} b d^{7} n^{5} x^{2} + 60 \, {\left(d x + c\right)}^{n} D a b^{2} c^{3} d^{4} n^{4} x^{3} + 20 \, {\left(d x + c\right)}^{n} C b^{3} c^{3} d^{4} n^{4} x^{3} - 192 \, {\left(d x + c\right)}^{n} D a^{2} b c^{2} d^{5} n^{4} x^{3} - 192 \, {\left(d x + c\right)}^{n} C a b^{2} c^{2} d^{5} n^{4} x^{3} - 64 \, {\left(d x + c\right)}^{n} B b^{3} c^{2} d^{5} n^{4} x^{3} + 163 \, {\left(d x + c\right)}^{n} D a^{3} c d^{6} n^{4} x^{3} + 489 \, {\left(d x + c\right)}^{n} C a^{2} b c d^{6} n^{4} x^{3} + 489 \, {\left(d x + c\right)}^{n} B a b^{2} c d^{6} n^{4} x^{3} + 163 \, {\left(d x + c\right)}^{n} A b^{3} c d^{6} n^{4} x^{3} + 247 \, {\left(d x + c\right)}^{n} C a^{3} d^{7} n^{4} x^{3} + 741 \, {\left(d x + c\right)}^{n} B a^{2} b d^{7} n^{4} x^{3} + 741 \, {\left(d x + c\right)}^{n} A a b^{2} d^{7} n^{4} x^{3} + 180 \, {\left(d x + c\right)}^{n} D b^{3} c^{3} d^{4} n^{3} x^{4} - 795 \, {\left(d x + c\right)}^{n} D a b^{2} c^{2} d^{5} n^{3} x^{4} - 265 \, {\left(d x + c\right)}^{n} C b^{3} c^{2} d^{5} n^{3} x^{4} + 1203 \, {\left(d x + c\right)}^{n} D a^{2} b c d^{6} n^{3} x^{4} + 1203 \, {\left(d x + c\right)}^{n} C a b^{2} c d^{6} n^{3} x^{4} + 401 \, {\left(d x + c\right)}^{n} B b^{3} c d^{6} n^{3} x^{4} + 1056 \, {\left(d x + c\right)}^{n} D a^{3} d^{7} n^{3} x^{4} + 3168 \, {\left(d x + c\right)}^{n} C a^{2} b d^{7} n^{3} x^{4} + 3168 \, {\left(d x + c\right)}^{n} B a b^{2} d^{7} n^{3} x^{4} + 1056 \, {\left(d x + c\right)}^{n} A b^{3} d^{7} n^{3} x^{4} - 300 \, {\left(d x + c\right)}^{n} D b^{3} c^{2} d^{5} n^{2} x^{5} + 1122 \, {\left(d x + c\right)}^{n} D a b^{2} c d^{6} n^{2} x^{5} + 374 \, {\left(d x + c\right)}^{n} C b^{3} c d^{6} n^{2} x^{5} + 6432 \, {\left(d x + c\right)}^{n} D a^{2} b d^{7} n^{2} x^{5} + 6432 \, {\left(d x + c\right)}^{n} C a b^{2} d^{7} n^{2} x^{5} + 2144 \, {\left(d x + c\right)}^{n} B b^{3} d^{7} n^{2} x^{5} + 120 \, {\left(d x + c\right)}^{n} D b^{3} c d^{6} n x^{6} + 6114 \, {\left(d x + c\right)}^{n} D a b^{2} d^{7} n x^{6} + 2038 \, {\left(d x + c\right)}^{n} C b^{3} d^{7} n x^{6} + 720 \, {\left(d x + c\right)}^{n} D b^{3} d^{7} x^{7} + {\left(d x + c\right)}^{n} A a^{3} c d^{6} n^{6} - 2 \, {\left(d x + c\right)}^{n} C a^{3} c^{2} d^{5} n^{5} x - 6 \, {\left(d x + c\right)}^{n} B a^{2} b c^{2} d^{5} n^{5} x - 6 \, {\left(d x + c\right)}^{n} A a b^{2} c^{2} d^{5} n^{5} x + 25 \, {\left(d x + c\right)}^{n} B a^{3} c d^{6} n^{5} x + 75 \, {\left(d x + c\right)}^{n} A a^{2} b c d^{6} n^{5} x + 27 \, {\left(d x + c\right)}^{n} A a^{3} d^{7} n^{5} x + 36 \, {\left(d x + c\right)}^{n} D a^{2} b c^{3} d^{4} n^{4} x^{2} + 36 \, {\left(d x + c\right)}^{n} C a b^{2} c^{3} d^{4} n^{4} x^{2} + 12 \, {\left(d x + c\right)}^{n} B b^{3} c^{3} d^{4} n^{4} x^{2} - 57 \, {\left(d x + c\right)}^{n} D a^{3} c^{2} d^{5} n^{4} x^{2} - 171 \, {\left(d x + c\right)}^{n} C a^{2} b c^{2} d^{5} n^{4} x^{2} - 171 \, {\left(d x + c\right)}^{n} B a b^{2} c^{2} d^{5} n^{4} x^{2} - 57 \, {\left(d x + c\right)}^{n} A b^{3} c^{2} d^{5} n^{4} x^{2} + 201 \, {\left(d x + c\right)}^{n} C a^{3} c d^{6} n^{4} x^{2} + 603 \, {\left(d x + c\right)}^{n} B a^{2} b c d^{6} n^{4} x^{2} + 603 \, {\left(d x + c\right)}^{n} A a b^{2} c d^{6} n^{4} x^{2} + 270 \, {\left(d x + c\right)}^{n} B a^{3} d^{7} n^{4} x^{2} + 810 \, {\left(d x + c\right)}^{n} A a^{2} b d^{7} n^{4} x^{2} - 120 \, {\left(d x + c\right)}^{n} D b^{3} c^{4} d^{3} n^{3} x^{3} + 600 \, {\left(d x + c\right)}^{n} D a b^{2} c^{3} d^{4} n^{3} x^{3} + 200 \, {\left(d x + c\right)}^{n} C b^{3} c^{3} d^{4} n^{3} x^{3} - 996 \, {\left(d x + c\right)}^{n} D a^{2} b c^{2} d^{5} n^{3} x^{3} - 996 \, {\left(d x + c\right)}^{n} C a b^{2} c^{2} d^{5} n^{3} x^{3} - 332 \, {\left(d x + c\right)}^{n} B b^{3} c^{2} d^{5} n^{3} x^{3} + 567 \, {\left(d x + c\right)}^{n} D a^{3} c d^{6} n^{3} x^{3} + 1701 \, {\left(d x + c\right)}^{n} C a^{2} b c d^{6} n^{3} x^{3} + 1701 \, {\left(d x + c\right)}^{n} B a b^{2} c d^{6} n^{3} x^{3} + 567 \, {\left(d x + c\right)}^{n} A b^{3} c d^{6} n^{3} x^{3} + 1219 \, {\left(d x + c\right)}^{n} C a^{3} d^{7} n^{3} x^{3} + 3657 \, {\left(d x + c\right)}^{n} B a^{2} b d^{7} n^{3} x^{3} + 3657 \, {\left(d x + c\right)}^{n} A a b^{2} d^{7} n^{3} x^{3} + 330 \, {\left(d x + c\right)}^{n} D b^{3} c^{3} d^{4} n^{2} x^{4} - 1245 \, {\left(d x + c\right)}^{n} D a b^{2} c^{2} d^{5} n^{2} x^{4} - 415 \, {\left(d x + c\right)}^{n} C b^{3} c^{2} d^{5} n^{2} x^{4} + 1620 \, {\left(d x + c\right)}^{n} D a^{2} b c d^{6} n^{2} x^{4} + 1620 \, {\left(d x + c\right)}^{n} C a b^{2} c d^{6} n^{2} x^{4} + 540 \, {\left(d x + c\right)}^{n} B b^{3} c d^{6} n^{2} x^{4} + 2545 \, {\left(d x + c\right)}^{n} D a^{3} d^{7} n^{2} x^{4} + 7635 \, {\left(d x + c\right)}^{n} C a^{2} b d^{7} n^{2} x^{4} + 7635 \, {\left(d x + c\right)}^{n} B a b^{2} d^{7} n^{2} x^{4} + 2545 \, {\left(d x + c\right)}^{n} A b^{3} d^{7} n^{2} x^{4} - 144 \, {\left(d x + c\right)}^{n} D b^{3} c^{2} d^{5} n x^{5} + 504 \, {\left(d x + c\right)}^{n} D a b^{2} c d^{6} n x^{5} + 168 \, {\left(d x + c\right)}^{n} C b^{3} c d^{6} n x^{5} + 7236 \, {\left(d x + c\right)}^{n} D a^{2} b d^{7} n x^{5} + 7236 \, {\left(d x + c\right)}^{n} C a b^{2} d^{7} n x^{5} + 2412 \, {\left(d x + c\right)}^{n} B b^{3} d^{7} n x^{5} + 2520 \, {\left(d x + c\right)}^{n} D a b^{2} d^{7} x^{6} + 840 \, {\left(d x + c\right)}^{n} C b^{3} d^{7} x^{6} - {\left(d x + c\right)}^{n} B a^{3} c^{2} d^{5} n^{5} - 3 \, {\left(d x + c\right)}^{n} A a^{2} b c^{2} d^{5} n^{5} + 27 \, {\left(d x + c\right)}^{n} A a^{3} c d^{6} n^{5} + 6 \, {\left(d x + c\right)}^{n} D a^{3} c^{3} d^{4} n^{4} x + 18 \, {\left(d x + c\right)}^{n} C a^{2} b c^{3} d^{4} n^{4} x + 18 \, {\left(d x + c\right)}^{n} B a b^{2} c^{3} d^{4} n^{4} x + 6 \, {\left(d x + c\right)}^{n} A b^{3} c^{3} d^{4} n^{4} x - 44 \, {\left(d x + c\right)}^{n} C a^{3} c^{2} d^{5} n^{4} x - 132 \, {\left(d x + c\right)}^{n} B a^{2} b c^{2} d^{5} n^{4} x - 132 \, {\left(d x + c\right)}^{n} A a b^{2} c^{2} d^{5} n^{4} x + 245 \, {\left(d x + c\right)}^{n} B a^{3} c d^{6} n^{4} x + 735 \, {\left(d x + c\right)}^{n} A a^{2} b c d^{6} n^{4} x + 295 \, {\left(d x + c\right)}^{n} A a^{3} d^{7} n^{4} x - 180 \, {\left(d x + c\right)}^{n} D a b^{2} c^{4} d^{3} n^{3} x^{2} - 60 \, {\left(d x + c\right)}^{n} C b^{3} c^{4} d^{3} n^{3} x^{2} + 504 \, {\left(d x + c\right)}^{n} D a^{2} b c^{3} d^{4} n^{3} x^{2} + 504 \, {\left(d x + c\right)}^{n} C a b^{2} c^{3} d^{4} n^{3} x^{2} + 168 \, {\left(d x + c\right)}^{n} B b^{3} c^{3} d^{4} n^{3} x^{2} - 375 \, {\left(d x + c\right)}^{n} D a^{3} c^{2} d^{5} n^{3} x^{2} - 1125 \, {\left(d x + c\right)}^{n} C a^{2} b c^{2} d^{5} n^{3} x^{2} - 1125 \, {\left(d x + c\right)}^{n} B a b^{2} c^{2} d^{5} n^{3} x^{2} - 375 \, {\left(d x + c\right)}^{n} A b^{3} c^{2} d^{5} n^{3} x^{2} + 817 \, {\left(d x + c\right)}^{n} C a^{3} c d^{6} n^{3} x^{2} + 2451 \, {\left(d x + c\right)}^{n} B a^{2} b c d^{6} n^{3} x^{2} + 2451 \, {\left(d x + c\right)}^{n} A a b^{2} c d^{6} n^{3} x^{2} + 1420 \, {\left(d x + c\right)}^{n} B a^{3} d^{7} n^{3} x^{2} + 4260 \, {\left(d x + c\right)}^{n} A a^{2} b d^{7} n^{3} x^{2} - 360 \, {\left(d x + c\right)}^{n} D b^{3} c^{4} d^{3} n^{2} x^{3} + 1380 \, {\left(d x + c\right)}^{n} D a b^{2} c^{3} d^{4} n^{2} x^{3} + 460 \, {\left(d x + c\right)}^{n} C b^{3} c^{3} d^{4} n^{2} x^{3} - 1824 \, {\left(d x + c\right)}^{n} D a^{2} b c^{2} d^{5} n^{2} x^{3} - 1824 \, {\left(d x + c\right)}^{n} C a b^{2} c^{2} d^{5} n^{2} x^{3} - 608 \, {\left(d x + c\right)}^{n} B b^{3} c^{2} d^{5} n^{2} x^{3} + 844 \, {\left(d x + c\right)}^{n} D a^{3} c d^{6} n^{2} x^{3} + 2532 \, {\left(d x + c\right)}^{n} C a^{2} b c d^{6} n^{2} x^{3} + 2532 \, {\left(d x + c\right)}^{n} B a b^{2} c d^{6} n^{2} x^{3} + 844 \, {\left(d x + c\right)}^{n} A b^{3} c d^{6} n^{2} x^{3} + 3112 \, {\left(d x + c\right)}^{n} C a^{3} d^{7} n^{2} x^{3} + 9336 \, {\left(d x + c\right)}^{n} B a^{2} b d^{7} n^{2} x^{3} + 9336 \, {\left(d x + c\right)}^{n} A a b^{2} d^{7} n^{2} x^{3} + 180 \, {\left(d x + c\right)}^{n} D b^{3} c^{3} d^{4} n x^{4} - 630 \, {\left(d x + c\right)}^{n} D a b^{2} c^{2} d^{5} n x^{4} - 210 \, {\left(d x + c\right)}^{n} C b^{3} c^{2} d^{5} n x^{4} + 756 \, {\left(d x + c\right)}^{n} D a^{2} b c d^{6} n x^{4} + 756 \, {\left(d x + c\right)}^{n} C a b^{2} c d^{6} n x^{4} + 252 \, {\left(d x + c\right)}^{n} B b^{3} c d^{6} n x^{4} + 2952 \, {\left(d x + c\right)}^{n} D a^{3} d^{7} n x^{4} + 8856 \, {\left(d x + c\right)}^{n} C a^{2} b d^{7} n x^{4} + 8856 \, {\left(d x + c\right)}^{n} B a b^{2} d^{7} n x^{4} + 2952 \, {\left(d x + c\right)}^{n} A b^{3} d^{7} n x^{4} + 3024 \, {\left(d x + c\right)}^{n} D a^{2} b d^{7} x^{5} + 3024 \, {\left(d x + c\right)}^{n} C a b^{2} d^{7} x^{5} + 1008 \, {\left(d x + c\right)}^{n} B b^{3} d^{7} x^{5} + 2 \, {\left(d x + c\right)}^{n} C a^{3} c^{3} d^{4} n^{4} + 6 \, {\left(d x + c\right)}^{n} B a^{2} b c^{3} d^{4} n^{4} + 6 \, {\left(d x + c\right)}^{n} A a b^{2} c^{3} d^{4} n^{4} - 25 \, {\left(d x + c\right)}^{n} B a^{3} c^{2} d^{5} n^{4} - 75 \, {\left(d x + c\right)}^{n} A a^{2} b c^{2} d^{5} n^{4} + 295 \, {\left(d x + c\right)}^{n} A a^{3} c d^{6} n^{4} - 72 \, {\left(d x + c\right)}^{n} D a^{2} b c^{4} d^{3} n^{3} x - 72 \, {\left(d x + c\right)}^{n} C a b^{2} c^{4} d^{3} n^{3} x - 24 \, {\left(d x + c\right)}^{n} B b^{3} c^{4} d^{3} n^{3} x + 108 \, {\left(d x + c\right)}^{n} D a^{3} c^{3} d^{4} n^{3} x + 324 \, {\left(d x + c\right)}^{n} C a^{2} b c^{3} d^{4} n^{3} x + 324 \, {\left(d x + c\right)}^{n} B a b^{2} c^{3} d^{4} n^{3} x + 108 \, {\left(d x + c\right)}^{n} A b^{3} c^{3} d^{4} n^{3} x - 358 \, {\left(d x + c\right)}^{n} C a^{3} c^{2} d^{5} n^{3} x - 1074 \, {\left(d x + c\right)}^{n} B a^{2} b c^{2} d^{5} n^{3} x - 1074 \, {\left(d x + c\right)}^{n} A a b^{2} c^{2} d^{5} n^{3} x + 1175 \, {\left(d x + c\right)}^{n} B a^{3} c d^{6} n^{3} x + 3525 \, {\left(d x + c\right)}^{n} A a^{2} b c d^{6} n^{3} x + 1665 \, {\left(d x + c\right)}^{n} A a^{3} d^{7} n^{3} x + 360 \, {\left(d x + c\right)}^{n} D b^{3} c^{5} d^{2} n^{2} x^{2} - 1440 \, {\left(d x + c\right)}^{n} D a b^{2} c^{4} d^{3} n^{2} x^{2} - 480 \, {\left(d x + c\right)}^{n} C b^{3} c^{4} d^{3} n^{2} x^{2} + 1980 \, {\left(d x + c\right)}^{n} D a^{2} b c^{3} d^{4} n^{2} x^{2} + 1980 \, {\left(d x + c\right)}^{n} C a b^{2} c^{3} d^{4} n^{2} x^{2} + 660 \, {\left(d x + c\right)}^{n} B b^{3} c^{3} d^{4} n^{2} x^{2} - 951 \, {\left(d x + c\right)}^{n} D a^{3} c^{2} d^{5} n^{2} x^{2} - 2853 \, {\left(d x + c\right)}^{n} C a^{2} b c^{2} d^{5} n^{2} x^{2} - 2853 \, {\left(d x + c\right)}^{n} B a b^{2} c^{2} d^{5} n^{2} x^{2} - 951 \, {\left(d x + c\right)}^{n} A b^{3} c^{2} d^{5} n^{2} x^{2} + 1478 \, {\left(d x + c\right)}^{n} C a^{3} c d^{6} n^{2} x^{2} + 4434 \, {\left(d x + c\right)}^{n} B a^{2} b c d^{6} n^{2} x^{2} + 4434 \, {\left(d x + c\right)}^{n} A a b^{2} c d^{6} n^{2} x^{2} + 3929 \, {\left(d x + c\right)}^{n} B a^{3} d^{7} n^{2} x^{2} + 11787 \, {\left(d x + c\right)}^{n} A a^{2} b d^{7} n^{2} x^{2} - 240 \, {\left(d x + c\right)}^{n} D b^{3} c^{4} d^{3} n x^{3} + 840 \, {\left(d x + c\right)}^{n} D a b^{2} c^{3} d^{4} n x^{3} + 280 \, {\left(d x + c\right)}^{n} C b^{3} c^{3} d^{4} n x^{3} - 1008 \, {\left(d x + c\right)}^{n} D a^{2} b c^{2} d^{5} n x^{3} - 1008 \, {\left(d x + c\right)}^{n} C a b^{2} c^{2} d^{5} n x^{3} - 336 \, {\left(d x + c\right)}^{n} B b^{3} c^{2} d^{5} n x^{3} + 420 \, {\left(d x + c\right)}^{n} D a^{3} c d^{6} n x^{3} + 1260 \, {\left(d x + c\right)}^{n} C a^{2} b c d^{6} n x^{3} + 1260 \, {\left(d x + c\right)}^{n} B a b^{2} c d^{6} n x^{3} + 420 \, {\left(d x + c\right)}^{n} A b^{3} c d^{6} n x^{3} + 3796 \, {\left(d x + c\right)}^{n} C a^{3} d^{7} n x^{3} + 11388 \, {\left(d x + c\right)}^{n} B a^{2} b d^{7} n x^{3} + 11388 \, {\left(d x + c\right)}^{n} A a b^{2} d^{7} n x^{3} + 1260 \, {\left(d x + c\right)}^{n} D a^{3} d^{7} x^{4} + 3780 \, {\left(d x + c\right)}^{n} C a^{2} b d^{7} x^{4} + 3780 \, {\left(d x + c\right)}^{n} B a b^{2} d^{7} x^{4} + 1260 \, {\left(d x + c\right)}^{n} A b^{3} d^{7} x^{4} - 6 \, {\left(d x + c\right)}^{n} D a^{3} c^{4} d^{3} n^{3} - 18 \, {\left(d x + c\right)}^{n} C a^{2} b c^{4} d^{3} n^{3} - 18 \, {\left(d x + c\right)}^{n} B a b^{2} c^{4} d^{3} n^{3} - 6 \, {\left(d x + c\right)}^{n} A b^{3} c^{4} d^{3} n^{3} + 44 \, {\left(d x + c\right)}^{n} C a^{3} c^{3} d^{4} n^{3} + 132 \, {\left(d x + c\right)}^{n} B a^{2} b c^{3} d^{4} n^{3} + 132 \, {\left(d x + c\right)}^{n} A a b^{2} c^{3} d^{4} n^{3} - 245 \, {\left(d x + c\right)}^{n} B a^{3} c^{2} d^{5} n^{3} - 735 \, {\left(d x + c\right)}^{n} A a^{2} b c^{2} d^{5} n^{3} + 1665 \, {\left(d x + c\right)}^{n} A a^{3} c d^{6} n^{3} + 360 \, {\left(d x + c\right)}^{n} D a b^{2} c^{5} d^{2} n^{2} x + 120 \, {\left(d x + c\right)}^{n} C b^{3} c^{5} d^{2} n^{2} x - 936 \, {\left(d x + c\right)}^{n} D a^{2} b c^{4} d^{3} n^{2} x - 936 \, {\left(d x + c\right)}^{n} C a b^{2} c^{4} d^{3} n^{2} x - 312 \, {\left(d x + c\right)}^{n} B b^{3} c^{4} d^{3} n^{2} x + 642 \, {\left(d x + c\right)}^{n} D a^{3} c^{3} d^{4} n^{2} x + 1926 \, {\left(d x + c\right)}^{n} C a^{2} b c^{3} d^{4} n^{2} x + 1926 \, {\left(d x + c\right)}^{n} B a b^{2} c^{3} d^{4} n^{2} x + 642 \, {\left(d x + c\right)}^{n} A b^{3} c^{3} d^{4} n^{2} x - 1276 \, {\left(d x + c\right)}^{n} C a^{3} c^{2} d^{5} n^{2} x - 3828 \, {\left(d x + c\right)}^{n} B a^{2} b c^{2} d^{5} n^{2} x - 3828 \, {\left(d x + c\right)}^{n} A a b^{2} c^{2} d^{5} n^{2} x + 2754 \, {\left(d x + c\right)}^{n} B a^{3} c d^{6} n^{2} x + 8262 \, {\left(d x + c\right)}^{n} A a^{2} b c d^{6} n^{2} x + 5104 \, {\left(d x + c\right)}^{n} A a^{3} d^{7} n^{2} x + 360 \, {\left(d x + c\right)}^{n} D b^{3} c^{5} d^{2} n x^{2} - 1260 \, {\left(d x + c\right)}^{n} D a b^{2} c^{4} d^{3} n x^{2} - 420 \, {\left(d x + c\right)}^{n} C b^{3} c^{4} d^{3} n x^{2} + 1512 \, {\left(d x + c\right)}^{n} D a^{2} b c^{3} d^{4} n x^{2} + 1512 \, {\left(d x + c\right)}^{n} C a b^{2} c^{3} d^{4} n x^{2} + 504 \, {\left(d x + c\right)}^{n} B b^{3} c^{3} d^{4} n x^{2} - 630 \, {\left(d x + c\right)}^{n} D a^{3} c^{2} d^{5} n x^{2} - 1890 \, {\left(d x + c\right)}^{n} C a^{2} b c^{2} d^{5} n x^{2} - 1890 \, {\left(d x + c\right)}^{n} B a b^{2} c^{2} d^{5} n x^{2} - 630 \, {\left(d x + c\right)}^{n} A b^{3} c^{2} d^{5} n x^{2} + 840 \, {\left(d x + c\right)}^{n} C a^{3} c d^{6} n x^{2} + 2520 \, {\left(d x + c\right)}^{n} B a^{2} b c d^{6} n x^{2} + 2520 \, {\left(d x + c\right)}^{n} A a b^{2} c d^{6} n x^{2} + 5274 \, {\left(d x + c\right)}^{n} B a^{3} d^{7} n x^{2} + 15822 \, {\left(d x + c\right)}^{n} A a^{2} b d^{7} n x^{2} + 1680 \, {\left(d x + c\right)}^{n} C a^{3} d^{7} x^{3} + 5040 \, {\left(d x + c\right)}^{n} B a^{2} b d^{7} x^{3} + 5040 \, {\left(d x + c\right)}^{n} A a b^{2} d^{7} x^{3} + 72 \, {\left(d x + c\right)}^{n} D a^{2} b c^{5} d^{2} n^{2} + 72 \, {\left(d x + c\right)}^{n} C a b^{2} c^{5} d^{2} n^{2} + 24 \, {\left(d x + c\right)}^{n} B b^{3} c^{5} d^{2} n^{2} - 108 \, {\left(d x + c\right)}^{n} D a^{3} c^{4} d^{3} n^{2} - 324 \, {\left(d x + c\right)}^{n} C a^{2} b c^{4} d^{3} n^{2} - 324 \, {\left(d x + c\right)}^{n} B a b^{2} c^{4} d^{3} n^{2} - 108 \, {\left(d x + c\right)}^{n} A b^{3} c^{4} d^{3} n^{2} + 358 \, {\left(d x + c\right)}^{n} C a^{3} c^{3} d^{4} n^{2} + 1074 \, {\left(d x + c\right)}^{n} B a^{2} b c^{3} d^{4} n^{2} + 1074 \, {\left(d x + c\right)}^{n} A a b^{2} c^{3} d^{4} n^{2} - 1175 \, {\left(d x + c\right)}^{n} B a^{3} c^{2} d^{5} n^{2} - 3525 \, {\left(d x + c\right)}^{n} A a^{2} b c^{2} d^{5} n^{2} + 5104 \, {\left(d x + c\right)}^{n} A a^{3} c d^{6} n^{2} - 720 \, {\left(d x + c\right)}^{n} D b^{3} c^{6} d n x + 2520 \, {\left(d x + c\right)}^{n} D a b^{2} c^{5} d^{2} n x + 840 \, {\left(d x + c\right)}^{n} C b^{3} c^{5} d^{2} n x - 3024 \, {\left(d x + c\right)}^{n} D a^{2} b c^{4} d^{3} n x - 3024 \, {\left(d x + c\right)}^{n} C a b^{2} c^{4} d^{3} n x - 1008 \, {\left(d x + c\right)}^{n} B b^{3} c^{4} d^{3} n x + 1260 \, {\left(d x + c\right)}^{n} D a^{3} c^{3} d^{4} n x + 3780 \, {\left(d x + c\right)}^{n} C a^{2} b c^{3} d^{4} n x + 3780 \, {\left(d x + c\right)}^{n} B a b^{2} c^{3} d^{4} n x + 1260 \, {\left(d x + c\right)}^{n} A b^{3} c^{3} d^{4} n x - 1680 \, {\left(d x + c\right)}^{n} C a^{3} c^{2} d^{5} n x - 5040 \, {\left(d x + c\right)}^{n} B a^{2} b c^{2} d^{5} n x - 5040 \, {\left(d x + c\right)}^{n} A a b^{2} c^{2} d^{5} n x + 2520 \, {\left(d x + c\right)}^{n} B a^{3} c d^{6} n x + 7560 \, {\left(d x + c\right)}^{n} A a^{2} b c d^{6} n x + 8028 \, {\left(d x + c\right)}^{n} A a^{3} d^{7} n x + 2520 \, {\left(d x + c\right)}^{n} B a^{3} d^{7} x^{2} + 7560 \, {\left(d x + c\right)}^{n} A a^{2} b d^{7} x^{2} - 360 \, {\left(d x + c\right)}^{n} D a b^{2} c^{6} d n - 120 \, {\left(d x + c\right)}^{n} C b^{3} c^{6} d n + 936 \, {\left(d x + c\right)}^{n} D a^{2} b c^{5} d^{2} n + 936 \, {\left(d x + c\right)}^{n} C a b^{2} c^{5} d^{2} n + 312 \, {\left(d x + c\right)}^{n} B b^{3} c^{5} d^{2} n - 642 \, {\left(d x + c\right)}^{n} D a^{3} c^{4} d^{3} n - 1926 \, {\left(d x + c\right)}^{n} C a^{2} b c^{4} d^{3} n - 1926 \, {\left(d x + c\right)}^{n} B a b^{2} c^{4} d^{3} n - 642 \, {\left(d x + c\right)}^{n} A b^{3} c^{4} d^{3} n + 1276 \, {\left(d x + c\right)}^{n} C a^{3} c^{3} d^{4} n + 3828 \, {\left(d x + c\right)}^{n} B a^{2} b c^{3} d^{4} n + 3828 \, {\left(d x + c\right)}^{n} A a b^{2} c^{3} d^{4} n - 2754 \, {\left(d x + c\right)}^{n} B a^{3} c^{2} d^{5} n - 8262 \, {\left(d x + c\right)}^{n} A a^{2} b c^{2} d^{5} n + 8028 \, {\left(d x + c\right)}^{n} A a^{3} c d^{6} n + 5040 \, {\left(d x + c\right)}^{n} A a^{3} d^{7} x + 720 \, {\left(d x + c\right)}^{n} D b^{3} c^{7} - 2520 \, {\left(d x + c\right)}^{n} D a b^{2} c^{6} d - 840 \, {\left(d x + c\right)}^{n} C b^{3} c^{6} d + 