\(\int \frac {f+g x}{(d+e x)^2 (a+b x+c x^2)^3} \, dx\) [2377]

Optimal result

Integrand size = 25, antiderivative size = 1043 \[ \int \frac {f+g x}{(d+e x)^2 \left (a+b x+c x^2\right )^3} \, dx=\frac {e \left (6 c^4 d^4 f-b^3 e^3 (3 b e f-2 b d g-a e g)-b c e^2 \left (7 a^2 e^2 g-a b e (21 e f-13 d g)-3 b^2 d (e f-d g)\right )+c^3 d^2 (4 a e (6 e f-d g)-3 b d (4 e f+d g))-c^2 e \left (2 a^2 e^2 (15 e f-22 d g)+6 a b d e (4 e f+d g)-b^2 d^2 (3 e f+7 d g)\right )\right )}{\left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^3 (d+e x)}-\frac {b c d f-b^2 e f+2 a c e f-2 a c d g+a b e g+c (2 c d f+2 a e g-b (e f+d g)) x}{2 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) (d+e x) \left (a+b x+c x^2\right )^2}-\frac {4 a c e (2 c d-b e) (2 c d f+2 a e g-b (e f+d g))-\left (b c d-b^2 e+2 a c e\right ) \left (6 c^2 d^2 f-b e (3 b e f-2 b d g-a e g)+c (2 a e (5 e f-2 d g)-b d (2 e f+3 d g))\right )-c \left (12 c^3 d^3 f+b^2 e^2 (3 b e f-2 b d g-a e g)+2 c^2 d (2 a e (9 e f-2 d g)-3 b d (3 e f+d g))+c e \left (11 b^2 d^2 g+16 a^2 e^2 g-2 a b e (9 e f+5 d g)\right )\right ) x}{2 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2 (d+e x) \left (a+b x+c x^2\right )}-\frac {\left (12 c^6 d^6 f+b^5 e^5 (3 b e f-2 b d g-a e g)+b^3 c e^4 \left (10 a^2 e^2 g-b^2 d (6 e f-5 d g)-10 a b e (3 e f-2 d g)\right )-10 a b c^2 e^4 \left (3 a^2 e^2 g-b^2 d (6 e f-5 d g)-3 a b e (3 e f-2 d g)\right )-10 c^3 e^2 \left (2 b^3 d^4 g-8 a b^2 d^3 e g+6 a^3 e^3 (e f-2 d g)+3 a^2 b d e^2 (6 e f-d g)\right )+2 c^5 d^4 (2 a e (15 e f-2 d g)-3 b d (6 e f+d g))+10 c^4 d^2 e \left (2 a^2 e^2 (9 e f-4 d g)-a b d e (12 e f+d g)+b^2 d^2 (3 e f+2 d g)\right )\right ) \text {arctanh}\left (\frac {b+2 c x}{\sqrt {b^2-4 a c}}\right )}{\left (b^2-4 a c\right )^{5/2} \left (c d^2-b d e+a e^2\right )^4}+\frac {e^4 (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log (d+e x)}{\left (c d^2-b d e+a e^2\right )^4}-\frac {e^4 (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log \left (a+b x+c x^2\right )}{2 \left (c d^2-b d e+a e^2\right )^4} \]

[Out]

e*(6*c^4*d^4*f-b^3*e^3*(-a*e*g-2*b*d*g+3*b*e*f)-b*c*e^2*(7*a^2*e^2*g-a*b*e*(-13*d*g+21*e*f)-3*b^2*d*(-d*g+e*f)
)+c^3*d^2*(4*a*e*(-d*g+6*e*f)-3*b*d*(d*g+4*e*f))-c^2*e*(2*a^2*e^2*(-22*d*g+15*e*f)+6*a*b*d*e*(d*g+4*e*f)-b^2*d
^2*(7*d*g+3*e*f)))/(-4*a*c+b^2)^2/(a*e^2-b*d*e+c*d^2)^3/(e*x+d)+1/2*(-b*c*d*f+b^2*e*f-2*a*c*e*f+2*a*c*d*g-a*b*
e*g-c*(2*c*d*f+2*a*e*g-b*(d*g+e*f))*x)/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/(e*x+d)/(c*x^2+b*x+a)^2+1/2*(-4*a*c*e*
(-b*e+2*c*d)*(2*c*d*f+2*a*e*g-b*(d*g+e*f))+(2*a*c*e-b^2*e+b*c*d)*(6*c^2*d^2*f-b*e*(-a*e*g-2*b*d*g+3*b*e*f)+c*(
2*a*e*(-2*d*g+5*e*f)-b*d*(3*d*g+2*e*f)))+c*(12*c^3*d^3*f+b^2*e^2*(-a*e*g-2*b*d*g+3*b*e*f)+2*c^2*d*(2*a*e*(-2*d
*g+9*e*f)-3*b*d*(d*g+3*e*f))+c*e*(11*b^2*d^2*g+16*a^2*e^2*g-2*a*b*e*(5*d*g+9*e*f)))*x)/(-4*a*c+b^2)^2/(a*e^2-b
*d*e+c*d^2)^2/(e*x+d)/(c*x^2+b*x+a)-(12*c^6*d^6*f+b^5*e^5*(-a*e*g-2*b*d*g+3*b*e*f)+b^3*c*e^4*(10*a^2*e^2*g-b^2
*d*(-5*d*g+6*e*f)-10*a*b*e*(-2*d*g+3*e*f))-10*a*b*c^2*e^4*(3*a^2*e^2*g-b^2*d*(-5*d*g+6*e*f)-3*a*b*e*(-2*d*g+3*
e*f))-10*c^3*e^2*(2*b^3*d^4*g-8*a*b^2*d^3*e*g+6*a^3*e^3*(-2*d*g+e*f)+3*a^2*b*d*e^2*(-d*g+6*e*f))+2*c^5*d^4*(2*
a*e*(-2*d*g+15*e*f)-3*b*d*(d*g+6*e*f))+10*c^4*d^2*e*(2*a^2*e^2*(-4*d*g+9*e*f)-a*b*d*e*(d*g+12*e*f)+b^2*d^2*(2*
d*g+3*e*f)))*arctanh((2*c*x+b)/(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(5/2)/(a*e^2-b*d*e+c*d^2)^4+e^4*(c*d*(-5*d*g+6
*e*f)-e*(-a*e*g-2*b*d*g+3*b*e*f))*ln(e*x+d)/(a*e^2-b*d*e+c*d^2)^4-1/2*e^4*(c*d*(-5*d*g+6*e*f)-e*(-a*e*g-2*b*d*
g+3*b*e*f))*ln(c*x^2+b*x+a)/(a*e^2-b*d*e+c*d^2)^4

Rubi [A] (verified)

Time = 4.25 (sec) , antiderivative size = 1043, normalized size of antiderivative = 1.00, number of steps used = 8, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.240, Rules used = {836, 814, 648, 632, 212, 642} \[ \int \frac {f+g x}{(d+e x)^2 \left (a+b x+c x^2\right )^3} \, dx=\frac {(c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log (d+e x) e^4}{\left (c d^2-b e d+a e^2\right )^4}-\frac {(c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log \left (c x^2+b x+a\right ) e^4}{2 \left (c d^2-b e d+a e^2\right )^4}+\frac {\left (6 c^4 f d^4+c^3 (4 a e (6 e f-d g)-3 b d (4 e f+d g)) d^2-b^3 e^3 (3 b e f-2 b d g-a e g)-b c e^2 \left (-3 d (e f-d g) b^2-a e (21 e f-13 d g) b+7 a^2 e^2 g\right )-c^2 e \left (-b^2 (3 e f+7 d g) d^2+6 a b e (4 e f+d g) d+2 a^2 e^2 (15 e f-22 d g)\right )\right ) e}{\left (b^2-4 a c\right )^2 \left (c d^2-b e d+a e^2\right )^3 (d+e x)}-\frac {\left (12 c^6 f d^6+2 c^5 (2 a e (15 e f-2 d g)-3 b d (6 e f+d g)) d^4+10 c^4 e \left (b^2 (3 e f+2 d g) d^2-a b e (12 e f+d g) d+2 a^2 e^2 (9 e f-4 d g)\right ) d^2+b^5 e^5 (3 b e f-2 b d g-a e g)+b^3 c e^4 \left (-d (6 e f-5 d g) b^2-10 a e (3 e f-2 d g) b+10 a^2 e^2 g\right )-10 a b c^2 e^4 \left (-d (6 e f-5 d g) b^2-3 a e (3 e f-2 d g) b+3 a^2 e^2 g\right )-10 c^3 e^2 \left (2 b^3 g d^4-8 a b^2 e g d^3+3 a^2 b e^2 (6 e f-d g) d+6 a^3 e^3 (e f-2 d g)\right )\right ) \text {arctanh}\left (\frac {b+2 c x}{\sqrt {b^2-4 a c}}\right )}{\left (b^2-4 a c\right )^{5/2} \left (c d^2-b e d+a e^2\right )^4}-\frac {4 a c e (2 c d-b e) (2 c d f+2 a e g-b (e f+d g))-\left (-e b^2+c d b+2 a c e\right ) \left (6 c^2 f d^2-b e (3 b e f-2 b d g-a e g)+c (2 a e (5 e f-2 d g)-b d (2 e f+3 d g))\right )-c \left (12 c^3 f d^3+2 c^2 (2 a e (9 e f-2 d g)-3 b d (3 e f+d g)) d+b^2 e^2 (3 b e f-2 b d g-a e g)+c e \left (11 b^2 g d^2+16 a^2 e^2 g-2 a b e (9 e f+5 d g)\right )\right ) x}{2 \left (b^2-4 a c\right )^2 \left (c d^2-b e d+a e^2\right )^2 (d+e x) \left (c x^2+b x+a\right )}-\frac {-e f b^2+c d f b+a e g b+2 a c e f-2 a c d g+c (2 c d f+2 a e g-b (e f+d g)) x}{2 \left (b^2-4 a c\right ) \left (c d^2-b e d+a e^2\right ) (d+e x) \left (c x^2+b x+a\right )^2} \]

[In]

Int[(f + g*x)/((d + e*x)^2*(a + b*x + c*x^2)^3),x]

[Out]

(e*(6*c^4*d^4*f - b^3*e^3*(3*b*e*f - 2*b*d*g - a*e*g) - b*c*e^2*(7*a^2*e^2*g - a*b*e*(21*e*f - 13*d*g) - 3*b^2
*d*(e*f - d*g)) + c^3*d^2*(4*a*e*(6*e*f - d*g) - 3*b*d*(4*e*f + d*g)) - c^2*e*(2*a^2*e^2*(15*e*f - 22*d*g) + 6
*a*b*d*e*(4*e*f + d*g) - b^2*d^2*(3*e*f + 7*d*g))))/((b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)) - (b
*c*d*f - b^2*e*f + 2*a*c*e*f - 2*a*c*d*g + a*b*e*g + c*(2*c*d*f + 2*a*e*g - b*(e*f + d*g))*x)/(2*(b^2 - 4*a*c)
*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*(a + b*x + c*x^2)^2) - (4*a*c*e*(2*c*d - b*e)*(2*c*d*f + 2*a*e*g - b*(e*f +
d*g)) - (b*c*d - b^2*e + 2*a*c*e)*(6*c^2*d^2*f - b*e*(3*b*e*f - 2*b*d*g - a*e*g) + c*(2*a*e*(5*e*f - 2*d*g) -
b*d*(2*e*f + 3*d*g))) - c*(12*c^3*d^3*f + b^2*e^2*(3*b*e*f - 2*b*d*g - a*e*g) + 2*c^2*d*(2*a*e*(9*e*f - 2*d*g
) - 3*b*d*(3*e*f + d*g)) + c*e*(11*b^2*d^2*g + 16*a^2*e^2*g - 2*a*b*e*(9*e*f + 5*d*g)))*x)/(2*(b^2 - 4*a*c)^2*
(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)*(a + b*x + c*x^2)) - ((12*c^6*d^6*f + b^5*e^5*(3*b*e*f - 2*b*d*g - a*e*g)
+ b^3*c*e^4*(10*a^2*e^2*g - b^2*d*(6*e*f - 5*d*g) - 10*a*b*e*(3*e*f - 2*d*g)) - 10*a*b*c^2*e^4*(3*a^2*e^2*g -
b^2*d*(6*e*f - 5*d*g) - 3*a*b*e*(3*e*f - 2*d*g)) - 10*c^3*e^2*(2*b^3*d^4*g - 8*a*b^2*d^3*e*g + 6*a^3*e^3*(e*f
- 2*d*g) + 3*a^2*b*d*e^2*(6*e*f - d*g)) + 2*c^5*d^4*(2*a*e*(15*e*f - 2*d*g) - 3*b*d*(6*e*f + d*g)) + 10*c^4*d^
2*e*(2*a^2*e^2*(9*e*f - 4*d*g) - a*b*d*e*(12*e*f + d*g) + b^2*d^2*(3*e*f + 2*d*g)))*ArcTanh[(b + 2*c*x)/Sqrt[b
^2 - 4*a*c]])/((b^2 - 4*a*c)^(5/2)*(c*d^2 - b*d*e + a*e^2)^4) + (e^4*(c*d*(6*e*f - 5*d*g) - e*(3*b*e*f - 2*b*d
*g - a*e*g))*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^4 - (e^4*(c*d*(6*e*f - 5*d*g) - e*(3*b*e*f - 2*b*d*g - a*e*
g))*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^4)

Rule 212

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

Rule 632

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 642

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 648

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 814

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 836

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*} \text {integral}& = -\frac {b c d f-b^2 e f+2 a c e f-2 a c d g+a b e g+c (2 c d f+2 a e g-b (e f+d g)) x}{2 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) (d+e x) \left (a+b x+c x^2\right )^2}-\frac {\int \frac {6 c^2 d^2 f-b e (3 b e f-2 b d g-a e g)+c (2 a e (5 e f-2 d g)-b d (2 e f+3 d g))+4 c e (2 c d f+2 a e g-b (e f+d g)) x}{(d+e x)^2 \left (a+b x+c x^2\right )^2} \, dx}{2 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right )} \\ & = -\frac {b c d f-b^2 e f+2 a c e f-2 a c d g+a b e g+c (2 c d f+2 a e g-b (e f+d g)) x}{2 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) (d+e x) \left (a+b x+c x^2\right )^2}-\frac {4 a c e (2 c d-b e) (2 c d f+2 a e g-b (e f+d g))-\left (b c d-b^2 e+2 a c e\right ) \left (6 c^2 d^2 f-b e (3 b e f-2 b d g-a e g)+c (2 a e (5 e f-2 d g)-b d (2 e f+3 d g))\right )-c \left (12 c^3 d^3 f+b^2 e^2 (3 b e f-2 b d g-a e g)+2 c^2 d (2 a e (9 e f-2 d g)-3 b d (3 e f+d g))+c e \left (11 b^2 d^2 g+16 a^2 e^2 g-2 a b e (9 e f+5 d g)\right )\right ) x}{2 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2 (d+e x) \left (a+b x+c x^2\right )}+\frac {\int \frac {-2 \left (2 c e (b d (c d-b e)+a e (4 c d-b e)) (2 c d f+2 a e g-b (e f+d g))-\frac {1}{2} \left (2 c^2 d^2-2 b^2 e^2+6 a c e^2\right ) \left (6 c^2 d^2 f-b e (3 b e f-2 b d g-a e g)+c (2 a e (5 e f-2 d g)-b d (2 e f+3 d g))\right )\right )+2 c e \left (12 c^3 d^3 f+b^2 e^2 (3 b e f-2 b d g-a e g)+2 c^2 d (2 a e (9 e f-2 d g)-3 b d (3 e f+d g))+c e \left (11 b^2 d^2 g+16 a^2 e^2 g-2 a b e (9 e f+5 d g)\right )\right ) x}{(d+e x)^2 \left (a+b x+c x^2\right )} \, dx}{2 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2} \\ & = -\frac {b c d f-b^2 e f+2 a c e f-2 a c d g+a b e g+c (2 c d f+2 a e g-b (e f+d g)) x}{2 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) (d+e x) \left (a+b x+c x^2\right )^2}-\frac {4 a c e (2 c d-b e) (2 c d f+2 a e g-b (e f+d g))-\left (b c d-b^2 e+2 a c e\right ) \left (6 c^2 d^2 f-b e (3 b e f-2 b d g-a e g)+c (2 a e (5 e f-2 d g)-b d (2 e f+3 d g))\right )-c \left (12 c^3 d^3 f+b^2 e^2 (3 b e f-2 b d g-a e g)+2 c^2 d (2 a e (9 e f-2 d g)-3 b d (3 e f+d g))+c e \left (11 b^2 d^2 g+16 a^2 e^2 g-2 a b e (9 e f+5 d g)\right )\right ) x}{2 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2 (d+e x) \left (a+b x+c x^2\right )}+\frac {\int \left (\frac {2 e^2 \left (-6 c^4 d^4 f+b^3 e^3 (3 b e f-2 b d g-a e g)+b c e^2 \left (7 a^2 e^2 g-a b e (21 e f-13 d g)-3 b^2 d (e f-d g)\right )-c^3 d^2 (4 a e (6 e f-d g)-3 b d (4 e f+d g))+c^2 e \left (2 a^2 e^2 (15 e f-22 d g)+6 a b d e (4 e f+d g)-b^2 d^2 (3 e f+7 d g)\right )\right )}{\left (c d^2-b d e+a e^2\right ) (d+e x)^2}+\frac {2 \left (b^2-4 a c\right )^2 e^5 (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g))}{\left (c d^2-b d e+a e^2\right )^2 (d+e x)}+\frac {2 \left (6 c^6 d^6 f+b^5 e^5 (3 b e f-2 b d g-a e g)-c^3 e^2 \left (10 b^3 d^4 g-40 a b^2 d^3 e g+a^2 b d e^2 (138 e f-55 d g)+30 a^3 e^3 (e f-2 d g)\right )-a b c^2 e^4 \left (23 a^2 e^2 g-9 b^2 d (6 e f-5 d g)-23 a b e (3 e f-2 d g)\right )+b^3 c e^4 \left (9 a^2 e^2 g-b^2 d (6 e f-5 d g)-9 a b e (3 e f-2 d g)\right )+c^5 d^4 (2 a e (15 e f-2 d g)-3 b d (6 e f+d g))+5 c^4 d^2 e \left (2 a^2 e^2 (9 e f-4 d g)-a b d e (12 e f+d g)+b^2 d^2 (3 e f+2 d g)\right )-c \left (b^2-4 a c\right )^2 e^4 (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) x\right )}{\left (c d^2-b d e+a e^2\right )^2 \left (a+b x+c x^2\right )}\right ) \, dx}{2 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2} \\ & = \frac {e \left (6 c^4 d^4 f-b^3 e^3 (3 b e f-2 b d g-a e g)-b c e^2 \left (7 a^2 e^2 g-a b e (21 e f-13 d g)-3 b^2 d (e f-d g)\right )+c^3 d^2 (4 a e (6 e f-d g)-3 b d (4 e f+d g))-c^2 e \left (2 a^2 e^2 (15 e f-22 d g)+6 a b d e (4 e f+d g)-b^2 d^2 (3 e f+7 d g)\right )\right )}{\left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^3 (d+e x)}-\frac {b c d f-b^2 e f+2 a c e f-2 a c d g+a b e g+c (2 c d f+2 a e g-b (e f+d g)) x}{2 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) (d+e x) \left (a+b x+c x^2\right )^2}-\frac {4 a c e (2 c d-b e) (2 c d f+2 a e g-b (e f+d g))-\left (b c d-b^2 e+2 a c e\right ) \left (6 c^2 d^2 f-b e (3 b e f-2 b d g-a e g)+c (2 a e (5 e f-2 d g)-b d (2 e f+3 d g))\right )-c \left (12 c^3 d^3 f+b^2 e^2 (3 b e f-2 b d g-a e g)+2 c^2 d (2 a e (9 e f-2 d g)-3 b d (3 e f+d g))+c e \left (11 b^2 d^2 g+16 a^2 e^2 g-2 a b e (9 e f+5 d g)\right )\right ) x}{2 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2 (d+e x) \left (a+b x+c x^2\right )}+\frac {e^4 (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log (d+e x)}{\left (c d^2-b d e+a e^2\right )^4}+\frac {\int \frac {6 c^6 d^6 f+b^5 e^5 (3 b e f-2 b d g-a e g)-c^3 e^2 \left (10 b^3 d^4 g-40 a b^2 d^3 e g+a^2 b d e^2 (138 e f-55 d g)+30 a^3 e^3 (e f-2 d g)\right )-a b c^2 e^4 \left (23 a^2 e^2 g-9 b^2 d (6 e f-5 d g)-23 a b e (3 e f-2 d g)\right )+b^3 c e^4 \left (9 a^2 e^2 g-b^2 d (6 e f-5 d g)-9 a b e (3 e f-2 d g)\right )+c^5 d^4 (2 a e (15 e f-2 d g)-3 b d (6 e f+d g))+5 c^4 d^2 e \left (2 a^2 e^2 (9 e f-4 d g)-a b d e (12 e f+d g)+b^2 d^2 (3 e f+2 d g)\right )-c \left (b^2-4 a c\right )^2 e^4 (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) x}{a+b x+c x^2} \, dx}{\left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^4} \\ & = \frac {e \left (6 c^4 d^4 f-b^3 e^3 (3 b e f-2 b d g-a e g)-b c e^2 \left (7 a^2 e^2 g-a b e (21 e f-13 d g)-3 b^2 d (e f-d g)\right )+c^3 d^2 (4 a e (6 e f-d g)-3 b d (4 e f+d g))-c^2 e \left (2 a^2 e^2 (15 e f-22 d g)+6 a b d e (4 e f+d g)-b^2 d^2 (3 e f+7 d g)\right )\right )}{\left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^3 (d+e x)}-\frac {b c d f-b^2 e f+2 a c e f-2 a c d g+a b e g+c (2 c d f+2 a e g-b (e f+d g)) x}{2 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) (d+e x) \left (a+b x+c x^2\right )^2}-\frac {4 a c e (2 c d-b e) (2 c d f+2 a e g-b (e f+d g))-\left (b c d-b^2 e+2 a c e\right ) \left (6 c^2 d^2 f-b e (3 b e f-2 b d g-a e g)+c (2 a e (5 e f-2 d g)-b d (2 e f+3 d g))\right )-c \left (12 c^3 d^3 f+b^2 e^2 (3 b e f-2 b d g-a e g)+2 c^2 d (2 a e (9 e f-2 d g)-3 b d (3 e f+d g))+c e \left (11 b^2 d^2 g+16 a^2 e^2 g-2 a b e (9 e f+5 d g)\right )\right ) x}{2 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2 (d+e x) \left (a+b x+c x^2\right )}+\frac {e^4 (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log (d+e x)}{\left (c d^2-b d e+a e^2\right )^4}-\frac {\left (e^4 (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g))\right ) \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 )^4}+\frac {\left (12 c^6 d^6 f+b^5 e^5 (3 b e f-2 b d g-a e g)+b^3 c e^4 \left (10 a^2 e^2 g-b^2 d (6 e f-5 d g)-10 a b e (3 e f-2 d g)\right )-10 a b c^2 e^4 \left (3 a^2 e^2 g-b^2 d (6 e f-5 d g)-3 a b e (3 e f-2 d g)\right )-10 c^3 e^2 \left (2 b^3 d^4 g-8 a b^2 d^3 e g+6 a^3 e^3 (e f-2 d g)+3 a^2 b d e^2 (6 e f-d g)\right )+2 c^5 d^4 (2 a e (15 e f-2 d g)-3 b d (6 e f+d g))+10 c^4 d^2 e \left (2 a^2 e^2 (9 e f-4 d g)-a b d e (12 e f+d g)+b^2 d^2 (3 e f+2 d g)\right )\right ) \int \frac {1}{a+b x+c x^2} \, dx}{2 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^4} \\ & = \frac {e \left (6 c^4 d^4 f-b^3 e^3 (3 b e f-2 b d g-a e g)-b c e^2 \left (7 a^2 e^2 g-a b e (21 e f-13 d g)-3 b^2 d (e f-d g)\right )+c^3 d^2 (4 a e (6 e f-d g)-3 b d (4 e f+d g))-c^2 e \left (2 a^2 e^2 (15 e f-22 d g)+6 a b d e (4 e f+d g)-b^2 d^2 (3 e f+7 d g)\right )\right )}{\left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^3 (d+e x)}-\frac {b c d f-b^2 e f+2 a c e f-2 a c d g+a b e g+c (2 c d f+2 a e g-b (e f+d g)) x}{2 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) (d+e x) \left (a+b x+c x^2\right )^2}-\frac {4 a c e (2 c d-b e) (2 c d f+2 a e g-b (e f+d g))-\left (b c d-b^2 e+2 a c e\right ) \left (6 c^2 d^2 f-b e (3 b e f-2 b d g-a e g)+c (2 a e (5 e f-2 d g)-b d (2 e f+3 d g))\right )-c \left (12 c^3 d^3 f+b^2 e^2 (3 b e f-2 b d g-a e g)+2 c^2 d (2 a e (9 e f-2 d g)-3 b d (3 e f+d g))+c e \left (11 b^2 d^2 g+16 a^2 e^2 g-2 a b e (9 e f+5 d g)\right )\right ) x}{2 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2 (d+e x) \left (a+b x+c x^2\right )}+\frac {e^4 (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log (d+e x)}{\left (c d^2-b d e+a e^2\right )^4}-\frac {e^4 (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log \left (a+b x+c x^2\right )}{2 \left (c d^2-b d e+a e^2\right )^4}-\frac {\left (12 c^6 d^6 f+b^5 e^5 (3 b e f-2 b d g-a e g)+b^3 c e^4 \left (10 a^2 e^2 g-b^2 d (6 e f-5 d g)-10 a b e (3 e f-2 d g)\right )-10 a b c^2 e^4 \left (3 a^2 e^2 g-b^2 d (6 e f-5 d g)-3 a b e (3 e f-2 d g)\right )-10 c^3 e^2 \left (2 b^3 d^4 g-8 a b^2 d^3 e g+6 a^3 e^3 (e f-2 d g)+3 a^2 b d e^2 (6 e f-d g)\right )+2 c^5 d^4 (2 a e (15 e f-2 d g)-3 b d (6 e f+d g))+10 c^4 d^2 e \left (2 a^2 e^2 (9 e f-4 d g)-a b d e (12 e f+d g)+b^2 d^2 (3 e f+2 d g)\right )\right ) \text {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 )^2 \left (c d^2-b d e+a e^2\right )^4} \\ & = \frac {e \left (6 c^4 d^4 f-b^3 e^3 (3 b e f-2 b d g-a e g)-b c e^2 \left (7 a^2 e^2 g-a b e (21 e f-13 d g)-3 b^2 d (e f-d g)\right )+c^3 d^2 (4 a e (6 e f-d g)-3 b d (4 e f+d g))-c^2 e \left (2 a^2 e^2 (15 e f-22 d g)+6 a b d e (4 e f+d g)-b^2 d^2 (3 e f+7 d g)\right )\right )}{\left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^3 (d+e x)}-\frac {b c d f-b^2 e f+2 a c e f-2 a c d g+a b e g+c (2 c d f+2 a e g-b (e f+d g)) x}{2 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) (d+e x) \left (a+b x+c x^2\right )^2}-\frac {4 a c e (2 c d-b e) (2 c d f+2 a e g-b (e f+d g))-\left (b c d-b^2 e+2 a c e\right ) \left (6 c^2 d^2 f-b e (3 b e f-2 b d g-a e g)+c (2 a e (5 e f-2 d g)-b d (2 e f+3 d g))\right )-c \left (12 c^3 d^3 f+b^2 e^2 (3 b e f-2 b d g-a e g)+2 c^2 d (2 a e (9 e f-2 d g)-3 b d (3 e f+d g))+c e \left (11 b^2 d^2 g+16 a^2 e^2 g-2 a b e (9 e f+5 d g)\right )\right ) x}{2 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2 (d+e x) \left (a+b x+c x^2\right )}-\frac {\left (12 c^6 d^6 f+b^5 e^5 (3 b e f-2 b d g-a e g)+b^3 c e^4 \left (10 a^2 e^2 g-b^2 d (6 e f-5 d g)-10 a b e (3 e f-2 d g)\right )-10 a b c^2 e^4 \left (3 a^2 e^2 g-b^2 d (6 e f-5 d g)-3 a b e (3 e f-2 d g)\right )-10 c^3 e^2 \left (2 b^3 d^4 g-8 a b^2 d^3 e g+6 a^3 e^3 (e f-2 d g)+3 a^2 b d e^2 (6 e f-d g)\right )+2 c^5 d^4 (2 a e (15 e f-2 d g)-3 b d (6 e f+d g))+10 c^4 d^2 e \left (2 a^2 e^2 (9 e f-4 d g)-a b d e (12 e f+d g)+b^2 d^2 (3 e f+2 d g)\right )\right ) \tanh ^{-1}\left (\frac {b+2 c x}{\sqrt {b^2-4 a c}}\right )}{\left (b^2-4 a c\right )^{5/2} \left (c d^2-b d e+a e^2\right )^4}+\frac {e^4 (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log (d+e x)}{\left (c d^2-b d e+a e^2\right )^4}-\frac {e^4 (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log \left (a+b x+c x^2\right )}{2 \left (c d^2-b d e+a e^2\right )^4} \\ \end{align*}

