3.2227 \(\int \frac {1}{(d+e x) (a+b x+c x^2)^5} \, dx\)

Optimal. Leaf size=1324 \[ \frac {\log (d+e x) e^9}{\left (c d^2-b e d+a e^2\right )^5}-\frac {\log \left (c x^2+b x+a\right ) e^9}{2 \left (c d^2-b e d+a e^2\right )^5}-\frac {\left (140 c^9 d^9-90 c^8 e (7 b d-8 a e) d^7+72 c^7 e^2 \left (15 b^2 d^2-35 a b e d+21 a^2 e^2\right ) d^5-84 c^6 e^3 \left (10 b^3 d^3-36 a b^2 e d^2+45 a^2 b e^2 d-20 a^3 e^3\right ) d^3+252 c^5 e^4 \left (b^4 d^4-5 a b^3 e d^3+10 a^2 b^2 e^2 d^2-10 a^3 b e^3 d+5 a^4 e^4\right ) d-b^9 e^9-630 a^4 b c^4 e^9+420 a^3 b^3 c^3 e^9-126 a^2 b^5 c^2 e^9+18 a b^7 c e^9\right ) \tanh ^{-1}\left (\frac {b+2 c x}{\sqrt {b^2-4 a c}}\right )}{\left (b^2-4 a c\right )^{9/2} \left (c d^2-e (b d-a e)\right )^5}+\frac {2 e^7 b^8+c d e^6 b^7+c e^5 \left (c d^2-31 a e^2\right ) b^6+c^2 d e^4 \left (c d^2-14 a e^2\right ) b^5-c^2 e^3 \left (125 c^2 d^4+13 a c e^2 d^2-178 a^2 e^4\right ) b^4+c^3 d e^2 \left (295 c^2 d^4+492 a c e^2 d^2+69 a^2 e^4\right ) b^3-c^3 e \left (245 c^3 d^6+725 a c^2 e^2 d^4+699 a^2 c e^4 d^2+443 a^3 e^6\right ) b^2+2 c^4 d \left (35 c^3 d^6+145 a c^2 e^2 d^4+233 a^2 c e^4 d^2+187 a^3 e^6\right ) b+256 a^4 c^4 e^7+2 c (2 c d-b e) \left (35 c^6 d^6-5 c^5 e (21 b d-29 a e) d^4+c^4 e^2 \left (95 b^2 d^2-290 a b e d+233 a^2 e^2\right ) d^2-b^6 e^6-3 b^4 c e^5 (b d-5 a e)-b^2 c^2 e^4 \left (7 b^2 d^2-44 a b e d+82 a^2 e^2\right )-c^3 e^3 \left (15 b^3 d^3-101 a b^2 e d^2+233 a^2 b e^2 d-187 a^3 e^3\right )\right ) x}{2 \left (b^2-4 a c\right )^4 \left (c d^2-b e d+a e^2\right )^4 \left (c x^2+b x+a\right )}+\frac {5 a c e \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right ) (2 c d-b e)^2-2 c \left (35 c^4 d^4-10 c^3 e (7 b d-11 a e) d^2+3 b^4 e^4+2 b^2 c e^3 (5 b d-17 a e)+c^2 e^2 \left (25 b^2 d^2-110 a b e d+123 a^2 e^2\right )\right ) x (2 c d-b e)-\left (-e b^2+c d b+2 a c e\right ) \left (70 c^4 d^4-15 c^3 e (7 b d-10 a e) d^2+6 b^4 e^4+2 b^2 c e^3 (5 b d-24 a e)+3 c^2 e^2 \left (5 b^2 d^2-25 a b e d+32 a^2 e^2\right )\right )}{12 \left (b^2-4 a c\right )^3 \left (c d^2-b e d+a e^2\right )^3 \left (c x^2+b x+a\right )^2}-\frac {7 a c e (2 c d-b e)^2-2 c \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right ) x (2 c d-b e)-\left (-e b^2+c d b+2 a c e\right ) \left (14 c^2 d^2-4 b^2 e^2-c e (7 b d-16 a e)\right )}{12 \left (b^2-4 a c\right )^2 \left (c d^2-b e d+a e^2\right )^2 \left (c x^2+b x+a\right )^3}-\frac {-e b^2+c d b+2 a c e+c (2 c d-b e) x}{4 \left (b^2-4 a c\right ) \left (c d^2-b e d+a e^2\right ) \left (c x^2+b x+a\right )^4} \]

[Out]

1/4*(-b*c*d+b^2*e-2*a*c*e-c*(-b*e+2*c*d)*x)/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/(c*x^2+b*x+a)^4+1/12*(-7*a*c*e*(-
b*e+2*c*d)^2+(2*a*c*e-b^2*e+b*c*d)*(14*c^2*d^2-4*b^2*e^2-c*e*(-16*a*e+7*b*d))+2*c*(-b*e+2*c*d)*(7*c^2*d^2-2*b^
2*e^2-c*e*(-15*a*e+7*b*d))*x)/(-4*a*c+b^2)^2/(a*e^2-b*d*e+c*d^2)^2/(c*x^2+b*x+a)^3+1/12*(5*a*c*e*(-b*e+2*c*d)^
2*(7*c^2*d^2-2*b^2*e^2-c*e*(-15*a*e+7*b*d))-(2*a*c*e-b^2*e+b*c*d)*(70*c^4*d^4+6*b^4*e^4+2*b^2*c*e^3*(-24*a*e+5
*b*d)-15*c^3*d^2*e*(-10*a*e+7*b*d)+3*c^2*e^2*(32*a^2*e^2-25*a*b*d*e+5*b^2*d^2))-2*c*(-b*e+2*c*d)*(35*c^4*d^4+3
*b^4*e^4+2*b^2*c*e^3*(-17*a*e+5*b*d)-10*c^3*d^2*e*(-11*a*e+7*b*d)+c^2*e^2*(123*a^2*e^2-110*a*b*d*e+25*b^2*d^2)
)*x)/(-4*a*c+b^2)^3/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2+1/2*(b^7*c*d*e^6+2*b^8*e^7+256*a^4*c^4*e^7+b^6*c*e^5
*(-31*a*e^2+c*d^2)+b^5*c^2*d*e^4*(-14*a*e^2+c*d^2)-b^4*c^2*e^3*(-178*a^2*e^4+13*a*c*d^2*e^2+125*c^2*d^4)+b^3*c
^3*d*e^2*(69*a^2*e^4+492*a*c*d^2*e^2+295*c^2*d^4)+2*b*c^4*d*(187*a^3*e^6+233*a^2*c*d^2*e^4+145*a*c^2*d^4*e^2+3
5*c^3*d^6)-b^2*c^3*e*(443*a^3*e^6+699*a^2*c*d^2*e^4+725*a*c^2*d^4*e^2+245*c^3*d^6)+2*c*(-b*e+2*c*d)*(35*c^6*d^
6-b^6*e^6-5*c^5*d^4*e*(-29*a*e+21*b*d)-3*b^4*c*e^5*(-5*a*e+b*d)-b^2*c^2*e^4*(82*a^2*e^2-44*a*b*d*e+7*b^2*d^2)+
c^4*d^2*e^2*(233*a^2*e^2-290*a*b*d*e+95*b^2*d^2)-c^3*e^3*(-187*a^3*e^3+233*a^2*b*d*e^2-101*a*b^2*d^2*e+15*b^3*
d^3))*x)/(-4*a*c+b^2)^4/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)-(140*c^9*d^9-b^9*e^9+18*a*b^7*c*e^9-126*a^2*b^5*c^
2*e^9+420*a^3*b^3*c^3*e^9-630*a^4*b*c^4*e^9-90*c^8*d^7*e*(-8*a*e+7*b*d)+72*c^7*d^5*e^2*(21*a^2*e^2-35*a*b*d*e+
15*b^2*d^2)-84*c^6*d^3*e^3*(-20*a^3*e^3+45*a^2*b*d*e^2-36*a*b^2*d^2*e+10*b^3*d^3)+252*c^5*d*e^4*(5*a^4*e^4-10*
a^3*b*d*e^3+10*a^2*b^2*d^2*e^2-5*a*b^3*d^3*e+b^4*d^4))*arctanh((2*c*x+b)/(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(9/2
)/(c*d^2-e*(-a*e+b*d))^5+e^9*ln(e*x+d)/(a*e^2-b*d*e+c*d^2)^5-1/2*e^9*ln(c*x^2+b*x+a)/(a*e^2-b*d*e+c*d^2)^5

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Rubi [A]  time = 13.90, antiderivative size = 1324, normalized size of antiderivative = 1.00, number of steps used = 10, number of rules used = 7, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.350, Rules used = {740, 822, 800, 634, 618, 206, 628} \[ \frac {\log (d+e x) e^9}{\left (c d^2-b e d+a e^2\right )^5}-\frac {\log \left (c x^2+b x+a\right ) e^9}{2 \left (c d^2-b e d+a e^2\right )^5}-\frac {\left (140 c^9 d^9-90 c^8 e (7 b d-8 a e) d^7+72 c^7 e^2 \left (15 b^2 d^2-35 a b e d+21 a^2 e^2\right ) d^5-84 c^6 e^3 \left (10 b^3 d^3-36 a b^2 e d^2+45 a^2 b e^2 d-20 a^3 e^3\right ) d^3+252 c^5 e^4 \left (b^4 d^4-5 a b^3 e d^3+10 a^2 b^2 e^2 d^2-10 a^3 b e^3 d+5 a^4 e^4\right ) d-b^9 e^9-630 a^4 b c^4 e^9+420 a^3 b^3 c^3 e^9-126 a^2 b^5 c^2 e^9+18 a b^7 c e^9\right ) \tanh ^{-1}\left (\frac {b+2 c x}{\sqrt {b^2-4 a c}}\right )}{\left (b^2-4 a c\right )^{9/2} \left (c d^2-e (b d-a e)\right )^5}+\frac {2 e^7 b^8+c d e^6 b^7+c e^5 \left (c d^2-31 a e^2\right ) b^6+c^2 d e^4 \left (c d^2-14 a e^2\right ) b^5-c^2 e^3 \left (125 c^2 d^4+13 a c e^2 d^2-178 a^2 e^4\right ) b^4+c^3 d e^2 \left (295 c^2 d^4+492 a c e^2 d^2+69 a^2 e^4\right ) b^3-c^3 e \left (245 c^3 d^6+725 a c^2 e^2 d^4+699 a^2 c e^4 d^2+443 a^3 e^6\right ) b^2+2 c^4 d \left (35 c^3 d^6+145 a c^2 e^2 d^4+233 a^2 c e^4 d^2+187 a^3 e^6\right ) b+256 a^4 c^4 e^7+2 c (2 c d-b e) \left (35 c^6 d^6-5 c^5 e (21 b d-29 a e) d^4+c^4 e^2 \left (95 b^2 d^2-290 a b e d+233 a^2 e^2\right ) d^2-b^6 e^6-3 b^4 c e^5 (b d-5 a e)-b^2 c^2 e^4 \left (7 b^2 d^2-44 a b e d+82 a^2 e^2\right )-c^3 e^3 \left (15 b^3 d^3-101 a b^2 e d^2+233 a^2 b e^2 d-187 a^3 e^3\right )\right ) x}{2 \left (b^2-4 a c\right )^4 \left (c d^2-b e d+a e^2\right )^4 \left (c x^2+b x+a\right )}+\frac {5 a c e \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right ) (2 c d-b e)^2-2 c \left (35 c^4 d^4-10 c^3 e (7 b d-11 a e) d^2+3 b^4 e^4+2 b^2 c e^3 (5 b d-17 a e)+c^2 e^2 \left (25 b^2 d^2-110 a b e d+123 a^2 e^2\right )\right ) x (2 c d-b e)-\left (-e b^2+c d b+2 a c e\right ) \left (70 c^4 d^4-15 c^3 e (7 b d-10 a e) d^2+6 b^4 e^4+2 b^2 c e^3 (5 b d-24 a e)+3 c^2 e^2 \left (5 b^2 d^2-25 a b e d+32 a^2 e^2\right )\right )}{12 \left (b^2-4 a c\right )^3 \left (c d^2-b e d+a e^2\right )^3 \left (c x^2+b x+a\right )^2}-\frac {7 a c e (2 c d-b e)^2-2 c \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right ) x (2 c d-b e)-\left (-e b^2+c d b+2 a c e\right ) \left (14 c^2 d^2-4 b^2 e^2-c e (7 b d-16 a e)\right )}{12 \left (b^2-4 a c\right )^2 \left (c d^2-b e d+a e^2\right )^2 \left (c x^2+b x+a\right )^3}-\frac {-e b^2+c d b+2 a c e+c (2 c d-b e) x}{4 \left (b^2-4 a c\right ) \left (c d^2-b e d+a e^2\right ) \left (c x^2+b x+a\right )^4} \]

Antiderivative was successfully verified.

[In]

Int[1/((d + e*x)*(a + b*x + c*x^2)^5),x]

[Out]

-(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x)/(4*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^4) -
(7*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(14*c^2*d^2 - 4*b^2*e^2 - c*e*(7*b*d - 16*a*e)) - 2*c*(2
*c*d - b*e)*(7*c^2*d^2 - 2*b^2*e^2 - c*e*(7*b*d - 15*a*e))*x)/(12*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(a
+ b*x + c*x^2)^3) + (5*a*c*e*(2*c*d - b*e)^2*(7*c^2*d^2 - 2*b^2*e^2 - c*e*(7*b*d - 15*a*e)) - (b*c*d - b^2*e
+ 2*a*c*e)*(70*c^4*d^4 + 6*b^4*e^4 + 2*b^2*c*e^3*(5*b*d - 24*a*e) - 15*c^3*d^2*e*(7*b*d - 10*a*e) + 3*c^2*e^2*
(5*b^2*d^2 - 25*a*b*d*e + 32*a^2*e^2)) - 2*c*(2*c*d - b*e)*(35*c^4*d^4 + 3*b^4*e^4 + 2*b^2*c*e^3*(5*b*d - 17*a
*e) - 10*c^3*d^2*e*(7*b*d - 11*a*e) + c^2*e^2*(25*b^2*d^2 - 110*a*b*d*e + 123*a^2*e^2))*x)/(12*(b^2 - 4*a*c)^3
*(c*d^2 - b*d*e + a*e^2)^3*(a + b*x + c*x^2)^2) + (b^7*c*d*e^6 + 2*b^8*e^7 + 256*a^4*c^4*e^7 + b^6*c*e^5*(c*d^
2 - 31*a*e^2) + b^5*c^2*d*e^4*(c*d^2 - 14*a*e^2) - b^4*c^2*e^3*(125*c^2*d^4 + 13*a*c*d^2*e^2 - 178*a^2*e^4) +
b^3*c^3*d*e^2*(295*c^2*d^4 + 492*a*c*d^2*e^2 + 69*a^2*e^4) + 2*b*c^4*d*(35*c^3*d^6 + 145*a*c^2*d^4*e^2 + 233*a
^2*c*d^2*e^4 + 187*a^3*e^6) - b^2*c^3*e*(245*c^3*d^6 + 725*a*c^2*d^4*e^2 + 699*a^2*c*d^2*e^4 + 443*a^3*e^6) +
2*c*(2*c*d - b*e)*(35*c^6*d^6 - b^6*e^6 - 5*c^5*d^4*e*(21*b*d - 29*a*e) - 3*b^4*c*e^5*(b*d - 5*a*e) - b^2*c^2*
e^4*(7*b^2*d^2 - 44*a*b*d*e + 82*a^2*e^2) + c^4*d^2*e^2*(95*b^2*d^2 - 290*a*b*d*e + 233*a^2*e^2) - c^3*e^3*(15
*b^3*d^3 - 101*a*b^2*d^2*e + 233*a^2*b*d*e^2 - 187*a^3*e^3))*x)/(2*(b^2 - 4*a*c)^4*(c*d^2 - b*d*e + a*e^2)^4*(
a + b*x + c*x^2)) - ((140*c^9*d^9 - b^9*e^9 + 18*a*b^7*c*e^9 - 126*a^2*b^5*c^2*e^9 + 420*a^3*b^3*c^3*e^9 - 630
*a^4*b*c^4*e^9 - 90*c^8*d^7*e*(7*b*d - 8*a*e) + 72*c^7*d^5*e^2*(15*b^2*d^2 - 35*a*b*d*e + 21*a^2*e^2) - 84*c^6
*d^3*e^3*(10*b^3*d^3 - 36*a*b^2*d^2*e + 45*a^2*b*d*e^2 - 20*a^3*e^3) + 252*c^5*d*e^4*(b^4*d^4 - 5*a*b^3*d^3*e
+ 10*a^2*b^2*d^2*e^2 - 10*a^3*b*d*e^3 + 5*a^4*e^4))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(9/
2)*(c*d^2 - e*(b*d - a*e))^5) + (e^9*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^5 - (e^9*Log[a + b*x + c*x^2])/(2*(
c*d^2 - b*d*e + a*e^2)^5)

Rule 206

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTanh[(Rt[-b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[-b, 2]), x]
/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])

Rule 618

Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> Dist[-2, Subst[Int[1/Simp[b^2 - 4*a*c - x^2, x], x]
, x, b + 2*c*x], x] /; FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]

Rule 628

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

Rule 634

Int[((d_.) + (e_.)*(x_))/((a_) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Dist[(2*c*d - b*e)/(2*c), Int[1/(a +
b*x + c*x^2), x], x] + Dist[e/(2*c), Int[(b + 2*c*x)/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c, d, e}, x] &
& NeQ[2*c*d - b*e, 0] && NeQ[b^2 - 4*a*c, 0] &&  !NiceSqrtQ[b^2 - 4*a*c]

Rule 740

Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((d + e*x)^(m + 1)*(
b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c)*(c*d^2 - b*d*e
+ a*e^2)), x] + Dist[1/((p + 1)*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)), Int[(d + e*x)^m*Simp[b*c*d*e*(2*p - m
+ 2) + b^2*e^2*(m + p + 2) - 2*c^2*d^2*(2*p + 3) - 2*a*c*e^2*(m + 2*p + 3) - c*e*(2*c*d - b*e)*(m + 2*p + 4)*x
, x]*(a + b*x + c*x^2)^(p + 1), 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] && LtQ[p, -1] && IntQuadraticQ[a, b, c, d, e, m, p, x]

Rule 800

Int[(((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_)))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Int[Exp
andIntegrand[((d + e*x)^m*(f + g*x))/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c, d, e, f, g}, x] && NeQ[b^2 -
4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && IntegerQ[m]

Rule 822

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp
[((d + e*x)^(m + 1)*(f*(b*c*d - b^2*e + 2*a*c*e) - a*g*(2*c*d - b*e) + c*(f*(2*c*d - b*e) - g*(b*d - 2*a*e))*x
)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)), x] + Dist[1/((p + 1)*(b^2 - 4*a*
c)*(c*d^2 - b*d*e + a*e^2)), Int[(d + e*x)^m*(a + b*x + c*x^2)^(p + 1)*Simp[f*(b*c*d*e*(2*p - m + 2) + b^2*e^2
*(p + m + 2) - 2*c^2*d^2*(2*p + 3) - 2*a*c*e^2*(m + 2*p + 3)) - g*(a*e*(b*e - 2*c*d*m + b*e*m) - b*d*(3*c*d -
b*e + 2*c*d*p - b*e*p)) + c*e*(g*(b*d - 2*a*e) - f*(2*c*d - b*e))*(m + 2*p + 4)*x, x], x], x] /; FreeQ[{a, b,
c, d, e, f, g, m}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && LtQ[p, -1] && (IntegerQ[m] ||
IntegerQ[p] || IntegersQ[2*m, 2*p])

Rubi steps

\begin {align*} \int \frac {1}{(d+e x) \left (a+b x+c x^2\right )^5} \, dx &=-\frac {b c d-b^2 e+2 a c e+c (2 c d-b e) x}{4 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \left (a+b x+c x^2\right )^4}-\frac {\int \frac {14 c^2 d^2-4 b^2 e^2-c e (7 b d-16 a e)+7 c e (2 c d-b e) x}{(d+e x) \left (a+b x+c x^2\right )^4} \, dx}{4 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right )}\\ &=-\frac {b c d-b^2 e+2 a c e+c (2 c d-b e) x}{4 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \left (a+b x+c x^2\right )^4}-\frac {7 a c e (2 c d-b e)^2-\left (b c d-b^2 e+2 a c e\right ) \left (14 c^2 d^2-4 b^2 e^2-c e (7 b d-16 a e)\right )-2 c (2 c d-b e) \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right ) x}{12 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2 \left (a+b x+c x^2\right )^3}+\frac {\int \frac {2 \left (70 c^4 d^4+6 b^4 e^4+2 b^2 c e^3 (5 b d-24 a e)-15 c^3 d^2 e (7 b d-10 a e)+3 c^2 e^2 \left (5 b^2 d^2-25 a b d e+32 a^2 e^2\right )\right )+10 c e (2 c d-b e) \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right ) x}{(d+e x) \left (a+b x+c x^2\right )^3} \, dx}{12 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2}\\ &=-\frac {b c d-b^2 e+2 a c e+c (2 c d-b e) x}{4 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \left (a+b x+c x^2\right )^4}-\frac {7 a c e (2 c d-b e)^2-\left (b c d-b^2 e+2 a c e\right ) \left (14 c^2 d^2-4 b^2 e^2-c e (7 b d-16 a e)\right )-2 c (2 c d-b e) \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right ) x}{12 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2 \left (a+b x+c x^2\right )^3}+\frac {5 a c e (2 c d-b e)^2 \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right )-\left (b c d-b^2 e+2 a c e\right ) \left (70 c^4 d^4+6 b^4 e^4+2 b^2 c e^3 (5 b d-24 a e)-15 c^3 d^2 e (7 b d-10 a e)+3 c^2 e^2 \left (5 b^2 d^2-25 a b d e+32 a^2 e^2\right )\right )-2 c (2 c d-b e) \left (35 c^4 d^4+3 b^4 e^4+2 b^2 c e^3 (5 b d-17 a e)-10 c^3 d^2 e (7 b d-11 a e)+c^2 e^2 \left (25 b^2 d^2-110 a b d e+123 a^2 e^2\right )\right ) x}{12 \left (b^2-4 a c\right )^3 \left (c d^2-b d e+a e^2\right )^3 \left (a+b x+c x^2\right )^2}-\frac {\int \frac {12 \left (70 c^6 d^6-2 b^6 e^6-5 c^5 d^4 e (35 b d-44 a e)-3 b^4 c e^5 (b d-8 a e)+6 c^4 d^2 e^2 \left (20 b^2 d^2-55 a b d e+41 a^2 e^2\right )-2 b^2 c^2 e^4 \left (2 b^2 d^2-17 a b d e+48 a^2 e^2\right )-c^3 e^3 \left (5 b^3 d^3-42 a b^2 d^2 e+123 a^2 b d e^2-128 a^3 e^3\right )\right )+12 c e (2 c d-b e) \left (35 c^4 d^4+3 b^4 e^4+2 b^2 c e^3 (5 b d-17 a e)-10 c^3 d^2 e (7 b d-11 a e)+c^2 e^2 \left (25 b^2 d^2-110 a b d e+123 a^2 e^2\right )\right ) x}{(d+e x) \left (a+b x+c x^2\right )^2} \, dx}{24 \left (b^2-4 a c\right )^3 \left (c d^2-b d e+a e^2\right )^3}\\ &=-\frac {b c d-b^2 e+2 a c e+c (2 c d-b e) x}{4 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \left (a+b x+c x^2\right )^4}-\frac {7 a c e (2 c d-b e)^2-\left (b c d-b^2 e+2 a c e\right ) \left (14 c^2 d^2-4 b^2 e^2-c e (7 b d-16 a e)\right )-2 c (2 c d-b e) \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right ) x}{12 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2 \left (a+b x+c x^2\right )^3}+\frac {5 a c e (2 c d-b e)^2 \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right )-\left (b c d-b^2 e+2 a c e\right ) \left (70 c^4 d^4+6 b^4 e^4+2 b^2 c e^3 (5 b d-24 a e)-15 c^3 d^2 e (7 b d-10 a e)+3 c^2 e^2 \left (5 b^2 d^2-25 a b d e+32 a^2 e^2\right )\right )-2 c (2 c d-b e) \left (35 c^4 d^4+3 b^4 e^4+2 b^2 c e^3 (5 b d-17 a e)-10 c^3 d^2 e (7 b d-11 a e)+c^2 e^2 \left (25 b^2 d^2-110 a b d e+123 a^2 e^2\right )\right ) x}{12 \left (b^2-4 a c\right )^3 \left (c d^2-b d e+a e^2\right )^3 \left (a+b x+c x^2\right )^2}+\frac {b^7 c d e^6+2 b^8 e^7+256 a^4 c^4 e^7+b^6 c e^5 \left (c d^2-31 a e^2\right )+b^5 c^2 d e^4 \left (c d^2-14 a e^2\right )-b^4 c^2 e^3 \left (125 c^2 d^4+13 a c d^2 e^2-178 a^2 e^4\right )+b^3 c^3 d e^2 \left (295 c^2 d^4+492 a c d^2 e^2+69 a^2 e^4\right )+2 b c^4 d \left (35 c^3 d^6+145 a c^2 d^4 e^2+233 a^2 c d^2 e^4+187 a^3 e^6\right )-b^2 c^3 e \left (245 c^3 d^6+725 a c^2 d^4 e^2+699 a^2 c d^2 e^4+443 a^3 e^6\right )+2 c (2 c d-b e) \left (35 c^6 d^6-b^6 e^6-5 c^5 d^4 e (21 b d-29 a e)-3 b^4 c e^5 (b d-5 a e)-b^2 c^2 e^4 \left (7 b^2 d^2-44 a b d e+82 a^2 e^2\right )+c^4 d^2 e^2 \left (95 b^2 d^2-290 a b d e+233 a^2 e^2\right )-c^3 e^3 \left (15 b^3 d^3-101 a b^2 d^2 e+233 a^2 b d e^2-187 a^3 e^3\right )\right ) x}{2 \left (b^2-4 a c\right )^4 \left (c d^2-b d e+a e^2\right )^4 \left (a+b x+c x^2\right )}+\frac {\int \frac {24 \left (70 c^8 d^8+b^8 e^8-5 c^7 d^6 e (49 b d-58 a e)+b^6 c e^7 (b d-16 a e)+b^4 c^2 e^6 \left (b^2 d^2-15 a b d e+96 a^2 e^2\right )+c^6 d^4 e^2 \left (295 b^2 d^2-725 a b d e+466 a^2 e^2\right )-c^5 d^2 e^3 \left (125 b^3 d^3-492 a b^2 d^2 e+699 a^2 b d e^2-374 a^3 e^3\right )+b^2 c^3 e^5 \left (b^3 d^3-14 a b^2 d^2 e+82 a^2 b d e^2-256 a^3 e^3\right )+c^4 e^4 \left (b^4 d^4-13 a b^3 d^3 e+69 a^2 b^2 d^2 e^2-187 a^3 b d e^3+256 a^4 e^4\right )\right )+24 c e (2 c d-b e) \left (35 c^6 d^6-b^6 e^6-5 c^5 d^4 e (21 b d-29 a e)-3 b^4 c e^5 (b d-5 a e)-b^2 c^2 e^4 \left (7 b^2 d^2-44 a b d e+82 a^2 e^2\right )+c^4 d^2 e^2 \left (95 b^2 d^2-290 a b d e+233 a^2 e^2\right )-c^3 e^3 \left (15 b^3 d^3-101 a b^2 d^2 e+233 a^2 b d e^2-187 a^3 e^3\right )\right ) x}{(d+e x) \left (a+b x+c x^2\right )} \, dx}{24 \left (b^2-4 a c\right )^4 \left (c d^2-b d e+a e^2\right )^4}\\ &=-\frac {b c d-b^2 e+2 a c e+c (2 c d-b e) x}{4 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \left (a+b x+c x^2\right )^4}-\frac {7 a c e (2 c d-b e)^2-\left (b c d-b^2 e+2 a c e\right ) \left (14 c^2 d^2-4 b^2 e^2-c e (7 b d-16 a e)\right )-2 c (2 c d-b e) \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right ) x}{12 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2 \left (a+b x+c x^2\right )^3}+\frac {5 a c e (2 c d-b e)^2 \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right )-\left (b c d-b^2 e+2 a c e\right ) \left (70 c^4 d^4+6 b^4 e^4+2 b^2 c e^3 (5 b d-24 a e)-15 c^3 d^2 e (7 b d-10 a e)+3 c^2 e^2 \left (5 b^2 d^2-25 a b d e+32 a^2 e^2\right )\right )-2 c (2 c d-b e) \left (35 c^4 d^4+3 b^4 e^4+2 b^2 c e^3 (5 b d-17 a e)-10 c^3 d^2 e (7 b d-11 a e)+c^2 e^2 \left (25 b^2 d^2-110 a b d e+123 a^2 e^2\right )\right ) x}{12 \left (b^2-4 a c\right )^3 \left (c d^2-b d e+a e^2\right )^3 \left (a+b x+c x^2\right )^2}+\frac {b^7 c d e^6+2 b^8 e^7+256 a^4 c^4 e^7+b^6 c e^5 \left (c d^2-31 a e^2\right )+b^5 c^2 d e^4 \left (c d^2-14 a e^2\right )-b^4 c^2 e^3 \left (125 c^2 d^4+13 a c d^2 e^2-178 a^2 e^4\right )+b^3 c^3 d e^2 \left (295 c^2 d^4+492 a c d^2 e^2+69 a^2 e^4\right )+2 b c^4 d \left (35 c^3 d^6+145 a c^2 d^4 e^2+233 a^2 c d^2 e^4+187 a^3 e^6\right )-b^2 c^3 e \left (245 c^3 d^6+725 a c^2 d^4 e^2+699 a^2 c d^2 e^4+443 a^3 e^6\right )+2 c (2 c d-b e) \left (35 c^6 d^6-b^6 e^6-5 c^5 d^4 e (21 b d-29 a e)-3 b^4 c e^5 (b d-5 a e)-b^2 c^2 e^4 \left (7 b^2 d^2-44 a b d e+82 a^2 e^2\right )+c^4 d^2 e^2 \left (95 b^2 d^2-290 a b d e+233 a^2 e^2\right )-c^3 e^3 \left (15 b^3 d^3-101 a b^2 d^2 e+233 a^2 b d e^2-187 a^3 e^3\right )\right ) x}{2 \left (b^2-4 a c\right )^4 \left (c d^2-b d e+a e^2\right )^4 \left (a+b x+c x^2\right )}+\frac {\int \left (\frac {24 \left (b^2-4 a c\right )^4 e^{10}}{\left (c d^2-b d e+a e^2\right ) (d+e x)}+\frac {24 \left (70 c^9 d^9-b^9 e^9+17 a b^7 c e^9-111 a^2 b^5 c^2 e^9+338 a^3 b^3 c^3 e^9-443 a^4 b c^4 e^9-45 c^8 d^7 e (7 b d-8 a e)+36 c^7 d^5 e^2 \left (15 b^2 d^2-35 a b d e+21 a^2 e^2\right )-42 c^6 d^3 e^3 \left (10 b^3 d^3-36 a b^2 d^2 e+45 a^2 b d e^2-20 a^3 e^3\right )+126 c^5 d e^4 \left (b^4 d^4-5 a b^3 d^3 e+10 a^2 b^2 d^2 e^2-10 a^3 b d e^3+5 a^4 e^4\right )-c \left (b^2-4 a c\right )^4 e^9 x\right )}{\left (c d^2-b d e+a e^2\right ) \left (a+b x+c x^2\right )}\right ) \, dx}{24 \left (b^2-4 a c\right )^4 \left (c d^2-b d e+a e^2\right )^4}\\ &=-\frac {b c d-b^2 e+2 a c e+c (2 c d-b e) x}{4 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \left (a+b x+c x^2\right )^4}-\frac {7 a c e (2 c d-b e)^2-\left (b c d-b^2 e+2 a c e\right ) \left (14 c^2 d^2-4 b^2 e^2-c e (7 b d-16 a e)\right )-2 c (2 c d-b e) \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right ) x}{12 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2 \left (a+b x+c x^2\right )^3}+\frac {5 a c e (2 c d-b e)^2 \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right )-\left (b c d-b^2 e+2 a c e\right ) \left (70 c^4 d^4+6 b^4 e^4+2 b^2 c e^3 (5 b d-24 a e)-15 c^3 d^2 e (7 b d-10 a e)+3 c^2 e^2 \left (5 b^2 d^2-25 a b d e+32 a^2 e^2\right )\right )-2 c (2 c d-b e) \left (35 c^4 d^4+3 b^4 e^4+2 b^2 c e^3 (5 b d-17 a e)-10 c^3 d^2 e (7 b d-11 a e)+c^2 e^2 \left (25 b^2 d^2-110 a b d e+123 a^2 e^2\right )\right ) x}{12 \left (b^2-4 a c\right )^3 \left (c d^2-b d e+a e^2\right )^3 \left (a+b x+c x^2\right )^2}+\frac {b^7 c d e^6+2 b^8 e^7+256 a^4 c^4 e^7+b^6 c e^5 \left (c d^2-31 a e^2\right )+b^5 c^2 d e^4 \left (c d^2-14 a e^2\right )-b^4 c^2 e^3 \left (125 c^2 d^4+13 a c d^2 e^2-178 a^2 e^4\right )+b^3 c^3 d e^2 \left (295 c^2 d^4+492 a c d^2 e^2+69 a^2 e^4\right )+2 b c^4 d \left (35 c^3 d^6+145 a c^2 d^4 e^2+233 a^2 c d^2 e^4+187 a^3 e^6\right )-b^2 c^3 e \left (245 c^3 d^6+725 a c^2 d^4 e^2+699 a^2 c d^2 e^4+443 a^3 e^6\right )+2 c (2 c d-b e) \left (35 c^6 d^6-b^6 e^6-5 c^5 d^4 e (21 b d-29 a e)-3 b^4 c e^5 (b d-5 a e)-b^2 c^2 e^4 \left (7 b^2 d^2-44 a b d e+82 a^2 e^2\right )+c^4 d^2 e^2 \left (95 b^2 d^2-290 a b d e+233 a^2 e^2\right )-c^3 e^3 \left (15 b^3 d^3-101 a b^2 d^2 e+233 a^2 b d e^2-187 a^3 e^3\right )\right ) x}{2 \left (b^2-4 a c\right )^4 \left (c d^2-b d e+a e^2\right )^4 \left (a+b x+c x^2\right )}+\frac {e^9 \log (d+e x)}{\left (c d^2-b d e+a e^2\right )^5}+\frac {\int \frac {70 c^9 d^9-b^9 e^9+17 a b^7 c e^9-111 a^2 b^5 c^2 e^9+338 a^3 b^3 c^3 e^9-443 a^4 b c^4 e^9-45 c^8 d^7 e (7 b d-8 a e)+36 c^7 d^5 e^2 \left (15 b^2 d^2-35 a b d e+21 a^2 e^2\right )-42 c^6 d^3 e^3 \left (10 b^3 d^3-36 a b^2 d^2 e+45 a^2 b d e^2-20 a^3 e^3\right )+126 c^5 d e^4 \left (b^4 d^4-5 a b^3 d^3 e+10 a^2 b^2 d^2 e^2-10 a^3 b d e^3+5 a^4 e^4\right )-c \left (b^2-4 a c\right )^4 e^9 x}{a+b x+c x^2} \, dx}{\left (b^2-4 a c\right )^4 \left (c d^2-b d e+a e^2\right )^5}\\ &=-\frac {b c d-b^2 e+2 a c e+c (2 c d-b e) x}{4 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \left (a+b x+c x^2\right )^4}-\frac {7 a c e (2 c d-b e)^2-\left (b c d-b^2 e+2 a c e\right ) \left (14 c^2 d^2-4 b^2 e^2-c e (7 b d-16 a e)\right )-2 c (2 c d-b e) \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right ) x}{12 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2 \left (a+b x+c x^2\right )^3}+\frac {5 a c e (2 c d-b e)^2 \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right )-\left (b c d-b^2 e+2 a c e\right ) \left (70 c^4 d^4+6 b^4 e^4+2 b^2 c e^3 (5 b d-24 a e)-15 c^3 d^2 e (7 b d-10 a e)+3 c^2 e^2 \left (5 b^2 d^2-25 a b d e+32 a^2 e^2\right )\right )-2 c (2 c d-b e) \left (35 c^4 d^4+3 b^4 e^4+2 b^2 c e^3 (5 b d-17 a e)-10 c^3 d^2 e (7 b d-11 a e)+c^2 e^2 \left (25 b^2 d^2-110 a b d e+123 a^2 e^2\right )\right ) x}{12 \left (b^2-4 a c\right )^3 \left (c d^2-b d e+a e^2\right )^3 \left (a+b x+c x^2\right )^2}+\frac {b^7 c d e^6+2 b^8 e^7+256 a^4 c^4 e^7+b^6 c e^5 \left (c d^2-31 a e^2\right )+b^5 c^2 d e^4 \left (c d^2-14 a e^2\right )-b^4 c^2 e^3 \left (125 c^2 d^4+13 a c d^2 e^2-178 a^2 e^4\right )+b^3 c^3 d e^2 \left (295 c^2 d^4+492 a c d^2 e^2+69 a^2 e^4\right )+2 b c^4 d \left (35 c^3 d^6+145 a c^2 d^4 e^2+233 a^2 c d^2 e^4+187 a^3 e^6\right )-b^2 c^3 e \left (245 c^3 d^6+725 a c^2 d^4 e^2+699 a^2 c d^2 e^4+443 a^3 e^6\right )+2 c (2 c d-b e) \left (35 c^6 d^6-b^6 e^6-5 c^5 d^4 e (21 b d-29 a e)-3 b^4 c e^5 (b d-5 a e)-b^2 c^2 e^4 \left (7 b^2 d^2-44 a b d e+82 a^2 e^2\right )+c^4 d^2 e^2 \left (95 b^2 d^2-290 a b d e+233 a^2 e^2\right )-c^3 e^3 \left (15 b^3 d^3-101 a b^2 d^2 e+233 a^2 b d e^2-187 a^3 e^3\right )\right ) x}{2 \left (b^2-4 a c\right )^4 \left (c d^2-b d e+a e^2\right )^4 \left (a+b x+c x^2\right )}+\frac {e^9 \log (d+e x)}{\left (c d^2-b d e+a e^2\right )^5}-\frac {e^9 \int \frac {b+2 c x}{a+b x+c x^2} \, dx}{2 \left (c d^2-b d e+a e^2\right )^5}+\frac {\left (140 c^9 d^9-b^9 e^9+18 a b^7 c e^9-126 a^2 b^5 c^2 e^9+420 a^3 b^3 c^3 e^9-630 a^4 b c^4 e^9-90 c^8 d^7 e (7 b d-8 a e)+72 c^7 d^5 e^2 \left (15 b^2 d^2-35 a b d e+21 a^2 e^2\right )-84 c^6 d^3 e^3 \left (10 b^3 d^3-36 a b^2 d^2 e+45 a^2 b d e^2-20 a^3 e^3\right )+252 c^5 d e^4 \left (b^4 d^4-5 a b^3 d^3 e+10 a^2 b^2 d^2 e^2-10 a^3 b d e^3+5 a^4 e^4\right )\right ) \int \frac {1}{a+b x+c x^2} \, dx}{2 \left (b^2-4 a c\right )^4 \left (c d^2-b d e+a e^2\right )^5}\\ &=-\frac {b c d-b^2 e+2 a c e+c (2 c d-b e) x}{4 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \left (a+b x+c x^2\right )^4}-\frac {7 a c e (2 c d-b e)^2-\left (b c d-b^2 e+2 a c e\right ) \left (14 c^2 d^2-4 b^2 e^2-c e (7 b d-16 a e)\right )-2 c (2 c d-b e) \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right ) x}{12 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2 \left (a+b x+c x^2\right )^3}+\frac {5 a c e (2 c d-b e)^2 \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right )-\left (b c d-b^2 e+2 a c e\right ) \left (70 c^4 d^4+6 b^4 e^4+2 b^2 c e^3 (5 b d-24 a e)-15 c^3 d^2 e (7 b d-10 a e)+3 c^2 e^2 \left (5 b^2 d^2-25 a b d e+32 a^2 e^2\right )\right )-2 c (2 c d-b e) \left (35 c^4 d^4+3 b^4 e^4+2 b^2 c e^3 (5 b d-17 a e)-10 c^3 d^2 e (7 b d-11 a e)+c^2 e^2 \left (25 b^2 d^2-110 a b d e+123 a^2 e^2\right )\right ) x}{12 \left (b^2-4 a c\right )^3 \left (c d^2-b d e+a e^2\right )^3 \left (a+b x+c x^2\right )^2}+\frac {b^7 c d e^6+2 b^8 e^7+256 a^4 c^4 e^7+b^6 c e^5 \left (c d^2-31 a e^2\right )+b^5 c^2 d e^4 \left (c d^2-14 a e^2\right )-b^4 c^2 e^3 \left (125 c^2 d^4+13 a c d^2 e^2-178 a^2 e^4\right )+b^3 c^3 d e^2 \left (295 c^2 d^4+492 a c d^2 e^2+69 a^2 e^4\right )+2 b c^4 d \left (35 c^3 d^6+145 a c^2 d^4 e^2+233 a^2 c d^2 e^4+187 a^3 e^6\right )-b^2 c^3 e \left (245 c^3 d^6+725 a c^2 d^4 e^2+699 a^2 c d^2 e^4+443 a^3 e^6\right )+2 c (2 c d-b e) \left (35 c^6 d^6-b^6 e^6-5 c^5 d^4 e (21 b d-29 a e)-3 b^4 c e^5 (b d-5 a e)-b^2 c^2 e^4 \left (7 b^2 d^2-44 a b d e+82 a^2 e^2\right )+c^4 d^2 e^2 \left (95 b^2 d^2-290 a b d e+233 a^2 e^2\right )-c^3 e^3 \left (15 b^3 d^3-101 a b^2 d^2 e+233 a^2 b d e^2-187 a^3 e^3\right )\right ) x}{2 \left (b^2-4 a c\right )^4 \left (c d^2-b d e+a e^2\right )^4 \left (a+b x+c x^2\right )}+\frac {e^9 \log (d+e x)}{\left (c d^2-b d e+a e^2\right )^5}-\frac {e^9 \log \left (a+b x+c x^2\right )}{2 \left (c d^2-b d e+a e^2\right )^5}-\frac {\left (140 c^9 d^9-b^9 e^9+18 a b^7 c e^9-126 a^2 b^5 c^2 e^9+420 a^3 b^3 c^3 e^9-630 a^4 b c^4 e^9-90 c^8 d^7 e (7 b d-8 a e)+72 c^7 d^5 e^2 \left (15 b^2 d^2-35 a b d e+21 a^2 e^2\right )-84 c^6 d^3 e^3 \left (10 b^3 d^3-36 a b^2 d^2 e+45 a^2 b d e^2-20 a^3 e^3\right )+252 c^5 d e^4 \left (b^4 d^4-5 a b^3 d^3 e+10 a^2 b^2 d^2 e^2-10 a^3 b d e^3+5 a^4 e^4\right )\right ) \operatorname {Subst}\left (\int \frac {1}{b^2-4 a c-x^2} \, dx,x,b+2 c x\right )}{\left (b^2-4 a c\right )^4 \left (c d^2-b d e+a e^2\right )^5}\\ &=-\frac {b c d-b^2 e+2 a c e+c (2 c d-b e) x}{4 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \left (a+b x+c x^2\right )^4}-\frac {7 a c e (2 c d-b e)^2-\left (b c d-b^2 e+2 a c e\right ) \left (14 c^2 d^2-4 b^2 e^2-c e (7 b d-16 a e)\right )-2 c (2 c d-b e) \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right ) x}{12 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2 \left (a+b x+c x^2\right )^3}+\frac {5 a c e (2 c d-b e)^2 \left (7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right )-\left (b c d-b^2 e+2 a c e\right ) \left (70 c^4 d^4+6 b^4 e^4+2 b^2 c e^3 (5 b d-24 a e)-15 c^3 d^2 e (7 b d-10 a e)+3 c^2 e^2 \left (5 b^2 d^2-25 a b d e+32 a^2 e^2\right )\right )-2 c (2 c d-b e) \left (35 c^4 d^4+3 b^4 e^4+2 b^2 c e^3 (5 b d-17 a e)-10 c^3 d^2 e (7 b d-11 a e)+c^2 e^2 \left (25 b^2 d^2-110 a b d e+123 a^2 e^2\right )\right ) x}{12 \left (b^2-4 a c\right )^3 \left (c d^2-b d e+a e^2\right )^3 \left (a+b x+c x^2\right )^2}+\frac {b^7 c d e^6+2 b^8 e^7+256 a^4 c^4 e^7+b^6 c e^5 \left (c d^2-31 a e^2\right )+b^5 c^2 d e^4 \left (c d^2-14 a e^2\right )-b^4 c^2 e^3 \left (125 c^2 d^4+13 a c d^2 e^2-178 a^2 e^4\right )+b^3 c^3 d e^2 \left (295 c^2 d^4+492 a c d^2 e^2+69 a^2 e^4\right )+2 b c^4 d \left (35 c^3 d^6+145 a c^2 d^4 e^2+233 a^2 c d^2 e^4+187 a^3 e^6\right )-b^2 c^3 e \left (245 c^3 d^6+725 a c^2 d^4 e^2+699 a^2 c d^2 e^4+443 a^3 e^6\right )+2 c (2 c d-b e) \left (35 c^6 d^6-b^6 e^6-5 c^5 d^4 e (21 b d-29 a e)-3 b^4 c e^5 (b d-5 a e)-b^2 c^2 e^4 \left (7 b^2 d^2-44 a b d e+82 a^2 e^2\right )+c^4 d^2 e^2 \left (95 b^2 d^2-290 a b d e+233 a^2 e^2\right )-c^3 e^3 \left (15 b^3 d^3-101 a b^2 d^2 e+233 a^2 b d e^2-187 a^3 e^3\right )\right ) x}{2 \left (b^2-4 a c\right )^4 \left (c d^2-b d e+a e^2\right )^4 \left (a+b x+c x^2\right )}-\frac {\left (140 c^9 d^9-b^9 e^9+18 a b^7 c e^9-126 a^2 b^5 c^2 e^9+420 a^3 b^3 c^3 e^9-630 a^4 b c^4 e^9-90 c^8 d^7 e (7 b d-8 a e)+72 c^7 d^5 e^2 \left (15 b^2 d^2-35 a b d e+21 a^2 e^2\right )-84 c^6 d^3 e^3 \left (10 b^3 d^3-36 a b^2 d^2 e+45 a^2 b d e^2-20 a^3 e^3\right )+252 c^5 d e^4 \left (b^4 d^4-5 a b^3 d^3 e+10 a^2 b^2 d^2 e^2-10 a^3 b d e^3+5 a^4 e^4\right )\right ) \tanh ^{-1}\left (\frac {b+2 c x}{\sqrt {b^2-4 a c}}\right )}{\left (b^2-4 a c\right )^{9/2} \left (c d^2-e (b d-a e)\right )^5}+\frac {e^9 \log (d+e x)}{\left (c d^2-b d e+a e^2\right )^5}-\frac {e^9 \log \left (a+b x+c x^2\right )}{2 \left (c d^2-b d e+a e^2\right )^5}\\ \end {align*}

