3.1.72 \(\int x (b+2 c x^2) (a+b x^2+c x^4)^{13} \, dx\)
Optimal. Leaf size=18 \[ \frac {1}{28} \left (a+b x^2+c x^4\right )^{14} \]
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Rubi [A] time = 0.33, antiderivative size = 18, normalized size of antiderivative = 1.00,
number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used =
{1247, 629} \begin {gather*} \frac {1}{28} \left (a+b x^2+c x^4\right )^{14} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[x*(b + 2*c*x^2)*(a + b*x^2 + c*x^4)^13,x]
[Out]
(a + b*x^2 + c*x^4)^14/28
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]
Rule 1247
Int[(x_)*((d_) + (e_.)*(x_)^2)^(q_.)*((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4)^(p_.), x_Symbol] :> Dist[1/2, Subst[
Int[(d + e*x)^q*(a + b*x + c*x^2)^p, x], x, x^2], x] /; FreeQ[{a, b, c, d, e, p, q}, x]
Rubi steps
\begin {align*} \int x \left (b+2 c x^2\right ) \left (a+b x^2+c x^4\right )^{13} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int (b+2 c x) \left (a+b x+c x^2\right )^{13} \, dx,x,x^2\right )\\ &=\frac {1}{28} \left (a+b x^2+c x^4\right )^{14}\\ \end {align*}
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Mathematica [B] time = 0.18, size = 233, normalized size = 12.94 \begin {gather*} \frac {1}{28} x^2 \left (b+c x^2\right ) \left (14 a^{13}+91 a^{12} x^2 \left (b+c x^2\right )+364 a^{11} x^4 \left (b+c x^2\right )^2+1001 a^{10} x^6 \left (b+c x^2\right )^3+2002 a^9 x^8 \left (b+c x^2\right )^4+3003 a^8 x^{10} \left (b+c x^2\right )^5+3432 a^7 x^{12} \left (b+c x^2\right )^6+3003 a^6 x^{14} \left (b+c x^2\right )^7+2002 a^5 x^{16} \left (b+c x^2\right )^8+1001 a^4 x^{18} \left (b+c x^2\right )^9+364 a^3 x^{20} \left (b+c x^2\right )^{10}+91 a^2 x^{22} \left (b+c x^2\right )^{11}+14 a x^{24} \left (b+c x^2\right )^{12}+x^{26} \left (b+c x^2\right )^{13}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[x*(b + 2*c*x^2)*(a + b*x^2 + c*x^4)^13,x]
[Out]
(x^2*(b + c*x^2)*(14*a^13 + 91*a^12*x^2*(b + c*x^2) + 364*a^11*x^4*(b + c*x^2)^2 + 1001*a^10*x^6*(b + c*x^2)^3
+ 2002*a^9*x^8*(b + c*x^2)^4 + 3003*a^8*x^10*(b + c*x^2)^5 + 3432*a^7*x^12*(b + c*x^2)^6 + 3003*a^6*x^14*(b +
c*x^2)^7 + 2002*a^5*x^16*(b + c*x^2)^8 + 1001*a^4*x^18*(b + c*x^2)^9 + 364*a^3*x^20*(b + c*x^2)^10 + 91*a^2*x
^22*(b + c*x^2)^11 + 14*a*x^24*(b + c*x^2)^12 + x^26*(b + c*x^2)^13))/28