Mathematica [A] (verified)

Time = 5.11 (sec) , antiderivative size = 1050, normalized size of antiderivative = 1.01 \[ \int \frac {f+g x}{(d+e x)^2 \left (a+b x+c x^2\right )^3} \, dx=\frac {1}{2} \left (-\frac {2 e^4 (e f-d g)}{\left (c d^2+e (-b d+a e)\right )^3 (d+e x)}+\frac {-b^3 e^2 f+b^2 e (a e g+c f (2 d-e x))+b c (c d (-d f+2 e f x+d g x)+a e (3 e f-2 d g+e g x))-2 c \left (a^2 e^2 g+c^2 d^2 f x-a c \left (d^2 g+e^2 f x-2 d e (f+g x)\right )\right )}{\left (b^2-4 a c\right ) \left (c d^2+e (-b d+a e)\right )^2 (a+x (b+c x))^2}+\frac {2 b^5 e^3 (2 e f-d g)+b^4 \left (-2 a e^4 g+c e^2 \left (-7 d e f+6 d^2 g+4 e^2 f x-2 d e g x\right )\right )+2 b c^2 \left (3 c^2 d^3 (-d f+4 e f x+d g x)+a^2 e^3 (23 e f-22 d g+7 e g x)+2 a c d e \left (-6 d e f+d^2 g+12 e^2 f x+3 d e g x\right )\right )-b^3 c e \left (a e^2 (29 e f-13 d g+2 e g x)+c d \left (7 d^2 g+6 e^2 f x+3 d e (f-2 g x)\right )\right )+b^2 c \left (15 a^2 e^4 g+c^2 d^2 \left (3 d^2 g-6 e^2 f x+2 d e (6 f-7 g x)\right )-2 a c e^2 \left (9 d^2 g+13 e^2 f x-d e (28 f+5 g x)\right )\right )-4 c^2 \left (4 a^3 e^4 g+3 c^3 d^4 f x-2 a c^2 d^2 e (-6 e f+d g) x+a^2 c e^2 \left (-12 d^2 g-7 e^2 f x+2 d e (8 f+7 g x)\right )\right )}{\left (b^2-4 a c\right )^2 \left (-c d^2+e (b d-a e)\right )^3 (a+x (b+c x))}-\frac {2 \left (-12 c^6 d^6 f+b^5 e^5 (-3 b e f+2 b d g+a e g)+b^3 c e^4 \left (-10 a^2 e^2 g+b^2 d (6 e f-5 d g)+10 a b e (3 e f-2 d g)\right )-10 c^3 e^2 \left (-2 b^3 d^4 g+8 a b^2 d^3 e g-6 a^3 e^3 (e f-2 d g)+3 a^2 b d e^2 (-6 e f+d g)\right )+2 c^5 d^4 (3 b d (6 e f+d g)+2 a e (-15 e f+2 d g))-10 c^4 d^2 e \left (2 a^2 e^2 (9 e f-4 d g)-a b d e (12 e f+d g)+b^2 d^2 (3 e f+2 d g)\right )+10 a b c^2 e^4 \left (3 a^2 e^2 g+3 a b e (-3 e f+2 d g)+b^2 d (-6 e f+5 d g)\right )\right ) \arctan \left (\frac {b+2 c x}{\sqrt {-b^2+4 a c}}\right )}{\left (-b^2+4 a c\right )^{5/2} \left (c d^2+e (-b d+a e)\right )^4}-\frac {2 e^4 (c d (-6 e f+5 d g)+e (3 b e f-2 b d g-a e g)) \log (d+e x)}{\left (c d^2+e (-b d+a e)\right )^4}+\frac {e^4 (c d (-6 e f+5 d g)+e (3 b e f-2 b d g-a e g)) \log (a+x (b+c x))}{\left (c d^2+e (-b d+a e)\right )^4}\right ) \]

[In]

Integrate[(f + g*x)/((d + e*x)^2*(a + b*x + c*x^2)^3),x]

[Out]

((-2*e^4*(e*f - d*g))/((c*d^2 + e*(-(b*d) + a*e))^3*(d + e*x)) + (-(b^3*e^2*f) + b^2*e*(a*e*g + c*f*(2*d - e*x
)) + b*c*(c*d*(-(d*f) + 2*e*f*x + d*g*x) + a*e*(3*e*f - 2*d*g + e*g*x)) - 2*c*(a^2*e^2*g + c^2*d^2*f*x - a*c*(
d^2*g + e^2*f*x - 2*d*e*(f + g*x))))/((b^2 - 4*a*c)*(c*d^2 + e*(-(b*d) + a*e))^2*(a + x*(b + c*x))^2) + (2*b^5
*e^3*(2*e*f - d*g) + b^4*(-2*a*e^4*g + c*e^2*(-7*d*e*f + 6*d^2*g + 4*e^2*f*x - 2*d*e*g*x)) + 2*b*c^2*(3*c^2*d^
3*(-(d*f) + 4*e*f*x + d*g*x) + a^2*e^3*(23*e*f - 22*d*g + 7*e*g*x) + 2*a*c*d*e*(-6*d*e*f + d^2*g + 12*e^2*f*x
+ 3*d*e*g*x)) - b^3*c*e*(a*e^2*(29*e*f - 13*d*g + 2*e*g*x) + c*d*(7*d^2*g + 6*e^2*f*x + 3*d*e*(f - 2*g*x))) +
b^2*c*(15*a^2*e^4*g + c^2*d^2*(3*d^2*g - 6*e^2*f*x + 2*d*e*(6*f - 7*g*x)) - 2*a*c*e^2*(9*d^2*g + 13*e^2*f*x -
d*e*(28*f + 5*g*x))) - 4*c^2*(4*a^3*e^4*g + 3*c^3*d^4*f*x - 2*a*c^2*d^2*e*(-6*e*f + d*g)*x + a^2*c*e^2*(-12*d^
2*g - 7*e^2*f*x + 2*d*e*(8*f + 7*g*x))))/((b^2 - 4*a*c)^2*(-(c*d^2) + e*(b*d - a*e))^3*(a + x*(b + c*x))) - (2
*(-12*c^6*d^6*f + b^5*e^5*(-3*b*e*f + 2*b*d*g + a*e*g) + b^3*c*e^4*(-10*a^2*e^2*g + b^2*d*(6*e*f - 5*d*g) + 10
*a*b*e*(3*e*f - 2*d*g)) - 10*c^3*e^2*(-2*b^3*d^4*g + 8*a*b^2*d^3*e*g - 6*a^3*e^3*(e*f - 2*d*g) + 3*a^2*b*d*e^2
*(-6*e*f + d*g)) + 2*c^5*d^4*(3*b*d*(6*e*f + d*g) + 2*a*e*(-15*e*f + 2*d*g)) - 10*c^4*d^2*e*(2*a^2*e^2*(9*e*f
- 4*d*g) - a*b*d*e*(12*e*f + d*g) + b^2*d^2*(3*e*f + 2*d*g)) + 10*a*b*c^2*e^4*(3*a^2*e^2*g + 3*a*b*e*(-3*e*f +
2*d*g) + b^2*d*(-6*e*f + 5*d*g)))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/((-b^2 + 4*a*c)^(5/2)*(c*d^2 + e*(-
(b*d) + a*e))^4) - (2*e^4*(c*d*(-6*e*f + 5*d*g) + e*(3*b*e*f - 2*b*d*g - a*e*g))*Log[d + e*x])/(c*d^2 + e*(-(b
*d) + a*e))^4 + (e^4*(c*d*(-6*e*f + 5*d*g) + e*(3*b*e*f - 2*b*d*g - a*e*g))*Log[a + x*(b + c*x)])/(c*d^2 + e*(
-(b*d) + a*e))^4)/2

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(3176\) vs. \(2(1033)=2066\).

Time = 1.51 (sec) , antiderivative size = 3177, normalized size of antiderivative = 3.05

method	result	size
default	\(\text {Expression too large to display}\)	\(3177\)
risch	\(\text {Expression too large to display}\)	\(1882175\)

[In]

int((g*x+f)/(e*x+d)^2/(c*x^2+b*x+a)^3,x,method=_RETURNVERBOSE)

[Out]

e^4*(a*e^2*g+2*b*d*e*g-3*b*e^2*f-5*c*d^2*g+6*c*d*e*f)/(a*e^2-b*d*e+c*d^2)^4*ln(e*x+d)+(d*g-e*f)*e^4/(a*e^2-b*d
*e+c*d^2)^3/(e*x+d)-1/(a*e^2-b*d*e+c*d^2)^4*((c^2*(7*a^3*b*c*e^6*g-28*a^3*c^2*d*e^5*g+14*a^3*c^2*e^6*f-a^2*b^3
*e^6*g-2*a^2*b^2*c*d*e^5*g-13*a^2*b^2*c*e^6*f+41*a^2*b*c^2*d^2*e^4*g+10*a^2*b*c^2*d*e^5*f-24*a^2*c^3*d^3*e^3*g
-10*a^2*c^3*d^2*e^4*f+2*a*b^4*e^6*f-3*a*b^3*c*d^2*e^4*g+10*a*b^3*c*d*e^5*f-8*a*b^2*c^2*d^3*e^3*g-40*a*b^2*c^2*
d^2*e^4*f+5*a*b*c^3*d^4*e^2*g+60*a*b*c^3*d^3*e^3*f+4*a*c^4*d^5*e*g-30*a*c^4*d^4*e^2*f+b^5*d^2*e^4*g-2*b^5*d*e^
5*f-4*b^4*c*d^3*e^3*g+5*b^4*c*d^2*e^4*f+10*b^3*c^2*d^4*e^2*g-10*b^2*c^3*d^5*e*g-15*b^2*c^3*d^4*e^2*f+3*b*c^4*d
^6*g+18*b*c^4*d^5*e*f-6*c^5*d^6*f)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3-1/2*c*(16*a^4*c^2*e^6*g-29*a^3*b^2*c*e^6*g+8
4*a^3*b*c^2*d*e^5*g-74*a^3*b*c^2*e^6*f-32*a^3*c^3*d^2*e^4*g+64*a^3*c^3*d*e^5*f+4*a^2*b^4*e^6*g+6*a^2*b^3*c*d*e
^5*g+55*a^2*b^3*c*e^6*f-123*a^2*b^2*c^2*d^2*e^4*g-30*a^2*b^2*c^2*d*e^5*f+136*a^2*b*c^3*d^3*e^3*g-66*a^2*b*c^3*
d^2*e^4*f-48*a^2*c^4*d^4*e^2*g+64*a^2*c^4*d^3*e^3*f-8*a*b^5*e^6*f+15*a*b^4*c*d^2*e^4*g-42*a*b^4*c*d*e^5*f-8*a*
b^3*c^2*d^3*e^3*g+168*a*b^3*c^2*d^2*e^4*f+9*a*b^2*c^3*d^4*e^2*g-212*a*b^2*c^3*d^3*e^3*f-12*a*b*c^4*d^5*e*g+90*
a*b*c^4*d^4*e^2*f-4*b^6*d^2*e^4*g+8*b^6*d*e^5*f+16*b^5*c*d^3*e^3*g-21*b^5*c*d^2*e^4*f-33*b^4*c^2*d^4*e^2*g+4*b
^4*c^2*d^3*e^3*f+30*b^3*c^3*d^5*e*g+45*b^3*c^3*d^4*e^2*f-9*b^2*c^4*d^6*g-54*b^2*c^4*d^5*e*f+18*b*c^5*d^6*f)/(1
6*a^2*c^2-8*a*b^2*c+b^4)*x^2+(a^4*b*c^2*e^6*g-36*a^4*c^3*d*e^5*g+18*a^4*c^3*e^6*f+6*a^3*b^3*c*e^6*g-18*a^3*b^2
*c^2*d*e^5*g+7*a^3*b^2*c^2*e^6*f+79*a^3*b*c^3*d^2*e^4*g-26*a^3*b*c^3*d*e^5*f-40*a^3*c^4*d^3*e^3*g-6*a^3*c^4*d^
2*e^4*f-a^2*b^5*e^6*g-12*a^2*b^4*c*e^6*f+14*a^2*b^3*c^2*d^2*e^4*g+20*a^2*b^3*c^2*d*e^5*f-64*a^2*b^2*c^3*d^3*e^
3*g-6*a^2*b^2*c^3*d^2*e^4*f+51*a^2*b*c^4*d^4*e^2*g+36*a^2*b*c^4*d^3*e^3*f-4*a^2*c^5*d^5*e*g-34*a^2*c^5*d^4*e^2
*f+2*a*b^6*e^6*f-4*a*b^5*c*d^2*e^4*g+8*a*b^5*c*d*e^5*f+12*a*b^4*c^2*d^3*e^3*g-39*a*b^4*c^2*d^2*e^4*f-3*a*b^3*c
^3*d^4*e^2*g+52*a*b^3*c^3*d^3*e^3*f-10*a*b^2*c^4*d^5*e*g-43*a*b^2*c^4*d^4*e^2*f+5*a*b*c^5*d^6*g+30*a*b*c^5*d^5
*e*f-10*a*c^6*d^6*f+b^7*d^2*e^4*g-2*b^7*d*e^5*f-4*b^6*c*d^3*e^3*g+6*b^6*c*d^2*e^4*f+6*b^5*c^2*d^4*e^2*g-4*b^5*
c^2*d^3*e^3*f-4*b^4*c^3*d^5*e*g-4*b^4*c^3*d^4*e^2*f+b^3*c^4*d^6*g+6*b^3*c^4*d^5*e*f-2*b^2*c^5*d^6*f)/(16*a^2*c
^2-8*a*b^2*c+b^4)*x-1/2*(24*a^5*c^2*e^6*g-21*a^4*b^2*c*e^6*g+20*a^4*b*c^2*d*e^5*g-58*a^4*b*c^2*e^6*f-24*a^4*c^
3*d^2*e^4*g+80*a^4*c^3*d*e^5*f+3*a^3*b^4*e^6*g+12*a^3*b^3*c*d*e^5*g+36*a^3*b^3*c*e^6*f-59*a^3*b^2*c^2*d^2*e^4*
g+2*a^3*b^2*c^2*d*e^5*f+104*a^3*b*c^3*d^3*e^3*g-138*a^3*b*c^3*d^2*e^4*f-56*a^3*c^4*d^4*e^2*g+96*a^3*c^4*d^3*e^
3*f-2*a^2*b^5*d*e^5*g-5*a^2*b^5*e^6*f+9*a^2*b^4*c*d^2*e^4*g-34*a^2*b^4*c*d*e^5*f-12*a^2*b^3*c^2*d^3*e^3*g+113*
a^2*b^3*c^2*d^2*e^4*f-7*a^2*b^2*c^3*d^4*e^2*g-84*a^2*b^2*c^3*d^3*e^3*f+20*a^2*b*c^4*d^5*e*g-6*a^2*b*c^4*d^4*e^
2*f-8*a^2*c^5*d^6*g+16*a^2*c^5*d^5*e*f-a*b^6*d^2*e^4*g+6*a*b^6*d*e^5*f+4*a*b^5*c*d^3*e^3*g-10*a*b^5*c*d^2*e^4*
f-6*a*b^4*c^2*d^4*e^2*g-16*a*b^4*c^2*d^3*e^3*f+4*a*b^3*c^3*d^5*e*g+48*a*b^3*c^3*d^4*e^2*f-a*b^2*c^4*d^6*g-38*a
*b^2*c^4*d^5*e*f+10*a*b*c^5*d^6*f-b^7*d^2*e^4*f+4*b^6*c*d^3*e^3*f-6*b^5*c^2*d^4*e^2*f+4*b^4*c^3*d^5*e*f-b^3*c^
4*d^6*f)/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^2+b*x+a)^2+1/(16*a^2*c^2-8*a*b^2*c+b^4)*(1/2*(16*a^3*c^3*e^6*g-8*a^2
*b^2*c^2*e^6*g+32*a^2*b*c^3*d*e^5*g-48*a^2*b*c^3*e^6*f-80*a^2*c^4*d^2*e^4*g+96*a^2*c^4*d*e^5*f+a*b^4*c*e^6*g-1
6*a*b^3*c^2*d*e^5*g+24*a*b^3*c^2*e^6*f+40*a*b^2*c^3*d^2*e^4*g-48*a*b^2*c^3*d*e^5*f+2*b^5*c*d*e^5*g-3*b^5*c*e^6
*f-5*b^4*c^2*d^2*e^4*g+6*b^4*c^2*d*e^5*f)/c*ln(c*x^2+b*x+a)+2*(-9*a^2*b^3*c*e^6*g-6*c^6*d^6*f+27*a*b^4*c*e^6*f
-5*b^5*c*d^2*e^4*g+6*b^5*c*d*e^5*f+10*b^3*c^3*d^4*e^2*g-10*b^2*c^4*d^5*e*g-18*a*b^4*c*d*e^5*g+a*b^5*e^6*g+2*b^
6*d*e^5*g+3*b*c^5*d^6*g+30*a^3*c^3*e^6*f+46*a^2*b^2*c^2*d*e^5*g-55*a^2*b*c^3*d^2*e^4*g+138*a^2*b*c^3*d*e^5*f+4
5*a*b^3*c^2*d^2*e^4*g-54*a*b^3*c^2*d*e^5*f-40*a*b^2*c^3*d^3*e^3*g+5*a*b*c^4*d^4*e^2*g+60*a*b*c^4*d^3*e^3*f-3*b
^6*e^6*f-1/2*(16*a^3*c^3*e^6*g-8*a^2*b^2*c^2*e^6*g+32*a^2*b*c^3*d*e^5*g-48*a^2*b*c^3*e^6*f-80*a^2*c^4*d^2*e^4*
g+96*a^2*c^4*d*e^5*f+a*b^4*c*e^6*g-16*a*b^3*c^2*d*e^5*g+24*a*b^3*c^2*e^6*f+40*a*b^2*c^3*d^2*e^4*g-48*a*b^2*c^3
*d*e^5*f+2*b^5*c*d*e^5*g-3*b^5*c*e^6*f-5*b^4*c^2*d^2*e^4*g+6*b^4*c^2*d*e^5*f)*b/c+23*a^3*b*c^2*e^6*g-60*a^3*c^
3*d*e^5*g-69*a^2*b^2*c^2*e^6*f+40*a^2*c^4*d^3*e^3*g-90*a^2*c^4*d^2*e^4*f+4*a*c^5*d^5*e*g-30*a*c^5*d^4*e^2*f-15
*b^2*c^4*d^4*e^2*f+18*b*c^5*d^5*e*f)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))))

Fricas [F(-1)]

Timed out. \[ \int \frac {f+g x}{(d+e x)^2 \left (a+b x+c x^2\right )^3} \, dx=\text {Timed out} \]

[In]

integrate((g*x+f)/(e*x+d)^2/(c*x^2+b*x+a)^3,x, algorithm="fricas")

[Out]

Timed out

Sympy [F(-1)]

Timed out. \[ \int \frac {f+g x}{(d+e x)^2 \left (a+b x+c x^2\right )^3} \, dx=\text {Timed out} \]

[In]

integrate((g*x+f)/(e*x+d)**2/(c*x**2+b*x+a)**3,x)

[Out]

Timed out

Maxima [F(-2)]

Exception generated. \[ \int \frac {f+g x}{(d+e x)^2 \left (a+b x+c x^2\right )^3} \, dx=\text {Exception raised: ValueError} \]

[In]

integrate((g*x+f)/(e*x+d)^2/(c*x^2+b*x+a)^3,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 deta

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 3633 vs. \(2 (1032) = 2064\).

