\(\int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^2} \, dx\) [82]

Optimal result

Integrand size = 45, antiderivative size = 509 \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^2} \, dx=-\frac {\left (a^2 \left (c^2 C-2 B c d-C d^2-A \left (c^2-d^2\right )\right )-b^2 \left (c^2 C-2 B c d-C d^2-A \left (c^2-d^2\right )\right )+2 a b \left (2 c (A-C) d-B \left (c^2-d^2\right )\right )\right ) x}{\left (a^2+b^2\right )^2 \left (c^2+d^2\right )^2}+\frac {b \left (3 a^3 b B d-2 a^4 C d+b^4 (B c-2 A d)-a^2 b^2 (B c+4 A d)+a b^3 (2 A c-2 c C+B d)\right ) \log (a \cos (e+f x)+b \sin (e+f x))}{\left (a^2+b^2\right )^2 (b c-a d)^3 f}+\frac {d \left (b \left (2 c^4 C-3 B c^3 d+4 A c^2 d^2-B c d^3+2 A d^4\right )-a d^2 \left (2 c (A-C) d-B \left (c^2-d^2\right )\right )\right ) \log (c \cos (e+f x)+d \sin (e+f x))}{(b c-a d)^3 \left (c^2+d^2\right )^2 f}-\frac {d \left (b^2 c (c C-B d)-a b B \left (c^2+d^2\right )+a^2 \left (2 c^2 C-B c d+C d^2\right )+A \left (a^2 d^2+b^2 \left (c^2+2 d^2\right )\right )\right )}{\left (a^2+b^2\right ) (b c-a d)^2 \left (c^2+d^2\right ) f (c+d \tan (e+f x))}-\frac {A b^2-a (b B-a C)}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x)) (c+d \tan (e+f x))} \]

[Out]

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

Rubi [A] (verified)

Time = 2.29 (sec) , antiderivative size = 508, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {3730, 3732, 3611} \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^2} \, dx=-\frac {d \left (a^2 A d^2+a^2 \left (-B c d+2 c^2 C+C d^2\right )-a b B \left (c^2+d^2\right )+A b^2 \left (c^2+2 d^2\right )+b^2 c (c C-B d)\right )}{f \left (a^2+b^2\right ) \left (c^2+d^2\right ) (b c-a d)^2 (c+d \tan (e+f x))}-\frac {x \left (a^2 \left (-A \left (c^2-d^2\right )-2 B c d+c^2 C-C d^2\right )+2 a b \left (2 c d (A-C)-B \left (c^2-d^2\right )\right )-b^2 \left (-A \left (c^2-d^2\right )-2 B c d+c^2 C-C d^2\right )\right )}{\left (a^2+b^2\right )^2 \left (c^2+d^2\right )^2}-\frac {A b^2-a (b B-a C)}{f \left (a^2+b^2\right ) (b c-a d) (a+b \tan (e+f x)) (c+d \tan (e+f x))}+\frac {b \left (-2 a^4 C d+3 a^3 b B d-a^2 b^2 (4 A d+B c)+a b^3 (2 A c+B d-2 c C)+b^4 (B c-2 A d)\right ) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left (a^2+b^2\right )^2 (b c-a d)^3}+\frac {d \left (b \left (4 A c^2 d^2+2 A d^4-3 B c^3 d-B c d^3+2 c^4 C\right )-a d^2 \left (2 c d (A-C)-B \left (c^2-d^2\right )\right )\right ) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left (c^2+d^2\right )^2 (b c-a d)^3} \]

[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])^2),x]

[Out]

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

Rule 3611

Int[((c_) + (d_.)*tan[(e_.) + (f_.)*(x_)])/((a_) + (b_.)*tan[(e_.) + (f_.)*(x_)]), x_Symbol] :> Simp[(c/(b*f))
*Log[RemoveContent[a*Cos[e + f*x] + b*Sin[e + f*x], x]], 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 3730

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*Ta
n[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 3732

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

Mathematica [A] (verified)

Time = 9.12 (sec) , antiderivative size = 984, normalized size of antiderivative = 1.93 \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^2} \, dx=-\frac {A b^2-a (b B-a C)}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x)) (c+d \tan (e+f x))}-\frac {-\frac {\frac {b (b c-a d)^2 \left (2 a A b c^2-a^2 B c^2+b^2 B c^2-2 a b c^2 C+2 a^2 A c d-2 A b^2 c d+4 a b B c d-2 a^2 c C d+2 b^2 c C d-2 a A b d^2+a^2 B d^2-b^2 B d^2+2 a b C d^2-\frac {\sqrt {-b^2} \left (a^2 \left (c^2 C-2 B c d-C d^2-A \left (c^2-d^2\right )\right )-b^2 \left (c^2 C-2 B c d-C d^2-A \left (c^2-d^2\right )\right )+2 a b \left (2 c (A-C) d-B \left (c^2-d^2\right )\right )\right )}{b}\right ) \log \left (\sqrt {-b^2}-b \tan (e+f x)\right )}{2 \left (a^2+b^2\right ) \left (c^2+d^2\right )}-\frac {b^2 \left (c^2+d^2\right ) \left (3 a^3 b B d-2 a^4 C d+b^4 (B c-2 A d)-a^2 b^2 (B c+4 A d)+a b^3 (2 A c-2 c C+B d)\right ) \log (a+b \tan (e+f x))}{\left (a^2+b^2\right ) (b c-a d)}+\frac {b (b c-a d)^2 \left (2 a A b c^2-a^2 B c^2+b^2 B c^2-2 a b c^2 C+2 a^2 A c d-2 A b^2 c d+4 a b B c d-2 a^2 c C d+2 b^2 c C d-2 a A b d^2+a^2 B d^2-b^2 B d^2+2 a b C d^2+\frac {\sqrt {-b^2} \left (a^2 \left (c^2 C-2 B c d-C d^2-A \left (c^2-d^2\right )\right )-b^2 \left (c^2 C-2 B c d-C d^2-A \left (c^2-d^2\right )\right )+2 a b \left (2 c (A-C) d-B \left (c^2-d^2\right )\right )\right )}{b}\right ) \log \left (\sqrt {-b^2}+b \tan (e+f x)\right )}{2 \left (a^2+b^2\right ) \left (c^2+d^2\right )}-\frac {b \left (a^2+b^2\right ) d \left (b \left (2 c^4 C-3 B c^3 d+4 A c^2 d^2-B c d^3+2 A d^4\right )-a d^2 \left (2 c (A-C) d-B \left (c^2-d^2\right )\right )\right ) \log (c+d \tan (e+f x))}{(b c-a d) \left (c^2+d^2\right )}}{b (-b c+a d) \left (c^2+d^2\right ) f}-\frac {-c \left (-2 c \left (A b^2-a (b B-a C)\right ) d+(A b-a B-b C) d (b c-a d)\right )+d^2 \left (2 A b^2 d-a A (b c-a d)-(b B-a C) (b c+a d)\right )}{(-b c+a d) \left (c^2+d^2\right ) f (c+d \tan (e+f x))}}{\left (a^2+b^2\right ) (b c-a d)} \]

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

Maple [A] (verified)

Time = 1.81 (sec) , antiderivative size = 577, normalized size of antiderivative = 1.13

method	result	size
derivativedivides	\(\frac {\frac {b \left (4 A \,a^{2} b^{2} d -2 A a \,b^{3} c +2 A \,b^{4} d -3 a^{3} b B d +B \,a^{2} b^{2} c -B a \,b^{3} d -B \,b^{4} c +2 a^{4} C d +2 C a \,b^{3} c \right ) \ln \left (a +b \tan \left (f x +e \right )\right )}{\left (a d -b c \right )^{3} \left (a^{2}+b^{2}\right )^{2}}-\frac {\left (A \,b^{2}-B a b +C \,a^{2}\right ) b}{\left (a d -b c \right )^{2} \left (a^{2}+b^{2}\right ) \left (a +b \tan \left (f x +e \right )\right )}+\frac {\frac {\left (-2 A \,a^{2} c d -2 A a b \,c^{2}+2 A a b \,d^{2}+2 A \,b^{2} c d +B \,a^{2} c^{2}-B \,a^{2} d^{2}-4 B a b c d -B \,b^{2} c^{2}+B \,b^{2} d^{2}+2 C \,a^{2} c d +2 C a b \,c^{2}-2 C a b \,d^{2}-2 C \,b^{2} c d \right ) \ln \left (1+\tan \left (f x +e \right )^{2}\right )}{2}+\left (A \,a^{2} c^{2}-A \,a^{2} d^{2}-4 A a b c d -A \,b^{2} c^{2}+A \,b^{2} d^{2}+2 B \,a^{2} c d +2 B a b \,c^{2}-2 B a b \,d^{2}-2 B \,b^{2} c d -C \,a^{2} c^{2}+a^{2} C \,d^{2}+4 C a b c d +C \,b^{2} c^{2}-C \,b^{2} d^{2}\right ) \arctan \left (\tan \left (f x +e \right )\right )}{\left (a^{2}+b^{2}\right )^{2} \left (c^{2}+d^{2}\right )^{2}}+\frac {d \left (2 A a c \,d^{3}-4 A b \,c^{2} d^{2}-2 A b \,d^{4}-B a \,c^{2} d^{2}+B a \,d^{4}+3 B b \,c^{3} d +B b c \,d^{3}-2 C a c \,d^{3}-2 C b \,c^{4}\right ) \ln \left (c +d \tan \left (f x +e \right )\right )}{\left (a d -b c \right )^{3} \left (c^{2}+d^{2}\right )^{2}}-\frac {\left (A \,d^{2}-B c d +c^{2} C \right ) d}{\left (a d -b c \right )^{2} \left (c^{2}+d^{2}\right ) \left (c +d \tan \left (f x +e \right )\right )}}{f}\)	\(577\)
default	\(\frac {\frac {b \left (4 A \,a^{2} b^{2} d -2 A a \,b^{3} c +2 A \,b^{4} d -3 a^{3} b B d +B \,a^{2} b^{2} c -B a \,b^{3} d -B \,b^{4} c +2 a^{4} C d +2 C a \,b^{3} c \right ) \ln \left (a +b \tan \left (f x +e \right )\right )}{\left (a d -b c \right )^{3} \left (a^{2}+b^{2}\right )^{2}}-\frac {\left (A \,b^{2}-B a b +C \,a^{2}\right ) b}{\left (a d -b c \right )^{2} \left (a^{2}+b^{2}\right ) \left (a +b \tan \left (f x +e \right )\right )}+\frac {\frac {\left (-2 A \,a^{2} c d -2 A a b \,c^{2}+2 A a b \,d^{2}+2 A \,b^{2} c d +B \,a^{2} c^{2}-B \,a^{2} d^{2}-4 B a b c d -B \,b^{2} c^{2}+B \,b^{2} d^{2}+2 C \,a^{2} c d +2 C a b \,c^{2}-2 C a b \,d^{2}-2 C \,b^{2} c d \right ) \ln \left (1+\tan \left (f x +e \right )^{2}\right )}{2}+\left (A \,a^{2} c^{2}-A \,a^{2} d^{2}-4 A a b c d -A \,b^{2} c^{2}+A \,b^{2} d^{2}+2 B \,a^{2} c d +2 B a b \,c^{2}-2 B a b \,d^{2}-2 B \,b^{2} c d -C \,a^{2} c^{2}+a^{2} C \,d^{2}+4 C a b c d +C \,b^{2} c^{2}-C \,b^{2} d^{2}\right ) \arctan \left (\tan \left (f x +e \right )\right )}{\left (a^{2}+b^{2}\right )^{2} \left (c^{2}+d^{2}\right )^{2}}+\frac {d \left (2 A a c \,d^{3}-4 A b \,c^{2} d^{2}-2 A b \,d^{4}-B a \,c^{2} d^{2}+B a \,d^{4}+3 B b \,c^{3} d +B b c \,d^{3}-2 C a c \,d^{3}-2 C b \,c^{4}\right ) \ln \left (c +d \tan \left (f x +e \right )\right )}{\left (a d -b c \right )^{3} \left (c^{2}+d^{2}\right )^{2}}-\frac {\left (A \,d^{2}-B c d +c^{2} C \right ) d}{\left (a d -b c \right )^{2} \left (c^{2}+d^{2}\right ) \left (c +d \tan \left (f x +e \right )\right )}}{f}\)	\(577\)
norman	\(\text {Expression too large to display}\)	\(1348\)
risch	\(\text {Expression too large to display}\)	\(9078\)
parallelrisch	\(\text {Expression too large to display}\)	\(12926\)

[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))^2,x,method=_RETURNVERBOSE)

[Out]

1/f*(b*(4*A*a^2*b^2*d-2*A*a*b^3*c+2*A*b^4*d-3*B*a^3*b*d+B*a^2*b^2*c-B*a*b^3*d-B*b^4*c+2*C*a^4*d+2*C*a*b^3*c)/(
a*d-b*c)^3/(a^2+b^2)^2*ln(a+b*tan(f*x+e))-(A*b^2-B*a*b+C*a^2)*b/(a*d-b*c)^2/(a^2+b^2)/(a+b*tan(f*x+e))+1/(a^2+
b^2)^2/(c^2+d^2)^2*(1/2*(-2*A*a^2*c*d-2*A*a*b*c^2+2*A*a*b*d^2+2*A*b^2*c*d+B*a^2*c^2-B*a^2*d^2-4*B*a*b*c*d-B*b^
2*c^2+B*b^2*d^2+2*C*a^2*c*d+2*C*a*b*c^2-2*C*a*b*d^2-2*C*b^2*c*d)*ln(1+tan(f*x+e)^2)+(A*a^2*c^2-A*a^2*d^2-4*A*a
*b*c*d-A*b^2*c^2+A*b^2*d^2+2*B*a^2*c*d+2*B*a*b*c^2-2*B*a*b*d^2-2*B*b^2*c*d-C*a^2*c^2+C*a^2*d^2+4*C*a*b*c*d+C*b
^2*c^2-C*b^2*d^2)*arctan(tan(f*x+e)))+d*(2*A*a*c*d^3-4*A*b*c^2*d^2-2*A*b*d^4-B*a*c^2*d^2+B*a*d^4+3*B*b*c^3*d+B
*b*c*d^3-2*C*a*c*d^3-2*C*b*c^4)/(a*d-b*c)^3/(c^2+d^2)^2*ln(c+d*tan(f*x+e))-(A*d^2-B*c*d+C*c^2)*d/(a*d-b*c)^2/(
c^2+d^2)/(c+d*tan(f*x+e)))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 4174 vs. \(2 (512) = 1024\).

Time = 3.54 (sec) , antiderivative size = 4174, normalized size of antiderivative = 8.20 \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^2} \, dx=\text {Too large to display} \]

[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))^2,x, algorithm="fricas")

[Out]

-1/2*(2*(C*a^2*b^4 - B*a*b^5 + A*b^6)*c^6 - 2*(C*a^3*b^3 - B*a^2*b^4 + A*a*b^5)*c^5*d + 4*(C*a^2*b^4 - B*a*b^5
+ A*b^6)*c^4*d^2 + 2*(C*a^5*b + 2*B*a^2*b^4 - (2*A - C)*a*b^5)*c^3*d^3 - 2*(C*a^6 + B*a^5*b + 2*C*a^4*b^2 + 2
*B*a^3*b^3 + 2*B*a*b^5 - A*b^6)*c^2*d^4 + 2*(B*a^6 + A*a^5*b + 2*B*a^4*b^2 + (2*A - C)*a^3*b^3 + 2*B*a^2*b^4)*
c*d^5 - 2*(A*a^6 + 2*A*a^4*b^2 + A*a^2*b^4)*d^6 - 2*(((A - C)*a^3*b^3 + 2*B*a^2*b^4 - (A - C)*a*b^5)*c^6 - (3*
(A - C)*a^4*b^2 + 4*B*a^3*b^3 + (A - C)*a^2*b^4 + 2*B*a*b^5)*c^5*d + (3*(A - C)*a^5*b + 8*(A - C)*a^3*b^3 + 4*
B*a^2*b^4 + (A - C)*a*b^5)*c^4*d^2 - ((A - C)*a^6 - 4*B*a^5*b + 8*(A - C)*a^4*b^2 + 3*(A - C)*a^2*b^4)*c^3*d^3
- (2*B*a^6 - (A - C)*a^5*b + 4*B*a^4*b^2 - 3*(A - C)*a^3*b^3)*c^2*d^4 + ((A - C)*a^6 + 2*B*a^5*b - (A - C)*a^
4*b^2)*c*d^5)*f*x - 2*((C*a^3*b^3 - B*a^2*b^4 + A*a*b^5)*c^5*d + (B*a^3*b^3 - (A - 2*C)*a^2*b^4 + C*b^6)*c^4*d
^2 - (C*a^5*b + B*a^4*b^2 + 4*B*a^2*b^4 - (2*A - C)*a*b^5 + B*b^6)*c^3*d^3 + (B*a^5*b + (A - 2*C)*a^4*b^2 + 4*
B*a^3*b^3 + B*a*b^5 + A*b^6)*c^2*d^4 - (A*a^5*b + (2*A - C)*a^3*b^3 + B*a^2*b^4)*c*d^5 - (C*a^4*b^2 - B*a^3*b^
3 + A*a^2*b^4)*d^6 + (((A - C)*a^2*b^4 + 2*B*a*b^5 - (A - C)*b^6)*c^5*d - (3*(A - C)*a^3*b^3 + 4*B*a^2*b^4 + (
A - C)*a*b^5 + 2*B*b^6)*c^4*d^2 + (3*(A - C)*a^4*b^2 + 8*(A - C)*a^2*b^4 + 4*B*a*b^5 + (A - C)*b^6)*c^3*d^3 -
((A - C)*a^5*b - 4*B*a^4*b^2 + 8*(A - C)*a^3*b^3 + 3*(A - C)*a*b^5)*c^2*d^4 - (2*B*a^5*b - (A - C)*a^4*b^2 + 4
*B*a^3*b^3 - 3*(A - C)*a^2*b^4)*c*d^5 + ((A - C)*a^5*b + 2*B*a^4*b^2 - (A - C)*a^3*b^3)*d^6)*f*x)*tan(f*x + e)
^2 + ((B*a^3*b^3 - 2*(A - C)*a^2*b^4 - B*a*b^5)*c^6 + (2*C*a^5*b - 3*B*a^4*b^2 + 4*A*a^3*b^3 - B*a^2*b^4 + 2*A
*a*b^5)*c^5*d + 2*(B*a^3*b^3 - 2*(A - C)*a^2*b^4 - B*a*b^5)*c^4*d^2 + 2*(2*C*a^5*b - 3*B*a^4*b^2 + 4*A*a^3*b^3
- B*a^2*b^4 + 2*A*a*b^5)*c^3*d^3 + (B*a^3*b^3 - 2*(A - C)*a^2*b^4 - B*a*b^5)*c^2*d^4 + (2*C*a^5*b - 3*B*a^4*b
^2 + 4*A*a^3*b^3 - B*a^2*b^4 + 2*A*a*b^5)*c*d^5 + ((B*a^2*b^4 - 2*(A - C)*a*b^5 - B*b^6)*c^5*d + (2*C*a^4*b^2
- 3*B*a^3*b^3 + 4*A*a^2*b^4 - B*a*b^5 + 2*A*b^6)*c^4*d^2 + 2*(B*a^2*b^4 - 2*(A - C)*a*b^5 - B*b^6)*c^3*d^3 + 2
*(2*C*a^4*b^2 - 3*B*a^3*b^3 + 4*A*a^2*b^4 - B*a*b^5 + 2*A*b^6)*c^2*d^4 + (B*a^2*b^4 - 2*(A - C)*a*b^5 - B*b^6)
*c*d^5 + (2*C*a^4*b^2 - 3*B*a^3*b^3 + 4*A*a^2*b^4 - B*a*b^5 + 2*A*b^6)*d^6)*tan(f*x + e)^2 + ((B*a^2*b^4 - 2*(
A - C)*a*b^5 - B*b^6)*c^6 + 2*(C*a^4*b^2 - B*a^3*b^3 + (A + C)*a^2*b^4 - B*a*b^5 + A*b^6)*c^5*d + (2*C*a^5*b -
3*B*a^4*b^2 + 4*A*a^3*b^3 + B*a^2*b^4 - 2*(A - 2*C)*a*b^5 - 2*B*b^6)*c^4*d^2 + 4*(C*a^4*b^2 - B*a^3*b^3 + (A
+ C)*a^2*b^4 - B*a*b^5 + A*b^6)*c^3*d^3 + (4*C*a^5*b - 6*B*a^4*b^2 + 8*A*a^3*b^3 - B*a^2*b^4 + 2*(A + C)*a*b^5
- B*b^6)*c^2*d^4 + 2*(C*a^4*b^2 - B*a^3*b^3 + (A + C)*a^2*b^4 - B*a*b^5 + A*b^6)*c*d^5 + (2*C*a^5*b - 3*B*a^4
*b^2 + 4*A*a^3*b^3 - B*a^2*b^4 + 2*A*a*b^5)*d^6)*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)) - (2*(C*a^5*b + 2*C*a^3*b^3 + C*a*b^5)*c^5*d - 3*(B*a^5*b + 2*B*a^3*b^3 + B*a*b^5)*
c^4*d^2 + (B*a^6 + 4*A*a^5*b + 2*B*a^4*b^2 + 8*A*a^3*b^3 + B*a^2*b^4 + 4*A*a*b^5)*c^3*d^3 - (2*(A - C)*a^6 + B
*a^5*b + 4*(A - C)*a^4*b^2 + 2*B*a^3*b^3 + 2*(A - C)*a^2*b^4 + B*a*b^5)*c^2*d^4 - (B*a^6 - 2*A*a^5*b + 2*B*a^4
*b^2 - 4*A*a^3*b^3 + B*a^2*b^4 - 2*A*a*b^5)*c*d^5 + (2*(C*a^4*b^2 + 2*C*a^2*b^4 + C*b^6)*c^4*d^2 - 3*(B*a^4*b^
2 + 2*B*a^2*b^4 + B*b^6)*c^3*d^3 + (B*a^5*b + 4*A*a^4*b^2 + 2*B*a^3*b^3 + 8*A*a^2*b^4 + B*a*b^5 + 4*A*b^6)*c^2
*d^4 - (2*(A - C)*a^5*b + B*a^4*b^2 + 4*(A - C)*a^3*b^3 + 2*B*a^2*b^4 + 2*(A - C)*a*b^5 + B*b^6)*c*d^5 - (B*a^
5*b - 2*A*a^4*b^2 + 2*B*a^3*b^3 - 4*A*a^2*b^4 + B*a*b^5 - 2*A*b^6)*d^6)*tan(f*x + e)^2 + (2*(C*a^4*b^2 + 2*C*a
^2*b^4 + C*b^6)*c^5*d + (2*C*a^5*b - 3*B*a^4*b^2 + 4*C*a^3*b^3 - 6*B*a^2*b^4 + 2*C*a*b^5 - 3*B*b^6)*c^4*d^2 -
2*(B*a^5*b - 2*A*a^4*b^2 + 2*B*a^3*b^3 - 4*A*a^2*b^4 + B*a*b^5 - 2*A*b^6)*c^3*d^3 + (B*a^6 + 2*(A + C)*a^5*b +
B*a^4*b^2 + 4*(A + C)*a^3*b^3 - B*a^2*b^4 + 2*(A + C)*a*b^5 - B*b^6)*c^2*d^4 - 2*((A - C)*a^6 + B*a^5*b + (A
- 2*C)*a^4*b^2 + 2*B*a^3*b^3 - (A + C)*a^2*b^4 + B*a*b^5 - A*b^6)*c*d^5 - (B*a^6 - 2*A*a^5*b + 2*B*a^4*b^2 - 4
*A*a^3*b^3 + B*a^2*b^4 - 2*A*a*b^5)*d^6)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(ta
n(f*x + e)^2 + 1)) - 2*((C*a^3*b^3 - B*a^2*b^4 + A*a*b^5)*c^6 - (C*a^4*b^2 - B*a^3*b^3 + (A + C)*a^2*b^4 - B*a
*b^5 + A*b^6)*c^5*d + (C*a^5*b + 5*C*a^3*b^3 - 3*B*a^2*b^4 + (3*A + C)*a*b^5)*c^4*d^2 - (C*a^6 + B*a^5*b + 5*C
*a^4*b^2 + (2*A + 5*C)*a^2*b^4 - B*a*b^5 + (2*A + C)*b^6)*c^3*d^3 + (B*a^6 + (A + C)*a^5*b + 3*B*a^4*b^2 + (2*
A + 5*C)*a^3*b^3 + (4*A + C)*a*b^5 + B*b^6)*c^2*d^4 - (A*a^6 + B*a^5*b + (3*A + C)*a^4*b^2 + B*a^3*b^3 + (4*A
+ C)*a^2*b^4 + 2*A*b^6)*c*d^5 + (A*a^5*b + (2*A + C)*a^3*b^3 - B*a^2*b^4 + 2*A*a*b^5)*d^6 + (((A - C)*a^2*b^4
+ 2*B*a*b^5 - (A - C)*b^6)*c^6 - 2*((A - C)*a^3*b^3 + B*a^2*b^4 + (A - C)*a*b^5 + B*b^6)*c^5*d - (4*B*a^3*b^3
- 7*(A - C)*a^2*b^4 - 2*B*a*b^5 - (A - C)*b^6)*c^4*d^2 + 2*((A - C)*a^5*b + 2*B*a^4*b^2 + 2*B*a^2*b^4 - (A - C
)*a*b^5)*c^3*d^3 - ((A - C)*a^6 - 2*B*a^5*b + 7*(A - C)*a^4*b^2 + 4*B*a^3*b^3)*c^2*d^4 - 2*(B*a^6 - (A - C)*a^
5*b + B*a^4*b^2 - (A - C)*a^3*b^3)*c*d^5 + ((A - C)*a^6 + 2*B*a^5*b - (A - C)*a^4*b^2)*d^6)*f*x)*tan(f*x + e))
/(((a^4*b^4 + 2*a^2*b^6 + b^8)*c^7*d - 3*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*c^6*d^2 + (3*a^6*b^2 + 8*a^4*b^4 + 7*a^
2*b^6 + 2*b^8)*c^5*d^3 - (a^7*b + 8*a^5*b^3 + 13*a^3*b^5 + 6*a*b^7)*c^4*d^4 + (6*a^6*b^2 + 13*a^4*b^4 + 8*a^2*
b^6 + b^8)*c^3*d^5 - (2*a^7*b + 7*a^5*b^3 + 8*a^3*b^5 + 3*a*b^7)*c^2*d^6 + 3*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c
*d^7 - (a^7*b + 2*a^5*b^3 + a^3*b^5)*d^8)*f*tan(f*x + e)^2 + ((a^4*b^4 + 2*a^2*b^6 + b^8)*c^8 - 2*(a^5*b^3 + 2
*a^3*b^5 + a*b^7)*c^7*d + 2*(a^4*b^4 + 2*a^2*b^6 + b^8)*c^6*d^2 + 2*(a^7*b - 3*a^3*b^5 - 2*a*b^7)*c^5*d^3 - (a
^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*c^4*d^4 + 2*(2*a^7*b + 3*a^5*b^3 - a*b^7)*c^3*d^5 - 2*(a^8 + 2*a^6*b^2 + a^4
*b^4)*c^2*d^6 + 2*(a^7*b + 2*a^5*b^3 + a^3*b^5)*c*d^7 - (a^8 + 2*a^6*b^2 + a^4*b^4)*d^8)*f*tan(f*x + e) + ((a^
5*b^3 + 2*a^3*b^5 + a*b^7)*c^8 - 3*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^7*d + (3*a^7*b + 8*a^5*b^3 + 7*a^3*b^5 +
2*a*b^7)*c^6*d^2 - (a^8 + 8*a^6*b^2 + 13*a^4*b^4 + 6*a^2*b^6)*c^5*d^3 + (6*a^7*b + 13*a^5*b^3 + 8*a^3*b^5 + a*
b^7)*c^4*d^4 - (2*a^8 + 7*a^6*b^2 + 8*a^4*b^4 + 3*a^2*b^6)*c^3*d^5 + 3*(a^7*b + 2*a^5*b^3 + a^3*b^5)*c^2*d^6 -
(a^8 + 2*a^6*b^2 + a^4*b^4)*c*d^7)*f)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^2} \, dx=\text {Exception raised: NotImplementedError} \]

[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))**2,x)

[Out]

Exception raised: NotImplementedError >> no valid subset found

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1185 vs. \(2 (512) = 1024\).

Time = 0.41 (sec) , antiderivative size = 1185, normalized size of antiderivative = 2.33 \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^2} \, dx=\text {Too large to display} \]

[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))^2,x, algorithm="maxima")

[Out]

1/2*(2*(((A - C)*a^2 + 2*B*a*b - (A - C)*b^2)*c^2 + 2*(B*a^2 - 2*(A - C)*a*b - B*b^2)*c*d - ((A - C)*a^2 + 2*B
*a*b - (A - C)*b^2)*d^2)*(f*x + e)/((a^4 + 2*a^2*b^2 + b^4)*c^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*c^2*d^2 + (a^4 + 2
*a^2*b^2 + b^4)*d^4) - 2*((B*a^2*b^3 - 2*(A - C)*a*b^4 - B*b^5)*c + (2*C*a^4*b - 3*B*a^3*b^2 + 4*A*a^2*b^3 - B
*a*b^4 + 2*A*b^5)*d)*log(b*tan(f*x + e) + a)/((a^4*b^3 + 2*a^2*b^5 + b^7)*c^3 - 3*(a^5*b^2 + 2*a^3*b^4 + a*b^6
)*c^2*d + 3*(a^6*b + 2*a^4*b^3 + a^2*b^5)*c*d^2 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d^3) + 2*(2*C*b*c^4*d - 3*B*b*c^
3*d^2 + (B*a + 4*A*b)*c^2*d^3 - (2*(A - C)*a + B*b)*c*d^4 - (B*a - 2*A*b)*d^5)*log(d*tan(f*x + e) + c)/(b^3*c^
7 - 3*a*b^2*c^6*d + 3*a^2*b*c*d^6 - a^3*d^7 + (3*a^2*b + 2*b^3)*c^5*d^2 - (a^3 + 6*a*b^2)*c^4*d^3 + (6*a^2*b +
b^3)*c^3*d^4 - (2*a^3 + 3*a*b^2)*c^2*d^5) + ((B*a^2 - 2*(A - C)*a*b - B*b^2)*c^2 - 2*((A - C)*a^2 + 2*B*a*b -
(A - C)*b^2)*c*d - (B*a^2 - 2*(A - C)*a*b - B*b^2)*d^2)*log(tan(f*x + e)^2 + 1)/((a^4 + 2*a^2*b^2 + b^4)*c^4
+ 2*(a^4 + 2*a^2*b^2 + b^4)*c^2*d^2 + (a^4 + 2*a^2*b^2 + b^4)*d^4) - 2*((C*a^2*b - B*a*b^2 + A*b^3)*c^3 + (C*a
^3 + C*a*b^2)*c^2*d - (B*a^3 - C*a^2*b + 2*B*a*b^2 - A*b^3)*c*d^2 + (A*a^3 + A*a*b^2)*d^3 + ((2*C*a^2*b - B*a*
b^2 + (A + C)*b^3)*c^2*d - (B*a^2*b + B*b^3)*c*d^2 + ((A + C)*a^2*b - B*a*b^2 + 2*A*b^3)*d^3)*tan(f*x + e))/((
a^3*b^2 + a*b^4)*c^5 - 2*(a^4*b + a^2*b^3)*c^4*d + (a^5 + 2*a^3*b^2 + a*b^4)*c^3*d^2 - 2*(a^4*b + a^2*b^3)*c^2
*d^3 + (a^5 + a^3*b^2)*c*d^4 + ((a^2*b^3 + b^5)*c^4*d - 2*(a^3*b^2 + a*b^4)*c^3*d^2 + (a^4*b + 2*a^2*b^3 + b^5
)*c^2*d^3 - 2*(a^3*b^2 + a*b^4)*c*d^4 + (a^4*b + a^2*b^3)*d^5)*tan(f*x + e)^2 + ((a^2*b^3 + b^5)*c^5 - (a^3*b^
2 + a*b^4)*c^4*d - (a^4*b - b^5)*c^3*d^2 + (a^5 - a*b^4)*c^2*d^3 - (a^4*b + a^2*b^3)*c*d^4 + (a^5 + a^3*b^2)*d
^5)*tan(f*x + e)))/f

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 2823 vs. \(2 (512) = 1024\).

