\(\int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^3 (c+d \tan (e+f x))} \, dx\) [76]

Optimal result

Integrand size = 45, antiderivative size = 477 \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^3 (c+d \tan (e+f x))} \, dx=\frac {\left (a^3 (A c-c C+B d)-3 a b^2 (A c-c C+B d)+3 a^2 b (B c-(A-C) d)-b^3 (B c-(A-C) d)\right ) x}{\left (a^2+b^2\right )^3 \left (c^2+d^2\right )}+\frac {\left (3 a b^5 B c^2-3 a^5 b B d^2+a^6 C d^2+3 a^4 b^2 d (B c+2 A d-C d)+b^6 \left (c (c C-B d)-A \left (c^2-d^2\right )\right )-a^3 b^3 \left (8 c (A-C) d+B \left (c^2-d^2\right )\right )-3 a^2 b^4 \left (c (c C+2 B d)-A \left (c^2+d^2\right )\right )\right ) \log (a \cos (e+f x)+b \sin (e+f x))}{\left (a^2+b^2\right )^3 (b c-a d)^3 f}-\frac {d^2 \left (c^2 C-B c d+A d^2\right ) \log (c \cos (e+f x)+d \sin (e+f x))}{(b c-a d)^3 \left (c^2+d^2\right ) f}-\frac {A b^2-a (b B-a C)}{2 \left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x))^2}-\frac {2 a b^3 c (A-C)+2 a^3 b B d-a^4 C d+b^4 (B c-A d)-a^2 b^2 (B c+3 A d-C d)}{\left (a^2+b^2\right )^2 (b c-a d)^2 f (a+b \tan (e+f x))} \]

[Out]

(a^3*(A*c+B*d-C*c)-3*a*b^2*(A*c+B*d-C*c)+3*a^2*b*(B*c-(A-C)*d)-b^3*(B*c-(A-C)*d))*x/(a^2+b^2)^3/(c^2+d^2)+(3*a
*b^5*B*c^2-3*a^5*b*B*d^2+a^6*C*d^2+3*a^4*b^2*d*(2*A*d+B*c-C*d)+b^6*(c*(-B*d+C*c)-A*(c^2-d^2))-a^3*b^3*(8*c*(A-
C)*d+B*(c^2-d^2))-3*a^2*b^4*(c*(2*B*d+C*c)-A*(c^2+d^2)))*ln(a*cos(f*x+e)+b*sin(f*x+e))/(a^2+b^2)^3/(-a*d+b*c)^
3/f-d^2*(A*d^2-B*c*d+C*c^2)*ln(c*cos(f*x+e)+d*sin(f*x+e))/(-a*d+b*c)^3/(c^2+d^2)/f+1/2*(-A*b^2+a*(B*b-C*a))/(a
^2+b^2)/(-a*d+b*c)/f/(a+b*tan(f*x+e))^2+(-2*a*b^3*c*(A-C)-2*a^3*b*B*d+a^4*C*d-b^4*(-A*d+B*c)+a^2*b^2*(3*A*d+B*
c-C*d))/(a^2+b^2)^2/(-a*d+b*c)^2/f/(a+b*tan(f*x+e))

Rubi [A] (verified)

Time = 1.94 (sec) , antiderivative size = 477, 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} \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^3 (c+d \tan (e+f x))} \, dx=-\frac {A b^2-a (b B-a C)}{2 f \left (a^2+b^2\right ) (b c-a d) (a+b \tan (e+f x))^2}+\frac {x \left (a^3 (A c+B d-c C)+3 a^2 b (B c-d (A-C))-3 a b^2 (A c+B d-c C)-b^3 (B c-d (A-C))\right )}{\left (a^2+b^2\right )^3 \left (c^2+d^2\right )}-\frac {a^4 (-C) d+2 a^3 b B d-a^2 b^2 (3 A d+B c-C d)+2 a b^3 c (A-C)+b^4 (B c-A d)}{f \left (a^2+b^2\right )^2 (b c-a d)^2 (a+b \tan (e+f x))}+\frac {\left (a^6 C d^2-3 a^5 b B d^2+3 a^4 b^2 d (2 A d+B c-C d)-a^3 b^3 \left (8 c d (A-C)+B \left (c^2-d^2\right )\right )-3 a^2 b^4 \left (c (2 B d+c C)-A \left (c^2+d^2\right )\right )+3 a b^5 B c^2+b^6 \left (c (c C-B d)-A \left (c^2-d^2\right )\right )\right ) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left (a^2+b^2\right )^3 (b c-a d)^3}-\frac {d^2 \left (A d^2-B c d+c^2 C\right ) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left (c^2+d^2\right ) (b c-a d)^3} \]

[In]

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

[Out]

