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3.2549 \(\int (d+e x)^m (a+b x+c x^2)^4 \, dx\)

Optimal. Leaf size=485 \[ \frac{(d+e x)^{m+5} \left (6 c^2 e^2 \left (a^2 e^2-10 a b d e+15 b^2 d^2\right )-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right )}{e^9 (m+5)}+\frac{2 (d+e x)^{m+3} \left (a e^2-b d e+c d^2\right )^2 \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{e^9 (m+3)}-\frac{4 (2 c d-b e) (d+e x)^{m+4} \left (a e^2-b d e+c d^2\right ) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{e^9 (m+4)}-\frac{4 c (2 c d-b e) (d+e x)^{m+6} \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{e^9 (m+6)}+\frac{2 c^2 (d+e x)^{m+7} \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{e^9 (m+7)}+\frac{(d+e x)^{m+1} \left (a e^2-b d e+c d^2\right )^4}{e^9 (m+1)}-\frac{4 (2 c d-b e) (d+e x)^{m+2} \left (a e^2-b d e+c d^2\right )^3}{e^9 (m+2)}-\frac{4 c^3 (2 c d-b e) (d+e x)^{m+8}}{e^9 (m+8)}+\frac{c^4 (d+e x)^{m+9}}{e^9 (m+9)} \]

[Out]

((c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^(1 + m))/(e^9*(1 + m)) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d +
e*x)^(2 + m))/(e^9*(2 + m)) + (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d +
 e*x)^(3 + m))/(e^9*(3 + m)) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*
a*e))*(d + e*x)^(4 + m))/(e^9*(4 + m)) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(
7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^(5 + m))/(e^9*(5 + m)) - (4*c*(2*c*d
 - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(6 + m))/(e^9*(6 + m)) + (2*c^2*(14*c^2*d^2 + 3*
b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(7 + m))/(e^9*(7 + m)) - (4*c^3*(2*c*d - b*e)*(d + e*x)^(8 + m))/(e^9
*(8 + m)) + (c^4*(d + e*x)^(9 + m))/(e^9*(9 + m))

________________________________________________________________________________________

Rubi [A]  time = 0.38575, antiderivative size = 485, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {698} \[ \frac{(d+e x)^{m+5} \left (6 c^2 e^2 \left (a^2 e^2-10 a b d e+15 b^2 d^2\right )-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right )}{e^9 (m+5)}+\frac{2 (d+e x)^{m+3} \left (a e^2-b d e+c d^2\right )^2 \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{e^9 (m+3)}-\frac{4 (2 c d-b e) (d+e x)^{m+4} \left (a e^2-b d e+c d^2\right ) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{e^9 (m+4)}-\frac{4 c (2 c d-b e) (d+e x)^{m+6} \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{e^9 (m+6)}+\frac{2 c^2 (d+e x)^{m+7} \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{e^9 (m+7)}+\frac{(d+e x)^{m+1} \left (a e^2-b d e+c d^2\right )^4}{e^9 (m+1)}-\frac{4 (2 c d-b e) (d+e x)^{m+2} \left (a e^2-b d e+c d^2\right )^3}{e^9 (m+2)}-\frac{4 c^3 (2 c d-b e) (d+e x)^{m+8}}{e^9 (m+8)}+\frac{c^4 (d+e x)^{m+9}}{e^9 (m+9)} \]

Antiderivative was successfully verified.

[In]

Int[(d + e*x)^m*(a + b*x + c*x^2)^4,x]

[Out]

((c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^(1 + m))/(e^9*(1 + m)) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d +
e*x)^(2 + m))/(e^9*(2 + m)) + (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d +
 e*x)^(3 + m))/(e^9*(3 + m)) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*
a*e))*(d + e*x)^(4 + m))/(e^9*(4 + m)) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(
7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^(5 + m))/(e^9*(5 + m)) - (4*c*(2*c*d
 - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(6 + m))/(e^9*(6 + m)) + (2*c^2*(14*c^2*d^2 + 3*
b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(7 + m))/(e^9*(7 + m)) - (4*c^3*(2*c*d - b*e)*(d + e*x)^(8 + m))/(e^9
*(8 + m)) + (c^4*(d + e*x)^(9 + m))/(e^9*(9 + m))

Rule 698

Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[ExpandIntegrand[(d +
 e*x)^m*(a + b*x + c*x^2)^p, x], x] /; FreeQ[{a, b, c, d, e, m}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*
e + a*e^2, 0] && NeQ[2*c*d - b*e, 0] && IntegerQ[p] && (GtQ[p, 0] || (EqQ[a, 0] && IntegerQ[m]))

Rubi steps

\begin{align*} \int (d+e x)^m \left (a+b x+c x^2\right )^4 \, dx &=\int \left (\frac{\left (c d^2-b d e+a e^2\right )^4 (d+e x)^m}{e^8}+\frac{4 (-2 c d+b e) \left (c d^2-b d e+a e^2\right )^3 (d+e x)^{1+m}}{e^8}+\frac{2 \left (c d^2-b d e+a e^2\right )^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right ) (d+e x)^{2+m}}{e^8}+\frac{4 (2 c d-b e) \left (c d^2-b d e+a e^2\right ) \left (-7 c^2 d^2+7 b c d e-b^2 e^2-3 a c e^2\right ) (d+e x)^{3+m}}{e^8}+\frac{\left (70 c^4 d^4+b^4 e^4-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+6 c^2 e^2 \left (15 b^2 d^2-10 a b d e+a^2 e^2\right )\right ) (d+e x)^{4+m}}{e^8}+\frac{4 c (2 c d-b e) \left (-7 c^2 d^2-b^2 e^2+c e (7 b d-3 a e)\right ) (d+e x)^{5+m}}{e^8}+\frac{2 c^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right ) (d+e x)^{6+m}}{e^8}-\frac{4 c^3 (2 c d-b e) (d+e x)^{7+m}}{e^8}+\frac{c^4 (d+e x)^{8+m}}{e^8}\right ) \, dx\\ &=\frac{\left (c d^2-b d e+a e^2\right )^4 (d+e x)^{1+m}}{e^9 (1+m)}-\frac{4 (2 c d-b e) \left (c d^2-b d e+a e^2\right )^3 (d+e x)^{2+m}}{e^9 (2+m)}+\frac{2 \left (c d^2-b d e+a e^2\right )^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right ) (d+e x)^{3+m}}{e^9 (3+m)}-\frac{4 (2 c d-b e) \left (c d^2-b d e+a e^2\right ) \left (7 c^2 d^2+b^2 e^2-c e (7 b d-3 a e)\right ) (d+e x)^{4+m}}{e^9 (4+m)}+\frac{\left (70 c^4 d^4+b^4 e^4-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+6 c^2 e^2 \left (15 b^2 d^2-10 a b d e+a^2 e^2\right )\right ) (d+e x)^{5+m}}{e^9 (5+m)}-\frac{4 c (2 c d-b e) \left (7 c^2 d^2+b^2 e^2-c e (7 b d-3 a e)\right ) (d+e x)^{6+m}}{e^9 (6+m)}+\frac{2 c^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right ) (d+e x)^{7+m}}{e^9 (7+m)}-\frac{4 c^3 (2 c d-b e) (d+e x)^{8+m}}{e^9 (8+m)}+\frac{c^4 (d+e x)^{9+m}}{e^9 (9+m)}\\ \end{align*}

Mathematica [B]  time = 4.38169, size = 1309, normalized size = 2.7 \[ \frac{(d+e x)^{m+1} \left ((a+x (b+c x))^4-\frac{4 (d+e x) (b e (m+15)+2 c (e (m+8) x-7 d)) (a+x (b+c x))^3}{e^2 (m+8) (m+9)}-\frac{12 (d+e x) \left (c e^4 (m+2) (m+3) (m+4) (m+5) (a+x (b+c x))^2 \left (-28 d^2 (5 d-e (m+6) x) c^3+2 e \left (7 b d (d (m+21)-2 e (m+6) x)+2 a e \left (d \left (m^2+3 m-33\right )+e \left (m^2+14 m+48\right ) x\right )\right ) c^2-b e^2 \left (-2 a e (11 m+81)+b d \left (m^2+17 m+156\right )+b e \left (m^2+7 m+6\right ) x\right ) c-2 b^3 e^3 (m+1)\right )-2 \left ((m+2) (m+3) \left (c e (m+5) \left (c e (b d-2 a e) (m+7) \left (-d e (m+15) b^2+14 \left (c d^2+a e^2\right ) b+4 a c d e (m+1)\right )-(b d (5 c d-2 b e)+a e (2 c d (m+1)-b e (m+2))) \left (28 c^2 d^2-b^2 e^2 (m+1)+4 c e (a e (m+8)-7 b d)\right )\right )-(3 c d-b e) \left (c e (2 c d-b e) (m+7) \left (-d e (m+15) b^2+14 \left (c d^2+a e^2\right ) b+4 a c d e (m+1)\right )-\left (10 c^2 d^2-b^2 e^2 (m+4)+c e (b d (m-3)+2 a e (m+6))\right ) \left (28 c^2 d^2-b^2 e^2 (m+1)+4 c e (a e (m+8)-7 b d)\right )\right )+c e (m+4) \left (c e (2 c d-b e) (m+7) \left (-d e (m+15) b^2+14 \left (c d^2+a e^2\right ) b+4 a c d e (m+1)\right )-\left (10 c^2 d^2-b^2 e^2 (m+4)+c e (b d (m-3)+2 a e (m+6))\right ) \left (28 c^2 d^2-b^2 e^2 (m+1)+4 c e (a e (m+8)-7 b d)\right )\right ) x\right ) (a+x (b+c x)) e^2+(2 c d-b e) (m+3) \left (840 c^5 d^6-40 c^4 e \left (63 b d+a e \left (2 m^2+6 m-59\right )\right ) d^4+4 c^3 e^2 \left (5 b^2 \left (m^2+3 m+128\right ) d^2+20 a b e \left (2 m^2+6 m-59\right ) d-2 a^2 e^2 \left (2 m^3+34 m^2+88 m-259\right )\right ) d^2+b^4 e^5 (b d-a e) \left (m^3+7 m^2+14 m+8\right )-b^2 c e^4 \left (m^2+3 m+2\right ) \left (b^2 (m-16) d^2+8 a b e (m+9) d-4 a^2 e^2 (2 m+13)\right )-8 c^2 e^3 \left (5 b^3 \left (m^2+3 m+23\right ) d^3-a b^2 e \left (m^3+2 m^2-m+313\right ) d^2-a^2 b e^2 \left (2 m^3+34 m^2+88 m-259\right ) d+a^3 e^3 \left (2 m^3+24 m^2+58 m-69\right )\right )\right )+(m+2) \left (-1680 c^6 d^6+80 c^5 e \left (63 b d+a e \left (2 m^2-m-66\right )\right ) d^4-4 c^4 e^2 \left (5 b^2 \left (2 m^2-m+249\right ) d^2+40 a b e \left (2 m^2-m-66\right ) d-12 a^2 e^2 \left (m^3+8 m^2-11 m-123\right )\right ) d^2+b^6 e^6 \left (m^3+8 m^2+19 m+12\right )-b^4 c e^5 \left (m^2+4 m+3\right ) (b d (3 m-8)+a e (9 m+56))+b^2 c^2 e^4 (m+1) \left (3 b^2 \left (m^2-13 m+12\right ) d^2+8 a b e \left (3 m^2+11 m-39\right ) d+12 a^2 e^2 \left (2 m^2+24 m+69\right )\right )-8 c^3 e^3 \left (-5 b^3 \left (2 m^2-m+39\right ) d^3+3 a b^2 e \left (m^3-2 m^2-6 m+207\right ) d^2+6 a^2 b e^2 \left (m^3+8 m^2-11 m-123\right ) d+2 a^3 e^3 \left (m^3+18 m^2+104 m+192\right )\right )\right ) (d+e x)\right )\right )}{c^2 e^8 (m+2) (m+3) (m+4) (m+5) (m+6) (m+7) (m+8) (m+9)}\right )}{e (m+1)} \]

Antiderivative was successfully verified.