Time = 1.07 (sec) , antiderivative size = 2823, normalized size of antiderivative = 5.55 \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^2} \, dx=\text {Too large to display} \]

[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))^2,x, algorithm="giac")

[Out]

1/2*(2*(A*a^2*c^2 - C*a^2*c^2 + 2*B*a*b*c^2 - A*b^2*c^2 + C*b^2*c^2 + 2*B*a^2*c*d - 4*A*a*b*c*d + 4*C*a*b*c*d
- 2*B*b^2*c*d - A*a^2*d^2 + C*a^2*d^2 - 2*B*a*b*d^2 + A*b^2*d^2 - C*b^2*d^2)*(f*x + e)/(a^4*c^4 + 2*a^2*b^2*c^
4 + b^4*c^4 + 2*a^4*c^2*d^2 + 4*a^2*b^2*c^2*d^2 + 2*b^4*c^2*d^2 + a^4*d^4 + 2*a^2*b^2*d^4 + b^4*d^4) + (B*a^2*
c^2 - 2*A*a*b*c^2 + 2*C*a*b*c^2 - B*b^2*c^2 - 2*A*a^2*c*d + 2*C*a^2*c*d - 4*B*a*b*c*d + 2*A*b^2*c*d - 2*C*b^2*
c*d - B*a^2*d^2 + 2*A*a*b*d^2 - 2*C*a*b*d^2 + B*b^2*d^2)*log(tan(f*x + e)^2 + 1)/(a^4*c^4 + 2*a^2*b^2*c^4 + b^
4*c^4 + 2*a^4*c^2*d^2 + 4*a^2*b^2*c^2*d^2 + 2*b^4*c^2*d^2 + a^4*d^4 + 2*a^2*b^2*d^4 + b^4*d^4) - 2*(B*a^2*b^4*
c - 2*A*a*b^5*c + 2*C*a*b^5*c - B*b^6*c + 2*C*a^4*b^2*d - 3*B*a^3*b^3*d + 4*A*a^2*b^4*d - B*a*b^5*d + 2*A*b^6*
d)*log(abs(b*tan(f*x + e) + a))/(a^4*b^4*c^3 + 2*a^2*b^6*c^3 + b^8*c^3 - 3*a^5*b^3*c^2*d - 6*a^3*b^5*c^2*d - 3
*a*b^7*c^2*d + 3*a^6*b^2*c*d^2 + 6*a^4*b^4*c*d^2 + 3*a^2*b^6*c*d^2 - a^7*b*d^3 - 2*a^5*b^3*d^3 - a^3*b^5*d^3)
+ 2*(2*C*b*c^4*d^2 - 3*B*b*c^3*d^3 + B*a*c^2*d^4 + 4*A*b*c^2*d^4 - 2*A*a*c*d^5 + 2*C*a*c*d^5 - B*b*c*d^5 - B*a
*d^6 + 2*A*b*d^6)*log(abs(d*tan(f*x + e) + c))/(b^3*c^7*d - 3*a*b^2*c^6*d^2 + 3*a^2*b*c^5*d^3 + 2*b^3*c^5*d^3
- a^3*c^4*d^4 - 6*a*b^2*c^4*d^4 + 6*a^2*b*c^3*d^5 + b^3*c^3*d^5 - 2*a^3*c^2*d^6 - 3*a*b^2*c^2*d^6 + 3*a^2*b*c*
d^7 - a^3*d^8) + (B*a^2*b^3*c^4*d*tan(f*x + e)^2 - 2*A*a*b^4*c^4*d*tan(f*x + e)^2 + 2*C*a*b^4*c^4*d*tan(f*x +
e)^2 - B*b^5*c^4*d*tan(f*x + e)^2 - 2*B*a^3*b^2*c^3*d^2*tan(f*x + e)^2 + 2*A*a^2*b^3*c^3*d^2*tan(f*x + e)^2 -
2*C*a^2*b^3*c^3*d^2*tan(f*x + e)^2 - 2*B*a*b^4*c^3*d^2*tan(f*x + e)^2 + 2*A*b^5*c^3*d^2*tan(f*x + e)^2 - 2*C*b
^5*c^3*d^2*tan(f*x + e)^2 + B*a^4*b*c^2*d^3*tan(f*x + e)^2 + 2*A*a^3*b^2*c^2*d^3*tan(f*x + e)^2 - 2*C*a^3*b^2*
c^2*d^3*tan(f*x + e)^2 + 6*B*a^2*b^3*c^2*d^3*tan(f*x + e)^2 - 2*A*a*b^4*c^2*d^3*tan(f*x + e)^2 + 2*C*a*b^4*c^2
*d^3*tan(f*x + e)^2 + B*b^5*c^2*d^3*tan(f*x + e)^2 - 2*A*a^4*b*c*d^4*tan(f*x + e)^2 + 2*C*a^4*b*c*d^4*tan(f*x
+ e)^2 - 2*B*a^3*b^2*c*d^4*tan(f*x + e)^2 - 2*A*a^2*b^3*c*d^4*tan(f*x + e)^2 + 2*C*a^2*b^3*c*d^4*tan(f*x + e)^
2 - 2*B*a*b^4*c*d^4*tan(f*x + e)^2 - B*a^4*b*d^5*tan(f*x + e)^2 + 2*A*a^3*b^2*d^5*tan(f*x + e)^2 - 2*C*a^3*b^2
*d^5*tan(f*x + e)^2 + B*a^2*b^3*d^5*tan(f*x + e)^2 + B*a^2*b^3*c^5*tan(f*x + e) - 2*A*a*b^4*c^5*tan(f*x + e) +
2*C*a*b^4*c^5*tan(f*x + e) - B*b^5*c^5*tan(f*x + e) - 4*C*a^4*b*c^4*d*tan(f*x + e) + B*a^3*b^2*c^4*d*tan(f*x
+ e) - 2*A*a^2*b^3*c^4*d*tan(f*x + e) - 6*C*a^2*b^3*c^4*d*tan(f*x + e) - B*a*b^4*c^4*d*tan(f*x + e) - 4*C*b^5*
c^4*d*tan(f*x + e) + B*a^4*b*c^3*d^2*tan(f*x + e) + 4*A*a^3*b^2*c^3*d^2*tan(f*x + e) - 4*C*a^3*b^2*c^3*d^2*tan
(f*x + e) + 8*B*a^2*b^3*c^3*d^2*tan(f*x + e) + 3*B*b^5*c^3*d^2*tan(f*x + e) + B*a^5*c^2*d^3*tan(f*x + e) - 2*A
*a^4*b*c^2*d^3*tan(f*x + e) - 6*C*a^4*b*c^2*d^3*tan(f*x + e) + 8*B*a^3*b^2*c^2*d^3*tan(f*x + e) - 12*A*a^2*b^3
*c^2*d^3*tan(f*x + e) - 4*C*a^2*b^3*c^2*d^3*tan(f*x + e) + 3*B*a*b^4*c^2*d^3*tan(f*x + e) - 6*A*b^5*c^2*d^3*ta
n(f*x + e) - 2*C*b^5*c^2*d^3*tan(f*x + e) - 2*A*a^5*c*d^4*tan(f*x + e) + 2*C*a^5*c*d^4*tan(f*x + e) - B*a^4*b*
c*d^4*tan(f*x + e) + 3*B*a^2*b^3*c*d^4*tan(f*x + e) + 2*B*b^5*c*d^4*tan(f*x + e) - B*a^5*d^5*tan(f*x + e) - 4*
C*a^4*b*d^5*tan(f*x + e) + 3*B*a^3*b^2*d^5*tan(f*x + e) - 6*A*a^2*b^3*d^5*tan(f*x + e) - 2*C*a^2*b^3*d^5*tan(f
*x + e) + 2*B*a*b^4*d^5*tan(f*x + e) - 4*A*b^5*d^5*tan(f*x + e) - 2*C*a^4*b*c^5 + 3*B*a^3*b^2*c^5 - 4*A*a^2*b^
3*c^5 + B*a*b^4*c^5 - 2*A*b^5*c^5 - 2*C*a^5*c^4*d - 2*B*a^4*b*c^4*d + 2*A*a^3*b^2*c^4*d - 6*C*a^3*b^2*c^4*d -
2*B*a^2*b^3*c^4*d + 2*A*a*b^4*c^4*d - 4*C*a*b^4*c^4*d + 3*B*a^5*c^3*d^2 + 2*A*a^4*b*c^3*d^2 - 6*C*a^4*b*c^3*d^
2 + 14*B*a^3*b^2*c^3*d^2 - 6*A*a^2*b^3*c^3*d^2 - 2*C*a^2*b^3*c^3*d^2 + 7*B*a*b^4*c^3*d^2 - 4*A*b^5*c^3*d^2 - 4
*A*a^5*c^2*d^3 - 2*B*a^4*b*c^2*d^3 - 6*A*a^3*b^2*c^2*d^3 - 2*C*a^3*b^2*c^2*d^3 - 2*B*a^2*b^3*c^2*d^3 - 2*A*a*b
^4*c^2*d^3 - 2*C*a*b^4*c^2*d^3 + B*a^5*c*d^4 + 2*A*a^4*b*c*d^4 - 4*C*a^4*b*c*d^4 + 7*B*a^3*b^2*c*d^4 - 2*A*a^2
*b^3*c*d^4 - 2*C*a^2*b^3*c*d^4 + 4*B*a*b^4*c*d^4 - 2*A*b^5*c*d^4 - 2*A*a^5*d^5 - 4*A*a^3*b^2*d^5 - 2*A*a*b^4*d
^5)/((a^4*b^2*c^6 + 2*a^2*b^4*c^6 + b^6*c^6 - 2*a^5*b*c^5*d - 4*a^3*b^3*c^5*d - 2*a*b^5*c^5*d + a^6*c^4*d^2 +
4*a^4*b^2*c^4*d^2 + 5*a^2*b^4*c^4*d^2 + 2*b^6*c^4*d^2 - 4*a^5*b*c^3*d^3 - 8*a^3*b^3*c^3*d^3 - 4*a*b^5*c^3*d^3
+ 2*a^6*c^2*d^4 + 5*a^4*b^2*c^2*d^4 + 4*a^2*b^4*c^2*d^4 + b^6*c^2*d^4 - 2*a^5*b*c*d^5 - 4*a^3*b^3*c*d^5 - 2*a*
b^5*c*d^5 + a^6*d^6 + 2*a^4*b^2*d^6 + a^2*b^4*d^6)*(b*d*tan(f*x + e)^2 + b*c*tan(f*x + e) + a*d*tan(f*x + e) +
a*c)))/f

Mupad [B] (verification not implemented)

Time = 25.22 (sec) , antiderivative size = 73684, normalized size of antiderivative = 144.76 \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^2} \, dx=\text {Too large to display} \]

[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))^2),x)

[Out]