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x \left (b+2 c x^2\right ) \left (a+b x^2+c x^4\right )^{13} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
IntegrateAlgebraic[x*(b + 2*c*x^2)*(a + b*x^2 + c*x^4)^13,x]
[Out]
IntegrateAlgebraic[x*(b + 2*c*x^2)*(a + b*x^2 + c*x^4)^13, x]
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fricas [B] time = 0.76, size = 1454, normalized size = 80.78
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x*(2*c*x^2+b)*(c*x^4+b*x^2+a)^13,x, algorithm="fricas")
[Out]
1/28*x^56*c^14 + 1/2*x^54*c^13*b + 13/4*x^52*c^12*b^2 + 1/2*x^52*c^13*a + 13*x^50*c^11*b^3 + 13/2*x^50*c^12*b*
a + 143/4*x^48*c^10*b^4 + 39*x^48*c^11*b^2*a + 13/4*x^48*c^12*a^2 + 143/2*x^46*c^9*b^5 + 143*x^46*c^10*b^3*a +
39*x^46*c^11*b*a^2 + 429/4*x^44*c^8*b^6 + 715/2*x^44*c^9*b^4*a + 429/2*x^44*c^10*b^2*a^2 + 13*x^44*c^11*a^3 +
858/7*x^42*c^7*b^7 + 1287/2*x^42*c^8*b^5*a + 715*x^42*c^9*b^3*a^2 + 143*x^42*c^10*b*a^3 + 429/4*x^40*c^6*b^8
+ 858*x^40*c^7*b^6*a + 6435/4*x^40*c^8*b^4*a^2 + 715*x^40*c^9*b^2*a^3 + 143/4*x^40*c^10*a^4 + 143/2*x^38*c^5*b
^9 + 858*x^38*c^6*b^7*a + 2574*x^38*c^7*b^5*a^2 + 2145*x^38*c^8*b^3*a^3 + 715/2*x^38*c^9*b*a^4 + 143/4*x^36*c^
4*b^10 + 1287/2*x^36*c^5*b^8*a + 3003*x^36*c^6*b^6*a^2 + 4290*x^36*c^7*b^4*a^3 + 6435/4*x^36*c^8*b^2*a^4 + 143
/2*x^36*c^9*a^5 + 13*x^34*c^3*b^11 + 715/2*x^34*c^4*b^9*a + 2574*x^34*c^5*b^7*a^2 + 6006*x^34*c^6*b^5*a^3 + 42
90*x^34*c^7*b^3*a^4 + 1287/2*x^34*c^8*b*a^5 + 13/4*x^32*c^2*b^12 + 143*x^32*c^3*b^10*a + 6435/4*x^32*c^4*b^8*a
^2 + 6006*x^32*c^5*b^6*a^3 + 15015/2*x^32*c^6*b^4*a^4 + 2574*x^32*c^7*b^2*a^5 + 429/4*x^32*c^8*a^6 + 1/2*x^30*
c*b^13 + 39*x^30*c^2*b^11*a + 715*x^30*c^3*b^9*a^2 + 4290*x^30*c^4*b^7*a^3 + 9009*x^30*c^5*b^5*a^4 + 6006*x^30
*c^6*b^3*a^5 + 858*x^30*c^7*b*a^6 + 1/28*x^28*b^14 + 13/2*x^28*c*b^12*a + 429/2*x^28*c^2*b^10*a^2 + 2145*x^28*
c^3*b^8*a^3 + 15015/2*x^28*c^4*b^6*a^4 + 9009*x^28*c^5*b^4*a^5 + 3003*x^28*c^6*b^2*a^6 + 858/7*x^28*c^7*a^7 +
1/2*x^26*b^13*a + 39*x^26*c*b^11*a^2 + 715*x^26*c^2*b^9*a^3 + 4290*x^26*c^3*b^7*a^4 + 9009*x^26*c^4*b^5*a^5 +
6006*x^26*c^5*b^3*a^6 + 858*x^26*c^6*b*a^7 + 13/4*x^24*b^12*a^2 + 143*x^24*c*b^10*a^3 + 6435/4*x^24*c^2*b^8*a^
4 + 6006*x^24*c^3*b^6*a^5 + 15015/2*x^24*c^4*b^4*a^6 + 2574*x^24*c^5*b^2*a^7 + 429/4*x^24*c^6*a^8 + 13*x^22*b^
11*a^3 + 715/2*x^22*c*b^9*a^4 + 2574*x^22*c^2*b^7*a^5 + 6006*x^22*c^3*b^5*a^6 + 4290*x^22*c^4*b^3*a^7 + 1287/2
