\(\int (b+2 c x) (-a+b x+c x^2)^{13} \, dx\) [97]

Optimal result

Integrand size = 21, antiderivative size = 18 \[ \int (b+2 c x) \left (-a+b x+c x^2\right )^{13} \, dx=\frac {1}{14} \left (a-b x-c x^2\right )^{14} \]

[Out]

1/14*(-c*x^2-b*x+a)^14

Rubi [A] (verified)

Time = 0.04 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {643} \[ \int (b+2 c x) \left (-a+b x+c x^2\right )^{13} \, dx=\frac {1}{14} \left (a-b x-c x^2\right )^{14} \]

[In]

Int[(b + 2*c*x)*(-a + b*x + c*x^2)^13,x]

[Out]

(a - b*x - c*x^2)^14/14

Rule 643

Int[((d_) + (e_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Simp[d*((a + b*x + c*x^2)^(p +
1)/(b*(p + 1))), x] /; FreeQ[{a, b, c, d, e, p}, x] && EqQ[2*c*d - b*e, 0] && NeQ[p, -1]

Rubi steps \begin{align*} \text {integral}& = \frac {1}{14} \left (a-b x-c x^2\right )^{14} \\ \end{align*}

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(201\) vs. \(2(18)=36\).

Time = 0.11 (sec) , antiderivative size = 201, normalized size of antiderivative = 11.17 \[ \int (b+2 c x) \left (-a+b x+c x^2\right )^{13} \, dx=\frac {1}{14} x (b+c x) \left (-14 a^{13}+91 a^{12} x (b+c x)-364 a^{11} x^2 (b+c x)^2+1001 a^{10} x^3 (b+c x)^3-2002 a^9 x^4 (b+c x)^4+3003 a^8 x^5 (b+c x)^5-3432 a^7 x^6 (b+c x)^6+3003 a^6 x^7 (b+c x)^7-2002 a^5 x^8 (b+c x)^8+1001 a^4 x^9 (b+c x)^9-364 a^3 x^{10} (b+c x)^{10}+91 a^2 x^{11} (b+c x)^{11}-14 a x^{12} (b+c x)^{12}+x^{13} (b+c x)^{13}\right ) \]

[In]

Integrate[(b + 2*c*x)*(-a + b*x + c*x^2)^13,x]

[Out]

(x*(b + c*x)*(-14*a^13 + 91*a^12*x*(b + c*x) - 364*a^11*x^2*(b + c*x)^2 + 1001*a^10*x^3*(b + c*x)^3 - 2002*a^9
*x^4*(b + c*x)^4 + 3003*a^8*x^5*(b + c*x)^5 - 3432*a^7*x^6*(b + c*x)^6 + 3003*a^6*x^7*(b + c*x)^7 - 2002*a^5*x
^8*(b + c*x)^8 + 1001*a^4*x^9*(b + c*x)^9 - 364*a^3*x^10*(b + c*x)^10 + 91*a^2*x^11*(b + c*x)^11 - 14*a*x^12*(
b + c*x)^12 + x^13*(b + c*x)^13))/14

Maple [A] (verified)

Time = 0.82 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94

method	result	size
default	\(\frac {\left (c \,x^{2}+b x -a \right )^{14}}{14}\)	\(17\)
norman	\(\text {Expression too large to display}\)	\(1228\)
gosper	\(\text {Expression too large to display}\)	\(1451\)
parallelrisch	\(\text {Expression too large to display}\)	\(1451\)
risch	\(\text {Expression too large to display}\)	\(1456\)

[In]

int((2*c*x+b)*(c*x^2+b*x-a)^13,x,method=_RETURNVERBOSE)

[Out]

1/14*(c*x^2+b*x-a)^14

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1238 vs. \(2 (16) = 32\).