(symsum(log((tan(e + f*x)*(4*A^3*a^3*b^4*d^7 + B^3*a^2*b^5*d^7 + 4*A^3*b^7*c^3*d^4 + 2*C^3*a^5*b^2*d^7 + B^3*b
^7*c^2*d^5 + 2*C^3*b^7*c^5*d^2 + 4*A^2*B*b^7*d^7 - 4*B^3*a^2*b^5*c^2*d^5 - 3*B^3*a^2*b^5*c^4*d^3 + 10*B^3*a^3*
b^4*c^3*d^4 - 3*B^3*a^4*b^3*c^2*d^5 - 4*A*B^2*a*b^6*d^7 - 4*A*B^2*b^7*c*d^6 + 2*B^3*a*b^6*c*d^6 - 6*A*B^2*a^3*
b^4*d^7 + 8*A^2*B*a^2*b^5*d^7 - 3*A^2*B*a^4*b^3*d^7 + 4*A*C^2*a^3*b^4*d^7 - 4*A*C^2*a^5*b^2*d^7 - 8*A^2*C*a^3*
b^4*d^7 + 2*A^2*C*a^5*b^2*d^7 - 6*A*B^2*b^7*c^3*d^4 - 3*B*C^2*a^4*b^3*d^7 + 8*A^2*B*b^7*c^2*d^5 - 3*A^2*B*b^7*
c^4*d^3 + 4*A*C^2*b^7*c^3*d^4 - 4*A*C^2*b^7*c^5*d^2 - 8*A^2*C*b^7*c^3*d^4 + 2*A^2*C*b^7*c^5*d^2 - 3*B*C^2*b^7*
c^4*d^3 - 4*A^3*a*b^6*c^2*d^5 - 4*A^3*a^2*b^5*c*d^6 + 6*B^3*a*b^6*c^3*d^4 + 6*B^3*a^3*b^4*c*d^6 - 2*C^3*a*b^6*
c^4*d^3 - 2*C^3*a^4*b^3*c*d^6 - 10*A*B^2*a^2*b^5*c^3*d^4 - 10*A*B^2*a^3*b^4*c^2*d^5 + 18*A^2*B*a^2*b^5*c^2*d^5
+ 2*B*C^2*a^2*b^5*c^2*d^5 + 4*B*C^2*a^4*b^3*c^4*d^3 + 2*B^2*C*a^2*b^5*c^3*d^4 + 2*B^2*C*a^2*b^5*c^5*d^2 + 2*B
^2*C*a^3*b^4*c^2*d^5 - 6*B^2*C*a^3*b^4*c^4*d^3 - 6*B^2*C*a^4*b^3*c^3*d^4 + 2*B^2*C*a^5*b^2*c^2*d^5 + 10*A*B*C*
a^4*b^3*d^7 + 10*A*B*C*b^7*c^4*d^3 - 8*A^2*B*a*b^6*c*d^6 - 2*A*B^2*a*b^6*c^2*d^5 + 6*A*B^2*a*b^6*c^4*d^3 - 2*A
*B^2*a^2*b^5*c*d^6 + 6*A*B^2*a^4*b^3*c*d^6 - 4*A^2*B*a*b^6*c^3*d^4 - 4*A^2*B*a^3*b^4*c*d^6 - 4*A*C^2*a*b^6*c^2
*d^5 + 4*A*C^2*a*b^6*c^4*d^3 - 4*A*C^2*a^2*b^5*c*d^6 + 4*A*C^2*a^4*b^3*c*d^6 + 8*A^2*C*a*b^6*c^2*d^5 - 2*A^2*C
*a*b^6*c^4*d^3 + 8*A^2*C*a^2*b^5*c*d^6 - 2*A^2*C*a^4*b^3*c*d^6 + 4*B*C^2*a*b^6*c^3*d^4 + 4*B*C^2*a*b^6*c^5*d^2
+ 4*B*C^2*a^3*b^4*c*d^6 + 4*B*C^2*a^5*b^2*c*d^6 - 4*B^2*C*a*b^6*c^2*d^5 - 10*B^2*C*a*b^6*c^4*d^3 - 4*B^2*C*a^
2*b^5*c*d^6 - 10*B^2*C*a^4*b^3*c*d^6 - 4*A*B*C*a^2*b^5*c^2*d^5 + 8*A*B*C*a^2*b^5*c^4*d^3 + 8*A*B*C*a^4*b^3*c^2
*d^5 + 8*A*B*C*a*b^6*c*d^6 - 4*A*B*C*a*b^6*c^5*d^2 - 4*A*B*C*a^5*b^2*c*d^6))/(a^8*d^8 + b^8*c^8 + 2*a^2*b^6*c^
8 + a^4*b^4*c^8 + a^4*b^4*d^8 + 2*a^6*b^2*d^8 + 2*a^8*c^2*d^6 + a^8*c^4*d^4 + b^8*c^4*d^4 + 2*b^8*c^6*d^2 - 4*
a*b^7*c^3*d^5 - 8*a*b^7*c^5*d^3 - 4*a^3*b^5*c*d^7 - 8*a^3*b^5*c^7*d - 8*a^5*b^3*c*d^7 - 4*a^5*b^3*c^7*d - 8*a^
7*b*c^3*d^5 - 4*a^7*b*c^5*d^3 + 6*a^2*b^6*c^2*d^6 + 14*a^2*b^6*c^4*d^4 + 10*a^2*b^6*c^6*d^2 - 16*a^3*b^5*c^3*d
^5 - 20*a^3*b^5*c^5*d^3 + 14*a^4*b^4*c^2*d^6 + 26*a^4*b^4*c^4*d^4 + 14*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^3*d^5 -
16*a^5*b^3*c^5*d^3 + 10*a^6*b^2*c^2*d^6 + 14*a^6*b^2*c^4*d^4 + 6*a^6*b^2*c^6*d^2 - 4*a*b^7*c^7*d - 4*a^7*b*c*d
^7) - (4*A^2*C*b^7*d^7 - 6*A^3*a^2*b^5*d^7 - B^3*a^3*b^4*d^7 - 6*A^3*b^7*c^2*d^5 - B^3*b^7*c^3*d^4 - 4*A^3*b^7
*d^7 - 8*A^3*a^2*b^5*c^2*d^5 - 3*B^3*a^2*b^5*c^3*d^4 - 3*B^3*a^3*b^4*c^2*d^5 + 2*C^3*a^2*b^5*c^4*d^3 + 2*C^3*a
^4*b^3*c^2*d^5 + 4*C^3*a^4*b^3*c^4*d^3 + 4*A^2*B*a*b^6*d^7 + 4*A^2*B*b^7*c*d^6 + 4*A^3*a*b^6*c*d^6 + A*B^2*a^2
*b^5*d^7 - 3*A*B^2*a^4*b^3*d^7 + 9*A^2*B*a^3*b^4*d^7 + 2*A*C^2*a^2*b^5*d^7 + 4*A*C^2*a^4*b^3*d^7 + 4*A^2*C*a^2
*b^5*d^7 - 4*A^2*C*a^4*b^3*d^7 + A*B^2*b^7*c^2*d^5 - 3*A*B^2*b^7*c^4*d^3 - B*C^2*a^3*b^4*d^7 - 2*B*C^2*a^5*b^2
*d^7 + 9*A^2*B*b^7*c^3*d^4 + B^2*C*a^2*b^5*d^7 + 3*B^2*C*a^4*b^3*d^7 + 2*A*C^2*b^7*c^2*d^5 + 4*A*C^2*b^7*c^4*d
^3 + 4*A^2*C*b^7*c^2*d^5 - 4*A^2*C*b^7*c^4*d^3 - B*C^2*b^7*c^3*d^4 - 2*B*C^2*b^7*c^5*d^2 + B^2*C*b^7*c^2*d^5 +
3*B^2*C*b^7*c^4*d^3 + 2*A^3*a*b^6*c^3*d^4 + 2*A^3*a^3*b^4*c*d^6 + B^3*a*b^6*c^2*d^5 + 3*B^3*a*b^6*c^4*d^3 + B
^3*a^2*b^5*c*d^6 + 3*B^3*a^4*b^3*c*d^6 + 2*C^3*a*b^6*c^3*d^4 + 2*C^3*a*b^6*c^5*d^2 + 2*C^3*a^3*b^4*c*d^6 + 2*C
^3*a^5*b^2*c*d^6 - 4*A*B*C*a*b^6*d^7 - 4*A*B*C*b^7*c*d^6 + 14*A*B^2*a^2*b^5*c^2*d^5 + 3*A*B^2*a^2*b^5*c^4*d^3
- 10*A*B^2*a^3*b^4*c^3*d^4 + 3*A*B^2*a^4*b^3*c^2*d^5 + 7*A^2*B*a^2*b^5*c^3*d^4 + 7*A^2*B*a^3*b^4*c^2*d^5 + 8*A
*C^2*a^2*b^5*c^2*d^5 + 4*A*C^2*a^2*b^5*c^4*d^3 + 4*A*C^2*a^4*b^3*c^2*d^5 - 4*A*C^2*a^4*b^3*c^4*d^3 - 6*A^2*C*a
^2*b^5*c^4*d^3 - 6*A^2*C*a^4*b^3*c^2*d^5 - B*C^2*a^2*b^5*c^3*d^4 + 2*B*C^2*a^2*b^5*c^5*d^2 - B*C^2*a^3*b^4*c^2
*d^5 - 6*B*C^2*a^3*b^4*c^4*d^3 - 6*B*C^2*a^4*b^3*c^3*d^4 + 2*B*C^2*a^5*b^2*c^2*d^5 - 6*B^2*C*a^2*b^5*c^2*d^5 -
B^2*C*a^2*b^5*c^4*d^3 + 10*B^2*C*a^3*b^4*c^3*d^4 - B^2*C*a^4*b^3*c^2*d^5 - 8*A*B*C*a^3*b^4*d^7 + 2*A*B*C*a^5*
b^2*d^7 - 8*A*B*C*b^7*c^3*d^4 + 2*A*B*C*b^7*c^5*d^2 - 6*A*B^2*a*b^6*c*d^6 + 4*A*C^2*a*b^6*c*d^6 - 8*A^2*C*a*b^
6*c*d^6 + 2*B^2*C*a*b^6*c*d^6 - 8*A*B^2*a*b^6*c^3*d^4 - 8*A*B^2*a^3*b^4*c*d^6 - A^2*B*a*b^6*c^2*d^5 - 3*A^2*B*
a*b^6*c^4*d^3 - A^2*B*a^2*b^5*c*d^6 - 3*A^2*B*a^4*b^3*c*d^6 - 2*A*C^2*a*b^6*c^3*d^4 - 4*A*C^2*a*b^6*c^5*d^2 -
2*A*C^2*a^3*b^4*c*d^6 - 4*A*C^2*a^5*b^2*c*d^6 - 2*A^2*C*a*b^6*c^3*d^4 + 2*A^2*C*a*b^6*c^5*d^2 - 2*A^2*C*a^3*b^
4*c*d^6 + 2*A^2*C*a^5*b^2*c*d^6 - 3*B*C^2*a*b^6*c^2*d^5 - 5*B*C^2*a*b^6*c^4*d^3 - 3*B*C^2*a^2*b^5*c*d^6 - 5*B*
C^2*a^4*b^3*c*d^6 + 4*B^2*C*a*b^6*c^3*d^4 - 2*B^2*C*a*b^6*c^5*d^2 + 4*B^2*C*a^3*b^4*c*d^6 - 2*B^2*C*a^5*b^2*c*
d^6 - 6*A*B*C*a^2*b^5*c^3*d^4 - 2*A*B*C*a^2*b^5*c^5*d^2 - 6*A*B*C*a^3*b^4*c^2*d^5 + 6*A*B*C*a^3*b^4*c^4*d^3 +
6*A*B*C*a^4*b^3*c^3*d^4 - 2*A*B*C*a^5*b^2*c^2*d^5 + 4*A*B*C*a*b^6*c^2*d^5 + 8*A*B*C*a*b^6*c^4*d^3 + 4*A*B*C*a^
2*b^5*c*d^6 + 8*A*B*C*a^4*b^3*c*d^6)/(a^8*d^8 + b^8*c^8 + 2*a^2*b^6*c^8 + a^4*b^4*c^8 + a^4*b^4*d^8 + 2*a^6*b^
2*d^8 + 2*a^8*c^2*d^6 + a^8*c^4*d^4 + b^8*c^4*d^4 + 2*b^8*c^6*d^2 - 4*a*b^7*c^3*d^5 - 8*a*b^7*c^5*d^3 - 4*a^3*
b^5*c*d^7 - 8*a^3*b^5*c^7*d - 8*a^5*b^3*c*d^7 - 4*a^5*b^3*c^7*d - 8*a^7*b*c^3*d^5 - 4*a^7*b*c^5*d^3 + 6*a^2*b^
6*c^2*d^6 + 14*a^2*b^6*c^4*d^4 + 10*a^2*b^6*c^6*d^2 - 16*a^3*b^5*c^3*d^5 - 20*a^3*b^5*c^5*d^3 + 14*a^4*b^4*c^2
*d^6 + 26*a^4*b^4*c^4*d^4 + 14*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^3*d^5 - 16*a^5*b^3*c^5*d^3 + 10*a^6*b^2*c^2*d^6
+ 14*a^6*b^2*c^4*d^4 + 6*a^6*b^2*c^6*d^2 - 4*a*b^7*c^7*d - 4*a^7*b*c*d^7) - root(144*a^13*b*c^5*d^9*f^4 + 144*
a^9*b^5*c*d^13*f^4 + 144*a^5*b^9*c^13*d*f^4 + 144*a*b^13*c^9*d^5*f^4 + 96*a^13*b*c^7*d^7*f^4 + 96*a^13*b*c^3*d
^11*f^4 + 96*a^11*b^3*c*d^13*f^4 + 96*a^7*b^7*c^13*d*f^4 + 96*a^7*b^7*c*d^13*f^4 + 96*a^3*b^11*c^13*d*f^4 + 96
*a*b^13*c^11*d^3*f^4 + 96*a*b^13*c^7*d^7*f^4 + 24*a^13*b*c^9*d^5*f^4 + 24*a^9*b^5*c^13*d*f^4 + 24*a^5*b^9*c*d^
13*f^4 + 24*a*b^13*c^5*d^9*f^4 + 24*a^13*b*c*d^13*f^4 + 24*a*b^13*c^13*d*f^4 + 3648*a^7*b^7*c^7*d^7*f^4 - 3188
*a^8*b^6*c^6*d^8*f^4 - 3188*a^6*b^8*c^8*d^6*f^4 - 2912*a^8*b^6*c^8*d^6*f^4 - 2912*a^6*b^8*c^6*d^8*f^4 + 2592*a
^9*b^5*c^7*d^7*f^4 + 2592*a^7*b^7*c^9*d^5*f^4 + 2592*a^7*b^7*c^5*d^9*f^4 + 2592*a^5*b^9*c^7*d^7*f^4 + 2168*a^9
*b^5*c^5*d^9*f^4 + 2168*a^5*b^9*c^9*d^5*f^4 - 1776*a^10*b^4*c^6*d^8*f^4 - 1776*a^8*b^6*c^4*d^10*f^4 - 1776*a^6
*b^8*c^10*d^4*f^4 - 1776*a^4*b^10*c^8*d^6*f^4 + 1568*a^9*b^5*c^9*d^5*f^4 + 1568*a^5*b^9*c^5*d^9*f^4 - 1344*a^1
0*b^4*c^8*d^6*f^4 - 1344*a^8*b^6*c^10*d^4*f^4 - 1344*a^6*b^8*c^4*d^10*f^4 - 1344*a^4*b^10*c^6*d^8*f^4 - 1164*a
^10*b^4*c^4*d^10*f^4 - 1164*a^4*b^10*c^10*d^4*f^4 + 896*a^11*b^3*c^5*d^9*f^4 + 896*a^9*b^5*c^3*d^11*f^4 + 896*
a^5*b^9*c^11*d^3*f^4 + 896*a^3*b^11*c^9*d^5*f^4 + 864*a^11*b^3*c^7*d^7*f^4 + 864*a^7*b^7*c^11*d^3*f^4 + 864*a^
7*b^7*c^3*d^11*f^4 + 864*a^3*b^11*c^7*d^7*f^4 - 480*a^10*b^4*c^10*d^4*f^4 - 480*a^4*b^10*c^4*d^10*f^4 + 464*a^
11*b^3*c^3*d^11*f^4 + 464*a^3*b^11*c^11*d^3*f^4 - 424*a^12*b^2*c^6*d^8*f^4 - 424*a^8*b^6*c^2*d^12*f^4 - 424*a^
6*b^8*c^12*d^2*f^4 - 424*a^2*b^12*c^8*d^6*f^4 + 416*a^11*b^3*c^9*d^5*f^4 + 416*a^9*b^5*c^11*d^3*f^4 + 416*a^5*
b^9*c^3*d^11*f^4 + 416*a^3*b^11*c^5*d^9*f^4 - 336*a^12*b^2*c^4*d^10*f^4 - 336*a^10*b^4*c^2*d^12*f^4 - 336*a^4*
b^10*c^12*d^2*f^4 - 336*a^2*b^12*c^10*d^4*f^4 - 256*a^12*b^2*c^8*d^6*f^4 - 256*a^8*b^6*c^12*d^2*f^4 - 256*a^6*
b^8*c^2*d^12*f^4 - 256*a^2*b^12*c^6*d^8*f^4 - 124*a^12*b^2*c^2*d^12*f^4 - 124*a^2*b^12*c^12*d^2*f^4 + 80*a^11*
b^3*c^11*d^3*f^4 + 80*a^3*b^11*c^3*d^11*f^4 - 60*a^12*b^2*c^10*d^4*f^4 - 60*a^10*b^4*c^12*d^2*f^4 - 60*a^4*b^1
0*c^2*d^12*f^4 - 60*a^2*b^12*c^4*d^10*f^4 - 24*b^14*c^10*d^4*f^4 - 16*b^14*c^12*d^2*f^4 - 16*b^14*c^8*d^6*f^4
- 4*b^14*c^6*d^8*f^4 - 24*a^14*c^4*d^10*f^4 - 16*a^14*c^6*d^8*f^4 - 16*a^14*c^2*d^12*f^4 - 4*a^14*c^8*d^6*f^4
- 24*a^10*b^4*d^14*f^4 - 16*a^12*b^2*d^14*f^4 - 16*a^8*b^6*d^14*f^4 - 4*a^6*b^8*d^14*f^4 - 24*a^4*b^10*c^14*f^
4 - 16*a^6*b^8*c^14*f^4 - 16*a^2*b^12*c^14*f^4 - 4*a^8*b^6*c^14*f^4 - 4*b^14*c^14*f^4 - 4*a^14*d^14*f^4 + 36*A
*C*a^9*b*c*d^9*f^2 + 36*A*C*a*b^9*c^9*d*f^2 + 32*A*C*a*b^9*c*d^9*f^2 - 552*B*C*a^7*b^3*c^4*d^6*f^2 - 552*B*C*a
^4*b^6*c^7*d^3*f^2 - 408*B*C*a^5*b^5*c^4*d^6*f^2 - 408*B*C*a^4*b^6*c^5*d^5*f^2 + 360*B*C*a^6*b^4*c^3*d^7*f^2 +
360*B*C*a^3*b^7*c^6*d^4*f^2 - 248*B*C*a^7*b^3*c^2*d^8*f^2 - 248*B*C*a^2*b^8*c^7*d^3*f^2 + 184*B*C*a^6*b^4*c^5
*d^5*f^2 + 184*B*C*a^5*b^5*c^6*d^4*f^2 + 152*B*C*a^8*b^2*c^3*d^7*f^2 - 152*B*C*a^5*b^5*c^2*d^8*f^2 + 152*B*C*a
^3*b^7*c^8*d^2*f^2 - 152*B*C*a^2*b^8*c^5*d^5*f^2 - 104*B*C*a^7*b^3*c^6*d^4*f^2 - 104*B*C*a^6*b^4*c^7*d^3*f^2 +
64*B*C*a^8*b^2*c^5*d^5*f^2 + 64*B*C*a^5*b^5*c^8*d^2*f^2 - 56*B*C*a^4*b^6*c^3*d^7*f^2 - 56*B*C*a^3*b^7*c^4*d^6
*f^2 - 24*B*C*a^8*b^2*c^7*d^3*f^2 - 24*B*C*a^7*b^3*c^8*d^2*f^2 - 24*B*C*a^3*b^7*c^2*d^8*f^2 - 24*B*C*a^2*b^8*c
^3*d^7*f^2 - 696*A*C*a^5*b^5*c^5*d^5*f^2 + 536*A*C*a^6*b^4*c^6*d^4*f^2 + 536*A*C*a^6*b^4*c^4*d^6*f^2 + 536*A*C
*a^4*b^6*c^6*d^4*f^2 + 472*A*C*a^4*b^6*c^4*d^6*f^2 - 232*A*C*a^7*b^3*c^5*d^5*f^2 - 232*A*C*a^5*b^5*c^7*d^3*f^2
+ 216*A*C*a^3*b^7*c^3*d^7*f^2 + 168*A*C*a^7*b^3*c^3*d^7*f^2 + 168*A*C*a^3*b^7*c^7*d^3*f^2 - 154*A*C*a^8*b^2*c
^2*d^8*f^2 - 154*A*C*a^2*b^8*c^8*d^2*f^2 + 62*A*C*a^8*b^2*c^6*d^4*f^2 + 62*A*C*a^6*b^4*c^8*d^2*f^2 - 40*A*C*a^
7*b^3*c^7*d^3*f^2 - 40*A*C*a^5*b^5*c^3*d^7*f^2 - 40*A*C*a^3*b^7*c^5*d^5*f^2 + 32*A*C*a^6*b^4*c^2*d^8*f^2 + 32*
A*C*a^2*b^8*c^6*d^4*f^2 - 32*A*C*a^2*b^8*c^2*d^8*f^2 + 30*A*C*a^4*b^6*c^2*d^8*f^2 + 30*A*C*a^2*b^8*c^4*d^6*f^2
+ 16*A*C*a^8*b^2*c^4*d^6*f^2 + 16*A*C*a^4*b^6*c^8*d^2*f^2 - 488*A*B*a^6*b^4*c^3*d^7*f^2 - 488*A*B*a^3*b^7*c^6
*d^4*f^2 + 440*A*B*a^7*b^3*c^4*d^6*f^2 + 440*A*B*a^4*b^6*c^7*d^3*f^2 - 360*A*B*a^6*b^4*c^5*d^5*f^2 - 360*A*B*a
^5*b^5*c^6*d^4*f^2 - 192*A*B*a^8*b^2*c^3*d^7*f^2 - 192*A*B*a^3*b^7*c^8*d^2*f^2 - 168*A*B*a^3*b^7*c^2*d^8*f^2 -
168*A*B*a^2*b^8*c^3*d^7*f^2 - 152*A*B*a^4*b^6*c^3*d^7*f^2 - 152*A*B*a^3*b^7*c^4*d^6*f^2 - 120*A*B*a^8*b^2*c^5
*d^5*f^2 + 120*A*B*a^7*b^3*c^2*d^8*f^2 - 120*A*B*a^5*b^5*c^8*d^2*f^2 + 120*A*B*a^5*b^5*c^4*d^6*f^2 - 120*A*B*a
^5*b^5*c^2*d^8*f^2 + 120*A*B*a^4*b^6*c^5*d^5*f^2 + 120*A*B*a^2*b^8*c^7*d^3*f^2 - 120*A*B*a^2*b^8*c^5*d^5*f^2 +
40*A*B*a^7*b^3*c^6*d^4*f^2 + 40*A*B*a^6*b^4*c^7*d^3*f^2 - 72*B*C*a^9*b*c^4*d^6*f^2 - 72*B*C*a^4*b^6*c^9*d*f^2
- 64*B*C*a^4*b^6*c*d^9*f^2 - 64*B*C*a*b^9*c^4*d^6*f^2 - 32*B*C*a^8*b^2*c*d^9*f^2 - 32*B*C*a*b^9*c^8*d^2*f^2 -
16*B*C*a^2*b^8*c*d^9*f^2 - 16*B*C*a*b^9*c^2*d^8*f^2 + 8*B*C*a^9*b*c^6*d^4*f^2 - 8*B*C*a^9*b*c^2*d^8*f^2 + 8*B
*C*a^6*b^4*c^9*d*f^2 - 8*B*C*a^2*b^8*c^9*d*f^2 + 104*A*C*a^7*b^3*c*d^9*f^2 + 104*A*C*a*b^9*c^7*d^3*f^2 + 96*A*
C*a^3*b^7*c*d^9*f^2 + 96*A*C*a*b^9*c^3*d^7*f^2 + 72*A*C*a^9*b*c^3*d^7*f^2 + 72*A*C*a^3*b^7*c^9*d*f^2 + 68*A*C*
a^5*b^5*c*d^9*f^2 + 68*A*C*a*b^9*c^5*d^5*f^2 - 28*A*C*a^9*b*c^5*d^5*f^2 - 28*A*C*a^5*b^5*c^9*d*f^2 + 80*A*B*a^
9*b*c^4*d^6*f^2 + 80*A*B*a^4*b^6*c^9*d*f^2 + 24*A*B*a^8*b^2*c*d^9*f^2 - 24*A*B*a^6*b^4*c*d^9*f^2 + 24*A*B*a^4*
b^6*c*d^9*f^2 - 24*A*B*a^2*b^8*c*d^9*f^2 + 24*A*B*a*b^9*c^8*d^2*f^2 - 24*A*B*a*b^9*c^6*d^4*f^2 + 24*A*B*a*b^9*
c^4*d^6*f^2 - 24*A*B*a*b^9*c^2*d^8*f^2 - 32*B*C*b^10*c^7*d^3*f^2 - 8*B*C*b^10*c^5*d^5*f^2 + 34*A*C*b^10*c^6*d^
4*f^2 + 16*B*C*a^10*c^3*d^7*f^2 + 16*A*C*b^10*c^4*d^6*f^2 - 12*A*C*b^10*c^8*d^2*f^2 - 96*A*B*b^10*c^5*d^5*f^2
- 72*A*B*b^10*c^3*d^7*f^2 - 32*B*C*a^7*b^3*d^10*f^2 - 28*A*C*a^10*c^2*d^8*f^2 - 24*A*B*b^10*c^7*d^3*f^2 - 8*B*
C*a^5*b^5*d^10*f^2 + 2*A*C*a^10*c^4*d^6*f^2 + 34*A*C*a^6*b^4*d^10*f^2 + 16*B*C*a^3*b^7*c^10*f^2 + 16*A*C*a^4*b
^6*d^10*f^2 - 16*A*B*a^10*c^3*d^7*f^2 - 12*A*C*a^8*b^2*d^10*f^2 - 96*A*B*a^5*b^5*d^10*f^2 - 72*A*B*a^3*b^7*d^1
0*f^2 - 28*A*C*a^2*b^8*c^10*f^2 - 24*A*B*a^7*b^3*d^10*f^2 + 2*A*C*a^4*b^6*c^10*f^2 - 16*A*B*a^3*b^7*c^10*f^2 +
444*C^2*a^5*b^5*c^5*d^5*f^2 + 148*C^2*a^7*b^3*c^5*d^5*f^2 + 148*C^2*a^5*b^5*c^7*d^3*f^2 + 148*C^2*a^5*b^5*c^3
*d^7*f^2 + 148*C^2*a^3*b^7*c^5*d^5*f^2 - 140*C^2*a^6*b^4*c^6*d^4*f^2 - 140*C^2*a^6*b^4*c^4*d^6*f^2 - 140*C^2*a
^4*b^6*c^6*d^4*f^2 - 140*C^2*a^4*b^6*c^4*d^6*f^2 + 109*C^2*a^8*b^2*c^2*d^8*f^2 + 109*C^2*a^2*b^8*c^8*d^2*f^2 +
48*C^2*a^8*b^2*c^4*d^6*f^2 + 48*C^2*a^6*b^4*c^2*d^8*f^2 + 48*C^2*a^4*b^6*c^8*d^2*f^2 + 48*C^2*a^2*b^8*c^6*d^4
*f^2 + 20*C^2*a^7*b^3*c^7*d^3*f^2 - 20*C^2*a^7*b^3*c^3*d^7*f^2 - 20*C^2*a^3*b^7*c^7*d^3*f^2 + 20*C^2*a^3*b^7*c
^3*d^7*f^2 + 17*C^2*a^8*b^2*c^6*d^4*f^2 + 17*C^2*a^6*b^4*c^8*d^2*f^2 + 17*C^2*a^4*b^6*c^2*d^8*f^2 + 17*C^2*a^2
*b^8*c^4*d^6*f^2 + 16*C^2*a^8*b^2*c^8*d^2*f^2 + 16*C^2*a^2*b^8*c^2*d^8*f^2 - 396*B^2*a^5*b^5*c^5*d^5*f^2 + 308
*B^2*a^6*b^4*c^4*d^6*f^2 + 308*B^2*a^4*b^6*c^6*d^4*f^2 + 300*B^2*a^4*b^6*c^4*d^6*f^2 + 284*B^2*a^6*b^4*c^6*d^4
*f^2 - 132*B^2*a^7*b^3*c^5*d^5*f^2 - 132*B^2*a^5*b^5*c^7*d^3*f^2 - 84*B^2*a^5*b^5*c^3*d^7*f^2 - 84*B^2*a^3*b^7
*c^5*d^5*f^2 + 61*B^2*a^4*b^6*c^2*d^8*f^2 + 61*B^2*a^2*b^8*c^4*d^6*f^2 - 59*B^2*a^8*b^2*c^2*d^8*f^2 - 59*B^2*a
^2*b^8*c^8*d^2*f^2 + 56*B^2*a^6*b^4*c^2*d^8*f^2 + 56*B^2*a^2*b^8*c^6*d^4*f^2 + 52*B^2*a^7*b^3*c^3*d^7*f^2 + 52
*B^2*a^3*b^7*c^7*d^3*f^2 + 44*B^2*a^3*b^7*c^3*d^7*f^2 + 33*B^2*a^8*b^2*c^6*d^4*f^2 + 33*B^2*a^6*b^4*c^8*d^2*f^
2 + 20*B^2*a^8*b^2*c^4*d^6*f^2 - 20*B^2*a^7*b^3*c^7*d^3*f^2 + 20*B^2*a^4*b^6*c^8*d^2*f^2 + 8*B^2*a^2*b^8*c^2*d
^8*f^2 + 337*A^2*a^4*b^6*c^2*d^8*f^2 + 337*A^2*a^2*b^8*c^4*d^6*f^2 + 272*A^2*a^2*b^8*c^2*d^8*f^2 + 252*A^2*a^5
*b^5*c^5*d^5*f^2 + 244*A^2*a^4*b^6*c^4*d^6*f^2 - 236*A^2*a^3*b^7*c^3*d^7*f^2 + 176*A^2*a^6*b^4*c^2*d^8*f^2 + 1
76*A^2*a^2*b^8*c^6*d^4*f^2 - 148*A^2*a^7*b^3*c^3*d^7*f^2 - 148*A^2*a^3*b^7*c^7*d^3*f^2 - 140*A^2*a^6*b^4*c^6*d
^4*f^2 + 109*A^2*a^8*b^2*c^2*d^8*f^2 + 109*A^2*a^2*b^8*c^8*d^2*f^2 - 108*A^2*a^5*b^5*c^3*d^7*f^2 - 108*A^2*a^3
*b^7*c^5*d^5*f^2 + 84*A^2*a^7*b^3*c^5*d^5*f^2 + 84*A^2*a^5*b^5*c^7*d^3*f^2 + 32*A^2*a^8*b^2*c^4*d^6*f^2 + 32*A
^2*a^4*b^6*c^8*d^2*f^2 + 20*A^2*a^7*b^3*c^7*d^3*f^2 - 15*A^2*a^8*b^2*c^6*d^4*f^2 - 15*A^2*a^6*b^4*c^8*d^2*f^2
- 12*A^2*a^6*b^4*c^4*d^6*f^2 - 12*A^2*a^4*b^6*c^6*d^4*f^2 + 8*B*C*b^10*c^9*d*f^2 - 16*B*C*a^10*c*d^9*f^2 - 16*
A*B*b^10*c^9*d*f^2 - 16*A*B*b^10*c*d^9*f^2 + 8*B*C*a^9*b*d^10*f^2 - 16*B*C*a*b^9*c^10*f^2 + 16*A*B*a^10*c*d^9*
f^2 - 16*A*B*a^9*b*d^10*f^2 - 16*A*B*a*b^9*d^10*f^2 + 16*A*B*a*b^9*c^10*f^2 + 22*C^2*a^9*b*c^5*d^5*f^2 + 22*C^
2*a^5*b^5*c^9*d*f^2 + 22*C^2*a^5*b^5*c*d^9*f^2 + 22*C^2*a*b^9*c^5*d^5*f^2 - 20*C^2*a^9*b*c^3*d^7*f^2 - 20*C^2*
a^7*b^3*c*d^9*f^2 - 20*C^2*a^3*b^7*c^9*d*f^2 - 20*C^2*a*b^9*c^7*d^3*f^2 + 36*B^2*a^7*b^3*c*d^9*f^2 + 36*B^2*a*
b^9*c^7*d^3*f^2 + 28*B^2*a^9*b*c^3*d^7*f^2 + 28*B^2*a^3*b^7*c^9*d*f^2 + 24*B^2*a^3*b^7*c*d^9*f^2 + 24*B^2*a*b^
9*c^3*d^7*f^2 - 18*B^2*a^9*b*c^5*d^5*f^2 - 18*B^2*a^5*b^5*c^9*d*f^2 + 6*B^2*a^5*b^5*c*d^9*f^2 + 6*B^2*a*b^9*c^
5*d^5*f^2 - 96*A^2*a^3*b^7*c*d^9*f^2 - 96*A^2*a*b^9*c^3*d^7*f^2 - 90*A^2*a^5*b^5*c*d^9*f^2 - 90*A^2*a*b^9*c^5*
d^5*f^2 - 84*A^2*a^7*b^3*c*d^9*f^2 - 84*A^2*a*b^9*c^7*d^3*f^2 - 52*A^2*a^9*b*c^3*d^7*f^2 - 52*A^2*a^3*b^7*c^9*
d*f^2 + 6*A^2*a^9*b*c^5*d^5*f^2 + 6*A^2*a^5*b^5*c^9*d*f^2 - 10*C^2*a^9*b*c*d^9*f^2 - 10*C^2*a*b^9*c^9*d*f^2 +
14*B^2*a^9*b*c*d^9*f^2 + 14*B^2*a*b^9*c^9*d*f^2 + 8*B^2*a*b^9*c*d^9*f^2 - 32*A^2*a*b^9*c*d^9*f^2 - 26*A^2*a^9*
b*c*d^9*f^2 - 26*A^2*a*b^9*c^9*d*f^2 + 2*A*C*b^10*c^10*f^2 + 2*A*C*a^10*d^10*f^2 + 14*C^2*b^10*c^8*d^2*f^2 - C
^2*b^10*c^6*d^4*f^2 + 31*B^2*b^10*c^6*d^4*f^2 + 20*B^2*b^10*c^4*d^6*f^2 + 14*C^2*a^10*c^2*d^8*f^2 + 4*B^2*b^10
*c^2*d^8*f^2 + 2*B^2*b^10*c^8*d^2*f^2 - C^2*a^10*c^4*d^6*f^2 + 80*A^2*b^10*c^4*d^6*f^2 + 64*A^2*b^10*c^2*d^8*f
^2 + 31*A^2*b^10*c^6*d^4*f^2 + 14*C^2*a^8*b^2*d^10*f^2 + 14*A^2*b^10*c^8*d^2*f^2 - 10*B^2*a^10*c^2*d^8*f^2 + 3
*B^2*a^10*c^4*d^6*f^2 - C^2*a^6*b^4*d^10*f^2 + 31*B^2*a^6*b^4*d^10*f^2 + 20*B^2*a^4*b^6*d^10*f^2 + 14*C^2*a^2*
b^8*c^10*f^2 + 14*A^2*a^10*c^2*d^8*f^2 + 4*B^2*a^2*b^8*d^10*f^2 + 2*B^2*a^8*b^2*d^10*f^2 - C^2*a^4*b^6*c^10*f^
2 - A^2*a^10*c^4*d^6*f^2 + 80*A^2*a^4*b^6*d^10*f^2 + 64*A^2*a^2*b^8*d^10*f^2 + 31*A^2*a^6*b^4*d^10*f^2 + 14*A^
2*a^8*b^2*d^10*f^2 - 10*B^2*a^2*b^8*c^10*f^2 + 3*B^2*a^4*b^6*c^10*f^2 + 14*A^2*a^2*b^8*c^10*f^2 - A^2*a^4*b^6*
c^10*f^2 - C^2*b^10*c^10*f^2 - C^2*a^10*d^10*f^2 + 16*A^2*b^10*d^10*f^2 + 3*B^2*b^10*c^10*f^2 + 3*B^2*a^10*d^1
0*f^2 - A^2*b^10*c^10*f^2 - A^2*a^10*d^10*f^2 - 96*A*B*C*a*b^7*c*d^7*f - 28*A*B*C*a^7*b*c*d^7*f - 28*A*B*C*a*b
^7*c^7*d*f + 484*A*B*C*a^4*b^4*c^4*d^4*f - 424*A*B*C*a^3*b^5*c^3*d^5*f + 320*A*B*C*a^2*b^6*c^2*d^6*f - 176*A*B
*C*a^6*b^2*c^2*d^6*f - 176*A*B*C*a^2*b^6*c^6*d^2*f + 158*A*B*C*a^4*b^4*c^2*d^6*f + 158*A*B*C*a^2*b^6*c^4*d^4*f
- 136*A*B*C*a^5*b^3*c^5*d^3*f - 34*A*B*C*a^6*b^2*c^4*d^4*f - 34*A*B*C*a^4*b^4*c^6*d^2*f + 28*A*B*C*a^5*b^3*c^
3*d^5*f + 28*A*B*C*a^3*b^5*c^5*d^3*f + 308*A*B*C*a^5*b^3*c*d^7*f + 308*A*B*C*a*b^7*c^5*d^3*f + 20*A*B*C*a^7*b*
c^3*d^5*f + 20*A*B*C*a^3*b^5*c^7*d*f + 30*B*C^2*a^7*b*c*d^7*f + 30*B*C^2*a*b^7*c^7*d*f + 160*A^2*B*a*b^7*c*d^7
*f - 2*A^2*B*a^7*b*c*d^7*f - 2*A^2*B*a*b^7*c^7*d*f - 96*A*B*C*b^8*c^4*d^4*f + 34*A*B*C*b^8*c^6*d^2*f - 32*A*B*
C*b^8*c^2*d^6*f + 2*A*B*C*a^8*c^2*d^6*f - 96*A*B*C*a^4*b^4*d^8*f + 34*A*B*C*a^6*b^2*d^8*f - 32*A*B*C*a^2*b^6*d
^8*f + 2*A*B*C*a^2*b^6*c^8*f - 210*B*C^2*a^4*b^4*c^4*d^4*f - 182*B^2*C*a^5*b^3*c^2*d^6*f - 182*B^2*C*a^2*b^6*c
^5*d^3*f + 180*B*C^2*a^5*b^3*c^5*d^3*f + 180*B*C^2*a^3*b^5*c^3*d^5*f - 166*B^2*C*a^5*b^3*c^4*d^4*f - 166*B^2*C
*a^4*b^4*c^5*d^3*f + 152*B*C^2*a^6*b^2*c^2*d^6*f + 152*B*C^2*a^2*b^6*c^6*d^2*f - 112*B^2*C*a^3*b^5*c^2*d^6*f -
112*B^2*C*a^2*b^6*c^3*d^5*f + 94*B^2*C*a^4*b^4*c^3*d^5*f + 94*B^2*C*a^3*b^5*c^4*d^4*f - 80*B*C^2*a^2*b^6*c^2*
d^6*f + 66*B*C^2*a^5*b^3*c^3*d^5*f + 66*B*C^2*a^3*b^5*c^5*d^3*f + 46*B^2*C*a^6*b^2*c^3*d^5*f + 46*B^2*C*a^3*b^
5*c^6*d^2*f + 33*B*C^2*a^6*b^2*c^4*d^4*f + 33*B*C^2*a^4*b^4*c^6*d^2*f + 24*B^2*C*a^6*b^2*c^5*d^3*f + 24*B^2*C*
a^5*b^3*c^6*d^2*f - 16*B*C^2*a^6*b^2*c^6*d^2*f - 15*B*C^2*a^4*b^4*c^2*d^6*f - 15*B*C^2*a^2*b^6*c^4*d^4*f - 190
*A^2*C*a^4*b^4*c^3*d^5*f - 190*A^2*C*a^3*b^5*c^4*d^4*f + 182*A^2*C*a^5*b^3*c^2*d^6*f + 182*A^2*C*a^2*b^6*c^5*d
^3*f + 160*A^2*C*a^3*b^5*c^2*d^6*f + 160*A^2*C*a^2*b^6*c^3*d^5*f - 150*A*C^2*a^5*b^3*c^2*d^6*f - 150*A*C^2*a^2
*b^6*c^5*d^3*f - 126*A*C^2*a^5*b^3*c^4*d^4*f - 126*A*C^2*a^4*b^4*c^5*d^3*f + 126*A*C^2*a^4*b^4*c^3*d^5*f + 126
*A*C^2*a^3*b^5*c^4*d^4*f - 96*A*C^2*a^3*b^5*c^2*d^6*f - 96*A*C^2*a^2*b^6*c^3*d^5*f + 94*A^2*C*a^5*b^3*c^4*d^4*
f + 94*A^2*C*a^4*b^4*c^5*d^3*f + 54*A*C^2*a^6*b^2*c^3*d^5*f + 54*A*C^2*a^3*b^5*c^6*d^2*f + 32*A*C^2*a^6*b^2*c^
5*d^3*f + 32*A*C^2*a^5*b^3*c^6*d^2*f - 22*A^2*C*a^6*b^2*c^3*d^5*f - 22*A^2*C*a^3*b^5*c^6*d^2*f + 500*A^2*B*a^3
*b^5*c^3*d^5*f - 290*A^2*B*a^4*b^4*c^4*d^4*f - 256*A^2*B*a^2*b^6*c^2*d^6*f - 230*A*B^2*a^4*b^4*c^3*d^5*f - 230
*A*B^2*a^3*b^5*c^4*d^4*f + 142*A*B^2*a^5*b^3*c^2*d^6*f + 142*A*B^2*a^2*b^6*c^5*d^3*f - 127*A^2*B*a^4*b^4*c^2*d
^6*f - 127*A^2*B*a^2*b^6*c^4*d^4*f + 86*A*B^2*a^5*b^3*c^4*d^4*f + 86*A*B^2*a^4*b^4*c^5*d^3*f + 80*A*B^2*a^3*b^
5*c^2*d^6*f + 80*A*B^2*a^2*b^6*c^3*d^5*f + 40*A^2*B*a^6*b^2*c^2*d^6*f + 40*A^2*B*a^2*b^6*c^6*d^2*f + 34*A^2*B*
a^5*b^3*c^3*d^5*f + 34*A^2*B*a^3*b^5*c^5*d^3*f - 30*A*B^2*a^6*b^2*c^3*d^5*f - 30*A*B^2*a^3*b^5*c^6*d^2*f + 20*
A^2*B*a^5*b^3*c^5*d^3*f - 15*A^2*B*a^6*b^2*c^4*d^4*f - 15*A^2*B*a^4*b^4*c^6*d^2*f - 98*B^2*C*a^6*b^2*c*d^7*f -