*x^22*c^5*b*a^8 + 143/4*x^20*b^10*a^4 + 1287/2*x^20*c*b^8*a^5 + 3003*x^20*c^2*b^6*a^6 + 4290*x^20*c^3*b^4*a^7
+ 6435/4*x^20*c^4*b^2*a^8 + 143/2*x^20*c^5*a^9 + 143/2*x^18*b^9*a^5 + 858*x^18*c*b^7*a^6 + 2574*x^18*c^2*b^5*a
^7 + 2145*x^18*c^3*b^3*a^8 + 715/2*x^18*c^4*b*a^9 + 429/4*x^16*b^8*a^6 + 858*x^16*c*b^6*a^7 + 6435/4*x^16*c^2*
b^4*a^8 + 715*x^16*c^3*b^2*a^9 + 143/4*x^16*c^4*a^10 + 858/7*x^14*b^7*a^7 + 1287/2*x^14*c*b^5*a^8 + 715*x^14*c
^2*b^3*a^9 + 143*x^14*c^3*b*a^10 + 429/4*x^12*b^6*a^8 + 715/2*x^12*c*b^4*a^9 + 429/2*x^12*c^2*b^2*a^10 + 13*x^
12*c^3*a^11 + 143/2*x^10*b^5*a^9 + 143*x^10*c*b^3*a^10 + 39*x^10*c^2*b*a^11 + 143/4*x^8*b^4*a^10 + 39*x^8*c*b^
2*a^11 + 13/4*x^8*c^2*a^12 + 13*x^6*b^3*a^11 + 13/2*x^6*c*b*a^12 + 13/4*x^4*b^2*a^12 + 1/2*x^4*c*a^13 + 1/2*x^
2*b*a^13
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giac [B] time = 0.66, size = 246, normalized size = 13.67 \begin {gather*} \frac {1}{28} \, {\left (c x^{4} + b x^{2}\right )}^{14} + \frac {1}{2} \, {\left (c x^{4} + b x^{2}\right )}^{13} a + \frac {13}{4} \, {\left (c x^{4} + b x^{2}\right )}^{12} a^{2} + 13 \, {\left (c x^{4} + b x^{2}\right )}^{11} a^{3} + \frac {143}{4} \, {\left (c x^{4} + b x^{2}\right )}^{10} a^{4} + \frac {143}{2} \, {\left (c x^{4} + b x^{2}\right )}^{9} a^{5} + \frac {429}{4} \, {\left (c x^{4} + b x^{2}\right )}^{8} a^{6} + \frac {858}{7} \, {\left (c x^{4} + b x^{2}\right )}^{7} a^{7} + \frac {429}{4} \, {\left (c x^{4} + b x^{2}\right )}^{6} a^{8} + \frac {143}{2} \, {\left (c x^{4} + b x^{2}\right )}^{5} a^{9} + \frac {143}{4} \, {\left (c x^{4} + b x^{2}\right )}^{4} a^{10} + 13 \, {\left (c x^{4} + b x^{2}\right )}^{3} a^{11} + \frac {13}{4} \, {\left (c x^{4} + b x^{2}\right )}^{2} a^{12} + \frac {1}{2} \, {\left (c x^{4} + b x^{2}\right )} a^{13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x*(2*c*x^2+b)*(c*x^4+b*x^2+a)^13,x, algorithm="giac")
[Out]
1/28*(c*x^4 + b*x^2)^14 + 1/2*(c*x^4 + b*x^2)^13*a + 13/4*(c*x^4 + b*x^2)^12*a^2 + 13*(c*x^4 + b*x^2)^11*a^3 +
143/4*(c*x^4 + b*x^2)^10*a^4 + 143/2*(c*x^4 + b*x^2)^9*a^5 + 429/4*(c*x^4 + b*x^2)^8*a^6 + 858/7*(c*x^4 + b*x
^2)^7*a^7 + 429/4*(c*x^4 + b*x^2)^6*a^8 + 143/2*(c*x^4 + b*x^2)^5*a^9 + 143/4*(c*x^4 + b*x^2)^4*a^10 + 13*(c*x
^4 + b*x^2)^3*a^11 + 13/4*(c*x^4 + b*x^2)^2*a^12 + 1/2*(c*x^4 + b*x^2)*a^13
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maple [B] time = 0.00, size = 46552, normalized size = 2586.22 \begin {gather*} \text {output too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(x*(2*c*x^2+b)*(c*x^4+b*x^2+a)^13,x)