[In]

Integrate[(d + e*x)^m*(a + b*x + c*x^2)^4,x]

[Out]

((d + e*x)^(1 + m)*((a + x*(b + c*x))^4 - (4*(d + e*x)*(a + x*(b + c*x))^3*(b*e*(15 + m) + 2*c*(-7*d + e*(8 +
m)*x)))/(e^2*(8 + m)*(9 + m)) - (12*(d + e*x)*(-2*((2*c*d - b*e)*(3 + m)*(840*c^5*d^6 + b^4*e^5*(b*d - a*e)*(8
 + 14*m + 7*m^2 + m^3) - b^2*c*e^4*(2 + 3*m + m^2)*(b^2*d^2*(-16 + m) + 8*a*b*d*e*(9 + m) - 4*a^2*e^2*(13 + 2*
m)) - 40*c^4*d^4*e*(63*b*d + a*e*(-59 + 6*m + 2*m^2)) + 4*c^3*d^2*e^2*(5*b^2*d^2*(128 + 3*m + m^2) + 20*a*b*d*
e*(-59 + 6*m + 2*m^2) - 2*a^2*e^2*(-259 + 88*m + 34*m^2 + 2*m^3)) - 8*c^2*e^3*(5*b^3*d^3*(23 + 3*m + m^2) - a*
b^2*d^2*e*(313 - m + 2*m^2 + m^3) + a^3*e^3*(-69 + 58*m + 24*m^2 + 2*m^3) - a^2*b*d*e^2*(-259 + 88*m + 34*m^2
+ 2*m^3))) + (2 + m)*(-1680*c^6*d^6 + b^6*e^6*(12 + 19*m + 8*m^2 + m^3) - b^4*c*e^5*(3 + 4*m + m^2)*(b*d*(-8 +
 3*m) + a*e*(56 + 9*m)) + 80*c^5*d^4*e*(63*b*d + a*e*(-66 - m + 2*m^2)) + b^2*c^2*e^4*(1 + m)*(3*b^2*d^2*(12 -
 13*m + m^2) + 12*a^2*e^2*(69 + 24*m + 2*m^2) + 8*a*b*d*e*(-39 + 11*m + 3*m^2)) - 4*c^4*d^2*e^2*(40*a*b*d*e*(-
66 - m + 2*m^2) + 5*b^2*d^2*(249 - m + 2*m^2) - 12*a^2*e^2*(-123 - 11*m + 8*m^2 + m^3)) - 8*c^3*e^3*(-5*b^3*d^
3*(39 - m + 2*m^2) + 3*a*b^2*d^2*e*(207 - 6*m - 2*m^2 + m^3) + 6*a^2*b*d*e^2*(-123 - 11*m + 8*m^2 + m^3) + 2*a
^3*e^3*(192 + 104*m + 18*m^2 + m^3)))*(d + e*x) + e^2*(2 + m)*(3 + m)*(c*e*(5 + m)*(c*e*(b*d - 2*a*e)*(7 + m)*
(14*b*(c*d^2 + a*e^2) + 4*a*c*d*e*(1 + m) - b^2*d*e*(15 + m)) - (b*d*(5*c*d - 2*b*e) + a*e*(2*c*d*(1 + m) - b*
e*(2 + m)))*(28*c^2*d^2 - b^2*e^2*(1 + m) + 4*c*e*(-7*b*d + a*e*(8 + m)))) - (3*c*d - b*e)*(c*e*(2*c*d - b*e)*
(7 + m)*(14*b*(c*d^2 + a*e^2) + 4*a*c*d*e*(1 + m) - b^2*d*e*(15 + m)) - (10*c^2*d^2 - b^2*e^2*(4 + m) + c*e*(b
*d*(-3 + m) + 2*a*e*(6 + m)))*(28*c^2*d^2 - b^2*e^2*(1 + m) + 4*c*e*(-7*b*d + a*e*(8 + m)))) + c*e*(4 + m)*(c*
e*(2*c*d - b*e)*(7 + m)*(14*b*(c*d^2 + a*e^2) + 4*a*c*d*e*(1 + m) - b^2*d*e*(15 + m)) - (10*c^2*d^2 - b^2*e^2*
(4 + m) + c*e*(b*d*(-3 + m) + 2*a*e*(6 + m)))*(28*c^2*d^2 - b^2*e^2*(1 + m) + 4*c*e*(-7*b*d + a*e*(8 + m))))*x
)*(a + x*(b + c*x))) + c*e^4*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(a + x*(b + c*x))^2*(-2*b^3*e^3*(1 + m) - 28*c^3*
d^2*(5*d - e*(6 + m)*x) - b*c*e^2*(-2*a*e*(81 + 11*m) + b*d*(156 + 17*m + m^2) + b*e*(6 + 7*m + m^2)*x) + 2*c^
2*e*(7*b*d*(d*(21 + m) - 2*e*(6 + m)*x) + 2*a*e*(d*(-33 + 3*m + m^2) + e*(48 + 14*m + m^2)*x)))))/(c^2*e^8*(2
+ m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(7 + m)*(8 + m)*(9 + m))))/(e*(1 + m))

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Maple [B]  time = 0.083, size = 7696, normalized size = 15.9 \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*(c*x^2+b*x+a)^4,x)

[Out]

result too large to display

________________________________________________________________________________________

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*(c*x^2+b*x+a)^4,x, algorithm="maxima")

[Out]

Exception raised: ValueError

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Fricas [B]  time = 3.32018, size = 13875, normalized size = 28.61 \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*(c*x^2+b*x+a)^4,x, algorithm="fricas")

[Out]

