Integrand size = 26, antiderivative size = 171 \[ \int \left (A+B x+C x^2\right ) \left (2+3 x-5 x^2+x^3\right )^3 \, dx=8 A x+2 (9 A+2 B) x^2-\frac {2}{3} (3 A-18 B-4 C) x^3-\frac {3}{4} (47 A+2 B-12 C) x^4+\frac {3}{5} (17 A-47 B-2 C) x^5+\frac {1}{2} (64 A+17 B-47 C) x^6-\frac {1}{7} (209 A-192 B-51 C) x^7+\frac {1}{8} (84 A-209 B+192 C) x^8-\frac {1}{9} (15 A-84 B+209 C) x^9+\frac {1}{10} (A-15 B+84 C) x^{10}+\frac {1}{11} (B-15 C) x^{11}+\frac {C x^{12}}{12} \] Output:
8*A*x+2*(9*A+2*B)*x^2-2/3*(3*A-18*B-4*C)*x^3-3/4*(47*A+2*B-12*C)*x^4+3/5*( 17*A-47*B-2*C)*x^5+1/2*(64*A+17*B-47*C)*x^6-1/7*(209*A-192*B-51*C)*x^7+1/8 *(84*A-209*B+192*C)*x^8-1/9*(15*A-84*B+209*C)*x^9+1/10*(A-15*B+84*C)*x^10+ 1/11*(B-15*C)*x^11+1/12*C*x^12
Time = 0.05 (sec) , antiderivative size = 171, normalized size of antiderivative = 1.00 \[ \int \left (A+B x+C x^2\right ) \left (2+3 x-5 x^2+x^3\right )^3 \, dx=8 A x+2 (9 A+2 B) x^2-\frac {2}{3} (3 A-18 B-4 C) x^3-\frac {3}{4} (47 A+2 B-12 C) x^4+\frac {3}{5} (17 A-47 B-2 C) x^5+\frac {1}{2} (64 A+17 B-47 C) x^6+\frac {1}{7} (-209 A+192 B+51 C) x^7+\frac {1}{8} (84 A-209 B+192 C) x^8+\frac {1}{9} (-15 A+84 B-209 C) x^9+\frac {1}{10} (A-15 B+84 C) x^{10}+\frac {1}{11} (B-15 C) x^{11}+\frac {C x^{12}}{12} \] Input:
Integrate[(A + B*x + C*x^2)*(2 + 3*x - 5*x^2 + x^3)^3,x]
Output:
8*A*x + 2*(9*A + 2*B)*x^2 - (2*(3*A - 18*B - 4*C)*x^3)/3 - (3*(47*A + 2*B - 12*C)*x^4)/4 + (3*(17*A - 47*B - 2*C)*x^5)/5 + ((64*A + 17*B - 47*C)*x^6 )/2 + ((-209*A + 192*B + 51*C)*x^7)/7 + ((84*A - 209*B + 192*C)*x^8)/8 + ( (-15*A + 84*B - 209*C)*x^9)/9 + ((A - 15*B + 84*C)*x^10)/10 + ((B - 15*C)* x^11)/11 + (C*x^12)/12
Time = 0.81 (sec) , antiderivative size = 171, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2188, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \left (x^3-5 x^2+3 x+2\right )^3 \left (A+B x+C x^2\right ) \, dx\) |
| \(\Big \downarrow \) 2188 |
| \(\displaystyle \int \left (x^9 (A-15 B+84 C)-x^8 (15 A-84 B+209 C)+x^7 (84 A-209 B+192 C)-x^6 (209 A-192 B-51 C)+3 x^5 (64 A+17 B-47 C)+3 x^4 (17 A-47 B-2 C)-3 x^3 (47 A+2 B-12 C)-2 x^2 (3 A-18 B-4 C)+4 x (9 A+2 B)+8 A+x^{10} (B-15 C)+C x^{11}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{10} x^{10} (A-15 B+84 C)-\frac {1}{9} x^9 (15 A-84 B+209 C)+\frac {1}{8} x^8 (84 A-209 B+192 C)-\frac {1}{7} x^7 (209 A-192 B-51 C)+\frac {1}{2} x^6 (64 A+17 B-47 C)+\frac {3}{5} x^5 (17 A-47 B-2 C)-\frac {3}{4} x^4 (47 A+2 B-12 C)-\frac {2}{3} x^3 (3 A-18 B-4 C)+2 x^2 (9 A+2 B)+8 A x+\frac {1}{11} x^{11} (B-15 C)+\frac {C x^{12}}{12}\) |