[Out]
result too large to display
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maxima [B] time = 0.49, size = 1240, normalized size = 68.89
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x*(2*c*x^2+b)*(c*x^4+b*x^2+a)^13,x, algorithm="maxima")
[Out]
1/28*c^14*x^56 + 1/2*b*c^13*x^54 + 1/4*(13*b^2*c^12 + 2*a*c^13)*x^52 + 13/2*(2*b^3*c^11 + a*b*c^12)*x^50 + 13/
4*(11*b^4*c^10 + 12*a*b^2*c^11 + a^2*c^12)*x^48 + 13/2*(11*b^5*c^9 + 22*a*b^3*c^10 + 6*a^2*b*c^11)*x^46 + 13/4
*(33*b^6*c^8 + 110*a*b^4*c^9 + 66*a^2*b^2*c^10 + 4*a^3*c^11)*x^44 + 143/14*(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^42 + 143/4*(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^40 + 143/2*(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^38 + 143/4*(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^36 + 13/2*(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^34 + 13/4*(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^32 + 1/2*(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^30 + 1/28*(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^28 + 1/2*(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^26 + 13/4*(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^24 + 13/2*(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^22 + 143/4*(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^20 + 143/2*(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^18 + 143/4*(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^16 + 1/2*a^13*b*x^2 + 143/14*(12*a^7*b^7 + 63*a^8*b^5*c + 70*a^9*b^3*c^2 + 14*a^1
0*b*c^3)*x^14 + 13/4*(33*a^8*b^6 + 110*a^9*b^4*c + 66*a^10*b^2*c^2 + 4*a^11*c^3)*x^12 + 13/2*(11*a^9*b^5 + 22*
a^10*b^3*c + 6*a^11*b*c^2)*x^10 + 13/4*(11*a^10*b^4 + 12*a^11*b^2*c + a^12*c^2)*x^8 + 13/2*(2*a^11*b^3 + a^12*
b*c)*x^6 + 1/4*(13*a^12*b^2 + 2*a^13*c)*x^4
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mupad [B] time = 3.23, size = 1210, normalized size = 67.22
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(x*(b + 2*c*x^2)*(a + b*x^2 + c*x^4)^13,x)
[Out]
x^24*((13*a^2*b^12)/4 + (429*a^8*c^6)/4 + 143*a^3*b^10*c + (6435*a^4*b^8*c^2)/4 + 6006*a^5*b^6*c^3 + (15015*a^
6*b^4*c^4)/2 + 2574*a^7*b^2*c^5) + x^32*((429*a^6*c^8)/4 + (13*b^12*c^2)/4 + 143*a*b^10*c^3 + (6435*a^2*b^8*c^