(a^4*d*e^8*m^8 + 40320*c^4*d^9 - 181440*b*c^3*d^8*e - 725760*a^3*b*d^2*e^7 + 362880*a^4*d*e^8 + 103680*(3*b^2*
c^2 + 2*a*c^3)*d^7*e^2 - 241920*(b^3*c + 3*a*b*c^2)*d^6*e^3 + 72576*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^4 - 3
62880*(a*b^3 + 3*a^2*b*c)*d^4*e^5 + 241920*(3*a^2*b^2 + 2*a^3*c)*d^3*e^6 + (c^4*e^9*m^8 + 36*c^4*e^9*m^7 + 546
*c^4*e^9*m^6 + 4536*c^4*e^9*m^5 + 22449*c^4*e^9*m^4 + 67284*c^4*e^9*m^3 + 118124*c^4*e^9*m^2 + 109584*c^4*e^9*
m + 40320*c^4*e^9)*x^9 + (181440*b*c^3*e^9 + (c^4*d*e^8 + 4*b*c^3*e^9)*m^8 + 4*(7*c^4*d*e^8 + 37*b*c^3*e^9)*m^
7 + 14*(23*c^4*d*e^8 + 164*b*c^3*e^9)*m^6 + 56*(35*c^4*d*e^8 + 347*b*c^3*e^9)*m^5 + 7*(967*c^4*d*e^8 + 13948*b
*c^3*e^9)*m^4 + 28*(469*c^4*d*e^8 + 10579*b*c^3*e^9)*m^3 + 36*(363*c^4*d*e^8 + 14584*b*c^3*e^9)*m^2 + 144*(35*
c^4*d*e^8 + 3407*b*c^3*e^9)*m)*x^8 - 4*(a^3*b*d^2*e^7 - 11*a^4*d*e^8)*m^7 + 2*(51840*(3*b^2*c^2 + 2*a*c^3)*e^9
 + (2*b*c^3*d*e^8 + (3*b^2*c^2 + 2*a*c^3)*e^9)*m^8 - 2*(2*c^4*d^2*e^7 - 30*b*c^3*d*e^8 - 19*(3*b^2*c^2 + 2*a*c
^3)*e^9)*m^7 - 4*(21*c^4*d^2*e^7 - 182*b*c^3*d*e^8 - 151*(3*b^2*c^2 + 2*a*c^3)*e^9)*m^6 - 14*(50*c^4*d^2*e^7 -
 330*b*c^3*d*e^8 - 373*(3*b^2*c^2 + 2*a*c^3)*e^9)*m^5 - 7*(420*c^4*d^2*e^7 - 2354*b*c^3*d*e^8 - 3817*(3*b^2*c^
2 + 2*a*c^3)*e^9)*m^4 - 28*(232*c^4*d^2*e^7 - 1170*b*c^3*d*e^8 - 2939*(3*b^2*c^2 + 2*a*c^3)*e^9)*m^3 - 36*(196
*c^4*d^2*e^7 - 922*b*c^3*d*e^8 - 4101*(3*b^2*c^2 + 2*a*c^3)*e^9)*m^2 - 144*(20*c^4*d^2*e^7 - 90*b*c^3*d*e^8 -
967*(3*b^2*c^2 + 2*a*c^3)*e^9)*m)*x^7 - 2*(84*a^3*b*d^2*e^7 - 413*a^4*d*e^8 - 2*(3*a^2*b^2 + 2*a^3*c)*d^3*e^6)
*m^6 + 2*(120960*(b^3*c + 3*a*b*c^2)*e^9 + ((3*b^2*c^2 + 2*a*c^3)*d*e^8 + 2*(b^3*c + 3*a*b*c^2)*e^9)*m^8 - 2*(
7*b*c^3*d^2*e^7 - 16*(3*b^2*c^2 + 2*a*c^3)*d*e^8 - 39*(b^3*c + 3*a*b*c^2)*e^9)*m^7 + 4*(7*c^4*d^3*e^6 - 84*b*c
^3*d^2*e^7 + 103*(3*b^2*c^2 + 2*a*c^3)*d*e^8 + 318*(b^3*c + 3*a*b*c^2)*e^9)*m^6 + 2*(210*c^4*d^3*e^6 - 1540*b*
c^3*d^2*e^7 + 1375*(3*b^2*c^2 + 2*a*c^3)*d*e^8 + 5634*(b^3*c + 3*a*b*c^2)*e^9)*m^5 + (2380*c^4*d^3*e^6 - 13860
*b*c^3*d^2*e^7 + 10219*(3*b^2*c^2 + 2*a*c^3)*d*e^8 + 58938*(b^3*c + 3*a*b*c^2)*e^9)*m^4 + 2*(3150*c^4*d^3*e^6
- 16093*b*c^3*d^2*e^7 + 10489*(3*b^2*c^2 + 2*a*c^3)*d*e^8 + 92511*(b^3*c + 3*a*b*c^2)*e^9)*m^3 + 4*(1918*c^4*d
^3*e^6 - 9051*b*c^3*d^2*e^7 + 5442*(3*b^2*c^2 + 2*a*c^3)*d*e^8 + 84307*(b^3*c + 3*a*b*c^2)*e^9)*m^2 + 48*(70*c
^4*d^3*e^6 - 315*b*c^3*d^2*e^7 + 180*(3*b^2*c^2 + 2*a*c^3)*d*e^8 + 6709*(b^3*c + 3*a*b*c^2)*e^9)*m)*x^6 - 4*(7
42*a^3*b*d^2*e^7 - 2156*a^4*d*e^8 + 6*(a*b^3 + 3*a^2*b*c)*d^4*e^5 - 39*(3*a^2*b^2 + 2*a^3*c)*d^3*e^6)*m^5 + (7
2576*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^9 + (4*(b^3*c + 3*a*b*c^2)*d*e^8 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^9)*m
^8 - 4*(3*(3*b^2*c^2 + 2*a*c^3)*d^2*e^7 - 34*(b^3*c + 3*a*b*c^2)*d*e^8 - 10*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^9
)*m^7 + 2*(84*b*c^3*d^3*e^6 - 162*(3*b^2*c^2 + 2*a*c^3)*d^2*e^7 + 932*(b^3*c + 3*a*b*c^2)*d*e^8 + 335*(b^4 + 1
2*a*b^2*c + 6*a^2*c^2)*e^9)*m^6 - 4*(84*c^4*d^4*e^5 - 798*b*c^3*d^3*e^6 + 831*(3*b^2*c^2 + 2*a*c^3)*d^2*e^7 -
3304*(b^3*c + 3*a*b*c^2)*d*e^8 - 1525*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^9)*m^5 - (3360*c^4*d^4*e^5 - 21000*b*c^
3*d^3*e^6 + 16380*(3*b^2*c^2 + 2*a*c^3)*d^2*e^7 - 51796*(b^3*c + 3*a*b*c^2)*d*e^8 - 32773*(b^4 + 12*a*b^2*c +
6*a^2*c^2)*e^9)*m^4 - 4*(2940*c^4*d^4*e^5 - 15330*b*c^3*d^3*e^6 + 10182*(3*b^2*c^2 + 2*a*c^3)*d^2*e^7 - 27766*
(b^3*c + 3*a*b*c^2)*d*e^8 - 26365*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^9)*m^3 - 12*(1400*c^4*d^4*e^5 - 6636*b*c^3*
d^3*e^6 + 4008*(3*b^2*c^2 + 2*a*c^3)*d^2*e^7 - 9928*(b^3*c + 3*a*b*c^2)*d*e^8 - 16365*(b^4 + 12*a*b^2*c + 6*a^
2*c^2)*e^9)*m^2 - 144*(56*c^4*d^4*e^5 - 252*b*c^3*d^3*e^6 + 144*(3*b^2*c^2 + 2*a*c^3)*d^2*e^7 - 336*(b^3*c + 3
*a*b*c^2)*d*e^8 - 1325*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^9)*m)*x^5 - (28560*a^3*b*d^2*e^7 - 54649*a^4*d*e^8 - 2
4*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^4 + 840*(a*b^3 + 3*a^2*b*c)*d^4*e^5 - 2500*(3*a^2*b^2 + 2*a^3*c)*d^3*e^
6)*m^4 + (362880*(a*b^3 + 3*a^2*b*c)*e^9 + ((b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^8 + 4*(a*b^3 + 3*a^2*b*c)*e^9)*
m^8 - 4*(5*(b^3*c + 3*a*b*c^2)*d^2*e^7 - 9*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^8 - 41*(a*b^3 + 3*a^2*b*c)*e^9)*
m^7 + 2*(30*(3*b^2*c^2 + 2*a*c^3)*d^3*e^6 - 300*(b^3*c + 3*a*b*c^2)*d^2*e^7 + 263*(b^4 + 12*a*b^2*c + 6*a^2*c^
2)*d*e^8 + 1412*(a*b^3 + 3*a^2*b*c)*e^9)*m^6 - 4*(210*b*c^3*d^4*e^5 - 345*(3*b^2*c^2 + 2*a*c^3)*d^3*e^6 + 1730
*(b^3*c + 3*a*b*c^2)*d^2*e^7 - 999*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^8 - 6626*(a*b^3 + 3*a^2*b*c)*e^9)*m^5 +
(1680*c^4*d^5*e^4 - 12600*b*c^3*d^4*e^5 + 11100*(3*b^2*c^2 + 2*a*c^3)*d^3*e^6 - 38400*(b^3*c + 3*a*b*c^2)*d^2*
e^7 + 16789*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^8 + 147076*(a*b^3 + 3*a^2*b*c)*e^9)*m^4 + 4*(2520*c^4*d^5*e^4 -
 13650*b*c^3*d^4*e^5 + 9375*(3*b^2*c^2 + 2*a*c^3)*d^3*e^6 - 26345*(b^3*c + 3*a*b*c^2)*d^2*e^7 + 9576*(b^4 + 12
*a*b^2*c + 6*a^2*c^2)*d*e^8 + 122249*(a*b^3 + 3*a^2*b*c)*e^9)*m^3 + 12*(1540*c^4*d^5*e^4 - 7350*b*c^3*d^4*e^5
+ 4470*(3*b^2*c^2 + 2*a*c^3)*d^3*e^6 - 11150*(b^3*c + 3*a*b*c^2)*d^2*e^7 + 3597*(b^4 + 12*a*b^2*c + 6*a^2*c^2)
*d*e^8 + 78228*(a*b^3 + 3*a^2*b*c)*e^9)*m^2 + 144*(70*c^4*d^5*e^4 - 315*b*c^3*d^4*e^5 + 180*(3*b^2*c^2 + 2*a*c
^3)*d^3*e^6 - 420*(b^3*c + 3*a*b*c^2)*d^2*e^7 + 126*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^8 + 6499*(a*b^3 + 3*a^2