Time = 0.26 (sec) , antiderivative size = 1238, normalized size of antiderivative = 68.78 \[ \int (b+2 c x) \left (-a+b x+c x^2\right )^{13} \, dx=\text {Too large to display} \]

[In]

integrate((2*c*x+b)*(c*x^2+b*x-a)^13,x, algorithm="fricas")

[Out]

1/14*c^14*x^28 + b*c^13*x^27 + 1/2*(13*b^2*c^12 - 2*a*c^13)*x^26 + 13*(2*b^3*c^11 - a*b*c^12)*x^25 + 13/2*(11*
b^4*c^10 - 12*a*b^2*c^11 + a^2*c^12)*x^24 + 13*(11*b^5*c^9 - 22*a*b^3*c^10 + 6*a^2*b*c^11)*x^23 + 13/2*(33*b^6
*c^8 - 110*a*b^4*c^9 + 66*a^2*b^2*c^10 - 4*a^3*c^11)*x^22 + 143/7*(12*b^7*c^7 - 63*a*b^5*c^8 + 70*a^2*b^3*c^9
- 14*a^3*b*c^10)*x^21 + 143/2*(3*b^8*c^6 - 24*a*b^6*c^7 + 45*a^2*b^4*c^8 - 20*a^3*b^2*c^9 + a^4*c^10)*x^20 + 1
43*(b^9*c^5 - 12*a*b^7*c^6 + 36*a^2*b^5*c^7 - 30*a^3*b^3*c^8 + 5*a^4*b*c^9)*x^19 + 143/2*(b^10*c^4 - 18*a*b^8*
c^5 + 84*a^2*b^6*c^6 - 120*a^3*b^4*c^7 + 45*a^4*b^2*c^8 - 2*a^5*c^9)*x^18 + 13*(2*b^11*c^3 - 55*a*b^9*c^4 + 39
6*a^2*b^7*c^5 - 924*a^3*b^5*c^6 + 660*a^4*b^3*c^7 - 99*a^5*b*c^8)*x^17 + 13/2*(b^12*c^2 - 44*a*b^10*c^3 + 495*
a^2*b^8*c^4 - 1848*a^3*b^6*c^5 + 2310*a^4*b^4*c^6 - 792*a^5*b^2*c^7 + 33*a^6*c^8)*x^16 + (b^13*c - 78*a*b^11*c
^2 + 1430*a^2*b^9*c^3 - 8580*a^3*b^7*c^4 + 18018*a^4*b^5*c^5 - 12012*a^5*b^3*c^6 + 1716*a^6*b*c^7)*x^15 - a^13
*b*x + 1/14*(b^14 - 182*a*b^12*c + 6006*a^2*b^10*c^2 - 60060*a^3*b^8*c^3 + 210210*a^4*b^6*c^4 - 252252*a^5*b^4
*c^5 + 84084*a^6*b^2*c^6 - 3432*a^7*c^7)*x^14 - (a*b^13 - 78*a^2*b^11*c + 1430*a^3*b^9*c^2 - 8580*a^4*b^7*c^3
+ 18018*a^5*b^5*c^4 - 12012*a^6*b^3*c^5 + 1716*a^7*b*c^6)*x^13 + 13/2*(a^2*b^12 - 44*a^3*b^10*c + 495*a^4*b^8*
c^2 - 1848*a^5*b^6*c^3 + 2310*a^6*b^4*c^4 - 792*a^7*b^2*c^5 + 33*a^8*c^6)*x^12 - 13*(2*a^3*b^11 - 55*a^4*b^9*c
+ 396*a^5*b^7*c^2 - 924*a^6*b^5*c^3 + 660*a^7*b^3*c^4 - 99*a^8*b*c^5)*x^11 + 143/2*(a^4*b^10 - 18*a^5*b^8*c +
84*a^6*b^6*c^2 - 120*a^7*b^4*c^3 + 45*a^8*b^2*c^4 - 2*a^9*c^5)*x^10 - 143*(a^5*b^9 - 12*a^6*b^7*c + 36*a^7*b^
5*c^2 - 30*a^8*b^3*c^3 + 5*a^9*b*c^4)*x^9 + 143/2*(3*a^6*b^8 - 24*a^7*b^6*c + 45*a^8*b^4*c^2 - 20*a^9*b^2*c^3
+ a^10*c^4)*x^8 - 143/7*(12*a^7*b^7 - 63*a^8*b^5*c + 70*a^9*b^3*c^2 - 14*a^10*b*c^3)*x^7 + 13/2*(33*a^8*b^6 -
110*a^9*b^4*c + 66*a^10*b^2*c^2 - 4*a^11*c^3)*x^6 - 13*(11*a^9*b^5 - 22*a^10*b^3*c + 6*a^11*b*c^2)*x^5 + 13/2*
(11*a^10*b^4 - 12*a^11*b^2*c + a^12*c^2)*x^4 - 13*(2*a^11*b^3 - a^12*b*c)*x^3 + 1/2*(13*a^12*b^2 - 2*a^13*c)*x
^2

