3.89 \(\int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^3} \, dx\)

Optimal. Leaf size=861 \[ \frac {\left (-3 C d a^4+4 b B d a^3-b^2 (B c+(5 A+C) d) a^2+2 b^3 (A c-C c+B d) a+b^4 (B c-3 A d)\right ) \log (a \cos (e+f x)+b \sin (e+f x)) b^2}{\left (a^2+b^2\right )^2 (b c-a d)^4 f}-\frac {\left (\left (C c^3-3 B d c^2-3 C d^2 c+B d^3-A \left (c^3-3 c d^2\right )\right ) a^2+2 b \left ((A-C) d \left (3 c^2-d^2\right )-B \left (c^3-3 c d^2\right )\right ) a+b^2 \left (A c^3-C c^3+3 B d c^2-3 A d^2 c+3 C d^2 c-B d^3\right )\right ) x}{\left (a^2+b^2\right )^2 \left (c^2+d^2\right )^3}+\frac {d \left (a^2 \left ((A-C) d \left (3 c^2-d^2\right )-B \left (c^3-3 c d^2\right )\right ) d^3-2 a b \left (c (A-C) d \left (5 c^2+d^2\right )-B \left (2 c^4-3 d^2 c^2-d^4\right )\right ) d^2+b^2 \left (3 C c^6-6 B d c^5+(10 A-C) d^2 c^4-3 B d^3 c^3+9 A d^4 c^2-B d^5 c+3 A d^6\right )\right ) \log (c \cos (e+f x)+d \sin (e+f x))}{(b c-a d)^4 \left (c^2+d^2\right )^3 f}-\frac {d \left (d^2 \left (2 c C d+B \left (c^2-d^2\right )\right ) a^3+b \left (3 C c^4-3 B d c^3+2 C d^2 c^2-B d^3 c+C d^4\right ) a^2+b^2 \left (2 c C d^3-B \left (c^4+d^2 c^2+2 d^4\right )\right ) a+b^3 c \left (2 C c^3-3 B d c^2-B d^3\right )-A \left (-\left (\left (c^4+6 d^2 c^2+3 d^4\right ) b^3\right )+2 a c d^3 b^2-2 a^2 d^2 \left (2 c^2+d^2\right ) b+2 a^3 c d^3\right )\right )}{\left (a^2+b^2\right ) (b c-a d)^3 \left (c^2+d^2\right )^2 f (c+d \tan (e+f x))}-\frac {d \left (\left (3 C c^2-B d c+2 C d^2\right ) a^2-2 b B \left (c^2+d^2\right ) a+b^2 c (c C-B d)+A \left (\left (2 c^2+3 d^2\right ) b^2+a^2 d^2\right )\right )}{2 \left (a^2+b^2\right ) (b c-a d)^2 \left (c^2+d^2\right ) f (c+d \tan (e+f x))^2}-\frac {A b^2-a (b B-a C)}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x)) (c+d \tan (e+f x))^2} \]

[Out]

-(b^2*(A*c^3-3*A*c*d^2+3*B*c^2*d-B*d^3-C*c^3+3*C*c*d^2)+a^2*(c^3*C-3*B*c^2*d-3*c*C*d^2+B*d^3-A*(c^3-3*c*d^2))+
2*a*b*((A-C)*d*(3*c^2-d^2)-B*(c^3-3*c*d^2)))*x/(a^2+b^2)^2/(c^2+d^2)^3+b^2*(4*a^3*b*B*d-3*a^4*C*d+b^4*(-3*A*d+
B*c)+2*a*b^3*(A*c+B*d-C*c)-a^2*b^2*(B*c+(5*A+C)*d))*ln(a*cos(f*x+e)+b*sin(f*x+e))/(a^2+b^2)^2/(-a*d+b*c)^4/f+d
*(b^2*(3*c^6*C-6*B*c^5*d+c^4*(10*A-C)*d^2-3*B*c^3*d^3+9*A*c^2*d^4-B*c*d^5+3*A*d^6)+a^2*d^3*((A-C)*d*(3*c^2-d^2
)-B*(c^3-3*c*d^2))-2*a*b*d^2*(c*(A-C)*d*(5*c^2+d^2)-B*(2*c^4-3*c^2*d^2-d^4)))*ln(c*cos(f*x+e)+d*sin(f*x+e))/(-
a*d+b*c)^4/(c^2+d^2)^3/f-1/2*d*(b^2*c*(-B*d+C*c)-2*a*b*B*(c^2+d^2)+a^2*(-B*c*d+3*C*c^2+2*C*d^2)+A*(a^2*d^2+b^2
*(2*c^2+3*d^2)))/(a^2+b^2)/(-a*d+b*c)^2/(c^2+d^2)/f/(c+d*tan(f*x+e))^2+(-A*b^2+a*(B*b-C*a))/(a^2+b^2)/(-a*d+b*
c)/f/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^2-d*(b^3*c*(-3*B*c^2*d-B*d^3+2*C*c^3)+a^2*b*(-3*B*c^3*d-B*c*d^3+3*C*c^4
+2*C*c^2*d^2+C*d^4)+a^3*d^2*(2*c*C*d+B*(c^2-d^2))+a*b^2*(2*c*C*d^3-B*(c^4+c^2*d^2+2*d^4))-A*(2*a^3*c*d^3+2*a*b
^2*c*d^3-2*a^2*b*d^2*(2*c^2+d^2)-b^3*(c^4+6*c^2*d^2+3*d^4)))/(a^2+b^2)/(-a*d+b*c)^3/(c^2+d^2)^2/f/(c+d*tan(f*x
+e))

________________________________________________________________________________________

Rubi [A]  time = 4.28, antiderivative size = 860, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 3, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {3649, 3651, 3530} \[ \frac {\left (-3 C d a^4+4 b B d a^3-b^2 (B c+(5 A+C) d) a^2+2 b^3 (A c-C c+B d) a+b^4 (B c-3 A d)\right ) \log (a \cos (e+f x)+b \sin (e+f x)) b^2}{\left (a^2+b^2\right )^2 (b c-a d)^4 f}-\frac {\left (\left (C c^3-3 B d c^2-3 C d^2 c+B d^3-A \left (c^3-3 c d^2\right )\right ) a^2+2 b \left ((A-C) d \left (3 c^2-d^2\right )-B \left (c^3-3 c d^2\right )\right ) a+b^2 \left (A c^3-C c^3+3 B d c^2-3 A d^2 c+3 C d^2 c-B d^3\right )\right ) x}{\left (a^2+b^2\right )^2 \left (c^2+d^2\right )^3}+\frac {d \left (a^2 \left ((A-C) d \left (3 c^2-d^2\right )-B \left (c^3-3 c d^2\right )\right ) d^3-2 a b \left (c (A-C) d \left (5 c^2+d^2\right )-B \left (2 c^4-3 d^2 c^2-d^4\right )\right ) d^2+b^2 \left (3 C c^6-6 B d c^5+(10 A-C) d^2 c^4-3 B d^3 c^3+9 A d^4 c^2-B d^5 c+3 A d^6\right )\right ) \log (c \cos (e+f x)+d \sin (e+f x))}{(b c-a d)^4 \left (c^2+d^2\right )^3 f}-\frac {d \left (d^2 \left (2 c C d+B \left (c^2-d^2\right )\right ) a^3+b \left (3 C c^4-3 B d c^3+2 C d^2 c^2-B d^3 c+C d^4\right ) a^2+b^2 \left (2 c C d^3-B \left (c^4+d^2 c^2+2 d^4\right )\right ) a+b^3 c \left (2 C c^3-3 B d c^2-B d^3\right )-A \left (-\left (c^4+6 d^2 c^2+3 d^4\right ) b^3+2 a c d^3 b^2-2 a^2 d^2 \left (2 c^2+d^2\right ) b+2 a^3 c d^3\right )\right )}{\left (a^2+b^2\right ) (b c-a d)^3 \left (c^2+d^2\right )^2 f (c+d \tan (e+f x))}-\frac {d \left (A d^2 a^2+\left (3 C c^2-B d c+2 C d^2\right ) a^2-2 b B \left (c^2+d^2\right ) a+b^2 c (c C-B d)+A b^2 \left (2 c^2+3 d^2\right )\right )}{2 \left (a^2+b^2\right ) (b c-a d)^2 \left (c^2+d^2\right ) f (c+d \tan (e+f x))^2}-\frac {A b^2-a (b B-a C)}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x)) (c+d \tan (e+f x))^2} \]

Antiderivative was successfully verified.

[In]

Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^3),x]

[Out]

-(((b^2*(A*c^3 - c^3*C + 3*B*c^2*d - 3*A*c*d^2 + 3*c*C*d^2 - B*d^3) + a^2*(c^3*C - 3*B*c^2*d - 3*c*C*d^2 + B*d
^3 - A*(c^3 - 3*c*d^2)) + 2*a*b*((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2)))*x)/((a^2 + b^2)^2*(c^2 + d^2)^3
)) + (b^2*(4*a^3*b*B*d - 3*a^4*C*d + b^4*(B*c - 3*A*d) + 2*a*b^3*(A*c - c*C + B*d) - a^2*b^2*(B*c + (5*A + C)*
d))*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^2*(b*c - a*d)^4*f) + (d*(b^2*(3*c^6*C - 6*B*c^5*d + c^4
*(10*A - C)*d^2 - 3*B*c^3*d^3 + 9*A*c^2*d^4 - B*c*d^5 + 3*A*d^6) + a^2*d^3*((A - C)*d*(3*c^2 - d^2) - B*(c^3 -
3*c*d^2)) - 2*a*b*d^2*(c*(A - C)*d*(5*c^2 + d^2) - B*(2*c^4 - 3*c^2*d^2 - d^4)))*Log[c*Cos[e + f*x] + d*Sin[e
+ f*x]])/((b*c - a*d)^4*(c^2 + d^2)^3*f) - (d*(a^2*A*d^2 + b^2*c*(c*C - B*d) - 2*a*b*B*(c^2 + d^2) + A*b^2*(2
*c^2 + 3*d^2) + a^2*(3*c^2*C - B*c*d + 2*C*d^2)))/(2*(a^2 + b^2)*(b*c - a*d)^2*(c^2 + d^2)*f*(c + d*Tan[e + f*
x])^2) - (A*b^2 - a*(b*B - a*C))/((a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^2) - (d*
(b^3*c*(2*c^3*C - 3*B*c^2*d - B*d^3) + a^2*b*(3*c^4*C - 3*B*c^3*d + 2*c^2*C*d^2 - B*c*d^3 + C*d^4) + a^3*d^2*(
2*c*C*d + B*(c^2 - d^2)) + a*b^2*(2*c*C*d^3 - B*(c^4 + c^2*d^2 + 2*d^4)) - A*(2*a^3*c*d^3 + 2*a*b^2*c*d^3 - 2*
a^2*b*d^2*(2*c^2 + d^2) - b^3*(c^4 + 6*c^2*d^2 + 3*d^4))))/((a^2 + b^2)*(b*c - a*d)^3*(c^2 + d^2)^2*f*(c + d*T
an[e + f*x]))

Rule 3530

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

Rule 3649

Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_)*((c_.) + (d_.)*tan[(e_.) + (f_.)*(x_)])^(n_)*((A_.) + (B_.)*t
an[(e_.) + (f_.)*(x_)] + (C_.)*tan[(e_.) + (f_.)*(x_)]^2), x_Symbol] :> Simp[((A*b^2 - a*(b*B - a*C))*(a + b*T
an[e + f*x])^(m + 1)*(c + d*Tan[e + f*x])^(n + 1))/(f*(m + 1)*(b*c - a*d)*(a^2 + b^2)), x] + Dist[1/((m + 1)*(
b*c - a*d)*(a^2 + b^2)), Int[(a + b*Tan[e + f*x])^(m + 1)*(c + d*Tan[e + f*x])^n*Simp[A*(a*(b*c - a*d)*(m + 1)
- b^2*d*(m + n + 2)) + (b*B - a*C)*(b*c*(m + 1) + a*d*(n + 1)) - (m + 1)*(b*c - a*d)*(A*b - a*B - b*C)*Tan[e
+ f*x] - d*(A*b^2 - a*(b*B - a*C))*(m + n + 2)*Tan[e + f*x]^2, x], x], x] /; FreeQ[{a, b, c, d, e, f, A, B, C,
n}, x] && NeQ[b*c - a*d, 0] && NeQ[a^2 + b^2, 0] && NeQ[c^2 + d^2, 0] && LtQ[m, -1] &&  !(ILtQ[n, -1] && ( !I
ntegerQ[m] || (EqQ[c, 0] && NeQ[a, 0])))

Rule 3651

Int[((A_.) + (B_.)*tan[(e_.) + (f_.)*(x_)] + (C_.)*tan[(e_.) + (f_.)*(x_)]^2)/(((a_) + (b_.)*tan[(e_.) + (f_.)
*(x_)])*((c_.) + (d_.)*tan[(e_.) + (f_.)*(x_)])), x_Symbol] :> Simp[((a*(A*c - c*C + B*d) + b*(B*c - A*d + C*d
))*x)/((a^2 + b^2)*(c^2 + d^2)), x] + (Dist[(A*b^2 - a*b*B + a^2*C)/((b*c - a*d)*(a^2 + b^2)), Int[(b - a*Tan[
e + f*x])/(a + b*Tan[e + f*x]), x], x] - Dist[(c^2*C - B*c*d + A*d^2)/((b*c - a*d)*(c^2 + d^2)), Int[(d - c*Ta
n[e + f*x])/(c + d*Tan[e + f*x]), x], x]) /; FreeQ[{a, b, c, d, e, f, A, B, C}, x] && NeQ[b*c - a*d, 0] && NeQ
[a^2 + b^2, 0] && NeQ[c^2 + d^2, 0]

Rubi steps

\begin {align*} \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^3} \, dx &=-\frac {A b^2-a (b B-a C)}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x)) (c+d \tan (e+f x))^2}-\frac {\int \frac {3 A b^2 d-a A (b c-a d)-(b B-a C) (b c+2 a d)+(A b-a B-b C) (b c-a d) \tan (e+f x)+3 \left (A b^2-a (b B-a C)\right ) d \tan ^2(e+f x)}{(a+b \tan (e+f x)) (c+d \tan (e+f x))^3} \, dx}{\left (a^2+b^2\right ) (b c-a d)}\\ &=-\frac {d \left (a^2 A d^2+b^2 c (c C-B d)-2 a b B \left (c^2+d^2\right )+A b^2 \left (2 c^2+3 d^2\right )+a^2 \left (3 c^2 C-B c d+2 C d^2\right )\right )}{2 \left (a^2+b^2\right ) (b c-a d)^2 \left (c^2+d^2\right ) f (c+d \tan (e+f x))^2}-\frac {A b^2-a (b B-a C)}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x)) (c+d \tan (e+f x))^2}-\frac {\int \frac {-2 \left (a^3 d^2 (A c-c C+B d)-a^2 b (2 A+C) d \left (c^2+d^2\right )+b^3 (B c-3 A d) \left (c^2+d^2\right )+a b^2 (A c-c C+B d) \left (c^2+2 d^2\right )\right )-2 (b c-a d)^2 (b c C-b B d-A (b c+a d)+a (B c+C d)) \tan (e+f x)+2 b d \left (a^2 A d^2+b^2 c (c C-B d)-2 a b B \left (c^2+d^2\right )+A b^2 \left (2 c^2+3 d^2\right )+a^2 \left (3 c^2 C-B c d+2 C d^2\right )\right ) \tan ^2(e+f x)}{(a+b \tan (e+f x)) (c+d \tan (e+f x))^2} \, dx}{2 \left (a^2+b^2\right ) (b c-a d)^2 \left (c^2+d^2\right )}\\ &=-\frac {d \left (a^2 A d^2+b^2 c (c C-B d)-2 a b B \left (c^2+d^2\right )+A b^2 \left (2 c^2+3 d^2\right )+a^2 \left (3 c^2 C-B c d+2 C d^2\right )\right )}{2 \left (a^2+b^2\right ) (b c-a d)^2 \left (c^2+d^2\right ) f (c+d \tan (e+f x))^2}-\frac {A b^2-a (b B-a C)}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x)) (c+d \tan (e+f x))^2}-\frac {d \left (b^3 c \left (2 c^3 C-3 B c^2 d-B d^3\right )+a^2 b \left (3 c^4 C-3 B c^3 d+2 c^2 C d^2-B c d^3+C d^4\right )+a^3 d^2 \left (2 c C d+B \left (c^2-d^2\right )\right )+a b^2 \left (2 c C d^3-B \left (c^4+c^2 d^2+2 d^4\right )\right )-A \left (2 a^3 c d^3+2 a b^2 c d^3-2 a^2 b d^2 \left (2 c^2+d^2\right )-b^3 \left (c^4+6 c^2 d^2+3 d^4\right )\right )\right )}{\left (a^2+b^2\right ) (b c-a d)^3 \left (c^2+d^2\right )^2 f (c+d \tan (e+f x))}-\frac {\int \frac {2 \left (\left (a c d-b \left (c^2+d^2\right )\right ) \left (a^3 d^2 (A c-c C+B d)-a^2 b (2 A+C) d \left (c^2+d^2\right )+b^3 (B c-3 A d) \left (c^2+d^2\right )+a b^2 (A c-c C+B d) \left (c^2+2 d^2\right )\right )+a d^2 \left (2 b^3 c^2 (c C-B d)-a b^2 c^2 (B c+C d)+a^3 d^2 (B c+C d)+a^2 b (c C-B d) \left (3 c^2+d^2\right )+A \left (a b^2 c^2 d+2 a^2 b c d^2-a^3 d^3+b^3 \left (c^3+3 c d^2\right )\right )\right )\right )+2 (b c-a d)^3 \left (2 a A c d-2 a c C d+A b \left (c^2-d^2\right )-a B \left (c^2-d^2\right )-b \left (c^2 C-2 B c d-C d^2\right )\right ) \tan (e+f x)+2 b d \left (b^3 c \left (2 c^3 C-3 B c^2 d-B d^3\right )+a^2 b \left (3 c^4 C-3 B c^3 d+2 c^2 C d^2-B c d^3+C d^4\right )+a^3 d^2 \left (2 c C d+B \left (c^2-d^2\right )\right )+a b^2 \left (2 c C d^3-B \left (c^4+c^2 d^2+2 d^4\right )\right )-A \left (2 a^3 c d^3+2 a b^2 c d^3-2 a^2 b d^2 \left (2 c^2+d^2\right )-b^3 \left (c^4+6 c^2 d^2+3 d^4\right )\right )\right ) \tan ^2(e+f x)}{(a+b \tan (e+f x)) (c+d \tan (e+f x))} \, dx}{2 \left (a^2+b^2\right ) (b c-a d)^3 \left (c^2+d^2\right )^2}\\ &=-\frac {\left (b^2 \left (A c^3-c^3 C+3 B c^2 d-3 A c d^2+3 c C d^2-B d^3\right )+a^2 \left (c^3 C-3 B c^2 d-3 c C d^2+B d^3-A \left (c^3-3 c d^2\right )\right )+2 a b \left ((A-C) d \left (3 c^2-d^2\right )-B \left (c^3-3 c d^2\right )\right )\right ) x}{\left (a^2+b^2\right )^2 \left (c^2+d^2\right )^3}-\frac {d \left (a^2 A d^2+b^2 c (c C-B d)-2 a b B \left (c^2+d^2\right )+A b^2 \left (2 c^2+3 d^2\right )+a^2 \left (3 c^2 C-B c d+2 C d^2\right )\right )}{2 \left (a^2+b^2\right ) (b c-a d)^2 \left (c^2+d^2\right ) f (c+d \tan (e+f x))^2}-\frac {A b^2-a (b B-a C)}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x)) (c+d \tan (e+f x))^2}-\frac {d \left (b^3 c \left (2 c^3 C-3 B c^2 d-B d^3\right )+a^2 b \left (3 c^4 C-3 B c^3 d+2 c^2 C d^2-B c d^3+C d^4\right )+a^3 d^2 \left (2 c C d+B \left (c^2-d^2\right )\right )+a b^2 \left (2 c C d^3-B \left (c^4+c^2 d^2+2 d^4\right )\right )-A \left (2 a^3 c d^3+2 a b^2 c d^3-2 a^2 b d^2 \left (2 c^2+d^2\right )-b^3 \left (c^4+6 c^2 d^2+3 d^4\right )\right )\right )}{\left (a^2+b^2\right ) (b c-a d)^3 \left (c^2+d^2\right )^2 f (c+d \tan (e+f x))}+\frac {\left (b^2 \left (4 a^3 b B d-3 a^4 C d+b^4 (B c-3 A d)+2 a b^3 (A c-c C+B d)-a^2 b^2 (B c+(5 A+C) d)\right )\right ) \int \frac {b-a \tan (e+f x)}{a+b \tan (e+f x)} \, dx}{\left (a^2+b^2\right )^2 (b c-a d)^4}+\frac {\left (d \left (b^2 \left (3 c^6 C-6 B c^5 d+c^4 (10 A-C) d^2-3 B c^3 d^3+9 A c^2 d^4-B c d^5+3 A d^6\right )+a^2 d^3 \left ((A-C) d \left (3 c^2-d^2\right )-B \left (c^3-3 c d^2\right )\right )-2 a b d^2 \left (c (A-C) d \left (5 c^2+d^2\right )-B \left (2 c^4-3 c^2 d^2-d^4\right )\right )\right )\right ) \int \frac {d-c \tan (e+f x)}{c+d \tan (e+f x)} \, dx}{(b c-a d)^4 \left (c^2+d^2\right )^3}\\ &=-\frac {\left (b^2 \left (A c^3-c^3 C+3 B c^2 d-3 A c d^2+3 c C d^2-B d^3\right )+a^2 \left (c^3 C-3 B c^2 d-3 c C d^2+B d^3-A \left (c^3-3 c d^2\right )\right )+2 a b \left ((A-C) d \left (3 c^2-d^2\right )-B \left (c^3-3 c d^2\right )\right )\right ) x}{\left (a^2+b^2\right )^2 \left (c^2+d^2\right )^3}+\frac {b^2 \left (4 a^3 b B d-3 a^4 C d+b^4 (B c-3 A d)+2 a b^3 (A c-c C+B d)-a^2 b^2 (B c+(5 A+C) d)\right ) \log (a \cos (e+f x)+b \sin (e+f x))}{\left (a^2+b^2\right )^2 (b c-a d)^4 f}+\frac {d \left (b^2 \left (3 c^6 C-6 B c^5 d+c^4 (10 A-C) d^2-3 B c^3 d^3+9 A c^2 d^4-B c d^5+3 A d^6\right )+a^2 d^3 \left ((A-C) d \left (3 c^2-d^2\right )-B \left (c^3-3 c d^2\right )\right )-2 a b d^2 \left (c (A-C) d \left (5 c^2+d^2\right )-B \left (2 c^4-3 c^2 d^2-d^4\right )\right )\right ) \log (c \cos (e+f x)+d \sin (e+f x))}{(b c-a d)^4 \left (c^2+d^2\right )^3 f}-\frac {d \left (a^2 A d^2+b^2 c (c C-B d)-2 a b B \left (c^2+d^2\right )+A b^2 \left (2 c^2+3 d^2\right )+a^2 \left (3 c^2 C-B c d+2 C d^2\right )\right )}{2 \left (a^2+b^2\right ) (b c-a d)^2 \left (c^2+d^2\right ) f (c+d \tan (e+f x))^2}-\frac {A b^2-a (b B-a C)}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x)) (c+d \tan (e+f x))^2}-\frac {d \left (b^3 c \left (2 c^3 C-3 B c^2 d-B d^3\right )+a^2 b \left (3 c^4 C-3 B c^3 d+2 c^2 C d^2-B c d^3+C d^4\right )+a^3 d^2 \left (2 c C d+B \left (c^2-d^2\right )\right )+a b^2 \left (2 c C d^3-B \left (c^4+c^2 d^2+2 d^4\right )\right )-A \left (2 a^3 c d^3+2 a b^2 c d^3-2 a^2 b d^2 \left (2 c^2+d^2\right )-b^3 \left (c^4+6 c^2 d^2+3 d^4\right )\right )\right )}{\left (a^2+b^2\right ) (b c-a d)^3 \left (c^2+d^2\right )^2 f (c+d \tan (e+f x))}\\ \end {align*}

________________________________________________________________________________________

Mathematica [B]  time = 8.74, size = 1732, normalized size = 2.01 \[ -\frac {A b^2-a (b B-a C)}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x)) (c+d \tan (e+f x))^2}-\frac {-\frac {d^2 \left (3 A d b^2-a A (b c-a d)-(b B-a C) (b c+2 a d)\right )-c \left ((A b-C b-a B) d (b c-a d)-3 c \left (A b^2-a (b B-a C)\right ) d\right )}{2 (a d-b c) \left (c^2+d^2\right ) f (c+d \tan (e+f x))^2}-\frac {-\frac {d^2 \left (\left (2 b d^2-2 c (a d-b c)\right ) \left (3 A d b^2-a A (b c-a d)-(b B-a C) (b c+2 a d)\right )-2 a d \left ((A b-C b-a B) d (b c-a d)-3 c \left (A b^2-a (b B-a C)\right ) d\right )\right )-c \left (2 d (a d-b c) \left (-3 \left (A b^2-a (b B-a C)\right ) d^2+\left (3 A d b^2-a A (b c-a d)-(b B-a C) (b c+2 a d)\right ) d-c (A b-C b-a B) (b c-a d)\right )-2 b c \left (d^2 \left (3 A d b^2-a A (b c-a d)-(b B-a C) (b c+2 a d)\right )-c \left ((A b-C b-a B) d (b c-a d)-3 c \left (A b^2-a (b B-a C)\right ) d\right )\right )\right )}{(a d-b c) \left (c^2+d^2\right ) f (c+d \tan (e+f x))}-\frac {-\frac {2 \left (c^2+d^2\right )^2 \left (-3 C d a^4+4 b B d a^3-b^2 (B c+(5 A+C) d) a^2+2 b^3 (A c-C c+B d) a+b^4 (B c-3 A d)\right ) \log (a+b \tan (e+f x)) b^3}{\left (a^2+b^2\right ) (b c-a d)}-\frac {2 \left (a^2+b^2\right ) d \left (a^2 \left ((A-C) d \left (3 c^2-d^2\right )-B \left (c^3-3 c d^2\right )\right ) d^3-2 a b \left (c (A-C) d \left (5 c^2+d^2\right )-B \left (2 c^4-3 d^2 c^2-d^4\right )\right ) d^2+b^2 \left (3 C c^6-6 B d c^5+(10 A-C) d^2 c^4-3 B d^3 c^3+9 A d^4 c^2-B d^5 c+3 A d^6\right )\right ) \log (c+d \tan (e+f x)) b}{(b c-a d) \left (c^2+d^2\right )}-\frac {(b c-a d)^3 \left (\sqrt {-b^2} \left (A c^3 b^3-B d^3 b^3-3 A c d^2 b^3+3 c C d^2 b^3-c^3 C b^3+3 B c^2 d b^3-2 a B c^3 b^2-2 a A d^3 b^2+2 a C d^3 b^2+6 a B c d^2 b^2+6 a A c^2 d b^2-6 a c^2 C d b^2-a^2 A c^3 b+a^2 B d^3 b+3 a^2 A c d^2 b-3 a^2 c C d^2 b+a^2 c^3 C b-3 a^2 B c^2 d b\right )-b^2 \left (2 a A b c^3-a^2 B c^3+b^2 B c^3-2 a b C c^3-3 A b^2 d c^2+3 a^2 A d c^2+6 a b B d c^2-3 a^2 C d c^2+3 b^2 C d c^2-6 a A b d^2 c+3 a^2 B d^2 c-3 b^2 B d^2 c+6 a b C d^2 c+A b^2 d^3-a^2 A d^3-2 a b B d^3+a^2 C d^3-b^2 C d^3\right )\right ) \log \left (\sqrt {-b^2}-b \tan (e+f x)\right )}{\left (a^2+b^2\right ) \left (c^2+d^2\right ) b}+\frac {(b c-a d)^3 \left (\left (2 a A b c^3-a^2 B c^3+b^2 B c^3-2 a b C c^3-3 A b^2 d c^2+3 a^2 A d c^2+6 a b B d c^2-3 a^2 C d c^2+3 b^2 C d c^2-6 a A b d^2 c+3 a^2 B d^2 c-3 b^2 B d^2 c+6 a b C d^2 c+A b^2 d^3-a^2 A d^3-2 a b B d^3+a^2 C d^3-b^2 C d^3\right ) b^2+\sqrt {-b^2} \left (A c^3 b^3-B d^3 b^3-3 A c d^2 b^3+3 c C d^2 b^3-c^3 C b^3+3 B c^2 d b^3-2 a B c^3 b^2-2 a A d^3 b^2+2 a C d^3 b^2+6 a B c d^2 b^2+6 a A c^2 d b^2-6 a c^2 C d b^2-a^2 A c^3 b+a^2 B d^3 b+3 a^2 A c d^2 b-3 a^2 c C d^2 b+a^2 c^3 C b-3 a^2 B c^2 d b\right )\right ) \log \left (b \tan (e+f x)+\sqrt {-b^2}\right )}{\left (a^2+b^2\right ) \left (c^2+d^2\right ) b}}{b (a d-b c) \left (c^2+d^2\right ) f}}{2 (a d-b c) \left (c^2+d^2\right )}}{\left (a^2+b^2\right ) (b c-a d)} \]

Warning: Unable to verify antiderivative.

[In]

Integrate[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^3),x]

[Out]

-((A*b^2 - a*(b*B - a*C))/((a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^2)) - (-1/2*(-(
c*(-3*c*(A*b^2 - a*(b*B - a*C))*d + (A*b - a*B - b*C)*d*(b*c - a*d))) + d^2*(3*A*b^2*d - a*A*(b*c - a*d) - (b*
B - a*C)*(b*c + 2*a*d)))/((-(b*c) + a*d)*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^2) - (-((-(((b*c - a*d)^3*(-(b^2*(
2*a*A*b*c^3 - a^2*B*c^3 + b^2*B*c^3 - 2*a*b*c^3*C + 3*a^2*A*c^2*d - 3*A*b^2*c^2*d + 6*a*b*B*c^2*d - 3*a^2*c^2*
C*d + 3*b^2*c^2*C*d - 6*a*A*b*c*d^2 + 3*a^2*B*c*d^2 - 3*b^2*B*c*d^2 + 6*a*b*c*C*d^2 - a^2*A*d^3 + A*b^2*d^3 -
2*a*b*B*d^3 + a^2*C*d^3 - b^2*C*d^3)) + Sqrt[-b^2]*(-(a^2*A*b*c^3) + A*b^3*c^3 - 2*a*b^2*B*c^3 + a^2*b*c^3*C -
b^3*c^3*C + 6*a*A*b^2*c^2*d - 3*a^2*b*B*c^2*d + 3*b^3*B*c^2*d - 6*a*b^2*c^2*C*d + 3*a^2*A*b*c*d^2 - 3*A*b^3*c
*d^2 + 6*a*b^2*B*c*d^2 - 3*a^2*b*c*C*d^2 + 3*b^3*c*C*d^2 - 2*a*A*b^2*d^3 + a^2*b*B*d^3 - b^3*B*d^3 + 2*a*b^2*C
*d^3))*Log[Sqrt[-b^2] - b*Tan[e + f*x]])/(b*(a^2 + b^2)*(c^2 + d^2))) - (2*b^3*(c^2 + d^2)^2*(4*a^3*b*B*d - 3*
a^4*C*d + b^4*(B*c - 3*A*d) + 2*a*b^3*(A*c - c*C + B*d) - a^2*b^2*(B*c + (5*A + C)*d))*Log[a + b*Tan[e + f*x]]
)/((a^2 + b^2)*(b*c - a*d)) + ((b*c - a*d)^3*(b^2*(2*a*A*b*c^3 - a^2*B*c^3 + b^2*B*c^3 - 2*a*b*c^3*C + 3*a^2*A
*c^2*d - 3*A*b^2*c^2*d + 6*a*b*B*c^2*d - 3*a^2*c^2*C*d + 3*b^2*c^2*C*d - 6*a*A*b*c*d^2 + 3*a^2*B*c*d^2 - 3*b^2
*B*c*d^2 + 6*a*b*c*C*d^2 - a^2*A*d^3 + A*b^2*d^3 - 2*a*b*B*d^3 + a^2*C*d^3 - b^2*C*d^3) + Sqrt[-b^2]*(-(a^2*A*
b*c^3) + A*b^3*c^3 - 2*a*b^2*B*c^3 + a^2*b*c^3*C - b^3*c^3*C + 6*a*A*b^2*c^2*d - 3*a^2*b*B*c^2*d + 3*b^3*B*c^2
*d - 6*a*b^2*c^2*C*d + 3*a^2*A*b*c*d^2 - 3*A*b^3*c*d^2 + 6*a*b^2*B*c*d^2 - 3*a^2*b*c*C*d^2 + 3*b^3*c*C*d^2 - 2
*a*A*b^2*d^3 + a^2*b*B*d^3 - b^3*B*d^3 + 2*a*b^2*C*d^3))*Log[Sqrt[-b^2] + b*Tan[e + f*x]])/(b*(a^2 + b^2)*(c^2
+ d^2)) - (2*b*(a^2 + b^2)*d*(b^2*(3*c^6*C - 6*B*c^5*d + c^4*(10*A - C)*d^2 - 3*B*c^3*d^3 + 9*A*c^2*d^4 - B*c
*d^5 + 3*A*d^6) + a^2*d^3*((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2)) - 2*a*b*d^2*(c*(A - C)*d*(5*c^2 + d^2)
- B*(2*c^4 - 3*c^2*d^2 - d^4)))*Log[c + d*Tan[e + f*x]])/((b*c - a*d)*(c^2 + d^2)))/(b*(-(b*c) + a*d)*(c^2 +
d^2)*f)) - (d^2*(-2*a*d*(-3*c*(A*b^2 - a*(b*B - a*C))*d + (A*b - a*B - b*C)*d*(b*c - a*d)) + (2*b*d^2 - 2*c*(-
(b*c) + a*d))*(3*A*b^2*d - a*A*(b*c - a*d) - (b*B - a*C)*(b*c + 2*a*d))) - c*(2*d*(-(b*c) + a*d)*(-3*(A*b^2 -
a*(b*B - a*C))*d^2 - c*(A*b - a*B - b*C)*(b*c - a*d) + d*(3*A*b^2*d - a*A*(b*c - a*d) - (b*B - a*C)*(b*c + 2*a
*d))) - 2*b*c*(-(c*(-3*c*(A*b^2 - a*(b*B - a*C))*d + (A*b - a*B - b*C)*d*(b*c - a*d))) + d^2*(3*A*b^2*d - a*A*
(b*c - a*d) - (b*B - a*C)*(b*c + 2*a*d)))))/((-(b*c) + a*d)*(c^2 + d^2)*f*(c + d*Tan[e + f*x])))/(2*(-(b*c) +
a*d)*(c^2 + d^2)))/((a^2 + b^2)*(b*c - a*d))

________________________________________________________________________________________

fricas [B]  time = 20.87, size = 9567, normalized size = 11.11 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/2*(2*(C*a^2*b^5 - B*a*b^6 + A*b^7)*c^9 - 2*(C*a^3*b^4 - B*a^2*b^5 + A*a*b^6)*c^8*d + 6*(C*a^2*b^5 - B*a*b^6
+ A*b^7)*c^7*d^2 + (7*C*a^5*b^2 + 8*C*a^3*b^4 + 6*B*a^2*b^5 - (6*A - 7*C)*a*b^6)*c^6*d^3 - (10*C*a^6*b + 9*B*
a^5*b^2 + 20*C*a^4*b^3 + 18*B*a^3*b^4 + 4*C*a^2*b^5 + 15*B*a*b^6 - 6*A*b^7)*c^5*d^4 + (3*C*a^7 + 14*B*a^6*b +
(11*A + 7*C)*a^5*b^2 + 28*B*a^4*b^3 + (22*A - C)*a^3*b^4 + 20*B*a^2*b^5 + (5*A + C)*a*b^6)*c^4*d^5 - (5*B*a^7
+ 2*(9*A - C)*a^6*b + 13*B*a^5*b^2 + 4*(9*A - C)*a^4*b^3 + 11*B*a^3*b^4 + 2*(9*A - 2*C)*a^2*b^5 + 5*B*a*b^6 -
2*A*b^7)*c^3*d^6 + ((7*A - 3*C)*a^7 + 2*B*a^6*b + (19*A - 6*C)*a^5*b^2 + 4*B*a^4*b^3 + (17*A - 5*C)*a^3*b^4 +
4*B*a^2*b^5 + 3*A*a*b^6)*c^2*d^7 + (B*a^7 - 6*A*a^6*b + 2*B*a^5*b^2 - 12*A*a^4*b^3 + B*a^3*b^4 - 6*A*a^2*b^5)*
c*d^8 + (A*a^7 + 2*A*a^5*b^2 + A*a^3*b^4)*d^9 - (2*(C*a^3*b^4 - B*a^2*b^5 + A*a*b^6)*c^7*d^2 + (3*C*a^4*b^3 +
2*B*a^3*b^4 - 2*(A - 5*C)*a^2*b^5 + 5*C*b^7)*c^6*d^3 - (6*C*a^5*b^2 + 7*B*a^4*b^3 + 6*C*a^3*b^4 + 20*B*a^2*b^5
- 6*(A - C)*a*b^6 + 7*B*b^7)*c^5*d^4 + (C*a^6*b + 10*B*a^5*b^2 + (9*A - 5*C)*a^4*b^3 + 26*B*a^3*b^4 + (12*A -
C)*a^2*b^5 + 10*B*a*b^6 + (9*A - C)*b^7)*c^4*d^5 - (3*B*a^6*b + 2*(7*A - 3*C)*a^5*b^2 + 7*B*a^4*b^3 + 2*(14*A
- 9*C)*a^3*b^4 + 11*B*a^2*b^5 + 2*(4*A - 3*C)*a*b^6 + B*b^7)*c^3*d^6 + (5*(A - C)*a^6*b - 2*B*a^5*b^2 + (13*A
- 16*C)*a^4*b^3 + 2*B*a^3*b^4 + 5*(A - C)*a^2*b^5 - 2*B*a*b^6 + 3*A*b^7)*c^2*d^7 + (3*B*a^6*b - 2*A*a^5*b^2 +
6*B*a^4*b^3 - 2*(2*A - C)*a^3*b^4 + B*a^2*b^5)*c*d^8 - (A*a^6*b + 2*(A + C)*a^4*b^3 - 2*B*a^3*b^4 + 3*A*a^2*b
^5)*d^9 + 2*(((A - C)*a^2*b^5 + 2*B*a*b^6 - (A - C)*b^7)*c^7*d^2 - (4*(A - C)*a^3*b^4 + 5*B*a^2*b^5 + 2*(A - C
)*a*b^6 + 3*B*b^7)*c^6*d^3 + 3*(2*(A - C)*a^4*b^3 + 5*(A - C)*a^2*b^5 + 2*B*a*b^6 + (A - C)*b^7)*c^5*d^4 - (4*
(A - C)*a^5*b^2 - 10*B*a^4*b^3 + 20*(A - C)*a^3*b^4 - 5*B*a^2*b^5 + 10*(A - C)*a*b^6 - B*b^7)*c^4*d^5 + ((A -
C)*a^6*b - 10*B*a^5*b^2 + 5*(A - C)*a^4*b^3 - 20*B*a^3*b^4 + 10*(A - C)*a^2*b^5 - 4*B*a*b^6)*c^3*d^6 + 3*(B*a^
6*b + 2*(A - C)*a^5*b^2 + 5*B*a^4*b^3 + 2*B*a^2*b^5)*c^2*d^7 - (3*(A - C)*a^6*b + 2*B*a^5*b^2 + 5*(A - C)*a^4*
b^3 + 4*B*a^3*b^4)*c*d^8 - (B*a^6*b - 2*(A - C)*a^5*b^2 - B*a^4*b^3)*d^9)*f*x)*tan(f*x + e)^3 - 2*(((A - C)*a^
3*b^4 + 2*B*a^2*b^5 - (A - C)*a*b^6)*c^9 - (4*(A - C)*a^4*b^3 + 5*B*a^3*b^4 + 2*(A - C)*a^2*b^5 + 3*B*a*b^6)*c
^8*d + 3*(2*(A - C)*a^5*b^2 + 5*(A - C)*a^3*b^4 + 2*B*a^2*b^5 + (A - C)*a*b^6)*c^7*d^2 - (4*(A - C)*a^6*b - 10
*B*a^5*b^2 + 20*(A - C)*a^4*b^3 - 5*B*a^3*b^4 + 10*(A - C)*a^2*b^5 - B*a*b^6)*c^6*d^3 + ((A - C)*a^7 - 10*B*a^
6*b + 5*(A - C)*a^5*b^2 - 20*B*a^4*b^3 + 10*(A - C)*a^3*b^4 - 4*B*a^2*b^5)*c^5*d^4 + 3*(B*a^7 + 2*(A - C)*a^6*
b + 5*B*a^5*b^2 + 2*B*a^3*b^4)*c^4*d^5 - (3*(A - C)*a^7 + 2*B*a^6*b + 5*(A - C)*a^5*b^2 + 4*B*a^4*b^3)*c^3*d^6
- (B*a^7 - 2*(A - C)*a^6*b - B*a^5*b^2)*c^2*d^7)*f*x - (4*(C*a^3*b^4 - B*a^2*b^5 + A*a*b^6)*c^8*d + 2*(C*a^4*
b^3 + 2*B*a^3*b^4 - (2*A - 5*C)*a^2*b^5 + B*a*b^6 - (A - 3*C)*b^7)*c^7*d^2 - (3*C*a^5*b^2 + 8*B*a^4*b^3 - 8*C*
a^3*b^4 + 30*B*a^2*b^5 - (14*A - 3*C)*a*b^6 + 8*B*b^7)*c^6*d^3 - (4*C*a^6*b - 5*B*a^5*b^2 - 2*(5*A - 13*C)*a^4
*b^3 - 22*B*a^3*b^4 - 2*(4*A - 11*C)*a^2*b^5 - 11*B*a*b^6 - 2*(2*A - 3*C)*b^7)*c^5*d^4 + (C*a^7 + 6*B*a^6*b -
(7*A - 13*C)*a^5*b^2 + 18*B*a^4*b^3 - (14*A - 41*C)*a^3*b^4 + 11*(A + C)*a*b^6 + 6*B*b^7)*c^4*d^5 - (3*B*a^7 +
8*A*a^6*b + 19*B*a^5*b^2 + 2*(11*A + 6*C)*a^4*b^3 + 17*B*a^3*b^4 + 2*(16*A + 3*C)*a^2*b^5 + 7*B*a*b^6 + 12*A*
b^7)*c^3*d^6 + (5*(A - C)*a^7 + 4*B*a^6*b + (25*A - 14*C)*a^5*b^2 + 10*B*a^4*b^3 + (35*A - 3*C)*a^3*b^4 - 2*B*
a^2*b^5 + (25*A - 4*C)*a*b^6 + 2*B*b^7)*c^2*d^7 + (3*B*a^7 - 4*(2*A - C)*a^6*b + 6*B*a^5*b^2 - 4*(5*A - C)*a^4
*b^3 + 7*B*a^3*b^4 - 2*(10*A - C)*a^2*b^5 + 2*B*a*b^6 - 6*A*b^7)*c*d^8 - (A*a^7 + 2*B*a^6*b - 2*A*a^5*b^2 + 4*
B*a^4*b^3 - (7*A + 2*C)*a^3*b^4 + 4*B*a^2*b^5 - 6*A*a*b^6)*d^9 + 2*(2*((A - C)*a^2*b^5 + 2*B*a*b^6 - (A - C)*b
^7)*c^8*d - (7*(A - C)*a^3*b^4 + 8*B*a^2*b^5 + 5*(A - C)*a*b^6 + 6*B*b^7)*c^7*d^2 + (8*(A - C)*a^4*b^3 - 5*B*a
^3*b^4 + 28*(A - C)*a^2*b^5 + 9*B*a*b^6 + 6*(A - C)*b^7)*c^6*d^3 - (2*(A - C)*a^5*b^2 - 20*B*a^4*b^3 + 25*(A -
C)*a^3*b^4 - 16*B*a^2*b^5 + 17*(A - C)*a*b^6 - 2*B*b^7)*c^5*d^4 - (2*(A - C)*a^6*b + 10*B*a^5*b^2 + 10*(A - C
)*a^4*b^3 + 35*B*a^3*b^4 - 10*(A - C)*a^2*b^5 + 7*B*a*b^6)*c^4*d^5 + ((A - C)*a^7 - 4*B*a^6*b + 17*(A - C)*a^5
*b^2 + 10*B*a^4*b^3 + 10*(A - C)*a^3*b^4 + 8*B*a^2*b^5)*c^3*d^6 + (3*B*a^7 + 11*B*a^5*b^2 - 10*(A - C)*a^4*b^3
- 2*B*a^3*b^4)*c^2*d^7 - (3*(A - C)*a^7 + 4*B*a^6*b + (A - C)*a^5*b^2 + 2*B*a^4*b^3)*c*d^8 - (B*a^7 - 2*(A -
C)*a^6*b - B*a^5*b^2)*d^9)*f*x)*tan(f*x + e)^2 + ((B*a^3*b^4 - 2*(A - C)*a^2*b^5 - B*a*b^6)*c^9 + (3*C*a^5*b^2
- 4*B*a^4*b^3 + (5*A + C)*a^3*b^4 - 2*B*a^2*b^5 + 3*A*a*b^6)*c^8*d + 3*(B*a^3*b^4 - 2*(A - C)*a^2*b^5 - B*a*b
^6)*c^7*d^2 + 3*(3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A + C)*a^3*b^4 - 2*B*a^2*b^5 + 3*A*a*b^6)*c^6*d^3 + 3*(B*a^3*b
^4 - 2*(A - C)*a^2*b^5 - B*a*b^6)*c^5*d^4 + 3*(3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A + C)*a^3*b^4 - 2*B*a^2*b^5 + 3
*A*a*b^6)*c^4*d^5 + (B*a^3*b^4 - 2*(A - C)*a^2*b^5 - B*a*b^6)*c^3*d^6 + (3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A + C)
*a^3*b^4 - 2*B*a^2*b^5 + 3*A*a*b^6)*c^2*d^7 + ((B*a^2*b^5 - 2*(A - C)*a*b^6 - B*b^7)*c^7*d^2 + (3*C*a^4*b^3 -
4*B*a^3*b^4 + (5*A + C)*a^2*b^5 - 2*B*a*b^6 + 3*A*b^7)*c^6*d^3 + 3*(B*a^2*b^5 - 2*(A - C)*a*b^6 - B*b^7)*c^5*d
^4 + 3*(3*C*a^4*b^3 - 4*B*a^3*b^4 + (5*A + C)*a^2*b^5 - 2*B*a*b^6 + 3*A*b^7)*c^4*d^5 + 3*(B*a^2*b^5 - 2*(A - C
)*a*b^6 - B*b^7)*c^3*d^6 + 3*(3*C*a^4*b^3 - 4*B*a^3*b^4 + (5*A + C)*a^2*b^5 - 2*B*a*b^6 + 3*A*b^7)*c^2*d^7 + (
B*a^2*b^5 - 2*(A - C)*a*b^6 - B*b^7)*c*d^8 + (3*C*a^4*b^3 - 4*B*a^3*b^4 + (5*A + C)*a^2*b^5 - 2*B*a*b^6 + 3*A*
b^7)*d^9)*tan(f*x + e)^3 + (2*(B*a^2*b^5 - 2*(A - C)*a*b^6 - B*b^7)*c^8*d + (6*C*a^4*b^3 - 7*B*a^3*b^4 + 4*(2*
A + C)*a^2*b^5 - 5*B*a*b^6 + 6*A*b^7)*c^7*d^2 + (3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A + C)*a^3*b^4 + 4*B*a^2*b^5 -
3*(3*A - 4*C)*a*b^6 - 6*B*b^7)*c^6*d^3 + 3*(6*C*a^4*b^3 - 7*B*a^3*b^4 + 4*(2*A + C)*a^2*b^5 - 5*B*a*b^6 + 6*A
*b^7)*c^5*d^4 + 3*(3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A + C)*a^3*b^4 - (A - 4*C)*a*b^6 - 2*B*b^7)*c^4*d^5 + 3*(6*C
*a^4*b^3 - 7*B*a^3*b^4 + 4*(2*A + C)*a^2*b^5 - 5*B*a*b^6 + 6*A*b^7)*c^3*d^6 + (9*C*a^5*b^2 - 12*B*a^4*b^3 + 3*
(5*A + C)*a^3*b^4 - 4*B*a^2*b^5 + (5*A + 4*C)*a*b^6 - 2*B*b^7)*c^2*d^7 + (6*C*a^4*b^3 - 7*B*a^3*b^4 + 4*(2*A +
C)*a^2*b^5 - 5*B*a*b^6 + 6*A*b^7)*c*d^8 + (3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A + C)*a^3*b^4 - 2*B*a^2*b^5 + 3*A*
a*b^6)*d^9)*tan(f*x + e)^2 + ((B*a^2*b^5 - 2*(A - C)*a*b^6 - B*b^7)*c^9 + (3*C*a^4*b^3 - 2*B*a^3*b^4 + (A + 5*
C)*a^2*b^5 - 4*B*a*b^6 + 3*A*b^7)*c^8*d + (6*C*a^5*b^2 - 8*B*a^4*b^3 + 2*(5*A + C)*a^3*b^4 - B*a^2*b^5 + 6*C*a
*b^6 - 3*B*b^7)*c^7*d^2 + 3*(3*C*a^4*b^3 - 2*B*a^3*b^4 + (A + 5*C)*a^2*b^5 - 4*B*a*b^6 + 3*A*b^7)*c^6*d^3 + 3*
(6*C*a^5*b^2 - 8*B*a^4*b^3 + 2*(5*A + C)*a^3*b^4 - 3*B*a^2*b^5 + 2*(2*A + C)*a*b^6 - B*b^7)*c^5*d^4 + 3*(3*C*a
^4*b^3 - 2*B*a^3*b^4 + (A + 5*C)*a^2*b^5 - 4*B*a*b^6 + 3*A*b^7)*c^4*d^5 + (18*C*a^5*b^2 - 24*B*a^4*b^3 + 6*(5*
A + C)*a^3*b^4 - 11*B*a^2*b^5 + 2*(8*A + C)*a*b^6 - B*b^7)*c^3*d^6 + (3*C*a^4*b^3 - 2*B*a^3*b^4 + (A + 5*C)*a^
2*b^5 - 4*B*a*b^6 + 3*A*b^7)*c^2*d^7 + 2*(3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A + C)*a^3*b^4 - 2*B*a^2*b^5 + 3*A*a*
b^6)*c*d^8)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - (3*(C*a^
5*b^2 + 2*C*a^3*b^4 + C*a*b^6)*c^8*d - 6*(B*a^5*b^2 + 2*B*a^3*b^4 + B*a*b^6)*c^7*d^2 + (4*B*a^6*b + (10*A - C)
*a^5*b^2 + 8*B*a^4*b^3 + 2*(10*A - C)*a^3*b^4 + 4*B*a^2*b^5 + (10*A - C)*a*b^6)*c^6*d^3 - (B*a^7 + 10*(A - C)*
a^6*b + 5*B*a^5*b^2 + 20*(A - C)*a^4*b^3 + 7*B*a^3*b^4 + 10*(A - C)*a^2*b^5 + 3*B*a*b^6)*c^5*d^4 + 3*((A - C)*
a^7 - 2*B*a^6*b + (5*A - 2*C)*a^5*b^2 - 4*B*a^4*b^3 + (7*A - C)*a^3*b^4 - 2*B*a^2*b^5 + 3*A*a*b^6)*c^4*d^5 + (
3*B*a^7 - 2*(A - C)*a^6*b + 5*B*a^5*b^2 - 4*(A - C)*a^4*b^3 + B*a^3*b^4 - 2*(A - C)*a^2*b^5 - B*a*b^6)*c^3*d^6
- ((A - C)*a^7 + 2*B*a^6*b - (A + 2*C)*a^5*b^2 + 4*B*a^4*b^3 - (5*A + C)*a^3*b^4 + 2*B*a^2*b^5 - 3*A*a*b^6)*c
^2*d^7 + (3*(C*a^4*b^3 + 2*C*a^2*b^5 + C*b^7)*c^6*d^3 - 6*(B*a^4*b^3 + 2*B*a^2*b^5 + B*b^7)*c^5*d^4 + (4*B*a^5
*b^2 + (10*A - C)*a^4*b^3 + 8*B*a^3*b^4 + 2*(10*A - C)*a^2*b^5 + 4*B*a*b^6 + (10*A - C)*b^7)*c^4*d^5 - (B*a^6*
b + 10*(A - C)*a^5*b^2 + 5*B*a^4*b^3 + 20*(A - C)*a^3*b^4 + 7*B*a^2*b^5 + 10*(A - C)*a*b^6 + 3*B*b^7)*c^3*d^6
+ 3*((A - C)*a^6*b - 2*B*a^5*b^2 + (5*A - 2*C)*a^4*b^3 - 4*B*a^3*b^4 + (7*A - C)*a^2*b^5 - 2*B*a*b^6 + 3*A*b^7
)*c^2*d^7 + (3*B*a^6*b - 2*(A - C)*a^5*b^2 + 5*B*a^4*b^3 - 4*(A - C)*a^3*b^4 + B*a^2*b^5 - 2*(A - C)*a*b^6 - B
*b^7)*c*d^8 - ((A - C)*a^6*b + 2*B*a^5*b^2 - (A + 2*C)*a^4*b^3 + 4*B*a^3*b^4 - (5*A + C)*a^2*b^5 + 2*B*a*b^6 -
3*A*b^7)*d^9)*tan(f*x + e)^3 + (6*(C*a^4*b^3 + 2*C*a^2*b^5 + C*b^7)*c^7*d^2 + 3*(C*a^5*b^2 - 4*B*a^4*b^3 + 2*
C*a^3*b^4 - 8*B*a^2*b^5 + C*a*b^6 - 4*B*b^7)*c^6*d^3 + 2*(B*a^5*b^2 + (10*A - C)*a^4*b^3 + 2*B*a^3*b^4 + 2*(10
*A - C)*a^2*b^5 + B*a*b^6 + (10*A - C)*b^7)*c^5*d^4 + (2*B*a^6*b - (10*A - 19*C)*a^5*b^2 - 2*B*a^4*b^3 - 2*(10
*A - 19*C)*a^3*b^4 - 10*B*a^2*b^5 - (10*A - 19*C)*a*b^6 - 6*B*b^7)*c^4*d^5 - (B*a^7 + 4*(A - C)*a^6*b + 17*B*a
^5*b^2 - 2*(5*A + 4*C)*a^4*b^3 + 31*B*a^3*b^4 - 4*(8*A + C)*a^2*b^5 + 15*B*a*b^6 - 18*A*b^7)*c^3*d^6 + (3*(A -
C)*a^7 + (11*A - 2*C)*a^5*b^2 - 2*B*a^4*b^3 + (13*A + 5*C)*a^3*b^4 - 4*B*a^2*b^5 + (5*A + 4*C)*a*b^6 - 2*B*b^
7)*c^2*d^7 + (3*B*a^7 - 4*(A - C)*a^6*b + B*a^5*b^2 - 2*(A - 4*C)*a^4*b^3 - 7*B*a^3*b^4 + 4*(2*A + C)*a^2*b^5
- 5*B*a*b^6 + 6*A*b^7)*c*d^8 - ((A - C)*a^7 + 2*B*a^6*b - (A + 2*C)*a^5*b^2 + 4*B*a^4*b^3 - (5*A + C)*a^3*b^4
+ 2*B*a^2*b^5 - 3*A*a*b^6)*d^9)*tan(f*x + e)^2 + (3*(C*a^4*b^3 + 2*C*a^2*b^5 + C*b^7)*c^8*d + 6*(C*a^5*b^2 - B
*a^4*b^3 + 2*C*a^3*b^4 - 2*B*a^2*b^5 + C*a*b^6 - B*b^7)*c^7*d^2 - (8*B*a^5*b^2 - (10*A - C)*a^4*b^3 + 16*B*a^3
*b^4 - 2*(10*A - C)*a^2*b^5 + 8*B*a*b^6 - (10*A - C)*b^7)*c^6*d^3 + (7*B*a^6*b + 2*(5*A + 4*C)*a^5*b^2 + 11*B*
a^4*b^3 + 4*(5*A + 4*C)*a^3*b^4 + B*a^2*b^5 + 2*(5*A + 4*C)*a*b^6 - 3*B*b^7)*c^5*d^4 - (2*B*a^7 + 17*(A - C)*a
^6*b + 16*B*a^5*b^2 + (25*A - 34*C)*a^4*b^3 + 26*B*a^3*b^4 - (A + 17*C)*a^2*b^5 + 12*B*a*b^6 - 9*A*b^7)*c^4*d^
5 + (6*(A - C)*a^7 - 9*B*a^6*b + 2*(14*A - 5*C)*a^5*b^2 - 19*B*a^4*b^3 + 2*(19*A - C)*a^3*b^4 - 11*B*a^2*b^5 +
2*(8*A + C)*a*b^6 - B*b^7)*c^3*d^6 + (6*B*a^7 - 5*(A - C)*a^6*b + 8*B*a^5*b^2 - (7*A - 10*C)*a^4*b^3 - 2*B*a^
3*b^4 + (A + 5*C)*a^2*b^5 - 4*B*a*b^6 + 3*A*b^7)*c^2*d^7 - 2*((A - C)*a^7 + 2*B*a^6*b - (A + 2*C)*a^5*b^2 + 4*
B*a^4*b^3 - (5*A + C)*a^3*b^4 + 2*B*a^2*b^5 - 3*A*a*b^6)*c*d^8)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*
tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (2*(C*a^3*b^4 - B*a^2*b^5 + A*a*b^6)*c^9 - 2*(C*a^4*b^3 - B*a^3*b^
4 + (A + 2*C)*a^2*b^5 - 2*B*a*b^6 + 2*A*b^7)*c^8*d + 2*(3*C*a^5*b^2 + 11*C*a^3*b^4 - 5*B*a^2*b^5 + (5*A + 3*C)
*a*b^6)*c^7*d^2 - (8*C*a^6*b + 8*B*a^5*b^2 + 29*C*a^4*b^3 + 10*B*a^3*b^4 + 2*(3*A + 17*C)*a^2*b^5 - 4*B*a*b^6
+ (12*A + 7*C)*b^7)*c^6*d^3 + (2*C*a^7 + 12*B*a^6*b + 2*(5*A + 4*C)*a^5*b^2 + 33*B*a^4*b^3 + 4*(5*A + 7*C)*a^3
*b^4 + 12*B*a^2*b^5 + 4*(7*A + C)*a*b^6 + 9*B*b^7)*c^5*d^4 - (4*B*a^7 + (16*A - 9*C)*a^6*b + 16*B*a^5*b^2 + (4
3*A - 11*C)*a^4*b^3 + 14*B*a^3*b^4 + (44*A + 5*C)*a^2*b^5 - 4*B*a*b^6 + (23*A + C)*b^7)*c^4*d^5 + (6*(A - C)*a
^7 - 7*B*a^6*b + 2*(12*A - 7*C)*a^5*b^2 - 11*B*a^4*b^3 + 2*(15*A + 2*C)*a^3*b^4 - 15*B*a^2*b^5 + 2*(13*A - C)*
a*b^6 + 3*B*b^7)*c^3*d^6 + (6*B*a^7 + (5*A - C)*a^6*b + 12*B*a^5*b^2 + (5*A - 4*C)*a^4*b^3 + 8*B*a^3*b^4 - (7*
A + 5*C)*a^2*b^5 + 4*B*a*b^6 - 9*A*b^7)*c^2*d^7 - (2*(3*A - 2*C)*a^7 + B*a^6*b + 2*(5*A - 4*C)*a^5*b^2 + 2*B*a
^4*b^3 + 2*(A - 4*C)*a^3*b^4 + 5*B*a^2*b^5 - 6*A*a*b^6)*c*d^8 - (2*B*a^7 - 3*A*a^6*b + 4*B*a^5*b^2 - 6*A*a^4*b
^3 + 2*B*a^3*b^4 - 3*A*a^2*b^5)*d^9 + 2*(((A - C)*a^2*b^5 + 2*B*a*b^6 - (A - C)*b^7)*c^9 - (2*(A - C)*a^3*b^4
+ B*a^2*b^5 + 4*(A - C)*a*b^6 + 3*B*b^7)*c^8*d - (2*(A - C)*a^4*b^3 + 10*B*a^3*b^4 - 11*(A - C)*a^2*b^5 - 3*(A
- C)*b^7)*c^7*d^2 + (8*(A - C)*a^5*b^2 + 10*B*a^4*b^3 + 10*(A - C)*a^3*b^4 + 17*B*a^2*b^5 - 4*(A - C)*a*b^6 +
B*b^7)*c^6*d^3 - (7*(A - C)*a^6*b - 10*B*a^5*b^2 + 35*(A - C)*a^4*b^3 + 10*B*a^3*b^4 + 10*(A - C)*a^2*b^5 + 2
*B*a*b^6)*c^5*d^4 + (2*(A - C)*a^7 - 17*B*a^6*b + 16*(A - C)*a^5*b^2 - 25*B*a^4*b^3 + 20*(A - C)*a^3*b^4 - 2*B
*a^2*b^5)*c^4*d^5 + (6*B*a^7 + 9*(A - C)*a^6*b + 28*B*a^5*b^2 - 5*(A - C)*a^4*b^3 + 8*B*a^3*b^4)*c^3*d^6 - (6*
(A - C)*a^7 + 5*B*a^6*b + 8*(A - C)*a^5*b^2 + 7*B*a^4*b^3)*c^2*d^7 - 2*(B*a^7 - 2*(A - C)*a^6*b - B*a^5*b^2)*c
*d^8)*f*x)*tan(f*x + e))/(((a^4*b^5 + 2*a^2*b^7 + b^9)*c^10*d^2 - 4*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*c^9*d^3 + 3*
(2*a^6*b^3 + 5*a^4*b^5 + 4*a^2*b^7 + b^9)*c^8*d^4 - 4*(a^7*b^2 + 5*a^5*b^4 + 7*a^3*b^6 + 3*a*b^8)*c^7*d^5 + (a
^8*b + 20*a^6*b^3 + 40*a^4*b^5 + 24*a^2*b^7 + 3*b^9)*c^6*d^6 - 12*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*c^
5*d^7 + (3*a^8*b + 24*a^6*b^3 + 40*a^4*b^5 + 20*a^2*b^7 + b^9)*c^4*d^8 - 4*(3*a^7*b^2 + 7*a^5*b^4 + 5*a^3*b^6
+ a*b^8)*c^3*d^9 + 3*(a^8*b + 4*a^6*b^3 + 5*a^4*b^5 + 2*a^2*b^7)*c^2*d^10 - 4*(a^7*b^2 + 2*a^5*b^4 + a^3*b^6)*
c*d^11 + (a^8*b + 2*a^6*b^3 + a^4*b^5)*d^12)*f*tan(f*x + e)^3 + (2*(a^4*b^5 + 2*a^2*b^7 + b^9)*c^11*d - 7*(a^5
*b^4 + 2*a^3*b^6 + a*b^8)*c^10*d^2 + 2*(4*a^6*b^3 + 11*a^4*b^5 + 10*a^2*b^7 + 3*b^9)*c^9*d^3 - (2*a^7*b^2 + 25
*a^5*b^4 + 44*a^3*b^6 + 21*a*b^8)*c^8*d^4 - 2*(a^8*b - 10*a^6*b^3 - 26*a^4*b^5 - 18*a^2*b^7 - 3*b^9)*c^7*d^5 +
(a^9 - 4*a^7*b^2 - 32*a^5*b^4 - 48*a^3*b^6 - 21*a*b^8)*c^6*d^6 - 2*(3*a^8*b - 6*a^6*b^3 - 22*a^4*b^5 - 14*a^2
*b^7 - b^9)*c^5*d^7 + (3*a^9 - 16*a^5*b^4 - 20*a^3*b^6 - 7*a*b^8)*c^4*d^8 - 2*(3*a^8*b + 2*a^6*b^3 - 5*a^4*b^5
- 4*a^2*b^7)*c^3*d^9 + (3*a^9 + 4*a^7*b^2 - a^5*b^4 - 2*a^3*b^6)*c^2*d^10 - 2*(a^8*b + 2*a^6*b^3 + a^4*b^5)*c
*d^11 + (a^9 + 2*a^7*b^2 + a^5*b^4)*d^12)*f*tan(f*x + e)^2 + ((a^4*b^5 + 2*a^2*b^7 + b^9)*c^12 - 2*(a^5*b^4 +
2*a^3*b^6 + a*b^8)*c^11*d - (2*a^6*b^3 + a^4*b^5 - 4*a^2*b^7 - 3*b^9)*c^10*d^2 + 2*(4*a^7*b^2 + 5*a^5*b^4 - 2*
a^3*b^6 - 3*a*b^8)*c^9*d^3 - (7*a^8*b + 20*a^6*b^3 + 16*a^4*b^5 - 3*b^9)*c^8*d^4 + 2*(a^9 + 14*a^7*b^2 + 22*a^
5*b^4 + 6*a^3*b^6 - 3*a*b^8)*c^7*d^5 - (21*a^8*b + 48*a^6*b^3 + 32*a^4*b^5 + 4*a^2*b^7 - b^9)*c^6*d^6 + 2*(3*a
^9 + 18*a^7*b^2 + 26*a^5*b^4 + 10*a^3*b^6 - a*b^8)*c^5*d^7 - (21*a^8*b + 44*a^6*b^3 + 25*a^4*b^5 + 2*a^2*b^7)*
c^4*d^8 + 2*(3*a^9 + 10*a^7*b^2 + 11*a^5*b^4 + 4*a^3*b^6)*c^3*d^9 - 7*(a^8*b + 2*a^6*b^3 + a^4*b^5)*c^2*d^10 +
2*(a^9 + 2*a^7*b^2 + a^5*b^4)*c*d^11)*f*tan(f*x + e) + ((a^5*b^4 + 2*a^3*b^6 + a*b^8)*c^12 - 4*(a^6*b^3 + 2*a
^4*b^5 + a^2*b^7)*c^11*d + 3*(2*a^7*b^2 + 5*a^5*b^4 + 4*a^3*b^6 + a*b^8)*c^10*d^2 - 4*(a^8*b + 5*a^6*b^3 + 7*a
^4*b^5 + 3*a^2*b^7)*c^9*d^3 + (a^9 + 20*a^7*b^2 + 40*a^5*b^4 + 24*a^3*b^6 + 3*a*b^8)*c^8*d^4 - 12*(a^8*b + 3*a
^6*b^3 + 3*a^4*b^5 + a^2*b^7)*c^7*d^5 + (3*a^9 + 24*a^7*b^2 + 40*a^5*b^4 + 20*a^3*b^6 + a*b^8)*c^6*d^6 - 4*(3*
a^8*b + 7*a^6*b^3 + 5*a^4*b^5 + a^2*b^7)*c^5*d^7 + 3*(a^9 + 4*a^7*b^2 + 5*a^5*b^4 + 2*a^3*b^6)*c^4*d^8 - 4*(a^
8*b + 2*a^6*b^3 + a^4*b^5)*c^3*d^9 + (a^9 + 2*a^7*b^2 + a^5*b^4)*c^2*d^10)*f)

