### 3.99 $$\int x^2 (b+2 c x^3) (-a+b x^3+c x^6)^{13} \, dx$$

Optimal. Leaf size=20 $\frac{1}{42} \left (a-b x^3-c x^6\right )^{14}$

[Out]

(a - b*x^3 - c*x^6)^14/42

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Rubi [A]  time = 0.310304, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 28, $$\frac{\text{number of rules}}{\text{integrand size}}$$ = 0.071, Rules used = {1468, 629} $\frac{1}{42} \left (a-b x^3-c x^6\right )^{14}$

Antiderivative was successfully veriﬁed.

[In]

Int[x^2*(b + 2*c*x^3)*(-a + b*x^3 + c*x^6)^13,x]

[Out]

(a - b*x^3 - c*x^6)^14/42

Rule 1468

Int[(x_)^(m_.)*((a_) + (c_.)*(x_)^(n2_.) + (b_.)*(x_)^(n_))^(p_.)*((d_) + (e_.)*(x_)^(n_))^(q_.), x_Symbol] :>
Dist[1/n, Subst[Int[(d + e*x)^q*(a + b*x + c*x^2)^p, x], x, x^n], x] /; FreeQ[{a, b, c, d, e, m, n, p, q}, x]
&& EqQ[n2, 2*n] && EqQ[Simplify[m - n + 1], 0]

Rule 629

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*} \int x^2 \left (b+2 c x^3\right ) \left (-a+b x^3+c x^6\right )^{13} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int (b+2 c x) \left (-a+b x+c x^2\right )^{13} \, dx,x,x^3\right )\\ &=\frac{1}{42} \left (a-b x^3-c x^6\right )^{14}\\ \end{align*}

Mathematica [B]  time = 0.164877, size = 233, normalized size = 11.65 $\frac{1}{42} x^3 \left (b+c x^3\right ) \left (91 a^2 x^{33} \left (b+c x^3\right )^{11}-364 a^3 x^{30} \left (b+c x^3\right )^{10}+1001 a^4 x^{27} \left (b+c x^3\right )^9-2002 a^5 x^{24} \left (b+c x^3\right )^8+3003 a^6 x^{21} \left (b+c x^3\right )^7-3432 a^7 x^{18} \left (b+c x^3\right )^6+3003 a^8 x^{15} \left (b+c x^3\right )^5-2002 a^9 x^{12} \left (b+c x^3\right )^4+1001 a^{10} x^9 \left (b+c x^3\right )^3-364 a^{11} x^6 \left (b+c x^3\right )^2+91 a^{12} x^3 \left (b+c x^3\right )-14 a^{13}-14 a x^{36} \left (b+c x^3\right )^{12}+x^{39} \left (b+c x^3\right )^{13}\right )$

Antiderivative was successfully veriﬁed.

[In]

Integrate[x^2*(b + 2*c*x^3)*(-a + b*x^3 + c*x^6)^13,x]

[Out]

(x^3*(b + c*x^3)*(-14*a^13 + 91*a^12*x^3*(b + c*x^3) - 364*a^11*x^6*(b + c*x^3)^2 + 1001*a^10*x^9*(b + c*x^3)^
3 - 2002*a^9*x^12*(b + c*x^3)^4 + 3003*a^8*x^15*(b + c*x^3)^5 - 3432*a^7*x^18*(b + c*x^3)^6 + 3003*a^6*x^21*(b
+ c*x^3)^7 - 2002*a^5*x^24*(b + c*x^3)^8 + 1001*a^4*x^27*(b + c*x^3)^9 - 364*a^3*x^30*(b + c*x^3)^10 + 91*a^2
*x^33*(b + c*x^3)^11 - 14*a*x^36*(b + c*x^3)^12 + x^39*(b + c*x^3)^13))/42

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Maple [B]  time = 0.001, size = 47688, normalized size = 2384.4 \begin{align*} \text{output too large to display} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(x^2*(2*c*x^3+b)*(c*x^6+b*x^3-a)^13,x)

[Out]

result too large to display

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Maxima [B]  time = 1.06222, size = 1677, normalized size = 83.85 \begin{align*} \text{result too large to display} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3-a)^13,x, algorithm="maxima")

[Out]