Input:
Int[(A + B*x + C*x^2)*(2 + 3*x - 5*x^2 + x^3)^3,x]
Output:
8*A*x + 2*(9*A + 2*B)*x^2 - (2*(3*A - 18*B - 4*C)*x^3)/3 - (3*(47*A + 2*B - 12*C)*x^4)/4 + (3*(17*A - 47*B - 2*C)*x^5)/5 + ((64*A + 17*B - 47*C)*x^6 )/2 - ((209*A - 192*B - 51*C)*x^7)/7 + ((84*A - 209*B + 192*C)*x^8)/8 - (( 15*A - 84*B + 209*C)*x^9)/9 + ((A - 15*B + 84*C)*x^10)/10 + ((B - 15*C)*x^ 11)/11 + (C*x^12)/12
Int[(Pq_)*((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[Expand Integrand[Pq*(a + b*x + c*x^2)^p, x], x] /; FreeQ[{a, b, c}, x] && PolyQ[Pq , x] && IGtQ[p, -2]
Time = 0.23 (sec) , antiderivative size = 146, normalized size of antiderivative = 0.85
| method | result | size |
| norman | \(\frac {C \,x^{12}}{12}+\left (\frac {B}{11}-\frac {15 C}{11}\right ) x^{11}+\left (\frac {A}{10}-\frac {3 B}{2}+\frac {42 C}{5}\right ) x^{10}+\left (-\frac {5 A}{3}+\frac {28 B}{3}-\frac {209 C}{9}\right ) x^{9}+\left (\frac {21 A}{2}-\frac {209 B}{8}+24 C \right ) x^{8}+\left (-\frac {209 A}{7}+\frac {192 B}{7}+\frac {51 C}{7}\right ) x^{7}+\left (32 A +\frac {17 B}{2}-\frac {47 C}{2}\right ) x^{6}+\left (\frac {51 A}{5}-\frac {141 B}{5}-\frac {6 C}{5}\right ) x^{5}+\left (-\frac {141 A}{4}-\frac {3 B}{2}+9 C \right ) x^{4}+\left (-2 A +12 B +\frac {8 C}{3}\right ) x^{3}+\left (18 A +4 B \right ) x^{2}+8 A x\) | \(146\) |
| default | \(\frac {C \,x^{12}}{12}+\frac {\left (B -15 C \right ) x^{11}}{11}+\frac {\left (A -15 B +84 C \right ) x^{10}}{10}+\frac {\left (-15 A +84 B -209 C \right ) x^{9}}{9}+\frac {\left (84 A -209 B +192 C \right ) x^{8}}{8}+\frac {\left (-209 A +192 B +51 C \right ) x^{7}}{7}+\frac {\left (192 A +51 B -141 C \right ) x^{6}}{6}+\frac {\left (51 A -141 B -6 C \right ) x^{5}}{5}+\frac {\left (-141 A -6 B +36 C \right ) x^{4}}{4}+\frac {\left (-6 A +36 B +8 C \right ) x^{3}}{3}+\frac {\left (36 A +8 B \right ) x^{2}}{2}+8 A x\) | \(152\) |
| orering | \(\frac {x \left (2310 C \,x^{11}+2520 B \,x^{10}-37800 x^{10} C +2772 A \,x^{9}-41580 x^{9} B +232848 C \,x^{9}-46200 x^{8} A +258720 B \,x^{8}-643720 x^{8} C +291060 x^{7} A -724185 x^{7} B +665280 x^{7} C -827640 x^{6} A +760320 x^{6} B +201960 C \,x^{6}+887040 x^{5} A +235620 B \,x^{5}-651420 x^{5} C +282744 x^{4} A -781704 x^{4} B -33264 C \,x^{4}-977130 x^{3} A -41580 B \,x^{3}+249480 C \,x^{3}-55440 A \,x^{2}+332640 B \,x^{2}+73920 C \,x^{2}+498960 A x +110880 B x +221760 A \right )}{27720}\) | \(178\) |