________________________________________________________________________________________

giac [B]  time = 90.12, size = 3176, normalized size = 3.69 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*(2*(A*a^2*c^3 - C*a^2*c^3 + 2*B*a*b*c^3 - A*b^2*c^3 + C*b^2*c^3 + 3*B*a^2*c^2*d - 6*A*a*b*c^2*d + 6*C*a*b*
c^2*d - 3*B*b^2*c^2*d - 3*A*a^2*c*d^2 + 3*C*a^2*c*d^2 - 6*B*a*b*c*d^2 + 3*A*b^2*c*d^2 - 3*C*b^2*c*d^2 - B*a^2*
d^3 + 2*A*a*b*d^3 - 2*C*a*b*d^3 + B*b^2*d^3)*(f*x + e)/(a^4*c^6 + 2*a^2*b^2*c^6 + b^4*c^6 + 3*a^4*c^4*d^2 + 6*
a^2*b^2*c^4*d^2 + 3*b^4*c^4*d^2 + 3*a^4*c^2*d^4 + 6*a^2*b^2*c^2*d^4 + 3*b^4*c^2*d^4 + a^4*d^6 + 2*a^2*b^2*d^6
+ b^4*d^6) + (B*a^2*c^3 - 2*A*a*b*c^3 + 2*C*a*b*c^3 - B*b^2*c^3 - 3*A*a^2*c^2*d + 3*C*a^2*c^2*d - 6*B*a*b*c^2*
d + 3*A*b^2*c^2*d - 3*C*b^2*c^2*d - 3*B*a^2*c*d^2 + 6*A*a*b*c*d^2 - 6*C*a*b*c*d^2 + 3*B*b^2*c*d^2 + A*a^2*d^3
- C*a^2*d^3 + 2*B*a*b*d^3 - A*b^2*d^3 + C*b^2*d^3)*log(tan(f*x + e)^2 + 1)/(a^4*c^6 + 2*a^2*b^2*c^6 + b^4*c^6
+ 3*a^4*c^4*d^2 + 6*a^2*b^2*c^4*d^2 + 3*b^4*c^4*d^2 + 3*a^4*c^2*d^4 + 6*a^2*b^2*c^2*d^4 + 3*b^4*c^2*d^4 + a^4*
d^6 + 2*a^2*b^2*d^6 + b^4*d^6) - 2*(B*a^2*b^5*c - 2*A*a*b^6*c + 2*C*a*b^6*c - B*b^7*c + 3*C*a^4*b^3*d - 4*B*a^
3*b^4*d + 5*A*a^2*b^5*d + C*a^2*b^5*d - 2*B*a*b^6*d + 3*A*b^7*d)*log(abs(b*tan(f*x + e) + a))/(a^4*b^5*c^4 + 2
*a^2*b^7*c^4 + b^9*c^4 - 4*a^5*b^4*c^3*d - 8*a^3*b^6*c^3*d - 4*a*b^8*c^3*d + 6*a^6*b^3*c^2*d^2 + 12*a^4*b^5*c^
2*d^2 + 6*a^2*b^7*c^2*d^2 - 4*a^7*b^2*c*d^3 - 8*a^5*b^4*c*d^3 - 4*a^3*b^6*c*d^3 + a^8*b*d^4 + 2*a^6*b^3*d^4 +
a^4*b^5*d^4) + 2*(3*C*b^2*c^6*d^2 - 6*B*b^2*c^5*d^3 + 4*B*a*b*c^4*d^4 + 10*A*b^2*c^4*d^4 - C*b^2*c^4*d^4 - B*a
^2*c^3*d^5 - 10*A*a*b*c^3*d^5 + 10*C*a*b*c^3*d^5 - 3*B*b^2*c^3*d^5 + 3*A*a^2*c^2*d^6 - 3*C*a^2*c^2*d^6 - 6*B*a
*b*c^2*d^6 + 9*A*b^2*c^2*d^6 + 3*B*a^2*c*d^7 - 2*A*a*b*c*d^7 + 2*C*a*b*c*d^7 - B*b^2*c*d^7 - A*a^2*d^8 + C*a^2
*d^8 - 2*B*a*b*d^8 + 3*A*b^2*d^8)*log(abs(d*tan(f*x + e) + c))/(b^4*c^10*d - 4*a*b^3*c^9*d^2 + 6*a^2*b^2*c^8*d
^3 + 3*b^4*c^8*d^3 - 4*a^3*b*c^7*d^4 - 12*a*b^3*c^7*d^4 + a^4*c^6*d^5 + 18*a^2*b^2*c^6*d^5 + 3*b^4*c^6*d^5 - 1
2*a^3*b*c^5*d^6 - 12*a*b^3*c^5*d^6 + 3*a^4*c^4*d^7 + 18*a^2*b^2*c^4*d^7 + b^4*c^4*d^7 - 12*a^3*b*c^3*d^8 - 4*a
*b^3*c^3*d^8 + 3*a^4*c^2*d^9 + 6*a^2*b^2*c^2*d^9 - 4*a^3*b*c*d^10 + a^4*d^11) + 2*(B*a^2*b^5*c*tan(f*x + e) -
2*A*a*b^6*c*tan(f*x + e) + 2*C*a*b^6*c*tan(f*x + e) - B*b^7*c*tan(f*x + e) + 3*C*a^4*b^3*d*tan(f*x + e) - 4*B*
a^3*b^4*d*tan(f*x + e) + 5*A*a^2*b^5*d*tan(f*x + e) + C*a^2*b^5*d*tan(f*x + e) - 2*B*a*b^6*d*tan(f*x + e) + 3*
A*b^7*d*tan(f*x + e) - C*a^4*b^3*c + 2*B*a^3*b^4*c - 3*A*a^2*b^5*c + C*a^2*b^5*c - A*b^7*c + 4*C*a^5*b^2*d - 5
*B*a^4*b^3*d + 6*A*a^3*b^4*d + 2*C*a^3*b^4*d - 3*B*a^2*b^5*d + 4*A*a*b^6*d)/((a^4*b^4*c^4 + 2*a^2*b^6*c^4 + b^
8*c^4 - 4*a^5*b^3*c^3*d - 8*a^3*b^5*c^3*d - 4*a*b^7*c^3*d + 6*a^6*b^2*c^2*d^2 + 12*a^4*b^4*c^2*d^2 + 6*a^2*b^6
*c^2*d^2 - 4*a^7*b*c*d^3 - 8*a^5*b^3*c*d^3 - 4*a^3*b^5*c*d^3 + a^8*d^4 + 2*a^6*b^2*d^4 + a^4*b^4*d^4)*(b*tan(f
*x + e) + a)) - (9*C*b^2*c^6*d^3*tan(f*x + e)^2 - 18*B*b^2*c^5*d^4*tan(f*x + e)^2 + 12*B*a*b*c^4*d^5*tan(f*x +
e)^2 + 30*A*b^2*c^4*d^5*tan(f*x + e)^2 - 3*C*b^2*c^4*d^5*tan(f*x + e)^2 - 3*B*a^2*c^3*d^6*tan(f*x + e)^2 - 30
*A*a*b*c^3*d^6*tan(f*x + e)^2 + 30*C*a*b*c^3*d^6*tan(f*x + e)^2 - 9*B*b^2*c^3*d^6*tan(f*x + e)^2 + 9*A*a^2*c^2
*d^7*tan(f*x + e)^2 - 9*C*a^2*c^2*d^7*tan(f*x + e)^2 - 18*B*a*b*c^2*d^7*tan(f*x + e)^2 + 27*A*b^2*c^2*d^7*tan(
f*x + e)^2 + 9*B*a^2*c*d^8*tan(f*x + e)^2 - 6*A*a*b*c*d^8*tan(f*x + e)^2 + 6*C*a*b*c*d^8*tan(f*x + e)^2 - 3*B*
b^2*c*d^8*tan(f*x + e)^2 - 3*A*a^2*d^9*tan(f*x + e)^2 + 3*C*a^2*d^9*tan(f*x + e)^2 - 6*B*a*b*d^9*tan(f*x + e)^
2 + 9*A*b^2*d^9*tan(f*x + e)^2 + 22*C*b^2*c^7*d^2*tan(f*x + e) - 4*C*a*b*c^6*d^3*tan(f*x + e) - 42*B*b^2*c^6*d
^3*tan(f*x + e) + 32*B*a*b*c^5*d^4*tan(f*x + e) + 68*A*b^2*c^5*d^4*tan(f*x + e) - 2*C*b^2*c^5*d^4*tan(f*x + e)
- 8*B*a^2*c^4*d^5*tan(f*x + e) - 72*A*a*b*c^4*d^5*tan(f*x + e) + 60*C*a*b*c^4*d^5*tan(f*x + e) - 26*B*b^2*c^4
*d^5*tan(f*x + e) + 22*A*a^2*c^3*d^6*tan(f*x + e) - 22*C*a^2*c^3*d^6*tan(f*x + e) - 28*B*a*b*c^3*d^6*tan(f*x +
e) + 66*A*b^2*c^3*d^6*tan(f*x + e) + 18*B*a^2*c^2*d^7*tan(f*x + e) - 28*A*a*b*c^2*d^7*tan(f*x + e) + 16*C*a*b
*c^2*d^7*tan(f*x + e) - 8*B*b^2*c^2*d^7*tan(f*x + e) - 2*A*a^2*c*d^8*tan(f*x + e) + 2*C*a^2*c*d^8*tan(f*x + e)
- 12*B*a*b*c*d^8*tan(f*x + e) + 22*A*b^2*c*d^8*tan(f*x + e) + 2*B*a^2*d^9*tan(f*x + e) - 4*A*a*b*d^9*tan(f*x
+ e) + 14*C*b^2*c^8*d - 6*C*a*b*c^7*d^2 - 25*B*b^2*c^7*d^2 + C*a^2*c^6*d^3 + 22*B*a*b*c^6*d^3 + 39*A*b^2*c^6*d
^3 + 3*C*b^2*c^6*d^3 - 6*B*a^2*c^5*d^4 - 44*A*a*b*c^5*d^4 + 26*C*a*b*c^5*d^4 - 19*B*b^2*c^5*d^4 + 14*A*a^2*c^4
*d^5 - 11*C*a^2*c^4*d^5 - 6*B*a*b*c^4*d^5 + 41*A*b^2*c^4*d^5 + C*b^2*c^4*d^5 + 7*B*a^2*c^3*d^6 - 26*A*a*b*c^3*
d^6 + 8*C*a*b*c^3*d^6 - 6*B*b^2*c^3*d^6 + 3*A*a^2*c^2*d^7 - 4*B*a*b*c^2*d^7 + 14*A*b^2*c^2*d^7 + B*a^2*c*d^8 -
6*A*a*b*c*d^8 + A*a^2*d^9)/((b^4*c^10 - 4*a*b^3*c^9*d + 6*a^2*b^2*c^8*d^2 + 3*b^4*c^8*d^2 - 4*a^3*b*c^7*d^3 -
12*a*b^3*c^7*d^3 + a^4*c^6*d^4 + 18*a^2*b^2*c^6*d^4 + 3*b^4*c^6*d^4 - 12*a^3*b*c^5*d^5 - 12*a*b^3*c^5*d^5 + 3
*a^4*c^4*d^6 + 18*a^2*b^2*c^4*d^6 + b^4*c^4*d^6 - 12*a^3*b*c^3*d^7 - 4*a*b^3*c^3*d^7 + 3*a^4*c^2*d^8 + 6*a^2*b
^2*c^2*d^8 - 4*a^3*b*c*d^9 + a^4*d^10)*(d*tan(f*x + e) + c)^2))/f

________________________________________________________________________________________

maple [B]  time = 0.62, size = 3364, normalized size = 3.91 \[ \text {output too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x)

[Out]

2/f*d^4/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*a*c+2/f*d/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*C*b*c^4+
3/f*d^5/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a^2*c^2-3/f*d^5/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e)
)*C*a^2*c^2+3/f*d/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*b^2*c^6-1/f*d^3/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*
tan(f*x+e))*C*b^2*c^4-5/f*b^4/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a^2*d-3/f/(a^2+b^2)^2/(c^2+d^2)^3*A
*arctan(tan(f*x+e))*a^2*c*d^2+2/f/(a^2+b^2)^2/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a*b*d^3+3/f/(a^2+b^2)^2/(c^2+d^
2)^3*A*arctan(tan(f*x+e))*b^2*c*d^2+3/f/(a^2+b^2)^2/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a^2*c^2*d-1/f/(a^2+b^2)^2
/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a*b*c^3+3/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*b^2*c^2*d-3/2/f/(
a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a^2*c*d^2+1/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a*b*d^3
+10/f*d^3/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*b^2*c^4+9/f*d^5/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+
e))*A*b^2*c^2-1/f*d^4/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a^2*c^3-1/f*b^4/(a*d-b*c)^4/(a^2+b^2)^2*ln(
a+b*tan(f*x+e))*C*a^2*d-2/f*b^5/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*C*a*c-2/f*d^4/(a*d-b*c)^3/(c^2+d^2)
^2/(c+d*tan(f*x+e))*A*a*c+4/f*d^3/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*A*b*c^2+1/f*d^3/(a*d-b*c)^3/(c^2+d^
2)^2/(c+d*tan(f*x+e))*B*a*c^2-3/f*d^2/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*b*c^3-1/f*d^4/(a*d-b*c)^3/(c^
2+d^2)^2/(c+d*tan(f*x+e))*B*b*c-3/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a^2*c^2*d+3/f/(a^2+b^2)^2/(
c^2+d^2)^3*C*arctan(tan(f*x+e))*a^2*c*d^2-2/f/(a^2+b^2)^2/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a*b*d^3-3/f/(a^2+b^
2)^2/(c^2+d^2)^3*C*arctan(tan(f*x+e))*b^2*c*d^2+2/f*b^5/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*A*a*c+4/f*b
^3/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*a^3*B*d-1/f*b^4/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a^2
*c+2/f*b^5/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*a*d-3/f*b^2/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))
*a^4*C*d+3/f*d^6/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a^2*c-2/f*d^7/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan
(f*x+e))*B*a*b-6/f*d^2/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*b^2*c^5-3/f*d^4/(a*d-b*c)^4/(c^2+d^2)^3*ln
(c+d*tan(f*x+e))*B*b^2*c^3-1/f*d^6/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*b^2*c+2/f/(a^2+b^2)^2/(c^2+d^2
)^3*B*arctan(tan(f*x+e))*a*b*c^3-3/f/(a^2+b^2)^2/(c^2+d^2)^3*B*arctan(tan(f*x+e))*b^2*c^2*d-3/2/f/(a^2+b^2)^2/
(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*b^2*c^2*d+3/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*b^2*c*d^2+3/2/f/
(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a^2*c^2*d+1/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a*b*c^
3-3/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a*b*c*d^2+6/f/(a^2+b^2)^2/(c^2+d^2)^3*C*arctan(tan(f*x+e))*
a*b*c^2*d-3/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a*b*c^2*d-1/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*
x+e)^2)*B*b^2*c^3-1/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*C*a^2*d^3-3/f*b^6/(a*d-b*c)^4/(a^2+b^2)^2*l
n(a+b*tan(f*x+e))*A*d+1/f*b^6/(a*d-b*c)^4/(a^2+b^2)^2*ln(a+b*tan(f*x+e))*B*c-1/f*b^3/(a*d-b*c)^3/(a^2+b^2)/(a+
b*tan(f*x+e))*B*a+1/f*b^2/(a*d-b*c)^3/(a^2+b^2)/(a+b*tan(f*x+e))*a^2*C+2/f*d^5/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*ta
n(f*x+e))*A*b-1/f*d^5/(a*d-b*c)^3/(c^2+d^2)^2/(c+d*tan(f*x+e))*B*a-1/f*d^7/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(
f*x+e))*A*a^2+3/f*d^7/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*b^2+1/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(
f*x+e)^2)*C*b^2*d^3+1/f/(a^2+b^2)^2/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a^2*c^3-1/f/(a^2+b^2)^2/(c^2+d^2)^3*A*arc
tan(tan(f*x+e))*b^2*c^3-1/f/(a^2+b^2)^2/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a^2*d^3+1/f/(a^2+b^2)^2/(c^2+d^2)^3*B
*arctan(tan(f*x+e))*b^2*d^3-1/f/(a^2+b^2)^2/(c^2+d^2)^3*C*arctan(tan(f*x+e))*a^2*c^3+1/f/(a^2+b^2)^2/(c^2+d^2)
^3*C*arctan(tan(f*x+e))*b^2*c^3+1/f*d^7/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a^2+1/2/f*d^2/(a*d-b*c)^2
/(c^2+d^2)/(c+d*tan(f*x+e))^2*B*c-1/2/f*d/(a*d-b*c)^2/(c^2+d^2)/(c+d*tan(f*x+e))^2*c^2*C+1/2/f/(a^2+b^2)^2/(c^
2+d^2)^3*ln(1+tan(f*x+e)^2)*A*a^2*d^3-1/2/f/(a^2+b^2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*A*b^2*d^3+1/2/f/(a^2+b^
2)^2/(c^2+d^2)^3*ln(1+tan(f*x+e)^2)*B*a^2*c^3-2/f*d^6/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*A*a*b*c+4/f*d
^3/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a*b*c^4+2/f*d^6/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*C*a
*b*c-6/f*d^5/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(f*x+e))*B*a*b*c^2+10/f*d^4/(a*d-b*c)^4/(c^2+d^2)^3*ln(c+d*tan(
f*x+e))*C*a*b*c^3-6/f/(a^2+b^2)^2/(c^2+d^2)^3*B*arctan(tan(f*x+e))*a*b*c*d^2-10/f*d^4/(a*d-b*c)^4/(c^2+d^2)^3*
ln(c+d*tan(f*x+e))*A*a*b*c^3-6/f/(a^2+b^2)^2/(c^2+d^2)^3*A*arctan(tan(f*x+e))*a*b*c^2*d-1/2/f*d^3/(a*d-b*c)^2/
(c^2+d^2)/(c+d*tan(f*x+e))^2*A+1/f*b^4/(a*d-b*c)^3/(a^2+b^2)/(a+b*tan(f*x+e))*A+3/f/(a^2+b^2)^2/(c^2+d^2)^3*ln
(1+tan(f*x+e)^2)*A*a*b*c*d^2

________________________________________________________________________________________

maxima [B]  time = 0.79, size = 2537, normalized size = 2.95 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x, algorithm="maxima")

[Out]

1/2*(2*(((A - C)*a^2 + 2*B*a*b - (A - C)*b^2)*c^3 + 3*(B*a^2 - 2*(A - C)*a*b - B*b^2)*c^2*d - 3*((A - C)*a^2 +
2*B*a*b - (A - C)*b^2)*c*d^2 - (B*a^2 - 2*(A - C)*a*b - B*b^2)*d^3)*(f*x + e)/((a^4 + 2*a^2*b^2 + b^4)*c^6 +
3*(a^4 + 2*a^2*b^2 + b^4)*c^4*d^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*c^2*d^4 + (a^4 + 2*a^2*b^2 + b^4)*d^6) - 2*((B*a
^2*b^4 - 2*(A - C)*a*b^5 - B*b^6)*c + (3*C*a^4*b^2 - 4*B*a^3*b^3 + (5*A + C)*a^2*b^4 - 2*B*a*b^5 + 3*A*b^6)*d)
*log(b*tan(f*x + e) + a)/((a^4*b^4 + 2*a^2*b^6 + b^8)*c^4 - 4*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*c^3*d + 6*(a^6*b^2
+ 2*a^4*b^4 + a^2*b^6)*c^2*d^2 - 4*(a^7*b + 2*a^5*b^3 + a^3*b^5)*c*d^3 + (a^8 + 2*a^6*b^2 + a^4*b^4)*d^4) + 2
*(3*C*b^2*c^6*d - 6*B*b^2*c^5*d^2 + (4*B*a*b + (10*A - C)*b^2)*c^4*d^3 - (B*a^2 + 10*(A - C)*a*b + 3*B*b^2)*c^
3*d^4 + 3*((A - C)*a^2 - 2*B*a*b + 3*A*b^2)*c^2*d^5 + (3*B*a^2 - 2*(A - C)*a*b - B*b^2)*c*d^6 - ((A - C)*a^2 +
2*B*a*b - 3*A*b^2)*d^7)*log(d*tan(f*x + e) + c)/(b^4*c^10 - 4*a*b^3*c^9*d - 4*a^3*b*c*d^9 + a^4*d^10 + 3*(2*a
^2*b^2 + b^4)*c^8*d^2 - 4*(a^3*b + 3*a*b^3)*c^7*d^3 + (a^4 + 18*a^2*b^2 + 3*b^4)*c^6*d^4 - 12*(a^3*b + a*b^3)*
c^5*d^5 + (3*a^4 + 18*a^2*b^2 + b^4)*c^4*d^6 - 4*(3*a^3*b + a*b^3)*c^3*d^7 + 3*(a^4 + 2*a^2*b^2)*c^2*d^8) + ((
B*a^2 - 2*(A - C)*a*b - B*b^2)*c^3 - 3*((A - C)*a^2 + 2*B*a*b - (A - C)*b^2)*c^2*d - 3*(B*a^2 - 2*(A - C)*a*b
- B*b^2)*c*d^2 + ((A - C)*a^2 + 2*B*a*b - (A - C)*b^2)*d^3)*log(tan(f*x + e)^2 + 1)/((a^4 + 2*a^2*b^2 + b^4)*c
^6 + 3*(a^4 + 2*a^2*b^2 + b^4)*c^4*d^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*c^2*d^4 + (a^4 + 2*a^2*b^2 + b^4)*d^6) - (2
*(C*a^2*b^2 - B*a*b^3 + A*b^4)*c^6 + 5*(C*a^3*b + C*a*b^3)*c^5*d - (C*a^4 + 7*B*a^3*b - 3*C*a^2*b^2 + 11*B*a*b
^3 - 4*A*b^4)*c^4*d^2 + (3*B*a^4 + (9*A + C)*a^3*b + 3*B*a^2*b^2 + (9*A + C)*a*b^3)*c^3*d^3 - ((5*A - 3*C)*a^4
+ 3*B*a^3*b + 5*(A - C)*a^2*b^2 + 5*B*a*b^3 - 2*A*b^4)*c^2*d^4 - (B*a^4 - 5*A*a^3*b + B*a^2*b^2 - 5*A*a*b^3)*
c*d^5 - (A*a^4 + A*a^2*b^2)*d^6 + 2*((3*C*a^2*b^2 - B*a*b^3 + (A + 2*C)*b^4)*c^4*d^2 - 3*(B*a^2*b^2 + B*b^4)*c
^3*d^3 + (B*a^3*b + 2*(2*A + C)*a^2*b^2 - B*a*b^3 + 6*A*b^4)*c^2*d^4 - (2*(A - C)*a^3*b + B*a^2*b^2 + 2*(A - C
)*a*b^3 + B*b^4)*c*d^5 - (B*a^3*b - (2*A + C)*a^2*b^2 + 2*B*a*b^3 - 3*A*b^4)*d^6)*tan(f*x + e)^2 + ((9*C*a^2*b
^2 - 4*B*a*b^3 + (4*A + 5*C)*b^4)*c^5*d + (3*C*a^3*b - 7*B*a^2*b^2 + 3*C*a*b^3 - 7*B*b^4)*c^4*d^2 - (3*B*a^3*b
- 9*(A + C)*a^2*b^2 + 11*B*a*b^3 - (17*A + C)*b^4)*c^3*d^3 + (2*B*a^4 + 3*(A + C)*a^3*b - B*a^2*b^2 + 3*(A +
C)*a*b^3 - 3*B*b^4)*c^2*d^4 - (4*(A - C)*a^4 + 3*B*a^3*b - (A + 8*C)*a^2*b^2 + 7*B*a*b^3 - 9*A*b^4)*c*d^5 - (2
*B*a^4 - 3*A*a^3*b + 2*B*a^2*b^2 - 3*A*a*b^3)*d^6)*tan(f*x + e))/((a^3*b^3 + a*b^5)*c^9 - 3*(a^4*b^2 + a^2*b^4
)*c^8*d + (3*a^5*b + 5*a^3*b^3 + 2*a*b^5)*c^7*d^2 - (a^6 + 7*a^4*b^2 + 6*a^2*b^4)*c^6*d^3 + (6*a^5*b + 7*a^3*b
^3 + a*b^5)*c^5*d^4 - (2*a^6 + 5*a^4*b^2 + 3*a^2*b^4)*c^4*d^5 + 3*(a^5*b + a^3*b^3)*c^3*d^6 - (a^6 + a^4*b^2)*
c^2*d^7 + ((a^2*b^4 + b^6)*c^7*d^2 - 3*(a^3*b^3 + a*b^5)*c^6*d^3 + (3*a^4*b^2 + 5*a^2*b^4 + 2*b^6)*c^5*d^4 - (
a^5*b + 7*a^3*b^3 + 6*a*b^5)*c^4*d^5 + (6*a^4*b^2 + 7*a^2*b^4 + b^6)*c^3*d^6 - (2*a^5*b + 5*a^3*b^3 + 3*a*b^5)
*c^2*d^7 + 3*(a^4*b^2 + a^2*b^4)*c*d^8 - (a^5*b + a^3*b^3)*d^9)*tan(f*x + e)^3 + (2*(a^2*b^4 + b^6)*c^8*d - 5*
(a^3*b^3 + a*b^5)*c^7*d^2 + (3*a^4*b^2 + 7*a^2*b^4 + 4*b^6)*c^6*d^3 + (a^5*b - 9*a^3*b^3 - 10*a*b^5)*c^5*d^4 -
(a^6 - 5*a^4*b^2 - 8*a^2*b^4 - 2*b^6)*c^4*d^5 + (2*a^5*b - 3*a^3*b^3 - 5*a*b^5)*c^3*d^6 - (2*a^6 - a^4*b^2 -
3*a^2*b^4)*c^2*d^7 + (a^5*b + a^3*b^3)*c*d^8 - (a^6 + a^4*b^2)*d^9)*tan(f*x + e)^2 + ((a^2*b^4 + b^6)*c^9 - (a
^3*b^3 + a*b^5)*c^8*d - (3*a^4*b^2 + a^2*b^4 - 2*b^6)*c^7*d^2 + (5*a^5*b + 3*a^3*b^3 - 2*a*b^5)*c^6*d^3 - (2*a
^6 + 8*a^4*b^2 + 5*a^2*b^4 - b^6)*c^5*d^4 + (10*a^5*b + 9*a^3*b^3 - a*b^5)*c^4*d^5 - (4*a^6 + 7*a^4*b^2 + 3*a^
2*b^4)*c^3*d^6 + 5*(a^5*b + a^3*b^3)*c^2*d^7 - 2*(a^6 + a^4*b^2)*c*d^8)*tan(f*x + e)))/f

________________________________________________________________________________________

mupad [B]  time = 47.93, size = 128666, normalized size = 149.44 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((A + B*tan(e + f*x) + C*tan(e + f*x)^2)/((a + b*tan(e + f*x))^2*(c + d*tan(e + f*x))^3),x)

[Out]