1/42*c^14*x^84 + 1/3*b*c^13*x^81 + 1/6*(13*b^2*c^12 - 2*a*c^13)*x^78 + 13/3*(2*b^3*c^11 - a*b*c^12)*x^75 + 13/
6*(11*b^4*c^10 - 12*a*b^2*c^11 + a^2*c^12)*x^72 + 13/3*(11*b^5*c^9 - 22*a*b^3*c^10 + 6*a^2*b*c^11)*x^69 + 13/6
*(33*b^6*c^8 - 110*a*b^4*c^9 + 66*a^2*b^2*c^10 - 4*a^3*c^11)*x^66 + 143/21*(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^63 + 143/6*(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^60 + 143/3*(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^57 + 143/6*(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^54 + 13/3*(2*b^11*c^3 - 55*a
*b^9*c^4 + 396*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^51 + 13/6*(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^48 + 1/3*(b^1
3*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^45 + 1/42*(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^42 - 1/3*(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^39 + 13/6*(a^2*b^12 - 44*a^3*b^10*c + 49
5*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^36 - 13/3*(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^33 + 143/6*(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^30 - 143/3*(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^27 + 143/6*(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^24 - 143/21*(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^21 + 1
3/6*(33*a^8*b^6 - 110*a^9*b^4*c + 66*a^10*b^2*c^2 - 4*a^11*c^3)*x^18 - 1/3*a^13*b*x^3 - 13/3*(11*a^9*b^5 - 22*
a^10*b^3*c + 6*a^11*b*c^2)*x^15 + 13/6*(11*a^10*b^4 - 12*a^11*b^2*c + a^12*c^2)*x^12 - 13/3*(2*a^11*b^3 - a^12
*b*c)*x^9 + 1/6*(13*a^12*b^2 - 2*a^13*c)*x^6

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Fricas [B]  time = 0.967692, size = 3594, normalized size = 179.7 \begin{align*} \text{result too large to display} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3-a)^13,x, algorithm="fricas")

[Out]

1/42*x^84*c^14 + 1/3*x^81*c^13*b + 13/6*x^78*c^12*b^2 - 1/3*x^78*c^13*a + 26/3*x^75*c^11*b^3 - 13/3*x^75*c^12*
b*a + 143/6*x^72*c^10*b^4 - 26*x^72*c^11*b^2*a + 13/6*x^72*c^12*a^2 + 143/3*x^69*c^9*b^5 - 286/3*x^69*c^10*b^3
*a + 26*x^69*c^11*b*a^2 + 143/2*x^66*c^8*b^6 - 715/3*x^66*c^9*b^4*a + 143*x^66*c^10*b^2*a^2 - 26/3*x^66*c^11*a
^3 + 572/7*x^63*c^7*b^7 - 429*x^63*c^8*b^5*a + 1430/3*x^63*c^9*b^3*a^2 - 286/3*x^63*c^10*b*a^3 + 143/2*x^60*c^