| gosper | \(9 C \,x^{4}+\frac {8}{3} C \,x^{3}+4 B \,x^{2}+18 A \,x^{2}-\frac {141}{4} x^{4} A +\frac {51}{5} x^{5} A -\frac {5}{3} A \,x^{9}-\frac {3}{2} B \,x^{10}+24 x^{8} C -\frac {209}{7} x^{7} A +\frac {28}{3} x^{9} B +\frac {21}{2} x^{8} A +\frac {192}{7} x^{7} B +\frac {51}{7} x^{7} C +32 x^{6} A +\frac {17}{2} x^{6} B +\frac {1}{10} x^{10} A +\frac {42}{5} x^{10} C +8 A x +\frac {1}{11} B \,x^{11}+\frac {1}{12} C \,x^{12}-\frac {209}{8} B \,x^{8}-\frac {141}{5} B \,x^{5}-\frac {47}{2} C \,x^{6}+12 B \,x^{3}-\frac {15}{11} C \,x^{11}-\frac {209}{9} C \,x^{9}-2 x^{3} A -\frac {3}{2} x^{4} B -\frac {6}{5} x^{5} C\) | \(180\) |
| risch | \(9 C \,x^{4}+\frac {8}{3} C \,x^{3}+4 B \,x^{2}+18 A \,x^{2}-\frac {141}{4} x^{4} A +\frac {51}{5} x^{5} A -\frac {5}{3} A \,x^{9}-\frac {3}{2} B \,x^{10}+24 x^{8} C -\frac {209}{7} x^{7} A +\frac {28}{3} x^{9} B +\frac {21}{2} x^{8} A +\frac {192}{7} x^{7} B +\frac {51}{7} x^{7} C +32 x^{6} A +\frac {17}{2} x^{6} B +\frac {1}{10} x^{10} A +\frac {42}{5} x^{10} C +8 A x +\frac {1}{11} B \,x^{11}+\frac {1}{12} C \,x^{12}-\frac {209}{8} B \,x^{8}-\frac {141}{5} B \,x^{5}-\frac {47}{2} C \,x^{6}+12 B \,x^{3}-\frac {15}{11} C \,x^{11}-\frac {209}{9} C \,x^{9}-2 x^{3} A -\frac {3}{2} x^{4} B -\frac {6}{5} x^{5} C\) | \(180\) |
| parallelrisch | \(9 C \,x^{4}+\frac {8}{3} C \,x^{3}+4 B \,x^{2}+18 A \,x^{2}-\frac {141}{4} x^{4} A +\frac {51}{5} x^{5} A -\frac {5}{3} A \,x^{9}-\frac {3}{2} B \,x^{10}+24 x^{8} C -\frac {209}{7} x^{7} A +\frac {28}{3} x^{9} B +\frac {21}{2} x^{8} A +\frac {192}{7} x^{7} B +\frac {51}{7} x^{7} C +32 x^{6} A +\frac {17}{2} x^{6} B +\frac {1}{10} x^{10} A +\frac {42}{5} x^{10} C +8 A x +\frac {1}{11} B \,x^{11}+\frac {1}{12} C \,x^{12}-\frac {209}{8} B \,x^{8}-\frac {141}{5} B \,x^{5}-\frac {47}{2} C \,x^{6}+12 B \,x^{3}-\frac {15}{11} C \,x^{11}-\frac {209}{9} C \,x^{9}-2 x^{3} A -\frac {3}{2} x^{4} B -\frac {6}{5} x^{5} C\) | \(180\) |
Input:
int((C*x^2+B*x+A)*(x^3-5*x^2+3*x+2)^3,x,method=_RETURNVERBOSE)
Output:
1/12*C*x^12+(1/11*B-15/11*C)*x^11+(1/10*A-3/2*B+42/5*C)*x^10+(-5/3*A+28/3* B-209/9*C)*x^9+(21/2*A-209/8*B+24*C)*x^8+(-209/7*A+192/7*B+51/7*C)*x^7+(32 *A+17/2*B-47/2*C)*x^6+(51/5*A-141/5*B-6/5*C)*x^5+(-141/4*A-3/2*B+9*C)*x^4+ (-2*A+12*B+8/3*C)*x^3+(18*A+4*B)*x^2+8*A*x
