3.367 $$\int (d+e x)^m (3+2 x+5 x^2)^3 (2+x+3 x^2-5 x^3+4 x^4) \, dx$$

Optimal. Leaf size=588 $\frac{\left (5 d^2-2 d e+3 e^2\right )^3 \left (3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right ) (d+e x)^{m+1}}{e^{11} (m+1)}-\frac{\left (5 d^2-2 d e+3 e^2\right )^2 \left (108 d^3 e^2-20 d^2 e^3+169 d^4 e+200 d^5+86 d e^4-15 e^5\right ) (d+e x)^{m+2}}{e^{11} (m+2)}+\frac{3 \left (5 d^2-2 d e+3 e^2\right ) \left (792 d^4 e^2+58 d^3 e^3+547 d^2 e^4+660 d^5 e+1500 d^6-156 d e^5+53 e^6\right ) (d+e x)^{m+3}}{e^{11} (m+3)}-\frac{2 \left (21420 d^5 e^2+1715 d^4 e^3+9990 d^3 e^4-2550 d^2 e^5+1050 d^6 e+30000 d^7+2218 d e^6-287 e^7\right ) (d+e x)^{m+4}}{e^{11} (m+4)}+\frac{\left (53550 d^4 e^2+3430 d^3 e^3+14985 d^2 e^4+3150 d^5 e+105000 d^6-2550 d e^5+1109 e^6\right ) (d+e x)^{m+5}}{e^{11} (m+5)}-\frac{6 \left (7140 d^3 e^2+343 d^2 e^3+525 d^4 e+21000 d^5+999 d e^4-85 e^5\right ) (d+e x)^{m+6}}{e^{11} (m+6)}+\frac{\left (21420 d^2 e^2+2100 d^3 e+105000 d^4+686 d e^3+999 e^4\right ) (d+e x)^{m+7}}{e^{11} (m+7)}-\frac{2 \left (450 d^2 e+30000 d^3+3060 d e^2+49 e^3\right ) (d+e x)^{m+8}}{e^{11} (m+8)}+\frac{45 \left (500 d^2+5 d e+17 e^2\right ) (d+e x)^{m+9}}{e^{11} (m+9)}-\frac{25 (200 d+e) (d+e x)^{m+10}}{e^{11} (m+10)}+\frac{500 (d+e x)^{m+11}}{e^{11} (m+11)}$

[Out]

((5*d^2 - 2*d*e + 3*e^2)^3*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*(d + e*x)^(1 + m))/(e^11*(1 + m)) - (
(5*d^2 - 2*d*e + 3*e^2)^2*(200*d^5 + 169*d^4*e + 108*d^3*e^2 - 20*d^2*e^3 + 86*d*e^4 - 15*e^5)*(d + e*x)^(2 +
m))/(e^11*(2 + m)) + (3*(5*d^2 - 2*d*e + 3*e^2)*(1500*d^6 + 660*d^5*e + 792*d^4*e^2 + 58*d^3*e^3 + 547*d^2*e^4
- 156*d*e^5 + 53*e^6)*(d + e*x)^(3 + m))/(e^11*(3 + m)) - (2*(30000*d^7 + 1050*d^6*e + 21420*d^5*e^2 + 1715*d
^4*e^3 + 9990*d^3*e^4 - 2550*d^2*e^5 + 2218*d*e^6 - 287*e^7)*(d + e*x)^(4 + m))/(e^11*(4 + m)) + ((105000*d^6
+ 3150*d^5*e + 53550*d^4*e^2 + 3430*d^3*e^3 + 14985*d^2*e^4 - 2550*d*e^5 + 1109*e^6)*(d + e*x)^(5 + m))/(e^11*
(5 + m)) - (6*(21000*d^5 + 525*d^4*e + 7140*d^3*e^2 + 343*d^2*e^3 + 999*d*e^4 - 85*e^5)*(d + e*x)^(6 + m))/(e^
11*(6 + m)) + ((105000*d^4 + 2100*d^3*e + 21420*d^2*e^2 + 686*d*e^3 + 999*e^4)*(d + e*x)^(7 + m))/(e^11*(7 + m
)) - (2*(30000*d^3 + 450*d^2*e + 3060*d*e^2 + 49*e^3)*(d + e*x)^(8 + m))/(e^11*(8 + m)) + (45*(500*d^2 + 5*d*e
+ 17*e^2)*(d + e*x)^(9 + m))/(e^11*(9 + m)) - (25*(200*d + e)*(d + e*x)^(10 + m))/(e^11*(10 + m)) + (500*(d +
e*x)^(11 + m))/(e^11*(11 + m))

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Rubi [A]  time = 0.364184, antiderivative size = 588, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 38, $$\frac{\text{number of rules}}{\text{integrand size}}$$ = 0.026, Rules used = {1628} $\frac{\left (5 d^2-2 d e+3 e^2\right )^3 \left (3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right ) (d+e x)^{m+1}}{e^{11} (m+1)}-\frac{\left (5 d^2-2 d e+3 e^2\right )^2 \left (108 d^3 e^2-20 d^2 e^3+169 d^4 e+200 d^5+86 d e^4-15 e^5\right ) (d+e x)^{m+2}}{e^{11} (m+2)}+\frac{3 \left (5 d^2-2 d e+3 e^2\right ) \left (792 d^4 e^2+58 d^3 e^3+547 d^2 e^4+660 d^5 e+1500 d^6-156 d e^5+53 e^6\right ) (d+e x)^{m+3}}{e^{11} (m+3)}-\frac{2 \left (21420 d^5 e^2+1715 d^4 e^3+9990 d^3 e^4-2550 d^2 e^5+1050 d^6 e+30000 d^7+2218 d e^6-287 e^7\right ) (d+e x)^{m+4}}{e^{11} (m+4)}+\frac{\left (53550 d^4 e^2+3430 d^3 e^3+14985 d^2 e^4+3150 d^5 e+105000 d^6-2550 d e^5+1109 e^6\right ) (d+e x)^{m+5}}{e^{11} (m+5)}-\frac{6 \left (7140 d^3 e^2+343 d^2 e^3+525 d^4 e+21000 d^5+999 d e^4-85 e^5\right ) (d+e x)^{m+6}}{e^{11} (m+6)}+\frac{\left (21420 d^2 e^2+2100 d^3 e+105000 d^4+686 d e^3+999 e^4\right ) (d+e x)^{m+7}}{e^{11} (m+7)}-\frac{2 \left (450 d^2 e+30000 d^3+3060 d e^2+49 e^3\right ) (d+e x)^{m+8}}{e^{11} (m+8)}+\frac{45 \left (500 d^2+5 d e+17 e^2\right ) (d+e x)^{m+9}}{e^{11} (m+9)}-\frac{25 (200 d+e) (d+e x)^{m+10}}{e^{11} (m+10)}+\frac{500 (d+e x)^{m+11}}{e^{11} (m+11)}$

Antiderivative was successfully veriﬁed.

[In]

Int[(d + e*x)^m*(3 + 2*x + 5*x^2)^3*(2 + x + 3*x^2 - 5*x^3 + 4*x^4),x]

[Out]

((5*d^2 - 2*d*e + 3*e^2)^3*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*(d + e*x)^(1 + m))/(e^11*(1 + m)) - (
(5*d^2 - 2*d*e + 3*e^2)^2*(200*d^5 + 169*d^4*e + 108*d^3*e^2 - 20*d^2*e^3 + 86*d*e^4 - 15*e^5)*(d + e*x)^(2 +
m))/(e^11*(2 + m)) + (3*(5*d^2 - 2*d*e + 3*e^2)*(1500*d^6 + 660*d^5*e + 792*d^4*e^2 + 58*d^3*e^3 + 547*d^2*e^4
- 156*d*e^5 + 53*e^6)*(d + e*x)^(3 + m))/(e^11*(3 + m)) - (2*(30000*d^7 + 1050*d^6*e + 21420*d^5*e^2 + 1715*d
^4*e^3 + 9990*d^3*e^4 - 2550*d^2*e^5 + 2218*d*e^6 - 287*e^7)*(d + e*x)^(4 + m))/(e^11*(4 + m)) + ((105000*d^6
+ 3150*d^5*e + 53550*d^4*e^2 + 3430*d^3*e^3 + 14985*d^2*e^4 - 2550*d*e^5 + 1109*e^6)*(d + e*x)^(5 + m))/(e^11*
(5 + m)) - (6*(21000*d^5 + 525*d^4*e + 7140*d^3*e^2 + 343*d^2*e^3 + 999*d*e^4 - 85*e^5)*(d + e*x)^(6 + m))/(e^
11*(6 + m)) + ((105000*d^4 + 2100*d^3*e + 21420*d^2*e^2 + 686*d*e^3 + 999*e^4)*(d + e*x)^(7 + m))/(e^11*(7 + m
)) - (2*(30000*d^3 + 450*d^2*e + 3060*d*e^2 + 49*e^3)*(d + e*x)^(8 + m))/(e^11*(8 + m)) + (45*(500*d^2 + 5*d*e
+ 17*e^2)*(d + e*x)^(9 + m))/(e^11*(9 + m)) - (25*(200*d + e)*(d + e*x)^(10 + m))/(e^11*(10 + m)) + (500*(d +
e*x)^(11 + m))/(e^11*(11 + m))

Rule 1628

Int[(Pq_)*((d_.) + (e_.)*(x_))^(m_.)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[ExpandIntegra
nd[(d + e*x)^m*Pq*(a + b*x + c*x^2)^p, x], x] /; FreeQ[{a, b, c, d, e, m}, x] && PolyQ[Pq, x] && IGtQ[p, -2]