*b*c)*e^9)*m)*x^4 - 4*(40369*a^3*b*d^2*e^7 - 53669*a^4*d*e^8 + 120*(b^3*c + 3*a*b*c^2)*d^6*e^3 - 180*(b^4 + 12
*a*b^2*c + 6*a^2*c^2)*d^5*e^4 + 2910*(a*b^3 + 3*a^2*b*c)*d^4*e^5 - 5265*(3*a^2*b^2 + 2*a^3*c)*d^3*e^6)*m^3 + 2
*(120960*(3*a^2*b^2 + 2*a^3*c)*e^9 + (2*(a*b^3 + 3*a^2*b*c)*d*e^8 + (3*a^2*b^2 + 2*a^3*c)*e^9)*m^8 - 2*((b^4 +
 12*a*b^2*c + 6*a^2*c^2)*d^2*e^7 - 38*(a*b^3 + 3*a^2*b*c)*d*e^8 - 21*(3*a^2*b^2 + 2*a^3*c)*e^9)*m^7 + 2*(20*(b
^3*c + 3*a*b*c^2)*d^3*e^6 - 33*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^7 + 592*(a*b^3 + 3*a^2*b*c)*d*e^8 + 372*(3
*a^2*b^2 + 2*a^3*c)*e^9)*m^6 - 2*(60*(3*b^2*c^2 + 2*a*c^3)*d^4*e^5 - 540*(b^3*c + 3*a*b*c^2)*d^3*e^6 + 427*(b^
4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^7 - 4850*(a*b^3 + 3*a^2*b*c)*d*e^8 - 3609*(3*a^2*b^2 + 2*a^3*c)*e^9)*m^5 + (
1680*b*c^3*d^5*e^4 - 2400*(3*b^2*c^2 + 2*a*c^3)*d^4*e^5 + 10600*(b^3*c + 3*a*b*c^2)*d^3*e^6 - 5430*(b^4 + 12*a
*b^2*c + 6*a^2*c^2)*d^2*e^7 + 44438*(a*b^3 + 3*a^2*b*c)*d*e^8 + 41619*(3*a^2*b^2 + 2*a^3*c)*e^9)*m^4 - 4*(840*
c^4*d^6*e^3 - 5040*b*c^3*d^5*e^4 + 3750*(3*b^2*c^2 + 2*a*c^3)*d^4*e^5 - 11250*(b^3*c + 3*a*b*c^2)*d^3*e^6 + 43
22*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^7 - 27796*(a*b^3 + 3*a^2*b*c)*d*e^8 - 36117*(3*a^2*b^2 + 2*a^3*c)*e^9)
*m^3 - 4*(2520*c^4*d^6*e^3 - 12180*b*c^3*d^5*e^4 + 7500*(3*b^2*c^2 + 2*a*c^3)*d^4*e^5 - 18940*(b^3*c + 3*a*b*c
^2)*d^3*e^6 + 6186*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^7 - 33954*(a*b^3 + 3*a^2*b*c)*d*e^8 - 72569*(3*a^2*b^2
 + 2*a^3*c)*e^9)*m^2 - 48*(140*c^4*d^6*e^3 - 630*b*c^3*d^5*e^4 + 360*(3*b^2*c^2 + 2*a*c^3)*d^4*e^5 - 840*(b^3*
c + 3*a*b*c^2)*d^3*e^6 + 252*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^7 - 1260*(a*b^3 + 3*a^2*b*c)*d*e^8 - 6289*(3
*a^2*b^2 + 2*a^3*c)*e^9)*m)*x^3 - 4*(133938*a^3*b*d^2*e^7 - 127251*a^4*d*e^8 - 360*(3*b^2*c^2 + 2*a*c^3)*d^7*e
^2 + 2880*(b^3*c + 3*a*b*c^2)*d^6*e^3 - 2010*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^4 + 19950*(a*b^3 + 3*a^2*b*c
)*d^4*e^5 - 24574*(3*a^2*b^2 + 2*a^3*c)*d^3*e^6)*m^2 + 2*(362880*a^3*b*e^9 + (2*a^3*b*e^9 + (3*a^2*b^2 + 2*a^3
*c)*d*e^8)*m^8 + 2*(43*a^3*b*e^9 - 3*(a*b^3 + 3*a^2*b*c)*d^2*e^7 + 20*(3*a^2*b^2 + 2*a^3*c)*d*e^8)*m^7 + 2*(78
4*a^3*b*e^9 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^6 - 108*(a*b^3 + 3*a^2*b*c)*d^2*e^7 + 332*(3*a^2*b^2 + 2*
a^3*c)*d*e^8)*m^6 + 2*(7882*a^3*b*e^9 - 60*(b^3*c + 3*a*b*c^2)*d^4*e^5 + 93*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3
*e^6 - 1560*(a*b^3 + 3*a^2*b*c)*d^2*e^7 + 2945*(3*a^2*b^2 + 2*a^3*c)*d*e^8)*m^5 + (95018*a^3*b*e^9 + 360*(3*b^
2*c^2 + 2*a*c^3)*d^5*e^4 - 3000*(b^3*c + 3*a*b*c^2)*d^4*e^5 + 2190*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^6 - 22
860*(a*b^3 + 3*a^2*b*c)*d^2*e^7 + 29839*(3*a^2*b^2 + 2*a^3*c)*d*e^8)*m^4 - 2*(2520*b*c^3*d^6*e^3 - 174307*a^3*
b*e^9 - 3240*(3*b^2*c^2 + 2*a*c^3)*d^5*e^4 + 12900*(b^3*c + 3*a*b*c^2)*d^4*e^5 - 5955*(b^4 + 12*a*b^2*c + 6*a^
2*c^2)*d^3*e^6 + 43797*(a*b^3 + 3*a^2*b*c)*d^2*e^7 - 42395*(3*a^2*b^2 + 2*a^3*c)*d*e^8)*m^3 + 12*(840*c^4*d^7*
e^2 - 4200*b*c^3*d^6*e^3 + 62511*a^3*b*e^9 + 2670*(3*b^2*c^2 + 2*a*c^3)*d^5*e^4 - 6950*(b^3*c + 3*a*b*c^2)*d^4
*e^5 + 2337*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^6 - 13197*(a*b^3 + 3*a^2*b*c)*d^2*e^7 + 10058*(3*a^2*b^2 + 2*
a^3*c)*d*e^8)*m^2 + 144*(70*c^4*d^7*e^2 - 315*b*c^3*d^6*e^3 + 5869*a^3*b*e^9 + 180*(3*b^2*c^2 + 2*a*c^3)*d^5*e
^4 - 420*(b^3*c + 3*a*b*c^2)*d^4*e^5 + 126*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^6 - 630*(a*b^3 + 3*a^2*b*c)*d^
2*e^7 + 420*(3*a^2*b^2 + 2*a^3*c)*d*e^8)*m)*x^2 - 48*(420*b*c^3*d^8*e + 20094*a^3*b*d^2*e^7 - 13827*a^4*d*e^8
- 510*(3*b^2*c^2 + 2*a*c^3)*d^7*e^2 + 1910*(b^3*c + 3*a*b*c^2)*d^6*e^3 - 825*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^
5*e^4 + 5637*(a*b^3 + 3*a^2*b*c)*d^4*e^5 - 5018*(3*a^2*b^2 + 2*a^3*c)*d^3*e^6)*m + (362880*a^4*e^9 + (4*a^3*b*
d*e^8 + a^4*e^9)*m^8 + 4*(42*a^3*b*d*e^8 + 11*a^4*e^9 - (3*a^2*b^2 + 2*a^3*c)*d^2*e^7)*m^7 + 2*(1484*a^3*b*d*e
^8 + 413*a^4*e^9 + 12*(a*b^3 + 3*a^2*b*c)*d^3*e^6 - 78*(3*a^2*b^2 + 2*a^3*c)*d^2*e^7)*m^6 + 4*(7140*a^3*b*d*e^
8 + 2156*a^4*e^9 - 6*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^5 + 210*(a*b^3 + 3*a^2*b*c)*d^3*e^6 - 625*(3*a^2*b^2
 + 2*a^3*c)*d^2*e^7)*m^5 + (161476*a^3*b*d*e^8 + 54649*a^4*e^9 + 480*(b^3*c + 3*a*b*c^2)*d^5*e^4 - 720*(b^4 +
12*a*b^2*c + 6*a^2*c^2)*d^4*e^5 + 11640*(a*b^3 + 3*a^2*b*c)*d^3*e^6 - 21060*(3*a^2*b^2 + 2*a^3*c)*d^2*e^7)*m^4
 + 4*(133938*a^3*b*d*e^8 + 53669*a^4*e^9 - 360*(3*b^2*c^2 + 2*a*c^3)*d^6*e^3 + 2880*(b^3*c + 3*a*b*c^2)*d^5*e^
4 - 2010*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^5 + 19950*(a*b^3 + 3*a^2*b*c)*d^3*e^6 - 24574*(3*a^2*b^2 + 2*a^3
*c)*d^2*e^7)*m^3 + 12*(1680*b*c^3*d^7*e^2 + 80376*a^3*b*d*e^8 + 42417*a^4*e^9 - 2040*(3*b^2*c^2 + 2*a*c^3)*d^6
*e^3 + 7640*(b^3*c + 3*a*b*c^2)*d^5*e^4 - 3300*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^5 + 22548*(a*b^3 + 3*a^2*b
*c)*d^3*e^6 - 20072*(3*a^2*b^2 + 2*a^3*c)*d^2*e^7)*m^2 - 144*(280*c^4*d^8*e - 1260*b*c^3*d^7*e^2 - 5040*a^3*b*
d*e^8 - 4609*a^4*e^9 + 720*(3*b^2*c^2 + 2*a*c^3)*d^6*e^3 - 1680*(b^3*c + 3*a*b*c^2)*d^5*e^4 + 504*(b^4 + 12*a*
b^2*c + 6*a^2*c^2)*d^4*e^5 - 2520*(a*b^3 + 3*a^2*b*c)*d^3*e^6 + 1680*(3*a^2*b^2 + 2*a^3*c)*d^2*e^7)*m)*x)*(e*x
 + d)^m/(e^9*m^9 + 45*e^9*m^8 + 870*e^9*m^7 + 9450*e^9*m^6 + 63273*e^9*m^5 + 269325*e^9*m^4 + 723680*e^9*m^3 +
 1172700*e^9*m^2 + 1026576*e^9*m + 362880*e^9)