((a^3*(A*c - c*C + B*d) - 3*a*b^2*(A*c - c*C + B*d) + 3*a^2*b*(B*c - (A - C)*d) - b^3*(B*c - (A - C)*d))*x)/((
a^2 + b^2)^3*(c^2 + d^2)) + ((3*a*b^5*B*c^2 - 3*a^5*b*B*d^2 + a^6*C*d^2 + 3*a^4*b^2*d*(B*c + 2*A*d - C*d) + b^
6*(c*(c*C - B*d) - A*(c^2 - d^2)) - a^3*b^3*(8*c*(A - C)*d + B*(c^2 - d^2)) - 3*a^2*b^4*(c*(c*C + 2*B*d) - A*(
c^2 + d^2)))*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^3*(b*c - a*d)^3*f) - (d^2*(c^2*C - B*c*d + A*d
^2)*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)^3*(c^2 + d^2)*f) - (A*b^2 - a*(b*B - a*C))/(2*(a^2 + b^
2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])^2) - (2*a*b^3*c*(A - C) + 2*a^3*b*B*d - a^4*C*d + b^4*(B*c - A*d) - a^2*
b^2*(B*c + 3*A*d - C*d))/((a^2 + b^2)^2*(b*c - a*d)^2*f*(a + b*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)}{2 \left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x))^2}-\frac {\int \frac {-2 \left (a b c (A-C)-a^2 A d+b^2 (B c-A d)\right )+2 (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))^2 (c+d \tan (e+f x))} \, dx}{2 \left (a^2+b^2\right ) (b c-a d)} \\ & = -\frac {A b^2-a (b B-a C)}{2 \left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x))^2}-\frac {2 a b^3 c (A-C)+2 a^3 b B d-a^4 C d+b^4 (B c-A d)-a^2 b^2 (B c+3 A d-C d)}{\left (a^2+b^2\right )^2 (b c-a d)^2 f (a+b \tan (e+f x))}+\frac {\int \frac {2 \left (2 a b^3 B c^2-2 a^3 b c (A-C) d+a^4 A d^2+b^4 \left (c (c C-B d)-A \left (c^2-d^2\right )\right )-a^2 b^2 \left (c (c C+3 B d)-A \left (c^2+2 d^2\right )\right )\right )+2 \left (a^2 B-b^2 B-2 a b (A-C)\right ) (b c-a d)^2 \tan (e+f x)-2 d \left (2 a b^3 c (A-C)+2 a^3 b B d-a^4 C d+b^4 (B c-A d)-a^2 b^2 (B c+3 A d-C d)\right ) \tan ^2(e+f x)}{(a+b \tan (e+f x)) (c+d \tan (e+f x))} \, dx}{2 \left (a^2+b^2\right )^2 (b c-a d)^2} \\ & = \frac {\left (a^3 (A c-c C+B d)-3 a b^2 (A c-c C+B d)+3 a^2 b (B c-(A-C) d)-b^3 (B c-(A-C) d)\right ) x}{\left (a^2+b^2\right )^3 \left (c^2+d^2\right )}-\frac {A b^2-a (b B-a C)}{2 \left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x))^2}-\frac {2 a b^3 c (A-C)+2 a^3 b B d-a^4 C d+b^4 (B c-A d)-a^2 b^2 (B c+3 A d-C d)}{\left (a^2+b^2\right )^2 (b c-a d)^2 f (a+b \tan (e+f x))}-\frac {\left (d^2 \left (c^2 C-B c d+A d^2\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 )}+\frac {\left (3 a b^5 B c^2-3 a^5 b B d^2+a^6 C d^2+3 a^4 b^2 d (B c+2 A d-C d)+b^6 \left (c (c C-B d)-A \left (c^2-d^2\right )\right )-a^3 b^3 \left (8 c (A-C) d+B \left (c^2-d^2\right )\right )-3 a^2 b^4 \left (c (c C+2 B d)-A \left (c^2+d^2\right )\right )\right ) \int \frac {b-a \tan (e+f x)}{a+b \tan (e+f x)} \, dx}{\left (a^2+b^2\right )^3 (b c-a d)^3} \\ & = \frac {\left (a^3 (A c-c C+B d)-3 a b^2 (A c-c C+B d)+3 a^2 b (B c-(A-C) d)-b^3 (B c-(A-C) d)\right ) x}{\left (a^2+b^2\right )^3 \left (c^2+d^2\right )}+\frac {\left (3 a b^5 B c^2-3 a^5 b B d^2+a^6 C d^2+3 a^4 b^2 d (B c+2 A d-C d)+b^6 \left (c (c C-B d)-A \left (c^2-d^2\right )\right )-a^3 b^3 \left (8 c (A-C) d+B \left (c^2-d^2\right )\right )-3 a^2 b^4 \left (c (c C+2 B d)-A \left (c^2+d^2\right )\right )\right ) \log (a \cos (e+f x)+b \sin (e+f x))}{\left (a^2+b^2\right )^3 (b c-a d)^3 f}-\frac {d^2 \left (c^2 C-B c d+A d^2\right ) \log (c \cos (e+f x)+d \sin (e+f x))}{(b c-a d)^3 \left (c^2+d^2\right ) f}-\frac {A b^2-a (b B-a C)}{2 \left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x))^2}-\frac {2 a b^3 c (A-C)+2 a^3 b B d-a^4 C d+b^4 (B c-A d)-a^2 b^2 (B c+3 A d-C d)}{\left (a^2+b^2\right )^2 (b c-a d)^2 f (a+b \tan (e+f x))} \\ \end{align*}

Mathematica [A] (verified)