98*B^2*C*a*b^7*c^6*d^2*f - 90*B*C^2*a^5*b^3*c*d^7*f - 90*B*C^2*a*b^7*c^5*d^3*f + 48*B^2*C*a^4*b^4*c*d^7*f + 4
8*B^2*C*a*b^7*c^4*d^4*f + 40*B^2*C*a^2*b^6*c*d^7*f + 40*B^2*C*a*b^7*c^2*d^6*f - 32*B*C^2*a^3*b^5*c*d^7*f - 32*
B*C^2*a*b^7*c^3*d^5*f + 26*B^2*C*a^7*b*c^2*d^6*f + 26*B^2*C*a^2*b^6*c^7*d*f - 26*B*C^2*a^7*b*c^3*d^5*f - 26*B*
C^2*a^3*b^5*c^7*d*f - 8*B^2*C*a^7*b*c^4*d^4*f - 8*B^2*C*a^4*b^4*c^7*d*f - 224*A^2*C*a^4*b^4*c*d^7*f - 224*A^2*
C*a*b^7*c^4*d^4*f - 96*A^2*C*a^2*b^6*c*d^7*f - 96*A^2*C*a*b^7*c^2*d^6*f + 96*A*C^2*a^4*b^4*c*d^7*f + 96*A*C^2*
a*b^7*c^4*d^4*f - 66*A*C^2*a^6*b^2*c*d^7*f - 66*A*C^2*a*b^7*c^6*d^2*f + 64*A*C^2*a^2*b^6*c*d^7*f + 64*A*C^2*a*
b^7*c^2*d^6*f + 34*A^2*C*a^6*b^2*c*d^7*f + 34*A^2*C*a*b^7*c^6*d^2*f + 34*A*C^2*a^7*b*c^2*d^6*f + 34*A*C^2*a^2*
b^6*c^7*d*f - 2*A^2*C*a^7*b*c^2*d^6*f - 2*A^2*C*a^2*b^6*c^7*d*f - 208*A*B^2*a^4*b^4*c*d^7*f - 208*A*B^2*a*b^7*
c^4*d^4*f + 160*A^2*B*a^3*b^5*c*d^7*f + 160*A^2*B*a*b^7*c^3*d^5*f - 154*A^2*B*a^5*b^3*c*d^7*f - 154*A^2*B*a*b^
7*c^5*d^3*f - 112*A*B^2*a^2*b^6*c*d^7*f - 112*A*B^2*a*b^7*c^2*d^6*f + 58*A*B^2*a^6*b^2*c*d^7*f + 58*A*B^2*a*b^
7*c^6*d^2*f - 10*A*B^2*a^7*b*c^2*d^6*f - 10*A*B^2*a^2*b^6*c^7*d*f + 6*A^2*B*a^7*b*c^3*d^5*f + 6*A^2*B*a^3*b^5*
c^7*d*f + 32*B^2*C*b^8*c^5*d^3*f - 17*B*C^2*b^8*c^6*d^2*f + 8*B^2*C*b^8*c^3*d^5*f + 64*A^2*C*b^8*c^3*d^5*f - 3
2*A^2*C*b^8*c^5*d^3*f + 32*A*C^2*b^8*c^5*d^3*f - B*C^2*a^8*c^2*d^6*f + 112*A^2*B*b^8*c^4*d^4*f - 64*A*B^2*b^8*
c^5*d^3*f + 32*B^2*C*a^5*b^3*d^8*f - 17*B*C^2*a^6*b^2*d^8*f + 16*A^2*B*b^8*c^2*d^6*f + 16*A*B^2*b^8*c^3*d^5*f
+ 8*B^2*C*a^3*b^5*d^8*f - A^2*B*b^8*c^6*d^2*f + 64*A^2*C*a^3*b^5*d^8*f - 32*A^2*C*a^5*b^3*d^8*f + 32*A*C^2*a^5
*b^3*d^8*f - A^2*B*a^8*c^2*d^6*f - B*C^2*a^2*b^6*c^8*f + 112*A^2*B*a^4*b^4*d^8*f - 64*A*B^2*a^5*b^3*d^8*f + 16
*A^2*B*a^2*b^6*d^8*f + 16*A*B^2*a^3*b^5*d^8*f - A^2*B*a^6*b^2*d^8*f - A^2*B*a^2*b^6*c^8*f - 8*B^3*a*b^7*c*d^7*
f - 2*B^3*a^7*b*c*d^7*f - 2*B^3*a*b^7*c^7*d*f - 6*B^2*C*b^8*c^7*d*f + 32*A^2*C*b^8*c*d^7*f + 6*A^2*C*b^8*c^7*d
*f - 6*A*C^2*b^8*c^7*d*f - 2*B^2*C*a^8*c*d^7*f + 16*A*B^2*b^8*c*d^7*f - 6*B^2*C*a^7*b*d^8*f - 6*A^2*C*a^8*c*d^
7*f + 6*A*C^2*a^8*c*d^7*f - 2*A*B^2*b^8*c^7*d*f + 32*A^2*C*a*b^7*d^8*f + 6*A^2*C*a^7*b*d^8*f - 6*A*C^2*a^7*b*d
^8*f - 2*B^2*C*a*b^7*c^8*f + 2*A*B^2*a^8*c*d^7*f + 16*A*B^2*a*b^7*d^8*f - 6*A^2*C*a*b^7*c^8*f + 6*A*C^2*a*b^7*
c^8*f - 2*A*B^2*a^7*b*d^8*f + 2*A*B^2*a*b^7*c^8*f - 50*C^3*a^6*b^2*c^3*d^5*f + 50*C^3*a^5*b^3*c^2*d^6*f - 50*C
^3*a^3*b^5*c^6*d^2*f + 50*C^3*a^2*b^6*c^5*d^3*f + 42*C^3*a^5*b^3*c^4*d^4*f + 42*C^3*a^4*b^4*c^5*d^3*f - 42*C^3
*a^4*b^4*c^3*d^5*f - 42*C^3*a^3*b^5*c^4*d^4*f - 32*C^3*a^6*b^2*c^5*d^3*f - 32*C^3*a^5*b^3*c^6*d^2*f + 32*C^3*a
^3*b^5*c^2*d^6*f + 32*C^3*a^2*b^6*c^3*d^5*f + 94*B^3*a^4*b^4*c^4*d^4*f + 48*B^3*a^2*b^6*c^2*d^6*f - 44*B^3*a^3
*b^5*c^3*d^5*f - 32*B^3*a^6*b^2*c^2*d^6*f - 32*B^3*a^2*b^6*c^6*d^2*f + 29*B^3*a^4*b^4*c^2*d^6*f + 29*B^3*a^2*b
^6*c^4*d^4*f - 20*B^3*a^5*b^3*c^5*d^3*f + 18*B^3*a^5*b^3*c^3*d^5*f + 18*B^3*a^3*b^5*c^5*d^3*f - 3*B^3*a^6*b^2*
c^4*d^4*f - 3*B^3*a^4*b^4*c^6*d^2*f + 106*A^3*a^4*b^4*c^3*d^5*f + 106*A^3*a^3*b^5*c^4*d^4*f - 96*A^3*a^3*b^5*c
^2*d^6*f - 96*A^3*a^2*b^6*c^3*d^5*f - 82*A^3*a^5*b^3*c^2*d^6*f - 82*A^3*a^2*b^6*c^5*d^3*f + 18*A^3*a^6*b^2*c^3
*d^5*f + 18*A^3*a^3*b^5*c^6*d^2*f - 10*A^3*a^5*b^3*c^4*d^4*f - 10*A^3*a^4*b^4*c^5*d^3*f - 22*C^3*a^7*b*c^2*d^6
*f + 22*C^3*a^6*b^2*c*d^7*f - 22*C^3*a^2*b^6*c^7*d*f + 22*C^3*a*b^7*c^6*d^2*f - 2*A*B*C*b^8*c^8*f - 2*A*B*C*a^
8*d^8*f + 62*B^3*a^5*b^3*c*d^7*f + 62*B^3*a*b^7*c^5*d^3*f + 16*B^3*a^3*b^5*c*d^7*f + 16*B^3*a*b^7*c^3*d^5*f +
6*B^3*a^7*b*c^3*d^5*f + 6*B^3*a^3*b^5*c^7*d*f + 128*A^3*a^4*b^4*c*d^7*f + 128*A^3*a*b^7*c^4*d^4*f + 32*A^3*a^2
*b^6*c*d^7*f + 32*A^3*a*b^7*c^2*d^6*f - 10*A^3*a^7*b*c^2*d^6*f + 10*A^3*a^6*b^2*c*d^7*f - 10*A^3*a^2*b^6*c^7*d
*f + 10*A^3*a*b^7*c^6*d^2*f + 11*B^3*b^8*c^6*d^2*f - 8*B^3*b^8*c^4*d^4*f - 4*B^3*b^8*c^2*d^6*f - 64*A^3*b^8*c^
3*d^5*f - B^3*a^8*c^2*d^6*f + 11*B^3*a^6*b^2*d^8*f - 8*B^3*a^4*b^4*d^8*f - 4*B^3*a^2*b^6*d^8*f - 64*A^3*a^3*b^
5*d^8*f - B^3*a^2*b^6*c^8*f + 2*C^3*b^8*c^7*d*f - 2*C^3*a^8*c*d^7*f - 32*A^3*b^8*c*d^7*f + 2*C^3*a^7*b*d^8*f -
2*A^3*b^8*c^7*d*f - 2*C^3*a*b^7*c^8*f + 2*A^3*a^8*c*d^7*f - 32*A^3*a*b^7*d^8*f - 2*A^3*a^7*b*d^8*f + 2*A^3*a*
b^7*c^8*f - 16*A^2*B*b^8*d^8*f + B*C^2*b^8*c^8*f + B*C^2*a^8*d^8*f + A^2*B*b^8*c^8*f + A^2*B*a^8*d^8*f + B^3*b
^8*c^8*f + B^3*a^8*d^8*f - 4*A*B^2*C*a^5*b*c*d^5 - 4*A*B^2*C*a*b^5*c^5*d + 4*A*B^2*C*a*b^5*c*d^5 + 22*A^2*B*C*
a^3*b^3*c^2*d^4 + 22*A^2*B*C*a^2*b^4*c^3*d^3 - 20*A*B^2*C*a^3*b^3*c^3*d^3 + 14*A*B^2*C*a^4*b^2*c^2*d^4 + 14*A*
B^2*C*a^2*b^4*c^4*d^2 - 14*A*B*C^2*a^3*b^3*c^2*d^4 - 14*A*B*C^2*a^2*b^4*c^3*d^3 + 12*A*B*C^2*a^4*b^2*c^3*d^3 +
12*A*B*C^2*a^3*b^3*c^4*d^2 - 6*A^2*B*C*a^4*b^2*c^3*d^3 - 6*A^2*B*C*a^3*b^3*c^4*d^2 - 4*A*B^2*C*a^2*b^4*c^2*d^
4 + 22*A*B*C^2*a^4*b^2*c*d^5 + 22*A*B*C^2*a*b^5*c^4*d^2 - 20*A^2*B*C*a^4*b^2*c*d^5 - 20*A^2*B*C*a*b^5*c^4*d^2
+ 10*A*B*C^2*a^2*b^4*c*d^5 + 10*A*B*C^2*a*b^5*c^2*d^4 - 8*A^2*B*C*a^2*b^4*c*d^5 - 8*A^2*B*C*a*b^5*c^2*d^4 + 4*
A*B^2*C*a^3*b^3*c*d^5 + 4*A*B^2*C*a*b^5*c^3*d^3 - 4*A*B*C^2*a^5*b*c^2*d^4 - 4*A*B*C^2*a^2*b^4*c^5*d + 2*A^2*B*
C*a^5*b*c^2*d^4 + 2*A^2*B*C*a^2*b^4*c^5*d - 8*B^3*C*a^4*b^2*c*d^5 - 8*B^3*C*a*b^5*c^4*d^2 - 8*B*C^3*a^4*b^2*c*
d^5 - 8*B*C^3*a*b^5*c^4*d^2 - 4*B^3*C*a^2*b^4*c*d^5 - 4*B^3*C*a*b^5*c^2*d^4 + 4*B^2*C^2*a^5*b*c*d^5 + 4*B^2*C^
2*a*b^5*c^5*d - 4*B*C^3*a^2*b^4*c*d^5 - 4*B*C^3*a*b^5*c^2*d^4 + 2*B^3*C*a^5*b*c^2*d^4 + 2*B^3*C*a^2*b^4*c^5*d
+ 2*B^2*C^2*a*b^5*c*d^5 + 2*B*C^3*a^5*b*c^2*d^4 + 2*B*C^3*a^2*b^4*c^5*d + 24*A^3*C*a^3*b^3*c*d^5 + 24*A^3*C*a*
b^5*c^3*d^3 - 24*A^2*C^2*a*b^5*c*d^5 + 12*A^2*C^2*a^5*b*c*d^5 + 12*A^2*C^2*a*b^5*c^5*d + 8*A*C^3*a^3*b^3*c*d^5
+ 8*A*C^3*a*b^5*c^3*d^3 + 6*A^3*B*a^4*b^2*c*d^5 + 6*A^3*B*a*b^5*c^4*d^2 - 6*A^2*B^2*a*b^5*c*d^5 + 6*A*B^3*a^4
*b^2*c*d^5 + 6*A*B^3*a*b^5*c^4*d^2 + 2*A^3*B*a^2*b^4*c*d^5 + 2*A^3*B*a*b^5*c^2*d^4 + 2*A*B^3*a^2*b^4*c*d^5 + 2
*A*B^3*a*b^5*c^2*d^4 + 20*A^2*B*C*b^6*c^3*d^3 - 10*A*B*C^2*b^6*c^3*d^3 - 2*A*B^2*C*b^6*c^4*d^2 - 2*A*B^2*C*b^6
*c^2*d^4 + 20*A^2*B*C*a^3*b^3*d^6 - 10*A*B*C^2*a^3*b^3*d^6 - 2*A*B^2*C*a^4*b^2*d^6 - 2*A*B^2*C*a^2*b^4*d^6 + 1
0*B^2*C^2*a^3*b^3*c^3*d^3 + 4*B^2*C^2*a^4*b^2*c^4*d^2 - 3*B^2*C^2*a^4*b^2*c^2*d^4 - 3*B^2*C^2*a^2*b^4*c^4*d^2
+ 2*B^2*C^2*a^2*b^4*c^2*d^4 + 40*A^2*C^2*a^2*b^4*c^2*d^4 - 16*A^2*C^2*a^4*b^2*c^2*d^4 - 16*A^2*C^2*a^2*b^4*c^4
*d^2 + 4*A^2*C^2*a^4*b^2*c^4*d^2 + 18*A^2*B^2*a^2*b^4*c^2*d^4 + 10*A^2*B^2*a^3*b^3*c^3*d^3 - 3*A^2*B^2*a^4*b^2
*c^2*d^4 - 3*A^2*B^2*a^2*b^4*c^4*d^2 + 24*A^3*C*a*b^5*c*d^5 - 12*A*C^3*a^5*b*c*d^5 - 12*A*C^3*a*b^5*c^5*d + 8*
A*C^3*a*b^5*c*d^5 - 4*A^3*C*a^5*b*c*d^5 - 4*A^3*C*a*b^5*c^5*d + 8*A^2*B*C*b^6*c*d^5 + 4*A*B*C^2*b^6*c^5*d - 4*
A*B*C^2*b^6*c*d^5 - 2*A^2*B*C*b^6*c^5*d + 8*A^2*B*C*a*b^5*d^6 + 4*A*B*C^2*a^5*b*d^6 - 4*A*B*C^2*a*b^5*d^6 - 2*
A^2*B*C*a^5*b*d^6 - 6*B^3*C*a^4*b^2*c^3*d^3 - 6*B^3*C*a^3*b^3*c^4*d^2 - 6*B*C^3*a^4*b^2*c^3*d^3 - 6*B*C^3*a^3*
b^3*c^4*d^2 + 2*B^3*C*a^3*b^3*c^2*d^4 + 2*B^3*C*a^2*b^4*c^3*d^3 + 2*B^2*C^2*a^3*b^3*c*d^5 + 2*B^2*C^2*a*b^5*c^
3*d^3 + 2*B*C^3*a^3*b^3*c^2*d^4 + 2*B*C^3*a^2*b^4*c^3*d^3 - 48*A^3*C*a^2*b^4*c^2*d^4 - 24*A^2*C^2*a^3*b^3*c*d^
5 - 24*A^2*C^2*a*b^5*c^3*d^3 - 16*A*C^3*a^2*b^4*c^2*d^4 + 8*A^3*C*a^4*b^2*c^2*d^4 + 8*A^3*C*a^2*b^4*c^4*d^2 -
8*A*C^3*a^4*b^2*c^4*d^2 + 8*A*C^3*a^4*b^2*c^2*d^4 + 8*A*C^3*a^2*b^4*c^4*d^2 - 10*A^3*B*a^3*b^3*c^2*d^4 - 10*A^
3*B*a^2*b^4*c^3*d^3 - 10*A*B^3*a^3*b^3*c^2*d^4 - 10*A*B^3*a^2*b^4*c^3*d^3 - 6*A^2*B^2*a^3*b^3*c*d^5 - 6*A^2*B^
2*a*b^5*c^3*d^3 + 3*B^2*C^2*b^6*c^4*d^2 - 8*A^2*C^2*b^6*c^4*d^2 + 8*A^2*C^2*b^6*c^2*d^4 + 9*A^2*B^2*b^6*c^2*d^
4 + 3*B^2*C^2*a^4*b^2*d^6 + 3*A^2*B^2*b^6*c^4*d^2 - 8*A^2*C^2*a^4*b^2*d^6 + 8*A^2*C^2*a^2*b^4*d^6 + 9*A^2*B^2*
a^2*b^4*d^6 + 3*A^2*B^2*a^4*b^2*d^6 + 2*B^4*a^3*b^3*c*d^5 + 2*B^4*a*b^5*c^3*d^3 - 8*A^4*a^3*b^3*c*d^5 - 8*A^4*
a*b^5*c^3*d^3 - 16*A^3*C*b^6*c^2*d^4 + 4*A^3*C*b^6*c^4*d^2 + 4*A*C^3*b^6*c^4*d^2 - 10*A^3*B*b^6*c^3*d^3 - 10*A
*B^3*b^6*c^3*d^3 - 16*A^3*C*a^2*b^4*d^6 + 4*A^3*C*a^4*b^2*d^6 + 4*A*C^3*a^4*b^2*d^6 - 10*A^3*B*a^3*b^3*d^6 - 1
0*A*B^3*a^3*b^3*d^6 + 4*C^4*a^5*b*c*d^5 + 4*C^4*a*b^5*c^5*d + 2*B^4*a*b^5*c*d^5 - 8*A^4*a*b^5*c*d^5 - 2*B^3*C*
b^6*c^5*d - 2*B*C^3*b^6*c^5*d - 4*A^3*B*b^6*c*d^5 - 4*A*B^3*b^6*c*d^5 - 2*B^3*C*a^5*b*d^6 - 2*B*C^3*a^5*b*d^6
- 4*A^3*B*a*b^5*d^6 - 4*A*B^3*a*b^5*d^6 + 4*C^4*a^4*b^2*c^4*d^2 + 4*C^4*a^2*b^4*c^2*d^4 + 10*B^4*a^3*b^3*c^3*d
^3 - 3*B^4*a^4*b^2*c^2*d^4 - 3*B^4*a^2*b^4*c^4*d^2 - 2*B^4*a^2*b^4*c^2*d^4 + 20*A^4*a^2*b^4*c^2*d^4 + B^2*C^2*
b^6*c^2*d^4 + B^2*C^2*a^2*b^4*d^6 - 8*A^3*C*b^6*d^6 + 3*B^4*b^6*c^4*d^2 + 8*A^4*b^6*c^2*d^4 + 3*B^4*a^4*b^2*d^
6 + 8*A^4*a^2*b^4*d^6 + 4*A^2*C^2*b^6*d^6 + 4*A^2*B^2*b^6*d^6 + 4*A^4*b^6*d^6 + B^4*b^6*c^2*d^4 + B^4*a^2*b^4*
d^6, f, k)*((16*A^2*a^3*b^6*d^9 + A^2*a^5*b^4*d^9 + 2*A^2*a^7*b^2*d^9 + 8*B^2*a^3*b^6*d^9 + 9*B^2*a^5*b^4*d^9
+ 16*A^2*b^9*c^3*d^6 + A^2*b^9*c^5*d^4 + 2*A^2*b^9*c^7*d^2 + C^2*a^5*b^4*d^9 + 2*C^2*a^7*b^2*d^9 + 8*B^2*b^9*c
^3*d^6 + 9*B^2*b^9*c^5*d^4 + C^2*b^9*c^5*d^4 + 2*C^2*b^9*c^7*d^2 + 16*A^2*a*b^8*d^9 + 16*A^2*b^9*c*d^8 - 14*A^
2*a^2*b^7*c^3*d^6 - 4*A^2*a^2*b^7*c^5*d^4 + 6*A^2*a^2*b^7*c^7*d^2 - 14*A^2*a^3*b^6*c^2*d^7 - 6*A^2*a^3*b^6*c^4
*d^5 - 12*A^2*a^3*b^6*c^6*d^3 - 6*A^2*a^4*b^5*c^3*d^6 + 7*A^2*a^4*b^5*c^5*d^4 - 4*A^2*a^5*b^4*c^2*d^7 + 7*A^2*
a^5*b^4*c^4*d^5 - 12*A^2*a^6*b^3*c^3*d^6 + 6*A^2*a^7*b^2*c^2*d^7 + 18*B^2*a^2*b^7*c^3*d^6 + 2*B^2*a^2*b^7*c^5*
d^4 - 4*B^2*a^2*b^7*c^7*d^2 + 18*B^2*a^3*b^6*c^2*d^7 - 20*B^2*a^3*b^6*c^4*d^5 + 6*B^2*a^3*b^6*c^6*d^3 - 20*B^2
*a^4*b^5*c^3*d^6 - 19*B^2*a^4*b^5*c^5*d^4 + 2*B^2*a^5*b^4*c^2*d^7 - 19*B^2*a^5*b^4*c^4*d^5 + 6*B^2*a^6*b^3*c^3
*d^6 - 4*B^2*a^7*b^2*c^2*d^7 + 2*C^2*a^2*b^7*c^3*d^6 + 12*C^2*a^2*b^7*c^5*d^4 + 6*C^2*a^2*b^7*c^7*d^2 + 2*C^2*
a^3*b^6*c^2*d^7 + 10*C^2*a^3*b^6*c^4*d^5 - 28*C^2*a^3*b^6*c^6*d^3 + 10*C^2*a^4*b^5*c^3*d^6 + 7*C^2*a^4*b^5*c^5
*d^4 + 12*C^2*a^5*b^4*c^2*d^7 + 7*C^2*a^5*b^4*c^4*d^5 - 16*C^2*a^5*b^4*c^6*d^3 - 28*C^2*a^6*b^3*c^3*d^6 - 16*C
^2*a^6*b^3*c^5*d^4 + 6*C^2*a^7*b^2*c^2*d^7 - 24*A*B*a^2*b^7*d^9 - 24*A*B*a^4*b^5*d^9 + A*B*a^6*b^3*d^9 + 16*A*
C*a^3*b^6*d^9 + 14*A*C*a^5*b^4*d^9 - 4*A*C*a^7*b^2*d^9 - 24*A*B*b^9*c^2*d^7 - 24*A*B*b^9*c^4*d^5 + A*B*b^9*c^6
*d^3 - 8*B*C*a^4*b^5*d^9 - 9*B*C*a^6*b^3*d^9 + 16*A*C*b^9*c^3*d^6 + 14*A*C*b^9*c^5*d^4 - 4*A*C*b^9*c^7*d^2 - 8
*B*C*b^9*c^4*d^5 - 9*B*C*b^9*c^6*d^3 - A^2*a*b^8*c^8*d - A^2*a^8*b*c*d^8 + B^2*a*b^8*c^8*d + B^2*a^8*b*c*d^8 -
C^2*a*b^8*c^8*d - C^2*a^8*b*c*d^8 - 3*A^2*a*b^8*c^4*d^5 - 8*A^2*a*b^8*c^6*d^3 - 3*A^2*a^4*b^5*c*d^8 - 8*A^2*a
^6*b^3*c*d^8 + 8*B^2*a*b^8*c^2*d^7 - 11*B^2*a*b^8*c^4*d^5 + 2*B^2*a*b^8*c^6*d^3 + 8*B^2*a^2*b^7*c*d^8 - 11*B^2
*a^4*b^5*c*d^8 + 2*B^2*a^6*b^3*c*d^8 + 13*C^2*a*b^8*c^4*d^5 - 8*C^2*a*b^8*c^6*d^3 + 13*C^2*a^4*b^5*c*d^8 - 8*C
^2*a^6*b^3*c*d^8 - A*B*a^8*b*d^9 - A*B*b^9*c^8*d + B*C*a^8*b*d^9 + B*C*b^9*c^8*d - 16*A*B*a*b^8*c*d^8 + 2*A*C*
a*b^8*c^8*d + 2*A*C*a^8*b*c*d^8 + 24*A*B*a*b^8*c^3*d^6 + 2*A*B*a*b^8*c^5*d^4 + 2*A*B*a*b^8*c^7*d^2 + A*B*a^2*b
^7*c^8*d + 24*A*B*a^3*b^6*c*d^8 + 2*A*B*a^5*b^4*c*d^8 + 2*A*B*a^7*b^2*c*d^8 + A*B*a^8*b*c^2*d^7 + 16*A*C*a*b^8
*c^2*d^7 - 26*A*C*a*b^8*c^4*d^5 + 16*A*C*a^2*b^7*c*d^8 - 26*A*C*a^4*b^5*c*d^8 - 24*B*C*a*b^8*c^3*d^6 + 14*B*C*
a*b^8*c^5*d^4 - 2*B*C*a*b^8*c^7*d^2 - B*C*a^2*b^7*c^8*d - 24*B*C*a^3*b^6*c*d^8 + 14*B*C*a^5*b^4*c*d^8 - 2*B*C*
a^7*b^2*c*d^8 - B*C*a^8*b*c^2*d^7 - 64*A*B*a^2*b^7*c^2*d^7 - 25*A*B*a^2*b^7*c^4*d^5 + 8*A*B*a^2*b^7*c^6*d^3 +
108*A*B*a^3*b^6*c^3*d^6 + 6*A*B*a^3*b^6*c^5*d^4 - 6*A*B*a^3*b^6*c^7*d^2 - 25*A*B*a^4*b^5*c^2*d^7 + 34*A*B*a^4*
b^5*c^4*d^5 + 15*A*B*a^4*b^5*c^6*d^3 + 6*A*B*a^5*b^4*c^3*d^6 - 20*A*B*a^5*b^4*c^5*d^4 + 8*A*B*a^6*b^3*c^2*d^7
+ 15*A*B*a^6*b^3*c^4*d^5 - 6*A*B*a^7*b^2*c^3*d^6 + 44*A*C*a^2*b^7*c^3*d^6 + 8*A*C*a^2*b^7*c^5*d^4 - 12*A*C*a^2
*b^7*c^7*d^2 + 44*A*C*a^3*b^6*c^2*d^7 - 36*A*C*a^3*b^6*c^4*d^5 + 8*A*C*a^3*b^6*c^6*d^3 - 36*A*C*a^4*b^5*c^3*d^
6 - 30*A*C*a^4*b^5*c^5*d^4 + 8*A*C*a^5*b^4*c^2*d^7 - 30*A*C*a^5*b^4*c^4*d^5 + 8*A*C*a^6*b^3*c^3*d^6 - 12*A*C*a
^7*b^2*c^2*d^7 - 15*B*C*a^2*b^7*c^4*d^5 - 8*B*C*a^2*b^7*c^6*d^3 - 44*B*C*a^3*b^6*c^3*d^6 + 58*B*C*a^3*b^6*c^5*
d^4 + 6*B*C*a^3*b^6*c^7*d^2 - 15*B*C*a^4*b^5*c^2*d^7 - 34*B*C*a^4*b^5*c^4*d^5 - 7*B*C*a^4*b^5*c^6*d^3 + 58*B*C
*a^5*b^4*c^3*d^6 + 68*B*C*a^5*b^4*c^5*d^4 - 8*B*C*a^6*b^3*c^2*d^7 - 7*B*C*a^6*b^3*c^4*d^5 + 6*B*C*a^7*b^2*c^3*
d^6)/(a^8*d^8 + b^8*c^8 + 2*a^2*b^6*c^8 + a^4*b^4*c^8 + a^4*b^4*d^8 + 2*a^6*b^2*d^8 + 2*a^8*c^2*d^6 + a^8*c^4*
d^4 + b^8*c^4*d^4 + 2*b^8*c^6*d^2 - 4*a*b^7*c^3*d^5 - 8*a*b^7*c^5*d^3 - 4*a^3*b^5*c*d^7 - 8*a^3*b^5*c^7*d - 8*
a^5*b^3*c*d^7 - 4*a^5*b^3*c^7*d - 8*a^7*b*c^3*d^5 - 4*a^7*b*c^5*d^3 + 6*a^2*b^6*c^2*d^6 + 14*a^2*b^6*c^4*d^4 +
10*a^2*b^6*c^6*d^2 - 16*a^3*b^5*c^3*d^5 - 20*a^3*b^5*c^5*d^3 + 14*a^4*b^4*c^2*d^6 + 26*a^4*b^4*c^4*d^4 + 14*a
^4*b^4*c^6*d^2 - 20*a^5*b^3*c^3*d^5 - 16*a^5*b^3*c^5*d^3 + 10*a^6*b^2*c^2*d^6 + 14*a^6*b^2*c^4*d^4 + 6*a^6*b^2
*c^6*d^2 - 4*a*b^7*c^7*d - 4*a^7*b*c*d^7) + root(144*a^13*b*c^5*d^9*f^4 + 144*a^9*b^5*c*d^13*f^4 + 144*a^5*b^9
*c^13*d*f^4 + 144*a*b^13*c^9*d^5*f^4 + 96*a^13*b*c^7*d^7*f^4 + 96*a^13*b*c^3*d^11*f^4 + 96*a^11*b^3*c*d^13*f^4
+ 96*a^7*b^7*c^13*d*f^4 + 96*a^7*b^7*c*d^13*f^4 + 96*a^3*b^11*c^13*d*f^4 + 96*a*b^13*c^11*d^3*f^4 + 96*a*b^13
*c^7*d^7*f^4 + 24*a^13*b*c^9*d^5*f^4 + 24*a^9*b^5*c^13*d*f^4 + 24*a^5*b^9*c*d^13*f^4 + 24*a*b^13*c^5*d^9*f^4 +
24*a^13*b*c*d^13*f^4 + 24*a*b^13*c^13*d*f^4 + 3648*a^7*b^7*c^7*d^7*f^4 - 3188*a^8*b^6*c^6*d^8*f^4 - 3188*a^6*
b^8*c^8*d^6*f^4 - 2912*a^8*b^6*c^8*d^6*f^4 - 2912*a^6*b^8*c^6*d^8*f^4 + 2592*a^9*b^5*c^7*d^7*f^4 + 2592*a^7*b^
7*c^9*d^5*f^4 + 2592*a^7*b^7*c^5*d^9*f^4 + 2592*a^5*b^9*c^7*d^7*f^4 + 2168*a^9*b^5*c^5*d^9*f^4 + 2168*a^5*b^9*
c^9*d^5*f^4 - 1776*a^10*b^4*c^6*d^8*f^4 - 1776*a^8*b^6*c^4*d^10*f^4 - 1776*a^6*b^8*c^10*d^4*f^4 - 1776*a^4*b^1
0*c^8*d^6*f^4 + 1568*a^9*b^5*c^9*d^5*f^4 + 1568*a^5*b^9*c^5*d^9*f^4 - 1344*a^10*b^4*c^8*d^6*f^4 - 1344*a^8*b^6
*c^10*d^4*f^4 - 1344*a^6*b^8*c^4*d^10*f^4 - 1344*a^4*b^10*c^6*d^8*f^4 - 1164*a^10*b^4*c^4*d^10*f^4 - 1164*a^4*
b^10*c^10*d^4*f^4 + 896*a^11*b^3*c^5*d^9*f^4 + 896*a^9*b^5*c^3*d^11*f^4 + 896*a^5*b^9*c^11*d^3*f^4 + 896*a^3*b
^11*c^9*d^5*f^4 + 864*a^11*b^3*c^7*d^7*f^4 + 864*a^7*b^7*c^11*d^3*f^4 + 864*a^7*b^7*c^3*d^11*f^4 + 864*a^3*b^1
1*c^7*d^7*f^4 - 480*a^10*b^4*c^10*d^4*f^4 - 480*a^4*b^10*c^4*d^10*f^4 + 464*a^11*b^3*c^3*d^11*f^4 + 464*a^3*b^
11*c^11*d^3*f^4 - 424*a^12*b^2*c^6*d^8*f^4 - 424*a^8*b^6*c^2*d^12*f^4 - 424*a^6*b^8*c^12*d^2*f^4 - 424*a^2*b^1
2*c^8*d^6*f^4 + 416*a^11*b^3*c^9*d^5*f^4 + 416*a^9*b^5*c^11*d^3*f^4 + 416*a^5*b^9*c^3*d^11*f^4 + 416*a^3*b^11*
c^5*d^9*f^4 - 336*a^12*b^2*c^4*d^10*f^4 - 336*a^10*b^4*c^2*d^12*f^4 - 336*a^4*b^10*c^12*d^2*f^4 - 336*a^2*b^12
*c^10*d^4*f^4 - 256*a^12*b^2*c^8*d^6*f^4 - 256*a^8*b^6*c^12*d^2*f^4 - 256*a^6*b^8*c^2*d^12*f^4 - 256*a^2*b^12*
c^6*d^8*f^4 - 124*a^12*b^2*c^2*d^12*f^4 - 124*a^2*b^12*c^12*d^2*f^4 + 80*a^11*b^3*c^11*d^3*f^4 + 80*a^3*b^11*c
^3*d^11*f^4 - 60*a^12*b^2*c^10*d^4*f^4 - 60*a^10*b^4*c^12*d^2*f^4 - 60*a^4*b^10*c^2*d^12*f^4 - 60*a^2*b^12*c^4
*d^10*f^4 - 24*b^14*c^10*d^4*f^4 - 16*b^14*c^12*d^2*f^4 - 16*b^14*c^8*d^6*f^4 - 4*b^14*c^6*d^8*f^4 - 24*a^14*c
^4*d^10*f^4 - 16*a^14*c^6*d^8*f^4 - 16*a^14*c^2*d^12*f^4 - 4*a^14*c^8*d^6*f^4 - 24*a^10*b^4*d^14*f^4 - 16*a^12
*b^2*d^14*f^4 - 16*a^8*b^6*d^14*f^4 - 4*a^6*b^8*d^14*f^4 - 24*a^4*b^10*c^14*f^4 - 16*a^6*b^8*c^14*f^4 - 16*a^2
*b^12*c^14*f^4 - 4*a^8*b^6*c^14*f^4 - 4*b^14*c^14*f^4 - 4*a^14*d^14*f^4 + 36*A*C*a^9*b*c*d^9*f^2 + 36*A*C*a*b^
9*c^9*d*f^2 + 32*A*C*a*b^9*c*d^9*f^2 - 552*B*C*a^7*b^3*c^4*d^6*f^2 - 552*B*C*a^4*b^6*c^7*d^3*f^2 - 408*B*C*a^5
*b^5*c^4*d^6*f^2 - 408*B*C*a^4*b^6*c^5*d^5*f^2 + 360*B*C*a^6*b^4*c^3*d^7*f^2 + 360*B*C*a^3*b^7*c^6*d^4*f^2 - 2
48*B*C*a^7*b^3*c^2*d^8*f^2 - 248*B*C*a^2*b^8*c^7*d^3*f^2 + 184*B*C*a^6*b^4*c^5*d^5*f^2 + 184*B*C*a^5*b^5*c^6*d
^4*f^2 + 152*B*C*a^8*b^2*c^3*d^7*f^2 - 152*B*C*a^5*b^5*c^2*d^8*f^2 + 152*B*C*a^3*b^7*c^8*d^2*f^2 - 152*B*C*a^2
*b^8*c^5*d^5*f^2 - 104*B*C*a^7*b^3*c^6*d^4*f^2 - 104*B*C*a^6*b^4*c^7*d^3*f^2 + 64*B*C*a^8*b^2*c^5*d^5*f^2 + 64
*B*C*a^5*b^5*c^8*d^2*f^2 - 56*B*C*a^4*b^6*c^3*d^7*f^2 - 56*B*C*a^3*b^7*c^4*d^6*f^2 - 24*B*C*a^8*b^2*c^7*d^3*f^
2 - 24*B*C*a^7*b^3*c^8*d^2*f^2 - 24*B*C*a^3*b^7*c^2*d^8*f^2 - 24*B*C*a^2*b^8*c^3*d^7*f^2 - 696*A*C*a^5*b^5*c^5
*d^5*f^2 + 536*A*C*a^6*b^4*c^6*d^4*f^2 + 536*A*C*a^6*b^4*c^4*d^6*f^2 + 536*A*C*a^4*b^6*c^6*d^4*f^2 + 472*A*C*a
^4*b^6*c^4*d^6*f^2 - 232*A*C*a^7*b^3*c^5*d^5*f^2 - 232*A*C*a^5*b^5*c^7*d^3*f^2 + 216*A*C*a^3*b^7*c^3*d^7*f^2 +
168*A*C*a^7*b^3*c^3*d^7*f^2 + 168*A*C*a^3*b^7*c^7*d^3*f^2 - 154*A*C*a^8*b^2*c^2*d^8*f^2 - 154*A*C*a^2*b^8*c^8
*d^2*f^2 + 62*A*C*a^8*b^2*c^6*d^4*f^2 + 62*A*C*a^6*b^4*c^8*d^2*f^2 - 40*A*C*a^7*b^3*c^7*d^3*f^2 - 40*A*C*a^5*b
^5*c^3*d^7*f^2 - 40*A*C*a^3*b^7*c^5*d^5*f^2 + 32*A*C*a^6*b^4*c^2*d^8*f^2 + 32*A*C*a^2*b^8*c^6*d^4*f^2 - 32*A*C
*a^2*b^8*c^2*d^8*f^2 + 30*A*C*a^4*b^6*c^2*d^8*f^2 + 30*A*C*a^2*b^8*c^4*d^6*f^2 + 16*A*C*a^8*b^2*c^4*d^6*f^2 +
16*A*C*a^4*b^6*c^8*d^2*f^2 - 488*A*B*a^6*b^4*c^3*d^7*f^2 - 488*A*B*a^3*b^7*c^6*d^4*f^2 + 440*A*B*a^7*b^3*c^4*d
^6*f^2 + 440*A*B*a^4*b^6*c^7*d^3*f^2 - 360*A*B*a^6*b^4*c^5*d^5*f^2 - 360*A*B*a^5*b^5*c^6*d^4*f^2 - 192*A*B*a^8
*b^2*c^3*d^7*f^2 - 192*A*B*a^3*b^7*c^8*d^2*f^2 - 168*A*B*a^3*b^7*c^2*d^8*f^2 - 168*A*B*a^2*b^8*c^3*d^7*f^2 - 1
52*A*B*a^4*b^6*c^3*d^7*f^2 - 152*A*B*a^3*b^7*c^4*d^6*f^2 - 120*A*B*a^8*b^2*c^5*d^5*f^2 + 120*A*B*a^7*b^3*c^2*d
^8*f^2 - 120*A*B*a^5*b^5*c^8*d^2*f^2 + 120*A*B*a^5*b^5*c^4*d^6*f^2 - 120*A*B*a^5*b^5*c^2*d^8*f^2 + 120*A*B*a^4
*b^6*c^5*d^5*f^2 + 120*A*B*a^2*b^8*c^7*d^3*f^2 - 120*A*B*a^2*b^8*c^5*d^5*f^2 + 40*A*B*a^7*b^3*c^6*d^4*f^2 + 40
*A*B*a^6*b^4*c^7*d^3*f^2 - 72*B*C*a^9*b*c^4*d^6*f^2 - 72*B*C*a^4*b^6*c^9*d*f^2 - 64*B*C*a^4*b^6*c*d^9*f^2 - 64
*B*C*a*b^9*c^4*d^6*f^2 - 32*B*C*a^8*b^2*c*d^9*f^2 - 32*B*C*a*b^9*c^8*d^2*f^2 - 16*B*C*a^2*b^8*c*d^9*f^2 - 16*B
*C*a*b^9*c^2*d^8*f^2 + 8*B*C*a^9*b*c^6*d^4*f^2 - 8*B*C*a^9*b*c^2*d^8*f^2 + 8*B*C*a^6*b^4*c^9*d*f^2 - 8*B*C*a^2
*b^8*c^9*d*f^2 + 104*A*C*a^7*b^3*c*d^9*f^2 + 104*A*C*a*b^9*c^7*d^3*f^2 + 96*A*C*a^3*b^7*c*d^9*f^2 + 96*A*C*a*b
^9*c^3*d^7*f^2 + 72*A*C*a^9*b*c^3*d^7*f^2 + 72*A*C*a^3*b^7*c^9*d*f^2 + 68*A*C*a^5*b^5*c*d^9*f^2 + 68*A*C*a*b^9
*c^5*d^5*f^2 - 28*A*C*a^9*b*c^5*d^5*f^2 - 28*A*C*a^5*b^5*c^9*d*f^2 + 80*A*B*a^9*b*c^4*d^6*f^2 + 80*A*B*a^4*b^6
*c^9*d*f^2 + 24*A*B*a^8*b^2*c*d^9*f^2 - 24*A*B*a^6*b^4*c*d^9*f^2 + 24*A*B*a^4*b^6*c*d^9*f^2 - 24*A*B*a^2*b^8*c
*d^9*f^2 + 24*A*B*a*b^9*c^8*d^2*f^2 - 24*A*B*a*b^9*c^6*d^4*f^2 + 24*A*B*a*b^9*c^4*d^6*f^2 - 24*A*B*a*b^9*c^2*d
^8*f^2 - 32*B*C*b^10*c^7*d^3*f^2 - 8*B*C*b^10*c^5*d^5*f^2 + 34*A*C*b^10*c^6*d^4*f^2 + 16*B*C*a^10*c^3*d^7*f^2
+ 16*A*C*b^10*c^4*d^6*f^2 - 12*A*C*b^10*c^8*d^2*f^2 - 96*A*B*b^10*c^5*d^5*f^2 - 72*A*B*b^10*c^3*d^7*f^2 - 32*B
*C*a^7*b^3*d^10*f^2 - 28*A*C*a^10*c^2*d^8*f^2 - 24*A*B*b^10*c^7*d^3*f^2 - 8*B*C*a^5*b^5*d^10*f^2 + 2*A*C*a^10*
c^4*d^6*f^2 + 34*A*C*a^6*b^4*d^10*f^2 + 16*B*C*a^3*b^7*c^10*f^2 + 16*A*C*a^4*b^6*d^10*f^2 - 16*A*B*a^10*c^3*d^
7*f^2 - 12*A*C*a^8*b^2*d^10*f^2 - 96*A*B*a^5*b^5*d^10*f^2 - 72*A*B*a^3*b^7*d^10*f^2 - 28*A*C*a^2*b^8*c^10*f^2
- 24*A*B*a^7*b^3*d^10*f^2 + 2*A*C*a^4*b^6*c^10*f^2 - 16*A*B*a^3*b^7*c^10*f^2 + 444*C^2*a^5*b^5*c^5*d^5*f^2 + 1