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1326 vs. \(2 (12) = 24\).

Time = 0.15 (sec) , antiderivative size = 1326, normalized size of antiderivative = 73.67 \[ \int (b+2 c x) \left (-a+b x+c x^2\right )^{13} \, dx=\text {Too large to display} \]

[In]

integrate((2*c*x+b)*(c*x**2+b*x-a)**13,x)

[Out]

-a**13*b*x + b*c**13*x**27 + c**14*x**28/14 + x**26*(-a*c**13 + 13*b**2*c**12/2) + x**25*(-13*a*b*c**12 + 26*b
**3*c**11) + x**24*(13*a**2*c**12/2 - 78*a*b**2*c**11 + 143*b**4*c**10/2) + x**23*(78*a**2*b*c**11 - 286*a*b**
3*c**10 + 143*b**5*c**9) + x**22*(-26*a**3*c**11 + 429*a**2*b**2*c**10 - 715*a*b**4*c**9 + 429*b**6*c**8/2) +
x**21*(-286*a**3*b*c**10 + 1430*a**2*b**3*c**9 - 1287*a*b**5*c**8 + 1716*b**7*c**7/7) + x**20*(143*a**4*c**10/
2 - 1430*a**3*b**2*c**9 + 6435*a**2*b**4*c**8/2 - 1716*a*b**6*c**7 + 429*b**8*c**6/2) + x**19*(715*a**4*b*c**9
- 4290*a**3*b**3*c**8 + 5148*a**2*b**5*c**7 - 1716*a*b**7*c**6 + 143*b**9*c**5) + x**18*(-143*a**5*c**9 + 643
5*a**4*b**2*c**8/2 - 8580*a**3*b**4*c**7 + 6006*a**2*b**6*c**6 - 1287*a*b**8*c**5 + 143*b**10*c**4/2) + x**17*
(-1287*a**5*b*c**8 + 8580*a**4*b**3*c**7 - 12012*a**3*b**5*c**6 + 5148*a**2*b**7*c**5 - 715*a*b**9*c**4 + 26*b
**11*c**3) + x**16*(429*a**6*c**8/2 - 5148*a**5*b**2*c**7 + 15015*a**4*b**4*c**6 - 12012*a**3*b**6*c**5 + 6435
*a**2*b**8*c**4/2 - 286*a*b**10*c**3 + 13*b**12*c**2/2) + x**15*(1716*a**6*b*c**7 - 12012*a**5*b**3*c**6 + 180
18*a**4*b**5*c**5 - 8580*a**3*b**7*c**4 + 1430*a**2*b**9*c**3 - 78*a*b**11*c**2 + b**13*c) + x**14*(-1716*a**7
*c**7/7 + 6006*a**6*b**2*c**6 - 18018*a**5*b**4*c**5 + 15015*a**4*b**6*c**4 - 4290*a**3*b**8*c**3 + 429*a**2*b
**10*c**2 - 13*a*b**12*c + b**14/14) + x**13*(-1716*a**7*b*c**6 + 12012*a**6*b**3*c**5 - 18018*a**5*b**5*c**4
+ 8580*a**4*b**7*c**3 - 1430*a**3*b**9*c**2 + 78*a**2*b**11*c - a*b**13) + x**12*(429*a**8*c**6/2 - 5148*a**7*
b**2*c**5 + 15015*a**6*b**4*c**4 - 12012*a**5*b**6*c**3 + 6435*a**4*b**8*c**2/2 - 286*a**3*b**10*c + 13*a**2*b
**12/2) + x**11*(1287*a**8*b*c**5 - 8580*a**7*b**3*c**4 + 12012*a**6*b**5*c**3 - 5148*a**5*b**7*c**2 + 715*a**
4*b**9*c - 26*a**3*b**11) + x**10*(-143*a**9*c**5 + 6435*a**8*b**2*c**4/2 - 8580*a**7*b**4*c**3 + 6006*a**6*b*
*6*c**2 - 1287*a**5*b**8*c + 143*a**4*b**10/2) + x**9*(-715*a**9*b*c**4 + 4290*a**8*b**3*c**3 - 5148*a**7*b**5
*c**2 + 1716*a**6*b**7*c - 143*a**5*b**9) + x**8*(143*a**10*c**4/2 - 1430*a**9*b**2*c**3 + 6435*a**8*b**4*c**2
/2 - 1716*a**7*b**6*c + 429*a**6*b**8/2) + x**7*(286*a**10*b*c**3 - 1430*a**9*b**3*c**2 + 1287*a**8*b**5*c - 1
716*a**7*b**7/7) + x**6*(-26*a**11*c**3 + 429*a**10*b**2*c**2 - 715*a**9*b**4*c + 429*a**8*b**6/2) + x**5*(-78
*a**11*b*c**2 + 286*a**10*b**3*c - 143*a**9*b**5) + x**4*(13*a**12*c**2/2 - 78*a**11*b**2*c + 143*a**10*b**4/2
) + x**3*(13*a**12*b*c - 26*a**11*b**3) + x**2*(-a**13*c + 13*a**12*b**2/2)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.89 \[ \int (b+2 c x) \left (-a+b x+c x^2\right )^{13} \, dx=\frac {1}{14} \, {\left (c x^{2} + b x - a\right )}^{14} \]