Time = 0.76 (sec) , antiderivative size = 3633, normalized size of antiderivative = 3.48 \[ \int \frac {f+g x}{(d+e x)^2 \left (a+b x+c x^2\right )^3} \, dx=\text {Too large to display} \]

[In]

integrate((g*x+f)/(e*x+d)^2/(c*x^2+b*x+a)^3,x, algorithm="giac")

[Out]

-1/2*(6*c*d*e^5*f - 3*b*e^6*f - 5*c*d^2*e^4*g + 2*b*d*e^5*g + a*e^6*g)*log(c - 2*c*d/(e*x + d) + c*d^2/(e*x +
d)^2 + b*e/(e*x + d) - b*d*e/(e*x + d)^2 + a*e^2/(e*x + d)^2)/(c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 + 4
*a*c^3*d^6*e^2 - 4*b^3*c*d^5*e^3 - 12*a*b*c^2*d^5*e^3 + b^4*d^4*e^4 + 12*a*b^2*c*d^4*e^4 + 6*a^2*c^2*d^4*e^4 -
4*a*b^3*d^3*e^5 - 12*a^2*b*c*d^3*e^5 + 6*a^2*b^2*d^2*e^6 + 4*a^3*c*d^2*e^6 - 4*a^3*b*d*e^7 + a^4*e^8) - (e^11
*f/(e*x + d) - d*e^10*g/(e*x + d))/(c^3*d^6*e^6 - 3*b*c^2*d^5*e^7 + 3*b^2*c*d^4*e^8 + 3*a*c^2*d^4*e^8 - b^3*d^
3*e^9 - 6*a*b*c*d^3*e^9 + 3*a*b^2*d^2*e^10 + 3*a^2*c*d^2*e^10 - 3*a^2*b*d*e^11 + a^3*e^12) + (12*c^6*d^6*e^2*f
- 36*b*c^5*d^5*e^3*f + 30*b^2*c^4*d^4*e^4*f + 60*a*c^5*d^4*e^4*f - 120*a*b*c^4*d^3*e^5*f + 180*a^2*c^4*d^2*e^
6*f - 6*b^5*c*d*e^7*f + 60*a*b^3*c^2*d*e^7*f - 180*a^2*b*c^3*d*e^7*f + 3*b^6*e^8*f - 30*a*b^4*c*e^8*f + 90*a^2
*b^2*c^2*e^8*f - 60*a^3*c^3*e^8*f - 6*b*c^5*d^6*e^2*g + 20*b^2*c^4*d^5*e^3*g - 8*a*c^5*d^5*e^3*g - 20*b^3*c^3*
d^4*e^4*g - 10*a*b*c^4*d^4*e^4*g + 80*a*b^2*c^3*d^3*e^5*g - 80*a^2*c^4*d^3*e^5*g + 5*b^5*c*d^2*e^6*g - 50*a*b^
3*c^2*d^2*e^6*g + 30*a^2*b*c^3*d^2*e^6*g - 2*b^6*d*e^7*g + 20*a*b^4*c*d*e^7*g - 60*a^2*b^2*c^2*d*e^7*g + 120*a
^3*c^3*d*e^7*g - a*b^5*e^8*g + 10*a^2*b^3*c*e^8*g - 30*a^3*b*c^2*e^8*g)*arctan((2*c*d - 2*c*d^2/(e*x + d) - b*
e + 2*b*d*e/(e*x + d) - 2*a*e^2/(e*x + d))/(sqrt(-b^2 + 4*a*c)*e))/((b^4*c^4*d^8 - 8*a*b^2*c^5*d^8 + 16*a^2*c^
6*d^8 - 4*b^5*c^3*d^7*e + 32*a*b^3*c^4*d^7*e - 64*a^2*b*c^5*d^7*e + 6*b^6*c^2*d^6*e^2 - 44*a*b^4*c^3*d^6*e^2 +
64*a^2*b^2*c^4*d^6*e^2 + 64*a^3*c^5*d^6*e^2 - 4*b^7*c*d^5*e^3 + 20*a*b^5*c^2*d^5*e^3 + 32*a^2*b^3*c^3*d^5*e^3
- 192*a^3*b*c^4*d^5*e^3 + b^8*d^4*e^4 + 4*a*b^6*c*d^4*e^4 - 74*a^2*b^4*c^2*d^4*e^4 + 144*a^3*b^2*c^3*d^4*e^4
+ 96*a^4*c^4*d^4*e^4 - 4*a*b^7*d^3*e^5 + 20*a^2*b^5*c*d^3*e^5 + 32*a^3*b^3*c^2*d^3*e^5 - 192*a^4*b*c^3*d^3*e^5
+ 6*a^2*b^6*d^2*e^6 - 44*a^3*b^4*c*d^2*e^6 + 64*a^4*b^2*c^2*d^2*e^6 + 64*a^5*c^3*d^2*e^6 - 4*a^3*b^5*d*e^7 +
32*a^4*b^3*c*d*e^7 - 64*a^5*b*c^2*d*e^7 + a^4*b^4*e^8 - 8*a^5*b^2*c*e^8 + 16*a^6*c^2*e^8)*sqrt(-b^2 + 4*a*c)*e
^2) + 1/2*(12*c^7*d^5*e*f - 30*b*c^6*d^4*e^2*f + 16*b^2*c^5*d^3*e^3*f + 56*a*c^6*d^3*e^3*f + 6*b^3*c^4*d^2*e^4
*f - 84*a*b*c^5*d^2*e^4*f - 14*b^4*c^3*d*e^5*f + 100*a*b^2*c^4*d*e^5*f - 116*a^2*c^5*d*e^5*f + 5*b^5*c^2*e^6*f
- 36*a*b^3*c^3*e^6*f + 58*a^2*b*c^4*e^6*f - 6*b*c^6*d^5*e*g + 17*b^2*c^5*d^4*e^2*g - 8*a*c^6*d^4*e^2*g - 12*b
^3*c^4*d^3*e^3*g - 12*a*b*c^5*d^3*e^3*g + 8*b^4*c^3*d^2*e^4*g - 34*a*b^2*c^4*d^2*e^4*g + 128*a^2*c^5*d^2*e^4*g
- 2*b^5*c^2*d*e^5*g + 18*a*b^3*c^3*d*e^5*g - 70*a^2*b*c^4*d*e^5*g - 3*a*b^4*c^2*e^6*g + 21*a^2*b^2*c^3*e^6*g
- 24*a^3*c^4*e^6*g - 2*(18*c^7*d^6*e^2*f - 54*b*c^6*d^5*e^3*f + 47*b^2*c^5*d^4*e^4*f + 82*a*c^6*d^4*e^4*f - 4*
b^3*c^4*d^3*e^5*f - 164*a*b*c^5*d^3*e^5*f - 29*b^4*c^3*d^2*e^6*f + 244*a*b^2*c^4*d^2*e^6*f - 242*a^2*c^5*d^2*e
^6*f + 22*b^5*c^2*d*e^7*f - 162*a*b^3*c^3*d*e^7*f + 242*a^2*b*c^4*d*e^7*f - 5*b^6*c*e^8*f + 38*a*b^4*c^2*e^8*f
- 71*a^2*b^2*c^3*e^8*f + 14*a^3*c^4*e^8*f - 9*b*c^6*d^6*e^2*g + 30*b^2*c^5*d^5*e^3*g - 12*a*c^6*d^5*e^3*g - 3
1*b^3*c^4*d^4*e^4*g - 11*a*b*c^5*d^4*e^4*g + 24*b^4*c^3*d^3*e^5*g - 64*a*b^2*c^4*d^3*e^5*g + 232*a^2*c^5*d^3*e
^5*g - 11*b^5*c^2*d^2*e^6*g + 67*a*b^3*c^3*d^2*e^6*g - 227*a^2*b*c^4*d^2*e^6*g + 2*b^6*c*d*e^7*g - 24*a*b^4*c^
2*d*e^7*g + 110*a^2*b^2*c^3*d*e^7*g - 76*a^3*c^4*d*e^7*g + 3*a*b^5*c*e^8*g - 22*a^2*b^3*c^2*e^8*g + 31*a^3*b*c
^3*e^8*g)/((e*x + d)*e) + (36*c^7*d^7*e^3*f - 126*b*c^6*d^6*e^4*f + 144*b^2*c^5*d^5*e^5*f + 180*a*c^6*d^5*e^5*
f - 45*b^3*c^4*d^4*e^6*f - 450*a*b*c^5*d^4*e^6*f - 70*b^4*c^3*d^3*e^7*f + 740*a*b^2*c^4*d^3*e^7*f - 580*a^2*c^
5*d^3*e^7*f + 87*b^5*c^2*d^2*e^8*f - 660*a*b^3*c^3*d^2*e^8*f + 870*a^2*b*c^4*d^2*e^8*f - 36*b^6*c*d*e^9*f + 25
8*a*b^4*c^2*d*e^9*f - 372*a^2*b^2*c^3*d*e^9*f - 84*a^3*c^4*d*e^9*f + 5*b^7*e^10*f - 34*a*b^5*c*e^10*f + 41*a^2
*b^3*c^2*e^10*f + 42*a^3*b*c^3*e^10*f - 18*b*c^6*d^7*e^3*g + 69*b^2*c^5*d^6*e^4*g - 24*a*c^6*d^6*e^4*g - 90*b^
3*c^4*d^5*e^5*g - 18*a*b*c^5*d^5*e^5*g + 80*b^4*c^3*d^4*e^6*g - 145*a*b^2*c^4*d^4*e^6*g + 560*a^2*c^5*d^4*e^6*
g - 50*b^5*c^2*d^3*e^7*g + 250*a*b^3*c^3*d^3*e^7*g - 830*a^2*b*c^4*d^3*e^7*g + 16*b^6*c*d^2*e^8*g - 129*a*b^4*
c^2*d^2*e^8*g + 471*a^2*b^2*c^3*d^2*e^8*g - 88*a^3*c^4*d^2*e^8*g - 2*b^7*d*e^9*g + 32*a*b^5*c*d*e^9*g - 160*a^
2*b^3*c^2*d*e^9*g + 130*a^3*b*c^3*d*e^9*g - 3*a*b^6*e^10*g + 19*a^2*b^4*c*e^10*g - 11*a^3*b^2*c^2*e^10*g - 32*
a^4*c^3*e^10*g)/((e*x + d)^2*e^2) - 2*(6*c^7*d^8*e^4*f - 24*b*c^6*d^7*e^5*f + 33*b^2*c^5*d^6*e^6*f + 36*a*c^6*
d^6*e^6*f - 15*b^3*c^4*d^5*e^7*f - 108*a*b*c^5*d^5*e^7*f - 15*b^4*c^3*d^4*e^8*f + 195*a*b^2*c^4*d^4*e^8*f - 12
0*a^2*c^5*d^4*e^8*f + 27*b^5*c^2*d^3*e^9*f - 210*a*b^3*c^3*d^3*e^9*f + 240*a^2*b*c^4*d^3*e^9*f - 15*b^6*c*d^2*
e^10*f + 99*a*b^4*c^2*d^2*e^10*f - 81*a^2*b^2*c^3*d^2*e^10*f - 132*a^3*c^4*d^2*e^10*f + 3*b^7*d*e^11*f - 12*a*
b^5*c*d*e^11*f - 39*a^2*b^3*c^2*d*e^11*f + 132*a^3*b*c^3*d*e^11*f - 3*a*b^6*e^12*f + 24*a^2*b^4*c*e^12*f - 51*
a^3*b^2*c^2*e^12*f + 18*a^4*c^3*e^12*f - 3*b*c^6*d^8*e^4*g + 13*b^2*c^5*d^7*e^5*g - 4*a*c^6*d^7*e^5*g - 20*b^3
*c^4*d^6*e^6*g - 4*a*b*c^5*d^6*e^6*g + 20*b^4*c^3*d^5*e^7*g - 25*a*b^2*c^4*d^5*e^7*g + 116*a^2*c^5*d^5*e^7*g -
15*b^5*c^2*d^4*e^8*g + 65*a*b^3*c^3*d^4*e^8*g - 230*a^2*b*c^4*d^4*e^8*g + 6*b^6*c*d^3*e^9*g - 39*a*b^4*c^2*d^
3*e^9*g + 131*a^2*b^2*c^3*d^3*e^9*g + 52*a^3*c^4*d^3*e^9*g - b^7*d^2*e^10*g + 11*a*b^5*c*d^2*e^10*g - 46*a^2*b
^3*c^2*d^2*e^10*g - 12*a^3*b*c^3*d^2*e^10*g - a*b^6*d*e^11*g + a^2*b^4*c*d*e^11*g + 41*a^3*b^2*c^2*d*e^11*g -
68*a^4*c^3*d*e^11*g + 2*a^2*b^5*e^12*g - 15*a^3*b^3*c*e^12*g + 25*a^4*b*c^2*e^12*g)/((e*x + d)^3*e^3))/((c*d^2
- b*d*e + a*e^2)^4*(b^2 - 4*a*c)^2*(c - 2*c*d/(e*x + d) + c*d^2/(e*x + d)^2 + b*e/(e*x + d) - b*d*e/(e*x + d)
^2 + a*e^2/(e*x + d)^2)^2)

Mupad [B] (verification not implemented)

Time = 22.09 (sec) , antiderivative size = 40079, normalized size of antiderivative = 38.43 \[ \int \frac {f+g x}{(d+e x)^2 \left (a+b x+c x^2\right )^3} \, dx=\text {Too large to display} \]

[In]

int((f + g*x)/((d + e*x)^2*(a + b*x + c*x^2)^3),x)

[Out]