(((2*A*b^4*c^6 - A*a^4*d^6 - 2*B*a*b^3*c^6 - B*a^4*c*d^5 - A*a^2*b^2*d^6 - 5*A*a^4*c^2*d^4 + 2*C*a^2*b^2*c^6 +
2*A*b^4*c^2*d^4 + 4*A*b^4*c^4*d^2 + 3*B*a^4*c^3*d^3 + 3*C*a^4*c^2*d^4 - C*a^4*c^4*d^2 + 9*A*a*b^3*c^3*d^3 + 9
*A*a^3*b*c^3*d^3 - 5*B*a*b^3*c^2*d^4 - 11*B*a*b^3*c^4*d^2 - B*a^2*b^2*c*d^5 - 3*B*a^3*b*c^2*d^4 - 7*B*a^3*b*c^
4*d^2 + C*a*b^3*c^3*d^3 + C*a^3*b*c^3*d^3 - 5*A*a^2*b^2*c^2*d^4 + 3*B*a^2*b^2*c^3*d^3 + 5*C*a^2*b^2*c^2*d^4 +
3*C*a^2*b^2*c^4*d^2 + 5*A*a*b^3*c*d^5 + 5*A*a^3*b*c*d^5 + 5*C*a*b^3*c^5*d + 5*C*a^3*b*c^5*d)/(2*(a^3*d^3 - b^3
*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^2*c^4 + a^2*d^4 + b^2*c^4 + b^2*d^4 + 2*a^2*c^2*d^2 + 2*b^2*c^2*d^2))
+ (tan(e + f*x)*(3*A*a*b^3*d^6 - 2*B*a^4*d^6 + 3*A*a^3*b*d^6 - 4*A*a^4*c*d^5 + 9*A*b^4*c*d^5 + 4*A*b^4*c^5*d
+ 4*C*a^4*c*d^5 + 5*C*b^4*c^5*d - 2*B*a^2*b^2*d^6 + 17*A*b^4*c^3*d^3 + 2*B*a^4*c^2*d^4 - 3*B*b^4*c^2*d^4 - 7*B
*b^4*c^4*d^2 + C*b^4*c^3*d^3 + 3*A*a*b^3*c^2*d^4 + A*a^2*b^2*c*d^5 + 3*A*a^3*b*c^2*d^4 - 11*B*a*b^3*c^3*d^3 -
3*B*a^3*b*c^3*d^3 + 3*C*a*b^3*c^2*d^4 + 3*C*a*b^3*c^4*d^2 + 8*C*a^2*b^2*c*d^5 + 9*C*a^2*b^2*c^5*d + 3*C*a^3*b*
c^2*d^4 + 3*C*a^3*b*c^4*d^2 + 9*A*a^2*b^2*c^3*d^3 - B*a^2*b^2*c^2*d^4 - 7*B*a^2*b^2*c^4*d^2 + 9*C*a^2*b^2*c^3*
d^3 - 7*B*a*b^3*c*d^5 - 4*B*a*b^3*c^5*d - 3*B*a^3*b*c*d^5))/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*
d^2)*(a^2*c^4 + a^2*d^4 + b^2*c^4 + b^2*d^4 + 2*a^2*c^2*d^2 + 2*b^2*c^2*d^2)) + (tan(e + f*x)^2*(3*A*b^4*d^6 -
2*B*a*b^3*d^6 - B*a^3*b*d^6 - B*b^4*c*d^5 + 2*A*a^2*b^2*d^6 + 6*A*b^4*c^2*d^4 + A*b^4*c^4*d^2 + C*a^2*b^2*d^6
- 3*B*b^4*c^3*d^3 + 2*C*b^4*c^4*d^2 - B*a*b^3*c^2*d^4 - B*a*b^3*c^4*d^2 - B*a^2*b^2*c*d^5 + B*a^3*b*c^2*d^4 +
4*A*a^2*b^2*c^2*d^4 - 3*B*a^2*b^2*c^3*d^3 + 2*C*a^2*b^2*c^2*d^4 + 3*C*a^2*b^2*c^4*d^2 - 2*A*a*b^3*c*d^5 - 2*A
*a^3*b*c*d^5 + 2*C*a*b^3*c*d^5 + 2*C*a^3*b*c*d^5))/((a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^2*c
^4 + a^2*d^4 + b^2*c^4 + b^2*d^4 + 2*a^2*c^2*d^2 + 2*b^2*c^2*d^2)))/(tan(e + f*x)*(b*c^2 + 2*a*c*d) + a*c^2 +
tan(e + f*x)^2*(a*d^2 + 2*b*c*d) + b*d^2*tan(e + f*x)^3) + symsum(log((3*A^3*a^3*b^6*d^10 - A^3*a^5*b^4*d^10 +
4*B^3*a^2*b^7*d^10 + 6*B^3*a^4*b^5*d^10 + 24*A^3*b^9*c^3*d^7 + 27*A^3*b^9*c^5*d^5 + C^3*a^5*b^4*d^10 + B^3*b^
9*c^2*d^8 + 4*B^3*b^9*c^4*d^6 + 7*B^3*b^9*c^6*d^4 + 9*A^2*B*b^9*d^10 + 9*A^3*b^9*c*d^9 + 26*A^3*a^2*b^7*c^3*d^
7 + 31*A^3*a^2*b^7*c^5*d^5 + 16*A^3*a^3*b^6*c^2*d^8 - 11*A^3*a^3*b^6*c^4*d^6 - 6*A^3*a^4*b^5*c^3*d^7 + 3*A^3*a
^5*b^4*c^2*d^8 + 5*B^3*a^2*b^7*c^2*d^8 - 14*B^3*a^2*b^7*c^4*d^6 + 9*B^3*a^2*b^7*c^6*d^4 + 28*B^3*a^3*b^6*c^3*d
^7 + 19*B^3*a^3*b^6*c^5*d^5 + 6*B^3*a^4*b^5*c^2*d^8 - 20*B^3*a^4*b^5*c^4*d^6 + 7*B^3*a^5*b^4*c^3*d^7 + C^3*a^2
*b^7*c^3*d^7 - 4*C^3*a^2*b^7*c^5*d^5 - 9*C^3*a^2*b^7*c^7*d^3 - 7*C^3*a^3*b^6*c^2*d^8 - 28*C^3*a^3*b^6*c^4*d^6
+ 3*C^3*a^3*b^6*c^6*d^4 + 15*C^3*a^4*b^5*c^3*d^7 - 9*C^3*a^4*b^5*c^7*d^3 - 3*C^3*a^5*b^4*c^2*d^8 - 24*C^3*a^5*
b^4*c^4*d^6 + 6*C^3*a^6*b^3*c^3*d^7 - 12*A*B^2*a*b^8*d^10 - 6*A*B^2*b^9*c*d^9 - 9*A^2*C*b^9*c*d^9 + 4*B^3*a*b^
8*c*d^9 - 17*A*B^2*a^3*b^6*d^10 + 3*A*B^2*a^5*b^4*d^10 + 12*A^2*B*a^2*b^7*d^10 - 7*A^2*B*a^4*b^5*d^10 + 3*A*C^
2*a^3*b^6*d^10 - 3*A*C^2*a^5*b^4*d^10 - 6*A^2*C*a^3*b^6*d^10 + 3*A^2*C*a^5*b^4*d^10 - 20*A*B^2*b^9*c^3*d^7 - 2
8*A*B^2*b^9*c^5*d^5 + 6*A*B^2*b^9*c^7*d^3 - B*C^2*a^4*b^5*d^10 + 3*B*C^2*a^6*b^3*d^10 + 21*A^2*B*b^9*c^2*d^8 +
13*A^2*B*b^9*c^4*d^6 - 27*A^2*B*b^9*c^6*d^4 - 4*B^2*C*a^3*b^6*d^10 - 9*B^2*C*a^5*b^4*d^10 - 3*A*C^2*b^9*c^3*d
^7 - 9*A*C^2*b^9*c^7*d^3 - 21*A^2*C*b^9*c^3*d^7 - 27*A^2*C*b^9*c^5*d^5 + 9*A^2*C*b^9*c^7*d^3 + B*C^2*b^9*c^4*d
^6 + 3*B*C^2*b^9*c^8*d^2 - B^2*C*b^9*c^3*d^7 - 2*B^2*C*b^9*c^5*d^5 - 9*B^2*C*b^9*c^7*d^3 - 3*A^3*a*b^8*c^2*d^8
- 31*A^3*a*b^8*c^4*d^6 - 8*A^3*a*b^8*c^6*d^4 + 3*A^3*a^2*b^7*c*d^9 - 10*A^3*a^4*b^5*c*d^9 + 11*B^3*a*b^8*c^3*
d^7 + 5*B^3*a*b^8*c^5*d^5 - 6*B^3*a*b^8*c^7*d^3 + B^3*a^3*b^6*c*d^9 - 5*B^3*a^5*b^4*c*d^9 - 2*C^3*a*b^8*c^4*d^
6 - C^3*a*b^8*c^6*d^4 - 3*C^3*a*b^8*c^8*d^2 - 2*C^3*a^4*b^5*c*d^9 - 6*C^3*a^6*b^3*c*d^9 - 4*A*B^2*a^2*b^7*c^3*
d^7 - 77*A*B^2*a^2*b^7*c^5*d^5 - 6*A*B^2*a^2*b^7*c^7*d^3 - 60*A*B^2*a^3*b^6*c^2*d^8 + 25*A*B^2*a^3*b^6*c^4*d^6
+ 28*A*B^2*a^3*b^6*c^6*d^4 + 44*A*B^2*a^4*b^5*c^3*d^7 - 17*A*B^2*a^4*b^5*c^5*d^5 - 21*A*B^2*a^5*b^4*c^2*d^8 +
4*A*B^2*a^5*b^4*c^4*d^6 + 71*A^2*B*a^2*b^7*c^2*d^8 + 86*A^2*B*a^2*b^7*c^4*d^6 - 13*A^2*B*a^2*b^7*c^6*d^4 - 11
6*A^2*B*a^3*b^6*c^3*d^7 - 37*A^2*B*a^3*b^6*c^5*d^5 + 16*A^2*B*a^4*b^5*c^2*d^8 + 35*A^2*B*a^4*b^5*c^4*d^6 - 9*A
^2*B*a^5*b^4*c^3*d^7 - 30*A*C^2*a^2*b^7*c^3*d^7 - 15*A*C^2*a^2*b^7*c^5*d^5 + 30*A*C^2*a^3*b^6*c^2*d^8 + 45*A*C
^2*a^3*b^6*c^4*d^6 - 6*A*C^2*a^3*b^6*c^6*d^4 - 63*A*C^2*a^4*b^5*c^3*d^7 - 27*A*C^2*a^4*b^5*c^5*d^5 + 9*A*C^2*a
^4*b^5*c^7*d^3 + 9*A*C^2*a^5*b^4*c^2*d^8 + 48*A*C^2*a^5*b^4*c^4*d^6 - 12*A*C^2*a^6*b^3*c^3*d^7 + 3*A^2*C*a^2*b
^7*c^3*d^7 - 12*A^2*C*a^2*b^7*c^5*d^5 + 9*A^2*C*a^2*b^7*c^7*d^3 - 39*A^2*C*a^3*b^6*c^2*d^8 - 6*A^2*C*a^3*b^6*c
^4*d^6 + 3*A^2*C*a^3*b^6*c^6*d^4 + 54*A^2*C*a^4*b^5*c^3*d^7 + 27*A^2*C*a^4*b^5*c^5*d^5 - 9*A^2*C*a^5*b^4*c^2*d
^8 - 24*A^2*C*a^5*b^4*c^4*d^6 + 6*A^2*C*a^6*b^3*c^3*d^7 + 11*B*C^2*a^2*b^7*c^2*d^8 + 47*B*C^2*a^2*b^7*c^4*d^6
+ 17*B*C^2*a^2*b^7*c^6*d^4 - 3*B*C^2*a^2*b^7*c^8*d^2 + 16*B*C^2*a^3*b^6*c^3*d^7 - 25*B*C^2*a^3*b^6*c^5*d^5 + 1
2*B*C^2*a^3*b^6*c^7*d^3 - 17*B*C^2*a^4*b^5*c^2*d^8 + 47*B*C^2*a^4*b^5*c^4*d^6 + 27*B*C^2*a^4*b^5*c^6*d^4 + 39*
B*C^2*a^5*b^4*c^3*d^7 - 12*B*C^2*a^5*b^4*c^5*d^5 - 18*B*C^2*a^6*b^3*c^2*d^8 + 3*B*C^2*a^6*b^3*c^4*d^6 - 35*B^2
*C*a^2*b^7*c^3*d^7 + 26*B^2*C*a^2*b^7*c^5*d^5 + 3*B^2*C*a^2*b^7*c^7*d^3 + 9*B^2*C*a^3*b^6*c^2*d^8 - 16*B^2*C*a
^3*b^6*c^4*d^6 - 37*B^2*C*a^3*b^6*c^6*d^4 - 68*B^2*C*a^4*b^5*c^3*d^7 - 4*B^2*C*a^4*b^5*c^5*d^5 + 9*B^2*C*a^5*b
^4*c^2*d^8 + 14*B^2*C*a^5*b^4*c^4*d^6 - 6*B^2*C*a^6*b^3*c^3*d^7 + 6*A*B*C*a^2*b^7*d^10 + 17*A*B*C*a^4*b^5*d^10
- 3*A*B*C*a^6*b^3*d^10 + 6*A*B*C*b^9*c^2*d^8 + 13*A*B*C*b^9*c^4*d^6 + 36*A*B*C*b^9*c^6*d^4 - 3*A*B*C*b^9*c^8*
d^2 - 24*A^2*B*a*b^8*c*d^9 - 19*A*B^2*a*b^8*c^2*d^8 + 37*A*B^2*a*b^8*c^4*d^6 + 32*A*B^2*a*b^8*c^6*d^4 + 11*A*B
^2*a^2*b^7*c*d^9 + 25*A*B^2*a^4*b^5*c*d^9 - 81*A^2*B*a*b^8*c^3*d^7 - 15*A^2*B*a*b^8*c^5*d^5 + 6*A^2*B*a*b^8*c^
7*d^3 - 23*A^2*B*a^3*b^6*c*d^9 + 11*A^2*B*a^5*b^4*c*d^9 - 3*A*C^2*a*b^8*c^2*d^8 - 27*A*C^2*a*b^8*c^4*d^6 - 6*A
*C^2*a*b^8*c^6*d^4 + 6*A*C^2*a*b^8*c^8*d^2 - 15*A*C^2*a^2*b^7*c*d^9 - 15*A*C^2*a^4*b^5*c*d^9 + 12*A*C^2*a^6*b^
3*c*d^9 + 6*A^2*C*a*b^8*c^2*d^8 + 60*A^2*C*a*b^8*c^4*d^6 + 15*A^2*C*a*b^8*c^6*d^4 - 3*A^2*C*a*b^8*c^8*d^2 + 12
*A^2*C*a^2*b^7*c*d^9 + 27*A^2*C*a^4*b^5*c*d^9 - 6*A^2*C*a^6*b^3*c*d^9 + 3*B*C^2*a*b^8*c^3*d^7 + 9*B*C^2*a*b^8*
c^5*d^5 + 18*B*C^2*a*b^8*c^7*d^3 + 13*B*C^2*a^3*b^6*c*d^9 + 23*B*C^2*a^5*b^4*c*d^9 - 8*B^2*C*a*b^8*c^2*d^8 - 2
8*B^2*C*a*b^8*c^4*d^6 - 29*B^2*C*a*b^8*c^6*d^4 + 3*B^2*C*a*b^8*c^8*d^2 - 14*B^2*C*a^2*b^7*c*d^9 - 16*B^2*C*a^4
*b^5*c*d^9 + 6*B^2*C*a^6*b^3*c*d^9 - 28*A*B*C*a^2*b^7*c^2*d^8 - 79*A*B*C*a^2*b^7*c^4*d^6 + 14*A*B*C*a^2*b^7*c^
6*d^4 + 3*A*B*C*a^2*b^7*c^8*d^2 + 100*A*B*C*a^3*b^6*c^3*d^7 + 62*A*B*C*a^3*b^6*c^5*d^5 - 12*A*B*C*a^3*b^6*c^7*
d^3 + 28*A*B*C*a^4*b^5*c^2*d^8 - 55*A*B*C*a^4*b^5*c^4*d^6 - 18*A*B*C*a^4*b^5*c^6*d^4 - 30*A*B*C*a^5*b^4*c^3*d^
7 + 12*A*B*C*a^5*b^4*c^5*d^5 + 18*A*B*C*a^6*b^3*c^2*d^8 - 3*A*B*C*a^6*b^3*c^4*d^6 + 24*A*B*C*a*b^8*c*d^9 + 78*
A*B*C*a*b^8*c^3*d^7 + 6*A*B*C*a*b^8*c^5*d^5 - 24*A*B*C*a*b^8*c^7*d^3 + 10*A*B*C*a^3*b^6*c*d^9 - 34*A*B*C*a^5*b
^4*c*d^9)/(a^10*d^14 + b^10*c^14 + 2*a^2*b^8*c^14 + a^4*b^6*c^14 + a^6*b^4*d^14 + 2*a^8*b^2*d^14 + 4*a^10*c^2*
d^12 + 6*a^10*c^4*d^10 + 4*a^10*c^6*d^8 + a^10*c^8*d^6 + b^10*c^6*d^8 + 4*b^10*c^8*d^6 + 6*b^10*c^10*d^4 + 4*b
^10*c^12*d^2 - 6*a*b^9*c^5*d^9 - 24*a*b^9*c^7*d^7 - 36*a*b^9*c^9*d^5 - 24*a*b^9*c^11*d^3 - 12*a^3*b^7*c^13*d -
6*a^5*b^5*c*d^13 - 6*a^5*b^5*c^13*d - 12*a^7*b^3*c*d^13 - 24*a^9*b*c^3*d^11 - 36*a^9*b*c^5*d^9 - 24*a^9*b*c^7
*d^7 - 6*a^9*b*c^9*d^5 + 15*a^2*b^8*c^4*d^10 + 62*a^2*b^8*c^6*d^8 + 98*a^2*b^8*c^8*d^6 + 72*a^2*b^8*c^10*d^4 +
23*a^2*b^8*c^12*d^2 - 20*a^3*b^7*c^3*d^11 - 92*a^3*b^7*c^5*d^9 - 168*a^3*b^7*c^7*d^7 - 152*a^3*b^7*c^9*d^5 -
68*a^3*b^7*c^11*d^3 + 15*a^4*b^6*c^2*d^12 + 90*a^4*b^6*c^4*d^10 + 211*a^4*b^6*c^6*d^8 + 244*a^4*b^6*c^8*d^6 +
141*a^4*b^6*c^10*d^4 + 34*a^4*b^6*c^12*d^2 - 64*a^5*b^5*c^3*d^11 - 202*a^5*b^5*c^5*d^9 - 288*a^5*b^5*c^7*d^7 -
202*a^5*b^5*c^9*d^5 - 64*a^5*b^5*c^11*d^3 + 34*a^6*b^4*c^2*d^12 + 141*a^6*b^4*c^4*d^10 + 244*a^6*b^4*c^6*d^8
+ 211*a^6*b^4*c^8*d^6 + 90*a^6*b^4*c^10*d^4 + 15*a^6*b^4*c^12*d^2 - 68*a^7*b^3*c^3*d^11 - 152*a^7*b^3*c^5*d^9
- 168*a^7*b^3*c^7*d^7 - 92*a^7*b^3*c^9*d^5 - 20*a^7*b^3*c^11*d^3 + 23*a^8*b^2*c^2*d^12 + 72*a^8*b^2*c^4*d^10 +
98*a^8*b^2*c^6*d^8 + 62*a^8*b^2*c^8*d^6 + 15*a^8*b^2*c^10*d^4 - 6*a*b^9*c^13*d - 6*a^9*b*c*d^13) - root(640*a
^15*b*c^7*d^13*f^4 + 640*a*b^15*c^13*d^7*f^4 + 480*a^15*b*c^9*d^11*f^4 + 480*a^15*b*c^5*d^15*f^4 + 480*a*b^15*
c^15*d^5*f^4 + 480*a*b^15*c^11*d^9*f^4 + 192*a^15*b*c^11*d^9*f^4 + 192*a^15*b*c^3*d^17*f^4 + 192*a^11*b^5*c*d^
19*f^4 + 192*a^5*b^11*c^19*d*f^4 + 192*a*b^15*c^17*d^3*f^4 + 192*a*b^15*c^9*d^11*f^4 + 128*a^13*b^3*c*d^19*f^4
+ 128*a^9*b^7*c*d^19*f^4 + 128*a^7*b^9*c^19*d*f^4 + 128*a^3*b^13*c^19*d*f^4 + 32*a^15*b*c^13*d^7*f^4 + 32*a^9
*b^7*c^19*d*f^4 + 32*a^7*b^9*c*d^19*f^4 + 32*a*b^15*c^7*d^13*f^4 + 32*a^15*b*c*d^19*f^4 + 32*a*b^15*c^19*d*f^4
- 47088*a^8*b^8*c^10*d^10*f^4 + 42432*a^9*b^7*c^9*d^11*f^4 + 42432*a^7*b^9*c^11*d^9*f^4 + 39328*a^9*b^7*c^11*
d^9*f^4 + 39328*a^7*b^9*c^9*d^11*f^4 - 36912*a^8*b^8*c^12*d^8*f^4 - 36912*a^8*b^8*c^8*d^12*f^4 - 34256*a^10*b^
6*c^10*d^10*f^4 - 34256*a^6*b^10*c^10*d^10*f^4 - 31152*a^10*b^6*c^8*d^12*f^4 - 31152*a^6*b^10*c^12*d^8*f^4 + 2
8128*a^9*b^7*c^7*d^13*f^4 + 28128*a^7*b^9*c^13*d^7*f^4 + 24160*a^11*b^5*c^9*d^11*f^4 + 24160*a^5*b^11*c^11*d^9
*f^4 - 23088*a^10*b^6*c^12*d^8*f^4 - 23088*a^6*b^10*c^8*d^12*f^4 + 22272*a^9*b^7*c^13*d^7*f^4 + 22272*a^7*b^9*
c^7*d^13*f^4 + 19072*a^11*b^5*c^11*d^9*f^4 + 19072*a^5*b^11*c^9*d^11*f^4 + 18624*a^11*b^5*c^7*d^13*f^4 + 18624
*a^5*b^11*c^13*d^7*f^4 - 17328*a^8*b^8*c^14*d^6*f^4 - 17328*a^8*b^8*c^6*d^14*f^4 - 17232*a^10*b^6*c^6*d^14*f^4
- 17232*a^6*b^10*c^14*d^6*f^4 - 13520*a^12*b^4*c^8*d^12*f^4 - 13520*a^4*b^12*c^12*d^8*f^4 - 12464*a^12*b^4*c^
10*d^10*f^4 - 12464*a^4*b^12*c^10*d^10*f^4 + 10880*a^9*b^7*c^5*d^15*f^4 + 10880*a^7*b^9*c^15*d^5*f^4 - 9072*a^
10*b^6*c^14*d^6*f^4 - 9072*a^6*b^10*c^6*d^14*f^4 + 8928*a^11*b^5*c^13*d^7*f^4 + 8928*a^5*b^11*c^7*d^13*f^4 - 8
880*a^12*b^4*c^6*d^14*f^4 - 8880*a^4*b^12*c^14*d^6*f^4 + 8480*a^11*b^5*c^5*d^15*f^4 + 8480*a^5*b^11*c^15*d^5*f
^4 + 7200*a^9*b^7*c^15*d^5*f^4 + 7200*a^7*b^9*c^5*d^15*f^4 - 6912*a^12*b^4*c^12*d^8*f^4 - 6912*a^4*b^12*c^8*d^
12*f^4 + 6400*a^13*b^3*c^9*d^11*f^4 + 6400*a^3*b^13*c^11*d^9*f^4 + 5920*a^13*b^3*c^7*d^13*f^4 + 5920*a^3*b^13*
c^13*d^7*f^4 - 5392*a^10*b^6*c^4*d^16*f^4 - 5392*a^6*b^10*c^16*d^4*f^4 - 4428*a^8*b^8*c^16*d^4*f^4 - 4428*a^8*
b^8*c^4*d^16*f^4 + 4128*a^13*b^3*c^11*d^9*f^4 + 4128*a^3*b^13*c^9*d^11*f^4 - 3328*a^12*b^4*c^4*d^16*f^4 - 3328
*a^4*b^12*c^16*d^4*f^4 + 3264*a^13*b^3*c^5*d^15*f^4 + 3264*a^3*b^13*c^15*d^5*f^4 - 2480*a^14*b^2*c^8*d^12*f^4
- 2480*a^2*b^14*c^12*d^8*f^4 + 2240*a^11*b^5*c^15*d^5*f^4 + 2240*a^5*b^11*c^5*d^15*f^4 - 2128*a^12*b^4*c^14*d^
6*f^4 - 2128*a^4*b^12*c^6*d^14*f^4 + 2112*a^9*b^7*c^3*d^17*f^4 + 2112*a^7*b^9*c^17*d^3*f^4 + 2048*a^11*b^5*c^3
*d^17*f^4 + 2048*a^5*b^11*c^17*d^3*f^4 - 2000*a^14*b^2*c^6*d^14*f^4 - 2000*a^2*b^14*c^14*d^6*f^4 - 1792*a^10*b
^6*c^16*d^4*f^4 - 1792*a^6*b^10*c^4*d^16*f^4 - 1776*a^14*b^2*c^10*d^10*f^4 - 1776*a^2*b^14*c^10*d^10*f^4 + 147
2*a^13*b^3*c^13*d^7*f^4 + 1472*a^3*b^13*c^7*d^13*f^4 + 1088*a^9*b^7*c^17*d^3*f^4 + 1088*a^7*b^9*c^3*d^17*f^4 +
992*a^13*b^3*c^3*d^17*f^4 + 992*a^3*b^13*c^17*d^3*f^4 - 912*a^14*b^2*c^4*d^16*f^4 - 912*a^2*b^14*c^16*d^4*f^4
- 768*a^10*b^6*c^2*d^18*f^4 - 768*a^6*b^10*c^18*d^2*f^4 - 688*a^14*b^2*c^12*d^8*f^4 - 688*a^2*b^14*c^8*d^12*f
^4 - 592*a^12*b^4*c^2*d^18*f^4 - 592*a^4*b^12*c^18*d^2*f^4 - 472*a^8*b^8*c^18*d^2*f^4 - 472*a^8*b^8*c^2*d^18*f
^4 - 280*a^12*b^4*c^16*d^4*f^4 - 280*a^4*b^12*c^4*d^16*f^4 + 224*a^13*b^3*c^15*d^5*f^4 + 224*a^11*b^5*c^17*d^3
*f^4 + 224*a^5*b^11*c^3*d^17*f^4 + 224*a^3*b^13*c^5*d^15*f^4 - 208*a^14*b^2*c^2*d^18*f^4 - 208*a^2*b^14*c^18*d
^2*f^4 - 112*a^14*b^2*c^14*d^6*f^4 - 112*a^10*b^6*c^18*d^2*f^4 - 112*a^6*b^10*c^2*d^18*f^4 - 112*a^2*b^14*c^6*
d^14*f^4 - 80*b^16*c^14*d^6*f^4 - 60*b^16*c^16*d^4*f^4 - 60*b^16*c^12*d^8*f^4 - 24*b^16*c^18*d^2*f^4 - 24*b^16
*c^10*d^10*f^4 - 4*b^16*c^8*d^12*f^4 - 80*a^16*c^6*d^14*f^4 - 60*a^16*c^8*d^12*f^4 - 60*a^16*c^4*d^16*f^4 - 24
*a^16*c^10*d^10*f^4 - 24*a^16*c^2*d^18*f^4 - 4*a^16*c^12*d^8*f^4 - 24*a^12*b^4*d^20*f^4 - 16*a^14*b^2*d^20*f^4
- 16*a^10*b^6*d^20*f^4 - 4*a^8*b^8*d^20*f^4 - 24*a^4*b^12*c^20*f^4 - 16*a^6*b^10*c^20*f^4 - 16*a^2*b^14*c^20*
f^4 - 4*a^8*b^8*c^20*f^4 - 4*b^16*c^20*f^4 - 4*a^16*d^20*f^4 + 56*A*C*a*b^11*c^13*d*f^2 - 48*A*C*a^11*b*c*d^13
*f^2 + 48*A*C*a*b^11*c*d^13*f^2 + 5904*B*C*a^6*b^6*c^7*d^7*f^2 - 5016*B*C*a^5*b^7*c^8*d^6*f^2 - 4608*B*C*a^7*b
^5*c^6*d^8*f^2 - 4512*B*C*a^5*b^7*c^6*d^8*f^2 - 4384*B*C*a^7*b^5*c^8*d^6*f^2 + 3056*B*C*a^8*b^4*c^7*d^7*f^2 +
2256*B*C*a^4*b^8*c^7*d^7*f^2 - 1824*B*C*a^3*b^9*c^8*d^6*f^2 + 1632*B*C*a^9*b^3*c^4*d^10*f^2 - 1400*B*C*a^8*b^4
*c^3*d^11*f^2 - 1320*B*C*a^4*b^8*c^11*d^3*f^2 - 1248*B*C*a^3*b^9*c^6*d^8*f^2 + 1152*B*C*a^3*b^9*c^10*d^4*f^2 -
1072*B*C*a^9*b^3*c^6*d^8*f^2 + 1068*B*C*a^6*b^6*c^9*d^5*f^2 - 1004*B*C*a^4*b^8*c^5*d^9*f^2 - 968*B*C*a^6*b^6*
c^3*d^11*f^2 - 864*B*C*a^8*b^4*c^5*d^9*f^2 - 828*B*C*a^4*b^8*c^9*d^5*f^2 - 792*B*C*a^4*b^8*c^3*d^11*f^2 - 792*
B*C*a^2*b^10*c^11*d^3*f^2 - 776*B*C*a^9*b^3*c^8*d^6*f^2 + 688*B*C*a^7*b^5*c^4*d^10*f^2 - 672*B*C*a^10*b^2*c^3*
d^11*f^2 - 592*B*C*a^2*b^10*c^9*d^5*f^2 + 544*B*C*a^10*b^2*c^7*d^7*f^2 - 492*B*C*a^2*b^10*c^5*d^9*f^2 + 480*B*
C*a^5*b^7*c^10*d^4*f^2 - 392*B*C*a^10*b^2*c^5*d^9*f^2 + 332*B*C*a^8*b^4*c^9*d^5*f^2 - 328*B*C*a^6*b^6*c^11*d^3
*f^2 + 320*B*C*a^9*b^3*c^2*d^12*f^2 + 272*B*C*a^3*b^9*c^12*d^2*f^2 - 248*B*C*a^5*b^7*c^4*d^10*f^2 - 248*B*C*a^
2*b^10*c^3*d^11*f^2 - 208*B*C*a^7*b^5*c^10*d^4*f^2 - 192*B*C*a^5*b^7*c^2*d^12*f^2 + 144*B*C*a^2*b^10*c^7*d^7*f
^2 - 96*B*C*a^3*b^9*c^4*d^10*f^2 + 88*B*C*a^5*b^7*c^12*d^2*f^2 - 72*B*C*a^8*b^4*c^11*d^3*f^2 + 48*B*C*a^9*b^3*
c^10*d^4*f^2 - 48*B*C*a^7*b^5*c^12*d^2*f^2 - 48*B*C*a^7*b^5*c^2*d^12*f^2 - 48*B*C*a^3*b^9*c^2*d^12*f^2 - 12*B*
C*a^10*b^2*c^9*d^5*f^2 + 4*B*C*a^6*b^6*c^5*d^9*f^2 + 5824*A*C*a^7*b^5*c^5*d^9*f^2 - 4378*A*C*a^8*b^4*c^6*d^8*f
^2 + 4296*A*C*a^5*b^7*c^5*d^9*f^2 - 3912*A*C*a^6*b^6*c^6*d^8*f^2 - 3672*A*C*a^5*b^7*c^9*d^5*f^2 + 3594*A*C*a^4
*b^8*c^8*d^6*f^2 + 3236*A*C*a^6*b^6*c^8*d^6*f^2 + 2816*A*C*a^9*b^3*c^5*d^9*f^2 + 2624*A*C*a^3*b^9*c^5*d^9*f^2
+ 2432*A*C*a^7*b^5*c^7*d^7*f^2 - 2366*A*C*a^8*b^4*c^4*d^10*f^2 + 2298*A*C*a^4*b^8*c^10*d^4*f^2 + 1872*A*C*a^3*
b^9*c^7*d^7*f^2 + 1848*A*C*a^6*b^6*c^10*d^4*f^2 - 1644*A*C*a^6*b^6*c^4*d^10*f^2 - 1488*A*C*a^7*b^5*c^9*d^5*f^2
- 1408*A*C*a^3*b^9*c^9*d^5*f^2 - 1308*A*C*a^4*b^8*c^6*d^8*f^2 + 1248*A*C*a^5*b^7*c^7*d^7*f^2 - 1012*A*C*a^10*
b^2*c^6*d^8*f^2 + 1008*A*C*a^7*b^5*c^3*d^11*f^2 + 992*A*C*a^5*b^7*c^3*d^11*f^2 + 928*A*C*a^3*b^9*c^3*d^11*f^2
+ 848*A*C*a^9*b^3*c^7*d^7*f^2 + 636*A*C*a^2*b^10*c^8*d^6*f^2 - 628*A*C*a^10*b^2*c^4*d^10*f^2 - 600*A*C*a^2*b^1
0*c^6*d^8*f^2 - 576*A*C*a^5*b^7*c^11*d^3*f^2 + 572*A*C*a^2*b^10*c^10*d^4*f^2 + 464*A*C*a^8*b^4*c^8*d^6*f^2 + 3
04*A*C*a^6*b^6*c^2*d^12*f^2 - 304*A*C*a^4*b^8*c^4*d^10*f^2 + 296*A*C*a^4*b^8*c^2*d^12*f^2 + 260*A*C*a^8*b^4*c^
10*d^4*f^2 - 232*A*C*a^9*b^3*c^9*d^5*f^2 - 232*A*C*a^2*b^10*c^12*d^2*f^2 + 228*A*C*a^10*b^2*c^2*d^12*f^2 - 188
*A*C*a^2*b^10*c^4*d^10*f^2 + 144*A*C*a^3*b^9*c^11*d^3*f^2 + 116*A*C*a^6*b^6*c^12*d^2*f^2 + 112*A*C*a^9*b^3*c^3
*d^11*f^2 - 112*A*C*a^7*b^5*c^11*d^3*f^2 + 92*A*C*a^10*b^2*c^8*d^6*f^2 + 74*A*C*a^4*b^8*c^12*d^2*f^2 + 62*A*C*
a^8*b^4*c^2*d^12*f^2 + 40*A*C*a^2*b^10*c^2*d^12*f^2 - 7008*A*B*a^6*b^6*c^7*d^7*f^2 - 4032*A*B*a^4*b^8*c^7*d^7*
f^2 + 3952*A*B*a^7*b^5*c^8*d^6*f^2 + 3648*A*B*a^5*b^7*c^8*d^6*f^2 - 3392*A*B*a^8*b^4*c^7*d^7*f^2 + 3264*A*B*a^
7*b^5*c^6*d^8*f^2 - 2992*A*B*a^5*b^7*c^4*d^10*f^2 - 2368*A*B*a^7*b^5*c^4*d^10*f^2 - 2304*A*B*a^3*b^9*c^4*d^10*
f^2 - 1968*A*B*a^6*b^6*c^9*d^5*f^2 - 1872*A*B*a^9*b^3*c^4*d^10*f^2 - 1728*A*B*a^2*b^10*c^7*d^7*f^2 + 1712*A*B*
a^8*b^4*c^3*d^11*f^2 + 1536*A*B*a^5*b^7*c^6*d^8*f^2 - 1536*A*B*a^3*b^9*c^10*d^4*f^2 - 1392*A*B*a^5*b^7*c^2*d^1
2*f^2 + 1328*A*B*a^6*b^6*c^3*d^11*f^2 - 1104*A*B*a^3*b^9*c^2*d^12*f^2 - 1056*A*B*a^3*b^9*c^6*d^8*f^2 + 976*A*B
*a^9*b^3*c^6*d^8*f^2 + 960*A*B*a^4*b^8*c^11*d^3*f^2 + 936*A*B*a^8*b^4*c^5*d^9*f^2 - 912*A*B*a^5*b^7*c^10*d^4*f
^2 + 848*A*B*a^9*b^3*c^8*d^6*f^2 - 816*A*B*a^7*b^5*c^2*d^12*f^2 + 816*A*B*a^4*b^8*c^3*d^11*f^2 + 768*A*B*a^10*
b^2*c^3*d^11*f^2 + 672*A*B*a^3*b^9*c^8*d^6*f^2 - 632*A*B*a^8*b^4*c^9*d^5*f^2 - 608*A*B*a^2*b^10*c^9*d^5*f^2 -
552*A*B*a^4*b^8*c^9*d^5*f^2 - 544*A*B*a^10*b^2*c^7*d^7*f^2 - 480*A*B*a^2*b^10*c^5*d^9*f^2 + 464*A*B*a^10*b^2*c
^5*d^9*f^2 - 464*A*B*a^9*b^3*c^2*d^12*f^2 + 432*A*B*a^2*b^10*c^11*d^3*f^2 - 368*A*B*a^3*b^9*c^12*d^2*f^2 - 256
*A*B*a^6*b^6*c^5*d^9*f^2 - 208*A*B*a^5*b^7*c^12*d^2*f^2 + 176*A*B*a^4*b^8*c^5*d^9*f^2 + 112*A*B*a^7*b^5*c^10*d
^4*f^2 + 112*A*B*a^6*b^6*c^11*d^3*f^2 - 16*A*B*a^2*b^10*c^3*d^11*f^2 - 576*B*C*a*b^11*c^8*d^6*f^2 + 400*B*C*a^
11*b*c^4*d^10*f^2 - 288*B*C*a*b^11*c^6*d^8*f^2 - 176*B*C*a^11*b*c^6*d^8*f^2 + 128*B*C*a*b^11*c^10*d^4*f^2 - 10
8*B*C*a^4*b^8*c*d^13*f^2 - 104*B*C*a*b^11*c^4*d^10*f^2 - 92*B*C*a^4*b^8*c^13*d*f^2 - 60*B*C*a^8*b^4*c*d^13*f^2
- 60*B*C*a^6*b^6*c*d^13*f^2 + 48*B*C*a^11*b*c^2*d^12*f^2 - 40*B*C*a^2*b^10*c*d^13*f^2 - 28*B*C*a^2*b^10*c^13*
d*f^2 - 24*B*C*a*b^11*c^12*d^2*f^2 + 20*B*C*a^10*b^2*c*d^13*f^2 - 16*B*C*a*b^11*c^2*d^12*f^2 + 12*B*C*a^6*b^6*
c^13*d*f^2 + 912*A*C*a*b^11*c^7*d^7*f^2 + 808*A*C*a*b^11*c^5*d^9*f^2 + 432*A*C*a^11*b*c^5*d^9*f^2 + 336*A*C*a*
b^11*c^3*d^11*f^2 + 224*A*C*a*b^11*c^11*d^3*f^2 - 112*A*C*a^11*b*c^3*d^11*f^2 + 112*A*C*a^3*b^9*c*d^13*f^2 - 8
8*A*C*a^9*b^3*c*d^13*f^2 + 80*A*C*a^3*b^9*c^13*d*f^2 + 56*A*C*a^5*b^7*c*d^13*f^2 + 48*A*C*a*b^11*c^9*d^5*f^2 -
40*A*C*a^5*b^7*c^13*d*f^2 - 16*A*C*a^11*b*c^7*d^7*f^2 + 16*A*C*a^7*b^5*c*d^13*f^2 - 496*A*B*a*b^11*c^4*d^10*f
^2 - 400*A*B*a^11*b*c^4*d^10*f^2 + 288*A*B*a*b^11*c^8*d^6*f^2 - 288*A*B*a*b^11*c^6*d^8*f^2 - 272*A*B*a*b^11*c^
2*d^12*f^2 + 240*A*B*a^6*b^6*c*d^13*f^2 - 224*A*B*a*b^11*c^10*d^4*f^2 + 192*A*B*a^8*b^4*c*d^13*f^2 + 192*A*B*a
^4*b^8*c*d^13*f^2 + 176*A*B*a^11*b*c^6*d^8*f^2 + 104*A*B*a^4*b^8*c^13*d*f^2 - 48*A*B*a^11*b*c^2*d^12*f^2 + 16*
A*B*a^10*b^2*c*d^13*f^2 + 16*A*B*a^2*b^10*c^13*d*f^2 + 16*A*B*a^2*b^10*c*d^13*f^2 - 112*B*C*b^12*c^11*d^3*f^2
+ 4*B*C*b^12*c^5*d^9*f^2 + 150*A*C*b^12*c^10*d^4*f^2 - 80*B*C*a^12*c^3*d^11*f^2 + 66*A*C*b^12*c^8*d^6*f^2 - 30
*A*C*b^12*c^12*d^2*f^2 + 24*B*C*a^12*c^5*d^9*f^2 - 12*A*C*b^12*c^4*d^10*f^2 - 576*A*B*b^12*c^7*d^7*f^2 - 432*A
*B*b^12*c^9*d^5*f^2 - 400*A*B*b^12*c^5*d^9*f^2 - 144*A*B*b^12*c^3*d^11*f^2 - 96*B*C*a^7*b^5*d^14*f^2 - 72*B*C*
a^5*b^7*d^14*f^2 - 66*A*C*a^12*c^4*d^10*f^2 + 54*A*C*a^12*c^2*d^12*f^2 - 32*A*B*b^12*c^11*d^3*f^2 - 24*B*C*a^9
*b^3*d^14*f^2 - 16*B*C*a^3*b^9*d^14*f^2 + 2*A*C*a^12*c^6*d^8*f^2 + 116*A*C*a^6*b^6*d^14*f^2 + 100*A*C*a^4*b^8*
d^14*f^2 + 80*A*B*a^12*c^3*d^11*f^2 + 24*A*C*a^2*b^10*d^14*f^2 - 24*A*B*a^12*c^5*d^9*f^2 + 22*A*C*a^8*b^4*d^14
*f^2 + 16*B*C*a^3*b^9*c^14*f^2 + 8*A*C*a^10*b^2*d^14*f^2 - 192*A*B*a^5*b^7*d^14*f^2 - 176*A*B*a^3*b^9*d^14*f^2
- 48*A*B*a^7*b^5*d^14*f^2 - 28*A*C*a^2*b^10*c^14*f^2 + 2*A*C*a^4*b^8*c^14*f^2 - 16*A*B*a^3*b^9*c^14*f^2 + 250
8*C^2*a^6*b^6*c^6*d^8*f^2 + 2376*C^2*a^5*b^7*c^9*d^5*f^2 + 2357*C^2*a^8*b^4*c^6*d^8*f^2 - 2048*C^2*a^7*b^5*c^5
*d^9*f^2 + 1304*C^2*a^3*b^9*c^9*d^5*f^2 + 1303*C^2*a^8*b^4*c^4*d^10*f^2 + 1212*C^2*a^6*b^6*c^4*d^10*f^2 - 1203
*C^2*a^4*b^8*c^8*d^6*f^2 - 1192*C^2*a^9*b^3*c^5*d^9*f^2 + 1062*C^2*a^4*b^8*c^6*d^8*f^2 + 984*C^2*a^7*b^5*c^9*d
^5*f^2 - 952*C^2*a^6*b^6*c^8*d^6*f^2 + 768*C^2*a^5*b^7*c^7*d^7*f^2 - 681*C^2*a^4*b^8*c^10*d^4*f^2 - 672*C^2*a^
5*b^7*c^5*d^9*f^2 - 480*C^2*a^6*b^6*c^10*d^4*f^2 + 458*C^2*a^10*b^2*c^6*d^8*f^2 - 448*C^2*a^7*b^5*c^7*d^7*f^2
+ 422*C^2*a^4*b^8*c^4*d^10*f^2 + 372*C^2*a^2*b^10*c^6*d^8*f^2 + 360*C^2*a^5*b^7*c^11*d^3*f^2 + 312*C^2*a^3*b^9
*c^7*d^7*f^2 + 278*C^2*a^10*b^2*c^4*d^10*f^2 - 232*C^2*a^9*b^3*c^7*d^7*f^2 + 194*C^2*a^2*b^10*c^12*d^2*f^2 + 1
76*C^2*a^9*b^3*c^9*d^5*f^2 + 152*C^2*a^5*b^7*c^3*d^11*f^2 + 124*C^2*a^2*b^10*c^4*d^10*f^2 - 120*C^2*a^7*b^5*c^
3*d^11*f^2 - 114*C^2*a^10*b^2*c^2*d^12*f^2 - 102*C^2*a^2*b^10*c^8*d^6*f^2 + 101*C^2*a^4*b^8*c^12*d^2*f^2 + 100
*C^2*a^6*b^6*c^2*d^12*f^2 - 88*C^2*a^3*b^9*c^5*d^9*f^2 + 77*C^2*a^8*b^4*c^2*d^12*f^2 + 72*C^2*a^3*b^9*c^11*d^3
*f^2 - 64*C^2*a^10*b^2*c^8*d^6*f^2 + 64*C^2*a^3*b^9*c^3*d^11*f^2 - 58*C^2*a^2*b^10*c^10*d^4*f^2 + 56*C^2*a^7*b
^5*c^11*d^3*f^2 + 56*C^2*a^6*b^6*c^12*d^2*f^2 + 40*C^2*a^9*b^3*c^3*d^11*f^2 + 36*C^2*a^8*b^4*c^12*d^2*f^2 + 32
*C^2*a^4*b^8*c^2*d^12*f^2 + 26*C^2*a^8*b^4*c^10*d^4*f^2 + 16*C^2*a^2*b^10*c^2*d^12*f^2 + 2*C^2*a^8*b^4*c^8*d^6
*f^2 + 2277*B^2*a^4*b^8*c^8*d^6*f^2 + 2144*B^2*a^7*b^5*c^5*d^9*f^2 - 2112*B^2*a^5*b^7*c^9*d^5*f^2 + 2028*B^2*a
^6*b^6*c^8*d^6*f^2 - 1671*B^2*a^8*b^4*c^6*d^8*f^2 + 1275*B^2*a^4*b^8*c^10*d^4*f^2 + 1176*B^2*a^5*b^7*c^5*d^9*f
^2 + 1096*B^2*a^9*b^3*c^5*d^9*f^2 - 1044*B^2*a^6*b^6*c^6*d^8*f^2 + 984*B^2*a^6*b^6*c^10*d^4*f^2 - 968*B^2*a^3*
b^9*c^9*d^5*f^2 - 888*B^2*a^7*b^5*c^9*d^5*f^2 + 672*B^2*a^7*b^5*c^7*d^7*f^2 + 664*B^2*a^3*b^9*c^5*d^9*f^2 - 64
9*B^2*a^8*b^4*c^4*d^10*f^2 + 618*B^2*a^2*b^10*c^8*d^6*f^2 + 514*B^2*a^4*b^8*c^4*d^10*f^2 + 460*B^2*a^6*b^6*c^2
*d^12*f^2 + 422*B^2*a^8*b^4*c^8*d^6*f^2 + 406*B^2*a^2*b^10*c^10*d^4*f^2 - 382*B^2*a^10*b^2*c^6*d^8*f^2 + 368*B
^2*a^4*b^8*c^2*d^12*f^2 - 312*B^2*a^5*b^7*c^11*d^3*f^2 + 312*B^2*a^3*b^9*c^7*d^7*f^2 + 248*B^2*a^9*b^3*c^7*d^7
*f^2 + 245*B^2*a^8*b^4*c^2*d^12*f^2 - 192*B^2*a^5*b^7*c^7*d^7*f^2 - 184*B^2*a^9*b^3*c^3*d^11*f^2 + 182*B^2*a^1
0*b^2*c^2*d^12*f^2 + 176*B^2*a^3*b^9*c^3*d^11*f^2 + 174*B^2*a^4*b^8*c^6*d^8*f^2 - 170*B^2*a^10*b^2*c^4*d^10*f^
2 - 152*B^2*a^9*b^3*c^9*d^5*f^2 + 152*B^2*a^2*b^10*c^4*d^10*f^2 + 142*B^2*a^8*b^4*c^10*d^4*f^2 - 90*B^2*a^2*b^
10*c^12*d^2*f^2 + 88*B^2*a^2*b^10*c^2*d^12*f^2 + 84*B^2*a^10*b^2*c^8*d^6*f^2 + 84*B^2*a^2*b^10*c^6*d^8*f^2 + 6
0*B^2*a^6*b^6*c^12*d^2*f^2 - 56*B^2*a^7*b^5*c^11*d^3*f^2 + 53*B^2*a^4*b^8*c^12*d^2*f^2 + 24*B^2*a^7*b^5*c^3*d^
11*f^2 + 24*B^2*a^6*b^6*c^4*d^10*f^2 + 24*B^2*a^3*b^9*c^11*d^3*f^2 - 8*B^2*a^5*b^7*c^3*d^11*f^2 + 4566*A^2*a^4
*b^8*c^6*d^8*f^2 + 4284*A^2*a^6*b^6*c^6*d^8*f^2 - 3776*A^2*a^7*b^5*c^5*d^9*f^2 - 3624*A^2*a^5*b^7*c^5*d^9*f^2
+ 3122*A^2*a^4*b^8*c^4*d^10*f^2 + 3108*A^2*a^2*b^10*c^6*d^8*f^2 + 2741*A^2*a^8*b^4*c^6*d^8*f^2 + 2592*A^2*a^6*
b^6*c^4*d^10*f^2 - 2536*A^2*a^3*b^9*c^5*d^9*f^2 + 2224*A^2*a^2*b^10*c^4*d^10*f^2 - 2184*A^2*a^3*b^9*c^7*d^7*f^
2 - 2016*A^2*a^5*b^7*c^7*d^7*f^2 - 1984*A^2*a^7*b^5*c^7*d^7*f^2 + 1626*A^2*a^2*b^10*c^8*d^6*f^2 - 1624*A^2*a^9
*b^3*c^5*d^9*f^2 + 1603*A^2*a^8*b^4*c^4*d^10*f^2 + 1296*A^2*a^5*b^7*c^9*d^5*f^2 - 1144*A^2*a^5*b^7*c^3*d^11*f^
2 - 992*A^2*a^3*b^9*c^3*d^11*f^2 + 968*A^2*a^4*b^8*c^2*d^12*f^2 - 888*A^2*a^7*b^5*c^3*d^11*f^2 + 849*A^2*a^4*b
^8*c^8*d^6*f^2 + 808*A^2*a^2*b^10*c^2*d^12*f^2 - 616*A^2*a^9*b^3*c^7*d^7*f^2 + 554*A^2*a^10*b^2*c^6*d^8*f^2 +
504*A^2*a^7*b^5*c^9*d^5*f^2 - 504*A^2*a^6*b^6*c^10*d^4*f^2 + 460*A^2*a^6*b^6*c^2*d^12*f^2 + 350*A^2*a^10*b^2*c
^4*d^10*f^2 + 350*A^2*a^2*b^10*c^10*d^4*f^2 - 321*A^2*a^4*b^8*c^10*d^4*f^2 + 216*A^2*a^5*b^7*c^11*d^3*f^2 - 21
6*A^2*a^3*b^9*c^11*d^3*f^2 + 182*A^2*a^2*b^10*c^12*d^2*f^2 - 152*A^2*a^9*b^3*c^3*d^11*f^2 - 124*A^2*a^6*b^6*c^
8*d^6*f^2 - 114*A^2*a^10*b^2*c^2*d^12*f^2 + 104*A^2*a^3*b^9*c^9*d^5*f^2 + 77*A^2*a^8*b^4*c^2*d^12*f^2 + 74*A^2
*a^8*b^4*c^8*d^6*f^2 - 70*A^2*a^8*b^4*c^10*d^4*f^2 + 56*A^2*a^9*b^3*c^9*d^5*f^2 + 56*A^2*a^7*b^5*c^11*d^3*f^2
+ 41*A^2*a^4*b^8*c^12*d^2*f^2 - 28*A^2*a^10*b^2*c^8*d^6*f^2 - 28*A^2*a^6*b^6*c^12*d^2*f^2 + 12*B*C*b^12*c^13*d
*f^2 + 24*B*C*a^12*c*d^13*f^2 - 24*A*B*b^12*c^13*d*f^2 - 24*A*B*b^12*c*d^13*f^2 - 16*B*C*a^11*b*d^14*f^2 - 24*
A*B*a^12*c*d^13*f^2 - 16*B*C*a*b^11*c^14*f^2 - 48*A*B*a*b^11*d^14*f^2 + 16*A*B*a^11*b*d^14*f^2 + 16*A*B*a*b^11
*c^14*f^2 - 216*C^2*a^11*b*c^5*d^9*f^2 + 216*C^2*a*b^11*c^9*d^5*f^2 + 56*C^2*a^11*b*c^3*d^11*f^2 + 56*C^2*a^9*
b^3*c*d^13*f^2 + 56*C^2*a^5*b^7*c*d^13*f^2 + 40*C^2*a^7*b^5*c*d^13*f^2 - 40*C^2*a*b^11*c^11*d^3*f^2 + 32*C^2*a
^5*b^7*c^13*d*f^2 - 24*C^2*a*b^11*c^7*d^7*f^2 - 16*C^2*a^3*b^9*c^13*d*f^2 + 16*C^2*a^3*b^9*c*d^13*f^2 + 8*C^2*
a^11*b*c^7*d^7*f^2 - 8*C^2*a*b^11*c^5*d^9*f^2 + 264*B^2*a*b^11*c^7*d^7*f^2 + 224*B^2*a*b^11*c^5*d^9*f^2 + 168*
B^2*a^11*b*c^5*d^9*f^2 - 112*B^2*a^9*b^3*c*d^13*f^2 - 104*B^2*a^11*b*c^3*d^11*f^2 - 104*B^2*a^7*b^5*c*d^13*f^2
+ 96*B^2*a*b^11*c^3*d^11*f^2 + 88*B^2*a*b^11*c^11*d^3*f^2 - 72*B^2*a*b^11*c^9*d^5*f^2 - 64*B^2*a^5*b^7*c*d^13
*f^2 + 32*B^2*a^3*b^9*c^13*d*f^2 - 24*B^2*a^11*b*c^7*d^7*f^2 - 24*B^2*a^5*b^7*c^13*d*f^2 + 16*B^2*a^3*b^9*c*d^
13*f^2 - 888*A^2*a*b^11*c^7*d^7*f^2 - 800*A^2*a*b^11*c^5*d^9*f^2 - 336*A^2*a*b^11*c^3*d^11*f^2 - 264*A^2*a*b^1
1*c^9*d^5*f^2 - 216*A^2*a^11*b*c^5*d^9*f^2 - 184*A^2*a*b^11*c^11*d^3*f^2 - 128*A^2*a^3*b^9*c*d^13*f^2 - 112*A^
2*a^5*b^7*c*d^13*f^2 - 64*A^2*a^3*b^9*c^13*d*f^2 + 56*A^2*a^11*b*c^3*d^11*f^2 - 56*A^2*a^7*b^5*c*d^13*f^2 + 32
*A^2*a^9*b^3*c*d^13*f^2 + 8*A^2*a^11*b*c^7*d^7*f^2 + 8*A^2*a^5*b^7*c^13*d*f^2 + 24*C^2*a^11*b*c*d^13*f^2 - 16*
C^2*a*b^11*c^13*d*f^2 - 40*B^2*a^11*b*c*d^13*f^2 + 24*B^2*a*b^11*c^13*d*f^2 + 16*B^2*a*b^11*c*d^13*f^2 - 48*A^
2*a*b^11*c*d^13*f^2 - 40*A^2*a*b^11*c^13*d*f^2 + 24*A^2*a^11*b*c*d^13*f^2 - 6*A*C*a^12*d^14*f^2 + 2*A*C*b^12*c
^14*f^2 + 33*C^2*b^12*c^12*d^2*f^2 - 27*C^2*b^12*c^10*d^4*f^2 + 3*C^2*b^12*c^8*d^6*f^2 + 117*B^2*b^12*c^10*d^4
*f^2 + 111*B^2*b^12*c^8*d^6*f^2 + 72*B^2*b^12*c^6*d^8*f^2 + 33*C^2*a^12*c^4*d^10*f^2 - 27*C^2*a^12*c^2*d^12*f^
2 + 24*B^2*b^12*c^4*d^10*f^2 + 4*B^2*b^12*c^2*d^12*f^2 - 3*B^2*b^12*c^12*d^2*f^2 - C^2*a^12*c^6*d^8*f^2 + 720*
A^2*b^12*c^6*d^8*f^2 + 552*A^2*b^12*c^4*d^10*f^2 + 471*A^2*b^12*c^8*d^6*f^2 + 216*A^2*b^12*c^2*d^12*f^2 + 93*A
^2*b^12*c^10*d^4*f^2 + 33*B^2*a^12*c^2*d^12*f^2 + 33*A^2*b^12*c^12*d^2*f^2 + 31*C^2*a^8*b^4*d^14*f^2 - 27*B^2*
a^12*c^4*d^10*f^2 + 20*C^2*a^6*b^6*d^14*f^2 + 4*C^2*a^4*b^8*d^14*f^2 + 3*B^2*a^12*c^6*d^8*f^2 + 2*C^2*a^10*b^2
*d^14*f^2 + 80*B^2*a^6*b^6*d^14*f^2 + 64*B^2*a^4*b^8*d^14*f^2 + 33*A^2*a^12*c^4*d^10*f^2 + 31*B^2*a^8*b^4*d^14
*f^2 - 27*A^2*a^12*c^2*d^12*f^2 + 16*B^2*a^2*b^10*d^14*f^2 + 14*C^2*a^2*b^10*c^14*f^2 + 14*B^2*a^10*b^2*d^14*f
^2 - C^2*a^4*b^8*c^14*f^2 - A^2*a^12*c^6*d^8*f^2 + 120*A^2*a^2*b^10*d^14*f^2 + 112*A^2*a^4*b^8*d^14*f^2 - 17*A
^2*a^8*b^4*d^14*f^2 - 10*B^2*a^2*b^10*c^14*f^2 - 10*A^2*a^10*b^2*d^14*f^2 + 8*A^2*a^6*b^6*d^14*f^2 + 3*B^2*a^4
*b^8*c^14*f^2 + 14*A^2*a^2*b^10*c^14*f^2 - A^2*a^4*b^8*c^14*f^2 + 3*C^2*a^12*d^14*f^2 - C^2*b^12*c^14*f^2 + 36
*A^2*b^12*d^14*f^2 + 3*B^2*b^12*c^14*f^2 - B^2*a^12*d^14*f^2 + 3*A^2*a^12*d^14*f^2 - A^2*b^12*c^14*f^2 - 44*A*
B*C*a*b^9*c^10*d*f + 3816*A*B*C*a^5*b^5*c^4*d^7*f + 2920*A*B*C*a^2*b^8*c^5*d^6*f - 2736*A*B*C*a^3*b^7*c^6*d^5*
f - 2672*A*B*C*a^4*b^6*c^3*d^8*f + 1996*A*B*C*a^4*b^6*c^7*d^4*f - 1412*A*B*C*a^6*b^4*c^5*d^6*f + 1120*A*B*C*a^
3*b^7*c^2*d^9*f + 1080*A*B*C*a^2*b^8*c^7*d^4*f + 1040*A*B*C*a^5*b^5*c^2*d^9*f + 684*A*B*C*a^4*b^6*c^5*d^6*f +
592*A*B*C*a^3*b^7*c^4*d^7*f - 560*A*B*C*a^7*b^3*c^2*d^9*f - 448*A*B*C*a^2*b^8*c^3*d^8*f - 400*A*B*C*a^5*b^5*c^
8*d^3*f - 398*A*B*C*a^2*b^8*c^9*d^2*f - 312*A*B*C*a^6*b^4*c^3*d^8*f + 166*A*B*C*a^8*b^2*c^3*d^8*f + 136*A*B*C*
a^5*b^5*c^6*d^5*f + 128*A*B*C*a^7*b^3*c^6*d^5*f - 100*A*B*C*a^6*b^4*c^7*d^4*f + 64*A*B*C*a^7*b^3*c^4*d^7*f - 6
4*A*B*C*a^4*b^6*c^9*d^2*f - 32*A*B*C*a^3*b^7*c^8*d^3*f - 16*A*B*C*a^8*b^2*c^5*d^6*f - 1312*A*B*C*a*b^9*c^4*d^7
*f + 996*A*B*C*a*b^9*c^8*d^3*f + 728*A*B*C*a^6*b^4*c*d^10*f - 624*A*B*C*a*b^9*c^6*d^5*f - 584*A*B*C*a^2*b^8*c*
d^10*f - 512*A*B*C*a^4*b^6*c*d^10*f - 320*A*B*C*a*b^9*c^2*d^9*f - 98*A*B*C*a^8*b^2*c*d^10*f + 36*A*B*C*a^9*b*c
^2*d^9*f + 32*A*B*C*a^3*b^7*c^10*d*f - 16*A*B*C*a^9*b*c^4*d^7*f + 46*B*C^2*a*b^9*c^10*d*f - 16*B^2*C*a*b^9*c*d
^10*f - 2*B^2*C*a^9*b*c*d^10*f + 312*A^2*C*a*b^9*c*d^10*f - 48*A*C^2*a*b^9*c*d^10*f - 6*A^2*C*a^9*b*c*d^10*f +
6*A*C^2*a^9*b*c*d^10*f + 208*A*B^2*a*b^9*c*d^10*f - 2*A^2*B*a*b^9*c^10*d*f + 2*A*B^2*a^9*b*c*d^10*f - 480*A*B
*C*b^10*c^7*d^4*f + 78*A*B*C*b^10*c^9*d^2*f - 64*A*B*C*b^10*c^5*d^6*f + 2*A*B*C*a^10*c^3*d^8*f - 224*A*B*C*a^5
*b^5*d^11*f + 80*A*B*C*a^7*b^3*d^11*f - 32*A*B*C*a^3*b^7*d^11*f + 2*A*B*C*a^2*b^8*c^11*f - 1692*B*C^2*a^5*b^5*
c^4*d^7*f - 1500*B^2*C*a^5*b^5*c^5*d^6*f - 1464*B^2*C*a^3*b^7*c^5*d^6*f + 1426*B*C^2*a^6*b^4*c^5*d^6*f - 1158*
B^2*C*a^6*b^4*c^4*d^7*f + 1152*B*C^2*a^3*b^7*c^6*d^5*f + 1026*B^2*C*a^4*b^6*c^6*d^5*f - 974*B*C^2*a^4*b^6*c^7*
d^4*f + 960*B^2*C*a^5*b^5*c^3*d^8*f - 884*B*C^2*a^2*b^8*c^5*d^6*f - 764*B^2*C*a^5*b^5*c^7*d^4*f + 752*B^2*C*a^
2*b^8*c^4*d^7*f - 752*B*C^2*a^3*b^7*c^4*d^7*f + 738*B^2*C*a^4*b^6*c^4*d^7*f - 688*B^2*C*a^6*b^4*c^2*d^9*f - 67
5*B^2*C*a^2*b^8*c^8*d^3*f + 560*B*C^2*a^5*b^5*c^8*d^3*f + 496*B*C^2*a^7*b^3*c^2*d^9*f + 496*B*C^2*a^4*b^6*c^3*
d^8*f - 468*B*C^2*a^2*b^8*c^7*d^4*f + 456*B^2*C*a^7*b^3*c^3*d^8*f - 452*B^2*C*a^4*b^6*c^8*d^3*f - 416*B*C^2*a^
3*b^7*c^2*d^9*f + 378*B*C^2*a^4*b^6*c^5*d^6*f + 376*B*C^2*a^3*b^7*c^8*d^3*f - 360*B^2*C*a^2*b^8*c^6*d^5*f + 35
5*B*C^2*a^2*b^8*c^9*d^2*f + 346*B^2*C*a^6*b^4*c^6*d^5*f - 320*B^2*C*a^4*b^6*c^2*d^9*f + 268*B^2*C*a^2*b^8*c^2*
d^9*f + 216*B^2*C*a^3*b^7*c^7*d^4*f - 203*B*C^2*a^8*b^2*c^3*d^8*f - 184*B*C^2*a^7*b^3*c^6*d^5*f + 170*B*C^2*a^
6*b^4*c^7*d^4*f + 160*B^2*C*a^7*b^3*c^5*d^6*f - 160*B*C^2*a^5*b^5*c^2*d^9*f - 140*B^2*C*a^8*b^2*c^4*d^7*f - 13
6*B*C^2*a^2*b^8*c^3*d^8*f + 112*B^2*C*a^3*b^7*c^9*d^2*f + 91*B^2*C*a^8*b^2*c^2*d^9*f + 88*B*C^2*a^7*b^3*c^4*d^
7*f + 72*B^2*C*a^6*b^4*c^8*d^3*f - 64*B^2*C*a^3*b^7*c^3*d^8*f - 60*B*C^2*a^6*b^4*c^3*d^8*f + 56*B*C^2*a^4*b^6*
c^9*d^2*f + 52*B*C^2*a^5*b^5*c^6*d^5*f - 48*B^2*C*a^7*b^3*c^7*d^4*f + 48*B^2*C*a^5*b^5*c^9*d^2*f + 44*B*C^2*a^
8*b^2*c^5*d^6*f - 36*B*C^2*a^6*b^4*c^9*d^2*f + 12*B^2*C*a^8*b^2*c^6*d^5*f - 2958*A^2*C*a^4*b^6*c^4*d^7*f - 193
2*A^2*C*a^2*b^8*c^4*d^7*f + 1848*A^2*C*a^3*b^7*c^5*d^6*f + 1728*A^2*C*a^3*b^7*c^3*d^8*f + 1524*A^2*C*a^5*b^5*c
^5*d^6*f + 1374*A*C^2*a^4*b^6*c^4*d^7*f - 1272*A*C^2*a^3*b^7*c^5*d^6*f - 1236*A*C^2*a^5*b^5*c^5*d^6*f + 1116*A
*C^2*a^2*b^8*c^4*d^7*f - 1110*A^2*C*a^4*b^6*c^6*d^5*f + 1038*A*C^2*a^4*b^6*c^6*d^5*f - 768*A^2*C*a^2*b^8*c^2*d
^9*f - 696*A^2*C*a^3*b^7*c^7*d^4*f - 666*A*C^2*a^6*b^4*c^4*d^7*f + 564*A^2*C*a^2*b^8*c^6*d^5*f - 564*A*C^2*a^5
*b^5*c^7*d^4*f - 555*A*C^2*a^2*b^8*c^8*d^3*f + 519*A^2*C*a^2*b^8*c^8*d^3*f - 480*A*C^2*a^3*b^7*c^3*d^8*f + 456
*A*C^2*a^5*b^5*c^3*d^8*f - 420*A*C^2*a^6*b^4*c^2*d^9*f + 408*A*C^2*a^3*b^7*c^7*d^4*f + 408*A*C^2*a^2*b^8*c^2*d
^9*f + 348*A^2*C*a^6*b^4*c^2*d^9*f - 348*A*C^2*a^2*b^8*c^6*d^5*f + 342*A*C^2*a^6*b^4*c^6*d^5*f - 336*A*C^2*a^4
*b^6*c^8*d^3*f + 324*A^2*C*a^5*b^5*c^7*d^4*f - 312*A^2*C*a^4*b^6*c^2*d^9*f + 264*A^2*C*a^4*b^6*c^8*d^3*f + 240
*A*C^2*a^7*b^3*c^5*d^6*f + 195*A*C^2*a^8*b^2*c^2*d^9*f - 174*A^2*C*a^6*b^4*c^6*d^5*f + 144*A*C^2*a^3*b^7*c^9*d
^2*f - 123*A^2*C*a^8*b^2*c^2*d^9*f + 120*A*C^2*a^7*b^3*c^3*d^8*f + 108*A*C^2*a^6*b^4*c^8*d^3*f - 102*A^2*C*a^6
*b^4*c^4*d^7*f - 96*A^2*C*a^8*b^2*c^4*d^7*f + 72*A^2*C*a^7*b^3*c^3*d^8*f + 72*A*C^2*a^5*b^5*c^9*d^2*f + 48*A^2
*C*a^7*b^3*c^5*d^6*f - 48*A^2*C*a^3*b^7*c^9*d^2*f - 48*A*C^2*a^4*b^6*c^2*d^9*f - 24*A^2*C*a^5*b^5*c^3*d^8*f -
12*A*C^2*a^8*b^2*c^4*d^7*f + 2736*A^2*B*a^3*b^7*c^6*d^5*f + 2464*A^2*B*a^4*b^6*c^3*d^8*f - 2298*A*B^2*a^4*b^6*
c^4*d^7*f - 2252*A^2*B*a^2*b^8*c^5*d^6*f - 1692*A^2*B*a^5*b^5*c^4*d^7*f - 1592*A*B^2*a^2*b^8*c^4*d^7*f - 1338*
A*B^2*a^4*b^6*c^6*d^5*f + 1320*A*B^2*a^3*b^7*c^5*d^6*f + 1212*A*B^2*a^5*b^5*c^5*d^6*f - 1056*A*B^2*a^5*b^5*c^3
*d^8*f + 1024*A^2*B*a^3*b^7*c^4*d^7*f - 1022*A^2*B*a^4*b^6*c^7*d^4*f - 880*A^2*B*a^5*b^5*c^2*d^9*f - 846*A^2*B
*a^4*b^6*c^5*d^6*f - 840*A*B^2*a^3*b^7*c^7*d^4*f + 760*A*B^2*a^6*b^4*c^2*d^9*f - 704*A^2*B*a^3*b^7*c^2*d^9*f +
688*A*B^2*a^3*b^7*c^3*d^8*f + 660*A^2*B*a^6*b^4*c^3*d^8*f - 612*A^2*B*a^2*b^8*c^7*d^4*f + 462*A*B^2*a^6*b^4*c
^4*d^7*f + 459*A*B^2*a^2*b^8*c^8*d^3*f - 412*A*B^2*a^2*b^8*c^2*d^9*f - 408*A*B^2*a^7*b^3*c^3*d^8*f + 388*A^2*B
*a^5*b^5*c^6*d^5*f + 296*A^2*B*a^2*b^8*c^3*d^8*f + 288*A*B^2*a^2*b^8*c^6*d^5*f + 284*A*B^2*a^5*b^5*c^7*d^4*f +
236*A*B^2*a^4*b^6*c^8*d^3*f - 226*A*B^2*a^6*b^4*c^6*d^5*f + 212*A*B^2*a^4*b^6*c^2*d^9*f + 202*A^2*B*a^6*b^4*c
^5*d^6*f - 152*A^2*B*a^7*b^3*c^4*d^7*f + 88*A^2*B*a^3*b^7*c^8*d^3*f + 79*A^2*B*a^2*b^8*c^9*d^2*f - 70*A^2*B*a^
6*b^4*c^7*d^4*f + 68*A*B^2*a^8*b^2*c^4*d^7*f + 64*A^2*B*a^7*b^3*c^2*d^9*f - 64*A*B^2*a^3*b^7*c^9*d^2*f + 56*A^
2*B*a^7*b^3*c^6*d^5*f + 56*A^2*B*a^5*b^5*c^8*d^3*f + 37*A^2*B*a^8*b^2*c^3*d^8*f - 28*A^2*B*a^8*b^2*c^5*d^6*f -
28*A^2*B*a^4*b^6*c^9*d^2*f + 17*A*B^2*a^8*b^2*c^2*d^9*f - 16*A*B^2*a^7*b^3*c^5*d^6*f + 24*A*B*C*b^10*c*d^10*f
- 6*A*B*C*a^10*c*d^10*f + 48*A*B*C*a*b^9*d^11*f + 4*A*B*C*a^9*b*d^11*f + 432*B^2*C*a*b^9*c^7*d^4*f - 376*B*C^
2*a^6*b^4*c*d^10*f - 354*B*C^2*a*b^9*c^8*d^3*f + 352*B^2*C*a^5*b^5*c*d^10*f + 320*B^2*C*a*b^9*c^5*d^6*f + 256*
B^2*C*a^3*b^7*c*d^10*f - 232*B^2*C*a^7*b^3*c*d^10*f - 210*B^2*C*a*b^9*c^9*d^2*f - 152*B*C^2*a^4*b^6*c*d^10*f +
85*B*C^2*a^8*b^2*c*d^10*f + 72*B^2*C*a*b^9*c^3*d^8*f - 48*B*C^2*a*b^9*c^6*d^5*f - 40*B*C^2*a^3*b^7*c^10*d*f +
40*B*C^2*a^2*b^8*c*d^10*f + 37*B^2*C*a^2*b^8*c^10*d*f + 22*B^2*C*a^9*b*c^3*d^8*f - 18*B*C^2*a^9*b*c^2*d^9*f +
16*B*C^2*a*b^9*c^2*d^9*f - 12*B^2*C*a^4*b^6*c^10*d*f + 8*B*C^2*a^9*b*c^4*d^7*f + 8*B*C^2*a*b^9*c^4*d^7*f - 98
4*A^2*C*a*b^9*c^7*d^4*f + 672*A^2*C*a*b^9*c^3*d^8*f + 552*A*C^2*a*b^9*c^7*d^4*f - 504*A^2*C*a^5*b^5*c*d^10*f -
408*A^2*C*a*b^9*c^5*d^6*f + 408*A*C^2*a*b^9*c^5*d^6*f + 336*A*C^2*a^5*b^5*c*d^10*f - 216*A*C^2*a^7*b^3*c*d^10
*f + 192*A*C^2*a^3*b^7*c*d^10*f - 162*A*C^2*a*b^9*c^9*d^2*f + 120*A^2*C*a^7*b^3*c*d^10*f + 96*A^2*C*a^3*b^7*c*
d^10*f + 90*A^2*C*a*b^9*c^9*d^2*f + 66*A^2*C*a^9*b*c^3*d^8*f - 66*A*C^2*a^9*b*c^3*d^8*f + 57*A*C^2*a^2*b^8*c^1
0*d*f - 48*A*C^2*a*b^9*c^3*d^8*f - 9*A^2*C*a^2*b^8*c^10*d*f + 1736*A^2*B*a*b^9*c^4*d^7*f + 1248*A^2*B*a*b^9*c^
6*d^5*f - 1008*A*B^2*a*b^9*c^7*d^4*f + 772*A^2*B*a^4*b^6*c*d^10*f - 688*A*B^2*a^5*b^5*c*d^10*f - 608*A*B^2*a*b
^9*c^5*d^6*f + 436*A^2*B*a^2*b^8*c*d^10*f - 426*A^2*B*a*b^9*c^8*d^3*f + 312*A*B^2*a*b^9*c^3*d^8*f + 304*A^2*B*
a*b^9*c^2*d^9*f - 244*A^2*B*a^6*b^4*c*d^10*f - 160*A*B^2*a^3*b^7*c*d^10*f + 114*A*B^2*a*b^9*c^9*d^2*f + 88*A*B
^2*a^7*b^3*c*d^10*f - 22*A*B^2*a^9*b*c^3*d^8*f - 18*A^2*B*a^9*b*c^2*d^9*f + 13*A^2*B*a^8*b^2*c*d^10*f - 13*A*B
^2*a^2*b^8*c^10*d*f + 8*A^2*B*a^9*b*c^4*d^7*f + 8*A^2*B*a^3*b^7*c^10*d*f + 111*B^2*C*b^10*c^8*d^3*f - 39*B*C^2
*b^10*c^9*d^2*f + 24*B*C^2*b^10*c^7*d^4*f - 4*B^2*C*b^10*c^2*d^9*f - 4*B*C^2*b^10*c^5*d^6*f + 432*A^2*C*b^10*c
^6*d^5*f + 192*A^2*C*b^10*c^4*d^7*f - 111*A^2*C*b^10*c^8*d^3*f + 111*A*C^2*b^10*c^8*d^3*f - 72*A*C^2*b^10*c^6*