________________________________________________________________________________________

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*(c*x**2+b*x+a)**4,x)

[Out]

Timed out

________________________________________________________________________________________

Giac [B]  time = 2.19686, size = 17743, normalized size = 36.58 \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*(c*x^2+b*x+a)^4,x, algorithm="giac")

[Out]

((x*e + d)^m*c^4*m^8*x^9*e^9 + (x*e + d)^m*c^4*d*m^8*x^8*e^8 + 4*(x*e + d)^m*b*c^3*m^8*x^8*e^9 + 36*(x*e + d)^
m*c^4*m^7*x^9*e^9 + 4*(x*e + d)^m*b*c^3*d*m^8*x^7*e^8 + 28*(x*e + d)^m*c^4*d*m^7*x^8*e^8 - 8*(x*e + d)^m*c^4*d
^2*m^7*x^7*e^7 + 6*(x*e + d)^m*b^2*c^2*m^8*x^7*e^9 + 4*(x*e + d)^m*a*c^3*m^8*x^7*e^9 + 148*(x*e + d)^m*b*c^3*m
^7*x^8*e^9 + 546*(x*e + d)^m*c^4*m^6*x^9*e^9 + 6*(x*e + d)^m*b^2*c^2*d*m^8*x^6*e^8 + 4*(x*e + d)^m*a*c^3*d*m^8
*x^6*e^8 + 120*(x*e + d)^m*b*c^3*d*m^7*x^7*e^8 + 322*(x*e + d)^m*c^4*d*m^6*x^8*e^8 - 28*(x*e + d)^m*b*c^3*d^2*
m^7*x^6*e^7 - 168*(x*e + d)^m*c^4*d^2*m^6*x^7*e^7 + 56*(x*e + d)^m*c^4*d^3*m^6*x^6*e^6 + 4*(x*e + d)^m*b^3*c*m
^8*x^6*e^9 + 12*(x*e + d)^m*a*b*c^2*m^8*x^6*e^9 + 228*(x*e + d)^m*b^2*c^2*m^7*x^7*e^9 + 152*(x*e + d)^m*a*c^3*
m^7*x^7*e^9 + 2296*(x*e + d)^m*b*c^3*m^6*x^8*e^9 + 4536*(x*e + d)^m*c^4*m^5*x^9*e^9 + 4*(x*e + d)^m*b^3*c*d*m^
8*x^5*e^8 + 12*(x*e + d)^m*a*b*c^2*d*m^8*x^5*e^8 + 192*(x*e + d)^m*b^2*c^2*d*m^7*x^6*e^8 + 128*(x*e + d)^m*a*c
^3*d*m^7*x^6*e^8 + 1456*(x*e + d)^m*b*c^3*d*m^6*x^7*e^8 + 1960*(x*e + d)^m*c^4*d*m^5*x^8*e^8 - 36*(x*e + d)^m*
b^2*c^2*d^2*m^7*x^5*e^7 - 24*(x*e + d)^m*a*c^3*d^2*m^7*x^5*e^7 - 672*(x*e + d)^m*b*c^3*d^2*m^6*x^6*e^7 - 1400*
(x*e + d)^m*c^4*d^2*m^5*x^7*e^7 + 168*(x*e + d)^m*b*c^3*d^3*m^6*x^5*e^6 + 840*(x*e + d)^m*c^4*d^3*m^5*x^6*e^6
- 336*(x*e + d)^m*c^4*d^4*m^5*x^5*e^5 + (x*e + d)^m*b^4*m^8*x^5*e^9 + 12*(x*e + d)^m*a*b^2*c*m^8*x^5*e^9 + 6*(
x*e + d)^m*a^2*c^2*m^8*x^5*e^9 + 156*(x*e + d)^m*b^3*c*m^7*x^6*e^9 + 468*(x*e + d)^m*a*b*c^2*m^7*x^6*e^9 + 362
4*(x*e + d)^m*b^2*c^2*m^6*x^7*e^9 + 2416*(x*e + d)^m*a*c^3*m^6*x^7*e^9 + 19432*(x*e + d)^m*b*c^3*m^5*x^8*e^9 +
 22449*(x*e + d)^m*c^4*m^4*x^9*e^9 + (x*e + d)^m*b^4*d*m^8*x^4*e^8 + 12*(x*e + d)^m*a*b^2*c*d*m^8*x^4*e^8 + 6*
(x*e + d)^m*a^2*c^2*d*m^8*x^4*e^8 + 136*(x*e + d)^m*b^3*c*d*m^7*x^5*e^8 + 408*(x*e + d)^m*a*b*c^2*d*m^7*x^5*e^
8 + 2472*(x*e + d)^m*b^2*c^2*d*m^6*x^6*e^8 + 1648*(x*e + d)^m*a*c^3*d*m^6*x^6*e^8 + 9240*(x*e + d)^m*b*c^3*d*m
^5*x^7*e^8 + 6769*(x*e + d)^m*c^4*d*m^4*x^8*e^8 - 20*(x*e + d)^m*b^3*c*d^2*m^7*x^4*e^7 - 60*(x*e + d)^m*a*b*c^
2*d^2*m^7*x^4*e^7 - 972*(x*e + d)^m*b^2*c^2*d^2*m^6*x^5*e^7 - 648*(x*e + d)^m*a*c^3*d^2*m^6*x^5*e^7 - 6160*(x*
e + d)^m*b*c^3*d^2*m^5*x^6*e^7 - 5880*(x*e + d)^m*c^4*d^2*m^4*x^7*e^7 + 180*(x*e + d)^m*b^2*c^2*d^3*m^6*x^4*e^
6 + 120*(x*e + d)^m*a*c^3*d^3*m^6*x^4*e^6 + 3192*(x*e + d)^m*b*c^3*d^3*m^5*x^5*e^6 + 4760*(x*e + d)^m*c^4*d^3*
m^4*x^6*e^6 - 840*(x*e + d)^m*b*c^3*d^4*m^5*x^4*e^5 - 3360*(x*e + d)^m*c^4*d^4*m^4*x^5*e^5 + 1680*(x*e + d)^m*
c^4*d^5*m^4*x^4*e^4 + 4*(x*e + d)^m*a*b^3*m^8*x^4*e^9 + 12*(x*e + d)^m*a^2*b*c*m^8*x^4*e^9 + 40*(x*e + d)^m*b^
4*m^7*x^5*e^9 + 480*(x*e + d)^m*a*b^2*c*m^7*x^5*e^9 + 240*(x*e + d)^m*a^2*c^2*m^7*x^5*e^9 + 2544*(x*e + d)^m*b
^3*c*m^6*x^6*e^9 + 7632*(x*e + d)^m*a*b*c^2*m^6*x^6*e^9 + 31332*(x*e + d)^m*b^2*c^2*m^5*x^7*e^9 + 20888*(x*e +
 d)^m*a*c^3*m^5*x^7*e^9 + 97636*(x*e + d)^m*b*c^3*m^4*x^8*e^9 + 67284*(x*e + d)^m*c^4*m^3*x^9*e^9 + 4*(x*e + d
)^m*a*b^3*d*m^8*x^3*e^8 + 12*(x*e + d)^m*a^2*b*c*d*m^8*x^3*e^8 + 36*(x*e + d)^m*b^4*d*m^7*x^4*e^8 + 432*(x*e +
 d)^m*a*b^2*c*d*m^7*x^4*e^8 + 216*(x*e + d)^m*a^2*c^2*d*m^7*x^4*e^8 + 1864*(x*e + d)^m*b^3*c*d*m^6*x^5*e^8 + 5
592*(x*e + d)^m*a*b*c^2*d*m^6*x^5*e^8 + 16500*(x*e + d)^m*b^2*c^2*d*m^5*x^6*e^8 + 11000*(x*e + d)^m*a*c^3*d*m^
5*x^6*e^8 + 32956*(x*e + d)^m*b*c^3*d*m^4*x^7*e^8 + 13132*(x*e + d)^m*c^4*d*m^3*x^8*e^8 - 4*(x*e + d)^m*b^4*d^
2*m^7*x^3*e^7 - 48*(x*e + d)^m*a*b^2*c*d^2*m^7*x^3*e^7 - 24*(x*e + d)^m*a^2*c^2*d^2*m^7*x^3*e^7 - 600*(x*e + d
)^m*b^3*c*d^2*m^6*x^4*e^7 - 1800*(x*e + d)^m*a*b*c^2*d^2*m^6*x^4*e^7 - 9972*(x*e + d)^m*b^2*c^2*d^2*m^5*x^5*e^
7 - 6648*(x*e + d)^m*a*c^3*d^2*m^5*x^5*e^7 - 27720*(x*e + d)^m*b*c^3*d^2*m^4*x^6*e^7 - 12992*(x*e + d)^m*c^4*d
^2*m^3*x^7*e^7 + 80*(x*e + d)^m*b^3*c*d^3*m^6*x^3*e^6 + 240*(x*e + d)^m*a*b*c^2*d^3*m^6*x^3*e^6 + 4140*(x*e +
d)^m*b^2*c^2*d^3*m^5*x^4*e^6 + 2760*(x*e + d)^m*a*c^3*d^3*m^5*x^4*e^6 + 21000*(x*e + d)^m*b*c^3*d^3*m^4*x^5*e^
6 + 12600*(x*e + d)^m*c^4*d^3*m^3*x^6*e^6 - 720*(x*e + d)^m*b^2*c^2*d^4*m^5*x^3*e^5 - 480*(x*e + d)^m*a*c^3*d^
4*m^5*x^3*e^5 - 12600*(x*e + d)^m*b*c^3*d^4*m^4*x^4*e^5 - 11760*(x*e + d)^m*c^4*d^4*m^3*x^5*e^5 + 3360*(x*e +
d)^m*b*c^3*d^5*m^4*x^3*e^4 + 10080*(x*e + d)^m*c^4*d^5*m^3*x^4*e^4 - 6720*(x*e + d)^m*c^4*d^6*m^3*x^3*e^3 + 6*
(x*e + d)^m*a^2*b^2*m^8*x^3*e^9 + 4*(x*e + d)^m*a^3*c*m^8*x^3*e^9 + 164*(x*e + d)^m*a*b^3*m^7*x^4*e^9 + 492*(x
*e + d)^m*a^2*b*c*m^7*x^4*e^9 + 670*(x*e + d)^m*b^4*m^6*x^5*e^9 + 8040*(x*e + d)^m*a*b^2*c*m^6*x^5*e^9 + 4020*
(x*e + d)^m*a^2*c^2*m^6*x^5*e^9 + 22536*(x*e + d)^m*b^3*c*m^5*x^6*e^9 + 67608*(x*e + d)^m*a*b*c^2*m^5*x^6*e^9
+ 160314*(x*e + d)^m*b^2*c^2*m^4*x^7*e^9 + 106876*(x*e + d)^m*a*c^3*m^4*x^7*e^9 + 296212*(x*e + d)^m*b*c^3*m^3
*x^8*e^9 + 118124*(x*e + d)^m*c^4*m^2*x^9*e^9 + 6*(x*e + d)^m*a^2*b^2*d*m^8*x^2*e^8 + 4*(x*e + d)^m*a^3*c*d*m^
8*x^2*e^8 + 152*(x*e + d)^m*a*b^3*d*m^7*x^3*e^8 + 456*(x*e + d)^m*a^2*b*c*d*m^7*x^3*e^8 + 526*(x*e + d)^m*b^4*
d*m^6*x^4*e^8 + 6312*(x*e + d)^m*a*b^2*c*d*m^6*x^4*e^8 + 3156*(x*e + d)^m*a^2*c^2*d*m^6*x^4*e^8 + 13216*(x*e +
 d)^m*b^3*c*d*m^5*x^5*e^8 + 39648*(x*e + d)^m*a*b*c^2*d*m^5*x^5*e^8 + 61314*(x*e + d)^m*b^2*c^2*d*m^4*x^6*e^8
+ 40876*(x*e + d)^m*a*c^3*d*m^4*x^6*e^8 + 65520*(x*e + d)^m*b*c^3*d*m^3*x^7*e^8 + 13068*(x*e + d)^m*c^4*d*m^2*