3024 \, {\left(d x + c\right)}^{n} D a^{2} b c^{5} d^{2} + 3024 \, {\left(d x + c\right)}^{n} C a b^{2} c^{5} d^{2} + 1008 \, {\left(d x + c\right)}^{n} B b^{3} c^{5} d^{2} - 1260 \, {\left(d x + c\right)}^{n} D a^{3} c^{4} d^{3} - 3780 \, {\left(d x + c\right)}^{n} C a^{2} b c^{4} d^{3} - 3780 \, {\left(d x + c\right)}^{n} B a b^{2} c^{4} d^{3} - 1260 \, {\left(d x + c\right)}^{n} A b^{3} c^{4} d^{3} + 1680 \, {\left(d x + c\right)}^{n} C a^{3} c^{3} d^{4} + 5040 \, {\left(d x + c\right)}^{n} B a^{2} b c^{3} d^{4} + 5040 \, {\left(d x + c\right)}^{n} A a b^{2} c^{3} d^{4} - 2520 \, {\left(d x + c\right)}^{n} B a^{3} c^{2} d^{5} - 7560 \, {\left(d x + c\right)}^{n} A a^{2} b c^{2} d^{5} + 5040 \, {\left(d x + c\right)}^{n} A a^{3} c d^{6}}{d^{7} n^{7} + 28 \, d^{7} n^{6} + 322 \, d^{7} n^{5} + 1960 \, d^{7} n^{4} + 6769 \, d^{7} n^{3} + 13132 \, d^{7} n^{2} + 13068 \, d^{7} n + 5040 \, d^{7}}"," ",0,"((d*x + c)^n*D*b^3*d^7*n^6*x^7 + (d*x + c)^n*D*b^3*c*d^6*n^6*x^6 + 3*(d*x + c)^n*D*a*b^2*d^7*n^6*x^6 + (d*x + c)^n*C*b^3*d^7*n^6*x^6 + 21*(d*x + c)^n*D*b^3*d^7*n^5*x^7 + 3*(d*x + c)^n*D*a*b^2*c*d^6*n^6*x^5 + (d*x + c)^n*C*b^3*c*d^6*n^6*x^5 + 3*(d*x + c)^n*D*a^2*b*d^7*n^6*x^5 + 3*(d*x + c)^n*C*a*b^2*d^7*n^6*x^5 + (d*x + c)^n*B*b^3*d^7*n^6*x^5 + 15*(d*x + c)^n*D*b^3*c*d^6*n^5*x^6 + 66*(d*x + c)^n*D*a*b^2*d^7*n^5*x^6 + 22*(d*x + c)^n*C*b^3*d^7*n^5*x^6 + 175*(d*x + c)^n*D*b^3*d^7*n^4*x^7 + 3*(d*x + c)^n*D*a^2*b*c*d^6*n^6*x^4 + 3*(d*x + c)^n*C*a*b^2*c*d^6*n^6*x^4 + (d*x + c)^n*B*b^3*c*d^6*n^6*x^4 + (d*x + c)^n*D*a^3*d^7*n^6*x^4 + 3*(d*x + c)^n*C*a^2*b*d^7*n^6*x^4 + 3*(d*x + c)^n*B*a*b^2*d^7*n^6*x^4 + (d*x + c)^n*A*b^3*d^7*n^6*x^4 - 6*(d*x + c)^n*D*b^3*c^2*d^5*n^5*x^5 + 51*(d*x + c)^n*D*a*b^2*c*d^6*n^5*x^5 + 17*(d*x + c)^n*C*b^3*c*d^6*n^5*x^5 + 69*(d*x + c)^n*D*a^2*b*d^7*n^5*x^5 + 69*(d*x + c)^n*C*a*b^2*d^7*n^5*x^5 + 23*(d*x + c)^n*B*b^3*d^7*n^5*x^5 + 85*(d*x + c)^n*D*b^3*c*d^6*n^4*x^6 + 570*(d*x + c)^n*D*a*b^2*d^7*n^4*x^6 + 190*(d*x + c)^n*C*b^3*d^7*n^4*x^6 + 735*(d*x + c)^n*D*b^3*d^7*n^3*x^7 + (d*x + c)^n*D*a^3*c*d^6*n^6*x^3 + 3*(d*x + c)^n*C*a^2*b*c*d^6*n^6*x^3 + 3*(d*x + c)^n*B*a*b^2*c*d^6*n^6*x^3 + (d*x + c)^n*A*b^3*c*d^6*n^6*x^3 + (d*x + c)^n*C*a^3*d^7*n^6*x^3 + 3*(d*x + c)^n*B*a^2*b*d^7*n^6*x^3 + 3*(d*x + c)^n*A*a*b^2*d^7*n^6*x^3 - 15*(d*x + c)^n*D*a*b^2*c^2*d^5*n^5*x^4 - 5*(d*x + c)^n*C*b^3*c^2*d^5*n^5*x^4 + 57*(d*x + c)^n*D*a^2*b*c*d^6*n^5*x^4 + 57*(d*x + c)^n*C*a*b^2*c*d^6*n^5*x^4 + 19*(d*x + c)^n*B*b^3*c*d^6*n^5*x^4 + 24*(d*x + c)^n*D*a^3*d^7*n^5*x^4 + 72*(d*x + c)^n*C*a^2*b*d^7*n^5*x^4 + 72*(d*x + c)^n*B*a*b^2*d^7*n^5*x^4 + 24*(d*x + c)^n*A*b^3*d^7*n^5*x^4 - 60*(d*x + c)^n*D*b^3*c^2*d^5*n^4*x^5 + 315*(d*x + c)^n*D*a*b^2*c*d^6*n^4*x^5 + 105*(d*x + c)^n*C*b^3*c*d^6*n^4*x^5 + 621*(d*x + c)^n*D*a^2*b*d^7*n^4*x^5 + 621*(d*x + c)^n*C*a*b^2*d^7*n^4*x^5 + 207*(d*x + c)^n*B*b^3*d^7*n^4*x^5 + 225*(d*x + c)^n*D*b^3*c*d^6*n^3*x^6 + 2460*(d*x + c)^n*D*a*b^2*d^7*n^3*x^6 + 820*(d*x + c)^n*C*b^3*d^7*n^3*x^6 + 1624*(d*x + c)^n*D*b^3*d^7*n^2*x^7 + (d*x + c)^n*C*a^3*c*d^6*n^6*x^2 + 3*(d*x + c)^n*B*a^2*b*c*d^6*n^6*x^2 + 3*(d*x + c)^n*A*a*b^2*c*d^6*n^6*x^2 + (d*x + c)^n*B*a^3*d^7*n^6*x^2 + 3*(d*x + c)^n*A*a^2*b*d^7*n^6*x^2 - 12*(d*x + c)^n*D*a^2*b*c^2*d^5*n^5*x^3 - 12*(d*x + c)^n*C*a*b^2*c^2*d^5*n^5*x^3 - 4*(d*x + c)^n*B*b^3*c^2*d^5*n^5*x^3 + 21*(d*x + c)^n*D*a^3*c*d^6*n^5*x^3 + 63*(d*x + c)^n*C*a^2*b*c*d^6*n^5*x^3 + 63*(d*x + c)^n*B*a*b^2*c*d^6*n^5*x^3 + 21*(d*x + c)^n*A*b^3*c*d^6*n^5*x^3 + 25*(d*x + c)^n*C*a^3*d^7*n^5*x^3 + 75*(d*x + c)^n*B*a^2*b*d^7*n^5*x^3 + 75*(d*x + c)^n*A*a*b^2*d^7*n^5*x^3 + 30*(d*x + c)^n*D*b^3*c^3*d^4*n^4*x^4 - 195*(d*x + c)^n*D*a*b^2*c^2*d^5*n^4*x^4 - 65*(d*x + c)^n*C*b^3*c^2*d^5*n^4*x^4 + 393*(d*x + c)^n*D*a^2*b*c*d^6*n^4*x^4 + 393*(d*x + c)^n*C*a*b^2*c*d^6*n^4*x^4 + 131*(d*x + c)^n*B*b^3*c*d^6*n^4*x^4 + 226*(d*x + c)^n*D*a^3*d^7*n^4*x^4 + 678*(d*x + c)^n*C*a^2*b*d^7*n^4*x^4 + 678*(d*x + c)^n*B*a*b^2*d^7*n^4*x^4 + 226*(d*x + c)^n*A*b^3*d^7*n^4*x^4 - 210*(d*x + c)^n*D*b^3*c^2*d^5*n^3*x^5 + 885*(d*x + c)^n*D*a*b^2*c*d^6*n^3*x^5 + 295*(d*x + c)^n*C*b^3*c*d^6*n^3*x^5 + 2775*(d*x + c)^n*D*a^2*b*d^7*n^3*x^5 + 2775*(d*x + c)^n*C*a*b^2*d^7*n^3*x^5 + 925*(d*x + c)^n*B*b^3*d^7*n^3*x^5 + 274*(d*x + c)^n*D*b^3*c*d^6*n^2*x^6 + 5547*(d*x + c)^n*D*a*b^2*d^7*n^2*x^6 + 1849*(d*x + c)^n*C*b^3*d^7*n^2*x^6 + 1764*(d*x + c)^n*D*b^3*d^7*n*x^7 + (d*x + c)^n*B*a^3*c*d^6*n^6*x + 3*(d*x + c)^n*A*a^2*b*c*d^6*n^6*x + (d*x + c)^n*A*a^3*d^7*n^6*x - 3*(d*x + c)^n*D*a^3*c^2*d^5*n^5*x^2 - 9*(d*x + c)^n*C*a^2*b*c^2*d^5*n^5*x^2 - 9*(d*x + c)^n*B*a*b^2*c^2*d^5*n^5*x^2 - 3*(d*x + c)^n*A*b^3*c^2*d^5*n^5*x^2 + 23*(d*x + c)^n*C*a^3*c*d^6*n^5*x^2 + 69*(d*x + c)^n*B*a^2*b*c*d^6*n^5*x^2 + 69*(d*x + c)^n*A*a*b^2*c*d^6*n^5*x^2 + 26*(d*x + c)^n*B*a^3*d^7*n^5*x^2 + 78*(d*x + c)^n*A*a^2*b*d^7*n^5*x^2 + 60*(d*x + c)^n*D*a*b^2*c^3*d^4*n^4*x^3 + 20*(d*x + c)^n*C*b^3*c^3*d^4*n^4*x^3 - 192*(d*x + c)^n*D*a^2*b*c^2*d^5*n^4*x^3 - 192*(d*x + c)^n*C*a*b^2*c^2*d^5*n^4*x^3 - 64*(d*x + c)^n*B*b^3*c^2*d^5*n^4*x^3 + 163*(d*x + c)^n*D*a^3*c*d^6*n^4*x^3 + 489*(d*x + c)^n*C*a^2*b*c*d^6*n^4*x^3 + 489*(d*x + c)^n*B*a*b^2*c*d^6*n^4*x^3 + 163*(d*x + c)^n*A*b^3*c*d^6*n^4*x^3 + 247*(d*x + c)^n*C*a^3*d^7*n^4*x^3 + 741*(d*x + c)^n*B*a^2*b*d^7*n^4*x^3 + 741*(d*x + c)^n*A*a*b^2*d^7*n^4*x^3 + 180*(d*x + c)^n*D*b^3*c^3*d^4*n^3*x^4 - 795*(d*x + c)^n*D*a*b^2*c^2*d^5*n^3*x^4 - 265*(d*x + c)^n*C*b^3*c^2*d^5*n^3*x^4 + 1203*(d*x + c)^n*D*a^2*b*c*d^6*n^3*x^4 + 1203*(d*x + c)^n*C*a*b^2*c*d^6*n^3*x^4 + 401*(d*x + c)^n*B*b^3*c*d^6*n^3*x^4 + 1056*(d*x + c)^n*D*a^3*d^7*n^3*x^4 + 3168*(d*x + c)^n*C*a^2*b*d^7*n^3*x^4 + 3168*(d*x + c)^n*B*a*b^2*d^7*n^3*x^4 + 1056*(d*x + c)^n*A*b^3*d^7*n^3*x^4 - 300*(d*x + c)^n*D*b^3*c^2*d^5*n^2*x^5 + 1122*(d*x + c)^n*D*a*b^2*c*d^6*n^2*x^5 + 374*(d*x + c)^n*C*b^3*c*d^6*n^2*x^5 + 6432*(d*x + c)^n*D*a^2*b*d^7*n^2*x^5 + 6432*(d*x + c)^n*C*a*b^2*d^7*n^2*x^5 + 2144*(d*x + c)^n*B*b^3*d^7*n^2*x^5 + 120*(d*x + c)^n*D*b^3*c*d^6*n*x^6 + 6114*(d*x + c)^n*D*a*b^2*d^7*n*x^6 + 2038*(d*x + c)^n*C*b^3*d^7*n*x^6 + 720*(d*x + c)^n*D*b^3*d^7*x^7 + (d*x + c)^n*A*a^3*c*d^6*n^6 - 2*(d*x + c)^n*C*a^3*c^2*d^5*n^5*x - 6*(d*x + c)^n*B*a^2*b*c^2*d^5*n^5*x - 6*(d*x + c)^n*A*a*b^2*c^2*d^5*n^5*x + 25*(d*x + c)^n*B*a^3*c*d^6*n^5*x + 75*(d*x + c)^n*A*a^2*b*c*d^6*n^5*x + 27*(d*x + c)^n*A*a^3*d^7*n^5*x + 36*(d*x + c)^n*D*a^2*b*c^3*d^4*n^4*x^2 + 36*(d*x + c)^n*C*a*b^2*c^3*d^4*n^4*x^2 + 12*(d*x + c)^n*B*b^3*c^3*d^4*n^4*x^2 - 57*(d*x + c)^n*D*a^3*c^2*d^5*n^4*x^2 - 171*(d*x + c)^n*C*a^2*b*c^2*d^5*n^4*x^2 - 171*(d*x + c)^n*B*a*b^2*c^2*d^5*n^4*x^2 - 57*(d*x + c)^n*A*b^3*c^2*d^5*n^4*x^2 + 201*(d*x + c)^n*C*a^3*c*d^6*n^4*x^2 + 603*(d*x + c)^n*B*a^2*b*c*d^6*n^4*x^2 + 603*(d*x + c)^n*A*a*b^2*c*d^6*n^4*x^2 + 270*(d*x + c)^n*B*a^3*d^7*n^4*x^2 + 810*(d*x + c)^n*A*a^2*b*d^7*n^4*x^2 - 120*(d*x + c)^n*D*b^3*c^4*d^3*n^3*x^3 + 600*(d*x + c)^n*D*a*b^2*c^3*d^4*n^3*x^3 + 200*(d*x + c)^n*C*b^3*c^3*d^4*n^3*x^3 - 996*(d*x + c)^n*D*a^2*b*c^2*d^5*n^3*x^3 - 996*(d*x + c)^n*C*a*b^2*c^2*d^5*n^3*x^3 - 332*(d*x + c)^n*B*b^3*c^2*d^5*n^3*x^3 + 567*(d*x + c)^n*D*a^3*c*d^6*n^3*x^3 + 1701*(d*x + c)^n*C*a^2*b*c*d^6*n^3*x^3 + 1701*(d*x + c)^n*B*a*b^2*c*d^6*n^3*x^3 + 567*(d*x + c)^n*A*b^3*c*d^6*n^3*x^3 + 1219*(d*x + c)^n*C*a^3*d^7*n^3*x^3 + 3657*(d*x + c)^n*B*a^2*b*d^7*n^3*x^3 + 3657*(d*x + c)^n*A*a*b^2*d^7*n^3*x^3 + 330*(d*x + c)^n*D*b^3*c^3*d^4*n^2*x^4 - 1245*(d*x + c)^n*D*a*b^2*c^2*d^5*n^2*x^4 - 415*(d*x + c)^n*C*b^3*c^2*d^5*n^2*x^4 + 1620*(d*x + c)^n*D*a^2*b*c*d^6*n^2*x^4 + 1620*(d*x + c)^n*C*a*b^2*c*d^6*n^2*x^4 + 540*(d*x + c)^n*B*b^3*c*d^6*n^2*x^4 + 2545*(d*x + c)^n*D*a^3*d^7*n^2*x^4 + 7635*(d*x + c)^n*C*a^2*b*d^7*n^2*x^4 + 7635*(d*x + c)^n*B*a*b^2*d^7*n^2*x^4 + 2545*(d*x + c)^n*A*b^3*d^7*n^2*x^4 - 144*(d*x + c)^n*D*b^3*c^2*d^5*n*x^5 + 504*(d*x + c)^n*D*a*b^2*c*d^6*n*x^5 + 168*(d*x + c)^n*C*b^3*c*d^6*n*x^5 + 7236*(d*x + c)^n*D*a^2*b*d^7*n*x^5 + 7236*(d*x + c)^n*C*a*b^2*d^7*n*x^5 + 2412*(d*x + c)^n*B*b^3*d^7*n*x^5 + 2520*(d*x + c)^n*D*a*b^2*d^7*x^6 + 840*(d*x + c)^n*C*b^3*d^7*x^6 - (d*x + c)^n*B*a^3*c^2*d^5*n^5 - 3*(d*x + c)^n*A*a^2*b*c^2*d^5*n^5 + 27*(d*x + c)^n*A*a^3*c*d^6*n^5 + 6*(d*x + c)^n*D*a^3*c^3*d^4*n^4*x + 18*(d*x + c)^n*C*a^2*b*c^3*d^4*n^4*x + 18*(d*x + c)^n*B*a*b^2*c^3*d^4*n^4*x + 6*(d*x + c)^n*A*b^3*c^3*d^4*n^4*x - 44*(d*x + c)^n*C*a^3*c^2*d^5*n^4*x - 132*(d*x + c)^n*B*a^2*b*c^2*d^5*n^4*x - 132*(d*x + c)^n*A*a*b^2*c^2*d^5*n^4*x + 245*(d*x + c)^n*B*a^3*c*d^6*n^4*x + 735*(d*x + c)^n*A*a^2*b*c*d^6*n^4*x + 295*(d*x + c)^n*A*a^3*d^7*n^4*x - 180*(d*x + c)^n*D*a*b^2*c^4*d^3*n^3*x^2 - 60*(d*x + c)^n*C*b^3*c^4*d^3*n^3*x^2 + 504*(d*x + c)^n*D*a^2*b*c^3*d^4*n^3*x^2 + 504*(d*x + c)^n*C*a*b^2*c^3*d^4*n^3*x^2 + 168*(d*x + c)^n*B*b^3*c^3*d^4*n^3*x^2 - 375*(d*x + c)^n*D*a^3*c^2*d^5*n^3*x^2 - 1125*(d*x + c)^n*C*a^2*b*c^2*d^5*n^3*x^2 - 1125*(d*x + c)^n*B*a*b^2*c^2*d^5*n^3*x^2 - 375*(d*x + c)^n*A*b^3*c^2*d^5*n^3*x^2 + 817*(d*x + c)^n*C*a^3*c*d^6*n^3*x^2 + 2451*(d*x + c)^n*B*a^2*b*c*d^6*n^3*x^2 + 2451*(d*x + c)^n*A*a*b^2*c*d^6*n^3*x^2 + 1420*(d*x + c)^n*B*a^3*d^7*n^3*x^2 + 4260*(d*x + c)^n*A*a^2*b*d^7*n^3*x^2 - 360*(d*x + c)^n*D*b^3*c^4*d^3*n^2*x^3 + 1380*(d*x + c)^n*D*a*b^2*c^3*d^4*n^2*x^3 + 460*(d*x + c)^n*C*b^3*c^3*d^4*n^2*x^3 - 1824*(d*x + c)^n*D*a^2*b*c^2*d^5*n^2*x^3 - 1824*(d*x + c)^n*C*a*b^2*c^2*d^5*n^2*x^3 - 608*(d*x + c)^n*B*b^3*c^2*d^5*n^2*x^3 + 844*(d*x + c)^n*D*a^3*c*d^6*n^2*x^3 + 2532*(d*x + c)^n*C*a^2*b*c*d^6*n^2*x^3 + 2532*(d*x + c)^n*B*a*b^2*c*d^6*n^2*x^3 + 844*(d*x + c)^n*A*b^3*c*d^6*n^2*x^3 + 3112*(d*x + c)^n*C*a^3*d^7*n^2*x^3 + 9336*(d*x + c)^n*B*a^2*b*d^7*n^2*x^3 + 9336*(d*x + c)^n*A*a*b^2*d^7*n^2*x^3 + 180*(d*x + c)^n*D*b^3*c^3*d^4*n*x^4 - 630*(d*x + c)^n*D*a*b^2*c^2*d^5*n*x^4 - 210*(d*x + c)^n*C*b^3*c^2*d^5*n*x^4 + 756*(d*x + c)^n*D*a^2*b*c*d^6*n*x^4 + 756*(d*x + c)^n*C*a*b^2*c*d^6*n*x^4 + 252*(d*x + c)^n*B*b^3*c*d^6*n*x^4 + 2952*(d*x + c)^n*D*a^3*d^7*n*x^4 + 8856*(d*x + c)^n*C*a^2*b*d^7*n*x^4 + 8856*(d*x + c)^n*B*a*b^2*d^7*n*x^4 + 2952*(d*x + c)^n*A*b^3*d^7*n*x^4 + 3024*(d*x + c)^n*D*a^2*b*d^7*x^5 + 3024*(d*x + c)^n*C*a*b^2*d^7*x^5 + 1008*(d*x + c)^n*B*b^3*d^7*x^5 + 2*(d*x + c)^n*C*a^3*c^3*d^4*n^4 + 6*(d*x + c)^n*B*a^2*b*c^3*d^4*n^4 + 6*(d*x + c)^n*A*a*b^2*c^3*d^4*n^4 - 25*(d*x + c)^n*B*a^3*c^2*d^5*n^4 - 75*(d*x + c)^n*A*a^2*b*c^2*d^5*n^4 + 295*(d*x + c)^n*A*a^3*c*d^6*n^4 - 72*(d*x + c)^n*D*a^2*b*c^4*d^3*n^3*x - 72*(d*x + c)^n*C*a*b^2*c^4*d^3*n^3*x - 24*(d*x + c)^n*B*b^3*c^4*d^3*n^3*x + 108*(d*x + c)^n*D*a^3*c^3*d^4*n^3*x + 324*(d*x + c)^n*C*a^2*b*c^3*d^4*n^3*x + 324*(d*x + c)^n*B*a*b^2*c^3*d^4*n^3*x + 108*(d*x + c)^n*A*b^3*c^3*d^4*n^3*x - 358*(d*x + c)^n*C*a^3*c^2*d^5*n^3*x - 1074*(d*x + c)^n*B*a^2*b*c^2*d^5*n^3*x - 1074*(d*x + c)^n*A*a*b^2*c^2*d^5*n^3*x + 1175*(d*x + c)^n*B*a^3*c*d^6*n^3*x + 3525*(d*x + c)^n*A*a^2*b*c*d^6*n^3*x + 1665*(d*x + c)^n*A*a^3*d^7*n^3*x + 360*(d*x + c)^n*D*b^3*c^5*d^2*n^2*x^2 - 1440*(d*x + c)^n*D*a*b^2*c^4*d^3*n^2*x^2 - 480*(d*x + c)^n*C*b^3*c^4*d^3*n^2*x^2 + 1980*(d*x + c)^n*D*a^2*b*c^3*d^4*n^2*x^2 + 1980*(d*x + c)^n*C*a*b^2*c^3*d^4*n^2*x^2 + 660*(d*x + c)^n*B*b^3*c^3*d^4*n^2*x^2 - 951*(d*x + c)^n*D*a^3*c^2*d^5*n^2*x^2 - 2853*(d*x + c)^n*C*a^2*b*c^2*d^5*n^2*x^2 - 2853*(d*x + c)^n*B*a*b^2*c^2*d^5*n^2*x^2 - 951*(d*x + c)^n*A*b^3*c^2*d^5*n^2*x^2 + 1478*(d*x + c)^n*C*a^3*c*d^6*n^2*x^2 + 4434*(d*x + c)^n*B*a^2*b*c*d^6*n^2*x^2 + 4434*(d*x + c)^n*A*a*b^2*c*d^6*n^2*x^2 + 3929*(d*x + c)^n*B*a^3*d^7*n^2*x^2 + 11787*(d*x + c)^n*A*a^2*b*d^7*n^2*x^2 - 240*(d*x + c)^n*D*b^3*c^4*d^3*n*x^3 + 840*(d*x + c)^n*D*a*b^2*c^3*d^4*n*x^3 + 280*(d*x + c)^n*C*b^3*c^3*d^4*n*x^3 - 1008*(d*x + c)^n*D*a^2*b*c^2*d^5*n*x^3 - 1008*(d*x + c)^n*C*a*b^2*c^2*d^5*n*x^3 - 336*(d*x + c)^n*B*b^3*c^2*d^5*n*x^3 + 420*(d*x + c)^n*D*a^3*c*d^6*n*x^3 + 1260*(d*x + c)^n*C*a^2*b*c*d^6*n*x^3 + 1260*(d*x + c)^n*B*a*b^2*c*d^6*n*x^3 + 420*(d*x + c)^n*A*b^3*c*d^6*n*x^3 + 3796*(d*x + c)^n*C*a^3*d^7*n*x^3 + 11388*(d*x + c)^n*B*a^2*b*d^7*n*x^3 + 11388*(d*x + c)^n*A*a*b^2*d^7*n*x^3 + 1260*(d*x + c)^n*D*a^3*d^7*x^4 + 3780*(d*x + c)^n*C*a^2*b*d^7*x^4 + 3780*(d*x + c)^n*B*a*b^2*d^7*x^4 + 1260*(d*x + c)^n*A*b^3*d^7*x^4 - 6*(d*x + c)^n*D*a^3*c^4*d^3*n^3 - 18*(d*x + c)^n*C*a^2*b*c^4*d^3*n^3 - 18*(d*x + c)^n*B*a*b^2*c^4*d^3*n^3 - 6*(d*x + c)^n*A*b^3*c^4*d^3*n^3 + 44*(d*x + c)^n*C*a^3*c^3*d^4*n^3 + 132*(d*x + c)^n*B*a^2*b*c^3*d^4*n^3 + 132*(d*x + c)^n*A*a*b^2*c^3*d^4*n^3 - 245*(d*x + c)^n*B*a^3*c^2*d^5*n^3 - 735*(d*x + c)^n*A*a^2*b*c^2*d^5*n^3 + 1665*(d*x + c)^n*A*a^3*c*d^6*n^3 + 360*(d*x + c)^n*D*a*b^2*c^5*d^2*n^2*x + 120*(d*x + c)^n*C*b^3*c^5*d^2*n^2*x - 936*(d*x + c)^n*D*a^2*b*c^4*d^3*n^2*x - 936*(d*x + c)^n*C*a*b^2*c^4*d^3*n^2*x - 312*(d*x + c)^n*B*b^3*c^4*d^3*n^2*x + 642*(d*x + c)^n*D*a^3*c^3*d^4*n^2*x + 1926*(d*x + c)^n*C*a^2*b*c^3*d^4*n^2*x + 1926*(d*x + c)^n*B*a*b^2*c^3*d^4*n^2*x + 642*(d*x + c)^n*A*b^3*c^3*d^4*n^2*x - 1276*(d*x + c)^n*C*a^3*c^2*d^5*n^2*x - 3828*(d*x + c)^n*B*a^2*b*c^2*d^5*n^2*x - 3828*(d*x + c)^n*A*a*b^2*c^2*d^5*n^2*x + 2754*(d*x + c)^n*B*a^3*c*d^6*n^2*x + 8262*(d*x + c)^n*A*a^2*b*c*d^6*n^2*x + 5104*(d*x + c)^n*A*a^3*d^7*n^2*x + 360*(d*x + c)^n*D*b^3*c^5*d^2*n*x^2 - 1260*(d*x + c)^n*D*a*b^2*c^4*d^3*n*x^2 - 420*(d*x + c)^n*C*b^3*c^4*d^3*n*x^2 + 1512*(d*x + c)^n*D*a^2*b*c^3*d^4*n*x^2 + 1512*(d*x + c)^n*C*a*b^2*c^3*d^4*n*x^2 + 504*(d*x + c)^n*B*b^3*c^3*d^4*n*x^2 - 630*(d*x + c)^n*D*a^3*c^2*d^5*n*x^2 - 1890*(d*x + c)^n*C*a^2*b*c^2*d^5*n*x^2 - 1890*(d*x + c)^n*B*a*b^2*c^2*d^5*n*x^2 - 630*(d*x + c)^n*A*b^3*c^2*d^5*n*x^2 + 840*(d*x + c)^n*C*a^3*c*d^6*n*x^2 + 2520*(d*x + c)^n*B*a^2*b*c*d^6*n*x^2 + 2520*(d*x + c)^n*A*a*b^2*c*d^6*n*x^2 + 5274*(d*x + c)^n*B*a^3*d^7*n*x^2 + 15822*(d*x + c)^n*A*a^2*b*d^7*n*x^2 + 1680*(d*x + c)^n*C*a^3*d^7*x^3 + 5040*(d*x + c)^n*B*a^2*b*d^7*x^3 + 5040*(d*x + c)^n*A*a*b^2*d^7*x^3 + 72*(d*x + c)^n*D*a^2*b*c^5*d^2*n^2 + 72*(d*x + c)^n*C*a*b^2*c^5*d^2*n^2 + 24*(d*x + c)^n*B*b^3*c^5*d^2*n^2 - 108*(d*x + c)^n*D*a^3*c^4*d^3*n^2 - 324*(d*x + c)^n*C*a^2*b*c^4*d^3*n^2 - 324*(d*x + c)^n*B*a*b^2*c^4*d^3*n^2 - 108*(d*x + c)^n*A*b^3*c^4*d^3*n^2 + 358*(d*x + c)^n*C*a^3*c^3*d^4*n^2 + 1074*(d*x + c)^n*B*a^2*b*c^3*d^4*n^2 + 1074*(d*x + c)^n*A*a*b^2*c^3*d^4*n^2 - 1175*(d*x + c)^n*B*a^3*c^2*d^5*n^2 - 3525*(d*x + c)^n*A*a^2*b*c^2*d^5*n^2 + 5104*(d*x + c)^n*A*a^3*c*d^6*n^2 - 720*(d*x + c)^n*D*b^3*c^6*d*n*x + 2520*(d*x + c)^n*D*a*b^2*c^5*d^2*n*x + 840*(d*x + c)^n*C*b^3*c^5*d^2*n*x - 3024*(d*x + c)^n*D*a^2*b*c^4*d^3*n*x - 3024*(d*x + c)^n*C*a*b^2*c^4*d^3*n*x - 1008*(d*x + c)^n*B*b^3*c^4*d^3*n*x + 1260*(d*x + c)^n*D*a^3*c^3*d^4*n*x + 3780*(d*x + c)^n*C*a^2*b*c^3*d^4*n*x + 3780*(d*x + c)^n*B*a*b^2*c^3*d^4*n*x + 1260*(d*x + c)^n*A*b^3*c^3*d^4*n*x - 1680*(d*x + c)^n*C*a^3*c^2*d^5*n*x - 5040*(d*x + c)^n*B*a^2*b*c^2*d^5*n*x - 5040*(d*x + c)^n*A*a*b^2*c^2*d^5*n*x + 2520*(d*x + c)^n*B*a^3*c*d^6*n*x + 7560*(d*x + c)^n*A*a^2*b*c*d^6*n*x + 8028*(d*x + c)^n*A*a^3*d^7*n*x + 2520*(d*x + c)^n*B*a^3*d^7*x^2 + 7560*(d*x + c)^n*A*a^2*b*d^7*x^2 - 360*(d*x + c)^n*D*a*b^2*c^6*d*n - 120*(d*x + c)^n*C*b^3*c^6*d*n + 936*(d*x + c)^n*D*a^2*b*c^5*d^2*n + 936*(d*x + c)^n*C*a*b^2*c^5*d^2*n + 312*(d*x + c)^n*B*b^3*c^5*d^2*n - 642*(d*x + c)^n*D*a^3*c^4*d^3*n - 1926*(d*x + c)^n*C*a^2*b*c^4*d^3*n - 1926*(d*x + c)^n*B*a*b^2*c^4*d^3*n - 642*(d*x + c)^n*A*b^3*c^4*d^3*n + 1276*(d*x + c)^n*C*a^3*c^3*d^4*n + 3828*(d*x + c)^n*B*a^2*b*c^3*d^4*n + 3828*(d*x + c)^n*A*a*b^2*c^3*d^4*n - 2754*(d*x + c)^n*B*a^3*c^2*d^5*n - 8262*(d*x + c)^n*A*a^2*b*c^2*d^5*n + 8028*(d*x + c)^n*A*a^3*c*d^6*n + 5040*(d*x + c)^n*A*a^3*d^7*x + 720*(d*x + c)^n*D*b^3*c^7 - 2520*(d*x + c)^n*D*a*b^2*c^6*d - 840*(d*x + c)^n*C*b^3*c^6*d + 3024*(d*x + c)^n*D*a^2*b*c^5*d^2 + 3024*(d*x + c)^n*C*a*b^2*c^5*d^2 + 1008*(d*x + c)^n*B*b^3*c^5*d^2 - 1260*(d*x + c)^n*D*a^3*c^4*d^3 - 3780*(d*x + c)^n*C*a^2*b*c^4*d^3 - 3780*(d*x + c)^n*B*a*b^2*c^4*d^3 - 1260*(d*x + c)^n*A*b^3*c^4*d^3 + 1680*(d*x + c)^n*C*a^3*c^3*d^4 + 5040*(d*x + c)^n*B*a^2*b*c^3*d^4 + 5040*(d*x + c)^n*A*a*b^2*c^3*d^4 - 2520*(d*x + c)^n*B*a^3*c^2*d^5 - 7560*(d*x + c)^n*A*a^2*b*c^2*d^5 + 5040*(d*x + c)^n*A*a^3*c*d^6)/(d^7*n^7 + 28*d^7*n^6 + 322*d^7*n^5 + 1960*d^7*n^4 + 6769*d^7*n^3 + 13132*d^7*n^2 + 13068*d^7*n + 5040*d^7)","B",0
26,1,4972,0,1.477049," ","integrate((b*x+a)^2*(d*x+c)^n*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\frac{{\left(d x + c\right)}^{n} D b^{2} d^{6} n^{5} x^{6} + {\left(d x + c\right)}^{n} D b^{2} c d^{5} n^{5} x^{5} + 2 \, {\left(d x + c\right)}^{n} D a b d^{6} n^{5} x^{5} + {\left(d x + c\right)}^{n} C b^{2} d^{6} n^{5} x^{5} + 15 \, {\left(d x + c\right)}^{n} D b^{2} d^{6} n^{4} x^{6} + 2 \, {\left(d x + c\right)}^{n} D a b c d^{5} n^{5} x^{4} + {\left(d x + c\right)}^{n} C b^{2} c d^{5} n^{5} x^{4} + {\left(d x + c\right)}^{n} D a^{2} d^{6} n^{5} x^{4} + 2 \, {\left(d x + c\right)}^{n} C a b d^{6} n^{5} x^{4} + {\left(d x + c\right)}^{n} B b^{2} d^{6} n^{5} x^{4} + 10 \, {\left(d x + c\right)}^{n} D b^{2} c d^{5} n^{4} x^{5} + 32 \, {\left(d x + c\right)}^{n} D a b d^{6} n^{4} x^{5} + 16 \, {\left(d x + c\right)}^{n} C b^{2} d^{6} n^{4} x^{5} + 85 \, {\left(d x + c\right)}^{n} D b^{2} d^{6} n^{3} x^{6} + {\left(d x + c\right)}^{n} D a^{2} c d^{5} n^{5} x^{3} + 2 \, {\left(d x + c\right)}^{n} C a b c d^{5} n^{5} x^{3} + {\left(d x + c\right)}^{n} B b^{2} c d^{5} n^{5} x^{3} + {\left(d x + c\right)}^{n} C a^{2} d^{6} n^{5} x^{3} + 2 \, {\left(d x + c\right)}^{n} B a b d^{6} n^{5} x^{3} + {\left(d x + c\right)}^{n} A b^{2} d^{6} n^{5} x^{3} - 5 \, {\left(d x + c\right)}^{n} D b^{2} c^{2} d^{4} n^{4} x^{4} + 24 \, {\left(d x + c\right)}^{n} D a b c d^{5} n^{4} x^{4} + 12 \, {\left(d x + c\right)}^{n} C b^{2} c d^{5} n^{4} x^{4} + 17 \, {\left(d x + c\right)}^{n} D a^{2} d^{6} n^{4} x^{4} + 34 \, {\left(d x + c\right)}^{n} C a b d^{6} n^{4} x^{4} + 17 \, {\left(d x + c\right)}^{n} B b^{2} d^{6} n^{4} x^{4} + 35 \, {\left(d x + c\right)}^{n} D b^{2} c d^{5} n^{3} x^{5} + 190 \, {\left(d x + c\right)}^{n} D a b d^{6} n^{3} x^{5} + 95 \, {\left(d x + c\right)}^{n} C b^{2} d^{6} n^{3} x^{5} + 225 \, {\left(d x + c\right)}^{n} D