d^5*f + 12*A*C^2*b^10*c^4*d^7*f - 3*B^2*C*a^10*c^2*d^9*f - B*C^2*a^10*c^3*d^8*f + 456*A^2*B*b^10*c^7*d^4*f - 2
88*A^2*B*b^10*c^3*d^8*f + 252*A*B^2*b^10*c^6*d^5*f + 192*A*B^2*b^10*c^4*d^7*f - 183*A*B^2*b^10*c^8*d^3*f - 148
*A^2*B*b^10*c^5*d^6*f + 112*B^2*C*a^6*b^4*d^11*f + 76*A*B^2*b^10*c^2*d^9*f - 64*B*C^2*a^7*b^3*d^11*f + 16*B^2*
C*a^4*b^6*d^11*f - 16*B^2*C*a^2*b^8*d^11*f + 16*B*C^2*a^5*b^5*d^11*f + 16*B*C^2*a^3*b^7*d^11*f - 9*A^2*C*a^10*
c^2*d^9*f + 9*A*C^2*a^10*c^2*d^9*f - 3*A^2*B*b^10*c^9*d^2*f - B^2*C*a^8*b^2*d^11*f + 96*A^2*C*a^4*b^6*d^11*f -
84*A^2*C*a^6*b^4*d^11*f + 72*A*C^2*a^6*b^4*d^11*f - 24*A*C^2*a^4*b^6*d^11*f - 24*A*C^2*a^2*b^8*d^11*f - 21*A*
C^2*a^8*b^2*d^11*f + 12*A^2*C*a^2*b^8*d^11*f + 9*A^2*C*a^8*b^2*d^11*f + 3*A*B^2*a^10*c^2*d^9*f - A^2*B*a^10*c^
3*d^8*f - B*C^2*a^2*b^8*c^11*f + 176*A*B^2*a^4*b^6*d^11*f + 136*A^2*B*a^5*b^5*d^11*f - 128*A^2*B*a^3*b^7*d^11*
f + 112*A*B^2*a^2*b^8*d^11*f - 64*A*B^2*a^6*b^4*d^11*f - 16*A^2*B*a^7*b^3*d^11*f - A^2*B*a^2*b^8*c^11*f - 2*C^
3*a^9*b*c*d^10*f - 2*B^3*a*b^9*c^10*d*f - 264*A^3*a*b^9*c*d^10*f + 2*A^3*a^9*b*c*d^10*f - 9*B^2*C*b^10*c^10*d*
f + 9*A^2*C*b^10*c^10*d*f - 9*A*C^2*b^10*c^10*d*f + 3*B*C^2*a^10*c*d^10*f - 132*A^2*B*b^10*c*d^10*f - 3*A*B^2*
b^10*c^10*d*f - 2*B*C^2*a^9*b*d^11*f + 3*A^2*B*a^10*c*d^10*f - 2*B^2*C*a*b^9*c^11*f - 120*A^2*B*a*b^9*d^11*f -
6*A^2*C*a*b^9*c^11*f + 6*A*C^2*a*b^9*c^11*f - 2*A^2*B*a^9*b*d^11*f + 2*A*B^2*a*b^9*c^11*f + 520*C^3*a^3*b^7*c
^5*d^6*f + 460*C^3*a^5*b^5*c^5*d^6*f - 418*C^3*a^4*b^6*c^6*d^5*f + 406*C^3*a^6*b^4*c^4*d^7*f + 268*C^3*a^5*b^5
*c^7*d^4*f - 266*C^3*a^6*b^4*c^6*d^5*f + 233*C^3*a^2*b^8*c^8*d^3*f - 176*C^3*a^7*b^3*c^5*d^6*f + 164*C^3*a^6*b
^4*c^2*d^9*f + 140*C^3*a^2*b^8*c^6*d^5*f + 136*C^3*a^4*b^6*c^2*d^9*f - 128*C^3*a^3*b^7*c^9*d^2*f + 128*C^3*a^3
*b^7*c^3*d^8*f - 108*C^3*a^6*b^4*c^8*d^3*f - 104*C^3*a^7*b^3*c^3*d^8*f - 104*C^3*a^5*b^5*c^3*d^8*f + 100*C^3*a
^4*b^6*c^8*d^3*f - 89*C^3*a^8*b^2*c^2*d^9*f - 72*C^3*a^5*b^5*c^9*d^2*f + 40*C^3*a^8*b^2*c^4*d^7*f - 40*C^3*a^3
*b^7*c^7*d^4*f - 28*C^3*a^2*b^8*c^4*d^7*f - 16*C^3*a^2*b^8*c^2*d^9*f - 2*C^3*a^4*b^6*c^4*d^7*f + 828*B^3*a^5*b
^5*c^4*d^7*f + 408*B^3*a^2*b^8*c^5*d^6*f + 390*B^3*a^4*b^6*c^7*d^4*f - 372*B^3*a^4*b^6*c^3*d^8*f - 336*B^3*a^3
*b^7*c^6*d^5*f - 314*B^3*a^6*b^4*c^5*d^6*f + 288*B^3*a^3*b^7*c^4*d^7*f + 216*B^3*a^2*b^8*c^7*d^4*f - 176*B^3*a
^7*b^3*c^2*d^9*f + 128*B^3*a^3*b^7*c^2*d^9*f + 108*B^3*a^5*b^5*c^6*d^5*f + 88*B^3*a^7*b^3*c^4*d^7*f + 72*B^3*a
^5*b^5*c^2*d^9*f - 68*B^3*a^2*b^8*c^3*d^8*f - 65*B^3*a^2*b^8*c^9*d^2*f - 56*B^3*a^5*b^5*c^8*d^3*f + 40*B^3*a^7
*b^3*c^6*d^5*f + 37*B^3*a^8*b^2*c^3*d^8*f + 30*B^3*a^4*b^6*c^5*d^6*f - 28*B^3*a^8*b^2*c^5*d^6*f + 24*B^3*a^3*b
^7*c^8*d^3*f - 4*B^3*a^4*b^6*c^9*d^2*f - 2*B^3*a^6*b^4*c^7*d^4*f + 1586*A^3*a^4*b^6*c^4*d^7*f - 1376*A^3*a^3*b
^7*c^3*d^8*f - 1096*A^3*a^3*b^7*c^5*d^6*f + 844*A^3*a^2*b^8*c^4*d^7*f - 748*A^3*a^5*b^5*c^5*d^6*f + 490*A^3*a^
4*b^6*c^6*d^5*f + 376*A^3*a^2*b^8*c^2*d^9*f + 362*A^3*a^6*b^4*c^4*d^7*f - 356*A^3*a^2*b^8*c^6*d^5*f - 328*A^3*
a^5*b^5*c^3*d^8*f + 328*A^3*a^3*b^7*c^7*d^4*f + 224*A^3*a^4*b^6*c^2*d^9*f - 197*A^3*a^2*b^8*c^8*d^3*f - 112*A^
3*a^7*b^3*c^5*d^6*f + 98*A^3*a^6*b^4*c^6*d^5*f - 92*A^3*a^6*b^4*c^2*d^9*f - 88*A^3*a^7*b^3*c^3*d^8*f + 68*A^3*
a^8*b^2*c^4*d^7*f + 32*A^3*a^3*b^7*c^9*d^2*f - 28*A^3*a^5*b^5*c^7*d^4*f - 28*A^3*a^4*b^6*c^8*d^3*f + 17*A^3*a^
8*b^2*c^2*d^9*f + 104*C^3*a^7*b^3*c*d^10*f + 54*C^3*a*b^9*c^9*d^2*f - 40*C^3*a*b^9*c^7*d^4*f - 35*C^3*a^2*b^8*
c^10*d*f + 22*C^3*a^9*b*c^3*d^8*f + 16*C^3*a^5*b^5*c*d^10*f - 16*C^3*a^3*b^7*c*d^10*f + 8*C^3*a*b^9*c^5*d^6*f
- 2*A*B*C*b^10*c^11*f + 198*B^3*a*b^9*c^8*d^3*f + 192*B^3*a^6*b^4*c*d^10*f - 128*B^3*a*b^9*c^4*d^7*f - 80*B^3*
a^2*b^8*c*d^10*f - 56*B^3*a*b^9*c^2*d^9*f - 24*B^3*a*b^9*c^6*d^5*f - 18*B^3*a^9*b*c^2*d^9*f - 16*B^3*a^4*b^6*c
*d^10*f + 13*B^3*a^8*b^2*c*d^10*f + 8*B^3*a^9*b*c^4*d^7*f + 8*B^3*a^3*b^7*c^10*d*f - 624*A^3*a*b^9*c^3*d^8*f +
472*A^3*a*b^9*c^7*d^4*f - 272*A^3*a^3*b^7*c*d^10*f + 152*A^3*a^5*b^5*c*d^10*f - 22*A^3*a^9*b*c^3*d^8*f + 18*A
^3*a*b^9*c^9*d^2*f - 13*A^3*a^2*b^8*c^10*d*f - 8*A^3*a^7*b^3*c*d^10*f - 8*A^3*a*b^9*c^5*d^6*f + A*B^2*a^8*b^2*
d^11*f - C^3*b^10*c^8*d^3*f - 60*B^3*b^10*c^7*d^4*f - 32*B^3*b^10*c^5*d^6*f + 21*B^3*b^10*c^9*d^2*f - 12*B^3*b
^10*c^3*d^8*f - 3*C^3*a^10*c^2*d^9*f - 360*A^3*b^10*c^6*d^5*f - 204*A^3*b^10*c^4*d^7*f + 11*C^3*a^8*b^2*d^11*f
- 8*C^3*a^6*b^4*d^11*f - 4*C^3*a^4*b^6*d^11*f - B^3*a^10*c^3*d^8*f - 64*B^3*a^5*b^5*d^11*f - 32*B^3*a^3*b^7*d
^11*f + 3*A^3*a^10*c^2*d^9*f - 68*A^3*a^4*b^6*d^11*f + 20*A^3*a^6*b^4*d^11*f + 12*A^3*a^2*b^8*d^11*f - B^3*a^2
*b^8*c^11*f + 3*C^3*b^10*c^10*d*f + 3*B^3*a^10*c*d^10*f - 3*A^3*b^10*c^10*d*f - 2*C^3*a*b^9*c^11*f - 2*B^3*a^9
*b*d^11*f + 2*A^3*a*b^9*c^11*f - 36*A^2*C*b^10*d^11*f + 3*A^2*C*a^10*d^11*f - 3*A*C^2*a^10*d^11*f - A*B^2*a^10
*d^11*f + 36*A^3*b^10*d^11*f - A^3*a^10*d^11*f + A^3*b^10*c^8*d^3*f + A^3*a^8*b^2*d^11*f + B^2*C*a^10*d^11*f +
B*C^2*b^10*c^11*f + A^2*B*b^10*c^11*f + C^3*a^10*d^11*f + B^3*b^10*c^11*f - 6*A*B^2*C*a*b^7*c^7*d + 4*A*B^2*C
*a*b^7*c*d^7 + 168*A^2*B*C*a^3*b^5*c^2*d^6 + 144*A*B*C^2*a^4*b^4*c^3*d^5 - 129*A^2*B*C*a^4*b^4*c^3*d^5 - 96*A*
B*C^2*a^3*b^5*c^2*d^6 + 84*A*B*C^2*a^2*b^6*c^3*d^5 + 72*A^2*B*C*a^3*b^5*c^4*d^4 - 72*A^2*B*C*a^2*b^6*c^3*d^5 +
64*A*B^2*C*a^4*b^4*c^4*d^4 - 60*A*B*C^2*a^3*b^5*c^4*d^4 + 57*A^2*B*C*a^2*b^6*c^5*d^3 - 56*A*B^2*C*a^3*b^5*c^5
*d^3 - 39*A*B^2*C*a^4*b^4*c^2*d^6 - 38*A*B^2*C*a^5*b^3*c^3*d^5 + 36*A*B^2*C*a^3*b^5*c^3*d^5 + 36*A*B*C^2*a^4*b
^4*c^5*d^3 - 30*A*B*C^2*a^2*b^6*c^5*d^3 + 27*A*B^2*C*a^2*b^6*c^6*d^2 - 24*A*B^2*C*a^2*b^6*c^2*d^6 - 24*A*B*C^2
*a^5*b^3*c^4*d^4 + 24*A*B*C^2*a^3*b^5*c^6*d^2 + 18*A^2*B*C*a^5*b^3*c^2*d^6 - 18*A^2*B*C*a^4*b^4*c^5*d^3 - 15*A
*B^2*C*a^2*b^6*c^4*d^4 + 12*A^2*B*C*a^5*b^3*c^4*d^4 - 12*A^2*B*C*a^3*b^5*c^6*d^2 + 9*A*B^2*C*a^6*b^2*c^2*d^6 +
6*A*B*C^2*a^6*b^2*c^3*d^5 - 3*A^2*B*C*a^6*b^2*c^3*d^5 + 60*A^2*B*C*a*b^7*c^2*d^6 - 51*A^2*B*C*a^4*b^4*c*d^7 +
48*A*B*C^2*a*b^7*c^6*d^2 - 42*A^2*B*C*a^2*b^6*c*d^7 - 42*A^2*B*C*a*b^7*c^6*d^2 + 36*A*B*C^2*a^4*b^4*c*d^7 + 3
6*A*B*C^2*a^2*b^6*c*d^7 + 36*A*B*C^2*a*b^7*c^4*d^4 - 30*A^2*B*C*a*b^7*c^4*d^4 + 24*A*B^2*C*a*b^7*c^3*d^5 - 24*
A*B*C^2*a*b^7*c^2*d^6 + 18*A*B^2*C*a^5*b^3*c*d^7 - 18*A*B*C^2*a^6*b^2*c*d^7 + 12*A*B^2*C*a^3*b^5*c*d^7 + 9*A^2
*B*C*a^6*b^2*c*d^7 + 6*A*B^2*C*a*b^7*c^5*d^3 - 6*A*B*C^2*a^2*b^6*c^7*d + 3*A^2*B*C*a^2*b^6*c^7*d - 18*B^3*C*a*
b^7*c^6*d^2 - 18*B*C^3*a*b^7*c^6*d^2 - 14*B^3*C*a*b^7*c^4*d^4 - 14*B*C^3*a*b^7*c^4*d^4 - 10*B^3*C*a^2*b^6*c*d^
7 - 10*B*C^3*a^2*b^6*c*d^7 + 9*B^3*C*a^6*b^2*c*d^7 + 9*B*C^3*a^6*b^2*c*d^7 - 7*B^3*C*a^4*b^4*c*d^7 - 7*B*C^3*a
^4*b^4*c*d^7 + 6*B^2*C^2*a*b^7*c^7*d - 4*B^3*C*a*b^7*c^2*d^6 + 4*B^2*C^2*a*b^7*c*d^7 - 4*B*C^3*a*b^7*c^2*d^6 +
3*B^3*C*a^2*b^6*c^7*d + 3*B*C^3*a^2*b^6*c^7*d + 144*A^3*C*a*b^7*c^3*d^5 + 62*A^3*C*a*b^7*c^5*d^3 + 48*A*C^3*a
*b^7*c^3*d^5 - 36*A^2*C^2*a*b^7*c*d^7 + 26*A*C^3*a*b^7*c^5*d^3 + 20*A^3*C*a^3*b^5*c*d^7 + 18*A^2*C^2*a*b^7*c^7
*d - 18*A*C^3*a^5*b^3*c*d^7 - 6*A^3*C*a^5*b^3*c*d^7 - 4*A*C^3*a^3*b^5*c*d^7 - 32*A^3*B*a*b^7*c^2*d^6 - 32*A*B^
3*a*b^7*c^2*d^6 + 22*A^3*B*a^4*b^4*c*d^7 + 22*A*B^3*a^4*b^4*c*d^7 + 16*A^3*B*a^2*b^6*c*d^7 + 16*A*B^3*a^2*b^6*
c*d^7 + 12*A^3*B*a*b^7*c^6*d^2 + 12*A*B^3*a*b^7*c^6*d^2 + 8*A^3*B*a*b^7*c^4*d^4 - 8*A^2*B^2*a*b^7*c*d^7 + 8*A*
B^3*a*b^7*c^4*d^4 + 57*A^2*B*C*b^8*c^5*d^3 + 36*A^2*B*C*b^8*c^3*d^5 - 30*A*B*C^2*b^8*c^5*d^3 - 18*A*B*C^2*b^8*
c^3*d^5 - 9*A*B^2*C*b^8*c^4*d^4 - 3*A*B^2*C*b^8*c^6*d^2 - 2*A*B^2*C*b^8*c^2*d^6 + 36*A^2*B*C*a^3*b^5*d^8 + 24*
A*B*C^2*a^5*b^3*d^8 - 18*A^2*B*C*a^5*b^3*d^8 - 12*A*B*C^2*a^3*b^5*d^8 - 3*A*B^2*C*a^6*b^2*d^8 - 3*A*B^2*C*a^4*
b^4*d^8 - 2*A*B^2*C*a^2*b^6*d^8 + 34*B^2*C^2*a^5*b^3*c^3*d^5 + 28*B^2*C^2*a^3*b^5*c^5*d^3 + 24*B^2*C^2*a^4*b^4
*c^2*d^6 - 20*B^2*C^2*a^4*b^4*c^4*d^4 + 12*B^2*C^2*a^3*b^5*c^3*d^5 + 12*B^2*C^2*a^2*b^6*c^2*d^6 - 9*B^2*C^2*a^
6*b^2*c^2*d^6 + 9*B^2*C^2*a^4*b^4*c^6*d^2 + 9*B^2*C^2*a^2*b^6*c^4*d^4 - 3*B^2*C^2*a^2*b^6*c^6*d^2 + 159*A^2*C^
2*a^2*b^6*c^4*d^4 - 156*A^2*C^2*a^3*b^5*c^3*d^5 + 90*A^2*C^2*a^5*b^3*c^3*d^5 + 78*A^2*C^2*a^2*b^6*c^2*d^6 - 63
*A^2*C^2*a^4*b^4*c^4*d^4 - 27*A^2*C^2*a^6*b^2*c^2*d^6 - 27*A^2*C^2*a^2*b^6*c^6*d^2 - 18*A^2*C^2*a^4*b^4*c^2*d^
6 + 9*A^2*C^2*a^4*b^4*c^6*d^2 + 66*A^2*B^2*a^2*b^6*c^2*d^6 + 60*A^2*B^2*a^2*b^6*c^4*d^4 - 48*A^2*B^2*a^3*b^5*c
^3*d^5 + 42*A^2*B^2*a^4*b^4*c^2*d^6 + 28*A^2*B^2*a^3*b^5*c^5*d^3 - 17*A^2*B^2*a^4*b^4*c^4*d^4 - 6*A^2*B^2*a^2*
b^6*c^6*d^2 + 4*A^2*B^2*a^5*b^3*c^3*d^5 + 36*A^3*C*a*b^7*c*d^7 - 18*A*C^3*a*b^7*c^7*d + 12*A*C^3*a*b^7*c*d^7 -
6*A^3*C*a*b^7*c^7*d + 12*A^2*B*C*b^8*c*d^7 + 6*A*B*C^2*b^8*c^7*d - 6*A*B*C^2*b^8*c*d^7 - 3*A^2*B*C*b^8*c^7*d
+ 24*A^2*B*C*a*b^7*d^8 - 12*A*B*C^2*a*b^7*d^8 - 53*B^3*C*a^4*b^4*c^3*d^5 - 53*B*C^3*a^4*b^4*c^3*d^5 - 32*B^3*C
*a^2*b^6*c^3*d^5 - 32*B*C^3*a^2*b^6*c^3*d^5 - 18*B^3*C*a^4*b^4*c^5*d^3 - 18*B*C^3*a^4*b^4*c^5*d^3 + 16*B^3*C*a
^3*b^5*c^4*d^4 + 16*B*C^3*a^3*b^5*c^4*d^4 + 12*B^3*C*a^5*b^3*c^4*d^4 - 12*B^3*C*a^3*b^5*c^6*d^2 + 12*B^2*C^2*a
*b^7*c^3*d^5 + 12*B*C^3*a^5*b^3*c^4*d^4 - 12*B*C^3*a^3*b^5*c^6*d^2 + 8*B^3*C*a^3*b^5*c^2*d^6 + 8*B*C^3*a^3*b^5
*c^2*d^6 - 6*B^3*C*a^5*b^3*c^2*d^6 - 6*B^2*C^2*a^5*b^3*c*d^7 + 6*B^2*C^2*a*b^7*c^5*d^3 - 6*B*C^3*a^5*b^3*c^2*d
^6 - 3*B^3*C*a^6*b^2*c^3*d^5 - 3*B*C^3*a^6*b^2*c^3*d^5 - 175*A^3*C*a^2*b^6*c^4*d^4 + 164*A^3*C*a^3*b^5*c^3*d^5
- 144*A^2*C^2*a*b^7*c^3*d^5 - 124*A^3*C*a^2*b^6*c^2*d^6 - 90*A*C^3*a^5*b^3*c^3*d^5 - 73*A*C^3*a^2*b^6*c^4*d^4
- 66*A^2*C^2*a*b^7*c^5*d^3 + 44*A*C^3*a^3*b^5*c^3*d^5 + 36*A*C^3*a^4*b^4*c^4*d^4 - 30*A^3*C*a^5*b^3*c^3*d^5 +
30*A^3*C*a^4*b^4*c^4*d^4 + 27*A*C^3*a^6*b^2*c^2*d^6 + 21*A*C^3*a^4*b^4*c^2*d^6 + 18*A^2*C^2*a^5*b^3*c*d^7 - 1
8*A*C^3*a^4*b^4*c^6*d^2 - 16*A*C^3*a^2*b^6*c^2*d^6 - 15*A^3*C*a^4*b^4*c^2*d^6 + 15*A^3*C*a^2*b^6*c^6*d^2 - 12*
A^2*C^2*a^3*b^5*c*d^7 + 9*A^3*C*a^6*b^2*c^2*d^6 + 9*A*C^3*a^2*b^6*c^6*d^2 - 80*A^3*B*a^3*b^5*c^2*d^6 - 80*A*B^
3*a^3*b^5*c^2*d^6 + 38*A^3*B*a^4*b^4*c^3*d^5 + 38*A*B^3*a^4*b^4*c^3*d^5 - 36*A^2*B^2*a*b^7*c^3*d^5 - 28*A^3*B*
a^3*b^5*c^4*d^4 - 28*A^3*B*a^2*b^6*c^5*d^3 - 28*A*B^3*a^3*b^5*c^4*d^4 - 28*A*B^3*a^2*b^6*c^5*d^3 + 20*A^3*B*a^
2*b^6*c^3*d^5 + 20*A*B^3*a^2*b^6*c^3*d^5 - 12*A^3*B*a^5*b^3*c^2*d^6 - 12*A^2*B^2*a^5*b^3*c*d^7 - 12*A^2*B^2*a^
3*b^5*c*d^7 - 12*A^2*B^2*a*b^7*c^5*d^3 - 12*A*B^3*a^5*b^3*c^2*d^6 + 6*B^2*C^2*b^8*c^6*d^2 + 3*B^2*C^2*b^8*c^4*
d^4 + 36*A^2*C^2*b^8*c^4*d^4 + 27*A^2*C^2*b^8*c^2*d^6 - 18*A^2*C^2*b^8*c^6*d^2 + 33*A^2*B^2*b^8*c^4*d^4 + 28*A
^2*B^2*b^8*c^2*d^6 + 9*B^2*C^2*a^4*b^4*d^8 + 6*A^2*B^2*b^8*c^6*d^2 + 4*B^2*C^2*a^2*b^6*d^8 + 3*B^2*C^2*a^6*b^2
*d^8 - 30*A^2*C^2*a^4*b^4*d^8 + 9*A^2*C^2*a^6*b^2*d^8 + 16*A^2*B^2*a^2*b^6*d^8 + 3*A^2*B^2*a^4*b^4*d^8 + 6*C^4
*a^5*b^3*c*d^7 + 4*C^4*a^3*b^5*c*d^7 - 2*C^4*a*b^7*c^5*d^3 - 12*B^4*a^5*b^3*c*d^7 + 12*B^4*a*b^7*c^3*d^5 + 8*B
^4*a*b^7*c^5*d^3 - 4*B^4*a^3*b^5*c*d^7 - 48*A^4*a*b^7*c^3*d^5 - 20*A^4*a*b^7*c^5*d^3 - 8*A^4*a^3*b^5*c*d^7 - 6
3*A^3*C*b^8*c^4*d^4 - 54*A^3*C*b^8*c^2*d^6 + 9*A^3*C*b^8*c^6*d^2 + 9*A*C^3*b^8*c^6*d^2 - 3*A*C^3*b^8*c^4*d^4 -
28*A^3*B*b^8*c^5*d^3 - 28*A*B^3*b^8*c^5*d^3 - 18*A^3*B*b^8*c^3*d^5 - 18*A*B^3*b^8*c^3*d^5 - 10*B^3*C*a^5*b^3*
d^8 - 10*B*C^3*a^5*b^3*d^8 - 4*B^3*C*a^3*b^5*d^8 - 4*B*C^3*a^3*b^5*d^8 + 23*A^3*C*a^4*b^4*d^8 - 18*A^3*C*a^2*b
^6*d^8 + 11*A*C^3*a^4*b^4*d^8 - 9*A*C^3*a^6*b^2*d^8 + 6*A*C^3*a^2*b^6*d^8 - 3*A^3*C*a^6*b^2*d^8 - 20*A^3*B*a^3
*b^5*d^8 - 20*A*B^3*a^3*b^5*d^8 + 4*A^3*B*a^5*b^3*d^8 + 4*A*B^3*a^5*b^3*d^8 + B^3*C*a^2*b^6*c^5*d^3 + B*C^3*a^
2*b^6*c^5*d^3 + 6*C^4*a*b^7*c^7*d + 4*B^4*a*b^7*c*d^7 - 12*A^4*a*b^7*c*d^7 - 3*B^3*C*b^8*c^7*d - 3*B*C^3*b^8*c
^7*d - 6*A^3*B*b^8*c*d^7 - 6*A*B^3*b^8*c*d^7 - 12*A^3*B*a*b^7*d^8 - 12*A*B^3*a*b^7*d^8 + 30*C^4*a^5*b^3*c^3*d^
5 + 19*C^4*a^2*b^6*c^4*d^4 - 9*C^4*a^6*b^2*c^2*d^6 + 9*C^4*a^4*b^4*c^6*d^2 + 4*C^4*a^3*b^5*c^3*d^5 + 4*C^4*a^2
*b^6*c^2*d^6 - 3*C^4*a^4*b^4*c^4*d^4 - 3*C^4*a^4*b^4*c^2*d^6 + 3*C^4*a^2*b^6*c^6*d^2 + 28*B^4*a^3*b^5*c^5*d^3
+ 27*B^4*a^4*b^4*c^2*d^6 - 17*B^4*a^4*b^4*c^4*d^4 - 10*B^4*a^2*b^6*c^4*d^4 + 8*B^4*a^3*b^5*c^3*d^5 + 8*B^4*a^2
*b^6*c^2*d^6 - 6*B^4*a^2*b^6*c^6*d^2 + 4*B^4*a^5*b^3*c^3*d^5 + 70*A^4*a^2*b^6*c^4*d^4 + 58*A^4*a^2*b^6*c^2*d^6
- 56*A^4*a^3*b^5*c^3*d^5 + 15*A^4*a^4*b^4*c^2*d^6 + B^2*C^2*b^8*c^2*d^6 - 18*A^3*C*b^8*d^8 + B^3*C*b^8*c^5*d^
3 + B*C^3*b^8*c^5*d^3 + 6*B^4*b^8*c^6*d^2 + 3*B^4*b^8*c^4*d^4 + 30*A^4*b^8*c^4*d^4 + 27*A^4*b^8*c^2*d^6 + 3*C^
4*a^6*b^2*d^8 + 8*B^4*a^4*b^4*d^8 + 4*B^4*a^2*b^6*d^8 + 12*A^4*a^2*b^6*d^8 - 5*A^4*a^4*b^4*d^8 + 9*A^2*C^2*b^8
*d^8 + 9*A^2*B^2*b^8*d^8 + 9*A^4*b^8*d^8 + B^4*b^8*c^2*d^6 + C^4*a^4*b^4*d^8, f, k)*(root(640*a^15*b*c^7*d^13*
f^4 + 640*a*b^15*c^13*d^7*f^4 + 480*a^15*b*c^9*d^11*f^4 + 480*a^15*b*c^5*d^15*f^4 + 480*a*b^15*c^15*d^5*f^4 +
480*a*b^15*c^11*d^9*f^4 + 192*a^15*b*c^11*d^9*f^4 + 192*a^15*b*c^3*d^17*f^4 + 192*a^11*b^5*c*d^19*f^4 + 192*a^
5*b^11*c^19*d*f^4 + 192*a*b^15*c^17*d^3*f^4 + 192*a*b^15*c^9*d^11*f^4 + 128*a^13*b^3*c*d^19*f^4 + 128*a^9*b^7*
c*d^19*f^4 + 128*a^7*b^9*c^19*d*f^4 + 128*a^3*b^13*c^19*d*f^4 + 32*a^15*b*c^13*d^7*f^4 + 32*a^9*b^7*c^19*d*f^4
+ 32*a^7*b^9*c*d^19*f^4 + 32*a*b^15*c^7*d^13*f^4 + 32*a^15*b*c*d^19*f^4 + 32*a*b^15*c^19*d*f^4 - 47088*a^8*b^
8*c^10*d^10*f^4 + 42432*a^9*b^7*c^9*d^11*f^4 + 42432*a^7*b^9*c^11*d^9*f^4 + 39328*a^9*b^7*c^11*d^9*f^4 + 39328
*a^7*b^9*c^9*d^11*f^4 - 36912*a^8*b^8*c^12*d^8*f^4 - 36912*a^8*b^8*c^8*d^12*f^4 - 34256*a^10*b^6*c^10*d^10*f^4
- 34256*a^6*b^10*c^10*d^10*f^4 - 31152*a^10*b^6*c^8*d^12*f^4 - 31152*a^6*b^10*c^12*d^8*f^4 + 28128*a^9*b^7*c^
7*d^13*f^4 + 28128*a^7*b^9*c^13*d^7*f^4 + 24160*a^11*b^5*c^9*d^11*f^4 + 24160*a^5*b^11*c^11*d^9*f^4 - 23088*a^
10*b^6*c^12*d^8*f^4 - 23088*a^6*b^10*c^8*d^12*f^4 + 22272*a^9*b^7*c^13*d^7*f^4 + 22272*a^7*b^9*c^7*d^13*f^4 +
19072*a^11*b^5*c^11*d^9*f^4 + 19072*a^5*b^11*c^9*d^11*f^4 + 18624*a^11*b^5*c^7*d^13*f^4 + 18624*a^5*b^11*c^13*
d^7*f^4 - 17328*a^8*b^8*c^14*d^6*f^4 - 17328*a^8*b^8*c^6*d^14*f^4 - 17232*a^10*b^6*c^6*d^14*f^4 - 17232*a^6*b^
10*c^14*d^6*f^4 - 13520*a^12*b^4*c^8*d^12*f^4 - 13520*a^4*b^12*c^12*d^8*f^4 - 12464*a^12*b^4*c^10*d^10*f^4 - 1
2464*a^4*b^12*c^10*d^10*f^4 + 10880*a^9*b^7*c^5*d^15*f^4 + 10880*a^7*b^9*c^15*d^5*f^4 - 9072*a^10*b^6*c^14*d^6
*f^4 - 9072*a^6*b^10*c^6*d^14*f^4 + 8928*a^11*b^5*c^13*d^7*f^4 + 8928*a^5*b^11*c^7*d^13*f^4 - 8880*a^12*b^4*c^
6*d^14*f^4 - 8880*a^4*b^12*c^14*d^6*f^4 + 8480*a^11*b^5*c^5*d^15*f^4 + 8480*a^5*b^11*c^15*d^5*f^4 + 7200*a^9*b
^7*c^15*d^5*f^4 + 7200*a^7*b^9*c^5*d^15*f^4 - 6912*a^12*b^4*c^12*d^8*f^4 - 6912*a^4*b^12*c^8*d^12*f^4 + 6400*a
^13*b^3*c^9*d^11*f^4 + 6400*a^3*b^13*c^11*d^9*f^4 + 5920*a^13*b^3*c^7*d^13*f^4 + 5920*a^3*b^13*c^13*d^7*f^4 -
5392*a^10*b^6*c^4*d^16*f^4 - 5392*a^6*b^10*c^16*d^4*f^4 - 4428*a^8*b^8*c^16*d^4*f^4 - 4428*a^8*b^8*c^4*d^16*f^
4 + 4128*a^13*b^3*c^11*d^9*f^4 + 4128*a^3*b^13*c^9*d^11*f^4 - 3328*a^12*b^4*c^4*d^16*f^4 - 3328*a^4*b^12*c^16*
d^4*f^4 + 3264*a^13*b^3*c^5*d^15*f^4 + 3264*a^3*b^13*c^15*d^5*f^4 - 2480*a^14*b^2*c^8*d^12*f^4 - 2480*a^2*b^14
*c^12*d^8*f^4 + 2240*a^11*b^5*c^15*d^5*f^4 + 2240*a^5*b^11*c^5*d^15*f^4 - 2128*a^12*b^4*c^14*d^6*f^4 - 2128*a^
4*b^12*c^6*d^14*f^4 + 2112*a^9*b^7*c^3*d^17*f^4 + 2112*a^7*b^9*c^17*d^3*f^4 + 2048*a^11*b^5*c^3*d^17*f^4 + 204
8*a^5*b^11*c^17*d^3*f^4 - 2000*a^14*b^2*c^6*d^14*f^4 - 2000*a^2*b^14*c^14*d^6*f^4 - 1792*a^10*b^6*c^16*d^4*f^4
- 1792*a^6*b^10*c^4*d^16*f^4 - 1776*a^14*b^2*c^10*d^10*f^4 - 1776*a^2*b^14*c^10*d^10*f^4 + 1472*a^13*b^3*c^13
*d^7*f^4 + 1472*a^3*b^13*c^7*d^13*f^4 + 1088*a^9*b^7*c^17*d^3*f^4 + 1088*a^7*b^9*c^3*d^17*f^4 + 992*a^13*b^3*c
^3*d^17*f^4 + 992*a^3*b^13*c^17*d^3*f^4 - 912*a^14*b^2*c^4*d^16*f^4 - 912*a^2*b^14*c^16*d^4*f^4 - 768*a^10*b^6
*c^2*d^18*f^4 - 768*a^6*b^10*c^18*d^2*f^4 - 688*a^14*b^2*c^12*d^8*f^4 - 688*a^2*b^14*c^8*d^12*f^4 - 592*a^12*b
^4*c^2*d^18*f^4 - 592*a^4*b^12*c^18*d^2*f^4 - 472*a^8*b^8*c^18*d^2*f^4 - 472*a^8*b^8*c^2*d^18*f^4 - 280*a^12*b
^4*c^16*d^4*f^4 - 280*a^4*b^12*c^4*d^16*f^4 + 224*a^13*b^3*c^15*d^5*f^4 + 224*a^11*b^5*c^17*d^3*f^4 + 224*a^5*
b^11*c^3*d^17*f^4 + 224*a^3*b^13*c^5*d^15*f^4 - 208*a^14*b^2*c^2*d^18*f^4 - 208*a^2*b^14*c^18*d^2*f^4 - 112*a^
14*b^2*c^14*d^6*f^4 - 112*a^10*b^6*c^18*d^2*f^4 - 112*a^6*b^10*c^2*d^18*f^4 - 112*a^2*b^14*c^6*d^14*f^4 - 80*b
^16*c^14*d^6*f^4 - 60*b^16*c^16*d^4*f^4 - 60*b^16*c^12*d^8*f^4 - 24*b^16*c^18*d^2*f^4 - 24*b^16*c^10*d^10*f^4
- 4*b^16*c^8*d^12*f^4 - 80*a^16*c^6*d^14*f^4 - 60*a^16*c^8*d^12*f^4 - 60*a^16*c^4*d^16*f^4 - 24*a^16*c^10*d^10
*f^4 - 24*a^16*c^2*d^18*f^4 - 4*a^16*c^12*d^8*f^4 - 24*a^12*b^4*d^20*f^4 - 16*a^14*b^2*d^20*f^4 - 16*a^10*b^6*
d^20*f^4 - 4*a^8*b^8*d^20*f^4 - 24*a^4*b^12*c^20*f^4 - 16*a^6*b^10*c^20*f^4 - 16*a^2*b^14*c^20*f^4 - 4*a^8*b^8
*c^20*f^4 - 4*b^16*c^20*f^4 - 4*a^16*d^20*f^4 + 56*A*C*a*b^11*c^13*d*f^2 - 48*A*C*a^11*b*c*d^13*f^2 + 48*A*C*a
*b^11*c*d^13*f^2 + 5904*B*C*a^6*b^6*c^7*d^7*f^2 - 5016*B*C*a^5*b^7*c^8*d^6*f^2 - 4608*B*C*a^7*b^5*c^6*d^8*f^2
- 4512*B*C*a^5*b^7*c^6*d^8*f^2 - 4384*B*C*a^7*b^5*c^8*d^6*f^2 + 3056*B*C*a^8*b^4*c^7*d^7*f^2 + 2256*B*C*a^4*b^
8*c^7*d^7*f^2 - 1824*B*C*a^3*b^9*c^8*d^6*f^2 + 1632*B*C*a^9*b^3*c^4*d^10*f^2 - 1400*B*C*a^8*b^4*c^3*d^11*f^2 -
1320*B*C*a^4*b^8*c^11*d^3*f^2 - 1248*B*C*a^3*b^9*c^6*d^8*f^2 + 1152*B*C*a^3*b^9*c^10*d^4*f^2 - 1072*B*C*a^9*b
^3*c^6*d^8*f^2 + 1068*B*C*a^6*b^6*c^9*d^5*f^2 - 1004*B*C*a^4*b^8*c^5*d^9*f^2 - 968*B*C*a^6*b^6*c^3*d^11*f^2 -
864*B*C*a^8*b^4*c^5*d^9*f^2 - 828*B*C*a^4*b^8*c^9*d^5*f^2 - 792*B*C*a^4*b^8*c^3*d^11*f^2 - 792*B*C*a^2*b^10*c^
11*d^3*f^2 - 776*B*C*a^9*b^3*c^8*d^6*f^2 + 688*B*C*a^7*b^5*c^4*d^10*f^2 - 672*B*C*a^10*b^2*c^3*d^11*f^2 - 592*
B*C*a^2*b^10*c^9*d^5*f^2 + 544*B*C*a^10*b^2*c^7*d^7*f^2 - 492*B*C*a^2*b^10*c^5*d^9*f^2 + 480*B*C*a^5*b^7*c^10*
d^4*f^2 - 392*B*C*a^10*b^2*c^5*d^9*f^2 + 332*B*C*a^8*b^4*c^9*d^5*f^2 - 328*B*C*a^6*b^6*c^11*d^3*f^2 + 320*B*C*
a^9*b^3*c^2*d^12*f^2 + 272*B*C*a^3*b^9*c^12*d^2*f^2 - 248*B*C*a^5*b^7*c^4*d^10*f^2 - 248*B*C*a^2*b^10*c^3*d^11
*f^2 - 208*B*C*a^7*b^5*c^10*d^4*f^2 - 192*B*C*a^5*b^7*c^2*d^12*f^2 + 144*B*C*a^2*b^10*c^7*d^7*f^2 - 96*B*C*a^3
*b^9*c^4*d^10*f^2 + 88*B*C*a^5*b^7*c^12*d^2*f^2 - 72*B*C*a^8*b^4*c^11*d^3*f^2 + 48*B*C*a^9*b^3*c^10*d^4*f^2 -
48*B*C*a^7*b^5*c^12*d^2*f^2 - 48*B*C*a^7*b^5*c^2*d^12*f^2 - 48*B*C*a^3*b^9*c^2*d^12*f^2 - 12*B*C*a^10*b^2*c^9*
d^5*f^2 + 4*B*C*a^6*b^6*c^5*d^9*f^2 + 5824*A*C*a^7*b^5*c^5*d^9*f^2 - 4378*A*C*a^8*b^4*c^6*d^8*f^2 + 4296*A*C*a
^5*b^7*c^5*d^9*f^2 - 3912*A*C*a^6*b^6*c^6*d^8*f^2 - 3672*A*C*a^5*b^7*c^9*d^5*f^2 + 3594*A*C*a^4*b^8*c^8*d^6*f^
2 + 3236*A*C*a^6*b^6*c^8*d^6*f^2 + 2816*A*C*a^9*b^3*c^5*d^9*f^2 + 2624*A*C*a^3*b^9*c^5*d^9*f^2 + 2432*A*C*a^7*
b^5*c^7*d^7*f^2 - 2366*A*C*a^8*b^4*c^4*d^10*f^2 + 2298*A*C*a^4*b^8*c^10*d^4*f^2 + 1872*A*C*a^3*b^9*c^7*d^7*f^2
+ 1848*A*C*a^6*b^6*c^10*d^4*f^2 - 1644*A*C*a^6*b^6*c^4*d^10*f^2 - 1488*A*C*a^7*b^5*c^9*d^5*f^2 - 1408*A*C*a^3
*b^9*c^9*d^5*f^2 - 1308*A*C*a^4*b^8*c^6*d^8*f^2 + 1248*A*C*a^5*b^7*c^7*d^7*f^2 - 1012*A*C*a^10*b^2*c^6*d^8*f^2
+ 1008*A*C*a^7*b^5*c^3*d^11*f^2 + 992*A*C*a^5*b^7*c^3*d^11*f^2 + 928*A*C*a^3*b^9*c^3*d^11*f^2 + 848*A*C*a^9*b
^3*c^7*d^7*f^2 + 636*A*C*a^2*b^10*c^8*d^6*f^2 - 628*A*C*a^10*b^2*c^4*d^10*f^2 - 600*A*C*a^2*b^10*c^6*d^8*f^2 -
576*A*C*a^5*b^7*c^11*d^3*f^2 + 572*A*C*a^2*b^10*c^10*d^4*f^2 + 464*A*C*a^8*b^4*c^8*d^6*f^2 + 304*A*C*a^6*b^6*
c^2*d^12*f^2 - 304*A*C*a^4*b^8*c^4*d^10*f^2 + 296*A*C*a^4*b^8*c^2*d^12*f^2 + 260*A*C*a^8*b^4*c^10*d^4*f^2 - 23
2*A*C*a^9*b^3*c^9*d^5*f^2 - 232*A*C*a^2*b^10*c^12*d^2*f^2 + 228*A*C*a^10*b^2*c^2*d^12*f^2 - 188*A*C*a^2*b^10*c
^4*d^10*f^2 + 144*A*C*a^3*b^9*c^11*d^3*f^2 + 116*A*C*a^6*b^6*c^12*d^2*f^2 + 112*A*C*a^9*b^3*c^3*d^11*f^2 - 112
*A*C*a^7*b^5*c^11*d^3*f^2 + 92*A*C*a^10*b^2*c^8*d^6*f^2 + 74*A*C*a^4*b^8*c^12*d^2*f^2 + 62*A*C*a^8*b^4*c^2*d^1
2*f^2 + 40*A*C*a^2*b^10*c^2*d^12*f^2 - 7008*A*B*a^6*b^6*c^7*d^7*f^2 - 4032*A*B*a^4*b^8*c^7*d^7*f^2 + 3952*A*B*
a^7*b^5*c^8*d^6*f^2 + 3648*A*B*a^5*b^7*c^8*d^6*f^2 - 3392*A*B*a^8*b^4*c^7*d^7*f^2 + 3264*A*B*a^7*b^5*c^6*d^8*f
^2 - 2992*A*B*a^5*b^7*c^4*d^10*f^2 - 2368*A*B*a^7*b^5*c^4*d^10*f^2 - 2304*A*B*a^3*b^9*c^4*d^10*f^2 - 1968*A*B*
a^6*b^6*c^9*d^5*f^2 - 1872*A*B*a^9*b^3*c^4*d^10*f^2 - 1728*A*B*a^2*b^10*c^7*d^7*f^2 + 1712*A*B*a^8*b^4*c^3*d^1
1*f^2 + 1536*A*B*a^5*b^7*c^6*d^8*f^2 - 1536*A*B*a^3*b^9*c^10*d^4*f^2 - 1392*A*B*a^5*b^7*c^2*d^12*f^2 + 1328*A*
B*a^6*b^6*c^3*d^11*f^2 - 1104*A*B*a^3*b^9*c^2*d^12*f^2 - 1056*A*B*a^3*b^9*c^6*d^8*f^2 + 976*A*B*a^9*b^3*c^6*d^
8*f^2 + 960*A*B*a^4*b^8*c^11*d^3*f^2 + 936*A*B*a^8*b^4*c^5*d^9*f^2 - 912*A*B*a^5*b^7*c^10*d^4*f^2 + 848*A*B*a^
9*b^3*c^8*d^6*f^2 - 816*A*B*a^7*b^5*c^2*d^12*f^2 + 816*A*B*a^4*b^8*c^3*d^11*f^2 + 768*A*B*a^10*b^2*c^3*d^11*f^
2 + 672*A*B*a^3*b^9*c^8*d^6*f^2 - 632*A*B*a^8*b^4*c^9*d^5*f^2 - 608*A*B*a^2*b^10*c^9*d^5*f^2 - 552*A*B*a^4*b^8
*c^9*d^5*f^2 - 544*A*B*a^10*b^2*c^7*d^7*f^2 - 480*A*B*a^2*b^10*c^5*d^9*f^2 + 464*A*B*a^10*b^2*c^5*d^9*f^2 - 46
4*A*B*a^9*b^3*c^2*d^12*f^2 + 432*A*B*a^2*b^10*c^11*d^3*f^2 - 368*A*B*a^3*b^9*c^12*d^2*f^2 - 256*A*B*a^6*b^6*c^
5*d^9*f^2 - 208*A*B*a^5*b^7*c^12*d^2*f^2 + 176*A*B*a^4*b^8*c^5*d^9*f^2 + 112*A*B*a^7*b^5*c^10*d^4*f^2 + 112*A*
B*a^6*b^6*c^11*d^3*f^2 - 16*A*B*a^2*b^10*c^3*d^11*f^2 - 576*B*C*a*b^11*c^8*d^6*f^2 + 400*B*C*a^11*b*c^4*d^10*f
^2 - 288*B*C*a*b^11*c^6*d^8*f^2 - 176*B*C*a^11*b*c^6*d^8*f^2 + 128*B*C*a*b^11*c^10*d^4*f^2 - 108*B*C*a^4*b^8*c
*d^13*f^2 - 104*B*C*a*b^11*c^4*d^10*f^2 - 92*B*C*a^4*b^8*c^13*d*f^2 - 60*B*C*a^8*b^4*c*d^13*f^2 - 60*B*C*a^6*b
^6*c*d^13*f^2 + 48*B*C*a^11*b*c^2*d^12*f^2 - 40*B*C*a^2*b^10*c*d^13*f^2 - 28*B*C*a^2*b^10*c^13*d*f^2 - 24*B*C*
a*b^11*c^12*d^2*f^2 + 20*B*C*a^10*b^2*c*d^13*f^2 - 16*B*C*a*b^11*c^2*d^12*f^2 + 12*B*C*a^6*b^6*c^13*d*f^2 + 91
2*A*C*a*b^11*c^7*d^7*f^2 + 808*A*C*a*b^11*c^5*d^9*f^2 + 432*A*C*a^11*b*c^5*d^9*f^2 + 336*A*C*a*b^11*c^3*d^11*f
^2 + 224*A*C*a*b^11*c^11*d^3*f^2 - 112*A*C*a^11*b*c^3*d^11*f^2 + 112*A*C*a^3*b^9*c*d^13*f^2 - 88*A*C*a^9*b^3*c
*d^13*f^2 + 80*A*C*a^3*b^9*c^13*d*f^2 + 56*A*C*a^5*b^7*c*d^13*f^2 + 48*A*C*a*b^11*c^9*d^5*f^2 - 40*A*C*a^5*b^7
*c^13*d*f^2 - 16*A*C*a^11*b*c^7*d^7*f^2 + 16*A*C*a^7*b^5*c*d^13*f^2 - 496*A*B*a*b^11*c^4*d^10*f^2 - 400*A*B*a^
11*b*c^4*d^10*f^2 + 288*A*B*a*b^11*c^8*d^6*f^2 - 288*A*B*a*b^11*c^6*d^8*f^2 - 272*A*B*a*b^11*c^2*d^12*f^2 + 24
0*A*B*a^6*b^6*c*d^13*f^2 - 224*A*B*a*b^11*c^10*d^4*f^2 + 192*A*B*a^8*b^4*c*d^13*f^2 + 192*A*B*a^4*b^8*c*d^13*f
^2 + 176*A*B*a^11*b*c^6*d^8*f^2 + 104*A*B*a^4*b^8*c^13*d*f^2 - 48*A*B*a^11*b*c^2*d^12*f^2 + 16*A*B*a^10*b^2*c*
d^13*f^2 + 16*A*B*a^2*b^10*c^13*d*f^2 + 16*A*B*a^2*b^10*c*d^13*f^2 - 112*B*C*b^12*c^11*d^3*f^2 + 4*B*C*b^12*c^
5*d^9*f^2 + 150*A*C*b^12*c^10*d^4*f^2 - 80*B*C*a^12*c^3*d^11*f^2 + 66*A*C*b^12*c^8*d^6*f^2 - 30*A*C*b^12*c^12*
d^2*f^2 + 24*B*C*a^12*c^5*d^9*f^2 - 12*A*C*b^12*c^4*d^10*f^2 - 576*A*B*b^12*c^7*d^7*f^2 - 432*A*B*b^12*c^9*d^5
*f^2 - 400*A*B*b^12*c^5*d^9*f^2 - 144*A*B*b^12*c^3*d^11*f^2 - 96*B*C*a^7*b^5*d^14*f^2 - 72*B*C*a^5*b^7*d^14*f^
2 - 66*A*C*a^12*c^4*d^10*f^2 + 54*A*C*a^12*c^2*d^12*f^2 - 32*A*B*b^12*c^11*d^3*f^2 - 24*B*C*a^9*b^3*d^14*f^2 -
16*B*C*a^3*b^9*d^14*f^2 + 2*A*C*a^12*c^6*d^8*f^2 + 116*A*C*a^6*b^6*d^14*f^2 + 100*A*C*a^4*b^8*d^14*f^2 + 80*A
*B*a^12*c^3*d^11*f^2 + 24*A*C*a^2*b^10*d^14*f^2 - 24*A*B*a^12*c^5*d^9*f^2 + 22*A*C*a^8*b^4*d^14*f^2 + 16*B*C*a
^3*b^9*c^14*f^2 + 8*A*C*a^10*b^2*d^14*f^2 - 192*A*B*a^5*b^7*d^14*f^2 - 176*A*B*a^3*b^9*d^14*f^2 - 48*A*B*a^7*b
^5*d^14*f^2 - 28*A*C*a^2*b^10*c^14*f^2 + 2*A*C*a^4*b^8*c^14*f^2 - 16*A*B*a^3*b^9*c^14*f^2 + 2508*C^2*a^6*b^6*c
^6*d^8*f^2 + 2376*C^2*a^5*b^7*c^9*d^5*f^2 + 2357*C^2*a^8*b^4*c^6*d^8*f^2 - 2048*C^2*a^7*b^5*c^5*d^9*f^2 + 1304
*C^2*a^3*b^9*c^9*d^5*f^2 + 1303*C^2*a^8*b^4*c^4*d^10*f^2 + 1212*C^2*a^6*b^6*c^4*d^10*f^2 - 1203*C^2*a^4*b^8*c^
8*d^6*f^2 - 1192*C^2*a^9*b^3*c^5*d^9*f^2 + 1062*C^2*a^4*b^8*c^6*d^8*f^2 + 984*C^2*a^7*b^5*c^9*d^5*f^2 - 952*C^
2*a^6*b^6*c^8*d^6*f^2 + 768*C^2*a^5*b^7*c^7*d^7*f^2 - 681*C^2*a^4*b^8*c^10*d^4*f^2 - 672*C^2*a^5*b^7*c^5*d^9*f
^2 - 480*C^2*a^6*b^6*c^10*d^4*f^2 + 458*C^2*a^10*b^2*c^6*d^8*f^2 - 448*C^2*a^7*b^5*c^7*d^7*f^2 + 422*C^2*a^4*b
^8*c^4*d^10*f^2 + 372*C^2*a^2*b^10*c^6*d^8*f^2 + 360*C^2*a^5*b^7*c^11*d^3*f^2 + 312*C^2*a^3*b^9*c^7*d^7*f^2 +
278*C^2*a^10*b^2*c^4*d^10*f^2 - 232*C^2*a^9*b^3*c^7*d^7*f^2 + 194*C^2*a^2*b^10*c^12*d^2*f^2 + 176*C^2*a^9*b^3*
c^9*d^5*f^2 + 152*C^2*a^5*b^7*c^3*d^11*f^2 + 124*C^2*a^2*b^10*c^4*d^10*f^2 - 120*C^2*a^7*b^5*c^3*d^11*f^2 - 11
4*C^2*a^10*b^2*c^2*d^12*f^2 - 102*C^2*a^2*b^10*c^8*d^6*f^2 + 101*C^2*a^4*b^8*c^12*d^2*f^2 + 100*C^2*a^6*b^6*c^
2*d^12*f^2 - 88*C^2*a^3*b^9*c^5*d^9*f^2 + 77*C^2*a^8*b^4*c^2*d^12*f^2 + 72*C^2*a^3*b^9*c^11*d^3*f^2 - 64*C^2*a
^10*b^2*c^8*d^6*f^2 + 64*C^2*a^3*b^9*c^3*d^11*f^2 - 58*C^2*a^2*b^10*c^10*d^4*f^2 + 56*C^2*a^7*b^5*c^11*d^3*f^2
+ 56*C^2*a^6*b^6*c^12*d^2*f^2 + 40*C^2*a^9*b^3*c^3*d^11*f^2 + 36*C^2*a^8*b^4*c^12*d^2*f^2 + 32*C^2*a^4*b^8*c^
2*d^12*f^2 + 26*C^2*a^8*b^4*c^10*d^4*f^2 + 16*C^2*a^2*b^10*c^2*d^12*f^2 + 2*C^2*a^8*b^4*c^8*d^6*f^2 + 2277*B^2
*a^4*b^8*c^8*d^6*f^2 + 2144*B^2*a^7*b^5*c^5*d^9*f^2 - 2112*B^2*a^5*b^7*c^9*d^5*f^2 + 2028*B^2*a^6*b^6*c^8*d^6*
f^2 - 1671*B^2*a^8*b^4*c^6*d^8*f^2 + 1275*B^2*a^4*b^8*c^10*d^4*f^2 + 1176*B^2*a^5*b^7*c^5*d^9*f^2 + 1096*B^2*a
^9*b^3*c^5*d^9*f^2 - 1044*B^2*a^6*b^6*c^6*d^8*f^2 + 984*B^2*a^6*b^6*c^10*d^4*f^2 - 968*B^2*a^3*b^9*c^9*d^5*f^2
- 888*B^2*a^7*b^5*c^9*d^5*f^2 + 672*B^2*a^7*b^5*c^7*d^7*f^2 + 664*B^2*a^3*b^9*c^5*d^9*f^2 - 649*B^2*a^8*b^4*c
^4*d^10*f^2 + 618*B^2*a^2*b^10*c^8*d^6*f^2 + 514*B^2*a^4*b^8*c^4*d^10*f^2 + 460*B^2*a^6*b^6*c^2*d^12*f^2 + 422
*B^2*a^8*b^4*c^8*d^6*f^2 + 406*B^2*a^2*b^10*c^10*d^4*f^2 - 382*B^2*a^10*b^2*c^6*d^8*f^2 + 368*B^2*a^4*b^8*c^2*
d^12*f^2 - 312*B^2*a^5*b^7*c^11*d^3*f^2 + 312*B^2*a^3*b^9*c^7*d^7*f^2 + 248*B^2*a^9*b^3*c^7*d^7*f^2 + 245*B^2*
a^8*b^4*c^2*d^12*f^2 - 192*B^2*a^5*b^7*c^7*d^7*f^2 - 184*B^2*a^9*b^3*c^3*d^11*f^2 + 182*B^2*a^10*b^2*c^2*d^12*
f^2 + 176*B^2*a^3*b^9*c^3*d^11*f^2 + 174*B^2*a^4*b^8*c^6*d^8*f^2 - 170*B^2*a^10*b^2*c^4*d^10*f^2 - 152*B^2*a^9
*b^3*c^9*d^5*f^2 + 152*B^2*a^2*b^10*c^4*d^10*f^2 + 142*B^2*a^8*b^4*c^10*d^4*f^2 - 90*B^2*a^2*b^10*c^12*d^2*f^2
+ 88*B^2*a^2*b^10*c^2*d^12*f^2 + 84*B^2*a^10*b^2*c^8*d^6*f^2 + 84*B^2*a^2*b^10*c^6*d^8*f^2 + 60*B^2*a^6*b^6*c
^12*d^2*f^2 - 56*B^2*a^7*b^5*c^11*d^3*f^2 + 53*B^2*a^4*b^8*c^12*d^2*f^2 + 24*B^2*a^7*b^5*c^3*d^11*f^2 + 24*B^2
*a^6*b^6*c^4*d^10*f^2 + 24*B^2*a^3*b^9*c^11*d^3*f^2 - 8*B^2*a^5*b^7*c^3*d^11*f^2 + 4566*A^2*a^4*b^8*c^6*d^8*f^
2 + 4284*A^2*a^6*b^6*c^6*d^8*f^2 - 3776*A^2*a^7*b^5*c^5*d^9*f^2 - 3624*A^2*a^5*b^7*c^5*d^9*f^2 + 3122*A^2*a^4*
b^8*c^4*d^10*f^2 + 3108*A^2*a^2*b^10*c^6*d^8*f^2 + 2741*A^2*a^8*b^4*c^6*d^8*f^2 + 2592*A^2*a^6*b^6*c^4*d^10*f^
2 - 2536*A^2*a^3*b^9*c^5*d^9*f^2 + 2224*A^2*a^2*b^10*c^4*d^10*f^2 - 2184*A^2*a^3*b^9*c^7*d^7*f^2 - 2016*A^2*a^
5*b^7*c^7*d^7*f^2 - 1984*A^2*a^7*b^5*c^7*d^7*f^2 + 1626*A^2*a^2*b^10*c^8*d^6*f^2 - 1624*A^2*a^9*b^3*c^5*d^9*f^
2 + 1603*A^2*a^8*b^4*c^4*d^10*f^2 + 1296*A^2*a^5*b^7*c^9*d^5*f^2 - 1144*A^2*a^5*b^7*c^3*d^11*f^2 - 992*A^2*a^3
*b^9*c^3*d^11*f^2 + 968*A^2*a^4*b^8*c^2*d^12*f^2 - 888*A^2*a^7*b^5*c^3*d^11*f^2 + 849*A^2*a^4*b^8*c^8*d^6*f^2
+ 808*A^2*a^2*b^10*c^2*d^12*f^2 - 616*A^2*a^9*b^3*c^7*d^7*f^2 + 554*A^2*a^10*b^2*c^6*d^8*f^2 + 504*A^2*a^7*b^5
*c^9*d^5*f^2 - 504*A^2*a^6*b^6*c^10*d^4*f^2 + 460*A^2*a^6*b^6*c^2*d^12*f^2 + 350*A^2*a^10*b^2*c^4*d^10*f^2 + 3
50*A^2*a^2*b^10*c^10*d^4*f^2 - 321*A^2*a^4*b^8*c^10*d^4*f^2 + 216*A^2*a^5*b^7*c^11*d^3*f^2 - 216*A^2*a^3*b^9*c
^11*d^3*f^2 + 182*A^2*a^2*b^10*c^12*d^2*f^2 - 152*A^2*a^9*b^3*c^3*d^11*f^2 - 124*A^2*a^6*b^6*c^8*d^6*f^2 - 114
*A^2*a^10*b^2*c^2*d^12*f^2 + 104*A^2*a^3*b^9*c^9*d^5*f^2 + 77*A^2*a^8*b^4*c^2*d^12*f^2 + 74*A^2*a^8*b^4*c^8*d^
6*f^2 - 70*A^2*a^8*b^4*c^10*d^4*f^2 + 56*A^2*a^9*b^3*c^9*d^5*f^2 + 56*A^2*a^7*b^5*c^11*d^3*f^2 + 41*A^2*a^4*b^
8*c^12*d^2*f^2 - 28*A^2*a^10*b^2*c^8*d^6*f^2 - 28*A^2*a^6*b^6*c^12*d^2*f^2 + 12*B*C*b^12*c^13*d*f^2 + 24*B*C*a
^12*c*d^13*f^2 - 24*A*B*b^12*c^13*d*f^2 - 24*A*B*b^12*c*d^13*f^2 - 16*B*C*a^11*b*d^14*f^2 - 24*A*B*a^12*c*d^13
*f^2 - 16*B*C*a*b^11*c^14*f^2 - 48*A*B*a*b^11*d^14*f^2 + 16*A*B*a^11*b*d^14*f^2 + 16*A*B*a*b^11*c^14*f^2 - 216
*C^2*a^11*b*c^5*d^9*f^2 + 216*C^2*a*b^11*c^9*d^5*f^2 + 56*C^2*a^11*b*c^3*d^11*f^2 + 56*C^2*a^9*b^3*c*d^13*f^2
+ 56*C^2*a^5*b^7*c*d^13*f^2 + 40*C^2*a^7*b^5*c*d^13*f^2 - 40*C^2*a*b^11*c^11*d^3*f^2 + 32*C^2*a^5*b^7*c^13*d*f
^2 - 24*C^2*a*b^11*c^7*d^7*f^2 - 16*C^2*a^3*b^9*c^13*d*f^2 + 16*C^2*a^3*b^9*c*d^13*f^2 + 8*C^2*a^11*b*c^7*d^7*
f^2 - 8*C^2*a*b^11*c^5*d^9*f^2 + 264*B^2*a*b^11*c^7*d^7*f^2 + 224*B^2*a*b^11*c^5*d^9*f^2 + 168*B^2*a^11*b*c^5*
d^9*f^2 - 112*B^2*a^9*b^3*c*d^13*f^2 - 104*B^2*a^11*b*c^3*d^11*f^2 - 104*B^2*a^7*b^5*c*d^13*f^2 + 96*B^2*a*b^1
1*c^3*d^11*f^2 + 88*B^2*a*b^11*c^11*d^3*f^2 - 72*B^2*a*b^11*c^9*d^5*f^2 - 64*B^2*a^5*b^7*c*d^13*f^2 + 32*B^2*a
^3*b^9*c^13*d*f^2 - 24*B^2*a^11*b*c^7*d^7*f^2 - 24*B^2*a^5*b^7*c^13*d*f^2 + 16*B^2*a^3*b^9*c*d^13*f^2 - 888*A^
2*a*b^11*c^7*d^7*f^2 - 800*A^2*a*b^11*c^5*d^9*f^2 - 336*A^2*a*b^11*c^3*d^11*f^2 - 264*A^2*a*b^11*c^9*d^5*f^2 -
216*A^2*a^11*b*c^5*d^9*f^2 - 184*A^2*a*b^11*c^11*d^3*f^2 - 128*A^2*a^3*b^9*c*d^13*f^2 - 112*A^2*a^5*b^7*c*d^1
3*f^2 - 64*A^2*a^3*b^9*c^13*d*f^2 + 56*A^2*a^11*b*c^3*d^11*f^2 - 56*A^2*a^7*b^5*c*d^13*f^2 + 32*A^2*a^9*b^3*c*
d^13*f^2 + 8*A^2*a^11*b*c^7*d^7*f^2 + 8*A^2*a^5*b^7*c^13*d*f^2 + 24*C^2*a^11*b*c*d^13*f^2 - 16*C^2*a*b^11*c^13
*d*f^2 - 40*B^2*a^11*b*c*d^13*f^2 + 24*B^2*a*b^11*c^13*d*f^2 + 16*B^2*a*b^11*c*d^13*f^2 - 48*A^2*a*b^11*c*d^13
*f^2 - 40*A^2*a*b^11*c^13*d*f^2 + 24*A^2*a^11*b*c*d^13*f^2 - 6*A*C*a^12*d^14*f^2 + 2*A*C*b^12*c^14*f^2 + 33*C^
2*b^12*c^12*d^2*f^2 - 27*C^2*b^12*c^10*d^4*f^2 + 3*C^2*b^12*c^8*d^6*f^2 + 117*B^2*b^12*c^10*d^4*f^2 + 111*B^2*
b^12*c^8*d^6*f^2 + 72*B^2*b^12*c^6*d^8*f^2 + 33*C^2*a^12*c^4*d^10*f^2 - 27*C^2*a^12*c^2*d^12*f^2 + 24*B^2*b^12
*c^4*d^10*f^2 + 4*B^2*b^12*c^2*d^12*f^2 - 3*B^2*b^12*c^12*d^2*f^2 - C^2*a^12*c^6*d^8*f^2 + 720*A^2*b^12*c^6*d^
8*f^2 + 552*A^2*b^12*c^4*d^10*f^2 + 471*A^2*b^12*c^8*d^6*f^2 + 216*A^2*b^12*c^2*d^12*f^2 + 93*A^2*b^12*c^10*d^
4*f^2 + 33*B^2*a^12*c^2*d^12*f^2 + 33*A^2*b^12*c^12*d^2*f^2 + 31*C^2*a^8*b^4*d^14*f^2 - 27*B^2*a^12*c^4*d^10*f
^2 + 20*C^2*a^6*b^6*d^14*f^2 + 4*C^2*a^4*b^8*d^14*f^2 + 3*B^2*a^12*c^6*d^8*f^2 + 2*C^2*a^10*b^2*d^14*f^2 + 80*
B^2*a^6*b^6*d^14*f^2 + 64*B^2*a^4*b^8*d^14*f^2 + 33*A^2*a^12*c^4*d^10*f^2 + 31*B^2*a^8*b^4*d^14*f^2 - 27*A^2*a
^12*c^2*d^12*f^2 + 16*B^2*a^2*b^10*d^14*f^2 + 14*C^2*a^2*b^10*c^14*f^2 + 14*B^2*a^10*b^2*d^14*f^2 - C^2*a^4*b^
8*c^14*f^2 - A^2*a^12*c^6*d^8*f^2 + 120*A^2*a^2*b^10*d^14*f^2 + 112*A^2*a^4*b^8*d^14*f^2 - 17*A^2*a^8*b^4*d^14
*f^2 - 10*B^2*a^2*b^10*c^14*f^2 - 10*A^2*a^10*b^2*d^14*f^2 + 8*A^2*a^6*b^6*d^14*f^2 + 3*B^2*a^4*b^8*c^14*f^2 +
14*A^2*a^2*b^10*c^14*f^2 - A^2*a^4*b^8*c^14*f^2 + 3*C^2*a^12*d^14*f^2 - C^2*b^12*c^14*f^2 + 36*A^2*b^12*d^14*
f^2 + 3*B^2*b^12*c^14*f^2 - B^2*a^12*d^14*f^2 + 3*A^2*a^12*d^14*f^2 - A^2*b^12*c^14*f^2 - 44*A*B*C*a*b^9*c^10*
d*f + 3816*A*B*C*a^5*b^5*c^4*d^7*f + 2920*A*B*C*a^2*b^8*c^5*d^6*f - 2736*A*B*C*a^3*b^7*c^6*d^5*f - 2672*A*B*C*
a^4*b^6*c^3*d^8*f + 1996*A*B*C*a^4*b^6*c^7*d^4*f - 1412*A*B*C*a^6*b^4*c^5*d^6*f + 1120*A*B*C*a^3*b^7*c^2*d^9*f
+ 1080*A*B*C*a^2*b^8*c^7*d^4*f + 1040*A*B*C*a^5*b^5*c^2*d^9*f + 684*A*B*C*a^4*b^6*c^5*d^6*f + 592*A*B*C*a^3*b
^7*c^4*d^7*f - 560*A*B*C*a^7*b^3*c^2*d^9*f - 448*A*B*C*a^2*b^8*c^3*d^8*f - 400*A*B*C*a^5*b^5*c^8*d^3*f - 398*A
*B*C*a^2*b^8*c^9*d^2*f - 312*A*B*C*a^6*b^4*c^3*d^8*f + 166*A*B*C*a^8*b^2*c^3*d^8*f + 136*A*B*C*a^5*b^5*c^6*d^5
*f + 128*A*B*C*a^7*b^3*c^6*d^5*f - 100*A*B*C*a^6*b^4*c^7*d^4*f + 64*A*B*C*a^7*b^3*c^4*d^7*f - 64*A*B*C*a^4*b^6
*c^9*d^2*f - 32*A*B*C*a^3*b^7*c^8*d^3*f - 16*A*B*C*a^8*b^2*c^5*d^6*f - 1312*A*B*C*a*b^9*c^4*d^7*f + 996*A*B*C*
a*b^9*c^8*d^3*f + 728*A*B*C*a^6*b^4*c*d^10*f - 624*A*B*C*a*b^9*c^6*d^5*f - 584*A*B*C*a^2*b^8*c*d^10*f - 512*A*
B*C*a^4*b^6*c*d^10*f - 320*A*B*C*a*b^9*c^2*d^9*f - 98*A*B*C*a^8*b^2*c*d^10*f + 36*A*B*C*a^9*b*c^2*d^9*f + 32*A
*B*C*a^3*b^7*c^10*d*f - 16*A*B*C*a^9*b*c^4*d^7*f + 46*B*C^2*a*b^9*c^10*d*f - 16*B^2*C*a*b^9*c*d^10*f - 2*B^2*C
*a^9*b*c*d^10*f + 312*A^2*C*a*b^9*c*d^10*f - 48*A*C^2*a*b^9*c*d^10*f - 6*A^2*C*a^9*b*c*d^10*f + 6*A*C^2*a^9*b*
c*d^10*f + 208*A*B^2*a*b^9*c*d^10*f - 2*A^2*B*a*b^9*c^10*d*f + 2*A*B^2*a^9*b*c*d^10*f - 480*A*B*C*b^10*c^7*d^4
*f + 78*A*B*C*b^10*c^9*d^2*f - 64*A*B*C*b^10*c^5*d^6*f + 2*A*B*C*a^10*c^3*d^8*f - 224*A*B*C*a^5*b^5*d^11*f + 8
0*A*B*C*a^7*b^3*d^11*f - 32*A*B*C*a^3*b^7*d^11*f + 2*A*B*C*a^2*b^8*c^11*f - 1692*B*C^2*a^5*b^5*c^4*d^7*f - 150
0*B^2*C*a^5*b^5*c^5*d^6*f - 1464*B^2*C*a^3*b^7*c^5*d^6*f + 1426*B*C^2*a^6*b^4*c^5*d^6*f - 1158*B^2*C*a^6*b^4*c
^4*d^7*f + 1152*B*C^2*a^3*b^7*c^6*d^5*f + 1026*B^2*C*a^4*b^6*c^6*d^5*f - 974*B*C^2*a^4*b^6*c^7*d^4*f + 960*B^2
*C*a^5*b^5*c^3*d^8*f - 884*B*C^2*a^2*b^8*c^5*d^6*f - 764*B^2*C*a^5*b^5*c^7*d^4*f + 752*B^2*C*a^2*b^8*c^4*d^7*f
- 752*B*C^2*a^3*b^7*c^4*d^7*f + 738*B^2*C*a^4*b^6*c^4*d^7*f - 688*B^2*C*a^6*b^4*c^2*d^9*f - 675*B^2*C*a^2*b^8
*c^8*d^3*f + 560*B*C^2*a^5*b^5*c^8*d^3*f + 496*B*C^2*a^7*b^3*c^2*d^9*f + 496*B*C^2*a^4*b^6*c^3*d^8*f - 468*B*C
^2*a^2*b^8*c^7*d^4*f + 456*B^2*C*a^7*b^3*c^3*d^8*f - 452*B^2*C*a^4*b^6*c^8*d^3*f - 416*B*C^2*a^3*b^7*c^2*d^9*f
+ 378*B*C^2*a^4*b^6*c^5*d^6*f + 376*B*C^2*a^3*b^7*c^8*d^3*f - 360*B^2*C*a^2*b^8*c^6*d^5*f + 355*B*C^2*a^2*b^8
*c^9*d^2*f + 346*B^2*C*a^6*b^4*c^6*d^5*f - 320*B^2*C*a^4*b^6*c^2*d^9*f + 268*B^2*C*a^2*b^8*c^2*d^9*f + 216*B^2
*C*a^3*b^7*c^7*d^4*f - 203*B*C^2*a^8*b^2*c^3*d^8*f - 184*B*C^2*a^7*b^3*c^6*d^5*f + 170*B*C^2*a^6*b^4*c^7*d^4*f
+ 160*B^2*C*a^7*b^3*c^5*d^6*f - 160*B*C^2*a^5*b^5*c^2*d^9*f - 140*B^2*C*a^8*b^2*c^4*d^7*f - 136*B*C^2*a^2*b^8
*c^3*d^8*f + 112*B^2*C*a^3*b^7*c^9*d^2*f + 91*B^2*C*a^8*b^2*c^2*d^9*f + 88*B*C^2*a^7*b^3*c^4*d^7*f + 72*B^2*C*
a^6*b^4*c^8*d^3*f - 64*B^2*C*a^3*b^7*c^3*d^8*f - 60*B*C^2*a^6*b^4*c^3*d^8*f + 56*B*C^2*a^4*b^6*c^9*d^2*f + 52*
B*C^2*a^5*b^5*c^6*d^5*f - 48*B^2*C*a^7*b^3*c^7*d^4*f + 48*B^2*C*a^5*b^5*c^9*d^2*f + 44*B*C^2*a^8*b^2*c^5*d^6*f
- 36*B*C^2*a^6*b^4*c^9*d^2*f + 12*B^2*C*a^8*b^2*c^6*d^5*f - 2958*A^2*C*a^4*b^6*c^4*d^7*f - 1932*A^2*C*a^2*b^8
*c^4*d^7*f + 1848*A^2*C*a^3*b^7*c^5*d^6*f + 1728*A^2*C*a^3*b^7*c^3*d^8*f + 1524*A^2*C*a^5*b^5*c^5*d^6*f + 1374
*A*C^2*a^4*b^6*c^4*d^7*f - 1272*A*C^2*a^3*b^7*c^5*d^6*f - 1236*A*C^2*a^5*b^5*c^5*d^6*f + 1116*A*C^2*a^2*b^8*c^
4*d^7*f - 1110*A^2*C*a^4*b^6*c^6*d^5*f + 1038*A*C^2*a^4*b^6*c^6*d^5*f - 768*A^2*C*a^2*b^8*c^2*d^9*f - 696*A^2*
C*a^3*b^7*c^7*d^4*f - 666*A*C^2*a^6*b^4*c^4*d^7*f + 564*A^2*C*a^2*b^8*c^6*d^5*f - 564*A*C^2*a^5*b^5*c^7*d^4*f
- 555*A*C^2*a^2*b^8*c^8*d^3*f + 519*A^2*C*a^2*b^8*c^8*d^3*f - 480*A*C^2*a^3*b^7*c^3*d^8*f + 456*A*C^2*a^5*b^5*
c^3*d^8*f - 420*A*C^2*a^6*b^4*c^2*d^9*f + 408*A*C^2*a^3*b^7*c^7*d^4*f + 408*A*C^2*a^2*b^8*c^2*d^9*f + 348*A^2*
C*a^6*b^4*c^2*d^9*f - 348*A*C^2*a^2*b^8*c^6*d^5*f + 342*A*C^2*a^6*b^4*c^6*d^5*f - 336*A*C^2*a^4*b^6*c^8*d^3*f
+ 324*A^2*C*a^5*b^5*c^7*d^4*f - 312*A^2*C*a^4*b^6*c^2*d^9*f + 264*A^2*C*a^4*b^6*c^8*d^3*f + 240*A*C^2*a^7*b^3*