x^8*e^8 - 12*(x*e + d)^m*a*b^3*d^2*m^7*x^2*e^7 - 36*(x*e + d)^m*a^2*b*c*d^2*m^7*x^2*e^7 - 132*(x*e + d)^m*b^4*
d^2*m^6*x^3*e^7 - 1584*(x*e + d)^m*a*b^2*c*d^2*m^6*x^3*e^7 - 792*(x*e + d)^m*a^2*c^2*d^2*m^6*x^3*e^7 - 6920*(x
*e + d)^m*b^3*c*d^2*m^5*x^4*e^7 - 20760*(x*e + d)^m*a*b*c^2*d^2*m^5*x^4*e^7 - 49140*(x*e + d)^m*b^2*c^2*d^2*m^
4*x^5*e^7 - 32760*(x*e + d)^m*a*c^3*d^2*m^4*x^5*e^7 - 64372*(x*e + d)^m*b*c^3*d^2*m^3*x^6*e^7 - 14112*(x*e + d
)^m*c^4*d^2*m^2*x^7*e^7 + 12*(x*e + d)^m*b^4*d^3*m^6*x^2*e^6 + 144*(x*e + d)^m*a*b^2*c*d^3*m^6*x^2*e^6 + 72*(x
*e + d)^m*a^2*c^2*d^3*m^6*x^2*e^6 + 2160*(x*e + d)^m*b^3*c*d^3*m^5*x^3*e^6 + 6480*(x*e + d)^m*a*b*c^2*d^3*m^5*
x^3*e^6 + 33300*(x*e + d)^m*b^2*c^2*d^3*m^4*x^4*e^6 + 22200*(x*e + d)^m*a*c^3*d^3*m^4*x^4*e^6 + 61320*(x*e + d
)^m*b*c^3*d^3*m^3*x^5*e^6 + 15344*(x*e + d)^m*c^4*d^3*m^2*x^6*e^6 - 240*(x*e + d)^m*b^3*c*d^4*m^5*x^2*e^5 - 72
0*(x*e + d)^m*a*b*c^2*d^4*m^5*x^2*e^5 - 14400*(x*e + d)^m*b^2*c^2*d^4*m^4*x^3*e^5 - 9600*(x*e + d)^m*a*c^3*d^4
*m^4*x^3*e^5 - 54600*(x*e + d)^m*b*c^3*d^4*m^3*x^4*e^5 - 16800*(x*e + d)^m*c^4*d^4*m^2*x^5*e^5 + 2160*(x*e + d
)^m*b^2*c^2*d^5*m^4*x^2*e^4 + 1440*(x*e + d)^m*a*c^3*d^5*m^4*x^2*e^4 + 40320*(x*e + d)^m*b*c^3*d^5*m^3*x^3*e^4
 + 18480*(x*e + d)^m*c^4*d^5*m^2*x^4*e^4 - 10080*(x*e + d)^m*b*c^3*d^6*m^3*x^2*e^3 - 20160*(x*e + d)^m*c^4*d^6
*m^2*x^3*e^3 + 20160*(x*e + d)^m*c^4*d^7*m^2*x^2*e^2 + 4*(x*e + d)^m*a^3*b*m^8*x^2*e^9 + 252*(x*e + d)^m*a^2*b
^2*m^7*x^3*e^9 + 168*(x*e + d)^m*a^3*c*m^7*x^3*e^9 + 2824*(x*e + d)^m*a*b^3*m^6*x^4*e^9 + 8472*(x*e + d)^m*a^2
*b*c*m^6*x^4*e^9 + 6100*(x*e + d)^m*b^4*m^5*x^5*e^9 + 73200*(x*e + d)^m*a*b^2*c*m^5*x^5*e^9 + 36600*(x*e + d)^
m*a^2*c^2*m^5*x^5*e^9 + 117876*(x*e + d)^m*b^3*c*m^4*x^6*e^9 + 353628*(x*e + d)^m*a*b*c^2*m^4*x^6*e^9 + 493752
*(x*e + d)^m*b^2*c^2*m^3*x^7*e^9 + 329168*(x*e + d)^m*a*c^3*m^3*x^7*e^9 + 525024*(x*e + d)^m*b*c^3*m^2*x^8*e^9
 + 109584*(x*e + d)^m*c^4*m*x^9*e^9 + 4*(x*e + d)^m*a^3*b*d*m^8*x*e^8 + 240*(x*e + d)^m*a^2*b^2*d*m^7*x^2*e^8
+ 160*(x*e + d)^m*a^3*c*d*m^7*x^2*e^8 + 2368*(x*e + d)^m*a*b^3*d*m^6*x^3*e^8 + 7104*(x*e + d)^m*a^2*b*c*d*m^6*
x^3*e^8 + 3996*(x*e + d)^m*b^4*d*m^5*x^4*e^8 + 47952*(x*e + d)^m*a*b^2*c*d*m^5*x^4*e^8 + 23976*(x*e + d)^m*a^2
*c^2*d*m^5*x^4*e^8 + 51796*(x*e + d)^m*b^3*c*d*m^4*x^5*e^8 + 155388*(x*e + d)^m*a*b*c^2*d*m^4*x^5*e^8 + 125868
*(x*e + d)^m*b^2*c^2*d*m^3*x^6*e^8 + 83912*(x*e + d)^m*a*c^3*d*m^3*x^6*e^8 + 66384*(x*e + d)^m*b*c^3*d*m^2*x^7
*e^8 + 5040*(x*e + d)^m*c^4*d*m*x^8*e^8 - 12*(x*e + d)^m*a^2*b^2*d^2*m^7*x*e^7 - 8*(x*e + d)^m*a^3*c*d^2*m^7*x
*e^7 - 432*(x*e + d)^m*a*b^3*d^2*m^6*x^2*e^7 - 1296*(x*e + d)^m*a^2*b*c*d^2*m^6*x^2*e^7 - 1708*(x*e + d)^m*b^4
*d^2*m^5*x^3*e^7 - 20496*(x*e + d)^m*a*b^2*c*d^2*m^5*x^3*e^7 - 10248*(x*e + d)^m*a^2*c^2*d^2*m^5*x^3*e^7 - 384
00*(x*e + d)^m*b^3*c*d^2*m^4*x^4*e^7 - 115200*(x*e + d)^m*a*b*c^2*d^2*m^4*x^4*e^7 - 122184*(x*e + d)^m*b^2*c^2
*d^2*m^3*x^5*e^7 - 81456*(x*e + d)^m*a*c^3*d^2*m^3*x^5*e^7 - 72408*(x*e + d)^m*b*c^3*d^2*m^2*x^6*e^7 - 5760*(x
*e + d)^m*c^4*d^2*m*x^7*e^7 + 24*(x*e + d)^m*a*b^3*d^3*m^6*x*e^6 + 72*(x*e + d)^m*a^2*b*c*d^3*m^6*x*e^6 + 372*
(x*e + d)^m*b^4*d^3*m^5*x^2*e^6 + 4464*(x*e + d)^m*a*b^2*c*d^3*m^5*x^2*e^6 + 2232*(x*e + d)^m*a^2*c^2*d^3*m^5*
x^2*e^6 + 21200*(x*e + d)^m*b^3*c*d^3*m^4*x^3*e^6 + 63600*(x*e + d)^m*a*b*c^2*d^3*m^4*x^3*e^6 + 112500*(x*e +
d)^m*b^2*c^2*d^3*m^3*x^4*e^6 + 75000*(x*e + d)^m*a*c^3*d^3*m^3*x^4*e^6 + 79632*(x*e + d)^m*b*c^3*d^3*m^2*x^5*e
^6 + 6720*(x*e + d)^m*c^4*d^3*m*x^6*e^6 - 24*(x*e + d)^m*b^4*d^4*m^5*x*e^5 - 288*(x*e + d)^m*a*b^2*c*d^4*m^5*x
*e^5 - 144*(x*e + d)^m*a^2*c^2*d^4*m^5*x*e^5 - 6000*(x*e + d)^m*b^3*c*d^4*m^4*x^2*e^5 - 18000*(x*e + d)^m*a*b*
c^2*d^4*m^4*x^2*e^5 - 90000*(x*e + d)^m*b^2*c^2*d^4*m^3*x^3*e^5 - 60000*(x*e + d)^m*a*c^3*d^4*m^3*x^3*e^5 - 88
200*(x*e + d)^m*b*c^3*d^4*m^2*x^4*e^5 - 8064*(x*e + d)^m*c^4*d^4*m*x^5*e^5 + 480*(x*e + d)^m*b^3*c*d^5*m^4*x*e
^4 + 1440*(x*e + d)^m*a*b*c^2*d^5*m^4*x*e^4 + 38880*(x*e + d)^m*b^2*c^2*d^5*m^3*x^2*e^4 + 25920*(x*e + d)^m*a*
c^3*d^5*m^3*x^2*e^4 + 97440*(x*e + d)^m*b*c^3*d^5*m^2*x^3*e^4 + 10080*(x*e + d)^m*c^4*d^5*m*x^4*e^4 - 4320*(x*
e + d)^m*b^2*c^2*d^6*m^3*x*e^3 - 2880*(x*e + d)^m*a*c^3*d^6*m^3*x*e^3 - 100800*(x*e + d)^m*b*c^3*d^6*m^2*x^2*e
^3 - 13440*(x*e + d)^m*c^4*d^6*m*x^3*e^3 + 20160*(x*e + d)^m*b*c^3*d^7*m^2*x*e^2 + 20160*(x*e + d)^m*c^4*d^7*m
*x^2*e^2 - 40320*(x*e + d)^m*c^4*d^8*m*x*e + (x*e + d)^m*a^4*m^8*x*e^9 + 172*(x*e + d)^m*a^3*b*m^7*x^2*e^9 + 4
464*(x*e + d)^m*a^2*b^2*m^6*x^3*e^9 + 2976*(x*e + d)^m*a^3*c*m^6*x^3*e^9 + 26504*(x*e + d)^m*a*b^3*m^5*x^4*e^9
 + 79512*(x*e + d)^m*a^2*b*c*m^5*x^4*e^9 + 32773*(x*e + d)^m*b^4*m^4*x^5*e^9 + 393276*(x*e + d)^m*a*b^2*c*m^4*
x^5*e^9 + 196638*(x*e + d)^m*a^2*c^2*m^4*x^5*e^9 + 370044*(x*e + d)^m*b^3*c*m^3*x^6*e^9 + 1110132*(x*e + d)^m*
a*b*c^2*m^3*x^6*e^9 + 885816*(x*e + d)^m*b^2*c^2*m^2*x^7*e^9 + 590544*(x*e + d)^m*a*c^3*m^2*x^7*e^9 + 490608*(
x*e + d)^m*b*c^3*m*x^8*e^9 + 40320*(x*e + d)^m*c^4*x^9*e^9 + (x*e + d)^m*a^4*d*m^8*e^8 + 168*(x*e + d)^m*a^3*b
*d*m^7*x*e^8 + 3984*(x*e + d)^m*a^2*b^2*d*m^6*x^2*e^8 + 2656*(x*e + d)^m*a^3*c*d*m^6*x^2*e^8 + 19400*(x*e + d)
^m*a*b^3*d*m^5*x^3*e^8 + 58200*(x*e + d)^m*a^2*b*c*d*m^5*x^3*e^8 + 16789*(x*e + d)^m*b^4*d*m^4*x^4*e^8 + 20146
8*(x*e + d)^m*a*b^2*c*d*m^4*x^4*e^8 + 100734*(x*e + d)^m*a^2*c^2*d*m^4*x^4*e^8 + 111064*(x*e + d)^m*b^3*c*d*m^
3*x^5*e^8 + 333192*(x*e + d)^m*a*b*c^2*d*m^3*x^5*e^8 + 130608*(x*e + d)^m*b^2*c^2*d*m^2*x^6*e^8 + 87072*(x*e +
 d)^m*a*c^3*d*m^2*x^6*e^8 + 25920*(x*e + d)^m*b*c^3*d*m*x^7*e^8 - 4*(x*e + d)^m*a^3*b*d^2*m^7*e^7 - 468*(x*e +
 d)^m*a^2*b^2*d^2*m^6*x*e^7 - 312*(x*e + d)^m*a^3*c*d^2*m^6*x*e^7 - 6240*(x*e + d)^m*a*b^3*d^2*m^5*x^2*e^7 - 1
8720*(x*e + d)^m*a^2*b*c*d^2*m^5*x^2*e^7 - 10860*(x*e + d)^m*b^4*d^2*m^4*x^3*e^7 - 130320*(x*e + d)^m*a*b^2*c*