48*C^2*a^7*b^3*c^5*d^5*f^2 + 148*C^2*a^5*b^5*c^7*d^3*f^2 + 148*C^2*a^5*b^5*c^3*d^7*f^2 + 148*C^2*a^3*b^7*c^5*d
^5*f^2 - 140*C^2*a^6*b^4*c^6*d^4*f^2 - 140*C^2*a^6*b^4*c^4*d^6*f^2 - 140*C^2*a^4*b^6*c^6*d^4*f^2 - 140*C^2*a^4
*b^6*c^4*d^6*f^2 + 109*C^2*a^8*b^2*c^2*d^8*f^2 + 109*C^2*a^2*b^8*c^8*d^2*f^2 + 48*C^2*a^8*b^2*c^4*d^6*f^2 + 48
*C^2*a^6*b^4*c^2*d^8*f^2 + 48*C^2*a^4*b^6*c^8*d^2*f^2 + 48*C^2*a^2*b^8*c^6*d^4*f^2 + 20*C^2*a^7*b^3*c^7*d^3*f^
2 - 20*C^2*a^7*b^3*c^3*d^7*f^2 - 20*C^2*a^3*b^7*c^7*d^3*f^2 + 20*C^2*a^3*b^7*c^3*d^7*f^2 + 17*C^2*a^8*b^2*c^6*
d^4*f^2 + 17*C^2*a^6*b^4*c^8*d^2*f^2 + 17*C^2*a^4*b^6*c^2*d^8*f^2 + 17*C^2*a^2*b^8*c^4*d^6*f^2 + 16*C^2*a^8*b^
2*c^8*d^2*f^2 + 16*C^2*a^2*b^8*c^2*d^8*f^2 - 396*B^2*a^5*b^5*c^5*d^5*f^2 + 308*B^2*a^6*b^4*c^4*d^6*f^2 + 308*B
^2*a^4*b^6*c^6*d^4*f^2 + 300*B^2*a^4*b^6*c^4*d^6*f^2 + 284*B^2*a^6*b^4*c^6*d^4*f^2 - 132*B^2*a^7*b^3*c^5*d^5*f
^2 - 132*B^2*a^5*b^5*c^7*d^3*f^2 - 84*B^2*a^5*b^5*c^3*d^7*f^2 - 84*B^2*a^3*b^7*c^5*d^5*f^2 + 61*B^2*a^4*b^6*c^
2*d^8*f^2 + 61*B^2*a^2*b^8*c^4*d^6*f^2 - 59*B^2*a^8*b^2*c^2*d^8*f^2 - 59*B^2*a^2*b^8*c^8*d^2*f^2 + 56*B^2*a^6*
b^4*c^2*d^8*f^2 + 56*B^2*a^2*b^8*c^6*d^4*f^2 + 52*B^2*a^7*b^3*c^3*d^7*f^2 + 52*B^2*a^3*b^7*c^7*d^3*f^2 + 44*B^
2*a^3*b^7*c^3*d^7*f^2 + 33*B^2*a^8*b^2*c^6*d^4*f^2 + 33*B^2*a^6*b^4*c^8*d^2*f^2 + 20*B^2*a^8*b^2*c^4*d^6*f^2 -
20*B^2*a^7*b^3*c^7*d^3*f^2 + 20*B^2*a^4*b^6*c^8*d^2*f^2 + 8*B^2*a^2*b^8*c^2*d^8*f^2 + 337*A^2*a^4*b^6*c^2*d^8
*f^2 + 337*A^2*a^2*b^8*c^4*d^6*f^2 + 272*A^2*a^2*b^8*c^2*d^8*f^2 + 252*A^2*a^5*b^5*c^5*d^5*f^2 + 244*A^2*a^4*b
^6*c^4*d^6*f^2 - 236*A^2*a^3*b^7*c^3*d^7*f^2 + 176*A^2*a^6*b^4*c^2*d^8*f^2 + 176*A^2*a^2*b^8*c^6*d^4*f^2 - 148
*A^2*a^7*b^3*c^3*d^7*f^2 - 148*A^2*a^3*b^7*c^7*d^3*f^2 - 140*A^2*a^6*b^4*c^6*d^4*f^2 + 109*A^2*a^8*b^2*c^2*d^8
*f^2 + 109*A^2*a^2*b^8*c^8*d^2*f^2 - 108*A^2*a^5*b^5*c^3*d^7*f^2 - 108*A^2*a^3*b^7*c^5*d^5*f^2 + 84*A^2*a^7*b^
3*c^5*d^5*f^2 + 84*A^2*a^5*b^5*c^7*d^3*f^2 + 32*A^2*a^8*b^2*c^4*d^6*f^2 + 32*A^2*a^4*b^6*c^8*d^2*f^2 + 20*A^2*
a^7*b^3*c^7*d^3*f^2 - 15*A^2*a^8*b^2*c^6*d^4*f^2 - 15*A^2*a^6*b^4*c^8*d^2*f^2 - 12*A^2*a^6*b^4*c^4*d^6*f^2 - 1
2*A^2*a^4*b^6*c^6*d^4*f^2 + 8*B*C*b^10*c^9*d*f^2 - 16*B*C*a^10*c*d^9*f^2 - 16*A*B*b^10*c^9*d*f^2 - 16*A*B*b^10
*c*d^9*f^2 + 8*B*C*a^9*b*d^10*f^2 - 16*B*C*a*b^9*c^10*f^2 + 16*A*B*a^10*c*d^9*f^2 - 16*A*B*a^9*b*d^10*f^2 - 16
*A*B*a*b^9*d^10*f^2 + 16*A*B*a*b^9*c^10*f^2 + 22*C^2*a^9*b*c^5*d^5*f^2 + 22*C^2*a^5*b^5*c^9*d*f^2 + 22*C^2*a^5
*b^5*c*d^9*f^2 + 22*C^2*a*b^9*c^5*d^5*f^2 - 20*C^2*a^9*b*c^3*d^7*f^2 - 20*C^2*a^7*b^3*c*d^9*f^2 - 20*C^2*a^3*b
^7*c^9*d*f^2 - 20*C^2*a*b^9*c^7*d^3*f^2 + 36*B^2*a^7*b^3*c*d^9*f^2 + 36*B^2*a*b^9*c^7*d^3*f^2 + 28*B^2*a^9*b*c
^3*d^7*f^2 + 28*B^2*a^3*b^7*c^9*d*f^2 + 24*B^2*a^3*b^7*c*d^9*f^2 + 24*B^2*a*b^9*c^3*d^7*f^2 - 18*B^2*a^9*b*c^5
*d^5*f^2 - 18*B^2*a^5*b^5*c^9*d*f^2 + 6*B^2*a^5*b^5*c*d^9*f^2 + 6*B^2*a*b^9*c^5*d^5*f^2 - 96*A^2*a^3*b^7*c*d^9
*f^2 - 96*A^2*a*b^9*c^3*d^7*f^2 - 90*A^2*a^5*b^5*c*d^9*f^2 - 90*A^2*a*b^9*c^5*d^5*f^2 - 84*A^2*a^7*b^3*c*d^9*f
^2 - 84*A^2*a*b^9*c^7*d^3*f^2 - 52*A^2*a^9*b*c^3*d^7*f^2 - 52*A^2*a^3*b^7*c^9*d*f^2 + 6*A^2*a^9*b*c^5*d^5*f^2
+ 6*A^2*a^5*b^5*c^9*d*f^2 - 10*C^2*a^9*b*c*d^9*f^2 - 10*C^2*a*b^9*c^9*d*f^2 + 14*B^2*a^9*b*c*d^9*f^2 + 14*B^2*
a*b^9*c^9*d*f^2 + 8*B^2*a*b^9*c*d^9*f^2 - 32*A^2*a*b^9*c*d^9*f^2 - 26*A^2*a^9*b*c*d^9*f^2 - 26*A^2*a*b^9*c^9*d
*f^2 + 2*A*C*b^10*c^10*f^2 + 2*A*C*a^10*d^10*f^2 + 14*C^2*b^10*c^8*d^2*f^2 - C^2*b^10*c^6*d^4*f^2 + 31*B^2*b^1
0*c^6*d^4*f^2 + 20*B^2*b^10*c^4*d^6*f^2 + 14*C^2*a^10*c^2*d^8*f^2 + 4*B^2*b^10*c^2*d^8*f^2 + 2*B^2*b^10*c^8*d^
2*f^2 - C^2*a^10*c^4*d^6*f^2 + 80*A^2*b^10*c^4*d^6*f^2 + 64*A^2*b^10*c^2*d^8*f^2 + 31*A^2*b^10*c^6*d^4*f^2 + 1
4*C^2*a^8*b^2*d^10*f^2 + 14*A^2*b^10*c^8*d^2*f^2 - 10*B^2*a^10*c^2*d^8*f^2 + 3*B^2*a^10*c^4*d^6*f^2 - C^2*a^6*
b^4*d^10*f^2 + 31*B^2*a^6*b^4*d^10*f^2 + 20*B^2*a^4*b^6*d^10*f^2 + 14*C^2*a^2*b^8*c^10*f^2 + 14*A^2*a^10*c^2*d
^8*f^2 + 4*B^2*a^2*b^8*d^10*f^2 + 2*B^2*a^8*b^2*d^10*f^2 - C^2*a^4*b^6*c^10*f^2 - A^2*a^10*c^4*d^6*f^2 + 80*A^
2*a^4*b^6*d^10*f^2 + 64*A^2*a^2*b^8*d^10*f^2 + 31*A^2*a^6*b^4*d^10*f^2 + 14*A^2*a^8*b^2*d^10*f^2 - 10*B^2*a^2*
b^8*c^10*f^2 + 3*B^2*a^4*b^6*c^10*f^2 + 14*A^2*a^2*b^8*c^10*f^2 - A^2*a^4*b^6*c^10*f^2 - C^2*b^10*c^10*f^2 - C
^2*a^10*d^10*f^2 + 16*A^2*b^10*d^10*f^2 + 3*B^2*b^10*c^10*f^2 + 3*B^2*a^10*d^10*f^2 - A^2*b^10*c^10*f^2 - A^2*
a^10*d^10*f^2 - 96*A*B*C*a*b^7*c*d^7*f - 28*A*B*C*a^7*b*c*d^7*f - 28*A*B*C*a*b^7*c^7*d*f + 484*A*B*C*a^4*b^4*c
^4*d^4*f - 424*A*B*C*a^3*b^5*c^3*d^5*f + 320*A*B*C*a^2*b^6*c^2*d^6*f - 176*A*B*C*a^6*b^2*c^2*d^6*f - 176*A*B*C
*a^2*b^6*c^6*d^2*f + 158*A*B*C*a^4*b^4*c^2*d^6*f + 158*A*B*C*a^2*b^6*c^4*d^4*f - 136*A*B*C*a^5*b^3*c^5*d^3*f -
34*A*B*C*a^6*b^2*c^4*d^4*f - 34*A*B*C*a^4*b^4*c^6*d^2*f + 28*A*B*C*a^5*b^3*c^3*d^5*f + 28*A*B*C*a^3*b^5*c^5*d
^3*f + 308*A*B*C*a^5*b^3*c*d^7*f + 308*A*B*C*a*b^7*c^5*d^3*f + 20*A*B*C*a^7*b*c^3*d^5*f + 20*A*B*C*a^3*b^5*c^7
*d*f + 30*B*C^2*a^7*b*c*d^7*f + 30*B*C^2*a*b^7*c^7*d*f + 160*A^2*B*a*b^7*c*d^7*f - 2*A^2*B*a^7*b*c*d^7*f - 2*A
^2*B*a*b^7*c^7*d*f - 96*A*B*C*b^8*c^4*d^4*f + 34*A*B*C*b^8*c^6*d^2*f - 32*A*B*C*b^8*c^2*d^6*f + 2*A*B*C*a^8*c^
2*d^6*f - 96*A*B*C*a^4*b^4*d^8*f + 34*A*B*C*a^6*b^2*d^8*f - 32*A*B*C*a^2*b^6*d^8*f + 2*A*B*C*a^2*b^6*c^8*f - 2
10*B*C^2*a^4*b^4*c^4*d^4*f - 182*B^2*C*a^5*b^3*c^2*d^6*f - 182*B^2*C*a^2*b^6*c^5*d^3*f + 180*B*C^2*a^5*b^3*c^5
*d^3*f + 180*B*C^2*a^3*b^5*c^3*d^5*f - 166*B^2*C*a^5*b^3*c^4*d^4*f - 166*B^2*C*a^4*b^4*c^5*d^3*f + 152*B*C^2*a
^6*b^2*c^2*d^6*f + 152*B*C^2*a^2*b^6*c^6*d^2*f - 112*B^2*C*a^3*b^5*c^2*d^6*f - 112*B^2*C*a^2*b^6*c^3*d^5*f + 9
4*B^2*C*a^4*b^4*c^3*d^5*f + 94*B^2*C*a^3*b^5*c^4*d^4*f - 80*B*C^2*a^2*b^6*c^2*d^6*f + 66*B*C^2*a^5*b^3*c^3*d^5
*f + 66*B*C^2*a^3*b^5*c^5*d^3*f + 46*B^2*C*a^6*b^2*c^3*d^5*f + 46*B^2*C*a^3*b^5*c^6*d^2*f + 33*B*C^2*a^6*b^2*c
^4*d^4*f + 33*B*C^2*a^4*b^4*c^6*d^2*f + 24*B^2*C*a^6*b^2*c^5*d^3*f + 24*B^2*C*a^5*b^3*c^6*d^2*f - 16*B*C^2*a^6
*b^2*c^6*d^2*f - 15*B*C^2*a^4*b^4*c^2*d^6*f - 15*B*C^2*a^2*b^6*c^4*d^4*f - 190*A^2*C*a^4*b^4*c^3*d^5*f - 190*A
^2*C*a^3*b^5*c^4*d^4*f + 182*A^2*C*a^5*b^3*c^2*d^6*f + 182*A^2*C*a^2*b^6*c^5*d^3*f + 160*A^2*C*a^3*b^5*c^2*d^6
*f + 160*A^2*C*a^2*b^6*c^3*d^5*f - 150*A*C^2*a^5*b^3*c^2*d^6*f - 150*A*C^2*a^2*b^6*c^5*d^3*f - 126*A*C^2*a^5*b
^3*c^4*d^4*f - 126*A*C^2*a^4*b^4*c^5*d^3*f + 126*A*C^2*a^4*b^4*c^3*d^5*f + 126*A*C^2*a^3*b^5*c^4*d^4*f - 96*A*
C^2*a^3*b^5*c^2*d^6*f - 96*A*C^2*a^2*b^6*c^3*d^5*f + 94*A^2*C*a^5*b^3*c^4*d^4*f + 94*A^2*C*a^4*b^4*c^5*d^3*f +
54*A*C^2*a^6*b^2*c^3*d^5*f + 54*A*C^2*a^3*b^5*c^6*d^2*f + 32*A*C^2*a^6*b^2*c^5*d^3*f + 32*A*C^2*a^5*b^3*c^6*d
^2*f - 22*A^2*C*a^6*b^2*c^3*d^5*f - 22*A^2*C*a^3*b^5*c^6*d^2*f + 500*A^2*B*a^3*b^5*c^3*d^5*f - 290*A^2*B*a^4*b
^4*c^4*d^4*f - 256*A^2*B*a^2*b^6*c^2*d^6*f - 230*A*B^2*a^4*b^4*c^3*d^5*f - 230*A*B^2*a^3*b^5*c^4*d^4*f + 142*A
*B^2*a^5*b^3*c^2*d^6*f + 142*A*B^2*a^2*b^6*c^5*d^3*f - 127*A^2*B*a^4*b^4*c^2*d^6*f - 127*A^2*B*a^2*b^6*c^4*d^4
*f + 86*A*B^2*a^5*b^3*c^4*d^4*f + 86*A*B^2*a^4*b^4*c^5*d^3*f + 80*A*B^2*a^3*b^5*c^2*d^6*f + 80*A*B^2*a^2*b^6*c
^3*d^5*f + 40*A^2*B*a^6*b^2*c^2*d^6*f + 40*A^2*B*a^2*b^6*c^6*d^2*f + 34*A^2*B*a^5*b^3*c^3*d^5*f + 34*A^2*B*a^3
*b^5*c^5*d^3*f - 30*A*B^2*a^6*b^2*c^3*d^5*f - 30*A*B^2*a^3*b^5*c^6*d^2*f + 20*A^2*B*a^5*b^3*c^5*d^3*f - 15*A^2
*B*a^6*b^2*c^4*d^4*f - 15*A^2*B*a^4*b^4*c^6*d^2*f - 98*B^2*C*a^6*b^2*c*d^7*f - 98*B^2*C*a*b^7*c^6*d^2*f - 90*B
*C^2*a^5*b^3*c*d^7*f - 90*B*C^2*a*b^7*c^5*d^3*f + 48*B^2*C*a^4*b^4*c*d^7*f + 48*B^2*C*a*b^7*c^4*d^4*f + 40*B^2
*C*a^2*b^6*c*d^7*f + 40*B^2*C*a*b^7*c^2*d^6*f - 32*B*C^2*a^3*b^5*c*d^7*f - 32*B*C^2*a*b^7*c^3*d^5*f + 26*B^2*C
*a^7*b*c^2*d^6*f + 26*B^2*C*a^2*b^6*c^7*d*f - 26*B*C^2*a^7*b*c^3*d^5*f - 26*B*C^2*a^3*b^5*c^7*d*f - 8*B^2*C*a^
7*b*c^4*d^4*f - 8*B^2*C*a^4*b^4*c^7*d*f - 224*A^2*C*a^4*b^4*c*d^7*f - 224*A^2*C*a*b^7*c^4*d^4*f - 96*A^2*C*a^2
*b^6*c*d^7*f - 96*A^2*C*a*b^7*c^2*d^6*f + 96*A*C^2*a^4*b^4*c*d^7*f + 96*A*C^2*a*b^7*c^4*d^4*f - 66*A*C^2*a^6*b
^2*c*d^7*f - 66*A*C^2*a*b^7*c^6*d^2*f + 64*A*C^2*a^2*b^6*c*d^7*f + 64*A*C^2*a*b^7*c^2*d^6*f + 34*A^2*C*a^6*b^2
*c*d^7*f + 34*A^2*C*a*b^7*c^6*d^2*f + 34*A*C^2*a^7*b*c^2*d^6*f + 34*A*C^2*a^2*b^6*c^7*d*f - 2*A^2*C*a^7*b*c^2*
d^6*f - 2*A^2*C*a^2*b^6*c^7*d*f - 208*A*B^2*a^4*b^4*c*d^7*f - 208*A*B^2*a*b^7*c^4*d^4*f + 160*A^2*B*a^3*b^5*c*
d^7*f + 160*A^2*B*a*b^7*c^3*d^5*f - 154*A^2*B*a^5*b^3*c*d^7*f - 154*A^2*B*a*b^7*c^5*d^3*f - 112*A*B^2*a^2*b^6*
c*d^7*f - 112*A*B^2*a*b^7*c^2*d^6*f + 58*A*B^2*a^6*b^2*c*d^7*f + 58*A*B^2*a*b^7*c^6*d^2*f - 10*A*B^2*a^7*b*c^2
*d^6*f - 10*A*B^2*a^2*b^6*c^7*d*f + 6*A^2*B*a^7*b*c^3*d^5*f + 6*A^2*B*a^3*b^5*c^7*d*f + 32*B^2*C*b^8*c^5*d^3*f
- 17*B*C^2*b^8*c^6*d^2*f + 8*B^2*C*b^8*c^3*d^5*f + 64*A^2*C*b^8*c^3*d^5*f - 32*A^2*C*b^8*c^5*d^3*f + 32*A*C^2
*b^8*c^5*d^3*f - B*C^2*a^8*c^2*d^6*f + 112*A^2*B*b^8*c^4*d^4*f - 64*A*B^2*b^8*c^5*d^3*f + 32*B^2*C*a^5*b^3*d^8
*f - 17*B*C^2*a^6*b^2*d^8*f + 16*A^2*B*b^8*c^2*d^6*f + 16*A*B^2*b^8*c^3*d^5*f + 8*B^2*C*a^3*b^5*d^8*f - A^2*B*
b^8*c^6*d^2*f + 64*A^2*C*a^3*b^5*d^8*f - 32*A^2*C*a^5*b^3*d^8*f + 32*A*C^2*a^5*b^3*d^8*f - A^2*B*a^8*c^2*d^6*f
- B*C^2*a^2*b^6*c^8*f + 112*A^2*B*a^4*b^4*d^8*f - 64*A*B^2*a^5*b^3*d^8*f + 16*A^2*B*a^2*b^6*d^8*f + 16*A*B^2*
a^3*b^5*d^8*f - A^2*B*a^6*b^2*d^8*f - A^2*B*a^2*b^6*c^8*f - 8*B^3*a*b^7*c*d^7*f - 2*B^3*a^7*b*c*d^7*f - 2*B^3*
a*b^7*c^7*d*f - 6*B^2*C*b^8*c^7*d*f + 32*A^2*C*b^8*c*d^7*f + 6*A^2*C*b^8*c^7*d*f - 6*A*C^2*b^8*c^7*d*f - 2*B^2
*C*a^8*c*d^7*f + 16*A*B^2*b^8*c*d^7*f - 6*B^2*C*a^7*b*d^8*f - 6*A^2*C*a^8*c*d^7*f + 6*A*C^2*a^8*c*d^7*f - 2*A*
B^2*b^8*c^7*d*f + 32*A^2*C*a*b^7*d^8*f + 6*A^2*C*a^7*b*d^8*f - 6*A*C^2*a^7*b*d^8*f - 2*B^2*C*a*b^7*c^8*f + 2*A
*B^2*a^8*c*d^7*f + 16*A*B^2*a*b^7*d^8*f - 6*A^2*C*a*b^7*c^8*f + 6*A*C^2*a*b^7*c^8*f - 2*A*B^2*a^7*b*d^8*f + 2*
A*B^2*a*b^7*c^8*f - 50*C^3*a^6*b^2*c^3*d^5*f + 50*C^3*a^5*b^3*c^2*d^6*f - 50*C^3*a^3*b^5*c^6*d^2*f + 50*C^3*a^
2*b^6*c^5*d^3*f + 42*C^3*a^5*b^3*c^4*d^4*f + 42*C^3*a^4*b^4*c^5*d^3*f - 42*C^3*a^4*b^4*c^3*d^5*f - 42*C^3*a^3*
b^5*c^4*d^4*f - 32*C^3*a^6*b^2*c^5*d^3*f - 32*C^3*a^5*b^3*c^6*d^2*f + 32*C^3*a^3*b^5*c^2*d^6*f + 32*C^3*a^2*b^
6*c^3*d^5*f + 94*B^3*a^4*b^4*c^4*d^4*f + 48*B^3*a^2*b^6*c^2*d^6*f - 44*B^3*a^3*b^5*c^3*d^5*f - 32*B^3*a^6*b^2*
c^2*d^6*f - 32*B^3*a^2*b^6*c^6*d^2*f + 29*B^3*a^4*b^4*c^2*d^6*f + 29*B^3*a^2*b^6*c^4*d^4*f - 20*B^3*a^5*b^3*c^
5*d^3*f + 18*B^3*a^5*b^3*c^3*d^5*f + 18*B^3*a^3*b^5*c^5*d^3*f - 3*B^3*a^6*b^2*c^4*d^4*f - 3*B^3*a^4*b^4*c^6*d^
2*f + 106*A^3*a^4*b^4*c^3*d^5*f + 106*A^3*a^3*b^5*c^4*d^4*f - 96*A^3*a^3*b^5*c^2*d^6*f - 96*A^3*a^2*b^6*c^3*d^
5*f - 82*A^3*a^5*b^3*c^2*d^6*f - 82*A^3*a^2*b^6*c^5*d^3*f + 18*A^3*a^6*b^2*c^3*d^5*f + 18*A^3*a^3*b^5*c^6*d^2*
f - 10*A^3*a^5*b^3*c^4*d^4*f - 10*A^3*a^4*b^4*c^5*d^3*f - 22*C^3*a^7*b*c^2*d^6*f + 22*C^3*a^6*b^2*c*d^7*f - 22
*C^3*a^2*b^6*c^7*d*f + 22*C^3*a*b^7*c^6*d^2*f - 2*A*B*C*b^8*c^8*f - 2*A*B*C*a^8*d^8*f + 62*B^3*a^5*b^3*c*d^7*f
+ 62*B^3*a*b^7*c^5*d^3*f + 16*B^3*a^3*b^5*c*d^7*f + 16*B^3*a*b^7*c^3*d^5*f + 6*B^3*a^7*b*c^3*d^5*f + 6*B^3*a^
3*b^5*c^7*d*f + 128*A^3*a^4*b^4*c*d^7*f + 128*A^3*a*b^7*c^4*d^4*f + 32*A^3*a^2*b^6*c*d^7*f + 32*A^3*a*b^7*c^2*
d^6*f - 10*A^3*a^7*b*c^2*d^6*f + 10*A^3*a^6*b^2*c*d^7*f - 10*A^3*a^2*b^6*c^7*d*f + 10*A^3*a*b^7*c^6*d^2*f + 11
*B^3*b^8*c^6*d^2*f - 8*B^3*b^8*c^4*d^4*f - 4*B^3*b^8*c^2*d^6*f - 64*A^3*b^8*c^3*d^5*f - B^3*a^8*c^2*d^6*f + 11
*B^3*a^6*b^2*d^8*f - 8*B^3*a^4*b^4*d^8*f - 4*B^3*a^2*b^6*d^8*f - 64*A^3*a^3*b^5*d^8*f - B^3*a^2*b^6*c^8*f + 2*
C^3*b^8*c^7*d*f - 2*C^3*a^8*c*d^7*f - 32*A^3*b^8*c*d^7*f + 2*C^3*a^7*b*d^8*f - 2*A^3*b^8*c^7*d*f - 2*C^3*a*b^7
*c^8*f + 2*A^3*a^8*c*d^7*f - 32*A^3*a*b^7*d^8*f - 2*A^3*a^7*b*d^8*f + 2*A^3*a*b^7*c^8*f - 16*A^2*B*b^8*d^8*f +
B*C^2*b^8*c^8*f + B*C^2*a^8*d^8*f + A^2*B*b^8*c^8*f + A^2*B*a^8*d^8*f + B^3*b^8*c^8*f + B^3*a^8*d^8*f - 4*A*B
^2*C*a^5*b*c*d^5 - 4*A*B^2*C*a*b^5*c^5*d + 4*A*B^2*C*a*b^5*c*d^5 + 22*A^2*B*C*a^3*b^3*c^2*d^4 + 22*A^2*B*C*a^2
*b^4*c^3*d^3 - 20*A*B^2*C*a^3*b^3*c^3*d^3 + 14*A*B^2*C*a^4*b^2*c^2*d^4 + 14*A*B^2*C*a^2*b^4*c^4*d^2 - 14*A*B*C
^2*a^3*b^3*c^2*d^4 - 14*A*B*C^2*a^2*b^4*c^3*d^3 + 12*A*B*C^2*a^4*b^2*c^3*d^3 + 12*A*B*C^2*a^3*b^3*c^4*d^2 - 6*
A^2*B*C*a^4*b^2*c^3*d^3 - 6*A^2*B*C*a^3*b^3*c^4*d^2 - 4*A*B^2*C*a^2*b^4*c^2*d^4 + 22*A*B*C^2*a^4*b^2*c*d^5 + 2
2*A*B*C^2*a*b^5*c^4*d^2 - 20*A^2*B*C*a^4*b^2*c*d^5 - 20*A^2*B*C*a*b^5*c^4*d^2 + 10*A*B*C^2*a^2*b^4*c*d^5 + 10*
A*B*C^2*a*b^5*c^2*d^4 - 8*A^2*B*C*a^2*b^4*c*d^5 - 8*A^2*B*C*a*b^5*c^2*d^4 + 4*A*B^2*C*a^3*b^3*c*d^5 + 4*A*B^2*
C*a*b^5*c^3*d^3 - 4*A*B*C^2*a^5*b*c^2*d^4 - 4*A*B*C^2*a^2*b^4*c^5*d + 2*A^2*B*C*a^5*b*c^2*d^4 + 2*A^2*B*C*a^2*
b^4*c^5*d - 8*B^3*C*a^4*b^2*c*d^5 - 8*B^3*C*a*b^5*c^4*d^2 - 8*B*C^3*a^4*b^2*c*d^5 - 8*B*C^3*a*b^5*c^4*d^2 - 4*
B^3*C*a^2*b^4*c*d^5 - 4*B^3*C*a*b^5*c^2*d^4 + 4*B^2*C^2*a^5*b*c*d^5 + 4*B^2*C^2*a*b^5*c^5*d - 4*B*C^3*a^2*b^4*
c*d^5 - 4*B*C^3*a*b^5*c^2*d^4 + 2*B^3*C*a^5*b*c^2*d^4 + 2*B^3*C*a^2*b^4*c^5*d + 2*B^2*C^2*a*b^5*c*d^5 + 2*B*C^
3*a^5*b*c^2*d^4 + 2*B*C^3*a^2*b^4*c^5*d + 24*A^3*C*a^3*b^3*c*d^5 + 24*A^3*C*a*b^5*c^3*d^3 - 24*A^2*C^2*a*b^5*c
*d^5 + 12*A^2*C^2*a^5*b*c*d^5 + 12*A^2*C^2*a*b^5*c^5*d + 8*A*C^3*a^3*b^3*c*d^5 + 8*A*C^3*a*b^5*c^3*d^3 + 6*A^3
*B*a^4*b^2*c*d^5 + 6*A^3*B*a*b^5*c^4*d^2 - 6*A^2*B^2*a*b^5*c*d^5 + 6*A*B^3*a^4*b^2*c*d^5 + 6*A*B^3*a*b^5*c^4*d
^2 + 2*A^3*B*a^2*b^4*c*d^5 + 2*A^3*B*a*b^5*c^2*d^4 + 2*A*B^3*a^2*b^4*c*d^5 + 2*A*B^3*a*b^5*c^2*d^4 + 20*A^2*B*
C*b^6*c^3*d^3 - 10*A*B*C^2*b^6*c^3*d^3 - 2*A*B^2*C*b^6*c^4*d^2 - 2*A*B^2*C*b^6*c^2*d^4 + 20*A^2*B*C*a^3*b^3*d^
6 - 10*A*B*C^2*a^3*b^3*d^6 - 2*A*B^2*C*a^4*b^2*d^6 - 2*A*B^2*C*a^2*b^4*d^6 + 10*B^2*C^2*a^3*b^3*c^3*d^3 + 4*B^
2*C^2*a^4*b^2*c^4*d^2 - 3*B^2*C^2*a^4*b^2*c^2*d^4 - 3*B^2*C^2*a^2*b^4*c^4*d^2 + 2*B^2*C^2*a^2*b^4*c^2*d^4 + 40
*A^2*C^2*a^2*b^4*c^2*d^4 - 16*A^2*C^2*a^4*b^2*c^2*d^4 - 16*A^2*C^2*a^2*b^4*c^4*d^2 + 4*A^2*C^2*a^4*b^2*c^4*d^2
+ 18*A^2*B^2*a^2*b^4*c^2*d^4 + 10*A^2*B^2*a^3*b^3*c^3*d^3 - 3*A^2*B^2*a^4*b^2*c^2*d^4 - 3*A^2*B^2*a^2*b^4*c^4
*d^2 + 24*A^3*C*a*b^5*c*d^5 - 12*A*C^3*a^5*b*c*d^5 - 12*A*C^3*a*b^5*c^5*d + 8*A*C^3*a*b^5*c*d^5 - 4*A^3*C*a^5*
b*c*d^5 - 4*A^3*C*a*b^5*c^5*d + 8*A^2*B*C*b^6*c*d^5 + 4*A*B*C^2*b^6*c^5*d - 4*A*B*C^2*b^6*c*d^5 - 2*A^2*B*C*b^
6*c^5*d + 8*A^2*B*C*a*b^5*d^6 + 4*A*B*C^2*a^5*b*d^6 - 4*A*B*C^2*a*b^5*d^6 - 2*A^2*B*C*a^5*b*d^6 - 6*B^3*C*a^4*
b^2*c^3*d^3 - 6*B^3*C*a^3*b^3*c^4*d^2 - 6*B*C^3*a^4*b^2*c^3*d^3 - 6*B*C^3*a^3*b^3*c^4*d^2 + 2*B^3*C*a^3*b^3*c^
2*d^4 + 2*B^3*C*a^2*b^4*c^3*d^3 + 2*B^2*C^2*a^3*b^3*c*d^5 + 2*B^2*C^2*a*b^5*c^3*d^3 + 2*B*C^3*a^3*b^3*c^2*d^4
+ 2*B*C^3*a^2*b^4*c^3*d^3 - 48*A^3*C*a^2*b^4*c^2*d^4 - 24*A^2*C^2*a^3*b^3*c*d^5 - 24*A^2*C^2*a*b^5*c^3*d^3 - 1
6*A*C^3*a^2*b^4*c^2*d^4 + 8*A^3*C*a^4*b^2*c^2*d^4 + 8*A^3*C*a^2*b^4*c^4*d^2 - 8*A*C^3*a^4*b^2*c^4*d^2 + 8*A*C^
3*a^4*b^2*c^2*d^4 + 8*A*C^3*a^2*b^4*c^4*d^2 - 10*A^3*B*a^3*b^3*c^2*d^4 - 10*A^3*B*a^2*b^4*c^3*d^3 - 10*A*B^3*a
^3*b^3*c^2*d^4 - 10*A*B^3*a^2*b^4*c^3*d^3 - 6*A^2*B^2*a^3*b^3*c*d^5 - 6*A^2*B^2*a*b^5*c^3*d^3 + 3*B^2*C^2*b^6*
c^4*d^2 - 8*A^2*C^2*b^6*c^4*d^2 + 8*A^2*C^2*b^6*c^2*d^4 + 9*A^2*B^2*b^6*c^2*d^4 + 3*B^2*C^2*a^4*b^2*d^6 + 3*A^
2*B^2*b^6*c^4*d^2 - 8*A^2*C^2*a^4*b^2*d^6 + 8*A^2*C^2*a^2*b^4*d^6 + 9*A^2*B^2*a^2*b^4*d^6 + 3*A^2*B^2*a^4*b^2*
d^6 + 2*B^4*a^3*b^3*c*d^5 + 2*B^4*a*b^5*c^3*d^3 - 8*A^4*a^3*b^3*c*d^5 - 8*A^4*a*b^5*c^3*d^3 - 16*A^3*C*b^6*c^2
*d^4 + 4*A^3*C*b^6*c^4*d^2 + 4*A*C^3*b^6*c^4*d^2 - 10*A^3*B*b^6*c^3*d^3 - 10*A*B^3*b^6*c^3*d^3 - 16*A^3*C*a^2*
b^4*d^6 + 4*A^3*C*a^4*b^2*d^6 + 4*A*C^3*a^4*b^2*d^6 - 10*A^3*B*a^3*b^3*d^6 - 10*A*B^3*a^3*b^3*d^6 + 4*C^4*a^5*
b*c*d^5 + 4*C^4*a*b^5*c^5*d + 2*B^4*a*b^5*c*d^5 - 8*A^4*a*b^5*c*d^5 - 2*B^3*C*b^6*c^5*d - 2*B*C^3*b^6*c^5*d -
4*A^3*B*b^6*c*d^5 - 4*A*B^3*b^6*c*d^5 - 2*B^3*C*a^5*b*d^6 - 2*B*C^3*a^5*b*d^6 - 4*A^3*B*a*b^5*d^6 - 4*A*B^3*a*
b^5*d^6 + 4*C^4*a^4*b^2*c^4*d^2 + 4*C^4*a^2*b^4*c^2*d^4 + 10*B^4*a^3*b^3*c^3*d^3 - 3*B^4*a^4*b^2*c^2*d^4 - 3*B
^4*a^2*b^4*c^4*d^2 - 2*B^4*a^2*b^4*c^2*d^4 + 20*A^4*a^2*b^4*c^2*d^4 + B^2*C^2*b^6*c^2*d^4 + B^2*C^2*a^2*b^4*d^
6 - 8*A^3*C*b^6*d^6 + 3*B^4*b^6*c^4*d^2 + 8*A^4*b^6*c^2*d^4 + 3*B^4*a^4*b^2*d^6 + 8*A^4*a^2*b^4*d^6 + 4*A^2*C^
2*b^6*d^6 + 4*A^2*B^2*b^6*d^6 + 4*A^4*b^6*d^6 + B^4*b^6*c^2*d^4 + B^4*a^2*b^4*d^6, f, k)*(root(144*a^13*b*c^5*
d^9*f^4 + 144*a^9*b^5*c*d^13*f^4 + 144*a^5*b^9*c^13*d*f^4 + 144*a*b^13*c^9*d^5*f^4 + 96*a^13*b*c^7*d^7*f^4 + 9
6*a^13*b*c^3*d^11*f^4 + 96*a^11*b^3*c*d^13*f^4 + 96*a^7*b^7*c^13*d*f^4 + 96*a^7*b^7*c*d^13*f^4 + 96*a^3*b^11*c
^13*d*f^4 + 96*a*b^13*c^11*d^3*f^4 + 96*a*b^13*c^7*d^7*f^4 + 24*a^13*b*c^9*d^5*f^4 + 24*a^9*b^5*c^13*d*f^4 + 2
4*a^5*b^9*c*d^13*f^4 + 24*a*b^13*c^5*d^9*f^4 + 24*a^13*b*c*d^13*f^4 + 24*a*b^13*c^13*d*f^4 + 3648*a^7*b^7*c^7*
d^7*f^4 - 3188*a^8*b^6*c^6*d^8*f^4 - 3188*a^6*b^8*c^8*d^6*f^4 - 2912*a^8*b^6*c^8*d^6*f^4 - 2912*a^6*b^8*c^6*d^
8*f^4 + 2592*a^9*b^5*c^7*d^7*f^4 + 2592*a^7*b^7*c^9*d^5*f^4 + 2592*a^7*b^7*c^5*d^9*f^4 + 2592*a^5*b^9*c^7*d^7*
f^4 + 2168*a^9*b^5*c^5*d^9*f^4 + 2168*a^5*b^9*c^9*d^5*f^4 - 1776*a^10*b^4*c^6*d^8*f^4 - 1776*a^8*b^6*c^4*d^10*
f^4 - 1776*a^6*b^8*c^10*d^4*f^4 - 1776*a^4*b^10*c^8*d^6*f^4 + 1568*a^9*b^5*c^9*d^5*f^4 + 1568*a^5*b^9*c^5*d^9*
f^4 - 1344*a^10*b^4*c^8*d^6*f^4 - 1344*a^8*b^6*c^10*d^4*f^4 - 1344*a^6*b^8*c^4*d^10*f^4 - 1344*a^4*b^10*c^6*d^
8*f^4 - 1164*a^10*b^4*c^4*d^10*f^4 - 1164*a^4*b^10*c^10*d^4*f^4 + 896*a^11*b^3*c^5*d^9*f^4 + 896*a^9*b^5*c^3*d
^11*f^4 + 896*a^5*b^9*c^11*d^3*f^4 + 896*a^3*b^11*c^9*d^5*f^4 + 864*a^11*b^3*c^7*d^7*f^4 + 864*a^7*b^7*c^11*d^
3*f^4 + 864*a^7*b^7*c^3*d^11*f^4 + 864*a^3*b^11*c^7*d^7*f^4 - 480*a^10*b^4*c^10*d^4*f^4 - 480*a^4*b^10*c^4*d^1
0*f^4 + 464*a^11*b^3*c^3*d^11*f^4 + 464*a^3*b^11*c^11*d^3*f^4 - 424*a^12*b^2*c^6*d^8*f^4 - 424*a^8*b^6*c^2*d^1
2*f^4 - 424*a^6*b^8*c^12*d^2*f^4 - 424*a^2*b^12*c^8*d^6*f^4 + 416*a^11*b^3*c^9*d^5*f^4 + 416*a^9*b^5*c^11*d^3*
f^4 + 416*a^5*b^9*c^3*d^11*f^4 + 416*a^3*b^11*c^5*d^9*f^4 - 336*a^12*b^2*c^4*d^10*f^4 - 336*a^10*b^4*c^2*d^12*
f^4 - 336*a^4*b^10*c^12*d^2*f^4 - 336*a^2*b^12*c^10*d^4*f^4 - 256*a^12*b^2*c^8*d^6*f^4 - 256*a^8*b^6*c^12*d^2*
f^4 - 256*a^6*b^8*c^2*d^12*f^4 - 256*a^2*b^12*c^6*d^8*f^4 - 124*a^12*b^2*c^2*d^12*f^4 - 124*a^2*b^12*c^12*d^2*
f^4 + 80*a^11*b^3*c^11*d^3*f^4 + 80*a^3*b^11*c^3*d^11*f^4 - 60*a^12*b^2*c^10*d^4*f^4 - 60*a^10*b^4*c^12*d^2*f^
4 - 60*a^4*b^10*c^2*d^12*f^4 - 60*a^2*b^12*c^4*d^10*f^4 - 24*b^14*c^10*d^4*f^4 - 16*b^14*c^12*d^2*f^4 - 16*b^1
4*c^8*d^6*f^4 - 4*b^14*c^6*d^8*f^4 - 24*a^14*c^4*d^10*f^4 - 16*a^14*c^6*d^8*f^4 - 16*a^14*c^2*d^12*f^4 - 4*a^1
4*c^8*d^6*f^4 - 24*a^10*b^4*d^14*f^4 - 16*a^12*b^2*d^14*f^4 - 16*a^8*b^6*d^14*f^4 - 4*a^6*b^8*d^14*f^4 - 24*a^
4*b^10*c^14*f^4 - 16*a^6*b^8*c^14*f^4 - 16*a^2*b^12*c^14*f^4 - 4*a^8*b^6*c^14*f^4 - 4*b^14*c^14*f^4 - 4*a^14*d
^14*f^4 + 36*A*C*a^9*b*c*d^9*f^2 + 36*A*C*a*b^9*c^9*d*f^2 + 32*A*C*a*b^9*c*d^9*f^2 - 552*B*C*a^7*b^3*c^4*d^6*f
^2 - 552*B*C*a^4*b^6*c^7*d^3*f^2 - 408*B*C*a^5*b^5*c^4*d^6*f^2 - 408*B*C*a^4*b^6*c^5*d^5*f^2 + 360*B*C*a^6*b^4
*c^3*d^7*f^2 + 360*B*C*a^3*b^7*c^6*d^4*f^2 - 248*B*C*a^7*b^3*c^2*d^8*f^2 - 248*B*C*a^2*b^8*c^7*d^3*f^2 + 184*B
*C*a^6*b^4*c^5*d^5*f^2 + 184*B*C*a^5*b^5*c^6*d^4*f^2 + 152*B*C*a^8*b^2*c^3*d^7*f^2 - 152*B*C*a^5*b^5*c^2*d^8*f
^2 + 152*B*C*a^3*b^7*c^8*d^2*f^2 - 152*B*C*a^2*b^8*c^5*d^5*f^2 - 104*B*C*a^7*b^3*c^6*d^4*f^2 - 104*B*C*a^6*b^4
*c^7*d^3*f^2 + 64*B*C*a^8*b^2*c^5*d^5*f^2 + 64*B*C*a^5*b^5*c^8*d^2*f^2 - 56*B*C*a^4*b^6*c^3*d^7*f^2 - 56*B*C*a