6*b^8 - 572*x^60*c^7*b^6*a + 2145/2*x^60*c^8*b^4*a^2 - 1430/3*x^60*c^9*b^2*a^3 + 143/6*x^60*c^10*a^4 + 143/3*x
^57*c^5*b^9 - 572*x^57*c^6*b^7*a + 1716*x^57*c^7*b^5*a^2 - 1430*x^57*c^8*b^3*a^3 + 715/3*x^57*c^9*b*a^4 + 143/
6*x^54*c^4*b^10 - 429*x^54*c^5*b^8*a + 2002*x^54*c^6*b^6*a^2 - 2860*x^54*c^7*b^4*a^3 + 2145/2*x^54*c^8*b^2*a^4
- 143/3*x^54*c^9*a^5 + 26/3*x^51*c^3*b^11 - 715/3*x^51*c^4*b^9*a + 1716*x^51*c^5*b^7*a^2 - 4004*x^51*c^6*b^5*
a^3 + 2860*x^51*c^7*b^3*a^4 - 429*x^51*c^8*b*a^5 + 13/6*x^48*c^2*b^12 - 286/3*x^48*c^3*b^10*a + 2145/2*x^48*c^
4*b^8*a^2 - 4004*x^48*c^5*b^6*a^3 + 5005*x^48*c^6*b^4*a^4 - 1716*x^48*c^7*b^2*a^5 + 143/2*x^48*c^8*a^6 + 1/3*x
^45*c*b^13 - 26*x^45*c^2*b^11*a + 1430/3*x^45*c^3*b^9*a^2 - 2860*x^45*c^4*b^7*a^3 + 6006*x^45*c^5*b^5*a^4 - 40
04*x^45*c^6*b^3*a^5 + 572*x^45*c^7*b*a^6 + 1/42*x^42*b^14 - 13/3*x^42*c*b^12*a + 143*x^42*c^2*b^10*a^2 - 1430*
x^42*c^3*b^8*a^3 + 5005*x^42*c^4*b^6*a^4 - 6006*x^42*c^5*b^4*a^5 + 2002*x^42*c^6*b^2*a^6 - 572/7*x^42*c^7*a^7
- 1/3*x^39*b^13*a + 26*x^39*c*b^11*a^2 - 1430/3*x^39*c^2*b^9*a^3 + 2860*x^39*c^3*b^7*a^4 - 6006*x^39*c^4*b^5*a
^5 + 4004*x^39*c^5*b^3*a^6 - 572*x^39*c^6*b*a^7 + 13/6*x^36*b^12*a^2 - 286/3*x^36*c*b^10*a^3 + 2145/2*x^36*c^2
*b^8*a^4 - 4004*x^36*c^3*b^6*a^5 + 5005*x^36*c^4*b^4*a^6 - 1716*x^36*c^5*b^2*a^7 + 143/2*x^36*c^6*a^8 - 26/3*x
^33*b^11*a^3 + 715/3*x^33*c*b^9*a^4 - 1716*x^33*c^2*b^7*a^5 + 4004*x^33*c^3*b^5*a^6 - 2860*x^33*c^4*b^3*a^7 +
429*x^33*c^5*b*a^8 + 143/6*x^30*b^10*a^4 - 429*x^30*c*b^8*a^5 + 2002*x^30*c^2*b^6*a^6 - 2860*x^30*c^3*b^4*a^7
+ 2145/2*x^30*c^4*b^2*a^8 - 143/3*x^30*c^5*a^9 - 143/3*x^27*b^9*a^5 + 572*x^27*c*b^7*a^6 - 1716*x^27*c^2*b^5*a
^7 + 1430*x^27*c^3*b^3*a^8 - 715/3*x^27*c^4*b*a^9 + 143/2*x^24*b^8*a^6 - 572*x^24*c*b^6*a^7 + 2145/2*x^24*c^2*
b^4*a^8 - 1430/3*x^24*c^3*b^2*a^9 + 143/6*x^24*c^4*a^10 - 572/7*x^21*b^7*a^7 + 429*x^21*c*b^5*a^8 - 1430/3*x^2
1*c^2*b^3*a^9 + 286/3*x^21*c^3*b*a^10 + 143/2*x^18*b^6*a^8 - 715/3*x^18*c*b^4*a^9 + 143*x^18*c^2*b^2*a^10 - 26
/3*x^18*c^3*a^11 - 143/3*x^15*b^5*a^9 + 286/3*x^15*c*b^3*a^10 - 26*x^15*c^2*b*a^11 + 143/6*x^12*b^4*a^10 - 26*
x^12*c*b^2*a^11 + 13/6*x^12*c^2*a^12 - 26/3*x^9*b^3*a^11 + 13/3*x^9*c*b*a^12 + 13/6*x^6*b^2*a^12 - 1/3*x^6*c*a
^13 - 1/3*x^3*b*a^13