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Mathematica [A]  time = 6.58, size = 1601, normalized size = 1.21 \[ \frac {\log (d+e x) e^9}{\left (c d^2-b e d+a e^2\right )^5}-\frac {\log \left (c x^2+b x+a\right ) e^9}{2 \left (c d^2-b e d+a e^2\right )^5}+\frac {\left (-140 c^9 d^9+630 b c^8 e d^8-720 a c^8 e^2 d^7-1080 b^2 c^7 e^2 d^7+2520 a b c^7 e^3 d^6+840 b^3 c^6 e^3 d^6-1512 a^2 c^7 e^4 d^5-3024 a b^2 c^6 e^4 d^5-252 b^4 c^5 e^4 d^5+3780 a^2 b c^6 e^5 d^4+1260 a b^3 c^5 e^5 d^4-1680 a^3 c^6 e^6 d^3-2520 a^2 b^2 c^5 e^6 d^3+2520 a^3 b c^5 e^7 d^2-1260 a^4 c^5 e^8 d+b^9 e^9+630 a^4 b c^4 e^9-420 a^3 b^3 c^3 e^9+126 a^2 b^5 c^2 e^9-18 a b^7 c e^9\right ) \tan ^{-1}\left (\frac {b+2 c x}{\sqrt {4 a c-b^2}}\right )}{\left (b^2-4 a c\right )^4 \sqrt {4 a c-b^2} \left (-c d^2+b e d-a e^2\right )^5}+\frac {2 e^7 b^8+c d e^6 b^7+2 c e^7 x b^7-31 a c e^7 b^6+c^2 d^2 e^5 b^6+2 c^2 d e^6 x b^6-14 a c^2 d e^6 b^5+c^3 d^3 e^4 b^5-30 a c^2 e^7 x b^5+2 c^3 d^2 e^5 x b^5+178 a^2 c^2 e^7 b^4-13 a c^3 d^2 e^5 b^4-125 c^4 d^4 e^3 b^4-28 a c^3 d e^6 x b^4+2 c^4 d^3 e^4 x b^4+69 a^2 c^3 d e^6 b^3+492 a c^4 d^3 e^4 b^3+295 c^5 d^5 e^2 b^3+164 a^2 c^3 e^7 x b^3-26 a c^4 d^2 e^5 x b^3-250 c^5 d^4 e^3 x b^3-443 a^3 c^3 e^7 b^2-699 a^2 c^4 d^2 e^5 b^2-725 a c^5 d^4 e^3 b^2-245 c^6 d^6 e b^2+138 a^2 c^4 d e^6 x b^2+984 a c^5 d^3 e^4 x b^2+590 c^6 d^5 e^2 x b^2+70 c^7 d^7 b+374 a^3 c^4 d e^6 b+466 a^2 c^5 d^3 e^4 b+290 a c^6 d^5 e^2 b-374 a^3 c^4 e^7 x b-1398 a^2 c^5 d^2 e^5 x b-1450 a c^6 d^4 e^3 x b-490 c^7 d^6 e x b+256 a^4 c^4 e^7+140 c^8 d^7 x+748 a^3 c^5 d e^6 x+932 a^2 c^6 d^3 e^4 x+580 a c^7 d^5 e^2 x}{2 \left (4 a c-b^2\right )^4 \left (c d^2-b e d+a e^2\right )^4 \left (c x^2+b x+a\right )}+\frac {-6 e^5 b^6-4 c d e^4 b^5-6 c e^5 x b^5+70 a c e^5 b^4-5 c^2 d^2 e^3 b^4-8 c^2 d e^4 x b^4+42 a c^2 d e^4 b^3+120 c^3 d^3 e^2 b^3+68 a c^2 e^5 x b^3-10 c^3 d^2 e^3 x b^3-267 a^2 c^2 e^5 b^2-330 a c^3 d^2 e^3 b^2-175 c^4 d^4 e b^2+84 a c^3 d e^4 x b^2+240 c^4 d^3 e^2 x b^2+70 c^5 d^5 b+246 a^2 c^3 d e^4 b+220 a c^4 d^3 e^2 b-246 a^2 c^3 e^5 x b-660 a c^4 d^2 e^3 x b-350 c^5 d^4 e x b+192 a^3 c^3 e^5+140 c^6 d^5 x+492 a^2 c^4 d e^4 x+440 a c^5 d^3 e^2 x}{12 \left (4 a c-b^2\right )^3 \left (c d^2-b e d+a e^2\right )^3 \left (c x^2+b x+a\right )^2}+\frac {4 e^3 b^4+3 c d e^2 b^3+4 c e^3 x b^3-31 a c e^3 b^2-21 c^2 d^2 e b^2+6 c^2 d e^2 x b^2+14 c^3 d^3 b+30 a c^2 d e^2 b-30 a c^2 e^3 x b-42 c^3 d^2 e x b+32 a^2 c^2 e^3+28 c^4 d^3 x+60 a c^3 d e^2 x}{12 \left (4 a c-b^2\right )^2 \left (c d^2-b e d+a e^2\right )^2 \left (c x^2+b x+a\right )^3}+\frac {-e b^2+c d b-c e x b+2 a c e+2 c^2 d x}{4 \left (4 a c-b^2\right ) \left (c d^2-b e d+a e^2\right ) \left (c x^2+b x+a\right )^4} \]

Antiderivative was successfully verified.

[In]

Integrate[1/((d + e*x)*(a + b*x + c*x^2)^5),x]

[Out]

(b*c*d - b^2*e + 2*a*c*e + 2*c^2*d*x - b*c*e*x)/(4*(-b^2 + 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^4)
+ (14*b*c^3*d^3 - 21*b^2*c^2*d^2*e + 3*b^3*c*d*e^2 + 30*a*b*c^2*d*e^2 + 4*b^4*e^3 - 31*a*b^2*c*e^3 + 32*a^2*c
^2*e^3 + 28*c^4*d^3*x - 42*b*c^3*d^2*e*x + 6*b^2*c^2*d*e^2*x + 60*a*c^3*d*e^2*x + 4*b^3*c*e^3*x - 30*a*b*c^2*e
^3*x)/(12*(-b^2 + 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)^3) + (70*b*c^5*d^5 - 175*b^2*c^4*d^4*e
+ 120*b^3*c^3*d^3*e^2 + 220*a*b*c^4*d^3*e^2 - 5*b^4*c^2*d^2*e^3 - 330*a*b^2*c^3*d^2*e^3 - 4*b^5*c*d*e^4 + 42*a
*b^3*c^2*d*e^4 + 246*a^2*b*c^3*d*e^4 - 6*b^6*e^5 + 70*a*b^4*c*e^5 - 267*a^2*b^2*c^2*e^5 + 192*a^3*c^3*e^5 + 14
0*c^6*d^5*x - 350*b*c^5*d^4*e*x + 240*b^2*c^4*d^3*e^2*x + 440*a*c^5*d^3*e^2*x - 10*b^3*c^3*d^2*e^3*x - 660*a*b
*c^4*d^2*e^3*x - 8*b^4*c^2*d*e^4*x + 84*a*b^2*c^3*d*e^4*x + 492*a^2*c^4*d*e^4*x - 6*b^5*c*e^5*x + 68*a*b^3*c^2
*e^5*x - 246*a^2*b*c^3*e^5*x)/(12*(-b^2 + 4*a*c)^3*(c*d^2 - b*d*e + a*e^2)^3*(a + b*x + c*x^2)^2) + (70*b*c^7*
d^7 - 245*b^2*c^6*d^6*e + 295*b^3*c^5*d^5*e^2 + 290*a*b*c^6*d^5*e^2 - 125*b^4*c^4*d^4*e^3 - 725*a*b^2*c^5*d^4*
e^3 + b^5*c^3*d^3*e^4 + 492*a*b^3*c^4*d^3*e^4 + 466*a^2*b*c^5*d^3*e^4 + b^6*c^2*d^2*e^5 - 13*a*b^4*c^3*d^2*e^5
- 699*a^2*b^2*c^4*d^2*e^5 + b^7*c*d*e^6 - 14*a*b^5*c^2*d*e^6 + 69*a^2*b^3*c^3*d*e^6 + 374*a^3*b*c^4*d*e^6 + 2
*b^8*e^7 - 31*a*b^6*c*e^7 + 178*a^2*b^4*c^2*e^7 - 443*a^3*b^2*c^3*e^7 + 256*a^4*c^4*e^7 + 140*c^8*d^7*x - 490*
b*c^7*d^6*e*x + 590*b^2*c^6*d^5*e^2*x + 580*a*c^7*d^5*e^2*x - 250*b^3*c^5*d^4*e^3*x - 1450*a*b*c^6*d^4*e^3*x +
2*b^4*c^4*d^3*e^4*x + 984*a*b^2*c^5*d^3*e^4*x + 932*a^2*c^6*d^3*e^4*x + 2*b^5*c^3*d^2*e^5*x - 26*a*b^3*c^4*d^
2*e^5*x - 1398*a^2*b*c^5*d^2*e^5*x + 2*b^6*c^2*d*e^6*x - 28*a*b^4*c^3*d*e^6*x + 138*a^2*b^2*c^4*d*e^6*x + 748*
a^3*c^5*d*e^6*x + 2*b^7*c*e^7*x - 30*a*b^5*c^2*e^7*x + 164*a^2*b^3*c^3*e^7*x - 374*a^3*b*c^4*e^7*x)/(2*(-b^2 +
4*a*c)^4*(c*d^2 - b*d*e + a*e^2)^4*(a + b*x + c*x^2)) + ((-140*c^9*d^9 + 630*b*c^8*d^8*e - 1080*b^2*c^7*d^7*e
^2 - 720*a*c^8*d^7*e^2 + 840*b^3*c^6*d^6*e^3 + 2520*a*b*c^7*d^6*e^3 - 252*b^4*c^5*d^5*e^4 - 3024*a*b^2*c^6*d^5
*e^4 - 1512*a^2*c^7*d^5*e^4 + 1260*a*b^3*c^5*d^4*e^5 + 3780*a^2*b*c^6*d^4*e^5 - 2520*a^2*b^2*c^5*d^3*e^6 - 168
0*a^3*c^6*d^3*e^6 + 2520*a^3*b*c^5*d^2*e^7 - 1260*a^4*c^5*d*e^8 + b^9*e^9 - 18*a*b^7*c*e^9 + 126*a^2*b^5*c^2*e
^9 - 420*a^3*b^3*c^3*e^9 + 630*a^4*b*c^4*e^9)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/((b^2 - 4*a*c)^4*Sqrt[-b
^2 + 4*a*c]*(-(c*d^2) + b*d*e - a*e^2)^5) + (e^9*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^5 - (e^9*Log[a + b*x +
c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^5)

________________________________________________________________________________________

fricas [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x+d)/(c*x^2+b*x+a)^5,x, algorithm="fricas")

[Out]

Timed out

________________________________________________________________________________________

giac [B]  time = 0.48, size = 6368, normalized size = 4.81 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x+d)/(c*x^2+b*x+a)^5,x, algorithm="giac")

[Out]