Rubi steps

\begin{align*} \int (d+e x)^m \left (3+2 x+5 x^2\right )^3 \left (2+x+3 x^2-5 x^3+4 x^4\right ) \, dx &=\int \left (\frac{\left (5 d^2-2 d e+3 e^2\right )^3 \left (4 d^4+5 d^3 e+3 d^2 e^2-d e^3+2 e^4\right ) (d+e x)^m}{e^{10}}+\frac{\left (5 d^2-2 d e+3 e^2\right )^2 \left (-200 d^5-169 d^4 e-108 d^3 e^2+20 d^2 e^3-86 d e^4+15 e^5\right ) (d+e x)^{1+m}}{e^{10}}+\frac{3 \left (7500 d^8+300 d^7 e+7140 d^6 e^2+686 d^5 e^3+4995 d^4 e^4-1700 d^3 e^5+2218 d^2 e^6-574 d e^7+159 e^8\right ) (d+e x)^{2+m}}{e^{10}}+\frac{2 \left (-30000 d^7-1050 d^6 e-21420 d^5 e^2-1715 d^4 e^3-9990 d^3 e^4+2550 d^2 e^5-2218 d e^6+287 e^7\right ) (d+e x)^{3+m}}{e^{10}}+\frac{\left (105000 d^6+3150 d^5 e+53550 d^4 e^2+3430 d^3 e^3+14985 d^2 e^4-2550 d e^5+1109 e^6\right ) (d+e x)^{4+m}}{e^{10}}+\frac{6 \left (-21000 d^5-525 d^4 e-7140 d^3 e^2-343 d^2 e^3-999 d e^4+85 e^5\right ) (d+e x)^{5+m}}{e^{10}}+\frac{\left (105000 d^4+2100 d^3 e+21420 d^2 e^2+686 d e^3+999 e^4\right ) (d+e x)^{6+m}}{e^{10}}-\frac{2 \left (30000 d^3+450 d^2 e+3060 d e^2+49 e^3\right ) (d+e x)^{7+m}}{e^{10}}+\frac{45 \left (500 d^2+5 d e+17 e^2\right ) (d+e x)^{8+m}}{e^{10}}-\frac{25 (200 d+e) (d+e x)^{9+m}}{e^{10}}+\frac{500 (d+e x)^{10+m}}{e^{10}}\right ) \, dx\\ &=\frac{\left (5 d^2-2 d e+3 e^2\right )^3 \left (4 d^4+5 d^3 e+3 d^2 e^2-d e^3+2 e^4\right ) (d+e x)^{1+m}}{e^{11} (1+m)}-\frac{\left (5 d^2-2 d e+3 e^2\right )^2 \left (200 d^5+169 d^4 e+108 d^3 e^2-20 d^2 e^3+86 d e^4-15 e^5\right ) (d+e x)^{2+m}}{e^{11} (2+m)}+\frac{3 \left (5 d^2-2 d e+3 e^2\right ) \left (1500 d^6+660 d^5 e+792 d^4 e^2+58 d^3 e^3+547 d^2 e^4-156 d e^5+53 e^6\right ) (d+e x)^{3+m}}{e^{11} (3+m)}-\frac{2 \left (30000 d^7+1050 d^6 e+21420 d^5 e^2+1715 d^4 e^3+9990 d^3 e^4-2550 d^2 e^5+2218 d e^6-287 e^7\right ) (d+e x)^{4+m}}{e^{11} (4+m)}+\frac{\left (105000 d^6+3150 d^5 e+53550 d^4 e^2+3430 d^3 e^3+14985 d^2 e^4-2550 d e^5+1109 e^6\right ) (d+e x)^{5+m}}{e^{11} (5+m)}-\frac{6 \left (21000 d^5+525 d^4 e+7140 d^3 e^2+343 d^2 e^3+999 d e^4-85 e^5\right ) (d+e x)^{6+m}}{e^{11} (6+m)}+\frac{\left (105000 d^4+2100 d^3 e+21420 d^2 e^2+686 d e^3+999 e^4\right ) (d+e x)^{7+m}}{e^{11} (7+m)}-\frac{2 \left (30000 d^3+450 d^2 e+3060 d e^2+49 e^3\right ) (d+e x)^{8+m}}{e^{11} (8+m)}+\frac{45 \left (500 d^2+5 d e+17 e^2\right ) (d+e x)^{9+m}}{e^{11} (9+m)}-\frac{25 (200 d+e) (d+e x)^{10+m}}{e^{11} (10+m)}+\frac{500 (d+e x)^{11+m}}{e^{11} (11+m)}\\ \end{align*}

Mathematica [A]  time = 0.410217, size = 537, normalized size = 0.91 $\frac{(d+e x)^{m+1} \left (\frac{45 \left (500 d^2+5 d e+17 e^2\right ) (d+e x)^8}{m+9}-\frac{2 \left (450 d^2 e+30000 d^3+3060 d e^2+49 e^3\right ) (d+e x)^7}{m+8}+\frac{\left (21420 d^2 e^2+2100 d^3 e+105000 d^4+686 d e^3+999 e^4\right ) (d+e x)^6}{m+7}-\frac{6 \left (7140 d^3 e^2+343 d^2 e^3+525 d^4 e+21000 d^5+999 d e^4-85 e^5\right ) (d+e x)^5}{m+6}+\frac{\left (53550 d^4 e^2+3430 d^3 e^3+14985 d^2 e^4+3150 d^5 e+105000 d^6-2550 d e^5+1109 e^6\right ) (d+e x)^4}{m+5}-\frac{2 \left (21420 d^5 e^2+1715 d^4 e^3+9990 d^3 e^4-2550 d^2 e^5+1050 d^6 e+30000 d^7+2218 d e^6-287 e^7\right ) (d+e x)^3}{m+4}+\frac{3 \left (5 d^2-2 d e+3 e^2\right ) \left (792 d^4 e^2+58 d^3 e^3+547 d^2 e^4+660 d^5 e+1500 d^6-156 d e^5+53 e^6\right ) (d+e x)^2}{m+3}-\frac{\left (5 d^2-2 d e+3 e^2\right )^2 \left (108 d^3 e^2-20 d^2 e^3+169 d^4 e+200 d^5+86 d e^4-15 e^5\right ) (d+e x)}{m+2}+\frac{\left (5 d^2-2 d e+3 e^2\right )^3 \left (3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right )}{m+1}+\frac{500 (d+e x)^{10}}{m+11}-\frac{25 (200 d+e) (d+e x)^9}{m+10}\right )}{e^{11}}$

Antiderivative was successfully veriﬁed.

[In]

Integrate[(d + e*x)^m*(3 + 2*x + 5*x^2)^3*(2 + x + 3*x^2 - 5*x^3 + 4*x^4),x]

[Out]

((d + e*x)^(1 + m)*(((5*d^2 - 2*d*e + 3*e^2)^3*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4))/(1 + m) - ((5*d^
2 - 2*d*e + 3*e^2)^2*(200*d^5 + 169*d^4*e + 108*d^3*e^2 - 20*d^2*e^3 + 86*d*e^4 - 15*e^5)*(d + e*x))/(2 + m) +
(3*(5*d^2 - 2*d*e + 3*e^2)*(1500*d^6 + 660*d^5*e + 792*d^4*e^2 + 58*d^3*e^3 + 547*d^2*e^4 - 156*d*e^5 + 53*e^
6)*(d + e*x)^2)/(3 + m) - (2*(30000*d^7 + 1050*d^6*e + 21420*d^5*e^2 + 1715*d^4*e^3 + 9990*d^3*e^4 - 2550*d^2*
e^5 + 2218*d*e^6 - 287*e^7)*(d + e*x)^3)/(4 + m) + ((105000*d^6 + 3150*d^5*e + 53550*d^4*e^2 + 3430*d^3*e^3 +
14985*d^2*e^4 - 2550*d*e^5 + 1109*e^6)*(d + e*x)^4)/(5 + m) - (6*(21000*d^5 + 525*d^4*e + 7140*d^3*e^2 + 343*d
^2*e^3 + 999*d*e^4 - 85*e^5)*(d + e*x)^5)/(6 + m) + ((105000*d^4 + 2100*d^3*e + 21420*d^2*e^2 + 686*d*e^3 + 99
9*e^4)*(d + e*x)^6)/(7 + m) - (2*(30000*d^3 + 450*d^2*e + 3060*d*e^2 + 49*e^3)*(d + e*x)^7)/(8 + m) + (45*(500
*d^2 + 5*d*e + 17*e^2)*(d + e*x)^8)/(9 + m) - (25*(200*d + e)*(d + e*x)^9)/(10 + m) + (500*(d + e*x)^10)/(11 +
m)))/e^11

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Maple [B]  time = 0.082, size = 5924, normalized size = 10.1 \begin{align*} \text{output too large to display} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((e*x+d)^m*(5*x^2+2*x+3)^3*(4*x^4-5*x^3+3*x^2+x+2),x)

[Out]

result too large to display

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Maxima [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x+d)^m*(5*x^2+2*x+3)^3*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm="maxima")

[Out]

Exception raised: ValueError

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Fricas [B]  time = 1.84756, size = 14657, normalized size = 24.93 \begin{align*} \text{result too large to display} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x+d)^m*(5*x^2+2*x+3)^3*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm="fricas")

[Out]