symsum(log(root(286720*a^9*b*c^8*d^7*e^9*z^3 + 286720*a^8*b*c^9*d^9*e^7*z^3 + 172032*a^10*b*c^7*d^5*e^11*z^3 +
172032*a^7*b*c^10*d^11*e^5*z^3 + 57344*a^11*b*c^6*d^3*e^13*z^3 + 57344*a^6*b*c^11*d^13*e^3*z^3 - 10240*a^11*b
^3*c^4*d*e^15*z^3 - 10240*a^4*b^3*c^11*d^15*e*z^3 + 5120*a^10*b^5*c^3*d*e^15*z^3 + 5120*a^3*b^5*c^10*d^15*e*z^
3 - 1280*a^9*b^7*c^2*d*e^15*z^3 - 1280*a^2*b^7*c^9*d^15*e*z^3 - 1232*a^5*b^12*c*d^4*e^12*z^3 - 1232*a*b^12*c^5
*d^12*e^4*z^3 + 1064*a^6*b^11*c*d^3*e^13*z^3 + 1064*a*b^11*c^6*d^13*e^3*z^3 + 840*a^4*b^13*c*d^5*e^11*z^3 + 84
0*a*b^13*c^4*d^11*e^5*z^3 - 552*a^7*b^10*c*d^2*e^14*z^3 - 552*a*b^10*c^7*d^14*e^2*z^3 - 280*a^3*b^14*c*d^6*e^1
0*z^3 - 280*a*b^14*c^3*d^10*e^6*z^3 - 8*a^2*b^15*c*d^7*e^9*z^3 - 8*a*b^15*c^2*d^9*e^7*z^3 + 8192*a^12*b*c^5*d*
e^15*z^3 + 8192*a^5*b*c^12*d^15*e*z^3 + 160*a^8*b^9*c*d*e^15*z^3 + 160*a*b^9*c^8*d^15*e*z^3 + 36*a*b^16*c*d^8*
e^8*z^3 - 483840*a^8*b^2*c^8*d^8*e^8*z^3 - 365568*a^7*b^5*c^6*d^7*e^9*z^3 - 365568*a^6*b^5*c^7*d^9*e^7*z^3 - 3
58400*a^9*b^2*c^7*d^6*e^10*z^3 - 358400*a^7*b^2*c^9*d^10*e^6*z^3 + 241920*a^7*b^4*c^7*d^8*e^8*z^3 + 215040*a^8
*b^4*c^6*d^6*e^10*z^3 + 215040*a^8*b^3*c^7*d^7*e^9*z^3 + 215040*a^7*b^3*c^8*d^9*e^7*z^3 + 215040*a^6*b^4*c^8*d
^10*e^6*z^3 - 193536*a^8*b^5*c^5*d^5*e^11*z^3 - 193536*a^5*b^5*c^8*d^11*e^5*z^3 - 136192*a^10*b^2*c^6*d^4*e^12
*z^3 - 136192*a^6*b^2*c^10*d^12*e^4*z^3 + 133056*a^6*b^6*c^6*d^8*e^8*z^3 + 125440*a^9*b^4*c^5*d^4*e^12*z^3 + 1
25440*a^5*b^4*c^9*d^12*e^4*z^3 - 109944*a^5*b^8*c^5*d^8*e^8*z^3 + 106752*a^6*b^7*c^5*d^7*e^9*z^3 + 106752*a^5*
b^7*c^6*d^9*e^7*z^3 + 80640*a^7*b^7*c^4*d^5*e^11*z^3 + 80640*a^4*b^7*c^7*d^11*e^5*z^3 - 77280*a^6*b^8*c^4*d^6*
e^10*z^3 - 77280*a^4*b^8*c^6*d^10*e^6*z^3 + 71680*a^9*b^3*c^6*d^5*e^11*z^3 + 71680*a^6*b^3*c^9*d^11*e^5*z^3 +
69888*a^7*b^6*c^5*d^6*e^10*z^3 + 69888*a^5*b^6*c^7*d^10*e^6*z^3 - 35840*a^9*b^5*c^4*d^3*e^13*z^3 - 35840*a^4*b
^5*c^9*d^13*e^3*z^3 + 30720*a^10*b^4*c^4*d^2*e^14*z^3 + 30720*a^4*b^4*c^10*d^14*e^2*z^3 + 26880*a^8*b^7*c^3*d^
3*e^13*z^3 + 26880*a^3*b^7*c^8*d^13*e^3*z^3 + 21510*a^4*b^10*c^4*d^8*e^8*z^3 + 18536*a^5*b^10*c^3*d^6*e^10*z^3
+ 18536*a^3*b^10*c^5*d^10*e^6*z^3 - 18480*a^7*b^8*c^3*d^4*e^12*z^3 - 18480*a^3*b^8*c^7*d^12*e^4*z^3 - 18432*a
^11*b^2*c^5*d^2*e^14*z^3 - 18432*a^5*b^2*c^11*d^14*e^2*z^3 - 16640*a^9*b^6*c^3*d^2*e^14*z^3 - 16640*a^3*b^6*c^
9*d^14*e^2*z^3 - 14336*a^10*b^3*c^5*d^3*e^13*z^3 - 14336*a^5*b^3*c^10*d^13*e^3*z^3 - 13440*a^8*b^6*c^4*d^4*e^1
2*z^3 - 13440*a^4*b^6*c^8*d^12*e^4*z^3 + 13280*a^5*b^9*c^4*d^7*e^9*z^3 + 13280*a^4*b^9*c^5*d^9*e^7*z^3 - 10840
*a^4*b^11*c^3*d^7*e^9*z^3 - 10840*a^3*b^11*c^4*d^9*e^7*z^3 + 7868*a^6*b^10*c^2*d^4*e^12*z^3 + 7868*a^2*b^10*c^
6*d^12*e^4*z^3 - 7840*a^7*b^9*c^2*d^3*e^13*z^3 - 7840*a^2*b^9*c^7*d^13*e^3*z^3 - 5600*a^6*b^9*c^3*d^5*e^11*z^3
- 5600*a^3*b^9*c^6*d^11*e^5*z^3 + 4320*a^8*b^8*c^2*d^2*e^14*z^3 + 4320*a^2*b^8*c^8*d^14*e^2*z^3 - 3528*a^5*b^
11*c^2*d^5*e^11*z^3 - 3528*a^2*b^11*c^5*d^11*e^5*z^3 + 1520*a^3*b^13*c^2*d^7*e^9*z^3 + 1520*a^2*b^13*c^3*d^9*e
^7*z^3 - 700*a^4*b^12*c^2*d^6*e^10*z^3 - 700*a^2*b^12*c^4*d^10*e^6*z^3 - 540*a^2*b^14*c^2*d^8*e^8*z^3 + 480*a^
3*b^12*c^3*d^8*e^8*z^3 - 8*b^17*c*d^9*e^7*z^3 - 8*b^11*c^7*d^15*e*z^3 - 8*a^7*b^11*d*e^15*z^3 - 8*a*b^17*d^7*e
^9*z^3 - 20*a^9*b^8*c*e^16*z^3 - 20*a*b^8*c^9*d^16*z^3 + 70*b^14*c^4*d^12*e^4*z^3 - 56*b^15*c^3*d^11*e^5*z^3 -
56*b^13*c^5*d^13*e^3*z^3 + 28*b^16*c^2*d^10*e^6*z^3 + 28*b^12*c^6*d^14*e^2*z^3 - 71680*a^9*c^9*d^8*e^8*z^3 -
57344*a^10*c^8*d^6*e^10*z^3 - 57344*a^8*c^10*d^10*e^6*z^3 - 28672*a^11*c^7*d^4*e^12*z^3 - 28672*a^7*c^11*d^12*
e^4*z^3 - 8192*a^12*c^6*d^2*e^14*z^3 - 8192*a^6*c^12*d^14*e^2*z^3 + 70*a^4*b^14*d^4*e^12*z^3 - 56*a^5*b^13*d^3
*e^13*z^3 - 56*a^3*b^15*d^5*e^11*z^3 + 28*a^6*b^12*d^2*e^14*z^3 + 28*a^2*b^16*d^6*e^10*z^3 + 1280*a^12*b^2*c^4
*e^16*z^3 - 640*a^11*b^4*c^3*e^16*z^3 + 160*a^10*b^6*c^2*e^16*z^3 + 1280*a^4*b^2*c^12*d^16*z^3 - 640*a^3*b^4*c
^11*d^16*z^3 + 160*a^2*b^6*c^10*d^16*z^3 - 1024*a^13*c^5*e^16*z^3 - 1024*a^5*c^13*d^16*z^3 + b^18*d^8*e^8*z^3
+ b^10*c^8*d^16*z^3 + a^8*b^10*e^16*z^3 + 96*a*b*c^10*d^10*e^2*f*g*z + 69900*a^4*b^2*c^6*d^3*e^9*f*g*z - 64590
*a^4*b^3*c^5*d^2*e^10*f*g*z - 40200*a^3*b^4*c^5*d^3*e^9*f*g*z + 32820*a^3*b^5*c^4*d^2*e^10*f*g*z + 10680*a^2*b
^6*c^4*d^3*e^9*f*g*z + 10500*a^3*b^3*c^6*d^4*e^8*f*g*z + 8820*a^2*b^3*c^7*d^6*e^6*f*g*z - 8460*a^2*b^7*c^3*d^2
*e^10*f*g*z - 5880*a^3*b^2*c^7*d^5*e^7*f*g*z - 5040*a^2*b^4*c^6*d^5*e^7*f*g*z - 3240*a^2*b^2*c^8*d^7*e^5*f*g*z
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*c^5*d*e^11*f*g*z + 24180*a^4*b^4*c^4*d*e^11*f*g*z - 9720*a^3*b^6*c^3*d*e^11*f*g*z + 3690*a*b^3*c^8*d^8*e^4*f*
g*z - 3360*a^3*b*c^8*d^6*e^6*f*g*z - 3240*a*b^4*c^7*d^7*e^5*f*g*z + 2160*a^2*b^8*c^2*d*e^11*f*g*z - 2100*a^4*b
*c^7*d^4*e^8*f*g*z - 1500*a*b^2*c^9*d^9*e^3*f*g*z - 1320*a*b^8*c^3*d^3*e^9*f*g*z - 1260*a^2*b*c^9*d^8*e^4*f*g*
z + 1080*a*b^9*c^2*d^2*e^10*f*g*z + 924*a*b^6*c^5*d^5*e^7*f*g*z + 252*a*b^5*c^6*d^6*e^6*f*g*z - 150*a*b^7*c^4*
d^4*e^8*f*g*z + 48*a*c^11*d^11*e*f*g*z - 660*b^4*c^8*d^9*e^3*f*g*z + 570*b^3*c^9*d^10*e^2*f*g*z + 270*b^5*c^7*
d^8*e^4*f*g*z + 84*b^6*c^6*d^7*e^5*f*g*z + 60*b^10*c^2*d^3*e^9*f*g*z - 60*b^8*c^4*d^5*e^7*f*g*z - 42*b^7*c^5*d
^6*e^6*f*g*z + 30*b^9*c^3*d^4*e^8*f*g*z - 59280*a^5*c^7*d^3*e^9*f*g*z + 3360*a^4*c^8*d^5*e^7*f*g*z + 2400*a^3*
c^9*d^7*e^5*f*g*z + 720*a^2*c^10*d^9*e^3*f*g*z + 7410*a^5*b^3*c^4*e^12*f*g*z - 3810*a^4*b^5*c^3*e^12*f*g*z + 9
60*a^3*b^7*c^2*e^12*f*g*z + 4872*a^6*b*c^5*d*e^11*g^2*z + 90*a*b^10*c*d^2*e^10*g^2*z + 80*a^2*b^9*c*d*e^11*g^2
*z - 33048*a^5*b*c^6*d*e^11*f^2*z + 1800*a*b*c^10*d^9*e^3*f^2*z - 720*a*b^9*c^2*d*e^11*f^2*z - 31575*a^4*b^2*c
^6*d^4*e^8*g^2*z + 24700*a^4*b^3*c^5*d^3*e^9*g^2*z + 16722*a^5*b^2*c^5*d^2*e^10*g^2*z + 15700*a^3*b^4*c^5*d^4*
e^8*g^2*z - 12140*a^3*b^5*c^4*d^3*e^9*g^2*z - 11640*a^4*b^4*c^4*d^2*e^10*g^2*z - 4485*a^2*b^6*c^4*d^4*e^8*g^2*
z + 4180*a^3*b^6*c^3*d^2*e^10*g^2*z + 3120*a^2*b^7*c^3*d^3*e^9*g^2*z - 1960*a^3*b^3*c^6*d^5*e^7*g^2*z + 1820*a
^3*b^2*c^7*d^6*e^6*g^2*z + 1596*a^2*b^5*c^5*d^5*e^7*g^2*z + 1185*a^2*b^2*c^8*d^8*e^4*g^2*z - 1080*a^2*b^3*c^7*
d^7*e^5*g^2*z - 840*a^2*b^8*c^2*d^2*e^10*g^2*z - 840*a^2*b^4*c^6*d^6*e^6*g^2*z - 50760*a^4*b^2*c^6*d^2*e^10*f^
2*z + 25380*a^3*b^4*c^5*d^2*e^10*f^2*z - 12600*a^3*b^2*c^7*d^4*e^8*f^2*z - 10080*a^2*b^2*c^8*d^6*e^6*f^2*z - 6
030*a^2*b^6*c^4*d^2*e^10*f^2*z + 3150*a^2*b^4*c^6*d^4*e^8*f^2*z + 2520*a^2*b^3*c^7*d^5*e^7*f^2*z - 1260*a^2*b^
5*c^5*d^3*e^9*f^2*z - 228*b^2*c^10*d^11*e*f*g*z - 54*b^11*c*d^2*e^10*f*g*z + 12816*a^6*c^6*d*e^11*f*g*z - 5508
*a^6*b*c^5*e^12*f*g*z - 120*a^2*b^9*c*e^12*f*g*z - 24*a*b*c^10*d^11*e*g^2*z - 18360*a^5*b*c^6*d^3*e^9*g^2*z -
5340*a^5*b^3*c^4*d*e^11*g^2*z + 2580*a^4*b^5*c^3*d*e^11*g^2*z + 1680*a^4*b*c^7*d^5*e^7*g^2*z + 1380*a*b^5*c^6*
d^7*e^5*g^2*z - 1050*a*b^4*c^7*d^8*e^4*g^2*z - 686*a*b^6*c^5*d^6*e^6*g^2*z - 640*a^3*b^7*c^2*d*e^11*g^2*z + 57
0*a*b^8*c^3*d^4*e^8*g^2*z - 400*a*b^9*c^2*d^3*e^9*g^2*z - 280*a^2*b*c^9*d^9*e^3*g^2*z + 260*a*b^3*c^8*d^9*e^3*
g^2*z + 80*a^3*b*c^8*d^7*e^5*g^2*z + 50*a*b^2*c^9*d^10*e^2*g^2*z + 44460*a^4*b^3*c^5*d*e^11*f^2*z - 22860*a^3*
b^5*c^4*d*e^11*f^2*z + 15120*a^3*b*c^8*d^5*e^7*f^2*z + 12600*a^4*b*c^7*d^3*e^9*f^2*z + 7920*a^2*b*c^9*d^7*e^5*
f^2*z + 5760*a^2*b^7*c^3*d*e^11*f^2*z - 3060*a*b^2*c^9*d^8*e^4*f^2*z + 1440*a*b^3*c^8*d^7*e^5*f^2*z - 1260*a*b
^5*c^6*d^5*e^7*f^2*z + 1260*a*b^4*c^7*d^6*e^6*f^2*z + 720*a*b^8*c^3*d^2*e^10*f^2*z + 180*a*b^7*c^4*d^3*e^9*f^2
*z + 216*b*c^11*d^11*e*f^2*z + 36*b^11*c*d*e^11*f^2*z - 4*a*b^11*d*e^11*g^2*z + 180*a*b^10*c*e^12*f^2*z + 200*
b^5*c^7*d^9*e^3*g^2*z - 160*b^4*c^8*d^10*e^2*g^2*z - 85*b^6*c^6*d^8*e^4*g^2*z + 70*b^8*c^4*d^6*e^6*g^2*z - 56*
b^7*c^5*d^7*e^5*g^2*z - 25*b^10*c^2*d^4*e^8*g^2*z - 20*b^9*c^3*d^5*e^7*g^2*z + 24000*a^5*c^7*d^4*e^8*g^2*z - 1
1280*a^6*c^6*d^2*e^10*g^2*z - 1120*a^4*c^8*d^6*e^6*g^2*z + 540*b^3*c^9*d^9*e^3*f^2*z - 504*b^2*c^10*d^10*e^2*f
^2*z - 320*a^3*c^9*d^8*e^4*g^2*z - 225*b^4*c^8*d^8*e^4*f^2*z + 144*b^7*c^5*d^5*e^7*f^2*z - 126*b^6*c^6*d^6*e^6
*f^2*z - 45*b^8*c^4*d^4*e^8*f^2*z - 36*b^10*c^2*d^2*e^10*f^2*z + 36*b^5*c^7*d^7*e^5*f^2*z - 16*a^2*c^10*d^10*e
^2*g^2*z + 33048*a^5*c^7*d^2*e^10*f^2*z - 6300*a^4*c^8*d^4*e^8*f^2*z - 5040*a^3*c^9*d^6*e^6*f^2*z - 1980*a^2*c
^10*d^8*e^4*f^2*z - 1185*a^6*b^2*c^4*e^12*g^2*z + 630*a^5*b^4*c^3*e^12*g^2*z - 160*a^4*b^6*c^2*e^12*g^2*z - 11
565*a^4*b^4*c^4*e^12*f^2*z + 9612*a^5*b^2*c^5*e^12*f^2*z + 5760*a^3*b^6*c^3*e^12*f^2*z - 1440*a^2*b^8*c^2*e^12
*f^2*z + 12*b^12*d*e^11*f*g*z + 36*b*c^11*d^12*f*g*z + 6*a*b^11*e^12*f*g*z + 60*b^3*c^9*d^11*e*g^2*z + 20*b^11
*c*d^3*e^9*g^2*z - 360*a*c^11*d^10*e^2*f^2*z + 20*a^3*b^8*c*e^12*g^2*z - 4*b^12*d^2*e^10*g^2*z + 768*a^7*c^5*e
^12*g^2*z - 9*b^2*c^10*d^12*g^2*z - 900*a^6*c^6*e^12*f^2*z - a^2*b^10*e^12*g^2*z - 36*c^12*d^12*f^2*z - 9*b^12
*e^12*f^2*z + 4644*a*b^2*c^6*d^2*e^8*f^2*g + 3420*a^2*b*c^6*d^2*e^8*f*g^2 - 2436*a*b^2*c^6*d^3*e^7*f*g^2 - 214
2*a^2*b^2*c^5*d*e^9*f*g^2 - 1470*a*b^3*c^5*d^2*e^8*f*g^2 + 1020*a*b^4*c^4*d*e^9*f*g^2 + 732*a*b*c^7*d^4*e^6*f*
g^2 + 720*a*b*c^7*d^3*e^7*f^2*g - 648*a^2*b*c^6*d*e^9*f^2*g - 468*a*b^3*c^5*d*e^9*f^2*g + 981*a^2*b^2*c^5*d^2*
e^8*g^3 - 540*b^3*c^6*d^3*e^7*f^2*g + 468*b^2*c^7*d^4*e^6*f^2*g - 459*b^4*c^5*d^2*e^8*f^2*g - 438*b^2*c^7*d^5*
e^5*f*g^2 + 396*b^4*c^5*d^3*e^7*f*g^2 + 120*b^5*c^4*d^2*e^8*f*g^2 + 87*b^3*c^6*d^4*e^6*f*g^2 - 7452*a^2*c^7*d^
2*e^8*f^2*g + 2688*a^2*c^7*d^3*e^7*f*g^2 + 1512*a^2*b^2*c^5*e^10*f^2*g + 555*a^2*b^3*c^4*e^10*f*g^2 - 1184*a^2
*b*c^6*d^3*e^7*g^3 + 796*a*b^3*c^5*d^3*e^7*g^3 - 360*a*b^4*c^4*d^2*e^8*g^3 - 350*a^2*b^3*c^4*d*e^9*g^3 + 7*a*b
^2*c^6*d^4*e^6*g^3 + 216*b*c^8*d^5*e^5*f^2*g + 180*b*c^8*d^6*e^4*f*g^2 - 120*b^6*c^3*d*e^9*f*g^2 + 90*b^5*c^4*
d*e^9*f^2*g - 1332*a*c^8*d^4*e^6*f^2*g + 1008*a^3*c^6*d*e^9*f*g^2 + 240*a*c^8*d^5*e^5*f*g^2 - 1404*a^3*b*c^5*e
^10*f*g^2 - 765*a*b^4*c^4*e^10*f^2*g - 60*a*b^5*c^3*e^10*f*g^2 + 760*a^3*b*c^5*d*e^9*g^3 - 120*a*b*c^7*d^5*e^5
*g^3 + 40*a*b^5*c^3*d*e^9*g^3 - 1944*a*b*c^7*d^2*e^8*f^3 - 1728*a*b^2*c^6*d*e^9*f^3 - 180*c^9*d^6*e^4*f^2*g +
90*b^6*c^3*e^10*f^2*g + 900*a^3*c^6*e^10*f^2*g - 540*b*c^8*d^4*e^6*f^3 + 162*b^4*c^5*d*e^9*f^3 + 5400*a^2*c^7*
d*e^9*f^3 + 1296*a*c^8*d^3*e^7*f^3 - 2700*a^2*b*c^6*e^10*f^3 + 1188*a*b^3*c^5*e^10*f^3 + 138*b^3*c^6*d^5*e^5*g
^3 - 98*b^4*c^5*d^4*e^6*g^3 - 80*b^5*c^4*d^3*e^7*g^3 - 45*b^2*c^7*d^6*e^4*g^3 + 40*b^6*c^3*d^2*e^8*g^3 - 1264*
a^3*c^6*d^2*e^8*g^3 + 216*b^3*c^6*d^2*e^8*f^3 + 216*b^2*c^7*d^3*e^7*f^3 - 80*a^2*c^7*d^4*e^6*g^3 - 95*a^3*b^2*
c^4*e^10*g^3 + 10*a^2*b^4*c^3*e^10*g^3 + 216*c^9*d^5*e^5*f^3 + 256*a^4*c^5*e^10*g^3 - 135*b^5*c^4*e^10*f^3, z,
k)*(root(286720*a^9*b*c^8*d^7*e^9*z^3 + 286720*a^8*b*c^9*d^9*e^7*z^3 + 172032*a^10*b*c^7*d^5*e^11*z^3 + 17203
2*a^7*b*c^10*d^11*e^5*z^3 + 57344*a^11*b*c^6*d^3*e^13*z^3 + 57344*a^6*b*c^11*d^13*e^3*z^3 - 10240*a^11*b^3*c^4
*d*e^15*z^3 - 10240*a^4*b^3*c^11*d^15*e*z^3 + 5120*a^10*b^5*c^3*d*e^15*z^3 + 5120*a^3*b^5*c^10*d^15*e*z^3 - 12
80*a^9*b^7*c^2*d*e^15*z^3 - 1280*a^2*b^7*c^9*d^15*e*z^3 - 1232*a^5*b^12*c*d^4*e^12*z^3 - 1232*a*b^12*c^5*d^12*
e^4*z^3 + 1064*a^6*b^11*c*d^3*e^13*z^3 + 1064*a*b^11*c^6*d^13*e^3*z^3 + 840*a^4*b^13*c*d^5*e^11*z^3 + 840*a*b^
13*c^4*d^11*e^5*z^3 - 552*a^7*b^10*c*d^2*e^14*z^3 - 552*a*b^10*c^7*d^14*e^2*z^3 - 280*a^3*b^14*c*d^6*e^10*z^3
- 280*a*b^14*c^3*d^10*e^6*z^3 - 8*a^2*b^15*c*d^7*e^9*z^3 - 8*a*b^15*c^2*d^9*e^7*z^3 + 8192*a^12*b*c^5*d*e^15*z
^3 + 8192*a^5*b*c^12*d^15*e*z^3 + 160*a^8*b^9*c*d*e^15*z^3 + 160*a*b^9*c^8*d^15*e*z^3 + 36*a*b^16*c*d^8*e^8*z^
3 - 483840*a^8*b^2*c^8*d^8*e^8*z^3 - 365568*a^7*b^5*c^6*d^7*e^9*z^3 - 365568*a^6*b^5*c^7*d^9*e^7*z^3 - 358400*
a^9*b^2*c^7*d^6*e^10*z^3 - 358400*a^7*b^2*c^9*d^10*e^6*z^3 + 241920*a^7*b^4*c^7*d^8*e^8*z^3 + 215040*a^8*b^4*c
^6*d^6*e^10*z^3 + 215040*a^8*b^3*c^7*d^7*e^9*z^3 + 215040*a^7*b^3*c^8*d^9*e^7*z^3 + 215040*a^6*b^4*c^8*d^10*e^
6*z^3 - 193536*a^8*b^5*c^5*d^5*e^11*z^3 - 193536*a^5*b^5*c^8*d^11*e^5*z^3 - 136192*a^10*b^2*c^6*d^4*e^12*z^3 -
136192*a^6*b^2*c^10*d^12*e^4*z^3 + 133056*a^6*b^6*c^6*d^8*e^8*z^3 + 125440*a^9*b^4*c^5*d^4*e^12*z^3 + 125440*
a^5*b^4*c^9*d^12*e^4*z^3 - 109944*a^5*b^8*c^5*d^8*e^8*z^3 + 106752*a^6*b^7*c^5*d^7*e^9*z^3 + 106752*a^5*b^7*c^
6*d^9*e^7*z^3 + 80640*a^7*b^7*c^4*d^5*e^11*z^3 + 80640*a^4*b^7*c^7*d^11*e^5*z^3 - 77280*a^6*b^8*c^4*d^6*e^10*z
^3 - 77280*a^4*b^8*c^6*d^10*e^6*z^3 + 71680*a^9*b^3*c^6*d^5*e^11*z^3 + 71680*a^6*b^3*c^9*d^11*e^5*z^3 + 69888*
a^7*b^6*c^5*d^6*e^10*z^3 + 69888*a^5*b^6*c^7*d^10*e^6*z^3 - 35840*a^9*b^5*c^4*d^3*e^13*z^3 - 35840*a^4*b^5*c^9
*d^13*e^3*z^3 + 30720*a^10*b^4*c^4*d^2*e^14*z^3 + 30720*a^4*b^4*c^10*d^14*e^2*z^3 + 26880*a^8*b^7*c^3*d^3*e^13
*z^3 + 26880*a^3*b^7*c^8*d^13*e^3*z^3 + 21510*a^4*b^10*c^4*d^8*e^8*z^3 + 18536*a^5*b^10*c^3*d^6*e^10*z^3 + 185
36*a^3*b^10*c^5*d^10*e^6*z^3 - 18480*a^7*b^8*c^3*d^4*e^12*z^3 - 18480*a^3*b^8*c^7*d^12*e^4*z^3 - 18432*a^11*b^
2*c^5*d^2*e^14*z^3 - 18432*a^5*b^2*c^11*d^14*e^2*z^3 - 16640*a^9*b^6*c^3*d^2*e^14*z^3 - 16640*a^3*b^6*c^9*d^14
*e^2*z^3 - 14336*a^10*b^3*c^5*d^3*e^13*z^3 - 14336*a^5*b^3*c^10*d^13*e^3*z^3 - 13440*a^8*b^6*c^4*d^4*e^12*z^3