Time = 0.06 (sec) , antiderivative size = 151, normalized size of antiderivative = 0.88 \[ \int \left (A+B x+C x^2\right ) \left (2+3 x-5 x^2+x^3\right )^3 \, dx=\frac {1}{12} \, C x^{12} + \frac {1}{11} \, {\left (B - 15 \, C\right )} x^{11} + \frac {1}{10} \, {\left (A - 15 \, B + 84 \, C\right )} x^{10} - \frac {1}{9} \, {\left (15 \, A - 84 \, B + 209 \, C\right )} x^{9} + \frac {1}{8} \, {\left (84 \, A - 209 \, B + 192 \, C\right )} x^{8} - \frac {1}{7} \, {\left (209 \, A - 192 \, B - 51 \, C\right )} x^{7} + \frac {1}{2} \, {\left (64 \, A + 17 \, B - 47 \, C\right )} x^{6} + \frac {3}{5} \, {\left (17 \, A - 47 \, B - 2 \, C\right )} x^{5} - \frac {3}{4} \, {\left (47 \, A + 2 \, B - 12 \, C\right )} x^{4} - \frac {2}{3} \, {\left (3 \, A - 18 \, B - 4 \, C\right )} x^{3} + 2 \, {\left (9 \, A + 2 \, B\right )} x^{2} + 8 \, A x \] Input:
integrate((C*x^2+B*x+A)*(x^3-5*x^2+3*x+2)^3,x, algorithm="fricas")
Output:
1/12*C*x^12 + 1/11*(B - 15*C)*x^11 + 1/10*(A - 15*B + 84*C)*x^10 - 1/9*(15 *A - 84*B + 209*C)*x^9 + 1/8*(84*A - 209*B + 192*C)*x^8 - 1/7*(209*A - 192 *B - 51*C)*x^7 + 1/2*(64*A + 17*B - 47*C)*x^6 + 3/5*(17*A - 47*B - 2*C)*x^ 5 - 3/4*(47*A + 2*B - 12*C)*x^4 - 2/3*(3*A - 18*B - 4*C)*x^3 + 2*(9*A + 2* B)*x^2 + 8*A*x
Time = 0.05 (sec) , antiderivative size = 172, normalized size of antiderivative = 1.01 \[ \int \left (A+B x+C x^2\right ) \left (2+3 x-5 x^2+x^3\right )^3 \, dx=8 A x + \frac {C x^{12}}{12} + x^{11} \left (\frac {B}{11} - \frac {15 C}{11}\right ) + x^{10} \left (\frac {A}{10} - \frac {3 B}{2} + \frac {42 C}{5}\right ) + x^{9} \left (- \frac {5 A}{3} + \frac {28 B}{3} - \frac {209 C}{9}\right ) + x^{8} \cdot \left (\frac {21 A}{2} - \frac {209 B}{8} + 24 C\right ) + x^{7} \left (- \frac {209 A}{7} + \frac {192 B}{7} + \frac {51 C}{7}\right ) + x^{6} \cdot \left (32 A + \frac {17 B}{2} - \frac {47 C}{2}\right ) + x^{5} \cdot \left (\frac {51 A}{5} - \frac {141 B}{5} - \frac {6 C}{5}\right ) + x^{4} \left (- \frac {141 A}{4} - \frac {3 B}{2} + 9 C\right ) + x^{3} \left (- 2 A + 12 B + \frac {8 C}{3}\right ) + x^{2} \cdot \left (18 A + 4 B\right ) \] Input:
integrate((C*x**2+B*x+A)*(x**3-5*x**2+3*x+2)**3,x)
Output:
8*A*x + C*x**12/12 + x**11*(B/11 - 15*C/11) + x**10*(A/10 - 3*B/2 + 42*C/5 ) + x**9*(-5*A/3 + 28*B/3 - 209*C/9) + x**8*(21*A/2 - 209*B/8 + 24*C) + x* *7*(-209*A/7 + 192*B/7 + 51*C/7) + x**6*(32*A + 17*B/2 - 47*C/2) + x**5*(5 1*A/5 - 141*B/5 - 6*C/5) + x**4*(-141*A/4 - 3*B/2 + 9*C) + x**3*(-2*A + 12 *B + 8*C/3) + x**2*(18*A + 4*B)