(54*d*e^10*m^10 + 500*(e^11*m^10 + 55*e^11*m^9 + 1320*e^11*m^8 + 18150*e^11*m^7 + 157773*e^11*m^6 + 902055*e^1
1*m^5 + 3416930*e^11*m^4 + 8409500*e^11*m^3 + 12753576*e^11*m^2 + 10628640*e^11*m + 3628800*e^11)*x^11 + 18144
00000*d^11 + 99792000*d^10*e + 3392928000*d^9*e^2 + 488980800*d^8*e^3 + 5696697600*d^7*e^4 - 3392928000*d^6*e^
5 + 8853546240*d^5*e^6 - 5728060800*d^4*e^7 + 6346771200*d^3*e^8 - 2694384000*d^2*e^9 + 2155507200*d*e^10 - 25
*(3991680*e^11 - (20*d*e^10 - e^11)*m^10 - 4*(225*d*e^10 - 14*e^11)*m^9 - 15*(1160*d*e^10 - 91*e^11)*m^8 - 60*
(3150*d*e^10 - 317*e^11)*m^7 - 21*(60260*d*e^10 - 7963*e^11)*m^6 - 84*(64125*d*e^10 - 11492*e^11)*m^5 - 5*(289
4720*d*e^10 - 737251*e^11)*m^4 - 20*(1172700*d*e^10 - 456659*e^11)*m^3 - 36*(570320*d*e^10 - 386841*e^11)*m^2
- 144*(50400*d*e^10 - 80939*e^11)*m)*x^10 - 135*(d^2*e^9 - 26*d*e^10)*m^9 + 5*(678585600*e^11 - (5*d*e^10 - 15
3*e^11)*m^10 - (1000*d^2*e^9 + 235*d*e^10 - 8721*e^11)*m^9 - 6*(6000*d^2*e^9 + 785*d*e^10 - 36006*e^11)*m^8 -
6*(91000*d^2*e^9 + 8785*d*e^10 - 509031*e^11)*m^7 - 105*(43200*d^2*e^9 + 3445*d*e^10 - 259029*e^11)*m^6 - 21*(
1069000*d^2*e^9 + 74815*d*e^10 - 7560189*e^11)*m^5 - 2*(33642000*d^2*e^9 + 2145620*d*e^10 - 306036567*e^11)*m^
4 - 4*(29531000*d^2*e^9 + 1761185*d*e^10 - 382172121*e^11)*m^3 - 72*(1522000*d^2*e^9 + 86510*d*e^10 - 32587351
*e^11)*m^2 - 1440*(28000*d^2*e^9 + 1540*d*e^10 - 1370727*e^11)*m)*x^9 + 9*(106*d^3*e^8 - 945*d^2*e^9 + 11160*d
*e^10)*m^8 - (488980800*e^11 - (765*d*e^10 - 98*e^11)*m^10 - (225*d^2*e^9 + 37485*d*e^10 - 5684*e^11)*m^9 - 3*
(15000*d^3*e^8 + 2925*d^2*e^9 + 260100*d*e^10 - 47726*e^11)*m^8 - 42*(30000*d^3*e^8 + 3375*d^2*e^9 + 214965*d*
e^10 - 48958*e^11)*m^7 - 63*(230000*d^3*e^8 + 19650*d^2*e^9 + 1012095*d*e^10 - 294882*e^11)*m^6 - 63*(1400000*
d^3*e^8 + 101175*d^2*e^9 + 4503555*d*e^10 - 1743812*e^11)*m^5 - (304605000*d^3*e^8 + 19707975*d^2*e^9 + 790573
950*d*e^10 - 428393182*e^11)*m^4 - 4*(147735000*d^3*e^8 + 8860500*d^2*e^9 + 329712705*d*e^10 - 270109021*e^11)
*m^3 - 36*(16335000*d^3*e^8 + 929925*d^2*e^9 + 32795550*d*e^10 - 46438966*e^11)*m^2 - 5040*(45000*d^3*e^8 + 24
75*d^2*e^9 + 84150*d*e^10 - 280861*e^11)*m)*x^8 - 6*(574*d^4*e^7 - 9540*d^3*e^8 + 39015*d^2*e^9 - 277290*d*e^1
0)*m^7 + (5696697600*e^11 - (98*d*e^10 - 999*e^11)*m^10 - 3*(2040*d^2*e^9 + 1666*d*e^10 - 19647*e^11)*m^9 - 24
*(75*d^3*e^8 + 10710*d^2*e^9 + 4508*d*e^10 - 62937*e^11)*m^8 - 6*(60000*d^4*e^7 + 9600*d^3*e^8 + 740520*d^2*e^
9 + 216482*d*e^10 - 3677319*e^11)*m^7 - 3*(2520000*d^4*e^7 + 243600*d^3*e^8 + 13708800*d^2*e^9 + 3161774*d*e^1
0 - 67539393*e^11)*m^6 - 21*(3000000*d^4*e^7 + 228000*d^3*e^8 + 10581480*d^2*e^9 + 2069662*d*e^10 - 57933009*e
^11)*m^5 - 2*(132300000*d^4*e^7 + 8738100*d^3*e^8 + 357157080*d^2*e^9 + 62076434*d*e^10 - 2405021571*e^11)*m^4
- 36*(16240000*d^4*e^7 + 981400*d^3*e^8 + 36788680*d^2*e^9 + 5871278*d*e^10 - 341095341*e^11)*m^3 - 72*(88200
00*d^4*e^7 + 503100*d^3*e^8 + 17778600*d^2*e^9 + 2670010*d*e^10 - 266622111*e^11)*m^2 - 12960*(20000*d^4*e^7 +
1100*d^3*e^8 + 37400*d^2*e^9 + 5390*d*e^10 - 1264623*e^11)*m)*x^7 + 6*(4436*d^5*e^6 - 32144*d^4*e^7 + 247086*
d^3*e^8 - 615195*d^2*e^9 + 2939517*d*e^10)*m^6 + (3392928000*e^11 + 3*(333*d*e^10 + 170*e^11)*m^10 + (686*d^2*
e^9 + 52947*d*e^10 + 30600*e^11)*m^9 + 6*(7140*d^3*e^8 + 5145*d^2*e^9 + 198801*d*e^10 + 133025*e^11)*m^8 + 6*(
2100*d^4*e^7 + 257040*d^3*e^8 + 95354*d^2*e^9 + 2484513*d*e^10 + 1978800*e^11)*m^7 + 3*(840000*d^5*e^6 + 10920
0*d^4*e^7 + 7282800*d^3*e^8 + 1886500*d^2*e^9 + 37725237*d*e^10 + 37016310*e^11)*m^6 + 3*(12600000*d^5*e^6 + 1
050000*d^4*e^7 + 52264800*d^3*e^8 + 10813418*d^2*e^9 + 179179641*d*e^10 + 226287000*e^11)*m^5 + 42*(5100000*d^
5*e^6 + 348000*d^4*e^7 + 14635980*d^3*e^8 + 2609495*d^2*e^9 + 37733562*d*e^10 + 64999925*e^11)*m^4 + 4*(141750
000*d^5*e^6 + 8659350*d^4*e^7 + 327983040*d^3*e^8 + 52869334*d^2*e^9 + 692643663*d*e^10 + 1769460300*e^11)*m^3
+ 120*(5754000*d^5*e^6 + 329070*d^4*e^7 + 11659620*d^3*e^8 + 1755817*d^2*e^9 + 21444534*d*e^10 + 93454763*e^1
1)*m^2 + 7200*(42000*d^5*e^6 + 2310*d^4*e^7 + 78540*d^3*e^8 + 11319*d^2*e^9 + 131868*d*e^10 + 1344547*e^11)*m)
*x^6 - 3*(20400*d^6*e^5 - 452472*d^5*e^6 + 1526840*d^4*e^7 - 7212240*d^3*e^8 + 12236805*d^2*e^9 - 41597010*d*e
^10)*m^5 + (8853546240*e^11 + (510*d*e^10 + 1109*e^11)*m^10 - (5994*d^2*e^9 - 28050*d*e^10 - 67649*e^11)*m^9 -
12*(343*d^3*e^8 + 23976*d^2*e^9 - 54825*d*e^10 - 149715*e^11)*m^8 - 6*(42840*d^4*e^7 + 27440*d^3*e^8 + 953046
*d^2*e^9 - 1430550*d*e^10 - 4541355*e^11)*m^7 - 3*(25200*d^5*e^6 + 2656080*d^4*e^7 + 869848*d^3*e^8 + 20283696
*d^2*e^9 - 22710810*d*e^10 - 86713819*e^11)*m^6 - 3*(5040000*d^6*e^5 + 529200*d^5*e^6 + 30416400*d^4*e^7 + 696
9760*d^3*e^8 + 124932942*d^2*e^9 - 112732950*d*e^10 - 541448179*e^11)*m^5 - 2*(75600000*d^6*e^5 + 5481000*d^5*
e^6 + 242260200*d^4*e^7 + 45047562*d^3*e^8 + 675619704*d^2*e^9 - 519501300*d*e^10 - 3335910815*e^11)*m^4 - 4*(
132300000*d^6*e^5 + 8221500*d^5*e^6 + 316416240*d^4*e^7 + 51779280*d^3*e^8 + 688165146*d^2*e^9 - 470707050*d*e
^10 - 4412539105*e^11)*m^3 - 72*(10500000*d^6*e^5 + 602700*d^5*e^6 + 21434280*d^4*e^7 + 3239978*d^3*e^8 + 3972
4236*d^2*e^9 - 25005980*d*e^10 - 395561447*e^11)*m^2 - 288*(1260000*d^6*e^5 + 69300*d^5*e^6 + 2356200*d^4*e^7
+ 339570*d^3*e^8 + 3956040*d^2*e^9 - 2356200*d*e^10 - 86687203*e^11)*m)*x^5 + 3*(239760*d^7*e^4 - 918000*d^6*e
^5 + 9537400*d^5*e^6 - 19929280*d^4*e^7 + 64836702*d^3*e^8 - 79518915*d^2*e^9 + 198514620*d*e^10)*m^4 + (57280