b^{2} d^{6} n^{2} x^{6} + {\left(d x + c\right)}^{n} C a^{2} c d^{5} n^{5} x^{2} + 2 \, {\left(d x + c\right)}^{n} B a b c d^{5} n^{5} x^{2} + {\left(d x + c\right)}^{n} A b^{2} c d^{5} n^{5} x^{2} + {\left(d x + c\right)}^{n} B a^{2} d^{6} n^{5} x^{2} + 2 \, {\left(d x + c\right)}^{n} A a b d^{6} n^{5} x^{2} - 8 \, {\left(d x + c\right)}^{n} D a b c^{2} d^{4} n^{4} x^{3} - 4 \, {\left(d x + c\right)}^{n} C b^{2} c^{2} d^{4} n^{4} x^{3} + 14 \, {\left(d x + c\right)}^{n} D a^{2} c d^{5} n^{4} x^{3} + 28 \, {\left(d x + c\right)}^{n} C a b c d^{5} n^{4} x^{3} + 14 \, {\left(d x + c\right)}^{n} B b^{2} c d^{5} n^{4} x^{3} + 18 \, {\left(d x + c\right)}^{n} C a^{2} d^{6} n^{4} x^{3} + 36 \, {\left(d x + c\right)}^{n} B a b d^{6} n^{4} x^{3} + 18 \, {\left(d x + c\right)}^{n} A b^{2} d^{6} n^{4} x^{3} - 30 \, {\left(d x + c\right)}^{n} D b^{2} c^{2} d^{4} n^{3} x^{4} + 94 \, {\left(d x + c\right)}^{n} D a b c d^{5} n^{3} x^{4} + 47 \, {\left(d x + c\right)}^{n} C b^{2} c d^{5} n^{3} x^{4} + 107 \, {\left(d x + c\right)}^{n} D a^{2} d^{6} n^{3} x^{4} + 214 \, {\left(d x + c\right)}^{n} C a b d^{6} n^{3} x^{4} + 107 \, {\left(d x + c\right)}^{n} B b^{2} d^{6} n^{3} x^{4} + 50 \, {\left(d x + c\right)}^{n} D b^{2} c d^{5} n^{2} x^{5} + 520 \, {\left(d x + c\right)}^{n} D a b d^{6} n^{2} x^{5} + 260 \, {\left(d x + c\right)}^{n} C b^{2} d^{6} n^{2} x^{5} + 274 \, {\left(d x + c\right)}^{n} D b^{2} d^{6} n x^{6} + {\left(d x + c\right)}^{n} B a^{2} c d^{5} n^{5} x + 2 \, {\left(d x + c\right)}^{n} A a b c d^{5} n^{5} x + {\left(d x + c\right)}^{n} A a^{2} d^{6} n^{5} x - 3 \, {\left(d x + c\right)}^{n} D a^{2} c^{2} d^{4} n^{4} x^{2} - 6 \, {\left(d x + c\right)}^{n} C a b c^{2} d^{4} n^{4} x^{2} - 3 \, {\left(d x + c\right)}^{n} B b^{2} c^{2} d^{4} n^{4} x^{2} + 16 \, {\left(d x + c\right)}^{n} C a^{2} c d^{5} n^{4} x^{2} + 32 \, {\left(d x + c\right)}^{n} B a b c d^{5} n^{4} x^{2} + 16 \, {\left(d x + c\right)}^{n} A b^{2} c d^{5} n^{4} x^{2} + 19 \, {\left(d x + c\right)}^{n} B a^{2} d^{6} n^{4} x^{2} + 38 \, {\left(d x + c\right)}^{n} A a b d^{6} n^{4} x^{2} + 20 \, {\left(d x + c\right)}^{n} D b^{2} c^{3} d^{3} n^{3} x^{3} - 72 \, {\left(d x + c\right)}^{n} D a b c^{2} d^{4} n^{3} x^{3} - 36 \, {\left(d x + c\right)}^{n} C b^{2} c^{2} d^{4} n^{3} x^{3} + 65 \, {\left(d x + c\right)}^{n} D a^{2} c d^{5} n^{3} x^{3} + 130 \, {\left(d x + c\right)}^{n} C a b c d^{5} n^{3} x^{3} + 65 \, {\left(d x + c\right)}^{n} B b^{2} c d^{5} n^{3} x^{3} + 121 \, {\left(d x + c\right)}^{n} C a^{2} d^{6} n^{3} x^{3} + 242 \, {\left(d x + c\right)}^{n} B a b d^{6} n^{3} x^{3} + 121 \, {\left(d x + c\right)}^{n} A b^{2} d^{6} n^{3} x^{3} - 55 \, {\left(d x + c\right)}^{n} D b^{2} c^{2} d^{4} n^{2} x^{4} + 144 \, {\left(d x + c\right)}^{n} D a b c d^{5} n^{2} x^{4} + 72 \, {\left(d x + c\right)}^{n} C b^{2} c d^{5} n^{2} x^{4} + 307 \, {\left(d x + c\right)}^{n} D a^{2} d^{6} n^{2} x^{4} + 614 \, {\left(d x + c\right)}^{n} C a b d^{6} n^{2} x^{4} + 307 \, {\left(d x + c\right)}^{n} B b^{2} d^{6} n^{2} x^{4} + 24 \, {\left(d x + c\right)}^{n} D b^{2} c d^{5} n x^{5} + 648 \, {\left(d x + c\right)}^{n} D a b d^{6} n x^{5} + 324 \, {\left(d x + c\right)}^{n} C b^{2} d^{6} n x^{5} + 120 \, {\left(d x + c\right)}^{n} D b^{2} d^{6} x^{6} + {\left(d x + c\right)}^{n} A a^{2} c d^{5} n^{5} - 2 \, {\left(d x + c\right)}^{n} C a^{2} c^{2} d^{4} n^{4} x - 4 \, {\left(d x + c\right)}^{n} B a b c^{2} d^{4} n^{4} x - 2 \, {\left(d x + c\right)}^{n} A b^{2} c^{2} d^{4} n^{4} x + 18 \, {\left(d x + c\right)}^{n} B a^{2} c d^{5} n^{4} x + 36 \, {\left(d x + c\right)}^{n} A a b c d^{5} n^{4} x + 20 \, {\left(d x + c\right)}^{n} A a^{2} d^{6} n^{4} x + 24 \, {\left(d x + c\right)}^{n} D a b c^{3} d^{3} n^{3} x^{2} + 12 \, {\left(d x + c\right)}^{n} C b^{2} c^{3} d^{3} n^{3} x^{2} - 36 \, {\left(d x + c\right)}^{n} D a^{2} c^{2} d^{4} n^{3} x^{2} - 72 \, {\left(d x + c\right)}^{n} C a b c^{2} d^{4} n^{3} x^{2} - 36 \, {\left(d x + c\right)}^{n} B b^{2} c^{2} d^{4} n^{3} x^{2} + 89 \, {\left(d x + c\right)}^{n} C a^{2} c d^{5} n^{3} x^{2} + 178 \, {\left(d x + c\right)}^{n} B a b c d^{5} n^{3} x^{2} + 89 \, {\left(d x + c\right)}^{n} A b^{2} c d^{5} n^{3} x^{2} + 137 \, {\left(d x + c\right)}^{n} B a^{2} d^{6} n^{3} x^{2} + 274 \, {\left(d x + c\right)}^{n} A a b d^{6} n^{3} x^{2} + 60 \, {\left(d x + c\right)}^{n} D b^{2} c^{3} d^{3} n^{2} x^{3} - 160 \, {\left(d x + c\right)}^{n} D a b c^{2} d^{4} n^{2} x^{3} - 80 \, {\left(d x + c\right)}^{n} C b^{2} c^{2} d^{4} n^{2} x^{3} + 112 \, {\left(d x + c\right)}^{n} D a^{2} c d^{5} n^{2} x^{3} + 224 \, {\left(d x + c\right)}^{n} C a b c d^{5} n^{2} x^{3} + 112 \, {\left(d x + c\right)}^{n} B b^{2} c d^{5} n^{2} x^{3} + 372 \, {\left(d x + c\right)}^{n} C a^{2} d^{6} n^{2} x^{3} + 744 \, {\left(d x + c\right)}^{n} B a b d^{6} n^{2} x^{3} + 372 \, {\left(d x + c\right)}^{n} A b^{2} d^{6} n^{2} x^{3} - 30 \, {\left(d x + c\right)}^{n} D b^{2} c^{2} d^{4} n x^{4} + 72 \, {\left(d x + c\right)}^{n} D a b c d^{5} n x^{4} + 36 \, {\left(d x + c\right)}^{n} C b^{2} c d^{5} n x^{4} + 396 \, {\left(d x + c\right)}^{n} D a^{2} d^{6} n x^{4} + 792 \, {\left(d x + c\right)}^{n} C a b d^{6} n x^{4} + 396 \, {\left(d x + c\right)}^{n} B b^{2} d^{6} n x^{4} + 288 \, {\left(d x + c\right)}^{n} D a b d^{6} x^{5} + 144 \, {\left(d x + c\right)}^{n} C b^{2} d^{6} x^{5} - {\left(d x + c\right)}^{n} B a^{2} c^{2} d^{4} n^{4} - 2 \, {\left(d x + c\right)}^{n} A a b c^{2} d^{4} n^{4} + 20 \, {\left(d x + c\right)}^{n} A a^{2} c d^{5} n^{4} + 6 \, {\left(d x + c\right)}^{n} D a^{2} c^{3} d^{3} n^{3} x + 12 \, {\left(d x + c\right)}^{n} C a b c^{3} d^{3} n^{3} x + 6 \, {\left(d x + c\right)}^{n} B b^{2} c^{3} d^{3} n^{3} x - 30 \, {\left(d x + c\right)}^{n} C a^{2} c^{2} d^{4} n^{3} x - 60 \, {\left(d x + c\right)}^{n} B a b c^{2} d^{4} n^{3} x - 30 \, {\left(d x + c\right)}^{n} A b^{2} c^{2} d^{4} n^{3} x + 119 \, {\left(d x + c\right)}^{n} B a^{2} c d^{5} n^{3} x + 238 \, {\left(d x + c\right)}^{n} A a b c d^{5} n^{3} x + 155 \, {\left(d x + c\right)}^{n} A a^{2} d^{6} n^{3} x - 60 \, {\left(d x + c\right)}^{n} D b^{2} c^{4} d^{2} n^{2} x^{2} + 168 \, {\left(d x + c\right)}^{n} D a b c^{3} d^{3} n^{2} x^{2} + 84 \, {\left(d x + c\right)}^{n} C b^{2} c^{3} d^{3} n^{2} x^{2} - 123 \, {\left(d x + c\right)}^{n} D a^{2} c^{2} d^{4} n^{2} x^{2} - 246 \, {\left(d x + c\right)}^{n} C a b c^{2} d^{4} n^{2} x^{2} - 123 \, {\left(d x + c\right)}^{n} B b^{2} c^{2} d^{4} n^{2} x^{2} + 194 \, {\left(d x + c\right)}^{n} C a^{2} c d^{5} n^{2} x^{2} + 388 \, {\left(d x + c\right)}^{n} B a b c d^{5} n^{2} x^{2} + 194 \, {\left(d x + c\right)}^{n} A b^{2} c d^{5} n^{2} x^{2} + 461 \, {\left(d x + c\right)}^{n} B a^{2} d^{6} n^{2} x^{2} + 922 \, {\left(d x + c\right)}^{n} A a b d^{6} n^{2} x^{2} + 40 \, {\left(d x + c\right)}^{n} D b^{2} c^{3} d^{3} n x^{3} - 96 \, {\left(d x + c\right)}^{n} D a b c^{2} d^{4} n x^{3} - 48 \, {\left(d x + c\right)}^{n} C b^{2} c^{2} d^{4} n x^{3} + 60 \, {\left(d x + c\right)}^{n} D a^{2} c d^{5} n x^{3} + 120 \, {\left(d x + c\right)}^{n} C a b c d^{5} n x^{3} + 60 \, {\left(d x + c\right)}^{n} B b^{2} c d^{5} n x^{3} + 508 \, {\left(d x + c\right)}^{n} C a^{2} d^{6} n x^{3} + 1016 \, {\left(d x + c\right)}^{n} B a b d^{6} n x^{3} + 508 \, {\left(d x + c\right)}^{n} A b^{2} d^{6} n x^{3} + 180 \, {\left(d x + c\right)}^{n} D a^{2} d^{6} x^{4} + 360 \, {\left(d x + c\right)}^{n} C a b d^{6} x^{4} + 180 \, {\left(d x + c\right)}^{n} B b^{2} d^{6} x^{4} + 2 \, {\left(d x + c\right)}^{n} C a^{2} c^{3} d^{3} n^{3} + 4 \, {\left(d x + c\right)}^{n} B a b c^{3} d^{3} n^{3} + 2 \, {\left(d x + c\right)}^{n} A b^{2} c^{3} d^{3} n^{3} - 18 \, {\left(d x + c\right)}^{n} B a^{2} c^{2} d^{4} n^{3} - 36 \, {\left(d x + c\right)}^{n} A a b c^{2} d^{4} n^{3} + 155 \, {\left(d x + c\right)}^{n} A a^{2} c d^{5} n^{3} - 48 \, {\left(d x + c\right)}^{n} D a b c^{4} d^{2} n^{2} x - 24 \, {\left(d x + c\right)}^{n} C b^{2} c^{4} d^{2} n^{2} x + 66 \, {\left(d x + c\right)}^{n} D a^{2} c^{3} d^{3} n^{2} x + 132 \, {\left(d x + c\right)}^{n} C a b c^{3} d^{3} n^{2} x + 66 \, {\left(d x + c\right)}^{n} B b^{2} c^{3} d^{3} n^{2} x - 148 \, {\left(d x + c\right)}^{n} C a^{2} c^{2} d^{4} n^{2} x - 296 \, {\left(d x + c\right)}^{n} B a b c^{2} d^{4} n^{2} x - 148 \, {\left(d x + c\right)}^{n} A b^{2} c^{2} d^{4} n^{2} x + 342 \, {\left(d x + c\right)}^{n} B a^{2} c d^{5} n^{2} x + 684 \, {\left(d x + c\right)}^{n} A a b c d^{5} n^{2} x + 580 \, {\left(d x + c\right)}^{n} A a^{2} d^{6} n^{2} x - 60 \, {\left(d x + c\right)}^{n} D b^{2} c^{4} d^{2} n x^{2} + 144 \, {\left(d x + c\right)}^{n} D a b c^{3} d^{3} n x^{2} + 72 \, {\left(d x + c\right)}^{n} C b^{2} c^{3} d^{3} n x^{2} - 90 \, {\left(d x + c\right)}^{n} D a^{2} c^{2} d^{4} n x^{2} - 180 \, {\left(d x + c\right)}^{n} C a b c^{2} d^{4} n x^{2} - 90 \, {\left(d x + c\right)}^{n} B