[In]

integrate((2*c*x+b)*(c*x^2+b*x-a)^13,x, algorithm="maxima")

[Out]

1/14*(c*x^2 + b*x - a)^14

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 218 vs. \(2 (16) = 32\).

Time = 0.31 (sec) , antiderivative size = 218, normalized size of antiderivative = 12.11 \[ \int (b+2 c x) \left (-a+b x+c x^2\right )^{13} \, dx=\frac {1}{14} \, {\left (c x^{2} + b x\right )}^{14} - {\left (c x^{2} + b x\right )}^{13} a + \frac {13}{2} \, {\left (c x^{2} + b x\right )}^{12} a^{2} - 26 \, {\left (c x^{2} + b x\right )}^{11} a^{3} + \frac {143}{2} \, {\left (c x^{2} + b x\right )}^{10} a^{4} - 143 \, {\left (c x^{2} + b x\right )}^{9} a^{5} + \frac {429}{2} \, {\left (c x^{2} + b x\right )}^{8} a^{6} - \frac {1716}{7} \, {\left (c x^{2} + b x\right )}^{7} a^{7} + \frac {429}{2} \, {\left (c x^{2} + b x\right )}^{6} a^{8} - 143 \, {\left (c x^{2} + b x\right )}^{5} a^{9} + \frac {143}{2} \, {\left (c x^{2} + b x\right )}^{4} a^{10} - 26 \, {\left (c x^{2} + b x\right )}^{3} a^{11} + \frac {13}{2} \, {\left (c x^{2} + b x\right )}^{2} a^{12} - {\left (c x^{2} + b x\right )} a^{13} \]