- 13440*a^4*b^6*c^8*d^12*e^4*z^3 + 13280*a^5*b^9*c^4*d^7*e^9*z^3 + 13280*a^4*b^9*c^5*d^9*e^7*z^3 - 10840*a^4*b
^11*c^3*d^7*e^9*z^3 - 10840*a^3*b^11*c^4*d^9*e^7*z^3 + 7868*a^6*b^10*c^2*d^4*e^12*z^3 + 7868*a^2*b^10*c^6*d^12
*e^4*z^3 - 7840*a^7*b^9*c^2*d^3*e^13*z^3 - 7840*a^2*b^9*c^7*d^13*e^3*z^3 - 5600*a^6*b^9*c^3*d^5*e^11*z^3 - 560
0*a^3*b^9*c^6*d^11*e^5*z^3 + 4320*a^8*b^8*c^2*d^2*e^14*z^3 + 4320*a^2*b^8*c^8*d^14*e^2*z^3 - 3528*a^5*b^11*c^2
*d^5*e^11*z^3 - 3528*a^2*b^11*c^5*d^11*e^5*z^3 + 1520*a^3*b^13*c^2*d^7*e^9*z^3 + 1520*a^2*b^13*c^3*d^9*e^7*z^3
- 700*a^4*b^12*c^2*d^6*e^10*z^3 - 700*a^2*b^12*c^4*d^10*e^6*z^3 - 540*a^2*b^14*c^2*d^8*e^8*z^3 + 480*a^3*b^12
*c^3*d^8*e^8*z^3 - 8*b^17*c*d^9*e^7*z^3 - 8*b^11*c^7*d^15*e*z^3 - 8*a^7*b^11*d*e^15*z^3 - 8*a*b^17*d^7*e^9*z^3
- 20*a^9*b^8*c*e^16*z^3 - 20*a*b^8*c^9*d^16*z^3 + 70*b^14*c^4*d^12*e^4*z^3 - 56*b^15*c^3*d^11*e^5*z^3 - 56*b^
13*c^5*d^13*e^3*z^3 + 28*b^16*c^2*d^10*e^6*z^3 + 28*b^12*c^6*d^14*e^2*z^3 - 71680*a^9*c^9*d^8*e^8*z^3 - 57344*
a^10*c^8*d^6*e^10*z^3 - 57344*a^8*c^10*d^10*e^6*z^3 - 28672*a^11*c^7*d^4*e^12*z^3 - 28672*a^7*c^11*d^12*e^4*z^
3 - 8192*a^12*c^6*d^2*e^14*z^3 - 8192*a^6*c^12*d^14*e^2*z^3 + 70*a^4*b^14*d^4*e^12*z^3 - 56*a^5*b^13*d^3*e^13*
z^3 - 56*a^3*b^15*d^5*e^11*z^3 + 28*a^6*b^12*d^2*e^14*z^3 + 28*a^2*b^16*d^6*e^10*z^3 + 1280*a^12*b^2*c^4*e^16*
z^3 - 640*a^11*b^4*c^3*e^16*z^3 + 160*a^10*b^6*c^2*e^16*z^3 + 1280*a^4*b^2*c^12*d^16*z^3 - 640*a^3*b^4*c^11*d^
16*z^3 + 160*a^2*b^6*c^10*d^16*z^3 - 1024*a^13*c^5*e^16*z^3 - 1024*a^5*c^13*d^16*z^3 + b^18*d^8*e^8*z^3 + b^10
*c^8*d^16*z^3 + a^8*b^10*e^16*z^3 + 96*a*b*c^10*d^10*e^2*f*g*z + 69900*a^4*b^2*c^6*d^3*e^9*f*g*z - 64590*a^4*b
^3*c^5*d^2*e^10*f*g*z - 40200*a^3*b^4*c^5*d^3*e^9*f*g*z + 32820*a^3*b^5*c^4*d^2*e^10*f*g*z + 10680*a^2*b^6*c^4
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f*g*z - 5880*a^3*b^2*c^7*d^5*e^7*f*g*z - 5040*a^2*b^4*c^6*d^5*e^7*f*g*z - 3240*a^2*b^2*c^8*d^7*e^5*f*g*z - 126
0*a^2*b^5*c^5*d^4*e^8*f*g*z - 252*a*b^10*c*d*e^11*f*g*z + 55872*a^5*b*c^6*d^2*e^10*f*g*z - 30636*a^5*b^2*c^5*d
*e^11*f*g*z + 24180*a^4*b^4*c^4*d*e^11*f*g*z - 9720*a^3*b^6*c^3*d*e^11*f*g*z + 3690*a*b^3*c^8*d^8*e^4*f*g*z -
3360*a^3*b*c^8*d^6*e^6*f*g*z - 3240*a*b^4*c^7*d^7*e^5*f*g*z + 2160*a^2*b^8*c^2*d*e^11*f*g*z - 2100*a^4*b*c^7*d
^4*e^8*f*g*z - 1500*a*b^2*c^9*d^9*e^3*f*g*z - 1320*a*b^8*c^3*d^3*e^9*f*g*z - 1260*a^2*b*c^9*d^8*e^4*f*g*z + 10
80*a*b^9*c^2*d^2*e^10*f*g*z + 924*a*b^6*c^5*d^5*e^7*f*g*z + 252*a*b^5*c^6*d^6*e^6*f*g*z - 150*a*b^7*c^4*d^4*e^
8*f*g*z + 48*a*c^11*d^11*e*f*g*z - 660*b^4*c^8*d^9*e^3*f*g*z + 570*b^3*c^9*d^10*e^2*f*g*z + 270*b^5*c^7*d^8*e^
4*f*g*z + 84*b^6*c^6*d^7*e^5*f*g*z + 60*b^10*c^2*d^3*e^9*f*g*z - 60*b^8*c^4*d^5*e^7*f*g*z - 42*b^7*c^5*d^6*e^6
*f*g*z + 30*b^9*c^3*d^4*e^8*f*g*z - 59280*a^5*c^7*d^3*e^9*f*g*z + 3360*a^4*c^8*d^5*e^7*f*g*z + 2400*a^3*c^9*d^
7*e^5*f*g*z + 720*a^2*c^10*d^9*e^3*f*g*z + 7410*a^5*b^3*c^4*e^12*f*g*z - 3810*a^4*b^5*c^3*e^12*f*g*z + 960*a^3
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3048*a^5*b*c^6*d*e^11*f^2*z + 1800*a*b*c^10*d^9*e^3*f^2*z - 720*a*b^9*c^2*d*e^11*f^2*z - 31575*a^4*b^2*c^6*d^4
*e^8*g^2*z + 24700*a^4*b^3*c^5*d^3*e^9*g^2*z + 16722*a^5*b^2*c^5*d^2*e^10*g^2*z + 15700*a^3*b^4*c^5*d^4*e^8*g^
2*z - 12140*a^3*b^5*c^4*d^3*e^9*g^2*z - 11640*a^4*b^4*c^4*d^2*e^10*g^2*z - 4485*a^2*b^6*c^4*d^4*e^8*g^2*z + 41
80*a^3*b^6*c^3*d^2*e^10*g^2*z + 3120*a^2*b^7*c^3*d^3*e^9*g^2*z - 1960*a^3*b^3*c^6*d^5*e^7*g^2*z + 1820*a^3*b^2
*c^7*d^6*e^6*g^2*z + 1596*a^2*b^5*c^5*d^5*e^7*g^2*z + 1185*a^2*b^2*c^8*d^8*e^4*g^2*z - 1080*a^2*b^3*c^7*d^7*e^
5*g^2*z - 840*a^2*b^8*c^2*d^2*e^10*g^2*z - 840*a^2*b^4*c^6*d^6*e^6*g^2*z - 50760*a^4*b^2*c^6*d^2*e^10*f^2*z +
25380*a^3*b^4*c^5*d^2*e^10*f^2*z - 12600*a^3*b^2*c^7*d^4*e^8*f^2*z - 10080*a^2*b^2*c^8*d^6*e^6*f^2*z - 6030*a^
2*b^6*c^4*d^2*e^10*f^2*z + 3150*a^2*b^4*c^6*d^4*e^8*f^2*z + 2520*a^2*b^3*c^7*d^5*e^7*f^2*z - 1260*a^2*b^5*c^5*
d^3*e^9*f^2*z - 228*b^2*c^10*d^11*e*f*g*z - 54*b^11*c*d^2*e^10*f*g*z + 12816*a^6*c^6*d*e^11*f*g*z - 5508*a^6*b
*c^5*e^12*f*g*z - 120*a^2*b^9*c*e^12*f*g*z - 24*a*b*c^10*d^11*e*g^2*z - 18360*a^5*b*c^6*d^3*e^9*g^2*z - 5340*a
^5*b^3*c^4*d*e^11*g^2*z + 2580*a^4*b^5*c^3*d*e^11*g^2*z + 1680*a^4*b*c^7*d^5*e^7*g^2*z + 1380*a*b^5*c^6*d^7*e^
5*g^2*z - 1050*a*b^4*c^7*d^8*e^4*g^2*z - 686*a*b^6*c^5*d^6*e^6*g^2*z - 640*a^3*b^7*c^2*d*e^11*g^2*z + 570*a*b^
8*c^3*d^4*e^8*g^2*z - 400*a*b^9*c^2*d^3*e^9*g^2*z - 280*a^2*b*c^9*d^9*e^3*g^2*z + 260*a*b^3*c^8*d^9*e^3*g^2*z
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4*d*e^11*f^2*z + 15120*a^3*b*c^8*d^5*e^7*f^2*z + 12600*a^4*b*c^7*d^3*e^9*f^2*z + 7920*a^2*b*c^9*d^7*e^5*f^2*z
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*d^5*e^7*f^2*z + 1260*a*b^4*c^7*d^6*e^6*f^2*z + 720*a*b^8*c^3*d^2*e^10*f^2*z + 180*a*b^7*c^4*d^3*e^9*f^2*z + 2
16*b*c^11*d^11*e*f^2*z + 36*b^11*c*d*e^11*f^2*z - 4*a*b^11*d*e^11*g^2*z + 180*a*b^10*c*e^12*f^2*z + 200*b^5*c^
7*d^9*e^3*g^2*z - 160*b^4*c^8*d^10*e^2*g^2*z - 85*b^6*c^6*d^8*e^4*g^2*z + 70*b^8*c^4*d^6*e^6*g^2*z - 56*b^7*c^
5*d^7*e^5*g^2*z - 25*b^10*c^2*d^4*e^8*g^2*z - 20*b^9*c^3*d^5*e^7*g^2*z + 24000*a^5*c^7*d^4*e^8*g^2*z - 11280*a
^6*c^6*d^2*e^10*g^2*z - 1120*a^4*c^8*d^6*e^6*g^2*z + 540*b^3*c^9*d^9*e^3*f^2*z - 504*b^2*c^10*d^10*e^2*f^2*z -
320*a^3*c^9*d^8*e^4*g^2*z - 225*b^4*c^8*d^8*e^4*f^2*z + 144*b^7*c^5*d^5*e^7*f^2*z - 126*b^6*c^6*d^6*e^6*f^2*z
- 45*b^8*c^4*d^4*e^8*f^2*z - 36*b^10*c^2*d^2*e^10*f^2*z + 36*b^5*c^7*d^7*e^5*f^2*z - 16*a^2*c^10*d^10*e^2*g^2
*z + 33048*a^5*c^7*d^2*e^10*f^2*z - 6300*a^4*c^8*d^4*e^8*f^2*z - 5040*a^3*c^9*d^6*e^6*f^2*z - 1980*a^2*c^10*d^
8*e^4*f^2*z - 1185*a^6*b^2*c^4*e^12*g^2*z + 630*a^5*b^4*c^3*e^12*g^2*z - 160*a^4*b^6*c^2*e^12*g^2*z - 11565*a^
4*b^4*c^4*e^12*f^2*z + 9612*a^5*b^2*c^5*e^12*f^2*z + 5760*a^3*b^6*c^3*e^12*f^2*z - 1440*a^2*b^8*c^2*e^12*f^2*z
+ 12*b^12*d*e^11*f*g*z + 36*b*c^11*d^12*f*g*z + 6*a*b^11*e^12*f*g*z + 60*b^3*c^9*d^11*e*g^2*z + 20*b^11*c*d^3
*e^9*g^2*z - 360*a*c^11*d^10*e^2*f^2*z + 20*a^3*b^8*c*e^12*g^2*z - 4*b^12*d^2*e^10*g^2*z + 768*a^7*c^5*e^12*g^
2*z - 9*b^2*c^10*d^12*g^2*z - 900*a^6*c^6*e^12*f^2*z - a^2*b^10*e^12*g^2*z - 36*c^12*d^12*f^2*z - 9*b^12*e^12*
f^2*z + 4644*a*b^2*c^6*d^2*e^8*f^2*g + 3420*a^2*b*c^6*d^2*e^8*f*g^2 - 2436*a*b^2*c^6*d^3*e^7*f*g^2 - 2142*a^2*
b^2*c^5*d*e^9*f*g^2 - 1470*a*b^3*c^5*d^2*e^8*f*g^2 + 1020*a*b^4*c^4*d*e^9*f*g^2 + 732*a*b*c^7*d^4*e^6*f*g^2 +
720*a*b*c^7*d^3*e^7*f^2*g - 648*a^2*b*c^6*d*e^9*f^2*g - 468*a*b^3*c^5*d*e^9*f^2*g + 981*a^2*b^2*c^5*d^2*e^8*g^
3 - 540*b^3*c^6*d^3*e^7*f^2*g + 468*b^2*c^7*d^4*e^6*f^2*g - 459*b^4*c^5*d^2*e^8*f^2*g - 438*b^2*c^7*d^5*e^5*f*
g^2 + 396*b^4*c^5*d^3*e^7*f*g^2 + 120*b^5*c^4*d^2*e^8*f*g^2 + 87*b^3*c^6*d^4*e^6*f*g^2 - 7452*a^2*c^7*d^2*e^8*
f^2*g + 2688*a^2*c^7*d^3*e^7*f*g^2 + 1512*a^2*b^2*c^5*e^10*f^2*g + 555*a^2*b^3*c^4*e^10*f*g^2 - 1184*a^2*b*c^6
*d^3*e^7*g^3 + 796*a*b^3*c^5*d^3*e^7*g^3 - 360*a*b^4*c^4*d^2*e^8*g^3 - 350*a^2*b^3*c^4*d*e^9*g^3 + 7*a*b^2*c^6
*d^4*e^6*g^3 + 216*b*c^8*d^5*e^5*f^2*g + 180*b*c^8*d^6*e^4*f*g^2 - 120*b^6*c^3*d*e^9*f*g^2 + 90*b^5*c^4*d*e^9*
f^2*g - 1332*a*c^8*d^4*e^6*f^2*g + 1008*a^3*c^6*d*e^9*f*g^2 + 240*a*c^8*d^5*e^5*f*g^2 - 1404*a^3*b*c^5*e^10*f*
g^2 - 765*a*b^4*c^4*e^10*f^2*g - 60*a*b^5*c^3*e^10*f*g^2 + 760*a^3*b*c^5*d*e^9*g^3 - 120*a*b*c^7*d^5*e^5*g^3 +
40*a*b^5*c^3*d*e^9*g^3 - 1944*a*b*c^7*d^2*e^8*f^3 - 1728*a*b^2*c^6*d*e^9*f^3 - 180*c^9*d^6*e^4*f^2*g + 90*b^6
*c^3*e^10*f^2*g + 900*a^3*c^6*e^10*f^2*g - 540*b*c^8*d^4*e^6*f^3 + 162*b^4*c^5*d*e^9*f^3 + 5400*a^2*c^7*d*e^9*
f^3 + 1296*a*c^8*d^3*e^7*f^3 - 2700*a^2*b*c^6*e^10*f^3 + 1188*a*b^3*c^5*e^10*f^3 + 138*b^3*c^6*d^5*e^5*g^3 - 9
8*b^4*c^5*d^4*e^6*g^3 - 80*b^5*c^4*d^3*e^7*g^3 - 45*b^2*c^7*d^6*e^4*g^3 + 40*b^6*c^3*d^2*e^8*g^3 - 1264*a^3*c^
6*d^2*e^8*g^3 + 216*b^3*c^6*d^2*e^8*f^3 + 216*b^2*c^7*d^3*e^7*f^3 - 80*a^2*c^7*d^4*e^6*g^3 - 95*a^3*b^2*c^4*e^
10*g^3 + 10*a^2*b^4*c^3*e^10*g^3 + 216*c^9*d^5*e^5*f^3 + 256*a^4*c^5*e^10*g^3 - 135*b^5*c^4*e^10*f^3, z, k)*((
2048*a^11*c^6*d*e^14 - 256*a^11*b*c^5*e^15 - a^7*b^9*c*e^15 - b^9*c^8*d^14*e - b^16*c*d^7*e^8 + 16*a^8*b^7*c^2
*e^15 - 96*a^9*b^5*c^3*e^15 + 256*a^10*b^3*c^4*e^15 + 2048*a^5*c^12*d^13*e^2 + 12288*a^6*c^11*d^11*e^4 + 30720
*a^7*c^10*d^9*e^6 + 40960*a^8*c^9*d^7*e^8 + 30720*a^9*c^8*d^5*e^10 + 12288*a^10*c^7*d^3*e^12 + 5*b^10*c^7*d^13
*e^2 - 9*b^11*c^6*d^12*e^3 + 5*b^12*c^5*d^11*e^4 + 5*b^13*c^4*d^10*e^5 - 9*b^14*c^3*d^9*e^6 + 5*b^15*c^2*d^8*e
^7 + 352*a^2*b^6*c^9*d^13*e^2 + 16*a^2*b^7*c^8*d^12*e^3 - 1872*a^2*b^8*c^7*d^11*e^4 + 3499*a^2*b^9*c^6*d^10*e^
5 - 2549*a^2*b^10*c^5*d^9*e^6 + 438*a^2*b^11*c^4*d^8*e^7 + 334*a^2*b^12*c^3*d^7*e^8 - 113*a^2*b^13*c^2*d^6*e^9
- 512*a^3*b^4*c^10*d^13*e^2 - 2976*a^3*b^5*c^9*d^12*e^3 + 12352*a^3*b^6*c^8*d^11*e^4 - 16784*a^3*b^7*c^7*d^10
*e^5 + 6984*a^3*b^8*c^6*d^9*e^6 + 4157*a^3*b^9*c^5*d^8*e^7 - 4204*a^3*b^10*c^4*d^7*e^8 + 438*a^3*b^11*c^3*d^6*
e^9 + 284*a^3*b^12*c^2*d^5*e^10 - 768*a^4*b^2*c^11*d^13*e^2 + 11776*a^4*b^3*c^10*d^12*e^3 - 32512*a^4*b^4*c^9*
d^11*e^4 + 28704*a^4*b^5*c^8*d^10*e^5 + 13216*a^4*b^6*c^7*d^9*e^6 - 36752*a^4*b^7*c^6*d^8*e^7 + 15264*a^4*b^8*
c^5*d^7*e^8 + 4157*a^4*b^9*c^4*d^6*e^9 - 2549*a^4*b^10*c^3*d^5*e^10 - 285*a^4*b^11*c^2*d^4*e^11 + 26112*a^5*b^
2*c^10*d^11*e^4 + 14336*a^5*b^3*c^9*d^10*e^5 - 94720*a^5*b^4*c^8*d^9*e^6 + 88032*a^5*b^5*c^7*d^8*e^7 + 4480*a^
5*b^6*c^6*d^7*e^8 - 36752*a^5*b^7*c^5*d^6*e^9 + 6984*a^5*b^8*c^4*d^5*e^10 + 3499*a^5*b^9*c^3*d^4*e^11 + 70*a^5
*b^10*c^2*d^3*e^12 + 111360*a^6*b^2*c^9*d^9*e^6 - 14080*a^6*b^3*c^8*d^8*e^7 - 125440*a^6*b^4*c^7*d^7*e^8 + 880
32*a^6*b^5*c^6*d^6*e^9 + 13216*a^6*b^6*c^5*d^5*e^10 - 16784*a^6*b^7*c^4*d^4*e^11 - 1872*a^6*b^8*c^3*d^3*e^12 +
89*a^6*b^9*c^2*d^2*e^13 + 168960*a^7*b^2*c^8*d^7*e^8 - 14080*a^7*b^3*c^7*d^6*e^9 - 94720*a^7*b^4*c^6*d^5*e^10
+ 28704*a^7*b^5*c^5*d^4*e^11 + 12352*a^7*b^6*c^4*d^3*e^12 + 16*a^7*b^7*c^3*d^2*e^13 + 111360*a^8*b^2*c^7*d^5*
e^10 + 14336*a^8*b^3*c^6*d^4*e^11 - 32512*a^8*b^4*c^5*d^3*e^12 - 2976*a^8*b^5*c^4*d^2*e^13 + 26112*a^9*b^2*c^6
*d^3*e^12 + 11776*a^9*b^3*c^5*d^2*e^13 + 16*a*b^7*c^9*d^14*e + 5*a*b^15*c*d^6*e^9 - 256*a^4*b*c^12*d^14*e + 5*
a^6*b^10*c*d*e^14 - 72*a*b^8*c^8*d^13*e^2 + 89*a*b^9*c^7*d^12*e^3 + 70*a*b^10*c^6*d^11*e^4 - 285*a*b^11*c^5*d^
10*e^5 + 284*a*b^12*c^4*d^9*e^6 - 113*a*b^13*c^3*d^8*e^7 + 6*a*b^14*c^2*d^7*e^8 - 96*a^2*b^5*c^10*d^14*e - 9*a
^2*b^14*c*d^5*e^10 + 256*a^3*b^3*c^11*d^14*e + 5*a^3*b^13*c*d^4*e^11 + 5*a^4*b^12*c*d^3*e^12 - 14080*a^5*b*c^1
1*d^12*e^3 - 9*a^5*b^11*c*d^2*e^13 - 66816*a^6*b*c^10*d^10*e^5 - 131840*a^7*b*c^9*d^8*e^7 - 72*a^7*b^8*c^2*d*e
^14 - 131840*a^8*b*c^8*d^6*e^9 + 352*a^8*b^6*c^3*d*e^14 - 66816*a^9*b*c^7*d^4*e^11 - 512*a^9*b^4*c^4*d*e^14 -
14080*a^10*b*c^6*d^2*e^13 - 768*a^10*b^2*c^5*d*e^14)/(256*a^4*c^10*d^12 + a^6*b^8*e^12 + 256*a^10*c^4*e^12 + b
^8*c^6*d^12 + b^14*d^6*e^6 - 16*a*b^6*c^7*d^12 - 16*a^7*b^6*c*e^12 - 6*a*b^13*d^5*e^7 - 6*a^5*b^9*d*e^11 - 6*b
^9*c^5*d^11*e - 6*b^13*c*d^7*e^5 + 96*a^2*b^4*c^8*d^12 - 256*a^3*b^2*c^9*d^12 + 96*a^8*b^4*c^2*e^12 - 256*a^9*
b^2*c^3*e^12 + 15*a^2*b^12*d^4*e^8 - 20*a^3*b^11*d^3*e^9 + 15*a^4*b^10*d^2*e^10 + 1536*a^5*c^9*d^10*e^2 + 3840
*a^6*c^8*d^8*e^4 + 5120*a^7*c^7*d^6*e^6 + 3840*a^8*c^6*d^4*e^8 + 1536*a^9*c^5*d^2*e^10 + 15*b^10*c^4*d^10*e^2
- 20*b^11*c^3*d^9*e^3 + 15*b^12*c^2*d^8*e^4 + 1344*a^2*b^6*c^6*d^10*e^2 - 1440*a^2*b^7*c^5*d^9*e^3 + 495*a^2*b
^8*c^4*d^8*e^4 + 324*a^2*b^9*c^3*d^7*e^5 - 294*a^2*b^10*c^2*d^6*e^6 - 3264*a^3*b^4*c^7*d^10*e^2 + 2240*a^3*b^5
*c^6*d^9*e^3 + 1680*a^3*b^6*c^5*d^8*e^4 - 3264*a^3*b^7*c^4*d^7*e^5 + 1204*a^3*b^8*c^3*d^6*e^6 + 324*a^3*b^9*c^
2*d^5*e^7 + 2304*a^4*b^2*c^8*d^10*e^2 + 2560*a^4*b^3*c^7*d^9*e^3 - 10080*a^4*b^4*c^6*d^8*e^4 + 8064*a^4*b^5*c^
5*d^7*e^5 + 896*a^4*b^6*c^4*d^6*e^6 - 3264*a^4*b^7*c^3*d^5*e^7 + 495*a^4*b^8*c^2*d^4*e^8 + 11520*a^5*b^2*c^7*d
^8*e^4 - 13440*a^5*b^4*c^5*d^6*e^6 + 8064*a^5*b^5*c^4*d^5*e^7 + 1680*a^5*b^6*c^3*d^4*e^8 - 1440*a^5*b^7*c^2*d^
3*e^9 + 17920*a^6*b^2*c^6*d^6*e^6 - 10080*a^6*b^4*c^4*d^4*e^8 + 2240*a^6*b^5*c^3*d^3*e^9 + 1344*a^6*b^6*c^2*d^
2*e^10 + 11520*a^7*b^2*c^5*d^4*e^8 + 2560*a^7*b^3*c^4*d^3*e^9 - 3264*a^7*b^4*c^3*d^2*e^10 + 2304*a^8*b^2*c^4*d
^2*e^10 + 96*a*b^7*c^6*d^11*e + 14*a*b^12*c*d^6*e^6 - 1536*a^4*b*c^9*d^11*e + 96*a^6*b^7*c*d*e^11 - 1536*a^9*b
*c^4*d*e^11 - 234*a*b^8*c^5*d^10*e^2 + 290*a*b^9*c^4*d^9*e^3 - 180*a*b^10*c^3*d^8*e^4 + 36*a*b^11*c^2*d^7*e^5
- 576*a^2*b^5*c^7*d^11*e + 36*a^2*b^11*c*d^5*e^7 + 1536*a^3*b^3*c^8*d^11*e - 180*a^3*b^10*c*d^4*e^8 + 290*a^4*
b^9*c*d^3*e^9 - 7680*a^5*b*c^8*d^9*e^3 - 234*a^5*b^8*c*d^2*e^10 - 15360*a^6*b*c^7*d^7*e^5 - 15360*a^7*b*c^6*d^
5*e^7 - 576*a^7*b^5*c^2*d*e^11 - 7680*a^8*b*c^5*d^3*e^9 + 1536*a^8*b^3*c^3*d*e^11) - (x*(2*a^6*b^10*c*e^15 - 1
536*a^11*c^6*e^15 + 512*a^4*c^13*d^14*e + 2*b^8*c^9*d^14*e + 2*b^16*c*d^6*e^9 - 38*a^7*b^8*c^2*e^15 + 288*a^8*
b^6*c^3*e^15 - 1088*a^9*b^4*c^4*e^15 + 2048*a^10*b^2*c^5*e^15 + 1536*a^5*c^12*d^12*e^3 - 1536*a^6*c^11*d^10*e^
5 - 12800*a^7*c^10*d^8*e^7 - 23040*a^8*c^9*d^6*e^9 - 19968*a^9*c^8*d^4*e^11 - 8704*a^10*c^7*d^2*e^13 - 14*b^9*
c^8*d^13*e^2 + 44*b^10*c^7*d^12*e^3 - 82*b^11*c^6*d^11*e^4 + 100*b^12*c^5*d^10*e^5 - 82*b^13*c^4*d^9*e^6 + 44*