c^5*d^6*f + 195*A*C^2*a^8*b^2*c^2*d^9*f - 174*A^2*C*a^6*b^4*c^6*d^5*f + 144*A*C^2*a^3*b^7*c^9*d^2*f - 123*A^2*
C*a^8*b^2*c^2*d^9*f + 120*A*C^2*a^7*b^3*c^3*d^8*f + 108*A*C^2*a^6*b^4*c^8*d^3*f - 102*A^2*C*a^6*b^4*c^4*d^7*f
- 96*A^2*C*a^8*b^2*c^4*d^7*f + 72*A^2*C*a^7*b^3*c^3*d^8*f + 72*A*C^2*a^5*b^5*c^9*d^2*f + 48*A^2*C*a^7*b^3*c^5*
d^6*f - 48*A^2*C*a^3*b^7*c^9*d^2*f - 48*A*C^2*a^4*b^6*c^2*d^9*f - 24*A^2*C*a^5*b^5*c^3*d^8*f - 12*A*C^2*a^8*b^
2*c^4*d^7*f + 2736*A^2*B*a^3*b^7*c^6*d^5*f + 2464*A^2*B*a^4*b^6*c^3*d^8*f - 2298*A*B^2*a^4*b^6*c^4*d^7*f - 225
2*A^2*B*a^2*b^8*c^5*d^6*f - 1692*A^2*B*a^5*b^5*c^4*d^7*f - 1592*A*B^2*a^2*b^8*c^4*d^7*f - 1338*A*B^2*a^4*b^6*c
^6*d^5*f + 1320*A*B^2*a^3*b^7*c^5*d^6*f + 1212*A*B^2*a^5*b^5*c^5*d^6*f - 1056*A*B^2*a^5*b^5*c^3*d^8*f + 1024*A
^2*B*a^3*b^7*c^4*d^7*f - 1022*A^2*B*a^4*b^6*c^7*d^4*f - 880*A^2*B*a^5*b^5*c^2*d^9*f - 846*A^2*B*a^4*b^6*c^5*d^
6*f - 840*A*B^2*a^3*b^7*c^7*d^4*f + 760*A*B^2*a^6*b^4*c^2*d^9*f - 704*A^2*B*a^3*b^7*c^2*d^9*f + 688*A*B^2*a^3*
b^7*c^3*d^8*f + 660*A^2*B*a^6*b^4*c^3*d^8*f - 612*A^2*B*a^2*b^8*c^7*d^4*f + 462*A*B^2*a^6*b^4*c^4*d^7*f + 459*
A*B^2*a^2*b^8*c^8*d^3*f - 412*A*B^2*a^2*b^8*c^2*d^9*f - 408*A*B^2*a^7*b^3*c^3*d^8*f + 388*A^2*B*a^5*b^5*c^6*d^
5*f + 296*A^2*B*a^2*b^8*c^3*d^8*f + 288*A*B^2*a^2*b^8*c^6*d^5*f + 284*A*B^2*a^5*b^5*c^7*d^4*f + 236*A*B^2*a^4*
b^6*c^8*d^3*f - 226*A*B^2*a^6*b^4*c^6*d^5*f + 212*A*B^2*a^4*b^6*c^2*d^9*f + 202*A^2*B*a^6*b^4*c^5*d^6*f - 152*
A^2*B*a^7*b^3*c^4*d^7*f + 88*A^2*B*a^3*b^7*c^8*d^3*f + 79*A^2*B*a^2*b^8*c^9*d^2*f - 70*A^2*B*a^6*b^4*c^7*d^4*f
+ 68*A*B^2*a^8*b^2*c^4*d^7*f + 64*A^2*B*a^7*b^3*c^2*d^9*f - 64*A*B^2*a^3*b^7*c^9*d^2*f + 56*A^2*B*a^7*b^3*c^6
*d^5*f + 56*A^2*B*a^5*b^5*c^8*d^3*f + 37*A^2*B*a^8*b^2*c^3*d^8*f - 28*A^2*B*a^8*b^2*c^5*d^6*f - 28*A^2*B*a^4*b
^6*c^9*d^2*f + 17*A*B^2*a^8*b^2*c^2*d^9*f - 16*A*B^2*a^7*b^3*c^5*d^6*f + 24*A*B*C*b^10*c*d^10*f - 6*A*B*C*a^10
*c*d^10*f + 48*A*B*C*a*b^9*d^11*f + 4*A*B*C*a^9*b*d^11*f + 432*B^2*C*a*b^9*c^7*d^4*f - 376*B*C^2*a^6*b^4*c*d^1
0*f - 354*B*C^2*a*b^9*c^8*d^3*f + 352*B^2*C*a^5*b^5*c*d^10*f + 320*B^2*C*a*b^9*c^5*d^6*f + 256*B^2*C*a^3*b^7*c
*d^10*f - 232*B^2*C*a^7*b^3*c*d^10*f - 210*B^2*C*a*b^9*c^9*d^2*f - 152*B*C^2*a^4*b^6*c*d^10*f + 85*B*C^2*a^8*b
^2*c*d^10*f + 72*B^2*C*a*b^9*c^3*d^8*f - 48*B*C^2*a*b^9*c^6*d^5*f - 40*B*C^2*a^3*b^7*c^10*d*f + 40*B*C^2*a^2*b
^8*c*d^10*f + 37*B^2*C*a^2*b^8*c^10*d*f + 22*B^2*C*a^9*b*c^3*d^8*f - 18*B*C^2*a^9*b*c^2*d^9*f + 16*B*C^2*a*b^9
*c^2*d^9*f - 12*B^2*C*a^4*b^6*c^10*d*f + 8*B*C^2*a^9*b*c^4*d^7*f + 8*B*C^2*a*b^9*c^4*d^7*f - 984*A^2*C*a*b^9*c
^7*d^4*f + 672*A^2*C*a*b^9*c^3*d^8*f + 552*A*C^2*a*b^9*c^7*d^4*f - 504*A^2*C*a^5*b^5*c*d^10*f - 408*A^2*C*a*b^
9*c^5*d^6*f + 408*A*C^2*a*b^9*c^5*d^6*f + 336*A*C^2*a^5*b^5*c*d^10*f - 216*A*C^2*a^7*b^3*c*d^10*f + 192*A*C^2*
a^3*b^7*c*d^10*f - 162*A*C^2*a*b^9*c^9*d^2*f + 120*A^2*C*a^7*b^3*c*d^10*f + 96*A^2*C*a^3*b^7*c*d^10*f + 90*A^2
*C*a*b^9*c^9*d^2*f + 66*A^2*C*a^9*b*c^3*d^8*f - 66*A*C^2*a^9*b*c^3*d^8*f + 57*A*C^2*a^2*b^8*c^10*d*f - 48*A*C^
2*a*b^9*c^3*d^8*f - 9*A^2*C*a^2*b^8*c^10*d*f + 1736*A^2*B*a*b^9*c^4*d^7*f + 1248*A^2*B*a*b^9*c^6*d^5*f - 1008*
A*B^2*a*b^9*c^7*d^4*f + 772*A^2*B*a^4*b^6*c*d^10*f - 688*A*B^2*a^5*b^5*c*d^10*f - 608*A*B^2*a*b^9*c^5*d^6*f +
436*A^2*B*a^2*b^8*c*d^10*f - 426*A^2*B*a*b^9*c^8*d^3*f + 312*A*B^2*a*b^9*c^3*d^8*f + 304*A^2*B*a*b^9*c^2*d^9*f
- 244*A^2*B*a^6*b^4*c*d^10*f - 160*A*B^2*a^3*b^7*c*d^10*f + 114*A*B^2*a*b^9*c^9*d^2*f + 88*A*B^2*a^7*b^3*c*d^
10*f - 22*A*B^2*a^9*b*c^3*d^8*f - 18*A^2*B*a^9*b*c^2*d^9*f + 13*A^2*B*a^8*b^2*c*d^10*f - 13*A*B^2*a^2*b^8*c^10
*d*f + 8*A^2*B*a^9*b*c^4*d^7*f + 8*A^2*B*a^3*b^7*c^10*d*f + 111*B^2*C*b^10*c^8*d^3*f - 39*B*C^2*b^10*c^9*d^2*f
+ 24*B*C^2*b^10*c^7*d^4*f - 4*B^2*C*b^10*c^2*d^9*f - 4*B*C^2*b^10*c^5*d^6*f + 432*A^2*C*b^10*c^6*d^5*f + 192*
A^2*C*b^10*c^4*d^7*f - 111*A^2*C*b^10*c^8*d^3*f + 111*A*C^2*b^10*c^8*d^3*f - 72*A*C^2*b^10*c^6*d^5*f + 12*A*C^
2*b^10*c^4*d^7*f - 3*B^2*C*a^10*c^2*d^9*f - B*C^2*a^10*c^3*d^8*f + 456*A^2*B*b^10*c^7*d^4*f - 288*A^2*B*b^10*c
^3*d^8*f + 252*A*B^2*b^10*c^6*d^5*f + 192*A*B^2*b^10*c^4*d^7*f - 183*A*B^2*b^10*c^8*d^3*f - 148*A^2*B*b^10*c^5
*d^6*f + 112*B^2*C*a^6*b^4*d^11*f + 76*A*B^2*b^10*c^2*d^9*f - 64*B*C^2*a^7*b^3*d^11*f + 16*B^2*C*a^4*b^6*d^11*
f - 16*B^2*C*a^2*b^8*d^11*f + 16*B*C^2*a^5*b^5*d^11*f + 16*B*C^2*a^3*b^7*d^11*f - 9*A^2*C*a^10*c^2*d^9*f + 9*A
*C^2*a^10*c^2*d^9*f - 3*A^2*B*b^10*c^9*d^2*f - B^2*C*a^8*b^2*d^11*f + 96*A^2*C*a^4*b^6*d^11*f - 84*A^2*C*a^6*b
^4*d^11*f + 72*A*C^2*a^6*b^4*d^11*f - 24*A*C^2*a^4*b^6*d^11*f - 24*A*C^2*a^2*b^8*d^11*f - 21*A*C^2*a^8*b^2*d^1
1*f + 12*A^2*C*a^2*b^8*d^11*f + 9*A^2*C*a^8*b^2*d^11*f + 3*A*B^2*a^10*c^2*d^9*f - A^2*B*a^10*c^3*d^8*f - B*C^2
*a^2*b^8*c^11*f + 176*A*B^2*a^4*b^6*d^11*f + 136*A^2*B*a^5*b^5*d^11*f - 128*A^2*B*a^3*b^7*d^11*f + 112*A*B^2*a
^2*b^8*d^11*f - 64*A*B^2*a^6*b^4*d^11*f - 16*A^2*B*a^7*b^3*d^11*f - A^2*B*a^2*b^8*c^11*f - 2*C^3*a^9*b*c*d^10*
f - 2*B^3*a*b^9*c^10*d*f - 264*A^3*a*b^9*c*d^10*f + 2*A^3*a^9*b*c*d^10*f - 9*B^2*C*b^10*c^10*d*f + 9*A^2*C*b^1
0*c^10*d*f - 9*A*C^2*b^10*c^10*d*f + 3*B*C^2*a^10*c*d^10*f - 132*A^2*B*b^10*c*d^10*f - 3*A*B^2*b^10*c^10*d*f -
2*B*C^2*a^9*b*d^11*f + 3*A^2*B*a^10*c*d^10*f - 2*B^2*C*a*b^9*c^11*f - 120*A^2*B*a*b^9*d^11*f - 6*A^2*C*a*b^9*
c^11*f + 6*A*C^2*a*b^9*c^11*f - 2*A^2*B*a^9*b*d^11*f + 2*A*B^2*a*b^9*c^11*f + 520*C^3*a^3*b^7*c^5*d^6*f + 460*
C^3*a^5*b^5*c^5*d^6*f - 418*C^3*a^4*b^6*c^6*d^5*f + 406*C^3*a^6*b^4*c^4*d^7*f + 268*C^3*a^5*b^5*c^7*d^4*f - 26
6*C^3*a^6*b^4*c^6*d^5*f + 233*C^3*a^2*b^8*c^8*d^3*f - 176*C^3*a^7*b^3*c^5*d^6*f + 164*C^3*a^6*b^4*c^2*d^9*f +
140*C^3*a^2*b^8*c^6*d^5*f + 136*C^3*a^4*b^6*c^2*d^9*f - 128*C^3*a^3*b^7*c^9*d^2*f + 128*C^3*a^3*b^7*c^3*d^8*f
- 108*C^3*a^6*b^4*c^8*d^3*f - 104*C^3*a^7*b^3*c^3*d^8*f - 104*C^3*a^5*b^5*c^3*d^8*f + 100*C^3*a^4*b^6*c^8*d^3*
f - 89*C^3*a^8*b^2*c^2*d^9*f - 72*C^3*a^5*b^5*c^9*d^2*f + 40*C^3*a^8*b^2*c^4*d^7*f - 40*C^3*a^3*b^7*c^7*d^4*f
- 28*C^3*a^2*b^8*c^4*d^7*f - 16*C^3*a^2*b^8*c^2*d^9*f - 2*C^3*a^4*b^6*c^4*d^7*f + 828*B^3*a^5*b^5*c^4*d^7*f +
408*B^3*a^2*b^8*c^5*d^6*f + 390*B^3*a^4*b^6*c^7*d^4*f - 372*B^3*a^4*b^6*c^3*d^8*f - 336*B^3*a^3*b^7*c^6*d^5*f
- 314*B^3*a^6*b^4*c^5*d^6*f + 288*B^3*a^3*b^7*c^4*d^7*f + 216*B^3*a^2*b^8*c^7*d^4*f - 176*B^3*a^7*b^3*c^2*d^9*
f + 128*B^3*a^3*b^7*c^2*d^9*f + 108*B^3*a^5*b^5*c^6*d^5*f + 88*B^3*a^7*b^3*c^4*d^7*f + 72*B^3*a^5*b^5*c^2*d^9*
f - 68*B^3*a^2*b^8*c^3*d^8*f - 65*B^3*a^2*b^8*c^9*d^2*f - 56*B^3*a^5*b^5*c^8*d^3*f + 40*B^3*a^7*b^3*c^6*d^5*f
+ 37*B^3*a^8*b^2*c^3*d^8*f + 30*B^3*a^4*b^6*c^5*d^6*f - 28*B^3*a^8*b^2*c^5*d^6*f + 24*B^3*a^3*b^7*c^8*d^3*f -
4*B^3*a^4*b^6*c^9*d^2*f - 2*B^3*a^6*b^4*c^7*d^4*f + 1586*A^3*a^4*b^6*c^4*d^7*f - 1376*A^3*a^3*b^7*c^3*d^8*f -
1096*A^3*a^3*b^7*c^5*d^6*f + 844*A^3*a^2*b^8*c^4*d^7*f - 748*A^3*a^5*b^5*c^5*d^6*f + 490*A^3*a^4*b^6*c^6*d^5*f
+ 376*A^3*a^2*b^8*c^2*d^9*f + 362*A^3*a^6*b^4*c^4*d^7*f - 356*A^3*a^2*b^8*c^6*d^5*f - 328*A^3*a^5*b^5*c^3*d^8
*f + 328*A^3*a^3*b^7*c^7*d^4*f + 224*A^3*a^4*b^6*c^2*d^9*f - 197*A^3*a^2*b^8*c^8*d^3*f - 112*A^3*a^7*b^3*c^5*d
^6*f + 98*A^3*a^6*b^4*c^6*d^5*f - 92*A^3*a^6*b^4*c^2*d^9*f - 88*A^3*a^7*b^3*c^3*d^8*f + 68*A^3*a^8*b^2*c^4*d^7
*f + 32*A^3*a^3*b^7*c^9*d^2*f - 28*A^3*a^5*b^5*c^7*d^4*f - 28*A^3*a^4*b^6*c^8*d^3*f + 17*A^3*a^8*b^2*c^2*d^9*f
+ 104*C^3*a^7*b^3*c*d^10*f + 54*C^3*a*b^9*c^9*d^2*f - 40*C^3*a*b^9*c^7*d^4*f - 35*C^3*a^2*b^8*c^10*d*f + 22*C
^3*a^9*b*c^3*d^8*f + 16*C^3*a^5*b^5*c*d^10*f - 16*C^3*a^3*b^7*c*d^10*f + 8*C^3*a*b^9*c^5*d^6*f - 2*A*B*C*b^10*
c^11*f + 198*B^3*a*b^9*c^8*d^3*f + 192*B^3*a^6*b^4*c*d^10*f - 128*B^3*a*b^9*c^4*d^7*f - 80*B^3*a^2*b^8*c*d^10*
f - 56*B^3*a*b^9*c^2*d^9*f - 24*B^3*a*b^9*c^6*d^5*f - 18*B^3*a^9*b*c^2*d^9*f - 16*B^3*a^4*b^6*c*d^10*f + 13*B^
3*a^8*b^2*c*d^10*f + 8*B^3*a^9*b*c^4*d^7*f + 8*B^3*a^3*b^7*c^10*d*f - 624*A^3*a*b^9*c^3*d^8*f + 472*A^3*a*b^9*
c^7*d^4*f - 272*A^3*a^3*b^7*c*d^10*f + 152*A^3*a^5*b^5*c*d^10*f - 22*A^3*a^9*b*c^3*d^8*f + 18*A^3*a*b^9*c^9*d^
2*f - 13*A^3*a^2*b^8*c^10*d*f - 8*A^3*a^7*b^3*c*d^10*f - 8*A^3*a*b^9*c^5*d^6*f + A*B^2*a^8*b^2*d^11*f - C^3*b^
10*c^8*d^3*f - 60*B^3*b^10*c^7*d^4*f - 32*B^3*b^10*c^5*d^6*f + 21*B^3*b^10*c^9*d^2*f - 12*B^3*b^10*c^3*d^8*f -
3*C^3*a^10*c^2*d^9*f - 360*A^3*b^10*c^6*d^5*f - 204*A^3*b^10*c^4*d^7*f + 11*C^3*a^8*b^2*d^11*f - 8*C^3*a^6*b^
4*d^11*f - 4*C^3*a^4*b^6*d^11*f - B^3*a^10*c^3*d^8*f - 64*B^3*a^5*b^5*d^11*f - 32*B^3*a^3*b^7*d^11*f + 3*A^3*a
^10*c^2*d^9*f - 68*A^3*a^4*b^6*d^11*f + 20*A^3*a^6*b^4*d^11*f + 12*A^3*a^2*b^8*d^11*f - B^3*a^2*b^8*c^11*f + 3
*C^3*b^10*c^10*d*f + 3*B^3*a^10*c*d^10*f - 3*A^3*b^10*c^10*d*f - 2*C^3*a*b^9*c^11*f - 2*B^3*a^9*b*d^11*f + 2*A
^3*a*b^9*c^11*f - 36*A^2*C*b^10*d^11*f + 3*A^2*C*a^10*d^11*f - 3*A*C^2*a^10*d^11*f - A*B^2*a^10*d^11*f + 36*A^
3*b^10*d^11*f - A^3*a^10*d^11*f + A^3*b^10*c^8*d^3*f + A^3*a^8*b^2*d^11*f + B^2*C*a^10*d^11*f + B*C^2*b^10*c^1
1*f + A^2*B*b^10*c^11*f + C^3*a^10*d^11*f + B^3*b^10*c^11*f - 6*A*B^2*C*a*b^7*c^7*d + 4*A*B^2*C*a*b^7*c*d^7 +
168*A^2*B*C*a^3*b^5*c^2*d^6 + 144*A*B*C^2*a^4*b^4*c^3*d^5 - 129*A^2*B*C*a^4*b^4*c^3*d^5 - 96*A*B*C^2*a^3*b^5*c
^2*d^6 + 84*A*B*C^2*a^2*b^6*c^3*d^5 + 72*A^2*B*C*a^3*b^5*c^4*d^4 - 72*A^2*B*C*a^2*b^6*c^3*d^5 + 64*A*B^2*C*a^4
*b^4*c^4*d^4 - 60*A*B*C^2*a^3*b^5*c^4*d^4 + 57*A^2*B*C*a^2*b^6*c^5*d^3 - 56*A*B^2*C*a^3*b^5*c^5*d^3 - 39*A*B^2
*C*a^4*b^4*c^2*d^6 - 38*A*B^2*C*a^5*b^3*c^3*d^5 + 36*A*B^2*C*a^3*b^5*c^3*d^5 + 36*A*B*C^2*a^4*b^4*c^5*d^3 - 30
*A*B*C^2*a^2*b^6*c^5*d^3 + 27*A*B^2*C*a^2*b^6*c^6*d^2 - 24*A*B^2*C*a^2*b^6*c^2*d^6 - 24*A*B*C^2*a^5*b^3*c^4*d^
4 + 24*A*B*C^2*a^3*b^5*c^6*d^2 + 18*A^2*B*C*a^5*b^3*c^2*d^6 - 18*A^2*B*C*a^4*b^4*c^5*d^3 - 15*A*B^2*C*a^2*b^6*
c^4*d^4 + 12*A^2*B*C*a^5*b^3*c^4*d^4 - 12*A^2*B*C*a^3*b^5*c^6*d^2 + 9*A*B^2*C*a^6*b^2*c^2*d^6 + 6*A*B*C^2*a^6*
b^2*c^3*d^5 - 3*A^2*B*C*a^6*b^2*c^3*d^5 + 60*A^2*B*C*a*b^7*c^2*d^6 - 51*A^2*B*C*a^4*b^4*c*d^7 + 48*A*B*C^2*a*b
^7*c^6*d^2 - 42*A^2*B*C*a^2*b^6*c*d^7 - 42*A^2*B*C*a*b^7*c^6*d^2 + 36*A*B*C^2*a^4*b^4*c*d^7 + 36*A*B*C^2*a^2*b
^6*c*d^7 + 36*A*B*C^2*a*b^7*c^4*d^4 - 30*A^2*B*C*a*b^7*c^4*d^4 + 24*A*B^2*C*a*b^7*c^3*d^5 - 24*A*B*C^2*a*b^7*c
^2*d^6 + 18*A*B^2*C*a^5*b^3*c*d^7 - 18*A*B*C^2*a^6*b^2*c*d^7 + 12*A*B^2*C*a^3*b^5*c*d^7 + 9*A^2*B*C*a^6*b^2*c*
d^7 + 6*A*B^2*C*a*b^7*c^5*d^3 - 6*A*B*C^2*a^2*b^6*c^7*d + 3*A^2*B*C*a^2*b^6*c^7*d - 18*B^3*C*a*b^7*c^6*d^2 - 1
8*B*C^3*a*b^7*c^6*d^2 - 14*B^3*C*a*b^7*c^4*d^4 - 14*B*C^3*a*b^7*c^4*d^4 - 10*B^3*C*a^2*b^6*c*d^7 - 10*B*C^3*a^
2*b^6*c*d^7 + 9*B^3*C*a^6*b^2*c*d^7 + 9*B*C^3*a^6*b^2*c*d^7 - 7*B^3*C*a^4*b^4*c*d^7 - 7*B*C^3*a^4*b^4*c*d^7 +
6*B^2*C^2*a*b^7*c^7*d - 4*B^3*C*a*b^7*c^2*d^6 + 4*B^2*C^2*a*b^7*c*d^7 - 4*B*C^3*a*b^7*c^2*d^6 + 3*B^3*C*a^2*b^
6*c^7*d + 3*B*C^3*a^2*b^6*c^7*d + 144*A^3*C*a*b^7*c^3*d^5 + 62*A^3*C*a*b^7*c^5*d^3 + 48*A*C^3*a*b^7*c^3*d^5 -
36*A^2*C^2*a*b^7*c*d^7 + 26*A*C^3*a*b^7*c^5*d^3 + 20*A^3*C*a^3*b^5*c*d^7 + 18*A^2*C^2*a*b^7*c^7*d - 18*A*C^3*a
^5*b^3*c*d^7 - 6*A^3*C*a^5*b^3*c*d^7 - 4*A*C^3*a^3*b^5*c*d^7 - 32*A^3*B*a*b^7*c^2*d^6 - 32*A*B^3*a*b^7*c^2*d^6
+ 22*A^3*B*a^4*b^4*c*d^7 + 22*A*B^3*a^4*b^4*c*d^7 + 16*A^3*B*a^2*b^6*c*d^7 + 16*A*B^3*a^2*b^6*c*d^7 + 12*A^3*
B*a*b^7*c^6*d^2 + 12*A*B^3*a*b^7*c^6*d^2 + 8*A^3*B*a*b^7*c^4*d^4 - 8*A^2*B^2*a*b^7*c*d^7 + 8*A*B^3*a*b^7*c^4*d
^4 + 57*A^2*B*C*b^8*c^5*d^3 + 36*A^2*B*C*b^8*c^3*d^5 - 30*A*B*C^2*b^8*c^5*d^3 - 18*A*B*C^2*b^8*c^3*d^5 - 9*A*B
^2*C*b^8*c^4*d^4 - 3*A*B^2*C*b^8*c^6*d^2 - 2*A*B^2*C*b^8*c^2*d^6 + 36*A^2*B*C*a^3*b^5*d^8 + 24*A*B*C^2*a^5*b^3
*d^8 - 18*A^2*B*C*a^5*b^3*d^8 - 12*A*B*C^2*a^3*b^5*d^8 - 3*A*B^2*C*a^6*b^2*d^8 - 3*A*B^2*C*a^4*b^4*d^8 - 2*A*B
^2*C*a^2*b^6*d^8 + 34*B^2*C^2*a^5*b^3*c^3*d^5 + 28*B^2*C^2*a^3*b^5*c^5*d^3 + 24*B^2*C^2*a^4*b^4*c^2*d^6 - 20*B
^2*C^2*a^4*b^4*c^4*d^4 + 12*B^2*C^2*a^3*b^5*c^3*d^5 + 12*B^2*C^2*a^2*b^6*c^2*d^6 - 9*B^2*C^2*a^6*b^2*c^2*d^6 +
9*B^2*C^2*a^4*b^4*c^6*d^2 + 9*B^2*C^2*a^2*b^6*c^4*d^4 - 3*B^2*C^2*a^2*b^6*c^6*d^2 + 159*A^2*C^2*a^2*b^6*c^4*d
^4 - 156*A^2*C^2*a^3*b^5*c^3*d^5 + 90*A^2*C^2*a^5*b^3*c^3*d^5 + 78*A^2*C^2*a^2*b^6*c^2*d^6 - 63*A^2*C^2*a^4*b^
4*c^4*d^4 - 27*A^2*C^2*a^6*b^2*c^2*d^6 - 27*A^2*C^2*a^2*b^6*c^6*d^2 - 18*A^2*C^2*a^4*b^4*c^2*d^6 + 9*A^2*C^2*a
^4*b^4*c^6*d^2 + 66*A^2*B^2*a^2*b^6*c^2*d^6 + 60*A^2*B^2*a^2*b^6*c^4*d^4 - 48*A^2*B^2*a^3*b^5*c^3*d^5 + 42*A^2
*B^2*a^4*b^4*c^2*d^6 + 28*A^2*B^2*a^3*b^5*c^5*d^3 - 17*A^2*B^2*a^4*b^4*c^4*d^4 - 6*A^2*B^2*a^2*b^6*c^6*d^2 + 4
*A^2*B^2*a^5*b^3*c^3*d^5 + 36*A^3*C*a*b^7*c*d^7 - 18*A*C^3*a*b^7*c^7*d + 12*A*C^3*a*b^7*c*d^7 - 6*A^3*C*a*b^7*
c^7*d + 12*A^2*B*C*b^8*c*d^7 + 6*A*B*C^2*b^8*c^7*d - 6*A*B*C^2*b^8*c*d^7 - 3*A^2*B*C*b^8*c^7*d + 24*A^2*B*C*a*
b^7*d^8 - 12*A*B*C^2*a*b^7*d^8 - 53*B^3*C*a^4*b^4*c^3*d^5 - 53*B*C^3*a^4*b^4*c^3*d^5 - 32*B^3*C*a^2*b^6*c^3*d^
5 - 32*B*C^3*a^2*b^6*c^3*d^5 - 18*B^3*C*a^4*b^4*c^5*d^3 - 18*B*C^3*a^4*b^4*c^5*d^3 + 16*B^3*C*a^3*b^5*c^4*d^4
+ 16*B*C^3*a^3*b^5*c^4*d^4 + 12*B^3*C*a^5*b^3*c^4*d^4 - 12*B^3*C*a^3*b^5*c^6*d^2 + 12*B^2*C^2*a*b^7*c^3*d^5 +
12*B*C^3*a^5*b^3*c^4*d^4 - 12*B*C^3*a^3*b^5*c^6*d^2 + 8*B^3*C*a^3*b^5*c^2*d^6 + 8*B*C^3*a^3*b^5*c^2*d^6 - 6*B^
3*C*a^5*b^3*c^2*d^6 - 6*B^2*C^2*a^5*b^3*c*d^7 + 6*B^2*C^2*a*b^7*c^5*d^3 - 6*B*C^3*a^5*b^3*c^2*d^6 - 3*B^3*C*a^
6*b^2*c^3*d^5 - 3*B*C^3*a^6*b^2*c^3*d^5 - 175*A^3*C*a^2*b^6*c^4*d^4 + 164*A^3*C*a^3*b^5*c^3*d^5 - 144*A^2*C^2*
a*b^7*c^3*d^5 - 124*A^3*C*a^2*b^6*c^2*d^6 - 90*A*C^3*a^5*b^3*c^3*d^5 - 73*A*C^3*a^2*b^6*c^4*d^4 - 66*A^2*C^2*a
*b^7*c^5*d^3 + 44*A*C^3*a^3*b^5*c^3*d^5 + 36*A*C^3*a^4*b^4*c^4*d^4 - 30*A^3*C*a^5*b^3*c^3*d^5 + 30*A^3*C*a^4*b
^4*c^4*d^4 + 27*A*C^3*a^6*b^2*c^2*d^6 + 21*A*C^3*a^4*b^4*c^2*d^6 + 18*A^2*C^2*a^5*b^3*c*d^7 - 18*A*C^3*a^4*b^4
*c^6*d^2 - 16*A*C^3*a^2*b^6*c^2*d^6 - 15*A^3*C*a^4*b^4*c^2*d^6 + 15*A^3*C*a^2*b^6*c^6*d^2 - 12*A^2*C^2*a^3*b^5
*c*d^7 + 9*A^3*C*a^6*b^2*c^2*d^6 + 9*A*C^3*a^2*b^6*c^6*d^2 - 80*A^3*B*a^3*b^5*c^2*d^6 - 80*A*B^3*a^3*b^5*c^2*d
^6 + 38*A^3*B*a^4*b^4*c^3*d^5 + 38*A*B^3*a^4*b^4*c^3*d^5 - 36*A^2*B^2*a*b^7*c^3*d^5 - 28*A^3*B*a^3*b^5*c^4*d^4
- 28*A^3*B*a^2*b^6*c^5*d^3 - 28*A*B^3*a^3*b^5*c^4*d^4 - 28*A*B^3*a^2*b^6*c^5*d^3 + 20*A^3*B*a^2*b^6*c^3*d^5 +
20*A*B^3*a^2*b^6*c^3*d^5 - 12*A^3*B*a^5*b^3*c^2*d^6 - 12*A^2*B^2*a^5*b^3*c*d^7 - 12*A^2*B^2*a^3*b^5*c*d^7 - 1
2*A^2*B^2*a*b^7*c^5*d^3 - 12*A*B^3*a^5*b^3*c^2*d^6 + 6*B^2*C^2*b^8*c^6*d^2 + 3*B^2*C^2*b^8*c^4*d^4 + 36*A^2*C^
2*b^8*c^4*d^4 + 27*A^2*C^2*b^8*c^2*d^6 - 18*A^2*C^2*b^8*c^6*d^2 + 33*A^2*B^2*b^8*c^4*d^4 + 28*A^2*B^2*b^8*c^2*
d^6 + 9*B^2*C^2*a^4*b^4*d^8 + 6*A^2*B^2*b^8*c^6*d^2 + 4*B^2*C^2*a^2*b^6*d^8 + 3*B^2*C^2*a^6*b^2*d^8 - 30*A^2*C
^2*a^4*b^4*d^8 + 9*A^2*C^2*a^6*b^2*d^8 + 16*A^2*B^2*a^2*b^6*d^8 + 3*A^2*B^2*a^4*b^4*d^8 + 6*C^4*a^5*b^3*c*d^7
+ 4*C^4*a^3*b^5*c*d^7 - 2*C^4*a*b^7*c^5*d^3 - 12*B^4*a^5*b^3*c*d^7 + 12*B^4*a*b^7*c^3*d^5 + 8*B^4*a*b^7*c^5*d^
3 - 4*B^4*a^3*b^5*c*d^7 - 48*A^4*a*b^7*c^3*d^5 - 20*A^4*a*b^7*c^5*d^3 - 8*A^4*a^3*b^5*c*d^7 - 63*A^3*C*b^8*c^4
*d^4 - 54*A^3*C*b^8*c^2*d^6 + 9*A^3*C*b^8*c^6*d^2 + 9*A*C^3*b^8*c^6*d^2 - 3*A*C^3*b^8*c^4*d^4 - 28*A^3*B*b^8*c
^5*d^3 - 28*A*B^3*b^8*c^5*d^3 - 18*A^3*B*b^8*c^3*d^5 - 18*A*B^3*b^8*c^3*d^5 - 10*B^3*C*a^5*b^3*d^8 - 10*B*C^3*
a^5*b^3*d^8 - 4*B^3*C*a^3*b^5*d^8 - 4*B*C^3*a^3*b^5*d^8 + 23*A^3*C*a^4*b^4*d^8 - 18*A^3*C*a^2*b^6*d^8 + 11*A*C
^3*a^4*b^4*d^8 - 9*A*C^3*a^6*b^2*d^8 + 6*A*C^3*a^2*b^6*d^8 - 3*A^3*C*a^6*b^2*d^8 - 20*A^3*B*a^3*b^5*d^8 - 20*A
*B^3*a^3*b^5*d^8 + 4*A^3*B*a^5*b^3*d^8 + 4*A*B^3*a^5*b^3*d^8 + B^3*C*a^2*b^6*c^5*d^3 + B*C^3*a^2*b^6*c^5*d^3 +
6*C^4*a*b^7*c^7*d + 4*B^4*a*b^7*c*d^7 - 12*A^4*a*b^7*c*d^7 - 3*B^3*C*b^8*c^7*d - 3*B*C^3*b^8*c^7*d - 6*A^3*B*
b^8*c*d^7 - 6*A*B^3*b^8*c*d^7 - 12*A^3*B*a*b^7*d^8 - 12*A*B^3*a*b^7*d^8 + 30*C^4*a^5*b^3*c^3*d^5 + 19*C^4*a^2*
b^6*c^4*d^4 - 9*C^4*a^6*b^2*c^2*d^6 + 9*C^4*a^4*b^4*c^6*d^2 + 4*C^4*a^3*b^5*c^3*d^5 + 4*C^4*a^2*b^6*c^2*d^6 -
3*C^4*a^4*b^4*c^4*d^4 - 3*C^4*a^4*b^4*c^2*d^6 + 3*C^4*a^2*b^6*c^6*d^2 + 28*B^4*a^3*b^5*c^5*d^3 + 27*B^4*a^4*b^
4*c^2*d^6 - 17*B^4*a^4*b^4*c^4*d^4 - 10*B^4*a^2*b^6*c^4*d^4 + 8*B^4*a^3*b^5*c^3*d^5 + 8*B^4*a^2*b^6*c^2*d^6 -
6*B^4*a^2*b^6*c^6*d^2 + 4*B^4*a^5*b^3*c^3*d^5 + 70*A^4*a^2*b^6*c^4*d^4 + 58*A^4*a^2*b^6*c^2*d^6 - 56*A^4*a^3*b
^5*c^3*d^5 + 15*A^4*a^4*b^4*c^2*d^6 + B^2*C^2*b^8*c^2*d^6 - 18*A^3*C*b^8*d^8 + B^3*C*b^8*c^5*d^3 + B*C^3*b^8*c
^5*d^3 + 6*B^4*b^8*c^6*d^2 + 3*B^4*b^8*c^4*d^4 + 30*A^4*b^8*c^4*d^4 + 27*A^4*b^8*c^2*d^6 + 3*C^4*a^6*b^2*d^8 +
8*B^4*a^4*b^4*d^8 + 4*B^4*a^2*b^6*d^8 + 12*A^4*a^2*b^6*d^8 - 5*A^4*a^4*b^4*d^8 + 9*A^2*C^2*b^8*d^8 + 9*A^2*B^
2*b^8*d^8 + 9*A^4*b^8*d^8 + B^4*b^8*c^2*d^6 + C^4*a^4*b^4*d^8, f, k)*(root(640*a^15*b*c^7*d^13*f^4 + 640*a*b^1
5*c^13*d^7*f^4 + 480*a^15*b*c^9*d^11*f^4 + 480*a^15*b*c^5*d^15*f^4 + 480*a*b^15*c^15*d^5*f^4 + 480*a*b^15*c^11
*d^9*f^4 + 192*a^15*b*c^11*d^9*f^4 + 192*a^15*b*c^3*d^17*f^4 + 192*a^11*b^5*c*d^19*f^4 + 192*a^5*b^11*c^19*d*f
^4 + 192*a*b^15*c^17*d^3*f^4 + 192*a*b^15*c^9*d^11*f^4 + 128*a^13*b^3*c*d^19*f^4 + 128*a^9*b^7*c*d^19*f^4 + 12
8*a^7*b^9*c^19*d*f^4 + 128*a^3*b^13*c^19*d*f^4 + 32*a^15*b*c^13*d^7*f^4 + 32*a^9*b^7*c^19*d*f^4 + 32*a^7*b^9*c
*d^19*f^4 + 32*a*b^15*c^7*d^13*f^4 + 32*a^15*b*c*d^19*f^4 + 32*a*b^15*c^19*d*f^4 - 47088*a^8*b^8*c^10*d^10*f^4
+ 42432*a^9*b^7*c^9*d^11*f^4 + 42432*a^7*b^9*c^11*d^9*f^4 + 39328*a^9*b^7*c^11*d^9*f^4 + 39328*a^7*b^9*c^9*d^
11*f^4 - 36912*a^8*b^8*c^12*d^8*f^4 - 36912*a^8*b^8*c^8*d^12*f^4 - 34256*a^10*b^6*c^10*d^10*f^4 - 34256*a^6*b^
10*c^10*d^10*f^4 - 31152*a^10*b^6*c^8*d^12*f^4 - 31152*a^6*b^10*c^12*d^8*f^4 + 28128*a^9*b^7*c^7*d^13*f^4 + 28
128*a^7*b^9*c^13*d^7*f^4 + 24160*a^11*b^5*c^9*d^11*f^4 + 24160*a^5*b^11*c^11*d^9*f^4 - 23088*a^10*b^6*c^12*d^8
*f^4 - 23088*a^6*b^10*c^8*d^12*f^4 + 22272*a^9*b^7*c^13*d^7*f^4 + 22272*a^7*b^9*c^7*d^13*f^4 + 19072*a^11*b^5*
c^11*d^9*f^4 + 19072*a^5*b^11*c^9*d^11*f^4 + 18624*a^11*b^5*c^7*d^13*f^4 + 18624*a^5*b^11*c^13*d^7*f^4 - 17328
*a^8*b^8*c^14*d^6*f^4 - 17328*a^8*b^8*c^6*d^14*f^4 - 17232*a^10*b^6*c^6*d^14*f^4 - 17232*a^6*b^10*c^14*d^6*f^4
- 13520*a^12*b^4*c^8*d^12*f^4 - 13520*a^4*b^12*c^12*d^8*f^4 - 12464*a^12*b^4*c^10*d^10*f^4 - 12464*a^4*b^12*c
^10*d^10*f^4 + 10880*a^9*b^7*c^5*d^15*f^4 + 10880*a^7*b^9*c^15*d^5*f^4 - 9072*a^10*b^6*c^14*d^6*f^4 - 9072*a^6
*b^10*c^6*d^14*f^4 + 8928*a^11*b^5*c^13*d^7*f^4 + 8928*a^5*b^11*c^7*d^13*f^4 - 8880*a^12*b^4*c^6*d^14*f^4 - 88
80*a^4*b^12*c^14*d^6*f^4 + 8480*a^11*b^5*c^5*d^15*f^4 + 8480*a^5*b^11*c^15*d^5*f^4 + 7200*a^9*b^7*c^15*d^5*f^4
+ 7200*a^7*b^9*c^5*d^15*f^4 - 6912*a^12*b^4*c^12*d^8*f^4 - 6912*a^4*b^12*c^8*d^12*f^4 + 6400*a^13*b^3*c^9*d^1
1*f^4 + 6400*a^3*b^13*c^11*d^9*f^4 + 5920*a^13*b^3*c^7*d^13*f^4 + 5920*a^3*b^13*c^13*d^7*f^4 - 5392*a^10*b^6*c
^4*d^16*f^4 - 5392*a^6*b^10*c^16*d^4*f^4 - 4428*a^8*b^8*c^16*d^4*f^4 - 4428*a^8*b^8*c^4*d^16*f^4 + 4128*a^13*b
^3*c^11*d^9*f^4 + 4128*a^3*b^13*c^9*d^11*f^4 - 3328*a^12*b^4*c^4*d^16*f^4 - 3328*a^4*b^12*c^16*d^4*f^4 + 3264*
a^13*b^3*c^5*d^15*f^4 + 3264*a^3*b^13*c^15*d^5*f^4 - 2480*a^14*b^2*c^8*d^12*f^4 - 2480*a^2*b^14*c^12*d^8*f^4 +
2240*a^11*b^5*c^15*d^5*f^4 + 2240*a^5*b^11*c^5*d^15*f^4 - 2128*a^12*b^4*c^14*d^6*f^4 - 2128*a^4*b^12*c^6*d^14
*f^4 + 2112*a^9*b^7*c^3*d^17*f^4 + 2112*a^7*b^9*c^17*d^3*f^4 + 2048*a^11*b^5*c^3*d^17*f^4 + 2048*a^5*b^11*c^17
*d^3*f^4 - 2000*a^14*b^2*c^6*d^14*f^4 - 2000*a^2*b^14*c^14*d^6*f^4 - 1792*a^10*b^6*c^16*d^4*f^4 - 1792*a^6*b^1
0*c^4*d^16*f^4 - 1776*a^14*b^2*c^10*d^10*f^4 - 1776*a^2*b^14*c^10*d^10*f^4 + 1472*a^13*b^3*c^13*d^7*f^4 + 1472
*a^3*b^13*c^7*d^13*f^4 + 1088*a^9*b^7*c^17*d^3*f^4 + 1088*a^7*b^9*c^3*d^17*f^4 + 992*a^13*b^3*c^3*d^17*f^4 + 9
92*a^3*b^13*c^17*d^3*f^4 - 912*a^14*b^2*c^4*d^16*f^4 - 912*a^2*b^14*c^16*d^4*f^4 - 768*a^10*b^6*c^2*d^18*f^4 -
768*a^6*b^10*c^18*d^2*f^4 - 688*a^14*b^2*c^12*d^8*f^4 - 688*a^2*b^14*c^8*d^12*f^4 - 592*a^12*b^4*c^2*d^18*f^4
- 592*a^4*b^12*c^18*d^2*f^4 - 472*a^8*b^8*c^18*d^2*f^4 - 472*a^8*b^8*c^2*d^18*f^4 - 280*a^12*b^4*c^16*d^4*f^4
- 280*a^4*b^12*c^4*d^16*f^4 + 224*a^13*b^3*c^15*d^5*f^4 + 224*a^11*b^5*c^17*d^3*f^4 + 224*a^5*b^11*c^3*d^17*f
^4 + 224*a^3*b^13*c^5*d^15*f^4 - 208*a^14*b^2*c^2*d^18*f^4 - 208*a^2*b^14*c^18*d^2*f^4 - 112*a^14*b^2*c^14*d^6
*f^4 - 112*a^10*b^6*c^18*d^2*f^4 - 112*a^6*b^10*c^2*d^18*f^4 - 112*a^2*b^14*c^6*d^14*f^4 - 80*b^16*c^14*d^6*f^
4 - 60*b^16*c^16*d^4*f^4 - 60*b^16*c^12*d^8*f^4 - 24*b^16*c^18*d^2*f^4 - 24*b^16*c^10*d^10*f^4 - 4*b^16*c^8*d^
12*f^4 - 80*a^16*c^6*d^14*f^4 - 60*a^16*c^8*d^12*f^4 - 60*a^16*c^4*d^16*f^4 - 24*a^16*c^10*d^10*f^4 - 24*a^16*
c^2*d^18*f^4 - 4*a^16*c^12*d^8*f^4 - 24*a^12*b^4*d^20*f^4 - 16*a^14*b^2*d^20*f^4 - 16*a^10*b^6*d^20*f^4 - 4*a^
8*b^8*d^20*f^4 - 24*a^4*b^12*c^20*f^4 - 16*a^6*b^10*c^20*f^4 - 16*a^2*b^14*c^20*f^4 - 4*a^8*b^8*c^20*f^4 - 4*b
^16*c^20*f^4 - 4*a^16*d^20*f^4 + 56*A*C*a*b^11*c^13*d*f^2 - 48*A*C*a^11*b*c*d^13*f^2 + 48*A*C*a*b^11*c*d^13*f^
2 + 5904*B*C*a^6*b^6*c^7*d^7*f^2 - 5016*B*C*a^5*b^7*c^8*d^6*f^2 - 4608*B*C*a^7*b^5*c^6*d^8*f^2 - 4512*B*C*a^5*
b^7*c^6*d^8*f^2 - 4384*B*C*a^7*b^5*c^8*d^6*f^2 + 3056*B*C*a^8*b^4*c^7*d^7*f^2 + 2256*B*C*a^4*b^8*c^7*d^7*f^2 -
1824*B*C*a^3*b^9*c^8*d^6*f^2 + 1632*B*C*a^9*b^3*c^4*d^10*f^2 - 1400*B*C*a^8*b^4*c^3*d^11*f^2 - 1320*B*C*a^4*b
^8*c^11*d^3*f^2 - 1248*B*C*a^3*b^9*c^6*d^8*f^2 + 1152*B*C*a^3*b^9*c^10*d^4*f^2 - 1072*B*C*a^9*b^3*c^6*d^8*f^2
+ 1068*B*C*a^6*b^6*c^9*d^5*f^2 - 1004*B*C*a^4*b^8*c^5*d^9*f^2 - 968*B*C*a^6*b^6*c^3*d^11*f^2 - 864*B*C*a^8*b^4
*c^5*d^9*f^2 - 828*B*C*a^4*b^8*c^9*d^5*f^2 - 792*B*C*a^4*b^8*c^3*d^11*f^2 - 792*B*C*a^2*b^10*c^11*d^3*f^2 - 77
6*B*C*a^9*b^3*c^8*d^6*f^2 + 688*B*C*a^7*b^5*c^4*d^10*f^2 - 672*B*C*a^10*b^2*c^3*d^11*f^2 - 592*B*C*a^2*b^10*c^
9*d^5*f^2 + 544*B*C*a^10*b^2*c^7*d^7*f^2 - 492*B*C*a^2*b^10*c^5*d^9*f^2 + 480*B*C*a^5*b^7*c^10*d^4*f^2 - 392*B
*C*a^10*b^2*c^5*d^9*f^2 + 332*B*C*a^8*b^4*c^9*d^5*f^2 - 328*B*C*a^6*b^6*c^11*d^3*f^2 + 320*B*C*a^9*b^3*c^2*d^1
2*f^2 + 272*B*C*a^3*b^9*c^12*d^2*f^2 - 248*B*C*a^5*b^7*c^4*d^10*f^2 - 248*B*C*a^2*b^10*c^3*d^11*f^2 - 208*B*C*
a^7*b^5*c^10*d^4*f^2 - 192*B*C*a^5*b^7*c^2*d^12*f^2 + 144*B*C*a^2*b^10*c^7*d^7*f^2 - 96*B*C*a^3*b^9*c^4*d^10*f
^2 + 88*B*C*a^5*b^7*c^12*d^2*f^2 - 72*B*C*a^8*b^4*c^11*d^3*f^2 + 48*B*C*a^9*b^3*c^10*d^4*f^2 - 48*B*C*a^7*b^5*
c^12*d^2*f^2 - 48*B*C*a^7*b^5*c^2*d^12*f^2 - 48*B*C*a^3*b^9*c^2*d^12*f^2 - 12*B*C*a^10*b^2*c^9*d^5*f^2 + 4*B*C
*a^6*b^6*c^5*d^9*f^2 + 5824*A*C*a^7*b^5*c^5*d^9*f^2 - 4378*A*C*a^8*b^4*c^6*d^8*f^2 + 4296*A*C*a^5*b^7*c^5*d^9*
f^2 - 3912*A*C*a^6*b^6*c^6*d^8*f^2 - 3672*A*C*a^5*b^7*c^9*d^5*f^2 + 3594*A*C*a^4*b^8*c^8*d^6*f^2 + 3236*A*C*a^
6*b^6*c^8*d^6*f^2 + 2816*A*C*a^9*b^3*c^5*d^9*f^2 + 2624*A*C*a^3*b^9*c^5*d^9*f^2 + 2432*A*C*a^7*b^5*c^7*d^7*f^2
- 2366*A*C*a^8*b^4*c^4*d^10*f^2 + 2298*A*C*a^4*b^8*c^10*d^4*f^2 + 1872*A*C*a^3*b^9*c^7*d^7*f^2 + 1848*A*C*a^6
*b^6*c^10*d^4*f^2 - 1644*A*C*a^6*b^6*c^4*d^10*f^2 - 1488*A*C*a^7*b^5*c^9*d^5*f^2 - 1408*A*C*a^3*b^9*c^9*d^5*f^
2 - 1308*A*C*a^4*b^8*c^6*d^8*f^2 + 1248*A*C*a^5*b^7*c^7*d^7*f^2 - 1012*A*C*a^10*b^2*c^6*d^8*f^2 + 1008*A*C*a^7
*b^5*c^3*d^11*f^2 + 992*A*C*a^5*b^7*c^3*d^11*f^2 + 928*A*C*a^3*b^9*c^3*d^11*f^2 + 848*A*C*a^9*b^3*c^7*d^7*f^2
+ 636*A*C*a^2*b^10*c^8*d^6*f^2 - 628*A*C*a^10*b^2*c^4*d^10*f^2 - 600*A*C*a^2*b^10*c^6*d^8*f^2 - 576*A*C*a^5*b^
7*c^11*d^3*f^2 + 572*A*C*a^2*b^10*c^10*d^4*f^2 + 464*A*C*a^8*b^4*c^8*d^6*f^2 + 304*A*C*a^6*b^6*c^2*d^12*f^2 -
304*A*C*a^4*b^8*c^4*d^10*f^2 + 296*A*C*a^4*b^8*c^2*d^12*f^2 + 260*A*C*a^8*b^4*c^10*d^4*f^2 - 232*A*C*a^9*b^3*c
^9*d^5*f^2 - 232*A*C*a^2*b^10*c^12*d^2*f^2 + 228*A*C*a^10*b^2*c^2*d^12*f^2 - 188*A*C*a^2*b^10*c^4*d^10*f^2 + 1
44*A*C*a^3*b^9*c^11*d^3*f^2 + 116*A*C*a^6*b^6*c^12*d^2*f^2 + 112*A*C*a^9*b^3*c^3*d^11*f^2 - 112*A*C*a^7*b^5*c^
11*d^3*f^2 + 92*A*C*a^10*b^2*c^8*d^6*f^2 + 74*A*C*a^4*b^8*c^12*d^2*f^2 + 62*A*C*a^8*b^4*c^2*d^12*f^2 + 40*A*C*
a^2*b^10*c^2*d^12*f^2 - 7008*A*B*a^6*b^6*c^7*d^7*f^2 - 4032*A*B*a^4*b^8*c^7*d^7*f^2 + 3952*A*B*a^7*b^5*c^8*d^6
*f^2 + 3648*A*B*a^5*b^7*c^8*d^6*f^2 - 3392*A*B*a^8*b^4*c^7*d^7*f^2 + 3264*A*B*a^7*b^5*c^6*d^8*f^2 - 2992*A*B*a
^5*b^7*c^4*d^10*f^2 - 2368*A*B*a^7*b^5*c^4*d^10*f^2 - 2304*A*B*a^3*b^9*c^4*d^10*f^2 - 1968*A*B*a^6*b^6*c^9*d^5
*f^2 - 1872*A*B*a^9*b^3*c^4*d^10*f^2 - 1728*A*B*a^2*b^10*c^7*d^7*f^2 + 1712*A*B*a^8*b^4*c^3*d^11*f^2 + 1536*A*
B*a^5*b^7*c^6*d^8*f^2 - 1536*A*B*a^3*b^9*c^10*d^4*f^2 - 1392*A*B*a^5*b^7*c^2*d^12*f^2 + 1328*A*B*a^6*b^6*c^3*d
^11*f^2 - 1104*A*B*a^3*b^9*c^2*d^12*f^2 - 1056*A*B*a^3*b^9*c^6*d^8*f^2 + 976*A*B*a^9*b^3*c^6*d^8*f^2 + 960*A*B
*a^4*b^8*c^11*d^3*f^2 + 936*A*B*a^8*b^4*c^5*d^9*f^2 - 912*A*B*a^5*b^7*c^10*d^4*f^2 + 848*A*B*a^9*b^3*c^8*d^6*f
^2 - 816*A*B*a^7*b^5*c^2*d^12*f^2 + 816*A*B*a^4*b^8*c^3*d^11*f^2 + 768*A*B*a^10*b^2*c^3*d^11*f^2 + 672*A*B*a^3
*b^9*c^8*d^6*f^2 - 632*A*B*a^8*b^4*c^9*d^5*f^2 - 608*A*B*a^2*b^10*c^9*d^5*f^2 - 552*A*B*a^4*b^8*c^9*d^5*f^2 -
544*A*B*a^10*b^2*c^7*d^7*f^2 - 480*A*B*a^2*b^10*c^5*d^9*f^2 + 464*A*B*a^10*b^2*c^5*d^9*f^2 - 464*A*B*a^9*b^3*c
^2*d^12*f^2 + 432*A*B*a^2*b^10*c^11*d^3*f^2 - 368*A*B*a^3*b^9*c^12*d^2*f^2 - 256*A*B*a^6*b^6*c^5*d^9*f^2 - 208
*A*B*a^5*b^7*c^12*d^2*f^2 + 176*A*B*a^4*b^8*c^5*d^9*f^2 + 112*A*B*a^7*b^5*c^10*d^4*f^2 + 112*A*B*a^6*b^6*c^11*
d^3*f^2 - 16*A*B*a^2*b^10*c^3*d^11*f^2 - 576*B*C*a*b^11*c^8*d^6*f^2 + 400*B*C*a^11*b*c^4*d^10*f^2 - 288*B*C*a*
b^11*c^6*d^8*f^2 - 176*B*C*a^11*b*c^6*d^8*f^2 + 128*B*C*a*b^11*c^10*d^4*f^2 - 108*B*C*a^4*b^8*c*d^13*f^2 - 104
*B*C*a*b^11*c^4*d^10*f^2 - 92*B*C*a^4*b^8*c^13*d*f^2 - 60*B*C*a^8*b^4*c*d^13*f^2 - 60*B*C*a^6*b^6*c*d^13*f^2 +
48*B*C*a^11*b*c^2*d^12*f^2 - 40*B*C*a^2*b^10*c*d^13*f^2 - 28*B*C*a^2*b^10*c^13*d*f^2 - 24*B*C*a*b^11*c^12*d^2
*f^2 + 20*B*C*a^10*b^2*c*d^13*f^2 - 16*B*C*a*b^11*c^2*d^12*f^2 + 12*B*C*a^6*b^6*c^13*d*f^2 + 912*A*C*a*b^11*c^
7*d^7*f^2 + 808*A*C*a*b^11*c^5*d^9*f^2 + 432*A*C*a^11*b*c^5*d^9*f^2 + 336*A*C*a*b^11*c^3*d^11*f^2 + 224*A*C*a*
b^11*c^11*d^3*f^2 - 112*A*C*a^11*b*c^3*d^11*f^2 + 112*A*C*a^3*b^9*c*d^13*f^2 - 88*A*C*a^9*b^3*c*d^13*f^2 + 80*
A*C*a^3*b^9*c^13*d*f^2 + 56*A*C*a^5*b^7*c*d^13*f^2 + 48*A*C*a*b^11*c^9*d^5*f^2 - 40*A*C*a^5*b^7*c^13*d*f^2 - 1
6*A*C*a^11*b*c^7*d^7*f^2 + 16*A*C*a^7*b^5*c*d^13*f^2 - 496*A*B*a*b^11*c^4*d^10*f^2 - 400*A*B*a^11*b*c^4*d^10*f
^2 + 288*A*B*a*b^11*c^8*d^6*f^2 - 288*A*B*a*b^11*c^6*d^8*f^2 - 272*A*B*a*b^11*c^2*d^12*f^2 + 240*A*B*a^6*b^6*c
*d^13*f^2 - 224*A*B*a*b^11*c^10*d^4*f^2 + 192*A*B*a^8*b^4*c*d^13*f^2 + 192*A*B*a^4*b^8*c*d^13*f^2 + 176*A*B*a^
11*b*c^6*d^8*f^2 + 104*A*B*a^4*b^8*c^13*d*f^2 - 48*A*B*a^11*b*c^2*d^12*f^2 + 16*A*B*a^10*b^2*c*d^13*f^2 + 16*A
*B*a^2*b^10*c^13*d*f^2 + 16*A*B*a^2*b^10*c*d^13*f^2 - 112*B*C*b^12*c^11*d^3*f^2 + 4*B*C*b^12*c^5*d^9*f^2 + 150
*A*C*b^12*c^10*d^4*f^2 - 80*B*C*a^12*c^3*d^11*f^2 + 66*A*C*b^12*c^8*d^6*f^2 - 30*A*C*b^12*c^12*d^2*f^2 + 24*B*
C*a^12*c^5*d^9*f^2 - 12*A*C*b^12*c^4*d^10*f^2 - 576*A*B*b^12*c^7*d^7*f^2 - 432*A*B*b^12*c^9*d^5*f^2 - 400*A*B*
b^12*c^5*d^9*f^2 - 144*A*B*b^12*c^3*d^11*f^2 - 96*B*C*a^7*b^5*d^14*f^2 - 72*B*C*a^5*b^7*d^14*f^2 - 66*A*C*a^12
*c^4*d^10*f^2 + 54*A*C*a^12*c^2*d^12*f^2 - 32*A*B*b^12*c^11*d^3*f^2 - 24*B*C*a^9*b^3*d^14*f^2 - 16*B*C*a^3*b^9
*d^14*f^2 + 2*A*C*a^12*c^6*d^8*f^2 + 116*A*C*a^6*b^6*d^14*f^2 + 100*A*C*a^4*b^8*d^14*f^2 + 80*A*B*a^12*c^3*d^1
1*f^2 + 24*A*C*a^2*b^10*d^14*f^2 - 24*A*B*a^12*c^5*d^9*f^2 + 22*A*C*a^8*b^4*d^14*f^2 + 16*B*C*a^3*b^9*c^14*f^2
+ 8*A*C*a^10*b^2*d^14*f^2 - 192*A*B*a^5*b^7*d^14*f^2 - 176*A*B*a^3*b^9*d^14*f^2 - 48*A*B*a^7*b^5*d^14*f^2 - 2
8*A*C*a^2*b^10*c^14*f^2 + 2*A*C*a^4*b^8*c^14*f^2 - 16*A*B*a^3*b^9*c^14*f^2 + 2508*C^2*a^6*b^6*c^6*d^8*f^2 + 23
76*C^2*a^5*b^7*c^9*d^5*f^2 + 2357*C^2*a^8*b^4*c^6*d^8*f^2 - 2048*C^2*a^7*b^5*c^5*d^9*f^2 + 1304*C^2*a^3*b^9*c^
9*d^5*f^2 + 1303*C^2*a^8*b^4*c^4*d^10*f^2 + 1212*C^2*a^6*b^6*c^4*d^10*f^2 - 1203*C^2*a^4*b^8*c^8*d^6*f^2 - 119
2*C^2*a^9*b^3*c^5*d^9*f^2 + 1062*C^2*a^4*b^8*c^6*d^8*f^2 + 984*C^2*a^7*b^5*c^9*d^5*f^2 - 952*C^2*a^6*b^6*c^8*d
^6*f^2 + 768*C^2*a^5*b^7*c^7*d^7*f^2 - 681*C^2*a^4*b^8*c^10*d^4*f^2 - 672*C^2*a^5*b^7*c^5*d^9*f^2 - 480*C^2*a^
6*b^6*c^10*d^4*f^2 + 458*C^2*a^10*b^2*c^6*d^8*f^2 - 448*C^2*a^7*b^5*c^7*d^7*f^2 + 422*C^2*a^4*b^8*c^4*d^10*f^2
+ 372*C^2*a^2*b^10*c^6*d^8*f^2 + 360*C^2*a^5*b^7*c^11*d^3*f^2 + 312*C^2*a^3*b^9*c^7*d^7*f^2 + 278*C^2*a^10*b^
2*c^4*d^10*f^2 - 232*C^2*a^9*b^3*c^7*d^7*f^2 + 194*C^2*a^2*b^10*c^12*d^2*f^2 + 176*C^2*a^9*b^3*c^9*d^5*f^2 + 1
52*C^2*a^5*b^7*c^3*d^11*f^2 + 124*C^2*a^2*b^10*c^4*d^10*f^2 - 120*C^2*a^7*b^5*c^3*d^11*f^2 - 114*C^2*a^10*b^2*
c^2*d^12*f^2 - 102*C^2*a^2*b^10*c^8*d^6*f^2 + 101*C^2*a^4*b^8*c^12*d^2*f^2 + 100*C^2*a^6*b^6*c^2*d^12*f^2 - 88
*C^2*a^3*b^9*c^5*d^9*f^2 + 77*C^2*a^8*b^4*c^2*d^12*f^2 + 72*C^2*a^3*b^9*c^11*d^3*f^2 - 64*C^2*a^10*b^2*c^8*d^6
*f^2 + 64*C^2*a^3*b^9*c^3*d^11*f^2 - 58*C^2*a^2*b^10*c^10*d^4*f^2 + 56*C^2*a^7*b^5*c^11*d^3*f^2 + 56*C^2*a^6*b
^6*c^12*d^2*f^2 + 40*C^2*a^9*b^3*c^3*d^11*f^2 + 36*C^2*a^8*b^4*c^12*d^2*f^2 + 32*C^2*a^4*b^8*c^2*d^12*f^2 + 26
*C^2*a^8*b^4*c^10*d^4*f^2 + 16*C^2*a^2*b^10*c^2*d^12*f^2 + 2*C^2*a^8*b^4*c^8*d^6*f^2 + 2277*B^2*a^4*b^8*c^8*d^
6*f^2 + 2144*B^2*a^7*b^5*c^5*d^9*f^2 - 2112*B^2*a^5*b^7*c^9*d^5*f^2 + 2028*B^2*a^6*b^6*c^8*d^6*f^2 - 1671*B^2*
a^8*b^4*c^6*d^8*f^2 + 1275*B^2*a^4*b^8*c^10*d^4*f^2 + 1176*B^2*a^5*b^7*c^5*d^9*f^2 + 1096*B^2*a^9*b^3*c^5*d^9*
f^2 - 1044*B^2*a^6*b^6*c^6*d^8*f^2 + 984*B^2*a^6*b^6*c^10*d^4*f^2 - 968*B^2*a^3*b^9*c^9*d^5*f^2 - 888*B^2*a^7*
b^5*c^9*d^5*f^2 + 672*B^2*a^7*b^5*c^7*d^7*f^2 + 664*B^2*a^3*b^9*c^5*d^9*f^2 - 649*B^2*a^8*b^4*c^4*d^10*f^2 + 6
18*B^2*a^2*b^10*c^8*d^6*f^2 + 514*B^2*a^4*b^8*c^4*d^10*f^2 + 460*B^2*a^6*b^6*c^2*d^12*f^2 + 422*B^2*a^8*b^4*c^
8*d^6*f^2 + 406*B^2*a^2*b^10*c^10*d^4*f^2 - 382*B^2*a^10*b^2*c^6*d^8*f^2 + 368*B^2*a^4*b^8*c^2*d^12*f^2 - 312*
B^2*a^5*b^7*c^11*d^3*f^2 + 312*B^2*a^3*b^9*c^7*d^7*f^2 + 248*B^2*a^9*b^3*c^7*d^7*f^2 + 245*B^2*a^8*b^4*c^2*d^1
2*f^2 - 192*B^2*a^5*b^7*c^7*d^7*f^2 - 184*B^2*a^9*b^3*c^3*d^11*f^2 + 182*B^2*a^10*b^2*c^2*d^12*f^2 + 176*B^2*a
^3*b^9*c^3*d^11*f^2 + 174*B^2*a^4*b^8*c^6*d^8*f^2 - 170*B^2*a^10*b^2*c^4*d^10*f^2 - 152*B^2*a^9*b^3*c^9*d^5*f^
2 + 152*B^2*a^2*b^10*c^4*d^10*f^2 + 142*B^2*a^8*b^4*c^10*d^4*f^2 - 90*B^2*a^2*b^10*c^12*d^2*f^2 + 88*B^2*a^2*b
^10*c^2*d^12*f^2 + 84*B^2*a^10*b^2*c^8*d^6*f^2 + 84*B^2*a^2*b^10*c^6*d^8*f^2 + 60*B^2*a^6*b^6*c^12*d^2*f^2 - 5
6*B^2*a^7*b^5*c^11*d^3*f^2 + 53*B^2*a^4*b^8*c^12*d^2*f^2 + 24*B^2*a^7*b^5*c^3*d^11*f^2 + 24*B^2*a^6*b^6*c^4*d^
10*f^2 + 24*B^2*a^3*b^9*c^11*d^3*f^2 - 8*B^2*a^5*b^7*c^3*d^11*f^2 + 4566*A^2*a^4*b^8*c^6*d^8*f^2 + 4284*A^2*a^
6*b^6*c^6*d^8*f^2 - 3776*A^2*a^7*b^5*c^5*d^9*f^2 - 3624*A^2*a^5*b^7*c^5*d^9*f^2 + 3122*A^2*a^4*b^8*c^4*d^10*f^
2 + 3108*A^2*a^2*b^10*c^6*d^8*f^2 + 2741*A^2*a^8*b^4*c^6*d^8*f^2 + 2592*A^2*a^6*b^6*c^4*d^10*f^2 - 2536*A^2*a^
3*b^9*c^5*d^9*f^2 + 2224*A^2*a^2*b^10*c^4*d^10*f^2 - 2184*A^2*a^3*b^9*c^7*d^7*f^2 - 2016*A^2*a^5*b^7*c^7*d^7*f
^2 - 1984*A^2*a^7*b^5*c^7*d^7*f^2 + 1626*A^2*a^2*b^10*c^8*d^6*f^2 - 1624*A^2*a^9*b^3*c^5*d^9*f^2 + 1603*A^2*a^
8*b^4*c^4*d^10*f^2 + 1296*A^2*a^5*b^7*c^9*d^5*f^2 - 1144*A^2*a^5*b^7*c^3*d^11*f^2 - 992*A^2*a^3*b^9*c^3*d^11*f
^2 + 968*A^2*a^4*b^8*c^2*d^12*f^2 - 888*A^2*a^7*b^5*c^3*d^11*f^2 + 849*A^2*a^4*b^8*c^8*d^6*f^2 + 808*A^2*a^2*b
^10*c^2*d^12*f^2 - 616*A^2*a^9*b^3*c^7*d^7*f^2 + 554*A^2*a^10*b^2*c^6*d^8*f^2 + 504*A^2*a^7*b^5*c^9*d^5*f^2 -
504*A^2*a^6*b^6*c^10*d^4*f^2 + 460*A^2*a^6*b^6*c^2*d^12*f^2 + 350*A^2*a^10*b^2*c^4*d^10*f^2 + 350*A^2*a^2*b^10
*c^10*d^4*f^2 - 321*A^2*a^4*b^8*c^10*d^4*f^2 + 216*A^2*a^5*b^7*c^11*d^3*f^2 - 216*A^2*a^3*b^9*c^11*d^3*f^2 + 1
82*A^2*a^2*b^10*c^12*d^2*f^2 - 152*A^2*a^9*b^3*c^3*d^11*f^2 - 124*A^2*a^6*b^6*c^8*d^6*f^2 - 114*A^2*a^10*b^2*c
^2*d^12*f^2 + 104*A^2*a^3*b^9*c^9*d^5*f^2 + 77*A^2*a^8*b^4*c^2*d^12*f^2 + 74*A^2*a^8*b^4*c^8*d^6*f^2 - 70*A^2*
a^8*b^4*c^10*d^4*f^2 + 56*A^2*a^9*b^3*c^9*d^5*f^2 + 56*A^2*a^7*b^5*c^11*d^3*f^2 + 41*A^2*a^4*b^8*c^12*d^2*f^2
- 28*A^2*a^10*b^2*c^8*d^6*f^2 - 28*A^2*a^6*b^6*c^12*d^2*f^2 + 12*B*C*b^12*c^13*d*f^2 + 24*B*C*a^12*c*d^13*f^2
- 24*A*B*b^12*c^13*d*f^2 - 24*A*B*b^12*c*d^13*f^2 - 16*B*C*a^11*b*d^14*f^2 - 24*A*B*a^12*c*d^13*f^2 - 16*B*C*a
*b^11*c^14*f^2 - 48*A*B*a*b^11*d^14*f^2 + 16*A*B*a^11*b*d^14*f^2 + 16*A*B*a*b^11*c^14*f^2 - 216*C^2*a^11*b*c^5
*d^9*f^2 + 216*C^2*a*b^11*c^9*d^5*f^2 + 56*C^2*a^11*b*c^3*d^11*f^2 + 56*C^2*a^9*b^3*c*d^13*f^2 + 56*C^2*a^5*b^
7*c*d^13*f^2 + 40*C^2*a^7*b^5*c*d^13*f^2 - 40*C^2*a*b^11*c^11*d^3*f^2 + 32*C^2*a^5*b^7*c^13*d*f^2 - 24*C^2*a*b
^11*c^7*d^7*f^2 - 16*C^2*a^3*b^9*c^13*d*f^2 + 16*C^2*a^3*b^9*c*d^13*f^2 + 8*C^2*a^11*b*c^7*d^7*f^2 - 8*C^2*a*b
^11*c^5*d^9*f^2 + 264*B^2*a*b^11*c^7*d^7*f^2 + 224*B^2*a*b^11*c^5*d^9*f^2 + 168*B^2*a^11*b*c^5*d^9*f^2 - 112*B
^2*a^9*b^3*c*d^13*f^2 - 104*B^2*a^11*b*c^3*d^11*f^2 - 104*B^2*a^7*b^5*c*d^13*f^2 + 96*B^2*a*b^11*c^3*d^11*f^2
+ 88*B^2*a*b^11*c^11*d^3*f^2 - 72*B^2*a*b^11*c^9*d^5*f^2 - 64*B^2*a^5*b^7*c*d^13*f^2 + 32*B^2*a^3*b^9*c^13*d*f
^2 - 24*B^2*a^11*b*c^7*d^7*f^2 - 24*B^2*a^5*b^7*c^13*d*f^2 + 16*B^2*a^3*b^9*c*d^13*f^2 - 888*A^2*a*b^11*c^7*d^
7*f^2 - 800*A^2*a*b^11*c^5*d^9*f^2 - 336*A^2*a*b^11*c^3*d^11*f^2 - 264*A^2*a*b^11*c^9*d^5*f^2 - 216*A^2*a^11*b
*c^5*d^9*f^2 - 184*A^2*a*b^11*c^11*d^3*f^2 - 128*A^2*a^3*b^9*c*d^13*f^2 - 112*A^2*a^5*b^7*c*d^13*f^2 - 64*A^2*
a^3*b^9*c^13*d*f^2 + 56*A^2*a^11*b*c^3*d^11*f^2 - 56*A^2*a^7*b^5*c*d^13*f^2 + 32*A^2*a^9*b^3*c*d^13*f^2 + 8*A^
2*a^11*b*c^7*d^7*f^2 + 8*A^2*a^5*b^7*c^13*d*f^2 + 24*C^2*a^11*b*c*d^13*f^2 - 16*C^2*a*b^11*c^13*d*f^2 - 40*B^2
*a^11*b*c*d^13*f^2 + 24*B^2*a*b^11*c^13*d*f^2 + 16*B^2*a*b^11*c*d^13*f^2 - 48*A^2*a*b^11*c*d^13*f^2 - 40*A^2*a
*b^11*c^13*d*f^2 + 24*A^2*a^11*b*c*d^13*f^2 - 6*A*C*a^12*d^14*f^2 + 2*A*C*b^12*c^14*f^2 + 33*C^2*b^12*c^12*d^2
*f^2 - 27*C^2*b^12*c^10*d^4*f^2 + 3*C^2*b^12*c^8*d^6*f^2 + 117*B^2*b^12*c^10*d^4*f^2 + 111*B^2*b^12*c^8*d^6*f^
2 + 72*B^2*b^12*c^6*d^8*f^2 + 33*C^2*a^12*c^4*d^10*f^2 - 27*C^2*a^12*c^2*d^12*f^2 + 24*B^2*b^12*c^4*d^10*f^2 +
4*B^2*b^12*c^2*d^12*f^2 - 3*B^2*b^12*c^12*d^2*f^2 - C^2*a^12*c^6*d^8*f^2 + 720*A^2*b^12*c^6*d^8*f^2 + 552*A^2
*b^12*c^4*d^10*f^2 + 471*A^2*b^12*c^8*d^6*f^2 + 216*A^2*b^12*c^2*d^12*f^2 + 93*A^2*b^12*c^10*d^4*f^2 + 33*B^2*
a^12*c^2*d^12*f^2 + 33*A^2*b^12*c^12*d^2*f^2 + 31*C^2*a^8*b^4*d^14*f^2 - 27*B^2*a^12*c^4*d^10*f^2 + 20*C^2*a^6
*b^6*d^14*f^2 + 4*C^2*a^4*b^8*d^14*f^2 + 3*B^2*a^12*c^6*d^8*f^2 + 2*C^2*a^10*b^2*d^14*f^2 + 80*B^2*a^6*b^6*d^1
4*f^2 + 64*B^2*a^4*b^8*d^14*f^2 + 33*A^2*a^12*c^4*d^10*f^2 + 31*B^2*a^8*b^4*d^14*f^2 - 27*A^2*a^12*c^2*d^12*f^
2 + 16*B^2*a^2*b^10*d^14*f^2 + 14*C^2*a^2*b^10*c^14*f^2 + 14*B^2*a^10*b^2*d^14*f^2 - C^2*a^4*b^8*c^14*f^2 - A^
2*a^12*c^6*d^8*f^2 + 120*A^2*a^2*b^10*d^14*f^2 + 112*A^2*a^4*b^8*d^14*f^2 - 17*A^2*a^8*b^4*d^14*f^2 - 10*B^2*a
^2*b^10*c^14*f^2 - 10*A^2*a^10*b^2*d^14*f^2 + 8*A^2*a^6*b^6*d^14*f^2 + 3*B^2*a^4*b^8*c^14*f^2 + 14*A^2*a^2*b^1
0*c^14*f^2 - A^2*a^4*b^8*c^14*f^2 + 3*C^2*a^12*d^14*f^2 - C^2*b^12*c^14*f^2 + 36*A^2*b^12*d^14*f^2 + 3*B^2*b^1
2*c^14*f^2 - B^2*a^12*d^14*f^2 + 3*A^2*a^12*d^14*f^2 - A^2*b^12*c^14*f^2 - 44*A*B*C*a*b^9*c^10*d*f + 3816*A*B*
C*a^5*b^5*c^4*d^7*f + 2920*A*B*C*a^2*b^8*c^5*d^6*f - 2736*A*B*C*a^3*b^7*c^6*d^5*f - 2672*A*B*C*a^4*b^6*c^3*d^8
*f + 1996*A*B*C*a^4*b^6*c^7*d^4*f - 1412*A*B*C*a^6*b^4*c^5*d^6*f + 1120*A*B*C*a^3*b^7*c^2*d^9*f + 1080*A*B*C*a