d^2*m^4*x^3*e^7 - 65160*(x*e + d)^m*a^2*c^2*d^2*m^4*x^3*e^7 - 105380*(x*e + d)^m*b^3*c*d^2*m^3*x^4*e^7 - 31614
0*(x*e + d)^m*a*b*c^2*d^2*m^3*x^4*e^7 - 144288*(x*e + d)^m*b^2*c^2*d^2*m^2*x^5*e^7 - 96192*(x*e + d)^m*a*c^3*d
^2*m^2*x^5*e^7 - 30240*(x*e + d)^m*b*c^3*d^2*m*x^6*e^7 + 12*(x*e + d)^m*a^2*b^2*d^3*m^6*e^6 + 8*(x*e + d)^m*a^
3*c*d^3*m^6*e^6 + 840*(x*e + d)^m*a*b^3*d^3*m^5*x*e^6 + 2520*(x*e + d)^m*a^2*b*c*d^3*m^5*x*e^6 + 4380*(x*e + d
)^m*b^4*d^3*m^4*x^2*e^6 + 52560*(x*e + d)^m*a*b^2*c*d^3*m^4*x^2*e^6 + 26280*(x*e + d)^m*a^2*c^2*d^3*m^4*x^2*e^
6 + 90000*(x*e + d)^m*b^3*c*d^3*m^3*x^3*e^6 + 270000*(x*e + d)^m*a*b*c^2*d^3*m^3*x^3*e^6 + 160920*(x*e + d)^m*
b^2*c^2*d^3*m^2*x^4*e^6 + 107280*(x*e + d)^m*a*c^3*d^3*m^2*x^4*e^6 + 36288*(x*e + d)^m*b*c^3*d^3*m*x^5*e^6 - 2
4*(x*e + d)^m*a*b^3*d^4*m^5*e^5 - 72*(x*e + d)^m*a^2*b*c*d^4*m^5*e^5 - 720*(x*e + d)^m*b^4*d^4*m^4*x*e^5 - 864
0*(x*e + d)^m*a*b^2*c*d^4*m^4*x*e^5 - 4320*(x*e + d)^m*a^2*c^2*d^4*m^4*x*e^5 - 51600*(x*e + d)^m*b^3*c*d^4*m^3
*x^2*e^5 - 154800*(x*e + d)^m*a*b*c^2*d^4*m^3*x^2*e^5 - 180000*(x*e + d)^m*b^2*c^2*d^4*m^2*x^3*e^5 - 120000*(x
*e + d)^m*a*c^3*d^4*m^2*x^3*e^5 - 45360*(x*e + d)^m*b*c^3*d^4*m*x^4*e^5 + 24*(x*e + d)^m*b^4*d^5*m^4*e^4 + 288
*(x*e + d)^m*a*b^2*c*d^5*m^4*e^4 + 144*(x*e + d)^m*a^2*c^2*d^5*m^4*e^4 + 11520*(x*e + d)^m*b^3*c*d^5*m^3*x*e^4
 + 34560*(x*e + d)^m*a*b*c^2*d^5*m^3*x*e^4 + 192240*(x*e + d)^m*b^2*c^2*d^5*m^2*x^2*e^4 + 128160*(x*e + d)^m*a
*c^3*d^5*m^2*x^2*e^4 + 60480*(x*e + d)^m*b*c^3*d^5*m*x^3*e^4 - 480*(x*e + d)^m*b^3*c*d^6*m^3*e^3 - 1440*(x*e +
 d)^m*a*b*c^2*d^6*m^3*e^3 - 73440*(x*e + d)^m*b^2*c^2*d^6*m^2*x*e^3 - 48960*(x*e + d)^m*a*c^3*d^6*m^2*x*e^3 -
90720*(x*e + d)^m*b*c^3*d^6*m*x^2*e^3 + 4320*(x*e + d)^m*b^2*c^2*d^7*m^2*e^2 + 2880*(x*e + d)^m*a*c^3*d^7*m^2*
e^2 + 181440*(x*e + d)^m*b*c^3*d^7*m*x*e^2 - 20160*(x*e + d)^m*b*c^3*d^8*m*e + 40320*(x*e + d)^m*c^4*d^9 + 44*
(x*e + d)^m*a^4*m^7*x*e^9 + 3136*(x*e + d)^m*a^3*b*m^6*x^2*e^9 + 43308*(x*e + d)^m*a^2*b^2*m^5*x^3*e^9 + 28872
*(x*e + d)^m*a^3*c*m^5*x^3*e^9 + 147076*(x*e + d)^m*a*b^3*m^4*x^4*e^9 + 441228*(x*e + d)^m*a^2*b*c*m^4*x^4*e^9
 + 105460*(x*e + d)^m*b^4*m^3*x^5*e^9 + 1265520*(x*e + d)^m*a*b^2*c*m^3*x^5*e^9 + 632760*(x*e + d)^m*a^2*c^2*m
^3*x^5*e^9 + 674456*(x*e + d)^m*b^3*c*m^2*x^6*e^9 + 2023368*(x*e + d)^m*a*b*c^2*m^2*x^6*e^9 + 835488*(x*e + d)
^m*b^2*c^2*m*x^7*e^9 + 556992*(x*e + d)^m*a*c^3*m*x^7*e^9 + 181440*(x*e + d)^m*b*c^3*x^8*e^9 + 44*(x*e + d)^m*
a^4*d*m^7*e^8 + 2968*(x*e + d)^m*a^3*b*d*m^6*x*e^8 + 35340*(x*e + d)^m*a^2*b^2*d*m^5*x^2*e^8 + 23560*(x*e + d)
^m*a^3*c*d*m^5*x^2*e^8 + 88876*(x*e + d)^m*a*b^3*d*m^4*x^3*e^8 + 266628*(x*e + d)^m*a^2*b*c*d*m^4*x^3*e^8 + 38
304*(x*e + d)^m*b^4*d*m^3*x^4*e^8 + 459648*(x*e + d)^m*a*b^2*c*d*m^3*x^4*e^8 + 229824*(x*e + d)^m*a^2*c^2*d*m^
3*x^4*e^8 + 119136*(x*e + d)^m*b^3*c*d*m^2*x^5*e^8 + 357408*(x*e + d)^m*a*b*c^2*d*m^2*x^5*e^8 + 51840*(x*e + d
)^m*b^2*c^2*d*m*x^6*e^8 + 34560*(x*e + d)^m*a*c^3*d*m*x^6*e^8 - 168*(x*e + d)^m*a^3*b*d^2*m^6*e^7 - 7500*(x*e
+ d)^m*a^2*b^2*d^2*m^5*x*e^7 - 5000*(x*e + d)^m*a^3*c*d^2*m^5*x*e^7 - 45720*(x*e + d)^m*a*b^3*d^2*m^4*x^2*e^7
- 137160*(x*e + d)^m*a^2*b*c*d^2*m^4*x^2*e^7 - 34576*(x*e + d)^m*b^4*d^2*m^3*x^3*e^7 - 414912*(x*e + d)^m*a*b^
2*c*d^2*m^3*x^3*e^7 - 207456*(x*e + d)^m*a^2*c^2*d^2*m^3*x^3*e^7 - 133800*(x*e + d)^m*b^3*c*d^2*m^2*x^4*e^7 -
401400*(x*e + d)^m*a*b*c^2*d^2*m^2*x^4*e^7 - 62208*(x*e + d)^m*b^2*c^2*d^2*m*x^5*e^7 - 41472*(x*e + d)^m*a*c^3
*d^2*m*x^5*e^7 + 468*(x*e + d)^m*a^2*b^2*d^3*m^5*e^6 + 312*(x*e + d)^m*a^3*c*d^3*m^5*e^6 + 11640*(x*e + d)^m*a
*b^3*d^3*m^4*x*e^6 + 34920*(x*e + d)^m*a^2*b*c*d^3*m^4*x*e^6 + 23820*(x*e + d)^m*b^4*d^3*m^3*x^2*e^6 + 285840*
(x*e + d)^m*a*b^2*c*d^3*m^3*x^2*e^6 + 142920*(x*e + d)^m*a^2*c^2*d^3*m^3*x^2*e^6 + 151520*(x*e + d)^m*b^3*c*d^
3*m^2*x^3*e^6 + 454560*(x*e + d)^m*a*b*c^2*d^3*m^2*x^3*e^6 + 77760*(x*e + d)^m*b^2*c^2*d^3*m*x^4*e^6 + 51840*(
x*e + d)^m*a*c^3*d^3*m*x^4*e^6 - 840*(x*e + d)^m*a*b^3*d^4*m^4*e^5 - 2520*(x*e + d)^m*a^2*b*c*d^4*m^4*e^5 - 80
40*(x*e + d)^m*b^4*d^4*m^3*x*e^5 - 96480*(x*e + d)^m*a*b^2*c*d^4*m^3*x*e^5 - 48240*(x*e + d)^m*a^2*c^2*d^4*m^3
*x*e^5 - 166800*(x*e + d)^m*b^3*c*d^4*m^2*x^2*e^5 - 500400*(x*e + d)^m*a*b*c^2*d^4*m^2*x^2*e^5 - 103680*(x*e +
 d)^m*b^2*c^2*d^4*m*x^3*e^5 - 69120*(x*e + d)^m*a*c^3*d^4*m*x^3*e^5 + 720*(x*e + d)^m*b^4*d^5*m^3*e^4 + 8640*(
x*e + d)^m*a*b^2*c*d^5*m^3*e^4 + 4320*(x*e + d)^m*a^2*c^2*d^5*m^3*e^4 + 91680*(x*e + d)^m*b^3*c*d^5*m^2*x*e^4
+ 275040*(x*e + d)^m*a*b*c^2*d^5*m^2*x*e^4 + 155520*(x*e + d)^m*b^2*c^2*d^5*m*x^2*e^4 + 103680*(x*e + d)^m*a*c
^3*d^5*m*x^2*e^4 - 11520*(x*e + d)^m*b^3*c*d^6*m^2*e^3 - 34560*(x*e + d)^m*a*b*c^2*d^6*m^2*e^3 - 311040*(x*e +
 d)^m*b^2*c^2*d^6*m*x*e^3 - 207360*(x*e + d)^m*a*c^3*d^6*m*x*e^3 + 73440*(x*e + d)^m*b^2*c^2*d^7*m*e^2 + 48960
*(x*e + d)^m*a*c^3*d^7*m*e^2 - 181440*(x*e + d)^m*b*c^3*d^8*e + 826*(x*e + d)^m*a^4*m^6*x*e^9 + 31528*(x*e + d
)^m*a^3*b*m^5*x^2*e^9 + 249714*(x*e + d)^m*a^2*b^2*m^4*x^3*e^9 + 166476*(x*e + d)^m*a^3*c*m^4*x^3*e^9 + 488996
*(x*e + d)^m*a*b^3*m^3*x^4*e^9 + 1466988*(x*e + d)^m*a^2*b*c*m^3*x^4*e^9 + 196380*(x*e + d)^m*b^4*m^2*x^5*e^9
+ 2356560*(x*e + d)^m*a*b^2*c*m^2*x^5*e^9 + 1178280*(x*e + d)^m*a^2*c^2*m^2*x^5*e^9 + 644064*(x*e + d)^m*b^3*c
*m*x^6*e^9 + 1932192*(x*e + d)^m*a*b*c^2*m*x^6*e^9 + 311040*(x*e + d)^m*b^2*c^2*x^7*e^9 + 207360*(x*e + d)^m*a
*c^3*x^7*e^9 + 826*(x*e + d)^m*a^4*d*m^6*e^8 + 28560*(x*e + d)^m*a^3*b*d*m^5*x*e^8 + 179034*(x*e + d)^m*a^2*b^
2*d*m^4*x^2*e^8 + 119356*(x*e + d)^m*a^3*c*d*m^4*x^2*e^8 + 222368*(x*e + d)^m*a*b^3*d*m^3*x^3*e^8 + 667104*(x*
e + d)^m*a^2*b*c*d*m^3*x^3*e^8 + 43164*(x*e + d)^m*b^4*d*m^2*x^4*e^8 + 517968*(x*e + d)^m*a*b^2*c*d*m^2*x^4*e^
8 + 258984*(x*e + d)^m*a^2*c^2*d*m^2*x^4*e^8 + 48384*(x*e + d)^m*b^3*c*d*m*x^5*e^8 + 145152*(x*e + d)^m*a*b*c^