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Sympy [B]  time = 0.321249, size = 1394, normalized size = 69.7 \begin{align*} \text{result too large to display} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**2*(2*c*x**3+b)*(c*x**6+b*x**3-a)**13,x)

[Out]

-a**13*b*x**3/3 + b*c**13*x**81/3 + c**14*x**84/42 + x**78*(-a*c**13/3 + 13*b**2*c**12/6) + x**75*(-13*a*b*c**
12/3 + 26*b**3*c**11/3) + x**72*(13*a**2*c**12/6 - 26*a*b**2*c**11 + 143*b**4*c**10/6) + x**69*(26*a**2*b*c**1
1 - 286*a*b**3*c**10/3 + 143*b**5*c**9/3) + x**66*(-26*a**3*c**11/3 + 143*a**2*b**2*c**10 - 715*a*b**4*c**9/3
+ 143*b**6*c**8/2) + x**63*(-286*a**3*b*c**10/3 + 1430*a**2*b**3*c**9/3 - 429*a*b**5*c**8 + 572*b**7*c**7/7) +
x**60*(143*a**4*c**10/6 - 1430*a**3*b**2*c**9/3 + 2145*a**2*b**4*c**8/2 - 572*a*b**6*c**7 + 143*b**8*c**6/2)
+ x**57*(715*a**4*b*c**9/3 - 1430*a**3*b**3*c**8 + 1716*a**2*b**5*c**7 - 572*a*b**7*c**6 + 143*b**9*c**5/3) +
x**54*(-143*a**5*c**9/3 + 2145*a**4*b**2*c**8/2 - 2860*a**3*b**4*c**7 + 2002*a**2*b**6*c**6 - 429*a*b**8*c**5
+ 143*b**10*c**4/6) + x**51*(-429*a**5*b*c**8 + 2860*a**4*b**3*c**7 - 4004*a**3*b**5*c**6 + 1716*a**2*b**7*c**
5 - 715*a*b**9*c**4/3 + 26*b**11*c**3/3) + x**48*(143*a**6*c**8/2 - 1716*a**5*b**2*c**7 + 5005*a**4*b**4*c**6
- 4004*a**3*b**6*c**5 + 2145*a**2*b**8*c**4/2 - 286*a*b**10*c**3/3 + 13*b**12*c**2/6) + x**45*(572*a**6*b*c**7
- 4004*a**5*b**3*c**6 + 6006*a**4*b**5*c**5 - 2860*a**3*b**7*c**4 + 1430*a**2*b**9*c**3/3 - 26*a*b**11*c**2 +
b**13*c/3) + x**42*(-572*a**7*c**7/7 + 2002*a**6*b**2*c**6 - 6006*a**5*b**4*c**5 + 5005*a**4*b**6*c**4 - 1430
*a**3*b**8*c**3 + 143*a**2*b**10*c**2 - 13*a*b**12*c/3 + b**14/42) + x**39*(-572*a**7*b*c**6 + 4004*a**6*b**3*
c**5 - 6006*a**5*b**5*c**4 + 2860*a**4*b**7*c**3 - 1430*a**3*b**9*c**2/3 + 26*a**2*b**11*c - a*b**13/3) + x**3
6*(143*a**8*c**6/2 - 1716*a**7*b**2*c**5 + 5005*a**6*b**4*c**4 - 4004*a**5*b**6*c**3 + 2145*a**4*b**8*c**2/2 -
286*a**3*b**10*c/3 + 13*a**2*b**12/6) + x**33*(429*a**8*b*c**5 - 2860*a**7*b**3*c**4 + 4004*a**6*b**5*c**3 -
1716*a**5*b**7*c**2 + 715*a**4*b**9*c/3 - 26*a**3*b**11/3) + x**30*(-143*a**9*c**5/3 + 2145*a**8*b**2*c**4/2 -
2860*a**7*b**4*c**3 + 2002*a**6*b**6*c**2 - 429*a**5*b**8*c + 143*a**4*b**10/6) + x**27*(-715*a**9*b*c**4/3 +
1430*a**8*b**3*c**3 - 1716*a**7*b**5*c**2 + 572*a**6*b**7*c - 143*a**5*b**9/3) + x**24*(143*a**10*c**4/6 - 14
30*a**9*b**2*c**3/3 + 2145*a**8*b**4*c**2/2 - 572*a**7*b**6*c + 143*a**6*b**8/2) + x**21*(286*a**10*b*c**3/3 -
1430*a**9*b**3*c**2/3 + 429*a**8*b**5*c - 572*a**7*b**7/7) + x**18*(-26*a**11*c**3/3 + 143*a**10*b**2*c**2 -
715*a**9*b**4*c/3 + 143*a**8*b**6/2) + x**15*(-26*a**11*b*c**2 + 286*a**10*b**3*c/3 - 143*a**9*b**5/3) + x**12
*(13*a**12*c**2/6 - 26*a**11*b**2*c + 143*a**10*b**4/6) + x**9*(13*a**12*b*c/3 - 26*a**11*b**3/3) + x**6*(-a**
13*c/3 + 13*a**12*b**2/6)

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Giac [B]  time = 1.14009, size = 1963, normalized size = 98.15 \begin{align*} \text{result too large to display} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3-a)^13,x, algorithm="giac")

[Out]