-1/2*e^9*log(c*x^2 + b*x + a)/(c^5*d^10 - 5*b*c^4*d^9*e + 10*b^2*c^3*d^8*e^2 + 5*a*c^4*d^8*e^2 - 10*b^3*c^2*d^
7*e^3 - 20*a*b*c^3*d^7*e^3 + 5*b^4*c*d^6*e^4 + 30*a*b^2*c^2*d^6*e^4 + 10*a^2*c^3*d^6*e^4 - b^5*d^5*e^5 - 20*a*
b^3*c*d^5*e^5 - 30*a^2*b*c^2*d^5*e^5 + 5*a*b^4*d^4*e^6 + 30*a^2*b^2*c*d^4*e^6 + 10*a^3*c^2*d^4*e^6 - 10*a^2*b^
3*d^3*e^7 - 20*a^3*b*c*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 5*a^4*c*d^2*e^8 - 5*a^4*b*d*e^9 + a^5*e^10) + e^10*log(a
bs(x*e + d))/(c^5*d^10*e - 5*b*c^4*d^9*e^2 + 10*b^2*c^3*d^8*e^3 + 5*a*c^4*d^8*e^3 - 10*b^3*c^2*d^7*e^4 - 20*a*
b*c^3*d^7*e^4 + 5*b^4*c*d^6*e^5 + 30*a*b^2*c^2*d^6*e^5 + 10*a^2*c^3*d^6*e^5 - b^5*d^5*e^6 - 20*a*b^3*c*d^5*e^6
- 30*a^2*b*c^2*d^5*e^6 + 5*a*b^4*d^4*e^7 + 30*a^2*b^2*c*d^4*e^7 + 10*a^3*c^2*d^4*e^7 - 10*a^2*b^3*d^3*e^8 - 2
0*a^3*b*c*d^3*e^8 + 10*a^3*b^2*d^2*e^9 + 5*a^4*c*d^2*e^9 - 5*a^4*b*d*e^10 + a^5*e^11) + (140*c^9*d^9 - 630*b*c
^8*d^8*e + 1080*b^2*c^7*d^7*e^2 + 720*a*c^8*d^7*e^2 - 840*b^3*c^6*d^6*e^3 - 2520*a*b*c^7*d^6*e^3 + 252*b^4*c^5
*d^5*e^4 + 3024*a*b^2*c^6*d^5*e^4 + 1512*a^2*c^7*d^5*e^4 - 1260*a*b^3*c^5*d^4*e^5 - 3780*a^2*b*c^6*d^4*e^5 + 2
520*a^2*b^2*c^5*d^3*e^6 + 1680*a^3*c^6*d^3*e^6 - 2520*a^3*b*c^5*d^2*e^7 + 1260*a^4*c^5*d*e^8 - b^9*e^9 + 18*a*
b^7*c*e^9 - 126*a^2*b^5*c^2*e^9 + 420*a^3*b^3*c^3*e^9 - 630*a^4*b*c^4*e^9)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*
c))/((b^8*c^5*d^10 - 16*a*b^6*c^6*d^10 + 96*a^2*b^4*c^7*d^10 - 256*a^3*b^2*c^8*d^10 + 256*a^4*c^9*d^10 - 5*b^9
*c^4*d^9*e + 80*a*b^7*c^5*d^9*e - 480*a^2*b^5*c^6*d^9*e + 1280*a^3*b^3*c^7*d^9*e - 1280*a^4*b*c^8*d^9*e + 10*b
^10*c^3*d^8*e^2 - 155*a*b^8*c^4*d^8*e^2 + 880*a^2*b^6*c^5*d^8*e^2 - 2080*a^3*b^4*c^6*d^8*e^2 + 1280*a^4*b^2*c^
7*d^8*e^2 + 1280*a^5*c^8*d^8*e^2 - 10*b^11*c^2*d^7*e^3 + 140*a*b^9*c^3*d^7*e^3 - 640*a^2*b^7*c^4*d^7*e^3 + 640
*a^3*b^5*c^5*d^7*e^3 + 2560*a^4*b^3*c^6*d^7*e^3 - 5120*a^5*b*c^7*d^7*e^3 + 5*b^12*c*d^6*e^4 - 50*a*b^10*c^2*d^
6*e^4 + 10*a^2*b^8*c^3*d^6*e^4 + 1440*a^3*b^6*c^4*d^6*e^4 - 5440*a^4*b^4*c^5*d^6*e^4 + 5120*a^5*b^2*c^6*d^6*e^
4 + 2560*a^6*c^7*d^6*e^4 - b^13*d^5*e^5 - 4*a*b^11*c*d^5*e^5 + 194*a^2*b^9*c^2*d^5*e^5 - 1184*a^3*b^7*c^3*d^5*
e^5 + 1984*a^4*b^5*c^4*d^5*e^5 + 2560*a^5*b^3*c^5*d^5*e^5 - 7680*a^6*b*c^6*d^5*e^5 + 5*a*b^12*d^4*e^6 - 50*a^2
*b^10*c*d^4*e^6 + 10*a^3*b^8*c^2*d^4*e^6 + 1440*a^4*b^6*c^3*d^4*e^6 - 5440*a^5*b^4*c^4*d^4*e^6 + 5120*a^6*b^2*
c^5*d^4*e^6 + 2560*a^7*c^6*d^4*e^6 - 10*a^2*b^11*d^3*e^7 + 140*a^3*b^9*c*d^3*e^7 - 640*a^4*b^7*c^2*d^3*e^7 + 6
40*a^5*b^5*c^3*d^3*e^7 + 2560*a^6*b^3*c^4*d^3*e^7 - 5120*a^7*b*c^5*d^3*e^7 + 10*a^3*b^10*d^2*e^8 - 155*a^4*b^8
*c*d^2*e^8 + 880*a^5*b^6*c^2*d^2*e^8 - 2080*a^6*b^4*c^3*d^2*e^8 + 1280*a^7*b^2*c^4*d^2*e^8 + 1280*a^8*c^5*d^2*
e^8 - 5*a^4*b^9*d*e^9 + 80*a^5*b^7*c*d*e^9 - 480*a^6*b^5*c^2*d*e^9 + 1280*a^7*b^3*c^3*d*e^9 - 1280*a^8*b*c^4*d
*e^9 + a^5*b^8*e^10 - 16*a^6*b^6*c*e^10 + 96*a^7*b^4*c^2*e^10 - 256*a^8*b^2*c^3*e^10 + 256*a^9*c^4*e^10)*sqrt(
-b^2 + 4*a*c)) - 1/12*(3*b^7*c^5*d^9 - 50*a*b^5*c^6*d^9 + 326*a^2*b^3*c^7*d^9 - 1116*a^3*b*c^8*d^9 - 15*b^8*c^
4*d^8*e + 249*a*b^6*c^5*d^8*e - 1611*a^2*b^4*c^6*d^8*e + 5406*a^3*b^2*c^7*d^8*e - 384*a^4*c^8*d^8*e + 30*b^9*c
^3*d^7*e^2 - 480*a*b^7*c^4*d^7*e^2 + 2916*a^2*b^5*c^5*d^7*e^2 - 8688*a^3*b^3*c^6*d^7*e^2 - 3984*a^4*b*c^7*d^7*
e^2 - 30*b^10*c^2*d^6*e^3 + 430*a*b^8*c^3*d^6*e^3 - 2080*a^2*b^6*c^4*d^6*e^3 + 3132*a^3*b^4*c^5*d^6*e^3 + 1906
4*a^4*b^2*c^6*d^6*e^3 - 2048*a^5*c^7*d^6*e^3 + 15*b^11*c*d^5*e^4 - 150*a*b^9*c^2*d^5*e^4 + 4800*a^3*b^5*c^4*d^
5*e^4 - 25500*a^4*b^3*c^5*d^5*e^4 - 4680*a^5*b*c^6*d^5*e^4 - 3*b^12*d^4*e^5 - 15*a*b^10*c*d^4*e^5 + 639*a^2*b^
8*c^2*d^4*e^5 - 3984*a^3*b^6*c^3*d^4*e^5 + 7962*a^4*b^4*c^4*d^4*e^5 + 25524*a^5*b^2*c^5*d^4*e^5 - 4608*a^6*c^6
*d^4*e^5 + 16*a*b^11*d^3*e^6 - 154*a^2*b^9*c*d^3*e^6 - 96*a^3*b^7*c^2*d^3*e^6 + 5780*a^4*b^5*c^3*d^3*e^6 - 243
68*a^5*b^3*c^4*d^3*e^6 - 1104*a^6*b*c^5*d^3*e^6 - 36*a^2*b^10*d^2*e^7 + 498*a^3*b^8*c*d^2*e^7 - 2172*a^4*b^6*c
^2*d^2*e^7 + 1044*a^5*b^4*c^3*d^2*e^7 + 17016*a^6*b^2*c^4*d^2*e^7 - 6144*a^7*c^5*d^2*e^7 + 48*a^3*b^9*d*e^8 -
741*a^4*b^7*c*d*e^8 + 4158*a^5*b^5*c^2*d*e^8 - 9354*a^6*b^3*c^3*d*e^8 + 2244*a^7*b*c^4*d*e^8 - 25*a^4*b^8*e^9
+ 385*a^5*b^6*c*e^9 - 2175*a^6*b^4*c^2*e^9 + 5150*a^7*b^2*c^3*e^9 - 3200*a^8*c^4*e^9 - 12*(70*c^12*d^9 - 315*b
*c^11*d^8*e + 540*b^2*c^10*d^7*e^2 + 360*a*c^11*d^7*e^2 - 420*b^3*c^9*d^6*e^3 - 1260*a*b*c^10*d^6*e^3 + 126*b^
4*c^8*d^5*e^4 + 1512*a*b^2*c^9*d^5*e^4 + 756*a^2*c^10*d^5*e^4 - 630*a*b^3*c^8*d^4*e^5 - 1890*a^2*b*c^9*d^4*e^5
+ 1260*a^2*b^2*c^8*d^3*e^6 + 840*a^3*c^9*d^3*e^6 - 1260*a^3*b*c^8*d^2*e^7 - b^8*c^4*d*e^8 + 16*a*b^6*c^5*d*e^
8 - 96*a^2*b^4*c^6*d*e^8 + 256*a^3*b^2*c^7*d*e^8 + 374*a^4*c^8*d*e^8 + a*b^7*c^4*e^9 - 15*a^2*b^5*c^5*e^9 + 82
*a^3*b^3*c^6*e^9 - 187*a^4*b*c^7*e^9)*x^7 - 6*(490*b*c^11*d^9 - 2205*b^2*c^10*d^8*e + 3780*b^3*c^9*d^7*e^2 + 2
520*a*b*c^10*d^7*e^2 - 2940*b^4*c^8*d^6*e^3 - 8820*a*b^2*c^9*d^6*e^3 + 882*b^5*c^7*d^5*e^4 + 10584*a*b^3*c^8*d
^5*e^4 + 5292*a^2*b*c^9*d^5*e^4 - 4410*a*b^4*c^7*d^4*e^5 - 13230*a^2*b^2*c^8*d^4*e^5 + 8820*a^2*b^3*c^7*d^3*e^
6 + 5880*a^3*b*c^8*d^3*e^6 + b^8*c^4*d^2*e^7 - 16*a*b^6*c^5*d^2*e^7 + 96*a^2*b^4*c^6*d^2*e^7 - 9076*a^3*b^2*c^
7*d^2*e^7 + 256*a^4*c^8*d^2*e^7 - 8*b^9*c^3*d*e^8 + 128*a*b^7*c^4*d*e^8 - 768*a^2*b^5*c^5*d*e^8 + 2048*a^3*b^3
*c^6*d*e^8 + 2362*a^4*b*c^7*d*e^8 + 8*a*b^8*c^3*e^9 - 121*a^2*b^6*c^4*e^9 + 670*a^3*b^4*c^5*e^9 - 1565*a^4*b^2
*c^6*e^9 + 256*a^5*c^7*e^9)*x^6 - 4*(910*b^2*c^10*d^9 + 770*a*c^11*d^9 - 4095*b^3*c^9*d^8*e - 3465*a*b*c^10*d^
8*e + 7020*b^4*c^8*d^7*e^2 + 10620*a*b^2*c^9*d^7*e^2 + 3960*a^2*c^10*d^7*e^2 - 5460*b^5*c^7*d^6*e^3 - 21000*a*
b^3*c^8*d^6*e^3 - 13860*a^2*b*c^9*d^6*e^3 + 1638*b^6*c^6*d^5*e^4 + 21042*a*b^4*c^7*d^5*e^4 + 26460*a^2*b^2*c^8
*d^5*e^4 + 8316*a^3*c^9*d^5*e^4 - 8190*a*b^5*c^6*d^4*e^5 - 31500*a^2*b^3*c^7*d^4*e^5 - 20790*a^3*b*c^8*d^4*e^5
- b^8*c^4*d^3*e^6 + 16*a*b^6*c^5*d^3*e^6 + 16284*a^2*b^4*c^6*d^3*e^6 + 25036*a^3*b^2*c^7*d^3*e^6 + 8984*a^4*c
^8*d^3*e^6 + 6*b^9*c^3*d^2*e^7 - 96*a*b^7*c^4*d^2*e^7 + 576*a^2*b^5*c^5*d^2*e^7 - 17916*a^3*b^3*c^6*d^2*e^7 -
12324*a^4*b*c^7*d^2*e^7 - 18*b^10*c^2*d*e^8 + 276*a*b^8*c^3*d*e^8 - 1536*a^2*b^6*c^4*d*e^8 + 3456*a^3*b^4*c^5*
d*e^8 + 6654*a^4*b^2*c^6*d*e^8 + 3858*a^5*c^7*d*e^8 + 18*a*b^9*c^2*e^9 - 264*a^2*b^7*c^3*e^9 + 1381*a^3*b^5*c^
4*e^9 - 2809*a^4*b^3*c^5*e^9 - 777*a^5*b*c^6*e^9)*x^5 - (1750*b^3*c^9*d^9 + 7700*a*b*c^10*d^9 - 7875*b^4*c^8*d
^8*e - 34650*a*b^2*c^9*d^8*e + 13500*b^5*c^7*d^7*e^2 + 68400*a*b^3*c^8*d^7*e^2 + 39600*a^2*b*c^9*d^7*e^2 - 105
00*b^6*c^6*d^6*e^3 - 77700*a*b^4*c^7*d^6*e^3 - 138600*a^2*b^2*c^8*d^6*e^3 + 3150*b^7*c^5*d^5*e^4 + 51660*a*b^5
*c^6*d^5*e^4 + 185220*a^2*b^3*c^7*d^5*e^4 + 83160*a^3*b*c^8*d^5*e^4 + 3*b^8*c^4*d^4*e^5 - 15798*a*b^6*c^5*d^4*
e^5 - 116262*a^2*b^4*c^6*d^4*e^5 - 208668*a^3*b^2*c^7*d^4*e^5 + 768*a^4*c^8*d^4*e^5 - 16*b^9*c^3*d^3*e^6 + 256
*a*b^7*c^4*d^3*e^6 + 29964*a^2*b^5*c^5*d^3*e^6 + 163696*a^3*b^3*c^6*d^3*e^6 + 88304*a^4*b*c^7*d^3*e^6 + 36*b^1
0*c^2*d^2*e^7 - 552*a*b^8*c^3*d^2*e^7 + 3072*a^2*b^6*c^4*d^2*e^7 - 38412*a^3*b^4*c^5*d^2*e^7 - 135528*a^4*b^2*
c^6*d^2*e^7 + 6144*a^5*c^7*d^2*e^7 - 48*b^11*c*d*e^8 + 624*a*b^9*c^2*d*e^8 - 2304*a^2*b^7*c^3*d*e^8 - 1536*a^3
*b^5*c^4*d*e^8 + 40326*a^4*b^3*c^5*d*e^8 + 32436*a^5*b*c^6*d*e^8 + 48*a*b^10*c*e^9 - 612*a^2*b^8*c^2*e^9 + 227
2*a^3*b^6*c^3*e^9 + 473*a^4*b^4*c^4*e^9 - 20058*a^5*b^2*c^5*e^9 + 5376*a^6*c^6*e^9)*x^4 - 4*(42*b^4*c^8*d^9 +
1414*a*b^2*c^9*d^9 + 1022*a^2*c^10*d^9 - 189*b^5*c^7*d^8*e - 6363*a*b^3*c^8*d^8*e - 4599*a^2*b*c^9*d^8*e + 324
*b^6*c^6*d^7*e^2 + 11124*a*b^4*c^7*d^7*e^2 + 15156*a^2*b^2*c^8*d^7*e^2 + 5256*a^3*c^9*d^7*e^2 - 252*b^7*c^5*d^
6*e^3 - 9240*a*b^5*c^6*d^6*e^3 - 31584*a^2*b^3*c^7*d^6*e^3 - 18396*a^3*b*c^8*d^6*e^3 + 75*b^8*c^4*d^5*e^4 + 34
62*a*b^6*c^5*d^5*e^4 + 32778*a^2*b^4*c^6*d^5*e^4 + 37500*a^3*b^2*c^7*d^5*e^4 + 10884*a^4*c^8*d^5*e^4 + 3*b^9*c
^3*d^4*e^5 - 426*a*b^7*c^4*d^4*e^5 - 13572*a^2*b^5*c^5*d^4*e^5 - 48144*a^3*b^3*c^6*d^4*e^5 - 26826*a^4*b*c^7*d
^4*e^5 - 6*b^10*c^2*d^3*e^6 + 92*a*b^8*c^3*d^3*e^6 + 244*a^2*b^6*c^4*d^3*e^6 + 27108*a^3*b^4*c^5*d^3*e^6 + 348
52*a^4*b^2*c^6*d^3*e^6 + 11240*a^5*c^7*d^3*e^6 + 6*b^11*c*d^2*e^7 - 78*a*b^9*c^2*d^2*e^7 + 288*a^2*b^7*c^3*d^2
*e^7 - 564*a^3*b^5*c^4*d^2*e^7 - 28524*a^4*b^3*c^5*d^2*e^7 - 13788*a^5*b*c^6*d^2*e^7 - 3*b^12*d*e^8 + 12*a*b^1
0*c*d*e^8 + 270*a^2*b^8*c^2*d*e^8 - 2400*a^3*b^6*c^3*d*e^8 + 7098*a^4*b^4*c^4*d*e^8 + 8118*a^5*b^2*c^5*d*e^8 +
4590*a^6*c^6*d*e^8 + 3*a*b^11*e^9 - 15*a^2*b^9*c*e^9 - 204*a^3*b^7*c^2*e^9 + 1882*a^4*b^5*c^3*e^9 - 5089*a^5*
b^3*c^4*e^9 + 393*a^6*b*c^5*e^9)*x^3 + 2*(14*b^5*c^7*d^9 - 392*a*b^3*c^8*d^9 - 3066*a^2*b*c^9*d^9 - 63*b^6*c^6
*d^8*e + 1764*a*b^4*c^7*d^8*e + 13797*a^2*b^2*c^8*d^8*e + 108*b^7*c^5*d^7*e^2 - 2952*a*b^5*c^6*d^7*e^2 - 25668
*a^2*b^3*c^7*d^7*e^2 - 15768*a^3*b*c^8*d^7*e^2 - 85*b^8*c^4*d^6*e^3 + 2116*a*b^6*c^5*d^6*e^3 + 25356*a^2*b^4*c
^6*d^6*e^3 + 55444*a^3*b^2*c^7*d^6*e^3 - 256*a^4*c^8*d^6*e^3 + 30*b^9*c^3*d^5*e^4 - 480*a*b^7*c^4*d^5*e^4 - 13
374*a^2*b^5*c^5*d^5*e^4 - 71688*a^3*b^3*c^6*d^5*e^4 - 31884*a^4*b*c^7*d^5*e^4 - 9*b^10*c^2*d^4*e^5 + 12*a*b^8*
c^3*d^4*e^5 + 2382*a^2*b^6*c^4*d^4*e^5 + 39906*a^3*b^4*c^5*d^4*e^5 + 82014*a^4*b^2*c^6*d^4*e^5 - 1536*a^5*c^7*
d^4*e^5 + 8*b^11*c*d^3*e^6 - 104*a*b^9*c^2*d^3*e^6 + 636*a^2*b^7*c^3*d^3*e^6 - 6632*a^3*b^5*c^4*d^3*e^6 - 6398
8*a^4*b^3*c^5*d^3*e^6 - 30648*a^5*b*c^6*d^3*e^6 - 3*b^12*d^2*e^7 + 12*a*b^10*c*d^2*e^7 + 270*a^2*b^8*c^2*d^2*e
^7 - 2652*a^3*b^6*c^3*d^2*e^7 + 13776*a^4*b^4*c^4*d^2*e^7 + 50580*a^5*b^2*c^5*d^2*e^7 - 4608*a^6*c^6*d^2*e^7 +
24*a*b^11*d*e^8 - 312*a^2*b^9*c*d*e^8 + 1152*a^3*b^7*c^2*d*e^8 + 894*a^4*b^5*c^3*d*e^8 - 15816*a^5*b^3*c^4*d*
e^8 - 9162*a^6*b*c^5*d*e^8 - 21*a^2*b^10*e^9 + 274*a^3*b^8*c*e^9 - 1078*a^4*b^6*c^2*e^9 + 150*a^5*b^4*c^3*e^9
+ 7525*a^6*b^2*c^4*e^9 - 3328*a^7*c^5*e^9)*x^2 - 4*(2*b^6*c^6*d^9 - 38*a*b^4*c^7*d^9 + 348*a^2*b^2*c^8*d^9 + 5
58*a^3*c^9*d^9 - 9*b^7*c^5*d^8*e + 171*a*b^5*c^6*d^8*e - 1566*a^2*b^3*c^7*d^8*e - 2511*a^3*b*c^8*d^8*e + 15*b^
8*c^4*d^7*e^2 - 276*a*b^6*c^5*d^7*e^2 + 2448*a^2*b^4*c^6*d^7*e^2 + 6204*a^3*b^2*c^7*d^7*e^2 + 2760*a^4*c^8*d^7
*e^2 - 10*b^9*c^3*d^6*e^3 + 160*a*b^7*c^4*d^6*e^3 - 1212*a^2*b^5*c^5*d^6*e^3 - 10124*a^3*b^3*c^6*d^6*e^3 - 953
2*a^4*b*c^7*d^6*e^3 + 30*a*b^8*c^3*d^5*e^4 - 480*a^2*b^6*c^4*d^5*e^4 + 8802*a^3*b^4*c^5*d^5*e^4 + 15504*a^4*b^
2*c^6*d^5*e^4 + 5412*a^5*c^7*d^5*e^4 + 3*b^11*c*d^4*e^5 - 57*a*b^9*c^2*d^4*e^5 + 432*a^2*b^7*c^3*d^4*e^5 - 201
0*a^3*b^5*c^4*d^4*e^5 - 15954*a^4*b^3*c^5*d^4*e^5 - 12762*a^5*b*c^6*d^4*e^5 - b^12*d^3*e^6 + 4*a*b^10*c*d^3*e^
6 + 126*a^2*b^8*c^2*d^3*e^6 - 1460*a^3*b^6*c^3*d^3*e^6 + 8048*a^4*b^4*c^4*d^3*e^6 + 12684*a^5*b^2*c^5*d^3*e^6
+ 5160*a^6*c^6*d^3*e^6 + 6*a*b^11*d^2*e^7 - 78*a^2*b^9*c*d^2*e^7 + 252*a^3*b^7*c^2*d^2*e^7 + 876*a^4*b^5*c^3*d
^2*e^7 - 9336*a^5*b^3*c^4*d^2*e^7 - 5436*a^6*b*c^5*d^2*e^7 - 18*a^2*b^10*d*e^8 + 276*a^3*b^8*c*d*e^8 - 1518*a^
4*b^6*c^2*d*e^8 + 3114*a^5*b^4*c^3*d*e^8 + 1596*a^6*b^2*c^4*d*e^8 + 1950*a^7*c^5*d*e^8 + 13*a^3*b^9*e^9 - 196*
a^4*b^7*c*e^9 + 1068*a^5*b^5*c^2*e^9 - 2324*a^6*b^3*c^3*e^9 + 689*a^7*b*c^4*e^9)*x)/((c*d^2 - b*d*e + a*e^2)^5
*(c*x^2 + b*x + a)^4*(b^2 - 4*a*c)^4)

________________________________________________________________________________________

maple [B]  time = 0.15, size = 32834, normalized size = 24.80 \[ \text {output too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(e*x+d)/(c*x^2+b*x+a)^5,x)

[Out]

result too large to display

________________________________________________________________________________________

maxima [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: ValueError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x+d)/(c*x^2+b*x+a)^5,x, algorithm="maxima")

[Out]

Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'a
ssume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` f
or more details)Is 4*a*c-b^2 positive or negative?

________________________________________________________________________________________

mupad [B]  time = 23.60, size = 59814, normalized size = 45.18 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((d + e*x)*(a + b*x + c*x^2)^5),x)

[Out]