60800*e^11 + (1109*d*e^10 + 574*e^11)*m^10 - (2550*d^2*e^9 - 63213*d*e^10 - 35588*e^11)*m^9 + 6*(4995*d^3*e^8
- 21675*d^2*e^9 + 257288*d*e^10 + 160433*e^11)*m^8 + 6*(3430*d^4*e^7 + 219780*d^3*e^8 - 461550*d^2*e^9 + 35122
03*d*e^10 + 2483698*e^11)*m^7 + 15*(85680*d^5*e^6 + 49392*d^4*e^7 + 1554444*d^3*e^8 - 2122620*d^2*e^9 + 117232
39*d*e^10 + 9703470*e^11)*m^6 + 3*(126000*d^6*e^5 + 11566800*d^5*e^6 + 3361400*d^4*e^7 + 70329600*d^3*e^8 - 71
101650*d^2*e^9 + 306983399*d*e^10 + 310583364*e^11)*m^5 + 2*(37800000*d^7*e^4 + 3213000*d^6*e^5 + 158722200*d^
5*e^6 + 32104800*d^4*e^7 + 515019465*d^3*e^8 - 418887225*d^2*e^9 + 1494010421*d*e^10 + 1964946361*e^11)*m^4 +
4*(113400000*d^7*e^4 + 7276500*d^6*e^5 + 288206100*d^5*e^6 + 48409305*d^4*e^7 + 659010330*d^3*e^8 - 460978800*
d^2*e^9 + 1424518263*d*e^10 + 2670494533*e^11)*m^3 + 72*(11550000*d^7*e^4 + 666750*d^6*e^5 + 23847600*d^5*e^6
+ 3625510*d^4*e^7 + 44710245*d^3*e^8 - 28312225*d^2*e^9 + 79001833*d*e^10 + 245697543*e^11)*m^2 + 720*(630000*
d^7*e^4 + 34650*d^6*e^5 + 1178100*d^5*e^6 + 169785*d^4*e^7 + 1978020*d^3*e^8 - 1178100*d^2*e^9 + 3074148*d*e^1
0 + 22036147*e^11)*m)*x^4 + 12*(41160*d^8*e^3 + 2277720*d^7*e^4 - 4105500*d^6*e^5 + 26582730*d^5*e^6 - 3858686
3*d^4*e^7 + 91855890*d^3*e^8 - 84312180*d^2*e^9 + 157352130*d*e^10)*m^3 + (6346771200*e^11 + (574*d*e^10 + 477
*e^11)*m^10 - (4436*d^2*e^9 - 33866*d*e^10 - 30051*e^11)*m^9 + 24*(425*d^3*e^8 - 9981*d^2*e^9 + 35875*d*e^10 +
34503*e^11)*m^8 - 6*(19980*d^4*e^7 - 81600*d^3*e^8 + 909380*d^2*e^9 - 2053198*d*e^10 - 2183229*e^11)*m^7 - 3*
(27440*d^5*e^6 + 1638360*d^4*e^7 - 3202800*d^3*e^8 + 22641344*d^2*e^9 - 36198162*d*e^10 - 43730883*e^11)*m^6 -
3*(1713600*d^6*e^5 + 905520*d^5*e^6 + 26173800*d^4*e^7 - 32844000*d^3*e^8 + 166540748*d^2*e^9 - 201988878*d*e
^10 - 288179073*e^11)*m^5 - 2*(756000*d^7*e^4 + 61689600*d^6*e^5 + 16093560*d^5*e^6 + 304195500*d^4*e^7 - 2788
11900*d^3*e^8 + 1092467028*d^2*e^9 - 1055996410*d*e^10 - 1884673269*e^11)*m^4 - 4*(75600000*d^8*e^3 + 5292000*
d^7*e^4 + 224910000*d^6*e^5 + 40069260*d^5*e^6 + 573745680*d^4*e^7 - 419556600*d^3*e^8 + 1349320300*d^2*e^9 -
1086499918*d*e^10 - 2657980899*e^11)*m^3 - 24*(37800000*d^8*e^3 + 2205000*d^7*e^4 + 79682400*d^6*e^5 + 1223824
0*d^5*e^6 + 152467380*d^4*e^7 - 97540900*d^3*e^8 + 275018692*d^2*e^9 - 193842670*d*e^10 - 763013811*e^11)*m^2
- 4320*(140000*d^8*e^3 + 7700*d^7*e^4 + 261800*d^6*e^5 + 37730*d^5*e^6 + 439560*d^4*e^7 - 261800*d^3*e^8 + 683
144*d^2*e^9 - 441980*d*e^10 - 3946963*e^11)*m)*x^3 + 12*(2570400*d^9*e^2 + 1234800*d^8*e^3 + 32307660*d^7*e^4
- 36490500*d^6*e^5 + 165294232*d^5*e^6 - 177258088*d^4*e^7 + 320238402*d^3*e^8 - 224755965*d^2*e^9 + 316309212
*d*e^10)*m^2 + 3*(898128000*e^11 + 3*(53*d*e^10 + 15*e^11)*m^10 - (574*d^2*e^9 - 9699*d*e^10 - 2880*e^11)*m^9
+ (4436*d^3*e^8 - 32718*d^2*e^9 + 256626*d*e^10 + 80865*e^11)*m^8 - 2*(5100*d^4*e^7 - 115336*d^3*e^8 + 397782*
d^2*e^9 - 1926603*d*e^10 - 654210*e^11)*m^7 + (119880*d^5*e^6 - 469200*d^4*e^7 + 4994936*d^3*e^8 - 10728060*d^
2*e^9 + 36024471*d*e^10 + 13467195*e^11)*m^6 + (82320*d^6*e^5 + 4675320*d^5*e^6 - 8670000*d^4*e^7 + 57934160*d
^3*e^8 - 87138366*d^2*e^9 + 216130131*d*e^10 + 91755720*e^11)*m^5 + (5140800*d^7*e^4 + 2551920*d^6*e^5 + 69170
760*d^5*e^6 - 81192000*d^4*e^7 + 383753924*d^3*e^8 - 431689902*d^2*e^9 + 824188584*d*e^10 + 416767635*e^11)*m^
4 + 4*(378000*d^8*e^3 + 28274400*d^7*e^4 + 6770820*d^6*e^5 + 117512370*d^5*e^6 - 98809950*d^4*e^7 + 354356552*
d^3*e^8 - 312153254*d^2*e^9 + 473899341*d*e^10 + 309068145*e^11)*m^3 + 12*(25200000*d^9*e^2 + 1512000*d^8*e^3
+ 56120400*d^7*e^4 + 8842540*d^6*e^5 + 112906980*d^5*e^6 - 73978900*d^4*e^7 + 213535732*d^3*e^8 - 154064470*d^
2*e^9 + 192742980*d*e^10 + 188672355*e^11)*m^2 + 2160*(140000*d^9*e^2 + 7700*d^8*e^3 + 261800*d^7*e^4 + 37730*
d^6*e^5 + 439560*d^5*e^6 - 261800*d^4*e^7 + 683144*d^3*e^8 - 441980*d^2*e^9 + 489720*d*e^10 + 1047765*e^11)*m)
*x^2 + 144*(63000*d^10*e + 4498200*d^9*e^2 + 1025570*d^8*e^3 + 16893090*d^7*e^4 - 13427450*d^6*e^5 + 45284906*
d^5*e^6 - 37254035*d^4*e^7 + 52296690*d^3*e^8 - 28438425*d^2*e^9 + 30235140*d*e^10)*m + 3*(718502400*e^11 + 9*
(5*d*e^10 + 2*e^11)*m^10 - 3*(106*d^2*e^9 - 945*d*e^10 - 390*e^11)*m^9 + 2*(574*d^3*e^8 - 9540*d^2*e^9 + 39015
*d*e^10 + 16740*e^11)*m^8 - 2*(4436*d^4*e^7 - 32144*d^3*e^8 + 247086*d^2*e^9 - 615195*d*e^10 - 277290*e^11)*m^
7 + (20400*d^5*e^6 - 452472*d^4*e^7 + 1526840*d^3*e^8 - 7212240*d^2*e^9 + 12236805*d*e^10 + 5879034*e^11)*m^6
- (239760*d^6*e^5 - 918000*d^5*e^6 + 9537400*d^4*e^7 - 19929280*d^3*e^8 + 64836702*d^2*e^9 - 79518915*d*e^10 -
41597010*e^11)*m^5 - 4*(41160*d^7*e^4 + 2277720*d^6*e^5 - 4105500*d^5*e^6 + 26582730*d^4*e^7 - 38586863*d^3*e
^8 + 91855890*d^2*e^9 - 84312180*d*e^10 - 49628655*e^11)*m^4 - 4*(2570400*d^8*e^3 + 1234800*d^7*e^4 + 32307660
*d^6*e^5 - 36490500*d^5*e^6 + 165294232*d^4*e^7 - 177258088*d^3*e^8 + 320238402*d^2*e^9 - 224755965*d*e^10 - 1
57352130*e^11)*m^3 - 48*(63000*d^9*e^2 + 4498200*d^8*e^3 + 1025570*d^7*e^4 + 16893090*d^6*e^5 - 13427450*d^5*e
^6 + 45284906*d^4*e^7 - 37254035*d^3*e^8 + 52296690*d^2*e^9 - 28438425*d*e^10 - 26359101*e^11)*m^2 - 8640*(700
00*d^10*e + 3850*d^9*e^2 + 130900*d^8*e^3 + 18865*d^7*e^4 + 219780*d^6*e^5 - 130900*d^5*e^6 + 341572*d^4*e^7 -
220990*d^3*e^8 + 244860*d^2*e^9 - 103950*d*e^10 - 167973*e^11)*m)*x)*(e*x + d)^m/(e^11*m^11 + 66*e^11*m^10 +
1925*e^11*m^9 + 32670*e^11*m^8 + 357423*e^11*m^7 + 2637558*e^11*m^6 + 13339535*e^11*m^5 + 45995730*e^11*m^4 +
105258076*e^11*m^3 + 150917976*e^11*m^2 + 120543840*e^11*m + 39916800*e^11)