[In]

integrate((2*c*x+b)*(c*x^2+b*x-a)^13,x, algorithm="giac")

[Out]

1/14*(c*x^2 + b*x)^14 - (c*x^2 + b*x)^13*a + 13/2*(c*x^2 + b*x)^12*a^2 - 26*(c*x^2 + b*x)^11*a^3 + 143/2*(c*x^
2 + b*x)^10*a^4 - 143*(c*x^2 + b*x)^9*a^5 + 429/2*(c*x^2 + b*x)^8*a^6 - 1716/7*(c*x^2 + b*x)^7*a^7 + 429/2*(c*
x^2 + b*x)^6*a^8 - 143*(c*x^2 + b*x)^5*a^9 + 143/2*(c*x^2 + b*x)^4*a^10 - 26*(c*x^2 + b*x)^3*a^11 + 13/2*(c*x^
2 + b*x)^2*a^12 - (c*x^2 + b*x)*a^13

Mupad [B] (verification not implemented)

Time = 0.93 (sec) , antiderivative size = 1208, normalized size of antiderivative = 67.11 \[ \int (b+2 c x) \left (-a+b x+c x^2\right )^{13} \, dx=x^{12}\,\left (\frac {429\,a^8\,c^6}{2}-5148\,a^7\,b^2\,c^5+15015\,a^6\,b^4\,c^4-12012\,a^5\,b^6\,c^3+\frac {6435\,a^4\,b^8\,c^2}{2}-286\,a^3\,b^{10}\,c+\frac {13\,a^2\,b^{12}}{2}\right )+x^{16}\,\left (\frac {429\,a^6\,c^8}{2}-5148\,a^5\,b^2\,c^7+15015\,a^4\,b^4\,c^6-12012\,a^3\,b^6\,c^5+\frac {6435\,a^2\,b^8\,c^4}{2}-286\,a\,b^{10}\,c^3+\frac {13\,b^{12}\,c^2}{2}\right )-x^{13}\,\left (1716\,a^7\,b\,c^6-12012\,a^6\,b^3\,c^5+18018\,a^5\,b^5\,c^4-8580\,a^4\,b^7\,c^3+1430\,a^3\,b^9\,c^2-78\,a^2\,b^{11}\,c+a\,b^{13}\right )+x^{15}\,\left (1716\,a^6\,b\,c^7-12012\,a^5\,b^3\,c^6+18018\,a^4\,b^5\,c^5-8580\,a^3\,b^7\,c^4+1430\,a^2\,b^9\,c^3-78\,a\,b^{11}\,c^2+b^{13}\,c\right )+x^6\,\left (-26\,a^{11}\,c^3+429\,a^{10}\,b^2\,c^2-715\,a^9\,b^4\,c+\frac {429\,a^8\,b^6}{2}\right )-x^{22}\,\left (26\,a^3\,c^{11}-429\,a^2\,b^2\,c^{10}+715\,a\,b^4\,c^9-\frac {429\,b^6\,c^8}{2}\right )+x^{10}\,\left (-143\,a^9\,c^5+\frac {6435\,a^8\,b^2\,c^4}{2}-8580\,a^7\,b^4\,c^3+6006\,a^6\,b^6\,c^2-1287\,a^5\,b^8\,c+\frac {143\,a^4\,b^{10}}{2}\right )-x^{18}\,\left (143\,a^5\,c^9-\frac {6435\,a^4\,b^2\,c^8}{2}+8580\,a^3\,b^4\,c^7-6006\,a^2\,b^6\,c^6+1287\,a\,b^8\,c^5-\frac {143\,b^{10}\,c^4}{2}\right )+x^{14}\,\left (-\frac {1716\,a^7\,c^7}{7}+6006\,a^6\,b^2\,c^6-18018\,a^5\,b^4\,c^5+15015\,a^4\,b^6\,c^4-4290\,a^3\,b^8\,c^3+429\,a^2\,b^{10}\,c^2-13\,a\,b^{12}\,c+\frac {b^{14}}{14}\right )+x^8\,\left (\frac {143\,a^{10}\,c^4}{2}-1430\,a^9\,b^2\,c^3+\frac {6435\,a^8\,b^4\,c^2}{2}-1716\,a^7\,b^6\,c+\frac {429\,a^6\,b^8}{2}\right )+x^{20}\,\left (\frac {143\,a^4\,c^{10}}{2}-1430\,a^3\,b^2\,c^9+\frac {6435\,a^2\,b^4\,c^8}{2}-1716\,a\,b^6\,c^7+\frac {429\,b^8\,c^6}{2}\right )+\frac {c^{14}\,x^{28}}{14}-x^2\,\left (a^{13}\,c-\frac {13\,a^{12}\,b^2}{2}\right )+\frac {13\,a^{10}\,x^4\,\left (a^2\,c^2-12\,a\,b^2\,c+11\,b^4\right )}{2}+\frac {13\,c^{10}\,x^{24}\,\left (a^2\,c^2-12\,a\,b^2\,c+11\,b^4\right )}{2}+b\,c^{13}\,x^{27}-\frac {c^{12}\,x^{26}\,\left (2\,a\,c-13\,b^2\right )}{2}-a^{13}\,b\,x-\frac {143\,a^7\,b\,x^7\,\left (-14\,a^3\,c^3+70\,a^2\,b^2\,c^2-63\,a\,b^4\,c+12\,b^6\right )}{7}+\frac {143\,b\,c^7\,x^{21}\,\left (-14\,a^3\,c^3+70\,a^2\,b^2\,c^2-63\,a\,b^4\,c+12\,b^6\right )}{7}-143\,a^5\,b\,x^9\,\left (5\,a^4\,c^4-30\,a^3\,b^2\,c^3+36\,a^2\,b^4\,c^2-12\,a\,b^6\,c+b^8\right )+143\,b\,c^5\,x^{19}\,\left (5\,a^4\,c^4-30\,a^3\,b^2\,c^3+36\,a^2\,b^4\,c^2-12\,a\,b^6\,c+b^8\right )-13\,a^3\,b\,x^{11}\,\left (-99\,a^5\,c^5+660\,a^4\,b^2\,c^4-924\,a^3\,b^4\,c^3+396\,a^2\,b^6\,c^2-55\,a\,b^8\,c+2\,b^{10}\right )+13\,b\,c^3\,x^{17}\,\left (-99\,a^5\,c^5+660\,a^4\,b^2\,c^4-924\,a^3\,b^4\,c^3+396\,a^2\,b^6\,c^2-55\,a\,b^8\,c+2\,b^{10}\right )-13\,a^9\,b\,x^5\,\left (6\,a^2\,c^2-22\,a\,b^2\,c+11\,b^4\right )+13\,b\,c^9\,x^{23}\,\left (6\,a^2\,c^2-22\,a\,b^2\,c+11\,b^4\right )+13\,a^{11}\,b\,x^3\,\left (a\,c-2\,b^2\right )-13\,b\,c^{11}\,x^{25}\,\left (a\,c-2\,b^2\right ) \]

[In]

int((b + 2*c*x)*(b*x - a + c*x^2)^13,x)

[Out]