^3*b^7*c^4*d^6*f^2 - 24*B*C*a^8*b^2*c^7*d^3*f^2 - 24*B*C*a^7*b^3*c^8*d^2*f^2 - 24*B*C*a^3*b^7*c^2*d^8*f^2 - 24
*B*C*a^2*b^8*c^3*d^7*f^2 - 696*A*C*a^5*b^5*c^5*d^5*f^2 + 536*A*C*a^6*b^4*c^6*d^4*f^2 + 536*A*C*a^6*b^4*c^4*d^6
*f^2 + 536*A*C*a^4*b^6*c^6*d^4*f^2 + 472*A*C*a^4*b^6*c^4*d^6*f^2 - 232*A*C*a^7*b^3*c^5*d^5*f^2 - 232*A*C*a^5*b
^5*c^7*d^3*f^2 + 216*A*C*a^3*b^7*c^3*d^7*f^2 + 168*A*C*a^7*b^3*c^3*d^7*f^2 + 168*A*C*a^3*b^7*c^7*d^3*f^2 - 154
*A*C*a^8*b^2*c^2*d^8*f^2 - 154*A*C*a^2*b^8*c^8*d^2*f^2 + 62*A*C*a^8*b^2*c^6*d^4*f^2 + 62*A*C*a^6*b^4*c^8*d^2*f
^2 - 40*A*C*a^7*b^3*c^7*d^3*f^2 - 40*A*C*a^5*b^5*c^3*d^7*f^2 - 40*A*C*a^3*b^7*c^5*d^5*f^2 + 32*A*C*a^6*b^4*c^2
*d^8*f^2 + 32*A*C*a^2*b^8*c^6*d^4*f^2 - 32*A*C*a^2*b^8*c^2*d^8*f^2 + 30*A*C*a^4*b^6*c^2*d^8*f^2 + 30*A*C*a^2*b
^8*c^4*d^6*f^2 + 16*A*C*a^8*b^2*c^4*d^6*f^2 + 16*A*C*a^4*b^6*c^8*d^2*f^2 - 488*A*B*a^6*b^4*c^3*d^7*f^2 - 488*A
*B*a^3*b^7*c^6*d^4*f^2 + 440*A*B*a^7*b^3*c^4*d^6*f^2 + 440*A*B*a^4*b^6*c^7*d^3*f^2 - 360*A*B*a^6*b^4*c^5*d^5*f
^2 - 360*A*B*a^5*b^5*c^6*d^4*f^2 - 192*A*B*a^8*b^2*c^3*d^7*f^2 - 192*A*B*a^3*b^7*c^8*d^2*f^2 - 168*A*B*a^3*b^7
*c^2*d^8*f^2 - 168*A*B*a^2*b^8*c^3*d^7*f^2 - 152*A*B*a^4*b^6*c^3*d^7*f^2 - 152*A*B*a^3*b^7*c^4*d^6*f^2 - 120*A
*B*a^8*b^2*c^5*d^5*f^2 + 120*A*B*a^7*b^3*c^2*d^8*f^2 - 120*A*B*a^5*b^5*c^8*d^2*f^2 + 120*A*B*a^5*b^5*c^4*d^6*f
^2 - 120*A*B*a^5*b^5*c^2*d^8*f^2 + 120*A*B*a^4*b^6*c^5*d^5*f^2 + 120*A*B*a^2*b^8*c^7*d^3*f^2 - 120*A*B*a^2*b^8
*c^5*d^5*f^2 + 40*A*B*a^7*b^3*c^6*d^4*f^2 + 40*A*B*a^6*b^4*c^7*d^3*f^2 - 72*B*C*a^9*b*c^4*d^6*f^2 - 72*B*C*a^4
*b^6*c^9*d*f^2 - 64*B*C*a^4*b^6*c*d^9*f^2 - 64*B*C*a*b^9*c^4*d^6*f^2 - 32*B*C*a^8*b^2*c*d^9*f^2 - 32*B*C*a*b^9
*c^8*d^2*f^2 - 16*B*C*a^2*b^8*c*d^9*f^2 - 16*B*C*a*b^9*c^2*d^8*f^2 + 8*B*C*a^9*b*c^6*d^4*f^2 - 8*B*C*a^9*b*c^2
*d^8*f^2 + 8*B*C*a^6*b^4*c^9*d*f^2 - 8*B*C*a^2*b^8*c^9*d*f^2 + 104*A*C*a^7*b^3*c*d^9*f^2 + 104*A*C*a*b^9*c^7*d
^3*f^2 + 96*A*C*a^3*b^7*c*d^9*f^2 + 96*A*C*a*b^9*c^3*d^7*f^2 + 72*A*C*a^9*b*c^3*d^7*f^2 + 72*A*C*a^3*b^7*c^9*d
*f^2 + 68*A*C*a^5*b^5*c*d^9*f^2 + 68*A*C*a*b^9*c^5*d^5*f^2 - 28*A*C*a^9*b*c^5*d^5*f^2 - 28*A*C*a^5*b^5*c^9*d*f
^2 + 80*A*B*a^9*b*c^4*d^6*f^2 + 80*A*B*a^4*b^6*c^9*d*f^2 + 24*A*B*a^8*b^2*c*d^9*f^2 - 24*A*B*a^6*b^4*c*d^9*f^2
+ 24*A*B*a^4*b^6*c*d^9*f^2 - 24*A*B*a^2*b^8*c*d^9*f^2 + 24*A*B*a*b^9*c^8*d^2*f^2 - 24*A*B*a*b^9*c^6*d^4*f^2 +
24*A*B*a*b^9*c^4*d^6*f^2 - 24*A*B*a*b^9*c^2*d^8*f^2 - 32*B*C*b^10*c^7*d^3*f^2 - 8*B*C*b^10*c^5*d^5*f^2 + 34*A
*C*b^10*c^6*d^4*f^2 + 16*B*C*a^10*c^3*d^7*f^2 + 16*A*C*b^10*c^4*d^6*f^2 - 12*A*C*b^10*c^8*d^2*f^2 - 96*A*B*b^1
0*c^5*d^5*f^2 - 72*A*B*b^10*c^3*d^7*f^2 - 32*B*C*a^7*b^3*d^10*f^2 - 28*A*C*a^10*c^2*d^8*f^2 - 24*A*B*b^10*c^7*
d^3*f^2 - 8*B*C*a^5*b^5*d^10*f^2 + 2*A*C*a^10*c^4*d^6*f^2 + 34*A*C*a^6*b^4*d^10*f^2 + 16*B*C*a^3*b^7*c^10*f^2
+ 16*A*C*a^4*b^6*d^10*f^2 - 16*A*B*a^10*c^3*d^7*f^2 - 12*A*C*a^8*b^2*d^10*f^2 - 96*A*B*a^5*b^5*d^10*f^2 - 72*A
*B*a^3*b^7*d^10*f^2 - 28*A*C*a^2*b^8*c^10*f^2 - 24*A*B*a^7*b^3*d^10*f^2 + 2*A*C*a^4*b^6*c^10*f^2 - 16*A*B*a^3*
b^7*c^10*f^2 + 444*C^2*a^5*b^5*c^5*d^5*f^2 + 148*C^2*a^7*b^3*c^5*d^5*f^2 + 148*C^2*a^5*b^5*c^7*d^3*f^2 + 148*C
^2*a^5*b^5*c^3*d^7*f^2 + 148*C^2*a^3*b^7*c^5*d^5*f^2 - 140*C^2*a^6*b^4*c^6*d^4*f^2 - 140*C^2*a^6*b^4*c^4*d^6*f
^2 - 140*C^2*a^4*b^6*c^6*d^4*f^2 - 140*C^2*a^4*b^6*c^4*d^6*f^2 + 109*C^2*a^8*b^2*c^2*d^8*f^2 + 109*C^2*a^2*b^8
*c^8*d^2*f^2 + 48*C^2*a^8*b^2*c^4*d^6*f^2 + 48*C^2*a^6*b^4*c^2*d^8*f^2 + 48*C^2*a^4*b^6*c^8*d^2*f^2 + 48*C^2*a
^2*b^8*c^6*d^4*f^2 + 20*C^2*a^7*b^3*c^7*d^3*f^2 - 20*C^2*a^7*b^3*c^3*d^7*f^2 - 20*C^2*a^3*b^7*c^7*d^3*f^2 + 20
*C^2*a^3*b^7*c^3*d^7*f^2 + 17*C^2*a^8*b^2*c^6*d^4*f^2 + 17*C^2*a^6*b^4*c^8*d^2*f^2 + 17*C^2*a^4*b^6*c^2*d^8*f^
2 + 17*C^2*a^2*b^8*c^4*d^6*f^2 + 16*C^2*a^8*b^2*c^8*d^2*f^2 + 16*C^2*a^2*b^8*c^2*d^8*f^2 - 396*B^2*a^5*b^5*c^5
*d^5*f^2 + 308*B^2*a^6*b^4*c^4*d^6*f^2 + 308*B^2*a^4*b^6*c^6*d^4*f^2 + 300*B^2*a^4*b^6*c^4*d^6*f^2 + 284*B^2*a
^6*b^4*c^6*d^4*f^2 - 132*B^2*a^7*b^3*c^5*d^5*f^2 - 132*B^2*a^5*b^5*c^7*d^3*f^2 - 84*B^2*a^5*b^5*c^3*d^7*f^2 -
84*B^2*a^3*b^7*c^5*d^5*f^2 + 61*B^2*a^4*b^6*c^2*d^8*f^2 + 61*B^2*a^2*b^8*c^4*d^6*f^2 - 59*B^2*a^8*b^2*c^2*d^8*
f^2 - 59*B^2*a^2*b^8*c^8*d^2*f^2 + 56*B^2*a^6*b^4*c^2*d^8*f^2 + 56*B^2*a^2*b^8*c^6*d^4*f^2 + 52*B^2*a^7*b^3*c^
3*d^7*f^2 + 52*B^2*a^3*b^7*c^7*d^3*f^2 + 44*B^2*a^3*b^7*c^3*d^7*f^2 + 33*B^2*a^8*b^2*c^6*d^4*f^2 + 33*B^2*a^6*
b^4*c^8*d^2*f^2 + 20*B^2*a^8*b^2*c^4*d^6*f^2 - 20*B^2*a^7*b^3*c^7*d^3*f^2 + 20*B^2*a^4*b^6*c^8*d^2*f^2 + 8*B^2
*a^2*b^8*c^2*d^8*f^2 + 337*A^2*a^4*b^6*c^2*d^8*f^2 + 337*A^2*a^2*b^8*c^4*d^6*f^2 + 272*A^2*a^2*b^8*c^2*d^8*f^2
+ 252*A^2*a^5*b^5*c^5*d^5*f^2 + 244*A^2*a^4*b^6*c^4*d^6*f^2 - 236*A^2*a^3*b^7*c^3*d^7*f^2 + 176*A^2*a^6*b^4*c
^2*d^8*f^2 + 176*A^2*a^2*b^8*c^6*d^4*f^2 - 148*A^2*a^7*b^3*c^3*d^7*f^2 - 148*A^2*a^3*b^7*c^7*d^3*f^2 - 140*A^2
*a^6*b^4*c^6*d^4*f^2 + 109*A^2*a^8*b^2*c^2*d^8*f^2 + 109*A^2*a^2*b^8*c^8*d^2*f^2 - 108*A^2*a^5*b^5*c^3*d^7*f^2
- 108*A^2*a^3*b^7*c^5*d^5*f^2 + 84*A^2*a^7*b^3*c^5*d^5*f^2 + 84*A^2*a^5*b^5*c^7*d^3*f^2 + 32*A^2*a^8*b^2*c^4*
d^6*f^2 + 32*A^2*a^4*b^6*c^8*d^2*f^2 + 20*A^2*a^7*b^3*c^7*d^3*f^2 - 15*A^2*a^8*b^2*c^6*d^4*f^2 - 15*A^2*a^6*b^
4*c^8*d^2*f^2 - 12*A^2*a^6*b^4*c^4*d^6*f^2 - 12*A^2*a^4*b^6*c^6*d^4*f^2 + 8*B*C*b^10*c^9*d*f^2 - 16*B*C*a^10*c
*d^9*f^2 - 16*A*B*b^10*c^9*d*f^2 - 16*A*B*b^10*c*d^9*f^2 + 8*B*C*a^9*b*d^10*f^2 - 16*B*C*a*b^9*c^10*f^2 + 16*A
*B*a^10*c*d^9*f^2 - 16*A*B*a^9*b*d^10*f^2 - 16*A*B*a*b^9*d^10*f^2 + 16*A*B*a*b^9*c^10*f^2 + 22*C^2*a^9*b*c^5*d
^5*f^2 + 22*C^2*a^5*b^5*c^9*d*f^2 + 22*C^2*a^5*b^5*c*d^9*f^2 + 22*C^2*a*b^9*c^5*d^5*f^2 - 20*C^2*a^9*b*c^3*d^7
*f^2 - 20*C^2*a^7*b^3*c*d^9*f^2 - 20*C^2*a^3*b^7*c^9*d*f^2 - 20*C^2*a*b^9*c^7*d^3*f^2 + 36*B^2*a^7*b^3*c*d^9*f
^2 + 36*B^2*a*b^9*c^7*d^3*f^2 + 28*B^2*a^9*b*c^3*d^7*f^2 + 28*B^2*a^3*b^7*c^9*d*f^2 + 24*B^2*a^3*b^7*c*d^9*f^2
+ 24*B^2*a*b^9*c^3*d^7*f^2 - 18*B^2*a^9*b*c^5*d^5*f^2 - 18*B^2*a^5*b^5*c^9*d*f^2 + 6*B^2*a^5*b^5*c*d^9*f^2 +
6*B^2*a*b^9*c^5*d^5*f^2 - 96*A^2*a^3*b^7*c*d^9*f^2 - 96*A^2*a*b^9*c^3*d^7*f^2 - 90*A^2*a^5*b^5*c*d^9*f^2 - 90*
A^2*a*b^9*c^5*d^5*f^2 - 84*A^2*a^7*b^3*c*d^9*f^2 - 84*A^2*a*b^9*c^7*d^3*f^2 - 52*A^2*a^9*b*c^3*d^7*f^2 - 52*A^
2*a^3*b^7*c^9*d*f^2 + 6*A^2*a^9*b*c^5*d^5*f^2 + 6*A^2*a^5*b^5*c^9*d*f^2 - 10*C^2*a^9*b*c*d^9*f^2 - 10*C^2*a*b^
9*c^9*d*f^2 + 14*B^2*a^9*b*c*d^9*f^2 + 14*B^2*a*b^9*c^9*d*f^2 + 8*B^2*a*b^9*c*d^9*f^2 - 32*A^2*a*b^9*c*d^9*f^2
- 26*A^2*a^9*b*c*d^9*f^2 - 26*A^2*a*b^9*c^9*d*f^2 + 2*A*C*b^10*c^10*f^2 + 2*A*C*a^10*d^10*f^2 + 14*C^2*b^10*c
^8*d^2*f^2 - C^2*b^10*c^6*d^4*f^2 + 31*B^2*b^10*c^6*d^4*f^2 + 20*B^2*b^10*c^4*d^6*f^2 + 14*C^2*a^10*c^2*d^8*f^
2 + 4*B^2*b^10*c^2*d^8*f^2 + 2*B^2*b^10*c^8*d^2*f^2 - C^2*a^10*c^4*d^6*f^2 + 80*A^2*b^10*c^4*d^6*f^2 + 64*A^2*
b^10*c^2*d^8*f^2 + 31*A^2*b^10*c^6*d^4*f^2 + 14*C^2*a^8*b^2*d^10*f^2 + 14*A^2*b^10*c^8*d^2*f^2 - 10*B^2*a^10*c
^2*d^8*f^2 + 3*B^2*a^10*c^4*d^6*f^2 - C^2*a^6*b^4*d^10*f^2 + 31*B^2*a^6*b^4*d^10*f^2 + 20*B^2*a^4*b^6*d^10*f^2
+ 14*C^2*a^2*b^8*c^10*f^2 + 14*A^2*a^10*c^2*d^8*f^2 + 4*B^2*a^2*b^8*d^10*f^2 + 2*B^2*a^8*b^2*d^10*f^2 - C^2*a
^4*b^6*c^10*f^2 - A^2*a^10*c^4*d^6*f^2 + 80*A^2*a^4*b^6*d^10*f^2 + 64*A^2*a^2*b^8*d^10*f^2 + 31*A^2*a^6*b^4*d^
10*f^2 + 14*A^2*a^8*b^2*d^10*f^2 - 10*B^2*a^2*b^8*c^10*f^2 + 3*B^2*a^4*b^6*c^10*f^2 + 14*A^2*a^2*b^8*c^10*f^2
- A^2*a^4*b^6*c^10*f^2 - C^2*b^10*c^10*f^2 - C^2*a^10*d^10*f^2 + 16*A^2*b^10*d^10*f^2 + 3*B^2*b^10*c^10*f^2 +
3*B^2*a^10*d^10*f^2 - A^2*b^10*c^10*f^2 - A^2*a^10*d^10*f^2 - 96*A*B*C*a*b^7*c*d^7*f - 28*A*B*C*a^7*b*c*d^7*f
- 28*A*B*C*a*b^7*c^7*d*f + 484*A*B*C*a^4*b^4*c^4*d^4*f - 424*A*B*C*a^3*b^5*c^3*d^5*f + 320*A*B*C*a^2*b^6*c^2*d
^6*f - 176*A*B*C*a^6*b^2*c^2*d^6*f - 176*A*B*C*a^2*b^6*c^6*d^2*f + 158*A*B*C*a^4*b^4*c^2*d^6*f + 158*A*B*C*a^2
*b^6*c^4*d^4*f - 136*A*B*C*a^5*b^3*c^5*d^3*f - 34*A*B*C*a^6*b^2*c^4*d^4*f - 34*A*B*C*a^4*b^4*c^6*d^2*f + 28*A*
B*C*a^5*b^3*c^3*d^5*f + 28*A*B*C*a^3*b^5*c^5*d^3*f + 308*A*B*C*a^5*b^3*c*d^7*f + 308*A*B*C*a*b^7*c^5*d^3*f + 2
0*A*B*C*a^7*b*c^3*d^5*f + 20*A*B*C*a^3*b^5*c^7*d*f + 30*B*C^2*a^7*b*c*d^7*f + 30*B*C^2*a*b^7*c^7*d*f + 160*A^2
*B*a*b^7*c*d^7*f - 2*A^2*B*a^7*b*c*d^7*f - 2*A^2*B*a*b^7*c^7*d*f - 96*A*B*C*b^8*c^4*d^4*f + 34*A*B*C*b^8*c^6*d
^2*f - 32*A*B*C*b^8*c^2*d^6*f + 2*A*B*C*a^8*c^2*d^6*f - 96*A*B*C*a^4*b^4*d^8*f + 34*A*B*C*a^6*b^2*d^8*f - 32*A
*B*C*a^2*b^6*d^8*f + 2*A*B*C*a^2*b^6*c^8*f - 210*B*C^2*a^4*b^4*c^4*d^4*f - 182*B^2*C*a^5*b^3*c^2*d^6*f - 182*B
^2*C*a^2*b^6*c^5*d^3*f + 180*B*C^2*a^5*b^3*c^5*d^3*f + 180*B*C^2*a^3*b^5*c^3*d^5*f - 166*B^2*C*a^5*b^3*c^4*d^4
*f - 166*B^2*C*a^4*b^4*c^5*d^3*f + 152*B*C^2*a^6*b^2*c^2*d^6*f + 152*B*C^2*a^2*b^6*c^6*d^2*f - 112*B^2*C*a^3*b
^5*c^2*d^6*f - 112*B^2*C*a^2*b^6*c^3*d^5*f + 94*B^2*C*a^4*b^4*c^3*d^5*f + 94*B^2*C*a^3*b^5*c^4*d^4*f - 80*B*C^
2*a^2*b^6*c^2*d^6*f + 66*B*C^2*a^5*b^3*c^3*d^5*f + 66*B*C^2*a^3*b^5*c^5*d^3*f + 46*B^2*C*a^6*b^2*c^3*d^5*f + 4
6*B^2*C*a^3*b^5*c^6*d^2*f + 33*B*C^2*a^6*b^2*c^4*d^4*f + 33*B*C^2*a^4*b^4*c^6*d^2*f + 24*B^2*C*a^6*b^2*c^5*d^3
*f + 24*B^2*C*a^5*b^3*c^6*d^2*f - 16*B*C^2*a^6*b^2*c^6*d^2*f - 15*B*C^2*a^4*b^4*c^2*d^6*f - 15*B*C^2*a^2*b^6*c
^4*d^4*f - 190*A^2*C*a^4*b^4*c^3*d^5*f - 190*A^2*C*a^3*b^5*c^4*d^4*f + 182*A^2*C*a^5*b^3*c^2*d^6*f + 182*A^2*C
*a^2*b^6*c^5*d^3*f + 160*A^2*C*a^3*b^5*c^2*d^6*f + 160*A^2*C*a^2*b^6*c^3*d^5*f - 150*A*C^2*a^5*b^3*c^2*d^6*f -
150*A*C^2*a^2*b^6*c^5*d^3*f - 126*A*C^2*a^5*b^3*c^4*d^4*f - 126*A*C^2*a^4*b^4*c^5*d^3*f + 126*A*C^2*a^4*b^4*c
^3*d^5*f + 126*A*C^2*a^3*b^5*c^4*d^4*f - 96*A*C^2*a^3*b^5*c^2*d^6*f - 96*A*C^2*a^2*b^6*c^3*d^5*f + 94*A^2*C*a^
5*b^3*c^4*d^4*f + 94*A^2*C*a^4*b^4*c^5*d^3*f + 54*A*C^2*a^6*b^2*c^3*d^5*f + 54*A*C^2*a^3*b^5*c^6*d^2*f + 32*A*
C^2*a^6*b^2*c^5*d^3*f + 32*A*C^2*a^5*b^3*c^6*d^2*f - 22*A^2*C*a^6*b^2*c^3*d^5*f - 22*A^2*C*a^3*b^5*c^6*d^2*f +
500*A^2*B*a^3*b^5*c^3*d^5*f - 290*A^2*B*a^4*b^4*c^4*d^4*f - 256*A^2*B*a^2*b^6*c^2*d^6*f - 230*A*B^2*a^4*b^4*c
^3*d^5*f - 230*A*B^2*a^3*b^5*c^4*d^4*f + 142*A*B^2*a^5*b^3*c^2*d^6*f + 142*A*B^2*a^2*b^6*c^5*d^3*f - 127*A^2*B
*a^4*b^4*c^2*d^6*f - 127*A^2*B*a^2*b^6*c^4*d^4*f + 86*A*B^2*a^5*b^3*c^4*d^4*f + 86*A*B^2*a^4*b^4*c^5*d^3*f + 8
0*A*B^2*a^3*b^5*c^2*d^6*f + 80*A*B^2*a^2*b^6*c^3*d^5*f + 40*A^2*B*a^6*b^2*c^2*d^6*f + 40*A^2*B*a^2*b^6*c^6*d^2
*f + 34*A^2*B*a^5*b^3*c^3*d^5*f + 34*A^2*B*a^3*b^5*c^5*d^3*f - 30*A*B^2*a^6*b^2*c^3*d^5*f - 30*A*B^2*a^3*b^5*c
^6*d^2*f + 20*A^2*B*a^5*b^3*c^5*d^3*f - 15*A^2*B*a^6*b^2*c^4*d^4*f - 15*A^2*B*a^4*b^4*c^6*d^2*f - 98*B^2*C*a^6
*b^2*c*d^7*f - 98*B^2*C*a*b^7*c^6*d^2*f - 90*B*C^2*a^5*b^3*c*d^7*f - 90*B*C^2*a*b^7*c^5*d^3*f + 48*B^2*C*a^4*b
^4*c*d^7*f + 48*B^2*C*a*b^7*c^4*d^4*f + 40*B^2*C*a^2*b^6*c*d^7*f + 40*B^2*C*a*b^7*c^2*d^6*f - 32*B*C^2*a^3*b^5
*c*d^7*f - 32*B*C^2*a*b^7*c^3*d^5*f + 26*B^2*C*a^7*b*c^2*d^6*f + 26*B^2*C*a^2*b^6*c^7*d*f - 26*B*C^2*a^7*b*c^3
*d^5*f - 26*B*C^2*a^3*b^5*c^7*d*f - 8*B^2*C*a^7*b*c^4*d^4*f - 8*B^2*C*a^4*b^4*c^7*d*f - 224*A^2*C*a^4*b^4*c*d^
7*f - 224*A^2*C*a*b^7*c^4*d^4*f - 96*A^2*C*a^2*b^6*c*d^7*f - 96*A^2*C*a*b^7*c^2*d^6*f + 96*A*C^2*a^4*b^4*c*d^7
*f + 96*A*C^2*a*b^7*c^4*d^4*f - 66*A*C^2*a^6*b^2*c*d^7*f - 66*A*C^2*a*b^7*c^6*d^2*f + 64*A*C^2*a^2*b^6*c*d^7*f
+ 64*A*C^2*a*b^7*c^2*d^6*f + 34*A^2*C*a^6*b^2*c*d^7*f + 34*A^2*C*a*b^7*c^6*d^2*f + 34*A*C^2*a^7*b*c^2*d^6*f +
34*A*C^2*a^2*b^6*c^7*d*f - 2*A^2*C*a^7*b*c^2*d^6*f - 2*A^2*C*a^2*b^6*c^7*d*f - 208*A*B^2*a^4*b^4*c*d^7*f - 20
8*A*B^2*a*b^7*c^4*d^4*f + 160*A^2*B*a^3*b^5*c*d^7*f + 160*A^2*B*a*b^7*c^3*d^5*f - 154*A^2*B*a^5*b^3*c*d^7*f -
154*A^2*B*a*b^7*c^5*d^3*f - 112*A*B^2*a^2*b^6*c*d^7*f - 112*A*B^2*a*b^7*c^2*d^6*f + 58*A*B^2*a^6*b^2*c*d^7*f +
58*A*B^2*a*b^7*c^6*d^2*f - 10*A*B^2*a^7*b*c^2*d^6*f - 10*A*B^2*a^2*b^6*c^7*d*f + 6*A^2*B*a^7*b*c^3*d^5*f + 6*
A^2*B*a^3*b^5*c^7*d*f + 32*B^2*C*b^8*c^5*d^3*f - 17*B*C^2*b^8*c^6*d^2*f + 8*B^2*C*b^8*c^3*d^5*f + 64*A^2*C*b^8
*c^3*d^5*f - 32*A^2*C*b^8*c^5*d^3*f + 32*A*C^2*b^8*c^5*d^3*f - B*C^2*a^8*c^2*d^6*f + 112*A^2*B*b^8*c^4*d^4*f -
64*A*B^2*b^8*c^5*d^3*f + 32*B^2*C*a^5*b^3*d^8*f - 17*B*C^2*a^6*b^2*d^8*f + 16*A^2*B*b^8*c^2*d^6*f + 16*A*B^2*
b^8*c^3*d^5*f + 8*B^2*C*a^3*b^5*d^8*f - A^2*B*b^8*c^6*d^2*f + 64*A^2*C*a^3*b^5*d^8*f - 32*A^2*C*a^5*b^3*d^8*f
+ 32*A*C^2*a^5*b^3*d^8*f - A^2*B*a^8*c^2*d^6*f - B*C^2*a^2*b^6*c^8*f + 112*A^2*B*a^4*b^4*d^8*f - 64*A*B^2*a^5*
b^3*d^8*f + 16*A^2*B*a^2*b^6*d^8*f + 16*A*B^2*a^3*b^5*d^8*f - A^2*B*a^6*b^2*d^8*f - A^2*B*a^2*b^6*c^8*f - 8*B^
3*a*b^7*c*d^7*f - 2*B^3*a^7*b*c*d^7*f - 2*B^3*a*b^7*c^7*d*f - 6*B^2*C*b^8*c^7*d*f + 32*A^2*C*b^8*c*d^7*f + 6*A
^2*C*b^8*c^7*d*f - 6*A*C^2*b^8*c^7*d*f - 2*B^2*C*a^8*c*d^7*f + 16*A*B^2*b^8*c*d^7*f - 6*B^2*C*a^7*b*d^8*f - 6*
A^2*C*a^8*c*d^7*f + 6*A*C^2*a^8*c*d^7*f - 2*A*B^2*b^8*c^7*d*f + 32*A^2*C*a*b^7*d^8*f + 6*A^2*C*a^7*b*d^8*f - 6
*A*C^2*a^7*b*d^8*f - 2*B^2*C*a*b^7*c^8*f + 2*A*B^2*a^8*c*d^7*f + 16*A*B^2*a*b^7*d^8*f - 6*A^2*C*a*b^7*c^8*f +
6*A*C^2*a*b^7*c^8*f - 2*A*B^2*a^7*b*d^8*f + 2*A*B^2*a*b^7*c^8*f - 50*C^3*a^6*b^2*c^3*d^5*f + 50*C^3*a^5*b^3*c^
2*d^6*f - 50*C^3*a^3*b^5*c^6*d^2*f + 50*C^3*a^2*b^6*c^5*d^3*f + 42*C^3*a^5*b^3*c^4*d^4*f + 42*C^3*a^4*b^4*c^5*
d^3*f - 42*C^3*a^4*b^4*c^3*d^5*f - 42*C^3*a^3*b^5*c^4*d^4*f - 32*C^3*a^6*b^2*c^5*d^3*f - 32*C^3*a^5*b^3*c^6*d^
2*f + 32*C^3*a^3*b^5*c^2*d^6*f + 32*C^3*a^2*b^6*c^3*d^5*f + 94*B^3*a^4*b^4*c^4*d^4*f + 48*B^3*a^2*b^6*c^2*d^6*
f - 44*B^3*a^3*b^5*c^3*d^5*f - 32*B^3*a^6*b^2*c^2*d^6*f - 32*B^3*a^2*b^6*c^6*d^2*f + 29*B^3*a^4*b^4*c^2*d^6*f
+ 29*B^3*a^2*b^6*c^4*d^4*f - 20*B^3*a^5*b^3*c^5*d^3*f + 18*B^3*a^5*b^3*c^3*d^5*f + 18*B^3*a^3*b^5*c^5*d^3*f -
3*B^3*a^6*b^2*c^4*d^4*f - 3*B^3*a^4*b^4*c^6*d^2*f + 106*A^3*a^4*b^4*c^3*d^5*f + 106*A^3*a^3*b^5*c^4*d^4*f - 96
*A^3*a^3*b^5*c^2*d^6*f - 96*A^3*a^2*b^6*c^3*d^5*f - 82*A^3*a^5*b^3*c^2*d^6*f - 82*A^3*a^2*b^6*c^5*d^3*f + 18*A
^3*a^6*b^2*c^3*d^5*f + 18*A^3*a^3*b^5*c^6*d^2*f - 10*A^3*a^5*b^3*c^4*d^4*f - 10*A^3*a^4*b^4*c^5*d^3*f - 22*C^3
*a^7*b*c^2*d^6*f + 22*C^3*a^6*b^2*c*d^7*f - 22*C^3*a^2*b^6*c^7*d*f + 22*C^3*a*b^7*c^6*d^2*f - 2*A*B*C*b^8*c^8*
f - 2*A*B*C*a^8*d^8*f + 62*B^3*a^5*b^3*c*d^7*f + 62*B^3*a*b^7*c^5*d^3*f + 16*B^3*a^3*b^5*c*d^7*f + 16*B^3*a*b^
7*c^3*d^5*f + 6*B^3*a^7*b*c^3*d^5*f + 6*B^3*a^3*b^5*c^7*d*f + 128*A^3*a^4*b^4*c*d^7*f + 128*A^3*a*b^7*c^4*d^4*
f + 32*A^3*a^2*b^6*c*d^7*f + 32*A^3*a*b^7*c^2*d^6*f - 10*A^3*a^7*b*c^2*d^6*f + 10*A^3*a^6*b^2*c*d^7*f - 10*A^3
*a^2*b^6*c^7*d*f + 10*A^3*a*b^7*c^6*d^2*f + 11*B^3*b^8*c^6*d^2*f - 8*B^3*b^8*c^4*d^4*f - 4*B^3*b^8*c^2*d^6*f -
64*A^3*b^8*c^3*d^5*f - B^3*a^8*c^2*d^6*f + 11*B^3*a^6*b^2*d^8*f - 8*B^3*a^4*b^4*d^8*f - 4*B^3*a^2*b^6*d^8*f -
64*A^3*a^3*b^5*d^8*f - B^3*a^2*b^6*c^8*f + 2*C^3*b^8*c^7*d*f - 2*C^3*a^8*c*d^7*f - 32*A^3*b^8*c*d^7*f + 2*C^3
*a^7*b*d^8*f - 2*A^3*b^8*c^7*d*f - 2*C^3*a*b^7*c^8*f + 2*A^3*a^8*c*d^7*f - 32*A^3*a*b^7*d^8*f - 2*A^3*a^7*b*d^
8*f + 2*A^3*a*b^7*c^8*f - 16*A^2*B*b^8*d^8*f + B*C^2*b^8*c^8*f + B*C^2*a^8*d^8*f + A^2*B*b^8*c^8*f + A^2*B*a^8
*d^8*f + B^3*b^8*c^8*f + B^3*a^8*d^8*f - 4*A*B^2*C*a^5*b*c*d^5 - 4*A*B^2*C*a*b^5*c^5*d + 4*A*B^2*C*a*b^5*c*d^5
+ 22*A^2*B*C*a^3*b^3*c^2*d^4 + 22*A^2*B*C*a^2*b^4*c^3*d^3 - 20*A*B^2*C*a^3*b^3*c^3*d^3 + 14*A*B^2*C*a^4*b^2*c
^2*d^4 + 14*A*B^2*C*a^2*b^4*c^4*d^2 - 14*A*B*C^2*a^3*b^3*c^2*d^4 - 14*A*B*C^2*a^2*b^4*c^3*d^3 + 12*A*B*C^2*a^4
*b^2*c^3*d^3 + 12*A*B*C^2*a^3*b^3*c^4*d^2 - 6*A^2*B*C*a^4*b^2*c^3*d^3 - 6*A^2*B*C*a^3*b^3*c^4*d^2 - 4*A*B^2*C*
a^2*b^4*c^2*d^4 + 22*A*B*C^2*a^4*b^2*c*d^5 + 22*A*B*C^2*a*b^5*c^4*d^2 - 20*A^2*B*C*a^4*b^2*c*d^5 - 20*A^2*B*C*
a*b^5*c^4*d^2 + 10*A*B*C^2*a^2*b^4*c*d^5 + 10*A*B*C^2*a*b^5*c^2*d^4 - 8*A^2*B*C*a^2*b^4*c*d^5 - 8*A^2*B*C*a*b^
5*c^2*d^4 + 4*A*B^2*C*a^3*b^3*c*d^5 + 4*A*B^2*C*a*b^5*c^3*d^3 - 4*A*B*C^2*a^5*b*c^2*d^4 - 4*A*B*C^2*a^2*b^4*c^
5*d + 2*A^2*B*C*a^5*b*c^2*d^4 + 2*A^2*B*C*a^2*b^4*c^5*d - 8*B^3*C*a^4*b^2*c*d^5 - 8*B^3*C*a*b^5*c^4*d^2 - 8*B*
C^3*a^4*b^2*c*d^5 - 8*B*C^3*a*b^5*c^4*d^2 - 4*B^3*C*a^2*b^4*c*d^5 - 4*B^3*C*a*b^5*c^2*d^4 + 4*B^2*C^2*a^5*b*c*
d^5 + 4*B^2*C^2*a*b^5*c^5*d - 4*B*C^3*a^2*b^4*c*d^5 - 4*B*C^3*a*b^5*c^2*d^4 + 2*B^3*C*a^5*b*c^2*d^4 + 2*B^3*C*
a^2*b^4*c^5*d + 2*B^2*C^2*a*b^5*c*d^5 + 2*B*C^3*a^5*b*c^2*d^4 + 2*B*C^3*a^2*b^4*c^5*d + 24*A^3*C*a^3*b^3*c*d^5
+ 24*A^3*C*a*b^5*c^3*d^3 - 24*A^2*C^2*a*b^5*c*d^5 + 12*A^2*C^2*a^5*b*c*d^5 + 12*A^2*C^2*a*b^5*c^5*d + 8*A*C^3
*a^3*b^3*c*d^5 + 8*A*C^3*a*b^5*c^3*d^3 + 6*A^3*B*a^4*b^2*c*d^5 + 6*A^3*B*a*b^5*c^4*d^2 - 6*A^2*B^2*a*b^5*c*d^5
+ 6*A*B^3*a^4*b^2*c*d^5 + 6*A*B^3*a*b^5*c^4*d^2 + 2*A^3*B*a^2*b^4*c*d^5 + 2*A^3*B*a*b^5*c^2*d^4 + 2*A*B^3*a^2
*b^4*c*d^5 + 2*A*B^3*a*b^5*c^2*d^4 + 20*A^2*B*C*b^6*c^3*d^3 - 10*A*B*C^2*b^6*c^3*d^3 - 2*A*B^2*C*b^6*c^4*d^2 -
2*A*B^2*C*b^6*c^2*d^4 + 20*A^2*B*C*a^3*b^3*d^6 - 10*A*B*C^2*a^3*b^3*d^6 - 2*A*B^2*C*a^4*b^2*d^6 - 2*A*B^2*C*a
^2*b^4*d^6 + 10*B^2*C^2*a^3*b^3*c^3*d^3 + 4*B^2*C^2*a^4*b^2*c^4*d^2 - 3*B^2*C^2*a^4*b^2*c^2*d^4 - 3*B^2*C^2*a^
2*b^4*c^4*d^2 + 2*B^2*C^2*a^2*b^4*c^2*d^4 + 40*A^2*C^2*a^2*b^4*c^2*d^4 - 16*A^2*C^2*a^4*b^2*c^2*d^4 - 16*A^2*C
^2*a^2*b^4*c^4*d^2 + 4*A^2*C^2*a^4*b^2*c^4*d^2 + 18*A^2*B^2*a^2*b^4*c^2*d^4 + 10*A^2*B^2*a^3*b^3*c^3*d^3 - 3*A
^2*B^2*a^4*b^2*c^2*d^4 - 3*A^2*B^2*a^2*b^4*c^4*d^2 + 24*A^3*C*a*b^5*c*d^5 - 12*A*C^3*a^5*b*c*d^5 - 12*A*C^3*a*
b^5*c^5*d + 8*A*C^3*a*b^5*c*d^5 - 4*A^3*C*a^5*b*c*d^5 - 4*A^3*C*a*b^5*c^5*d + 8*A^2*B*C*b^6*c*d^5 + 4*A*B*C^2*
b^6*c^5*d - 4*A*B*C^2*b^6*c*d^5 - 2*A^2*B*C*b^6*c^5*d + 8*A^2*B*C*a*b^5*d^6 + 4*A*B*C^2*a^5*b*d^6 - 4*A*B*C^2*
a*b^5*d^6 - 2*A^2*B*C*a^5*b*d^6 - 6*B^3*C*a^4*b^2*c^3*d^3 - 6*B^3*C*a^3*b^3*c^4*d^2 - 6*B*C^3*a^4*b^2*c^3*d^3
- 6*B*C^3*a^3*b^3*c^4*d^2 + 2*B^3*C*a^3*b^3*c^2*d^4 + 2*B^3*C*a^2*b^4*c^3*d^3 + 2*B^2*C^2*a^3*b^3*c*d^5 + 2*B^
2*C^2*a*b^5*c^3*d^3 + 2*B*C^3*a^3*b^3*c^2*d^4 + 2*B*C^3*a^2*b^4*c^3*d^3 - 48*A^3*C*a^2*b^4*c^2*d^4 - 24*A^2*C^
2*a^3*b^3*c*d^5 - 24*A^2*C^2*a*b^5*c^3*d^3 - 16*A*C^3*a^2*b^4*c^2*d^4 + 8*A^3*C*a^4*b^2*c^2*d^4 + 8*A^3*C*a^2*
b^4*c^4*d^2 - 8*A*C^3*a^4*b^2*c^4*d^2 + 8*A*C^3*a^4*b^2*c^2*d^4 + 8*A*C^3*a^2*b^4*c^4*d^2 - 10*A^3*B*a^3*b^3*c
^2*d^4 - 10*A^3*B*a^2*b^4*c^3*d^3 - 10*A*B^3*a^3*b^3*c^2*d^4 - 10*A*B^3*a^2*b^4*c^3*d^3 - 6*A^2*B^2*a^3*b^3*c*
d^5 - 6*A^2*B^2*a*b^5*c^3*d^3 + 3*B^2*C^2*b^6*c^4*d^2 - 8*A^2*C^2*b^6*c^4*d^2 + 8*A^2*C^2*b^6*c^2*d^4 + 9*A^2*
B^2*b^6*c^2*d^4 + 3*B^2*C^2*a^4*b^2*d^6 + 3*A^2*B^2*b^6*c^4*d^2 - 8*A^2*C^2*a^4*b^2*d^6 + 8*A^2*C^2*a^2*b^4*d^
6 + 9*A^2*B^2*a^2*b^4*d^6 + 3*A^2*B^2*a^4*b^2*d^6 + 2*B^4*a^3*b^3*c*d^5 + 2*B^4*a*b^5*c^3*d^3 - 8*A^4*a^3*b^3*
c*d^5 - 8*A^4*a*b^5*c^3*d^3 - 16*A^3*C*b^6*c^2*d^4 + 4*A^3*C*b^6*c^4*d^2 + 4*A*C^3*b^6*c^4*d^2 - 10*A^3*B*b^6*
c^3*d^3 - 10*A*B^3*b^6*c^3*d^3 - 16*A^3*C*a^2*b^4*d^6 + 4*A^3*C*a^4*b^2*d^6 + 4*A*C^3*a^4*b^2*d^6 - 10*A^3*B*a
^3*b^3*d^6 - 10*A*B^3*a^3*b^3*d^6 + 4*C^4*a^5*b*c*d^5 + 4*C^4*a*b^5*c^5*d + 2*B^4*a*b^5*c*d^5 - 8*A^4*a*b^5*c*
d^5 - 2*B^3*C*b^6*c^5*d - 2*B*C^3*b^6*c^5*d - 4*A^3*B*b^6*c*d^5 - 4*A*B^3*b^6*c*d^5 - 2*B^3*C*a^5*b*d^6 - 2*B*
C^3*a^5*b*d^6 - 4*A^3*B*a*b^5*d^6 - 4*A*B^3*a*b^5*d^6 + 4*C^4*a^4*b^2*c^4*d^2 + 4*C^4*a^2*b^4*c^2*d^4 + 10*B^4
*a^3*b^3*c^3*d^3 - 3*B^4*a^4*b^2*c^2*d^4 - 3*B^4*a^2*b^4*c^4*d^2 - 2*B^4*a^2*b^4*c^2*d^4 + 20*A^4*a^2*b^4*c^2*
d^4 + B^2*C^2*b^6*c^2*d^4 + B^2*C^2*a^2*b^4*d^6 - 8*A^3*C*b^6*d^6 + 3*B^4*b^6*c^4*d^2 + 8*A^4*b^6*c^2*d^4 + 3*
B^4*a^4*b^2*d^6 + 8*A^4*a^2*b^4*d^6 + 4*A^2*C^2*b^6*d^6 + 4*A^2*B^2*b^6*d^6 + 4*A^4*b^6*d^6 + B^4*b^6*c^2*d^4
+ B^4*a^2*b^4*d^6, f, k)*((4*a^5*b^8*d^13 + 4*a^7*b^6*d^13 - 4*a^9*b^4*d^13 - 4*a^11*b^2*d^13 + 4*b^13*c^5*d^8