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x+d)**m*(5*x**2+2*x+3)**3*(4*x**4-5*x**3+3*x**2+x+2),x)

[Out]

Timed out

________________________________________________________________________________________

Giac [B]  time = 1.40895, size = 14796, normalized size = 25.16 \begin{align*} \text{result too large to display} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x+d)^m*(5*x^2+2*x+3)^3*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm="giac")

[Out]

(500*(x*e + d)^m*m^10*x^11*e^11 + 500*(x*e + d)^m*d*m^10*x^10*e^10 - 25*(x*e + d)^m*m^10*x^10*e^11 + 27500*(x*
e + d)^m*m^9*x^11*e^11 - 25*(x*e + d)^m*d*m^10*x^9*e^10 + 22500*(x*e + d)^m*d*m^9*x^10*e^10 - 5000*(x*e + d)^m
*d^2*m^9*x^9*e^9 + 765*(x*e + d)^m*m^10*x^9*e^11 - 1400*(x*e + d)^m*m^9*x^10*e^11 + 660000*(x*e + d)^m*m^8*x^1
1*e^11 + 765*(x*e + d)^m*d*m^10*x^8*e^10 - 1175*(x*e + d)^m*d*m^9*x^9*e^10 + 435000*(x*e + d)^m*d*m^8*x^10*e^1
0 + 225*(x*e + d)^m*d^2*m^9*x^8*e^9 - 180000*(x*e + d)^m*d^2*m^8*x^9*e^9 + 45000*(x*e + d)^m*d^3*m^8*x^8*e^8 -
98*(x*e + d)^m*m^10*x^8*e^11 + 43605*(x*e + d)^m*m^9*x^9*e^11 - 34125*(x*e + d)^m*m^8*x^10*e^11 + 9075000*(x*
e + d)^m*m^7*x^11*e^11 - 98*(x*e + d)^m*d*m^10*x^7*e^10 + 37485*(x*e + d)^m*d*m^9*x^8*e^10 - 23550*(x*e + d)^m
*d*m^8*x^9*e^10 + 4725000*(x*e + d)^m*d*m^7*x^10*e^10 - 6120*(x*e + d)^m*d^2*m^9*x^7*e^9 + 8775*(x*e + d)^m*d^
2*m^8*x^8*e^9 - 2730000*(x*e + d)^m*d^2*m^7*x^9*e^9 - 1800*(x*e + d)^m*d^3*m^8*x^7*e^8 + 1260000*(x*e + d)^m*d
^3*m^7*x^8*e^8 - 360000*(x*e + d)^m*d^4*m^7*x^7*e^7 + 999*(x*e + d)^m*m^10*x^7*e^11 - 5684*(x*e + d)^m*m^9*x^8
*e^11 + 1080180*(x*e + d)^m*m^8*x^9*e^11 - 475500*(x*e + d)^m*m^7*x^10*e^11 + 78886500*(x*e + d)^m*m^6*x^11*e^
11 + 999*(x*e + d)^m*d*m^10*x^6*e^10 - 4998*(x*e + d)^m*d*m^9*x^7*e^10 + 780300*(x*e + d)^m*d*m^8*x^8*e^10 - 2
63550*(x*e + d)^m*d*m^7*x^9*e^10 + 31636500*(x*e + d)^m*d*m^6*x^10*e^10 + 686*(x*e + d)^m*d^2*m^9*x^6*e^9 - 25
7040*(x*e + d)^m*d^2*m^8*x^7*e^9 + 141750*(x*e + d)^m*d^2*m^7*x^8*e^9 - 22680000*(x*e + d)^m*d^2*m^6*x^9*e^9 +
42840*(x*e + d)^m*d^3*m^8*x^6*e^8 - 57600*(x*e + d)^m*d^3*m^7*x^7*e^8 + 14490000*(x*e + d)^m*d^3*m^6*x^8*e^8
+ 12600*(x*e + d)^m*d^4*m^7*x^6*e^7 - 7560000*(x*e + d)^m*d^4*m^6*x^7*e^7 + 2520000*(x*e + d)^m*d^5*m^6*x^6*e^
6 + 510*(x*e + d)^m*m^10*x^6*e^11 + 58941*(x*e + d)^m*m^9*x^7*e^11 - 143178*(x*e + d)^m*m^8*x^8*e^11 + 1527093
0*(x*e + d)^m*m^7*x^9*e^11 - 4180575*(x*e + d)^m*m^6*x^10*e^11 + 451027500*(x*e + d)^m*m^5*x^11*e^11 + 510*(x*
e + d)^m*d*m^10*x^5*e^10 + 52947*(x*e + d)^m*d*m^9*x^6*e^10 - 108192*(x*e + d)^m*d*m^8*x^7*e^10 + 9028530*(x*e
+ d)^m*d*m^7*x^8*e^10 - 1808625*(x*e + d)^m*d*m^6*x^9*e^10 + 134662500*(x*e + d)^m*d*m^5*x^10*e^10 - 5994*(x*
e + d)^m*d^2*m^9*x^5*e^9 + 30870*(x*e + d)^m*d^2*m^8*x^6*e^9 - 4443120*(x*e + d)^m*d^2*m^7*x^7*e^9 + 1237950*(
x*e + d)^m*d^2*m^6*x^8*e^9 - 112245000*(x*e + d)^m*d^2*m^5*x^9*e^9 - 4116*(x*e + d)^m*d^3*m^8*x^5*e^8 + 154224
0*(x*e + d)^m*d^3*m^7*x^6*e^8 - 730800*(x*e + d)^m*d^3*m^6*x^7*e^8 + 88200000*(x*e + d)^m*d^3*m^5*x^8*e^8 - 25
7040*(x*e + d)^m*d^4*m^7*x^5*e^7 + 327600*(x*e + d)^m*d^4*m^6*x^6*e^7 - 63000000*(x*e + d)^m*d^4*m^5*x^7*e^7 -
75600*(x*e + d)^m*d^5*m^6*x^5*e^6 + 37800000*(x*e + d)^m*d^5*m^5*x^6*e^6 - 15120000*(x*e + d)^m*d^6*m^5*x^5*e
^5 + 1109*(x*e + d)^m*m^10*x^5*e^11 + 30600*(x*e + d)^m*m^9*x^6*e^11 + 1510488*(x*e + d)^m*m^8*x^7*e^11 - 2056
236*(x*e + d)^m*m^7*x^8*e^11 + 135990225*(x*e + d)^m*m^6*x^9*e^11 - 24133200*(x*e + d)^m*m^5*x^10*e^11 + 17084
65000*(x*e + d)^m*m^4*x^11*e^11 + 1109*(x*e + d)^m*d*m^10*x^4*e^10 + 28050*(x*e + d)^m*d*m^9*x^5*e^10 + 119280
6*(x*e + d)^m*d*m^8*x^6*e^10 - 1298892*(x*e + d)^m*d*m^7*x^7*e^10 + 63761985*(x*e + d)^m*d*m^6*x^8*e^10 - 7855
575*(x*e + d)^m*d*m^5*x^9*e^10 + 361840000*(x*e + d)^m*d*m^4*x^10*e^10 - 2550*(x*e + d)^m*d^2*m^9*x^4*e^9 - 28
7712*(x*e + d)^m*d^2*m^8*x^5*e^9 + 572124*(x*e + d)^m*d^2*m^7*x^6*e^9 - 41126400*(x*e + d)^m*d^2*m^6*x^7*e^9 +
6374025*(x*e + d)^m*d^2*m^5*x^8*e^9 - 336420000*(x*e + d)^m*d^2*m^4*x^9*e^9 + 29970*(x*e + d)^m*d^3*m^8*x^4*e
^8 - 164640*(x*e + d)^m*d^3*m^7*x^5*e^8 + 21848400*(x*e + d)^m*d^3*m^6*x^6*e^8 - 4788000*(x*e + d)^m*d^3*m^5*x
^7*e^8 + 304605000*(x*e + d)^m*d^3*m^4*x^8*e^8 + 20580*(x*e + d)^m*d^4*m^7*x^4*e^7 - 7968240*(x*e + d)^m*d^4*m
^6*x^5*e^7 + 3150000*(x*e + d)^m*d^4*m^5*x^6*e^7 - 264600000*(x*e + d)^m*d^4*m^4*x^7*e^7 + 1285200*(x*e + d)^m
*d^5*m^6*x^4*e^6 - 1587600*(x*e + d)^m*d^5*m^5*x^5*e^6 + 214200000*(x*e + d)^m*d^5*m^4*x^6*e^6 + 378000*(x*e +
d)^m*d^6*m^5*x^4*e^5 - 151200000*(x*e + d)^m*d^6*m^4*x^5*e^5 + 75600000*(x*e + d)^m*d^7*m^4*x^4*e^4 + 574*(x*
e + d)^m*m^10*x^4*e^11 + 67649*(x*e + d)^m*m^9*x^5*e^11 + 798150*(x*e + d)^m*m^8*x^6*e^11 + 22063914*(x*e + d)
^m*m^7*x^7*e^11 - 18577566*(x*e + d)^m*m^6*x^8*e^11 + 793819845*(x*e + d)^m*m^5*x^9*e^11 - 92156375*(x*e + d)^
m*m^4*x^10*e^11 + 4204750000*(x*e + d)^m*m^3*x^11*e^11 + 574*(x*e + d)^m*d*m^10*x^3*e^10 + 63213*(x*e + d)^m*d
*m^9*x^4*e^10 + 657900*(x*e + d)^m*d*m^8*x^5*e^10 + 14907078*(x*e + d)^m*d*m^7*x^6*e^10 - 9485322*(x*e + d)^m*
d*m^6*x^7*e^10 + 283723965*(x*e + d)^m*d*m^5*x^8*e^10 - 21456200*(x*e + d)^m*d*m^4*x^9*e^10 + 586350000*(x*e +
d)^m*d*m^3*x^10*e^10 - 4436*(x*e + d)^m*d^2*m^9*x^3*e^9 - 130050*(x*e + d)^m*d^2*m^8*x^4*e^9 - 5718276*(x*e +
d)^m*d^2*m^7*x^5*e^9 + 5659500*(x*e + d)^m*d^2*m^6*x^6*e^9 - 222211080*(x*e + d)^m*d^2*m^5*x^7*e^9 + 19707975
*(x*e + d)^m*d^2*m^4*x^8*e^9 - 590620000*(x*e + d)^m*d^2*m^3*x^9*e^9 + 10200*(x*e + d)^m*d^3*m^8*x^3*e^8 + 131
8680*(x*e + d)^m*d^3*m^7*x^4*e^8 - 2609544*(x*e + d)^m*d^3*m^6*x^5*e^8 + 156794400*(x*e + d)^m*d^3*m^5*x^6*e^8