4)/4 + 6006*a^3*b^6*c^5 + (15015*a^4*b^4*c^6)/2 + 2574*a^5*b^2*c^7) + x^26*((a*b^13)/2 + 39*a^2*b^11*c + 858*a
^7*b*c^6 + 715*a^3*b^9*c^2 + 4290*a^4*b^7*c^3 + 9009*a^5*b^5*c^4 + 6006*a^6*b^3*c^5) + x^30*((b^13*c)/2 + 39*a
*b^11*c^2 + 858*a^6*b*c^7 + 715*a^2*b^9*c^3 + 4290*a^3*b^7*c^4 + 9009*a^4*b^5*c^5 + 6006*a^5*b^3*c^6) + x^12*(
(429*a^8*b^6)/4 + 13*a^11*c^3 + (715*a^9*b^4*c)/2 + (429*a^10*b^2*c^2)/2) + x^44*(13*a^3*c^11 + (429*b^6*c^8)/
4 + (715*a*b^4*c^9)/2 + (429*a^2*b^2*c^10)/2) + x^20*((143*a^4*b^10)/4 + (143*a^9*c^5)/2 + (1287*a^5*b^8*c)/2
+ 3003*a^6*b^6*c^2 + 4290*a^7*b^4*c^3 + (6435*a^8*b^2*c^4)/4) + x^36*((143*a^5*c^9)/2 + (143*b^10*c^4)/4 + (12
87*a*b^8*c^5)/2 + 3003*a^2*b^6*c^6 + 4290*a^3*b^4*c^7 + (6435*a^4*b^2*c^8)/4) + x^28*(b^14/28 + (858*a^7*c^7)/
7 + (429*a^2*b^10*c^2)/2 + 2145*a^3*b^8*c^3 + (15015*a^4*b^6*c^4)/2 + 9009*a^5*b^4*c^5 + 3003*a^6*b^2*c^6 + (1
3*a*b^12*c)/2) + x^16*((429*a^6*b^8)/4 + (143*a^10*c^4)/4 + 858*a^7*b^6*c + (6435*a^8*b^4*c^2)/4 + 715*a^9*b^2
*c^3) + x^40*((143*a^4*c^10)/4 + (429*b^8*c^6)/4 + 858*a*b^6*c^7 + (6435*a^2*b^4*c^8)/4 + 715*a^3*b^2*c^9) + (
c^14*x^56)/28 + x^4*((a^13*c)/2 + (13*a^12*b^2)/4) + (13*a^10*x^8*(11*b^4 + a^2*c^2 + 12*a*b^2*c))/4 + (13*c^1
0*x^48*(11*b^4 + a^2*c^2 + 12*a*b^2*c))/4 + (a^13*b*x^2)/2 + (b*c^13*x^54)/2 + (c^12*x^52*(2*a*c + 13*b^2))/4
+ (143*a^7*b*x^14*(12*b^6 + 14*a^3*c^3 + 70*a^2*b^2*c^2 + 63*a*b^4*c))/14 + (143*b*c^7*x^42*(12*b^6 + 14*a^3*c
^3 + 70*a^2*b^2*c^2 + 63*a*b^4*c))/14 + (143*a^5*b*x^18*(b^8 + 5*a^4*c^4 + 36*a^2*b^4*c^2 + 30*a^3*b^2*c^3 + 1
2*a*b^6*c))/2 + (143*b*c^5*x^38*(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))/2 + (13*a^3*
b*x^22*(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))/2 + (13*b*c^3
*x^34*(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))/2 + (13*a^9*b*
x^10*(11*b^4 + 6*a^2*c^2 + 22*a*b^2*c))/2 + (13*b*c^9*x^46*(11*b^4 + 6*a^2*c^2 + 22*a*b^2*c))/2 + (13*a^11*b*x
^6*(a*c + 2*b^2))/2 + (13*b*c^11*x^50*(a*c + 2*b^2))/2
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sympy [B] time = 0.34, size = 1384, normalized size = 76.89
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x*(2*c*x**2+b)*(c*x**4+b*x**2+a)**13,x)
[Out]
a**13*b*x**2/2 + b*c**13*x**54/2 + c**14*x**56/28 + x**52*(a*c**13/2 + 13*b**2*c**12/4) + x**50*(13*a*b*c**12/
2 + 13*b**3*c**11) + x**48*(13*a**2*c**12/4 + 39*a*b**2*c**11 + 143*b**4*c**10/4) + x**46*(39*a**2*b*c**11 + 1