2*d*m*x^5*e^8 - 2968*(x*e + d)^m*a^3*b*d^2*m^5*e^7 - 63180*(x*e + d)^m*a^2*b^2*d^2*m^4*x*e^7 - 42120*(x*e + d)
^m*a^3*c*d^2*m^4*x*e^7 - 175188*(x*e + d)^m*a*b^3*d^2*m^3*x^2*e^7 - 525564*(x*e + d)^m*a^2*b*c*d^2*m^3*x^2*e^7
 - 49488*(x*e + d)^m*b^4*d^2*m^2*x^3*e^7 - 593856*(x*e + d)^m*a*b^2*c*d^2*m^2*x^3*e^7 - 296928*(x*e + d)^m*a^2
*c^2*d^2*m^2*x^3*e^7 - 60480*(x*e + d)^m*b^3*c*d^2*m*x^4*e^7 - 181440*(x*e + d)^m*a*b*c^2*d^2*m*x^4*e^7 + 7500
*(x*e + d)^m*a^2*b^2*d^3*m^4*e^6 + 5000*(x*e + d)^m*a^3*c*d^3*m^4*e^6 + 79800*(x*e + d)^m*a*b^3*d^3*m^3*x*e^6
+ 239400*(x*e + d)^m*a^2*b*c*d^3*m^3*x*e^6 + 56088*(x*e + d)^m*b^4*d^3*m^2*x^2*e^6 + 673056*(x*e + d)^m*a*b^2*
c*d^3*m^2*x^2*e^6 + 336528*(x*e + d)^m*a^2*c^2*d^3*m^2*x^2*e^6 + 80640*(x*e + d)^m*b^3*c*d^3*m*x^3*e^6 + 24192
0*(x*e + d)^m*a*b*c^2*d^3*m*x^3*e^6 - 11640*(x*e + d)^m*a*b^3*d^4*m^3*e^5 - 34920*(x*e + d)^m*a^2*b*c*d^4*m^3*
e^5 - 39600*(x*e + d)^m*b^4*d^4*m^2*x*e^5 - 475200*(x*e + d)^m*a*b^2*c*d^4*m^2*x*e^5 - 237600*(x*e + d)^m*a^2*
c^2*d^4*m^2*x*e^5 - 120960*(x*e + d)^m*b^3*c*d^4*m*x^2*e^5 - 362880*(x*e + d)^m*a*b*c^2*d^4*m*x^2*e^5 + 8040*(
x*e + d)^m*b^4*d^5*m^2*e^4 + 96480*(x*e + d)^m*a*b^2*c*d^5*m^2*e^4 + 48240*(x*e + d)^m*a^2*c^2*d^5*m^2*e^4 + 2
41920*(x*e + d)^m*b^3*c*d^5*m*x*e^4 + 725760*(x*e + d)^m*a*b*c^2*d^5*m*x*e^4 - 91680*(x*e + d)^m*b^3*c*d^6*m*e
^3 - 275040*(x*e + d)^m*a*b*c^2*d^6*m*e^3 + 311040*(x*e + d)^m*b^2*c^2*d^7*e^2 + 207360*(x*e + d)^m*a*c^3*d^7*
e^2 + 8624*(x*e + d)^m*a^4*m^5*x*e^9 + 190036*(x*e + d)^m*a^3*b*m^4*x^2*e^9 + 866808*(x*e + d)^m*a^2*b^2*m^3*x
^3*e^9 + 577872*(x*e + d)^m*a^3*c*m^3*x^3*e^9 + 938736*(x*e + d)^m*a*b^3*m^2*x^4*e^9 + 2816208*(x*e + d)^m*a^2
*b*c*m^2*x^4*e^9 + 190800*(x*e + d)^m*b^4*m*x^5*e^9 + 2289600*(x*e + d)^m*a*b^2*c*m*x^5*e^9 + 1144800*(x*e + d
)^m*a^2*c^2*m*x^5*e^9 + 241920*(x*e + d)^m*b^3*c*x^6*e^9 + 725760*(x*e + d)^m*a*b*c^2*x^6*e^9 + 8624*(x*e + d)
^m*a^4*d*m^5*e^8 + 161476*(x*e + d)^m*a^3*b*d*m^4*x*e^8 + 508740*(x*e + d)^m*a^2*b^2*d*m^3*x^2*e^8 + 339160*(x
*e + d)^m*a^3*c*d*m^3*x^2*e^8 + 271632*(x*e + d)^m*a*b^3*d*m^2*x^3*e^8 + 814896*(x*e + d)^m*a^2*b*c*d*m^2*x^3*
e^8 + 18144*(x*e + d)^m*b^4*d*m*x^4*e^8 + 217728*(x*e + d)^m*a*b^2*c*d*m*x^4*e^8 + 108864*(x*e + d)^m*a^2*c^2*
d*m*x^4*e^8 - 28560*(x*e + d)^m*a^3*b*d^2*m^4*e^7 - 294888*(x*e + d)^m*a^2*b^2*d^2*m^3*x*e^7 - 196592*(x*e + d
)^m*a^3*c*d^2*m^3*x*e^7 - 316728*(x*e + d)^m*a*b^3*d^2*m^2*x^2*e^7 - 950184*(x*e + d)^m*a^2*b*c*d^2*m^2*x^2*e^
7 - 24192*(x*e + d)^m*b^4*d^2*m*x^3*e^7 - 290304*(x*e + d)^m*a*b^2*c*d^2*m*x^3*e^7 - 145152*(x*e + d)^m*a^2*c^
2*d^2*m*x^3*e^7 + 63180*(x*e + d)^m*a^2*b^2*d^3*m^3*e^6 + 42120*(x*e + d)^m*a^3*c*d^3*m^3*e^6 + 270576*(x*e +
d)^m*a*b^3*d^3*m^2*x*e^6 + 811728*(x*e + d)^m*a^2*b*c*d^3*m^2*x*e^6 + 36288*(x*e + d)^m*b^4*d^3*m*x^2*e^6 + 43
5456*(x*e + d)^m*a*b^2*c*d^3*m*x^2*e^6 + 217728*(x*e + d)^m*a^2*c^2*d^3*m*x^2*e^6 - 79800*(x*e + d)^m*a*b^3*d^
4*m^2*e^5 - 239400*(x*e + d)^m*a^2*b*c*d^4*m^2*e^5 - 72576*(x*e + d)^m*b^4*d^4*m*x*e^5 - 870912*(x*e + d)^m*a*
b^2*c*d^4*m*x*e^5 - 435456*(x*e + d)^m*a^2*c^2*d^4*m*x*e^5 + 39600*(x*e + d)^m*b^4*d^5*m*e^4 + 475200*(x*e + d
)^m*a*b^2*c*d^5*m*e^4 + 237600*(x*e + d)^m*a^2*c^2*d^5*m*e^4 - 241920*(x*e + d)^m*b^3*c*d^6*e^3 - 725760*(x*e
+ d)^m*a*b*c^2*d^6*e^3 + 54649*(x*e + d)^m*a^4*m^4*x*e^9 + 697228*(x*e + d)^m*a^3*b*m^3*x^2*e^9 + 1741656*(x*e
 + d)^m*a^2*b^2*m^2*x^3*e^9 + 1161104*(x*e + d)^m*a^3*c*m^2*x^3*e^9 + 935856*(x*e + d)^m*a*b^3*m*x^4*e^9 + 280
7568*(x*e + d)^m*a^2*b*c*m*x^4*e^9 + 72576*(x*e + d)^m*b^4*x^5*e^9 + 870912*(x*e + d)^m*a*b^2*c*x^5*e^9 + 4354
56*(x*e + d)^m*a^2*c^2*x^5*e^9 + 54649*(x*e + d)^m*a^4*d*m^4*e^8 + 535752*(x*e + d)^m*a^3*b*d*m^3*x*e^8 + 7241
76*(x*e + d)^m*a^2*b^2*d*m^2*x^2*e^8 + 482784*(x*e + d)^m*a^3*c*d*m^2*x^2*e^8 + 120960*(x*e + d)^m*a*b^3*d*m*x
^3*e^8 + 362880*(x*e + d)^m*a^2*b*c*d*m*x^3*e^8 - 161476*(x*e + d)^m*a^3*b*d^2*m^3*e^7 - 722592*(x*e + d)^m*a^
2*b^2*d^2*m^2*x*e^7 - 481728*(x*e + d)^m*a^3*c*d^2*m^2*x*e^7 - 181440*(x*e + d)^m*a*b^3*d^2*m*x^2*e^7 - 544320
*(x*e + d)^m*a^2*b*c*d^2*m*x^2*e^7 + 294888*(x*e + d)^m*a^2*b^2*d^3*m^2*e^6 + 196592*(x*e + d)^m*a^3*c*d^3*m^2
*e^6 + 362880*(x*e + d)^m*a*b^3*d^3*m*x*e^6 + 1088640*(x*e + d)^m*a^2*b*c*d^3*m*x*e^6 - 270576*(x*e + d)^m*a*b
^3*d^4*m*e^5 - 811728*(x*e + d)^m*a^2*b*c*d^4*m*e^5 + 72576*(x*e + d)^m*b^4*d^5*e^4 + 870912*(x*e + d)^m*a*b^2
*c*d^5*e^4 + 435456*(x*e + d)^m*a^2*c^2*d^5*e^4 + 214676*(x*e + d)^m*a^4*m^3*x*e^9 + 1500264*(x*e + d)^m*a^3*b
*m^2*x^2*e^9 + 1811232*(x*e + d)^m*a^2*b^2*m*x^3*e^9 + 1207488*(x*e + d)^m*a^3*c*m*x^3*e^9 + 362880*(x*e + d)^
m*a*b^3*x^4*e^9 + 1088640*(x*e + d)^m*a^2*b*c*x^4*e^9 + 214676*(x*e + d)^m*a^4*d*m^3*e^8 + 964512*(x*e + d)^m*
a^3*b*d*m^2*x*e^8 + 362880*(x*e + d)^m*a^2*b^2*d*m*x^2*e^8 + 241920*(x*e + d)^m*a^3*c*d*m*x^2*e^8 - 535752*(x*
e + d)^m*a^3*b*d^2*m^2*e^7 - 725760*(x*e + d)^m*a^2*b^2*d^2*m*x*e^7 - 483840*(x*e + d)^m*a^3*c*d^2*m*x*e^7 + 7
22592*(x*e + d)^m*a^2*b^2*d^3*m*e^6 + 481728*(x*e + d)^m*a^3*c*d^3*m*e^6 - 362880*(x*e + d)^m*a*b^3*d^4*e^5 -
1088640*(x*e + d)^m*a^2*b*c*d^4*e^5 + 509004*(x*e + d)^m*a^4*m^2*x*e^9 + 1690272*(x*e + d)^m*a^3*b*m*x^2*e^9 +
 725760*(x*e + d)^m*a^2*b^2*x^3*e^9 + 483840*(x*e + d)^m*a^3*c*x^3*e^9 + 509004*(x*e + d)^m*a^4*d*m^2*e^8 + 72
5760*(x*e + d)^m*a^3*b*d*m*x*e^8 - 964512*(x*e + d)^m*a^3*b*d^2*m*e^7 + 725760*(x*e + d)^m*a^2*b^2*d^3*e^6 + 4
83840*(x*e + d)^m*a^3*c*d^3*e^6 + 663696*(x*e + d)^m*a^4*m*x*e^9 + 725760*(x*e + d)^m*a^3*b*x^2*e^9 + 663696*(
x*e + d)^m*a^4*d*m*e^8 - 725760*(x*e + d)^m*a^3*b*d^2*e^7 + 362880*(x*e + d)^m*a^4*x*e^9 + 362880*(x*e + d)^m*
a^4*d*e^8)/(m^9*e^9 + 45*m^8*e^9 + 870*m^7*e^9 + 9450*m^6*e^9 + 63273*m^5*e^9 + 269325*m^4*e^9 + 723680*m^3*e^
9 + 1172700*m^2*e^9 + 1026576*m*e^9 + 362880*e^9)

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