- 17476200*(x*e + d)^m*d^3*m^4*x^7*e^8 + 590940000*(x*e + d)^m*d^3*m^3*x^8*e^8 - 119880*(x*e + d)^m*d^4*m^7*x
^3*e^7 + 740880*(x*e + d)^m*d^4*m^6*x^4*e^7 - 91249200*(x*e + d)^m*d^4*m^5*x^5*e^7 + 14616000*(x*e + d)^m*d^4*
m^4*x^6*e^7 - 584640000*(x*e + d)^m*d^4*m^3*x^7*e^7 - 82320*(x*e + d)^m*d^5*m^6*x^3*e^6 + 34700400*(x*e + d)^m
*d^5*m^5*x^4*e^6 - 10962000*(x*e + d)^m*d^5*m^4*x^5*e^6 + 567000000*(x*e + d)^m*d^5*m^3*x^6*e^6 - 5140800*(x*e
+ d)^m*d^6*m^5*x^3*e^5 + 6426000*(x*e + d)^m*d^6*m^4*x^4*e^5 - 529200000*(x*e + d)^m*d^6*m^3*x^5*e^5 - 151200
0*(x*e + d)^m*d^7*m^4*x^3*e^4 + 453600000*(x*e + d)^m*d^7*m^3*x^4*e^4 - 302400000*(x*e + d)^m*d^8*m^3*x^3*e^3
+ 477*(x*e + d)^m*m^10*x^3*e^11 + 35588*(x*e + d)^m*m^9*x^4*e^11 + 1796580*(x*e + d)^m*m^8*x^5*e^11 + 11872800
*(x*e + d)^m*m^7*x^6*e^11 + 202618179*(x*e + d)^m*m^6*x^7*e^11 - 109860156*(x*e + d)^m*m^5*x^8*e^11 + 30603656
70*(x*e + d)^m*m^4*x^9*e^11 - 228329500*(x*e + d)^m*m^3*x^10*e^11 + 6376788000*(x*e + d)^m*m^2*x^11*e^11 + 477
*(x*e + d)^m*d*m^10*x^2*e^10 + 33866*(x*e + d)^m*d*m^9*x^3*e^10 + 1543728*(x*e + d)^m*d*m^8*x^4*e^10 + 8583300
*(x*e + d)^m*d*m^7*x^5*e^10 + 113175711*(x*e + d)^m*d*m^6*x^6*e^10 - 43462902*(x*e + d)^m*d*m^5*x^7*e^10 + 790
573950*(x*e + d)^m*d*m^4*x^8*e^10 - 35223700*(x*e + d)^m*d*m^3*x^9*e^10 + 513288000*(x*e + d)^m*d*m^2*x^10*e^1
0 - 1722*(x*e + d)^m*d^2*m^9*x^2*e^9 - 239544*(x*e + d)^m*d^2*m^8*x^3*e^9 - 2769300*(x*e + d)^m*d^2*m^7*x^4*e^
9 - 60851088*(x*e + d)^m*d^2*m^6*x^5*e^9 + 32440254*(x*e + d)^m*d^2*m^5*x^6*e^9 - 714314160*(x*e + d)^m*d^2*m^
4*x^7*e^9 + 35442000*(x*e + d)^m*d^2*m^3*x^8*e^9 - 547920000*(x*e + d)^m*d^2*m^2*x^9*e^9 + 13308*(x*e + d)^m*d
^3*m^8*x^2*e^8 + 489600*(x*e + d)^m*d^3*m^7*x^3*e^8 + 23316660*(x*e + d)^m*d^3*m^6*x^4*e^8 - 20909280*(x*e + d
)^m*d^3*m^5*x^5*e^8 + 614711160*(x*e + d)^m*d^3*m^4*x^6*e^8 - 35330400*(x*e + d)^m*d^3*m^3*x^7*e^8 + 588060000
*(x*e + d)^m*d^3*m^2*x^8*e^8 - 30600*(x*e + d)^m*d^4*m^7*x^2*e^7 - 4915080*(x*e + d)^m*d^4*m^6*x^3*e^7 + 10084
200*(x*e + d)^m*d^4*m^5*x^4*e^7 - 484520400*(x*e + d)^m*d^4*m^4*x^5*e^7 + 34637400*(x*e + d)^m*d^4*m^3*x^6*e^7
- 635040000*(x*e + d)^m*d^4*m^2*x^7*e^7 + 359640*(x*e + d)^m*d^5*m^6*x^2*e^6 - 2716560*(x*e + d)^m*d^5*m^5*x^
3*e^6 + 317444400*(x*e + d)^m*d^5*m^4*x^4*e^6 - 32886000*(x*e + d)^m*d^5*m^3*x^5*e^6 + 690480000*(x*e + d)^m*d
^5*m^2*x^6*e^6 + 246960*(x*e + d)^m*d^6*m^5*x^2*e^5 - 123379200*(x*e + d)^m*d^6*m^4*x^3*e^5 + 29106000*(x*e +
d)^m*d^6*m^3*x^4*e^5 - 756000000*(x*e + d)^m*d^6*m^2*x^5*e^5 + 15422400*(x*e + d)^m*d^7*m^4*x^2*e^4 - 21168000
*(x*e + d)^m*d^7*m^3*x^3*e^4 + 831600000*(x*e + d)^m*d^7*m^2*x^4*e^4 + 4536000*(x*e + d)^m*d^8*m^3*x^2*e^3 - 9
07200000*(x*e + d)^m*d^8*m^2*x^3*e^3 + 907200000*(x*e + d)^m*d^9*m^2*x^2*e^2 + 135*(x*e + d)^m*m^10*x^2*e^11 +
30051*(x*e + d)^m*m^9*x^3*e^11 + 962598*(x*e + d)^m*m^8*x^4*e^11 + 27248130*(x*e + d)^m*m^7*x^5*e^11 + 111048
930*(x*e + d)^m*m^6*x^6*e^11 + 1216593189*(x*e + d)^m*m^5*x^7*e^11 - 428393182*(x*e + d)^m*m^4*x^8*e^11 + 7643
442420*(x*e + d)^m*m^3*x^9*e^11 - 348156900*(x*e + d)^m*m^2*x^10*e^11 + 5314320000*(x*e + d)^m*m*x^11*e^11 + 1
35*(x*e + d)^m*d*m^10*x*e^10 + 29097*(x*e + d)^m*d*m^9*x^2*e^10 + 861000*(x*e + d)^m*d*m^8*x^3*e^10 + 21073218
*(x*e + d)^m*d*m^7*x^4*e^10 + 68132430*(x*e + d)^m*d*m^6*x^5*e^10 + 537538923*(x*e + d)^m*d*m^5*x^6*e^10 - 124
152868*(x*e + d)^m*d*m^4*x^7*e^10 + 1318850820*(x*e + d)^m*d*m^3*x^8*e^10 - 31143600*(x*e + d)^m*d*m^2*x^9*e^1
0 + 181440000*(x*e + d)^m*d*m*x^10*e^10 - 954*(x*e + d)^m*d^2*m^9*x*e^9 - 98154*(x*e + d)^m*d^2*m^8*x^2*e^9 -
5456280*(x*e + d)^m*d^2*m^7*x^3*e^9 - 31839300*(x*e + d)^m*d^2*m^6*x^4*e^9 - 374798826*(x*e + d)^m*d^2*m^5*x^5
*e^9 + 109598790*(x*e + d)^m*d^2*m^4*x^6*e^9 - 1324392480*(x*e + d)^m*d^2*m^3*x^7*e^9 + 33477300*(x*e + d)^m*d
^2*m^2*x^8*e^9 - 201600000*(x*e + d)^m*d^2*m*x^9*e^9 + 3444*(x*e + d)^m*d^3*m^8*x*e^8 + 692016*(x*e + d)^m*d^3
*m^7*x^2*e^8 + 9608400*(x*e + d)^m*d^3*m^6*x^3*e^8 + 210988800*(x*e + d)^m*d^3*m^5*x^4*e^8 - 90095124*(x*e + d
)^m*d^3*m^4*x^5*e^8 + 1311932160*(x*e + d)^m*d^3*m^3*x^6*e^8 - 36223200*(x*e + d)^m*d^3*m^2*x^7*e^8 + 22680000
0*(x*e + d)^m*d^3*m*x^8*e^8 - 26616*(x*e + d)^m*d^4*m^7*x*e^7 - 1407600*(x*e + d)^m*d^4*m^6*x^2*e^7 - 78521400
*(x*e + d)^m*d^4*m^5*x^3*e^7 + 64209600*(x*e + d)^m*d^4*m^4*x^4*e^7 - 1265664960*(x*e + d)^m*d^4*m^3*x^5*e^7 +
39488400*(x*e + d)^m*d^4*m^2*x^6*e^7 - 259200000*(x*e + d)^m*d^4*m*x^7*e^7 + 61200*(x*e + d)^m*d^5*m^6*x*e^6
+ 14025960*(x*e + d)^m*d^5*m^5*x^2*e^6 - 32187120*(x*e + d)^m*d^5*m^4*x^3*e^6 + 1152824400*(x*e + d)^m*d^5*m^3
*x^4*e^6 - 43394400*(x*e + d)^m*d^5*m^2*x^5*e^6 + 302400000*(x*e + d)^m*d^5*m*x^6*e^6 - 719280*(x*e + d)^m*d^6
*m^5*x*e^5 + 7655760*(x*e + d)^m*d^6*m^4*x^2*e^5 - 899640000*(x*e + d)^m*d^6*m^3*x^3*e^5 + 48006000*(x*e + d)^
m*d^6*m^2*x^4*e^5 - 362880000*(x*e + d)^m*d^6*m*x^5*e^5 - 493920*(x*e + d)^m*d^7*m^4*x*e^4 + 339292800*(x*e +
d)^m*d^7*m^3*x^2*e^4 - 52920000*(x*e + d)^m*d^7*m^2*x^3*e^4 + 453600000*(x*e + d)^m*d^7*m*x^4*e^4 - 30844800*(
x*e + d)^m*d^8*m^3*x*e^3 + 54432000*(x*e + d)^m*d^8*m^2*x^2*e^3 - 604800000*(x*e + d)^m*d^8*m*x^3*e^3 - 907200
0*(x*e + d)^m*d^9*m^2*x*e^2 + 907200000*(x*e + d)^m*d^9*m*x^2*e^2 - 1814400000*(x*e + d)^m*d^10*m*x*e + 54*(x*
e + d)^m*m^10*x*e^11 + 8640*(x*e + d)^m*m^9*x^2*e^11 + 828072*(x*e + d)^m*m^8*x^3*e^11 + 14902188*(x*e + d)^m*
m^7*x^4*e^11 + 260141457*(x*e + d)^m*m^6*x^5*e^11 + 678861000*(x*e + d)^m*m^5*x^6*e^11 + 4810043142*(x*e + d)^