b^14*c^3*d^8*e^7 - 14*b^15*c^2*d^7*e^8 - 1344*a^2*b^5*c^10*d^13*e^2 + 4128*a^2*b^6*c^9*d^12*e^3 - 7296*a^2*b^7
*c^8*d^11*e^4 + 7962*a^2*b^8*c^7*d^10*e^5 - 4962*a^2*b^9*c^6*d^9*e^6 + 834*a^2*b^10*c^5*d^8*e^7 + 1092*a^2*b^1
1*c^4*d^7*e^8 - 714*a^2*b^12*c^3*d^6*e^9 + 78*a^2*b^13*c^2*d^5*e^10 + 3584*a^3*b^3*c^11*d^13*e^2 - 10688*a^3*b
^4*c^10*d^12*e^3 + 17536*a^3*b^5*c^9*d^11*e^4 - 15712*a^3*b^6*c^8*d^10*e^5 + 3232*a^3*b^7*c^7*d^9*e^6 + 9326*a
^3*b^8*c^6*d^8*e^7 - 10232*a^3*b^9*c^5*d^7*e^8 + 3164*a^3*b^10*c^4*d^6*e^9 + 752*a^3*b^11*c^3*d^5*e^10 - 410*a
^3*b^12*c^2*d^4*e^11 + 9728*a^4*b^2*c^11*d^12*e^3 - 11776*a^4*b^3*c^10*d^11*e^4 - 1088*a^4*b^4*c^9*d^10*e^5 +
27968*a^4*b^5*c^8*d^9*e^6 - 44576*a^4*b^6*c^7*d^8*e^7 + 27392*a^4*b^7*c^6*d^7*e^8 + 2086*a^4*b^8*c^5*d^6*e^9 -
8882*a^4*b^9*c^4*d^5*e^10 + 1520*a^4*b^10*c^3*d^4*e^11 + 670*a^4*b^11*c^2*d^3*e^12 + 27648*a^5*b^2*c^10*d^10*
e^5 - 53760*a^5*b^3*c^9*d^9*e^6 + 56640*a^5*b^4*c^8*d^8*e^7 - 5376*a^5*b^5*c^7*d^7*e^8 - 45024*a^5*b^6*c^6*d^6
*e^9 + 29472*a^5*b^7*c^5*d^5*e^10 + 2802*a^5*b^8*c^4*d^4*e^11 - 4164*a^5*b^9*c^3*d^3*e^12 - 546*a^5*b^10*c^2*d
^2*e^13 + 5120*a^6*b^2*c^9*d^8*e^7 - 66560*a^6*b^3*c^8*d^7*e^8 + 96320*a^6*b^4*c^7*d^6*e^9 - 23744*a^6*b^5*c^6
*d^5*e^10 - 32032*a^6*b^6*c^5*d^4*e^11 + 10624*a^6*b^7*c^4*d^3*e^12 + 3902*a^6*b^8*c^3*d^2*e^13 - 43520*a^7*b^
2*c^8*d^6*e^9 - 48640*a^7*b^3*c^7*d^5*e^10 + 71872*a^7*b^4*c^6*d^4*e^11 - 2944*a^7*b^5*c^5*d^3*e^12 - 13472*a^
7*b^6*c^4*d^2*e^13 - 41472*a^8*b^2*c^7*d^4*e^11 - 32256*a^8*b^3*c^6*d^3*e^12 + 21312*a^8*b^4*c^5*d^2*e^13 - 81
92*a^9*b^2*c^6*d^2*e^13 - 32*a*b^6*c^10*d^14*e - 12*a*b^15*c*d^5*e^10 - 12*a^5*b^11*c*d*e^14 + 8704*a^10*b*c^6
*d*e^14 + 224*a*b^7*c^9*d^13*e^2 - 698*a*b^8*c^8*d^12*e^3 + 1276*a*b^9*c^7*d^11*e^4 - 1498*a*b^10*c^6*d^10*e^5
+ 1132*a*b^11*c^5*d^9*e^6 - 494*a*b^12*c^4*d^8*e^7 + 68*a*b^13*c^3*d^7*e^8 + 34*a*b^14*c^2*d^6*e^9 + 192*a^2*
b^4*c^11*d^14*e + 30*a^2*b^14*c*d^4*e^11 - 512*a^3*b^2*c^12*d^14*e - 40*a^3*b^13*c*d^3*e^12 - 3584*a^4*b*c^12*
d^13*e^2 + 30*a^4*b^12*c*d^2*e^13 - 9216*a^5*b*c^11*d^11*e^4 + 7680*a^6*b*c^10*d^9*e^6 + 226*a^6*b^9*c^2*d*e^1
4 + 51200*a^7*b*c^9*d^7*e^8 - 1696*a^7*b^7*c^3*d*e^14 + 69120*a^8*b*c^8*d^5*e^10 + 6336*a^8*b^5*c^4*d*e^14 + 3
9936*a^9*b*c^7*d^3*e^12 - 11776*a^9*b^3*c^5*d*e^14))/(256*a^4*c^10*d^12 + a^6*b^8*e^12 + 256*a^10*c^4*e^12 + b
^8*c^6*d^12 + b^14*d^6*e^6 - 16*a*b^6*c^7*d^12 - 16*a^7*b^6*c*e^12 - 6*a*b^13*d^5*e^7 - 6*a^5*b^9*d*e^11 - 6*b
^9*c^5*d^11*e - 6*b^13*c*d^7*e^5 + 96*a^2*b^4*c^8*d^12 - 256*a^3*b^2*c^9*d^12 + 96*a^8*b^4*c^2*e^12 - 256*a^9*
b^2*c^3*e^12 + 15*a^2*b^12*d^4*e^8 - 20*a^3*b^11*d^3*e^9 + 15*a^4*b^10*d^2*e^10 + 1536*a^5*c^9*d^10*e^2 + 3840
*a^6*c^8*d^8*e^4 + 5120*a^7*c^7*d^6*e^6 + 3840*a^8*c^6*d^4*e^8 + 1536*a^9*c^5*d^2*e^10 + 15*b^10*c^4*d^10*e^2
- 20*b^11*c^3*d^9*e^3 + 15*b^12*c^2*d^8*e^4 + 1344*a^2*b^6*c^6*d^10*e^2 - 1440*a^2*b^7*c^5*d^9*e^3 + 495*a^2*b
^8*c^4*d^8*e^4 + 324*a^2*b^9*c^3*d^7*e^5 - 294*a^2*b^10*c^2*d^6*e^6 - 3264*a^3*b^4*c^7*d^10*e^2 + 2240*a^3*b^5
*c^6*d^9*e^3 + 1680*a^3*b^6*c^5*d^8*e^4 - 3264*a^3*b^7*c^4*d^7*e^5 + 1204*a^3*b^8*c^3*d^6*e^6 + 324*a^3*b^9*c^
2*d^5*e^7 + 2304*a^4*b^2*c^8*d^10*e^2 + 2560*a^4*b^3*c^7*d^9*e^3 - 10080*a^4*b^4*c^6*d^8*e^4 + 8064*a^4*b^5*c^
5*d^7*e^5 + 896*a^4*b^6*c^4*d^6*e^6 - 3264*a^4*b^7*c^3*d^5*e^7 + 495*a^4*b^8*c^2*d^4*e^8 + 11520*a^5*b^2*c^7*d
^8*e^4 - 13440*a^5*b^4*c^5*d^6*e^6 + 8064*a^5*b^5*c^4*d^5*e^7 + 1680*a^5*b^6*c^3*d^4*e^8 - 1440*a^5*b^7*c^2*d^
3*e^9 + 17920*a^6*b^2*c^6*d^6*e^6 - 10080*a^6*b^4*c^4*d^4*e^8 + 2240*a^6*b^5*c^3*d^3*e^9 + 1344*a^6*b^6*c^2*d^
2*e^10 + 11520*a^7*b^2*c^5*d^4*e^8 + 2560*a^7*b^3*c^4*d^3*e^9 - 3264*a^7*b^4*c^3*d^2*e^10 + 2304*a^8*b^2*c^4*d
^2*e^10 + 96*a*b^7*c^6*d^11*e + 14*a*b^12*c*d^6*e^6 - 1536*a^4*b*c^9*d^11*e + 96*a^6*b^7*c*d*e^11 - 1536*a^9*b
*c^4*d*e^11 - 234*a*b^8*c^5*d^10*e^2 + 290*a*b^9*c^4*d^9*e^3 - 180*a*b^10*c^3*d^8*e^4 + 36*a*b^11*c^2*d^7*e^5
- 576*a^2*b^5*c^7*d^11*e + 36*a^2*b^11*c*d^5*e^7 + 1536*a^3*b^3*c^8*d^11*e - 180*a^3*b^10*c*d^4*e^8 + 290*a^4*
b^9*c*d^3*e^9 - 7680*a^5*b*c^8*d^9*e^3 - 234*a^5*b^8*c*d^2*e^10 - 15360*a^6*b*c^7*d^7*e^5 - 15360*a^7*b*c^6*d^
5*e^7 - 576*a^7*b^5*c^2*d*e^11 - 7680*a^8*b*c^5*d^3*e^9 + 1536*a^8*b^3*c^3*d*e^11)) + (480*a^8*c^6*e^13*f - 3*
a^3*b^10*c*e^13*f + a^4*b^9*c*e^13*g + 368*a^8*b*c^5*e^13*g + 96*a^2*c^12*d^12*e*f - 448*a^8*c^6*d*e^12*g + 6*
b^4*c^10*d^12*e*f + 3*b^13*c*d^3*e^10*f - 3*b^5*c^9*d^12*e*g - 2*b^13*c*d^4*e^9*g + 51*a^4*b^8*c^2*e^13*f - 33
3*a^5*b^6*c^3*e^13*f + 1014*a^6*b^4*c^4*e^13*f - 1344*a^7*b^2*c^5*e^13*f - 17*a^5*b^7*c^2*e^13*g + 111*a^6*b^5
*c^3*e^13*g - 328*a^7*b^3*c^4*e^13*g + 576*a^3*c^11*d^10*e^3*f + 1824*a^4*c^10*d^8*e^5*f + 3456*a^5*c^9*d^6*e^
7*f + 3744*a^6*c^8*d^4*e^9*f + 2112*a^7*c^7*d^2*e^11*f - 64*a^3*c^11*d^11*e^2*g - 704*a^4*c^10*d^9*e^4*g - 217
6*a^5*c^9*d^7*e^6*g - 2944*a^6*c^8*d^5*e^8*g - 1856*a^7*c^7*d^3*e^10*g - 30*b^5*c^9*d^11*e^2*f + 57*b^6*c^8*d^
10*e^3*f - 48*b^7*c^7*d^9*e^4*f + 15*b^8*c^6*d^8*e^5*f - 6*b^10*c^4*d^6*e^7*f + 15*b^11*c^3*d^5*e^8*f - 12*b^1
2*c^2*d^4*e^9*f + 16*b^6*c^8*d^11*e^2*g - 33*b^7*c^7*d^10*e^3*g + 30*b^8*c^6*d^9*e^4*g - 10*b^9*c^5*d^8*e^5*g
+ 5*b^10*c^4*d^7*e^6*g - 12*b^11*c^3*d^6*e^7*g + 9*b^12*c^2*d^5*e^8*g + 240*a*b^3*c^10*d^11*e^2*f - 420*a*b^4*
c^9*d^10*e^3*f + 246*a*b^5*c^8*d^9*e^4*f + 39*a*b^6*c^7*d^8*e^5*f - 36*a*b^7*c^6*d^7*e^6*f + 78*a*b^8*c^5*d^6*
e^7*f - 252*a*b^9*c^4*d^5*e^8*f + 186*a*b^10*c^3*d^4*e^9*f - 24*a*b^11*c^2*d^3*e^10*f - 480*a^2*b*c^11*d^11*e^
2*f - 2208*a^3*b*c^10*d^9*e^4*f - 150*a^3*b^9*c^2*d*e^12*f - 4032*a^4*b*c^9*d^7*e^6*f + 948*a^4*b^7*c^3*d*e^12
*f - 3648*a^5*b*c^8*d^5*e^8*f - 2706*a^5*b^5*c^4*d*e^12*f - 1632*a^6*b*c^7*d^3*e^10*f + 3024*a^6*b^3*c^5*d*e^1
2*f - 132*a*b^4*c^9*d^11*e^2*g + 264*a*b^5*c^8*d^10*e^3*g - 184*a*b^6*c^7*d^9*e^4*g - 17*a*b^7*c^6*d^8*e^5*g -
48*a*b^8*c^5*d^7*e^6*g + 212*a*b^9*c^4*d^6*e^7*g - 139*a*b^10*c^3*d^5*e^8*g + 15*a*b^11*c^2*d^4*e^9*g - 3*a^2
*b^11*c*d^2*e^11*g + 848*a^4*b*c^9*d^8*e^5*g + 18*a^4*b^8*c^2*d*e^12*g + 2432*a^5*b*c^8*d^6*e^7*g - 128*a^5*b^
6*c^3*d*e^12*g + 2928*a^6*b*c^7*d^4*e^9*g + 388*a^6*b^4*c^4*d*e^12*g + 1664*a^7*b*c^6*d^2*e^11*g - 288*a^7*b^2
*c^5*d*e^12*g + 624*a^2*b^2*c^10*d^10*e^3*f + 336*a^2*b^3*c^9*d^9*e^4*f - 918*a^2*b^4*c^8*d^8*e^5*f + 36*a^2*b
^5*c^7*d^7*e^6*f - 414*a^2*b^6*c^6*d^6*e^7*f + 1740*a^2*b^7*c^5*d^5*e^8*f - 1038*a^2*b^8*c^4*d^4*e^9*f - 126*a
^2*b^9*c^3*d^3*e^10*f + 135*a^2*b^10*c^2*d^2*e^11*f + 1632*a^3*b^2*c^9*d^8*e^5*f + 1440*a^3*b^3*c^8*d^7*e^6*f
+ 1320*a^3*b^4*c^7*d^6*e^7*f - 5892*a^3*b^5*c^6*d^5*e^8*f + 1974*a^3*b^6*c^5*d^4*e^9*f + 2004*a^3*b^7*c^4*d^3*
e^10*f - 690*a^3*b^8*c^3*d^2*e^11*f - 2976*a^4*b^2*c^8*d^6*e^7*f + 8928*a^4*b^3*c^7*d^5*e^8*f + 2010*a^4*b^4*c
^6*d^4*e^9*f - 7782*a^4*b^5*c^5*d^3*e^10*f + 981*a^4*b^6*c^4*d^2*e^11*f - 9456*a^5*b^2*c^7*d^4*e^9*f + 10608*a
^5*b^3*c^6*d^3*e^10*f + 2364*a^5*b^4*c^5*d^2*e^11*f - 6864*a^6*b^2*c^6*d^2*e^11*f + 288*a^2*b^2*c^10*d^11*e^2*
g - 528*a^2*b^3*c^9*d^10*e^3*g - 12*a^2*b^4*c^8*d^9*e^4*g + 669*a^2*b^5*c^7*d^8*e^5*g + 328*a^2*b^6*c^6*d^7*e^
6*g - 1430*a^2*b^7*c^5*d^6*e^7*g + 708*a^2*b^8*c^4*d^5*e^8*g + 101*a^2*b^9*c^3*d^4*e^9*g - 73*a^2*b^10*c^2*d^3
*e^10*g + 1248*a^3*b^2*c^9*d^9*e^4*g - 1976*a^3*b^3*c^8*d^8*e^5*g - 1736*a^3*b^4*c^7*d^7*e^6*g + 4488*a^3*b^5*
c^6*d^6*e^7*g - 1064*a^3*b^6*c^5*d^5*e^8*g - 1294*a^3*b^7*c^4*d^4*e^9*g + 348*a^3*b^8*c^3*d^3*e^10*g + 48*a^3*
b^9*c^2*d^2*e^11*g + 4032*a^4*b^2*c^8*d^7*e^6*g - 6176*a^4*b^3*c^7*d^6*e^7*g - 1592*a^4*b^4*c^6*d^5*e^8*g + 44
07*a^4*b^5*c^5*d^4*e^9*g - 504*a^4*b^6*c^4*d^3*e^10*g - 281*a^4*b^7*c^3*d^2*e^11*g + 5184*a^5*b^2*c^7*d^5*e^8*
g - 5912*a^5*b^3*c^6*d^4*e^9*g - 500*a^5*b^4*c^5*d^3*e^10*g + 816*a^5*b^5*c^4*d^2*e^11*g + 1824*a^6*b^2*c^6*d^
3*e^10*g - 1488*a^6*b^3*c^5*d^2*e^11*g - 48*a*b^2*c^11*d^12*e*f - 9*a*b^12*c*d^2*e^11*f + 9*a^2*b^11*c*d*e^12*
f - 288*a^7*b*c^6*d*e^12*f + 24*a*b^3*c^10*d^12*e*g + 5*a*b^12*c*d^3*e^10*g - 48*a^2*b*c^11*d^12*e*g - a^3*b^1
0*c*d*e^12*g)/(256*a^4*c^10*d^12 + a^6*b^8*e^12 + 256*a^10*c^4*e^12 + b^8*c^6*d^12 + b^14*d^6*e^6 - 16*a*b^6*c
^7*d^12 - 16*a^7*b^6*c*e^12 - 6*a*b^13*d^5*e^7 - 6*a^5*b^9*d*e^11 - 6*b^9*c^5*d^11*e - 6*b^13*c*d^7*e^5 + 96*a
^2*b^4*c^8*d^12 - 256*a^3*b^2*c^9*d^12 + 96*a^8*b^4*c^2*e^12 - 256*a^9*b^2*c^3*e^12 + 15*a^2*b^12*d^4*e^8 - 20
*a^3*b^11*d^3*e^9 + 15*a^4*b^10*d^2*e^10 + 1536*a^5*c^9*d^10*e^2 + 3840*a^6*c^8*d^8*e^4 + 5120*a^7*c^7*d^6*e^6
+ 3840*a^8*c^6*d^4*e^8 + 1536*a^9*c^5*d^2*e^10 + 15*b^10*c^4*d^10*e^2 - 20*b^11*c^3*d^9*e^3 + 15*b^12*c^2*d^8
*e^4 + 1344*a^2*b^6*c^6*d^10*e^2 - 1440*a^2*b^7*c^5*d^9*e^3 + 495*a^2*b^8*c^4*d^8*e^4 + 324*a^2*b^9*c^3*d^7*e^
5 - 294*a^2*b^10*c^2*d^6*e^6 - 3264*a^3*b^4*c^7*d^10*e^2 + 2240*a^3*b^5*c^6*d^9*e^3 + 1680*a^3*b^6*c^5*d^8*e^4
- 3264*a^3*b^7*c^4*d^7*e^5 + 1204*a^3*b^8*c^3*d^6*e^6 + 324*a^3*b^9*c^2*d^5*e^7 + 2304*a^4*b^2*c^8*d^10*e^2 +
2560*a^4*b^3*c^7*d^9*e^3 - 10080*a^4*b^4*c^6*d^8*e^4 + 8064*a^4*b^5*c^5*d^7*e^5 + 896*a^4*b^6*c^4*d^6*e^6 - 3
264*a^4*b^7*c^3*d^5*e^7 + 495*a^4*b^8*c^2*d^4*e^8 + 11520*a^5*b^2*c^7*d^8*e^4 - 13440*a^5*b^4*c^5*d^6*e^6 + 80
64*a^5*b^5*c^4*d^5*e^7 + 1680*a^5*b^6*c^3*d^4*e^8 - 1440*a^5*b^7*c^2*d^3*e^9 + 17920*a^6*b^2*c^6*d^6*e^6 - 100
80*a^6*b^4*c^4*d^4*e^8 + 2240*a^6*b^5*c^3*d^3*e^9 + 1344*a^6*b^6*c^2*d^2*e^10 + 11520*a^7*b^2*c^5*d^4*e^8 + 25
60*a^7*b^3*c^4*d^3*e^9 - 3264*a^7*b^4*c^3*d^2*e^10 + 2304*a^8*b^2*c^4*d^2*e^10 + 96*a*b^7*c^6*d^11*e + 14*a*b^
12*c*d^6*e^6 - 1536*a^4*b*c^9*d^11*e + 96*a^6*b^7*c*d*e^11 - 1536*a^9*b*c^4*d*e^11 - 234*a*b^8*c^5*d^10*e^2 +
290*a*b^9*c^4*d^9*e^3 - 180*a*b^10*c^3*d^8*e^4 + 36*a*b^11*c^2*d^7*e^5 - 576*a^2*b^5*c^7*d^11*e + 36*a^2*b^11*
c*d^5*e^7 + 1536*a^3*b^3*c^8*d^11*e - 180*a^3*b^10*c*d^4*e^8 + 290*a^4*b^9*c*d^3*e^9 - 7680*a^5*b*c^8*d^9*e^3
- 234*a^5*b^8*c*d^2*e^10 - 15360*a^6*b*c^7*d^7*e^5 - 15360*a^7*b*c^6*d^5*e^7 - 576*a^7*b^5*c^2*d*e^11 - 7680*a
^8*b*c^5*d^3*e^9 + 1536*a^8*b^3*c^3*d*e^11) + (x*(768*a^8*c^6*e^13*g - 1824*a^7*b*c^6*e^13*f + 3648*a^7*c^7*d*
e^12*f - 6*a^3*b^9*c^2*e^13*f + 99*a^4*b^7*c^3*e^13*f - 618*a^5*b^5*c^4*e^13*f + 1728*a^6*b^3*c^5*e^13*f + 2*a
^4*b^8*c^2*e^13*g - 33*a^5*b^6*c^3*e^13*g + 216*a^6*b^4*c^4*e^13*g - 656*a^7*b^2*c^5*e^13*g + 192*a^2*c^12*d^1
1*e^2*f + 1344*a^3*c^11*d^9*e^4*f + 6528*a^4*c^10*d^7*e^6*f + 13440*a^5*c^9*d^5*e^8*f + 11712*a^6*c^8*d^3*e^10
*f - 128*a^3*c^11*d^10*e^3*g - 2816*a^4*c^10*d^8*e^5*g - 6912*a^5*c^9*d^6*e^7*g - 5120*a^6*c^8*d^4*e^9*g - 128
*a^7*c^7*d^2*e^11*g + 12*b^4*c^10*d^11*e^2*f - 66*b^5*c^9*d^10*e^3*f + 144*b^6*c^8*d^9*e^4*f - 153*b^7*c^7*d^8
*e^5*f + 84*b^8*c^6*d^7*e^6*f - 42*b^9*c^5*d^6*e^7*f + 42*b^10*c^4*d^5*e^8*f - 27*b^11*c^3*d^4*e^9*f + 6*b^12*
c^2*d^3*e^10*f - 6*b^5*c^9*d^11*e^2*g + 35*b^6*c^8*d^10*e^3*g - 82*b^7*c^7*d^9*e^4*g + 88*b^8*c^6*d^8*e^5*g -
28*b^9*c^5*d^7*e^6*g - 23*b^10*c^4*d^6*e^7*g + 20*b^11*c^3*d^5*e^8*g - 4*b^12*c^2*d^4*e^9*g - 96*a*b^2*c^11*d^
11*e^2*f + 528*a*b^3*c^10*d^10*e^3*f - 1068*a*b^4*c^9*d^9*e^4*f + 846*a*b^5*c^8*d^8*e^5*f - 120*a*b^6*c^7*d^7*
e^6*f + 168*a*b^7*c^6*d^6*e^7*f - 588*a*b^8*c^5*d^5*e^8*f + 384*a*b^9*c^4*d^4*e^9*f - 36*a*b^10*c^3*d^3*e^10*f
- 18*a*b^11*c^2*d^2*e^11*f - 1056*a^2*b*c^11*d^10*e^3*f + 18*a^2*b^10*c^2*d*e^12*f - 6048*a^3*b*c^10*d^8*e^5*
f - 288*a^3*b^8*c^3*d*e^12*f - 22848*a^4*b*c^9*d^6*e^7*f + 1704*a^4*b^6*c^4*d*e^12*f - 33600*a^5*b*c^8*d^4*e^9
*f - 4188*a^5*b^4*c^5*d*e^12*f - 17568*a^6*b*c^7*d^2*e^11*f + 2400*a^6*b^2*c^6*d*e^12*f + 48*a*b^3*c^10*d^11*e
^2*g - 288*a*b^4*c^9*d^10*e^3*g + 654*a*b^5*c^8*d^9*e^4*g - 517*a*b^6*c^7*d^8*e^5*g - 284*a*b^7*c^6*d^7*e^6*g
+ 698*a*b^8*c^5*d^6*e^7*g - 344*a*b^9*c^4*d^5*e^8*g + 23*a*b^10*c^3*d^4*e^9*g + 10*a*b^11*c^2*d^3*e^10*g - 96*
a^2*b*c^11*d^11*e^2*g - 32*a^3*b*c^10*d^9*e^4*g - 2*a^3*b^9*c^2*d*e^12*g + 8000*a^4*b*c^9*d^7*e^6*g + 34*a^4*b
^7*c^3*d*e^12*g + 14016*a^5*b*c^8*d^5*e^8*g - 282*a^5*b^5*c^4*d*e^12*g + 4384*a^6*b*c^7*d^3*e^10*g + 1136*a^6*
b^3*c^5*d*e^12*g + 1632*a^2*b^2*c^10*d^9*e^4*f + 576*a^2*b^3*c^9*d^8*e^5*f - 2664*a^2*b^4*c^8*d^7*e^6*f - 756*
a^2*b^5*c^7*d^6*e^7*f + 4200*a^2*b^6*c^6*d^5*e^8*f - 1986*a^2*b^7*c^5*d^4*e^9*f - 408*a^2*b^8*c^4*d^3*e^10*f +
252*a^2*b^9*c^3*d^2*e^11*f + 5568*a^3*b^2*c^9*d^7*e^6*f + 8736*a^3*b^3*c^8*d^6*e^7*f - 15288*a^3*b^4*c^7*d^5*
e^8*f + 2268*a^3*b^5*c^6*d^4*e^9*f + 4824*a^3*b^6*c^5*d^3*e^10*f - 1104*a^3*b^7*c^4*d^2*e^11*f + 17472*a^4*b^2
*c^8*d^5*e^8*f + 13440*a^4*b^3*c^7*d^4*e^9*f - 16740*a^4*b^4*c^6*d^3*e^10*f + 246*a^4*b^5*c^5*d^2*e^11*f + 160
32*a^5*b^2*c^7*d^3*e^10*f + 9552*a^5*b^3*c^6*d^2*e^11*f + 624*a^2*b^2*c^10*d^10*e^3*g - 1296*a^2*b^3*c^9*d^9*e
^4*g - 264*a^2*b^4*c^8*d^8*e^5*g + 4116*a^2*b^5*c^7*d^7*e^6*g - 4674*a^2*b^6*c^6*d^6*e^7*g + 1296*a^2*b^7*c^5*
d^5*e^8*g + 438*a^2*b^8*c^4*d^4*e^9*g - 138*a^2*b^9*c^3*d^3*e^10*g - 6*a^2*b^10*c^2*d^2*e^11*g + 4400*a^3*b^2*
c^9*d^8*e^5*g - 12128*a^3*b^3*c^8*d^7*e^6*g + 9344*a^3*b^4*c^7*d^6*e^7*g + 1900*a^3*b^5*c^6*d^5*e^8*g - 3834*a
^3*b^6*c^5*d^4*e^9*g + 380*a^3*b^7*c^4*d^3*e^10*g + 94*a^3*b^8*c^3*d^2*e^11*g + 352*a^4*b^2*c^8*d^6*e^7*g - 14