b^{2} c^{2} d^{4} n x^{2} + 120 \, {\left(d x + c\right)}^{n} C a^{2} c d^{5} n x^{2} + 240 \, {\left(d x + c\right)}^{n} B a b c d^{5} n x^{2} + 120 \, {\left(d x + c\right)}^{n} A b^{2} c d^{5} n x^{2} + 702 \, {\left(d x + c\right)}^{n} B a^{2} d^{6} n x^{2} + 1404 \, {\left(d x + c\right)}^{n} A a b d^{6} n x^{2} + 240 \, {\left(d x + c\right)}^{n} C a^{2} d^{6} x^{3} + 480 \, {\left(d x + c\right)}^{n} B a b d^{6} x^{3} + 240 \, {\left(d x + c\right)}^{n} A b^{2} d^{6} x^{3} - 6 \, {\left(d x + c\right)}^{n} D a^{2} c^{4} d^{2} n^{2} - 12 \, {\left(d x + c\right)}^{n} C a b c^{4} d^{2} n^{2} - 6 \, {\left(d x + c\right)}^{n} B b^{2} c^{4} d^{2} n^{2} + 30 \, {\left(d x + c\right)}^{n} C a^{2} c^{3} d^{3} n^{2} + 60 \, {\left(d x + c\right)}^{n} B a b c^{3} d^{3} n^{2} + 30 \, {\left(d x + c\right)}^{n} A b^{2} c^{3} d^{3} n^{2} - 119 \, {\left(d x + c\right)}^{n} B a^{2} c^{2} d^{4} n^{2} - 238 \, {\left(d x + c\right)}^{n} A a b c^{2} d^{4} n^{2} + 580 \, {\left(d x + c\right)}^{n} A a^{2} c d^{5} n^{2} + 120 \, {\left(d x + c\right)}^{n} D b^{2} c^{5} d n x - 288 \, {\left(d x + c\right)}^{n} D a b c^{4} d^{2} n x - 144 \, {\left(d x + c\right)}^{n} C b^{2} c^{4} d^{2} n x + 180 \, {\left(d x + c\right)}^{n} D a^{2} c^{3} d^{3} n x + 360 \, {\left(d x + c\right)}^{n} C a b c^{3} d^{3} n x + 180 \, {\left(d x + c\right)}^{n} B b^{2} c^{3} d^{3} n x - 240 \, {\left(d x + c\right)}^{n} C a^{2} c^{2} d^{4} n x - 480 \, {\left(d x + c\right)}^{n} B a b c^{2} d^{4} n x - 240 \, {\left(d x + c\right)}^{n} A b^{2} c^{2} d^{4} n x + 360 \, {\left(d x + c\right)}^{n} B a^{2} c d^{5} n x + 720 \, {\left(d x + c\right)}^{n} A a b c d^{5} n x + 1044 \, {\left(d x + c\right)}^{n} A a^{2} d^{6} n x + 360 \, {\left(d x + c\right)}^{n} B a^{2} d^{6} x^{2} + 720 \, {\left(d x + c\right)}^{n} A a b d^{6} x^{2} + 48 \, {\left(d x + c\right)}^{n} D a b c^{5} d n + 24 \, {\left(d x + c\right)}^{n} C b^{2} c^{5} d n - 66 \, {\left(d x + c\right)}^{n} D a^{2} c^{4} d^{2} n - 132 \, {\left(d x + c\right)}^{n} C a b c^{4} d^{2} n - 66 \, {\left(d x + c\right)}^{n} B b^{2} c^{4} d^{2} n + 148 \, {\left(d x + c\right)}^{n} C a^{2} c^{3} d^{3} n + 296 \, {\left(d x + c\right)}^{n} B a b c^{3} d^{3} n + 148 \, {\left(d x + c\right)}^{n} A b^{2} c^{3} d^{3} n - 342 \, {\left(d x + c\right)}^{n} B a^{2} c^{2} d^{4} n - 684 \, {\left(d x + c\right)}^{n} A a b c^{2} d^{4} n + 1044 \, {\left(d x + c\right)}^{n} A a^{2} c d^{5} n + 720 \, {\left(d x + c\right)}^{n} A a^{2} d^{6} x - 120 \, {\left(d x + c\right)}^{n} D b^{2} c^{6} + 288 \, {\left(d x + c\right)}^{n} D a b c^{5} d + 144 \, {\left(d x + c\right)}^{n} C b^{2} c^{5} d - 180 \, {\left(d x + c\right)}^{n} D a^{2} c^{4} d^{2} - 360 \, {\left(d x + c\right)}^{n} C a b c^{4} d^{2} - 180 \, {\left(d x + c\right)}^{n} B b^{2} c^{4} d^{2} + 240 \, {\left(d x + c\right)}^{n} C a^{2} c^{3} d^{3} + 480 \, {\left(d x + c\right)}^{n} B a b c^{3} d^{3} + 240 \, {\left(d x + c\right)}^{n} A b^{2} c^{3} d^{3} - 360 \, {\left(d x + c\right)}^{n} B a^{2} c^{2} d^{4} - 720 \, {\left(d x + c\right)}^{n} A a b c^{2} d^{4} + 720 \, {\left(d x + c\right)}^{n} A a^{2} c d^{5}}{d^{6} n^{6} + 21 \, d^{6} n^{5} + 175 \, d^{6} n^{4} + 735 \, d^{6} n^{3} + 1624 \, d^{6} n^{2} + 1764 \, d^{6} n + 720 \, d^{6}}"," ",0,"((d*x + c)^n*D*b^2*d^6*n^5*x^6 + (d*x + c)^n*D*b^2*c*d^5*n^5*x^5 + 2*(d*x + c)^n*D*a*b*d^6*n^5*x^5 + (d*x + c)^n*C*b^2*d^6*n^5*x^5 + 15*(d*x + c)^n*D*b^2*d^6*n^4*x^6 + 2*(d*x + c)^n*D*a*b*c*d^5*n^5*x^4 + (d*x + c)^n*C*b^2*c*d^5*n^5*x^4 + (d*x + c)^n*D*a^2*d^6*n^5*x^4 + 2*(d*x + c)^n*C*a*b*d^6*n^5*x^4 + (d*x + c)^n*B*b^2*d^6*n^5*x^4 + 10*(d*x + c)^n*D*b^2*c*d^5*n^4*x^5 + 32*(d*x + c)^n*D*a*b*d^6*n^4*x^5 + 16*(d*x + c)^n*C*b^2*d^6*n^4*x^5 + 85*(d*x + c)^n*D*b^2*d^6*n^3*x^6 + (d*x + c)^n*D*a^2*c*d^5*n^5*x^3 + 2*(d*x + c)^n*C*a*b*c*d^5*n^5*x^3 + (d*x + c)^n*B*b^2*c*d^5*n^5*x^3 + (d*x + c)^n*C*a^2*d^6*n^5*x^3 + 2*(d*x + c)^n*B*a*b*d^6*n^5*x^3 + (d*x + c)^n*A*b^2*d^6*n^5*x^3 - 5*(d*x + c)^n*D*b^2*c^2*d^4*n^4*x^4 + 24*(d*x + c)^n*D*a*b*c*d^5*n^4*x^4 + 12*(d*x + c)^n*C*b^2*c*d^5*n^4*x^4 + 17*(d*x + c)^n*D*a^2*d^6*n^4*x^4 + 34*(d*x + c)^n*C*a*b*d^6*n^4*x^4 + 17*(d*x + c)^n*B*b^2*d^6*n^4*x^4 + 35*(d*x + c)^n*D*b^2*c*d^5*n^3*x^5 + 190*(d*x + c)^n*D*a*b*d^6*n^3*x^5 + 95*(d*x + c)^n*C*b^2*d^6*n^3*x^5 + 225*(d*x + c)^n*D*b^2*d^6*n^2*x^6 + (d*x + c)^n*C*a^2*c*d^5*n^5*x^2 + 2*(d*x + c)^n*B*a*b*c*d^5*n^5*x^2 + (d*x + c)^n*A*b^2*c*d^5*n^5*x^2 + (d*x + c)^n*B*a^2*d^6*n^5*x^2 + 2*(d*x + c)^n*A*a*b*d^6*n^5*x^2 - 8*(d*x + c)^n*D*a*b*c^2*d^4*n^4*x^3 - 4*(d*x + c)^n*C*b^2*c^2*d^4*n^4*x^3 + 14*(d*x + c)^n*D*a^2*c*d^5*n^4*x^3 + 28*(d*x + c)^n*C*a*b*c*d^5*n^4*x^3 + 14*(d*x + c)^n*B*b^2*c*d^5*n^4*x^3 + 18*(d*x + c)^n*C*a^2*d^6*n^4*x^3 + 36*(d*x + c)^n*B*a*b*d^6*n^4*x^3 + 18*(d*x + c)^n*A*b^2*d^6*n^4*x^3 - 30*(d*x + c)^n*D*b^2*c^2*d^4*n^3*x^4 + 94*(d*x + c)^n*D*a*b*c*d^5*n^3*x^4 + 47*(d*x + c)^n*C*b^2*c*d^5*n^3*x^4 + 107*(d*x + c)^n*D*a^2*d^6*n^3*x^4 + 214*(d*x + c)^n*C*a*b*d^6*n^3*x^4 + 107*(d*x + c)^n*B*b^2*d^6*n^3*x^4 + 50*(d*x + c)^n*D*b^2*c*d^5*n^2*x^5 + 520*(d*x + c)^n*D*a*b*d^6*n^2*x^5 + 260*(d*x + c)^n*C*b^2*d^6*n^2*x^5 + 274*(d*x + c)^n*D*b^2*d^6*n*x^6 + (d*x + c)^n*B*a^2*c*d^5*n^5*x + 2*(d*x + c)^n*A*a*b*c*d^5*n^5*x + (d*x + c)^n*A*a^2*d^6*n^5*x - 3*(d*x + c)^n*D*a^2*c^2*d^4*n^4*x^2 - 6*(d*x + c)^n*C*a*b*c^2*d^4*n^4*x^2 - 3*(d*x + c)^n*B*b^2*c^2*d^4*n^4*x^2 + 16*(d*x + c)^n*C*a^2*c*d^5*n^4*x^2 + 32*(d*x + c)^n*B*a*b*c*d^5*n^4*x^2 + 16*(d*x + c)^n*A*b^2*c*d^5*n^4*x^2 + 19*(d*x + c)^n*B*a^2*d^6*n^4*x^2 + 38*(d*x + c)^n*A*a*b*d^6*n^4*x^2 + 20*(d*x + c)^n*D*b^2*c^3*d^3*n^3*x^3 - 72*(d*x + c)^n*D*a*b*c^2*d^4*n^3*x^3 - 36*(d*x + c)^n*C*b^2*c^2*d^4*n^3*x^3 + 65*(d*x + c)^n*D*a^2*c*d^5*n^3*x^3 + 130*(d*x + c)^n*C*a*b*c*d^5*n^3*x^3 + 65*(d*x + c)^n*B*b^2*c*d^5*n^3*x^3 + 121*(d*x + c)^n*C*a^2*d^6*n^3*x^3 + 242*(d*x + c)^n*B*a*b*d^6*n^3*x^3 + 121*(d*x + c)^n*A*b^2*d^6*n^3*x^3 - 55*(d*x + c)^n*D*b^2*c^2*d^4*n^2*x^4 + 144*(d*x + c)^n*D*a*b*c*d^5*n^2*x^4 + 72*(d*x + c)^n*C*b^2*c*d^5*n^2*x^4 + 307*(d*x + c)^n*D*a^2*d^6*n^2*x^4 + 614*(d*x + c)^n*C*a*b*d^6*n^2*x^4 + 307*(d*x + c)^n*B*b^2*d^6*n^2*x^4 + 24*(d*x + c)^n*D*b^2*c*d^5*n*x^5 + 648*(d*x + c)^n*D*a*b*d^6*n*x^5 + 324*(d*x + c)^n*C*b^2*d^6*n*x^5 + 120*(d*x + c)^n*D*b^2*d^6*x^6 + (d*x + c)^n*A*a^2*c*d^5*n^5 - 2*(d*x + c)^n*C*a^2*c^2*d^4*n^4*x - 4*(d*x + c)^n*B*a*b*c^2*d^4*n^4*x - 2*(d*x + c)^n*A*b^2*c^2*d^4*n^4*x + 18*(d*x + c)^n*B*a^2*c*d^5*n^4*x + 36*(d*x + c)^n*A*a*b*c*d^5*n^4*x + 20*(d*x + c)^n*A*a^2*d^6*n^4*x + 24*(d*x + c)^n*D*a*b*c^3*d^3*n^3*x^2 + 12*(d*x + c)^n*C*b^2*c^3*d^3*n^3*x^2 - 36*(d*x + c)^n*D*a^2*c^2*d^4*n^3*x^2 - 72*(d*x + c)^n*C*a*b*c^2*d^4*n^3*x^2 - 36*(d*x + c)^n*B*b^2*c^2*d^4*n^3*x^2 + 89*(d*x + c)^n*C*a^2*c*d^5*n^3*x^2 + 178*(d*x + c)^n*B*a*b*c*d^5*n^3*x^2 + 89*(d*x + c)^n*A*b^2*c*d^5*n^3*x^2 + 137*(d*x + c)^n*B*a^2*d^6*n^3*x^2 + 274*(d*x + c)^n*A*a*b*d^6*n^3*x^2 + 60*(d*x + c)^n*D*b^2*c^3*d^3*n^2*x^3 - 160*(d*x + c)^n*D*a*b*c^2*d^4*n^2*x^3 - 80*(d*x + c)^n*C*b^2*c^2*d^4*n^2*x^3 + 112*(d*x + c)^n*D*a^2*c*d^5*n^2*x^3 + 224*(d*x + c)^n*C*a*b*c*d^5*n^2*x^3 + 112*(d*x + c)^n*B*b^2*c*d^5*n^2*x^3 + 372*(d*x + c)^n*C*a^2*d^6*n^2*x^3 + 744*(d*x + c)^n*B*a*b*d^6*n^2*x^3 + 372*(d*x + c)^n*A*b^2*d^6*n^2*x^3 - 30*(d*x + c)^n*D*b^2*c^2*d^4*n*x^4 + 72*(d*x + c)^n*D*a*b*c*d^5*n*x^4 + 36*(d*x + c)^n*C*b^2*c*d^5*n*x^4 + 396*(d*x + c)^n*D*a^2*d^6*n*x^4 + 792*(d*x + c)^n*C*a*b*d^6*n*x^4 + 396*(d*x + c)^n*B*b^2*d^6*n*x^4 + 288*(d*x + c)^n*D*a*b*d^6*x^5 + 144*(d*x + c)^n*C*b^2*d^6*x^5 - (d*x + c)^n*B*a^2*c^2*d^4*n^4 - 2*(d*x + c)^n*A*a*b*c^2*d^4*n^4 + 20*(d*x + c)^n*A*a^2*c*d^5*n^4 + 6*(d*x + c)^n*D*a^2*c^3*d^3*n^3*x + 12*(d*x + c)^n*C*a*b*c^3*d^3*n^3*x + 6*(d*x + c)^n*B*b^2*c^3*d^3*n^3*x - 30*(d*x + c)^n*C*a^2*c^2*d^4*n^3*x - 60*(d*x + c)^n*B*a*b*c^2*d^4*n^3*x - 30*(d*x + c)^n*A*b^2*c^2*d^4*n^3*x + 119*(d*x + c)^n*B*a^2*c*d^5*n^3*x + 238*(d*x + c)^n*A*a*b*c*d^5*n^3*x + 155*(d*x + c)^n*A*a^2*d^6*n^3*x - 60*(d*x + c)^n*D*b^2*c^4*d^2*n^2*x^2 + 168*(d*x + c)^n*D*a*b*c^3*d^3*n^2*x^2 + 84*(d*x + c)^n*C*b^2*c^3*d^3*n^2*x^2 - 123*(d*x + c)^n*D*a^2*c^2*d^4*n^2*x^2 - 246*(d*x + c)^n*C*a*b*c^2*d^4*n^2*x^2 - 123*(d*x + c)^n*B*b^2*c^2*d^4*n^2*x^2 + 194*(d*x + c)^n*C*a^2*c*d^5*n^2*x^2 + 388*(d*x + c)^n*B*a*b*c*d^5*n^2*x^2 + 194*(d*x + c)^n*A*b^2*c*d^5*n^2*x^2 + 461*(d*x + c)^n*B*a^2*d^6*n^2*x^2 + 922*(d*x + c)^n*A*a*b*d^6*n^2*x^2 + 40*(d*x + c)^n*D*b^2*c^3*d^3*n*x^3 - 96*(d*x + c)^n*D*a*b*c^2*d^4*n*x^3 - 48*(d*x + c)^n*C*b^2*c^2*d^4*n*x^3 + 60*(d*x + c)^n*D*a^2*c*d^5*n*x^3 + 120*(d*x + c)^n*C*a*b*c*d^5*n*x^3 + 60*(d*x + c)^n*B*b^2*c*d^5*n*x^3 + 508*(d*x + c)^n*C*a^2*d^6*n*x^3 + 1016*(d*x + c)^n*B*a*b*d^6*n*x^3 + 508*(d*x + c)^n*A*b^2*d^6*n*x^3 + 180*(d*x + c)^n*D*a^2*d^6*x^4 + 360*(d*x + c)^n*C*a*b*d^6*x^4 + 180*(d*x + c)^n*B*b^2*d^6*x^4 + 2*(d*x + c)^n*C*a^2*c^3*d^3*n^3 + 4*(d*x + c)^n*B*a*b*c^3*d^3*n^3 + 2*(d*x + c)^n*A*b^2*c^3*d^3*n^3 - 18*(d*x + c)^n*B*a^2*c^2*d^4*n^3 - 36*(d*x + c)^n*A*a*b*c^2*d^4*n^3 + 155*(d*x + c)^n*A*a^2*c*d^5*n^3 - 48*(d*x + c)^n*D*a*b*c^4*d^2*n^2*x - 24*(d*x + c)^n*C*b^2*c^4*d^2*n^2*x + 66*(d*x + c)^n*D*a^2*c^3*d^3*n^2*x + 132*(d*x + c)^n*C*a*b*c^3*d^3*n^2*x + 66*(d*x + c)^n*B*b^2*c^3*d^3*n^2*x - 148*(d*x + c)^n*C*a^2*c^2*d^4*n^2*x - 296*(d*x + c)^n*B*a*b*c^2*d^4*n^2*x - 148*(d*x + c)^n*A*b^2*c^2*d^4*n^2*x + 342*(d*x + c)^n*B*a^2*c*d^5*n^2*x + 684*(d*x + c)^n*A*a*b*c*d^5*n^2*x + 580*(d*x + c)^n*A*a^2*d^6*n^2*x - 60*(d*x + c)^n*D*b^2*c^4*d^2*n*x^2 + 144*(d*x + c)^n*D*a*b*c^3*d^3*n*x^2 + 72*(d*x + c)^n*C*b^2*c^3*d^3*n*x^2 - 90*(d*x + c)^n*D*a^2*c^2*d^4*n*x^2 - 180*(d*x + c)^n*C*a*b*c^2*d^4*n*x^2 - 90*(d*x + c)^n*B*b^2*c^2*d^4*n*x^2 + 120*(d*x + c)^n*C*a^2*c*d^5*n*x^2 + 240*(d*x + c)^n*B*a*b*c*d^5*n*x^2 + 120*(d*x + c)^n*A*b^2*c*d^5*n*x^2 + 702*(d*x + c)^n*B*a^2*d^6*n*x^2 + 1404*(d*x + c)^n*A*a*b*d^6*n*x^2 + 240*(d*x + c)^n*C*a^2*d^6*x^3 + 480*(d*x + c)^n*B*a*b*d^6*x^3 + 240*(d*x + c)^n*A*b^2*d^6*x^3 - 6*(d*x + c)^n*D*a^2*c^4*d^2*n^2 - 12*(d*x + c)^n*C*a*b*c^4*d^2*n^2 - 6*(d*x + c)^n*B*b^2*c^4*d^2*n^2 + 30*(d*x + c)^n*C*a^2*c^3*d^3*n^2 + 60*(d*x + c)^n*B*a*b*c^3*d^3*n^2 + 30*(d*x + c)^n*A*b^2*c^3*d^3*n^2 - 119*(d*x + c)^n*B*a^2*c^2*d^4*n^2 - 238*(d*x + c)^n*A*a*b*c^2*d^4*n^2 + 580*(d*x + c)^n*A*a^2*c*d^5*n^2 + 120*(d*x + c)^n*D*b^2*c^5*d*n*x - 288*(d*x + c)^n*D*a*b*c^4*d^2*n*x - 144*(d*x + c)^n*C*b^2*c^4*d^2*n*x + 180*(d*x + c)^n*D*a^2*c^3*d^3*n*x + 360*(d*x + c)^n*C*a*b*c^3*d^3*n*x + 180*(d*x + c)^n*B*b^2*c^3*d^3*n*x - 240*(d*x + c)^n*C*a^2*c^2*d^4*n*x - 480*(d*x + c)^n*B*a*b*c^2*d^4*n*x - 240*(d*x + c)^n*A*b^2*c^2*d^4*n*x + 360*(d*x + c)^n*B*a^2*c*d^5*n*x + 720*(d*x + c)^n*A*a*b*c*d^5*n*x + 1044*(d*x + c)^n*A*a^2*d^6*n*x + 360*(d*x + c)^n*B*a^2*d^6*x^2 + 720*(d*x + c)^n*A*a*b*d^6*x^2 + 48*(d*x + c)^n*D*a*b*c^5*d*n + 24*(d*x + c)^n*C*b^2*c^5*d*n - 66*(d*x + c)^n*D*a^2*c^4*d^2*n - 132*(d*x + c)^n*C*a*b*c^4*d^2*n - 66*(d*x + c)^n*B*b^2*c^4*d^2*n + 148*(d*x + c)^n*C*a^2*c^3*d^3*n + 296*(d*x + c)^n*B*a*b*c^3*d^3*n + 148*(d*x + c)^n*A*b^2*c^3*d^3*n - 342*(d*x + c)^n*B*a^2*c^2*d^4*n - 684*(d*x + c)^n*A*a*b*c^2*d^4*n + 1044*(d*x + c)^n*A*a^2*c*d^5*n + 720*(d*x + c)^n*A*a^2*d^6*x - 120*(d*x + c)^n*D*b^2*c^6 + 288*(d*x + c)^n*D*a*b*c^5*d + 144*(d*x + c)^n*C*b^2*c^5*d - 180*(d*x + c)^n*D*a^2*c^4*d^2 - 360*(d*x + c)^n*C*a*b*c^4*d^2 - 180*(d*x + c)^n*B*b^2*c^4*d^2 + 240*(d*x + c)^n*C*a^2*c^3*d^3 + 480*(d*x + c)^n*B*a*b*c^3*d^3 + 240*(d*x + c)^n*A*b^2*c^3*d^3 - 360*(d*x + c)^n*B*a^2*c^2*d^4 - 720*(d*x + c)^n*A*a*b*c^2*d^4 + 720*(d*x + c)^n*A*a^2*c*d^5)/(d^6*n^6 + 21*d^6*n^5 + 175*d^6*n^4 + 735*d^6*n^3 + 1624*d^6*n^2 + 1764*d^6*n + 720*d^6)","B",0
27,1,2224,0,1.390064," ","integrate((b*x+a)*(d*x+c)^n*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\frac{{\left(d x + c\right)}^{n} D b d^{5} n^{4} x^{5} + {\left(d x + c\right)}^{n} D b c d^{4} n^{4} x^{4} + {\left(d x + c\right)}^{n} D a d^{5} n^{4} x^{4} + {\left(d x + c\right)}^{n} C b d^{5} n^{4} x^{4} + 10 \, {\left(d x + c\right)}^{n} D b d^{5} n^{3} x^{5} + {\left(d x + c\right)}^{n} D a c d^{4} n^{4} x^{3} + {\left(d x + c\right)}^{n} C b c d^{4} n^{4} x^{3} + {\left(d x + c\right)}^{n} C a d^{5} n^{4} x^{3} + {\left(d x + c\right)}^{n} B b d^{5} n^{4} x^{3} + 6 \, {\left(d x + c\right)}^{n} D b c d^{4} n^{3} x^{4} + 11 \, {\left(d x + c\right)}^{n} D a d^{5} n^{3} x^{4} + 11 \, {\left(d x + c\right)}^{n} C b d^{5} n^{3} x^{4} + 35 \, {\left(d x + c\right)}^{n} D b d^{5} n^{2} x^{5} + {\left(d x + c\right)}^{n} C a c d^{4} n^{4} x^{2} + {\left(d x + c\right)}^{n} B b c d^{4} n^{4} x^{2} + {\left(d x + c\right)}^{n} B a d^{5} n^{4} x^{2} + {\left(d x + c\right)}^{n} A b d^{5} n^{4} x^{2} - 4 \, {\left(d x + c\right)}^{n} D b c^{2} d^{3} n^{3} x^{3} + 8 \, {\left(d x + c\right)}^{n} D a c d^{4} n^{3} x^{3} + 8 \, {\left(d x + c\right)}^{n} C b c d^{4} n^{3} x^{3} + 12 \, {\left(d x + c\right)}^{n} C a d^{5} n^{3} x^{3} + 12 \, {\left(d x + c\right)}^{n} B b d^{5} n^{3} x^{3} + 11 \, {\left(d x + c\right)}^{n} D b c d^{4} n^{2} x^{4} + 41 \, {\left(d x + c\right)}^{n} D a d^{5} n^{2} x^{4} + 41 \, {\left(d x + c\right)}^{n} C b d^{5} n^{2} x^{4} + 50 \, {\left(d x + c\right)}^{n} D b d^{5} n x^{5} + {\left(d x + c\right)}^{n} B a c d^{4} n^{4} x + {\left(d x + c\right)}^{n} A b c d^{4} n^{4} x + {\left(d x + c\right)}^{n} A a d^{5} n^{4} x - 3 \, {\left(d x + c\right)}^{n} D a c^{2} d^{3} n^{3} x^{2} - 3 \, {\left(d x + c\right)}^{n} C b c^{2} d^{3} n^{3} x^{2} + 10 \, {\left(d x + c\right)}^{n} C a c d^{4} n^{3} x^{2} + 10 \, {\left(d x + c\right)}^{n} B b c d^{4} n^{3} x^{2} + 13 \, {\left(d x + c\right)}^{n} B a d^{5} n^{3} x^{2} + 13 \, {\left(d x + c\right)}^{n} A b d^{5} n^{3} x^{2} - 12 \, {\left(d x + c\right)}^{n} D b c^{2} d^{3} n^{2} x^{3} + 17 \, {\left(d x + c\right)}^{n} D a c d^{4} n^{2} x^{3} + 17 \, {\left(d x + c\right)}^{n} C b c d^{4} n^{2} x^{3} + 49 \, {\left(d x + c\right)}^{n} C a d^{5} n^{2} x^{3} + 49 \, {\left(d x + c\right)}^{n} B b d^{5} n^{2} x^{3} + 6 \, {\left(d x + c\right)}^{n} D b c d^{4} n x^{4} + 61 \, {\left(d x + c\right)}^{n} D a d^{5} n x^{4} + 61 \, {\left(d x + c\right)}^{n} C b d^{5} n x^{4} + 24 \, {\left(d x + c\right)}^{n} D b d^{5} x^{5} + {\left(d x + c\right)}^{n} A a c d^{4} n^{4} - 2 \, {\left(d x + c\right)}^{n} C a c^{2} d^{3} n^{3} x - 2 \, {\left(d x + c\right)}^{n} B b c^{2} d^{3} n^{3} x + 12 \, {\left(d x + c\right)}^{n} B a c d^{4} n^{3} x + 12 \, {\left(d x + c\right)}^{n} A b c d^{4} n^{3} x + 14 \, {\left(d x + c\right)}^{n} A a d^{5} n^{3} x + 12 \, {\left(d x + c\right)}^{n} D b c^{3} d^{2} n^{2} x^{2} - 18 \, {\left(d x + c\right)}^{n} D a c^{2} d^{3} n^{2} x^{2} - 18 \, {\left(d x + c\right)}^{n} C b c^{2} d^{3} n^{2} x^{2} + 29 \, {\left(d x + c\right)}^{n} C a c d^{4} n^{2} x^{2} + 29 \, {\left(d x + c\right)}^{n} B b c d^{4} n^{2} x^{2} + 59 \, {\left(d x + c\right)}^{n} B a d^{5} n^{2} x^{2} + 59 \, {\left(d x + c\right)}^{n} A b d^{5} n^{2} x^{2} - 8 \, {\left(d x + c\right)}^{n} D b c^{2} d^{3} n x^{3} + 10 \, {\left(d x + c\right)}^{n} D a c d^{4} n x^{3} + 10 \, {\left(d x + c\right)}^{n} C b c d^{4} n x^{3} + 78 \, {\left(d x + c\right)}^{n} C a d^{5} n x^{3} + 78 \, {\left(d x + c\right)}^{n} B b d^{5} n x^{3} + 30 \, {\left(d x + c\right)}^{n} D a d^{5} x^{4} + 30 \, {\left(d x + c\right)}^{n} C b d^{5} x^{4} - {\left(d x + c\right)}^{n} B a c^{2} d^{3} n^{3} - {\left(d x + c\right)}^{n} A b c^{2} d^{3} n^{3} + 14 \, {\left(d x + c\right)}^{n} A a c d^{4} n^{3} + 6 \, {\left(d x + c\right)}^{n} D a c^{3} d^{2} n^{2} x + 6 \, {\left(d x + c\right)}^{n} C b c^{3} d^{2} n^{2} x - 18 \, {\left(d x + c\right)}^{n} C a c^{2} d^{3} n^{2} x - 18 \, {\left(d x + c\right)}^{n} B b c^{2} d^{3} n^{2} x + 47 \, {\left(d x + c\right)}^{n} B a c d^{4} n^{2} x + 47 \, {\left(d x + c\right)}^{n} A b c d^{4} n^{2} x + 71 \, {\left(d x + c\right)}^{n} A a d^{5} n^{2} x + 12 \, {\left(d x + c\right)}^{n} D b c^{3} d^{2} n x^{2} - 15 \, {\left(d x + c\right)}^{n} D a c^{2} d^{3} n x^{2} - 15 \, {\left(d x + c\right)}^{n} C b c^{2} d^{3} n x^{2} + 20 \, {\left(d x + c\right)}^{n} C a c d^{4} n x^{2} + 20 \, {\left(d x + c\right)}^{n} B b c d^{4} n x^{2} + 107 \, {\left(d x + c\right)}^{n} B a d^{5} n x^{2} + 107 \, {\left(d x + c\right)}^{n} A b d^{5} n x^{2} + 40 \, {\left(d x + c\right)}^{n} C a d^{5} x^{3} + 40 \, {\left(d x + c\right)}^{n} B b d^{5} x^{3} + 2 \, {\left(d x + c\right)}^{n} C a c^{3} d^{2} n^{2} + 2 \, {\left(d x + c\right)}^{n} B b c^{3} d^{2} n^{2} - 12 \, {\left(d x + c\right)}^{n} B a c^{2} d^{3} n^{2} - 12 \, {\left(d x + c\right)}^{n} A b c^{2} d^{3} n^{2} + 71 \, {\left(d x + c\right)}^{n} A a c d^{4} n^{2} - 24 \, {\left(d x + c\right)}^{n} D b c^{4} d n x + 30 \, {\left(d x + c\right)}^{n} D a c^{3} d^{2} n x + 30 \, {\left(d x + c\right)}^{n} C b c^{3} d^{2} n x - 40 \, {\left(d x + c\right)}^{n} C a c^{2} d^{3} n x - 40 \, {\left(d x + c\right)}^{n} B b c^{2} d^{3} n x + 60 \, {\left(d x + c\right)}^{n} B a c d^{4} n x + 60 \, {\left(d x + c\right)}^{n} A b c d^{4} n x + 154 \, {\left(d x + c\right)}^{n} A a d^{5} n x + 60 \, {\left(d x + c\right)}^{n} B a d^{5} x^{2} + 60 \, {\left(d x + c\right)}^{n} A b d^{5} x^{2} - 6 \, {\left(d x + c\right)}^{n} D a c^{4} d n - 6 \, {\left(d x + c\right)}^{n} C b c^{4} d n + 18 \, {\left(d x + c\right)}^{n} C a c^{3} d^{2} n + 18 \, {\left(d x + c\right)}^{n} B b c^{3} d^{2} n - 47 \, {\left(d x + c\right)}^{n} B a c^{2} d^{3} n - 47 \, {\left(d x + c\right)}^{n} A b c^{2} d^{3} n + 154 \, {\left(d x + c\right)}^{n} A a c d^{4} n + 120 \, {\left(d x + c\right)}^{n} A a d^{5} x + 24 \, {\left(d x + c\right)}^{n} D b c^{5} - 30 \, {\left(d x + c\right)}^{n} D a c^{4} d - 30 \, {\left(d x + c\right)}^{n} C b c^{4} d + 40 \, {\left(d x + c\right)}^{n} C a c^{3} d^{2} + 40 \, {\left(d x + c\right)}^{n} B b c^{3} d^{2} - 60 \, {\left(d x + c\right)}^{n} B a c^{2} d^{3} - 60 \, {\left(d x + c\right)}^{n} A b