Time = 8.92 (sec) , antiderivative size = 898, normalized size of antiderivative = 1.88 \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^3 (c+d \tan (e+f x))} \, dx=-\frac {A b^2-a (b B-a C)}{2 \left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x))^2}-\frac {-\frac {-\frac {b (b c-a d)^2 \left (3 a^2 A b c-A b^3 c-a^3 B c+3 a b^2 B c-3 a^2 b c C+b^3 c C+a^3 A d-3 a A b^2 d+3 a^2 b B d-b^3 B d-a^3 C d+3 a b^2 C d+\frac {\sqrt {-b^2} \left (a^3 (A c-c C+B d)-3 a b^2 (A c-c C+B d)+3 a^2 b (B c-(A-C) d)-b^3 (B c-(A-C) d)\right )}{b}\right ) \log \left (\sqrt {-b^2}-b \tan (e+f x)\right )}{\left (a^2+b^2\right ) \left (c^2+d^2\right )}+\frac {2 b \left (3 a b^5 B c^2-3 a^5 b B d^2+a^6 C d^2+3 a^4 b^2 d (B c+2 A d-C d)+b^6 \left (c (c C-B d)-A \left (c^2-d^2\right )\right )-a^3 b^3 \left (8 c (A-C) d+B \left (c^2-d^2\right )\right )-3 a^2 b^4 \left (c (c C+2 B d)-A \left (c^2+d^2\right )\right )\right ) \log (a+b \tan (e+f x))}{\left (a^2+b^2\right ) (b c-a d)}-\frac {b (b c-a d)^2 \left (3 a^2 A b c-A b^3 c-a^3 B c+3 a b^2 B c-3 a^2 b c C+b^3 c C+a^3 A d-3 a A b^2 d+3 a^2 b B d-b^3 B d-a^3 C d+3 a b^2 C d-\frac {\sqrt {-b^2} \left (a^3 (A c-c C+B d)-3 a b^2 (A c-c C+B d)+3 a^2 b (B c-(A-C) d)-b^3 (B c-(A-C) d)\right )}{b}\right ) \log \left (\sqrt {-b^2}+b \tan (e+f x)\right )}{\left (a^2+b^2\right ) \left (c^2+d^2\right )}-\frac {2 b \left (a^2+b^2\right )^2 d^2 \left (c^2 C-B c d+A d^2\right ) \log (c+d \tan (e+f x))}{(b c-a d) \left (c^2+d^2\right )}}{b \left (a^2+b^2\right ) (b c-a d) f}-\frac {-a \left (-2 a \left (A b^2-a (b B-a C)\right ) d+2 b (A b-a B-b C) (b c-a d)\right )-2 b^2 \left (a b c (A-C)-a^2 A d+b^2 (B c-A d)\right )}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x))}}{2 \left (a^2+b^2\right ) (b c-a d)} \]

[In]

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

[Out]

-1/2*(A*b^2 - a*(b*B - a*C))/((a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])^2) - (-((-((b*(b*c - a*d)^2*(3*a^
2*A*b*c - A*b^3*c - a^3*B*c + 3*a*b^2*B*c - 3*a^2*b*c*C + b^3*c*C + a^3*A*d - 3*a*A*b^2*d + 3*a^2*b*B*d - b^3*
B*d - a^3*C*d + 3*a*b^2*C*d + (Sqrt[-b^2]*(a^3*(A*c - c*C + B*d) - 3*a*b^2*(A*c - c*C + B*d) + 3*a^2*b*(B*c -
(A - C)*d) - b^3*(B*c - (A - C)*d)))/b)*Log[Sqrt[-b^2] - b*Tan[e + f*x]])/((a^2 + b^2)*(c^2 + d^2))) + (2*b*(3
*a*b^5*B*c^2 - 3*a^5*b*B*d^2 + a^6*C*d^2 + 3*a^4*b^2*d*(B*c + 2*A*d - C*d) + b^6*(c*(c*C - B*d) - A*(c^2 - d^2
)) - a^3*b^3*(8*c*(A - C)*d + B*(c^2 - d^2)) - 3*a^2*b^4*(c*(c*C + 2*B*d) - A*(c^2 + d^2)))*Log[a + b*Tan[e +
f*x]])/((a^2 + b^2)*(b*c - a*d)) - (b*(b*c - a*d)^2*(3*a^2*A*b*c - A*b^3*c - a^3*B*c + 3*a*b^2*B*c - 3*a^2*b*c
*C + b^3*c*C + a^3*A*d - 3*a*A*b^2*d + 3*a^2*b*B*d - b^3*B*d - a^3*C*d + 3*a*b^2*C*d - (Sqrt[-b^2]*(a^3*(A*c -
c*C + B*d) - 3*a*b^2*(A*c - c*C + B*d) + 3*a^2*b*(B*c - (A - C)*d) - b^3*(B*c - (A - C)*d)))/b)*Log[Sqrt[-b^2
] + b*Tan[e + f*x]])/((a^2 + b^2)*(c^2 + d^2)) - (2*b*(a^2 + b^2)^2*d^2*(c^2*C - B*c*d + A*d^2)*Log[c + d*Tan[
e + f*x]])/((b*c - a*d)*(c^2 + d^2)))/(b*(a^2 + b^2)*(b*c - a*d)*f)) - (-(a*(-2*a*(A*b^2 - a*(b*B - a*C))*d +
2*b*(A*b - a*B - b*C)*(b*c - a*d))) - 2*b^2*(a*b*c*(A - C) - a^2*A*d + b^2*(B*c - A*d)))/((a^2 + b^2)*(b*c - a
*d)*f*(a + b*Tan[e + f*x])))/(2*(a^2 + b^2)*(b*c - a*d))

Maple [A] (verified)

Time = 1.58 (sec) , antiderivative size = 647, normalized size of antiderivative = 1.36