+ 4*b^13*c^7*d^6 - 4*b^13*c^9*d^4 - 4*b^13*c^11*d^2 - 12*a*b^12*c^4*d^9 + 4*a*b^12*c^6*d^7 + 52*a*b^12*c^8*d^
5 + 44*a*b^12*c^10*d^3 + 16*a^3*b^10*c^12*d - 12*a^4*b^9*c*d^12 + 8*a^5*b^8*c^12*d + 4*a^6*b^7*c*d^12 + 52*a^8
*b^5*c*d^12 + 44*a^10*b^3*c*d^12 + 16*a^12*b*c^3*d^10 + 8*a^12*b*c^5*d^8 + 8*a^2*b^11*c^3*d^10 - 36*a^2*b^11*c
^5*d^8 - 140*a^2*b^11*c^7*d^6 - 140*a^2*b^11*c^9*d^4 - 44*a^2*b^11*c^11*d^2 + 8*a^3*b^10*c^2*d^11 + 28*a^3*b^1
0*c^4*d^9 + 148*a^3*b^10*c^6*d^7 + 260*a^3*b^10*c^8*d^5 + 148*a^3*b^10*c^10*d^3 + 28*a^4*b^9*c^3*d^10 - 56*a^4
*b^9*c^5*d^8 - 320*a^4*b^9*c^7*d^6 - 300*a^4*b^9*c^9*d^4 - 76*a^4*b^9*c^11*d^2 - 36*a^5*b^8*c^2*d^11 - 56*a^5*
b^8*c^4*d^9 + 160*a^5*b^8*c^6*d^7 + 332*a^5*b^8*c^8*d^5 + 164*a^5*b^8*c^10*d^3 + 148*a^6*b^7*c^3*d^10 + 160*a^
6*b^7*c^5*d^8 - 144*a^6*b^7*c^7*d^6 - 196*a^6*b^7*c^9*d^4 - 36*a^6*b^7*c^11*d^2 - 140*a^7*b^6*c^2*d^11 - 320*a
^7*b^6*c^4*d^9 - 144*a^7*b^6*c^6*d^7 + 92*a^7*b^6*c^8*d^5 + 60*a^7*b^6*c^10*d^3 + 260*a^8*b^5*c^3*d^10 + 332*a
^8*b^5*c^5*d^8 + 92*a^8*b^5*c^7*d^6 - 32*a^8*b^5*c^9*d^4 - 140*a^9*b^4*c^2*d^11 - 300*a^9*b^4*c^4*d^9 - 196*a^
9*b^4*c^6*d^7 - 32*a^9*b^4*c^8*d^5 + 148*a^10*b^3*c^3*d^10 + 164*a^10*b^3*c^5*d^8 + 60*a^10*b^3*c^7*d^6 - 44*a
^11*b^2*c^2*d^11 - 76*a^11*b^2*c^4*d^9 - 36*a^11*b^2*c^6*d^7 + 8*a*b^12*c^12*d + 8*a^12*b*c*d^12)/(a^8*d^8 + b
^8*c^8 + 2*a^2*b^6*c^8 + a^4*b^4*c^8 + a^4*b^4*d^8 + 2*a^6*b^2*d^8 + 2*a^8*c^2*d^6 + a^8*c^4*d^4 + b^8*c^4*d^4
+ 2*b^8*c^6*d^2 - 4*a*b^7*c^3*d^5 - 8*a*b^7*c^5*d^3 - 4*a^3*b^5*c*d^7 - 8*a^3*b^5*c^7*d - 8*a^5*b^3*c*d^7 - 4
*a^5*b^3*c^7*d - 8*a^7*b*c^3*d^5 - 4*a^7*b*c^5*d^3 + 6*a^2*b^6*c^2*d^6 + 14*a^2*b^6*c^4*d^4 + 10*a^2*b^6*c^6*d
^2 - 16*a^3*b^5*c^3*d^5 - 20*a^3*b^5*c^5*d^3 + 14*a^4*b^4*c^2*d^6 + 26*a^4*b^4*c^4*d^4 + 14*a^4*b^4*c^6*d^2 -
20*a^5*b^3*c^3*d^5 - 16*a^5*b^3*c^5*d^3 + 10*a^6*b^2*c^2*d^6 + 14*a^6*b^2*c^4*d^4 + 6*a^6*b^2*c^6*d^2 - 4*a*b^
7*c^7*d - 4*a^7*b*c*d^7) + (tan(e + f*x)*(6*a^12*b*d^13 + 6*b^13*c^12*d + 8*a^4*b^9*d^13 + 22*a^6*b^7*d^13 + 2
6*a^8*b^5*d^13 + 18*a^10*b^3*d^13 + 8*b^13*c^4*d^9 + 22*b^13*c^6*d^7 + 26*b^13*c^8*d^5 + 18*b^13*c^10*d^3 - 32
*a*b^12*c^3*d^10 - 84*a*b^12*c^5*d^8 - 92*a*b^12*c^7*d^6 - 60*a*b^12*c^9*d^4 - 20*a*b^12*c^11*d^2 + 10*a^2*b^1
1*c^12*d - 32*a^3*b^10*c*d^12 + 2*a^4*b^9*c^12*d - 84*a^5*b^8*c*d^12 - 2*a^6*b^7*c^12*d - 92*a^7*b^6*c*d^12 -
60*a^9*b^4*c*d^12 - 20*a^11*b^2*c*d^12 + 10*a^12*b*c^2*d^11 + 2*a^12*b*c^4*d^9 - 2*a^12*b*c^6*d^7 + 48*a^2*b^1
1*c^2*d^11 + 138*a^2*b^11*c^4*d^9 + 152*a^2*b^11*c^6*d^7 + 92*a^2*b^11*c^8*d^5 + 40*a^2*b^11*c^10*d^3 - 152*a^
3*b^10*c^3*d^10 - 196*a^3*b^10*c^5*d^8 - 92*a^3*b^10*c^7*d^6 - 44*a^3*b^10*c^9*d^4 - 28*a^3*b^10*c^11*d^2 + 13
8*a^4*b^9*c^2*d^11 + 220*a^4*b^9*c^4*d^9 + 50*a^4*b^9*c^6*d^7 - 46*a^4*b^9*c^8*d^5 - 4*a^4*b^9*c^10*d^3 - 196*
a^5*b^8*c^3*d^10 - 16*a^5*b^8*c^5*d^8 + 224*a^5*b^8*c^7*d^6 + 132*a^5*b^8*c^9*d^4 + 4*a^5*b^8*c^11*d^2 + 152*a
^6*b^7*c^2*d^11 + 50*a^6*b^7*c^4*d^9 - 320*a^6*b^7*c^6*d^7 - 294*a^6*b^7*c^8*d^5 - 56*a^6*b^7*c^10*d^3 - 92*a^
7*b^6*c^3*d^10 + 224*a^7*b^6*c^5*d^8 + 368*a^7*b^6*c^7*d^6 + 156*a^7*b^6*c^9*d^4 + 12*a^7*b^6*c^11*d^2 + 92*a^
8*b^5*c^2*d^11 - 46*a^8*b^5*c^4*d^9 - 294*a^8*b^5*c^6*d^7 - 212*a^8*b^5*c^8*d^5 - 30*a^8*b^5*c^10*d^3 - 44*a^9
*b^4*c^3*d^10 + 132*a^9*b^4*c^5*d^8 + 156*a^9*b^4*c^7*d^6 + 40*a^9*b^4*c^9*d^4 + 40*a^10*b^3*c^2*d^11 - 4*a^10
*b^3*c^4*d^9 - 56*a^10*b^3*c^6*d^7 - 30*a^10*b^3*c^8*d^5 - 28*a^11*b^2*c^3*d^10 + 4*a^11*b^2*c^5*d^8 + 12*a^11
*b^2*c^7*d^6))/(a^8*d^8 + b^8*c^8 + 2*a^2*b^6*c^8 + a^4*b^4*c^8 + a^4*b^4*d^8 + 2*a^6*b^2*d^8 + 2*a^8*c^2*d^6
+ a^8*c^4*d^4 + b^8*c^4*d^4 + 2*b^8*c^6*d^2 - 4*a*b^7*c^3*d^5 - 8*a*b^7*c^5*d^3 - 4*a^3*b^5*c*d^7 - 8*a^3*b^5*
c^7*d - 8*a^5*b^3*c*d^7 - 4*a^5*b^3*c^7*d - 8*a^7*b*c^3*d^5 - 4*a^7*b*c^5*d^3 + 6*a^2*b^6*c^2*d^6 + 14*a^2*b^6
*c^4*d^4 + 10*a^2*b^6*c^6*d^2 - 16*a^3*b^5*c^3*d^5 - 20*a^3*b^5*c^5*d^3 + 14*a^4*b^4*c^2*d^6 + 26*a^4*b^4*c^4*
d^4 + 14*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^3*d^5 - 16*a^5*b^3*c^5*d^3 + 10*a^6*b^2*c^2*d^6 + 14*a^6*b^2*c^4*d^4 +
6*a^6*b^2*c^6*d^2 - 4*a*b^7*c^7*d - 4*a^7*b*c*d^7)) - (C*a^10*b*d^11 - A*b^11*c^10*d - A*a^10*b*d^11 + C*b^11
*c^10*d - 8*A*a^2*b^9*d^11 - 16*A*a^4*b^7*d^11 - A*a^6*b^5*d^11 + 6*A*a^8*b^3*d^11 + 4*B*a^3*b^8*d^11 + 12*B*a
^5*b^6*d^11 + 4*B*a^7*b^4*d^11 - 4*B*a^9*b^2*d^11 - 8*A*b^11*c^2*d^9 - 16*A*b^11*c^4*d^7 - A*b^11*c^6*d^5 + 6*
A*b^11*c^8*d^3 - 7*C*a^6*b^5*d^11 - 6*C*a^8*b^3*d^11 + 4*B*b^11*c^3*d^8 + 12*B*b^11*c^5*d^6 + 4*B*b^11*c^7*d^4
- 4*B*b^11*c^9*d^2 - 7*C*b^11*c^6*d^5 - 6*C*b^11*c^8*d^3 + 56*A*a*b^10*c^3*d^8 + 54*A*a*b^10*c^5*d^6 + 12*A*a
*b^10*c^7*d^4 - 2*A*a*b^10*c^9*d^2 - 2*A*a^2*b^9*c^10*d + 56*A*a^3*b^8*c*d^10 - A*a^4*b^7*c^10*d + 54*A*a^5*b^
6*c*d^10 + 12*A*a^7*b^4*c*d^10 - 2*A*a^9*b^2*c*d^10 - 2*A*a^10*b*c^2*d^9 - A*a^10*b*c^4*d^7 - 4*B*a*b^10*c^2*d
^9 - 32*B*a*b^10*c^4*d^7 - 44*B*a*b^10*c^6*d^5 - 16*B*a*b^10*c^8*d^3 - 4*B*a^2*b^9*c*d^10 - 32*B*a^4*b^7*c*d^1
0 - 44*B*a^6*b^5*c*d^10 - 16*B*a^8*b^3*c*d^10 - 8*C*a*b^10*c^3*d^8 + 2*C*a*b^10*c^5*d^6 + 20*C*a*b^10*c^7*d^4
+ 10*C*a*b^10*c^9*d^2 + 2*C*a^2*b^9*c^10*d - 8*C*a^3*b^8*c*d^10 + C*a^4*b^7*c^10*d + 2*C*a^5*b^6*c*d^10 + 20*C
*a^7*b^4*c*d^10 + 10*C*a^9*b^2*c*d^10 + 2*C*a^10*b*c^2*d^9 + C*a^10*b*c^4*d^7 - 80*A*a^2*b^9*c^2*d^9 - 159*A*a
^2*b^9*c^4*d^7 - 80*A*a^2*b^9*c^6*d^5 + 5*A*a^2*b^9*c^8*d^3 + 212*A*a^3*b^8*c^3*d^8 + 228*A*a^3*b^8*c^5*d^6 +
76*A*a^3*b^8*c^7*d^4 + 4*A*a^3*b^8*c^9*d^2 - 159*A*a^4*b^7*c^2*d^9 - 332*A*a^4*b^7*c^4*d^7 - 204*A*a^4*b^7*c^6
*d^5 - 16*A*a^4*b^7*c^8*d^3 + 228*A*a^5*b^6*c^3*d^8 + 252*A*a^5*b^6*c^5*d^6 + 84*A*a^5*b^6*c^7*d^4 + 6*A*a^5*b
^6*c^9*d^2 - 80*A*a^6*b^5*c^2*d^9 - 204*A*a^6*b^5*c^4*d^7 - 140*A*a^6*b^5*c^6*d^5 - 15*A*a^6*b^5*c^8*d^3 + 76*
A*a^7*b^4*c^3*d^8 + 84*A*a^7*b^4*c^5*d^6 + 20*A*a^7*b^4*c^7*d^4 + 5*A*a^8*b^3*c^2*d^9 - 16*A*a^8*b^3*c^4*d^7 -
15*A*a^8*b^3*c^6*d^5 + 4*A*a^9*b^2*c^3*d^8 + 6*A*a^9*b^2*c^5*d^6 + 20*B*a^2*b^9*c^3*d^8 + 84*B*a^2*b^9*c^5*d^
6 + 60*B*a^2*b^9*c^7*d^4 + 20*B*a^3*b^8*c^2*d^9 - 44*B*a^3*b^8*c^4*d^7 - 100*B*a^3*b^8*c^6*d^5 - 40*B*a^3*b^8*
c^8*d^3 - 44*B*a^4*b^7*c^3*d^8 + 60*B*a^4*b^7*c^5*d^6 + 76*B*a^4*b^7*c^7*d^4 + 4*B*a^4*b^7*c^9*d^2 + 84*B*a^5*
b^6*c^2*d^9 + 60*B*a^5*b^6*c^4*d^7 - 36*B*a^5*b^6*c^6*d^5 - 24*B*a^5*b^6*c^8*d^3 - 100*B*a^6*b^5*c^3*d^8 - 36*
B*a^6*b^5*c^5*d^6 + 20*B*a^6*b^5*c^7*d^4 + 60*B*a^7*b^4*c^2*d^9 + 76*B*a^7*b^4*c^4*d^7 + 20*B*a^7*b^4*c^6*d^5
- 40*B*a^8*b^3*c^3*d^8 - 24*B*a^8*b^3*c^5*d^6 + 4*B*a^9*b^2*c^4*d^7 + 16*C*a^2*b^9*c^2*d^9 + 47*C*a^2*b^9*c^4*
d^7 + 16*C*a^2*b^9*c^6*d^5 - 13*C*a^2*b^9*c^8*d^3 - 84*C*a^3*b^8*c^3*d^8 - 100*C*a^3*b^8*c^5*d^6 - 12*C*a^3*b^
8*c^7*d^4 + 12*C*a^3*b^8*c^9*d^2 + 47*C*a^4*b^7*c^2*d^9 + 140*C*a^4*b^7*c^4*d^7 + 92*C*a^4*b^7*c^6*d^5 - 100*C
*a^5*b^6*c^3*d^8 - 156*C*a^5*b^6*c^5*d^6 - 52*C*a^5*b^6*c^7*d^4 + 2*C*a^5*b^6*c^9*d^2 + 16*C*a^6*b^5*c^2*d^9 +
92*C*a^6*b^5*c^4*d^7 + 76*C*a^6*b^5*c^6*d^5 + 7*C*a^6*b^5*c^8*d^3 - 12*C*a^7*b^4*c^3*d^8 - 52*C*a^7*b^4*c^5*d
^6 - 20*C*a^7*b^4*c^7*d^4 - 13*C*a^8*b^3*c^2*d^9 + 7*C*a^8*b^3*c^6*d^5 + 12*C*a^9*b^2*c^3*d^8 + 2*C*a^9*b^2*c^
5*d^6 + 16*A*a*b^10*c*d^10)/(a^8*d^8 + b^8*c^8 + 2*a^2*b^6*c^8 + a^4*b^4*c^8 + a^4*b^4*d^8 + 2*a^6*b^2*d^8 + 2
*a^8*c^2*d^6 + a^8*c^4*d^4 + b^8*c^4*d^4 + 2*b^8*c^6*d^2 - 4*a*b^7*c^3*d^5 - 8*a*b^7*c^5*d^3 - 4*a^3*b^5*c*d^7
- 8*a^3*b^5*c^7*d - 8*a^5*b^3*c*d^7 - 4*a^5*b^3*c^7*d - 8*a^7*b*c^3*d^5 - 4*a^7*b*c^5*d^3 + 6*a^2*b^6*c^2*d^6
+ 14*a^2*b^6*c^4*d^4 + 10*a^2*b^6*c^6*d^2 - 16*a^3*b^5*c^3*d^5 - 20*a^3*b^5*c^5*d^3 + 14*a^4*b^4*c^2*d^6 + 26
*a^4*b^4*c^4*d^4 + 14*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^3*d^5 - 16*a^5*b^3*c^5*d^3 + 10*a^6*b^2*c^2*d^6 + 14*a^6*
b^2*c^4*d^4 + 6*a^6*b^2*c^6*d^2 - 4*a*b^7*c^7*d - 4*a^7*b*c*d^7) + (tan(e + f*x)*(3*B*a^10*b*d^11 + 3*B*b^11*c
^10*d - 16*A*a^3*b^8*d^11 - 48*A*a^5*b^6*d^11 - 36*A*a^7*b^4*d^11 - 4*A*a^9*b^2*d^11 + 4*B*a^4*b^7*d^11 + 23*B
*a^6*b^5*d^11 + 22*B*a^8*b^3*d^11 - 16*A*b^11*c^3*d^8 - 48*A*b^11*c^5*d^6 - 36*A*b^11*c^7*d^4 - 4*A*b^11*c^9*d
^2 + 8*C*a^5*b^6*d^11 + 4*C*a^7*b^4*d^11 - 4*C*a^9*b^2*d^11 + 4*B*b^11*c^4*d^7 + 23*B*b^11*c^6*d^5 + 22*B*b^11
*c^8*d^3 + 8*C*b^11*c^5*d^6 + 4*C*b^11*c^7*d^4 - 4*C*b^11*c^9*d^2 + 16*A*a*b^10*c^2*d^9 + 80*A*a*b^10*c^4*d^7
+ 100*A*a*b^10*c^6*d^5 + 40*A*a*b^10*c^8*d^3 + 16*A*a^2*b^9*c*d^10 + 4*A*a^3*b^8*c^10*d + 80*A*a^4*b^7*c*d^10
+ 100*A*a^6*b^5*c*d^10 + 40*A*a^8*b^3*c*d^10 + 4*A*a^10*b*c^3*d^8 + 16*B*a*b^10*c^3*d^8 + 6*B*a*b^10*c^5*d^6 -
20*B*a*b^10*c^7*d^4 - 10*B*a*b^10*c^9*d^2 + 2*B*a^2*b^9*c^10*d + 16*B*a^3*b^8*c*d^10 - B*a^4*b^7*c^10*d + 6*B
*a^5*b^6*c*d^10 - 20*B*a^7*b^4*c*d^10 - 10*B*a^9*b^2*c*d^10 + 2*B*a^10*b*c^2*d^9 - B*a^10*b*c^4*d^7 - 40*C*a*b
^10*c^4*d^7 - 68*C*a*b^10*c^6*d^5 - 32*C*a*b^10*c^8*d^3 - 4*C*a^3*b^8*c^10*d - 40*C*a^4*b^7*c*d^10 - 68*C*a^6*
b^5*c*d^10 - 32*C*a^8*b^3*c*d^10 - 4*C*a^10*b*c^3*d^8 - 32*A*a^2*b^9*c^3*d^8 - 180*A*a^2*b^9*c^5*d^6 - 156*A*a
^2*b^9*c^7*d^4 - 24*A*a^2*b^9*c^9*d^2 - 32*A*a^3*b^8*c^2*d^9 + 116*A*a^3*b^8*c^4*d^7 + 204*A*a^3*b^8*c^6*d^5 +
76*A*a^3*b^8*c^8*d^3 + 116*A*a^4*b^7*c^3*d^8 - 84*A*a^4*b^7*c^5*d^6 - 140*A*a^4*b^7*c^7*d^4 - 20*A*a^4*b^7*c^
9*d^2 - 180*A*a^5*b^6*c^2*d^9 - 84*A*a^5*b^6*c^4*d^7 + 84*A*a^5*b^6*c^6*d^5 + 36*A*a^5*b^6*c^8*d^3 + 204*A*a^6
*b^5*c^3*d^8 + 84*A*a^6*b^5*c^5*d^6 - 20*A*a^6*b^5*c^7*d^4 - 156*A*a^7*b^4*c^2*d^9 - 140*A*a^7*b^4*c^4*d^7 - 2
0*A*a^7*b^4*c^6*d^5 + 76*A*a^8*b^3*c^3*d^8 + 36*A*a^8*b^3*c^5*d^6 - 24*A*a^9*b^2*c^2*d^9 - 20*A*a^9*b^2*c^4*d^
7 - 40*B*a^2*b^9*c^2*d^9 - 103*B*a^2*b^9*c^4*d^7 - 40*B*a^2*b^9*c^6*d^5 + 25*B*a^2*b^9*c^8*d^3 + 148*B*a^3*b^8
*c^3*d^8 + 180*B*a^3*b^8*c^5*d^6 + 44*B*a^3*b^8*c^7*d^4 - 4*B*a^3*b^8*c^9*d^2 - 103*B*a^4*b^7*c^2*d^9 - 284*B*
a^4*b^7*c^4*d^7 - 188*B*a^4*b^7*c^6*d^5 - 12*B*a^4*b^7*c^8*d^3 + 180*B*a^5*b^6*c^3*d^8 + 252*B*a^5*b^6*c^5*d^6
+ 84*B*a^5*b^6*c^7*d^4 + 6*B*a^5*b^6*c^9*d^2 - 40*B*a^6*b^5*c^2*d^9 - 188*B*a^6*b^5*c^4*d^7 - 140*B*a^6*b^5*c
^6*d^5 - 15*B*a^6*b^5*c^8*d^3 + 44*B*a^7*b^4*c^3*d^8 + 84*B*a^7*b^4*c^5*d^6 + 20*B*a^7*b^4*c^7*d^4 + 25*B*a^8*
b^3*c^2*d^9 - 12*B*a^8*b^3*c^4*d^7 - 15*B*a^8*b^3*c^6*d^5 - 4*B*a^9*b^2*c^3*d^8 + 6*B*a^9*b^2*c^5*d^6 + 32*C*a
^2*b^9*c^3*d^8 + 116*C*a^2*b^9*c^5*d^6 + 92*C*a^2*b^9*c^7*d^4 + 8*C*a^2*b^9*c^9*d^2 + 32*C*a^3*b^8*c^2*d^9 - 5
2*C*a^3*b^8*c^4*d^7 - 140*C*a^3*b^8*c^6*d^5 - 60*C*a^3*b^8*c^8*d^3 - 52*C*a^4*b^7*c^3*d^8 + 84*C*a^4*b^7*c^5*d
^6 + 108*C*a^4*b^7*c^7*d^4 + 12*C*a^4*b^7*c^9*d^2 + 116*C*a^5*b^6*c^2*d^9 + 84*C*a^5*b^6*c^4*d^7 - 52*C*a^5*b^
6*c^6*d^5 - 28*C*a^5*b^6*c^8*d^3 - 140*C*a^6*b^5*c^3*d^8 - 52*C*a^6*b^5*c^5*d^6 + 20*C*a^6*b^5*c^7*d^4 + 92*C*
a^7*b^4*c^2*d^9 + 108*C*a^7*b^4*c^4*d^7 + 20*C*a^7*b^4*c^6*d^5 - 60*C*a^8*b^3*c^3*d^8 - 28*C*a^8*b^3*c^5*d^6 +
8*C*a^9*b^2*c^2*d^9 + 12*C*a^9*b^2*c^4*d^7 + 4*A*a*b^10*c^10*d + 4*A*a^10*b*c*d^10 - 4*C*a*b^10*c^10*d - 4*C*
a^10*b*c*d^10))/(a^8*d^8 + b^8*c^8 + 2*a^2*b^6*c^8 + a^4*b^4*c^8 + a^4*b^4*d^8 + 2*a^6*b^2*d^8 + 2*a^8*c^2*d^6
+ a^8*c^4*d^4 + b^8*c^4*d^4 + 2*b^8*c^6*d^2 - 4*a*b^7*c^3*d^5 - 8*a*b^7*c^5*d^3 - 4*a^3*b^5*c*d^7 - 8*a^3*b^5
*c^7*d - 8*a^5*b^3*c*d^7 - 4*a^5*b^3*c^7*d - 8*a^7*b*c^3*d^5 - 4*a^7*b*c^5*d^3 + 6*a^2*b^6*c^2*d^6 + 14*a^2*b^
6*c^4*d^4 + 10*a^2*b^6*c^6*d^2 - 16*a^3*b^5*c^3*d^5 - 20*a^3*b^5*c^5*d^3 + 14*a^4*b^4*c^2*d^6 + 26*a^4*b^4*c^4
*d^4 + 14*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^3*d^5 - 16*a^5*b^3*c^5*d^3 + 10*a^6*b^2*c^2*d^6 + 14*a^6*b^2*c^4*d^4
+ 6*a^6*b^2*c^6*d^2 - 4*a*b^7*c^7*d - 4*a^7*b*c*d^7)) + (tan(e + f*x)*(8*A^2*b^9*d^9 + 8*A^2*a^2*b^7*d^9 + 18*
A^2*a^4*b^5*d^9 + 2*A^2*a^6*b^3*d^9 + 2*B^2*a^2*b^7*d^9 - 6*B^2*a^4*b^5*d^9 + 9*B^2*a^6*b^3*d^9 + 8*A^2*b^9*c^
2*d^7 + 18*A^2*b^9*c^4*d^5 + 2*A^2*b^9*c^6*d^3 + 2*C^2*a^4*b^5*d^9 - 14*C^2*a^6*b^3*d^9 + 2*B^2*b^9*c^2*d^7 -
6*B^2*b^9*c^4*d^5 + 9*B^2*b^9*c^6*d^3 + 2*C^2*b^9*c^4*d^5 - 14*C^2*b^9*c^6*d^3 + A^2*a^8*b*d^9 + A^2*b^9*c^8*d
+ C^2*a^8*b*d^9 + C^2*b^9*c^8*d + 28*A^2*a^2*b^7*c^2*d^7 + 54*A^2*a^2*b^7*c^4*d^5 + 6*A^2*a^2*b^7*c^6*d^3 - 9
6*A^2*a^3*b^6*c^3*d^6 - 20*A^2*a^3*b^6*c^5*d^4 + 54*A^2*a^4*b^5*c^2*d^7 + 42*A^2*a^4*b^5*c^4*d^5 - 20*A^2*a^5*
b^4*c^3*d^6 + 6*A^2*a^6*b^3*c^2*d^7 - 20*B^2*a^2*b^7*c^2*d^7 - 37*B^2*a^2*b^7*c^4*d^5 + 14*B^2*a^2*b^7*c^6*d^3
- 4*B^2*a^3*b^6*c^3*d^6 - 14*B^2*a^3*b^6*c^5*d^4 - 6*B^2*a^3*b^6*c^7*d^2 - 37*B^2*a^4*b^5*c^2*d^7 - 28*B^2*a^
4*b^5*c^4*d^5 + 9*B^2*a^4*b^5*c^6*d^3 - 14*B^2*a^5*b^4*c^3*d^6 + 14*B^2*a^6*b^3*c^2*d^7 + 9*B^2*a^6*b^3*c^4*d^
5 - 6*B^2*a^7*b^2*c^3*d^6 + 20*C^2*a^2*b^7*c^2*d^7 + 22*C^2*a^2*b^7*c^4*d^5 - 26*C^2*a^2*b^7*c^6*d^3 - 48*C^2*
a^3*b^6*c^3*d^6 - 28*C^2*a^3*b^6*c^5*d^4 + 8*C^2*a^3*b^6*c^7*d^2 + 22*C^2*a^4*b^5*c^2*d^7 + 18*C^2*a^4*b^5*c^4
*d^5 - 8*C^2*a^4*b^5*c^6*d^3 - 28*C^2*a^5*b^4*c^3*d^6 - 32*C^2*a^5*b^4*c^5*d^4 - 26*C^2*a^6*b^3*c^2*d^7 - 8*C^
2*a^6*b^3*c^4*d^5 + 8*C^2*a^6*b^3*c^6*d^3 + 8*C^2*a^7*b^2*c^3*d^6 + 4*A*B*a^3*b^6*d^9 - 20*A*B*a^5*b^4*d^9 + 2
*A*B*a^7*b^2*d^9 - 28*A*C*a^4*b^5*d^9 + 4*A*C*a^6*b^3*d^9 + 4*A*B*b^9*c^3*d^6 - 20*A*B*b^9*c^5*d^4 + 2*A*B*b^9
*c^7*d^2 + 28*B*C*a^5*b^4*d^9 - 6*B*C*a^7*b^2*d^9 - 28*A*C*b^9*c^4*d^5 + 4*A*C*b^9*c^6*d^3 + 28*B*C*b^9*c^5*d^
4 - 6*B*C*b^9*c^7*d^2 - 48*A^2*a*b^8*c*d^8 + 4*B^2*a*b^8*c*d^8 - 72*A^2*a*b^8*c^3*d^6 - 24*A^2*a*b^8*c^5*d^4 -
4*A^2*a*b^8*c^7*d^2 - 72*A^2*a^3*b^6*c*d^8 - 24*A^2*a^5*b^4*c*d^8 - 4*A^2*a^7*b^2*c*d^8 - 10*B^2*a*b^8*c^5*d^
4 - 2*B^2*a*b^8*c^7*d^2 + B^2*a^2*b^7*c^8*d - 10*B^2*a^5*b^4*c*d^8 - 2*B^2*a^7*b^2*c*d^8 + B^2*a^8*b*c^2*d^7 -
8*C^2*a*b^8*c^3*d^6 + 4*C^2*a*b^8*c^7*d^2 - 8*C^2*a^3*b^6*c*d^8 + 4*C^2*a^7*b^2*c*d^8 - 8*A*B*a*b^8*d^9 - 2*A
*C*a^8*b*d^9 - 8*A*B*b^9*c*d^8 - 2*A*C*b^9*c^8*d - 2*A*B*a*b^8*c^8*d - 2*A*B*a^8*b*c*d^8 + 16*A*C*a*b^8*c*d^8
+ 2*B*C*a*b^8*c^8*d + 2*B*C*a^8*b*c*d^8 + 28*A*B*a*b^8*c^2*d^7 + 48*A*B*a*b^8*c^4*d^5 + 2*A*B*a*b^8*c^6*d^3 +
28*A*B*a^2*b^7*c*d^8 + 48*A*B*a^4*b^5*c*d^8 + 2*A*B*a^6*b^3*c*d^8 + 16*A*C*a*b^8*c^3*d^6 - 8*A*C*a*b^8*c^5*d^4
+ 16*A*C*a^3*b^6*c*d^8 - 8*A*C*a^5*b^4*c*d^8 - 8*B*C*a*b^8*c^2*d^7 - 24*B*C*a*b^8*c^4*d^5 - 6*B*C*a*b^8*c^6*d
^3 - 8*B*C*a^2*b^7*c*d^8 - 24*B*C*a^4*b^5*c*d^8 - 6*B*C*a^6*b^3*c*d^8 + 52*A*B*a^2*b^7*c^3*d^6 - 22*A*B*a^2*b^
7*c^5*d^4 + 10*A*B*a^2*b^7*c^7*d^2 + 52*A*B*a^3*b^6*c^2*d^7 + 50*A*B*a^3*b^6*c^4*d^5 - 6*A*B*a^3*b^6*c^6*d^3 +
50*A*B*a^4*b^5*c^3*d^6 - 10*A*B*a^4*b^5*c^5*d^4 - 22*A*B*a^5*b^4*c^2*d^7 - 10*A*B*a^5*b^4*c^4*d^5 - 6*A*B*a^6
*b^3*c^3*d^6 + 10*A*B*a^7*b^2*c^2*d^7 - 40*A*C*a^2*b^7*c^2*d^7 - 84*A*C*a^2*b^7*c^4*d^5 + 12*A*C*a^2*b^7*c^6*d
^3 + 16*A*C*a^3*b^6*c^3*d^6 - 16*A*C*a^3*b^6*c^5*d^4 - 8*A*C*a^3*b^6*c^7*d^2 - 84*A*C*a^4*b^5*c^2*d^7 - 52*A*C
*a^4*b^5*c^4*d^5 + 16*A*C*a^4*b^5*c^6*d^3 - 16*A*C*a^5*b^4*c^3*d^6 + 12*A*C*a^6*b^3*c^2*d^7 + 16*A*C*a^6*b^3*c
^4*d^5 - 8*A*C*a^7*b^2*c^3*d^6 + 28*B*C*a^2*b^7*c^3*d^6 + 82*B*C*a^2*b^7*c^5*d^4 - 10*B*C*a^2*b^7*c^7*d^2 + 28
*B*C*a^3*b^6*c^2*d^7 + 10*B*C*a^3*b^6*c^4*d^5 - 10*B*C*a^3*b^6*c^6*d^3 + 10*B*C*a^4*b^5*c^3*d^6 + 50*B*C*a^4*b
^5*c^5*d^4 + 4*B*C*a^4*b^5*c^7*d^2 + 82*B*C*a^5*b^4*c^2*d^7 + 50*B*C*a^5*b^4*c^4*d^5 - 12*B*C*a^5*b^4*c^6*d^3
- 10*B*C*a^6*b^3*c^3*d^6 - 12*B*C*a^6*b^3*c^5*d^4 - 10*B*C*a^7*b^2*c^2*d^7 + 4*B*C*a^7*b^2*c^4*d^5))/(a^8*d^8
+ b^8*c^8 + 2*a^2*b^6*c^8 + a^4*b^4*c^8 + a^4*b^4*d^8 + 2*a^6*b^2*d^8 + 2*a^8*c^2*d^6 + a^8*c^4*d^4 + b^8*c^4*
d^4 + 2*b^8*c^6*d^2 - 4*a*b^7*c^3*d^5 - 8*a*b^7*c^5*d^3 - 4*a^3*b^5*c*d^7 - 8*a^3*b^5*c^7*d - 8*a^5*b^3*c*d^7
- 4*a^5*b^3*c^7*d - 8*a^7*b*c^3*d^5 - 4*a^7*b*c^5*d^3 + 6*a^2*b^6*c^2*d^6 + 14*a^2*b^6*c^4*d^4 + 10*a^2*b^6*c^
6*d^2 - 16*a^3*b^5*c^3*d^5 - 20*a^3*b^5*c^5*d^3 + 14*a^4*b^4*c^2*d^6 + 26*a^4*b^4*c^4*d^4 + 14*a^4*b^4*c^6*d^2
- 20*a^5*b^3*c^3*d^5 - 16*a^5*b^3*c^5*d^3 + 10*a^6*b^2*c^2*d^6 + 14*a^6*b^2*c^4*d^4 + 6*a^6*b^2*c^6*d^2 - 4*a
*b^7*c^7*d - 4*a^7*b*c*d^7)))*root(144*a^13*b*c^5*d^9*f^4 + 144*a^9*b^5*c*d^13*f^4 + 144*a^5*b^9*c^13*d*f^4 +
144*a*b^13*c^9*d^5*f^4 + 96*a^13*b*c^7*d^7*f^4 + 96*a^13*b*c^3*d^11*f^4 + 96*a^11*b^3*c*d^13*f^4 + 96*a^7*b^7*
c^13*d*f^4 + 96*a^7*b^7*c*d^13*f^4 + 96*a^3*b^11*c^13*d*f^4 + 96*a*b^13*c^11*d^3*f^4 + 96*a*b^13*c^7*d^7*f^4 +
24*a^13*b*c^9*d^5*f^4 + 24*a^9*b^5*c^13*d*f^4 + 24*a^5*b^9*c*d^13*f^4 + 24*a*b^13*c^5*d^9*f^4 + 24*a^13*b*c*d
^13*f^4 + 24*a*b^13*c^13*d*f^4 + 3648*a^7*b^7*c^7*d^7*f^4 - 3188*a^8*b^6*c^6*d^8*f^4 - 3188*a^6*b^8*c^8*d^6*f^
4 - 2912*a^8*b^6*c^8*d^6*f^4 - 2912*a^6*b^8*c^6*d^8*f^4 + 2592*a^9*b^5*c^7*d^7*f^4 + 2592*a^7*b^7*c^9*d^5*f^4
+ 2592*a^7*b^7*c^5*d^9*f^4 + 2592*a^5*b^9*c^7*d^7*f^4 + 2168*a^9*b^5*c^5*d^9*f^4 + 2168*a^5*b^9*c^9*d^5*f^4 -
1776*a^10*b^4*c^6*d^8*f^4 - 1776*a^8*b^6*c^4*d^10*f^4 - 1776*a^6*b^8*c^10*d^4*f^4 - 1776*a^4*b^10*c^8*d^6*f^4
+ 1568*a^9*b^5*c^9*d^5*f^4 + 1568*a^5*b^9*c^5*d^9*f^4 - 1344*a^10*b^4*c^8*d^6*f^4 - 1344*a^8*b^6*c^10*d^4*f^4
- 1344*a^6*b^8*c^4*d^10*f^4 - 1344*a^4*b^10*c^6*d^8*f^4 - 1164*a^10*b^4*c^4*d^10*f^4 - 1164*a^4*b^10*c^10*d^4*
f^4 + 896*a^11*b^3*c^5*d^9*f^4 + 896*a^9*b^5*c^3*d^11*f^4 + 896*a^5*b^9*c^11*d^3*f^4 + 896*a^3*b^11*c^9*d^5*f^
4 + 864*a^11*b^3*c^7*d^7*f^4 + 864*a^7*b^7*c^11*d^3*f^4 + 864*a^7*b^7*c^3*d^11*f^4 + 864*a^3*b^11*c^7*d^7*f^4
- 480*a^10*b^4*c^10*d^4*f^4 - 480*a^4*b^10*c^4*d^10*f^4 + 464*a^11*b^3*c^3*d^11*f^4 + 464*a^3*b^11*c^11*d^3*f^
4 - 424*a^12*b^2*c^6*d^8*f^4 - 424*a^8*b^6*c^2*d^12*f^4 - 424*a^6*b^8*c^12*d^2*f^4 - 424*a^2*b^12*c^8*d^6*f^4
+ 416*a^11*b^3*c^9*d^5*f^4 + 416*a^9*b^5*c^11*d^3*f^4 + 416*a^5*b^9*c^3*d^11*f^4 + 416*a^3*b^11*c^5*d^9*f^4 -
336*a^12*b^2*c^4*d^10*f^4 - 336*a^10*b^4*c^2*d^12*f^4 - 336*a^4*b^10*c^12*d^2*f^4 - 336*a^2*b^12*c^10*d^4*f^4
- 256*a^12*b^2*c^8*d^6*f^4 - 256*a^8*b^6*c^12*d^2*f^4 - 256*a^6*b^8*c^2*d^12*f^4 - 256*a^2*b^12*c^6*d^8*f^4 -
124*a^12*b^2*c^2*d^12*f^4 - 124*a^2*b^12*c^12*d^2*f^4 + 80*a^11*b^3*c^11*d^3*f^4 + 80*a^3*b^11*c^3*d^11*f^4 -
60*a^12*b^2*c^10*d^4*f^4 - 60*a^10*b^4*c^12*d^2*f^4 - 60*a^4*b^10*c^2*d^12*f^4 - 60*a^2*b^12*c^4*d^10*f^4 - 24
*b^14*c^10*d^4*f^4 - 16*b^14*c^12*d^2*f^4 - 16*b^14*c^8*d^6*f^4 - 4*b^14*c^6*d^8*f^4 - 24*a^14*c^4*d^10*f^4 -
16*a^14*c^6*d^8*f^4 - 16*a^14*c^2*d^12*f^4 - 4*a^14*c^8*d^6*f^4 - 24*a^10*b^4*d^14*f^4 - 16*a^12*b^2*d^14*f^4
- 16*a^8*b^6*d^14*f^4 - 4*a^6*b^8*d^14*f^4 - 24*a^4*b^10*c^14*f^4 - 16*a^6*b^8*c^14*f^4 - 16*a^2*b^12*c^14*f^4
- 4*a^8*b^6*c^14*f^4 - 4*b^14*c^14*f^4 - 4*a^14*d^14*f^4 + 36*A*C*a^9*b*c*d^9*f^2 + 36*A*C*a*b^9*c^9*d*f^2 +
32*A*C*a*b^9*c*d^9*f^2 - 552*B*C*a^7*b^3*c^4*d^6*f^2 - 552*B*C*a^4*b^6*c^7*d^3*f^2 - 408*B*C*a^5*b^5*c^4*d^6*f
^2 - 408*B*C*a^4*b^6*c^5*d^5*f^2 + 360*B*C*a^6*b^4*c^3*d^7*f^2 + 360*B*C*a^3*b^7*c^6*d^4*f^2 - 248*B*C*a^7*b^3
*c^2*d^8*f^2 - 248*B*C*a^2*b^8*c^7*d^3*f^2 + 184*B*C*a^6*b^4*c^5*d^5*f^2 + 184*B*C*a^5*b^5*c^6*d^4*f^2 + 152*B
*C*a^8*b^2*c^3*d^7*f^2 - 152*B*C*a^5*b^5*c^2*d^8*f^2 + 152*B*C*a^3*b^7*c^8*d^2*f^2 - 152*B*C*a^2*b^8*c^5*d^5*f
^2 - 104*B*C*a^7*b^3*c^6*d^4*f^2 - 104*B*C*a^6*b^4*c^7*d^3*f^2 + 64*B*C*a^8*b^2*c^5*d^5*f^2 + 64*B*C*a^5*b^5*c
^8*d^2*f^2 - 56*B*C*a^4*b^6*c^3*d^7*f^2 - 56*B*C*a^3*b^7*c^4*d^6*f^2 - 24*B*C*a^8*b^2*c^7*d^3*f^2 - 24*B*C*a^7
*b^3*c^8*d^2*f^2 - 24*B*C*a^3*b^7*c^2*d^8*f^2 - 24*B*C*a^2*b^8*c^3*d^7*f^2 - 696*A*C*a^5*b^5*c^5*d^5*f^2 + 536
*A*C*a^6*b^4*c^6*d^4*f^2 + 536*A*C*a^6*b^4*c^4*d^6*f^2 + 536*A*C*a^4*b^6*c^6*d^4*f^2 + 472*A*C*a^4*b^6*c^4*d^6
*f^2 - 232*A*C*a^7*b^3*c^5*d^5*f^2 - 232*A*C*a^5*b^5*c^7*d^3*f^2 + 216*A*C*a^3*b^7*c^3*d^7*f^2 + 168*A*C*a^7*b
^3*c^3*d^7*f^2 + 168*A*C*a^3*b^7*c^7*d^3*f^2 - 154*A*C*a^8*b^2*c^2*d^8*f^2 - 154*A*C*a^2*b^8*c^8*d^2*f^2 + 62*