Time = 0.03 (sec) , antiderivative size = 151, normalized size of antiderivative = 0.88 \[ \int \left (A+B x+C x^2\right ) \left (2+3 x-5 x^2+x^3\right )^3 \, dx=\frac {1}{12} \, C x^{12} + \frac {1}{11} \, {\left (B - 15 \, C\right )} x^{11} + \frac {1}{10} \, {\left (A - 15 \, B + 84 \, C\right )} x^{10} - \frac {1}{9} \, {\left (15 \, A - 84 \, B + 209 \, C\right )} x^{9} + \frac {1}{8} \, {\left (84 \, A - 209 \, B + 192 \, C\right )} x^{8} - \frac {1}{7} \, {\left (209 \, A - 192 \, B - 51 \, C\right )} x^{7} + \frac {1}{2} \, {\left (64 \, A + 17 \, B - 47 \, C\right )} x^{6} + \frac {3}{5} \, {\left (17 \, A - 47 \, B - 2 \, C\right )} x^{5} - \frac {3}{4} \, {\left (47 \, A + 2 \, B - 12 \, C\right )} x^{4} - \frac {2}{3} \, {\left (3 \, A - 18 \, B - 4 \, C\right )} x^{3} + 2 \, {\left (9 \, A + 2 \, B\right )} x^{2} + 8 \, A x \] Input:
integrate((C*x^2+B*x+A)*(x^3-5*x^2+3*x+2)^3,x, algorithm="maxima")
Output:
1/12*C*x^12 + 1/11*(B - 15*C)*x^11 + 1/10*(A - 15*B + 84*C)*x^10 - 1/9*(15 *A - 84*B + 209*C)*x^9 + 1/8*(84*A - 209*B + 192*C)*x^8 - 1/7*(209*A - 192 *B - 51*C)*x^7 + 1/2*(64*A + 17*B - 47*C)*x^6 + 3/5*(17*A - 47*B - 2*C)*x^ 5 - 3/4*(47*A + 2*B - 12*C)*x^4 - 2/3*(3*A - 18*B - 4*C)*x^3 + 2*(9*A + 2* B)*x^2 + 8*A*x
Time = 0.11 (sec) , antiderivative size = 179, normalized size of antiderivative = 1.05 \[ \int \left (A+B x+C x^2\right ) \left (2+3 x-5 x^2+x^3\right )^3 \, dx=\frac {1}{12} \, C x^{12} + \frac {1}{11} \, B x^{11} - \frac {15}{11} \, C x^{11} + \frac {1}{10} \, A x^{10} - \frac {3}{2} \, B x^{10} + \frac {42}{5} \, C x^{10} - \frac {5}{3} \, A x^{9} + \frac {28}{3} \, B x^{9} - \frac {209}{9} \, C x^{9} + \frac {21}{2} \, A x^{8} - \frac {209}{8} \, B x^{8} + 24 \, C x^{8} - \frac {209}{7} \, A x^{7} + \frac {192}{7} \, B x^{7} + \frac {51}{7} \, C x^{7} + 32 \, A x^{6} + \frac {17}{2} \, B x^{6} - \frac {47}{2} \, C x^{6} + \frac {51}{5} \, A x^{5} - \frac {141}{5} \, B x^{5} - \frac {6}{5} \, C x^{5} - \frac {141}{4} \, A x^{4} - \frac {3}{2} \, B x^{4} + 9 \, C x^{4} - 2 \, A x^{3} + 12 \, B x^{3} + \frac {8}{3} \, C x^{3} + 18 \, A x^{2} + 4 \, B x^{2} + 8 \, A x \] Input:
integrate((C*x^2+B*x+A)*(x^3-5*x^2+3*x+2)^3,x, algorithm="giac")
Output:
1/12*C*x^12 + 1/11*B*x^11 - 15/11*C*x^11 + 1/10*A*x^10 - 3/2*B*x^10 + 42/5 *C*x^10 - 5/3*A*x^9 + 28/3*B*x^9 - 209/9*C*x^9 + 21/2*A*x^8 - 209/8*B*x^8 + 24*C*x^8 - 209/7*A*x^7 + 192/7*B*x^7 + 51/7*C*x^7 + 32*A*x^6 + 17/2*B*x^ 6 - 47/2*C*x^6 + 51/5*A*x^5 - 141/5*B*x^5 - 6/5*C*x^5 - 141/4*A*x^4 - 3/2* B*x^4 + 9*C*x^4 - 2*A*x^3 + 12*B*x^3 + 8/3*C*x^3 + 18*A*x^2 + 4*B*x^2 + 8* A*x