((25*a^3*b^8*e^7 + 3200*a^7*c^4*e^7 - 3*b^7*c^4*d^7 - 3*b^11*d^3*e^4 + 50*a*b^5*c^5*d^7 + 1116*a^3*b*c^7*d^7 -
385*a^4*b^6*c*e^7 + 13*a*b^10*d^2*e^5 - 23*a^2*b^9*d*e^6 + 384*a^4*c^7*d^6*e + 12*b^8*c^3*d^6*e + 12*b^10*c*d
^4*e^3 - 326*a^2*b^3*c^6*d^7 + 2175*a^5*b^4*c^2*e^7 - 5150*a^6*b^2*c^3*e^7 + 1664*a^5*c^6*d^4*e^3 + 2944*a^6*c
^5*d^2*e^5 - 18*b^9*c^2*d^5*e^2 - 1681*a^2*b^5*c^4*d^5*e^2 + 598*a^2*b^6*c^3*d^4*e^3 + 314*a^2*b^7*c^2*d^3*e^4
+ 4724*a^3*b^3*c^5*d^5*e^2 + 307*a^3*b^4*c^4*d^4*e^3 - 2812*a^3*b^5*c^3*d^3*e^4 + 574*a^3*b^6*c^2*d^2*e^5 - 1
1522*a^4*b^2*c^5*d^4*e^3 + 9254*a^4*b^3*c^4*d^3*e^4 + 985*a^4*b^4*c^3*d^2*e^5 - 10910*a^5*b^2*c^4*d^2*e^5 - 19
9*a*b^6*c^4*d^6*e + 10*a*b^9*c*d^3*e^4 + 356*a^3*b^7*c*d*e^6 + 956*a^6*b*c^4*d*e^6 + 284*a*b^7*c^3*d^5*e^2 - 1
58*a*b^8*c^2*d^4*e^3 + 1285*a^2*b^4*c^5*d^6*e - 167*a^2*b^8*c*d^2*e^5 - 4290*a^3*b^2*c^6*d^6*e + 3252*a^4*b*c^
6*d^5*e^2 - 1983*a^4*b^5*c^2*d*e^6 + 3092*a^5*b*c^5*d^3*e^4 + 4204*a^5*b^3*c^3*d*e^6)/(12*(a^4*b^8*e^8 + 256*a
^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3
*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^
6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*
a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*
e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 +
512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512
*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^
6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024
*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5
+ 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*
c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)) + (x^7*(70*c^11*d^7 + b^7*c^4*e^7 - 15*a*b^5*c^5*e^7 - 187*a^3*b*c^7*e^
7 + 290*a*c^10*d^5*e^2 + 374*a^3*c^8*d*e^6 + b^6*c^5*d*e^6 + 82*a^2*b^3*c^6*e^7 + 466*a^2*c^9*d^3*e^4 + 295*b^
2*c^9*d^5*e^2 - 125*b^3*c^8*d^4*e^3 + b^4*c^7*d^3*e^4 + b^5*c^6*d^2*e^5 - 245*b*c^10*d^6*e - 725*a*b*c^9*d^4*e
^3 - 14*a*b^4*c^6*d*e^6 + 492*a*b^2*c^8*d^3*e^4 - 13*a*b^3*c^7*d^2*e^5 - 699*a^2*b*c^8*d^2*e^5 + 69*a^2*b^2*c^
7*d*e^6))/(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 1
6*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8
- 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2
+ 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3
*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e
^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 -
128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 115
2*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7
*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5
*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a
^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7) + (x^4*(48*b^10*c*e^7 + 5376*a^5*c^6*e^7 +
1750*b^3*c^8*d^7 - 612*a*b^8*c^2*e^7 - 6125*b^4*c^7*d^6*e + 12*b^9*c^2*d*e^6 + 2272*a^2*b^6*c^3*e^7 + 473*a^3
*b^4*c^4*e^7 - 20058*a^4*b^2*c^5*e^7 + 768*a^4*c^7*d^2*e^5 + 7375*b^5*c^6*d^5*e^2 - 3125*b^6*c^5*d^4*e^3 + 25*
b^7*c^4*d^3*e^4 + 28*b^8*c^3*d^2*e^5 + 7700*a*b*c^9*d^7 - 79750*a^2*b^2*c^7*d^4*e^3 + 65770*a^2*b^3*c^6*d^3*e^
4 - 18617*a^2*b^4*c^5*d^2*e^5 - 77658*a^3*b^2*c^6*d^2*e^5 - 26950*a*b^2*c^8*d^6*e - 32*a*b^7*c^3*d*e^6 + 37812
*a^4*b*c^6*d*e^6 + 39700*a*b^3*c^7*d^5*e^2 - 31875*a*b^4*c^6*d^4*e^3 + 12410*a*b^5*c^5*d^3*e^4 - 263*a*b^6*c^4
*d^2*e^5 + 31900*a^2*b*c^8*d^5*e^2 - 1063*a^2*b^5*c^4*d*e^6 + 51260*a^3*b*c^7*d^3*e^4 + 20268*a^3*b^3*c^5*d*e^
6))/(12*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*
a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 -
256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 +
1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d
^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4
- 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 1
28*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*
a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e
+ 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d
^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5
*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)) + (x^5*(770*a*c^10*d^7 + 910*b^2*c^9*d^7 +
18*b^9*c^2*e^7 - 264*a*b^7*c^3*e^7 - 777*a^4*b*c^6*e^7 + 3858*a^4*c^7*d*e^6 - 3185*b^3*c^8*d^6*e + 12*b^8*c^3*
d*e^6 + 1381*a^2*b^5*c^4*e^7 - 2809*a^3*b^3*c^5*e^7 + 3190*a^2*c^9*d^5*e^2 + 5126*a^3*c^8*d^3*e^4 + 3835*b^4*c
^7*d^5*e^2 - 1625*b^5*c^6*d^4*e^3 + 13*b^6*c^5*d^3*e^4 + 13*b^7*c^4*d^2*e^5 - 2695*a*b*c^9*d^6*e + 11470*a^2*b
^2*c^7*d^3*e^4 - 9230*a^2*b^3*c^6*d^2*e^5 - 155*a*b^6*c^4*d*e^6 + 7015*a*b^2*c^8*d^5*e^2 - 10800*a*b^3*c^7*d^4
*e^3 + 6407*a*b^4*c^6*d^3*e^4 - 158*a*b^5*c^5*d^2*e^5 - 7975*a^2*b*c^8*d^4*e^3 + 647*a^2*b^4*c^5*d*e^6 - 7689*
a^3*b*c^7*d^2*e^5 + 5877*a^3*b^2*c^6*d*e^6))/(3*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8
+ b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e -
4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^
2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512
*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b
^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^
5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^
4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4
*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 +
52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^
2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)) + (
x^3*(3*b^11*e^7 + 1022*a^2*c^9*d^7 + 42*b^4*c^7*d^7 + 1414*a*b^2*c^8*d^7 + 393*a^5*b*c^5*e^7 + 4590*a^5*c^6*d*
e^6 - 147*b^5*c^6*d^6*e - 204*a^2*b^7*c^2*e^7 + 1882*a^3*b^5*c^3*e^7 - 5089*a^4*b^3*c^4*e^7 + 4234*a^3*c^8*d^5
*e^2 + 6650*a^4*c^7*d^3*e^4 + 177*b^6*c^5*d^5*e^2 - 75*b^7*c^4*d^4*e^3 + 3*b^9*c^2*d^2*e^5 - 15*a*b^9*c*e^7 -
3*b^10*c*d*e^6 + 10165*a^2*b^2*c^7*d^5*e^2 - 16470*a^2*b^3*c^6*d^4*e^3 + 10175*a^2*b^4*c^5*d^3*e^4 - 437*a^2*b
^5*c^4*d^2*e^5 + 16750*a^3*b^2*c^6*d^3*e^4 - 14924*a^3*b^3*c^5*d^2*e^5 - 4949*a*b^3*c^7*d^6*e + 66*a*b^8*c^2*d
*e^6 - 3577*a^2*b*c^8*d^6*e + 6133*a*b^4*c^6*d^5*e^2 - 2960*a*b^5*c^5*d^4*e^3 + 325*a*b^6*c^4*d^3*e^4 - 26*a*b
^7*c^3*d^2*e^5 - 518*a^2*b^6*c^3*d*e^6 - 10585*a^3*b*c^7*d^4*e^3 + 2009*a^3*b^4*c^4*d*e^6 - 9591*a^4*b*c^6*d^2
*e^5 + 8511*a^4*b^2*c^5*d*e^6))/(3*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e
^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5
*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^
6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*
d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^
3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2
240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*
a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4
*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*
d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*
a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)) + (x*(13*a^2*b^9
*e^7 + 558*a^3*c^8*d^7 + 2*b^6*c^5*d^7 + b^11*d^2*e^5 - 38*a*b^4*c^6*d^7 - 196*a^3*b^7*c*e^7 + 689*a^6*b*c^4*e
^7 + 1950*a^6*c^5*d*e^6 - 7*b^7*c^4*d^6*e - 2*b^10*c*d^3*e^4 + 348*a^2*b^2*c^7*d^7 + 1068*a^4*b^5*c^2*e^7 - 23
24*a^5*b^3*c^3*e^7 + 2202*a^4*c^7*d^5*e^2 + 3210*a^5*c^6*d^3*e^4 + 8*b^8*c^3*d^5*e^2 - 2*b^9*c^2*d^4*e^3 - 5*a
*b^10*d*e^6 + 1268*a^2*b^4*c^5*d^5*e^2 - 77*a^2*b^5*c^4*d^4*e^3 - 412*a^2*b^6*c^3*d^3*e^4 - 2*a^2*b^7*c^2*d^2*
e^5 + 3903*a^3*b^2*c^6*d^5*e^2 - 5003*a^3*b^3*c^5*d^4*e^3 + 2531*a^3*b^4*c^4*d^3*e^4 + 598*a^3*b^5*c^3*d^2*e^5
+ 6224*a^4*b^2*c^5*d^3*e^4 - 4727*a^4*b^3*c^4*d^2*e^5 + 133*a*b^5*c^5*d^6*e - 11*a*b^9*c*d^2*e^5 + 80*a^2*b^8
*c*d*e^6 - 1953*a^3*b*c^7*d^6*e - 145*a*b^6*c^4*d^5*e^2 + 22*a*b^7*c^3*d^4*e^3 + 44*a*b^8*c^2*d^3*e^4 - 1218*a
^2*b^3*c^6*d^6*e - 450*a^3*b^6*c^2*d*e^6 - 5377*a^4*b*c^6*d^4*e^3 + 790*a^4*b^4*c^3*d*e^6 - 4175*a^5*b*c^5*d^2
*e^5 + 2285*a^5*b^2*c^4*d*e^6))/(3*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e
^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5
*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^
6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*
d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^
3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2
240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*
a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4
*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*
d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*
a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)) + (x^2*(21*a*b^1
0*e^7 - 3*b^11*d*e^6 + 3328*a^6*c^5*e^7 - 14*b^5*c^6*d^7 + 392*a*b^3*c^7*d^7 + 3066*a^2*b*c^8*d^7 - 274*a^2*b^
8*c*e^7 + 49*b^6*c^5*d^6*e + 5*b^10*c*d^2*e^5 + 1078*a^3*b^6*c^2*e^7 - 150*a^4*b^4*c^3*e^7 - 7525*a^5*b^2*c^4*
e^7 + 256*a^4*c^7*d^4*e^3 + 1280*a^5*c^6*d^2*e^5 - 59*b^7*c^4*d^5*e^2 + 26*b^8*c^3*d^4*e^3 - 4*b^9*c^2*d^3*e^4
+ 38*a*b^9*c*d*e^6 + 14545*a^2*b^3*c^6*d^5*e^2 - 9439*a^2*b^4*c^5*d^4*e^3 + 2341*a^2*b^5*c^4*d^3*e^4 + 530*a^
2*b^6*c^3*d^2*e^5 - 32011*a^3*b^2*c^6*d^4*e^3 + 25132*a^3*b^3*c^5*d^3*e^4 - 5335*a^3*b^4*c^4*d^2*e^5 - 30565*a
^4*b^2*c^5*d^2*e^5 - 1372*a*b^4*c^6*d^6*e + 12490*a^5*b*c^5*d*e^6 + 1594*a*b^5*c^5*d^5*e^2 - 571*a*b^6*c^4*d^4
*e^3 - 32*a*b^7*c^3*d^3*e^4 - 70*a*b^8*c^2*d^2*e^5 - 10731*a^2*b^2*c^7*d^6*e - 74*a^2*b^7*c^2*d*e^6 + 12702*a^
3*b*c^7*d^5*e^2 - 1044*a^3*b^5*c^3*d*e^6 + 19438*a^4*b*c^6*d^3*e^4 + 8291*a^4*b^3*c^4*d*e^6))/(6*(a^4*b^8*e^8
+ 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b
^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8
+ 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4
+ 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c
^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^
3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^
5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 +
512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7
- 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d
^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072
*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)) + (x^6*(490*b*c^10*d^7 + 256*a^4*c^7*e^7 + 8*b^8*c^3*e^7 - 121*a
*b^6*c^4*e^7 - 1715*b^2*c^9*d^6*e + 7*b^7*c^4*d*e^6 + 670*a^2*b^4*c^5*e^7 - 1565*a^3*b^2*c^6*e^7 + 2065*b^3*c^
8*d^5*e^2 - 875*b^4*c^7*d^4*e^3 + 7*b^5*c^6*d^3*e^4 + 7*b^6*c^5*d^2*e^5 - 4893*a^2*b^2*c^7*d^2*e^5 + 2030*a*b*
c^9*d^5*e^2 - 98*a*b^5*c^5*d*e^6 + 2618*a^3*b*c^7*d*e^6 - 5075*a*b^2*c^8*d^4*e^3 + 3444*a*b^3*c^7*d^3*e^4 - 91
*a*b^4*c^6*d^2*e^5 + 3262*a^2*b*c^8*d^3*e^4 + 483*a^2*b^3*c^6*d*e^6))/(2*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*
a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*
d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 2
56*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 +
6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^
4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*
d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*
e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6
+ 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7
- 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^
6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 102
4*a^6*b^3*c^3*d*e^7)))/(x^4*(b^4 + 6*a^2*c^2 + 12*a*b^2*c) + a^4 + c^4*x^8 + x^2*(4*a^3*c + 6*a^2*b^2) + x^6*(
4*a*c^3 + 6*b^2*c^2) + x^3*(4*a*b^3 + 12*a^2*b*c) + x^5*(4*b^3*c + 12*a*b*c^2) + 4*b*c^3*x^7 + 4*a^3*b*x) + sy
msum(log((b^15*c^2*e^17 + 4900*c^17*d^15*e^2 - 31*a*b^13*c^3*e^17 - 47872*a^7*b*c^9*e^17 + 40600*a*c^16*d^13*e
^4 + 95744*a^7*c^10*d*e^16 - 34300*b*c^16*d^14*e^3 + 2*b^14*c^3*d*e^16 + 418*a^2*b^11*c^4*e^17 - 3195*a^3*b^9*
c^5*e^17 + 14960*a^4*b^7*c^6*e^17 - 42784*a^5*b^5*c^7*e^17 + 68864*a^6*b^3*c^8*e^17 + 149340*a^2*c^15*d^11*e^6
+ 322640*a^3*c^14*d^9*e^8 + 451996*a^4*c^13*d^7*e^10 + 422808*a^5*c^12*d^5*e^12 + 259172*a^6*c^11*d^3*e^14 +
101325*b^2*c^15*d^13*e^4 - 162050*b^3*c^14*d^12*e^5 + 148415*b^4*c^13*d^11*e^6 - 74100*b^5*c^12*d^10*e^7 + 158
65*b^6*c^11*d^9*e^8 - 10*b^7*c^10*d^8*e^9 - 79*b^8*c^9*d^7*e^10 + 97*b^9*c^8*d^6*e^11 + 48*b^10*c^7*d^5*e^12 -
121*b^11*c^6*d^4*e^13 + 4*b^12*c^5*d^3*e^14 + 3*b^13*c^4*d^2*e^15 + 1438095*a^2*b^2*c^13*d^9*e^8 - 1272180*a^
2*b^3*c^12*d^8*e^9 + 435726*a^2*b^4*c^11*d^7*e^10 + 5952*a^2*b^5*c^10*d^6*e^11 + 10995*a^2*b^6*c^9*d^5*e^12 -
14960*a^2*b^7*c^8*d^4*e^13 - 7820*a^2*b^8*c^7*d^3*e^14 + 327*a^2*b^9*c^6*d^2*e^15 + 1806484*a^3*b^2*c^12*d^7*e
^10 - 893532*a^3*b^3*c^11*d^6*e^11 - 46060*a^3*b^4*c^10*d^5*e^12 + 47260*a^3*b^5*c^9*d^4*e^13 + 56800*a^3*b^6*
c^8*d^3*e^14 + 5688*a^3*b^7*c^7*d^2*e^15 + 1193355*a^4*b^2*c^11*d^5*e^12 - 60170*a^4*b^3*c^10*d^4*e^13 - 19644
5*a^4*b^4*c^9*d^3*e^14 - 58188*a^4*b^5*c^8*d^2*e^15 + 319694*a^5*b^2*c^10*d^3*e^14 + 211146*a^5*b^3*c^9*d^2*e^
15 - 243600*a*b*c^15*d^12*e^5 - 60*a*b^12*c^4*d*e^16 + 595230*a*b^2*c^14*d^11*e^6 - 743150*a*b^3*c^13*d^10*e^7
+ 476520*a*b^4*c^12*d^9*e^8 - 126780*a*b^5*c^11*d^8*e^9 + 1334*a*b^6*c^10*d^7*e^10 - 1342*a*b^7*c^9*d^6*e^11
- 1200*a*b^8*c^8*d^5*e^12 + 2175*a*b^9*c^7*d^4*e^13 + 392*a*b^10*c^6*d^3*e^14 - 87*a*b^11*c^5*d^2*e^15 - 74670
0*a^2*b*c^14*d^10*e^7 + 778*a^2*b^10*c^5*d*e^16 - 1290560*a^3*b*c^13*d^8*e^9 - 5164*a^3*b^8*c^6*d*e^16 - 13649
48*a^4*b*c^12*d^6*e^11 + 16814*a^4*b^6*c^7*d*e^16 - 882736*a^5*b*c^11*d^4*e^13 - 16012*a^5*b^4*c^8*d*e^16 - 31
8820*a^6*b*c^10*d^2*e^15 - 43111*a^6*b^2*c^9*d*e^16)/(a^8*b^16*e^16 + 65536*a^8*c^16*d^16 + 65536*a^16*c^8*e^1
6 + b^16*c^8*d^16 + b^24*d^8*e^8 - 32*a*b^14*c^9*d^16 - 32*a^9*b^14*c*e^16 - 8*a*b^23*d^7*e^9 - 8*a^7*b^17*d*e
^15 - 8*b^17*c^7*d^15*e - 8*b^23*c*d^9*e^7 + 448*a^2*b^12*c^10*d^16 - 3584*a^3*b^10*c^11*d^16 + 17920*a^4*b^8*
c^12*d^16 - 57344*a^5*b^6*c^13*d^16 + 114688*a^6*b^4*c^14*d^16 - 131072*a^7*b^2*c^15*d^16 + 448*a^10*b^12*c^2*
e^16 - 3584*a^11*b^10*c^3*e^16 + 17920*a^12*b^8*c^4*e^16 - 57344*a^13*b^6*c^5*e^16 + 114688*a^14*b^4*c^6*e^16
- 131072*a^15*b^2*c^7*e^16 + 28*a^2*b^22*d^6*e^10 - 56*a^3*b^21*d^5*e^11 + 70*a^4*b^20*d^4*e^12 - 56*a^5*b^19*
d^3*e^13 + 28*a^6*b^18*d^2*e^14 + 524288*a^9*c^15*d^14*e^2 + 1835008*a^10*c^14*d^12*e^4 + 3670016*a^11*c^13*d^
10*e^6 + 4587520*a^12*c^12*d^8*e^8 + 3670016*a^13*c^11*d^6*e^10 + 1835008*a^14*c^10*d^4*e^12 + 524288*a^15*c^9
*d^2*e^14 + 28*b^18*c^6*d^14*e^2 - 56*b^19*c^5*d^13*e^3 + 70*b^20*c^4*d^12*e^4 - 56*b^21*c^3*d^11*e^5 + 28*b^2
2*c^2*d^10*e^6 + 12288*a^2*b^14*c^8*d^14*e^2 - 23296*a^2*b^15*c^7*d^13*e^3 + 26012*a^2*b^16*c^6*d^12*e^4 - 162
96*a^2*b^17*c^5*d^11*e^5 + 4004*a^2*b^18*c^4*d^10*e^6 + 1232*a^2*b^19*c^3*d^9*e^7 - 924*a^2*b^20*c^2*d^8*e^8 -
96768*a^3*b^12*c^9*d^14*e^2 + 175616*a^3*b^13*c^8*d^13*e^3 - 176512*a^3*b^14*c^7*d^12*e^4 + 80640*a^3*b^15*c^
6*d^11*e^5 + 11704*a^3*b^16*c^5*d^10*e^6 - 28952*a^3*b^17*c^4*d^9*e^7 + 8624*a^3*b^18*c^3*d^8*e^8 + 1232*a^3*b
^19*c^2*d^7*e^9 + 473088*a^4*b^10*c^10*d^14*e^2 - 802816*a^4*b^11*c^9*d^13*e^3 + 664832*a^4*b^12*c^8*d^12*e^4
- 75264*a^4*b^13*c^7*d^11*e^5 - 315392*a^4*b^14*c^6*d^10*e^6 + 216832*a^4*b^15*c^5*d^9*e^7 - 12474*a^4*b^16*c^
4*d^8*e^8 - 28952*a^4*b^17*c^3*d^7*e^9 + 4004*a^4*b^18*c^2*d^6*e^10 - 1462272*a^5*b^8*c^11*d^14*e^2 + 2207744*
a^5*b^9*c^10*d^13*e^3 - 1103872*a^5*b^10*c^9*d^12*e^4 - 1204224*a^5*b^11*c^8*d^11*e^5 + 1931776*a^5*b^12*c^7*d
^10*e^6 - 670208*a^5*b^13*c^6*d^9*e^7 - 310464*a^5*b^14*c^5*d^8*e^8 + 216832*a^5*b^15*c^4*d^7*e^9 + 11704*a^5*
b^16*c^3*d^6*e^10 - 16296*a^5*b^17*c^2*d^5*e^11 + 2752512*a^6*b^6*c^12*d^14*e^2 - 3211264*a^6*b^7*c^11*d^13*e^
3 - 1103872*a^6*b^8*c^10*d^12*e^4 + 6623232*a^6*b^9*c^9*d^11*e^5 - 5519360*a^6*b^10*c^8*d^10*e^6 - 315392*a^6*
b^11*c^7*d^9*e^7 + 2454144*a^6*b^12*c^6*d^8*e^8 - 670208*a^6*b^13*c^5*d^7*e^9 - 315392*a^6*b^14*c^4*d^6*e^10 +
80640*a^6*b^15*c^3*d^5*e^11 + 26012*a^6*b^16*c^2*d^4*e^12 - 2752512*a^7*b^4*c^13*d^14*e^2 + 917504*a^7*b^5*c^
12*d^13*e^3 + 8486912*a^7*b^6*c^11*d^12*e^4 - 15138816*a^7*b^7*c^10*d^11*e^5 + 5361664*a^7*b^8*c^9*d^10*e^6 +
8876032*a^7*b^9*c^8*d^9*e^7 - 8008704*a^7*b^10*c^7*d^8*e^8 - 315392*a^7*b^11*c^6*d^7*e^9 + 1931776*a^7*b^12*c^
5*d^6*e^10 - 75264*a^7*b^13*c^4*d^5*e^11 - 176512*a^7*b^14*c^3*d^4*e^12 - 23296*a^7*b^15*c^2*d^3*e^13 + 786432
*a^8*b^2*c^14*d^14*e^2 + 3670016*a^8*b^3*c^13*d^13*e^3 - 14221312*a^8*b^4*c^12*d^12*e^4 + 13762560*a^8*b^5*c^1
1*d^11*e^5 + 10092544*a^8*b^6*c^10*d^10*e^6 - 26673152*a^8*b^7*c^9*d^9*e^7 + 10036224*a^8*b^8*c^8*d^8*e^8 + 88
76032*a^8*b^9*c^7*d^7*e^9 - 5519360*a^8*b^10*c^6*d^6*e^10 - 1204224*a^8*b^11*c^5*d^5*e^11 + 664832*a^8*b^12*c^
4*d^4*e^12 + 175616*a^8*b^13*c^3*d^3*e^13 + 12288*a^8*b^14*c^2*d^2*e^14 + 7340032*a^9*b^2*c^13*d^12*e^4 + 3670
016*a^9*b^3*c^12*d^11*e^5 - 30277632*a^9*b^4*c^11*d^10*e^6 + 30277632*a^9*b^5*c^10*d^9*e^7 + 8830976*a^9*b^6*c
^9*d^8*e^8 - 26673152*a^9*b^7*c^8*d^7*e^9 + 5361664*a^9*b^8*c^7*d^6*e^10 + 6623232*a^9*b^9*c^6*d^5*e^11 - 1103
872*a^9*b^10*c^5*d^4*e^12 - 802816*a^9*b^11*c^4*d^3*e^13 - 96768*a^9*b^12*c^3*d^2*e^14 + 20185088*a^10*b^2*c^1
2*d^10*e^6 - 37847040*a^10*b^4*c^10*d^8*e^8 + 30277632*a^10*b^5*c^9*d^7*e^9 + 10092544*a^10*b^6*c^8*d^6*e^10 -
15138816*a^10*b^7*c^7*d^5*e^11 - 1103872*a^10*b^8*c^6*d^4*e^12 + 2207744*a^10*b^9*c^5*d^3*e^13 + 473088*a^10*
b^10*c^4*d^2*e^14 + 27525120*a^11*b^2*c^11*d^8*e^8 - 30277632*a^11*b^4*c^9*d^6*e^10 + 13762560*a^11*b^5*c^8*d^
5*e^11 + 8486912*a^11*b^6*c^7*d^4*e^12 - 3211264*a^11*b^7*c^6*d^3*e^13 - 1462272*a^11*b^8*c^5*d^2*e^14 + 20185
088*a^12*b^2*c^10*d^6*e^10 + 3670016*a^12*b^3*c^9*d^5*e^11 - 14221312*a^12*b^4*c^8*d^4*e^12 + 917504*a^12*b^5*
c^7*d^3*e^13 + 2752512*a^12*b^6*c^6*d^2*e^14 + 7340032*a^13*b^2*c^9*d^4*e^12 + 3670016*a^13*b^3*c^8*d^3*e^13 -
2752512*a^13*b^4*c^7*d^2*e^14 + 786432*a^14*b^2*c^8*d^2*e^14 + 256*a*b^15*c^8*d^15*e + 24*a*b^22*c*d^8*e^8 -
524288*a^8*b*c^15*d^15*e + 256*a^8*b^15*c*d*e^15 - 524288*a^15*b*c^8*d*e^15 - 888*a*b^16*c^7*d^14*e^2 + 1736*a
*b^17*c^6*d^13*e^3 - 2072*a*b^18*c^5*d^12*e^4 + 1512*a*b^19*c^4*d^11*e^5 - 616*a*b^20*c^3*d^10*e^6 + 88*a*b^21
*c^2*d^9*e^7 - 3584*a^2*b^13*c^9*d^15*e + 88*a^2*b^21*c*d^7*e^9 + 28672*a^3*b^11*c^10*d^15*e - 616*a^3*b^20*c*
d^6*e^10 - 143360*a^4*b^9*c^11*d^15*e + 1512*a^4*b^19*c*d^5*e^11 + 458752*a^5*b^7*c^12*d^15*e - 2072*a^5*b^18*
c*d^4*e^12 - 917504*a^6*b^5*c^13*d^15*e + 1736*a^6*b^17*c*d^3*e^13 + 1048576*a^7*b^3*c^14*d^15*e - 888*a^7*b^1
6*c*d^2*e^14 - 3670016*a^9*b*c^14*d^13*e^3 - 3584*a^9*b^13*c^2*d*e^15 - 11010048*a^10*b*c^13*d^11*e^5 + 28672*
a^10*b^11*c^3*d*e^15 - 18350080*a^11*b*c^12*d^9*e^7 - 143360*a^11*b^9*c^4*d*e^15 - 18350080*a^12*b*c^11*d^7*e^
9 + 458752*a^12*b^7*c^5*d*e^15 - 11010048*a^13*b*c^10*d^5*e^11 - 917504*a^13*b^5*c^6*d*e^15 - 3670016*a^14*b*c
^9*d^3*e^13 + 1048576*a^14*b^3*c^7*d*e^15) - root(330301440*a^14*b*c^13*d^9*e^11*z^3 + 330301440*a^13*b*c^14*d
^11*e^9*z^3 + 220200960*a^15*b*c^12*d^7*e^13*z^3 + 220200960*a^12*b*c^15*d^13*e^7*z^3 + 94371840*a^16*b*c^11*d
^5*e^15*z^3 + 94371840*a^11*b*c^16*d^15*e^5*z^3 + 23592960*a^17*b*c^10*d^3*e^17*z^3 + 23592960*a^10*b*c^17*d^1
7*e^3*z^3 - 5898240*a^17*b^3*c^8*d*e^19*z^3 + 5898240*a^16*b^5*c^7*d*e^19*z^3 - 5898240*a^8*b^3*c^17*d^19*e*z^
3 + 5898240*a^7*b^5*c^16*d^19*e*z^3 - 3440640*a^15*b^7*c^6*d*e^19*z^3 - 3440640*a^6*b^7*c^15*d^19*e*z^3 + 1290
240*a^14*b^9*c^5*d*e^19*z^3 + 1290240*a^5*b^9*c^14*d^19*e*z^3 - 322560*a^13*b^11*c^4*d*e^19*z^3 - 322560*a^4*b
^11*c^13*d^19*e*z^3 + 53760*a^12*b^13*c^3*d*e^19*z^3 + 53760*a^3*b^13*c^12*d^19*e*z^3 + 8232*a^6*b^21*c*d^5*e^
15*z^3 + 8232*a*b^21*c^6*d^15*e^5*z^3 - 7200*a^7*b^20*c*d^4*e^16*z^3 - 7200*a*b^20*c^7*d^16*e^4*z^3 - 6300*a^5
*b^22*c*d^6*e^14*z^3 - 6300*a*b^22*c^5*d^14*e^6*z^3 - 5760*a^11*b^15*c^2*d*e^19*z^3 - 5760*a^2*b^15*c^11*d^19*
e*z^3 + 4230*a^8*b^19*c*d^3*e^17*z^3 + 4230*a*b^19*c^8*d^17*e^3*z^3 + 3060*a^4*b^23*c*d^7*e^13*z^3 + 3060*a*b^
23*c^4*d^13*e^7*z^3 - 1610*a^9*b^18*c*d^2*e^18*z^3 - 1610*a*b^18*c^9*d^18*e^2*z^3 - 780*a^3*b^24*c*d^8*e^12*z^
3 - 780*a*b^24*c^3*d^12*e^8*z^3 + 2621440*a^18*b*c^9*d*e^19*z^3 + 2621440*a^9*b*c^18*d^19*e*z^3 + 360*a^10*b^1
7*c*d*e^19*z^3 + 360*a*b^17*c^10*d^19*e*z^3 + 54*a*b^26*c*d^10*e^10*z^3 - 1073479680*a^12*b^5*c^11*d^9*e^11*z^
3 - 1073479680*a^11*b^5*c^12*d^11*e^9*z^3 - 706387968*a^10*b^8*c^10*d^10*e^10*z^3 - 677117952*a^13*b^2*c^13*d^
10*e^10*z^3 - 660602880*a^13*b^5*c^10*d^7*e^13*z^3 - 660602880*a^10*b^5*c^13*d^13*e^7*z^3 + 651755520*a^11*b^7
*c^10*d^9*e^11*z^3 + 651755520*a^10*b^7*c^11*d^11*e^9*z^3 + 608305152*a^12*b^4*c^12*d^10*e^10*z^3 - 536739840*
a^14*b^2*c^12*d^8*e^12*z^3 + 536739840*a^13*b^4*c^11*d^8*e^12*z^3 - 536739840*a^12*b^2*c^14*d^12*e^8*z^3 + 536
739840*a^11*b^4*c^13*d^12*e^8*z^3 - 534343680*a^11*b^8*c^9*d^8*e^12*z^3 - 534343680*a^9*b^8*c^11*d^12*e^8*z^3
+ 485621760*a^12*b^7*c^9*d^7*e^13*z^3 + 485621760*a^9*b^7*c^12*d^13*e^7*z^3 + 375717888*a^11*b^6*c^11*d^10*e^1
0*z^3 + 357826560*a^13*b^3*c^12*d^9*e^11*z^3 + 357826560*a^12*b^3*c^13*d^11*e^9*z^3 + 356415488*a^9*b^10*c^9*d
^10*e^10*z^3 + 342097920*a^14*b^4*c^10*d^6*e^14*z^3 + 342097920*a^10*b^4*c^14*d^14*e^6*z^3 + 296524800*a^10*b^
10*c^8*d^8*e^12*z^3 + 296524800*a^8*b^10*c^10*d^12*e^8*z^3 - 259522560*a^15*b^2*c^11*d^6*e^14*z^3 - 259522560*
a^11*b^2*c^15*d^14*e^6*z^3 + 223641600*a^12*b^6*c^10*d^8*e^12*z^3 + 223641600*a^10*b^6*c^12*d^12*e^8*z^3 + 222