method	result	size
derivativedivides	\(\frac {\frac {3 A \,a^{2} b^{2} d -2 A a \,b^{3} c +A \,b^{4} d -2 a^{3} b B d +B \,a^{2} b^{2} c -B \,b^{4} c +a^{4} C d -C \,a^{2} b^{2} d +2 C a \,b^{3} c}{\left (a d -b c \right )^{2} \left (a^{2}+b^{2}\right )^{2} \left (a +b \tan \left (f x +e \right )\right )}-\frac {\left (6 A \,a^{4} b^{2} d^{2}-8 A \,a^{3} b^{3} c d +3 A \,a^{2} b^{4} c^{2}+3 A \,a^{2} b^{4} d^{2}-A \,b^{6} c^{2}+A \,b^{6} d^{2}-3 a^{5} b B \,d^{2}+3 B \,a^{4} b^{2} c d -B \,a^{3} b^{3} c^{2}+B \,a^{3} b^{3} d^{2}-6 B \,a^{2} b^{4} c d +3 a \,b^{5} B \,c^{2}-B \,b^{6} c d +a^{6} C \,d^{2}-3 a^{4} b^{2} C \,d^{2}+8 C \,a^{3} b^{3} c d -3 C \,a^{2} b^{4} c^{2}+C \,b^{6} c^{2}\right ) \ln \left (a +b \tan \left (f x +e \right )\right )}{\left (a d -b c \right )^{3} \left (a^{2}+b^{2}\right )^{3}}+\frac {A \,b^{2}-B a b +C \,a^{2}}{2 \left (a d -b c \right ) \left (a^{2}+b^{2}\right ) \left (a +b \tan \left (f x +e \right )\right )^{2}}+\frac {\frac {\left (-A \,a^{3} d -3 A \,a^{2} b c +3 A a \,b^{2} d +A \,b^{3} c +B \,a^{3} c -3 B \,a^{2} b d -3 B a \,b^{2} c +B \,b^{3} d +a^{3} C d +3 C \,a^{2} b c -3 C a \,b^{2} d -C \,b^{3} c \right ) \ln \left (1+\tan \left (f x +e \right )^{2}\right )}{2}+\left (A \,a^{3} c -3 A \,a^{2} b d -3 A a \,b^{2} c +A \,b^{3} d +B \,a^{3} d +3 B \,a^{2} b c -3 B a \,b^{2} d -B \,b^{3} c -C \,a^{3} c +3 C \,a^{2} b d +3 C a \,b^{2} c -C \,b^{3} d \right ) \arctan \left (\tan \left (f x +e \right )\right )}{\left (a^{2}+b^{2}\right )^{3} \left (c^{2}+d^{2}\right )}+\frac {\left (A \,d^{2}-B c d +c^{2} C \right ) d^{2} \ln \left (c +d \tan \left (f x +e \right )\right )}{\left (a d -b c \right )^{3} \left (c^{2}+d^{2}\right )}}{f}\)	\(647\)
default	\(\frac {\frac {3 A \,a^{2} b^{2} d -2 A a \,b^{3} c +A \,b^{4} d -2 a^{3} b B d +B \,a^{2} b^{2} c -B \,b^{4} c +a^{4} C d -C \,a^{2} b^{2} d +2 C a \,b^{3} c}{\left (a d -b c \right )^{2} \left (a^{2}+b^{2}\right )^{2} \left (a +b \tan \left (f x +e \right )\right )}-\frac {\left (6 A \,a^{4} b^{2} d^{2}-8 A \,a^{3} b^{3} c d +3 A \,a^{2} b^{4} c^{2}+3 A \,a^{2} b^{4} d^{2}-A \,b^{6} c^{2}+A \,b^{6} d^{2}-3 a^{5} b B \,d^{2}+3 B \,a^{4} b^{2} c d -B \,a^{3} b^{3} c^{2}+B \,a^{3} b^{3} d^{2}-6 B \,a^{2} b^{4} c d +3 a \,b^{5} B \,c^{2}-B \,b^{6} c d +a^{6} C \,d^{2}-3 a^{4} b^{2} C \,d^{2}+8 C \,a^{3} b^{3} c d -3 C \,a^{2} b^{4} c^{2}+C \,b^{6} c^{2}\right ) \ln \left (a +b \tan \left (f x +e \right )\right )}{\left (a d -b c \right )^{3} \left (a^{2}+b^{2}\right )^{3}}+\frac {A \,b^{2}-B a b +C \,a^{2}}{2 \left (a d -b c \right ) \left (a^{2}+b^{2}\right ) \left (a +b \tan \left (f x +e \right )\right )^{2}}+\frac {\frac {\left (-A \,a^{3} d -3 A \,a^{2} b c +3 A a \,b^{2} d +A \,b^{3} c +B \,a^{3} c -3 B \,a^{2} b d -3 B a \,b^{2} c +B \,b^{3} d +a^{3} C d +3 C \,a^{2} b c -3 C a \,b^{2} d -C \,b^{3} c \right ) \ln \left (1+\tan \left (f x +e \right )^{2}\right )}{2}+\left (A \,a^{3} c -3 A \,a^{2} b d -3 A a \,b^{2} c +A \,b^{3} d +B \,a^{3} d +3 B \,a^{2} b c -3 B a \,b^{2} d -B \,b^{3} c -C \,a^{3} c +3 C \,a^{2} b d +3 C a \,b^{2} c -C \,b^{3} d \right ) \arctan \left (\tan \left (f x +e \right )\right )}{\left (a^{2}+b^{2}\right )^{3} \left (c^{2}+d^{2}\right )}+\frac {\left (A \,d^{2}-B c d +c^{2} C \right ) d^{2} \ln \left (c +d \tan \left (f x +e \right )\right )}{\left (a d -b c \right )^{3} \left (c^{2}+d^{2}\right )}}{f}\)	\(647\)
norman	\(\text {Expression too large to display}\)	\(1228\)
parallelrisch	\(\text {Expression too large to display}\)	\(9347\)
risch	\(\text {Expression too large to display}\)	\(12454\)

[In]

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

[Out]