m*m^4*x^7*e^11 - 1080436084*(x*e + d)^m*m^3*x^8*e^11 + 11731446360*(x*e + d)^m*m^2*x^9*e^11 - 291380400*(x*e +
d)^m*m*x^10*e^11 + 1814400000*(x*e + d)^m*x^11*e^11 + 54*(x*e + d)^m*d*m^10*e^10 + 8505*(x*e + d)^m*d*m^9*x*e
^10 + 769878*(x*e + d)^m*d*m^8*x^2*e^10 + 12319188*(x*e + d)^m*d*m^7*x^3*e^10 + 175848585*(x*e + d)^m*d*m^6*x^
4*e^10 + 338198850*(x*e + d)^m*d*m^5*x^5*e^10 + 1584809604*(x*e + d)^m*d*m^4*x^6*e^10 - 211366008*(x*e + d)^m*
d*m^3*x^7*e^10 + 1180639800*(x*e + d)^m*d*m^2*x^8*e^10 - 11088000*(x*e + d)^m*d*m*x^9*e^10 - 135*(x*e + d)^m*d
^2*m^9*e^9 - 57240*(x*e + d)^m*d^2*m^8*x*e^9 - 2386692*(x*e + d)^m*d^2*m^7*x^2*e^9 - 67924032*(x*e + d)^m*d^2*
m^6*x^3*e^9 - 213304950*(x*e + d)^m*d^2*m^5*x^4*e^9 - 1351239408*(x*e + d)^m*d^2*m^4*x^5*e^9 + 211477336*(x*e
+ d)^m*d^2*m^3*x^6*e^9 - 1280059200*(x*e + d)^m*d^2*m^2*x^7*e^9 + 12474000*(x*e + d)^m*d^2*m*x^8*e^9 + 954*(x*
e + d)^m*d^3*m^8*e^8 + 192864*(x*e + d)^m*d^3*m^7*x*e^8 + 14984808*(x*e + d)^m*d^3*m^6*x^2*e^8 + 98532000*(x*e
+ d)^m*d^3*m^5*x^3*e^8 + 1030038930*(x*e + d)^m*d^3*m^4*x^4*e^8 - 207117120*(x*e + d)^m*d^3*m^3*x^5*e^8 + 139
9154400*(x*e + d)^m*d^3*m^2*x^6*e^8 - 14256000*(x*e + d)^m*d^3*m*x^7*e^8 - 3444*(x*e + d)^m*d^4*m^7*e^7 - 1357
416*(x*e + d)^m*d^4*m^6*x*e^7 - 26010000*(x*e + d)^m*d^4*m^5*x^2*e^7 - 608391000*(x*e + d)^m*d^4*m^4*x^3*e^7 +
193637220*(x*e + d)^m*d^4*m^3*x^4*e^7 - 1543268160*(x*e + d)^m*d^4*m^2*x^5*e^7 + 16632000*(x*e + d)^m*d^4*m*x
^6*e^7 + 26616*(x*e + d)^m*d^5*m^6*e^6 + 2754000*(x*e + d)^m*d^5*m^5*x*e^6 + 207512280*(x*e + d)^m*d^5*m^4*x^2
*e^6 - 160277040*(x*e + d)^m*d^5*m^3*x^3*e^6 + 1717027200*(x*e + d)^m*d^5*m^2*x^4*e^6 - 19958400*(x*e + d)^m*d
^5*m*x^5*e^6 - 61200*(x*e + d)^m*d^6*m^5*e^5 - 27332640*(x*e + d)^m*d^6*m^4*x*e^5 + 81249840*(x*e + d)^m*d^6*m
^3*x^2*e^5 - 1912377600*(x*e + d)^m*d^6*m^2*x^3*e^5 + 24948000*(x*e + d)^m*d^6*m*x^4*e^5 + 719280*(x*e + d)^m*
d^7*m^4*e^4 - 14817600*(x*e + d)^m*d^7*m^3*x*e^4 + 2020334400*(x*e + d)^m*d^7*m^2*x^2*e^4 - 33264000*(x*e + d)
^m*d^7*m*x^3*e^4 + 493920*(x*e + d)^m*d^8*m^3*e^3 - 647740800*(x*e + d)^m*d^8*m^2*x*e^3 + 49896000*(x*e + d)^m
*d^8*m*x^2*e^3 + 30844800*(x*e + d)^m*d^9*m^2*e^2 - 99792000*(x*e + d)^m*d^9*m*x*e^2 + 9072000*(x*e + d)^m*d^1
0*m*e + 1814400000*(x*e + d)^m*d^11 + 3510*(x*e + d)^m*m^9*x*e^11 + 242595*(x*e + d)^m*m^8*x^2*e^11 + 13099374
*(x*e + d)^m*m^7*x^3*e^11 + 145552050*(x*e + d)^m*m^6*x^4*e^11 + 1624344537*(x*e + d)^m*m^5*x^5*e^11 + 2729996
850*(x*e + d)^m*m^4*x^6*e^11 + 12279432276*(x*e + d)^m*m^3*x^7*e^11 - 1671802776*(x*e + d)^m*m^2*x^8*e^11 + 98
69234400*(x*e + d)^m*m*x^9*e^11 - 99792000*(x*e + d)^m*x^10*e^11 + 3510*(x*e + d)^m*d*m^9*e^10 + 234090*(x*e +
d)^m*d*m^8*x*e^10 + 11559618*(x*e + d)^m*d*m^7*x^2*e^10 + 108594486*(x*e + d)^m*d*m^6*x^3*e^10 + 920950197*(x
*e + d)^m*d*m^5*x^4*e^10 + 1039002600*(x*e + d)^m*d*m^4*x^5*e^10 + 2770574652*(x*e + d)^m*d*m^3*x^6*e^10 - 192
240720*(x*e + d)^m*d*m^2*x^7*e^10 + 424116000*(x*e + d)^m*d*m*x^8*e^10 - 8505*(x*e + d)^m*d^2*m^8*e^9 - 148251
6*(x*e + d)^m*d^2*m^7*x*e^9 - 32184180*(x*e + d)^m*d^2*m^6*x^2*e^9 - 499622244*(x*e + d)^m*d^2*m^5*x^3*e^9 - 8
37774450*(x*e + d)^m*d^2*m^4*x^4*e^9 - 2752660584*(x*e + d)^m*d^2*m^3*x^5*e^9 + 210698040*(x*e + d)^m*d^2*m^2*
x^6*e^9 - 484704000*(x*e + d)^m*d^2*m*x^7*e^9 + 57240*(x*e + d)^m*d^3*m^7*e^8 + 4580520*(x*e + d)^m*d^3*m^6*x*
e^8 + 173802480*(x*e + d)^m*d^3*m^5*x^2*e^8 + 557623800*(x*e + d)^m*d^3*m^4*x^3*e^8 + 2636041320*(x*e + d)^m*d
^3*m^3*x^4*e^8 - 233278416*(x*e + d)^m*d^3*m^2*x^5*e^8 + 565488000*(x*e + d)^m*d^3*m*x^6*e^8 - 192864*(x*e + d
)^m*d^4*m^6*e^7 - 28612200*(x*e + d)^m*d^4*m^5*x*e^7 - 243576000*(x*e + d)^m*d^4*m^4*x^2*e^7 - 2294982720*(x*e
+ d)^m*d^4*m^3*x^3*e^7 + 261036720*(x*e + d)^m*d^4*m^2*x^4*e^7 - 678585600*(x*e + d)^m*d^4*m*x^5*e^7 + 135741
6*(x*e + d)^m*d^5*m^5*e^6 + 49266000*(x*e + d)^m*d^5*m^4*x*e^6 + 1410148440*(x*e + d)^m*d^5*m^3*x^2*e^6 - 2937
17760*(x*e + d)^m*d^5*m^2*x^3*e^6 + 848232000*(x*e + d)^m*d^5*m*x^4*e^6 - 2754000*(x*e + d)^m*d^6*m^4*e^5 - 38
7691920*(x*e + d)^m*d^6*m^3*x*e^5 + 318331440*(x*e + d)^m*d^6*m^2*x^2*e^5 - 1130976000*(x*e + d)^m*d^6*m*x^3*e
^5 + 27332640*(x*e + d)^m*d^7*m^3*e^4 - 147682080*(x*e + d)^m*d^7*m^2*x*e^4 + 1696464000*(x*e + d)^m*d^7*m*x^2
*e^4 + 14817600*(x*e + d)^m*d^8*m^2*e^3 - 3392928000*(x*e + d)^m*d^8*m*x*e^3 + 647740800*(x*e + d)^m*d^9*m*e^2
+ 99792000*(x*e + d)^m*d^10*e + 100440*(x*e + d)^m*m^8*x*e^11 + 3925260*(x*e + d)^m*m^7*x^2*e^11 + 131192649*
(x*e + d)^m*m^6*x^3*e^11 + 931750092*(x*e + d)^m*m^5*x^4*e^11 + 6671821630*(x*e + d)^m*m^4*x^5*e^11 + 70778412
00*(x*e + d)^m*m^3*x^6*e^11 + 19196791992*(x*e + d)^m*m^2*x^7*e^11 - 1415539440*(x*e + d)^m*m*x^8*e^11 + 33929
28000*(x*e + d)^m*x^9*e^11 + 100440*(x*e + d)^m*d*m^8*e^10 + 3691170*(x*e + d)^m*d*m^7*x*e^10 + 108073413*(x*e
+ d)^m*d*m^6*x^2*e^10 + 605966634*(x*e + d)^m*d*m^5*x^3*e^10 + 2988020842*(x*e + d)^m*d*m^4*x^4*e^10 + 188282
8200*(x*e + d)^m*d*m^3*x^5*e^10 + 2573344080*(x*e + d)^m*d*m^2*x^6*e^10 - 69854400*(x*e + d)^m*d*m*x^7*e^10 -
234090*(x*e + d)^m*d^2*m^7*e^9 - 21636720*(x*e + d)^m*d^2*m^6*x*e^9 - 261415098*(x*e + d)^m*d^2*m^5*x^2*e^9 -
2184934056*(x*e + d)^m*d^2*m^4*x^3*e^9 - 1843915200*(x*e + d)^m*d^2*m^3*x^4*e^9 - 2860144992*(x*e + d)^m*d^2*m
^2*x^5*e^9 + 81496800*(x*e + d)^m*d^2*m*x^6*e^9 + 1482516*(x*e + d)^m*d^3*m^6*e^8 + 59787840*(x*e + d)^m*d^3*m
^5*x*e^8 + 1151261772*(x*e + d)^m*d^3*m^4*x^2*e^8 + 1678226400*(x*e + d)^m*d^3*m^3*x^3*e^8 + 3219137640*(x*e +
d)^m*d^3*m^2*x^4*e^8 - 97796160*(x*e + d)^m*d^3*m*x^5*e^8 - 4580520*(x*e + d)^m*d^4*m^5*e^7 - 318992760*(x*e