1/42*c^14*x^84 + 1/3*b*c^13*x^81 + 13/6*b^2*c^12*x^78 - 1/3*a*c^13*x^78 + 26/3*b^3*c^11*x^75 - 13/3*a*b*c^12*x
^75 + 143/6*b^4*c^10*x^72 - 26*a*b^2*c^11*x^72 + 13/6*a^2*c^12*x^72 + 143/3*b^5*c^9*x^69 - 286/3*a*b^3*c^10*x^
69 + 26*a^2*b*c^11*x^69 + 143/2*b^6*c^8*x^66 - 715/3*a*b^4*c^9*x^66 + 143*a^2*b^2*c^10*x^66 - 26/3*a^3*c^11*x^
66 + 572/7*b^7*c^7*x^63 - 429*a*b^5*c^8*x^63 + 1430/3*a^2*b^3*c^9*x^63 - 286/3*a^3*b*c^10*x^63 + 143/2*b^8*c^6
*x^60 - 572*a*b^6*c^7*x^60 + 2145/2*a^2*b^4*c^8*x^60 - 1430/3*a^3*b^2*c^9*x^60 + 143/6*a^4*c^10*x^60 + 143/3*b
^9*c^5*x^57 - 572*a*b^7*c^6*x^57 + 1716*a^2*b^5*c^7*x^57 - 1430*a^3*b^3*c^8*x^57 + 715/3*a^4*b*c^9*x^57 + 143/
6*b^10*c^4*x^54 - 429*a*b^8*c^5*x^54 + 2002*a^2*b^6*c^6*x^54 - 2860*a^3*b^4*c^7*x^54 + 2145/2*a^4*b^2*c^8*x^54
- 143/3*a^5*c^9*x^54 + 26/3*b^11*c^3*x^51 - 715/3*a*b^9*c^4*x^51 + 1716*a^2*b^7*c^5*x^51 - 4004*a^3*b^5*c^6*x
^51 + 2860*a^4*b^3*c^7*x^51 - 429*a^5*b*c^8*x^51 + 13/6*b^12*c^2*x^48 - 286/3*a*b^10*c^3*x^48 + 2145/2*a^2*b^8
*c^4*x^48 - 4004*a^3*b^6*c^5*x^48 + 5005*a^4*b^4*c^6*x^48 - 1716*a^5*b^2*c^7*x^48 + 143/2*a^6*c^8*x^48 + 1/3*b
^13*c*x^45 - 26*a*b^11*c^2*x^45 + 1430/3*a^2*b^9*c^3*x^45 - 2860*a^3*b^7*c^4*x^45 + 6006*a^4*b^5*c^5*x^45 - 40
04*a^5*b^3*c^6*x^45 + 572*a^6*b*c^7*x^45 + 1/42*b^14*x^42 - 13/3*a*b^12*c*x^42 + 143*a^2*b^10*c^2*x^42 - 1430*
a^3*b^8*c^3*x^42 + 5005*a^4*b^6*c^4*x^42 - 6006*a^5*b^4*c^5*x^42 + 2002*a^6*b^2*c^6*x^42 - 572/7*a^7*c^7*x^42
- 1/3*a*b^13*x^39 + 26*a^2*b^11*c*x^39 - 1430/3*a^3*b^9*c^2*x^39 + 2860*a^4*b^7*c^3*x^39 - 6006*a^5*b^5*c^4*x^
39 + 4004*a^6*b^3*c^5*x^39 - 572*a^7*b*c^6*x^39 + 13/6*a^2*b^12*x^36 - 286/3*a^3*b^10*c*x^36 + 2145/2*a^4*b^8*
c^2*x^36 - 4004*a^5*b^6*c^3*x^36 + 5005*a^6*b^4*c^4*x^36 - 1716*a^7*b^2*c^5*x^36 + 143/2*a^8*c^6*x^36 - 26/3*a
^3*b^11*x^33 + 715/3*a^4*b^9*c*x^33 - 1716*a^5*b^7*c^2*x^33 + 4004*a^6*b^5*c^3*x^33 - 2860*a^7*b^3*c^4*x^33 +
429*a^8*b*c^5*x^33 + 143/6*a^4*b^10*x^30 - 429*a^5*b^8*c*x^30 + 2002*a^6*b^6*c^2*x^30 - 2860*a^7*b^4*c^3*x^30
+ 2145/2*a^8*b^2*c^4*x^30 - 143/3*a^9*c^5*x^30 - 143/3*a^5*b^9*x^27 + 572*a^6*b^7*c*x^27 - 1716*a^7*b^5*c^2*x^
27 + 1430*a^8*b^3*c^3*x^27 - 715/3*a^9*b*c^4*x^27 + 143/2*a^6*b^8*x^24 - 572*a^7*b^6*c*x^24 + 2145/2*a^8*b^4*c
^2*x^24 - 1430/3*a^9*b^2*c^3*x^24 + 143/6*a^10*c^4*x^24 - 572/7*a^7*b^7*x^21 + 429*a^8*b^5*c*x^21 - 1430/3*a^9
*b^3*c^2*x^21 + 286/3*a^10*b*c^3*x^21 + 143/2*a^8*b^6*x^18 - 715/3*a^9*b^4*c*x^18 + 143*a^10*b^2*c^2*x^18 - 26
/3*a^11*c^3*x^18 - 143/3*a^9*b^5*x^15 + 286/3*a^10*b^3*c*x^15 - 26*a^11*b*c^2*x^15 + 143/6*a^10*b^4*x^12 - 26*
a^11*b^2*c*x^12 + 13/6*a^12*c^2*x^12 - 26/3*a^11*b^3*x^9 + 13/3*a^12*b*c*x^9 + 13/6*a^12*b^2*x^6 - 1/3*a^13*c*
x^6 - 1/3*a^13*b*x^3