953472*a^13*b^7*c^8*d^5*e^15*z^3 + 222953472*a^8*b^7*c^13*d^15*e^5*z^3 - 217055232*a^14*b^5*c^9*d^5*e^15*z^3 -
217055232*a^9*b^5*c^14*d^15*e^5*z^3 - 201277440*a^12*b^8*c^8*d^6*e^14*z^3 - 201277440*a^8*b^8*c^12*d^14*e^6*z
^3 + 165150720*a^14*b^3*c^11*d^7*e^13*z^3 + 165150720*a^11*b^3*c^14*d^13*e^7*z^3 - 159344640*a^9*b^11*c^8*d^9*
e^11*z^3 - 159344640*a^8*b^11*c^9*d^11*e^9*z^3 + 150958080*a^11*b^10*c^7*d^6*e^14*z^3 + 150958080*a^7*b^10*c^1
1*d^14*e^6*z^3 + 130744320*a^15*b^4*c^9*d^4*e^16*z^3 + 130744320*a^9*b^4*c^15*d^16*e^4*z^3 - 93929472*a^12*b^9
*c^7*d^5*e^15*z^3 - 93929472*a^7*b^9*c^12*d^15*e^5*z^3 - 86261760*a^11*b^9*c^8*d^7*e^13*z^3 - 86261760*a^8*b^9
*c^11*d^13*e^7*z^3 + 78474240*a^8*b^13*c^7*d^9*e^11*z^3 + 78474240*a^7*b^13*c^8*d^11*e^9*z^3 - 72990720*a^14*b
^6*c^8*d^4*e^16*z^3 - 72990720*a^8*b^6*c^14*d^16*e^4*z^3 - 67829760*a^16*b^2*c^10*d^4*e^16*z^3 - 67829760*a^10
*b^2*c^16*d^16*e^4*z^3 - 64696320*a^10*b^11*c^7*d^7*e^13*z^3 - 64696320*a^7*b^11*c^10*d^13*e^7*z^3 - 63797760*
a^9*b^12*c^7*d^8*e^12*z^3 - 63797760*a^7*b^12*c^9*d^12*e^8*z^3 - 60622848*a^8*b^12*c^8*d^10*e^10*z^3 - 5031936
0*a^10*b^12*c^6*d^6*e^14*z^3 - 50319360*a^6*b^12*c^10*d^14*e^6*z^3 + 44513280*a^9*b^13*c^6*d^7*e^13*z^3 + 4451
3280*a^6*b^13*c^9*d^13*e^7*z^3 + 39813120*a^14*b^7*c^7*d^3*e^17*z^3 + 39813120*a^7*b^7*c^14*d^17*e^3*z^3 - 296
75520*a^13*b^9*c^6*d^3*e^17*z^3 - 29675520*a^6*b^9*c^13*d^17*e^3*z^3 + 27256320*a^12*b^10*c^6*d^4*e^16*z^3 + 2
7256320*a^6*b^10*c^12*d^16*e^4*z^3 - 23101440*a^15*b^6*c^7*d^2*e^18*z^3 - 23101440*a^7*b^6*c^15*d^18*e^2*z^3 -
21626880*a^16*b^3*c^9*d^3*e^17*z^3 - 21626880*a^9*b^3*c^16*d^17*e^3*z^3 + 20643840*a^16*b^4*c^8*d^2*e^18*z^3
+ 20643840*a^8*b^4*c^16*d^18*e^2*z^3 - 17694720*a^15*b^5*c^8*d^3*e^17*z^3 - 17694720*a^8*b^5*c^15*d^17*e^3*z^3
- 16423680*a^7*b^15*c^6*d^9*e^11*z^3 - 16423680*a^6*b^15*c^7*d^11*e^9*z^3 - 15724800*a^11*b^12*c^5*d^4*e^16*z
^3 - 15724800*a^5*b^12*c^11*d^16*e^4*z^3 + 14192640*a^14*b^8*c^6*d^2*e^18*z^3 + 14192640*a^6*b^8*c^14*d^18*e^2
*z^3 - 13762560*a^13*b^6*c^9*d^6*e^14*z^3 - 13762560*a^9*b^6*c^13*d^14*e^6*z^3 - 13508352*a^7*b^14*c^7*d^10*e^
10*z^3 + 12579840*a^12*b^11*c^5*d^3*e^17*z^3 + 12579840*a^5*b^11*c^12*d^17*e^3*z^3 - 12096000*a^8*b^15*c^5*d^7
*e^13*z^3 - 12096000*a^5*b^15*c^8*d^13*e^7*z^3 + 10063872*a^11*b^11*c^6*d^5*e^15*z^3 + 10063872*a^6*b^11*c^11*
d^15*e^5*z^3 + 8600592*a^6*b^16*c^6*d^10*e^10*z^3 + 7864320*a^15*b^3*c^10*d^5*e^15*z^3 + 7864320*a^10*b^3*c^15
*d^15*e^5*z^3 + 7354368*a^10*b^13*c^5*d^5*e^15*z^3 + 7354368*a^5*b^13*c^10*d^15*e^5*z^3 + 6842880*a^9*b^14*c^5
*d^6*e^14*z^3 + 6842880*a^5*b^14*c^9*d^14*e^6*z^3 - 5898240*a^17*b^2*c^9*d^2*e^18*z^3 - 5898240*a^9*b^2*c^17*d
^18*e^2*z^3 - 5857280*a^10*b^9*c^9*d^9*e^11*z^3 - 5857280*a^9*b^9*c^10*d^11*e^9*z^3 - 5806080*a^13*b^8*c^7*d^4
*e^16*z^3 - 5806080*a^7*b^8*c^13*d^16*e^4*z^3 + 5798520*a^7*b^16*c^5*d^8*e^12*z^3 + 5798520*a^5*b^16*c^7*d^12*
e^8*z^3 - 5483520*a^13*b^10*c^5*d^2*e^18*z^3 - 5483520*a^5*b^10*c^13*d^18*e^2*z^3 + 4864320*a^10*b^14*c^4*d^4*
e^16*z^3 + 4864320*a^4*b^14*c^10*d^16*e^4*z^3 - 4717440*a^8*b^14*c^6*d^8*e^12*z^3 - 4717440*a^6*b^14*c^8*d^12*
e^8*z^3 - 3820032*a^9*b^15*c^4*d^5*e^15*z^3 - 3820032*a^4*b^15*c^9*d^15*e^5*z^3 - 3386880*a^11*b^13*c^4*d^3*e^
17*z^3 - 3386880*a^4*b^13*c^11*d^17*e^3*z^3 - 1693692*a^5*b^18*c^5*d^10*e^10*z^3 + 1481760*a^7*b^17*c^4*d^7*e^
13*z^3 + 1481760*a^4*b^17*c^7*d^13*e^7*z^3 + 1397760*a^12*b^12*c^4*d^2*e^18*z^3 + 1397760*a^4*b^12*c^12*d^18*e
^2*z^3 - 1340430*a^6*b^18*c^4*d^8*e^12*z^3 - 1340430*a^4*b^18*c^6*d^12*e^8*z^3 - 923220*a^9*b^16*c^3*d^4*e^16*
z^3 - 923220*a^3*b^16*c^9*d^16*e^4*z^3 + 883872*a^8*b^17*c^3*d^5*e^15*z^3 + 883872*a^3*b^17*c^8*d^15*e^5*z^3 +
851760*a^6*b^17*c^5*d^9*e^11*z^3 + 851760*a^5*b^17*c^6*d^11*e^9*z^3 + 721440*a^8*b^16*c^4*d^6*e^14*z^3 + 7214
40*a^4*b^16*c^8*d^14*e^6*z^3 + 593280*a^10*b^15*c^3*d^3*e^17*z^3 + 593280*a^3*b^15*c^10*d^17*e^3*z^3 - 448440*
a^7*b^18*c^3*d^6*e^14*z^3 - 448440*a^3*b^18*c^7*d^14*e^6*z^3 + 311220*a^5*b^19*c^4*d^9*e^11*z^3 + 311220*a^4*b
^19*c^5*d^11*e^9*z^3 - 236160*a^11*b^14*c^3*d^2*e^18*z^3 - 236160*a^3*b^14*c^11*d^18*e^2*z^3 + 131040*a^5*b^20
*c^3*d^8*e^12*z^3 + 131040*a^3*b^20*c^5*d^12*e^8*z^3 + 126126*a^4*b^20*c^4*d^10*e^10*z^3 - 115272*a^7*b^19*c^2
*d^5*e^15*z^3 - 115272*a^2*b^19*c^7*d^15*e^5*z^3 + 108045*a^8*b^18*c^2*d^4*e^16*z^3 + 108045*a^2*b^18*c^8*d^16
*e^4*z^3 + 76860*a^6*b^20*c^2*d^6*e^14*z^3 + 76860*a^2*b^20*c^6*d^14*e^6*z^3 - 67080*a^4*b^21*c^3*d^9*e^11*z^3
- 67080*a^3*b^21*c^4*d^11*e^9*z^3 - 65880*a^9*b^17*c^2*d^3*e^17*z^3 - 65880*a^2*b^17*c^9*d^17*e^3*z^3 - 26280
*a^5*b^21*c^2*d^7*e^13*z^3 - 26280*a^2*b^21*c^5*d^13*e^7*z^3 + 25560*a^10*b^16*c^2*d^2*e^18*z^3 + 25560*a^2*b^
16*c^10*d^18*e^2*z^3 + 9240*a^6*b^19*c^3*d^7*e^13*z^3 + 9240*a^3*b^19*c^6*d^13*e^7*z^3 + 5304*a^3*b^22*c^3*d^1
0*e^10*z^3 + 4680*a^3*b^23*c^2*d^9*e^11*z^3 + 4680*a^2*b^23*c^3*d^11*e^9*z^3 - 1404*a^2*b^24*c^2*d^10*e^10*z^3
- 1170*a^4*b^22*c^2*d^8*e^12*z^3 - 1170*a^2*b^22*c^4*d^12*e^8*z^3 - 10*b^27*c*d^11*e^9*z^3 - 10*b^19*c^9*d^19
*e*z^3 - 10*a^9*b^19*d*e^19*z^3 - 10*a*b^27*d^9*e^11*z^3 - 36*a^11*b^16*c*e^20*z^3 - 36*a*b^16*c^11*d^20*z^3 -
66060288*a^14*c^14*d^10*e^10*z^3 - 55050240*a^15*c^13*d^8*e^12*z^3 - 55050240*a^13*c^15*d^12*e^8*z^3 - 314572
80*a^16*c^12*d^6*e^14*z^3 - 31457280*a^12*c^16*d^14*e^6*z^3 - 252*b^23*c^5*d^15*e^5*z^3 + 210*b^24*c^4*d^14*e^
6*z^3 + 210*b^22*c^6*d^16*e^4*z^3 - 120*b^25*c^3*d^13*e^7*z^3 - 120*b^21*c^7*d^17*e^3*z^3 + 45*b^26*c^2*d^12*e
^8*z^3 + 45*b^20*c^8*d^18*e^2*z^3 - 11796480*a^17*c^11*d^4*e^16*z^3 - 11796480*a^11*c^17*d^16*e^4*z^3 - 262144
0*a^18*c^10*d^2*e^18*z^3 - 2621440*a^10*c^18*d^18*e^2*z^3 - 252*a^5*b^23*d^5*e^15*z^3 + 210*a^6*b^22*d^4*e^16*
z^3 + 210*a^4*b^24*d^6*e^14*z^3 - 120*a^7*b^21*d^3*e^17*z^3 - 120*a^3*b^25*d^7*e^13*z^3 + 45*a^8*b^20*d^2*e^18
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6*c^6*e^20*z^3 - 129024*a^15*b^8*c^5*e^20*z^3 + 32256*a^14*b^10*c^4*e^20*z^3 - 5376*a^13*b^12*c^3*e^20*z^3 + 5
76*a^12*b^14*c^2*e^20*z^3 + 589824*a^8*b^2*c^18*d^20*z^3 - 589824*a^7*b^4*c^17*d^20*z^3 + 344064*a^6*b^6*c^16*
d^20*z^3 - 129024*a^5*b^8*c^15*d^20*z^3 + 32256*a^4*b^10*c^14*d^20*z^3 - 5376*a^3*b^12*c^13*d^20*z^3 + 576*a^2
*b^14*c^12*d^20*z^3 - 262144*a^19*c^9*e^20*z^3 - 262144*a^9*c^19*d^20*z^3 + b^28*d^10*e^10*z^3 + b^18*c^10*d^2
0*z^3 + a^10*b^18*e^20*z^3 + 403200*a*b*c^16*d^15*e^3*z + 396900*a^8*b*c^9*d*e^17*z - 12071430*a^4*b^2*c^12*d^
8*e^10*z + 11880120*a^3*b^3*c^12*d^9*e^9*z + 10349640*a^4*b^3*c^11*d^7*e^11*z - 9657144*a^3*b^2*c^13*d^10*e^8*
z - 9578520*a^5*b^2*c^11*d^6*e^12*z + 7733880*a^2*b^3*c^13*d^11*e^7*z - 7329420*a^3*b^4*c^11*d^8*e^10*z - 7012
656*a^2*b^4*c^12*d^10*e^8*z - 4859820*a^2*b^2*c^14*d^12*e^6*z + 4604040*a^5*b^3*c^10*d^5*e^13*z - 4365900*a^6*
b^2*c^10*d^4*e^14*z + 3448620*a^2*b^5*c^11*d^9*e^9*z - 3069360*a^4*b^4*c^10*d^6*e^12*z + 1723680*a^3*b^5*c^10*
d^7*e^11*z - 793800*a^7*b^2*c^9*d^2*e^16*z - 754110*a^2*b^6*c^10*d^8*e^10*z + 529200*a^6*b^4*c^8*d^2*e^16*z -
460404*a^4*b^5*c^9*d^5*e^13*z + 441000*a^6*b^3*c^9*d^3*e^15*z - 423360*a^5*b^5*c^8*d^3*e^15*z + 396900*a^5*b^4
*c^9*d^4*e^14*z - 158760*a^5*b^6*c^7*d^2*e^16*z + 143640*a^4*b^7*c^7*d^3*e^15*z + 123984*a^3*b^7*c^8*d^5*e^13*
z + 61560*a^2*b^7*c^9*d^7*e^11*z - 45360*a^3*b^8*c^7*d^4*e^14*z - 30240*a^2*b^8*c^8*d^6*e^12*z + 26460*a^4*b^6
*c^8*d^4*e^14*z + 22680*a^4*b^8*c^6*d^2*e^16*z - 21840*a^3*b^9*c^6*d^3*e^15*z + 17640*a^3*b^6*c^9*d^6*e^12*z -
10584*a^2*b^9*c^7*d^5*e^13*z + 9450*a^2*b^10*c^6*d^4*e^14*z - 1260*a^3*b^10*c^5*d^2*e^16*z + 1260*a^2*b^11*c^
5*d^3*e^15*z + 6894720*a^5*b*c^12*d^7*e^11*z + 6322680*a^4*b*c^13*d^9*e^9*z + 4974480*a^6*b*c^11*d^5*e^13*z +
3971520*a^3*b*c^14*d^11*e^7*z - 3178980*a*b^4*c^13*d^12*e^6*z + 2703960*a*b^3*c^14*d^13*e^5*z + 2268000*a*b^5*
c^12*d^11*e^7*z + 2116800*a^7*b*c^10*d^3*e^15*z + 1648080*a^2*b*c^15*d^13*e^5*z - 1394280*a*b^2*c^15*d^14*e^4*
z - 910224*a*b^6*c^11*d^10*e^8*z - 264600*a^7*b^3*c^8*d*e^17*z + 157500*a*b^7*c^10*d^9*e^9*z + 79380*a^6*b^5*c
^7*d*e^17*z - 11340*a^5*b^7*c^6*d*e^17*z - 9360*a*b^9*c^8*d^7*e^11*z + 6300*a*b^10*c^7*d^6*e^12*z + 5670*a*b^8
*c^9*d^8*e^10*z - 756*a*b^11*c^6*d^5*e^13*z + 630*a^4*b^9*c^5*d*e^17*z - 630*a*b^12*c^5*d^4*e^14*z - 573840*b^
4*c^14*d^14*e^4*z + 532980*b^5*c^13*d^13*e^5*z + 399000*b^3*c^15*d^15*e^3*z - 312480*b^6*c^12*d^12*e^6*z - 174
825*b^2*c^16*d^16*e^2*z + 105840*b^7*c^11*d^11*e^7*z - 15876*b^8*c^10*d^10*e^8*z + 540*b^11*c^7*d^7*e^11*z - 4
20*b^12*c^6*d^6*e^12*z - 315*b^10*c^8*d^8*e^10*z + 126*b^13*c^5*d^5*e^13*z + 70*b^9*c^9*d^9*e^9*z - 1723680*a^
5*c^13*d^8*e^10*z - 1658160*a^6*c^12*d^6*e^12*z - 1264536*a^4*c^14*d^10*e^8*z - 1058400*a^7*c^11*d^4*e^14*z -
661920*a^3*c^15*d^12*e^6*z - 396900*a^8*c^10*d^2*e^16*z - 235440*a^2*c^16*d^14*e^4*z + 574668*a^7*b^4*c^7*e^18
*z - 541593*a^8*b^2*c^8*e^18*z - 341838*a^6*b^6*c^6*e^18*z + 128898*a^5*b^8*c^5*e^18*z - 32256*a^4*b^10*c^4*e^
18*z + 5376*a^3*b^12*c^3*e^18*z - 576*a^2*b^14*c^2*e^18*z - 50400*a*c^17*d^16*e^2*z + 44100*b*c^17*d^17*e*z +
36*a*b^16*c*e^18*z + 196608*a^9*c^9*e^18*z - 4900*c^18*d^18*z - b^18*e^18*z - 113880*a^2*b*c^10*d^3*e^14 + 686
55*a*b^2*c^10*d^4*e^13 + 23445*a^2*b^3*c^8*d*e^16 - 7810*a*b^3*c^9*d^3*e^14 - 5445*a*b^4*c^8*d^2*e^15 - 77700*
a*b*c^11*d^5*e^12 - 69220*a^3*b*c^9*d*e^16 - 3600*a*b^5*c^7*d*e^16 + 33495*a^2*b^2*c^9*d^2*e^15 + 27825*b^2*c^
11*d^6*e^11 - 14875*b^3*c^10*d^5*e^12 + 715*b^4*c^9*d^4*e^13 + 495*b^5*c^8*d^3*e^14 + 330*b^6*c^7*d^2*e^15 + 6
9220*a^3*c^10*d^2*e^15 + 56940*a^2*c^11*d^4*e^13 - 48231*a^3*b^2*c^8*e^17 + 15156*a^2*b^4*c^7*e^17 - 19600*b*c
^12*d^7*e^10 + 210*b^7*c^6*d*e^16 + 25900*a*c^12*d^6*e^11 - 2226*a*b^6*c^6*e^17 + 4900*c^13*d^8*e^9 + 126*b^8*
c^5*e^17 + 65536*a^4*c^9*e^17, z, k)*((30208*a^12*c^10*d*e^17 - 113408*a^12*b*c^9*e^18 - 17920*a^4*c^18*d^17*e
- a^4*b^17*c*e^18 - 70*b^8*c^14*d^17*e - b^21*c*d^4*e^14 + 33*a^5*b^15*c^2*e^18 - 479*a^6*b^13*c^3*e^18 + 400
2*a^7*b^11*c^4*e^18 - 21115*a^8*b^9*c^5*e^18 + 72304*a^9*b^7*c^6*e^18 - 157472*a^10*b^5*c^7*e^18 + 199936*a^11
*b^3*c^8*e^18 - 128000*a^5*c^17*d^15*e^3 - 377856*a^6*c^16*d^13*e^5 - 566272*a^7*c^15*d^11*e^7 - 389120*a^8*c^
14*d^9*e^9 + 25600*a^9*c^13*d^7*e^11 + 230400*a^10*c^12*d^5*e^13 + 144384*a^11*c^11*d^3*e^15 + 525*b^9*c^13*d^
16*e^2 - 1695*b^10*c^12*d^15*e^3 + 3055*b^11*c^11*d^14*e^4 - 3321*b^12*c^10*d^13*e^5 + 2178*b^13*c^9*d^12*e^6
- 798*b^14*c^8*d^11*e^7 + 126*b^15*c^7*d^10*e^8 + b^18*c^4*d^7*e^11 - 3*b^19*c^3*d^6*e^12 + 3*b^20*c^2*d^5*e^1
3 + 50400*a^2*b^5*c^15*d^16*e^2 - 154720*a^2*b^6*c^14*d^15*e^3 + 242400*a^2*b^7*c^13*d^14*e^4 - 185940*a^2*b^8
*c^12*d^13*e^5 + 29500*a^2*b^9*c^11*d^12*e^6 + 50673*a^2*b^10*c^10*d^11*e^7 - 26667*a^2*b^11*c^9*d^10*e^8 - 60
*a^2*b^12*c^8*d^9*e^9 + 157*a^2*b^13*c^7*d^8*e^10 + 1427*a^2*b^14*c^6*d^7*e^11 - 1413*a^2*b^15*c^5*d^6*e^12 +
1310*a^2*b^16*c^4*d^5*e^13 - 215*a^2*b^17*c^3*d^4*e^14 - 126*a^2*b^18*c^2*d^3*e^15 - 134400*a^3*b^3*c^16*d^16*
e^2 + 385920*a^3*b^4*c^15*d^15*e^3 - 476800*a^3*b^5*c^14*d^14*e^4 + 67680*a^3*b^6*c^13*d^13*e^5 + 444480*a^3*b
^7*c^12*d^12*e^6 - 413140*a^3*b^8*c^11*d^11*e^7 + 77460*a^3*b^9*c^10*d^10*e^8 + 26955*a^3*b^10*c^9*d^9*e^9 + 1
4594*a^3*b^11*c^8*d^8*e^10 - 10786*a^3*b^12*c^7*d^7*e^11 + 8272*a^3*b^13*c^6*d^6*e^12 - 10235*a^3*b^14*c^5*d^5
*e^13 + 160*a^3*b^15*c^4*d^4*e^14 + 1718*a^3*b^16*c^3*d^3*e^15 + 198*a^3*b^17*c^2*d^2*e^16 - 305920*a^4*b^2*c^
16*d^15*e^3 - 32000*a^4*b^3*c^15*d^14*e^4 + 1157760*a^4*b^4*c^14*d^13*e^5 - 1712000*a^4*b^5*c^13*d^12*e^6 + 67
9840*a^4*b^6*c^12*d^11*e^7 + 331680*a^4*b^7*c^11*d^10*e^8 - 154400*a^4*b^8*c^10*d^9*e^9 - 95130*a^4*b^9*c^9*d^
8*e^10 - 15205*a^4*b^10*c^8*d^7*e^11 - 22359*a^4*b^11*c^7*d^6*e^12 + 56187*a^4*b^12*c^6*d^5*e^13 + 11200*a^4*b
^13*c^5*d^4*e^14 - 13125*a^4*b^14*c^4*d^3*e^15 - 2875*a^4*b^15*c^3*d^2*e^16 - 1771776*a^5*b^2*c^15*d^13*e^5 +
1061888*a^5*b^3*c^14*d^12*e^6 + 1314432*a^5*b^4*c^13*d^11*e^7 - 1759104*a^5*b^5*c^12*d^10*e^8 + 116000*a^5*b^6
*c^11*d^9*e^9 + 124000*a^5*b^7*c^10*d^8*e^10 + 362996*a^5*b^8*c^9*d^7*e^11 + 130532*a^5*b^9*c^8*d^6*e^12 - 242
047*a^5*b^10*c^7*d^5*e^13 - 109172*a^5*b^11*c^6*d^4*e^14 + 60181*a^5*b^12*c^5*d^3*e^15 + 24040*a^5*b^13*c^4*d^
2*e^16 - 3234560*a^6*b^2*c^14*d^11*e^7 + 1323264*a^6*b^3*c^13*d^10*e^8 + 925440*a^6*b^4*c^12*d^9*e^9 + 432448*
a^6*b^5*c^11*d^8*e^10 - 921376*a^6*b^6*c^10*d^7*e^11 - 1026272*a^6*b^7*c^9*d^6*e^12 + 662420*a^6*b^8*c^8*d^5*e
^13 + 580300*a^6*b^9*c^7*d^4*e^14 - 152557*a^6*b^10*c^6*d^3*e^15 - 127021*a^6*b^11*c^5*d^2*e^16 - 1557760*a^7*
b^2*c^13*d^9*e^9 - 1061888*a^7*b^3*c^12*d^8*e^10 - 362368*a^7*b^4*c^11*d^7*e^11 + 3244672*a^7*b^5*c^10*d^6*e^1
2 - 417760*a^7*b^6*c^9*d^5*e^13 - 1893440*a^7*b^7*c^8*d^4*e^14 + 68324*a^7*b^8*c^7*d^3*e^15 + 433164*a^7*b^9*c
^6*d^2*e^16 + 2488064*a^8*b^2*c^12*d^7*e^11 - 2878208*a^8*b^3*c^11*d^6*e^12 - 2389120*a^8*b^4*c^10*d^5*e^13 +
3295360*a^8*b^5*c^9*d^4*e^14 + 855008*a^8*b^6*c^8*d^3*e^15 - 908192*a^8*b^7*c^7*d^2*e^16 + 4115712*a^9*b^2*c^1
1*d^5*e^13 - 1638400*a^9*b^3*c^10*d^4*e^14 - 2550400*a^9*b^4*c^9*d^3*e^15 + 949120*a^9*b^5*c^8*d^2*e^16 + 2363
136*a^10*b^2*c^10*d^3*e^15 + 14080*a^10*b^3*c^9*d^2*e^16 + 1120*a*b^6*c^15*d^17*e + 4*a*b^20*c*d^3*e^15 + 4*a^
3*b^18*c*d*e^17 - 8400*a*b^7*c^14*d^16*e^2 + 26620*a*b^8*c^13*d^15*e^3 - 45700*a*b^9*c^12*d^14*e^4 + 44739*a*b
^10*c^11*d^13*e^5 - 23152*a*b^11*c^10*d^12*e^6 + 3885*a*b^12*c^9*d^11*e^7 + 1224*a*b^13*c^8*d^10*e^8 - 210*a*b
^14*c^7*d^9*e^9 - 127*a*b^15*c^6*d^8*e^10 - 31*a*b^16*c^5*d^7*e^11 + 98*a*b^17*c^4*d^6*e^12 - 95*a*b^18*c^3*d^
5*e^13 + 25*a*b^19*c^2*d^4*e^14 - 6720*a^2*b^4*c^16*d^17*e - 6*a^2*b^19*c*d^2*e^16 + 17920*a^3*b^2*c^17*d^17*e
+ 134400*a^4*b*c^17*d^16*e^2 - 133*a^4*b^16*c^2*d*e^17 + 814080*a^5*b*c^16*d^14*e^4 + 1949*a^5*b^14*c^3*d*e^1
7 + 1932288*a^6*b*c^15*d^12*e^6 - 16486*a^6*b^12*c^4*d*e^17 + 2024448*a^7*b*c^14*d^10*e^8 + 88433*a^7*b^10*c^5
*d*e^17 + 239104*a^8*b*c^13*d^8*e^10 - 309466*a^8*b^8*c^6*d*e^17 - 1608704*a^9*b*c^12*d^6*e^12 + 691712*a^9*b^
6*c^7*d*e^17 - 1668096*a^10*b*c^11*d^4*e^14 - 899776*a^10*b^4*c^8*d*e^17 - 705536*a^11*b*c^10*d^2*e^16 + 50662
4*a^11*b^2*c^9*d*e^17)/(a^8*b^16*e^16 + 65536*a^8*c^16*d^16 + 65536*a^16*c^8*e^16 + b^16*c^8*d^16 + b^24*d^8*e
^8 - 32*a*b^14*c^9*d^16 - 32*a^9*b^14*c*e^16 - 8*a*b^23*d^7*e^9 - 8*a^7*b^17*d*e^15 - 8*b^17*c^7*d^15*e - 8*b^
23*c*d^9*e^7 + 448*a^2*b^12*c^10*d^16 - 3584*a^3*b^10*c^11*d^16 + 17920*a^4*b^8*c^12*d^16 - 57344*a^5*b^6*c^13
*d^16 + 114688*a^6*b^4*c^14*d^16 - 131072*a^7*b^2*c^15*d^16 + 448*a^10*b^12*c^2*e^16 - 3584*a^11*b^10*c^3*e^16
+ 17920*a^12*b^8*c^4*e^16 - 57344*a^13*b^6*c^5*e^16 + 114688*a^14*b^4*c^6*e^16 - 131072*a^15*b^2*c^7*e^16 + 2
8*a^2*b^22*d^6*e^10 - 56*a^3*b^21*d^5*e^11 + 70*a^4*b^20*d^4*e^12 - 56*a^5*b^19*d^3*e^13 + 28*a^6*b^18*d^2*e^1
4 + 524288*a^9*c^15*d^14*e^2 + 1835008*a^10*c^14*d^12*e^4 + 3670016*a^11*c^13*d^10*e^6 + 4587520*a^12*c^12*d^8
*e^8 + 3670016*a^13*c^11*d^6*e^10 + 1835008*a^14*c^10*d^4*e^12 + 524288*a^15*c^9*d^2*e^14 + 28*b^18*c^6*d^14*e
^2 - 56*b^19*c^5*d^13*e^3 + 70*b^20*c^4*d^12*e^4 - 56*b^21*c^3*d^11*e^5 + 28*b^22*c^2*d^10*e^6 + 12288*a^2*b^1
4*c^8*d^14*e^2 - 23296*a^2*b^15*c^7*d^13*e^3 + 26012*a^2*b^16*c^6*d^12*e^4 - 16296*a^2*b^17*c^5*d^11*e^5 + 400
4*a^2*b^18*c^4*d^10*e^6 + 1232*a^2*b^19*c^3*d^9*e^7 - 924*a^2*b^20*c^2*d^8*e^8 - 96768*a^3*b^12*c^9*d^14*e^2 +
175616*a^3*b^13*c^8*d^13*e^3 - 176512*a^3*b^14*c^7*d^12*e^4 + 80640*a^3*b^15*c^6*d^11*e^5 + 11704*a^3*b^16*c^
5*d^10*e^6 - 28952*a^3*b^17*c^4*d^9*e^7 + 8624*a^3*b^18*c^3*d^8*e^8 + 1232*a^3*b^19*c^2*d^7*e^9 + 473088*a^4*b
^10*c^10*d^14*e^2 - 802816*a^4*b^11*c^9*d^13*e^3 + 664832*a^4*b^12*c^8*d^12*e^4 - 75264*a^4*b^13*c^7*d^11*e^5
- 315392*a^4*b^14*c^6*d^10*e^6 + 216832*a^4*b^15*c^5*d^9*e^7 - 12474*a^4*b^16*c^4*d^8*e^8 - 28952*a^4*b^17*c^3
*d^7*e^9 + 4004*a^4*b^18*c^2*d^6*e^10 - 1462272*a^5*b^8*c^11*d^14*e^2 + 2207744*a^5*b^9*c^10*d^13*e^3 - 110387
2*a^5*b^10*c^9*d^12*e^4 - 1204224*a^5*b^11*c^8*d^11*e^5 + 1931776*a^5*b^12*c^7*d^10*e^6 - 670208*a^5*b^13*c^6*
d^9*e^7 - 310464*a^5*b^14*c^5*d^8*e^8 + 216832*a^5*b^15*c^4*d^7*e^9 + 11704*a^5*b^16*c^3*d^6*e^10 - 16296*a^5*
b^17*c^2*d^5*e^11 + 2752512*a^6*b^6*c^12*d^14*e^2 - 3211264*a^6*b^7*c^11*d^13*e^3 - 1103872*a^6*b^8*c^10*d^12*
e^4 + 6623232*a^6*b^9*c^9*d^11*e^5 - 5519360*a^6*b^10*c^8*d^10*e^6 - 315392*a^6*b^11*c^7*d^9*e^7 + 2454144*a^6
*b^12*c^6*d^8*e^8 - 670208*a^6*b^13*c^5*d^7*e^9 - 315392*a^6*b^14*c^4*d^6*e^10 + 80640*a^6*b^15*c^3*d^5*e^11 +
26012*a^6*b^16*c^2*d^4*e^12 - 2752512*a^7*b^4*c^13*d^14*e^2 + 917504*a^7*b^5*c^12*d^13*e^3 + 8486912*a^7*b^6*
c^11*d^12*e^4 - 15138816*a^7*b^7*c^10*d^11*e^5 + 5361664*a^7*b^8*c^9*d^10*e^6 + 8876032*a^7*b^9*c^8*d^9*e^7 -
8008704*a^7*b^10*c^7*d^8*e^8 - 315392*a^7*b^11*c^6*d^7*e^9 + 1931776*a^7*b^12*c^5*d^6*e^10 - 75264*a^7*b^13*c^
4*d^5*e^11 - 176512*a^7*b^14*c^3*d^4*e^12 - 23296*a^7*b^15*c^2*d^3*e^13 + 786432*a^8*b^2*c^14*d^14*e^2 + 36700
16*a^8*b^3*c^13*d^13*e^3 - 14221312*a^8*b^4*c^12*d^12*e^4 + 13762560*a^8*b^5*c^11*d^11*e^5 + 10092544*a^8*b^6*
c^10*d^10*e^6 - 26673152*a^8*b^7*c^9*d^9*e^7 + 10036224*a^8*b^8*c^8*d^8*e^8 + 8876032*a^8*b^9*c^7*d^7*e^9 - 55
19360*a^8*b^10*c^6*d^6*e^10 - 1204224*a^8*b^11*c^5*d^5*e^11 + 664832*a^8*b^12*c^4*d^4*e^12 + 175616*a^8*b^13*c
^3*d^3*e^13 + 12288*a^8*b^14*c^2*d^2*e^14 + 7340032*a^9*b^2*c^13*d^12*e^4 + 3670016*a^9*b^3*c^12*d^11*e^5 - 30
277632*a^9*b^4*c^11*d^10*e^6 + 30277632*a^9*b^5*c^10*d^9*e^7 + 8830976*a^9*b^6*c^9*d^8*e^8 - 26673152*a^9*b^7*
c^8*d^7*e^9 + 5361664*a^9*b^8*c^7*d^6*e^10 + 6623232*a^9*b^9*c^6*d^5*e^11 - 1103872*a^9*b^10*c^5*d^4*e^12 - 80
2816*a^9*b^11*c^4*d^3*e^13 - 96768*a^9*b^12*c^3*d^2*e^14 + 20185088*a^10*b^2*c^12*d^10*e^6 - 37847040*a^10*b^4
*c^10*d^8*e^8 + 30277632*a^10*b^5*c^9*d^7*e^9 + 10092544*a^10*b^6*c^8*d^6*e^10 - 15138816*a^10*b^7*c^7*d^5*e^1
1 - 1103872*a^10*b^8*c^6*d^4*e^12 + 2207744*a^10*b^9*c^5*d^3*e^13 + 473088*a^10*b^10*c^4*d^2*e^14 + 27525120*a
^11*b^2*c^11*d^8*e^8 - 30277632*a^11*b^4*c^9*d^6*e^10 + 13762560*a^11*b^5*c^8*d^5*e^11 + 8486912*a^11*b^6*c^7*
d^4*e^12 - 3211264*a^11*b^7*c^6*d^3*e^13 - 1462272*a^11*b^8*c^5*d^2*e^14 + 20185088*a^12*b^2*c^10*d^6*e^10 + 3
670016*a^12*b^3*c^9*d^5*e^11 - 14221312*a^12*b^4*c^8*d^4*e^12 + 917504*a^12*b^5*c^7*d^3*e^13 + 2752512*a^12*b^
6*c^6*d^2*e^14 + 7340032*a^13*b^2*c^9*d^4*e^12 + 3670016*a^13*b^3*c^8*d^3*e^13 - 2752512*a^13*b^4*c^7*d^2*e^14
+ 786432*a^14*b^2*c^8*d^2*e^14 + 256*a*b^15*c^8*d^15*e + 24*a*b^22*c*d^8*e^8 - 524288*a^8*b*c^15*d^15*e + 256
*a^8*b^15*c*d*e^15 - 524288*a^15*b*c^8*d*e^15 - 888*a*b^16*c^7*d^14*e^2 + 1736*a*b^17*c^6*d^13*e^3 - 2072*a*b^
18*c^5*d^12*e^4 + 1512*a*b^19*c^4*d^11*e^5 - 616*a*b^20*c^3*d^10*e^6 + 88*a*b^21*c^2*d^9*e^7 - 3584*a^2*b^13*c
^9*d^15*e + 88*a^2*b^21*c*d^7*e^9 + 28672*a^3*b^11*c^10*d^15*e - 616*a^3*b^20*c*d^6*e^10 - 143360*a^4*b^9*c^11
*d^15*e + 1512*a^4*b^19*c*d^5*e^11 + 458752*a^5*b^7*c^12*d^15*e - 2072*a^5*b^18*c*d^4*e^12 - 917504*a^6*b^5*c^
13*d^15*e + 1736*a^6*b^17*c*d^3*e^13 + 1048576*a^7*b^3*c^14*d^15*e - 888*a^7*b^16*c*d^2*e^14 - 3670016*a^9*b*c
^14*d^13*e^3 - 3584*a^9*b^13*c^2*d*e^15 - 11010048*a^10*b*c^13*d^11*e^5 + 28672*a^10*b^11*c^3*d*e^15 - 1835008
0*a^11*b*c^12*d^9*e^7 - 143360*a^11*b^9*c^4*d*e^15 - 18350080*a^12*b*c^11*d^7*e^9 + 458752*a^12*b^7*c^5*d*e^15
- 11010048*a^13*b*c^10*d^5*e^11 - 917504*a^13*b^5*c^6*d*e^15 - 3670016*a^14*b*c^9*d^3*e^13 + 1048576*a^14*b^3
*c^7*d*e^15) - root(330301440*a^14*b*c^13*d^9*e^11*z^3 + 330301440*a^13*b*c^14*d^11*e^9*z^3 + 220200960*a^15*b
*c^12*d^7*e^13*z^3 + 220200960*a^12*b*c^15*d^13*e^7*z^3 + 94371840*a^16*b*c^11*d^5*e^15*z^3 + 94371840*a^11*b*
c^16*d^15*e^5*z^3 + 23592960*a^17*b*c^10*d^3*e^17*z^3 + 23592960*a^10*b*c^17*d^17*e^3*z^3 - 5898240*a^17*b^3*c
^8*d*e^19*z^3 + 5898240*a^16*b^5*c^7*d*e^19*z^3 - 5898240*a^8*b^3*c^17*d^19*e*z^3 + 5898240*a^7*b^5*c^16*d^19*
e*z^3 - 3440640*a^15*b^7*c^6*d*e^19*z^3 - 3440640*a^6*b^7*c^15*d^19*e*z^3 + 1290240*a^14*b^9*c^5*d*e^19*z^3 +
1290240*a^5*b^9*c^14*d^19*e*z^3 - 322560*a^13*b^11*c^4*d*e^19*z^3 - 322560*a^4*b^11*c^13*d^19*e*z^3 + 53760*a^
12*b^13*c^3*d*e^19*z^3 + 53760*a^3*b^13*c^12*d^19*e*z^3 + 8232*a^6*b^21*c*d^5*e^15*z^3 + 8232*a*b^21*c^6*d^15*
e^5*z^3 - 7200*a^7*b^20*c*d^4*e^16*z^3 - 7200*a*b^20*c^7*d^16*e^4*z^3 - 6300*a^5*b^22*c*d^6*e^14*z^3 - 6300*a*
b^22*c^5*d^14*e^6*z^3 - 5760*a^11*b^15*c^2*d*e^19*z^3 - 5760*a^2*b^15*c^11*d^19*e*z^3 + 4230*a^8*b^19*c*d^3*e^
17*z^3 + 4230*a*b^19*c^8*d^17*e^3*z^3 + 3060*a^4*b^23*c*d^7*e^13*z^3 + 3060*a*b^23*c^4*d^13*e^7*z^3 - 1610*a^9
*b^18*c*d^2*e^18*z^3 - 1610*a*b^18*c^9*d^18*e^2*z^3 - 780*a^3*b^24*c*d^8*e^12*z^3 - 780*a*b^24*c^3*d^12*e^8*z^
3 + 2621440*a^18*b*c^9*d*e^19*z^3 + 2621440*a^9*b*c^18*d^19*e*z^3 + 360*a^10*b^17*c*d*e^19*z^3 + 360*a*b^17*c^
10*d^19*e*z^3 + 54*a*b^26*c*d^10*e^10*z^3 - 1073479680*a^12*b^5*c^11*d^9*e^11*z^3 - 1073479680*a^11*b^5*c^12*d
^11*e^9*z^3 - 706387968*a^10*b^8*c^10*d^10*e^10*z^3 - 677117952*a^13*b^2*c^13*d^10*e^10*z^3 - 660602880*a^13*b
^5*c^10*d^7*e^13*z^3 - 660602880*a^10*b^5*c^13*d^13*e^7*z^3 + 651755520*a^11*b^7*c^10*d^9*e^11*z^3 + 651755520
*a^10*b^7*c^11*d^11*e^9*z^3 + 608305152*a^12*b^4*c^12*d^10*e^10*z^3 - 536739840*a^14*b^2*c^12*d^8*e^12*z^3 + 5