c^{2} d^{3} + 120 \, {\left(d x + c\right)}^{n} A a c d^{4}}{d^{5} n^{5} + 15 \, d^{5} n^{4} + 85 \, d^{5} n^{3} + 225 \, d^{5} n^{2} + 274 \, d^{5} n + 120 \, d^{5}}"," ",0,"((d*x + c)^n*D*b*d^5*n^4*x^5 + (d*x + c)^n*D*b*c*d^4*n^4*x^4 + (d*x + c)^n*D*a*d^5*n^4*x^4 + (d*x + c)^n*C*b*d^5*n^4*x^4 + 10*(d*x + c)^n*D*b*d^5*n^3*x^5 + (d*x + c)^n*D*a*c*d^4*n^4*x^3 + (d*x + c)^n*C*b*c*d^4*n^4*x^3 + (d*x + c)^n*C*a*d^5*n^4*x^3 + (d*x + c)^n*B*b*d^5*n^4*x^3 + 6*(d*x + c)^n*D*b*c*d^4*n^3*x^4 + 11*(d*x + c)^n*D*a*d^5*n^3*x^4 + 11*(d*x + c)^n*C*b*d^5*n^3*x^4 + 35*(d*x + c)^n*D*b*d^5*n^2*x^5 + (d*x + c)^n*C*a*c*d^4*n^4*x^2 + (d*x + c)^n*B*b*c*d^4*n^4*x^2 + (d*x + c)^n*B*a*d^5*n^4*x^2 + (d*x + c)^n*A*b*d^5*n^4*x^2 - 4*(d*x + c)^n*D*b*c^2*d^3*n^3*x^3 + 8*(d*x + c)^n*D*a*c*d^4*n^3*x^3 + 8*(d*x + c)^n*C*b*c*d^4*n^3*x^3 + 12*(d*x + c)^n*C*a*d^5*n^3*x^3 + 12*(d*x + c)^n*B*b*d^5*n^3*x^3 + 11*(d*x + c)^n*D*b*c*d^4*n^2*x^4 + 41*(d*x + c)^n*D*a*d^5*n^2*x^4 + 41*(d*x + c)^n*C*b*d^5*n^2*x^4 + 50*(d*x + c)^n*D*b*d^5*n*x^5 + (d*x + c)^n*B*a*c*d^4*n^4*x + (d*x + c)^n*A*b*c*d^4*n^4*x + (d*x + c)^n*A*a*d^5*n^4*x - 3*(d*x + c)^n*D*a*c^2*d^3*n^3*x^2 - 3*(d*x + c)^n*C*b*c^2*d^3*n^3*x^2 + 10*(d*x + c)^n*C*a*c*d^4*n^3*x^2 + 10*(d*x + c)^n*B*b*c*d^4*n^3*x^2 + 13*(d*x + c)^n*B*a*d^5*n^3*x^2 + 13*(d*x + c)^n*A*b*d^5*n^3*x^2 - 12*(d*x + c)^n*D*b*c^2*d^3*n^2*x^3 + 17*(d*x + c)^n*D*a*c*d^4*n^2*x^3 + 17*(d*x + c)^n*C*b*c*d^4*n^2*x^3 + 49*(d*x + c)^n*C*a*d^5*n^2*x^3 + 49*(d*x + c)^n*B*b*d^5*n^2*x^3 + 6*(d*x + c)^n*D*b*c*d^4*n*x^4 + 61*(d*x + c)^n*D*a*d^5*n*x^4 + 61*(d*x + c)^n*C*b*d^5*n*x^4 + 24*(d*x + c)^n*D*b*d^5*x^5 + (d*x + c)^n*A*a*c*d^4*n^4 - 2*(d*x + c)^n*C*a*c^2*d^3*n^3*x - 2*(d*x + c)^n*B*b*c^2*d^3*n^3*x + 12*(d*x + c)^n*B*a*c*d^4*n^3*x + 12*(d*x + c)^n*A*b*c*d^4*n^3*x + 14*(d*x + c)^n*A*a*d^5*n^3*x + 12*(d*x + c)^n*D*b*c^3*d^2*n^2*x^2 - 18*(d*x + c)^n*D*a*c^2*d^3*n^2*x^2 - 18*(d*x + c)^n*C*b*c^2*d^3*n^2*x^2 + 29*(d*x + c)^n*C*a*c*d^4*n^2*x^2 + 29*(d*x + c)^n*B*b*c*d^4*n^2*x^2 + 59*(d*x + c)^n*B*a*d^5*n^2*x^2 + 59*(d*x + c)^n*A*b*d^5*n^2*x^2 - 8*(d*x + c)^n*D*b*c^2*d^3*n*x^3 + 10*(d*x + c)^n*D*a*c*d^4*n*x^3 + 10*(d*x + c)^n*C*b*c*d^4*n*x^3 + 78*(d*x + c)^n*C*a*d^5*n*x^3 + 78*(d*x + c)^n*B*b*d^5*n*x^3 + 30*(d*x + c)^n*D*a*d^5*x^4 + 30*(d*x + c)^n*C*b*d^5*x^4 - (d*x + c)^n*B*a*c^2*d^3*n^3 - (d*x + c)^n*A*b*c^2*d^3*n^3 + 14*(d*x + c)^n*A*a*c*d^4*n^3 + 6*(d*x + c)^n*D*a*c^3*d^2*n^2*x + 6*(d*x + c)^n*C*b*c^3*d^2*n^2*x - 18*(d*x + c)^n*C*a*c^2*d^3*n^2*x - 18*(d*x + c)^n*B*b*c^2*d^3*n^2*x + 47*(d*x + c)^n*B*a*c*d^4*n^2*x + 47*(d*x + c)^n*A*b*c*d^4*n^2*x + 71*(d*x + c)^n*A*a*d^5*n^2*x + 12*(d*x + c)^n*D*b*c^3*d^2*n*x^2 - 15*(d*x + c)^n*D*a*c^2*d^3*n*x^2 - 15*(d*x + c)^n*C*b*c^2*d^3*n*x^2 + 20*(d*x + c)^n*C*a*c*d^4*n*x^2 + 20*(d*x + c)^n*B*b*c*d^4*n*x^2 + 107*(d*x + c)^n*B*a*d^5*n*x^2 + 107*(d*x + c)^n*A*b*d^5*n*x^2 + 40*(d*x + c)^n*C*a*d^5*x^3 + 40*(d*x + c)^n*B*b*d^5*x^3 + 2*(d*x + c)^n*C*a*c^3*d^2*n^2 + 2*(d*x + c)^n*B*b*c^3*d^2*n^2 - 12*(d*x + c)^n*B*a*c^2*d^3*n^2 - 12*(d*x + c)^n*A*b*c^2*d^3*n^2 + 71*(d*x + c)^n*A*a*c*d^4*n^2 - 24*(d*x + c)^n*D*b*c^4*d*n*x + 30*(d*x + c)^n*D*a*c^3*d^2*n*x + 30*(d*x + c)^n*C*b*c^3*d^2*n*x - 40*(d*x + c)^n*C*a*c^2*d^3*n*x - 40*(d*x + c)^n*B*b*c^2*d^3*n*x + 60*(d*x + c)^n*B*a*c*d^4*n*x + 60*(d*x + c)^n*A*b*c*d^4*n*x + 154*(d*x + c)^n*A*a*d^5*n*x + 60*(d*x + c)^n*B*a*d^5*x^2 + 60*(d*x + c)^n*A*b*d^5*x^2 - 6*(d*x + c)^n*D*a*c^4*d*n - 6*(d*x + c)^n*C*b*c^4*d*n + 18*(d*x + c)^n*C*a*c^3*d^2*n + 18*(d*x + c)^n*B*b*c^3*d^2*n - 47*(d*x + c)^n*B*a*c^2*d^3*n - 47*(d*x + c)^n*A*b*c^2*d^3*n + 154*(d*x + c)^n*A*a*c*d^4*n + 120*(d*x + c)^n*A*a*d^5*x + 24*(d*x + c)^n*D*b*c^5 - 30*(d*x + c)^n*D*a*c^4*d - 30*(d*x + c)^n*C*b*c^4*d + 40*(d*x + c)^n*C*a*c^3*d^2 + 40*(d*x + c)^n*B*b*c^3*d^2 - 60*(d*x + c)^n*B*a*c^2*d^3 - 60*(d*x + c)^n*A*b*c^2*d^3 + 120*(d*x + c)^n*A*a*c*d^4)/(d^5*n^5 + 15*d^5*n^4 + 85*d^5*n^3 + 225*d^5*n^2 + 274*d^5*n + 120*d^5)","B",0
28,1,728,0,1.316448," ","integrate((d*x+c)^n*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\frac{{\left(d x + c\right)}^{n} D d^{4} n^{3} x^{4} + {\left(d x + c\right)}^{n} D c d^{3} n^{3} x^{3} + {\left(d x + c\right)}^{n} C d^{4} n^{3} x^{3} + 6 \, {\left(d x + c\right)}^{n} D d^{4} n^{2} x^{4} + {\left(d x + c\right)}^{n} C c d^{3} n^{3} x^{2} + {\left(d x + c\right)}^{n} B d^{4} n^{3} x^{2} + 3 \, {\left(d x + c\right)}^{n} D c d^{3} n^{2} x^{3} + 7 \, {\left(d x + c\right)}^{n} C d^{4} n^{2} x^{3} + 11 \, {\left(d x + c\right)}^{n} D d^{4} n x^{4} + {\left(d x + c\right)}^{n} B c d^{3} n^{3} x + {\left(d x + c\right)}^{n} A d^{4} n^{3} x - 3 \, {\left(d x + c\right)}^{n} D c^{2} d^{2} n^{2} x^{2} + 5 \, {\left(d x + c\right)}^{n} C c d^{3} n^{2} x^{2} + 8 \, {\left(d x + c\right)}^{n} B d^{4} n^{2} x^{2} + 2 \, {\left(d x + c\right)}^{n} D c d^{3} n x^{3} + 14 \, {\left(d x + c\right)}^{n} C d^{4} n x^{3} + 6 \, {\left(d x + c\right)}^{n} D d^{4} x^{4} + {\left(d x + c\right)}^{n} A c d^{3} n^{3} - 2 \, {\left(d x + c\right)}^{n} C c^{2} d^{2} n^{2} x + 7 \, {\left(d x + c\right)}^{n} B c d^{3} n^{2} x + 9 \, {\left(d x + c\right)}^{n} A d^{4} n^{2} x - 3 \, {\left(d x + c\right)}^{n} D c^{2} d^{2} n x^{2} + 4 \, {\left(d x + c\right)}^{n} C c d^{3} n x^{2} + 19 \, {\left(d x + c\right)}^{n} B d^{4} n x^{2} + 8 \, {\left(d x + c\right)}^{n} C d^{4} x^{3} - {\left(d x + c\right)}^{n} B c^{2} d^{2} n^{2} + 9 \, {\left(d x + c\right)}^{n} A c d^{3} n^{2} + 6 \, {\left(d x + c\right)}^{n} D c^{3} d n x - 8 \, {\left(d x + c\right)}^{n} C c^{2} d^{2} n x + 12 \, {\left(d x + c\right)}^{n} B c d^{3} n x + 26 \, {\left(d x + c\right)}^{n} A d^{4} n x + 12 \, {\left(d x + c\right)}^{n} B d^{4} x^{2} + 2 \, {\left(d x + c\right)}^{n} C c^{3} d n - 7 \, {\left(d x + c\right)}^{n} B c^{2} d^{2} n + 26 \, {\left(d x + c\right)}^{n} A c d^{3} n + 24 \, {\left(d x + c\right)}^{n} A d^{4} x - 6 \, {\left(d x + c\right)}^{n} D c^{4} + 8 \, {\left(d x + c\right)}^{n} C c^{3} d - 12 \, {\left(d x + c\right)}^{n} B c^{2} d^{2} + 24 \, {\left(d x + c\right)}^{n} A c d^{3}}{d^{4} n^{4} + 10 \, d^{4} n^{3} + 35 \, d^{4} n^{2} + 50 \, d^{4} n + 24 \, d^{4}}"," ",0,"((d*x + c)^n*D*d^4*n^3*x^4 + (d*x + c)^n*D*c*d^3*n^3*x^3 + (d*x + c)^n*C*d^4*n^3*x^3 + 6*(d*x + c)^n*D*d^4*n^2*x^4 + (d*x + c)^n*C*c*d^3*n^3*x^2 + (d*x + c)^n*B*d^4*n^3*x^2 + 3*(d*x + c)^n*D*c*d^3*n^2*x^3 + 7*(d*x + c)^n*C*d^4*n^2*x^3 + 11*(d*x + c)^n*D*d^4*n*x^4 + (d*x + c)^n*B*c*d^3*n^3*x + (d*x + c)^n*A*d^4*n^3*x - 3*(d*x + c)^n*D*c^2*d^2*n^2*x^2 + 5*(d*x + c)^n*C*c*d^3*n^2*x^2 + 8*(d*x + c)^n*B*d^4*n^2*x^2 + 2*(d*x + c)^n*D*c*d^3*n*x^3 + 14*(d*x + c)^n*C*d^4*n*x^3 + 6*(d*x + c)^n*D*d^4*x^4 + (d*x + c)^n*A*c*d^3*n^3 - 2*(d*x + c)^n*C*c^2*d^2*n^2*x + 7*(d*x + c)^n*B*c*d^3*n^2*x + 9*(d*x + c)^n*A*d^4*n^2*x - 3*(d*x + c)^n*D*c^2*d^2*n*x^2 + 4*(d*x + c)^n*C*c*d^3*n*x^2 + 19*(d*x + c)^n*B*d^4*n*x^2 + 8*(d*x + c)^n*C*d^4*x^3 - (d*x + c)^n*B*c^2*d^2*n^2 + 9*(d*x + c)^n*A*c*d^3*n^2 + 6*(d*x + c)^n*D*c^3*d*n*x - 8*(d*x + c)^n*C*c^2*d^2*n*x + 12*(d*x + c)^n*B*c*d^3*n*x + 26*(d*x + c)^n*A*d^4*n*x + 12*(d*x + c)^n*B*d^4*x^2 + 2*(d*x + c)^n*C*c^3*d*n - 7*(d*x + c)^n*B*c^2*d^2*n + 26*(d*x + c)^n*A*c*d^3*n + 24*(d*x + c)^n*A*d^4*x - 6*(d*x + c)^n*D*c^4 + 8*(d*x + c)^n*C*c^3*d - 12*(d*x + c)^n*B*c^2*d^2 + 24*(d*x + c)^n*A*c*d^3)/(d^4*n^4 + 10*d^4*n^3 + 35*d^4*n^2 + 50*d^4*n + 24*d^4)","B",0
29,0,0,0,0.000000," ","integrate((d*x+c)^n*(D*x^3+C*x^2+B*x+A)/(b*x+a),x, algorithm=""giac"")","\int \frac{{\left(D x^{3} + C x^{2} + B x + A\right)} {\left(d x + c\right)}^{n}}{b x + a}\,{d x}"," ",0,"integrate((D*x^3 + C*x^2 + B*x + A)*(d*x + c)^n/(b*x + a), x)","F",0
30,0,0,0,0.000000," ","integrate((d*x+c)^n*(D*x^3+C*x^2+B*x+A)/(b*x+a)^2,x, algorithm=""giac"")","\int \frac{{\left(D x^{3} + C x^{2} + B x + A\right)} {\left(d x + c\right)}^{n}}{{\left(b x + a\right)}^{2}}\,{d x}"," ",0,"integrate((D*x^3 + C*x^2 + B*x + A)*(d*x + c)^n/(b*x + a)^2, x)","F",0
31,0,0,0,0.000000," ","integrate((d*x+c)^n*(D*x^3+C*x^2+B*x+A)/(b*x+a)^3,x, algorithm=""giac"")","\int \frac{{\left(D x^{3} + C x^{2} + B x + A\right)} {\left(d x + c\right)}^{n}}{{\left(b x + a\right)}^{3}}\,{d x}"," ",0,"integrate((D*x^3 + C*x^2 + B*x + A)*(d*x + c)^n/(b*x + a)^3, x)","F",0
32,0,0,0,0.000000," ","integrate((b*x+a)^m*(B*x+A)*(d*x+c)^n,x, algorithm=""giac"")","\int {\left(B x + A\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n}\,{d x}"," ",0,"integrate((B*x + A)*(b*x + a)^m*(d*x + c)^n, x)","F",0
33,0,0,0,0.000000," ","integrate((b*x+a)^m*(d*x+c)^n*(C*x^2+B*x+A),x, algorithm=""giac"")","\int {\left(C x^{2} + B x + A\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*(b*x + a)^m*(d*x + c)^n, x)","F",0
34,0,0,0,0.000000," ","integrate((b*x+a)^m*(d*x+c)^n*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\int {\left(D x^{3} + C x^{2} + B x + A\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n}\,{d x}"," ",0,"integrate((D*x^3 + C*x^2 + B*x + A)*(b*x + a)^m*(d*x + c)^n, x)","F",0