1/f*((3*A*a^2*b^2*d-2*A*a*b^3*c+A*b^4*d-2*B*a^3*b*d+B*a^2*b^2*c-B*b^4*c+C*a^4*d-C*a^2*b^2*d+2*C*a*b^3*c)/(a*d-
b*c)^2/(a^2+b^2)^2/(a+b*tan(f*x+e))-(6*A*a^4*b^2*d^2-8*A*a^3*b^3*c*d+3*A*a^2*b^4*c^2+3*A*a^2*b^4*d^2-A*b^6*c^2
+A*b^6*d^2-3*B*a^5*b*d^2+3*B*a^4*b^2*c*d-B*a^3*b^3*c^2+B*a^3*b^3*d^2-6*B*a^2*b^4*c*d+3*B*a*b^5*c^2-B*b^6*c*d+C
*a^6*d^2-3*C*a^4*b^2*d^2+8*C*a^3*b^3*c*d-3*C*a^2*b^4*c^2+C*b^6*c^2)/(a*d-b*c)^3/(a^2+b^2)^3*ln(a+b*tan(f*x+e))
+1/2*(A*b^2-B*a*b+C*a^2)/(a*d-b*c)/(a^2+b^2)/(a+b*tan(f*x+e))^2+1/(a^2+b^2)^3/(c^2+d^2)*(1/2*(-A*a^3*d-3*A*a^2
*b*c+3*A*a*b^2*d+A*b^3*c+B*a^3*c-3*B*a^2*b*d-3*B*a*b^2*c+B*b^3*d+C*a^3*d+3*C*a^2*b*c-3*C*a*b^2*d-C*b^3*c)*ln(1
+tan(f*x+e)^2)+(A*a^3*c-3*A*a^2*b*d-3*A*a*b^2*c+A*b^3*d+B*a^3*d+3*B*a^2*b*c-3*B*a*b^2*d-B*b^3*c-C*a^3*c+3*C*a^
2*b*d+3*C*a*b^2*c-C*b^3*d)*arctan(tan(f*x+e)))+(A*d^2-B*c*d+C*c^2)*d^2/(a*d-b*c)^3/(c^2+d^2)*ln(c+d*tan(f*x+e)
))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 3643 vs. \(2 (475) = 950\).

Time = 3.39 (sec) , antiderivative size = 3643, normalized size of antiderivative = 7.64 \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^3 (c+d \tan (e+f x))} \, dx=\text {Too large to display} \]

[In]

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

[Out]

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

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^3 (c+d \tan (e+f x))} \, dx=\text {Exception raised: NotImplementedError} \]

[In]

integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**3/(c+d*tan(f*x+e)),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. 1096 vs. \(2 (475) = 950\).

Time = 0.38 (sec) , antiderivative size = 1096, normalized size of antiderivative = 2.30 \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^3 (c+d \tan (e+f x))} \, dx=\text {Too large to display} \]

[In]

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

[Out]

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

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 2080 vs. \(2 (475) = 950\).

Time = 1.09 (sec) , antiderivative size = 2080, normalized size of antiderivative = 4.36 \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^3 (c+d \tan (e+f x))} \, dx=\text {Too large to display} \]

[In]

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

[Out]