^2*b^8*c^7*d^4*f + 1040*A*B*C*a^5*b^5*c^2*d^9*f + 684*A*B*C*a^4*b^6*c^5*d^6*f + 592*A*B*C*a^3*b^7*c^4*d^7*f -
560*A*B*C*a^7*b^3*c^2*d^9*f - 448*A*B*C*a^2*b^8*c^3*d^8*f - 400*A*B*C*a^5*b^5*c^8*d^3*f - 398*A*B*C*a^2*b^8*c^
9*d^2*f - 312*A*B*C*a^6*b^4*c^3*d^8*f + 166*A*B*C*a^8*b^2*c^3*d^8*f + 136*A*B*C*a^5*b^5*c^6*d^5*f + 128*A*B*C*
a^7*b^3*c^6*d^5*f - 100*A*B*C*a^6*b^4*c^7*d^4*f + 64*A*B*C*a^7*b^3*c^4*d^7*f - 64*A*B*C*a^4*b^6*c^9*d^2*f - 32
*A*B*C*a^3*b^7*c^8*d^3*f - 16*A*B*C*a^8*b^2*c^5*d^6*f - 1312*A*B*C*a*b^9*c^4*d^7*f + 996*A*B*C*a*b^9*c^8*d^3*f
+ 728*A*B*C*a^6*b^4*c*d^10*f - 624*A*B*C*a*b^9*c^6*d^5*f - 584*A*B*C*a^2*b^8*c*d^10*f - 512*A*B*C*a^4*b^6*c*d
^10*f - 320*A*B*C*a*b^9*c^2*d^9*f - 98*A*B*C*a^8*b^2*c*d^10*f + 36*A*B*C*a^9*b*c^2*d^9*f + 32*A*B*C*a^3*b^7*c^
10*d*f - 16*A*B*C*a^9*b*c^4*d^7*f + 46*B*C^2*a*b^9*c^10*d*f - 16*B^2*C*a*b^9*c*d^10*f - 2*B^2*C*a^9*b*c*d^10*f
+ 312*A^2*C*a*b^9*c*d^10*f - 48*A*C^2*a*b^9*c*d^10*f - 6*A^2*C*a^9*b*c*d^10*f + 6*A*C^2*a^9*b*c*d^10*f + 208*
A*B^2*a*b^9*c*d^10*f - 2*A^2*B*a*b^9*c^10*d*f + 2*A*B^2*a^9*b*c*d^10*f - 480*A*B*C*b^10*c^7*d^4*f + 78*A*B*C*b
^10*c^9*d^2*f - 64*A*B*C*b^10*c^5*d^6*f + 2*A*B*C*a^10*c^3*d^8*f - 224*A*B*C*a^5*b^5*d^11*f + 80*A*B*C*a^7*b^3
*d^11*f - 32*A*B*C*a^3*b^7*d^11*f + 2*A*B*C*a^2*b^8*c^11*f - 1692*B*C^2*a^5*b^5*c^4*d^7*f - 1500*B^2*C*a^5*b^5
*c^5*d^6*f - 1464*B^2*C*a^3*b^7*c^5*d^6*f + 1426*B*C^2*a^6*b^4*c^5*d^6*f - 1158*B^2*C*a^6*b^4*c^4*d^7*f + 1152
*B*C^2*a^3*b^7*c^6*d^5*f + 1026*B^2*C*a^4*b^6*c^6*d^5*f - 974*B*C^2*a^4*b^6*c^7*d^4*f + 960*B^2*C*a^5*b^5*c^3*
d^8*f - 884*B*C^2*a^2*b^8*c^5*d^6*f - 764*B^2*C*a^5*b^5*c^7*d^4*f + 752*B^2*C*a^2*b^8*c^4*d^7*f - 752*B*C^2*a^
3*b^7*c^4*d^7*f + 738*B^2*C*a^4*b^6*c^4*d^7*f - 688*B^2*C*a^6*b^4*c^2*d^9*f - 675*B^2*C*a^2*b^8*c^8*d^3*f + 56
0*B*C^2*a^5*b^5*c^8*d^3*f + 496*B*C^2*a^7*b^3*c^2*d^9*f + 496*B*C^2*a^4*b^6*c^3*d^8*f - 468*B*C^2*a^2*b^8*c^7*
d^4*f + 456*B^2*C*a^7*b^3*c^3*d^8*f - 452*B^2*C*a^4*b^6*c^8*d^3*f - 416*B*C^2*a^3*b^7*c^2*d^9*f + 378*B*C^2*a^
4*b^6*c^5*d^6*f + 376*B*C^2*a^3*b^7*c^8*d^3*f - 360*B^2*C*a^2*b^8*c^6*d^5*f + 355*B*C^2*a^2*b^8*c^9*d^2*f + 34
6*B^2*C*a^6*b^4*c^6*d^5*f - 320*B^2*C*a^4*b^6*c^2*d^9*f + 268*B^2*C*a^2*b^8*c^2*d^9*f + 216*B^2*C*a^3*b^7*c^7*
d^4*f - 203*B*C^2*a^8*b^2*c^3*d^8*f - 184*B*C^2*a^7*b^3*c^6*d^5*f + 170*B*C^2*a^6*b^4*c^7*d^4*f + 160*B^2*C*a^
7*b^3*c^5*d^6*f - 160*B*C^2*a^5*b^5*c^2*d^9*f - 140*B^2*C*a^8*b^2*c^4*d^7*f - 136*B*C^2*a^2*b^8*c^3*d^8*f + 11
2*B^2*C*a^3*b^7*c^9*d^2*f + 91*B^2*C*a^8*b^2*c^2*d^9*f + 88*B*C^2*a^7*b^3*c^4*d^7*f + 72*B^2*C*a^6*b^4*c^8*d^3
*f - 64*B^2*C*a^3*b^7*c^3*d^8*f - 60*B*C^2*a^6*b^4*c^3*d^8*f + 56*B*C^2*a^4*b^6*c^9*d^2*f + 52*B*C^2*a^5*b^5*c
^6*d^5*f - 48*B^2*C*a^7*b^3*c^7*d^4*f + 48*B^2*C*a^5*b^5*c^9*d^2*f + 44*B*C^2*a^8*b^2*c^5*d^6*f - 36*B*C^2*a^6
*b^4*c^9*d^2*f + 12*B^2*C*a^8*b^2*c^6*d^5*f - 2958*A^2*C*a^4*b^6*c^4*d^7*f - 1932*A^2*C*a^2*b^8*c^4*d^7*f + 18
48*A^2*C*a^3*b^7*c^5*d^6*f + 1728*A^2*C*a^3*b^7*c^3*d^8*f + 1524*A^2*C*a^5*b^5*c^5*d^6*f + 1374*A*C^2*a^4*b^6*
c^4*d^7*f - 1272*A*C^2*a^3*b^7*c^5*d^6*f - 1236*A*C^2*a^5*b^5*c^5*d^6*f + 1116*A*C^2*a^2*b^8*c^4*d^7*f - 1110*
A^2*C*a^4*b^6*c^6*d^5*f + 1038*A*C^2*a^4*b^6*c^6*d^5*f - 768*A^2*C*a^2*b^8*c^2*d^9*f - 696*A^2*C*a^3*b^7*c^7*d
^4*f - 666*A*C^2*a^6*b^4*c^4*d^7*f + 564*A^2*C*a^2*b^8*c^6*d^5*f - 564*A*C^2*a^5*b^5*c^7*d^4*f - 555*A*C^2*a^2
*b^8*c^8*d^3*f + 519*A^2*C*a^2*b^8*c^8*d^3*f - 480*A*C^2*a^3*b^7*c^3*d^8*f + 456*A*C^2*a^5*b^5*c^3*d^8*f - 420
*A*C^2*a^6*b^4*c^2*d^9*f + 408*A*C^2*a^3*b^7*c^7*d^4*f + 408*A*C^2*a^2*b^8*c^2*d^9*f + 348*A^2*C*a^6*b^4*c^2*d
^9*f - 348*A*C^2*a^2*b^8*c^6*d^5*f + 342*A*C^2*a^6*b^4*c^6*d^5*f - 336*A*C^2*a^4*b^6*c^8*d^3*f + 324*A^2*C*a^5
*b^5*c^7*d^4*f - 312*A^2*C*a^4*b^6*c^2*d^9*f + 264*A^2*C*a^4*b^6*c^8*d^3*f + 240*A*C^2*a^7*b^3*c^5*d^6*f + 195
*A*C^2*a^8*b^2*c^2*d^9*f - 174*A^2*C*a^6*b^4*c^6*d^5*f + 144*A*C^2*a^3*b^7*c^9*d^2*f - 123*A^2*C*a^8*b^2*c^2*d
^9*f + 120*A*C^2*a^7*b^3*c^3*d^8*f + 108*A*C^2*a^6*b^4*c^8*d^3*f - 102*A^2*C*a^6*b^4*c^4*d^7*f - 96*A^2*C*a^8*
b^2*c^4*d^7*f + 72*A^2*C*a^7*b^3*c^3*d^8*f + 72*A*C^2*a^5*b^5*c^9*d^2*f + 48*A^2*C*a^7*b^3*c^5*d^6*f - 48*A^2*
C*a^3*b^7*c^9*d^2*f - 48*A*C^2*a^4*b^6*c^2*d^9*f - 24*A^2*C*a^5*b^5*c^3*d^8*f - 12*A*C^2*a^8*b^2*c^4*d^7*f + 2
736*A^2*B*a^3*b^7*c^6*d^5*f + 2464*A^2*B*a^4*b^6*c^3*d^8*f - 2298*A*B^2*a^4*b^6*c^4*d^7*f - 2252*A^2*B*a^2*b^8
*c^5*d^6*f - 1692*A^2*B*a^5*b^5*c^4*d^7*f - 1592*A*B^2*a^2*b^8*c^4*d^7*f - 1338*A*B^2*a^4*b^6*c^6*d^5*f + 1320
*A*B^2*a^3*b^7*c^5*d^6*f + 1212*A*B^2*a^5*b^5*c^5*d^6*f - 1056*A*B^2*a^5*b^5*c^3*d^8*f + 1024*A^2*B*a^3*b^7*c^
4*d^7*f - 1022*A^2*B*a^4*b^6*c^7*d^4*f - 880*A^2*B*a^5*b^5*c^2*d^9*f - 846*A^2*B*a^4*b^6*c^5*d^6*f - 840*A*B^2
*a^3*b^7*c^7*d^4*f + 760*A*B^2*a^6*b^4*c^2*d^9*f - 704*A^2*B*a^3*b^7*c^2*d^9*f + 688*A*B^2*a^3*b^7*c^3*d^8*f +
660*A^2*B*a^6*b^4*c^3*d^8*f - 612*A^2*B*a^2*b^8*c^7*d^4*f + 462*A*B^2*a^6*b^4*c^4*d^7*f + 459*A*B^2*a^2*b^8*c
^8*d^3*f - 412*A*B^2*a^2*b^8*c^2*d^9*f - 408*A*B^2*a^7*b^3*c^3*d^8*f + 388*A^2*B*a^5*b^5*c^6*d^5*f + 296*A^2*B
*a^2*b^8*c^3*d^8*f + 288*A*B^2*a^2*b^8*c^6*d^5*f + 284*A*B^2*a^5*b^5*c^7*d^4*f + 236*A*B^2*a^4*b^6*c^8*d^3*f -
226*A*B^2*a^6*b^4*c^6*d^5*f + 212*A*B^2*a^4*b^6*c^2*d^9*f + 202*A^2*B*a^6*b^4*c^5*d^6*f - 152*A^2*B*a^7*b^3*c
^4*d^7*f + 88*A^2*B*a^3*b^7*c^8*d^3*f + 79*A^2*B*a^2*b^8*c^9*d^2*f - 70*A^2*B*a^6*b^4*c^7*d^4*f + 68*A*B^2*a^8
*b^2*c^4*d^7*f + 64*A^2*B*a^7*b^3*c^2*d^9*f - 64*A*B^2*a^3*b^7*c^9*d^2*f + 56*A^2*B*a^7*b^3*c^6*d^5*f + 56*A^2
*B*a^5*b^5*c^8*d^3*f + 37*A^2*B*a^8*b^2*c^3*d^8*f - 28*A^2*B*a^8*b^2*c^5*d^6*f - 28*A^2*B*a^4*b^6*c^9*d^2*f +
17*A*B^2*a^8*b^2*c^2*d^9*f - 16*A*B^2*a^7*b^3*c^5*d^6*f + 24*A*B*C*b^10*c*d^10*f - 6*A*B*C*a^10*c*d^10*f + 48*
A*B*C*a*b^9*d^11*f + 4*A*B*C*a^9*b*d^11*f + 432*B^2*C*a*b^9*c^7*d^4*f - 376*B*C^2*a^6*b^4*c*d^10*f - 354*B*C^2
*a*b^9*c^8*d^3*f + 352*B^2*C*a^5*b^5*c*d^10*f + 320*B^2*C*a*b^9*c^5*d^6*f + 256*B^2*C*a^3*b^7*c*d^10*f - 232*B
^2*C*a^7*b^3*c*d^10*f - 210*B^2*C*a*b^9*c^9*d^2*f - 152*B*C^2*a^4*b^6*c*d^10*f + 85*B*C^2*a^8*b^2*c*d^10*f + 7
2*B^2*C*a*b^9*c^3*d^8*f - 48*B*C^2*a*b^9*c^6*d^5*f - 40*B*C^2*a^3*b^7*c^10*d*f + 40*B*C^2*a^2*b^8*c*d^10*f + 3
7*B^2*C*a^2*b^8*c^10*d*f + 22*B^2*C*a^9*b*c^3*d^8*f - 18*B*C^2*a^9*b*c^2*d^9*f + 16*B*C^2*a*b^9*c^2*d^9*f - 12
*B^2*C*a^4*b^6*c^10*d*f + 8*B*C^2*a^9*b*c^4*d^7*f + 8*B*C^2*a*b^9*c^4*d^7*f - 984*A^2*C*a*b^9*c^7*d^4*f + 672*
A^2*C*a*b^9*c^3*d^8*f + 552*A*C^2*a*b^9*c^7*d^4*f - 504*A^2*C*a^5*b^5*c*d^10*f - 408*A^2*C*a*b^9*c^5*d^6*f + 4
08*A*C^2*a*b^9*c^5*d^6*f + 336*A*C^2*a^5*b^5*c*d^10*f - 216*A*C^2*a^7*b^3*c*d^10*f + 192*A*C^2*a^3*b^7*c*d^10*
f - 162*A*C^2*a*b^9*c^9*d^2*f + 120*A^2*C*a^7*b^3*c*d^10*f + 96*A^2*C*a^3*b^7*c*d^10*f + 90*A^2*C*a*b^9*c^9*d^
2*f + 66*A^2*C*a^9*b*c^3*d^8*f - 66*A*C^2*a^9*b*c^3*d^8*f + 57*A*C^2*a^2*b^8*c^10*d*f - 48*A*C^2*a*b^9*c^3*d^8
*f - 9*A^2*C*a^2*b^8*c^10*d*f + 1736*A^2*B*a*b^9*c^4*d^7*f + 1248*A^2*B*a*b^9*c^6*d^5*f - 1008*A*B^2*a*b^9*c^7
*d^4*f + 772*A^2*B*a^4*b^6*c*d^10*f - 688*A*B^2*a^5*b^5*c*d^10*f - 608*A*B^2*a*b^9*c^5*d^6*f + 436*A^2*B*a^2*b
^8*c*d^10*f - 426*A^2*B*a*b^9*c^8*d^3*f + 312*A*B^2*a*b^9*c^3*d^8*f + 304*A^2*B*a*b^9*c^2*d^9*f - 244*A^2*B*a^
6*b^4*c*d^10*f - 160*A*B^2*a^3*b^7*c*d^10*f + 114*A*B^2*a*b^9*c^9*d^2*f + 88*A*B^2*a^7*b^3*c*d^10*f - 22*A*B^2
*a^9*b*c^3*d^8*f - 18*A^2*B*a^9*b*c^2*d^9*f + 13*A^2*B*a^8*b^2*c*d^10*f - 13*A*B^2*a^2*b^8*c^10*d*f + 8*A^2*B*
a^9*b*c^4*d^7*f + 8*A^2*B*a^3*b^7*c^10*d*f + 111*B^2*C*b^10*c^8*d^3*f - 39*B*C^2*b^10*c^9*d^2*f + 24*B*C^2*b^1
0*c^7*d^4*f - 4*B^2*C*b^10*c^2*d^9*f - 4*B*C^2*b^10*c^5*d^6*f + 432*A^2*C*b^10*c^6*d^5*f + 192*A^2*C*b^10*c^4*
d^7*f - 111*A^2*C*b^10*c^8*d^3*f + 111*A*C^2*b^10*c^8*d^3*f - 72*A*C^2*b^10*c^6*d^5*f + 12*A*C^2*b^10*c^4*d^7*
f - 3*B^2*C*a^10*c^2*d^9*f - B*C^2*a^10*c^3*d^8*f + 456*A^2*B*b^10*c^7*d^4*f - 288*A^2*B*b^10*c^3*d^8*f + 252*
A*B^2*b^10*c^6*d^5*f + 192*A*B^2*b^10*c^4*d^7*f - 183*A*B^2*b^10*c^8*d^3*f - 148*A^2*B*b^10*c^5*d^6*f + 112*B^
2*C*a^6*b^4*d^11*f + 76*A*B^2*b^10*c^2*d^9*f - 64*B*C^2*a^7*b^3*d^11*f + 16*B^2*C*a^4*b^6*d^11*f - 16*B^2*C*a^
2*b^8*d^11*f + 16*B*C^2*a^5*b^5*d^11*f + 16*B*C^2*a^3*b^7*d^11*f - 9*A^2*C*a^10*c^2*d^9*f + 9*A*C^2*a^10*c^2*d
^9*f - 3*A^2*B*b^10*c^9*d^2*f - B^2*C*a^8*b^2*d^11*f + 96*A^2*C*a^4*b^6*d^11*f - 84*A^2*C*a^6*b^4*d^11*f + 72*
A*C^2*a^6*b^4*d^11*f - 24*A*C^2*a^4*b^6*d^11*f - 24*A*C^2*a^2*b^8*d^11*f - 21*A*C^2*a^8*b^2*d^11*f + 12*A^2*C*
a^2*b^8*d^11*f + 9*A^2*C*a^8*b^2*d^11*f + 3*A*B^2*a^10*c^2*d^9*f - A^2*B*a^10*c^3*d^8*f - B*C^2*a^2*b^8*c^11*f
+ 176*A*B^2*a^4*b^6*d^11*f + 136*A^2*B*a^5*b^5*d^11*f - 128*A^2*B*a^3*b^7*d^11*f + 112*A*B^2*a^2*b^8*d^11*f -
64*A*B^2*a^6*b^4*d^11*f - 16*A^2*B*a^7*b^3*d^11*f - A^2*B*a^2*b^8*c^11*f - 2*C^3*a^9*b*c*d^10*f - 2*B^3*a*b^9
*c^10*d*f - 264*A^3*a*b^9*c*d^10*f + 2*A^3*a^9*b*c*d^10*f - 9*B^2*C*b^10*c^10*d*f + 9*A^2*C*b^10*c^10*d*f - 9*
A*C^2*b^10*c^10*d*f + 3*B*C^2*a^10*c*d^10*f - 132*A^2*B*b^10*c*d^10*f - 3*A*B^2*b^10*c^10*d*f - 2*B*C^2*a^9*b*
d^11*f + 3*A^2*B*a^10*c*d^10*f - 2*B^2*C*a*b^9*c^11*f - 120*A^2*B*a*b^9*d^11*f - 6*A^2*C*a*b^9*c^11*f + 6*A*C^
2*a*b^9*c^11*f - 2*A^2*B*a^9*b*d^11*f + 2*A*B^2*a*b^9*c^11*f + 520*C^3*a^3*b^7*c^5*d^6*f + 460*C^3*a^5*b^5*c^5
*d^6*f - 418*C^3*a^4*b^6*c^6*d^5*f + 406*C^3*a^6*b^4*c^4*d^7*f + 268*C^3*a^5*b^5*c^7*d^4*f - 266*C^3*a^6*b^4*c
^6*d^5*f + 233*C^3*a^2*b^8*c^8*d^3*f - 176*C^3*a^7*b^3*c^5*d^6*f + 164*C^3*a^6*b^4*c^2*d^9*f + 140*C^3*a^2*b^8
*c^6*d^5*f + 136*C^3*a^4*b^6*c^2*d^9*f - 128*C^3*a^3*b^7*c^9*d^2*f + 128*C^3*a^3*b^7*c^3*d^8*f - 108*C^3*a^6*b
^4*c^8*d^3*f - 104*C^3*a^7*b^3*c^3*d^8*f - 104*C^3*a^5*b^5*c^3*d^8*f + 100*C^3*a^4*b^6*c^8*d^3*f - 89*C^3*a^8*
b^2*c^2*d^9*f - 72*C^3*a^5*b^5*c^9*d^2*f + 40*C^3*a^8*b^2*c^4*d^7*f - 40*C^3*a^3*b^7*c^7*d^4*f - 28*C^3*a^2*b^
8*c^4*d^7*f - 16*C^3*a^2*b^8*c^2*d^9*f - 2*C^3*a^4*b^6*c^4*d^7*f + 828*B^3*a^5*b^5*c^4*d^7*f + 408*B^3*a^2*b^8
*c^5*d^6*f + 390*B^3*a^4*b^6*c^7*d^4*f - 372*B^3*a^4*b^6*c^3*d^8*f - 336*B^3*a^3*b^7*c^6*d^5*f - 314*B^3*a^6*b
^4*c^5*d^6*f + 288*B^3*a^3*b^7*c^4*d^7*f + 216*B^3*a^2*b^8*c^7*d^4*f - 176*B^3*a^7*b^3*c^2*d^9*f + 128*B^3*a^3
*b^7*c^2*d^9*f + 108*B^3*a^5*b^5*c^6*d^5*f + 88*B^3*a^7*b^3*c^4*d^7*f + 72*B^3*a^5*b^5*c^2*d^9*f - 68*B^3*a^2*
b^8*c^3*d^8*f - 65*B^3*a^2*b^8*c^9*d^2*f - 56*B^3*a^5*b^5*c^8*d^3*f + 40*B^3*a^7*b^3*c^6*d^5*f + 37*B^3*a^8*b^
2*c^3*d^8*f + 30*B^3*a^4*b^6*c^5*d^6*f - 28*B^3*a^8*b^2*c^5*d^6*f + 24*B^3*a^3*b^7*c^8*d^3*f - 4*B^3*a^4*b^6*c
^9*d^2*f - 2*B^3*a^6*b^4*c^7*d^4*f + 1586*A^3*a^4*b^6*c^4*d^7*f - 1376*A^3*a^3*b^7*c^3*d^8*f - 1096*A^3*a^3*b^
7*c^5*d^6*f + 844*A^3*a^2*b^8*c^4*d^7*f - 748*A^3*a^5*b^5*c^5*d^6*f + 490*A^3*a^4*b^6*c^6*d^5*f + 376*A^3*a^2*
b^8*c^2*d^9*f + 362*A^3*a^6*b^4*c^4*d^7*f - 356*A^3*a^2*b^8*c^6*d^5*f - 328*A^3*a^5*b^5*c^3*d^8*f + 328*A^3*a^
3*b^7*c^7*d^4*f + 224*A^3*a^4*b^6*c^2*d^9*f - 197*A^3*a^2*b^8*c^8*d^3*f - 112*A^3*a^7*b^3*c^5*d^6*f + 98*A^3*a
^6*b^4*c^6*d^5*f - 92*A^3*a^6*b^4*c^2*d^9*f - 88*A^3*a^7*b^3*c^3*d^8*f + 68*A^3*a^8*b^2*c^4*d^7*f + 32*A^3*a^3
*b^7*c^9*d^2*f - 28*A^3*a^5*b^5*c^7*d^4*f - 28*A^3*a^4*b^6*c^8*d^3*f + 17*A^3*a^8*b^2*c^2*d^9*f + 104*C^3*a^7*
b^3*c*d^10*f + 54*C^3*a*b^9*c^9*d^2*f - 40*C^3*a*b^9*c^7*d^4*f - 35*C^3*a^2*b^8*c^10*d*f + 22*C^3*a^9*b*c^3*d^
8*f + 16*C^3*a^5*b^5*c*d^10*f - 16*C^3*a^3*b^7*c*d^10*f + 8*C^3*a*b^9*c^5*d^6*f - 2*A*B*C*b^10*c^11*f + 198*B^
3*a*b^9*c^8*d^3*f + 192*B^3*a^6*b^4*c*d^10*f - 128*B^3*a*b^9*c^4*d^7*f - 80*B^3*a^2*b^8*c*d^10*f - 56*B^3*a*b^
9*c^2*d^9*f - 24*B^3*a*b^9*c^6*d^5*f - 18*B^3*a^9*b*c^2*d^9*f - 16*B^3*a^4*b^6*c*d^10*f + 13*B^3*a^8*b^2*c*d^1
0*f + 8*B^3*a^9*b*c^4*d^7*f + 8*B^3*a^3*b^7*c^10*d*f - 624*A^3*a*b^9*c^3*d^8*f + 472*A^3*a*b^9*c^7*d^4*f - 272
*A^3*a^3*b^7*c*d^10*f + 152*A^3*a^5*b^5*c*d^10*f - 22*A^3*a^9*b*c^3*d^8*f + 18*A^3*a*b^9*c^9*d^2*f - 13*A^3*a^
2*b^8*c^10*d*f - 8*A^3*a^7*b^3*c*d^10*f - 8*A^3*a*b^9*c^5*d^6*f + A*B^2*a^8*b^2*d^11*f - C^3*b^10*c^8*d^3*f -
60*B^3*b^10*c^7*d^4*f - 32*B^3*b^10*c^5*d^6*f + 21*B^3*b^10*c^9*d^2*f - 12*B^3*b^10*c^3*d^8*f - 3*C^3*a^10*c^2
*d^9*f - 360*A^3*b^10*c^6*d^5*f - 204*A^3*b^10*c^4*d^7*f + 11*C^3*a^8*b^2*d^11*f - 8*C^3*a^6*b^4*d^11*f - 4*C^
3*a^4*b^6*d^11*f - B^3*a^10*c^3*d^8*f - 64*B^3*a^5*b^5*d^11*f - 32*B^3*a^3*b^7*d^11*f + 3*A^3*a^10*c^2*d^9*f -
68*A^3*a^4*b^6*d^11*f + 20*A^3*a^6*b^4*d^11*f + 12*A^3*a^2*b^8*d^11*f - B^3*a^2*b^8*c^11*f + 3*C^3*b^10*c^10*
d*f + 3*B^3*a^10*c*d^10*f - 3*A^3*b^10*c^10*d*f - 2*C^3*a*b^9*c^11*f - 2*B^3*a^9*b*d^11*f + 2*A^3*a*b^9*c^11*f
- 36*A^2*C*b^10*d^11*f + 3*A^2*C*a^10*d^11*f - 3*A*C^2*a^10*d^11*f - A*B^2*a^10*d^11*f + 36*A^3*b^10*d^11*f -
A^3*a^10*d^11*f + A^3*b^10*c^8*d^3*f + A^3*a^8*b^2*d^11*f + B^2*C*a^10*d^11*f + B*C^2*b^10*c^11*f + A^2*B*b^1
0*c^11*f + C^3*a^10*d^11*f + B^3*b^10*c^11*f - 6*A*B^2*C*a*b^7*c^7*d + 4*A*B^2*C*a*b^7*c*d^7 + 168*A^2*B*C*a^3
*b^5*c^2*d^6 + 144*A*B*C^2*a^4*b^4*c^3*d^5 - 129*A^2*B*C*a^4*b^4*c^3*d^5 - 96*A*B*C^2*a^3*b^5*c^2*d^6 + 84*A*B
*C^2*a^2*b^6*c^3*d^5 + 72*A^2*B*C*a^3*b^5*c^4*d^4 - 72*A^2*B*C*a^2*b^6*c^3*d^5 + 64*A*B^2*C*a^4*b^4*c^4*d^4 -
60*A*B*C^2*a^3*b^5*c^4*d^4 + 57*A^2*B*C*a^2*b^6*c^5*d^3 - 56*A*B^2*C*a^3*b^5*c^5*d^3 - 39*A*B^2*C*a^4*b^4*c^2*
d^6 - 38*A*B^2*C*a^5*b^3*c^3*d^5 + 36*A*B^2*C*a^3*b^5*c^3*d^5 + 36*A*B*C^2*a^4*b^4*c^5*d^3 - 30*A*B*C^2*a^2*b^
6*c^5*d^3 + 27*A*B^2*C*a^2*b^6*c^6*d^2 - 24*A*B^2*C*a^2*b^6*c^2*d^6 - 24*A*B*C^2*a^5*b^3*c^4*d^4 + 24*A*B*C^2*
a^3*b^5*c^6*d^2 + 18*A^2*B*C*a^5*b^3*c^2*d^6 - 18*A^2*B*C*a^4*b^4*c^5*d^3 - 15*A*B^2*C*a^2*b^6*c^4*d^4 + 12*A^
2*B*C*a^5*b^3*c^4*d^4 - 12*A^2*B*C*a^3*b^5*c^6*d^2 + 9*A*B^2*C*a^6*b^2*c^2*d^6 + 6*A*B*C^2*a^6*b^2*c^3*d^5 - 3
*A^2*B*C*a^6*b^2*c^3*d^5 + 60*A^2*B*C*a*b^7*c^2*d^6 - 51*A^2*B*C*a^4*b^4*c*d^7 + 48*A*B*C^2*a*b^7*c^6*d^2 - 42
*A^2*B*C*a^2*b^6*c*d^7 - 42*A^2*B*C*a*b^7*c^6*d^2 + 36*A*B*C^2*a^4*b^4*c*d^7 + 36*A*B*C^2*a^2*b^6*c*d^7 + 36*A
*B*C^2*a*b^7*c^4*d^4 - 30*A^2*B*C*a*b^7*c^4*d^4 + 24*A*B^2*C*a*b^7*c^3*d^5 - 24*A*B*C^2*a*b^7*c^2*d^6 + 18*A*B
^2*C*a^5*b^3*c*d^7 - 18*A*B*C^2*a^6*b^2*c*d^7 + 12*A*B^2*C*a^3*b^5*c*d^7 + 9*A^2*B*C*a^6*b^2*c*d^7 + 6*A*B^2*C
*a*b^7*c^5*d^3 - 6*A*B*C^2*a^2*b^6*c^7*d + 3*A^2*B*C*a^2*b^6*c^7*d - 18*B^3*C*a*b^7*c^6*d^2 - 18*B*C^3*a*b^7*c
^6*d^2 - 14*B^3*C*a*b^7*c^4*d^4 - 14*B*C^3*a*b^7*c^4*d^4 - 10*B^3*C*a^2*b^6*c*d^7 - 10*B*C^3*a^2*b^6*c*d^7 + 9
*B^3*C*a^6*b^2*c*d^7 + 9*B*C^3*a^6*b^2*c*d^7 - 7*B^3*C*a^4*b^4*c*d^7 - 7*B*C^3*a^4*b^4*c*d^7 + 6*B^2*C^2*a*b^7
*c^7*d - 4*B^3*C*a*b^7*c^2*d^6 + 4*B^2*C^2*a*b^7*c*d^7 - 4*B*C^3*a*b^7*c^2*d^6 + 3*B^3*C*a^2*b^6*c^7*d + 3*B*C
^3*a^2*b^6*c^7*d + 144*A^3*C*a*b^7*c^3*d^5 + 62*A^3*C*a*b^7*c^5*d^3 + 48*A*C^3*a*b^7*c^3*d^5 - 36*A^2*C^2*a*b^
7*c*d^7 + 26*A*C^3*a*b^7*c^5*d^3 + 20*A^3*C*a^3*b^5*c*d^7 + 18*A^2*C^2*a*b^7*c^7*d - 18*A*C^3*a^5*b^3*c*d^7 -
6*A^3*C*a^5*b^3*c*d^7 - 4*A*C^3*a^3*b^5*c*d^7 - 32*A^3*B*a*b^7*c^2*d^6 - 32*A*B^3*a*b^7*c^2*d^6 + 22*A^3*B*a^4
*b^4*c*d^7 + 22*A*B^3*a^4*b^4*c*d^7 + 16*A^3*B*a^2*b^6*c*d^7 + 16*A*B^3*a^2*b^6*c*d^7 + 12*A^3*B*a*b^7*c^6*d^2
+ 12*A*B^3*a*b^7*c^6*d^2 + 8*A^3*B*a*b^7*c^4*d^4 - 8*A^2*B^2*a*b^7*c*d^7 + 8*A*B^3*a*b^7*c^4*d^4 + 57*A^2*B*C
*b^8*c^5*d^3 + 36*A^2*B*C*b^8*c^3*d^5 - 30*A*B*C^2*b^8*c^5*d^3 - 18*A*B*C^2*b^8*c^3*d^5 - 9*A*B^2*C*b^8*c^4*d^
4 - 3*A*B^2*C*b^8*c^6*d^2 - 2*A*B^2*C*b^8*c^2*d^6 + 36*A^2*B*C*a^3*b^5*d^8 + 24*A*B*C^2*a^5*b^3*d^8 - 18*A^2*B
*C*a^5*b^3*d^8 - 12*A*B*C^2*a^3*b^5*d^8 - 3*A*B^2*C*a^6*b^2*d^8 - 3*A*B^2*C*a^4*b^4*d^8 - 2*A*B^2*C*a^2*b^6*d^
8 + 34*B^2*C^2*a^5*b^3*c^3*d^5 + 28*B^2*C^2*a^3*b^5*c^5*d^3 + 24*B^2*C^2*a^4*b^4*c^2*d^6 - 20*B^2*C^2*a^4*b^4*
c^4*d^4 + 12*B^2*C^2*a^3*b^5*c^3*d^5 + 12*B^2*C^2*a^2*b^6*c^2*d^6 - 9*B^2*C^2*a^6*b^2*c^2*d^6 + 9*B^2*C^2*a^4*
b^4*c^6*d^2 + 9*B^2*C^2*a^2*b^6*c^4*d^4 - 3*B^2*C^2*a^2*b^6*c^6*d^2 + 159*A^2*C^2*a^2*b^6*c^4*d^4 - 156*A^2*C^
2*a^3*b^5*c^3*d^5 + 90*A^2*C^2*a^5*b^3*c^3*d^5 + 78*A^2*C^2*a^2*b^6*c^2*d^6 - 63*A^2*C^2*a^4*b^4*c^4*d^4 - 27*
A^2*C^2*a^6*b^2*c^2*d^6 - 27*A^2*C^2*a^2*b^6*c^6*d^2 - 18*A^2*C^2*a^4*b^4*c^2*d^6 + 9*A^2*C^2*a^4*b^4*c^6*d^2
+ 66*A^2*B^2*a^2*b^6*c^2*d^6 + 60*A^2*B^2*a^2*b^6*c^4*d^4 - 48*A^2*B^2*a^3*b^5*c^3*d^5 + 42*A^2*B^2*a^4*b^4*c^
2*d^6 + 28*A^2*B^2*a^3*b^5*c^5*d^3 - 17*A^2*B^2*a^4*b^4*c^4*d^4 - 6*A^2*B^2*a^2*b^6*c^6*d^2 + 4*A^2*B^2*a^5*b^
3*c^3*d^5 + 36*A^3*C*a*b^7*c*d^7 - 18*A*C^3*a*b^7*c^7*d + 12*A*C^3*a*b^7*c*d^7 - 6*A^3*C*a*b^7*c^7*d + 12*A^2*
B*C*b^8*c*d^7 + 6*A*B*C^2*b^8*c^7*d - 6*A*B*C^2*b^8*c*d^7 - 3*A^2*B*C*b^8*c^7*d + 24*A^2*B*C*a*b^7*d^8 - 12*A*
B*C^2*a*b^7*d^8 - 53*B^3*C*a^4*b^4*c^3*d^5 - 53*B*C^3*a^4*b^4*c^3*d^5 - 32*B^3*C*a^2*b^6*c^3*d^5 - 32*B*C^3*a^
2*b^6*c^3*d^5 - 18*B^3*C*a^4*b^4*c^5*d^3 - 18*B*C^3*a^4*b^4*c^5*d^3 + 16*B^3*C*a^3*b^5*c^4*d^4 + 16*B*C^3*a^3*
b^5*c^4*d^4 + 12*B^3*C*a^5*b^3*c^4*d^4 - 12*B^3*C*a^3*b^5*c^6*d^2 + 12*B^2*C^2*a*b^7*c^3*d^5 + 12*B*C^3*a^5*b^
3*c^4*d^4 - 12*B*C^3*a^3*b^5*c^6*d^2 + 8*B^3*C*a^3*b^5*c^2*d^6 + 8*B*C^3*a^3*b^5*c^2*d^6 - 6*B^3*C*a^5*b^3*c^2
*d^6 - 6*B^2*C^2*a^5*b^3*c*d^7 + 6*B^2*C^2*a*b^7*c^5*d^3 - 6*B*C^3*a^5*b^3*c^2*d^6 - 3*B^3*C*a^6*b^2*c^3*d^5 -
3*B*C^3*a^6*b^2*c^3*d^5 - 175*A^3*C*a^2*b^6*c^4*d^4 + 164*A^3*C*a^3*b^5*c^3*d^5 - 144*A^2*C^2*a*b^7*c^3*d^5 -
124*A^3*C*a^2*b^6*c^2*d^6 - 90*A*C^3*a^5*b^3*c^3*d^5 - 73*A*C^3*a^2*b^6*c^4*d^4 - 66*A^2*C^2*a*b^7*c^5*d^3 +
44*A*C^3*a^3*b^5*c^3*d^5 + 36*A*C^3*a^4*b^4*c^4*d^4 - 30*A^3*C*a^5*b^3*c^3*d^5 + 30*A^3*C*a^4*b^4*c^4*d^4 + 27
*A*C^3*a^6*b^2*c^2*d^6 + 21*A*C^3*a^4*b^4*c^2*d^6 + 18*A^2*C^2*a^5*b^3*c*d^7 - 18*A*C^3*a^4*b^4*c^6*d^2 - 16*A
*C^3*a^2*b^6*c^2*d^6 - 15*A^3*C*a^4*b^4*c^2*d^6 + 15*A^3*C*a^2*b^6*c^6*d^2 - 12*A^2*C^2*a^3*b^5*c*d^7 + 9*A^3*
C*a^6*b^2*c^2*d^6 + 9*A*C^3*a^2*b^6*c^6*d^2 - 80*A^3*B*a^3*b^5*c^2*d^6 - 80*A*B^3*a^3*b^5*c^2*d^6 + 38*A^3*B*a
^4*b^4*c^3*d^5 + 38*A*B^3*a^4*b^4*c^3*d^5 - 36*A^2*B^2*a*b^7*c^3*d^5 - 28*A^3*B*a^3*b^5*c^4*d^4 - 28*A^3*B*a^2
*b^6*c^5*d^3 - 28*A*B^3*a^3*b^5*c^4*d^4 - 28*A*B^3*a^2*b^6*c^5*d^3 + 20*A^3*B*a^2*b^6*c^3*d^5 + 20*A*B^3*a^2*b
^6*c^3*d^5 - 12*A^3*B*a^5*b^3*c^2*d^6 - 12*A^2*B^2*a^5*b^3*c*d^7 - 12*A^2*B^2*a^3*b^5*c*d^7 - 12*A^2*B^2*a*b^7
*c^5*d^3 - 12*A*B^3*a^5*b^3*c^2*d^6 + 6*B^2*C^2*b^8*c^6*d^2 + 3*B^2*C^2*b^8*c^4*d^4 + 36*A^2*C^2*b^8*c^4*d^4 +
27*A^2*C^2*b^8*c^2*d^6 - 18*A^2*C^2*b^8*c^6*d^2 + 33*A^2*B^2*b^8*c^4*d^4 + 28*A^2*B^2*b^8*c^2*d^6 + 9*B^2*C^2
*a^4*b^4*d^8 + 6*A^2*B^2*b^8*c^6*d^2 + 4*B^2*C^2*a^2*b^6*d^8 + 3*B^2*C^2*a^6*b^2*d^8 - 30*A^2*C^2*a^4*b^4*d^8
+ 9*A^2*C^2*a^6*b^2*d^8 + 16*A^2*B^2*a^2*b^6*d^8 + 3*A^2*B^2*a^4*b^4*d^8 + 6*C^4*a^5*b^3*c*d^7 + 4*C^4*a^3*b^5
*c*d^7 - 2*C^4*a*b^7*c^5*d^3 - 12*B^4*a^5*b^3*c*d^7 + 12*B^4*a*b^7*c^3*d^5 + 8*B^4*a*b^7*c^5*d^3 - 4*B^4*a^3*b
^5*c*d^7 - 48*A^4*a*b^7*c^3*d^5 - 20*A^4*a*b^7*c^5*d^3 - 8*A^4*a^3*b^5*c*d^7 - 63*A^3*C*b^8*c^4*d^4 - 54*A^3*C
*b^8*c^2*d^6 + 9*A^3*C*b^8*c^6*d^2 + 9*A*C^3*b^8*c^6*d^2 - 3*A*C^3*b^8*c^4*d^4 - 28*A^3*B*b^8*c^5*d^3 - 28*A*B
^3*b^8*c^5*d^3 - 18*A^3*B*b^8*c^3*d^5 - 18*A*B^3*b^8*c^3*d^5 - 10*B^3*C*a^5*b^3*d^8 - 10*B*C^3*a^5*b^3*d^8 - 4
*B^3*C*a^3*b^5*d^8 - 4*B*C^3*a^3*b^5*d^8 + 23*A^3*C*a^4*b^4*d^8 - 18*A^3*C*a^2*b^6*d^8 + 11*A*C^3*a^4*b^4*d^8
- 9*A*C^3*a^6*b^2*d^8 + 6*A*C^3*a^2*b^6*d^8 - 3*A^3*C*a^6*b^2*d^8 - 20*A^3*B*a^3*b^5*d^8 - 20*A*B^3*a^3*b^5*d^
8 + 4*A^3*B*a^5*b^3*d^8 + 4*A*B^3*a^5*b^3*d^8 + B^3*C*a^2*b^6*c^5*d^3 + B*C^3*a^2*b^6*c^5*d^3 + 6*C^4*a*b^7*c^
7*d + 4*B^4*a*b^7*c*d^7 - 12*A^4*a*b^7*c*d^7 - 3*B^3*C*b^8*c^7*d - 3*B*C^3*b^8*c^7*d - 6*A^3*B*b^8*c*d^7 - 6*A
*B^3*b^8*c*d^7 - 12*A^3*B*a*b^7*d^8 - 12*A*B^3*a*b^7*d^8 + 30*C^4*a^5*b^3*c^3*d^5 + 19*C^4*a^2*b^6*c^4*d^4 - 9
*C^4*a^6*b^2*c^2*d^6 + 9*C^4*a^4*b^4*c^6*d^2 + 4*C^4*a^3*b^5*c^3*d^5 + 4*C^4*a^2*b^6*c^2*d^6 - 3*C^4*a^4*b^4*c
^4*d^4 - 3*C^4*a^4*b^4*c^2*d^6 + 3*C^4*a^2*b^6*c^6*d^2 + 28*B^4*a^3*b^5*c^5*d^3 + 27*B^4*a^4*b^4*c^2*d^6 - 17*
B^4*a^4*b^4*c^4*d^4 - 10*B^4*a^2*b^6*c^4*d^4 + 8*B^4*a^3*b^5*c^3*d^5 + 8*B^4*a^2*b^6*c^2*d^6 - 6*B^4*a^2*b^6*c
^6*d^2 + 4*B^4*a^5*b^3*c^3*d^5 + 70*A^4*a^2*b^6*c^4*d^4 + 58*A^4*a^2*b^6*c^2*d^6 - 56*A^4*a^3*b^5*c^3*d^5 + 15
*A^4*a^4*b^4*c^2*d^6 + B^2*C^2*b^8*c^2*d^6 - 18*A^3*C*b^8*d^8 + B^3*C*b^8*c^5*d^3 + B*C^3*b^8*c^5*d^3 + 6*B^4*
b^8*c^6*d^2 + 3*B^4*b^8*c^4*d^4 + 30*A^4*b^8*c^4*d^4 + 27*A^4*b^8*c^2*d^6 + 3*C^4*a^6*b^2*d^8 + 8*B^4*a^4*b^4*
d^8 + 4*B^4*a^2*b^6*d^8 + 12*A^4*a^2*b^6*d^8 - 5*A^4*a^4*b^4*d^8 + 9*A^2*C^2*b^8*d^8 + 9*A^2*B^2*b^8*d^8 + 9*A
^4*b^8*d^8 + B^4*b^8*c^2*d^6 + C^4*a^4*b^4*d^8, f, k)*((4*a^7*b^8*d^19 + 4*a^9*b^6*d^19 - 4*a^11*b^4*d^19 - 4*
a^13*b^2*d^19 + 4*b^15*c^7*d^12 + 12*b^15*c^9*d^10 + 8*b^15*c^11*d^8 - 8*b^15*c^13*d^6 - 12*b^15*c^15*d^4 - 4*
b^15*c^17*d^2 - 20*a*b^14*c^6*d^13 - 44*a*b^14*c^8*d^11 + 32*a*b^14*c^10*d^9 + 168*a*b^14*c^12*d^7 + 172*a*b^1
4*c^14*d^5 + 68*a*b^14*c^16*d^3 + 16*a^3*b^12*c^18*d + 8*a^5*b^10*c^18*d - 20*a^6*b^9*c*d^18 - 4*a^8*b^7*c*d^1
8 + 60*a^10*b^5*c*d^18 + 52*a^12*b^3*c*d^18 + 32*a^14*b*c^3*d^16 + 48*a^14*b*c^5*d^14 + 32*a^14*b*c^7*d^12 + 8
*a^14*b*c^9*d^10 + 36*a^2*b^13*c^5*d^14 + 32*a^2*b^13*c^7*d^12 - 292*a^2*b^13*c^9*d^10 - 768*a^2*b^13*c^11*d^8
- 772*a^2*b^13*c^13*d^6 - 352*a^2*b^13*c^15*d^4 - 60*a^2*b^13*c^17*d^2 - 20*a^3*b^12*c^4*d^15 + 64*a^3*b^12*c
^6*d^13 + 668*a^3*b^12*c^8*d^11 + 1648*a^3*b^12*c^10*d^9 + 1892*a^3*b^12*c^12*d^7 + 1088*a^3*b^12*c^14*d^5 + 2
76*a^3*b^12*c^16*d^3 - 20*a^4*b^11*c^3*d^16 - 104*a^4*b^11*c^5*d^14 - 640*a^4*b^11*c^7*d^12 - 2028*a^4*b^11*c^
9*d^10 - 3092*a^4*b^11*c^11*d^8 - 2368*a^4*b^11*c^13*d^6 - 856*a^4*b^11*c^15*d^4 - 108*a^4*b^11*c^17*d^2 + 36*
a^5*b^10*c^2*d^17 + 8*a^5*b^10*c^4*d^15 + 112*a^5*b^10*c^6*d^13 + 1404*a^5*b^10*c^8*d^11 + 3404*a^5*b^10*c^10*
d^9 + 3552*a^5*b^10*c^12*d^7 + 1752*a^5*b^10*c^14*d^5 + 348*a^5*b^10*c^16*d^3 + 64*a^6*b^9*c^3*d^16 + 392*a^6*
b^9*c^5*d^14 + 32*a^6*b^9*c^7*d^12 - 1864*a^6*b^9*c^9*d^10 - 3296*a^6*b^9*c^11*d^8 - 2360*a^6*b^9*c^13*d^6 - 7
04*a^6*b^9*c^15*d^4 - 52*a^6*b^9*c^17*d^2 - 32*a^7*b^8*c^2*d^17 - 568*a^7*b^8*c^4*d^15 - 1504*a^7*b^8*c^6*d^13
- 976*a^7*b^8*c^8*d^11 + 1120*a^7*b^8*c^10*d^9 + 1912*a^7*b^8*c^12*d^7 + 928*a^7*b^8*c^14*d^5 + 140*a^7*b^8*c
^16*d^3 + 472*a^8*b^7*c^3*d^16 + 2016*a^8*b^7*c^5*d^14 + 3076*a^8*b^7*c^7*d^12 + 1724*a^8*b^7*c^9*d^10 - 288*a
^8*b^7*c^11*d^8 - 664*a^8*b^7*c^13*d^6 - 188*a^8*b^7*c^15*d^4 - 240*a^9*b^6*c^2*d^17 - 1472*a^9*b^6*c^4*d^15 -
3316*a^9*b^6*c^6*d^13 - 3484*a^9*b^6*c^8*d^11 - 1592*a^9*b^6*c^10*d^9 - 104*a^9*b^6*c^12*d^7 + 92*a^9*b^6*c^1
4*d^5 + 704*a^10*b^5*c^3*d^16 + 2308*a^10*b^5*c^5*d^14 + 3392*a^10*b^5*c^7*d^12 + 2468*a^10*b^5*c^9*d^10 + 832
*a^10*b^5*c^11*d^8 + 92*a^10*b^5*c^13*d^6 - 240*a^11*b^4*c^2*d^17 - 1108*a^11*b^4*c^4*d^15 - 2112*a^11*b^4*c^6
*d^13 - 2028*a^11*b^4*c^8*d^11 - 976*a^11*b^4*c^10*d^9 - 188*a^11*b^4*c^12*d^7 + 348*a^12*b^3*c^3*d^16 + 872*a
^12*b^3*c^5*d^14 + 1048*a^12*b^3*c^7*d^12 + 612*a^12*b^3*c^9*d^10 + 140*a^12*b^3*c^11*d^8 - 68*a^13*b^2*c^2*d^
17 - 232*a^13*b^2*c^4*d^15 - 328*a^13*b^2*c^6*d^13 - 212*a^13*b^2*c^8*d^11 - 52*a^13*b^2*c^10*d^9 + 8*a*b^14*c
^18*d + 8*a^14*b*c*d^18)/(a^10*d^14 + b^10*c^14 + 2*a^2*b^8*c^14 + a^4*b^6*c^14 + a^6*b^4*d^14 + 2*a^8*b^2*d^1
4 + 4*a^10*c^2*d^12 + 6*a^10*c^4*d^10 + 4*a^10*c^6*d^8 + a^10*c^8*d^6 + b^10*c^6*d^8 + 4*b^10*c^8*d^6 + 6*b^10
*c^10*d^4 + 4*b^10*c^12*d^2 - 6*a*b^9*c^5*d^9 - 24*a*b^9*c^7*d^7 - 36*a*b^9*c^9*d^5 - 24*a*b^9*c^11*d^3 - 12*a
^3*b^7*c^13*d - 6*a^5*b^5*c*d^13 - 6*a^5*b^5*c^13*d - 12*a^7*b^3*c*d^13 - 24*a^9*b*c^3*d^11 - 36*a^9*b*c^5*d^9
- 24*a^9*b*c^7*d^7 - 6*a^9*b*c^9*d^5 + 15*a^2*b^8*c^4*d^10 + 62*a^2*b^8*c^6*d^8 + 98*a^2*b^8*c^8*d^6 + 72*a^2
*b^8*c^10*d^4 + 23*a^2*b^8*c^12*d^2 - 20*a^3*b^7*c^3*d^11 - 92*a^3*b^7*c^5*d^9 - 168*a^3*b^7*c^7*d^7 - 152*a^3
*b^7*c^9*d^5 - 68*a^3*b^7*c^11*d^3 + 15*a^4*b^6*c^2*d^12 + 90*a^4*b^6*c^4*d^10 + 211*a^4*b^6*c^6*d^8 + 244*a^4
*b^6*c^8*d^6 + 141*a^4*b^6*c^10*d^4 + 34*a^4*b^6*c^12*d^2 - 64*a^5*b^5*c^3*d^11 - 202*a^5*b^5*c^5*d^9 - 288*a^
5*b^5*c^7*d^7 - 202*a^5*b^5*c^9*d^5 - 64*a^5*b^5*c^11*d^3 + 34*a^6*b^4*c^2*d^12 + 141*a^6*b^4*c^4*d^10 + 244*a
^6*b^4*c^6*d^8 + 211*a^6*b^4*c^8*d^6 + 90*a^6*b^4*c^10*d^4 + 15*a^6*b^4*c^12*d^2 - 68*a^7*b^3*c^3*d^11 - 152*a
^7*b^3*c^5*d^9 - 168*a^7*b^3*c^7*d^7 - 92*a^7*b^3*c^9*d^5 - 20*a^7*b^3*c^11*d^3 + 23*a^8*b^2*c^2*d^12 + 72*a^8
*b^2*c^4*d^10 + 98*a^8*b^2*c^6*d^8 + 62*a^8*b^2*c^8*d^6 + 15*a^8*b^2*c^10*d^4 - 6*a*b^9*c^13*d - 6*a^9*b*c*d^1
3) + (tan(e + f*x)*(6*a^14*b*d^19 + 6*b^15*c^18*d + 8*a^6*b^9*d^19 + 22*a^8*b^7*d^19 + 26*a^10*b^5*d^19 + 18*a
^12*b^3*d^19 + 8*b^15*c^6*d^13 + 38*b^15*c^8*d^11 + 78*b^15*c^10*d^9 + 92*b^15*c^12*d^7 + 68*b^15*c^14*d^5 + 3
0*b^15*c^16*d^3 - 48*a*b^14*c^5*d^14 - 224*a*b^14*c^7*d^12 - 448*a*b^14*c^9*d^10 - 512*a*b^14*c^11*d^8 - 368*a
*b^14*c^13*d^6 - 160*a*b^14*c^15*d^4 - 32*a*b^14*c^17*d^2 + 10*a^2*b^13*c^18*d + 2*a^4*b^11*c^18*d - 48*a^5*b^
10*c*d^18 - 2*a^6*b^9*c^18*d - 128*a^7*b^8*c*d^18 - 144*a^9*b^6*c*d^18 - 96*a^11*b^4*c*d^18 - 32*a^13*b^2*c*d^
18 + 22*a^14*b*c^2*d^17 + 28*a^14*b*c^4*d^15 + 12*a^14*b*c^6*d^13 - 2*a^14*b*c^8*d^11 - 2*a^14*b*c^10*d^9 + 12
0*a^2*b^13*c^4*d^15 + 568*a^2*b^13*c^6*d^13 + 1138*a^2*b^13*c^8*d^11 + 1282*a^2*b^13*c^10*d^9 + 908*a^2*b^13*c
^12*d^7 + 412*a^2*b^13*c^14*d^5 + 106*a^2*b^13*c^16*d^3 - 160*a^3*b^12*c^3*d^16 - 832*a^3*b^12*c^5*d^14 - 1776
*a^3*b^12*c^7*d^12 - 2032*a^3*b^12*c^9*d^10 - 1408*a^3*b^12*c^11*d^8 - 672*a^3*b^12*c^13*d^6 - 240*a^3*b^12*c^
15*d^4 - 48*a^3*b^12*c^17*d^2 + 120*a^4*b^11*c^2*d^17 + 820*a^4*b^11*c^4*d^15 + 2044*a^4*b^11*c^6*d^13 + 2434*
a^4*b^11*c^8*d^11 + 1498*a^4*b^11*c^10*d^9 + 552*a^4*b^11*c^12*d^7 + 208*a^4*b^11*c^14*d^5 + 66*a^4*b^11*c^16*
d^3 - 608*a^5*b^10*c^3*d^16 - 1904*a^5*b^10*c^5*d^14 - 2384*a^5*b^10*c^7*d^12 - 976*a^5*b^10*c^9*d^10 + 448*a^
5*b^10*c^11*d^8 + 496*a^5*b^10*c^13*d^6 + 112*a^5*b^10*c^15*d^4 + 344*a^6*b^9*c^2*d^17 + 1428*a^6*b^9*c^4*d^15
+ 1988*a^6*b^9*c^6*d^13 + 214*a^6*b^9*c^8*d^11 - 2058*a^6*b^9*c^10*d^9 - 2000*a^6*b^9*c^12*d^7 - 688*a^6*b^9*
c^14*d^5 - 66*a^6*b^9*c^16*d^3 - 848*a^7*b^8*c^3*d^16 - 1520*a^7*b^8*c^5*d^14 + 80*a^7*b^8*c^7*d^12 + 3056*a^7
*b^8*c^9*d^10 + 3536*a^7*b^8*c^11*d^8 + 1648*a^7*b^8*c^13*d^6 + 304*a^7*b^8*c^15*d^4 + 16*a^7*b^8*c^17*d^2 + 4
06*a^8*b^7*c^2*d^17 + 1072*a^8*b^7*c^4*d^15 + 200*a^8*b^7*c^6*d^13 - 2626*a^8*b^7*c^8*d^11 - 4042*a^8*b^7*c^10
*d^9 - 2540*a^8*b^7*c^12*d^7 - 692*a^8*b^7*c^14*d^5 - 56*a^8*b^7*c^16*d^3 - 624*a^9*b^6*c^3*d^16 - 544*a^9*b^6
*c^5*d^14 + 1296*a^9*b^6*c^7*d^12 + 3184*a^9*b^6*c^9*d^10 + 2672*a^9*b^6*c^11*d^8 + 960*a^9*b^6*c^13*d^6 + 112
*a^9*b^6*c^15*d^4 + 282*a^10*b^5*c^2*d^17 + 568*a^10*b^5*c^4*d^15 - 168*a^10*b^5*c^6*d^13 - 1622*a^10*b^5*c^8*
d^11 - 1862*a^10*b^5*c^10*d^9 - 860*a^10*b^5*c^12*d^7 - 140*a^10*b^5*c^14*d^5 - 336*a^11*b^4*c^3*d^16 - 272*a^
11*b^4*c^5*d^14 + 352*a^11*b^4*c^7*d^12 + 768*a^11*b^4*c^9*d^10 + 496*a^11*b^4*c^11*d^8 + 112*a^11*b^4*c^13*d^
6 + 122*a^12*b^3*c^2*d^17 + 252*a^12*b^3*c^4*d^15 + 148*a^12*b^3*c^6*d^13 - 118*a^12*b^3*c^8*d^11 - 174*a^12*b
^3*c^10*d^9 - 56*a^12*b^3*c^12*d^7 - 112*a^13*b^2*c^3*d^16 - 128*a^13*b^2*c^5*d^14 - 32*a^13*b^2*c^7*d^12 + 32
*a^13*b^2*c^9*d^10 + 16*a^13*b^2*c^11*d^8))/(a^10*d^14 + b^10*c^14 + 2*a^2*b^8*c^14 + a^4*b^6*c^14 + a^6*b^4*d
^14 + 2*a^8*b^2*d^14 + 4*a^10*c^2*d^12 + 6*a^10*c^4*d^10 + 4*a^10*c^6*d^8 + a^10*c^8*d^6 + b^10*c^6*d^8 + 4*b^
10*c^8*d^6 + 6*b^10*c^10*d^4 + 4*b^10*c^12*d^2 - 6*a*b^9*c^5*d^9 - 24*a*b^9*c^7*d^7 - 36*a*b^9*c^9*d^5 - 24*a*
b^9*c^11*d^3 - 12*a^3*b^7*c^13*d - 6*a^5*b^5*c*d^13 - 6*a^5*b^5*c^13*d - 12*a^7*b^3*c*d^13 - 24*a^9*b*c^3*d^11
- 36*a^9*b*c^5*d^9 - 24*a^9*b*c^7*d^7 - 6*a^9*b*c^9*d^5 + 15*a^2*b^8*c^4*d^10 + 62*a^2*b^8*c^6*d^8 + 98*a^2*b
^8*c^8*d^6 + 72*a^2*b^8*c^10*d^4 + 23*a^2*b^8*c^12*d^2 - 20*a^3*b^7*c^3*d^11 - 92*a^3*b^7*c^5*d^9 - 168*a^3*b^
7*c^7*d^7 - 152*a^3*b^7*c^9*d^5 - 68*a^3*b^7*c^11*d^3 + 15*a^4*b^6*c^2*d^12 + 90*a^4*b^6*c^4*d^10 + 211*a^4*b^
6*c^6*d^8 + 244*a^4*b^6*c^8*d^6 + 141*a^4*b^6*c^10*d^4 + 34*a^4*b^6*c^12*d^2 - 64*a^5*b^5*c^3*d^11 - 202*a^5*b
^5*c^5*d^9 - 288*a^5*b^5*c^7*d^7 - 202*a^5*b^5*c^9*d^5 - 64*a^5*b^5*c^11*d^3 + 34*a^6*b^4*c^2*d^12 + 141*a^6*b
^4*c^4*d^10 + 244*a^6*b^4*c^6*d^8 + 211*a^6*b^4*c^8*d^6 + 90*a^6*b^4*c^10*d^4 + 15*a^6*b^4*c^12*d^2 - 68*a^7*b
^3*c^3*d^11 - 152*a^7*b^3*c^5*d^9 - 168*a^7*b^3*c^7*d^7 - 92*a^7*b^3*c^9*d^5 - 20*a^7*b^3*c^11*d^3 + 23*a^8*b^
2*c^2*d^12 + 72*a^8*b^2*c^4*d^10 + 98*a^8*b^2*c^6*d^8 + 62*a^8*b^2*c^8*d^6 + 15*a^8*b^2*c^10*d^4 - 6*a*b^9*c^1
3*d - 6*a^9*b*c*d^13)) - (C*b^13*c^15*d - A*b^13*c^15*d - B*a^12*b*d^16 + 12*A*a^3*b^10*d^16 + 20*A*a^5*b^8*d^
16 - 4*A*a^9*b^4*d^16 + 4*A*a^11*b^2*d^16 - 8*B*a^4*b^9*d^16 - 16*B*a^6*b^7*d^16 - B*a^8*b^5*d^16 + 6*B*a^10*b
^3*d^16 - 12*A*b^13*c^3*d^13 - 48*A*b^13*c^5*d^11 - 76*A*b^13*c^7*d^9 - 45*A*b^13*c^9*d^7 + 5*A*b^13*c^11*d^5
+ 9*A*b^13*c^13*d^3 + 4*C*a^5*b^8*d^16 + 12*C*a^7*b^6*d^16 + 4*C*a^9*b^4*d^16 - 4*C*a^11*b^2*d^16 + 4*B*b^13*c
^4*d^12 + 16*B*b^13*c^6*d^10 + 35*B*b^13*c^8*d^8 + 33*B*b^13*c^10*d^6 + 5*B*b^13*c^12*d^4 - 5*B*b^13*c^14*d^2
+ 4*C*b^13*c^7*d^9 - 3*C*b^13*c^9*d^7 - 17*C*b^13*c^11*d^5 - 9*C*b^13*c^13*d^3 + 36*A*a*b^12*c^2*d^14 + 176*A*
a*b^12*c^4*d^12 + 380*A*a*b^12*c^6*d^10 + 396*A*a*b^12*c^8*d^8 + 176*A*a*b^12*c^10*d^6 + 20*A*a*b^12*c^12*d^4
- 36*A*a^2*b^11*c*d^15 - 2*A*a^2*b^11*c^15*d - 92*A*a^4*b^9*c*d^15 - A*a^4*b^9*c^15*d - 56*A*a^6*b^7*c*d^15 +
3*A*a^8*b^5*c*d^15 + 2*A*a^10*b^3*c*d^15 - 3*A*a^12*b*c^3*d^13 - 3*A*a^12*b*c^5*d^11 - A*a^12*b*c^7*d^9 - 4*B*
a*b^12*c^3*d^13 - 24*B*a*b^12*c^5*d^11 - 116*B*a*b^12*c^7*d^9 - 196*B*a*b^12*c^9*d^7 - 120*B*a*b^12*c^11*d^5 -
20*B*a*b^12*c^13*d^3 + 20*B*a^3*b^10*c*d^15 + 68*B*a^5*b^8*c*d^15 + 56*B*a^7*b^6*c*d^15 + 4*B*a^9*b^4*c*d^15
- 4*B*a^11*b^2*c*d^15 - 3*B*a^12*b*c^2*d^14 - 3*B*a^12*b*c^4*d^12 - B*a^12*b*c^6*d^10 - 8*C*a*b^12*c^4*d^12 -
56*C*a*b^12*c^6*d^10 - 60*C*a*b^12*c^8*d^8 + 28*C*a*b^12*c^10*d^6 + 52*C*a*b^12*c^12*d^4 + 12*C*a*b^12*c^14*d^
2 + 2*C*a^2*b^11*c^15*d - 4*C*a^4*b^9*c*d^15 + C*a^4*b^9*c^15*d - 40*C*a^6*b^7*c*d^15 - 51*C*a^8*b^5*c*d^15 -
14*C*a^10*b^3*c*d^15 + 3*C*a^12*b*c^3*d^13 + 3*C*a^12*b*c^5*d^11 + C*a^12*b*c^7*d^9 - 260*A*a^2*b^11*c^3*d^13
- 780*A*a^2*b^11*c^5*d^11 - 1144*A*a^2*b^11*c^7*d^9 - 798*A*a^2*b^11*c^9*d^7 - 202*A*a^2*b^11*c^11*d^5 + 6*A*a
^2*b^11*c^13*d^3 + 204*A*a^3*b^10*c^2*d^14 + 876*A*a^3*b^10*c^4*d^12 + 1812*A*a^3*b^10*c^6*d^10 + 1872*A*a^3*b
^10*c^8*d^8 + 872*A*a^3*b^10*c^10*d^6 + 136*A*a^3*b^10*c^12*d^4 + 8*A*a^3*b^10*c^14*d^2 - 608*A*a^4*b^9*c^3*d^
13 - 1866*A*a^4*b^9*c^5*d^11 - 2802*A*a^4*b^9*c^7*d^9 - 2007*A*a^4*b^9*c^9*d^7 - 585*A*a^4*b^9*c^11*d^5 - 31*A
*a^4*b^9*c^13*d^3 + 264*A*a^5*b^8*c^2*d^14 + 1180*A*a^5*b^8*c^4*d^12 + 2528*A*a^5*b^8*c^6*d^10 + 2628*A*a^5*b^
8*c^8*d^8 + 1200*A*a^5*b^8*c^10*d^6 + 172*A*a^5*b^8*c^12*d^4 + 8*A*a^5*b^8*c^14*d^2 - 356*A*a^6*b^7*c^3*d^13 -
1320*A*a^6*b^7*c^5*d^11 - 2188*A*a^6*b^7*c^7*d^9 - 1588*A*a^6*b^7*c^9*d^7 - 448*A*a^6*b^7*c^11*d^5 - 28*A*a^6
*b^7*c^13*d^3 + 24*A*a^7*b^6*c^2*d^14 + 368*A*a^7*b^6*c^4*d^12 + 1112*A*a^7*b^6*c^6*d^10 + 1272*A*a^7*b^6*c^8*
d^8 + 560*A*a^7*b^6*c^10*d^6 + 56*A*a^7*b^6*c^12*d^4 + 33*A*a^8*b^5*c^3*d^13 - 165*A*a^8*b^5*c^5*d^11 - 487*A*
a^8*b^5*c^7*d^9 - 362*A*a^8*b^5*c^9*d^7 - 70*A*a^8*b^5*c^11*d^5 - 68*A*a^9*b^4*c^2*d^14 - 108*A*a^9*b^4*c^4*d^
12 + 28*A*a^9*b^4*c^6*d^10 + 128*A*a^9*b^4*c^8*d^8 + 56*A*a^9*b^4*c^10*d^6 + 26*A*a^10*b^3*c^3*d^13 + 18*A*a^1
0*b^3*c^5*d^11 - 34*A*a^10*b^3*c^7*d^9 - 28*A*a^10*b^3*c^9*d^7 + 4*A*a^11*b^2*c^2*d^14 + 4*A*a^11*b^2*c^4*d^12
+ 12*A*a^11*b^2*c^6*d^10 + 8*A*a^11*b^2*c^8*d^8 - 12*B*a^2*b^11*c^2*d^14 - 44*B*a^2*b^11*c^4*d^12 + 48*B*a^2*
b^11*c^6*d^10 + 302*B*a^2*b^11*c^8*d^8 + 342*B*a^2*b^11*c^10*d^6 + 118*B*a^2*b^11*c^12*d^4 - 2*B*a^2*b^11*c^14
*d^2 + 132*B*a^3*b^10*c^3*d^13 + 284*B*a^3*b^10*c^5*d^11 + 28*B*a^3*b^10*c^7*d^9 - 424*B*a^3*b^10*c^9*d^7 - 33
6*B*a^3*b^10*c^11*d^5 - 56*B*a^3*b^10*c^13*d^3 - 132*B*a^4*b^9*c^2*d^14 - 558*B*a^4*b^9*c^4*d^12 - 694*B*a^4*b
^9*c^6*d^10 - 27*B*a^4*b^9*c^8*d^8 + 411*B*a^4*b^9*c^10*d^6 + 181*B*a^4*b^9*c^12*d^4 + 3*B*a^4*b^9*c^14*d^2 +
496*B*a^5*b^8*c^3*d^13 + 1196*B*a^5*b^8*c^5*d^11 + 1032*B*a^5*b^8*c^7*d^9 + 84*B*a^5*b^8*c^9*d^7 - 216*B*a^5*b
^8*c^11*d^5 - 36*B*a^5*b^8*c^13*d^3 - 244*B*a^6*b^7*c^2*d^14 - 1064*B*a^6*b^7*c^4*d^12 - 1596*B*a^6*b^7*c^6*d^
10 - 828*B*a^6*b^7*c^8*d^8 + 68*B*a^6*b^7*c^12*d^4 + 488*B*a^7*b^6*c^3*d^13 + 1224*B*a^7*b^6*c^5*d^11 + 1208*B
*a^7*b^6*c^7*d^9 + 416*B*a^7*b^6*c^9*d^7 - 103*B*a^8*b^5*c^2*d^14 - 581*B*a^8*b^5*c^4*d^12 - 959*B*a^8*b^5*c^6
*d^10 - 582*B*a^8*b^5*c^8*d^8 - 102*B*a^8*b^5*c^10*d^6 + 132*B*a^9*b^4*c^3*d^13 + 356*B*a^9*b^4*c^5*d^11 + 332
*B*a^9*b^4*c^7*d^9 + 104*B*a^9*b^4*c^9*d^7 + 18*B*a^10*b^3*c^2*d^14 - 30*B*a^10*b^3*c^4*d^12 - 90*B*a^10*b^3*c
^6*d^10 - 48*B*a^10*b^3*c^8*d^8 + 4*B*a^11*b^2*c^3*d^13 + 20*B*a^11*b^2*c^5*d^11 + 12*B*a^11*b^2*c^7*d^9 + 20*
C*a^2*b^11*c^3*d^13 + 156*C*a^2*b^11*c^5*d^11 + 328*C*a^2*b^11*c^7*d^9 + 234*C*a^2*b^11*c^9*d^7 + 10*C*a^2*b^1
1*c^11*d^5 - 30*C*a^2*b^11*c^13*d^3 - 12*C*a^3*b^10*c^2*d^14 - 168*C*a^3*b^10*c^4*d^12 - 636*C*a^3*b^10*c^6*d^
10 - 828*C*a^3*b^10*c^8*d^8 - 344*C*a^3*b^10*c^10*d^6 + 20*C*a^3*b^10*c^12*d^4 + 16*C*a^3*b^10*c^14*d^2 + 56*C
*a^4*b^9*c^3*d^13 + 570*C*a^4*b^9*c^5*d^11 + 1218*C*a^4*b^9*c^7*d^9 + 951*C*a^4*b^9*c^9*d^7 + 225*C*a^4*b^9*c^
11*d^5 - 17*C*a^4*b^9*c^13*d^3 + 36*C*a^5*b^8*c^2*d^14 - 172*C*a^5*b^8*c^4*d^12 - 1004*C*a^5*b^8*c^6*d^10 - 14
52*C*a^5*b^8*c^8*d^8 - 732*C*a^5*b^8*c^10*d^6 - 76*C*a^5*b^8*c^12*d^4 + 4*C*a^5*b^8*c^14*d^2 - 124*C*a^6*b^7*c
^3*d^13 + 336*C*a^6*b^7*c^5*d^11 + 1132*C*a^6*b^7*c^7*d^9 + 964*C*a^6*b^7*c^9*d^7 + 256*C*a^6*b^7*c^11*d^5 + 4
*C*a^6*b^7*c^13*d^3 + 144*C*a^7*b^6*c^2*d^14 + 196*C*a^7*b^6*c^4*d^12 - 296*C*a^7*b^6*c^6*d^10 - 708*C*a^7*b^6
*c^8*d^8 - 392*C*a^7*b^6*c^10*d^6 - 44*C*a^7*b^6*c^12*d^4 - 237*C*a^8*b^5*c^3*d^13 - 171*C*a^8*b^5*c^5*d^11 +
223*C*a^8*b^5*c^7*d^9 + 266*C*a^8*b^5*c^9*d^7 + 58*C*a^8*b^5*c^11*d^5 + 92*C*a^9*b^4*c^2*d^14 + 204*C*a^9*b^4*
c^4*d^12 + 116*C*a^9*b^4*c^6*d^10 - 32*C*a^9*b^4*c^8*d^8 - 32*C*a^9*b^4*c^10*d^6 - 74*C*a^10*b^3*c^3*d^13 - 90
*C*a^10*b^3*c^5*d^11 - 14*C*a^10*b^3*c^7*d^9 + 16*C*a^10*b^3*c^9*d^7 - 4*C*a^11*b^2*c^2*d^14 - 4*C*a^11*b^2*c^
4*d^12 - 12*C*a^11*b^2*c^6*d^10 - 8*C*a^11*b^2*c^8*d^8 - A*a^12*b*c*d^15 + C*a^12*b*c*d^15)/(a^10*d^14 + b^10*
c^14 + 2*a^2*b^8*c^14 + a^4*b^6*c^14 + a^6*b^4*d^14 + 2*a^8*b^2*d^14 + 4*a^10*c^2*d^12 + 6*a^10*c^4*d^10 + 4*a
^10*c^6*d^8 + a^10*c^8*d^6 + b^10*c^6*d^8 + 4*b^10*c^8*d^6 + 6*b^10*c^10*d^4 + 4*b^10*c^12*d^2 - 6*a*b^9*c^5*d
^9 - 24*a*b^9*c^7*d^7 - 36*a*b^9*c^9*d^5 - 24*a*b^9*c^11*d^3 - 12*a^3*b^7*c^13*d - 6*a^5*b^5*c*d^13 - 6*a^5*b^
5*c^13*d - 12*a^7*b^3*c*d^13 - 24*a^9*b*c^3*d^11 - 36*a^9*b*c^5*d^9 - 24*a^9*b*c^7*d^7 - 6*a^9*b*c^9*d^5 + 15*
a^2*b^8*c^4*d^10 + 62*a^2*b^8*c^6*d^8 + 98*a^2*b^8*c^8*d^6 + 72*a^2*b^8*c^10*d^4 + 23*a^2*b^8*c^12*d^2 - 20*a^
3*b^7*c^3*d^11 - 92*a^3*b^7*c^5*d^9 - 168*a^3*b^7*c^7*d^7 - 152*a^3*b^7*c^9*d^5 - 68*a^3*b^7*c^11*d^3 + 15*a^4
*b^6*c^2*d^12 + 90*a^4*b^6*c^4*d^10 + 211*a^4*b^6*c^6*d^8 + 244*a^4*b^6*c^8*d^6 + 141*a^4*b^6*c^10*d^4 + 34*a^
4*b^6*c^12*d^2 - 64*a^5*b^5*c^3*d^11 - 202*a^5*b^5*c^5*d^9 - 288*a^5*b^5*c^7*d^7 - 202*a^5*b^5*c^9*d^5 - 64*a^