+ d)^m*d^4*m^4*x*e^7 - 1185719400*(x*e + d)^m*d^4*m^3*x^2*e^7 - 3659217120*(x*e + d)^m*d^4*m^2*x^3*e^7 + 12224
5200*(x*e + d)^m*d^4*m*x^4*e^7 + 28612200*(x*e + d)^m*d^5*m^4*e^6 + 437886000*(x*e + d)^m*d^5*m^3*x*e^6 + 4064
651280*(x*e + d)^m*d^5*m^2*x^2*e^6 - 162993600*(x*e + d)^m*d^5*m*x^3*e^6 - 49266000*(x*e + d)^m*d^6*m^3*e^5 -
2432604960*(x*e + d)^m*d^6*m^2*x*e^5 + 244490400*(x*e + d)^m*d^6*m*x^2*e^5 + 387691920*(x*e + d)^m*d^7*m^2*e^4
- 488980800*(x*e + d)^m*d^7*m*x*e^4 + 147682080*(x*e + d)^m*d^8*m*e^3 + 3392928000*(x*e + d)^m*d^9*e^2 + 1663
740*(x*e + d)^m*m^7*x*e^11 + 40401585*(x*e + d)^m*m^6*x^2*e^11 + 864537219*(x*e + d)^m*m^5*x^3*e^11 + 39298927
22*(x*e + d)^m*m^4*x^4*e^11 + 17650156420*(x*e + d)^m*m^3*x^5*e^11 + 11214571560*(x*e + d)^m*m^2*x^6*e^11 + 16
389514080*(x*e + d)^m*m*x^7*e^11 - 488980800*(x*e + d)^m*x^8*e^11 + 1663740*(x*e + d)^m*d*m^7*e^10 + 36710415*
(x*e + d)^m*d*m^6*x*e^10 + 648390393*(x*e + d)^m*d*m^5*x^2*e^10 + 2111992820*(x*e + d)^m*d*m^4*x^3*e^10 + 5698
073052*(x*e + d)^m*d*m^3*x^4*e^10 + 1800430560*(x*e + d)^m*d*m^2*x^5*e^10 + 949449600*(x*e + d)^m*d*m*x^6*e^10
- 3691170*(x*e + d)^m*d^2*m^6*e^9 - 194510106*(x*e + d)^m*d^2*m^5*x*e^9 - 1295069706*(x*e + d)^m*d^2*m^4*x^2*
e^9 - 5397281200*(x*e + d)^m*d^2*m^3*x^3*e^9 - 2038480200*(x*e + d)^m*d^2*m^2*x^4*e^9 - 1139339520*(x*e + d)^m
*d^2*m*x^5*e^9 + 21636720*(x*e + d)^m*d^3*m^5*e^8 + 463042356*(x*e + d)^m*d^3*m^4*x*e^8 + 4252278624*(x*e + d)
^m*d^3*m^3*x^2*e^8 + 2340981600*(x*e + d)^m*d^3*m^2*x^3*e^8 + 1424174400*(x*e + d)^m*d^3*m*x^4*e^8 - 59787840*
(x*e + d)^m*d^4*m^4*e^7 - 1983530784*(x*e + d)^m*d^4*m^3*x*e^7 - 2663240400*(x*e + d)^m*d^4*m^2*x^2*e^7 - 1898
899200*(x*e + d)^m*d^4*m*x^3*e^7 + 318992760*(x*e + d)^m*d^5*m^3*e^6 + 1933552800*(x*e + d)^m*d^5*m^2*x*e^6 +
2848348800*(x*e + d)^m*d^5*m*x^2*e^6 - 437886000*(x*e + d)^m*d^6*m^2*e^5 - 5696697600*(x*e + d)^m*d^6*m*x*e^5
+ 2432604960*(x*e + d)^m*d^7*m*e^4 + 488980800*(x*e + d)^m*d^8*e^3 + 17637102*(x*e + d)^m*m^6*x*e^11 + 2752671
60*(x*e + d)^m*m^5*x^2*e^11 + 3769346538*(x*e + d)^m*m^4*x^3*e^11 + 10681978132*(x*e + d)^m*m^3*x^4*e^11 + 284
80424184*(x*e + d)^m*m^2*x^5*e^11 + 9680738400*(x*e + d)^m*m*x^6*e^11 + 5696697600*(x*e + d)^m*x^7*e^11 + 1763
7102*(x*e + d)^m*d*m^6*e^10 + 238556745*(x*e + d)^m*d*m^5*x*e^10 + 2472565752*(x*e + d)^m*d*m^4*x^2*e^10 + 434
5999672*(x*e + d)^m*d*m^3*x^3*e^10 + 5688131976*(x*e + d)^m*d*m^2*x^4*e^10 + 678585600*(x*e + d)^m*d*m*x^5*e^1
0 - 36710415*(x*e + d)^m*d^2*m^5*e^9 - 1102270680*(x*e + d)^m*d^2*m^4*x*e^9 - 3745839048*(x*e + d)^m*d^2*m^3*x
^2*e^9 - 6600448608*(x*e + d)^m*d^2*m^2*x^3*e^9 - 848232000*(x*e + d)^m*d^2*m*x^4*e^9 + 194510106*(x*e + d)^m*
d^3*m^4*e^8 + 2127097056*(x*e + d)^m*d^3*m^3*x*e^8 + 7687286352*(x*e + d)^m*d^3*m^2*x^2*e^8 + 1130976000*(x*e
+ d)^m*d^3*m*x^3*e^8 - 463042356*(x*e + d)^m*d^4*m^3*e^7 - 6521026464*(x*e + d)^m*d^4*m^2*x*e^7 - 1696464000*(
x*e + d)^m*d^4*m*x^2*e^7 + 1983530784*(x*e + d)^m*d^5*m^2*e^6 + 3392928000*(x*e + d)^m*d^5*m*x*e^6 - 193355280
0*(x*e + d)^m*d^6*m*e^5 + 5696697600*(x*e + d)^m*d^7*e^4 + 124791030*(x*e + d)^m*m^5*x*e^11 + 1250302905*(x*e
+ d)^m*m^4*x^2*e^11 + 10631923596*(x*e + d)^m*m^3*x^3*e^11 + 17690223096*(x*e + d)^m*m^2*x^4*e^11 + 2496591446
4*(x*e + d)^m*m*x^5*e^11 + 3392928000*(x*e + d)^m*x^6*e^11 + 124791030*(x*e + d)^m*d*m^5*e^10 + 1011746160*(x*
e + d)^m*d*m^4*x*e^10 + 5686792092*(x*e + d)^m*d*m^3*x^2*e^10 + 4652224080*(x*e + d)^m*d*m^2*x^3*e^10 + 221338
6560*(x*e + d)^m*d*m*x^4*e^10 - 238556745*(x*e + d)^m*d^2*m^4*e^9 - 3842860824*(x*e + d)^m*d^2*m^3*x*e^9 - 554
6320920*(x*e + d)^m*d^2*m^2*x^2*e^9 - 2951182080*(x*e + d)^m*d^2*m*x^3*e^9 + 1102270680*(x*e + d)^m*d^3*m^3*e^
8 + 5364581040*(x*e + d)^m*d^3*m^2*x*e^8 + 4426773120*(x*e + d)^m*d^3*m*x^2*e^8 - 2127097056*(x*e + d)^m*d^4*m
^2*e^7 - 8853546240*(x*e + d)^m*d^4*m*x*e^7 + 6521026464*(x*e + d)^m*d^5*m*e^6 - 3392928000*(x*e + d)^m*d^6*e^
5 + 595543860*(x*e + d)^m*m^4*x*e^11 + 3708817740*(x*e + d)^m*m^3*x^2*e^11 + 18312331464*(x*e + d)^m*m^2*x^3*e
^11 + 15866025840*(x*e + d)^m*m*x^4*e^11 + 8853546240*(x*e + d)^m*x^5*e^11 + 595543860*(x*e + d)^m*d*m^4*e^10
+ 2697071580*(x*e + d)^m*d*m^3*x*e^10 + 6938747280*(x*e + d)^m*d*m^2*x^2*e^10 + 1909353600*(x*e + d)^m*d*m*x^3
*e^10 - 1011746160*(x*e + d)^m*d^2*m^3*e^9 - 7530723360*(x*e + d)^m*d^2*m^2*x*e^9 - 2864030400*(x*e + d)^m*d^2
*m*x^2*e^9 + 3842860824*(x*e + d)^m*d^3*m^2*e^8 + 5728060800*(x*e + d)^m*d^3*m*x*e^8 - 5364581040*(x*e + d)^m*
d^4*m*e^7 + 8853546240*(x*e + d)^m*d^5*e^6 + 1888225560*(x*e + d)^m*m^3*x*e^11 + 6792204780*(x*e + d)^m*m^2*x^
2*e^11 + 17050880160*(x*e + d)^m*m*x^3*e^11 + 5728060800*(x*e + d)^m*x^4*e^11 + 1888225560*(x*e + d)^m*d*m^3*e
^10 + 4095133200*(x*e + d)^m*d*m^2*x*e^10 + 3173385600*(x*e + d)^m*d*m*x^2*e^10 - 2697071580*(x*e + d)^m*d^2*m
^2*e^9 - 6346771200*(x*e + d)^m*d^2*m*x*e^9 + 7530723360*(x*e + d)^m*d^3*m*e^8 - 5728060800*(x*e + d)^m*d^4*e^
7 + 3795710544*(x*e + d)^m*m^2*x*e^11 + 6789517200*(x*e + d)^m*m*x^2*e^11 + 6346771200*(x*e + d)^m*x^3*e^11 +
3795710544*(x*e + d)^m*d*m^2*e^10 + 2694384000*(x*e + d)^m*d*m*x*e^10 - 4095133200*(x*e + d)^m*d^2*m*e^9 + 634
6771200*(x*e + d)^m*d^3*e^8 + 4353860160*(x*e + d)^m*m*x*e^11 + 2694384000*(x*e + d)^m*x^2*e^11 + 4353860160*(
x*e + d)^m*d*m*e^10 - 2694384000*(x*e + d)^m*d^2*e^9 + 2155507200*(x*e + d)^m*x*e^11 + 2155507200*(x*e + d)^m*
d*e^10)/(m^11*e^11 + 66*m^10*e^11 + 1925*m^9*e^11 + 32670*m^8*e^11 + 357423*m^7*e^11 + 2637558*m^6*e^11 + 1333
9535*m^5*e^11 + 45995730*m^4*e^11 + 105258076*m^3*e^11 + 150917976*m^2*e^11 + 120543840*m*e^11 + 39916800*e^11
)