x^12*((13*a^2*b^12)/2 + (429*a^8*c^6)/2 - 286*a^3*b^10*c + (6435*a^4*b^8*c^2)/2 - 12012*a^5*b^6*c^3 + 15015*a^
6*b^4*c^4 - 5148*a^7*b^2*c^5) + x^16*((429*a^6*c^8)/2 + (13*b^12*c^2)/2 - 286*a*b^10*c^3 + (6435*a^2*b^8*c^4)/
2 - 12012*a^3*b^6*c^5 + 15015*a^4*b^4*c^6 - 5148*a^5*b^2*c^7) - x^13*(a*b^13 - 78*a^2*b^11*c + 1716*a^7*b*c^6
+ 1430*a^3*b^9*c^2 - 8580*a^4*b^7*c^3 + 18018*a^5*b^5*c^4 - 12012*a^6*b^3*c^5) + x^15*(b^13*c - 78*a*b^11*c^2
+ 1716*a^6*b*c^7 + 1430*a^2*b^9*c^3 - 8580*a^3*b^7*c^4 + 18018*a^4*b^5*c^5 - 12012*a^5*b^3*c^6) + x^6*((429*a^
8*b^6)/2 - 26*a^11*c^3 - 715*a^9*b^4*c + 429*a^10*b^2*c^2) - x^22*(26*a^3*c^11 - (429*b^6*c^8)/2 + 715*a*b^4*c
^9 - 429*a^2*b^2*c^10) + x^10*((143*a^4*b^10)/2 - 143*a^9*c^5 - 1287*a^5*b^8*c + 6006*a^6*b^6*c^2 - 8580*a^7*b
^4*c^3 + (6435*a^8*b^2*c^4)/2) - x^18*(143*a^5*c^9 - (143*b^10*c^4)/2 + 1287*a*b^8*c^5 - 6006*a^2*b^6*c^6 + 85
80*a^3*b^4*c^7 - (6435*a^4*b^2*c^8)/2) + x^14*(b^14/14 - (1716*a^7*c^7)/7 + 429*a^2*b^10*c^2 - 4290*a^3*b^8*c^
3 + 15015*a^4*b^6*c^4 - 18018*a^5*b^4*c^5 + 6006*a^6*b^2*c^6 - 13*a*b^12*c) + x^8*((429*a^6*b^8)/2 + (143*a^10
*c^4)/2 - 1716*a^7*b^6*c + (6435*a^8*b^4*c^2)/2 - 1430*a^9*b^2*c^3) + x^20*((143*a^4*c^10)/2 + (429*b^8*c^6)/2
- 1716*a*b^6*c^7 + (6435*a^2*b^4*c^8)/2 - 1430*a^3*b^2*c^9) + (c^14*x^28)/14 - x^2*(a^13*c - (13*a^12*b^2)/2)
+ (13*a^10*x^4*(11*b^4 + a^2*c^2 - 12*a*b^2*c))/2 + (13*c^10*x^24*(11*b^4 + a^2*c^2 - 12*a*b^2*c))/2 + b*c^13
*x^27 - (c^12*x^26*(2*a*c - 13*b^2))/2 - a^13*b*x - (143*a^7*b*x^7*(12*b^6 - 14*a^3*c^3 + 70*a^2*b^2*c^2 - 63*
a*b^4*c))/7 + (143*b*c^7*x^21*(12*b^6 - 14*a^3*c^3 + 70*a^2*b^2*c^2 - 63*a*b^4*c))/7 - 143*a^5*b*x^9*(b^8 + 5*
a^4*c^4 + 36*a^2*b^4*c^2 - 30*a^3*b^2*c^3 - 12*a*b^6*c) + 143*b*c^5*x^19*(b^8 + 5*a^4*c^4 + 36*a^2*b^4*c^2 - 3
0*a^3*b^2*c^3 - 12*a*b^6*c) - 13*a^3*b*x^11*(2*b^10 - 99*a^5*c^5 + 396*a^2*b^6*c^2 - 924*a^3*b^4*c^3 + 660*a^4
*b^2*c^4 - 55*a*b^8*c) + 13*b*c^3*x^17*(2*b^10 - 99*a^5*c^5 + 396*a^2*b^6*c^2 - 924*a^3*b^4*c^3 + 660*a^4*b^2*
c^4 - 55*a*b^8*c) - 13*a^9*b*x^5*(11*b^4 + 6*a^2*c^2 - 22*a*b^2*c) + 13*b*c^9*x^23*(11*b^4 + 6*a^2*c^2 - 22*a*
b^2*c) + 13*a^11*b*x^3*(a*c - 2*b^2) - 13*b*c^11*x^25*(a*c - 2*b^2)