5*b^5*c^11*d^3 + 34*a^6*b^4*c^2*d^12 + 141*a^6*b^4*c^4*d^10 + 244*a^6*b^4*c^6*d^8 + 211*a^6*b^4*c^8*d^6 + 90*a
^6*b^4*c^10*d^4 + 15*a^6*b^4*c^12*d^2 - 68*a^7*b^3*c^3*d^11 - 152*a^7*b^3*c^5*d^9 - 168*a^7*b^3*c^7*d^7 - 92*a
^7*b^3*c^9*d^5 - 20*a^7*b^3*c^11*d^3 + 23*a^8*b^2*c^2*d^12 + 72*a^8*b^2*c^4*d^10 + 98*a^8*b^2*c^6*d^8 + 62*a^8
*b^2*c^8*d^6 + 15*a^8*b^2*c^10*d^4 - 6*a*b^9*c^13*d - 6*a^9*b*c*d^13) + (tan(e + f*x)*(3*C*a^12*b*d^16 - 3*A*a
^12*b*d^16 + 3*B*b^13*c^15*d + 24*A*a^4*b^9*d^16 + 56*A*a^6*b^7*d^16 + 25*A*a^8*b^5*d^16 - 10*A*a^10*b^3*d^16
- 16*B*a^5*b^8*d^16 - 48*B*a^7*b^6*d^16 - 36*B*a^9*b^4*d^16 - 4*B*a^11*b^2*d^16 - 24*A*b^13*c^4*d^12 - 104*A*b
^13*c^6*d^10 - 199*A*b^13*c^8*d^8 - 189*A*b^13*c^10*d^6 - 77*A*b^13*c^12*d^4 - 7*A*b^13*c^14*d^2 + 4*C*a^6*b^7
*d^16 + 23*C*a^8*b^5*d^16 + 22*C*a^10*b^3*d^16 + 8*B*b^13*c^5*d^11 + 24*B*b^13*c^7*d^9 + 51*B*b^13*c^9*d^7 + 6
5*B*b^13*c^11*d^5 + 33*B*b^13*c^13*d^3 - 4*C*b^13*c^6*d^10 + 7*C*b^13*c^8*d^8 + 21*C*b^13*c^10*d^6 + 5*C*b^13*
c^12*d^4 - 5*C*b^13*c^14*d^2 + 48*A*a*b^12*c^3*d^13 + 208*A*a*b^12*c^5*d^11 + 472*A*a*b^12*c^7*d^9 + 572*A*a*b
^12*c^9*d^7 + 324*A*a*b^12*c^11*d^5 + 68*A*a*b^12*c^13*d^3 - 48*A*a^3*b^10*c*d^15 + 4*A*a^3*b^10*c^15*d - 144*
A*a^5*b^8*c*d^15 - 104*A*a^7*b^6*c*d^15 + 4*A*a^9*b^4*c*d^15 + 12*A*a^11*b^2*c*d^15 - A*a^12*b*c^2*d^14 + 7*A*
a^12*b*c^4*d^12 + 5*A*a^12*b*c^6*d^10 + 64*B*a*b^12*c^6*d^10 + 100*B*a*b^12*c^8*d^8 - 4*B*a*b^12*c^10*d^6 - 52
*B*a*b^12*c^12*d^4 - 12*B*a*b^12*c^14*d^2 + 2*B*a^2*b^11*c^15*d + 24*B*a^4*b^9*c*d^15 - B*a^4*b^9*c^15*d + 120
*B*a^6*b^7*c*d^15 + 147*B*a^8*b^5*c*d^15 + 58*B*a^10*b^3*c*d^15 + 13*B*a^12*b*c^3*d^13 + 5*B*a^12*b*c^5*d^11 -
B*a^12*b*c^7*d^9 + 8*C*a*b^12*c^5*d^11 - 88*C*a*b^12*c^7*d^9 - 236*C*a*b^12*c^9*d^7 - 180*C*a*b^12*c^11*d^5 -
44*C*a*b^12*c^13*d^3 - 4*C*a^3*b^10*c^15*d + 24*C*a^5*b^8*c*d^15 + 8*C*a^7*b^6*c*d^15 - 28*C*a^9*b^4*c*d^15 -
12*C*a^11*b^2*c*d^15 + C*a^12*b*c^2*d^14 - 7*C*a^12*b*c^4*d^12 - 5*C*a^12*b*c^6*d^10 - 24*A*a^2*b^11*c^4*d^12
- 316*A*a^2*b^11*c^6*d^10 - 838*A*a^2*b^11*c^8*d^8 - 858*A*a^2*b^11*c^10*d^6 - 346*A*a^2*b^11*c^12*d^4 - 34*A
*a^2*b^11*c^14*d^2 - 192*A*a^3*b^10*c^3*d^13 - 200*A*a^3*b^10*c^5*d^11 + 472*A*a^3*b^10*c^7*d^9 + 1148*A*a^3*b
^10*c^9*d^7 + 756*A*a^3*b^10*c^11*d^5 + 140*A*a^3*b^10*c^13*d^3 + 200*A*a^4*b^9*c^2*d^14 + 790*A*a^4*b^9*c^4*d
^12 + 906*A*a^4*b^9*c^6*d^10 - 177*A*a^4*b^9*c^8*d^8 - 795*A*a^4*b^9*c^10*d^6 - 353*A*a^4*b^9*c^12*d^4 - 27*A*
a^4*b^9*c^14*d^2 - 936*A*a^5*b^8*c^3*d^13 - 2016*A*a^5*b^8*c^5*d^11 - 1512*A*a^5*b^8*c^7*d^9 + 72*A*a^5*b^8*c^
9*d^7 + 432*A*a^5*b^8*c^11*d^5 + 72*A*a^5*b^8*c^13*d^3 + 468*A*a^6*b^7*c^2*d^14 + 1768*A*a^6*b^7*c^4*d^12 + 25
24*A*a^6*b^7*c^6*d^10 + 1252*A*a^6*b^7*c^8*d^8 - 84*A*a^6*b^7*c^12*d^4 - 952*A*a^7*b^6*c^3*d^13 - 2264*A*a^7*b
^6*c^5*d^11 - 2088*A*a^7*b^6*c^7*d^9 - 672*A*a^7*b^6*c^9*d^7 + 283*A*a^8*b^5*c^2*d^14 + 1137*A*a^8*b^5*c^4*d^1
2 + 1651*A*a^8*b^5*c^6*d^10 + 898*A*a^8*b^5*c^8*d^8 + 126*A*a^8*b^5*c^10*d^6 - 268*A*a^9*b^4*c^3*d^13 - 716*A*
a^9*b^4*c^5*d^11 - 612*A*a^9*b^4*c^7*d^9 - 168*A*a^9*b^4*c^9*d^7 + 14*A*a^10*b^3*c^2*d^14 + 166*A*a^10*b^3*c^4
*d^12 + 250*A*a^10*b^3*c^6*d^10 + 108*A*a^10*b^3*c^8*d^8 - 12*A*a^11*b^2*c^3*d^13 - 60*A*a^11*b^2*c^5*d^11 - 3
6*A*a^11*b^2*c^7*d^9 - 32*B*a^2*b^11*c^3*d^13 - 280*B*a^2*b^11*c^5*d^11 - 612*B*a^2*b^11*c^7*d^9 - 474*B*a^2*b
^11*c^9*d^7 - 70*B*a^2*b^11*c^11*d^5 + 42*B*a^2*b^11*c^13*d^3 + 16*B*a^3*b^10*c^2*d^14 + 240*B*a^3*b^10*c^4*d^
12 + 968*B*a^3*b^10*c^6*d^10 + 1348*B*a^3*b^10*c^8*d^8 + 668*B*a^3*b^10*c^10*d^6 + 60*B*a^3*b^10*c^12*d^4 - 4*
B*a^3*b^10*c^14*d^2 + 8*B*a^4*b^9*c^3*d^13 - 814*B*a^4*b^9*c^5*d^11 - 2034*B*a^4*b^9*c^7*d^9 - 1731*B*a^4*b^9*
c^9*d^7 - 513*B*a^4*b^9*c^11*d^5 - 19*B*a^4*b^9*c^13*d^3 - 128*B*a^5*b^8*c^2*d^14 + 144*B*a^5*b^8*c^4*d^12 + 1
472*B*a^5*b^8*c^6*d^10 + 2232*B*a^5*b^8*c^8*d^8 + 1176*B*a^5*b^8*c^10*d^6 + 168*B*a^5*b^8*c^12*d^4 + 8*B*a^5*b
^8*c^14*d^2 + 460*B*a^6*b^7*c^3*d^13 - 152*B*a^6*b^7*c^5*d^11 - 1596*B*a^6*b^7*c^7*d^9 - 1524*B*a^6*b^7*c^9*d^
7 - 448*B*a^6*b^7*c^11*d^5 - 28*B*a^6*b^7*c^13*d^3 - 408*B*a^7*b^6*c^2*d^14 - 576*B*a^7*b^6*c^4*d^12 + 328*B*a
^7*b^6*c^6*d^10 + 1048*B*a^7*b^6*c^8*d^8 + 560*B*a^7*b^6*c^10*d^6 + 56*B*a^7*b^6*c^12*d^4 + 617*B*a^8*b^5*c^3*
d^13 + 587*B*a^8*b^5*c^5*d^11 - 159*B*a^8*b^5*c^7*d^9 - 346*B*a^8*b^5*c^9*d^7 - 70*B*a^8*b^5*c^11*d^5 - 316*B*
a^9*b^4*c^2*d^14 - 564*B*a^9*b^4*c^4*d^12 - 268*B*a^9*b^4*c^6*d^10 + 72*B*a^9*b^4*c^8*d^8 + 56*B*a^9*b^4*c^10*
d^6 + 210*B*a^10*b^3*c^3*d^13 + 218*B*a^10*b^3*c^5*d^11 + 38*B*a^10*b^3*c^7*d^9 - 28*B*a^10*b^3*c^9*d^7 - 52*B
*a^11*b^2*c^2*d^14 - 84*B*a^11*b^2*c^4*d^12 - 28*B*a^11*b^2*c^6*d^10 + 8*B*a^11*b^2*c^8*d^8 - 36*C*a^2*b^11*c^
4*d^12 + 52*C*a^2*b^11*c^6*d^10 + 382*C*a^2*b^11*c^8*d^8 + 474*C*a^2*b^11*c^10*d^6 + 190*C*a^2*b^11*c^12*d^4 +
10*C*a^2*b^11*c^14*d^2 + 96*C*a^3*b^10*c^3*d^13 + 344*C*a^3*b^10*c^5*d^11 + 104*C*a^3*b^10*c^7*d^9 - 524*C*a^
3*b^10*c^9*d^7 - 468*C*a^3*b^10*c^11*d^5 - 92*C*a^3*b^10*c^13*d^3 - 92*C*a^4*b^9*c^2*d^14 - 646*C*a^4*b^9*c^4*
d^12 - 942*C*a^4*b^9*c^6*d^10 - 87*C*a^4*b^9*c^8*d^8 + 543*C*a^4*b^9*c^10*d^6 + 257*C*a^4*b^9*c^12*d^4 + 15*C*
a^4*b^9*c^14*d^2 + 504*C*a^5*b^8*c^3*d^13 + 1512*C*a^5*b^8*c^5*d^11 + 1416*C*a^5*b^8*c^7*d^9 + 144*C*a^5*b^8*c
^9*d^7 - 288*C*a^5*b^8*c^11*d^5 - 48*C*a^5*b^8*c^13*d^3 - 204*C*a^6*b^7*c^2*d^14 - 1324*C*a^6*b^7*c^4*d^12 - 2
188*C*a^6*b^7*c^6*d^10 - 1168*C*a^6*b^7*c^8*d^8 - 24*C*a^6*b^7*c^10*d^6 + 72*C*a^6*b^7*c^12*d^4 + 568*C*a^7*b^
6*c^3*d^13 + 1688*C*a^7*b^6*c^5*d^11 + 1704*C*a^7*b^6*c^7*d^9 + 576*C*a^7*b^6*c^9*d^7 - 79*C*a^8*b^5*c^2*d^14
- 801*C*a^8*b^5*c^4*d^12 - 1387*C*a^8*b^5*c^6*d^10 - 802*C*a^8*b^5*c^8*d^8 - 114*C*a^8*b^5*c^10*d^6 + 172*C*a^
9*b^4*c^3*d^13 + 572*C*a^9*b^4*c^5*d^11 + 516*C*a^9*b^4*c^7*d^9 + 144*C*a^9*b^4*c^9*d^7 + 34*C*a^10*b^3*c^2*d^
14 - 94*C*a^10*b^3*c^4*d^12 - 202*C*a^10*b^3*c^6*d^10 - 96*C*a^10*b^3*c^8*d^8 + 12*C*a^11*b^2*c^3*d^13 + 60*C*
a^11*b^2*c^5*d^11 + 36*C*a^11*b^2*c^7*d^9 + 4*A*a*b^12*c^15*d + 7*B*a^12*b*c*d^15 - 4*C*a*b^12*c^15*d))/(a^10*
d^14 + b^10*c^14 + 2*a^2*b^8*c^14 + a^4*b^6*c^14 + a^6*b^4*d^14 + 2*a^8*b^2*d^14 + 4*a^10*c^2*d^12 + 6*a^10*c^
4*d^10 + 4*a^10*c^6*d^8 + a^10*c^8*d^6 + b^10*c^6*d^8 + 4*b^10*c^8*d^6 + 6*b^10*c^10*d^4 + 4*b^10*c^12*d^2 - 6
*a*b^9*c^5*d^9 - 24*a*b^9*c^7*d^7 - 36*a*b^9*c^9*d^5 - 24*a*b^9*c^11*d^3 - 12*a^3*b^7*c^13*d - 6*a^5*b^5*c*d^1
3 - 6*a^5*b^5*c^13*d - 12*a^7*b^3*c*d^13 - 24*a^9*b*c^3*d^11 - 36*a^9*b*c^5*d^9 - 24*a^9*b*c^7*d^7 - 6*a^9*b*c
^9*d^5 + 15*a^2*b^8*c^4*d^10 + 62*a^2*b^8*c^6*d^8 + 98*a^2*b^8*c^8*d^6 + 72*a^2*b^8*c^10*d^4 + 23*a^2*b^8*c^12
*d^2 - 20*a^3*b^7*c^3*d^11 - 92*a^3*b^7*c^5*d^9 - 168*a^3*b^7*c^7*d^7 - 152*a^3*b^7*c^9*d^5 - 68*a^3*b^7*c^11*
d^3 + 15*a^4*b^6*c^2*d^12 + 90*a^4*b^6*c^4*d^10 + 211*a^4*b^6*c^6*d^8 + 244*a^4*b^6*c^8*d^6 + 141*a^4*b^6*c^10
*d^4 + 34*a^4*b^6*c^12*d^2 - 64*a^5*b^5*c^3*d^11 - 202*a^5*b^5*c^5*d^9 - 288*a^5*b^5*c^7*d^7 - 202*a^5*b^5*c^9
*d^5 - 64*a^5*b^5*c^11*d^3 + 34*a^6*b^4*c^2*d^12 + 141*a^6*b^4*c^4*d^10 + 244*a^6*b^4*c^6*d^8 + 211*a^6*b^4*c^
8*d^6 + 90*a^6*b^4*c^10*d^4 + 15*a^6*b^4*c^12*d^2 - 68*a^7*b^3*c^3*d^11 - 152*a^7*b^3*c^5*d^9 - 168*a^7*b^3*c^
7*d^7 - 92*a^7*b^3*c^9*d^5 - 20*a^7*b^3*c^11*d^3 + 23*a^8*b^2*c^2*d^12 + 72*a^8*b^2*c^4*d^10 + 98*a^8*b^2*c^6*
d^8 + 62*a^8*b^2*c^8*d^6 + 15*a^8*b^2*c^10*d^4 - 6*a*b^9*c^13*d - 6*a^9*b*c*d^13)) + (36*A^2*a^3*b^8*d^13 - 4*
A^2*a^5*b^6*d^13 - 3*A^2*a^7*b^4*d^13 + 16*B^2*a^3*b^8*d^13 + 16*B^2*a^5*b^6*d^13 + B^2*a^7*b^4*d^13 + 2*B^2*a
^9*b^2*d^13 + 156*A^2*b^11*c^3*d^10 + 204*A^2*b^11*c^5*d^8 + 85*A^2*b^11*c^7*d^6 + 3*A^2*b^11*c^11*d^2 + 8*C^2
*a^5*b^6*d^13 + 9*C^2*a^7*b^4*d^13 + 4*B^2*b^11*c^3*d^10 + 28*B^2*b^11*c^5*d^8 + 45*B^2*b^11*c^7*d^6 + 24*B^2*
b^11*c^9*d^4 - B^2*b^11*c^11*d^2 + C^2*b^11*c^7*d^6 + 3*C^2*b^11*c^11*d^2 + 36*A^2*a*b^10*d^13 + 36*A^2*b^11*c
*d^12 + 168*A^2*a^2*b^9*c^3*d^10 + 393*A^2*a^2*b^9*c^5*d^8 + 43*A^2*a^2*b^9*c^7*d^6 + 5*A^2*a^2*b^9*c^9*d^4 +
7*A^2*a^2*b^9*c^11*d^2 + 8*A^2*a^3*b^8*c^2*d^11 - 417*A^2*a^3*b^8*c^4*d^9 - 411*A^2*a^3*b^8*c^6*d^7 - 7*A^2*a^
3*b^8*c^8*d^5 - 17*A^2*a^3*b^8*c^10*d^3 + 87*A^2*a^4*b^7*c^3*d^10 + 359*A^2*a^4*b^7*c^5*d^8 - 75*A^2*a^4*b^7*c
^7*d^6 + 9*A^2*a^4*b^7*c^9*d^4 + 17*A^2*a^5*b^6*c^2*d^11 - 205*A^2*a^5*b^6*c^4*d^9 - 13*A^2*a^5*b^6*c^6*d^7 +
37*A^2*a^5*b^6*c^8*d^5 + A^2*a^6*b^5*c^3*d^10 + 13*A^2*a^6*b^5*c^5*d^8 - 89*A^2*a^6*b^5*c^7*d^6 + 23*A^2*a^7*b
^4*c^2*d^11 + 23*A^2*a^7*b^4*c^4*d^9 + 93*A^2*a^7*b^4*c^6*d^7 - 53*A^2*a^8*b^3*c^5*d^8 - 8*A^2*a^9*b^2*c^2*d^1
1 + 16*A^2*a^9*b^2*c^4*d^9 + 48*B^2*a^2*b^9*c^3*d^10 - 47*B^2*a^2*b^9*c^5*d^8 + 131*B^2*a^2*b^9*c^7*d^6 + 9*B^
2*a^2*b^9*c^9*d^4 - 5*B^2*a^2*b^9*c^11*d^2 + 36*B^2*a^3*b^8*c^2*d^11 + 163*B^2*a^3*b^8*c^4*d^9 - 31*B^2*a^3*b^
8*c^6*d^7 - 199*B^2*a^3*b^8*c^8*d^5 + 7*B^2*a^3*b^8*c^10*d^3 - 49*B^2*a^4*b^7*c^3*d^10 - 209*B^2*a^4*b^7*c^5*d
^8 + 149*B^2*a^4*b^7*c^7*d^6 - 19*B^2*a^4*b^7*c^9*d^4 - 11*B^2*a^5*b^6*c^2*d^11 + 91*B^2*a^5*b^6*c^4*d^9 - 185
*B^2*a^5*b^6*c^6*d^7 - 127*B^2*a^5*b^6*c^8*d^5 - 39*B^2*a^6*b^5*c^3*d^10 + 13*B^2*a^6*b^5*c^5*d^8 + 119*B^2*a^
6*b^5*c^7*d^6 - 13*B^2*a^7*b^4*c^2*d^11 + 3*B^2*a^7*b^4*c^4*d^9 - 79*B^2*a^7*b^4*c^6*d^7 - 20*B^2*a^8*b^3*c^3*
d^10 + 43*B^2*a^8*b^3*c^5*d^8 + 12*B^2*a^9*b^2*c^2*d^11 - 14*B^2*a^9*b^2*c^4*d^9 + 36*C^2*a^2*b^9*c^3*d^10 + 1
41*C^2*a^2*b^9*c^5*d^8 - 65*C^2*a^2*b^9*c^7*d^6 + 17*C^2*a^2*b^9*c^9*d^4 + 7*C^2*a^2*b^9*c^11*d^2 + 20*C^2*a^3
*b^8*c^2*d^11 - 69*C^2*a^3*b^8*c^4*d^9 + 57*C^2*a^3*b^8*c^6*d^7 + 113*C^2*a^3*b^8*c^8*d^5 - 65*C^2*a^3*b^8*c^1
0*d^3 + 99*C^2*a^4*b^7*c^3*d^10 + 179*C^2*a^4*b^7*c^5*d^8 - 231*C^2*a^4*b^7*c^7*d^6 - 15*C^2*a^4*b^7*c^9*d^4 +
41*C^2*a^5*b^6*c^2*d^11 - 97*C^2*a^5*b^6*c^4*d^9 + 143*C^2*a^5*b^6*c^6*d^7 + 61*C^2*a^5*b^6*c^8*d^5 - 36*C^2*
a^5*b^6*c^10*d^3 - 11*C^2*a^6*b^5*c^3*d^10 - 119*C^2*a^6*b^5*c^5*d^8 - 221*C^2*a^6*b^5*c^7*d^6 - 36*C^2*a^6*b^
5*c^9*d^4 + 11*C^2*a^7*b^4*c^2*d^11 - 37*C^2*a^7*b^4*c^4*d^9 + 57*C^2*a^7*b^4*c^6*d^7 - 53*C^2*a^8*b^3*c^5*d^8
- 8*C^2*a^9*b^2*c^2*d^11 + 16*C^2*a^9*b^2*c^4*d^9 - 48*A*B*a^2*b^9*d^13 - 48*A*B*a^4*b^7*d^13 - A*B*a^8*b^3*d
^13 + 36*A*C*a^3*b^8*d^13 + 32*A*C*a^5*b^6*d^13 - 6*A*C*a^7*b^4*d^13 - 24*A*B*b^11*c^2*d^11 - 136*A*B*b^11*c^4
*d^9 - 200*A*B*b^11*c^6*d^7 - 89*A*B*b^11*c^8*d^5 + 6*A*B*b^11*c^10*d^3 - 24*B*C*a^4*b^7*d^13 - 24*B*C*a^6*b^5
*d^13 + B*C*a^8*b^3*d^13 - 12*A*C*b^11*c^3*d^10 + 12*A*C*b^11*c^5*d^8 + 58*A*C*b^11*c^7*d^6 + 36*A*C*b^11*c^9*
d^4 - 6*A*C*b^11*c^11*d^2 + 4*B*C*b^11*c^4*d^9 - 4*B*C*b^11*c^6*d^7 - 19*B*C*b^11*c^8*d^5 - 18*B*C*b^11*c^10*d
^3 - A^2*a*b^10*c^12*d + 2*A^2*a^10*b*c*d^12 + B^2*a*b^10*c^12*d - 2*B^2*a^10*b*c*d^12 - C^2*a*b^10*c^12*d + 2
*C^2*a^10*b*c*d^12 + 24*A^2*a*b^10*c^2*d^11 - 188*A^2*a*b^10*c^4*d^9 - 277*A^2*a*b^10*c^6*d^7 - 27*A^2*a*b^10*
c^8*d^5 - 15*A^2*a*b^10*c^10*d^3 - 44*A^2*a^4*b^7*c*d^12 - 29*A^2*a^6*b^5*c*d^12 + A^2*a^8*b^3*c*d^12 - 2*A^2*
a^10*b*c^3*d^10 + 20*B^2*a*b^10*c^2*d^11 + 72*B^2*a*b^10*c^4*d^9 + 47*B^2*a*b^10*c^6*d^7 - 89*B^2*a*b^10*c^8*d
^5 + 5*B^2*a*b^10*c^10*d^3 + 32*B^2*a^2*b^9*c*d^12 + 16*B^2*a^4*b^7*c*d^12 - 5*B^2*a^6*b^5*c*d^12 - 11*B^2*a^8
*b^3*c*d^12 + 2*B^2*a^10*b*c^3*d^10 - 8*C^2*a*b^10*c^4*d^9 - C^2*a*b^10*c^6*d^7 + 69*C^2*a*b^10*c^8*d^5 - 27*C
^2*a*b^10*c^10*d^3 + 16*C^2*a^4*b^7*c*d^12 - 5*C^2*a^6*b^5*c*d^12 + C^2*a^8*b^3*c*d^12 - 2*C^2*a^10*b*c^3*d^10
+ A*B*a^10*b*d^13 - A*B*b^11*c^12*d - B*C*a^10*b*d^13 + B*C*b^11*c^12*d - 72*A*B*a*b^10*c*d^12 + 2*A*C*a*b^10
*c^12*d - 4*A*C*a^10*b*c*d^12 - 160*A*B*a*b^10*c^3*d^10 + 56*A*B*a*b^10*c^5*d^8 + 312*A*B*a*b^10*c^7*d^6 - 8*A
*B*a*b^10*c^9*d^4 + A*B*a^2*b^9*c^12*d - 24*A*B*a^3*b^8*c*d^12 + 40*A*B*a^5*b^6*c*d^12 + 32*A*B*a^7*b^4*c*d^12
- 6*A*B*a^10*b*c^2*d^11 + A*B*a^10*b*c^4*d^9 + 84*A*C*a*b^10*c^2*d^11 + 268*A*C*a*b^10*c^4*d^9 + 206*A*C*a*b^
10*c^6*d^7 - 150*A*C*a*b^10*c^8*d^5 + 6*A*C*a*b^10*c^10*d^3 + 36*A*C*a^2*b^9*c*d^12 - 8*A*C*a^4*b^7*c*d^12 - 2
*A*C*a^6*b^5*c*d^12 - 2*A*C*a^8*b^3*c*d^12 + 4*A*C*a^10*b*c^3*d^10 - 20*B*C*a*b^10*c^3*d^10 - 116*B*C*a*b^10*c
^5*d^8 - 180*B*C*a*b^10*c^7*d^6 + 92*B*C*a*b^10*c^9*d^4 - B*C*a^2*b^9*c^12*d - 36*B*C*a^3*b^8*c*d^12 + 8*B*C*a
^5*b^6*c*d^12 + 4*B*C*a^7*b^4*c*d^12 + 6*B*C*a^10*b*c^2*d^11 - B*C*a^10*b*c^4*d^9 - 64*A*B*a^2*b^9*c^2*d^11 -
112*A*B*a^2*b^9*c^4*d^9 - 508*A*B*a^2*b^9*c^6*d^7 - 23*A*B*a^2*b^9*c^8*d^5 + 30*A*B*a^2*b^9*c^10*d^3 - 112*A*B
*a^3*b^8*c^3*d^10 + 480*A*B*a^3*b^8*c^5*d^8 + 584*A*B*a^3*b^8*c^7*d^6 - 56*A*B*a^3*b^8*c^9*d^4 - 8*A*B*a^3*b^8
*c^11*d^2 + 40*A*B*a^4*b^7*c^2*d^11 + 114*A*B*a^4*b^7*c^4*d^9 - 456*A*B*a^4*b^7*c^6*d^7 + 170*A*B*a^4*b^7*c^8*
d^5 + 28*A*B*a^4*b^7*c^10*d^3 - 104*A*B*a^5*b^6*c^3*d^10 + 368*A*B*a^5*b^6*c^5*d^8 + 104*A*B*a^5*b^6*c^7*d^6 -
56*A*B*a^5*b^6*c^9*d^4 + 52*A*B*a^6*b^5*c^2*d^11 - 50*A*B*a^6*b^5*c^4*d^9 - 176*A*B*a^6*b^5*c^6*d^7 + 70*A*B*
a^6*b^5*c^8*d^5 + 40*A*B*a^7*b^4*c^3*d^10 + 144*A*B*a^7*b^4*c^5*d^8 - 56*A*B*a^7*b^4*c^7*d^6 - 30*A*B*a^8*b^3*
c^2*d^11 - 105*A*B*a^8*b^3*c^4*d^9 + 28*A*B*a^8*b^3*c^6*d^7 + 40*A*B*a^9*b^2*c^3*d^10 - 8*A*B*a^9*b^2*c^5*d^8
- 60*A*C*a^2*b^9*c^3*d^10 - 318*A*C*a^2*b^9*c^5*d^8 + 166*A*C*a^2*b^9*c^7*d^6 + 14*A*C*a^2*b^9*c^9*d^4 - 14*A*
C*a^2*b^9*c^11*d^2 + 188*A*C*a^3*b^8*c^2*d^11 + 630*A*C*a^3*b^8*c^4*d^9 + 210*A*C*a^3*b^8*c^6*d^7 - 322*A*C*a^
3*b^8*c^8*d^5 + 10*A*C*a^3*b^8*c^10*d^3 - 330*A*C*a^4*b^7*c^3*d^10 - 754*A*C*a^4*b^7*c^5*d^8 + 162*A*C*a^4*b^7
*c^7*d^6 - 30*A*C*a^4*b^7*c^9*d^4 + 50*A*C*a^5*b^6*c^2*d^11 + 374*A*C*a^5*b^6*c^4*d^9 - 202*A*C*a^5*b^6*c^6*d^
7 - 206*A*C*a^5*b^6*c^8*d^5 - 134*A*C*a^6*b^5*c^3*d^10 - 110*A*C*a^6*b^5*c^5*d^8 + 166*A*C*a^6*b^5*c^7*d^6 - 3
4*A*C*a^7*b^4*c^2*d^11 + 14*A*C*a^7*b^4*c^4*d^9 - 150*A*C*a^7*b^4*c^6*d^7 + 106*A*C*a^8*b^3*c^5*d^8 + 16*A*C*a
^9*b^2*c^2*d^11 - 32*A*C*a^9*b^2*c^4*d^9 - 68*B*C*a^2*b^9*c^2*d^11 - 140*B*C*a^2*b^9*c^4*d^9 + 208*B*C*a^2*b^9
*c^6*d^7 - 109*B*C*a^2*b^9*c^8*d^5 - 30*B*C*a^2*b^9*c^10*d^3 + 4*B*C*a^3*b^8*c^3*d^10 - 300*B*C*a^3*b^8*c^5*d^
8 - 140*B*C*a^3*b^8*c^7*d^6 + 272*B*C*a^3*b^8*c^9*d^4 + 8*B*C*a^3*b^8*c^11*d^2 - 160*B*C*a^4*b^7*c^2*d^11 - 17
4*B*C*a^4*b^7*c^4*d^9 + 420*B*C*a^4*b^7*c^6*d^7 - 182*B*C*a^4*b^7*c^8*d^5 - 16*B*C*a^4*b^7*c^10*d^3 + 236*B*C*
a^5*b^6*c^3*d^10 - 116*B*C*a^5*b^6*c^5*d^8 + 196*B*C*a^5*b^6*c^7*d^6 + 188*B*C*a^5*b^6*c^9*d^4 - 64*B*C*a^6*b^
5*c^2*d^11 + 110*B*C*a^6*b^5*c^4*d^9 + 236*B*C*a^6*b^5*c^6*d^7 - 58*B*C*a^6*b^5*c^8*d^5 + 20*B*C*a^7*b^4*c^3*d
^10 - 132*B*C*a^7*b^4*c^5*d^8 + 44*B*C*a^7*b^4*c^7*d^6 + 30*B*C*a^8*b^3*c^2*d^11 + 105*B*C*a^8*b^3*c^4*d^9 - 2
8*B*C*a^8*b^3*c^6*d^7 - 40*B*C*a^9*b^2*c^3*d^10 + 8*B*C*a^9*b^2*c^5*d^8)/(a^10*d^14 + b^10*c^14 + 2*a^2*b^8*c^
14 + a^4*b^6*c^14 + a^6*b^4*d^14 + 2*a^8*b^2*d^14 + 4*a^10*c^2*d^12 + 6*a^10*c^4*d^10 + 4*a^10*c^6*d^8 + a^10*
c^8*d^6 + b^10*c^6*d^8 + 4*b^10*c^8*d^6 + 6*b^10*c^10*d^4 + 4*b^10*c^12*d^2 - 6*a*b^9*c^5*d^9 - 24*a*b^9*c^7*d
^7 - 36*a*b^9*c^9*d^5 - 24*a*b^9*c^11*d^3 - 12*a^3*b^7*c^13*d - 6*a^5*b^5*c*d^13 - 6*a^5*b^5*c^13*d - 12*a^7*b
^3*c*d^13 - 24*a^9*b*c^3*d^11 - 36*a^9*b*c^5*d^9 - 24*a^9*b*c^7*d^7 - 6*a^9*b*c^9*d^5 + 15*a^2*b^8*c^4*d^10 +
62*a^2*b^8*c^6*d^8 + 98*a^2*b^8*c^8*d^6 + 72*a^2*b^8*c^10*d^4 + 23*a^2*b^8*c^12*d^2 - 20*a^3*b^7*c^3*d^11 - 92
*a^3*b^7*c^5*d^9 - 168*a^3*b^7*c^7*d^7 - 152*a^3*b^7*c^9*d^5 - 68*a^3*b^7*c^11*d^3 + 15*a^4*b^6*c^2*d^12 + 90*
a^4*b^6*c^4*d^10 + 211*a^4*b^6*c^6*d^8 + 244*a^4*b^6*c^8*d^6 + 141*a^4*b^6*c^10*d^4 + 34*a^4*b^6*c^12*d^2 - 64
*a^5*b^5*c^3*d^11 - 202*a^5*b^5*c^5*d^9 - 288*a^5*b^5*c^7*d^7 - 202*a^5*b^5*c^9*d^5 - 64*a^5*b^5*c^11*d^3 + 34
*a^6*b^4*c^2*d^12 + 141*a^6*b^4*c^4*d^10 + 244*a^6*b^4*c^6*d^8 + 211*a^6*b^4*c^8*d^6 + 90*a^6*b^4*c^10*d^4 + 1
5*a^6*b^4*c^12*d^2 - 68*a^7*b^3*c^3*d^11 - 152*a^7*b^3*c^5*d^9 - 168*a^7*b^3*c^7*d^7 - 92*a^7*b^3*c^9*d^5 - 20
*a^7*b^3*c^11*d^3 + 23*a^8*b^2*c^2*d^12 + 72*a^8*b^2*c^4*d^10 + 98*a^8*b^2*c^6*d^8 + 62*a^8*b^2*c^8*d^6 + 15*a
^8*b^2*c^10*d^4 - 6*a*b^9*c^13*d - 6*a^9*b*c*d^13) - (tan(e + f*x)*(10*A^2*a^4*b^7*d^13 - 6*A^2*a^2*b^9*d^13 -
18*A^2*b^11*d^13 + 12*A^2*a^6*b^5*d^13 - 3*A^2*a^8*b^3*d^13 - 8*B^2*a^2*b^9*d^13 - 8*B^2*a^4*b^7*d^13 - 18*B^
2*a^6*b^5*d^13 - 2*B^2*a^8*b^3*d^13 - 54*A^2*b^11*c^2*d^11 - 18*A^2*b^11*c^4*d^9 + 20*A^2*b^11*c^6*d^7 - 65*A^
2*b^11*c^8*d^5 - 2*C^2*a^4*b^7*d^13 + 6*C^2*a^6*b^5*d^13 - 9*C^2*a^8*b^3*d^13 - 2*B^2*b^11*c^2*d^11 - 6*B^2*b^
11*c^4*d^9 + 12*B^2*b^11*c^6*d^7 + 66*B^2*b^11*c^8*d^5 - 18*B^2*b^11*c^10*d^3 + 2*C^2*b^11*c^6*d^7 - 29*C^2*b^
11*c^8*d^5 + 36*C^2*b^11*c^10*d^3 - B^2*a^10*b*d^13 - A^2*b^11*c^12*d - C^2*b^11*c^12*d - 158*A^2*a^2*b^9*c^2*
d^11 - 224*A^2*a^2*b^9*c^4*d^9 - 252*A^2*a^2*b^9*c^6*d^7 - 194*A^2*a^2*b^9*c^8*d^5 - 2*A^2*a^2*b^9*c^10*d^3 +
504*A^2*a^3*b^8*c^3*d^10 + 580*A^2*a^3*b^8*c^5*d^8 + 464*A^2*a^3*b^8*c^7*d^6 + 28*A^2*a^3*b^8*c^9*d^4 - 232*A^
2*a^4*b^7*c^2*d^11 - 446*A^2*a^4*b^7*c^4*d^9 - 452*A^2*a^4*b^7*c^6*d^7 - 128*A^2*a^4*b^7*c^8*d^5 + 248*A^2*a^5
*b^6*c^3*d^10 + 332*A^2*a^5*b^6*c^5*d^8 + 152*A^2*a^5*b^6*c^7*d^6 - 96*A^2*a^6*b^5*c^2*d^11 - 244*A^2*a^6*b^5*
c^4*d^9 - 144*A^2*a^6*b^5*c^6*d^7 + 120*A^2*a^7*b^4*c^3*d^10 + 132*A^2*a^7*b^4*c^5*d^8 - 34*A^2*a^8*b^3*c^2*d^
11 - 83*A^2*a^8*b^3*c^4*d^9 + 28*A^2*a^9*b^2*c^3*d^10 + 18*B^2*a^2*b^9*c^2*d^11 + 36*B^2*a^2*b^9*c^4*d^9 + 208
*B^2*a^2*b^9*c^6*d^7 + 179*B^2*a^2*b^9*c^8*d^5 - 32*B^2*a^2*b^9*c^10*d^3 + 128*B^2*a^3*b^8*c^3*d^10 + 180*B^2*
a^3*b^8*c^5*d^8 - 96*B^2*a^3*b^8*c^7*d^6 + 36*B^2*a^3*b^8*c^9*d^4 + 8*B^2*a^3*b^8*c^11*d^2 + 4*B^2*a^4*b^7*c^2
*d^11 - 36*B^2*a^4*b^7*c^4*d^9 + 164*B^2*a^4*b^7*c^6*d^7 + 76*B^2*a^4*b^7*c^8*d^5 - 16*B^2*a^4*b^7*c^10*d^3 +
208*B^2*a^5*b^6*c^3*d^10 + 148*B^2*a^5*b^6*c^5*d^8 + 16*B^2*a^5*b^6*c^7*d^6 - 84*B^2*a^6*b^5*c^2*d^11 - 134*B^
2*a^6*b^5*c^4*d^9 - 96*B^2*a^6*b^5*c^6*d^7 - 36*B^2*a^6*b^5*c^8*d^5 + 40*B^2*a^7*b^4*c^3*d^10 + 20*B^2*a^7*b^4
*c^5*d^8 + 48*B^2*a^7*b^4*c^7*d^6 - 4*B^2*a^8*b^3*c^2*d^11 + 22*B^2*a^8*b^3*c^4*d^9 - 28*B^2*a^8*b^3*c^6*d^7 -
12*B^2*a^9*b^2*c^3*d^10 + 8*B^2*a^9*b^2*c^5*d^8 - 8*C^2*a^2*b^9*c^2*d^11 + 16*C^2*a^2*b^9*c^4*d^9 - 132*C^2*a
^2*b^9*c^6*d^7 - 104*C^2*a^2*b^9*c^8*d^5 + 64*C^2*a^2*b^9*c^10*d^3 + 64*C^2*a^3*b^8*c^5*d^8 + 356*C^2*a^3*b^8*
c^7*d^6 + 64*C^2*a^3*b^8*c^9*d^4 - 12*C^2*a^3*b^8*c^11*d^2 + 44*C^2*a^4*b^7*c^2*d^11 + 178*C^2*a^4*b^7*c^4*d^9
- 68*C^2*a^4*b^7*c^6*d^7 - 68*C^2*a^4*b^7*c^8*d^5 + 12*C^2*a^4*b^7*c^10*d^3 - 4*C^2*a^5*b^6*c^3*d^10 + 80*C^2
*a^5*b^6*c^5*d^8 + 164*C^2*a^5*b^6*c^7*d^6 + 72*C^2*a^5*b^6*c^9*d^4 + 90*C^2*a^6*b^5*c^2*d^11 + 188*C^2*a^6*b^
5*c^4*d^9 + 120*C^2*a^6*b^5*c^6*d^7 + 6*C^2*a^6*b^5*c^8*d^5 - 18*C^2*a^6*b^5*c^10*d^3 + 36*C^2*a^7*b^4*c^3*d^1
0 - 60*C^2*a^7*b^4*c^7*d^6 - 28*C^2*a^8*b^3*c^2*d^11 - 53*C^2*a^8*b^3*c^4*d^9 + 18*C^2*a^8*b^3*c^6*d^7 + 28*C^
2*a^9*b^2*c^3*d^10 + 16*A*B*a^3*b^8*d^13 + 16*A*B*a^5*b^6*d^13 - 8*A*B*a^7*b^4*d^13 + 2*A*B*a^9*b^2*d^13 - 12*
A*C*a^2*b^9*d^13 + 10*A*C*a^4*b^7*d^13 + 12*A*C*a^8*b^3*d^13 + 36*A*B*b^11*c^3*d^10 - 36*A*B*b^11*c^5*d^8 - 13
2*A*B*b^11*c^7*d^6 + 60*A*B*b^11*c^9*d^4 - 4*A*B*b^11*c^11*d^2 + 8*B*C*a^3*b^8*d^13 - 4*B*C*a^5*b^6*d^13 + 20*
B*C*a^7*b^4*d^13 - 2*B*C*a^9*b^2*d^13 - 18*A*C*b^11*c^4*d^9 + 14*A*C*b^11*c^6*d^7 + 148*A*C*b^11*c^8*d^5 - 18*
A*C*b^11*c^10*d^3 + 6*B*C*b^11*c^5*d^8 + 18*B*C*b^11*c^7*d^6 - 114*B*C*b^11*c^9*d^4 + 10*B*C*b^11*c^11*d^2 + 9
6*A^2*a*b^10*c*d^12 - 8*B^2*a*b^10*c*d^12 + 336*A^2*a*b^10*c^3*d^10 + 372*A^2*a*b^10*c^5*d^8 + 320*A^2*a*b^10*
c^7*d^6 + 40*A^2*a*b^10*c^9*d^4 + 4*A^2*a*b^10*c^11*d^2 + 136*A^2*a^3*b^8*c*d^12 + 52*A^2*a^5*b^6*c*d^12 + 20*
A^2*a^7*b^4*c*d^12 + 4*A^2*a^9*b^2*c*d^12 - 4*A^2*a^10*b*c^2*d^11 - 16*B^2*a*b^10*c^3*d^10 + 52*B^2*a*b^10*c^5
*d^8 - 72*B^2*a*b^10*c^7*d^6 + 24*B^2*a*b^10*c^9*d^4 + 4*B^2*a*b^10*c^11*d^2 - B^2*a^2*b^9*c^12*d + 48*B^2*a^3
*b^8*c*d^12 + 92*B^2*a^5*b^6*c*d^12 + 36*B^2*a^7*b^4*c*d^12 + 4*B^2*a^9*b^2*c*d^12 + 2*B^2*a^10*b*c^2*d^11 - B
^2*a^10*b*c^4*d^9 - 24*C^2*a*b^10*c^5*d^8 + 140*C^2*a*b^10*c^7*d^6 + 4*C^2*a*b^10*c^9*d^4 - 8*C^2*a*b^10*c^11*
d^2 - 8*C^2*a^3*b^8*c*d^12 - 8*C^2*a^5*b^6*c*d^12 + 8*C^2*a^7*b^4*c*d^12 + 4*C^2*a^9*b^2*c*d^12 - 4*C^2*a^10*b
*c^2*d^11 + 24*A*B*a*b^10*d^13 + 12*A*B*b^11*c*d^12 + 2*A*C*b^11*c^12*d + 2*A*B*a*b^10*c^12*d - 4*A*B*a^10*b*c
*d^12 - 24*A*C*a*b^10*c*d^12 - 2*B*C*a*b^10*c^12*d + 4*B*C*a^10*b*c*d^12 + 16*A*B*a*b^10*c^2*d^11 - 136*A*B*a*
b^10*c^4*d^9 + 8*A*B*a*b^10*c^6*d^7 - 174*A*B*a*b^10*c^8*d^5 - 4*A*B*a*b^10*c^10*d^3 - 140*A*B*a^2*b^9*c*d^12
- 220*A*B*a^4*b^7*c*d^12 - 68*A*B*a^6*b^5*c*d^12 - 12*A*B*a^8*b^3*c*d^12 + 4*A*B*a^10*b*c^3*d^10 - 48*A*C*a*b^
10*c^3*d^10 + 84*A*C*a*b^10*c^5*d^8 - 172*A*C*a*b^10*c^7*d^6 + 28*A*C*a*b^10*c^9*d^4 + 4*A*C*a*b^10*c^11*d^2 +
16*A*C*a^3*b^8*c*d^12 + 28*A*C*a^5*b^6*c*d^12 - 28*A*C*a^7*b^4*c*d^12 - 8*A*C*a^9*b^2*c*d^12 + 8*A*C*a^10*b*c
^2*d^11 + 8*B*C*a*b^10*c^2*d^11 + 28*B*C*a*b^10*c^4*d^9 - 188*B*C*a*b^10*c^6*d^7 + 114*B*C*a*b^10*c^8*d^5 + 16
*B*C*a*b^10*c^10*d^3 + 20*B*C*a^2*b^9*c*d^12 - 14*B*C*a^4*b^7*c*d^12 - 52*B*C*a^6*b^5*c*d^12 - 6*B*C*a^8*b^3*c
*d^12 - 4*B*C*a^10*b*c^3*d^10 - 300*A*B*a^2*b^9*c^3*d^10 - 580*A*B*a^2*b^9*c^5*d^8 - 340*A*B*a^2*b^9*c^7*d^6 +
92*A*B*a^2*b^9*c^9*d^4 - 12*A*B*a^2*b^9*c^11*d^2 + 64*A*B*a^3*b^8*c^2*d^11 + 8*A*B*a^3*b^8*c^4*d^9 + 208*A*B*
a^3*b^8*c^6*d^7 - 200*A*B*a^3*b^8*c^8*d^5 - 420*A*B*a^4*b^7*c^3*d^10 - 596*A*B*a^4*b^7*c^5*d^8 - 100*A*B*a^4*b
^7*c^7*d^6 + 56*A*B*a^4*b^7*c^9*d^4 + 184*A*B*a^5*b^6*c^2*d^11 + 292*A*B*a^5*b^6*c^4*d^9 + 128*A*B*a^5*b^6*c^6
*d^7 - 28*A*B*a^5*b^6*c^8*d^5 - 84*A*B*a^6*b^5*c^3*d^10 + 60*A*B*a^6*b^5*c^5*d^8 + 92*A*B*a^6*b^5*c^7*d^6 + 32
*A*B*a^7*b^4*c^2*d^11 - 40*A*B*a^7*b^4*c^4*d^9 - 144*A*B*a^7*b^4*c^6*d^7 - 20*A*B*a^8*b^3*c^3*d^10 + 96*A*B*a^
8*b^3*c^5*d^8 + 20*A*B*a^9*b^2*c^2*d^11 - 30*A*B*a^9*b^2*c^4*d^9 + 112*A*C*a^2*b^9*c^2*d^11 + 172*A*C*a^2*b^9*
c^4*d^9 + 420*A*C*a^2*b^9*c^6*d^7 + 352*A*C*a^2*b^9*c^8*d^5 - 44*A*C*a^2*b^9*c^10*d^3 + 72*A*C*a^3*b^8*c^3*d^1
0 + 220*A*C*a^3*b^8*c^5*d^8 - 244*A*C*a^3*b^8*c^7*d^6 + 52*A*C*a^3*b^8*c^9*d^4 + 12*A*C*a^3*b^8*c^11*d^2 + 242
*A*C*a^4*b^7*c^2*d^11 + 304*A*C*a^4*b^7*c^4*d^9 + 484*A*C*a^4*b^7*c^6*d^7 + 142*A*C*a^4*b^7*c^8*d^5 - 30*A*C*a
^4*b^7*c^10*d^3 + 44*A*C*a^5*b^6*c^3*d^10 + 20*A*C*a^5*b^6*c^5*d^8 - 28*A*C*a^5*b^6*c^7*d^6 + 60*A*C*a^6*b^5*c
^2*d^11 + 92*A*C*a^6*b^5*c^4*d^9 - 12*A*C*a^6*b^5*c^6*d^7 - 60*A*C*a^6*b^5*c^8*d^5 - 156*A*C*a^7*b^4*c^3*d^10
- 132*A*C*a^7*b^4*c^5*d^8 + 60*A*C*a^7*b^4*c^7*d^6 + 62*A*C*a^8*b^3*c^2*d^11 + 136*A*C*a^8*b^3*c^4*d^9 - 18*A*
C*a^8*b^3*c^6*d^7 - 56*A*C*a^9*b^2*c^3*d^10 + 160*B*C*a^2*b^9*c^5*d^8 - 80*B*C*a^2*b^9*c^7*d^6 - 272*B*C*a^2*b
^9*c^9*d^4 + 12*B*C*a^2*b^9*c^11*d^2 - 88*B*C*a^3*b^8*c^2*d^11 - 332*B*C*a^3*b^8*c^4*d^9 - 652*B*C*a^3*b^8*c^6
*d^7 + 68*B*C*a^3*b^8*c^8*d^5 + 36*B*C*a^3*b^8*c^10*d^3 - 66*B*C*a^4*b^7*c^3*d^10 + 248*B*C*a^4*b^7*c^5*d^8 -
80*B*C*a^4*b^7*c^7*d^6 - 146*B*C*a^4*b^7*c^9*d^4 - 6*B*C*a^4*b^7*c^11*d^2 - 172*B*C*a^5*b^6*c^2*d^11 - 448*B*C
*a^5*b^6*c^4*d^9 - 404*B*C*a^5*b^6*c^6*d^7 - 68*B*C*a^5*b^6*c^8*d^5 + 24*B*C*a^5*b^6*c^10*d^3 - 96*B*C*a^6*b^5
*c^3*d^10 - 24*B*C*a^6*b^5*c^5*d^8 + 40*B*C*a^6*b^5*c^7*d^6 + 36*B*C*a^6*b^5*c^9*d^4 + 28*B*C*a^7*b^4*c^2*d^11
+ 100*B*C*a^7*b^4*c^4*d^9 + 132*B*C*a^7*b^4*c^6*d^7 - 24*B*C*a^7*b^4*c^8*d^5 - 10*B*C*a^8*b^3*c^3*d^10 - 102*
B*C*a^8*b^3*c^5*d^8 + 6*B*C*a^8*b^3*c^7*d^6 - 20*B*C*a^9*b^2*c^2*d^11 + 30*B*C*a^9*b^2*c^4*d^9))/(a^10*d^14 +
b^10*c^14 + 2*a^2*b^8*c^14 + a^4*b^6*c^14 + a^6*b^4*d^14 + 2*a^8*b^2*d^14 + 4*a^10*c^2*d^12 + 6*a^10*c^4*d^10
+ 4*a^10*c^6*d^8 + a^10*c^8*d^6 + b^10*c^6*d^8 + 4*b^10*c^8*d^6 + 6*b^10*c^10*d^4 + 4*b^10*c^12*d^2 - 6*a*b^9*
c^5*d^9 - 24*a*b^9*c^7*d^7 - 36*a*b^9*c^9*d^5 - 24*a*b^9*c^11*d^3 - 12*a^3*b^7*c^13*d - 6*a^5*b^5*c*d^13 - 6*a
^5*b^5*c^13*d - 12*a^7*b^3*c*d^13 - 24*a^9*b*c^3*d^11 - 36*a^9*b*c^5*d^9 - 24*a^9*b*c^7*d^7 - 6*a^9*b*c^9*d^5
+ 15*a^2*b^8*c^4*d^10 + 62*a^2*b^8*c^6*d^8 + 98*a^2*b^8*c^8*d^6 + 72*a^2*b^8*c^10*d^4 + 23*a^2*b^8*c^12*d^2 -
20*a^3*b^7*c^3*d^11 - 92*a^3*b^7*c^5*d^9 - 168*a^3*b^7*c^7*d^7 - 152*a^3*b^7*c^9*d^5 - 68*a^3*b^7*c^11*d^3 + 1
5*a^4*b^6*c^2*d^12 + 90*a^4*b^6*c^4*d^10 + 211*a^4*b^6*c^6*d^8 + 244*a^4*b^6*c^8*d^6 + 141*a^4*b^6*c^10*d^4 +
34*a^4*b^6*c^12*d^2 - 64*a^5*b^5*c^3*d^11 - 202*a^5*b^5*c^5*d^9 - 288*a^5*b^5*c^7*d^7 - 202*a^5*b^5*c^9*d^5 -
64*a^5*b^5*c^11*d^3 + 34*a^6*b^4*c^2*d^12 + 141*a^6*b^4*c^4*d^10 + 244*a^6*b^4*c^6*d^8 + 211*a^6*b^4*c^8*d^6 +
90*a^6*b^4*c^10*d^4 + 15*a^6*b^4*c^12*d^2 - 68*a^7*b^3*c^3*d^11 - 152*a^7*b^3*c^5*d^9 - 168*a^7*b^3*c^7*d^7 -
92*a^7*b^3*c^9*d^5 - 20*a^7*b^3*c^11*d^3 + 23*a^8*b^2*c^2*d^12 + 72*a^8*b^2*c^4*d^10 + 98*a^8*b^2*c^6*d^8 + 6
2*a^8*b^2*c^8*d^6 + 15*a^8*b^2*c^10*d^4 - 6*a*b^9*c^13*d - 6*a^9*b*c*d^13)) + (tan(e + f*x)*(4*B^3*a^5*b^4*d^1
0 - 12*A^3*a^2*b^7*d^10 - A^3*a^4*b^5*d^10 - 9*A^3*b^9*d^10 - 27*A^3*b^9*c^2*d^8 - 24*A^3*b^9*c^4*d^6 + 10*A^3
*b^9*c^6*d^4 + C^3*a^4*b^5*d^10 + B^3*b^9*c^3*d^7 + B^3*b^9*c^5*d^5 - C^3*b^9*c^6*d^4 + 3*C^3*b^9*c^8*d^2 + 9*
A^2*C*b^9*d^10 - 58*A^3*a^2*b^7*c^2*d^8 - 46*A^3*a^2*b^7*c^4*d^6 + 52*A^3*a^3*b^6*c^3*d^7 - 17*A^3*a^4*b^5*c^2
*d^8 + 16*B^3*a^2*b^7*c^3*d^7 - 26*B^3*a^2*b^7*c^5*d^5 - 6*B^3*a^2*b^7*c^7*d^3 - 8*B^3*a^3*b^6*c^2*d^8 + 20*B^
3*a^3*b^6*c^4*d^6 + 28*B^3*a^3*b^6*c^6*d^4 + 17*B^3*a^4*b^5*c^3*d^7 - 17*B^3*a^4*b^5*c^5*d^5 - 8*B^3*a^5*b^4*c
^2*d^8 + 4*B^3*a^5*b^4*c^4*d^6 + 4*C^3*a^2*b^7*c^2*d^8 - 2*C^3*a^2*b^7*c^4*d^6 + 6*C^3*a^2*b^7*c^6*d^4 + 20*C^
3*a^3*b^6*c^3*d^7 - 10*C^3*a^4*b^5*c^2*d^8 - 6*C^3*a^4*b^5*c^4*d^6 + 9*C^3*a^4*b^5*c^6*d^4 + 36*C^3*a^5*b^4*c^
3*d^7 - 12*C^3*a^6*b^3*c^2*d^8 + 12*A^2*B*a*b^8*d^10 + 15*A^2*B*b^9*c*d^9 + 12*A^3*a*b^8*c*d^9 - 4*A*B^2*a^2*b
^7*d^10 - 14*A*B^2*a^4*b^5*d^10 + 20*A^2*B*a^3*b^6*d^10 + 6*A*C^2*a^2*b^7*d^10 + 6*A*C^2*a^4*b^5*d^10 + 6*A^2*
C*a^2*b^7*d^10 - 6*A^2*C*a^4*b^5*d^10 - 7*A*B^2*b^9*c^2*d^8 - 15*A*B^2*b^9*c^4*d^6 - 24*A*B^2*b^9*c^6*d^4 - 4*
B*C^2*a^3*b^6*d^10 - 6*B*C^2*a^5*b^4*d^10 + 45*A^2*B*b^9*c^3*d^7 + 56*A^2*B*b^9*c^5*d^5 - 6*A^2*B*b^9*c^7*d^3
+ 4*B^2*C*a^2*b^7*d^10 + 8*B^2*C*a^4*b^5*d^10 - 3*B^2*C*a^6*b^3*d^10 + 3*A*C^2*b^9*c^4*d^6 + 21*A*C^2*b^9*c^6*
d^4 - 6*A*C^2*b^9*c^8*d^2 + 27*A^2*C*b^9*c^2*d^8 + 21*A^2*C*b^9*c^4*d^6 - 30*A^2*C*b^9*c^6*d^4 + 3*A^2*C*b^9*c
^8*d^2 - B*C^2*b^9*c^5*d^5 - 9*B*C^2*b^9*c^7*d^3 + B^2*C*b^9*c^2*d^8 + 3*B^2*C*b^9*c^4*d^6 + 6*B^2*C*b^9*c^6*d
^4 + 36*A^3*a*b^8*c^3*d^7 - 8*A^3*a*b^8*c^5*d^5 + 20*A^3*a^3*b^6*c*d^9 + 4*B^3*a*b^8*c^2*d^8 + 12*B^3*a*b^8*c^
4*d^6 + 24*B^3*a*b^8*c^6*d^4 + 4*B^3*a^2*b^7*c*d^9 + 2*B^3*a^4*b^5*c*d^9 + 8*C^3*a*b^8*c^5*d^5 + 4*C^3*a^3*b^6
*c*d^9 + 12*C^3*a^5*b^4*c*d^9 - 12*A*B*C*a*b^8*d^10 - 6*A*B*C*b^9*c*d^9 + 8*A*B^2*a^2*b^7*c^2*d^8 + 54*A*B^2*a
^2*b^7*c^4*d^6 - 22*A*B^2*a^2*b^7*c^6*d^4 - 92*A*B^2*a^3*b^6*c^3*d^7 - 56*A*B^2*a^3*b^6*c^5*d^5 - 7*A*B^2*a^4*
b^5*c^2*d^8 + 55*A*B^2*a^4*b^5*c^4*d^6 - 16*A*B^2*a^5*b^4*c^3*d^7 + 46*A^2*B*a^2*b^7*c^3*d^7 + 82*A^2*B*a^2*b^
7*c^5*d^5 + 68*A^2*B*a^3*b^6*c^2*d^8 - 16*A^2*B*a^3*b^6*c^4*d^6 - 33*A^2*B*a^4*b^5*c^3*d^7 + 16*A^2*B*a^5*b^4*
c^2*d^8 - 12*A*C^2*a^2*b^7*c^2*d^8 + 12*A*C^2*a^2*b^7*c^4*d^6 + 6*A*C^2*a^2*b^7*c^6*d^4 + 12*A*C^2*a^3*b^6*c^3
*d^7 + 30*A*C^2*a^4*b^5*c^2*d^8 + 39*A*C^2*a^4*b^5*c^4*d^6 - 9*A*C^2*a^4*b^5*c^6*d^4 - 72*A*C^2*a^5*b^4*c^3*d^
7 + 24*A*C^2*a^6*b^3*c^2*d^8 + 66*A^2*C*a^2*b^7*c^2*d^8 + 36*A^2*C*a^2*b^7*c^4*d^6 - 12*A^2*C*a^2*b^7*c^6*d^4
- 84*A^2*C*a^3*b^6*c^3*d^7 - 3*A^2*C*a^4*b^5*c^2*d^8 - 33*A^2*C*a^4*b^5*c^4*d^6 + 36*A^2*C*a^5*b^4*c^3*d^7 - 1
2*A^2*C*a^6*b^3*c^2*d^8 - 20*B*C^2*a^2*b^7*c^3*d^7 + 4*B*C^2*a^2*b^7*c^5*d^5 + 6*B*C^2*a^2*b^7*c^7*d^3 + 8*B*C
^2*a^3*b^6*c^2*d^8 + 32*B*C^2*a^3*b^6*c^4*d^6 - 12*B*C^2*a^3*b^6*c^6*d^4 - 66*B*C^2*a^4*b^5*c^3*d^7 - 21*B*C^2
*a^4*b^5*c^5*d^5 + 9*B*C^2*a^4*b^5*c^7*d^3 + 4*B*C^2*a^5*b^4*c^2*d^8 + 42*B*C^2*a^5*b^4*c^4*d^6 - 12*B*C^2*a^6
*b^3*c^3*d^7 - 2*B^2*C*a^2*b^7*c^2*d^8 - 63*B^2*C*a^2*b^7*c^4*d^6 - 2*B^2*C*a^2*b^7*c^6*d^4 + 3*B^2*C*a^2*b^7*
c^8*d^2 + 32*B^2*C*a^3*b^6*c^3*d^7 + 44*B^2*C*a^3*b^6*c^5*d^5 - 12*B^2*C*a^3*b^6*c^7*d^3 + 13*B^2*C*a^4*b^5*c^
2*d^8 - 73*B^2*C*a^4*b^5*c^4*d^6 - 18*B^2*C*a^4*b^5*c^6*d^4 + 4*B^2*C*a^5*b^4*c^3*d^7 + 12*B^2*C*a^5*b^4*c^5*d
^5 + 6*B^2*C*a^6*b^3*c^2*d^8 - 3*B^2*C*a^6*b^3*c^4*d^6 - 16*A*B*C*a^3*b^6*d^10 + 6*A*B*C*a^5*b^4*d^10 - 18*A*B
*C*b^9*c^3*d^7 - 28*A*B*C*b^9*c^5*d^5 + 24*A*B*C*b^9*c^7*d^3 - 16*A*B^2*a*b^8*c*d^9 + 12*A*C^2*a*b^8*c*d^9 - 2
4*A^2*C*a*b^8*c*d^9 + 4*B^2*C*a*b^8*c*d^9 - 56*A*B^2*a*b^8*c^3*d^7 - 28*A*B^2*a*b^8*c^5*d^5 + 12*A*B^2*a*b^8*c
^7*d^3 - 4*A*B^2*a^3*b^6*c*d^9 + 16*A*B^2*a^5*b^4*c*d^9 + 20*A^2*B*a*b^8*c^2*d^8 - 56*A^2*B*a*b^8*c^4*d^6 - 16
*A^2*B*a*b^8*c^6*d^4 - 4*A^2*B*a^2*b^7*c*d^9 - 33*A^2*B*a^4*b^5*c*d^9 + 36*A*C^2*a*b^8*c^3*d^7 - 24*A*C^2*a*b^
8*c^5*d^5 + 12*A*C^2*a^3*b^6*c*d^9 - 24*A*C^2*a^5*b^4*c*d^9 - 72*A^2*C*a*b^8*c^3*d^7 + 24*A^2*C*a*b^8*c^5*d^5
- 36*A^2*C*a^3*b^6*c*d^9 + 12*A^2*C*a^5*b^4*c*d^9 - 4*B*C^2*a*b^8*c^2*d^8 - 14*B*C^2*a*b^8*c^4*d^6 - 4*B*C^2*a
*b^8*c^6*d^4 + 6*B*C^2*a*b^8*c^8*d^2 - 10*B*C^2*a^2*b^7*c*d^9 - 12*B*C^2*a^4*b^5*c*d^9 + 12*B*C^2*a^6*b^3*c*d^
9 + 8*B^2*C*a*b^8*c^3*d^7 + 4*B^2*C*a*b^8*c^5*d^5 - 24*B^2*C*a*b^8*c^7*d^3 - 8*B^2*C*a^3*b^6*c*d^9 - 16*B^2*C*
a^5*b^4*c*d^9 + 28*A*B*C*a^2*b^7*c^3*d^7 - 32*A*B*C*a^2*b^7*c^5*d^5 + 12*A*B*C*a^2*b^7*c^7*d^3 - 76*A*B*C*a^3*
b^6*c^2*d^8 - 16*A*B*C*a^3*b^6*c^4*d^6 + 12*A*B*C*a^3*b^6*c^6*d^4 + 126*A*B*C*a^4*b^5*c^3*d^7 + 48*A*B*C*a^4*b
^5*c^5*d^5 - 20*A*B*C*a^5*b^4*c^2*d^8 - 42*A*B*C*a^5*b^4*c^4*d^6 + 12*A*B*C*a^6*b^3*c^3*d^7 - 16*A*B*C*a*b^8*c
^2*d^8 + 70*A*B*C*a*b^8*c^4*d^6 + 20*A*B*C*a*b^8*c^6*d^4 - 6*A*B*C*a*b^8*c^8*d^2 + 32*A*B*C*a^2*b^7*c*d^9 + 54
*A*B*C*a^4*b^5*c*d^9 - 12*A*B*C*a^6*b^3*c*d^9))/(a^10*d^14 + b^10*c^14 + 2*a^2*b^8*c^14 + a^4*b^6*c^14 + a^6*b
^4*d^14 + 2*a^8*b^2*d^14 + 4*a^10*c^2*d^12 + 6*a^10*c^4*d^10 + 4*a^10*c^6*d^8 + a^10*c^8*d^6 + b^10*c^6*d^8 +
4*b^10*c^8*d^6 + 6*b^10*c^10*d^4 + 4*b^10*c^12*d^2 - 6*a*b^9*c^5*d^9 - 24*a*b^9*c^7*d^7 - 36*a*b^9*c^9*d^5 - 2
4*a*b^9*c^11*d^3 - 12*a^3*b^7*c^13*d - 6*a^5*b^5*c*d^13 - 6*a^5*b^5*c^13*d - 12*a^7*b^3*c*d^13 - 24*a^9*b*c^3*
d^11 - 36*a^9*b*c^5*d^9 - 24*a^9*b*c^7*d^7 - 6*a^9*b*c^9*d^5 + 15*a^2*b^8*c^4*d^10 + 62*a^2*b^8*c^6*d^8 + 98*a
^2*b^8*c^8*d^6 + 72*a^2*b^8*c^10*d^4 + 23*a^2*b^8*c^12*d^2 - 20*a^3*b^7*c^3*d^11 - 92*a^3*b^7*c^5*d^9 - 168*a^
3*b^7*c^7*d^7 - 152*a^3*b^7*c^9*d^5 - 68*a^3*b^7*c^11*d^3 + 15*a^4*b^6*c^2*d^12 + 90*a^4*b^6*c^4*d^10 + 211*a^
4*b^6*c^6*d^8 + 244*a^4*b^6*c^8*d^6 + 141*a^4*b^6*c^10*d^4 + 34*a^4*b^6*c^12*d^2 - 64*a^5*b^5*c^3*d^11 - 202*a
^5*b^5*c^5*d^9 - 288*a^5*b^5*c^7*d^7 - 202*a^5*b^5*c^9*d^5 - 64*a^5*b^5*c^11*d^3 + 34*a^6*b^4*c^2*d^12 + 141*a
^6*b^4*c^4*d^10 + 244*a^6*b^4*c^6*d^8 + 211*a^6*b^4*c^8*d^6 + 90*a^6*b^4*c^10*d^4 + 15*a^6*b^4*c^12*d^2 - 68*a
^7*b^3*c^3*d^11 - 152*a^7*b^3*c^5*d^9 - 168*a^7*b^3*c^7*d^7 - 92*a^7*b^3*c^9*d^5 - 20*a^7*b^3*c^11*d^3 + 23*a^
8*b^2*c^2*d^12 + 72*a^8*b^2*c^4*d^10 + 98*a^8*b^2*c^6*d^8 + 62*a^8*b^2*c^8*d^6 + 15*a^8*b^2*c^10*d^4 - 6*a*b^9
*c^13*d - 6*a^9*b*c*d^13))*root(640*a^15*b*c^7*d^13*f^4 + 640*a*b^15*c^13*d^7*f^4 + 480*a^15*b*c^9*d^11*f^4 +
480*a^15*b*c^5*d^15*f^4 + 480*a*b^15*c^15*d^5*f^4 + 480*a*b^15*c^11*d^9*f^4 + 192*a^15*b*c^11*d^9*f^4 + 192*a^
15*b*c^3*d^17*f^4 + 192*a^11*b^5*c*d^19*f^4 + 192*a^5*b^11*c^19*d*f^4 + 192*a*b^15*c^17*d^3*f^4 + 192*a*b^15*c
^9*d^11*f^4 + 128*a^13*b^3*c*d^19*f^4 + 128*a^9*b^7*c*d^19*f^4 + 128*a^7*b^9*c^19*d*f^4 + 128*a^3*b^13*c^19*d*
f^4 + 32*a^15*b*c^13*d^7*f^4 + 32*a^9*b^7*c^19*d*f^4 + 32*a^7*b^9*c*d^19*f^4 + 32*a*b^15*c^7*d^13*f^4 + 32*a^1
5*b*c*d^19*f^4 + 32*a*b^15*c^19*d*f^4 - 47088*a^8*b^8*c^10*d^10*f^4 + 42432*a^9*b^7*c^9*d^11*f^4 + 42432*a^7*b
^9*c^11*d^9*f^4 + 39328*a^9*b^7*c^11*d^9*f^4 + 39328*a^7*b^9*c^9*d^11*f^4 - 36912*a^8*b^8*c^12*d^8*f^4 - 36912
*a^8*b^8*c^8*d^12*f^4 - 34256*a^10*b^6*c^10*d^10*f^4 - 34256*a^6*b^10*c^10*d^10*f^4 - 31152*a^10*b^6*c^8*d^12*
f^4 - 31152*a^6*b^10*c^12*d^8*f^4 + 28128*a^9*b^7*c^7*d^13*f^4 + 28128*a^7*b^9*c^13*d^7*f^4 + 24160*a^11*b^5*c
^9*d^11*f^4 + 24160*a^5*b^11*c^11*d^9*f^4 - 23088*a^10*b^6*c^12*d^8*f^4 - 23088*a^6*b^10*c^8*d^12*f^4 + 22272*
a^9*b^7*c^13*d^7*f^4 + 22272*a^7*b^9*c^7*d^13*f^4 + 19072*a^11*b^5*c^11*d^9*f^4 + 19072*a^5*b^11*c^9*d^11*f^4
+ 18624*a^11*b^5*c^7*d^13*f^4 + 18624*a^5*b^11*c^13*d^7*f^4 - 17328*a^8*b^8*c^14*d^6*f^4 - 17328*a^8*b^8*c^6*d
^14*f^4 - 17232*a^10*b^6*c^6*d^14*f^4 - 17232*a^6*b^10*c^14*d^6*f^4 - 13520*a^12*b^4*c^8*d^12*f^4 - 13520*a^4*
b^12*c^12*d^8*f^4 - 12464*a^12*b^4*c^10*d^10*f^4 - 12464*a^4*b^12*c^10*d^10*f^4 + 10880*a^9*b^7*c^5*d^15*f^4 +
10880*a^7*b^9*c^15*d^5*f^4 - 9072*a^10*b^6*c^14*d^6*f^4 - 9072*a^6*b^10*c^6*d^14*f^4 + 8928*a^11*b^5*c^13*d^7
*f^4 + 8928*a^5*b^11*c^7*d^13*f^4 - 8880*a^12*b^4*c^6*d^14*f^4 - 8880*a^4*b^12*c^14*d^6*f^4 + 8480*a^11*b^5*c^
5*d^15*f^4 + 8480*a^5*b^11*c^15*d^5*f^4 + 7200*a^9*b^7*c^15*d^5*f^4 + 7200*a^7*b^9*c^5*d^15*f^4 - 6912*a^12*b^
4*c^12*d^8*f^4 - 6912*a^4*b^12*c^8*d^12*f^4 + 6400*a^13*b^3*c^9*d^11*f^4 + 6400*a^3*b^13*c^11*d^9*f^4 + 5920*a
^13*b^3*c^7*d^13*f^4 + 5920*a^3*b^13*c^13*d^7*f^4 - 5392*a^10*b^6*c^4*d^16*f^4 - 5392*a^6*b^10*c^16*d^4*f^4 -
4428*a^8*b^8*c^16*d^4*f^4 - 4428*a^8*b^8*c^4*d^16*f^4 + 4128*a^13*b^3*c^11*d^9*f^4 + 4128*a^3*b^13*c^9*d^11*f^
4 - 3328*a^12*b^4*c^4*d^16*f^4 - 3328*a^4*b^12*c^16*d^4*f^4 + 3264*a^13*b^3*c^5*d^15*f^4 + 3264*a^3*b^13*c^15*
d^5*f^4 - 2480*a^14*b^2*c^8*d^12*f^4 - 2480*a^2*b^14*c^12*d^8*f^4 + 2240*a^11*b^5*c^15*d^5*f^4 + 2240*a^5*b^11
*c^5*d^15*f^4 - 2128*a^12*b^4*c^14*d^6*f^4 - 2128*a^4*b^12*c^6*d^14*f^4 + 2112*a^9*b^7*c^3*d^17*f^4 + 2112*a^7
*b^9*c^17*d^3*f^4 + 2048*a^11*b^5*c^3*d^17*f^4 + 2048*a^5*b^11*c^17*d^3*f^4 - 2000*a^14*b^2*c^6*d^14*f^4 - 200
0*a^2*b^14*c^14*d^6*f^4 - 1792*a^10*b^6*c^16*d^4*f^4 - 1792*a^6*b^10*c^4*d^16*f^4 - 1776*a^14*b^2*c^10*d^10*f^
4 - 1776*a^2*b^14*c^10*d^10*f^4 + 1472*a^13*b^3*c^13*d^7*f^4 + 1472*a^3*b^13*c^7*d^13*f^4 + 1088*a^9*b^7*c^17*
d^3*f^4 + 1088*a^7*b^9*c^3*d^17*f^4 + 992*a^13*b^3*c^3*d^17*f^4 + 992*a^3*b^13*c^17*d^3*f^4 - 912*a^14*b^2*c^4
*d^16*f^4 - 912*a^2*b^14*c^16*d^4*f^4 - 768*a^10*b^6*c^2*d^18*f^4 - 768*a^6*b^10*c^18*d^2*f^4 - 688*a^14*b^2*c
^12*d^8*f^4 - 688*a^2*b^14*c^8*d^12*f^4 - 592*a^12*b^4*c^2*d^18*f^4 - 592*a^4*b^12*c^18*d^2*f^4 - 472*a^8*b^8*
c^18*d^2*f^4 - 472*a^8*b^8*c^2*d^18*f^4 - 280*a^12*b^4*c^16*d^4*f^4 - 280*a^4*b^12*c^4*d^16*f^4 + 224*a^13*b^3
*c^15*d^5*f^4 + 224*a^11*b^5*c^17*d^3*f^4 + 224*a^5*b^11*c^3*d^17*f^4 + 224*a^3*b^13*c^5*d^15*f^4 - 208*a^14*b
^2*c^2*d^18*f^4 - 208*a^2*b^14*c^18*d^2*f^4 - 112*a^14*b^2*c^14*d^6*f^4 - 112*a^10*b^6*c^18*d^2*f^4 - 112*a^6*
b^10*c^2*d^18*f^4 - 112*a^2*b^14*c^6*d^14*f^4 - 80*b^16*c^14*d^6*f^4 - 60*b^16*c^16*d^4*f^4 - 60*b^16*c^12*d^8
*f^4 - 24*b^16*c^18*d^2*f^4 - 24*b^16*c^10*d^10*f^4 - 4*b^16*c^8*d^12*f^4 - 80*a^16*c^6*d^14*f^4 - 60*a^16*c^8
*d^12*f^4 - 60*a^16*c^4*d^16*f^4 - 24*a^16*c^10*d^10*f^4 - 24*a^16*c^2*d^18*f^4 - 4*a^16*c^12*d^8*f^4 - 24*a^1
2*b^4*d^20*f^4 - 16*a^14*b^2*d^20*f^4 - 16*a^10*b^6*d^20*f^4 - 4*a^8*b^8*d^20*f^4 - 24*a^4*b^12*c^20*f^4 - 16*