1/2*(2*(A*a^3*c - C*a^3*c + 3*B*a^2*b*c - 3*A*a*b^2*c + 3*C*a*b^2*c - B*b^3*c + B*a^3*d - 3*A*a^2*b*d + 3*C*a^
2*b*d - 3*B*a*b^2*d + A*b^3*d - C*b^3*d)*(f*x + e)/(a^6*c^2 + 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 + b^6*c^2 + a^6*d^
2 + 3*a^4*b^2*d^2 + 3*a^2*b^4*d^2 + b^6*d^2) + (B*a^3*c - 3*A*a^2*b*c + 3*C*a^2*b*c - 3*B*a*b^2*c + A*b^3*c -
C*b^3*c - A*a^3*d + C*a^3*d - 3*B*a^2*b*d + 3*A*a*b^2*d - 3*C*a*b^2*d + B*b^3*d)*log(tan(f*x + e)^2 + 1)/(a^6*
c^2 + 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 + b^6*c^2 + a^6*d^2 + 3*a^4*b^2*d^2 + 3*a^2*b^4*d^2 + b^6*d^2) - 2*(B*a^3*
b^4*c^2 - 3*A*a^2*b^5*c^2 + 3*C*a^2*b^5*c^2 - 3*B*a*b^6*c^2 + A*b^7*c^2 - C*b^7*c^2 - 3*B*a^4*b^3*c*d + 8*A*a^
3*b^4*c*d - 8*C*a^3*b^4*c*d + 6*B*a^2*b^5*c*d + B*b^7*c*d - C*a^6*b*d^2 + 3*B*a^5*b^2*d^2 - 6*A*a^4*b^3*d^2 +
3*C*a^4*b^3*d^2 - B*a^3*b^4*d^2 - 3*A*a^2*b^5*d^2 - A*b^7*d^2)*log(abs(b*tan(f*x + e) + a))/(a^6*b^4*c^3 + 3*a
^4*b^6*c^3 + 3*a^2*b^8*c^3 + b^10*c^3 - 3*a^7*b^3*c^2*d - 9*a^5*b^5*c^2*d - 9*a^3*b^7*c^2*d - 3*a*b^9*c^2*d +
3*a^8*b^2*c*d^2 + 9*a^6*b^4*c*d^2 + 9*a^4*b^6*c*d^2 + 3*a^2*b^8*c*d^2 - a^9*b*d^3 - 3*a^7*b^3*d^3 - 3*a^5*b^5*
d^3 - a^3*b^7*d^3) - 2*(C*c^2*d^3 - B*c*d^4 + A*d^5)*log(abs(d*tan(f*x + e) + c))/(b^3*c^5*d - 3*a*b^2*c^4*d^2
+ 3*a^2*b*c^3*d^3 + b^3*c^3*d^3 - a^3*c^2*d^4 - 3*a*b^2*c^2*d^4 + 3*a^2*b*c*d^5 - a^3*d^6) + (3*B*a^3*b^5*c^2
*tan(f*x + e)^2 - 9*A*a^2*b^6*c^2*tan(f*x + e)^2 + 9*C*a^2*b^6*c^2*tan(f*x + e)^2 - 9*B*a*b^7*c^2*tan(f*x + e)
^2 + 3*A*b^8*c^2*tan(f*x + e)^2 - 3*C*b^8*c^2*tan(f*x + e)^2 - 9*B*a^4*b^4*c*d*tan(f*x + e)^2 + 24*A*a^3*b^5*c
*d*tan(f*x + e)^2 - 24*C*a^3*b^5*c*d*tan(f*x + e)^2 + 18*B*a^2*b^6*c*d*tan(f*x + e)^2 + 3*B*b^8*c*d*tan(f*x +
e)^2 - 3*C*a^6*b^2*d^2*tan(f*x + e)^2 + 9*B*a^5*b^3*d^2*tan(f*x + e)^2 - 18*A*a^4*b^4*d^2*tan(f*x + e)^2 + 9*C
*a^4*b^4*d^2*tan(f*x + e)^2 - 3*B*a^3*b^5*d^2*tan(f*x + e)^2 - 9*A*a^2*b^6*d^2*tan(f*x + e)^2 - 3*A*b^8*d^2*ta
n(f*x + e)^2 + 8*B*a^4*b^4*c^2*tan(f*x + e) - 22*A*a^3*b^5*c^2*tan(f*x + e) + 22*C*a^3*b^5*c^2*tan(f*x + e) -
18*B*a^2*b^6*c^2*tan(f*x + e) + 2*A*a*b^7*c^2*tan(f*x + e) - 2*C*a*b^7*c^2*tan(f*x + e) - 2*B*b^8*c^2*tan(f*x
+ e) + 2*C*a^6*b^2*c*d*tan(f*x + e) - 24*B*a^5*b^3*c*d*tan(f*x + e) + 58*A*a^4*b^4*c*d*tan(f*x + e) - 52*C*a^4
*b^4*c*d*tan(f*x + e) + 32*B*a^3*b^5*c*d*tan(f*x + e) + 12*A*a^2*b^6*c*d*tan(f*x + e) - 6*C*a^2*b^6*c*d*tan(f*
x + e) + 8*B*a*b^7*c*d*tan(f*x + e) + 2*A*b^8*c*d*tan(f*x + e) - 8*C*a^7*b*d^2*tan(f*x + e) + 22*B*a^6*b^2*d^2
*tan(f*x + e) - 42*A*a^5*b^3*d^2*tan(f*x + e) + 18*C*a^5*b^3*d^2*tan(f*x + e) - 2*B*a^4*b^4*d^2*tan(f*x + e) -
26*A*a^3*b^5*d^2*tan(f*x + e) + 2*C*a^3*b^5*d^2*tan(f*x + e) - 8*A*a*b^7*d^2*tan(f*x + e) - C*a^6*b^2*c^2 + 6
*B*a^5*b^3*c^2 - 14*A*a^4*b^4*c^2 + 11*C*a^4*b^4*c^2 - 7*B*a^3*b^5*c^2 - 3*A*a^2*b^6*c^2 - B*a*b^7*c^2 - A*b^8
*c^2 + 4*C*a^7*b*c*d - 17*B*a^6*b^2*c*d + 36*A*a^5*b^3*c*d - 24*C*a^5*b^3*c*d + 10*B*a^4*b^4*c*d + 16*A*a^3*b^
5*c*d - 4*C*a^3*b^5*c*d + 3*B*a^2*b^6*c*d + 4*A*a*b^7*c*d - 6*C*a^8*d^2 + 14*B*a^7*b*d^2 - 25*A*a^6*b^2*d^2 +
7*C*a^6*b^2*d^2 + 3*B*a^5*b^3*d^2 - 19*A*a^4*b^4*d^2 + C*a^4*b^4*d^2 + B*a^3*b^5*d^2 - 6*A*a^2*b^6*d^2)/((a^6*
b^3*c^3 + 3*a^4*b^5*c^3 + 3*a^2*b^7*c^3 + b^9*c^3 - 3*a^7*b^2*c^2*d - 9*a^5*b^4*c^2*d - 9*a^3*b^6*c^2*d - 3*a*
b^8*c^2*d + 3*a^8*b*c*d^2 + 9*a^6*b^3*c*d^2 + 9*a^4*b^5*c*d^2 + 3*a^2*b^7*c*d^2 - a^9*d^3 - 3*a^7*b^2*d^3 - 3*
a^5*b^4*d^3 - a^3*b^6*d^3)*(b*tan(f*x + e) + a)^2))/f

Mupad [B] (verification not implemented)

Time = 22.52 (sec) , antiderivative size = 65819, normalized size of antiderivative = 137.99 \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^3 (c+d \tan (e+f x))} \, dx=\text {Too large to display} \]

[In]

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

[Out]