36739840*a^13*b^4*c^11*d^8*e^12*z^3 - 536739840*a^12*b^2*c^14*d^12*e^8*z^3 + 536739840*a^11*b^4*c^13*d^12*e^8*
z^3 - 534343680*a^11*b^8*c^9*d^8*e^12*z^3 - 534343680*a^9*b^8*c^11*d^12*e^8*z^3 + 485621760*a^12*b^7*c^9*d^7*e
^13*z^3 + 485621760*a^9*b^7*c^12*d^13*e^7*z^3 + 375717888*a^11*b^6*c^11*d^10*e^10*z^3 + 357826560*a^13*b^3*c^1
2*d^9*e^11*z^3 + 357826560*a^12*b^3*c^13*d^11*e^9*z^3 + 356415488*a^9*b^10*c^9*d^10*e^10*z^3 + 342097920*a^14*
b^4*c^10*d^6*e^14*z^3 + 342097920*a^10*b^4*c^14*d^14*e^6*z^3 + 296524800*a^10*b^10*c^8*d^8*e^12*z^3 + 29652480
0*a^8*b^10*c^10*d^12*e^8*z^3 - 259522560*a^15*b^2*c^11*d^6*e^14*z^3 - 259522560*a^11*b^2*c^15*d^14*e^6*z^3 + 2
23641600*a^12*b^6*c^10*d^8*e^12*z^3 + 223641600*a^10*b^6*c^12*d^12*e^8*z^3 + 222953472*a^13*b^7*c^8*d^5*e^15*z
^3 + 222953472*a^8*b^7*c^13*d^15*e^5*z^3 - 217055232*a^14*b^5*c^9*d^5*e^15*z^3 - 217055232*a^9*b^5*c^14*d^15*e
^5*z^3 - 201277440*a^12*b^8*c^8*d^6*e^14*z^3 - 201277440*a^8*b^8*c^12*d^14*e^6*z^3 + 165150720*a^14*b^3*c^11*d
^7*e^13*z^3 + 165150720*a^11*b^3*c^14*d^13*e^7*z^3 - 159344640*a^9*b^11*c^8*d^9*e^11*z^3 - 159344640*a^8*b^11*
c^9*d^11*e^9*z^3 + 150958080*a^11*b^10*c^7*d^6*e^14*z^3 + 150958080*a^7*b^10*c^11*d^14*e^6*z^3 + 130744320*a^1
5*b^4*c^9*d^4*e^16*z^3 + 130744320*a^9*b^4*c^15*d^16*e^4*z^3 - 93929472*a^12*b^9*c^7*d^5*e^15*z^3 - 93929472*a
^7*b^9*c^12*d^15*e^5*z^3 - 86261760*a^11*b^9*c^8*d^7*e^13*z^3 - 86261760*a^8*b^9*c^11*d^13*e^7*z^3 + 78474240*
a^8*b^13*c^7*d^9*e^11*z^3 + 78474240*a^7*b^13*c^8*d^11*e^9*z^3 - 72990720*a^14*b^6*c^8*d^4*e^16*z^3 - 72990720
*a^8*b^6*c^14*d^16*e^4*z^3 - 67829760*a^16*b^2*c^10*d^4*e^16*z^3 - 67829760*a^10*b^2*c^16*d^16*e^4*z^3 - 64696
320*a^10*b^11*c^7*d^7*e^13*z^3 - 64696320*a^7*b^11*c^10*d^13*e^7*z^3 - 63797760*a^9*b^12*c^7*d^8*e^12*z^3 - 63
797760*a^7*b^12*c^9*d^12*e^8*z^3 - 60622848*a^8*b^12*c^8*d^10*e^10*z^3 - 50319360*a^10*b^12*c^6*d^6*e^14*z^3 -
50319360*a^6*b^12*c^10*d^14*e^6*z^3 + 44513280*a^9*b^13*c^6*d^7*e^13*z^3 + 44513280*a^6*b^13*c^9*d^13*e^7*z^3
+ 39813120*a^14*b^7*c^7*d^3*e^17*z^3 + 39813120*a^7*b^7*c^14*d^17*e^3*z^3 - 29675520*a^13*b^9*c^6*d^3*e^17*z^
3 - 29675520*a^6*b^9*c^13*d^17*e^3*z^3 + 27256320*a^12*b^10*c^6*d^4*e^16*z^3 + 27256320*a^6*b^10*c^12*d^16*e^4
*z^3 - 23101440*a^15*b^6*c^7*d^2*e^18*z^3 - 23101440*a^7*b^6*c^15*d^18*e^2*z^3 - 21626880*a^16*b^3*c^9*d^3*e^1
7*z^3 - 21626880*a^9*b^3*c^16*d^17*e^3*z^3 + 20643840*a^16*b^4*c^8*d^2*e^18*z^3 + 20643840*a^8*b^4*c^16*d^18*e
^2*z^3 - 17694720*a^15*b^5*c^8*d^3*e^17*z^3 - 17694720*a^8*b^5*c^15*d^17*e^3*z^3 - 16423680*a^7*b^15*c^6*d^9*e
^11*z^3 - 16423680*a^6*b^15*c^7*d^11*e^9*z^3 - 15724800*a^11*b^12*c^5*d^4*e^16*z^3 - 15724800*a^5*b^12*c^11*d^
16*e^4*z^3 + 14192640*a^14*b^8*c^6*d^2*e^18*z^3 + 14192640*a^6*b^8*c^14*d^18*e^2*z^3 - 13762560*a^13*b^6*c^9*d
^6*e^14*z^3 - 13762560*a^9*b^6*c^13*d^14*e^6*z^3 - 13508352*a^7*b^14*c^7*d^10*e^10*z^3 + 12579840*a^12*b^11*c^
5*d^3*e^17*z^3 + 12579840*a^5*b^11*c^12*d^17*e^3*z^3 - 12096000*a^8*b^15*c^5*d^7*e^13*z^3 - 12096000*a^5*b^15*
c^8*d^13*e^7*z^3 + 10063872*a^11*b^11*c^6*d^5*e^15*z^3 + 10063872*a^6*b^11*c^11*d^15*e^5*z^3 + 8600592*a^6*b^1
6*c^6*d^10*e^10*z^3 + 7864320*a^15*b^3*c^10*d^5*e^15*z^3 + 7864320*a^10*b^3*c^15*d^15*e^5*z^3 + 7354368*a^10*b
^13*c^5*d^5*e^15*z^3 + 7354368*a^5*b^13*c^10*d^15*e^5*z^3 + 6842880*a^9*b^14*c^5*d^6*e^14*z^3 + 6842880*a^5*b^
14*c^9*d^14*e^6*z^3 - 5898240*a^17*b^2*c^9*d^2*e^18*z^3 - 5898240*a^9*b^2*c^17*d^18*e^2*z^3 - 5857280*a^10*b^9
*c^9*d^9*e^11*z^3 - 5857280*a^9*b^9*c^10*d^11*e^9*z^3 - 5806080*a^13*b^8*c^7*d^4*e^16*z^3 - 5806080*a^7*b^8*c^
13*d^16*e^4*z^3 + 5798520*a^7*b^16*c^5*d^8*e^12*z^3 + 5798520*a^5*b^16*c^7*d^12*e^8*z^3 - 5483520*a^13*b^10*c^
5*d^2*e^18*z^3 - 5483520*a^5*b^10*c^13*d^18*e^2*z^3 + 4864320*a^10*b^14*c^4*d^4*e^16*z^3 + 4864320*a^4*b^14*c^
10*d^16*e^4*z^3 - 4717440*a^8*b^14*c^6*d^8*e^12*z^3 - 4717440*a^6*b^14*c^8*d^12*e^8*z^3 - 3820032*a^9*b^15*c^4
*d^5*e^15*z^3 - 3820032*a^4*b^15*c^9*d^15*e^5*z^3 - 3386880*a^11*b^13*c^4*d^3*e^17*z^3 - 3386880*a^4*b^13*c^11
*d^17*e^3*z^3 - 1693692*a^5*b^18*c^5*d^10*e^10*z^3 + 1481760*a^7*b^17*c^4*d^7*e^13*z^3 + 1481760*a^4*b^17*c^7*
d^13*e^7*z^3 + 1397760*a^12*b^12*c^4*d^2*e^18*z^3 + 1397760*a^4*b^12*c^12*d^18*e^2*z^3 - 1340430*a^6*b^18*c^4*
d^8*e^12*z^3 - 1340430*a^4*b^18*c^6*d^12*e^8*z^3 - 923220*a^9*b^16*c^3*d^4*e^16*z^3 - 923220*a^3*b^16*c^9*d^16
*e^4*z^3 + 883872*a^8*b^17*c^3*d^5*e^15*z^3 + 883872*a^3*b^17*c^8*d^15*e^5*z^3 + 851760*a^6*b^17*c^5*d^9*e^11*
z^3 + 851760*a^5*b^17*c^6*d^11*e^9*z^3 + 721440*a^8*b^16*c^4*d^6*e^14*z^3 + 721440*a^4*b^16*c^8*d^14*e^6*z^3 +
593280*a^10*b^15*c^3*d^3*e^17*z^3 + 593280*a^3*b^15*c^10*d^17*e^3*z^3 - 448440*a^7*b^18*c^3*d^6*e^14*z^3 - 44
8440*a^3*b^18*c^7*d^14*e^6*z^3 + 311220*a^5*b^19*c^4*d^9*e^11*z^3 + 311220*a^4*b^19*c^5*d^11*e^9*z^3 - 236160*
a^11*b^14*c^3*d^2*e^18*z^3 - 236160*a^3*b^14*c^11*d^18*e^2*z^3 + 131040*a^5*b^20*c^3*d^8*e^12*z^3 + 131040*a^3
*b^20*c^5*d^12*e^8*z^3 + 126126*a^4*b^20*c^4*d^10*e^10*z^3 - 115272*a^7*b^19*c^2*d^5*e^15*z^3 - 115272*a^2*b^1
9*c^7*d^15*e^5*z^3 + 108045*a^8*b^18*c^2*d^4*e^16*z^3 + 108045*a^2*b^18*c^8*d^16*e^4*z^3 + 76860*a^6*b^20*c^2*
d^6*e^14*z^3 + 76860*a^2*b^20*c^6*d^14*e^6*z^3 - 67080*a^4*b^21*c^3*d^9*e^11*z^3 - 67080*a^3*b^21*c^4*d^11*e^9
*z^3 - 65880*a^9*b^17*c^2*d^3*e^17*z^3 - 65880*a^2*b^17*c^9*d^17*e^3*z^3 - 26280*a^5*b^21*c^2*d^7*e^13*z^3 - 2
6280*a^2*b^21*c^5*d^13*e^7*z^3 + 25560*a^10*b^16*c^2*d^2*e^18*z^3 + 25560*a^2*b^16*c^10*d^18*e^2*z^3 + 9240*a^
6*b^19*c^3*d^7*e^13*z^3 + 9240*a^3*b^19*c^6*d^13*e^7*z^3 + 5304*a^3*b^22*c^3*d^10*e^10*z^3 + 4680*a^3*b^23*c^2
*d^9*e^11*z^3 + 4680*a^2*b^23*c^3*d^11*e^9*z^3 - 1404*a^2*b^24*c^2*d^10*e^10*z^3 - 1170*a^4*b^22*c^2*d^8*e^12*
z^3 - 1170*a^2*b^22*c^4*d^12*e^8*z^3 - 10*b^27*c*d^11*e^9*z^3 - 10*b^19*c^9*d^19*e*z^3 - 10*a^9*b^19*d*e^19*z^
3 - 10*a*b^27*d^9*e^11*z^3 - 36*a^11*b^16*c*e^20*z^3 - 36*a*b^16*c^11*d^20*z^3 - 66060288*a^14*c^14*d^10*e^10*
z^3 - 55050240*a^15*c^13*d^8*e^12*z^3 - 55050240*a^13*c^15*d^12*e^8*z^3 - 31457280*a^16*c^12*d^6*e^14*z^3 - 31
457280*a^12*c^16*d^14*e^6*z^3 - 252*b^23*c^5*d^15*e^5*z^3 + 210*b^24*c^4*d^14*e^6*z^3 + 210*b^22*c^6*d^16*e^4*
z^3 - 120*b^25*c^3*d^13*e^7*z^3 - 120*b^21*c^7*d^17*e^3*z^3 + 45*b^26*c^2*d^12*e^8*z^3 + 45*b^20*c^8*d^18*e^2*
z^3 - 11796480*a^17*c^11*d^4*e^16*z^3 - 11796480*a^11*c^17*d^16*e^4*z^3 - 2621440*a^18*c^10*d^2*e^18*z^3 - 262
1440*a^10*c^18*d^18*e^2*z^3 - 252*a^5*b^23*d^5*e^15*z^3 + 210*a^6*b^22*d^4*e^16*z^3 + 210*a^4*b^24*d^6*e^14*z^
3 - 120*a^7*b^21*d^3*e^17*z^3 - 120*a^3*b^25*d^7*e^13*z^3 + 45*a^8*b^20*d^2*e^18*z^3 + 45*a^2*b^26*d^8*e^12*z^
3 + 589824*a^18*b^2*c^8*e^20*z^3 - 589824*a^17*b^4*c^7*e^20*z^3 + 344064*a^16*b^6*c^6*e^20*z^3 - 129024*a^15*b
^8*c^5*e^20*z^3 + 32256*a^14*b^10*c^4*e^20*z^3 - 5376*a^13*b^12*c^3*e^20*z^3 + 576*a^12*b^14*c^2*e^20*z^3 + 58
9824*a^8*b^2*c^18*d^20*z^3 - 589824*a^7*b^4*c^17*d^20*z^3 + 344064*a^6*b^6*c^16*d^20*z^3 - 129024*a^5*b^8*c^15
*d^20*z^3 + 32256*a^4*b^10*c^14*d^20*z^3 - 5376*a^3*b^12*c^13*d^20*z^3 + 576*a^2*b^14*c^12*d^20*z^3 - 262144*a
^19*c^9*e^20*z^3 - 262144*a^9*c^19*d^20*z^3 + b^28*d^10*e^10*z^3 + b^18*c^10*d^20*z^3 + a^10*b^18*e^20*z^3 + 4
03200*a*b*c^16*d^15*e^3*z + 396900*a^8*b*c^9*d*e^17*z - 12071430*a^4*b^2*c^12*d^8*e^10*z + 11880120*a^3*b^3*c^
12*d^9*e^9*z + 10349640*a^4*b^3*c^11*d^7*e^11*z - 9657144*a^3*b^2*c^13*d^10*e^8*z - 9578520*a^5*b^2*c^11*d^6*e
^12*z + 7733880*a^2*b^3*c^13*d^11*e^7*z - 7329420*a^3*b^4*c^11*d^8*e^10*z - 7012656*a^2*b^4*c^12*d^10*e^8*z -
4859820*a^2*b^2*c^14*d^12*e^6*z + 4604040*a^5*b^3*c^10*d^5*e^13*z - 4365900*a^6*b^2*c^10*d^4*e^14*z + 3448620*
a^2*b^5*c^11*d^9*e^9*z - 3069360*a^4*b^4*c^10*d^6*e^12*z + 1723680*a^3*b^5*c^10*d^7*e^11*z - 793800*a^7*b^2*c^
9*d^2*e^16*z - 754110*a^2*b^6*c^10*d^8*e^10*z + 529200*a^6*b^4*c^8*d^2*e^16*z - 460404*a^4*b^5*c^9*d^5*e^13*z
+ 441000*a^6*b^3*c^9*d^3*e^15*z - 423360*a^5*b^5*c^8*d^3*e^15*z + 396900*a^5*b^4*c^9*d^4*e^14*z - 158760*a^5*b
^6*c^7*d^2*e^16*z + 143640*a^4*b^7*c^7*d^3*e^15*z + 123984*a^3*b^7*c^8*d^5*e^13*z + 61560*a^2*b^7*c^9*d^7*e^11
*z - 45360*a^3*b^8*c^7*d^4*e^14*z - 30240*a^2*b^8*c^8*d^6*e^12*z + 26460*a^4*b^6*c^8*d^4*e^14*z + 22680*a^4*b^
8*c^6*d^2*e^16*z - 21840*a^3*b^9*c^6*d^3*e^15*z + 17640*a^3*b^6*c^9*d^6*e^12*z - 10584*a^2*b^9*c^7*d^5*e^13*z
+ 9450*a^2*b^10*c^6*d^4*e^14*z - 1260*a^3*b^10*c^5*d^2*e^16*z + 1260*a^2*b^11*c^5*d^3*e^15*z + 6894720*a^5*b*c
^12*d^7*e^11*z + 6322680*a^4*b*c^13*d^9*e^9*z + 4974480*a^6*b*c^11*d^5*e^13*z + 3971520*a^3*b*c^14*d^11*e^7*z
- 3178980*a*b^4*c^13*d^12*e^6*z + 2703960*a*b^3*c^14*d^13*e^5*z + 2268000*a*b^5*c^12*d^11*e^7*z + 2116800*a^7*
b*c^10*d^3*e^15*z + 1648080*a^2*b*c^15*d^13*e^5*z - 1394280*a*b^2*c^15*d^14*e^4*z - 910224*a*b^6*c^11*d^10*e^8
*z - 264600*a^7*b^3*c^8*d*e^17*z + 157500*a*b^7*c^10*d^9*e^9*z + 79380*a^6*b^5*c^7*d*e^17*z - 11340*a^5*b^7*c^
6*d*e^17*z - 9360*a*b^9*c^8*d^7*e^11*z + 6300*a*b^10*c^7*d^6*e^12*z + 5670*a*b^8*c^9*d^8*e^10*z - 756*a*b^11*c
^6*d^5*e^13*z + 630*a^4*b^9*c^5*d*e^17*z - 630*a*b^12*c^5*d^4*e^14*z - 573840*b^4*c^14*d^14*e^4*z + 532980*b^5
*c^13*d^13*e^5*z + 399000*b^3*c^15*d^15*e^3*z - 312480*b^6*c^12*d^12*e^6*z - 174825*b^2*c^16*d^16*e^2*z + 1058
40*b^7*c^11*d^11*e^7*z - 15876*b^8*c^10*d^10*e^8*z + 540*b^11*c^7*d^7*e^11*z - 420*b^12*c^6*d^6*e^12*z - 315*b
^10*c^8*d^8*e^10*z + 126*b^13*c^5*d^5*e^13*z + 70*b^9*c^9*d^9*e^9*z - 1723680*a^5*c^13*d^8*e^10*z - 1658160*a^
6*c^12*d^6*e^12*z - 1264536*a^4*c^14*d^10*e^8*z - 1058400*a^7*c^11*d^4*e^14*z - 661920*a^3*c^15*d^12*e^6*z - 3
96900*a^8*c^10*d^2*e^16*z - 235440*a^2*c^16*d^14*e^4*z + 574668*a^7*b^4*c^7*e^18*z - 541593*a^8*b^2*c^8*e^18*z
- 341838*a^6*b^6*c^6*e^18*z + 128898*a^5*b^8*c^5*e^18*z - 32256*a^4*b^10*c^4*e^18*z + 5376*a^3*b^12*c^3*e^18*
z - 576*a^2*b^14*c^2*e^18*z - 50400*a*c^17*d^16*e^2*z + 44100*b*c^17*d^17*e*z + 36*a*b^16*c*e^18*z + 196608*a^
9*c^9*e^18*z - 4900*c^18*d^18*z - b^18*e^18*z - 113880*a^2*b*c^10*d^3*e^14 + 68655*a*b^2*c^10*d^4*e^13 + 23445
*a^2*b^3*c^8*d*e^16 - 7810*a*b^3*c^9*d^3*e^14 - 5445*a*b^4*c^8*d^2*e^15 - 77700*a*b*c^11*d^5*e^12 - 69220*a^3*
b*c^9*d*e^16 - 3600*a*b^5*c^7*d*e^16 + 33495*a^2*b^2*c^9*d^2*e^15 + 27825*b^2*c^11*d^6*e^11 - 14875*b^3*c^10*d
^5*e^12 + 715*b^4*c^9*d^4*e^13 + 495*b^5*c^8*d^3*e^14 + 330*b^6*c^7*d^2*e^15 + 69220*a^3*c^10*d^2*e^15 + 56940
*a^2*c^11*d^4*e^13 - 48231*a^3*b^2*c^8*e^17 + 15156*a^2*b^4*c^7*e^17 - 19600*b*c^12*d^7*e^10 + 210*b^7*c^6*d*e
^16 + 25900*a*c^12*d^6*e^11 - 2226*a*b^6*c^6*e^17 + 4900*c^13*d^8*e^9 + 126*b^8*c^5*e^17 + 65536*a^4*c^9*e^17,
z, k)*((524288*a^17*c^10*d*e^18 - 65536*a^17*b*c^9*e^19 - a^9*b^17*c*e^19 - b^17*c^10*d^18*e - b^26*c*d^9*e^1
0 + 32*a^10*b^15*c^2*e^19 - 448*a^11*b^13*c^3*e^19 + 3584*a^12*b^11*c^4*e^19 - 17920*a^13*b^9*c^5*e^19 + 57344
*a^14*b^7*c^6*e^19 - 114688*a^15*b^5*c^7*e^19 + 131072*a^16*b^3*c^8*e^19 + 524288*a^9*c^18*d^17*e^2 + 4194304*
a^10*c^17*d^15*e^4 + 14680064*a^11*c^16*d^13*e^6 + 29360128*a^12*c^15*d^11*e^8 + 36700160*a^13*c^14*d^9*e^10 +
29360128*a^14*c^13*d^7*e^12 + 14680064*a^15*c^12*d^5*e^14 + 4194304*a^16*c^11*d^3*e^16 + 7*b^18*c^9*d^17*e^2
- 20*b^19*c^8*d^16*e^3 + 28*b^20*c^7*d^15*e^4 - 14*b^21*c^6*d^14*e^5 - 14*b^22*c^5*d^13*e^6 + 28*b^23*c^4*d^12
*e^7 - 20*b^24*c^3*d^11*e^8 + 7*b^25*c^2*d^10*e^9 + 2880*a^2*b^14*c^11*d^17*e^2 - 6624*a^2*b^15*c^10*d^16*e^3
+ 3648*a^2*b^16*c^9*d^15*e^4 + 12060*a^2*b^17*c^8*d^14*e^5 - 28028*a^2*b^18*c^7*d^13*e^6 + 26460*a^2*b^19*c^6*
d^12*e^7 - 11676*a^2*b^20*c^5*d^11*e^8 + 1012*a^2*b^21*c^4*d^10*e^9 + 940*a^2*b^22*c^3*d^9*e^10 - 204*a^2*b^23
*c^2*d^8*e^11 - 21504*a^3*b^12*c^12*d^17*e^2 + 38976*a^3*b^13*c^11*d^16*e^3 + 23040*a^3*b^14*c^10*d^15*e^4 - 1
97760*a^3*b^15*c^9*d^14*e^5 + 327264*a^3*b^16*c^8*d^13*e^6 - 248724*a^3*b^17*c^7*d^12*e^7 + 65576*a^3*b^18*c^6
*d^11*e^8 + 26180*a^3*b^19*c^5*d^10*e^9 - 18480*a^3*b^20*c^4*d^9*e^10 + 1012*a^3*b^21*c^3*d^8*e^11 + 808*a^3*b
^22*c^2*d^7*e^12 + 96768*a^4*b^10*c^13*d^17*e^2 - 96768*a^4*b^11*c^12*d^16*e^3 - 473088*a^4*b^12*c^11*d^15*e^4
+ 1639680*a^4*b^13*c^10*d^14*e^5 - 2177280*a^4*b^14*c^9*d^13*e^6 + 1212288*a^4*b^15*c^8*d^12*e^7 + 111552*a^4
*b^16*c^7*d^11*e^8 - 447678*a^4*b^17*c^6*d^10*e^9 + 139370*a^4*b^18*c^5*d^9*e^10 + 26180*a^4*b^19*c^4*d^8*e^11
- 11676*a^4*b^20*c^3*d^7*e^12 - 1414*a^4*b^21*c^2*d^6*e^13 - 258048*a^5*b^8*c^14*d^17*e^2 - 161280*a^5*b^9*c^
13*d^16*e^3 + 3182592*a^5*b^10*c^12*d^15*e^4 - 7999488*a^5*b^11*c^11*d^14*e^5 + 8429568*a^5*b^12*c^10*d^13*e^6
- 1994496*a^5*b^13*c^9*d^12*e^7 - 3709440*a^5*b^14*c^8*d^11*e^8 + 3030720*a^5*b^15*c^7*d^10*e^9 - 222992*a^5*
b^16*c^6*d^9*e^10 - 447678*a^5*b^17*c^5*d^8*e^11 + 65576*a^5*b^18*c^4*d^7*e^12 + 26460*a^5*b^19*c^3*d^6*e^13 +
1176*a^5*b^20*c^2*d^5*e^14 + 344064*a^6*b^6*c^15*d^17*e^2 + 1892352*a^6*b^7*c^14*d^16*e^3 - 11698176*a^6*b^8*
c^13*d^15*e^4 + 23439360*a^6*b^9*c^12*d^14*e^5 - 16558080*a^6*b^10*c^11*d^13*e^6 - 9633792*a^6*b^11*c^10*d^12*
e^7 + 22493184*a^6*b^12*c^9*d^11*e^8 - 9432192*a^6*b^13*c^8*d^10*e^9 - 3597440*a^6*b^14*c^7*d^9*e^10 + 3030720
*a^6*b^15*c^6*d^8*e^11 + 111552*a^6*b^16*c^5*d^7*e^12 - 248724*a^6*b^17*c^4*d^6*e^13 - 28028*a^6*b^18*c^3*d^5*
e^14 - 140*a^6*b^19*c^2*d^4*e^15 - 5750784*a^7*b^5*c^15*d^16*e^3 + 24772608*a^7*b^6*c^14*d^15*e^4 - 37847040*a
^7*b^7*c^13*d^14*e^5 + 1032192*a^7*b^8*c^12*d^13*e^6 + 63866880*a^7*b^9*c^11*d^12*e^7 - 65015808*a^7*b^10*c^10
*d^11*e^8 + 2128896*a^7*b^11*c^9*d^10*e^9 + 28272640*a^7*b^12*c^8*d^9*e^10 - 9432192*a^7*b^13*c^7*d^8*e^11 - 3
709440*a^7*b^14*c^6*d^7*e^12 + 1212288*a^7*b^15*c^5*d^6*e^13 + 327264*a^7*b^16*c^4*d^5*e^14 + 12060*a^7*b^17*c
^3*d^4*e^15 - 616*a^7*b^18*c^2*d^3*e^16 - 589824*a^8*b^2*c^17*d^17*e^2 + 8257536*a^8*b^3*c^16*d^16*e^3 - 27525
120*a^8*b^4*c^15*d^15*e^4 + 20643840*a^8*b^5*c^14*d^14*e^5 + 67436544*a^8*b^6*c^13*d^13*e^6 - 153452544*a^8*b^
7*c^12*d^12*e^7 + 74612736*a^8*b^8*c^11*d^11*e^8 + 82283520*a^8*b^9*c^10*d^10*e^9 - 91857920*a^8*b^10*c^9*d^9*
e^10 + 2128896*a^8*b^11*c^8*d^8*e^11 + 22493184*a^8*b^12*c^7*d^7*e^12 - 1994496*a^8*b^13*c^6*d^6*e^13 - 217728
0*a^8*b^14*c^5*d^5*e^14 - 197760*a^8*b^15*c^4*d^4*e^15 + 3648*a^8*b^16*c^3*d^3*e^16 + 567*a^8*b^17*c^2*d^2*e^1
7 + 9961472*a^9*b^2*c^16*d^15*e^4 + 24903680*a^9*b^3*c^15*d^14*e^5 - 128450560*a^9*b^4*c^14*d^13*e^6 + 1509294
08*a^9*b^5*c^13*d^12*e^7 + 66977792*a^9*b^6*c^12*d^11*e^8 - 262586368*a^9*b^7*c^11*d^10*e^9 + 124805120*a^9*b^
8*c^10*d^9*e^10 + 82283520*a^9*b^9*c^9*d^8*e^11 - 65015808*a^9*b^10*c^8*d^7*e^12 - 9633792*a^9*b^11*c^7*d^6*e^
13 + 8429568*a^9*b^12*c^6*d^5*e^14 + 1639680*a^9*b^13*c^5*d^4*e^15 + 23040*a^9*b^14*c^4*d^3*e^16 - 6624*a^9*b^
15*c^3*d^2*e^17 + 71565312*a^10*b^2*c^15*d^13*e^6 + 12845056*a^10*b^3*c^14*d^12*e^7 - 266076160*a^10*b^4*c^13*
d^11*e^8 + 310345728*a^10*b^5*c^12*d^10*e^9 + 47939584*a^10*b^6*c^11*d^9*e^10 - 262586368*a^10*b^7*c^10*d^8*e^
11 + 74612736*a^10*b^8*c^9*d^7*e^12 + 63866880*a^10*b^9*c^8*d^6*e^13 - 16558080*a^10*b^10*c^7*d^5*e^14 - 79994
88*a^10*b^11*c^6*d^4*e^15 - 473088*a^10*b^12*c^5*d^3*e^16 + 38976*a^10*b^13*c^4*d^2*e^17 + 187170816*a^11*b^2*
c^14*d^11*e^8 - 29360128*a^11*b^3*c^13*d^10*e^9 - 330301440*a^11*b^4*c^12*d^9*e^10 + 310345728*a^11*b^5*c^11*d
^8*e^11 + 66977792*a^11*b^6*c^10*d^7*e^12 - 153452544*a^11*b^7*c^9*d^6*e^13 + 1032192*a^11*b^8*c^8*d^5*e^14 +
23439360*a^11*b^9*c^7*d^4*e^15 + 3182592*a^11*b^10*c^6*d^3*e^16 - 96768*a^11*b^11*c^5*d^2*e^17 + 252313600*a^1
2*b^2*c^13*d^9*e^10 - 29360128*a^12*b^3*c^12*d^8*e^11 - 266076160*a^12*b^4*c^11*d^7*e^12 + 150929408*a^12*b^5*
c^10*d^6*e^13 + 67436544*a^12*b^6*c^9*d^5*e^14 - 37847040*a^12*b^7*c^8*d^4*e^15 - 11698176*a^12*b^8*c^7*d^3*e^
16 - 161280*a^12*b^9*c^6*d^2*e^17 + 187170816*a^13*b^2*c^12*d^7*e^12 + 12845056*a^13*b^3*c^11*d^6*e^13 - 12845
0560*a^13*b^4*c^10*d^5*e^14 + 20643840*a^13*b^5*c^9*d^4*e^15 + 24772608*a^13*b^6*c^8*d^3*e^16 + 1892352*a^13*b
^7*c^7*d^2*e^17 + 71565312*a^14*b^2*c^11*d^5*e^14 + 24903680*a^14*b^3*c^10*d^4*e^15 - 27525120*a^14*b^4*c^9*d^
3*e^16 - 5750784*a^14*b^5*c^8*d^2*e^17 + 9961472*a^15*b^2*c^10*d^3*e^16 + 8257536*a^15*b^3*c^9*d^2*e^17 + 32*a
*b^15*c^11*d^18*e + 7*a*b^25*c*d^8*e^11 - 65536*a^8*b*c^18*d^18*e + 7*a^8*b^18*c*d*e^18 - 216*a*b^16*c^10*d^17
*e^2 + 567*a*b^17*c^9*d^16*e^3 - 616*a*b^18*c^8*d^15*e^4 - 140*a*b^19*c^7*d^14*e^5 + 1176*a*b^20*c^6*d^13*e^6
- 1414*a*b^21*c^5*d^12*e^7 + 808*a*b^22*c^4*d^11*e^8 - 204*a*b^23*c^3*d^10*e^9 - 448*a^2*b^13*c^12*d^18*e - 20
*a^2*b^24*c*d^7*e^12 + 3584*a^3*b^11*c^13*d^18*e + 28*a^3*b^23*c*d^6*e^13 - 17920*a^4*b^9*c^14*d^18*e - 14*a^4
*b^22*c*d^5*e^14 + 57344*a^5*b^7*c^15*d^18*e - 14*a^5*b^21*c*d^4*e^15 - 114688*a^6*b^5*c^16*d^18*e + 28*a^6*b^
20*c*d^3*e^16 + 131072*a^7*b^3*c^17*d^18*e - 20*a^7*b^19*c*d^2*e^17 - 4784128*a^9*b*c^17*d^16*e^3 - 216*a^9*b^
16*c^2*d*e^18 - 31719424*a^10*b*c^16*d^14*e^5 + 2880*a^10*b^14*c^3*d*e^18 - 93585408*a^11*b*c^15*d^12*e^7 - 21
504*a^11*b^12*c^4*d*e^18 - 155058176*a^12*b*c^14*d^10*e^9 + 96768*a^12*b^10*c^5*d*e^18 - 155058176*a^13*b*c^13
*d^8*e^11 - 258048*a^13*b^8*c^6*d*e^18 - 93585408*a^14*b*c^12*d^6*e^13 + 344064*a^14*b^6*c^7*d*e^18 - 31719424
*a^15*b*c^11*d^4*e^15 - 4784128*a^16*b*c^10*d^2*e^17 - 589824*a^16*b^2*c^9*d*e^18)/(a^8*b^16*e^16 + 65536*a^8*
c^16*d^16 + 65536*a^16*c^8*e^16 + b^16*c^8*d^16 + b^24*d^8*e^8 - 32*a*b^14*c^9*d^16 - 32*a^9*b^14*c*e^16 - 8*a
*b^23*d^7*e^9 - 8*a^7*b^17*d*e^15 - 8*b^17*c^7*d^15*e - 8*b^23*c*d^9*e^7 + 448*a^2*b^12*c^10*d^16 - 3584*a^3*b
^10*c^11*d^16 + 17920*a^4*b^8*c^12*d^16 - 57344*a^5*b^6*c^13*d^16 + 114688*a^6*b^4*c^14*d^16 - 131072*a^7*b^2*
c^15*d^16 + 448*a^10*b^12*c^2*e^16 - 3584*a^11*b^10*c^3*e^16 + 17920*a^12*b^8*c^4*e^16 - 57344*a^13*b^6*c^5*e^
16 + 114688*a^14*b^4*c^6*e^16 - 131072*a^15*b^2*c^7*e^16 + 28*a^2*b^22*d^6*e^10 - 56*a^3*b^21*d^5*e^11 + 70*a^
4*b^20*d^4*e^12 - 56*a^5*b^19*d^3*e^13 + 28*a^6*b^18*d^2*e^14 + 524288*a^9*c^15*d^14*e^2 + 1835008*a^10*c^14*d
^12*e^4 + 3670016*a^11*c^13*d^10*e^6 + 4587520*a^12*c^12*d^8*e^8 + 3670016*a^13*c^11*d^6*e^10 + 1835008*a^14*c
^10*d^4*e^12 + 524288*a^15*c^9*d^2*e^14 + 28*b^18*c^6*d^14*e^2 - 56*b^19*c^5*d^13*e^3 + 70*b^20*c^4*d^12*e^4 -
56*b^21*c^3*d^11*e^5 + 28*b^22*c^2*d^10*e^6 + 12288*a^2*b^14*c^8*d^14*e^2 - 23296*a^2*b^15*c^7*d^13*e^3 + 260
12*a^2*b^16*c^6*d^12*e^4 - 16296*a^2*b^17*c^5*d^11*e^5 + 4004*a^2*b^18*c^4*d^10*e^6 + 1232*a^2*b^19*c^3*d^9*e^
7 - 924*a^2*b^20*c^2*d^8*e^8 - 96768*a^3*b^12*c^9*d^14*e^2 + 175616*a^3*b^13*c^8*d^13*e^3 - 176512*a^3*b^14*c^
7*d^12*e^4 + 80640*a^3*b^15*c^6*d^11*e^5 + 11704*a^3*b^16*c^5*d^10*e^6 - 28952*a^3*b^17*c^4*d^9*e^7 + 8624*a^3
*b^18*c^3*d^8*e^8 + 1232*a^3*b^19*c^2*d^7*e^9 + 473088*a^4*b^10*c^10*d^14*e^2 - 802816*a^4*b^11*c^9*d^13*e^3 +
664832*a^4*b^12*c^8*d^12*e^4 - 75264*a^4*b^13*c^7*d^11*e^5 - 315392*a^4*b^14*c^6*d^10*e^6 + 216832*a^4*b^15*c
^5*d^9*e^7 - 12474*a^4*b^16*c^4*d^8*e^8 - 28952*a^4*b^17*c^3*d^7*e^9 + 4004*a^4*b^18*c^2*d^6*e^10 - 1462272*a^
5*b^8*c^11*d^14*e^2 + 2207744*a^5*b^9*c^10*d^13*e^3 - 1103872*a^5*b^10*c^9*d^12*e^4 - 1204224*a^5*b^11*c^8*d^1
1*e^5 + 1931776*a^5*b^12*c^7*d^10*e^6 - 670208*a^5*b^13*c^6*d^9*e^7 - 310464*a^5*b^14*c^5*d^8*e^8 + 216832*a^5
*b^15*c^4*d^7*e^9 + 11704*a^5*b^16*c^3*d^6*e^10 - 16296*a^5*b^17*c^2*d^5*e^11 + 2752512*a^6*b^6*c^12*d^14*e^2
- 3211264*a^6*b^7*c^11*d^13*e^3 - 1103872*a^6*b^8*c^10*d^12*e^4 + 6623232*a^6*b^9*c^9*d^11*e^5 - 5519360*a^6*b
^10*c^8*d^10*e^6 - 315392*a^6*b^11*c^7*d^9*e^7 + 2454144*a^6*b^12*c^6*d^8*e^8 - 670208*a^6*b^13*c^5*d^7*e^9 -
315392*a^6*b^14*c^4*d^6*e^10 + 80640*a^6*b^15*c^3*d^5*e^11 + 26012*a^6*b^16*c^2*d^4*e^12 - 2752512*a^7*b^4*c^1
3*d^14*e^2 + 917504*a^7*b^5*c^12*d^13*e^3 + 8486912*a^7*b^6*c^11*d^12*e^4 - 15138816*a^7*b^7*c^10*d^11*e^5 + 5
361664*a^7*b^8*c^9*d^10*e^6 + 8876032*a^7*b^9*c^8*d^9*e^7 - 8008704*a^7*b^10*c^7*d^8*e^8 - 315392*a^7*b^11*c^6
*d^7*e^9 + 1931776*a^7*b^12*c^5*d^6*e^10 - 75264*a^7*b^13*c^4*d^5*e^11 - 176512*a^7*b^14*c^3*d^4*e^12 - 23296*
a^7*b^15*c^2*d^3*e^13 + 786432*a^8*b^2*c^14*d^14*e^2 + 3670016*a^8*b^3*c^13*d^13*e^3 - 14221312*a^8*b^4*c^12*d
^12*e^4 + 13762560*a^8*b^5*c^11*d^11*e^5 + 10092544*a^8*b^6*c^10*d^10*e^6 - 26673152*a^8*b^7*c^9*d^9*e^7 + 100
36224*a^8*b^8*c^8*d^8*e^8 + 8876032*a^8*b^9*c^7*d^7*e^9 - 5519360*a^8*b^10*c^6*d^6*e^10 - 1204224*a^8*b^11*c^5
*d^5*e^11 + 664832*a^8*b^12*c^4*d^4*e^12 + 175616*a^8*b^13*c^3*d^3*e^13 + 12288*a^8*b^14*c^2*d^2*e^14 + 734003
2*a^9*b^2*c^13*d^12*e^4 + 3670016*a^9*b^3*c^12*d^11*e^5 - 30277632*a^9*b^4*c^11*d^10*e^6 + 30277632*a^9*b^5*c^
10*d^9*e^7 + 8830976*a^9*b^6*c^9*d^8*e^8 - 26673152*a^9*b^7*c^8*d^7*e^9 + 5361664*a^9*b^8*c^7*d^6*e^10 + 66232
32*a^9*b^9*c^6*d^5*e^11 - 1103872*a^9*b^10*c^5*d^4*e^12 - 802816*a^9*b^11*c^4*d^3*e^13 - 96768*a^9*b^12*c^3*d^
2*e^14 + 20185088*a^10*b^2*c^12*d^10*e^6 - 37847040*a^10*b^4*c^10*d^8*e^8 + 30277632*a^10*b^5*c^9*d^7*e^9 + 10
092544*a^10*b^6*c^8*d^6*e^10 - 15138816*a^10*b^7*c^7*d^5*e^11 - 1103872*a^10*b^8*c^6*d^4*e^12 + 2207744*a^10*b
^9*c^5*d^3*e^13 + 473088*a^10*b^10*c^4*d^2*e^14 + 27525120*a^11*b^2*c^11*d^8*e^8 - 30277632*a^11*b^4*c^9*d^6*e