43*a*b**3*c**10 + 143*b**5*c**9/2) + x**44*(13*a**3*c**11 + 429*a**2*b**2*c**10/2 + 715*a*b**4*c**9/2 + 429*b*
*6*c**8/4) + x**42*(143*a**3*b*c**10 + 715*a**2*b**3*c**9 + 1287*a*b**5*c**8/2 + 858*b**7*c**7/7) + x**40*(143
*a**4*c**10/4 + 715*a**3*b**2*c**9 + 6435*a**2*b**4*c**8/4 + 858*a*b**6*c**7 + 429*b**8*c**6/4) + x**38*(715*a
**4*b*c**9/2 + 2145*a**3*b**3*c**8 + 2574*a**2*b**5*c**7 + 858*a*b**7*c**6 + 143*b**9*c**5/2) + x**36*(143*a**
5*c**9/2 + 6435*a**4*b**2*c**8/4 + 4290*a**3*b**4*c**7 + 3003*a**2*b**6*c**6 + 1287*a*b**8*c**5/2 + 143*b**10*
c**4/4) + x**34*(1287*a**5*b*c**8/2 + 4290*a**4*b**3*c**7 + 6006*a**3*b**5*c**6 + 2574*a**2*b**7*c**5 + 715*a*
b**9*c**4/2 + 13*b**11*c**3) + x**32*(429*a**6*c**8/4 + 2574*a**5*b**2*c**7 + 15015*a**4*b**4*c**6/2 + 6006*a*
*3*b**6*c**5 + 6435*a**2*b**8*c**4/4 + 143*a*b**10*c**3 + 13*b**12*c**2/4) + x**30*(858*a**6*b*c**7 + 6006*a**
5*b**3*c**6 + 9009*a**4*b**5*c**5 + 4290*a**3*b**7*c**4 + 715*a**2*b**9*c**3 + 39*a*b**11*c**2 + b**13*c/2) +
x**28*(858*a**7*c**7/7 + 3003*a**6*b**2*c**6 + 9009*a**5*b**4*c**5 + 15015*a**4*b**6*c**4/2 + 2145*a**3*b**8*c
**3 + 429*a**2*b**10*c**2/2 + 13*a*b**12*c/2 + b**14/28) + x**26*(858*a**7*b*c**6 + 6006*a**6*b**3*c**5 + 9009
*a**5*b**5*c**4 + 4290*a**4*b**7*c**3 + 715*a**3*b**9*c**2 + 39*a**2*b**11*c + a*b**13/2) + x**24*(429*a**8*c*
*6/4 + 2574*a**7*b**2*c**5 + 15015*a**6*b**4*c**4/2 + 6006*a**5*b**6*c**3 + 6435*a**4*b**8*c**2/4 + 143*a**3*b
**10*c + 13*a**2*b**12/4) + x**22*(1287*a**8*b*c**5/2 + 4290*a**7*b**3*c**4 + 6006*a**6*b**5*c**3 + 2574*a**5*
b**7*c**2 + 715*a**4*b**9*c/2 + 13*a**3*b**11) + x**20*(143*a**9*c**5/2 + 6435*a**8*b**2*c**4/4 + 4290*a**7*b*
*4*c**3 + 3003*a**6*b**6*c**2 + 1287*a**5*b**8*c/2 + 143*a**4*b**10/4) + x**18*(715*a**9*b*c**4/2 + 2145*a**8*
b**3*c**3 + 2574*a**7*b**5*c**2 + 858*a**6*b**7*c + 143*a**5*b**9/2) + x**16*(143*a**10*c**4/4 + 715*a**9*b**2
*c**3 + 6435*a**8*b**4*c**2/4 + 858*a**7*b**6*c + 429*a**6*b**8/4) + x**14*(143*a**10*b*c**3 + 715*a**9*b**3*c
**2 + 1287*a**8*b**5*c/2 + 858*a**7*b**7/7) + x**12*(13*a**11*c**3 + 429*a**10*b**2*c**2/2 + 715*a**9*b**4*c/2
+ 429*a**8*b**6/4) + x**10*(39*a**11*b*c**2 + 143*a**10*b**3*c + 143*a**9*b**5/2) + x**8*(13*a**12*c**2/4 + 3
9*a**11*b**2*c + 143*a**10*b**4/4) + x**6*(13*a**12*b*c/2 + 13*a**11*b**3) + x**4*(a**13*c/2 + 13*a**12*b**2/4
)
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