-(((A*b^5*c - 3*C*a^5*d - 3*A*a*b^4*d + B*a*b^4*c + 5*B*a^4*b*d + C*a^4*b*c + 5*A*a^2*b^3*c - 7*A*a^3*b^2*d -
3*B*a^3*b^2*c + B*a^2*b^3*d - 3*C*a^2*b^3*c + C*a^3*b^2*d)/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a^4 + b^4 + 2*a
^2*b^2)) - (tan(e + f*x)*(A*b^5*d - B*b^5*c - 2*A*a*b^4*c + 2*C*a*b^4*c + C*a^4*b*d + 3*A*a^2*b^3*d + B*a^2*b^
3*c - 2*B*a^3*b^2*d - C*a^2*b^3*d))/((a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a^4 + b^4 + 2*a^2*b^2)))/(a^2 + b^2*tan(
e + f*x)^2 + 2*a*b*tan(e + f*x)) - symsum(log(- (A^3*b^8*c^2*d^4 - 4*A^3*a^2*b^6*d^6 - 7*A^3*a^4*b^4*d^6 - A^3
*b^8*d^6 + A^2*C*b^8*d^6 - 3*A^3*a^2*b^6*c^2*d^4 - B^3*a^3*b^5*c^2*d^4 - C^3*a^2*b^6*c^2*d^4 - 2*C^3*a^3*b^5*c
^3*d^3 + 7*C^3*a^4*b^4*c^2*d^4 + A^2*B*a*b^7*d^6 + A^2*B*b^8*c*d^5 + A^3*a*b^7*c*d^5 + C^3*a^7*b*c*d^5 - A*B^2
*a^2*b^6*d^6 - 3*A*B^2*a^6*b^2*d^6 + 2*A^2*B*a^3*b^5*d^6 + 9*A^2*B*a^5*b^3*d^6 - A*C^2*a^2*b^6*d^6 - 4*A*C^2*a
^4*b^4*d^6 + A*C^2*a^6*b^2*d^6 + 5*A^2*C*a^2*b^6*d^6 + 11*A^2*C*a^4*b^4*d^6 - A^2*C*a^6*b^2*d^6 + A*C^2*b^8*c^
2*d^4 - 2*A^2*C*b^8*c^2*d^4 - B*C^2*b^8*c^3*d^3 + B^2*C*b^8*c^2*d^4 + 9*A^3*a^3*b^5*c*d^5 - B^3*a*b^7*c^2*d^4
+ B^3*a^2*b^6*c*d^5 + B^3*a^4*b^4*c*d^5 + 2*C^3*a*b^7*c^3*d^3 - 3*C^3*a^5*b^3*c*d^5 + A*B*C*a^7*b*d^6 - 2*A*B*
C*b^8*c*d^5 + 3*A*B^2*a^2*b^6*c^2*d^4 - A*B^2*a^4*b^4*c^2*d^4 + 3*A^2*B*a^3*b^5*c^2*d^4 - A*C^2*a^2*b^6*c^2*d^
4 + 4*A*C^2*a^3*b^5*c^3*d^3 - 14*A*C^2*a^4*b^4*c^2*d^4 + 5*A^2*C*a^2*b^6*c^2*d^4 - 2*A^2*C*a^3*b^5*c^3*d^3 + 7
*A^2*C*a^4*b^4*c^2*d^4 + 6*B*C^2*a^2*b^6*c^3*d^3 - 15*B*C^2*a^3*b^5*c^2*d^4 - B*C^2*a^4*b^4*c^3*d^3 + 3*B*C^2*
a^5*b^3*c^2*d^4 + 5*B^2*C*a^2*b^6*c^2*d^4 + 2*B^2*C*a^3*b^5*c^3*d^3 - 4*B^2*C*a^4*b^4*c^2*d^4 + A*B*C*a^3*b^5*
d^6 - 6*A*B*C*a^5*b^3*d^6 + A*B*C*b^8*c^3*d^3 + 2*A*C^2*a*b^7*c*d^5 - A*C^2*a^7*b*c*d^5 - 3*A^2*C*a*b^7*c*d^5
- 5*A*B^2*a^3*b^5*c*d^5 + 3*A*B^2*a^5*b^3*c*d^5 - 5*A^2*B*a*b^7*c^2*d^4 + 7*A^2*B*a^2*b^6*c*d^5 - 10*A^2*B*a^4
*b^4*c*d^5 - 4*A*C^2*a*b^7*c^3*d^3 + 12*A*C^2*a^3*b^5*c*d^5 + 9*A*C^2*a^5*b^3*c*d^5 + 2*A^2*C*a*b^7*c^3*d^3 -
21*A^2*C*a^3*b^5*c*d^5 - 6*A^2*C*a^5*b^3*c*d^5 - 2*B*C^2*a*b^7*c^2*d^4 + B*C^2*a^2*b^6*c*d^5 + 5*B*C^2*a^4*b^4
*c*d^5 - 4*B*C^2*a^6*b^2*c*d^5 - 2*B^2*C*a*b^7*c^3*d^3 - B^2*C*a^3*b^5*c*d^5 + 3*B^2*C*a^5*b^3*c*d^5 - 6*A*B*C
*a^2*b^6*c^3*d^3 + 12*A*B*C*a^3*b^5*c^2*d^4 + A*B*C*a^4*b^4*c^3*d^3 - 3*A*B*C*a^5*b^3*c^2*d^4 + 7*A*B*C*a*b^7*
c^2*d^4 - 11*A*B*C*a^2*b^6*c*d^5 + 2*A*B*C*a^4*b^4*c*d^5 + 3*A*B*C*a^6*b^2*c*d^5)/(a^12*d^4 + b^12*c^4 + 4*a^2
*b^10*c^4 + 6*a^4*b^8*c^4 + 4*a^6*b^6*c^4 + a^8*b^4*c^4 + a^4*b^8*d^4 + 4*a^6*b^6*d^4 + 6*a^8*b^4*d^4 + 4*a^10