Time = 21.63 (sec) , antiderivative size = 148, normalized size of antiderivative = 0.87 \[ \int \left (A+B x+C x^2\right ) \left (2+3 x-5 x^2+x^3\right )^3 \, dx=\frac {C\,x^{12}}{12}+\left (\frac {B}{11}-\frac {15\,C}{11}\right )\,x^{11}+\left (\frac {A}{10}-\frac {3\,B}{2}+\frac {42\,C}{5}\right )\,x^{10}+\left (\frac {28\,B}{3}-\frac {5\,A}{3}-\frac {209\,C}{9}\right )\,x^9+\left (\frac {21\,A}{2}-\frac {209\,B}{8}+24\,C\right )\,x^8+\left (\frac {192\,B}{7}-\frac {209\,A}{7}+\frac {51\,C}{7}\right )\,x^7+\left (32\,A+\frac {17\,B}{2}-\frac {47\,C}{2}\right )\,x^6+\left (\frac {51\,A}{5}-\frac {141\,B}{5}-\frac {6\,C}{5}\right )\,x^5+\left (9\,C-\frac {3\,B}{2}-\frac {141\,A}{4}\right )\,x^4+\left (12\,B-2\,A+\frac {8\,C}{3}\right )\,x^3+\left (18\,A+4\,B\right )\,x^2+8\,A\,x \] Input:
int((A + B*x + C*x^2)*(3*x - 5*x^2 + x^3 + 2)^3,x)
Output:
8*A*x + (C*x^12)/12 + x^3*(12*B - 2*A + (8*C)/3) + x^10*(A/10 - (3*B)/2 + (42*C)/5) + x^6*(32*A + (17*B)/2 - (47*C)/2) - x^4*((141*A)/4 + (3*B)/2 - 9*C) - x^5*((141*B)/5 - (51*A)/5 + (6*C)/5) - x^9*((5*A)/3 - (28*B)/3 + (2 09*C)/9) + x^8*((21*A)/2 - (209*B)/8 + 24*C) + x^7*((192*B)/7 - (209*A)/7 + (51*C)/7) + x^2*(18*A + 4*B) + x^11*(B/11 - (15*C)/11)
Time = 0.15 (sec) , antiderivative size = 177, normalized size of antiderivative = 1.04 \[ \int \left (A+B x+C x^2\right ) \left (2+3 x-5 x^2+x^3\right )^3 \, dx=\frac {x \left (2310 c \,x^{11}+2520 b \,x^{10}-37800 c \,x^{10}+2772 a \,x^{9}-41580 b \,x^{9}+232848 c \,x^{9}-46200 a \,x^{8}+258720 b \,x^{8}-643720 c \,x^{8}+291060 a \,x^{7}-724185 b \,x^{7}+665280 c \,x^{7}-827640 a \,x^{6}+760320 b \,x^{6}+201960 c \,x^{6}+887040 a \,x^{5}+235620 b \,x^{5}-651420 c \,x^{5}+282744 a \,x^{4}-781704 b \,x^{4}-33264 c \,x^{4}-977130 a \,x^{3}-41580 b \,x^{3}+249480 c \,x^{3}-55440 a \,x^{2}+332640 b \,x^{2}+73920 c \,x^{2}+498960 a x +110880 b x +221760 a \right )}{27720} \] Input:
int((C*x^2+B*x+A)*(x^3-5*x^2+3*x+2)^3,x)
Output:
(x*(2772*a*x**9 - 46200*a*x**8 + 291060*a*x**7 - 827640*a*x**6 + 887040*a* x**5 + 282744*a*x**4 - 977130*a*x**3 - 55440*a*x**2 + 498960*a*x + 221760* a + 2520*b*x**10 - 41580*b*x**9 + 258720*b*x**8 - 724185*b*x**7 + 760320*b *x**6 + 235620*b*x**5 - 781704*b*x**4 - 41580*b*x**3 + 332640*b*x**2 + 110 880*b*x + 2310*c*x**11 - 37800*c*x**10 + 232848*c*x**9 - 643720*c*x**8 + 6 65280*c*x**7 + 201960*c*x**6 - 651420*c*x**5 - 33264*c*x**4 + 249480*c*x** 3 + 73920*c*x**2))/27720