a^6*b^10*c^20*f^4 - 16*a^2*b^14*c^20*f^4 - 4*a^8*b^8*c^20*f^4 - 4*b^16*c^20*f^4 - 4*a^16*d^20*f^4 + 56*A*C*a*b
^11*c^13*d*f^2 - 48*A*C*a^11*b*c*d^13*f^2 + 48*A*C*a*b^11*c*d^13*f^2 + 5904*B*C*a^6*b^6*c^7*d^7*f^2 - 5016*B*C
*a^5*b^7*c^8*d^6*f^2 - 4608*B*C*a^7*b^5*c^6*d^8*f^2 - 4512*B*C*a^5*b^7*c^6*d^8*f^2 - 4384*B*C*a^7*b^5*c^8*d^6*
f^2 + 3056*B*C*a^8*b^4*c^7*d^7*f^2 + 2256*B*C*a^4*b^8*c^7*d^7*f^2 - 1824*B*C*a^3*b^9*c^8*d^6*f^2 + 1632*B*C*a^
9*b^3*c^4*d^10*f^2 - 1400*B*C*a^8*b^4*c^3*d^11*f^2 - 1320*B*C*a^4*b^8*c^11*d^3*f^2 - 1248*B*C*a^3*b^9*c^6*d^8*
f^2 + 1152*B*C*a^3*b^9*c^10*d^4*f^2 - 1072*B*C*a^9*b^3*c^6*d^8*f^2 + 1068*B*C*a^6*b^6*c^9*d^5*f^2 - 1004*B*C*a
^4*b^8*c^5*d^9*f^2 - 968*B*C*a^6*b^6*c^3*d^11*f^2 - 864*B*C*a^8*b^4*c^5*d^9*f^2 - 828*B*C*a^4*b^8*c^9*d^5*f^2
- 792*B*C*a^4*b^8*c^3*d^11*f^2 - 792*B*C*a^2*b^10*c^11*d^3*f^2 - 776*B*C*a^9*b^3*c^8*d^6*f^2 + 688*B*C*a^7*b^5
*c^4*d^10*f^2 - 672*B*C*a^10*b^2*c^3*d^11*f^2 - 592*B*C*a^2*b^10*c^9*d^5*f^2 + 544*B*C*a^10*b^2*c^7*d^7*f^2 -
492*B*C*a^2*b^10*c^5*d^9*f^2 + 480*B*C*a^5*b^7*c^10*d^4*f^2 - 392*B*C*a^10*b^2*c^5*d^9*f^2 + 332*B*C*a^8*b^4*c
^9*d^5*f^2 - 328*B*C*a^6*b^6*c^11*d^3*f^2 + 320*B*C*a^9*b^3*c^2*d^12*f^2 + 272*B*C*a^3*b^9*c^12*d^2*f^2 - 248*
B*C*a^5*b^7*c^4*d^10*f^2 - 248*B*C*a^2*b^10*c^3*d^11*f^2 - 208*B*C*a^7*b^5*c^10*d^4*f^2 - 192*B*C*a^5*b^7*c^2*
d^12*f^2 + 144*B*C*a^2*b^10*c^7*d^7*f^2 - 96*B*C*a^3*b^9*c^4*d^10*f^2 + 88*B*C*a^5*b^7*c^12*d^2*f^2 - 72*B*C*a
^8*b^4*c^11*d^3*f^2 + 48*B*C*a^9*b^3*c^10*d^4*f^2 - 48*B*C*a^7*b^5*c^12*d^2*f^2 - 48*B*C*a^7*b^5*c^2*d^12*f^2
- 48*B*C*a^3*b^9*c^2*d^12*f^2 - 12*B*C*a^10*b^2*c^9*d^5*f^2 + 4*B*C*a^6*b^6*c^5*d^9*f^2 + 5824*A*C*a^7*b^5*c^5
*d^9*f^2 - 4378*A*C*a^8*b^4*c^6*d^8*f^2 + 4296*A*C*a^5*b^7*c^5*d^9*f^2 - 3912*A*C*a^6*b^6*c^6*d^8*f^2 - 3672*A
*C*a^5*b^7*c^9*d^5*f^2 + 3594*A*C*a^4*b^8*c^8*d^6*f^2 + 3236*A*C*a^6*b^6*c^8*d^6*f^2 + 2816*A*C*a^9*b^3*c^5*d^
9*f^2 + 2624*A*C*a^3*b^9*c^5*d^9*f^2 + 2432*A*C*a^7*b^5*c^7*d^7*f^2 - 2366*A*C*a^8*b^4*c^4*d^10*f^2 + 2298*A*C
*a^4*b^8*c^10*d^4*f^2 + 1872*A*C*a^3*b^9*c^7*d^7*f^2 + 1848*A*C*a^6*b^6*c^10*d^4*f^2 - 1644*A*C*a^6*b^6*c^4*d^
10*f^2 - 1488*A*C*a^7*b^5*c^9*d^5*f^2 - 1408*A*C*a^3*b^9*c^9*d^5*f^2 - 1308*A*C*a^4*b^8*c^6*d^8*f^2 + 1248*A*C
*a^5*b^7*c^7*d^7*f^2 - 1012*A*C*a^10*b^2*c^6*d^8*f^2 + 1008*A*C*a^7*b^5*c^3*d^11*f^2 + 992*A*C*a^5*b^7*c^3*d^1
1*f^2 + 928*A*C*a^3*b^9*c^3*d^11*f^2 + 848*A*C*a^9*b^3*c^7*d^7*f^2 + 636*A*C*a^2*b^10*c^8*d^6*f^2 - 628*A*C*a^
10*b^2*c^4*d^10*f^2 - 600*A*C*a^2*b^10*c^6*d^8*f^2 - 576*A*C*a^5*b^7*c^11*d^3*f^2 + 572*A*C*a^2*b^10*c^10*d^4*
f^2 + 464*A*C*a^8*b^4*c^8*d^6*f^2 + 304*A*C*a^6*b^6*c^2*d^12*f^2 - 304*A*C*a^4*b^8*c^4*d^10*f^2 + 296*A*C*a^4*
b^8*c^2*d^12*f^2 + 260*A*C*a^8*b^4*c^10*d^4*f^2 - 232*A*C*a^9*b^3*c^9*d^5*f^2 - 232*A*C*a^2*b^10*c^12*d^2*f^2
+ 228*A*C*a^10*b^2*c^2*d^12*f^2 - 188*A*C*a^2*b^10*c^4*d^10*f^2 + 144*A*C*a^3*b^9*c^11*d^3*f^2 + 116*A*C*a^6*b
^6*c^12*d^2*f^2 + 112*A*C*a^9*b^3*c^3*d^11*f^2 - 112*A*C*a^7*b^5*c^11*d^3*f^2 + 92*A*C*a^10*b^2*c^8*d^6*f^2 +
74*A*C*a^4*b^8*c^12*d^2*f^2 + 62*A*C*a^8*b^4*c^2*d^12*f^2 + 40*A*C*a^2*b^10*c^2*d^12*f^2 - 7008*A*B*a^6*b^6*c^
7*d^7*f^2 - 4032*A*B*a^4*b^8*c^7*d^7*f^2 + 3952*A*B*a^7*b^5*c^8*d^6*f^2 + 3648*A*B*a^5*b^7*c^8*d^6*f^2 - 3392*
A*B*a^8*b^4*c^7*d^7*f^2 + 3264*A*B*a^7*b^5*c^6*d^8*f^2 - 2992*A*B*a^5*b^7*c^4*d^10*f^2 - 2368*A*B*a^7*b^5*c^4*
d^10*f^2 - 2304*A*B*a^3*b^9*c^4*d^10*f^2 - 1968*A*B*a^6*b^6*c^9*d^5*f^2 - 1872*A*B*a^9*b^3*c^4*d^10*f^2 - 1728
*A*B*a^2*b^10*c^7*d^7*f^2 + 1712*A*B*a^8*b^4*c^3*d^11*f^2 + 1536*A*B*a^5*b^7*c^6*d^8*f^2 - 1536*A*B*a^3*b^9*c^
10*d^4*f^2 - 1392*A*B*a^5*b^7*c^2*d^12*f^2 + 1328*A*B*a^6*b^6*c^3*d^11*f^2 - 1104*A*B*a^3*b^9*c^2*d^12*f^2 - 1
056*A*B*a^3*b^9*c^6*d^8*f^2 + 976*A*B*a^9*b^3*c^6*d^8*f^2 + 960*A*B*a^4*b^8*c^11*d^3*f^2 + 936*A*B*a^8*b^4*c^5
*d^9*f^2 - 912*A*B*a^5*b^7*c^10*d^4*f^2 + 848*A*B*a^9*b^3*c^8*d^6*f^2 - 816*A*B*a^7*b^5*c^2*d^12*f^2 + 816*A*B
*a^4*b^8*c^3*d^11*f^2 + 768*A*B*a^10*b^2*c^3*d^11*f^2 + 672*A*B*a^3*b^9*c^8*d^6*f^2 - 632*A*B*a^8*b^4*c^9*d^5*
f^2 - 608*A*B*a^2*b^10*c^9*d^5*f^2 - 552*A*B*a^4*b^8*c^9*d^5*f^2 - 544*A*B*a^10*b^2*c^7*d^7*f^2 - 480*A*B*a^2*
b^10*c^5*d^9*f^2 + 464*A*B*a^10*b^2*c^5*d^9*f^2 - 464*A*B*a^9*b^3*c^2*d^12*f^2 + 432*A*B*a^2*b^10*c^11*d^3*f^2
- 368*A*B*a^3*b^9*c^12*d^2*f^2 - 256*A*B*a^6*b^6*c^5*d^9*f^2 - 208*A*B*a^5*b^7*c^12*d^2*f^2 + 176*A*B*a^4*b^8
*c^5*d^9*f^2 + 112*A*B*a^7*b^5*c^10*d^4*f^2 + 112*A*B*a^6*b^6*c^11*d^3*f^2 - 16*A*B*a^2*b^10*c^3*d^11*f^2 - 57
6*B*C*a*b^11*c^8*d^6*f^2 + 400*B*C*a^11*b*c^4*d^10*f^2 - 288*B*C*a*b^11*c^6*d^8*f^2 - 176*B*C*a^11*b*c^6*d^8*f
^2 + 128*B*C*a*b^11*c^10*d^4*f^2 - 108*B*C*a^4*b^8*c*d^13*f^2 - 104*B*C*a*b^11*c^4*d^10*f^2 - 92*B*C*a^4*b^8*c
^13*d*f^2 - 60*B*C*a^8*b^4*c*d^13*f^2 - 60*B*C*a^6*b^6*c*d^13*f^2 + 48*B*C*a^11*b*c^2*d^12*f^2 - 40*B*C*a^2*b^
10*c*d^13*f^2 - 28*B*C*a^2*b^10*c^13*d*f^2 - 24*B*C*a*b^11*c^12*d^2*f^2 + 20*B*C*a^10*b^2*c*d^13*f^2 - 16*B*C*
a*b^11*c^2*d^12*f^2 + 12*B*C*a^6*b^6*c^13*d*f^2 + 912*A*C*a*b^11*c^7*d^7*f^2 + 808*A*C*a*b^11*c^5*d^9*f^2 + 43
2*A*C*a^11*b*c^5*d^9*f^2 + 336*A*C*a*b^11*c^3*d^11*f^2 + 224*A*C*a*b^11*c^11*d^3*f^2 - 112*A*C*a^11*b*c^3*d^11
*f^2 + 112*A*C*a^3*b^9*c*d^13*f^2 - 88*A*C*a^9*b^3*c*d^13*f^2 + 80*A*C*a^3*b^9*c^13*d*f^2 + 56*A*C*a^5*b^7*c*d
^13*f^2 + 48*A*C*a*b^11*c^9*d^5*f^2 - 40*A*C*a^5*b^7*c^13*d*f^2 - 16*A*C*a^11*b*c^7*d^7*f^2 + 16*A*C*a^7*b^5*c
*d^13*f^2 - 496*A*B*a*b^11*c^4*d^10*f^2 - 400*A*B*a^11*b*c^4*d^10*f^2 + 288*A*B*a*b^11*c^8*d^6*f^2 - 288*A*B*a
*b^11*c^6*d^8*f^2 - 272*A*B*a*b^11*c^2*d^12*f^2 + 240*A*B*a^6*b^6*c*d^13*f^2 - 224*A*B*a*b^11*c^10*d^4*f^2 + 1
92*A*B*a^8*b^4*c*d^13*f^2 + 192*A*B*a^4*b^8*c*d^13*f^2 + 176*A*B*a^11*b*c^6*d^8*f^2 + 104*A*B*a^4*b^8*c^13*d*f
^2 - 48*A*B*a^11*b*c^2*d^12*f^2 + 16*A*B*a^10*b^2*c*d^13*f^2 + 16*A*B*a^2*b^10*c^13*d*f^2 + 16*A*B*a^2*b^10*c*
d^13*f^2 - 112*B*C*b^12*c^11*d^3*f^2 + 4*B*C*b^12*c^5*d^9*f^2 + 150*A*C*b^12*c^10*d^4*f^2 - 80*B*C*a^12*c^3*d^
11*f^2 + 66*A*C*b^12*c^8*d^6*f^2 - 30*A*C*b^12*c^12*d^2*f^2 + 24*B*C*a^12*c^5*d^9*f^2 - 12*A*C*b^12*c^4*d^10*f
^2 - 576*A*B*b^12*c^7*d^7*f^2 - 432*A*B*b^12*c^9*d^5*f^2 - 400*A*B*b^12*c^5*d^9*f^2 - 144*A*B*b^12*c^3*d^11*f^
2 - 96*B*C*a^7*b^5*d^14*f^2 - 72*B*C*a^5*b^7*d^14*f^2 - 66*A*C*a^12*c^4*d^10*f^2 + 54*A*C*a^12*c^2*d^12*f^2 -
32*A*B*b^12*c^11*d^3*f^2 - 24*B*C*a^9*b^3*d^14*f^2 - 16*B*C*a^3*b^9*d^14*f^2 + 2*A*C*a^12*c^6*d^8*f^2 + 116*A*
C*a^6*b^6*d^14*f^2 + 100*A*C*a^4*b^8*d^14*f^2 + 80*A*B*a^12*c^3*d^11*f^2 + 24*A*C*a^2*b^10*d^14*f^2 - 24*A*B*a
^12*c^5*d^9*f^2 + 22*A*C*a^8*b^4*d^14*f^2 + 16*B*C*a^3*b^9*c^14*f^2 + 8*A*C*a^10*b^2*d^14*f^2 - 192*A*B*a^5*b^
7*d^14*f^2 - 176*A*B*a^3*b^9*d^14*f^2 - 48*A*B*a^7*b^5*d^14*f^2 - 28*A*C*a^2*b^10*c^14*f^2 + 2*A*C*a^4*b^8*c^1
4*f^2 - 16*A*B*a^3*b^9*c^14*f^2 + 2508*C^2*a^6*b^6*c^6*d^8*f^2 + 2376*C^2*a^5*b^7*c^9*d^5*f^2 + 2357*C^2*a^8*b
^4*c^6*d^8*f^2 - 2048*C^2*a^7*b^5*c^5*d^9*f^2 + 1304*C^2*a^3*b^9*c^9*d^5*f^2 + 1303*C^2*a^8*b^4*c^4*d^10*f^2 +
1212*C^2*a^6*b^6*c^4*d^10*f^2 - 1203*C^2*a^4*b^8*c^8*d^6*f^2 - 1192*C^2*a^9*b^3*c^5*d^9*f^2 + 1062*C^2*a^4*b^
8*c^6*d^8*f^2 + 984*C^2*a^7*b^5*c^9*d^5*f^2 - 952*C^2*a^6*b^6*c^8*d^6*f^2 + 768*C^2*a^5*b^7*c^7*d^7*f^2 - 681*
C^2*a^4*b^8*c^10*d^4*f^2 - 672*C^2*a^5*b^7*c^5*d^9*f^2 - 480*C^2*a^6*b^6*c^10*d^4*f^2 + 458*C^2*a^10*b^2*c^6*d
^8*f^2 - 448*C^2*a^7*b^5*c^7*d^7*f^2 + 422*C^2*a^4*b^8*c^4*d^10*f^2 + 372*C^2*a^2*b^10*c^6*d^8*f^2 + 360*C^2*a
^5*b^7*c^11*d^3*f^2 + 312*C^2*a^3*b^9*c^7*d^7*f^2 + 278*C^2*a^10*b^2*c^4*d^10*f^2 - 232*C^2*a^9*b^3*c^7*d^7*f^
2 + 194*C^2*a^2*b^10*c^12*d^2*f^2 + 176*C^2*a^9*b^3*c^9*d^5*f^2 + 152*C^2*a^5*b^7*c^3*d^11*f^2 + 124*C^2*a^2*b
^10*c^4*d^10*f^2 - 120*C^2*a^7*b^5*c^3*d^11*f^2 - 114*C^2*a^10*b^2*c^2*d^12*f^2 - 102*C^2*a^2*b^10*c^8*d^6*f^2
+ 101*C^2*a^4*b^8*c^12*d^2*f^2 + 100*C^2*a^6*b^6*c^2*d^12*f^2 - 88*C^2*a^3*b^9*c^5*d^9*f^2 + 77*C^2*a^8*b^4*c
^2*d^12*f^2 + 72*C^2*a^3*b^9*c^11*d^3*f^2 - 64*C^2*a^10*b^2*c^8*d^6*f^2 + 64*C^2*a^3*b^9*c^3*d^11*f^2 - 58*C^2
*a^2*b^10*c^10*d^4*f^2 + 56*C^2*a^7*b^5*c^11*d^3*f^2 + 56*C^2*a^6*b^6*c^12*d^2*f^2 + 40*C^2*a^9*b^3*c^3*d^11*f
^2 + 36*C^2*a^8*b^4*c^12*d^2*f^2 + 32*C^2*a^4*b^8*c^2*d^12*f^2 + 26*C^2*a^8*b^4*c^10*d^4*f^2 + 16*C^2*a^2*b^10
*c^2*d^12*f^2 + 2*C^2*a^8*b^4*c^8*d^6*f^2 + 2277*B^2*a^4*b^8*c^8*d^6*f^2 + 2144*B^2*a^7*b^5*c^5*d^9*f^2 - 2112
*B^2*a^5*b^7*c^9*d^5*f^2 + 2028*B^2*a^6*b^6*c^8*d^6*f^2 - 1671*B^2*a^8*b^4*c^6*d^8*f^2 + 1275*B^2*a^4*b^8*c^10
*d^4*f^2 + 1176*B^2*a^5*b^7*c^5*d^9*f^2 + 1096*B^2*a^9*b^3*c^5*d^9*f^2 - 1044*B^2*a^6*b^6*c^6*d^8*f^2 + 984*B^
2*a^6*b^6*c^10*d^4*f^2 - 968*B^2*a^3*b^9*c^9*d^5*f^2 - 888*B^2*a^7*b^5*c^9*d^5*f^2 + 672*B^2*a^7*b^5*c^7*d^7*f
^2 + 664*B^2*a^3*b^9*c^5*d^9*f^2 - 649*B^2*a^8*b^4*c^4*d^10*f^2 + 618*B^2*a^2*b^10*c^8*d^6*f^2 + 514*B^2*a^4*b
^8*c^4*d^10*f^2 + 460*B^2*a^6*b^6*c^2*d^12*f^2 + 422*B^2*a^8*b^4*c^8*d^6*f^2 + 406*B^2*a^2*b^10*c^10*d^4*f^2 -
382*B^2*a^10*b^2*c^6*d^8*f^2 + 368*B^2*a^4*b^8*c^2*d^12*f^2 - 312*B^2*a^5*b^7*c^11*d^3*f^2 + 312*B^2*a^3*b^9*
c^7*d^7*f^2 + 248*B^2*a^9*b^3*c^7*d^7*f^2 + 245*B^2*a^8*b^4*c^2*d^12*f^2 - 192*B^2*a^5*b^7*c^7*d^7*f^2 - 184*B
^2*a^9*b^3*c^3*d^11*f^2 + 182*B^2*a^10*b^2*c^2*d^12*f^2 + 176*B^2*a^3*b^9*c^3*d^11*f^2 + 174*B^2*a^4*b^8*c^6*d
^8*f^2 - 170*B^2*a^10*b^2*c^4*d^10*f^2 - 152*B^2*a^9*b^3*c^9*d^5*f^2 + 152*B^2*a^2*b^10*c^4*d^10*f^2 + 142*B^2
*a^8*b^4*c^10*d^4*f^2 - 90*B^2*a^2*b^10*c^12*d^2*f^2 + 88*B^2*a^2*b^10*c^2*d^12*f^2 + 84*B^2*a^10*b^2*c^8*d^6*
f^2 + 84*B^2*a^2*b^10*c^6*d^8*f^2 + 60*B^2*a^6*b^6*c^12*d^2*f^2 - 56*B^2*a^7*b^5*c^11*d^3*f^2 + 53*B^2*a^4*b^8
*c^12*d^2*f^2 + 24*B^2*a^7*b^5*c^3*d^11*f^2 + 24*B^2*a^6*b^6*c^4*d^10*f^2 + 24*B^2*a^3*b^9*c^11*d^3*f^2 - 8*B^
2*a^5*b^7*c^3*d^11*f^2 + 4566*A^2*a^4*b^8*c^6*d^8*f^2 + 4284*A^2*a^6*b^6*c^6*d^8*f^2 - 3776*A^2*a^7*b^5*c^5*d^
9*f^2 - 3624*A^2*a^5*b^7*c^5*d^9*f^2 + 3122*A^2*a^4*b^8*c^4*d^10*f^2 + 3108*A^2*a^2*b^10*c^6*d^8*f^2 + 2741*A^
2*a^8*b^4*c^6*d^8*f^2 + 2592*A^2*a^6*b^6*c^4*d^10*f^2 - 2536*A^2*a^3*b^9*c^5*d^9*f^2 + 2224*A^2*a^2*b^10*c^4*d
^10*f^2 - 2184*A^2*a^3*b^9*c^7*d^7*f^2 - 2016*A^2*a^5*b^7*c^7*d^7*f^2 - 1984*A^2*a^7*b^5*c^7*d^7*f^2 + 1626*A^
2*a^2*b^10*c^8*d^6*f^2 - 1624*A^2*a^9*b^3*c^5*d^9*f^2 + 1603*A^2*a^8*b^4*c^4*d^10*f^2 + 1296*A^2*a^5*b^7*c^9*d
^5*f^2 - 1144*A^2*a^5*b^7*c^3*d^11*f^2 - 992*A^2*a^3*b^9*c^3*d^11*f^2 + 968*A^2*a^4*b^8*c^2*d^12*f^2 - 888*A^2
*a^7*b^5*c^3*d^11*f^2 + 849*A^2*a^4*b^8*c^8*d^6*f^2 + 808*A^2*a^2*b^10*c^2*d^12*f^2 - 616*A^2*a^9*b^3*c^7*d^7*
f^2 + 554*A^2*a^10*b^2*c^6*d^8*f^2 + 504*A^2*a^7*b^5*c^9*d^5*f^2 - 504*A^2*a^6*b^6*c^10*d^4*f^2 + 460*A^2*a^6*
b^6*c^2*d^12*f^2 + 350*A^2*a^10*b^2*c^4*d^10*f^2 + 350*A^2*a^2*b^10*c^10*d^4*f^2 - 321*A^2*a^4*b^8*c^10*d^4*f^
2 + 216*A^2*a^5*b^7*c^11*d^3*f^2 - 216*A^2*a^3*b^9*c^11*d^3*f^2 + 182*A^2*a^2*b^10*c^12*d^2*f^2 - 152*A^2*a^9*
b^3*c^3*d^11*f^2 - 124*A^2*a^6*b^6*c^8*d^6*f^2 - 114*A^2*a^10*b^2*c^2*d^12*f^2 + 104*A^2*a^3*b^9*c^9*d^5*f^2 +
77*A^2*a^8*b^4*c^2*d^12*f^2 + 74*A^2*a^8*b^4*c^8*d^6*f^2 - 70*A^2*a^8*b^4*c^10*d^4*f^2 + 56*A^2*a^9*b^3*c^9*d
^5*f^2 + 56*A^2*a^7*b^5*c^11*d^3*f^2 + 41*A^2*a^4*b^8*c^12*d^2*f^2 - 28*A^2*a^10*b^2*c^8*d^6*f^2 - 28*A^2*a^6*
b^6*c^12*d^2*f^2 + 12*B*C*b^12*c^13*d*f^2 + 24*B*C*a^12*c*d^13*f^2 - 24*A*B*b^12*c^13*d*f^2 - 24*A*B*b^12*c*d^
13*f^2 - 16*B*C*a^11*b*d^14*f^2 - 24*A*B*a^12*c*d^13*f^2 - 16*B*C*a*b^11*c^14*f^2 - 48*A*B*a*b^11*d^14*f^2 + 1
6*A*B*a^11*b*d^14*f^2 + 16*A*B*a*b^11*c^14*f^2 - 216*C^2*a^11*b*c^5*d^9*f^2 + 216*C^2*a*b^11*c^9*d^5*f^2 + 56*
C^2*a^11*b*c^3*d^11*f^2 + 56*C^2*a^9*b^3*c*d^13*f^2 + 56*C^2*a^5*b^7*c*d^13*f^2 + 40*C^2*a^7*b^5*c*d^13*f^2 -
40*C^2*a*b^11*c^11*d^3*f^2 + 32*C^2*a^5*b^7*c^13*d*f^2 - 24*C^2*a*b^11*c^7*d^7*f^2 - 16*C^2*a^3*b^9*c^13*d*f^2
+ 16*C^2*a^3*b^9*c*d^13*f^2 + 8*C^2*a^11*b*c^7*d^7*f^2 - 8*C^2*a*b^11*c^5*d^9*f^2 + 264*B^2*a*b^11*c^7*d^7*f^
2 + 224*B^2*a*b^11*c^5*d^9*f^2 + 168*B^2*a^11*b*c^5*d^9*f^2 - 112*B^2*a^9*b^3*c*d^13*f^2 - 104*B^2*a^11*b*c^3*
d^11*f^2 - 104*B^2*a^7*b^5*c*d^13*f^2 + 96*B^2*a*b^11*c^3*d^11*f^2 + 88*B^2*a*b^11*c^11*d^3*f^2 - 72*B^2*a*b^1
1*c^9*d^5*f^2 - 64*B^2*a^5*b^7*c*d^13*f^2 + 32*B^2*a^3*b^9*c^13*d*f^2 - 24*B^2*a^11*b*c^7*d^7*f^2 - 24*B^2*a^5
*b^7*c^13*d*f^2 + 16*B^2*a^3*b^9*c*d^13*f^2 - 888*A^2*a*b^11*c^7*d^7*f^2 - 800*A^2*a*b^11*c^5*d^9*f^2 - 336*A^
2*a*b^11*c^3*d^11*f^2 - 264*A^2*a*b^11*c^9*d^5*f^2 - 216*A^2*a^11*b*c^5*d^9*f^2 - 184*A^2*a*b^11*c^11*d^3*f^2
- 128*A^2*a^3*b^9*c*d^13*f^2 - 112*A^2*a^5*b^7*c*d^13*f^2 - 64*A^2*a^3*b^9*c^13*d*f^2 + 56*A^2*a^11*b*c^3*d^11
*f^2 - 56*A^2*a^7*b^5*c*d^13*f^2 + 32*A^2*a^9*b^3*c*d^13*f^2 + 8*A^2*a^11*b*c^7*d^7*f^2 + 8*A^2*a^5*b^7*c^13*d
*f^2 + 24*C^2*a^11*b*c*d^13*f^2 - 16*C^2*a*b^11*c^13*d*f^2 - 40*B^2*a^11*b*c*d^13*f^2 + 24*B^2*a*b^11*c^13*d*f
^2 + 16*B^2*a*b^11*c*d^13*f^2 - 48*A^2*a*b^11*c*d^13*f^2 - 40*A^2*a*b^11*c^13*d*f^2 + 24*A^2*a^11*b*c*d^13*f^2
- 6*A*C*a^12*d^14*f^2 + 2*A*C*b^12*c^14*f^2 + 33*C^2*b^12*c^12*d^2*f^2 - 27*C^2*b^12*c^10*d^4*f^2 + 3*C^2*b^1
2*c^8*d^6*f^2 + 117*B^2*b^12*c^10*d^4*f^2 + 111*B^2*b^12*c^8*d^6*f^2 + 72*B^2*b^12*c^6*d^8*f^2 + 33*C^2*a^12*c
^4*d^10*f^2 - 27*C^2*a^12*c^2*d^12*f^2 + 24*B^2*b^12*c^4*d^10*f^2 + 4*B^2*b^12*c^2*d^12*f^2 - 3*B^2*b^12*c^12*
d^2*f^2 - C^2*a^12*c^6*d^8*f^2 + 720*A^2*b^12*c^6*d^8*f^2 + 552*A^2*b^12*c^4*d^10*f^2 + 471*A^2*b^12*c^8*d^6*f
^2 + 216*A^2*b^12*c^2*d^12*f^2 + 93*A^2*b^12*c^10*d^4*f^2 + 33*B^2*a^12*c^2*d^12*f^2 + 33*A^2*b^12*c^12*d^2*f^
2 + 31*C^2*a^8*b^4*d^14*f^2 - 27*B^2*a^12*c^4*d^10*f^2 + 20*C^2*a^6*b^6*d^14*f^2 + 4*C^2*a^4*b^8*d^14*f^2 + 3*
B^2*a^12*c^6*d^8*f^2 + 2*C^2*a^10*b^2*d^14*f^2 + 80*B^2*a^6*b^6*d^14*f^2 + 64*B^2*a^4*b^8*d^14*f^2 + 33*A^2*a^
12*c^4*d^10*f^2 + 31*B^2*a^8*b^4*d^14*f^2 - 27*A^2*a^12*c^2*d^12*f^2 + 16*B^2*a^2*b^10*d^14*f^2 + 14*C^2*a^2*b
^10*c^14*f^2 + 14*B^2*a^10*b^2*d^14*f^2 - C^2*a^4*b^8*c^14*f^2 - A^2*a^12*c^6*d^8*f^2 + 120*A^2*a^2*b^10*d^14*
f^2 + 112*A^2*a^4*b^8*d^14*f^2 - 17*A^2*a^8*b^4*d^14*f^2 - 10*B^2*a^2*b^10*c^14*f^2 - 10*A^2*a^10*b^2*d^14*f^2
+ 8*A^2*a^6*b^6*d^14*f^2 + 3*B^2*a^4*b^8*c^14*f^2 + 14*A^2*a^2*b^10*c^14*f^2 - A^2*a^4*b^8*c^14*f^2 + 3*C^2*a
^12*d^14*f^2 - C^2*b^12*c^14*f^2 + 36*A^2*b^12*d^14*f^2 + 3*B^2*b^12*c^14*f^2 - B^2*a^12*d^14*f^2 + 3*A^2*a^12
*d^14*f^2 - A^2*b^12*c^14*f^2 - 44*A*B*C*a*b^9*c^10*d*f + 3816*A*B*C*a^5*b^5*c^4*d^7*f + 2920*A*B*C*a^2*b^8*c^
5*d^6*f - 2736*A*B*C*a^3*b^7*c^6*d^5*f - 2672*A*B*C*a^4*b^6*c^3*d^8*f + 1996*A*B*C*a^4*b^6*c^7*d^4*f - 1412*A*
B*C*a^6*b^4*c^5*d^6*f + 1120*A*B*C*a^3*b^7*c^2*d^9*f + 1080*A*B*C*a^2*b^8*c^7*d^4*f + 1040*A*B*C*a^5*b^5*c^2*d
^9*f + 684*A*B*C*a^4*b^6*c^5*d^6*f + 592*A*B*C*a^3*b^7*c^4*d^7*f - 560*A*B*C*a^7*b^3*c^2*d^9*f - 448*A*B*C*a^2
*b^8*c^3*d^8*f - 400*A*B*C*a^5*b^5*c^8*d^3*f - 398*A*B*C*a^2*b^8*c^9*d^2*f - 312*A*B*C*a^6*b^4*c^3*d^8*f + 166
*A*B*C*a^8*b^2*c^3*d^8*f + 136*A*B*C*a^5*b^5*c^6*d^5*f + 128*A*B*C*a^7*b^3*c^6*d^5*f - 100*A*B*C*a^6*b^4*c^7*d
^4*f + 64*A*B*C*a^7*b^3*c^4*d^7*f - 64*A*B*C*a^4*b^6*c^9*d^2*f - 32*A*B*C*a^3*b^7*c^8*d^3*f - 16*A*B*C*a^8*b^2
*c^5*d^6*f - 1312*A*B*C*a*b^9*c^4*d^7*f + 996*A*B*C*a*b^9*c^8*d^3*f + 728*A*B*C*a^6*b^4*c*d^10*f - 624*A*B*C*a
*b^9*c^6*d^5*f - 584*A*B*C*a^2*b^8*c*d^10*f - 512*A*B*C*a^4*b^6*c*d^10*f - 320*A*B*C*a*b^9*c^2*d^9*f - 98*A*B*
C*a^8*b^2*c*d^10*f + 36*A*B*C*a^9*b*c^2*d^9*f + 32*A*B*C*a^3*b^7*c^10*d*f - 16*A*B*C*a^9*b*c^4*d^7*f + 46*B*C^
2*a*b^9*c^10*d*f - 16*B^2*C*a*b^9*c*d^10*f - 2*B^2*C*a^9*b*c*d^10*f + 312*A^2*C*a*b^9*c*d^10*f - 48*A*C^2*a*b^
9*c*d^10*f - 6*A^2*C*a^9*b*c*d^10*f + 6*A*C^2*a^9*b*c*d^10*f + 208*A*B^2*a*b^9*c*d^10*f - 2*A^2*B*a*b^9*c^10*d
*f + 2*A*B^2*a^9*b*c*d^10*f - 480*A*B*C*b^10*c^7*d^4*f + 78*A*B*C*b^10*c^9*d^2*f - 64*A*B*C*b^10*c^5*d^6*f + 2
*A*B*C*a^10*c^3*d^8*f - 224*A*B*C*a^5*b^5*d^11*f + 80*A*B*C*a^7*b^3*d^11*f - 32*A*B*C*a^3*b^7*d^11*f + 2*A*B*C
*a^2*b^8*c^11*f - 1692*B*C^2*a^5*b^5*c^4*d^7*f - 1500*B^2*C*a^5*b^5*c^5*d^6*f - 1464*B^2*C*a^3*b^7*c^5*d^6*f +
1426*B*C^2*a^6*b^4*c^5*d^6*f - 1158*B^2*C*a^6*b^4*c^4*d^7*f + 1152*B*C^2*a^3*b^7*c^6*d^5*f + 1026*B^2*C*a^4*b
^6*c^6*d^5*f - 974*B*C^2*a^4*b^6*c^7*d^4*f + 960*B^2*C*a^5*b^5*c^3*d^8*f - 884*B*C^2*a^2*b^8*c^5*d^6*f - 764*B
^2*C*a^5*b^5*c^7*d^4*f + 752*B^2*C*a^2*b^8*c^4*d^7*f - 752*B*C^2*a^3*b^7*c^4*d^7*f + 738*B^2*C*a^4*b^6*c^4*d^7
*f - 688*B^2*C*a^6*b^4*c^2*d^9*f - 675*B^2*C*a^2*b^8*c^8*d^3*f + 560*B*C^2*a^5*b^5*c^8*d^3*f + 496*B*C^2*a^7*b
^3*c^2*d^9*f + 496*B*C^2*a^4*b^6*c^3*d^8*f - 468*B*C^2*a^2*b^8*c^7*d^4*f + 456*B^2*C*a^7*b^3*c^3*d^8*f - 452*B
^2*C*a^4*b^6*c^8*d^3*f - 416*B*C^2*a^3*b^7*c^2*d^9*f + 378*B*C^2*a^4*b^6*c^5*d^6*f + 376*B*C^2*a^3*b^7*c^8*d^3
*f - 360*B^2*C*a^2*b^8*c^6*d^5*f + 355*B*C^2*a^2*b^8*c^9*d^2*f + 346*B^2*C*a^6*b^4*c^6*d^5*f - 320*B^2*C*a^4*b
^6*c^2*d^9*f + 268*B^2*C*a^2*b^8*c^2*d^9*f + 216*B^2*C*a^3*b^7*c^7*d^4*f - 203*B*C^2*a^8*b^2*c^3*d^8*f - 184*B
*C^2*a^7*b^3*c^6*d^5*f + 170*B*C^2*a^6*b^4*c^7*d^4*f + 160*B^2*C*a^7*b^3*c^5*d^6*f - 160*B*C^2*a^5*b^5*c^2*d^9
*f - 140*B^2*C*a^8*b^2*c^4*d^7*f - 136*B*C^2*a^2*b^8*c^3*d^8*f + 112*B^2*C*a^3*b^7*c^9*d^2*f + 91*B^2*C*a^8*b^
2*c^2*d^9*f + 88*B*C^2*a^7*b^3*c^4*d^7*f + 72*B^2*C*a^6*b^4*c^8*d^3*f - 64*B^2*C*a^3*b^7*c^3*d^8*f - 60*B*C^2*
a^6*b^4*c^3*d^8*f + 56*B*C^2*a^4*b^6*c^9*d^2*f + 52*B*C^2*a^5*b^5*c^6*d^5*f - 48*B^2*C*a^7*b^3*c^7*d^4*f + 48*
B^2*C*a^5*b^5*c^9*d^2*f + 44*B*C^2*a^8*b^2*c^5*d^6*f - 36*B*C^2*a^6*b^4*c^9*d^2*f + 12*B^2*C*a^8*b^2*c^6*d^5*f
- 2958*A^2*C*a^4*b^6*c^4*d^7*f - 1932*A^2*C*a^2*b^8*c^4*d^7*f + 1848*A^2*C*a^3*b^7*c^5*d^6*f + 1728*A^2*C*a^3
*b^7*c^3*d^8*f + 1524*A^2*C*a^5*b^5*c^5*d^6*f + 1374*A*C^2*a^4*b^6*c^4*d^7*f - 1272*A*C^2*a^3*b^7*c^5*d^6*f -
1236*A*C^2*a^5*b^5*c^5*d^6*f + 1116*A*C^2*a^2*b^8*c^4*d^7*f - 1110*A^2*C*a^4*b^6*c^6*d^5*f + 1038*A*C^2*a^4*b^
6*c^6*d^5*f - 768*A^2*C*a^2*b^8*c^2*d^9*f - 696*A^2*C*a^3*b^7*c^7*d^4*f - 666*A*C^2*a^6*b^4*c^4*d^7*f + 564*A^
2*C*a^2*b^8*c^6*d^5*f - 564*A*C^2*a^5*b^5*c^7*d^4*f - 555*A*C^2*a^2*b^8*c^8*d^3*f + 519*A^2*C*a^2*b^8*c^8*d^3*
f - 480*A*C^2*a^3*b^7*c^3*d^8*f + 456*A*C^2*a^5*b^5*c^3*d^8*f - 420*A*C^2*a^6*b^4*c^2*d^9*f + 408*A*C^2*a^3*b^
7*c^7*d^4*f + 408*A*C^2*a^2*b^8*c^2*d^9*f + 348*A^2*C*a^6*b^4*c^2*d^9*f - 348*A*C^2*a^2*b^8*c^6*d^5*f + 342*A*
C^2*a^6*b^4*c^6*d^5*f - 336*A*C^2*a^4*b^6*c^8*d^3*f + 324*A^2*C*a^5*b^5*c^7*d^4*f - 312*A^2*C*a^4*b^6*c^2*d^9*
f + 264*A^2*C*a^4*b^6*c^8*d^3*f + 240*A*C^2*a^7*b^3*c^5*d^6*f + 195*A*C^2*a^8*b^2*c^2*d^9*f - 174*A^2*C*a^6*b^
4*c^6*d^5*f + 144*A*C^2*a^3*b^7*c^9*d^2*f - 123*A^2*C*a^8*b^2*c^2*d^9*f + 120*A*C^2*a^7*b^3*c^3*d^8*f + 108*A*
C^2*a^6*b^4*c^8*d^3*f - 102*A^2*C*a^6*b^4*c^4*d^7*f - 96*A^2*C*a^8*b^2*c^4*d^7*f + 72*A^2*C*a^7*b^3*c^3*d^8*f
+ 72*A*C^2*a^5*b^5*c^9*d^2*f + 48*A^2*C*a^7*b^3*c^5*d^6*f - 48*A^2*C*a^3*b^7*c^9*d^2*f - 48*A*C^2*a^4*b^6*c^2*
d^9*f - 24*A^2*C*a^5*b^5*c^3*d^8*f - 12*A*C^2*a^8*b^2*c^4*d^7*f + 2736*A^2*B*a^3*b^7*c^6*d^5*f + 2464*A^2*B*a^
4*b^6*c^3*d^8*f - 2298*A*B^2*a^4*b^6*c^4*d^7*f - 2252*A^2*B*a^2*b^8*c^5*d^6*f - 1692*A^2*B*a^5*b^5*c^4*d^7*f -
1592*A*B^2*a^2*b^8*c^4*d^7*f - 1338*A*B^2*a^4*b^6*c^6*d^5*f + 1320*A*B^2*a^3*b^7*c^5*d^6*f + 1212*A*B^2*a^5*b
^5*c^5*d^6*f - 1056*A*B^2*a^5*b^5*c^3*d^8*f + 1024*A^2*B*a^3*b^7*c^4*d^7*f - 1022*A^2*B*a^4*b^6*c^7*d^4*f - 88
0*A^2*B*a^5*b^5*c^2*d^9*f - 846*A^2*B*a^4*b^6*c^5*d^6*f - 840*A*B^2*a^3*b^7*c^7*d^4*f + 760*A*B^2*a^6*b^4*c^2*
d^9*f - 704*A^2*B*a^3*b^7*c^2*d^9*f + 688*A*B^2*a^3*b^7*c^3*d^8*f + 660*A^2*B*a^6*b^4*c^3*d^8*f - 612*A^2*B*a^
2*b^8*c^7*d^4*f + 462*A*B^2*a^6*b^4*c^4*d^7*f + 459*A*B^2*a^2*b^8*c^8*d^3*f - 412*A*B^2*a^2*b^8*c^2*d^9*f - 40
8*A*B^2*a^7*b^3*c^3*d^8*f + 388*A^2*B*a^5*b^5*c^6*d^5*f + 296*A^2*B*a^2*b^8*c^3*d^8*f + 288*A*B^2*a^2*b^8*c^6*
d^5*f + 284*A*B^2*a^5*b^5*c^7*d^4*f + 236*A*B^2*a^4*b^6*c^8*d^3*f - 226*A*B^2*a^6*b^4*c^6*d^5*f + 212*A*B^2*a^
4*b^6*c^2*d^9*f + 202*A^2*B*a^6*b^4*c^5*d^6*f - 152*A^2*B*a^7*b^3*c^4*d^7*f + 88*A^2*B*a^3*b^7*c^8*d^3*f + 79*
A^2*B*a^2*b^8*c^9*d^2*f - 70*A^2*B*a^6*b^4*c^7*d^4*f + 68*A*B^2*a^8*b^2*c^4*d^7*f + 64*A^2*B*a^7*b^3*c^2*d^9*f
- 64*A*B^2*a^3*b^7*c^9*d^2*f + 56*A^2*B*a^7*b^3*c^6*d^5*f + 56*A^2*B*a^5*b^5*c^8*d^3*f + 37*A^2*B*a^8*b^2*c^3
*d^8*f - 28*A^2*B*a^8*b^2*c^5*d^6*f - 28*A^2*B*a^4*b^6*c^9*d^2*f + 17*A*B^2*a^8*b^2*c^2*d^9*f - 16*A*B^2*a^7*b
^3*c^5*d^6*f + 24*A*B*C*b^10*c*d^10*f - 6*A*B*C*a^10*c*d^10*f + 48*A*B*C*a*b^9*d^11*f + 4*A*B*C*a^9*b*d^11*f +
432*B^2*C*a*b^9*c^7*d^4*f - 376*B*C^2*a^6*b^4*c*d^10*f - 354*B*C^2*a*b^9*c^8*d^3*f + 352*B^2*C*a^5*b^5*c*d^10
*f + 320*B^2*C*a*b^9*c^5*d^6*f + 256*B^2*C*a^3*b^7*c*d^10*f - 232*B^2*C*a^7*b^3*c*d^10*f - 210*B^2*C*a*b^9*c^9
*d^2*f - 152*B*C^2*a^4*b^6*c*d^10*f + 85*B*C^2*a^8*b^2*c*d^10*f + 72*B^2*C*a*b^9*c^3*d^8*f - 48*B*C^2*a*b^9*c^
6*d^5*f - 40*B*C^2*a^3*b^7*c^10*d*f + 40*B*C^2*a^2*b^8*c*d^10*f + 37*B^2*C*a^2*b^8*c^10*d*f + 22*B^2*C*a^9*b*c
^3*d^8*f - 18*B*C^2*a^9*b*c^2*d^9*f + 16*B*C^2*a*b^9*c^2*d^9*f - 12*B^2*C*a^4*b^6*c^10*d*f + 8*B*C^2*a^9*b*c^4
*d^7*f + 8*B*C^2*a*b^9*c^4*d^7*f - 984*A^2*C*a*b^9*c^7*d^4*f + 672*A^2*C*a*b^9*c^3*d^8*f + 552*A*C^2*a*b^9*c^7
*d^4*f - 504*A^2*C*a^5*b^5*c*d^10*f - 408*A^2*C*a*b^9*c^5*d^6*f + 408*A*C^2*a*b^9*c^5*d^6*f + 336*A*C^2*a^5*b^
5*c*d^10*f - 216*A*C^2*a^7*b^3*c*d^10*f + 192*A*C^2*a^3*b^7*c*d^10*f - 162*A*C^2*a*b^9*c^9*d^2*f + 120*A^2*C*a
^7*b^3*c*d^10*f + 96*A^2*C*a^3*b^7*c*d^10*f + 90*A^2*C*a*b^9*c^9*d^2*f + 66*A^2*C*a^9*b*c^3*d^8*f - 66*A*C^2*a
^9*b*c^3*d^8*f + 57*A*C^2*a^2*b^8*c^10*d*f - 48*A*C^2*a*b^9*c^3*d^8*f - 9*A^2*C*a^2*b^8*c^10*d*f + 1736*A^2*B*
a*b^9*c^4*d^7*f + 1248*A^2*B*a*b^9*c^6*d^5*f - 1008*A*B^2*a*b^9*c^7*d^4*f + 772*A^2*B*a^4*b^6*c*d^10*f - 688*A
*B^2*a^5*b^5*c*d^10*f - 608*A*B^2*a*b^9*c^5*d^6*f + 436*A^2*B*a^2*b^8*c*d^10*f - 426*A^2*B*a*b^9*c^8*d^3*f + 3
12*A*B^2*a*b^9*c^3*d^8*f + 304*A^2*B*a*b^9*c^2*d^9*f - 244*A^2*B*a^6*b^4*c*d^10*f - 160*A*B^2*a^3*b^7*c*d^10*f
+ 114*A*B^2*a*b^9*c^9*d^2*f + 88*A*B^2*a^7*b^3*c*d^10*f - 22*A*B^2*a^9*b*c^3*d^8*f - 18*A^2*B*a^9*b*c^2*d^9*f
+ 13*A^2*B*a^8*b^2*c*d^10*f - 13*A*B^2*a^2*b^8*c^10*d*f + 8*A^2*B*a^9*b*c^4*d^7*f + 8*A^2*B*a^3*b^7*c^10*d*f
+ 111*B^2*C*b^10*c^8*d^3*f - 39*B*C^2*b^10*c^9*d^2*f + 24*B*C^2*b^10*c^7*d^4*f - 4*B^2*C*b^10*c^2*d^9*f - 4*B*
C^2*b^10*c^5*d^6*f + 432*A^2*C*b^10*c^6*d^5*f + 192*A^2*C*b^10*c^4*d^7*f - 111*A^2*C*b^10*c^8*d^3*f + 111*A*C^
2*b^10*c^8*d^3*f - 72*A*C^2*b^10*c^6*d^5*f + 12*A*C^2*b^10*c^4*d^7*f - 3*B^2*C*a^10*c^2*d^9*f - B*C^2*a^10*c^3
*d^8*f + 456*A^2*B*b^10*c^7*d^4*f - 288*A^2*B*b^10*c^3*d^8*f + 252*A*B^2*b^10*c^6*d^5*f + 192*A*B^2*b^10*c^4*d
^7*f - 183*A*B^2*b^10*c^8*d^3*f - 148*A^2*B*b^10*c^5*d^6*f + 112*B^2*C*a^6*b^4*d^11*f + 76*A*B^2*b^10*c^2*d^9*
f - 64*B*C^2*a^7*b^3*d^11*f + 16*B^2*C*a^4*b^6*d^11*f - 16*B^2*C*a^2*b^8*d^11*f + 16*B*C^2*a^5*b^5*d^11*f + 16
*B*C^2*a^3*b^7*d^11*f - 9*A^2*C*a^10*c^2*d^9*f + 9*A*C^2*a^10*c^2*d^9*f - 3*A^2*B*b^10*c^9*d^2*f - B^2*C*a^8*b
^2*d^11*f + 96*A^2*C*a^4*b^6*d^11*f - 84*A^2*C*a^6*b^4*d^11*f + 72*A*C^2*a^6*b^4*d^11*f - 24*A*C^2*a^4*b^6*d^1
1*f - 24*A*C^2*a^2*b^8*d^11*f - 21*A*C^2*a^8*b^2*d^11*f + 12*A^2*C*a^2*b^8*d^11*f + 9*A^2*C*a^8*b^2*d^11*f + 3
*A*B^2*a^10*c^2*d^9*f - A^2*B*a^10*c^3*d^8*f - B*C^2*a^2*b^8*c^11*f + 176*A*B^2*a^4*b^6*d^11*f + 136*A^2*B*a^5
*b^5*d^11*f - 128*A^2*B*a^3*b^7*d^11*f + 112*A*B^2*a^2*b^8*d^11*f - 64*A*B^2*a^6*b^4*d^11*f - 16*A^2*B*a^7*b^3
*d^11*f - A^2*B*a^2*b^8*c^11*f - 2*C^3*a^9*b*c*d^10*f - 2*B^3*a*b^9*c^10*d*f - 264*A^3*a*b^9*c*d^10*f + 2*A^3*
a^9*b*c*d^10*f - 9*B^2*C*b^10*c^10*d*f + 9*A^2*C*b^10*c^10*d*f - 9*A*C^2*b^10*c^10*d*f + 3*B*C^2*a^10*c*d^10*f
- 132*A^2*B*b^10*c*d^10*f - 3*A*B^2*b^10*c^10*d*f - 2*B*C^2*a^9*b*d^11*f + 3*A^2*B*a^10*c*d^10*f - 2*B^2*C*a*
b^9*c^11*f - 120*A^2*B*a*b^9*d^11*f - 6*A^2*C*a*b^9*c^11*f + 6*A*C^2*a*b^9*c^11*f - 2*A^2*B*a^9*b*d^11*f + 2*A
*B^2*a*b^9*c^11*f + 520*C^3*a^3*b^7*c^5*d^6*f + 460*C^3*a^5*b^5*c^5*d^6*f - 418*C^3*a^4*b^6*c^6*d^5*f + 406*C^
3*a^6*b^4*c^4*d^7*f + 268*C^3*a^5*b^5*c^7*d^4*f - 266*C^3*a^6*b^4*c^6*d^5*f + 233*C^3*a^2*b^8*c^8*d^3*f - 176*
C^3*a^7*b^3*c^5*d^6*f + 164*C^3*a^6*b^4*c^2*d^9*f + 140*C^3*a^2*b^8*c^6*d^5*f + 136*C^3*a^4*b^6*c^2*d^9*f - 12
8*C^3*a^3*b^7*c^9*d^2*f + 128*C^3*a^3*b^7*c^3*d^8*f - 108*C^3*a^6*b^4*c^8*d^3*f - 104*C^3*a^7*b^3*c^3*d^8*f -
104*C^3*a^5*b^5*c^3*d^8*f + 100*C^3*a^4*b^6*c^8*d^3*f - 89*C^3*a^8*b^2*c^2*d^9*f - 72*C^3*a^5*b^5*c^9*d^2*f +
40*C^3*a^8*b^2*c^4*d^7*f - 40*C^3*a^3*b^7*c^7*d^4*f - 28*C^3*a^2*b^8*c^4*d^7*f - 16*C^3*a^2*b^8*c^2*d^9*f - 2*
C^3*a^4*b^6*c^4*d^7*f + 828*B^3*a^5*b^5*c^4*d^7*f + 408*B^3*a^2*b^8*c^5*d^6*f + 390*B^3*a^4*b^6*c^7*d^4*f - 37
2*B^3*a^4*b^6*c^3*d^8*f - 336*B^3*a^3*b^7*c^6*d^5*f - 314*B^3*a^6*b^4*c^5*d^6*f + 288*B^3*a^3*b^7*c^4*d^7*f +
216*B^3*a^2*b^8*c^7*d^4*f - 176*B^3*a^7*b^3*c^2*d^9*f + 128*B^3*a^3*b^7*c^2*d^9*f + 108*B^3*a^5*b^5*c^6*d^5*f
+ 88*B^3*a^7*b^3*c^4*d^7*f + 72*B^3*a^5*b^5*c^2*d^9*f - 68*B^3*a^2*b^8*c^3*d^8*f - 65*B^3*a^2*b^8*c^9*d^2*f -
56*B^3*a^5*b^5*c^8*d^3*f + 40*B^3*a^7*b^3*c^6*d^5*f + 37*B^3*a^8*b^2*c^3*d^8*f + 30*B^3*a^4*b^6*c^5*d^6*f - 28
*B^3*a^8*b^2*c^5*d^6*f + 24*B^3*a^3*b^7*c^8*d^3*f - 4*B^3*a^4*b^6*c^9*d^2*f - 2*B^3*a^6*b^4*c^7*d^4*f + 1586*A
^3*a^4*b^6*c^4*d^7*f - 1376*A^3*a^3*b^7*c^3*d^8*f - 1096*A^3*a^3*b^7*c^5*d^6*f + 844*A^3*a^2*b^8*c^4*d^7*f - 7
48*A^3*a^5*b^5*c^5*d^6*f + 490*A^3*a^4*b^6*c^6*d^5*f + 376*A^3*a^2*b^8*c^2*d^9*f + 362*A^3*a^6*b^4*c^4*d^7*f -
356*A^3*a^2*b^8*c^6*d^5*f - 328*A^3*a^5*b^5*c^3*d^8*f + 328*A^3*a^3*b^7*c^7*d^4*f + 224*A^3*a^4*b^6*c^2*d^9*f
- 197*A^3*a^2*b^8*c^8*d^3*f - 112*A^3*a^7*b^3*c^5*d^6*f + 98*A^3*a^6*b^4*c^6*d^5*f - 92*A^3*a^6*b^4*c^2*d^9*f
- 88*A^3*a^7*b^3*c^3*d^8*f + 68*A^3*a^8*b^2*c^4*d^7*f + 32*A^3*a^3*b^7*c^9*d^2*f - 28*A^3*a^5*b^5*c^7*d^4*f -
28*A^3*a^4*b^6*c^8*d^3*f + 17*A^3*a^8*b^2*c^2*d^9*f + 104*C^3*a^7*b^3*c*d^10*f + 54*C^3*a*b^9*c^9*d^2*f - 40*
C^3*a*b^9*c^7*d^4*f - 35*C^3*a^2*b^8*c^10*d*f + 22*C^3*a^9*b*c^3*d^8*f + 16*C^3*a^5*b^5*c*d^10*f - 16*C^3*a^3*
b^7*c*d^10*f + 8*C^3*a*b^9*c^5*d^6*f - 2*A*B*C*b^10*c^11*f + 198*B^3*a*b^9*c^8*d^3*f + 192*B^3*a^6*b^4*c*d^10*
f - 128*B^3*a*b^9*c^4*d^7*f - 80*B^3*a^2*b^8*c*d^10*f - 56*B^3*a*b^9*c^2*d^9*f - 24*B^3*a*b^9*c^6*d^5*f - 18*B
^3*a^9*b*c^2*d^9*f - 16*B^3*a^4*b^6*c*d^10*f + 13*B^3*a^8*b^2*c*d^10*f + 8*B^3*a^9*b*c^4*d^7*f + 8*B^3*a^3*b^7
*c^10*d*f - 624*A^3*a*b^9*c^3*d^8*f + 472*A^3*a*b^9*c^7*d^4*f - 272*A^3*a^3*b^7*c*d^10*f + 152*A^3*a^5*b^5*c*d
^10*f - 22*A^3*a^9*b*c^3*d^8*f + 18*A^3*a*b^9*c^9*d^2*f - 13*A^3*a^2*b^8*c^10*d*f - 8*A^3*a^7*b^3*c*d^10*f - 8
*A^3*a*b^9*c^5*d^6*f + A*B^2*a^8*b^2*d^11*f - C^3*b^10*c^8*d^3*f - 60*B^3*b^10*c^7*d^4*f - 32*B^3*b^10*c^5*d^6
*f + 21*B^3*b^10*c^9*d^2*f - 12*B^3*b^10*c^3*d^8*f - 3*C^3*a^10*c^2*d^9*f - 360*A^3*b^10*c^6*d^5*f - 204*A^3*b
^10*c^4*d^7*f + 11*C^3*a^8*b^2*d^11*f - 8*C^3*a^6*b^4*d^11*f - 4*C^3*a^4*b^6*d^11*f - B^3*a^10*c^3*d^8*f - 64*
B^3*a^5*b^5*d^11*f - 32*B^3*a^3*b^7*d^11*f + 3*A^3*a^10*c^2*d^9*f - 68*A^3*a^4*b^6*d^11*f + 20*A^3*a^6*b^4*d^1
1*f + 12*A^3*a^2*b^8*d^11*f - B^3*a^2*b^8*c^11*f + 3*C^3*b^10*c^10*d*f + 3*B^3*a^10*c*d^10*f - 3*A^3*b^10*c^10
*d*f - 2*C^3*a*b^9*c^11*f - 2*B^3*a^9*b*d^11*f + 2*A^3*a*b^9*c^11*f - 36*A^2*C*b^10*d^11*f + 3*A^2*C*a^10*d^11
*f - 3*A*C^2*a^10*d^11*f - A*B^2*a^10*d^11*f + 36*A^3*b^10*d^11*f - A^3*a^10*d^11*f + A^3*b^10*c^8*d^3*f + A^3
*a^8*b^2*d^11*f + B^2*C*a^10*d^11*f + B*C^2*b^10*c^11*f + A^2*B*b^10*c^11*f + C^3*a^10*d^11*f + B^3*b^10*c^11*
f - 6*A*B^2*C*a*b^7*c^7*d + 4*A*B^2*C*a*b^7*c*d^7 + 168*A^2*B*C*a^3*b^5*c^2*d^6 + 144*A*B*C^2*a^4*b^4*c^3*d^5
- 129*A^2*B*C*a^4*b^4*c^3*d^5 - 96*A*B*C^2*a^3*b^5*c^2*d^6 + 84*A*B*C^2*a^2*b^6*c^3*d^5 + 72*A^2*B*C*a^3*b^5*c
^4*d^4 - 72*A^2*B*C*a^2*b^6*c^3*d^5 + 64*A*B^2*C*a^4*b^4*c^4*d^4 - 60*A*B*C^2*a^3*b^5*c^4*d^4 + 57*A^2*B*C*a^2
*b^6*c^5*d^3 - 56*A*B^2*C*a^3*b^5*c^5*d^3 - 39*A*B^2*C*a^4*b^4*c^2*d^6 - 38*A*B^2*C*a^5*b^3*c^3*d^5 + 36*A*B^2
*C*a^3*b^5*c^3*d^5 + 36*A*B*C^2*a^4*b^4*c^5*d^3 - 30*A*B*C^2*a^2*b^6*c^5*d^3 + 27*A*B^2*C*a^2*b^6*c^6*d^2 - 24
*A*B^2*C*a^2*b^6*c^2*d^6 - 24*A*B*C^2*a^5*b^3*c^4*d^4 + 24*A*B*C^2*a^3*b^5*c^6*d^2 + 18*A^2*B*C*a^5*b^3*c^2*d^
6 - 18*A^2*B*C*a^4*b^4*c^5*d^3 - 15*A*B^2*C*a^2*b^6*c^4*d^4 + 12*A^2*B*C*a^5*b^3*c^4*d^4 - 12*A^2*B*C*a^3*b^5*
c^6*d^2 + 9*A*B^2*C*a^6*b^2*c^2*d^6 + 6*A*B*C^2*a^6*b^2*c^3*d^5 - 3*A^2*B*C*a^6*b^2*c^3*d^5 + 60*A^2*B*C*a*b^7
*c^2*d^6 - 51*A^2*B*C*a^4*b^4*c*d^7 + 48*A*B*C^2*a*b^7*c^6*d^2 - 42*A^2*B*C*a^2*b^6*c*d^7 - 42*A^2*B*C*a*b^7*c
^6*d^2 + 36*A*B*C^2*a^4*b^4*c*d^7 + 36*A*B*C^2*a^2*b^6*c*d^7 + 36*A*B*C^2*a*b^7*c^4*d^4 - 30*A^2*B*C*a*b^7*c^4
*d^4 + 24*A*B^2*C*a*b^7*c^3*d^5 - 24*A*B*C^2*a*b^7*c^2*d^6 + 18*A*B^2*C*a^5*b^3*c*d^7 - 18*A*B*C^2*a^6*b^2*c*d
^7 + 12*A*B^2*C*a^3*b^5*c*d^7 + 9*A^2*B*C*a^6*b^2*c*d^7 + 6*A*B^2*C*a*b^7*c^5*d^3 - 6*A*B*C^2*a^2*b^6*c^7*d +
3*A^2*B*C*a^2*b^6*c^7*d - 18*B^3*C*a*b^7*c^6*d^2 - 18*B*C^3*a*b^7*c^6*d^2 - 14*B^3*C*a*b^7*c^4*d^4 - 14*B*C^3*
a*b^7*c^4*d^4 - 10*B^3*C*a^2*b^6*c*d^7 - 10*B*C^3*a^2*b^6*c*d^7 + 9*B^3*C*a^6*b^2*c*d^7 + 9*B*C^3*a^6*b^2*c*d^
7 - 7*B^3*C*a^4*b^4*c*d^7 - 7*B*C^3*a^4*b^4*c*d^7 + 6*B^2*C^2*a*b^7*c^7*d - 4*B^3*C*a*b^7*c^2*d^6 + 4*B^2*C^2*
a*b^7*c*d^7 - 4*B*C^3*a*b^7*c^2*d^6 + 3*B^3*C*a^2*b^6*c^7*d + 3*B*C^3*a^2*b^6*c^7*d + 144*A^3*C*a*b^7*c^3*d^5
+ 62*A^3*C*a*b^7*c^5*d^3 + 48*A*C^3*a*b^7*c^3*d^5 - 36*A^2*C^2*a*b^7*c*d^7 + 26*A*C^3*a*b^7*c^5*d^3 + 20*A^3*C
*a^3*b^5*c*d^7 + 18*A^2*C^2*a*b^7*c^7*d - 18*A*C^3*a^5*b^3*c*d^7 - 6*A^3*C*a^5*b^3*c*d^7 - 4*A*C^3*a^3*b^5*c*d
^7 - 32*A^3*B*a*b^7*c^2*d^6 - 32*A*B^3*a*b^7*c^2*d^6 + 22*A^3*B*a^4*b^4*c*d^7 + 22*A*B^3*a^4*b^4*c*d^7 + 16*A^
3*B*a^2*b^6*c*d^7 + 16*A*B^3*a^2*b^6*c*d^7 + 12*A^3*B*a*b^7*c^6*d^2 + 12*A*B^3*a*b^7*c^6*d^2 + 8*A^3*B*a*b^7*c
^4*d^4 - 8*A^2*B^2*a*b^7*c*d^7 + 8*A*B^3*a*b^7*c^4*d^4 + 57*A^2*B*C*b^8*c^5*d^3 + 36*A^2*B*C*b^8*c^3*d^5 - 30*
A*B*C^2*b^8*c^5*d^3 - 18*A*B*C^2*b^8*c^3*d^5 - 9*A*B^2*C*b^8*c^4*d^4 - 3*A*B^2*C*b^8*c^6*d^2 - 2*A*B^2*C*b^8*c
^2*d^6 + 36*A^2*B*C*a^3*b^5*d^8 + 24*A*B*C^2*a^5*b^3*d^8 - 18*A^2*B*C*a^5*b^3*d^8 - 12*A*B*C^2*a^3*b^5*d^8 - 3
*A*B^2*C*a^6*b^2*d^8 - 3*A*B^2*C*a^4*b^4*d^8 - 2*A*B^2*C*a^2*b^6*d^8 + 34*B^2*C^2*a^5*b^3*c^3*d^5 + 28*B^2*C^2
*a^3*b^5*c^5*d^3 + 24*B^2*C^2*a^4*b^4*c^2*d^6 - 20*B^2*C^2*a^4*b^4*c^4*d^4 + 12*B^2*C^2*a^3*b^5*c^3*d^5 + 12*B
^2*C^2*a^2*b^6*c^2*d^6 - 9*B^2*C^2*a^6*b^2*c^2*d^6 + 9*B^2*C^2*a^4*b^4*c^6*d^2 + 9*B^2*C^2*a^2*b^6*c^4*d^4 - 3
*B^2*C^2*a^2*b^6*c^6*d^2 + 159*A^2*C^2*a^2*b^6*c^4*d^4 - 156*A^2*C^2*a^3*b^5*c^3*d^5 + 90*A^2*C^2*a^5*b^3*c^3*
d^5 + 78*A^2*C^2*a^2*b^6*c^2*d^6 - 63*A^2*C^2*a^4*b^4*c^4*d^4 - 27*A^2*C^2*a^6*b^2*c^2*d^6 - 27*A^2*C^2*a^2*b^
6*c^6*d^2 - 18*A^2*C^2*a^4*b^4*c^2*d^6 + 9*A^2*C^2*a^4*b^4*c^6*d^2 + 66*A^2*B^2*a^2*b^6*c^2*d^6 + 60*A^2*B^2*a
^2*b^6*c^4*d^4 - 48*A^2*B^2*a^3*b^5*c^3*d^5 + 42*A^2*B^2*a^4*b^4*c^2*d^6 + 28*A^2*B^2*a^3*b^5*c^5*d^3 - 17*A^2
*B^2*a^4*b^4*c^4*d^4 - 6*A^2*B^2*a^2*b^6*c^6*d^2 + 4*A^2*B^2*a^5*b^3*c^3*d^5 + 36*A^3*C*a*b^7*c*d^7 - 18*A*C^3
*a*b^7*c^7*d + 12*A*C^3*a*b^7*c*d^7 - 6*A^3*C*a*b^7*c^7*d + 12*A^2*B*C*b^8*c*d^7 + 6*A*B*C^2*b^8*c^7*d - 6*A*B
*C^2*b^8*c*d^7 - 3*A^2*B*C*b^8*c^7*d + 24*A^2*B*C*a*b^7*d^8 - 12*A*B*C^2*a*b^7*d^8 - 53*B^3*C*a^4*b^4*c^3*d^5
- 53*B*C^3*a^4*b^4*c^3*d^5 - 32*B^3*C*a^2*b^6*c^3*d^5 - 32*B*C^3*a^2*b^6*c^3*d^5 - 18*B^3*C*a^4*b^4*c^5*d^3 -
18*B*C^3*a^4*b^4*c^5*d^3 + 16*B^3*C*a^3*b^5*c^4*d^4 + 16*B*C^3*a^3*b^5*c^4*d^4 + 12*B^3*C*a^5*b^3*c^4*d^4 - 12
*B^3*C*a^3*b^5*c^6*d^2 + 12*B^2*C^2*a*b^7*c^3*d^5 + 12*B*C^3*a^5*b^3*c^4*d^4 - 12*B*C^3*a^3*b^5*c^6*d^2 + 8*B^
3*C*a^3*b^5*c^2*d^6 + 8*B*C^3*a^3*b^5*c^2*d^6 - 6*B^3*C*a^5*b^3*c^2*d^6 - 6*B^2*C^2*a^5*b^3*c*d^7 + 6*B^2*C^2*
a*b^7*c^5*d^3 - 6*B*C^3*a^5*b^3*c^2*d^6 - 3*B^3*C*a^6*b^2*c^3*d^5 - 3*B*C^3*a^6*b^2*c^3*d^5 - 175*A^3*C*a^2*b^
6*c^4*d^4 + 164*A^3*C*a^3*b^5*c^3*d^5 - 144*A^2*C^2*a*b^7*c^3*d^5 - 124*A^3*C*a^2*b^6*c^2*d^6 - 90*A*C^3*a^5*b
^3*c^3*d^5 - 73*A*C^3*a^2*b^6*c^4*d^4 - 66*A^2*C^2*a*b^7*c^5*d^3 + 44*A*C^3*a^3*b^5*c^3*d^5 + 36*A*C^3*a^4*b^4
*c^4*d^4 - 30*A^3*C*a^5*b^3*c^3*d^5 + 30*A^3*C*a^4*b^4*c^4*d^4 + 27*A*C^3*a^6*b^2*c^2*d^6 + 21*A*C^3*a^4*b^4*c
^2*d^6 + 18*A^2*C^2*a^5*b^3*c*d^7 - 18*A*C^3*a^4*b^4*c^6*d^2 - 16*A*C^3*a^2*b^6*c^2*d^6 - 15*A^3*C*a^4*b^4*c^2
*d^6 + 15*A^3*C*a^2*b^6*c^6*d^2 - 12*A^2*C^2*a^3*b^5*c*d^7 + 9*A^3*C*a^6*b^2*c^2*d^6 + 9*A*C^3*a^2*b^6*c^6*d^2
- 80*A^3*B*a^3*b^5*c^2*d^6 - 80*A*B^3*a^3*b^5*c^2*d^6 + 38*A^3*B*a^4*b^4*c^3*d^5 + 38*A*B^3*a^4*b^4*c^3*d^5 -
36*A^2*B^2*a*b^7*c^3*d^5 - 28*A^3*B*a^3*b^5*c^4*d^4 - 28*A^3*B*a^2*b^6*c^5*d^3 - 28*A*B^3*a^3*b^5*c^4*d^4 - 2
8*A*B^3*a^2*b^6*c^5*d^3 + 20*A^3*B*a^2*b^6*c^3*d^5 + 20*A*B^3*a^2*b^6*c^3*d^5 - 12*A^3*B*a^5*b^3*c^2*d^6 - 12*
A^2*B^2*a^5*b^3*c*d^7 - 12*A^2*B^2*a^3*b^5*c*d^7 - 12*A^2*B^2*a*b^7*c^5*d^3 - 12*A*B^3*a^5*b^3*c^2*d^6 + 6*B^2
*C^2*b^8*c^6*d^2 + 3*B^2*C^2*b^8*c^4*d^4 + 36*A^2*C^2*b^8*c^4*d^4 + 27*A^2*C^2*b^8*c^2*d^6 - 18*A^2*C^2*b^8*c^
6*d^2 + 33*A^2*B^2*b^8*c^4*d^4 + 28*A^2*B^2*b^8*c^2*d^6 + 9*B^2*C^2*a^4*b^4*d^8 + 6*A^2*B^2*b^8*c^6*d^2 + 4*B^
2*C^2*a^2*b^6*d^8 + 3*B^2*C^2*a^6*b^2*d^8 - 30*A^2*C^2*a^4*b^4*d^8 + 9*A^2*C^2*a^6*b^2*d^8 + 16*A^2*B^2*a^2*b^
6*d^8 + 3*A^2*B^2*a^4*b^4*d^8 + 6*C^4*a^5*b^3*c*d^7 + 4*C^4*a^3*b^5*c*d^7 - 2*C^4*a*b^7*c^5*d^3 - 12*B^4*a^5*b
^3*c*d^7 + 12*B^4*a*b^7*c^3*d^5 + 8*B^4*a*b^7*c^5*d^3 - 4*B^4*a^3*b^5*c*d^7 - 48*A^4*a*b^7*c^3*d^5 - 20*A^4*a*
b^7*c^5*d^3 - 8*A^4*a^3*b^5*c*d^7 - 63*A^3*C*b^8*c^4*d^4 - 54*A^3*C*b^8*c^2*d^6 + 9*A^3*C*b^8*c^6*d^2 + 9*A*C^
3*b^8*c^6*d^2 - 3*A*C^3*b^8*c^4*d^4 - 28*A^3*B*b^8*c^5*d^3 - 28*A*B^3*b^8*c^5*d^3 - 18*A^3*B*b^8*c^3*d^5 - 18*
A*B^3*b^8*c^3*d^5 - 10*B^3*C*a^5*b^3*d^8 - 10*B*C^3*a^5*b^3*d^8 - 4*B^3*C*a^3*b^5*d^8 - 4*B*C^3*a^3*b^5*d^8 +
23*A^3*C*a^4*b^4*d^8 - 18*A^3*C*a^2*b^6*d^8 + 11*A*C^3*a^4*b^4*d^8 - 9*A*C^3*a^6*b^2*d^8 + 6*A*C^3*a^2*b^6*d^8
- 3*A^3*C*a^6*b^2*d^8 - 20*A^3*B*a^3*b^5*d^8 - 20*A*B^3*a^3*b^5*d^8 + 4*A^3*B*a^5*b^3*d^8 + 4*A*B^3*a^5*b^3*d
^8 + B^3*C*a^2*b^6*c^5*d^3 + B*C^3*a^2*b^6*c^5*d^3 + 6*C^4*a*b^7*c^7*d + 4*B^4*a*b^7*c*d^7 - 12*A^4*a*b^7*c*d^
7 - 3*B^3*C*b^8*c^7*d - 3*B*C^3*b^8*c^7*d - 6*A^3*B*b^8*c*d^7 - 6*A*B^3*b^8*c*d^7 - 12*A^3*B*a*b^7*d^8 - 12*A*
B^3*a*b^7*d^8 + 30*C^4*a^5*b^3*c^3*d^5 + 19*C^4*a^2*b^6*c^4*d^4 - 9*C^4*a^6*b^2*c^2*d^6 + 9*C^4*a^4*b^4*c^6*d^
2 + 4*C^4*a^3*b^5*c^3*d^5 + 4*C^4*a^2*b^6*c^2*d^6 - 3*C^4*a^4*b^4*c^4*d^4 - 3*C^4*a^4*b^4*c^2*d^6 + 3*C^4*a^2*
b^6*c^6*d^2 + 28*B^4*a^3*b^5*c^5*d^3 + 27*B^4*a^4*b^4*c^2*d^6 - 17*B^4*a^4*b^4*c^4*d^4 - 10*B^4*a^2*b^6*c^4*d^
4 + 8*B^4*a^3*b^5*c^3*d^5 + 8*B^4*a^2*b^6*c^2*d^6 - 6*B^4*a^2*b^6*c^6*d^2 + 4*B^4*a^5*b^3*c^3*d^5 + 70*A^4*a^2
*b^6*c^4*d^4 + 58*A^4*a^2*b^6*c^2*d^6 - 56*A^4*a^3*b^5*c^3*d^5 + 15*A^4*a^4*b^4*c^2*d^6 + B^2*C^2*b^8*c^2*d^6
- 18*A^3*C*b^8*d^8 + B^3*C*b^8*c^5*d^3 + B*C^3*b^8*c^5*d^3 + 6*B^4*b^8*c^6*d^2 + 3*B^4*b^8*c^4*d^4 + 30*A^4*b^
8*c^4*d^4 + 27*A^4*b^8*c^2*d^6 + 3*C^4*a^6*b^2*d^8 + 8*B^4*a^4*b^4*d^8 + 4*B^4*a^2*b^6*d^8 + 12*A^4*a^2*b^6*d^
8 - 5*A^4*a^4*b^4*d^8 + 9*A^2*C^2*b^8*d^8 + 9*A^2*B^2*b^8*d^8 + 9*A^4*b^8*d^8 + B^4*b^8*c^2*d^6 + C^4*a^4*b^4*
d^8, f, k), k, 1, 4))/f

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**2/(c+d*tan(f*x+e))**3,x)

[Out]

Exception raised: NotImplementedError

________________________________________________________________________________________