A*C*a^8*b^2*c^6*d^4*f^2 + 62*A*C*a^6*b^4*c^8*d^2*f^2 - 40*A*C*a^7*b^3*c^7*d^3*f^2 - 40*A*C*a^5*b^5*c^3*d^7*f^2
- 40*A*C*a^3*b^7*c^5*d^5*f^2 + 32*A*C*a^6*b^4*c^2*d^8*f^2 + 32*A*C*a^2*b^8*c^6*d^4*f^2 - 32*A*C*a^2*b^8*c^2*d
^8*f^2 + 30*A*C*a^4*b^6*c^2*d^8*f^2 + 30*A*C*a^2*b^8*c^4*d^6*f^2 + 16*A*C*a^8*b^2*c^4*d^6*f^2 + 16*A*C*a^4*b^6
*c^8*d^2*f^2 - 488*A*B*a^6*b^4*c^3*d^7*f^2 - 488*A*B*a^3*b^7*c^6*d^4*f^2 + 440*A*B*a^7*b^3*c^4*d^6*f^2 + 440*A
*B*a^4*b^6*c^7*d^3*f^2 - 360*A*B*a^6*b^4*c^5*d^5*f^2 - 360*A*B*a^5*b^5*c^6*d^4*f^2 - 192*A*B*a^8*b^2*c^3*d^7*f
^2 - 192*A*B*a^3*b^7*c^8*d^2*f^2 - 168*A*B*a^3*b^7*c^2*d^8*f^2 - 168*A*B*a^2*b^8*c^3*d^7*f^2 - 152*A*B*a^4*b^6
*c^3*d^7*f^2 - 152*A*B*a^3*b^7*c^4*d^6*f^2 - 120*A*B*a^8*b^2*c^5*d^5*f^2 + 120*A*B*a^7*b^3*c^2*d^8*f^2 - 120*A
*B*a^5*b^5*c^8*d^2*f^2 + 120*A*B*a^5*b^5*c^4*d^6*f^2 - 120*A*B*a^5*b^5*c^2*d^8*f^2 + 120*A*B*a^4*b^6*c^5*d^5*f
^2 + 120*A*B*a^2*b^8*c^7*d^3*f^2 - 120*A*B*a^2*b^8*c^5*d^5*f^2 + 40*A*B*a^7*b^3*c^6*d^4*f^2 + 40*A*B*a^6*b^4*c
^7*d^3*f^2 - 72*B*C*a^9*b*c^4*d^6*f^2 - 72*B*C*a^4*b^6*c^9*d*f^2 - 64*B*C*a^4*b^6*c*d^9*f^2 - 64*B*C*a*b^9*c^4
*d^6*f^2 - 32*B*C*a^8*b^2*c*d^9*f^2 - 32*B*C*a*b^9*c^8*d^2*f^2 - 16*B*C*a^2*b^8*c*d^9*f^2 - 16*B*C*a*b^9*c^2*d
^8*f^2 + 8*B*C*a^9*b*c^6*d^4*f^2 - 8*B*C*a^9*b*c^2*d^8*f^2 + 8*B*C*a^6*b^4*c^9*d*f^2 - 8*B*C*a^2*b^8*c^9*d*f^2
+ 104*A*C*a^7*b^3*c*d^9*f^2 + 104*A*C*a*b^9*c^7*d^3*f^2 + 96*A*C*a^3*b^7*c*d^9*f^2 + 96*A*C*a*b^9*c^3*d^7*f^2
+ 72*A*C*a^9*b*c^3*d^7*f^2 + 72*A*C*a^3*b^7*c^9*d*f^2 + 68*A*C*a^5*b^5*c*d^9*f^2 + 68*A*C*a*b^9*c^5*d^5*f^2 -
28*A*C*a^9*b*c^5*d^5*f^2 - 28*A*C*a^5*b^5*c^9*d*f^2 + 80*A*B*a^9*b*c^4*d^6*f^2 + 80*A*B*a^4*b^6*c^9*d*f^2 + 2
4*A*B*a^8*b^2*c*d^9*f^2 - 24*A*B*a^6*b^4*c*d^9*f^2 + 24*A*B*a^4*b^6*c*d^9*f^2 - 24*A*B*a^2*b^8*c*d^9*f^2 + 24*
A*B*a*b^9*c^8*d^2*f^2 - 24*A*B*a*b^9*c^6*d^4*f^2 + 24*A*B*a*b^9*c^4*d^6*f^2 - 24*A*B*a*b^9*c^2*d^8*f^2 - 32*B*
C*b^10*c^7*d^3*f^2 - 8*B*C*b^10*c^5*d^5*f^2 + 34*A*C*b^10*c^6*d^4*f^2 + 16*B*C*a^10*c^3*d^7*f^2 + 16*A*C*b^10*
c^4*d^6*f^2 - 12*A*C*b^10*c^8*d^2*f^2 - 96*A*B*b^10*c^5*d^5*f^2 - 72*A*B*b^10*c^3*d^7*f^2 - 32*B*C*a^7*b^3*d^1
0*f^2 - 28*A*C*a^10*c^2*d^8*f^2 - 24*A*B*b^10*c^7*d^3*f^2 - 8*B*C*a^5*b^5*d^10*f^2 + 2*A*C*a^10*c^4*d^6*f^2 +
34*A*C*a^6*b^4*d^10*f^2 + 16*B*C*a^3*b^7*c^10*f^2 + 16*A*C*a^4*b^6*d^10*f^2 - 16*A*B*a^10*c^3*d^7*f^2 - 12*A*C
*a^8*b^2*d^10*f^2 - 96*A*B*a^5*b^5*d^10*f^2 - 72*A*B*a^3*b^7*d^10*f^2 - 28*A*C*a^2*b^8*c^10*f^2 - 24*A*B*a^7*b
^3*d^10*f^2 + 2*A*C*a^4*b^6*c^10*f^2 - 16*A*B*a^3*b^7*c^10*f^2 + 444*C^2*a^5*b^5*c^5*d^5*f^2 + 148*C^2*a^7*b^3
*c^5*d^5*f^2 + 148*C^2*a^5*b^5*c^7*d^3*f^2 + 148*C^2*a^5*b^5*c^3*d^7*f^2 + 148*C^2*a^3*b^7*c^5*d^5*f^2 - 140*C
^2*a^6*b^4*c^6*d^4*f^2 - 140*C^2*a^6*b^4*c^4*d^6*f^2 - 140*C^2*a^4*b^6*c^6*d^4*f^2 - 140*C^2*a^4*b^6*c^4*d^6*f
^2 + 109*C^2*a^8*b^2*c^2*d^8*f^2 + 109*C^2*a^2*b^8*c^8*d^2*f^2 + 48*C^2*a^8*b^2*c^4*d^6*f^2 + 48*C^2*a^6*b^4*c
^2*d^8*f^2 + 48*C^2*a^4*b^6*c^8*d^2*f^2 + 48*C^2*a^2*b^8*c^6*d^4*f^2 + 20*C^2*a^7*b^3*c^7*d^3*f^2 - 20*C^2*a^7
*b^3*c^3*d^7*f^2 - 20*C^2*a^3*b^7*c^7*d^3*f^2 + 20*C^2*a^3*b^7*c^3*d^7*f^2 + 17*C^2*a^8*b^2*c^6*d^4*f^2 + 17*C
^2*a^6*b^4*c^8*d^2*f^2 + 17*C^2*a^4*b^6*c^2*d^8*f^2 + 17*C^2*a^2*b^8*c^4*d^6*f^2 + 16*C^2*a^8*b^2*c^8*d^2*f^2
+ 16*C^2*a^2*b^8*c^2*d^8*f^2 - 396*B^2*a^5*b^5*c^5*d^5*f^2 + 308*B^2*a^6*b^4*c^4*d^6*f^2 + 308*B^2*a^4*b^6*c^6
*d^4*f^2 + 300*B^2*a^4*b^6*c^4*d^6*f^2 + 284*B^2*a^6*b^4*c^6*d^4*f^2 - 132*B^2*a^7*b^3*c^5*d^5*f^2 - 132*B^2*a
^5*b^5*c^7*d^3*f^2 - 84*B^2*a^5*b^5*c^3*d^7*f^2 - 84*B^2*a^3*b^7*c^5*d^5*f^2 + 61*B^2*a^4*b^6*c^2*d^8*f^2 + 61
*B^2*a^2*b^8*c^4*d^6*f^2 - 59*B^2*a^8*b^2*c^2*d^8*f^2 - 59*B^2*a^2*b^8*c^8*d^2*f^2 + 56*B^2*a^6*b^4*c^2*d^8*f^
2 + 56*B^2*a^2*b^8*c^6*d^4*f^2 + 52*B^2*a^7*b^3*c^3*d^7*f^2 + 52*B^2*a^3*b^7*c^7*d^3*f^2 + 44*B^2*a^3*b^7*c^3*
d^7*f^2 + 33*B^2*a^8*b^2*c^6*d^4*f^2 + 33*B^2*a^6*b^4*c^8*d^2*f^2 + 20*B^2*a^8*b^2*c^4*d^6*f^2 - 20*B^2*a^7*b^
3*c^7*d^3*f^2 + 20*B^2*a^4*b^6*c^8*d^2*f^2 + 8*B^2*a^2*b^8*c^2*d^8*f^2 + 337*A^2*a^4*b^6*c^2*d^8*f^2 + 337*A^2
*a^2*b^8*c^4*d^6*f^2 + 272*A^2*a^2*b^8*c^2*d^8*f^2 + 252*A^2*a^5*b^5*c^5*d^5*f^2 + 244*A^2*a^4*b^6*c^4*d^6*f^2
- 236*A^2*a^3*b^7*c^3*d^7*f^2 + 176*A^2*a^6*b^4*c^2*d^8*f^2 + 176*A^2*a^2*b^8*c^6*d^4*f^2 - 148*A^2*a^7*b^3*c
^3*d^7*f^2 - 148*A^2*a^3*b^7*c^7*d^3*f^2 - 140*A^2*a^6*b^4*c^6*d^4*f^2 + 109*A^2*a^8*b^2*c^2*d^8*f^2 + 109*A^2
*a^2*b^8*c^8*d^2*f^2 - 108*A^2*a^5*b^5*c^3*d^7*f^2 - 108*A^2*a^3*b^7*c^5*d^5*f^2 + 84*A^2*a^7*b^3*c^5*d^5*f^2
+ 84*A^2*a^5*b^5*c^7*d^3*f^2 + 32*A^2*a^8*b^2*c^4*d^6*f^2 + 32*A^2*a^4*b^6*c^8*d^2*f^2 + 20*A^2*a^7*b^3*c^7*d^
3*f^2 - 15*A^2*a^8*b^2*c^6*d^4*f^2 - 15*A^2*a^6*b^4*c^8*d^2*f^2 - 12*A^2*a^6*b^4*c^4*d^6*f^2 - 12*A^2*a^4*b^6*
c^6*d^4*f^2 + 8*B*C*b^10*c^9*d*f^2 - 16*B*C*a^10*c*d^9*f^2 - 16*A*B*b^10*c^9*d*f^2 - 16*A*B*b^10*c*d^9*f^2 + 8
*B*C*a^9*b*d^10*f^2 - 16*B*C*a*b^9*c^10*f^2 + 16*A*B*a^10*c*d^9*f^2 - 16*A*B*a^9*b*d^10*f^2 - 16*A*B*a*b^9*d^1
0*f^2 + 16*A*B*a*b^9*c^10*f^2 + 22*C^2*a^9*b*c^5*d^5*f^2 + 22*C^2*a^5*b^5*c^9*d*f^2 + 22*C^2*a^5*b^5*c*d^9*f^2
+ 22*C^2*a*b^9*c^5*d^5*f^2 - 20*C^2*a^9*b*c^3*d^7*f^2 - 20*C^2*a^7*b^3*c*d^9*f^2 - 20*C^2*a^3*b^7*c^9*d*f^2 -
20*C^2*a*b^9*c^7*d^3*f^2 + 36*B^2*a^7*b^3*c*d^9*f^2 + 36*B^2*a*b^9*c^7*d^3*f^2 + 28*B^2*a^9*b*c^3*d^7*f^2 + 2
8*B^2*a^3*b^7*c^9*d*f^2 + 24*B^2*a^3*b^7*c*d^9*f^2 + 24*B^2*a*b^9*c^3*d^7*f^2 - 18*B^2*a^9*b*c^5*d^5*f^2 - 18*
B^2*a^5*b^5*c^9*d*f^2 + 6*B^2*a^5*b^5*c*d^9*f^2 + 6*B^2*a*b^9*c^5*d^5*f^2 - 96*A^2*a^3*b^7*c*d^9*f^2 - 96*A^2*
a*b^9*c^3*d^7*f^2 - 90*A^2*a^5*b^5*c*d^9*f^2 - 90*A^2*a*b^9*c^5*d^5*f^2 - 84*A^2*a^7*b^3*c*d^9*f^2 - 84*A^2*a*
b^9*c^7*d^3*f^2 - 52*A^2*a^9*b*c^3*d^7*f^2 - 52*A^2*a^3*b^7*c^9*d*f^2 + 6*A^2*a^9*b*c^5*d^5*f^2 + 6*A^2*a^5*b^
5*c^9*d*f^2 - 10*C^2*a^9*b*c*d^9*f^2 - 10*C^2*a*b^9*c^9*d*f^2 + 14*B^2*a^9*b*c*d^9*f^2 + 14*B^2*a*b^9*c^9*d*f^
2 + 8*B^2*a*b^9*c*d^9*f^2 - 32*A^2*a*b^9*c*d^9*f^2 - 26*A^2*a^9*b*c*d^9*f^2 - 26*A^2*a*b^9*c^9*d*f^2 + 2*A*C*b
^10*c^10*f^2 + 2*A*C*a^10*d^10*f^2 + 14*C^2*b^10*c^8*d^2*f^2 - C^2*b^10*c^6*d^4*f^2 + 31*B^2*b^10*c^6*d^4*f^2
+ 20*B^2*b^10*c^4*d^6*f^2 + 14*C^2*a^10*c^2*d^8*f^2 + 4*B^2*b^10*c^2*d^8*f^2 + 2*B^2*b^10*c^8*d^2*f^2 - C^2*a^
10*c^4*d^6*f^2 + 80*A^2*b^10*c^4*d^6*f^2 + 64*A^2*b^10*c^2*d^8*f^2 + 31*A^2*b^10*c^6*d^4*f^2 + 14*C^2*a^8*b^2*
d^10*f^2 + 14*A^2*b^10*c^8*d^2*f^2 - 10*B^2*a^10*c^2*d^8*f^2 + 3*B^2*a^10*c^4*d^6*f^2 - C^2*a^6*b^4*d^10*f^2 +
31*B^2*a^6*b^4*d^10*f^2 + 20*B^2*a^4*b^6*d^10*f^2 + 14*C^2*a^2*b^8*c^10*f^2 + 14*A^2*a^10*c^2*d^8*f^2 + 4*B^2
*a^2*b^8*d^10*f^2 + 2*B^2*a^8*b^2*d^10*f^2 - C^2*a^4*b^6*c^10*f^2 - A^2*a^10*c^4*d^6*f^2 + 80*A^2*a^4*b^6*d^10
*f^2 + 64*A^2*a^2*b^8*d^10*f^2 + 31*A^2*a^6*b^4*d^10*f^2 + 14*A^2*a^8*b^2*d^10*f^2 - 10*B^2*a^2*b^8*c^10*f^2 +
3*B^2*a^4*b^6*c^10*f^2 + 14*A^2*a^2*b^8*c^10*f^2 - A^2*a^4*b^6*c^10*f^2 - C^2*b^10*c^10*f^2 - C^2*a^10*d^10*f
^2 + 16*A^2*b^10*d^10*f^2 + 3*B^2*b^10*c^10*f^2 + 3*B^2*a^10*d^10*f^2 - A^2*b^10*c^10*f^2 - A^2*a^10*d^10*f^2
- 96*A*B*C*a*b^7*c*d^7*f - 28*A*B*C*a^7*b*c*d^7*f - 28*A*B*C*a*b^7*c^7*d*f + 484*A*B*C*a^4*b^4*c^4*d^4*f - 424
*A*B*C*a^3*b^5*c^3*d^5*f + 320*A*B*C*a^2*b^6*c^2*d^6*f - 176*A*B*C*a^6*b^2*c^2*d^6*f - 176*A*B*C*a^2*b^6*c^6*d
^2*f + 158*A*B*C*a^4*b^4*c^2*d^6*f + 158*A*B*C*a^2*b^6*c^4*d^4*f - 136*A*B*C*a^5*b^3*c^5*d^3*f - 34*A*B*C*a^6*
b^2*c^4*d^4*f - 34*A*B*C*a^4*b^4*c^6*d^2*f + 28*A*B*C*a^5*b^3*c^3*d^5*f + 28*A*B*C*a^3*b^5*c^5*d^3*f + 308*A*B
*C*a^5*b^3*c*d^7*f + 308*A*B*C*a*b^7*c^5*d^3*f + 20*A*B*C*a^7*b*c^3*d^5*f + 20*A*B*C*a^3*b^5*c^7*d*f + 30*B*C^
2*a^7*b*c*d^7*f + 30*B*C^2*a*b^7*c^7*d*f + 160*A^2*B*a*b^7*c*d^7*f - 2*A^2*B*a^7*b*c*d^7*f - 2*A^2*B*a*b^7*c^7
*d*f - 96*A*B*C*b^8*c^4*d^4*f + 34*A*B*C*b^8*c^6*d^2*f - 32*A*B*C*b^8*c^2*d^6*f + 2*A*B*C*a^8*c^2*d^6*f - 96*A
*B*C*a^4*b^4*d^8*f + 34*A*B*C*a^6*b^2*d^8*f - 32*A*B*C*a^2*b^6*d^8*f + 2*A*B*C*a^2*b^6*c^8*f - 210*B*C^2*a^4*b
^4*c^4*d^4*f - 182*B^2*C*a^5*b^3*c^2*d^6*f - 182*B^2*C*a^2*b^6*c^5*d^3*f + 180*B*C^2*a^5*b^3*c^5*d^3*f + 180*B
*C^2*a^3*b^5*c^3*d^5*f - 166*B^2*C*a^5*b^3*c^4*d^4*f - 166*B^2*C*a^4*b^4*c^5*d^3*f + 152*B*C^2*a^6*b^2*c^2*d^6
*f + 152*B*C^2*a^2*b^6*c^6*d^2*f - 112*B^2*C*a^3*b^5*c^2*d^6*f - 112*B^2*C*a^2*b^6*c^3*d^5*f + 94*B^2*C*a^4*b^
4*c^3*d^5*f + 94*B^2*C*a^3*b^5*c^4*d^4*f - 80*B*C^2*a^2*b^6*c^2*d^6*f + 66*B*C^2*a^5*b^3*c^3*d^5*f + 66*B*C^2*
a^3*b^5*c^5*d^3*f + 46*B^2*C*a^6*b^2*c^3*d^5*f + 46*B^2*C*a^3*b^5*c^6*d^2*f + 33*B*C^2*a^6*b^2*c^4*d^4*f + 33*
B*C^2*a^4*b^4*c^6*d^2*f + 24*B^2*C*a^6*b^2*c^5*d^3*f + 24*B^2*C*a^5*b^3*c^6*d^2*f - 16*B*C^2*a^6*b^2*c^6*d^2*f
- 15*B*C^2*a^4*b^4*c^2*d^6*f - 15*B*C^2*a^2*b^6*c^4*d^4*f - 190*A^2*C*a^4*b^4*c^3*d^5*f - 190*A^2*C*a^3*b^5*c
^4*d^4*f + 182*A^2*C*a^5*b^3*c^2*d^6*f + 182*A^2*C*a^2*b^6*c^5*d^3*f + 160*A^2*C*a^3*b^5*c^2*d^6*f + 160*A^2*C
*a^2*b^6*c^3*d^5*f - 150*A*C^2*a^5*b^3*c^2*d^6*f - 150*A*C^2*a^2*b^6*c^5*d^3*f - 126*A*C^2*a^5*b^3*c^4*d^4*f -
126*A*C^2*a^4*b^4*c^5*d^3*f + 126*A*C^2*a^4*b^4*c^3*d^5*f + 126*A*C^2*a^3*b^5*c^4*d^4*f - 96*A*C^2*a^3*b^5*c^
2*d^6*f - 96*A*C^2*a^2*b^6*c^3*d^5*f + 94*A^2*C*a^5*b^3*c^4*d^4*f + 94*A^2*C*a^4*b^4*c^5*d^3*f + 54*A*C^2*a^6*
b^2*c^3*d^5*f + 54*A*C^2*a^3*b^5*c^6*d^2*f + 32*A*C^2*a^6*b^2*c^5*d^3*f + 32*A*C^2*a^5*b^3*c^6*d^2*f - 22*A^2*
C*a^6*b^2*c^3*d^5*f - 22*A^2*C*a^3*b^5*c^6*d^2*f + 500*A^2*B*a^3*b^5*c^3*d^5*f - 290*A^2*B*a^4*b^4*c^4*d^4*f -
256*A^2*B*a^2*b^6*c^2*d^6*f - 230*A*B^2*a^4*b^4*c^3*d^5*f - 230*A*B^2*a^3*b^5*c^4*d^4*f + 142*A*B^2*a^5*b^3*c
^2*d^6*f + 142*A*B^2*a^2*b^6*c^5*d^3*f - 127*A^2*B*a^4*b^4*c^2*d^6*f - 127*A^2*B*a^2*b^6*c^4*d^4*f + 86*A*B^2*
a^5*b^3*c^4*d^4*f + 86*A*B^2*a^4*b^4*c^5*d^3*f + 80*A*B^2*a^3*b^5*c^2*d^6*f + 80*A*B^2*a^2*b^6*c^3*d^5*f + 40*
A^2*B*a^6*b^2*c^2*d^6*f + 40*A^2*B*a^2*b^6*c^6*d^2*f + 34*A^2*B*a^5*b^3*c^3*d^5*f + 34*A^2*B*a^3*b^5*c^5*d^3*f
- 30*A*B^2*a^6*b^2*c^3*d^5*f - 30*A*B^2*a^3*b^5*c^6*d^2*f + 20*A^2*B*a^5*b^3*c^5*d^3*f - 15*A^2*B*a^6*b^2*c^4
*d^4*f - 15*A^2*B*a^4*b^4*c^6*d^2*f - 98*B^2*C*a^6*b^2*c*d^7*f - 98*B^2*C*a*b^7*c^6*d^2*f - 90*B*C^2*a^5*b^3*c
*d^7*f - 90*B*C^2*a*b^7*c^5*d^3*f + 48*B^2*C*a^4*b^4*c*d^7*f + 48*B^2*C*a*b^7*c^4*d^4*f + 40*B^2*C*a^2*b^6*c*d
^7*f + 40*B^2*C*a*b^7*c^2*d^6*f - 32*B*C^2*a^3*b^5*c*d^7*f - 32*B*C^2*a*b^7*c^3*d^5*f + 26*B^2*C*a^7*b*c^2*d^6
*f + 26*B^2*C*a^2*b^6*c^7*d*f - 26*B*C^2*a^7*b*c^3*d^5*f - 26*B*C^2*a^3*b^5*c^7*d*f - 8*B^2*C*a^7*b*c^4*d^4*f
- 8*B^2*C*a^4*b^4*c^7*d*f - 224*A^2*C*a^4*b^4*c*d^7*f - 224*A^2*C*a*b^7*c^4*d^4*f - 96*A^2*C*a^2*b^6*c*d^7*f -
96*A^2*C*a*b^7*c^2*d^6*f + 96*A*C^2*a^4*b^4*c*d^7*f + 96*A*C^2*a*b^7*c^4*d^4*f - 66*A*C^2*a^6*b^2*c*d^7*f - 6
6*A*C^2*a*b^7*c^6*d^2*f + 64*A*C^2*a^2*b^6*c*d^7*f + 64*A*C^2*a*b^7*c^2*d^6*f + 34*A^2*C*a^6*b^2*c*d^7*f + 34*
A^2*C*a*b^7*c^6*d^2*f + 34*A*C^2*a^7*b*c^2*d^6*f + 34*A*C^2*a^2*b^6*c^7*d*f - 2*A^2*C*a^7*b*c^2*d^6*f - 2*A^2*
C*a^2*b^6*c^7*d*f - 208*A*B^2*a^4*b^4*c*d^7*f - 208*A*B^2*a*b^7*c^4*d^4*f + 160*A^2*B*a^3*b^5*c*d^7*f + 160*A^
2*B*a*b^7*c^3*d^5*f - 154*A^2*B*a^5*b^3*c*d^7*f - 154*A^2*B*a*b^7*c^5*d^3*f - 112*A*B^2*a^2*b^6*c*d^7*f - 112*
A*B^2*a*b^7*c^2*d^6*f + 58*A*B^2*a^6*b^2*c*d^7*f + 58*A*B^2*a*b^7*c^6*d^2*f - 10*A*B^2*a^7*b*c^2*d^6*f - 10*A*
B^2*a^2*b^6*c^7*d*f + 6*A^2*B*a^7*b*c^3*d^5*f + 6*A^2*B*a^3*b^5*c^7*d*f + 32*B^2*C*b^8*c^5*d^3*f - 17*B*C^2*b^
8*c^6*d^2*f + 8*B^2*C*b^8*c^3*d^5*f + 64*A^2*C*b^8*c^3*d^5*f - 32*A^2*C*b^8*c^5*d^3*f + 32*A*C^2*b^8*c^5*d^3*f
- B*C^2*a^8*c^2*d^6*f + 112*A^2*B*b^8*c^4*d^4*f - 64*A*B^2*b^8*c^5*d^3*f + 32*B^2*C*a^5*b^3*d^8*f - 17*B*C^2*
a^6*b^2*d^8*f + 16*A^2*B*b^8*c^2*d^6*f + 16*A*B^2*b^8*c^3*d^5*f + 8*B^2*C*a^3*b^5*d^8*f - A^2*B*b^8*c^6*d^2*f
+ 64*A^2*C*a^3*b^5*d^8*f - 32*A^2*C*a^5*b^3*d^8*f + 32*A*C^2*a^5*b^3*d^8*f - A^2*B*a^8*c^2*d^6*f - B*C^2*a^2*b
^6*c^8*f + 112*A^2*B*a^4*b^4*d^8*f - 64*A*B^2*a^5*b^3*d^8*f + 16*A^2*B*a^2*b^6*d^8*f + 16*A*B^2*a^3*b^5*d^8*f
- A^2*B*a^6*b^2*d^8*f - A^2*B*a^2*b^6*c^8*f - 8*B^3*a*b^7*c*d^7*f - 2*B^3*a^7*b*c*d^7*f - 2*B^3*a*b^7*c^7*d*f
- 6*B^2*C*b^8*c^7*d*f + 32*A^2*C*b^8*c*d^7*f + 6*A^2*C*b^8*c^7*d*f - 6*A*C^2*b^8*c^7*d*f - 2*B^2*C*a^8*c*d^7*f
+ 16*A*B^2*b^8*c*d^7*f - 6*B^2*C*a^7*b*d^8*f - 6*A^2*C*a^8*c*d^7*f + 6*A*C^2*a^8*c*d^7*f - 2*A*B^2*b^8*c^7*d*
f + 32*A^2*C*a*b^7*d^8*f + 6*A^2*C*a^7*b*d^8*f - 6*A*C^2*a^7*b*d^8*f - 2*B^2*C*a*b^7*c^8*f + 2*A*B^2*a^8*c*d^7
*f + 16*A*B^2*a*b^7*d^8*f - 6*A^2*C*a*b^7*c^8*f + 6*A*C^2*a*b^7*c^8*f - 2*A*B^2*a^7*b*d^8*f + 2*A*B^2*a*b^7*c^
8*f - 50*C^3*a^6*b^2*c^3*d^5*f + 50*C^3*a^5*b^3*c^2*d^6*f - 50*C^3*a^3*b^5*c^6*d^2*f + 50*C^3*a^2*b^6*c^5*d^3*
f + 42*C^3*a^5*b^3*c^4*d^4*f + 42*C^3*a^4*b^4*c^5*d^3*f - 42*C^3*a^4*b^4*c^3*d^5*f - 42*C^3*a^3*b^5*c^4*d^4*f
- 32*C^3*a^6*b^2*c^5*d^3*f - 32*C^3*a^5*b^3*c^6*d^2*f + 32*C^3*a^3*b^5*c^2*d^6*f + 32*C^3*a^2*b^6*c^3*d^5*f +
94*B^3*a^4*b^4*c^4*d^4*f + 48*B^3*a^2*b^6*c^2*d^6*f - 44*B^3*a^3*b^5*c^3*d^5*f - 32*B^3*a^6*b^2*c^2*d^6*f - 32
*B^3*a^2*b^6*c^6*d^2*f + 29*B^3*a^4*b^4*c^2*d^6*f + 29*B^3*a^2*b^6*c^4*d^4*f - 20*B^3*a^5*b^3*c^5*d^3*f + 18*B
^3*a^5*b^3*c^3*d^5*f + 18*B^3*a^3*b^5*c^5*d^3*f - 3*B^3*a^6*b^2*c^4*d^4*f - 3*B^3*a^4*b^4*c^6*d^2*f + 106*A^3*
a^4*b^4*c^3*d^5*f + 106*A^3*a^3*b^5*c^4*d^4*f - 96*A^3*a^3*b^5*c^2*d^6*f - 96*A^3*a^2*b^6*c^3*d^5*f - 82*A^3*a
^5*b^3*c^2*d^6*f - 82*A^3*a^2*b^6*c^5*d^3*f + 18*A^3*a^6*b^2*c^3*d^5*f + 18*A^3*a^3*b^5*c^6*d^2*f - 10*A^3*a^5
*b^3*c^4*d^4*f - 10*A^3*a^4*b^4*c^5*d^3*f - 22*C^3*a^7*b*c^2*d^6*f + 22*C^3*a^6*b^2*c*d^7*f - 22*C^3*a^2*b^6*c
^7*d*f + 22*C^3*a*b^7*c^6*d^2*f - 2*A*B*C*b^8*c^8*f - 2*A*B*C*a^8*d^8*f + 62*B^3*a^5*b^3*c*d^7*f + 62*B^3*a*b^
7*c^5*d^3*f + 16*B^3*a^3*b^5*c*d^7*f + 16*B^3*a*b^7*c^3*d^5*f + 6*B^3*a^7*b*c^3*d^5*f + 6*B^3*a^3*b^5*c^7*d*f
+ 128*A^3*a^4*b^4*c*d^7*f + 128*A^3*a*b^7*c^4*d^4*f + 32*A^3*a^2*b^6*c*d^7*f + 32*A^3*a*b^7*c^2*d^6*f - 10*A^3
*a^7*b*c^2*d^6*f + 10*A^3*a^6*b^2*c*d^7*f - 10*A^3*a^2*b^6*c^7*d*f + 10*A^3*a*b^7*c^6*d^2*f + 11*B^3*b^8*c^6*d
^2*f - 8*B^3*b^8*c^4*d^4*f - 4*B^3*b^8*c^2*d^6*f - 64*A^3*b^8*c^3*d^5*f - B^3*a^8*c^2*d^6*f + 11*B^3*a^6*b^2*d
^8*f - 8*B^3*a^4*b^4*d^8*f - 4*B^3*a^2*b^6*d^8*f - 64*A^3*a^3*b^5*d^8*f - B^3*a^2*b^6*c^8*f + 2*C^3*b^8*c^7*d*
f - 2*C^3*a^8*c*d^7*f - 32*A^3*b^8*c*d^7*f + 2*C^3*a^7*b*d^8*f - 2*A^3*b^8*c^7*d*f - 2*C^3*a*b^7*c^8*f + 2*A^3
*a^8*c*d^7*f - 32*A^3*a*b^7*d^8*f - 2*A^3*a^7*b*d^8*f + 2*A^3*a*b^7*c^8*f - 16*A^2*B*b^8*d^8*f + B*C^2*b^8*c^8
*f + B*C^2*a^8*d^8*f + A^2*B*b^8*c^8*f + A^2*B*a^8*d^8*f + B^3*b^8*c^8*f + B^3*a^8*d^8*f - 4*A*B^2*C*a^5*b*c*d
^5 - 4*A*B^2*C*a*b^5*c^5*d + 4*A*B^2*C*a*b^5*c*d^5 + 22*A^2*B*C*a^3*b^3*c^2*d^4 + 22*A^2*B*C*a^2*b^4*c^3*d^3 -
20*A*B^2*C*a^3*b^3*c^3*d^3 + 14*A*B^2*C*a^4*b^2*c^2*d^4 + 14*A*B^2*C*a^2*b^4*c^4*d^2 - 14*A*B*C^2*a^3*b^3*c^2
*d^4 - 14*A*B*C^2*a^2*b^4*c^3*d^3 + 12*A*B*C^2*a^4*b^2*c^3*d^3 + 12*A*B*C^2*a^3*b^3*c^4*d^2 - 6*A^2*B*C*a^4*b^
2*c^3*d^3 - 6*A^2*B*C*a^3*b^3*c^4*d^2 - 4*A*B^2*C*a^2*b^4*c^2*d^4 + 22*A*B*C^2*a^4*b^2*c*d^5 + 22*A*B*C^2*a*b^
5*c^4*d^2 - 20*A^2*B*C*a^4*b^2*c*d^5 - 20*A^2*B*C*a*b^5*c^4*d^2 + 10*A*B*C^2*a^2*b^4*c*d^5 + 10*A*B*C^2*a*b^5*
c^2*d^4 - 8*A^2*B*C*a^2*b^4*c*d^5 - 8*A^2*B*C*a*b^5*c^2*d^4 + 4*A*B^2*C*a^3*b^3*c*d^5 + 4*A*B^2*C*a*b^5*c^3*d^
3 - 4*A*B*C^2*a^5*b*c^2*d^4 - 4*A*B*C^2*a^2*b^4*c^5*d + 2*A^2*B*C*a^5*b*c^2*d^4 + 2*A^2*B*C*a^2*b^4*c^5*d - 8*
B^3*C*a^4*b^2*c*d^5 - 8*B^3*C*a*b^5*c^4*d^2 - 8*B*C^3*a^4*b^2*c*d^5 - 8*B*C^3*a*b^5*c^4*d^2 - 4*B^3*C*a^2*b^4*
c*d^5 - 4*B^3*C*a*b^5*c^2*d^4 + 4*B^2*C^2*a^5*b*c*d^5 + 4*B^2*C^2*a*b^5*c^5*d - 4*B*C^3*a^2*b^4*c*d^5 - 4*B*C^
3*a*b^5*c^2*d^4 + 2*B^3*C*a^5*b*c^2*d^4 + 2*B^3*C*a^2*b^4*c^5*d + 2*B^2*C^2*a*b^5*c*d^5 + 2*B*C^3*a^5*b*c^2*d^
4 + 2*B*C^3*a^2*b^4*c^5*d + 24*A^3*C*a^3*b^3*c*d^5 + 24*A^3*C*a*b^5*c^3*d^3 - 24*A^2*C^2*a*b^5*c*d^5 + 12*A^2*
C^2*a^5*b*c*d^5 + 12*A^2*C^2*a*b^5*c^5*d + 8*A*C^3*a^3*b^3*c*d^5 + 8*A*C^3*a*b^5*c^3*d^3 + 6*A^3*B*a^4*b^2*c*d
^5 + 6*A^3*B*a*b^5*c^4*d^2 - 6*A^2*B^2*a*b^5*c*d^5 + 6*A*B^3*a^4*b^2*c*d^5 + 6*A*B^3*a*b^5*c^4*d^2 + 2*A^3*B*a
^2*b^4*c*d^5 + 2*A^3*B*a*b^5*c^2*d^4 + 2*A*B^3*a^2*b^4*c*d^5 + 2*A*B^3*a*b^5*c^2*d^4 + 20*A^2*B*C*b^6*c^3*d^3
- 10*A*B*C^2*b^6*c^3*d^3 - 2*A*B^2*C*b^6*c^4*d^2 - 2*A*B^2*C*b^6*c^2*d^4 + 20*A^2*B*C*a^3*b^3*d^6 - 10*A*B*C^2
*a^3*b^3*d^6 - 2*A*B^2*C*a^4*b^2*d^6 - 2*A*B^2*C*a^2*b^4*d^6 + 10*B^2*C^2*a^3*b^3*c^3*d^3 + 4*B^2*C^2*a^4*b^2*
c^4*d^2 - 3*B^2*C^2*a^4*b^2*c^2*d^4 - 3*B^2*C^2*a^2*b^4*c^4*d^2 + 2*B^2*C^2*a^2*b^4*c^2*d^4 + 40*A^2*C^2*a^2*b
^4*c^2*d^4 - 16*A^2*C^2*a^4*b^2*c^2*d^4 - 16*A^2*C^2*a^2*b^4*c^4*d^2 + 4*A^2*C^2*a^4*b^2*c^4*d^2 + 18*A^2*B^2*
a^2*b^4*c^2*d^4 + 10*A^2*B^2*a^3*b^3*c^3*d^3 - 3*A^2*B^2*a^4*b^2*c^2*d^4 - 3*A^2*B^2*a^2*b^4*c^4*d^2 + 24*A^3*
C*a*b^5*c*d^5 - 12*A*C^3*a^5*b*c*d^5 - 12*A*C^3*a*b^5*c^5*d + 8*A*C^3*a*b^5*c*d^5 - 4*A^3*C*a^5*b*c*d^5 - 4*A^
3*C*a*b^5*c^5*d + 8*A^2*B*C*b^6*c*d^5 + 4*A*B*C^2*b^6*c^5*d - 4*A*B*C^2*b^6*c*d^5 - 2*A^2*B*C*b^6*c^5*d + 8*A^
2*B*C*a*b^5*d^6 + 4*A*B*C^2*a^5*b*d^6 - 4*A*B*C^2*a*b^5*d^6 - 2*A^2*B*C*a^5*b*d^6 - 6*B^3*C*a^4*b^2*c^3*d^3 -
6*B^3*C*a^3*b^3*c^4*d^2 - 6*B*C^3*a^4*b^2*c^3*d^3 - 6*B*C^3*a^3*b^3*c^4*d^2 + 2*B^3*C*a^3*b^3*c^2*d^4 + 2*B^3*
C*a^2*b^4*c^3*d^3 + 2*B^2*C^2*a^3*b^3*c*d^5 + 2*B^2*C^2*a*b^5*c^3*d^3 + 2*B*C^3*a^3*b^3*c^2*d^4 + 2*B*C^3*a^2*
b^4*c^3*d^3 - 48*A^3*C*a^2*b^4*c^2*d^4 - 24*A^2*C^2*a^3*b^3*c*d^5 - 24*A^2*C^2*a*b^5*c^3*d^3 - 16*A*C^3*a^2*b^
4*c^2*d^4 + 8*A^3*C*a^4*b^2*c^2*d^4 + 8*A^3*C*a^2*b^4*c^4*d^2 - 8*A*C^3*a^4*b^2*c^4*d^2 + 8*A*C^3*a^4*b^2*c^2*
d^4 + 8*A*C^3*a^2*b^4*c^4*d^2 - 10*A^3*B*a^3*b^3*c^2*d^4 - 10*A^3*B*a^2*b^4*c^3*d^3 - 10*A*B^3*a^3*b^3*c^2*d^4
- 10*A*B^3*a^2*b^4*c^3*d^3 - 6*A^2*B^2*a^3*b^3*c*d^5 - 6*A^2*B^2*a*b^5*c^3*d^3 + 3*B^2*C^2*b^6*c^4*d^2 - 8*A^
2*C^2*b^6*c^4*d^2 + 8*A^2*C^2*b^6*c^2*d^4 + 9*A^2*B^2*b^6*c^2*d^4 + 3*B^2*C^2*a^4*b^2*d^6 + 3*A^2*B^2*b^6*c^4*
d^2 - 8*A^2*C^2*a^4*b^2*d^6 + 8*A^2*C^2*a^2*b^4*d^6 + 9*A^2*B^2*a^2*b^4*d^6 + 3*A^2*B^2*a^4*b^2*d^6 + 2*B^4*a^
3*b^3*c*d^5 + 2*B^4*a*b^5*c^3*d^3 - 8*A^4*a^3*b^3*c*d^5 - 8*A^4*a*b^5*c^3*d^3 - 16*A^3*C*b^6*c^2*d^4 + 4*A^3*C
*b^6*c^4*d^2 + 4*A*C^3*b^6*c^4*d^2 - 10*A^3*B*b^6*c^3*d^3 - 10*A*B^3*b^6*c^3*d^3 - 16*A^3*C*a^2*b^4*d^6 + 4*A^
3*C*a^4*b^2*d^6 + 4*A*C^3*a^4*b^2*d^6 - 10*A^3*B*a^3*b^3*d^6 - 10*A*B^3*a^3*b^3*d^6 + 4*C^4*a^5*b*c*d^5 + 4*C^
4*a*b^5*c^5*d + 2*B^4*a*b^5*c*d^5 - 8*A^4*a*b^5*c*d^5 - 2*B^3*C*b^6*c^5*d - 2*B*C^3*b^6*c^5*d - 4*A^3*B*b^6*c*
d^5 - 4*A*B^3*b^6*c*d^5 - 2*B^3*C*a^5*b*d^6 - 2*B*C^3*a^5*b*d^6 - 4*A^3*B*a*b^5*d^6 - 4*A*B^3*a*b^5*d^6 + 4*C^
4*a^4*b^2*c^4*d^2 + 4*C^4*a^2*b^4*c^2*d^4 + 10*B^4*a^3*b^3*c^3*d^3 - 3*B^4*a^4*b^2*c^2*d^4 - 3*B^4*a^2*b^4*c^4
*d^2 - 2*B^4*a^2*b^4*c^2*d^4 + 20*A^4*a^2*b^4*c^2*d^4 + B^2*C^2*b^6*c^2*d^4 + B^2*C^2*a^2*b^4*d^6 - 8*A^3*C*b^
6*d^6 + 3*B^4*b^6*c^4*d^2 + 8*A^4*b^6*c^2*d^4 + 3*B^4*a^4*b^2*d^6 + 8*A^4*a^2*b^4*d^6 + 4*A^2*C^2*b^6*d^6 + 4*
A^2*B^2*b^6*d^6 + 4*A^4*b^6*d^6 + B^4*b^6*c^2*d^4 + B^4*a^2*b^4*d^6, f, k), k, 1, 4) - ((A*a^3*d^3 + A*b^3*c^3
+ A*a*b^2*d^3 - B*a*b^2*c^3 + C*a^2*b*c^3 + A*b^3*c*d^2 - B*a^3*c*d^2 + C*a^3*c^2*d - 2*B*a*b^2*c*d^2 + C*a*b
^2*c^2*d + C*a^2*b*c*d^2)/((a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a^2*c^2 + a^2*d^2 + b^2*c^2 + b^2*d^2)) + (tan(e +
f*x)*(2*A*b^3*d^3 + A*a^2*b*d^3 - B*a*b^2*d^3 + A*b^3*c^2*d + C*a^2*b*d^3 - B*b^3*c*d^2 + C*b^3*c^2*d - B*a*b
^2*c^2*d - B*a^2*b*c*d^2 + 2*C*a^2*b*c^2*d))/((a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a^2*c^2 + a^2*d^2 + b^2*c^2 + b
^2*d^2)))/(a*c + tan(e + f*x)*(a*d + b*c) + b*d*tan(e + f*x)^2))/f