944*a^4*b^3*c^7*d^5*e^8*g + 8560*a^4*b^4*c^6*d^4*e^9*g + 1298*a^4*b^5*c^5*d^3*e^10*g - 385*a^4*b^6*c^4*d^2*e^1
1*g - 1440*a^5*b^2*c^7*d^4*e^9*g - 6096*a^5*b^3*c^6*d^3*e^10*g + 96*a^5*b^4*c^5*d^2*e^11*g + 1328*a^6*b^2*c^6*
d^2*e^11*g - 1696*a^7*b*c^6*d*e^12*g))/(256*a^4*c^10*d^12 + a^6*b^8*e^12 + 256*a^10*c^4*e^12 + b^8*c^6*d^12 +
b^14*d^6*e^6 - 16*a*b^6*c^7*d^12 - 16*a^7*b^6*c*e^12 - 6*a*b^13*d^5*e^7 - 6*a^5*b^9*d*e^11 - 6*b^9*c^5*d^11*e
- 6*b^13*c*d^7*e^5 + 96*a^2*b^4*c^8*d^12 - 256*a^3*b^2*c^9*d^12 + 96*a^8*b^4*c^2*e^12 - 256*a^9*b^2*c^3*e^12 +
15*a^2*b^12*d^4*e^8 - 20*a^3*b^11*d^3*e^9 + 15*a^4*b^10*d^2*e^10 + 1536*a^5*c^9*d^10*e^2 + 3840*a^6*c^8*d^8*e
^4 + 5120*a^7*c^7*d^6*e^6 + 3840*a^8*c^6*d^4*e^8 + 1536*a^9*c^5*d^2*e^10 + 15*b^10*c^4*d^10*e^2 - 20*b^11*c^3*
d^9*e^3 + 15*b^12*c^2*d^8*e^4 + 1344*a^2*b^6*c^6*d^10*e^2 - 1440*a^2*b^7*c^5*d^9*e^3 + 495*a^2*b^8*c^4*d^8*e^4
+ 324*a^2*b^9*c^3*d^7*e^5 - 294*a^2*b^10*c^2*d^6*e^6 - 3264*a^3*b^4*c^7*d^10*e^2 + 2240*a^3*b^5*c^6*d^9*e^3 +
1680*a^3*b^6*c^5*d^8*e^4 - 3264*a^3*b^7*c^4*d^7*e^5 + 1204*a^3*b^8*c^3*d^6*e^6 + 324*a^3*b^9*c^2*d^5*e^7 + 23
04*a^4*b^2*c^8*d^10*e^2 + 2560*a^4*b^3*c^7*d^9*e^3 - 10080*a^4*b^4*c^6*d^8*e^4 + 8064*a^4*b^5*c^5*d^7*e^5 + 89
6*a^4*b^6*c^4*d^6*e^6 - 3264*a^4*b^7*c^3*d^5*e^7 + 495*a^4*b^8*c^2*d^4*e^8 + 11520*a^5*b^2*c^7*d^8*e^4 - 13440
*a^5*b^4*c^5*d^6*e^6 + 8064*a^5*b^5*c^4*d^5*e^7 + 1680*a^5*b^6*c^3*d^4*e^8 - 1440*a^5*b^7*c^2*d^3*e^9 + 17920*
a^6*b^2*c^6*d^6*e^6 - 10080*a^6*b^4*c^4*d^4*e^8 + 2240*a^6*b^5*c^3*d^3*e^9 + 1344*a^6*b^6*c^2*d^2*e^10 + 11520
*a^7*b^2*c^5*d^4*e^8 + 2560*a^7*b^3*c^4*d^3*e^9 - 3264*a^7*b^4*c^3*d^2*e^10 + 2304*a^8*b^2*c^4*d^2*e^10 + 96*a
*b^7*c^6*d^11*e + 14*a*b^12*c*d^6*e^6 - 1536*a^4*b*c^9*d^11*e + 96*a^6*b^7*c*d*e^11 - 1536*a^9*b*c^4*d*e^11 -
234*a*b^8*c^5*d^10*e^2 + 290*a*b^9*c^4*d^9*e^3 - 180*a*b^10*c^3*d^8*e^4 + 36*a*b^11*c^2*d^7*e^5 - 576*a^2*b^5*
c^7*d^11*e + 36*a^2*b^11*c*d^5*e^7 + 1536*a^3*b^3*c^8*d^11*e - 180*a^3*b^10*c*d^4*e^8 + 290*a^4*b^9*c*d^3*e^9
- 7680*a^5*b*c^8*d^9*e^3 - 234*a^5*b^8*c*d^2*e^10 - 15360*a^6*b*c^7*d^7*e^5 - 15360*a^7*b*c^6*d^5*e^7 - 576*a^
7*b^5*c^2*d*e^11 - 7680*a^8*b*c^5*d^3*e^9 + 1536*a^8*b^3*c^3*d*e^11)) - (1728*a^3*b^3*c^5*e^11*f^2 - 36*c^11*d
^9*e^2*f^2 - 738*a^2*b^5*c^4*e^11*f^2 - 9*b^9*c^2*e^11*f^2 - a^2*b^7*c^2*e^11*g^2 + 15*a^3*b^5*c^3*e^11*g^2 -
72*a^4*b^3*c^4*e^11*g^2 - 792*a^2*c^9*d^5*e^6*f^2 - 864*a^3*c^8*d^3*e^8*f^2 - 16*a^2*c^9*d^7*e^4*g^2 + 32*a^3*
c^8*d^5*e^6*g^2 + 1648*a^4*c^7*d^3*e^8*g^2 - 180*b^2*c^9*d^7*e^4*f^2 + 36*b^3*c^8*d^6*e^5*f^2 + 63*b^4*c^7*d^5
*e^6*f^2 - 45*b^6*c^5*d^3*e^8*f^2 + 9*b^7*c^4*d^2*e^9*f^2 - 9*b^2*c^9*d^9*e^2*g^2 + 42*b^3*c^8*d^8*e^3*g^2 - 6
7*b^4*c^7*d^7*e^4*g^2 + 39*b^5*c^6*d^6*e^5*g^2 + 4*b^6*c^5*d^5*e^6*g^2 - 17*b^7*c^4*d^4*e^7*g^2 + 12*b^8*c^3*d
^3*e^8*g^2 - 4*b^9*c^2*d^2*e^9*g^2 + 480*a^5*c^6*e^11*f*g + 135*a*b^7*c^3*e^11*f^2 - 1440*a^4*b*c^6*e^11*f^2 +
112*a^5*b*c^5*e^11*g^2 - 288*a*c^10*d^7*e^4*f^2 + 1980*a^4*c^7*d*e^10*f^2 + 144*b*c^10*d^8*e^3*f^2 - 704*a^5*
c^6*d*e^10*g^2 + 18*b^8*c^3*d*e^10*f^2 + 864*a*b*c^9*d^6*e^5*f^2 - 288*a*b^6*c^4*d*e^10*f^2 - 24*a*b*c^9*d^8*e
^3*g^2 - 4*a*b^8*c^2*d*e^10*g^2 - 90*a^2*b^6*c^3*e^11*f*g + 462*a^3*b^4*c^4*e^11*f*g - 912*a^4*b^2*c^5*e^11*f*
g + 144*a^2*c^9*d^6*e^5*f*g - 144*a^3*c^8*d^4*e^7*f*g - 4368*a^4*c^7*d^2*e^9*f*g - 156*b^2*c^9*d^8*e^3*f*g + 2
22*b^3*c^8*d^7*e^4*f*g - 90*b^4*c^7*d^6*e^5*f*g - 48*b^5*c^6*d^5*e^6*f*g + 36*b^6*c^5*d^4*e^7*f*g + 18*b^7*c^4
*d^3*e^8*f*g - 30*b^8*c^3*d^2*e^9*f*g - 684*a*b^2*c^8*d^5*e^6*f^2 - 216*a*b^3*c^7*d^4*e^7*f^2 + 450*a*b^4*c^6*
d^3*e^8*f^2 + 18*a*b^5*c^5*d^2*e^9*f^2 + 1872*a^2*b*c^8*d^4*e^7*f^2 + 1575*a^2*b^4*c^5*d*e^10*f^2 + 2016*a^3*b
*c^7*d^2*e^9*f^2 - 3348*a^3*b^2*c^6*d*e^10*f^2 + 20*a*b^2*c^8*d^7*e^4*g^2 + 102*a*b^3*c^7*d^6*e^5*g^2 - 180*a*
b^4*c^6*d^5*e^6*g^2 + 145*a*b^5*c^5*d^4*e^7*g^2 - 130*a*b^6*c^4*d^3*e^8*g^2 + 62*a*b^7*c^3*d^2*e^9*g^2 - 24*a^
2*b*c^8*d^6*e^5*g^2 + 58*a^2*b^6*c^3*d*e^10*g^2 + 168*a^3*b*c^7*d^4*e^7*g^2 - 310*a^3*b^4*c^4*d*e^10*g^2 - 125
6*a^4*b*c^6*d^2*e^9*g^2 + 735*a^4*b^2*c^5*d*e^10*g^2 + 6*a*b^8*c^2*e^11*f*g + 48*a*c^10*d^8*e^3*f*g + 36*b*c^1
0*d^9*e^2*f*g + 12*b^9*c^2*d*e^10*f*g - 1116*a^2*b^2*c^7*d^3*e^8*f^2 - 684*a^2*b^3*c^6*d^2*e^9*f^2 + 18*a^2*b^
2*c^7*d^5*e^6*g^2 - 98*a^2*b^3*c^6*d^4*e^7*g^2 + 585*a^2*b^4*c^5*d^3*e^8*g^2 - 399*a^2*b^5*c^4*d^2*e^9*g^2 - 1
692*a^3*b^2*c^6*d^3*e^8*g^2 + 1210*a^3*b^3*c^5*d^2*e^9*g^2 + 120*a*b*c^9*d^7*e^4*f*g - 180*a*b^7*c^3*d*e^10*f*
g + 3708*a^4*b*c^6*d*e^10*f*g - 684*a*b^2*c^8*d^6*e^5*f*g + 774*a*b^3*c^7*d^5*e^6*f*g - 186*a*b^4*c^6*d^4*e^7*
f*g - 258*a*b^5*c^5*d^3*e^8*f*g + 378*a*b^6*c^4*d^2*e^9*f*g + 192*a^2*b*c^8*d^5*e^6*f*g + 1086*a^2*b^5*c^4*d*e
^10*f*g - 24*a^3*b*c^7*d^3*e^8*f*g - 3150*a^3*b^3*c^5*d*e^10*f*g - 804*a^2*b^2*c^7*d^4*e^7*f*g + 1002*a^2*b^3*
c^6*d^3*e^8*f*g - 1770*a^2*b^4*c^5*d^2*e^9*f*g + 3900*a^3*b^2*c^6*d^2*e^9*f*g)/(256*a^4*c^10*d^12 + a^6*b^8*e^
12 + 256*a^10*c^4*e^12 + b^8*c^6*d^12 + b^14*d^6*e^6 - 16*a*b^6*c^7*d^12 - 16*a^7*b^6*c*e^12 - 6*a*b^13*d^5*e^
7 - 6*a^5*b^9*d*e^11 - 6*b^9*c^5*d^11*e - 6*b^13*c*d^7*e^5 + 96*a^2*b^4*c^8*d^12 - 256*a^3*b^2*c^9*d^12 + 96*a
^8*b^4*c^2*e^12 - 256*a^9*b^2*c^3*e^12 + 15*a^2*b^12*d^4*e^8 - 20*a^3*b^11*d^3*e^9 + 15*a^4*b^10*d^2*e^10 + 15
36*a^5*c^9*d^10*e^2 + 3840*a^6*c^8*d^8*e^4 + 5120*a^7*c^7*d^6*e^6 + 3840*a^8*c^6*d^4*e^8 + 1536*a^9*c^5*d^2*e^
10 + 15*b^10*c^4*d^10*e^2 - 20*b^11*c^3*d^9*e^3 + 15*b^12*c^2*d^8*e^4 + 1344*a^2*b^6*c^6*d^10*e^2 - 1440*a^2*b
^7*c^5*d^9*e^3 + 495*a^2*b^8*c^4*d^8*e^4 + 324*a^2*b^9*c^3*d^7*e^5 - 294*a^2*b^10*c^2*d^6*e^6 - 3264*a^3*b^4*c
^7*d^10*e^2 + 2240*a^3*b^5*c^6*d^9*e^3 + 1680*a^3*b^6*c^5*d^8*e^4 - 3264*a^3*b^7*c^4*d^7*e^5 + 1204*a^3*b^8*c^
3*d^6*e^6 + 324*a^3*b^9*c^2*d^5*e^7 + 2304*a^4*b^2*c^8*d^10*e^2 + 2560*a^4*b^3*c^7*d^9*e^3 - 10080*a^4*b^4*c^6
*d^8*e^4 + 8064*a^4*b^5*c^5*d^7*e^5 + 896*a^4*b^6*c^4*d^6*e^6 - 3264*a^4*b^7*c^3*d^5*e^7 + 495*a^4*b^8*c^2*d^4
*e^8 + 11520*a^5*b^2*c^7*d^8*e^4 - 13440*a^5*b^4*c^5*d^6*e^6 + 8064*a^5*b^5*c^4*d^5*e^7 + 1680*a^5*b^6*c^3*d^4
*e^8 - 1440*a^5*b^7*c^2*d^3*e^9 + 17920*a^6*b^2*c^6*d^6*e^6 - 10080*a^6*b^4*c^4*d^4*e^8 + 2240*a^6*b^5*c^3*d^3
*e^9 + 1344*a^6*b^6*c^2*d^2*e^10 + 11520*a^7*b^2*c^5*d^4*e^8 + 2560*a^7*b^3*c^4*d^3*e^9 - 3264*a^7*b^4*c^3*d^2
*e^10 + 2304*a^8*b^2*c^4*d^2*e^10 + 96*a*b^7*c^6*d^11*e + 14*a*b^12*c*d^6*e^6 - 1536*a^4*b*c^9*d^11*e + 96*a^6
*b^7*c*d*e^11 - 1536*a^9*b*c^4*d*e^11 - 234*a*b^8*c^5*d^10*e^2 + 290*a*b^9*c^4*d^9*e^3 - 180*a*b^10*c^3*d^8*e^
4 + 36*a*b^11*c^2*d^7*e^5 - 576*a^2*b^5*c^7*d^11*e + 36*a^2*b^11*c*d^5*e^7 + 1536*a^3*b^3*c^8*d^11*e - 180*a^3
*b^10*c*d^4*e^8 + 290*a^4*b^9*c*d^3*e^9 - 7680*a^5*b*c^8*d^9*e^3 - 234*a^5*b^8*c*d^2*e^10 - 15360*a^6*b*c^7*d^
7*e^5 - 15360*a^7*b*c^6*d^5*e^7 - 576*a^7*b^5*c^2*d*e^11 - 7680*a^8*b*c^5*d^3*e^9 + 1536*a^8*b^3*c^3*d*e^11) -
(x*(1260*a^3*b^2*c^6*e^11*f^2 - 9*b^8*c^3*e^11*f^2 - 36*c^11*d^8*e^3*f^2 - 621*a^2*b^4*c^5*e^11*f^2 - 900*a^4
*c^7*e^11*f^2 - a^2*b^6*c^3*e^11*g^2 + 14*a^3*b^4*c^4*e^11*g^2 - 49*a^4*b^2*c^5*e^11*g^2 - 216*a^2*c^9*d^4*e^7
*f^2 + 1440*a^3*c^8*d^2*e^9*f^2 - 16*a^2*c^9*d^6*e^5*g^2 + 352*a^3*c^8*d^4*e^7*g^2 - 1936*a^4*c^7*d^2*e^9*g^2
- 180*b^2*c^9*d^6*e^5*f^2 + 36*b^3*c^8*d^5*e^6*f^2 + 99*b^4*c^7*d^4*e^7*f^2 - 90*b^5*c^6*d^3*e^8*f^2 + 9*b^6*c
^5*d^2*e^9*f^2 - 9*b^2*c^9*d^8*e^3*g^2 + 42*b^3*c^8*d^7*e^4*g^2 - 67*b^4*c^7*d^6*e^5*g^2 + 54*b^5*c^6*d^5*e^6*
g^2 - 37*b^6*c^5*d^4*e^7*g^2 + 12*b^7*c^4*d^3*e^8*g^2 - 4*b^8*c^3*d^2*e^9*g^2 + 126*a*b^6*c^4*e^11*f^2 - 288*a
*c^10*d^6*e^5*f^2 + 144*b*c^10*d^7*e^4*f^2 + 18*b^7*c^4*d*e^10*f^2 + 864*a*b*c^9*d^5*e^6*f^2 - 270*a*b^5*c^5*d
*e^10*f^2 - 1440*a^3*b*c^7*d*e^10*f^2 - 24*a*b*c^9*d^7*e^4*g^2 - 4*a*b^7*c^3*d*e^10*g^2 + 616*a^4*b*c^6*d*e^10
*g^2 - 84*a^2*b^5*c^4*e^11*f*g + 354*a^3*b^3*c^5*e^11*f*g - 336*a^2*c^9*d^5*e^6*f*g - 2352*a^3*c^8*d^3*e^8*f*g
- 156*b^2*c^9*d^7*e^4*f*g + 222*b^3*c^8*d^6*e^5*f*g - 120*b^4*c^7*d^5*e^6*f*g + 6*b^5*c^6*d^4*e^7*f*g + 48*b^
6*c^5*d^3*e^8*f*g - 30*b^7*c^4*d^2*e^9*f*g - 972*a*b^2*c^8*d^4*e^7*f^2 + 504*a*b^3*c^7*d^3*e^8*f^2 + 162*a*b^4
*c^6*d^2*e^9*f^2 + 432*a^2*b*c^8*d^3*e^8*f^2 + 1188*a^2*b^3*c^6*d*e^10*f^2 + 20*a*b^2*c^8*d^6*e^5*g^2 - 18*a*b
^3*c^7*d^5*e^6*g^2 + 168*a*b^4*c^6*d^4*e^7*g^2 - 68*a*b^5*c^5*d^3*e^8*g^2 + 58*a*b^6*c^4*d^2*e^9*g^2 + 216*a^2
*b*c^8*d^5*e^6*g^2 + 54*a^2*b^5*c^4*d*e^10*g^2 + 472*a^3*b*c^7*d^3*e^8*g^2 - 270*a^3*b^3*c^5*d*e^10*g^2 + 6*a*
b^7*c^3*e^11*f*g - 420*a^4*b*c^6*e^11*f*g + 48*a*c^10*d^7*e^4*f*g + 2640*a^4*c^7*d*e^10*f*g + 36*b*c^10*d^8*e^
3*f*g + 12*b^8*c^3*d*e^10*f*g - 1404*a^2*b^2*c^7*d^2*e^9*f^2 - 798*a^2*b^2*c^7*d^4*e^7*g^2 + 214*a^2*b^3*c^6*d
^3*e^8*g^2 - 375*a^2*b^4*c^5*d^2*e^9*g^2 + 1060*a^3*b^2*c^6*d^2*e^9*g^2 + 120*a*b*c^9*d^6*e^5*f*g - 168*a*b^6*
c^4*d*e^10*f*g - 444*a*b^2*c^8*d^5*e^6*f*g + 342*a*b^3*c^7*d^4*e^7*f*g - 420*a*b^4*c^6*d^3*e^8*f*g + 258*a*b^5
*c^5*d^2*e^9*f*g + 1056*a^2*b*c^8*d^4*e^7*f*g + 1020*a^2*b^4*c^5*d*e^10*f*g + 2088*a^3*b*c^7*d^2*e^9*f*g - 296
4*a^3*b^2*c^6*d*e^10*f*g + 492*a^2*b^2*c^7*d^3*e^8*f*g - 822*a^2*b^3*c^6*d^2*e^9*f*g))/(256*a^4*c^10*d^12 + a^
6*b^8*e^12 + 256*a^10*c^4*e^12 + b^8*c^6*d^12 + b^14*d^6*e^6 - 16*a*b^6*c^7*d^12 - 16*a^7*b^6*c*e^12 - 6*a*b^1
3*d^5*e^7 - 6*a^5*b^9*d*e^11 - 6*b^9*c^5*d^11*e - 6*b^13*c*d^7*e^5 + 96*a^2*b^4*c^8*d^12 - 256*a^3*b^2*c^9*d^1
2 + 96*a^8*b^4*c^2*e^12 - 256*a^9*b^2*c^3*e^12 + 15*a^2*b^12*d^4*e^8 - 20*a^3*b^11*d^3*e^9 + 15*a^4*b^10*d^2*e
^10 + 1536*a^5*c^9*d^10*e^2 + 3840*a^6*c^8*d^8*e^4 + 5120*a^7*c^7*d^6*e^6 + 3840*a^8*c^6*d^4*e^8 + 1536*a^9*c^
5*d^2*e^10 + 15*b^10*c^4*d^10*e^2 - 20*b^11*c^3*d^9*e^3 + 15*b^12*c^2*d^8*e^4 + 1344*a^2*b^6*c^6*d^10*e^2 - 14
40*a^2*b^7*c^5*d^9*e^3 + 495*a^2*b^8*c^4*d^8*e^4 + 324*a^2*b^9*c^3*d^7*e^5 - 294*a^2*b^10*c^2*d^6*e^6 - 3264*a
^3*b^4*c^7*d^10*e^2 + 2240*a^3*b^5*c^6*d^9*e^3 + 1680*a^3*b^6*c^5*d^8*e^4 - 3264*a^3*b^7*c^4*d^7*e^5 + 1204*a^
3*b^8*c^3*d^6*e^6 + 324*a^3*b^9*c^2*d^5*e^7 + 2304*a^4*b^2*c^8*d^10*e^2 + 2560*a^4*b^3*c^7*d^9*e^3 - 10080*a^4
*b^4*c^6*d^8*e^4 + 8064*a^4*b^5*c^5*d^7*e^5 + 896*a^4*b^6*c^4*d^6*e^6 - 3264*a^4*b^7*c^3*d^5*e^7 + 495*a^4*b^8
*c^2*d^4*e^8 + 11520*a^5*b^2*c^7*d^8*e^4 - 13440*a^5*b^4*c^5*d^6*e^6 + 8064*a^5*b^5*c^4*d^5*e^7 + 1680*a^5*b^6
*c^3*d^4*e^8 - 1440*a^5*b^7*c^2*d^3*e^9 + 17920*a^6*b^2*c^6*d^6*e^6 - 10080*a^6*b^4*c^4*d^4*e^8 + 2240*a^6*b^5
*c^3*d^3*e^9 + 1344*a^6*b^6*c^2*d^2*e^10 + 11520*a^7*b^2*c^5*d^4*e^8 + 2560*a^7*b^3*c^4*d^3*e^9 - 3264*a^7*b^4
*c^3*d^2*e^10 + 2304*a^8*b^2*c^4*d^2*e^10 + 96*a*b^7*c^6*d^11*e + 14*a*b^12*c*d^6*e^6 - 1536*a^4*b*c^9*d^11*e
+ 96*a^6*b^7*c*d*e^11 - 1536*a^9*b*c^4*d*e^11 - 234*a*b^8*c^5*d^10*e^2 + 290*a*b^9*c^4*d^9*e^3 - 180*a*b^10*c^
3*d^8*e^4 + 36*a*b^11*c^2*d^7*e^5 - 576*a^2*b^5*c^7*d^11*e + 36*a^2*b^11*c*d^5*e^7 + 1536*a^3*b^3*c^8*d^11*e -
180*a^3*b^10*c*d^4*e^8 + 290*a^4*b^9*c*d^3*e^9 - 7680*a^5*b*c^8*d^9*e^3 - 234*a^5*b^8*c*d^2*e^10 - 15360*a^6*
b*c^7*d^7*e^5 - 15360*a^7*b*c^6*d^5*e^7 - 576*a^7*b^5*c^2*d*e^11 - 7680*a^8*b*c^5*d^3*e^9 + 1536*a^8*b^3*c^3*d
*e^11))*root(286720*a^9*b*c^8*d^7*e^9*z^3 + 286720*a^8*b*c^9*d^9*e^7*z^3 + 172032*a^10*b*c^7*d^5*e^11*z^3 + 17
2032*a^7*b*c^10*d^11*e^5*z^3 + 57344*a^11*b*c^6*d^3*e^13*z^3 + 57344*a^6*b*c^11*d^13*e^3*z^3 - 10240*a^11*b^3*
c^4*d*e^15*z^3 - 10240*a^4*b^3*c^11*d^15*e*z^3 + 5120*a^10*b^5*c^3*d*e^15*z^3 + 5120*a^3*b^5*c^10*d^15*e*z^3 -
1280*a^9*b^7*c^2*d*e^15*z^3 - 1280*a^2*b^7*c^9*d^15*e*z^3 - 1232*a^5*b^12*c*d^4*e^12*z^3 - 1232*a*b^12*c^5*d^
12*e^4*z^3 + 1064*a^6*b^11*c*d^3*e^13*z^3 + 1064*a*b^11*c^6*d^13*e^3*z^3 + 840*a^4*b^13*c*d^5*e^11*z^3 + 840*a
*b^13*c^4*d^11*e^5*z^3 - 552*a^7*b^10*c*d^2*e^14*z^3 - 552*a*b^10*c^7*d^14*e^2*z^3 - 280*a^3*b^14*c*d^6*e^10*z
^3 - 280*a*b^14*c^3*d^10*e^6*z^3 - 8*a^2*b^15*c*d^7*e^9*z^3 - 8*a*b^15*c^2*d^9*e^7*z^3 + 8192*a^12*b*c^5*d*e^1
5*z^3 + 8192*a^5*b*c^12*d^15*e*z^3 + 160*a^8*b^9*c*d*e^15*z^3 + 160*a*b^9*c^8*d^15*e*z^3 + 36*a*b^16*c*d^8*e^8
*z^3 - 483840*a^8*b^2*c^8*d^8*e^8*z^3 - 365568*a^7*b^5*c^6*d^7*e^9*z^3 - 365568*a^6*b^5*c^7*d^9*e^7*z^3 - 3584
00*a^9*b^2*c^7*d^6*e^10*z^3 - 358400*a^7*b^2*c^9*d^10*e^6*z^3 + 241920*a^7*b^4*c^7*d^8*e^8*z^3 + 215040*a^8*b^
4*c^6*d^6*e^10*z^3 + 215040*a^8*b^3*c^7*d^7*e^9*z^3 + 215040*a^7*b^3*c^8*d^9*e^7*z^3 + 215040*a^6*b^4*c^8*d^10
*e^6*z^3 - 193536*a^8*b^5*c^5*d^5*e^11*z^3 - 193536*a^5*b^5*c^8*d^11*e^5*z^3 - 136192*a^10*b^2*c^6*d^4*e^12*z^
3 - 136192*a^6*b^2*c^10*d^12*e^4*z^3 + 133056*a^6*b^6*c^6*d^8*e^8*z^3 + 125440*a^9*b^4*c^5*d^4*e^12*z^3 + 1254
40*a^5*b^4*c^9*d^12*e^4*z^3 - 109944*a^5*b^8*c^5*d^8*e^8*z^3 + 106752*a^6*b^7*c^5*d^7*e^9*z^3 + 106752*a^5*b^7
*c^6*d^9*e^7*z^3 + 80640*a^7*b^7*c^4*d^5*e^11*z^3 + 80640*a^4*b^7*c^7*d^11*e^5*z^3 - 77280*a^6*b^8*c^4*d^6*e^1
0*z^3 - 77280*a^4*b^8*c^6*d^10*e^6*z^3 + 71680*a^9*b^3*c^6*d^5*e^11*z^3 + 71680*a^6*b^3*c^9*d^11*e^5*z^3 + 698
88*a^7*b^6*c^5*d^6*e^10*z^3 + 69888*a^5*b^6*c^7*d^10*e^6*z^3 - 35840*a^9*b^5*c^4*d^3*e^13*z^3 - 35840*a^4*b^5*
c^9*d^13*e^3*z^3 + 30720*a^10*b^4*c^4*d^2*e^14*z^3 + 30720*a^4*b^4*c^10*d^14*e^2*z^3 + 26880*a^8*b^7*c^3*d^3*e
^13*z^3 + 26880*a^3*b^7*c^8*d^13*e^3*z^3 + 21510*a^4*b^10*c^4*d^8*e^8*z^3 + 18536*a^5*b^10*c^3*d^6*e^10*z^3 +