^10 + 13762560*a^11*b^5*c^8*d^5*e^11 + 8486912*a^11*b^6*c^7*d^4*e^12 - 3211264*a^11*b^7*c^6*d^3*e^13 - 1462272
*a^11*b^8*c^5*d^2*e^14 + 20185088*a^12*b^2*c^10*d^6*e^10 + 3670016*a^12*b^3*c^9*d^5*e^11 - 14221312*a^12*b^4*c
^8*d^4*e^12 + 917504*a^12*b^5*c^7*d^3*e^13 + 2752512*a^12*b^6*c^6*d^2*e^14 + 7340032*a^13*b^2*c^9*d^4*e^12 + 3
670016*a^13*b^3*c^8*d^3*e^13 - 2752512*a^13*b^4*c^7*d^2*e^14 + 786432*a^14*b^2*c^8*d^2*e^14 + 256*a*b^15*c^8*d
^15*e + 24*a*b^22*c*d^8*e^8 - 524288*a^8*b*c^15*d^15*e + 256*a^8*b^15*c*d*e^15 - 524288*a^15*b*c^8*d*e^15 - 88
8*a*b^16*c^7*d^14*e^2 + 1736*a*b^17*c^6*d^13*e^3 - 2072*a*b^18*c^5*d^12*e^4 + 1512*a*b^19*c^4*d^11*e^5 - 616*a
*b^20*c^3*d^10*e^6 + 88*a*b^21*c^2*d^9*e^7 - 3584*a^2*b^13*c^9*d^15*e + 88*a^2*b^21*c*d^7*e^9 + 28672*a^3*b^11
*c^10*d^15*e - 616*a^3*b^20*c*d^6*e^10 - 143360*a^4*b^9*c^11*d^15*e + 1512*a^4*b^19*c*d^5*e^11 + 458752*a^5*b^
7*c^12*d^15*e - 2072*a^5*b^18*c*d^4*e^12 - 917504*a^6*b^5*c^13*d^15*e + 1736*a^6*b^17*c*d^3*e^13 + 1048576*a^7
*b^3*c^14*d^15*e - 888*a^7*b^16*c*d^2*e^14 - 3670016*a^9*b*c^14*d^13*e^3 - 3584*a^9*b^13*c^2*d*e^15 - 11010048
*a^10*b*c^13*d^11*e^5 + 28672*a^10*b^11*c^3*d*e^15 - 18350080*a^11*b*c^12*d^9*e^7 - 143360*a^11*b^9*c^4*d*e^15
- 18350080*a^12*b*c^11*d^7*e^9 + 458752*a^12*b^7*c^5*d*e^15 - 11010048*a^13*b*c^10*d^5*e^11 - 917504*a^13*b^5
*c^6*d*e^15 - 3670016*a^14*b*c^9*d^3*e^13 + 1048576*a^14*b^3*c^7*d*e^15) + (x*(393216*a^17*c^10*e^19 - 2*a^8*b
^18*c*e^19 - 131072*a^8*c^19*d^18*e - 2*b^16*c^11*d^18*e - 2*b^26*c*d^8*e^11 + 70*a^9*b^16*c^2*e^19 - 1088*a^1
0*b^14*c^3*e^19 + 9856*a^11*b^12*c^4*e^19 - 57344*a^12*b^10*c^5*e^19 + 222208*a^13*b^8*c^6*e^19 - 573440*a^14*
b^6*c^7*e^19 + 950272*a^15*b^4*c^8*e^19 - 917504*a^16*b^2*c^9*e^19 - 655360*a^9*c^18*d^16*e^3 - 524288*a^10*c^
17*d^14*e^5 + 3670016*a^11*c^16*d^12*e^7 + 12845056*a^12*c^15*d^10*e^9 + 20185088*a^13*c^14*d^8*e^11 + 1835008
0*a^14*c^13*d^6*e^13 + 9961472*a^15*c^12*d^4*e^15 + 3014656*a^16*c^11*d^2*e^17 + 18*b^17*c^10*d^17*e^2 - 74*b^
18*c^9*d^16*e^3 + 184*b^19*c^8*d^15*e^4 - 308*b^20*c^7*d^14*e^5 + 364*b^21*c^6*d^13*e^6 - 308*b^22*c^5*d^12*e^
7 + 184*b^23*c^4*d^11*e^8 - 74*b^24*c^3*d^10*e^9 + 18*b^25*c^2*d^9*e^10 + 8064*a^2*b^13*c^12*d^17*e^2 - 32832*
a^2*b^14*c^11*d^16*e^3 + 79872*a^2*b^15*c^10*d^15*e^4 - 128520*a^2*b^16*c^9*d^14*e^5 + 141624*a^2*b^17*c^8*d^1
3*e^6 - 105056*a^2*b^18*c^7*d^12*e^7 + 47208*a^2*b^19*c^6*d^11*e^8 - 7392*a^2*b^20*c^5*d^10*e^9 - 3960*a^2*b^2
1*c^4*d^9*e^10 + 2112*a^2*b^22*c^3*d^8*e^11 - 168*a^2*b^23*c^2*d^7*e^12 - 64512*a^3*b^11*c^13*d^17*e^2 + 26073
6*a^3*b^12*c^12*d^16*e^3 - 623616*a^3*b^13*c^11*d^15*e^4 + 971520*a^3*b^14*c^10*d^14*e^5 - 1005312*a^3*b^15*c^
9*d^13*e^6 + 646968*a^3*b^16*c^8*d^12*e^7 - 177744*a^3*b^17*c^7*d^11*e^8 - 74536*a^3*b^18*c^6*d^10*e^9 + 80080
*a^3*b^19*c^5*d^9*e^10 - 19096*a^3*b^20*c^4*d^8*e^11 - 3056*a^3*b^21*c^3*d^7*e^12 + 1288*a^3*b^22*c^2*d^6*e^13
+ 322560*a^4*b^9*c^14*d^17*e^2 - 1290240*a^4*b^10*c^13*d^16*e^3 + 3010560*a^4*b^11*c^12*d^15*e^4 - 4462080*a^
4*b^12*c^11*d^14*e^5 + 4139520*a^4*b^13*c^10*d^13*e^6 - 1908480*a^4*b^14*c^9*d^12*e^7 - 430080*a^4*b^15*c^8*d^
11*e^8 + 1159620*a^4*b^16*c^7*d^10*e^9 - 574420*a^4*b^17*c^6*d^9*e^10 + 10780*a^4*b^18*c^5*d^8*e^11 + 70280*a^
4*b^19*c^4*d^7*e^12 - 8820*a^4*b^20*c^3*d^6*e^13 - 3220*a^4*b^21*c^2*d^5*e^14 - 1032192*a^5*b^7*c^15*d^17*e^2
+ 4064256*a^5*b^8*c^14*d^16*e^3 - 9117696*a^5*b^9*c^13*d^15*e^4 + 12386304*a^5*b^10*c^12*d^14*e^5 - 9031680*a^
5*b^11*c^11*d^13*e^6 - 75264*a^5*b^12*c^10*d^12*e^7 + 7160832*a^5*b^13*c^9*d^11*e^8 - 6475392*a^5*b^14*c^8*d^1
0*e^9 + 1586816*a^5*b^15*c^7*d^9*e^10 + 956340*a^5*b^16*c^6*d^8*e^11 - 551376*a^5*b^17*c^5*d^7*e^12 - 27832*a^
5*b^18*c^4*d^6*e^13 + 37632*a^5*b^19*c^3*d^5*e^14 + 4452*a^5*b^20*c^2*d^4*e^15 + 2064384*a^6*b^5*c^16*d^17*e^2
- 7913472*a^6*b^6*c^15*d^16*e^3 + 16515072*a^6*b^7*c^14*d^15*e^4 - 18493440*a^6*b^8*c^13*d^14*e^5 + 4214784*a
^6*b^9*c^12*d^13*e^6 + 19869696*a^6*b^10*c^11*d^12*e^7 - 30879744*a^6*b^11*c^10*d^11*e^8 + 17090304*a^6*b^12*c
^9*d^10*e^9 + 2858240*a^6*b^13*c^8*d^9*e^10 - 7480704*a^6*b^14*c^7*d^8*e^11 + 1849344*a^6*b^15*c^6*d^7*e^12 +
810264*a^6*b^16*c^5*d^6*e^13 - 210504*a^6*b^17*c^4*d^5*e^14 - 61040*a^6*b^18*c^3*d^4*e^15 - 3752*a^6*b^19*c^2*
d^3*e^16 - 2359296*a^7*b^3*c^17*d^17*e^2 + 8552448*a^7*b^4*c^16*d^16*e^3 - 14942208*a^7*b^5*c^15*d^15*e^4 + 68
81280*a^7*b^6*c^14*d^14*e^5 + 26148864*a^7*b^7*c^13*d^13*e^6 - 64598016*a^7*b^8*c^12*d^12*e^7 + 62988288*a^7*b
^9*c^11*d^11*e^8 - 10070016*a^7*b^10*c^10*d^10*e^9 - 35031040*a^7*b^11*c^9*d^9*e^10 + 26247936*a^7*b^12*c^8*d^
8*e^11 + 623616*a^7*b^13*c^7*d^7*e^12 - 5553408*a^7*b^14*c^6*d^6*e^13 + 327936*a^7*b^15*c^5*d^5*e^14 + 464280*
a^7*b^16*c^4*d^4*e^15 + 55248*a^7*b^17*c^3*d^3*e^16 + 1928*a^7*b^18*c^2*d^2*e^17 - 3538944*a^8*b^2*c^17*d^16*e
^3 + 1572864*a^8*b^3*c^16*d^15*e^4 + 17694720*a^8*b^4*c^15*d^14*e^5 - 57802752*a^8*b^5*c^14*d^13*e^6 + 8670412
8*a^8*b^6*c^13*d^12*e^7 - 44826624*a^8*b^7*c^12*d^11*e^8 - 61433856*a^8*b^8*c^11*d^10*e^9 + 108922880*a^8*b^9*
c^10*d^9*e^10 - 39333888*a^8*b^10*c^9*d^8*e^11 - 28274688*a^8*b^11*c^8*d^7*e^12 + 18891264*a^8*b^12*c^7*d^6*e^
13 + 2935296*a^8*b^13*c^6*d^5*e^14 - 2062080*a^8*b^14*c^5*d^4*e^15 - 466944*a^8*b^15*c^4*d^3*e^16 - 29394*a^8*
b^16*c^3*d^2*e^17 - 18350080*a^9*b^2*c^16*d^14*e^5 + 36700160*a^9*b^3*c^15*d^13*e^6 - 32112640*a^9*b^4*c^14*d^
12*e^7 - 45875200*a^9*b^5*c^13*d^11*e^8 + 164003840*a^9*b^6*c^12*d^10*e^9 - 149585920*a^9*b^7*c^11*d^9*e^10 -
21514240*a^9*b^8*c^10*d^8*e^11 + 104079360*a^9*b^9*c^9*d^7*e^12 - 28385280*a^9*b^10*c^8*d^6*e^13 - 21073920*a^
9*b^11*c^7*d^5*e^14 + 4784640*a^9*b^12*c^6*d^4*e^15 + 2472960*a^9*b^13*c^5*d^3*e^16 + 260160*a^9*b^14*c^4*d^2*
e^17 - 22020096*a^10*b^2*c^15*d^12*e^7 + 84410368*a^10*b^3*c^14*d^11*e^8 - 146341888*a^10*b^4*c^13*d^10*e^9 +
45416448*a^10*b^5*c^12*d^9*e^10 + 169050112*a^10*b^6*c^11*d^8*e^11 - 170131456*a^10*b^7*c^10*d^7*e^12 - 160849
92*a^10*b^8*c^9*d^6*e^13 + 63393792*a^10*b^9*c^8*d^5*e^14 - 946176*a^10*b^10*c^7*d^4*e^15 - 8343552*a^10*b^11*
c^6*d^3*e^16 - 1470336*a^10*b^12*c^5*d^2*e^17 + 22020096*a^11*b^2*c^14*d^10*e^9 + 91750400*a^11*b^3*c^13*d^9*e
^10 - 221577216*a^11*b^4*c^12*d^8*e^11 + 93585408*a^11*b^5*c^11*d^7*e^12 + 131661824*a^11*b^6*c^10*d^6*e^13 -
94961664*a^11*b^7*c^9*d^5*e^14 - 27095040*a^11*b^8*c^8*d^4*e^15 + 17031168*a^11*b^9*c^7*d^3*e^16 + 5483520*a^1
1*b^10*c^6*d^2*e^17 + 78905344*a^12*b^2*c^13*d^8*e^11 + 69730304*a^12*b^3*c^12*d^7*e^12 - 186253312*a^12*b^4*c
^11*d^6*e^13 + 44957696*a^12*b^5*c^10*d^5*e^14 + 75694080*a^12*b^6*c^9*d^4*e^15 - 16515072*a^12*b^7*c^8*d^3*e^
16 - 13396992*a^12*b^8*c^7*d^2*e^17 + 77070336*a^13*b^2*c^12*d^6*e^13 + 51380224*a^13*b^3*c^11*d^5*e^14 - 8716
2880*a^13*b^4*c^10*d^4*e^15 - 5505024*a^13*b^5*c^9*d^3*e^16 + 20299776*a^13*b^6*c^8*d^2*e^17 + 31457280*a^14*b
^2*c^11*d^4*e^15 + 28835840*a^14*b^3*c^10*d^3*e^16 - 16220160*a^14*b^4*c^9*d^2*e^17 + 2883584*a^15*b^2*c^10*d^
2*e^17 + 64*a*b^14*c^12*d^18*e + 16*a*b^25*c*d^7*e^12 + 16*a^7*b^19*c*d*e^18 - 3014656*a^16*b*c^10*d*e^18 - 57
6*a*b^15*c^11*d^17*e^2 + 2358*a*b^16*c^10*d^16*e^3 - 5808*a*b^17*c^9*d^15*e^4 + 9560*a*b^18*c^8*d^14*e^5 - 109
76*a*b^19*c^7*d^13*e^6 + 8820*a*b^20*c^6*d^12*e^7 - 4768*a*b^21*c^5*d^11*e^8 + 1528*a*b^22*c^4*d^10*e^9 - 160*
a*b^23*c^3*d^9*e^10 - 58*a*b^24*c^2*d^8*e^11 - 896*a^2*b^12*c^13*d^18*e - 56*a^2*b^24*c*d^6*e^13 + 7168*a^3*b^
10*c^14*d^18*e + 112*a^3*b^23*c*d^5*e^14 - 35840*a^4*b^8*c^15*d^18*e - 140*a^4*b^22*c*d^4*e^15 + 114688*a^5*b^
6*c^16*d^18*e + 112*a^5*b^21*c*d^3*e^16 - 229376*a^6*b^4*c^17*d^18*e - 56*a^6*b^20*c*d^2*e^17 + 262144*a^7*b^2
*c^18*d^18*e + 1179648*a^8*b*c^18*d^17*e^2 - 558*a^8*b^17*c^2*d*e^18 + 5242880*a^9*b*c^17*d^15*e^4 + 8640*a^9*
b^15*c^3*d*e^18 + 3670016*a^10*b*c^16*d^13*e^6 - 77952*a^10*b^13*c^4*d*e^18 - 22020096*a^11*b*c^15*d^11*e^8 +
451584*a^11*b^11*c^5*d*e^18 - 64225280*a^12*b*c^14*d^9*e^10 - 1741824*a^12*b^9*c^6*d*e^18 - 80740352*a^13*b*c^
13*d^7*e^12 + 4472832*a^13*b^7*c^7*d*e^18 - 55050240*a^14*b*c^12*d^5*e^14 - 7372800*a^14*b^5*c^8*d*e^18 - 1992
2944*a^15*b*c^11*d^3*e^16 + 7077888*a^15*b^3*c^9*d*e^18))/(a^8*b^16*e^16 + 65536*a^8*c^16*d^16 + 65536*a^16*c^
8*e^16 + b^16*c^8*d^16 + b^24*d^8*e^8 - 32*a*b^14*c^9*d^16 - 32*a^9*b^14*c*e^16 - 8*a*b^23*d^7*e^9 - 8*a^7*b^1
7*d*e^15 - 8*b^17*c^7*d^15*e - 8*b^23*c*d^9*e^7 + 448*a^2*b^12*c^10*d^16 - 3584*a^3*b^10*c^11*d^16 + 17920*a^4
*b^8*c^12*d^16 - 57344*a^5*b^6*c^13*d^16 + 114688*a^6*b^4*c^14*d^16 - 131072*a^7*b^2*c^15*d^16 + 448*a^10*b^12
*c^2*e^16 - 3584*a^11*b^10*c^3*e^16 + 17920*a^12*b^8*c^4*e^16 - 57344*a^13*b^6*c^5*e^16 + 114688*a^14*b^4*c^6*
e^16 - 131072*a^15*b^2*c^7*e^16 + 28*a^2*b^22*d^6*e^10 - 56*a^3*b^21*d^5*e^11 + 70*a^4*b^20*d^4*e^12 - 56*a^5*
b^19*d^3*e^13 + 28*a^6*b^18*d^2*e^14 + 524288*a^9*c^15*d^14*e^2 + 1835008*a^10*c^14*d^12*e^4 + 3670016*a^11*c^
13*d^10*e^6 + 4587520*a^12*c^12*d^8*e^8 + 3670016*a^13*c^11*d^6*e^10 + 1835008*a^14*c^10*d^4*e^12 + 524288*a^1
5*c^9*d^2*e^14 + 28*b^18*c^6*d^14*e^2 - 56*b^19*c^5*d^13*e^3 + 70*b^20*c^4*d^12*e^4 - 56*b^21*c^3*d^11*e^5 + 2
8*b^22*c^2*d^10*e^6 + 12288*a^2*b^14*c^8*d^14*e^2 - 23296*a^2*b^15*c^7*d^13*e^3 + 26012*a^2*b^16*c^6*d^12*e^4
- 16296*a^2*b^17*c^5*d^11*e^5 + 4004*a^2*b^18*c^4*d^10*e^6 + 1232*a^2*b^19*c^3*d^9*e^7 - 924*a^2*b^20*c^2*d^8*
e^8 - 96768*a^3*b^12*c^9*d^14*e^2 + 175616*a^3*b^13*c^8*d^13*e^3 - 176512*a^3*b^14*c^7*d^12*e^4 + 80640*a^3*b^
15*c^6*d^11*e^5 + 11704*a^3*b^16*c^5*d^10*e^6 - 28952*a^3*b^17*c^4*d^9*e^7 + 8624*a^3*b^18*c^3*d^8*e^8 + 1232*
a^3*b^19*c^2*d^7*e^9 + 473088*a^4*b^10*c^10*d^14*e^2 - 802816*a^4*b^11*c^9*d^13*e^3 + 664832*a^4*b^12*c^8*d^12
*e^4 - 75264*a^4*b^13*c^7*d^11*e^5 - 315392*a^4*b^14*c^6*d^10*e^6 + 216832*a^4*b^15*c^5*d^9*e^7 - 12474*a^4*b^
16*c^4*d^8*e^8 - 28952*a^4*b^17*c^3*d^7*e^9 + 4004*a^4*b^18*c^2*d^6*e^10 - 1462272*a^5*b^8*c^11*d^14*e^2 + 220
7744*a^5*b^9*c^10*d^13*e^3 - 1103872*a^5*b^10*c^9*d^12*e^4 - 1204224*a^5*b^11*c^8*d^11*e^5 + 1931776*a^5*b^12*
c^7*d^10*e^6 - 670208*a^5*b^13*c^6*d^9*e^7 - 310464*a^5*b^14*c^5*d^8*e^8 + 216832*a^5*b^15*c^4*d^7*e^9 + 11704
*a^5*b^16*c^3*d^6*e^10 - 16296*a^5*b^17*c^2*d^5*e^11 + 2752512*a^6*b^6*c^12*d^14*e^2 - 3211264*a^6*b^7*c^11*d^
13*e^3 - 1103872*a^6*b^8*c^10*d^12*e^4 + 6623232*a^6*b^9*c^9*d^11*e^5 - 5519360*a^6*b^10*c^8*d^10*e^6 - 315392
*a^6*b^11*c^7*d^9*e^7 + 2454144*a^6*b^12*c^6*d^8*e^8 - 670208*a^6*b^13*c^5*d^7*e^9 - 315392*a^6*b^14*c^4*d^6*e
^10 + 80640*a^6*b^15*c^3*d^5*e^11 + 26012*a^6*b^16*c^2*d^4*e^12 - 2752512*a^7*b^4*c^13*d^14*e^2 + 917504*a^7*b
^5*c^12*d^13*e^3 + 8486912*a^7*b^6*c^11*d^12*e^4 - 15138816*a^7*b^7*c^10*d^11*e^5 + 5361664*a^7*b^8*c^9*d^10*e
^6 + 8876032*a^7*b^9*c^8*d^9*e^7 - 8008704*a^7*b^10*c^7*d^8*e^8 - 315392*a^7*b^11*c^6*d^7*e^9 + 1931776*a^7*b^
12*c^5*d^6*e^10 - 75264*a^7*b^13*c^4*d^5*e^11 - 176512*a^7*b^14*c^3*d^4*e^12 - 23296*a^7*b^15*c^2*d^3*e^13 + 7
86432*a^8*b^2*c^14*d^14*e^2 + 3670016*a^8*b^3*c^13*d^13*e^3 - 14221312*a^8*b^4*c^12*d^12*e^4 + 13762560*a^8*b^
5*c^11*d^11*e^5 + 10092544*a^8*b^6*c^10*d^10*e^6 - 26673152*a^8*b^7*c^9*d^9*e^7 + 10036224*a^8*b^8*c^8*d^8*e^8
+ 8876032*a^8*b^9*c^7*d^7*e^9 - 5519360*a^8*b^10*c^6*d^6*e^10 - 1204224*a^8*b^11*c^5*d^5*e^11 + 664832*a^8*b^
12*c^4*d^4*e^12 + 175616*a^8*b^13*c^3*d^3*e^13 + 12288*a^8*b^14*c^2*d^2*e^14 + 7340032*a^9*b^2*c^13*d^12*e^4 +
3670016*a^9*b^3*c^12*d^11*e^5 - 30277632*a^9*b^4*c^11*d^10*e^6 + 30277632*a^9*b^5*c^10*d^9*e^7 + 8830976*a^9*
b^6*c^9*d^8*e^8 - 26673152*a^9*b^7*c^8*d^7*e^9 + 5361664*a^9*b^8*c^7*d^6*e^10 + 6623232*a^9*b^9*c^6*d^5*e^11 -
1103872*a^9*b^10*c^5*d^4*e^12 - 802816*a^9*b^11*c^4*d^3*e^13 - 96768*a^9*b^12*c^3*d^2*e^14 + 20185088*a^10*b^
2*c^12*d^10*e^6 - 37847040*a^10*b^4*c^10*d^8*e^8 + 30277632*a^10*b^5*c^9*d^7*e^9 + 10092544*a^10*b^6*c^8*d^6*e
^10 - 15138816*a^10*b^7*c^7*d^5*e^11 - 1103872*a^10*b^8*c^6*d^4*e^12 + 2207744*a^10*b^9*c^5*d^3*e^13 + 473088*
a^10*b^10*c^4*d^2*e^14 + 27525120*a^11*b^2*c^11*d^8*e^8 - 30277632*a^11*b^4*c^9*d^6*e^10 + 13762560*a^11*b^5*c
^8*d^5*e^11 + 8486912*a^11*b^6*c^7*d^4*e^12 - 3211264*a^11*b^7*c^6*d^3*e^13 - 1462272*a^11*b^8*c^5*d^2*e^14 +
20185088*a^12*b^2*c^10*d^6*e^10 + 3670016*a^12*b^3*c^9*d^5*e^11 - 14221312*a^12*b^4*c^8*d^4*e^12 + 917504*a^12
*b^5*c^7*d^3*e^13 + 2752512*a^12*b^6*c^6*d^2*e^14 + 7340032*a^13*b^2*c^9*d^4*e^12 + 3670016*a^13*b^3*c^8*d^3*e
^13 - 2752512*a^13*b^4*c^7*d^2*e^14 + 786432*a^14*b^2*c^8*d^2*e^14 + 256*a*b^15*c^8*d^15*e + 24*a*b^22*c*d^8*e
^8 - 524288*a^8*b*c^15*d^15*e + 256*a^8*b^15*c*d*e^15 - 524288*a^15*b*c^8*d*e^15 - 888*a*b^16*c^7*d^14*e^2 + 1
736*a*b^17*c^6*d^13*e^3 - 2072*a*b^18*c^5*d^12*e^4 + 1512*a*b^19*c^4*d^11*e^5 - 616*a*b^20*c^3*d^10*e^6 + 88*a
*b^21*c^2*d^9*e^7 - 3584*a^2*b^13*c^9*d^15*e + 88*a^2*b^21*c*d^7*e^9 + 28672*a^3*b^11*c^10*d^15*e - 616*a^3*b^
20*c*d^6*e^10 - 143360*a^4*b^9*c^11*d^15*e + 1512*a^4*b^19*c*d^5*e^11 + 458752*a^5*b^7*c^12*d^15*e - 2072*a^5*
b^18*c*d^4*e^12 - 917504*a^6*b^5*c^13*d^15*e + 1736*a^6*b^17*c*d^3*e^13 + 1048576*a^7*b^3*c^14*d^15*e - 888*a^
7*b^16*c*d^2*e^14 - 3670016*a^9*b*c^14*d^13*e^3 - 3584*a^9*b^13*c^2*d*e^15 - 11010048*a^10*b*c^13*d^11*e^5 + 2
8672*a^10*b^11*c^3*d*e^15 - 18350080*a^11*b*c^12*d^9*e^7 - 143360*a^11*b^9*c^4*d*e^15 - 18350080*a^12*b*c^11*d
^7*e^9 + 458752*a^12*b^7*c^5*d*e^15 - 11010048*a^13*b*c^10*d^5*e^11 - 917504*a^13*b^5*c^6*d*e^15 - 3670016*a^1
4*b*c^9*d^3*e^13 + 1048576*a^14*b^3*c^7*d*e^15)) + (x*(65*a^5*b^14*c^3*e^18 - 2*a^4*b^16*c^2*e^18 - 196608*a^1
2*c^10*e^18 - 926*a^6*b^12*c^4*e^18 + 7557*a^7*b^10*c^5*e^18 - 38800*a^8*b^8*c^6*e^18 + 129248*a^9*b^6*c^7*e^1
8 - 275200*a^10*b^4*c^8*e^18 + 345344*a^11*b^2*c^9*e^18 - 35840*a^4*c^18*d^16*e^2 - 291840*a^5*c^17*d^14*e^4 -
1047552*a^6*c^16*d^12*e^6 - 2180096*a^7*c^15*d^10*e^8 - 3023872*a^8*c^14*d^8*e^10 - 3038208*a^9*c^13*d^6*e^12
- 2184192*a^10*c^12*d^4*e^14 - 977920*a^11*c^11*d^2*e^16 - 140*b^8*c^14*d^16*e^2 + 1120*b^9*c^13*d^15*e^3 - 3
915*b^10*c^12*d^14*e^4 + 7805*b^11*c^11*d^13*e^5 - 9697*b^12*c^10*d^12*e^6 + 7677*b^13*c^9*d^11*e^7 - 3774*b^1
4*c^8*d^10*e^8 + 1050*b^15*c^7*d^9*e^9 - 127*b^16*c^6*d^8*e^10 + 5*b^17*c^5*d^7*e^11 - 9*b^18*c^4*d^6*e^12 + 7
*b^19*c^3*d^5*e^13 - 2*b^20*c^2*d^4*e^14 - 13440*a^2*b^4*c^16*d^16*e^2 + 107520*a^2*b^5*c^15*d^15*e^3 - 357600
*a^2*b^6*c^14*d^14*e^4 + 621600*a^2*b^7*c^13*d^13*e^5 - 552780*a^2*b^8*c^12*d^12*e^6 + 128040*a^2*b^9*c^11*d^1
1*e^7 + 203109*a^2*b^10*c^10*d^10*e^8 - 187245*a^2*b^11*c^9*d^9*e^9 + 47324*a^2*b^12*c^8*d^8*e^10 + 8854*a^2*b
^13*c^7*d^7*e^11 - 7585*a^2*b^14*c^6*d^6*e^12 + 2737*a^2*b^15*c^5*d^5*e^13 - 280*a^2*b^16*c^4*d^4*e^14 - 242*a
^2*b^17*c^3*d^3*e^15 - 12*a^2*b^18*c^2*d^2*e^16 + 35840*a^3*b^2*c^17*d^16*e^2 - 286720*a^3*b^3*c^16*d^15*e^3 +
892800*a^3*b^4*c^15*d^14*e^4 - 1232000*a^3*b^5*c^14*d^13*e^5 + 254560*a^3*b^6*c^13*d^12*e^6 + 1442880*a^3*b^7
*c^12*d^11*e^7 - 1823540*a^3*b^8*c^11*d^10*e^8 + 696100*a^3*b^9*c^10*d^9*e^9 + 183143*a^3*b^10*c^9*d^8*e^10 -
202932*a^3*b^11*c^8*d^7*e^11 + 50134*a^3*b^12*c^7*d^6*e^12 - 12200*a^3*b^13*c^6*d^5*e^13 - 1575*a^3*b^14*c^5*d
^4*e^14 + 3116*a^3*b^15*c^4*d^3*e^15 + 386*a^3*b^16*c^3*d^2*e^16 - 710400*a^4*b^2*c^16*d^14*e^4 - 44800*a^4*b^
3*c^15*d^13*e^5 + 3240320*a^4*b^4*c^14*d^12*e^6 - 5813760*a^4*b^5*c^13*d^11*e^7 + 3326240*a^4*b^6*c^12*d^10*e^
8 + 1426400*a^4*b^7*c^11*d^9*e^9 - 2481940*a^4*b^8*c^10*d^8*e^10 + 749840*a^4*b^9*c^9*d^7*e^11 + 54327*a^4*b^1
0*c^8*d^6*e^12 + 4099*a^4*b^11*c^7*d^5*e^13 + 26275*a^4*b^12*c^6*d^4*e^14 - 21795*a^4*b^13*c^5*d^3*e^15 - 5425
*a^4*b^14*c^4*d^2*e^16 - 5068032*a^5*b^2*c^15*d^12*e^6 + 3850752*a^5*b^3*c^14*d^11*e^7 + 4807296*a^5*b^4*c^13*
d^10*e^8 - 10646400*a^5*b^5*c^12*d^9*e^9 + 5374688*a^5*b^6*c^11*d^8*e^10 + 1271680*a^5*b^7*c^10*d^7*e^11 - 126
7084*a^5*b^8*c^9*d^6*e^12 - 83228*a^5*b^9*c^8*d^5*e^13 - 130219*a^5*b^10*c^7*d^4*e^14 + 92314*a^5*b^11*c^6*d^3
*e^15 + 43457*a^5*b^12*c^5*d^2*e^16 - 13469440*a^6*b^2*c^14*d^10*e^8 + 9731840*a^6*b^3*c^13*d^9*e^9 + 5220224*
a^6*b^4*c^12*d^8*e^10 - 10133504*a^6*b^5*c^11*d^7*e^11 + 1895264*a^6*b^6*c^10*d^6*e^12 + 1516768*a^6*b^7*c^9*d
^5*e^13 + 503420*a^6*b^8*c^8*d^4*e^14 - 251672*a^6*b^9*c^7*d^3*e^15 - 219985*a^6*b^10*c^6*d^2*e^16 - 18478336*
a^7*b^2*c^13*d^8*e^10 + 8510464*a^7*b^3*c^12*d^7*e^11 + 6884480*a^7*b^4*c^11*d^6*e^12 - 4658048*a^7*b^5*c^10*d
^5*e^13 - 2234080*a^7*b^6*c^9*d^4*e^14 + 359488*a^7*b^7*c^8*d^3*e^15 + 736388*a^7*b^8*c^7*d^2*e^16 - 14331136*
a^8*b^2*c^12*d^6*e^12 + 659200*a^8*b^3*c^11*d^5*e^13 + 6262400*a^8*b^4*c^10*d^4*e^14 + 487936*a^8*b^5*c^9*d^3*
e^15 - 1607584*a^8*b^6*c^8*d^2*e^16 - 5932800*a^9*b^2*c^11*d^4*e^14 - 3325440*a^9*b^3*c^10*d^3*e^15 + 1980800*
a^9*b^4*c^9*d^2*e^16 - 587008*a^10*b^2*c^10*d^2*e^16 + 977920*a^11*b*c^10*d*e^17 + 2240*a*b^6*c^15*d^16*e^2 -
17920*a*b^7*c^14*d^15*e^3 + 61500*a*b^8*c^13*d^14*e^4 - 116900*a*b^9*c^12*d^13*e^5 + 131263*a*b^10*c^11*d^12*e
^6 - 83238*a*b^11*c^10*d^11*e^7 + 21225*a*b^12*c^9*d^10*e^8 + 6240*a*b^13*c^8*d^9*e^9 - 5386*a*b^14*c^7*d^8*e^
10 + 846*a*b^15*c^6*d^7*e^11 + 289*a*b^16*c^5*d^6*e^12 - 212*a*b^17*c^4*d^5*e^13 + 45*a*b^18*c^3*d^4*e^14 + 8*
a*b^19*c^2*d^3*e^15 + 8*a^3*b^17*c^2*d*e^17 + 286720*a^4*b*c^17*d^15*e^3 - 261*a^4*b^15*c^3*d*e^17 + 2042880*a
^5*b*c^16*d^13*e^5 + 3736*a^5*b^13*c^4*d*e^17 + 6285312*a^6*b*c^15*d^11*e^7 - 30675*a^6*b^11*c^5*d*e^17 + 1090
0480*a^7*b*c^14*d^9*e^9 + 159260*a^7*b^9*c^6*d*e^17 + 12095488*a^8*b*c^13*d^7*e^11 - 542432*a^8*b^7*c^7*d*e^17
+ 9114624*a^9*b*c^12*d^5*e^13 + 1201024*a^9*b^5*c^8*d*e^17 + 4368384*a^10*b*c^11*d^3*e^15 - 1597184*a^10*b^3*
c^9*d*e^17))/(a^8*b^16*e^16 + 65536*a^8*c^16*d^16 + 65536*a^16*c^8*e^16 + b^16*c^8*d^16 + b^24*d^8*e^8 - 32*a*
b^14*c^9*d^16 - 32*a^9*b^14*c*e^16 - 8*a*b^23*d^7*e^9 - 8*a^7*b^17*d*e^15 - 8*b^17*c^7*d^15*e - 8*b^23*c*d^9*e
^7 + 448*a^2*b^12*c^10*d^16 - 3584*a^3*b^10*c^11*d^16 + 17920*a^4*b^8*c^12*d^16 - 57344*a^5*b^6*c^13*d^16 + 11
4688*a^6*b^4*c^14*d^16 - 131072*a^7*b^2*c^15*d^16 + 448*a^10*b^12*c^2*e^16 - 3584*a^11*b^10*c^3*e^16 + 17920*a
^12*b^8*c^4*e^16 - 57344*a^13*b^6*c^5*e^16 + 114688*a^14*b^4*c^6*e^16 - 131072*a^15*b^2*c^7*e^16 + 28*a^2*b^22
*d^6*e^10 - 56*a^3*b^21*d^5*e^11 + 70*a^4*b^20*d^4*e^12 - 56*a^5*b^19*d^3*e^13 + 28*a^6*b^18*d^2*e^14 + 524288
*a^9*c^15*d^14*e^2 + 1835008*a^10*c^14*d^12*e^4 + 3670016*a^11*c^13*d^10*e^6 + 4587520*a^12*c^12*d^8*e^8 + 367
0016*a^13*c^11*d^6*e^10 + 1835008*a^14*c^10*d^4*e^12 + 524288*a^15*c^9*d^2*e^14 + 28*b^18*c^6*d^14*e^2 - 56*b^
19*c^5*d^13*e^3 + 70*b^20*c^4*d^12*e^4 - 56*b^21*c^3*d^11*e^5 + 28*b^22*c^2*d^10*e^6 + 12288*a^2*b^14*c^8*d^14
*e^2 - 23296*a^2*b^15*c^7*d^13*e^3 + 26012*a^2*b^16*c^6*d^12*e^4 - 16296*a^2*b^17*c^5*d^11*e^5 + 4004*a^2*b^18
*c^4*d^10*e^6 + 1232*a^2*b^19*c^3*d^9*e^7 - 924*a^2*b^20*c^2*d^8*e^8 - 96768*a^3*b^12*c^9*d^14*e^2 + 175616*a^
3*b^13*c^8*d^13*e^3 - 176512*a^3*b^14*c^7*d^12*e^4 + 80640*a^3*b^15*c^6*d^11*e^5 + 11704*a^3*b^16*c^5*d^10*e^6
- 28952*a^3*b^17*c^4*d^9*e^7 + 8624*a^3*b^18*c^3*d^8*e^8 + 1232*a^3*b^19*c^2*d^7*e^9 + 473088*a^4*b^10*c^10*d
^14*e^2 - 802816*a^4*b^11*c^9*d^13*e^3 + 664832*a^4*b^12*c^8*d^12*e^4 - 75264*a^4*b^13*c^7*d^11*e^5 - 315392*a
^4*b^14*c^6*d^10*e^6 + 216832*a^4*b^15*c^5*d^9*e^7 - 12474*a^4*b^16*c^4*d^8*e^8 - 28952*a^4*b^17*c^3*d^7*e^9 +
4004*a^4*b^18*c^2*d^6*e^10 - 1462272*a^5*b^8*c^11*d^14*e^2 + 2207744*a^5*b^9*c^10*d^13*e^3 - 1103872*a^5*b^10
*c^9*d^12*e^4 - 1204224*a^5*b^11*c^8*d^11*e^5 + 1931776*a^5*b^12*c^7*d^10*e^6 - 670208*a^5*b^13*c^6*d^9*e^7 -
310464*a^5*b^14*c^5*d^8*e^8 + 216832*a^5*b^15*c^4*d^7*e^9 + 11704*a^5*b^16*c^3*d^6*e^10 - 16296*a^5*b^17*c^2*d
^5*e^11 + 2752512*a^6*b^6*c^12*d^14*e^2 - 3211264*a^6*b^7*c^11*d^13*e^3 - 1103872*a^6*b^8*c^10*d^12*e^4 + 6623
232*a^6*b^9*c^9*d^11*e^5 - 5519360*a^6*b^10*c^8*d^10*e^6 - 315392*a^6*b^11*c^7*d^9*e^7 + 2454144*a^6*b^12*c^6*
d^8*e^8 - 670208*a^6*b^13*c^5*d^7*e^9 - 315392*a^6*b^14*c^4*d^6*e^10 + 80640*a^6*b^15*c^3*d^5*e^11 + 26012*a^6
*b^16*c^2*d^4*e^12 - 2752512*a^7*b^4*c^13*d^14*e^2 + 917504*a^7*b^5*c^12*d^13*e^3 + 8486912*a^7*b^6*c^11*d^12*
e^4 - 15138816*a^7*b^7*c^10*d^11*e^5 + 5361664*a^7*b^8*c^9*d^10*e^6 + 8876032*a^7*b^9*c^8*d^9*e^7 - 8008704*a^
7*b^10*c^7*d^8*e^8 - 315392*a^7*b^11*c^6*d^7*e^9 + 1931776*a^7*b^12*c^5*d^6*e^10 - 75264*a^7*b^13*c^4*d^5*e^11
- 176512*a^7*b^14*c^3*d^4*e^12 - 23296*a^7*b^15*c^2*d^3*e^13 + 786432*a^8*b^2*c^14*d^14*e^2 + 3670016*a^8*b^3
*c^13*d^13*e^3 - 14221312*a^8*b^4*c^12*d^12*e^4 + 13762560*a^8*b^5*c^11*d^11*e^5 + 10092544*a^8*b^6*c^10*d^10*
e^6 - 26673152*a^8*b^7*c^9*d^9*e^7 + 10036224*a^8*b^8*c^8*d^8*e^8 + 8876032*a^8*b^9*c^7*d^7*e^9 - 5519360*a^8*
b^10*c^6*d^6*e^10 - 1204224*a^8*b^11*c^5*d^5*e^11 + 664832*a^8*b^12*c^4*d^4*e^12 + 175616*a^8*b^13*c^3*d^3*e^1
3 + 12288*a^8*b^14*c^2*d^2*e^14 + 7340032*a^9*b^2*c^13*d^12*e^4 + 3670016*a^9*b^3*c^12*d^11*e^5 - 30277632*a^9
*b^4*c^11*d^10*e^6 + 30277632*a^9*b^5*c^10*d^9*e^7 + 8830976*a^9*b^6*c^9*d^8*e^8 - 26673152*a^9*b^7*c^8*d^7*e^
9 + 5361664*a^9*b^8*c^7*d^6*e^10 + 6623232*a^9*b^9*c^6*d^5*e^11 - 1103872*a^9*b^10*c^5*d^4*e^12 - 802816*a^9*b
^11*c^4*d^3*e^13 - 96768*a^9*b^12*c^3*d^2*e^14 + 20185088*a^10*b^2*c^12*d^10*e^6 - 37847040*a^10*b^4*c^10*d^8*