18536*a^3*b^10*c^5*d^10*e^6*z^3 - 18480*a^7*b^8*c^3*d^4*e^12*z^3 - 18480*a^3*b^8*c^7*d^12*e^4*z^3 - 18432*a^11
*b^2*c^5*d^2*e^14*z^3 - 18432*a^5*b^2*c^11*d^14*e^2*z^3 - 16640*a^9*b^6*c^3*d^2*e^14*z^3 - 16640*a^3*b^6*c^9*d
^14*e^2*z^3 - 14336*a^10*b^3*c^5*d^3*e^13*z^3 - 14336*a^5*b^3*c^10*d^13*e^3*z^3 - 13440*a^8*b^6*c^4*d^4*e^12*z
^3 - 13440*a^4*b^6*c^8*d^12*e^4*z^3 + 13280*a^5*b^9*c^4*d^7*e^9*z^3 + 13280*a^4*b^9*c^5*d^9*e^7*z^3 - 10840*a^
4*b^11*c^3*d^7*e^9*z^3 - 10840*a^3*b^11*c^4*d^9*e^7*z^3 + 7868*a^6*b^10*c^2*d^4*e^12*z^3 + 7868*a^2*b^10*c^6*d
^12*e^4*z^3 - 7840*a^7*b^9*c^2*d^3*e^13*z^3 - 7840*a^2*b^9*c^7*d^13*e^3*z^3 - 5600*a^6*b^9*c^3*d^5*e^11*z^3 -
5600*a^3*b^9*c^6*d^11*e^5*z^3 + 4320*a^8*b^8*c^2*d^2*e^14*z^3 + 4320*a^2*b^8*c^8*d^14*e^2*z^3 - 3528*a^5*b^11*
c^2*d^5*e^11*z^3 - 3528*a^2*b^11*c^5*d^11*e^5*z^3 + 1520*a^3*b^13*c^2*d^7*e^9*z^3 + 1520*a^2*b^13*c^3*d^9*e^7*
z^3 - 700*a^4*b^12*c^2*d^6*e^10*z^3 - 700*a^2*b^12*c^4*d^10*e^6*z^3 - 540*a^2*b^14*c^2*d^8*e^8*z^3 + 480*a^3*b
^12*c^3*d^8*e^8*z^3 - 8*b^17*c*d^9*e^7*z^3 - 8*b^11*c^7*d^15*e*z^3 - 8*a^7*b^11*d*e^15*z^3 - 8*a*b^17*d^7*e^9*
z^3 - 20*a^9*b^8*c*e^16*z^3 - 20*a*b^8*c^9*d^16*z^3 + 70*b^14*c^4*d^12*e^4*z^3 - 56*b^15*c^3*d^11*e^5*z^3 - 56
*b^13*c^5*d^13*e^3*z^3 + 28*b^16*c^2*d^10*e^6*z^3 + 28*b^12*c^6*d^14*e^2*z^3 - 71680*a^9*c^9*d^8*e^8*z^3 - 573
44*a^10*c^8*d^6*e^10*z^3 - 57344*a^8*c^10*d^10*e^6*z^3 - 28672*a^11*c^7*d^4*e^12*z^3 - 28672*a^7*c^11*d^12*e^4
*z^3 - 8192*a^12*c^6*d^2*e^14*z^3 - 8192*a^6*c^12*d^14*e^2*z^3 + 70*a^4*b^14*d^4*e^12*z^3 - 56*a^5*b^13*d^3*e^
13*z^3 - 56*a^3*b^15*d^5*e^11*z^3 + 28*a^6*b^12*d^2*e^14*z^3 + 28*a^2*b^16*d^6*e^10*z^3 + 1280*a^12*b^2*c^4*e^
16*z^3 - 640*a^11*b^4*c^3*e^16*z^3 + 160*a^10*b^6*c^2*e^16*z^3 + 1280*a^4*b^2*c^12*d^16*z^3 - 640*a^3*b^4*c^11
*d^16*z^3 + 160*a^2*b^6*c^10*d^16*z^3 - 1024*a^13*c^5*e^16*z^3 - 1024*a^5*c^13*d^16*z^3 + b^18*d^8*e^8*z^3 + b
^10*c^8*d^16*z^3 + a^8*b^10*e^16*z^3 + 96*a*b*c^10*d^10*e^2*f*g*z + 69900*a^4*b^2*c^6*d^3*e^9*f*g*z - 64590*a^
4*b^3*c^5*d^2*e^10*f*g*z - 40200*a^3*b^4*c^5*d^3*e^9*f*g*z + 32820*a^3*b^5*c^4*d^2*e^10*f*g*z + 10680*a^2*b^6*
c^4*d^3*e^9*f*g*z + 10500*a^3*b^3*c^6*d^4*e^8*f*g*z + 8820*a^2*b^3*c^7*d^6*e^6*f*g*z - 8460*a^2*b^7*c^3*d^2*e^
10*f*g*z - 5880*a^3*b^2*c^7*d^5*e^7*f*g*z - 5040*a^2*b^4*c^6*d^5*e^7*f*g*z - 3240*a^2*b^2*c^8*d^7*e^5*f*g*z -
1260*a^2*b^5*c^5*d^4*e^8*f*g*z - 252*a*b^10*c*d*e^11*f*g*z + 55872*a^5*b*c^6*d^2*e^10*f*g*z - 30636*a^5*b^2*c^
5*d*e^11*f*g*z + 24180*a^4*b^4*c^4*d*e^11*f*g*z - 9720*a^3*b^6*c^3*d*e^11*f*g*z + 3690*a*b^3*c^8*d^8*e^4*f*g*z
- 3360*a^3*b*c^8*d^6*e^6*f*g*z - 3240*a*b^4*c^7*d^7*e^5*f*g*z + 2160*a^2*b^8*c^2*d*e^11*f*g*z - 2100*a^4*b*c^
7*d^4*e^8*f*g*z - 1500*a*b^2*c^9*d^9*e^3*f*g*z - 1320*a*b^8*c^3*d^3*e^9*f*g*z - 1260*a^2*b*c^9*d^8*e^4*f*g*z +
1080*a*b^9*c^2*d^2*e^10*f*g*z + 924*a*b^6*c^5*d^5*e^7*f*g*z + 252*a*b^5*c^6*d^6*e^6*f*g*z - 150*a*b^7*c^4*d^4
*e^8*f*g*z + 48*a*c^11*d^11*e*f*g*z - 660*b^4*c^8*d^9*e^3*f*g*z + 570*b^3*c^9*d^10*e^2*f*g*z + 270*b^5*c^7*d^8
*e^4*f*g*z + 84*b^6*c^6*d^7*e^5*f*g*z + 60*b^10*c^2*d^3*e^9*f*g*z - 60*b^8*c^4*d^5*e^7*f*g*z - 42*b^7*c^5*d^6*
e^6*f*g*z + 30*b^9*c^3*d^4*e^8*f*g*z - 59280*a^5*c^7*d^3*e^9*f*g*z + 3360*a^4*c^8*d^5*e^7*f*g*z + 2400*a^3*c^9
*d^7*e^5*f*g*z + 720*a^2*c^10*d^9*e^3*f*g*z + 7410*a^5*b^3*c^4*e^12*f*g*z - 3810*a^4*b^5*c^3*e^12*f*g*z + 960*
a^3*b^7*c^2*e^12*f*g*z + 4872*a^6*b*c^5*d*e^11*g^2*z + 90*a*b^10*c*d^2*e^10*g^2*z + 80*a^2*b^9*c*d*e^11*g^2*z
- 33048*a^5*b*c^6*d*e^11*f^2*z + 1800*a*b*c^10*d^9*e^3*f^2*z - 720*a*b^9*c^2*d*e^11*f^2*z - 31575*a^4*b^2*c^6*
d^4*e^8*g^2*z + 24700*a^4*b^3*c^5*d^3*e^9*g^2*z + 16722*a^5*b^2*c^5*d^2*e^10*g^2*z + 15700*a^3*b^4*c^5*d^4*e^8
*g^2*z - 12140*a^3*b^5*c^4*d^3*e^9*g^2*z - 11640*a^4*b^4*c^4*d^2*e^10*g^2*z - 4485*a^2*b^6*c^4*d^4*e^8*g^2*z +
4180*a^3*b^6*c^3*d^2*e^10*g^2*z + 3120*a^2*b^7*c^3*d^3*e^9*g^2*z - 1960*a^3*b^3*c^6*d^5*e^7*g^2*z + 1820*a^3*
b^2*c^7*d^6*e^6*g^2*z + 1596*a^2*b^5*c^5*d^5*e^7*g^2*z + 1185*a^2*b^2*c^8*d^8*e^4*g^2*z - 1080*a^2*b^3*c^7*d^7
*e^5*g^2*z - 840*a^2*b^8*c^2*d^2*e^10*g^2*z - 840*a^2*b^4*c^6*d^6*e^6*g^2*z - 50760*a^4*b^2*c^6*d^2*e^10*f^2*z
+ 25380*a^3*b^4*c^5*d^2*e^10*f^2*z - 12600*a^3*b^2*c^7*d^4*e^8*f^2*z - 10080*a^2*b^2*c^8*d^6*e^6*f^2*z - 6030
*a^2*b^6*c^4*d^2*e^10*f^2*z + 3150*a^2*b^4*c^6*d^4*e^8*f^2*z + 2520*a^2*b^3*c^7*d^5*e^7*f^2*z - 1260*a^2*b^5*c
^5*d^3*e^9*f^2*z - 228*b^2*c^10*d^11*e*f*g*z - 54*b^11*c*d^2*e^10*f*g*z + 12816*a^6*c^6*d*e^11*f*g*z - 5508*a^
6*b*c^5*e^12*f*g*z - 120*a^2*b^9*c*e^12*f*g*z - 24*a*b*c^10*d^11*e*g^2*z - 18360*a^5*b*c^6*d^3*e^9*g^2*z - 534
0*a^5*b^3*c^4*d*e^11*g^2*z + 2580*a^4*b^5*c^3*d*e^11*g^2*z + 1680*a^4*b*c^7*d^5*e^7*g^2*z + 1380*a*b^5*c^6*d^7
*e^5*g^2*z - 1050*a*b^4*c^7*d^8*e^4*g^2*z - 686*a*b^6*c^5*d^6*e^6*g^2*z - 640*a^3*b^7*c^2*d*e^11*g^2*z + 570*a
*b^8*c^3*d^4*e^8*g^2*z - 400*a*b^9*c^2*d^3*e^9*g^2*z - 280*a^2*b*c^9*d^9*e^3*g^2*z + 260*a*b^3*c^8*d^9*e^3*g^2
*z + 80*a^3*b*c^8*d^7*e^5*g^2*z + 50*a*b^2*c^9*d^10*e^2*g^2*z + 44460*a^4*b^3*c^5*d*e^11*f^2*z - 22860*a^3*b^5
*c^4*d*e^11*f^2*z + 15120*a^3*b*c^8*d^5*e^7*f^2*z + 12600*a^4*b*c^7*d^3*e^9*f^2*z + 7920*a^2*b*c^9*d^7*e^5*f^2
*z + 5760*a^2*b^7*c^3*d*e^11*f^2*z - 3060*a*b^2*c^9*d^8*e^4*f^2*z + 1440*a*b^3*c^8*d^7*e^5*f^2*z - 1260*a*b^5*
c^6*d^5*e^7*f^2*z + 1260*a*b^4*c^7*d^6*e^6*f^2*z + 720*a*b^8*c^3*d^2*e^10*f^2*z + 180*a*b^7*c^4*d^3*e^9*f^2*z
+ 216*b*c^11*d^11*e*f^2*z + 36*b^11*c*d*e^11*f^2*z - 4*a*b^11*d*e^11*g^2*z + 180*a*b^10*c*e^12*f^2*z + 200*b^5
*c^7*d^9*e^3*g^2*z - 160*b^4*c^8*d^10*e^2*g^2*z - 85*b^6*c^6*d^8*e^4*g^2*z + 70*b^8*c^4*d^6*e^6*g^2*z - 56*b^7
*c^5*d^7*e^5*g^2*z - 25*b^10*c^2*d^4*e^8*g^2*z - 20*b^9*c^3*d^5*e^7*g^2*z + 24000*a^5*c^7*d^4*e^8*g^2*z - 1128
0*a^6*c^6*d^2*e^10*g^2*z - 1120*a^4*c^8*d^6*e^6*g^2*z + 540*b^3*c^9*d^9*e^3*f^2*z - 504*b^2*c^10*d^10*e^2*f^2*
z - 320*a^3*c^9*d^8*e^4*g^2*z - 225*b^4*c^8*d^8*e^4*f^2*z + 144*b^7*c^5*d^5*e^7*f^2*z - 126*b^6*c^6*d^6*e^6*f^
2*z - 45*b^8*c^4*d^4*e^8*f^2*z - 36*b^10*c^2*d^2*e^10*f^2*z + 36*b^5*c^7*d^7*e^5*f^2*z - 16*a^2*c^10*d^10*e^2*
g^2*z + 33048*a^5*c^7*d^2*e^10*f^2*z - 6300*a^4*c^8*d^4*e^8*f^2*z - 5040*a^3*c^9*d^6*e^6*f^2*z - 1980*a^2*c^10
*d^8*e^4*f^2*z - 1185*a^6*b^2*c^4*e^12*g^2*z + 630*a^5*b^4*c^3*e^12*g^2*z - 160*a^4*b^6*c^2*e^12*g^2*z - 11565
*a^4*b^4*c^4*e^12*f^2*z + 9612*a^5*b^2*c^5*e^12*f^2*z + 5760*a^3*b^6*c^3*e^12*f^2*z - 1440*a^2*b^8*c^2*e^12*f^
2*z + 12*b^12*d*e^11*f*g*z + 36*b*c^11*d^12*f*g*z + 6*a*b^11*e^12*f*g*z + 60*b^3*c^9*d^11*e*g^2*z + 20*b^11*c*
d^3*e^9*g^2*z - 360*a*c^11*d^10*e^2*f^2*z + 20*a^3*b^8*c*e^12*g^2*z - 4*b^12*d^2*e^10*g^2*z + 768*a^7*c^5*e^12
*g^2*z - 9*b^2*c^10*d^12*g^2*z - 900*a^6*c^6*e^12*f^2*z - a^2*b^10*e^12*g^2*z - 36*c^12*d^12*f^2*z - 9*b^12*e^
12*f^2*z + 4644*a*b^2*c^6*d^2*e^8*f^2*g + 3420*a^2*b*c^6*d^2*e^8*f*g^2 - 2436*a*b^2*c^6*d^3*e^7*f*g^2 - 2142*a
^2*b^2*c^5*d*e^9*f*g^2 - 1470*a*b^3*c^5*d^2*e^8*f*g^2 + 1020*a*b^4*c^4*d*e^9*f*g^2 + 732*a*b*c^7*d^4*e^6*f*g^2
+ 720*a*b*c^7*d^3*e^7*f^2*g - 648*a^2*b*c^6*d*e^9*f^2*g - 468*a*b^3*c^5*d*e^9*f^2*g + 981*a^2*b^2*c^5*d^2*e^8
*g^3 - 540*b^3*c^6*d^3*e^7*f^2*g + 468*b^2*c^7*d^4*e^6*f^2*g - 459*b^4*c^5*d^2*e^8*f^2*g - 438*b^2*c^7*d^5*e^5
*f*g^2 + 396*b^4*c^5*d^3*e^7*f*g^2 + 120*b^5*c^4*d^2*e^8*f*g^2 + 87*b^3*c^6*d^4*e^6*f*g^2 - 7452*a^2*c^7*d^2*e
^8*f^2*g + 2688*a^2*c^7*d^3*e^7*f*g^2 + 1512*a^2*b^2*c^5*e^10*f^2*g + 555*a^2*b^3*c^4*e^10*f*g^2 - 1184*a^2*b*
c^6*d^3*e^7*g^3 + 796*a*b^3*c^5*d^3*e^7*g^3 - 360*a*b^4*c^4*d^2*e^8*g^3 - 350*a^2*b^3*c^4*d*e^9*g^3 + 7*a*b^2*
c^6*d^4*e^6*g^3 + 216*b*c^8*d^5*e^5*f^2*g + 180*b*c^8*d^6*e^4*f*g^2 - 120*b^6*c^3*d*e^9*f*g^2 + 90*b^5*c^4*d*e
^9*f^2*g - 1332*a*c^8*d^4*e^6*f^2*g + 1008*a^3*c^6*d*e^9*f*g^2 + 240*a*c^8*d^5*e^5*f*g^2 - 1404*a^3*b*c^5*e^10
*f*g^2 - 765*a*b^4*c^4*e^10*f^2*g - 60*a*b^5*c^3*e^10*f*g^2 + 760*a^3*b*c^5*d*e^9*g^3 - 120*a*b*c^7*d^5*e^5*g^
3 + 40*a*b^5*c^3*d*e^9*g^3 - 1944*a*b*c^7*d^2*e^8*f^3 - 1728*a*b^2*c^6*d*e^9*f^3 - 180*c^9*d^6*e^4*f^2*g + 90*
b^6*c^3*e^10*f^2*g + 900*a^3*c^6*e^10*f^2*g - 540*b*c^8*d^4*e^6*f^3 + 162*b^4*c^5*d*e^9*f^3 + 5400*a^2*c^7*d*e
^9*f^3 + 1296*a*c^8*d^3*e^7*f^3 - 2700*a^2*b*c^6*e^10*f^3 + 1188*a*b^3*c^5*e^10*f^3 + 138*b^3*c^6*d^5*e^5*g^3
- 98*b^4*c^5*d^4*e^6*g^3 - 80*b^5*c^4*d^3*e^7*g^3 - 45*b^2*c^7*d^6*e^4*g^3 + 40*b^6*c^3*d^2*e^8*g^3 - 1264*a^3
*c^6*d^2*e^8*g^3 + 216*b^3*c^6*d^2*e^8*f^3 + 216*b^2*c^7*d^3*e^7*f^3 - 80*a^2*c^7*d^4*e^6*g^3 - 95*a^3*b^2*c^4
*e^10*g^3 + 10*a^2*b^4*c^3*e^10*g^3 + 216*c^9*d^5*e^5*f^3 + 256*a^4*c^5*e^10*g^3 - 135*b^5*c^4*e^10*f^3, z, k)
, k, 1, 3) + ((b^6*d^2*e^3*f - 8*a^2*c^4*d^5*g - 32*a^4*c^2*e^5*f - b^3*c^3*d^5*f - 2*a^2*b^4*e^5*f + 10*a*b*c
^4*d^5*f - 5*a*b^5*d*e^4*f - a*b^2*c^3*d^5*g + 16*a^3*b^2*c*e^5*f + a*b^5*d^2*e^3*g + 5*a^2*b^4*d*e^4*g + 16*a
^2*c^4*d^4*e*f + 56*a^4*c^2*d*e^4*g + 3*b^4*c^2*d^4*e*f - 3*b^5*c*d^3*e^2*f + 80*a^3*c^3*d^2*e^3*f - 48*a^3*c^
3*d^3*e^2*g + 21*a*b^3*c^2*d^3*e^2*f - 9*a^2*b^3*c*d^2*e^3*g + 44*a^3*b*c^2*d^2*e^3*g - 56*a^2*b^2*c^2*d^2*e^3
*f + 6*a^2*b^2*c^2*d^3*e^2*g - 28*a*b^2*c^3*d^4*e*f + 2*a*b^4*c*d^2*e^3*f + 36*a^2*b^3*c*d*e^4*f - 58*a^3*b*c^
2*d*e^4*f + 3*a*b^3*c^2*d^4*e*g - 3*a*b^4*c*d^3*e^2*g + 12*a^2*b*c^3*d^4*e*g - 37*a^3*b^2*c*d*e^4*g)/(2*(16*a^
2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a
*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 +
24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3
*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*
e^4 - 96*a^3*b*c^3*d^3*e^3)) - (x^4*(30*a^2*c^4*e^5*f + 3*b^4*c^2*e^5*f - 6*c^6*d^4*e*f + 3*b*c^5*d^4*e*g - 21
*a*b^2*c^3*e^5*f - a*b^3*c^2*e^5*g + 7*a^2*b*c^3*e^5*g - 24*a*c^5*d^2*e^3*f + 4*a*c^5*d^3*e^2*g + 12*b*c^5*d^3
*e^2*f - 44*a^2*c^4*d*e^4*g - 3*b^3*c^3*d*e^4*f - 2*b^4*c^2*d*e^4*g - 3*b^2*c^4*d^2*e^3*f - 7*b^2*c^4*d^3*e^2*
g + 3*b^3*c^3*d^2*e^3*g + 24*a*b*c^4*d*e^4*f + 6*a*b*c^4*d^2*e^3*g + 13*a*b^2*c^3*d*e^4*g))/(16*a^2*c^5*d^6 +
a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4
- 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*
c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^
2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3
*b*c^3*d^3*e^3) - (x^2*(6*b^6*e^5*f + 100*a^3*c^3*e^5*f + 9*b^2*c^4*d^5*g - 2*a*b^5*e^5*g - 18*b*c^5*d^5*f - 4
*b^6*d*e^4*g - 36*a*b^4*c*e^5*f - 20*a*c^5*d^4*e*f + 12*a^2*b^3*c*e^5*g + 2*a^3*b*c^2*e^5*g - 152*a^3*c^3*d*e^
4*g + 32*b^2*c^4*d^4*e*f - 19*b^3*c^3*d^4*e*g + 2*b^5*c*d^2*e^3*g + 14*a^2*b^2*c^2*e^5*f - 112*a^2*c^4*d^2*e^3
*f + 40*a^2*c^4*d^3*e^2*g - b^3*c^3*d^3*e^2*f - 13*b^4*c^2*d^2*e^3*f + 6*b^4*c^2*d^3*e^2*g + 62*a*b^2*c^3*d^2*
e^3*f - 16*a*b^2*c^3*d^3*e^2*g + 5*a*b^3*c^2*d^2*e^3*g - 16*a^2*b*c^3*d^2*e^3*g - 5*a^2*b^2*c^2*d*e^4*g + 22*a
*b*c^4*d^4*e*g + 20*a*b^4*c*d*e^4*g - 32*a*b*c^4*d^3*e^2*f - a*b^3*c^2*d*e^4*f + 58*a^2*b*c^3*d*e^4*f))/(2*(16
*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 +
3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^
4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*
d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d
^2*e^4 - 96*a^3*b*c^3*d^3*e^3)) + (x^3*(12*c^6*d^5*f + 16*a^3*c^3*e^5*g - 6*b*c^5*d^5*g - 12*b^5*c*e^5*f + 4*a
*b^4*c*e^5*g - 8*a*c^5*d^4*e*g - 6*b*c^5*d^4*e*f + 8*b^5*c*d*e^4*g + 87*a*b^3*c^2*e^5*f - 138*a^2*b*c^3*e^5*f
+ 48*a*c^5*d^3*e^2*f + 36*a^2*c^4*d*e^4*f + 9*b^4*c^2*d*e^4*f + 5*b^2*c^4*d^4*e*g - 29*a^2*b^2*c^2*e^5*g + 8*a
^2*c^4*d^2*e^3*g - 30*b^2*c^4*d^3*e^2*f + 15*b^3*c^3*d^2*e^3*f + 15*b^3*c^3*d^3*e^2*g - 10*b^4*c^2*d^2*e^3*g -
4*a*b^2*c^3*d^2*e^3*g + 24*a*b*c^4*d^2*e^3*f - 78*a*b^2*c^3*d*e^4*f - 24*a*b*c^4*d^3*e^2*g - 53*a*b^3*c^2*d*e
^4*g + 150*a^2*b*c^3*d*e^4*g))/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 -
8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 4
8*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*
e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 -
21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)) + (x*(3*a^2*b^4*e^5*g + 4*b^2*c^4*d^5*f +
24*a^4*c^2*e^5*g - 2*b^3*c^3*d^5*g + 2*b^6*d^2*e^3*g - 9*a*b^5*e^5*f + 20*a*c^5*d^5*f - 3*b^6*d*e^4*f - 10*a*
b*c^4*d^5*g + 7*a*b^5*d*e^4*g + 68*a^2*b^3*c*e^5*f - 122*a^3*b*c^2*e^5*f - 21*a^3*b^2*c*e^5*g + 44*a^3*c^3*d*e
^4*f - 9*b^3*c^3*d^4*e*f + 5*b^5*c*d^2*e^3*f + 6*b^4*c^2*d^4*e*g - 6*b^5*c*d^3*e^2*g + 64*a^2*c^4*d^3*e^2*f +
24*a^3*c^3*d^2*e^3*g + 3*b^4*c^2*d^3*e^2*f + 14*a*b^2*c^3*d^3*e^2*f - 33*a*b^3*c^2*d^2*e^3*f + 16*a^2*b*c^3*d^
2*e^3*f - 70*a^2*b^2*c^2*d*e^4*f + 21*a*b^3*c^2*d^3*e^2*g - 72*a^2*b*c^3*d^3*e^2*g - 30*a*b*c^4*d^4*e*f + 26*a
*b^4*c*d*e^4*f + 40*a^2*b^2*c^2*d^2*e^3*g + 9*a*b^2*c^3*d^4*e*g - 15*a*b^4*c*d^2*e^3*g - 53*a^2*b^3*c*d*e^4*g
+ 106*a^3*b*c^2*d*e^4*g))/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*
b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3
*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 +
24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*
b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))/(x^2*(b^2*d + 2*a*b*e + 2*a*c*d) + x^3*(b^2*e
+ 2*a*c*e + 2*b*c*d) + x*(a^2*e + 2*a*b*d) + a^2*d + x^4*(c^2*d + 2*b*c*e) + c^2*e*x^5)