e^8 + 30277632*a^10*b^5*c^9*d^7*e^9 + 10092544*a^10*b^6*c^8*d^6*e^10 - 15138816*a^10*b^7*c^7*d^5*e^11 - 110387
2*a^10*b^8*c^6*d^4*e^12 + 2207744*a^10*b^9*c^5*d^3*e^13 + 473088*a^10*b^10*c^4*d^2*e^14 + 27525120*a^11*b^2*c^
11*d^8*e^8 - 30277632*a^11*b^4*c^9*d^6*e^10 + 13762560*a^11*b^5*c^8*d^5*e^11 + 8486912*a^11*b^6*c^7*d^4*e^12 -
3211264*a^11*b^7*c^6*d^3*e^13 - 1462272*a^11*b^8*c^5*d^2*e^14 + 20185088*a^12*b^2*c^10*d^6*e^10 + 3670016*a^1
2*b^3*c^9*d^5*e^11 - 14221312*a^12*b^4*c^8*d^4*e^12 + 917504*a^12*b^5*c^7*d^3*e^13 + 2752512*a^12*b^6*c^6*d^2*
e^14 + 7340032*a^13*b^2*c^9*d^4*e^12 + 3670016*a^13*b^3*c^8*d^3*e^13 - 2752512*a^13*b^4*c^7*d^2*e^14 + 786432*
a^14*b^2*c^8*d^2*e^14 + 256*a*b^15*c^8*d^15*e + 24*a*b^22*c*d^8*e^8 - 524288*a^8*b*c^15*d^15*e + 256*a^8*b^15*
c*d*e^15 - 524288*a^15*b*c^8*d*e^15 - 888*a*b^16*c^7*d^14*e^2 + 1736*a*b^17*c^6*d^13*e^3 - 2072*a*b^18*c^5*d^1
2*e^4 + 1512*a*b^19*c^4*d^11*e^5 - 616*a*b^20*c^3*d^10*e^6 + 88*a*b^21*c^2*d^9*e^7 - 3584*a^2*b^13*c^9*d^15*e
+ 88*a^2*b^21*c*d^7*e^9 + 28672*a^3*b^11*c^10*d^15*e - 616*a^3*b^20*c*d^6*e^10 - 143360*a^4*b^9*c^11*d^15*e +
1512*a^4*b^19*c*d^5*e^11 + 458752*a^5*b^7*c^12*d^15*e - 2072*a^5*b^18*c*d^4*e^12 - 917504*a^6*b^5*c^13*d^15*e
+ 1736*a^6*b^17*c*d^3*e^13 + 1048576*a^7*b^3*c^14*d^15*e - 888*a^7*b^16*c*d^2*e^14 - 3670016*a^9*b*c^14*d^13*e
^3 - 3584*a^9*b^13*c^2*d*e^15 - 11010048*a^10*b*c^13*d^11*e^5 + 28672*a^10*b^11*c^3*d*e^15 - 18350080*a^11*b*c
^12*d^9*e^7 - 143360*a^11*b^9*c^4*d*e^15 - 18350080*a^12*b*c^11*d^7*e^9 + 458752*a^12*b^7*c^5*d*e^15 - 1101004
8*a^13*b*c^10*d^5*e^11 - 917504*a^13*b^5*c^6*d*e^15 - 3670016*a^14*b*c^9*d^3*e^13 + 1048576*a^14*b^3*c^7*d*e^1
5)) + (x*(b^14*c^3*e^17 + 4900*c^17*d^14*e^3 - 30*a*b^12*c^4*e^17 + 40600*a*c^16*d^12*e^5 - 34300*b*c^16*d^13*
e^4 + 2*b^13*c^4*d*e^16 + 389*a^2*b^10*c^5*e^17 - 2834*a^3*b^8*c^6*e^17 + 12334*a^4*b^6*c^7*e^17 - 30668*a^5*b
^4*c^8*e^17 + 34969*a^6*b^2*c^9*e^17 + 149340*a^2*c^15*d^10*e^7 + 322640*a^3*c^14*d^8*e^9 + 434076*a^4*c^13*d^
6*e^11 + 348568*a^5*c^12*d^4*e^13 + 139876*a^6*c^11*d^2*e^15 + 101325*b^2*c^15*d^12*e^5 - 162050*b^3*c^14*d^11
*e^6 + 148415*b^4*c^13*d^10*e^7 - 74100*b^5*c^12*d^9*e^8 + 15865*b^6*c^11*d^8*e^9 - 10*b^7*c^10*d^7*e^10 - 149
*b^8*c^9*d^6*e^11 + 342*b^9*c^8*d^5*e^12 - 247*b^10*c^7*d^4*e^13 + 4*b^11*c^6*d^3*e^14 + 3*b^12*c^5*d^2*e^15 +
1438095*a^2*b^2*c^13*d^8*e^9 - 1272180*a^2*b^3*c^12*d^7*e^10 + 429006*a^2*b^4*c^11*d^6*e^11 + 29472*a^2*b^5*c
^10*d^5*e^12 - 12685*a^2*b^6*c^9*d^4*e^13 - 14560*a^2*b^7*c^8*d^3*e^14 - 510*a^2*b^8*c^7*d^2*e^15 + 1824404*a^
3*b^2*c^12*d^6*e^11 - 956252*a^3*b^3*c^11*d^5*e^12 + 1620*a^3*b^4*c^10*d^4*e^13 + 84860*a^3*b^5*c^9*d^3*e^14 +
17280*a^3*b^6*c^8*d^2*e^15 + 1192075*a^4*b^2*c^11*d^4*e^13 - 213770*a^4*b^3*c^10*d^3*e^14 - 115485*a^4*b^4*c^
9*d^2*e^15 + 313038*a^5*b^2*c^10*d^2*e^15 - 243600*a*b*c^15*d^11*e^6 - 58*a*b^11*c^5*d*e^16 - 139876*a^6*b*c^1
0*d*e^16 + 595230*a*b^2*c^14*d^10*e^7 - 743150*a*b^3*c^13*d^9*e^8 + 476520*a*b^4*c^12*d^8*e^9 - 126780*a*b^5*c
^11*d^7*e^10 + 2454*a*b^6*c^10*d^6*e^11 - 5262*a*b^7*c^9*d^5*e^12 + 3230*a*b^8*c^8*d^4*e^13 + 900*a*b^9*c^7*d^
3*e^14 - 84*a*b^10*c^6*d^2*e^15 - 746700*a^2*b*c^14*d^9*e^8 + 722*a^2*b^9*c^6*d*e^16 - 1290560*a^3*b*c^13*d^7*
e^10 - 3992*a^3*b^7*c^7*d*e^16 - 1302228*a^4*b*c^12*d^5*e^12 + 5332*a^4*b^5*c^8*d*e^16 - 697136*a^5*b*c^11*d^3
*e^14 + 35530*a^5*b^3*c^9*d*e^16))/(a^8*b^16*e^16 + 65536*a^8*c^16*d^16 + 65536*a^16*c^8*e^16 + b^16*c^8*d^16
+ b^24*d^8*e^8 - 32*a*b^14*c^9*d^16 - 32*a^9*b^14*c*e^16 - 8*a*b^23*d^7*e^9 - 8*a^7*b^17*d*e^15 - 8*b^17*c^7*d
^15*e - 8*b^23*c*d^9*e^7 + 448*a^2*b^12*c^10*d^16 - 3584*a^3*b^10*c^11*d^16 + 17920*a^4*b^8*c^12*d^16 - 57344*
a^5*b^6*c^13*d^16 + 114688*a^6*b^4*c^14*d^16 - 131072*a^7*b^2*c^15*d^16 + 448*a^10*b^12*c^2*e^16 - 3584*a^11*b
^10*c^3*e^16 + 17920*a^12*b^8*c^4*e^16 - 57344*a^13*b^6*c^5*e^16 + 114688*a^14*b^4*c^6*e^16 - 131072*a^15*b^2*
c^7*e^16 + 28*a^2*b^22*d^6*e^10 - 56*a^3*b^21*d^5*e^11 + 70*a^4*b^20*d^4*e^12 - 56*a^5*b^19*d^3*e^13 + 28*a^6*
b^18*d^2*e^14 + 524288*a^9*c^15*d^14*e^2 + 1835008*a^10*c^14*d^12*e^4 + 3670016*a^11*c^13*d^10*e^6 + 4587520*a
^12*c^12*d^8*e^8 + 3670016*a^13*c^11*d^6*e^10 + 1835008*a^14*c^10*d^4*e^12 + 524288*a^15*c^9*d^2*e^14 + 28*b^1
8*c^6*d^14*e^2 - 56*b^19*c^5*d^13*e^3 + 70*b^20*c^4*d^12*e^4 - 56*b^21*c^3*d^11*e^5 + 28*b^22*c^2*d^10*e^6 + 1
2288*a^2*b^14*c^8*d^14*e^2 - 23296*a^2*b^15*c^7*d^13*e^3 + 26012*a^2*b^16*c^6*d^12*e^4 - 16296*a^2*b^17*c^5*d^
11*e^5 + 4004*a^2*b^18*c^4*d^10*e^6 + 1232*a^2*b^19*c^3*d^9*e^7 - 924*a^2*b^20*c^2*d^8*e^8 - 96768*a^3*b^12*c^
9*d^14*e^2 + 175616*a^3*b^13*c^8*d^13*e^3 - 176512*a^3*b^14*c^7*d^12*e^4 + 80640*a^3*b^15*c^6*d^11*e^5 + 11704
*a^3*b^16*c^5*d^10*e^6 - 28952*a^3*b^17*c^4*d^9*e^7 + 8624*a^3*b^18*c^3*d^8*e^8 + 1232*a^3*b^19*c^2*d^7*e^9 +
473088*a^4*b^10*c^10*d^14*e^2 - 802816*a^4*b^11*c^9*d^13*e^3 + 664832*a^4*b^12*c^8*d^12*e^4 - 75264*a^4*b^13*c
^7*d^11*e^5 - 315392*a^4*b^14*c^6*d^10*e^6 + 216832*a^4*b^15*c^5*d^9*e^7 - 12474*a^4*b^16*c^4*d^8*e^8 - 28952*
a^4*b^17*c^3*d^7*e^9 + 4004*a^4*b^18*c^2*d^6*e^10 - 1462272*a^5*b^8*c^11*d^14*e^2 + 2207744*a^5*b^9*c^10*d^13*
e^3 - 1103872*a^5*b^10*c^9*d^12*e^4 - 1204224*a^5*b^11*c^8*d^11*e^5 + 1931776*a^5*b^12*c^7*d^10*e^6 - 670208*a
^5*b^13*c^6*d^9*e^7 - 310464*a^5*b^14*c^5*d^8*e^8 + 216832*a^5*b^15*c^4*d^7*e^9 + 11704*a^5*b^16*c^3*d^6*e^10
- 16296*a^5*b^17*c^2*d^5*e^11 + 2752512*a^6*b^6*c^12*d^14*e^2 - 3211264*a^6*b^7*c^11*d^13*e^3 - 1103872*a^6*b^
8*c^10*d^12*e^4 + 6623232*a^6*b^9*c^9*d^11*e^5 - 5519360*a^6*b^10*c^8*d^10*e^6 - 315392*a^6*b^11*c^7*d^9*e^7 +
2454144*a^6*b^12*c^6*d^8*e^8 - 670208*a^6*b^13*c^5*d^7*e^9 - 315392*a^6*b^14*c^4*d^6*e^10 + 80640*a^6*b^15*c^
3*d^5*e^11 + 26012*a^6*b^16*c^2*d^4*e^12 - 2752512*a^7*b^4*c^13*d^14*e^2 + 917504*a^7*b^5*c^12*d^13*e^3 + 8486
912*a^7*b^6*c^11*d^12*e^4 - 15138816*a^7*b^7*c^10*d^11*e^5 + 5361664*a^7*b^8*c^9*d^10*e^6 + 8876032*a^7*b^9*c^
8*d^9*e^7 - 8008704*a^7*b^10*c^7*d^8*e^8 - 315392*a^7*b^11*c^6*d^7*e^9 + 1931776*a^7*b^12*c^5*d^6*e^10 - 75264
*a^7*b^13*c^4*d^5*e^11 - 176512*a^7*b^14*c^3*d^4*e^12 - 23296*a^7*b^15*c^2*d^3*e^13 + 786432*a^8*b^2*c^14*d^14
*e^2 + 3670016*a^8*b^3*c^13*d^13*e^3 - 14221312*a^8*b^4*c^12*d^12*e^4 + 13762560*a^8*b^5*c^11*d^11*e^5 + 10092
544*a^8*b^6*c^10*d^10*e^6 - 26673152*a^8*b^7*c^9*d^9*e^7 + 10036224*a^8*b^8*c^8*d^8*e^8 + 8876032*a^8*b^9*c^7*
d^7*e^9 - 5519360*a^8*b^10*c^6*d^6*e^10 - 1204224*a^8*b^11*c^5*d^5*e^11 + 664832*a^8*b^12*c^4*d^4*e^12 + 17561
6*a^8*b^13*c^3*d^3*e^13 + 12288*a^8*b^14*c^2*d^2*e^14 + 7340032*a^9*b^2*c^13*d^12*e^4 + 3670016*a^9*b^3*c^12*d
^11*e^5 - 30277632*a^9*b^4*c^11*d^10*e^6 + 30277632*a^9*b^5*c^10*d^9*e^7 + 8830976*a^9*b^6*c^9*d^8*e^8 - 26673
152*a^9*b^7*c^8*d^7*e^9 + 5361664*a^9*b^8*c^7*d^6*e^10 + 6623232*a^9*b^9*c^6*d^5*e^11 - 1103872*a^9*b^10*c^5*d
^4*e^12 - 802816*a^9*b^11*c^4*d^3*e^13 - 96768*a^9*b^12*c^3*d^2*e^14 + 20185088*a^10*b^2*c^12*d^10*e^6 - 37847
040*a^10*b^4*c^10*d^8*e^8 + 30277632*a^10*b^5*c^9*d^7*e^9 + 10092544*a^10*b^6*c^8*d^6*e^10 - 15138816*a^10*b^7
*c^7*d^5*e^11 - 1103872*a^10*b^8*c^6*d^4*e^12 + 2207744*a^10*b^9*c^5*d^3*e^13 + 473088*a^10*b^10*c^4*d^2*e^14
+ 27525120*a^11*b^2*c^11*d^8*e^8 - 30277632*a^11*b^4*c^9*d^6*e^10 + 13762560*a^11*b^5*c^8*d^5*e^11 + 8486912*a
^11*b^6*c^7*d^4*e^12 - 3211264*a^11*b^7*c^6*d^3*e^13 - 1462272*a^11*b^8*c^5*d^2*e^14 + 20185088*a^12*b^2*c^10*
d^6*e^10 + 3670016*a^12*b^3*c^9*d^5*e^11 - 14221312*a^12*b^4*c^8*d^4*e^12 + 917504*a^12*b^5*c^7*d^3*e^13 + 275
2512*a^12*b^6*c^6*d^2*e^14 + 7340032*a^13*b^2*c^9*d^4*e^12 + 3670016*a^13*b^3*c^8*d^3*e^13 - 2752512*a^13*b^4*
c^7*d^2*e^14 + 786432*a^14*b^2*c^8*d^2*e^14 + 256*a*b^15*c^8*d^15*e + 24*a*b^22*c*d^8*e^8 - 524288*a^8*b*c^15*
d^15*e + 256*a^8*b^15*c*d*e^15 - 524288*a^15*b*c^8*d*e^15 - 888*a*b^16*c^7*d^14*e^2 + 1736*a*b^17*c^6*d^13*e^3
- 2072*a*b^18*c^5*d^12*e^4 + 1512*a*b^19*c^4*d^11*e^5 - 616*a*b^20*c^3*d^10*e^6 + 88*a*b^21*c^2*d^9*e^7 - 358
4*a^2*b^13*c^9*d^15*e + 88*a^2*b^21*c*d^7*e^9 + 28672*a^3*b^11*c^10*d^15*e - 616*a^3*b^20*c*d^6*e^10 - 143360*
a^4*b^9*c^11*d^15*e + 1512*a^4*b^19*c*d^5*e^11 + 458752*a^5*b^7*c^12*d^15*e - 2072*a^5*b^18*c*d^4*e^12 - 91750
4*a^6*b^5*c^13*d^15*e + 1736*a^6*b^17*c*d^3*e^13 + 1048576*a^7*b^3*c^14*d^15*e - 888*a^7*b^16*c*d^2*e^14 - 367
0016*a^9*b*c^14*d^13*e^3 - 3584*a^9*b^13*c^2*d*e^15 - 11010048*a^10*b*c^13*d^11*e^5 + 28672*a^10*b^11*c^3*d*e^
15 - 18350080*a^11*b*c^12*d^9*e^7 - 143360*a^11*b^9*c^4*d*e^15 - 18350080*a^12*b*c^11*d^7*e^9 + 458752*a^12*b^
7*c^5*d*e^15 - 11010048*a^13*b*c^10*d^5*e^11 - 917504*a^13*b^5*c^6*d*e^15 - 3670016*a^14*b*c^9*d^3*e^13 + 1048
576*a^14*b^3*c^7*d*e^15))*root(330301440*a^14*b*c^13*d^9*e^11*z^3 + 330301440*a^13*b*c^14*d^11*e^9*z^3 + 22020
0960*a^15*b*c^12*d^7*e^13*z^3 + 220200960*a^12*b*c^15*d^13*e^7*z^3 + 94371840*a^16*b*c^11*d^5*e^15*z^3 + 94371
840*a^11*b*c^16*d^15*e^5*z^3 + 23592960*a^17*b*c^10*d^3*e^17*z^3 + 23592960*a^10*b*c^17*d^17*e^3*z^3 - 5898240
*a^17*b^3*c^8*d*e^19*z^3 + 5898240*a^16*b^5*c^7*d*e^19*z^3 - 5898240*a^8*b^3*c^17*d^19*e*z^3 + 5898240*a^7*b^5
*c^16*d^19*e*z^3 - 3440640*a^15*b^7*c^6*d*e^19*z^3 - 3440640*a^6*b^7*c^15*d^19*e*z^3 + 1290240*a^14*b^9*c^5*d*
e^19*z^3 + 1290240*a^5*b^9*c^14*d^19*e*z^3 - 322560*a^13*b^11*c^4*d*e^19*z^3 - 322560*a^4*b^11*c^13*d^19*e*z^3
+ 53760*a^12*b^13*c^3*d*e^19*z^3 + 53760*a^3*b^13*c^12*d^19*e*z^3 + 8232*a^6*b^21*c*d^5*e^15*z^3 + 8232*a*b^2
1*c^6*d^15*e^5*z^3 - 7200*a^7*b^20*c*d^4*e^16*z^3 - 7200*a*b^20*c^7*d^16*e^4*z^3 - 6300*a^5*b^22*c*d^6*e^14*z^
3 - 6300*a*b^22*c^5*d^14*e^6*z^3 - 5760*a^11*b^15*c^2*d*e^19*z^3 - 5760*a^2*b^15*c^11*d^19*e*z^3 + 4230*a^8*b^
19*c*d^3*e^17*z^3 + 4230*a*b^19*c^8*d^17*e^3*z^3 + 3060*a^4*b^23*c*d^7*e^13*z^3 + 3060*a*b^23*c^4*d^13*e^7*z^3
- 1610*a^9*b^18*c*d^2*e^18*z^3 - 1610*a*b^18*c^9*d^18*e^2*z^3 - 780*a^3*b^24*c*d^8*e^12*z^3 - 780*a*b^24*c^3*
d^12*e^8*z^3 + 2621440*a^18*b*c^9*d*e^19*z^3 + 2621440*a^9*b*c^18*d^19*e*z^3 + 360*a^10*b^17*c*d*e^19*z^3 + 36
0*a*b^17*c^10*d^19*e*z^3 + 54*a*b^26*c*d^10*e^10*z^3 - 1073479680*a^12*b^5*c^11*d^9*e^11*z^3 - 1073479680*a^11
*b^5*c^12*d^11*e^9*z^3 - 706387968*a^10*b^8*c^10*d^10*e^10*z^3 - 677117952*a^13*b^2*c^13*d^10*e^10*z^3 - 66060
2880*a^13*b^5*c^10*d^7*e^13*z^3 - 660602880*a^10*b^5*c^13*d^13*e^7*z^3 + 651755520*a^11*b^7*c^10*d^9*e^11*z^3
+ 651755520*a^10*b^7*c^11*d^11*e^9*z^3 + 608305152*a^12*b^4*c^12*d^10*e^10*z^3 - 536739840*a^14*b^2*c^12*d^8*e
^12*z^3 + 536739840*a^13*b^4*c^11*d^8*e^12*z^3 - 536739840*a^12*b^2*c^14*d^12*e^8*z^3 + 536739840*a^11*b^4*c^1
3*d^12*e^8*z^3 - 534343680*a^11*b^8*c^9*d^8*e^12*z^3 - 534343680*a^9*b^8*c^11*d^12*e^8*z^3 + 485621760*a^12*b^
7*c^9*d^7*e^13*z^3 + 485621760*a^9*b^7*c^12*d^13*e^7*z^3 + 375717888*a^11*b^6*c^11*d^10*e^10*z^3 + 357826560*a
^13*b^3*c^12*d^9*e^11*z^3 + 357826560*a^12*b^3*c^13*d^11*e^9*z^3 + 356415488*a^9*b^10*c^9*d^10*e^10*z^3 + 3420
97920*a^14*b^4*c^10*d^6*e^14*z^3 + 342097920*a^10*b^4*c^14*d^14*e^6*z^3 + 296524800*a^10*b^10*c^8*d^8*e^12*z^3
+ 296524800*a^8*b^10*c^10*d^12*e^8*z^3 - 259522560*a^15*b^2*c^11*d^6*e^14*z^3 - 259522560*a^11*b^2*c^15*d^14*
e^6*z^3 + 223641600*a^12*b^6*c^10*d^8*e^12*z^3 + 223641600*a^10*b^6*c^12*d^12*e^8*z^3 + 222953472*a^13*b^7*c^8
*d^5*e^15*z^3 + 222953472*a^8*b^7*c^13*d^15*e^5*z^3 - 217055232*a^14*b^5*c^9*d^5*e^15*z^3 - 217055232*a^9*b^5*
c^14*d^15*e^5*z^3 - 201277440*a^12*b^8*c^8*d^6*e^14*z^3 - 201277440*a^8*b^8*c^12*d^14*e^6*z^3 + 165150720*a^14
*b^3*c^11*d^7*e^13*z^3 + 165150720*a^11*b^3*c^14*d^13*e^7*z^3 - 159344640*a^9*b^11*c^8*d^9*e^11*z^3 - 15934464
0*a^8*b^11*c^9*d^11*e^9*z^3 + 150958080*a^11*b^10*c^7*d^6*e^14*z^3 + 150958080*a^7*b^10*c^11*d^14*e^6*z^3 + 13
0744320*a^15*b^4*c^9*d^4*e^16*z^3 + 130744320*a^9*b^4*c^15*d^16*e^4*z^3 - 93929472*a^12*b^9*c^7*d^5*e^15*z^3 -
93929472*a^7*b^9*c^12*d^15*e^5*z^3 - 86261760*a^11*b^9*c^8*d^7*e^13*z^3 - 86261760*a^8*b^9*c^11*d^13*e^7*z^3
+ 78474240*a^8*b^13*c^7*d^9*e^11*z^3 + 78474240*a^7*b^13*c^8*d^11*e^9*z^3 - 72990720*a^14*b^6*c^8*d^4*e^16*z^3
- 72990720*a^8*b^6*c^14*d^16*e^4*z^3 - 67829760*a^16*b^2*c^10*d^4*e^16*z^3 - 67829760*a^10*b^2*c^16*d^16*e^4*
z^3 - 64696320*a^10*b^11*c^7*d^7*e^13*z^3 - 64696320*a^7*b^11*c^10*d^13*e^7*z^3 - 63797760*a^9*b^12*c^7*d^8*e^
12*z^3 - 63797760*a^7*b^12*c^9*d^12*e^8*z^3 - 60622848*a^8*b^12*c^8*d^10*e^10*z^3 - 50319360*a^10*b^12*c^6*d^6
*e^14*z^3 - 50319360*a^6*b^12*c^10*d^14*e^6*z^3 + 44513280*a^9*b^13*c^6*d^7*e^13*z^3 + 44513280*a^6*b^13*c^9*d
^13*e^7*z^3 + 39813120*a^14*b^7*c^7*d^3*e^17*z^3 + 39813120*a^7*b^7*c^14*d^17*e^3*z^3 - 29675520*a^13*b^9*c^6*
d^3*e^17*z^3 - 29675520*a^6*b^9*c^13*d^17*e^3*z^3 + 27256320*a^12*b^10*c^6*d^4*e^16*z^3 + 27256320*a^6*b^10*c^
12*d^16*e^4*z^3 - 23101440*a^15*b^6*c^7*d^2*e^18*z^3 - 23101440*a^7*b^6*c^15*d^18*e^2*z^3 - 21626880*a^16*b^3*
c^9*d^3*e^17*z^3 - 21626880*a^9*b^3*c^16*d^17*e^3*z^3 + 20643840*a^16*b^4*c^8*d^2*e^18*z^3 + 20643840*a^8*b^4*
c^16*d^18*e^2*z^3 - 17694720*a^15*b^5*c^8*d^3*e^17*z^3 - 17694720*a^8*b^5*c^15*d^17*e^3*z^3 - 16423680*a^7*b^1
5*c^6*d^9*e^11*z^3 - 16423680*a^6*b^15*c^7*d^11*e^9*z^3 - 15724800*a^11*b^12*c^5*d^4*e^16*z^3 - 15724800*a^5*b
^12*c^11*d^16*e^4*z^3 + 14192640*a^14*b^8*c^6*d^2*e^18*z^3 + 14192640*a^6*b^8*c^14*d^18*e^2*z^3 - 13762560*a^1
3*b^6*c^9*d^6*e^14*z^3 - 13762560*a^9*b^6*c^13*d^14*e^6*z^3 - 13508352*a^7*b^14*c^7*d^10*e^10*z^3 + 12579840*a
^12*b^11*c^5*d^3*e^17*z^3 + 12579840*a^5*b^11*c^12*d^17*e^3*z^3 - 12096000*a^8*b^15*c^5*d^7*e^13*z^3 - 1209600
0*a^5*b^15*c^8*d^13*e^7*z^3 + 10063872*a^11*b^11*c^6*d^5*e^15*z^3 + 10063872*a^6*b^11*c^11*d^15*e^5*z^3 + 8600
592*a^6*b^16*c^6*d^10*e^10*z^3 + 7864320*a^15*b^3*c^10*d^5*e^15*z^3 + 7864320*a^10*b^3*c^15*d^15*e^5*z^3 + 735
4368*a^10*b^13*c^5*d^5*e^15*z^3 + 7354368*a^5*b^13*c^10*d^15*e^5*z^3 + 6842880*a^9*b^14*c^5*d^6*e^14*z^3 + 684
2880*a^5*b^14*c^9*d^14*e^6*z^3 - 5898240*a^17*b^2*c^9*d^2*e^18*z^3 - 5898240*a^9*b^2*c^17*d^18*e^2*z^3 - 58572
80*a^10*b^9*c^9*d^9*e^11*z^3 - 5857280*a^9*b^9*c^10*d^11*e^9*z^3 - 5806080*a^13*b^8*c^7*d^4*e^16*z^3 - 5806080
*a^7*b^8*c^13*d^16*e^4*z^3 + 5798520*a^7*b^16*c^5*d^8*e^12*z^3 + 5798520*a^5*b^16*c^7*d^12*e^8*z^3 - 5483520*a
^13*b^10*c^5*d^2*e^18*z^3 - 5483520*a^5*b^10*c^13*d^18*e^2*z^3 + 4864320*a^10*b^14*c^4*d^4*e^16*z^3 + 4864320*
a^4*b^14*c^10*d^16*e^4*z^3 - 4717440*a^8*b^14*c^6*d^8*e^12*z^3 - 4717440*a^6*b^14*c^8*d^12*e^8*z^3 - 3820032*a
^9*b^15*c^4*d^5*e^15*z^3 - 3820032*a^4*b^15*c^9*d^15*e^5*z^3 - 3386880*a^11*b^13*c^4*d^3*e^17*z^3 - 3386880*a^
4*b^13*c^11*d^17*e^3*z^3 - 1693692*a^5*b^18*c^5*d^10*e^10*z^3 + 1481760*a^7*b^17*c^4*d^7*e^13*z^3 + 1481760*a^
4*b^17*c^7*d^13*e^7*z^3 + 1397760*a^12*b^12*c^4*d^2*e^18*z^3 + 1397760*a^4*b^12*c^12*d^18*e^2*z^3 - 1340430*a^
6*b^18*c^4*d^8*e^12*z^3 - 1340430*a^4*b^18*c^6*d^12*e^8*z^3 - 923220*a^9*b^16*c^3*d^4*e^16*z^3 - 923220*a^3*b^
16*c^9*d^16*e^4*z^3 + 883872*a^8*b^17*c^3*d^5*e^15*z^3 + 883872*a^3*b^17*c^8*d^15*e^5*z^3 + 851760*a^6*b^17*c^
5*d^9*e^11*z^3 + 851760*a^5*b^17*c^6*d^11*e^9*z^3 + 721440*a^8*b^16*c^4*d^6*e^14*z^3 + 721440*a^4*b^16*c^8*d^1
4*e^6*z^3 + 593280*a^10*b^15*c^3*d^3*e^17*z^3 + 593280*a^3*b^15*c^10*d^17*e^3*z^3 - 448440*a^7*b^18*c^3*d^6*e^
14*z^3 - 448440*a^3*b^18*c^7*d^14*e^6*z^3 + 311220*a^5*b^19*c^4*d^9*e^11*z^3 + 311220*a^4*b^19*c^5*d^11*e^9*z^
3 - 236160*a^11*b^14*c^3*d^2*e^18*z^3 - 236160*a^3*b^14*c^11*d^18*e^2*z^3 + 131040*a^5*b^20*c^3*d^8*e^12*z^3 +
131040*a^3*b^20*c^5*d^12*e^8*z^3 + 126126*a^4*b^20*c^4*d^10*e^10*z^3 - 115272*a^7*b^19*c^2*d^5*e^15*z^3 - 115
272*a^2*b^19*c^7*d^15*e^5*z^3 + 108045*a^8*b^18*c^2*d^4*e^16*z^3 + 108045*a^2*b^18*c^8*d^16*e^4*z^3 + 76860*a^
6*b^20*c^2*d^6*e^14*z^3 + 76860*a^2*b^20*c^6*d^14*e^6*z^3 - 67080*a^4*b^21*c^3*d^9*e^11*z^3 - 67080*a^3*b^21*c
^4*d^11*e^9*z^3 - 65880*a^9*b^17*c^2*d^3*e^17*z^3 - 65880*a^2*b^17*c^9*d^17*e^3*z^3 - 26280*a^5*b^21*c^2*d^7*e
^13*z^3 - 26280*a^2*b^21*c^5*d^13*e^7*z^3 + 25560*a^10*b^16*c^2*d^2*e^18*z^3 + 25560*a^2*b^16*c^10*d^18*e^2*z^
3 + 9240*a^6*b^19*c^3*d^7*e^13*z^3 + 9240*a^3*b^19*c^6*d^13*e^7*z^3 + 5304*a^3*b^22*c^3*d^10*e^10*z^3 + 4680*a
^3*b^23*c^2*d^9*e^11*z^3 + 4680*a^2*b^23*c^3*d^11*e^9*z^3 - 1404*a^2*b^24*c^2*d^10*e^10*z^3 - 1170*a^4*b^22*c^
2*d^8*e^12*z^3 - 1170*a^2*b^22*c^4*d^12*e^8*z^3 - 10*b^27*c*d^11*e^9*z^3 - 10*b^19*c^9*d^19*e*z^3 - 10*a^9*b^1
9*d*e^19*z^3 - 10*a*b^27*d^9*e^11*z^3 - 36*a^11*b^16*c*e^20*z^3 - 36*a*b^16*c^11*d^20*z^3 - 66060288*a^14*c^14
*d^10*e^10*z^3 - 55050240*a^15*c^13*d^8*e^12*z^3 - 55050240*a^13*c^15*d^12*e^8*z^3 - 31457280*a^16*c^12*d^6*e^
14*z^3 - 31457280*a^12*c^16*d^14*e^6*z^3 - 252*b^23*c^5*d^15*e^5*z^3 + 210*b^24*c^4*d^14*e^6*z^3 + 210*b^22*c^
6*d^16*e^4*z^3 - 120*b^25*c^3*d^13*e^7*z^3 - 120*b^21*c^7*d^17*e^3*z^3 + 45*b^26*c^2*d^12*e^8*z^3 + 45*b^20*c^
8*d^18*e^2*z^3 - 11796480*a^17*c^11*d^4*e^16*z^3 - 11796480*a^11*c^17*d^16*e^4*z^3 - 2621440*a^18*c^10*d^2*e^1
8*z^3 - 2621440*a^10*c^18*d^18*e^2*z^3 - 252*a^5*b^23*d^5*e^15*z^3 + 210*a^6*b^22*d^4*e^16*z^3 + 210*a^4*b^24*
d^6*e^14*z^3 - 120*a^7*b^21*d^3*e^17*z^3 - 120*a^3*b^25*d^7*e^13*z^3 + 45*a^8*b^20*d^2*e^18*z^3 + 45*a^2*b^26*
d^8*e^12*z^3 + 589824*a^18*b^2*c^8*e^20*z^3 - 589824*a^17*b^4*c^7*e^20*z^3 + 344064*a^16*b^6*c^6*e^20*z^3 - 12
9024*a^15*b^8*c^5*e^20*z^3 + 32256*a^14*b^10*c^4*e^20*z^3 - 5376*a^13*b^12*c^3*e^20*z^3 + 576*a^12*b^14*c^2*e^
20*z^3 + 589824*a^8*b^2*c^18*d^20*z^3 - 589824*a^7*b^4*c^17*d^20*z^3 + 344064*a^6*b^6*c^16*d^20*z^3 - 129024*a
^5*b^8*c^15*d^20*z^3 + 32256*a^4*b^10*c^14*d^20*z^3 - 5376*a^3*b^12*c^13*d^20*z^3 + 576*a^2*b^14*c^12*d^20*z^3
- 262144*a^19*c^9*e^20*z^3 - 262144*a^9*c^19*d^20*z^3 + b^28*d^10*e^10*z^3 + b^18*c^10*d^20*z^3 + a^10*b^18*e
^20*z^3 + 403200*a*b*c^16*d^15*e^3*z + 396900*a^8*b*c^9*d*e^17*z - 12071430*a^4*b^2*c^12*d^8*e^10*z + 11880120
*a^3*b^3*c^12*d^9*e^9*z + 10349640*a^4*b^3*c^11*d^7*e^11*z - 9657144*a^3*b^2*c^13*d^10*e^8*z - 9578520*a^5*b^2
*c^11*d^6*e^12*z + 7733880*a^2*b^3*c^13*d^11*e^7*z - 7329420*a^3*b^4*c^11*d^8*e^10*z - 7012656*a^2*b^4*c^12*d^
10*e^8*z - 4859820*a^2*b^2*c^14*d^12*e^6*z + 4604040*a^5*b^3*c^10*d^5*e^13*z - 4365900*a^6*b^2*c^10*d^4*e^14*z
+ 3448620*a^2*b^5*c^11*d^9*e^9*z - 3069360*a^4*b^4*c^10*d^6*e^12*z + 1723680*a^3*b^5*c^10*d^7*e^11*z - 793800
*a^7*b^2*c^9*d^2*e^16*z - 754110*a^2*b^6*c^10*d^8*e^10*z + 529200*a^6*b^4*c^8*d^2*e^16*z - 460404*a^4*b^5*c^9*
d^5*e^13*z + 441000*a^6*b^3*c^9*d^3*e^15*z - 423360*a^5*b^5*c^8*d^3*e^15*z + 396900*a^5*b^4*c^9*d^4*e^14*z - 1
58760*a^5*b^6*c^7*d^2*e^16*z + 143640*a^4*b^7*c^7*d^3*e^15*z + 123984*a^3*b^7*c^8*d^5*e^13*z + 61560*a^2*b^7*c
^9*d^7*e^11*z - 45360*a^3*b^8*c^7*d^4*e^14*z - 30240*a^2*b^8*c^8*d^6*e^12*z + 26460*a^4*b^6*c^8*d^4*e^14*z + 2
2680*a^4*b^8*c^6*d^2*e^16*z - 21840*a^3*b^9*c^6*d^3*e^15*z + 17640*a^3*b^6*c^9*d^6*e^12*z - 10584*a^2*b^9*c^7*
d^5*e^13*z + 9450*a^2*b^10*c^6*d^4*e^14*z - 1260*a^3*b^10*c^5*d^2*e^16*z + 1260*a^2*b^11*c^5*d^3*e^15*z + 6894
720*a^5*b*c^12*d^7*e^11*z + 6322680*a^4*b*c^13*d^9*e^9*z + 4974480*a^6*b*c^11*d^5*e^13*z + 3971520*a^3*b*c^14*
d^11*e^7*z - 3178980*a*b^4*c^13*d^12*e^6*z + 2703960*a*b^3*c^14*d^13*e^5*z + 2268000*a*b^5*c^12*d^11*e^7*z + 2
116800*a^7*b*c^10*d^3*e^15*z + 1648080*a^2*b*c^15*d^13*e^5*z - 1394280*a*b^2*c^15*d^14*e^4*z - 910224*a*b^6*c^
11*d^10*e^8*z - 264600*a^7*b^3*c^8*d*e^17*z + 157500*a*b^7*c^10*d^9*e^9*z + 79380*a^6*b^5*c^7*d*e^17*z - 11340
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56*a*b^11*c^6*d^5*e^13*z + 630*a^4*b^9*c^5*d*e^17*z - 630*a*b^12*c^5*d^4*e^14*z - 573840*b^4*c^14*d^14*e^4*z +
532980*b^5*c^13*d^13*e^5*z + 399000*b^3*c^15*d^15*e^3*z - 312480*b^6*c^12*d^12*e^6*z - 174825*b^2*c^16*d^16*e
^2*z + 105840*b^7*c^11*d^11*e^7*z - 15876*b^8*c^10*d^10*e^8*z + 540*b^11*c^7*d^7*e^11*z - 420*b^12*c^6*d^6*e^1
2*z - 315*b^10*c^8*d^8*e^10*z + 126*b^13*c^5*d^5*e^13*z + 70*b^9*c^9*d^9*e^9*z - 1723680*a^5*c^13*d^8*e^10*z -
1658160*a^6*c^12*d^6*e^12*z - 1264536*a^4*c^14*d^10*e^8*z - 1058400*a^7*c^11*d^4*e^14*z - 661920*a^3*c^15*d^1
2*e^6*z - 396900*a^8*c^10*d^2*e^16*z - 235440*a^2*c^16*d^14*e^4*z + 574668*a^7*b^4*c^7*e^18*z - 541593*a^8*b^2
*c^8*e^18*z - 341838*a^6*b^6*c^6*e^18*z + 128898*a^5*b^8*c^5*e^18*z - 32256*a^4*b^10*c^4*e^18*z + 5376*a^3*b^1
2*c^3*e^18*z - 576*a^2*b^14*c^2*e^18*z - 50400*a*c^17*d^16*e^2*z + 44100*b*c^17*d^17*e*z + 36*a*b^16*c*e^18*z
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^13 + 23445*a^2*b^3*c^8*d*e^16 - 7810*a*b^3*c^9*d^3*e^14 - 5445*a*b^4*c^8*d^2*e^15 - 77700*a*b*c^11*d^5*e^12 -
69220*a^3*b*c^9*d*e^16 - 3600*a*b^5*c^7*d*e^16 + 33495*a^2*b^2*c^9*d^2*e^15 + 27825*b^2*c^11*d^6*e^11 - 14875
*b^3*c^10*d^5*e^12 + 715*b^4*c^9*d^4*e^13 + 495*b^5*c^8*d^3*e^14 + 330*b^6*c^7*d^2*e^15 + 69220*a^3*c^10*d^2*e
^15 + 56940*a^2*c^11*d^4*e^13 - 48231*a^3*b^2*c^8*e^17 + 15156*a^2*b^4*c^7*e^17 - 19600*b*c^12*d^7*e^10 + 210*
b^7*c^6*d*e^16 + 25900*a*c^12*d^6*e^11 - 2226*a*b^6*c^6*e^17 + 4900*c^13*d^8*e^9 + 126*b^8*c^5*e^17 + 65536*a^
4*c^9*e^17, z, k), k, 1, 3)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x+d)/(c*x**2+b*x+a)**5,x)

[Out]

Timed out

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