*b^2*d^4 - 4*a^3*b^9*c*d^3 - 16*a^3*b^9*c^3*d - 16*a^5*b^7*c*d^3 - 24*a^5*b^7*c^3*d - 24*a^7*b^5*c*d^3 - 16*a^
7*b^5*c^3*d - 16*a^9*b^3*c*d^3 - 4*a^9*b^3*c^3*d + 6*a^2*b^10*c^2*d^2 + 24*a^4*b^8*c^2*d^2 + 36*a^6*b^6*c^2*d^
2 + 24*a^8*b^4*c^2*d^2 + 6*a^10*b^2*c^2*d^2 - 4*a*b^11*c^3*d - 4*a^11*b*c*d^3) - root(480*a^11*b^7*c*d^9*f^4 +
480*a^7*b^11*c^9*d*f^4 + 360*a^13*b^5*c*d^9*f^4 + 360*a^9*b^9*c^9*d*f^4 + 360*a^9*b^9*c*d^9*f^4 + 360*a^5*b^1
3*c^9*d*f^4 + 144*a^15*b^3*c*d^9*f^4 + 144*a^11*b^7*c^9*d*f^4 + 144*a^7*b^11*c*d^9*f^4 + 144*a^3*b^15*c^9*d*f^
4 + 48*a^17*b*c^3*d^7*f^4 + 48*a*b^17*c^7*d^3*f^4 + 24*a^17*b*c^5*d^5*f^4 + 24*a^13*b^5*c^9*d*f^4 + 24*a^5*b^1
3*c*d^9*f^4 + 24*a*b^17*c^5*d^5*f^4 + 24*a^17*b*c*d^9*f^4 + 24*a*b^17*c^9*d*f^4 + 3920*a^9*b^9*c^5*d^5*f^4 - 3
360*a^10*b^8*c^4*d^6*f^4 - 3360*a^8*b^10*c^6*d^4*f^4 + 3024*a^11*b^7*c^5*d^5*f^4 - 3024*a^10*b^8*c^6*d^4*f^4 -
3024*a^8*b^10*c^4*d^6*f^4 + 3024*a^7*b^11*c^5*d^5*f^4 + 2320*a^9*b^9*c^7*d^3*f^4 + 2320*a^9*b^9*c^3*d^7*f^4 -
2240*a^12*b^6*c^4*d^6*f^4 - 2240*a^6*b^12*c^6*d^4*f^4 + 2160*a^11*b^7*c^3*d^7*f^4 + 2160*a^7*b^11*c^7*d^3*f^4
- 1624*a^12*b^6*c^6*d^4*f^4 - 1624*a^6*b^12*c^4*d^6*f^4 + 1488*a^11*b^7*c^7*d^3*f^4 + 1488*a^7*b^11*c^3*d^7*f
^4 + 1344*a^13*b^5*c^5*d^5*f^4 + 1344*a^5*b^13*c^5*d^5*f^4 - 1320*a^10*b^8*c^2*d^8*f^4 - 1320*a^8*b^10*c^8*d^2
*f^4 + 1200*a^13*b^5*c^3*d^7*f^4 + 1200*a^5*b^13*c^7*d^3*f^4 - 1060*a^12*b^6*c^2*d^8*f^4 - 1060*a^6*b^12*c^8*d
^2*f^4 - 948*a^10*b^8*c^8*d^2*f^4 - 948*a^8*b^10*c^2*d^8*f^4 - 840*a^14*b^4*c^4*d^6*f^4 - 840*a^4*b^14*c^6*d^4
*f^4 + 528*a^13*b^5*c^7*d^3*f^4 + 528*a^5*b^13*c^3*d^7*f^4 - 480*a^14*b^4*c^6*d^4*f^4 - 480*a^14*b^4*c^2*d^8*f
^4 - 480*a^4*b^14*c^8*d^2*f^4 - 480*a^4*b^14*c^4*d^6*f^4 + 368*a^15*b^3*c^3*d^7*f^4 - 368*a^12*b^6*c^8*d^2*f^4
- 368*a^6*b^12*c^2*d^8*f^4 + 368*a^3*b^15*c^7*d^3*f^4 + 304*a^15*b^3*c^5*d^5*f^4 + 304*a^3*b^15*c^5*d^5*f^4 -
144*a^16*b^2*c^4*d^6*f^4 - 144*a^2*b^16*c^6*d^4*f^4 - 108*a^16*b^2*c^2*d^8*f^4 - 108*a^2*b^16*c^8*d^2*f^4 + 8
0*a^15*b^3*c^7*d^3*f^4 + 80*a^3*b^15*c^3*d^7*f^4 - 60*a^16*b^2*c^6*d^4*f^4 - 60*a^14*b^4*c^8*d^2*f^4 - 60*a^4*
b^14*c^2*d^8*f^4 - 60*a^2*b^16*c^4*d^6*f^4 - 8*b^18*c^8*d^2*f^4 - 4*b^18*c^6*d^4*f^4 - 8*a^18*c^2*d^8*f^4 - 4*
a^18*c^4*d^6*f^4 - 80*a^12*b^6*d^10*f^4 - 60*a^14*b^4*d^10*f^4 - 60*a^10*b^8*d^10*f^4 - 24*a^16*b^2*d^10*f^4 -
24*a^8*b^10*d^10*f^4 - 4*a^6*b^12*d^10*f^4 - 80*a^6*b^12*c^10*f^4 - 60*a^8*b^10*c^10*f^4 - 60*a^4*b^14*c^10*f
^4 - 24*a^10*b^8*c^10*f^4 - 24*a^2*b^16*c^10*f^4 - 4*a^12*b^6*c^10*f^4 - 4*b^18*c^10*f^4 - 4*a^18*d^10*f^4 - 1
2*A*C*a^11*b*c*d^7*f^2 - 12*A*C*a*b^11*c^7*d*f^2 - 912*B*C*a^5*b^7*c^4*d^4*f^2 - 792*B*C*a^8*b^4*c^3*d^5*f^2 +
792*B*C*a^4*b^8*c^5*d^3*f^2 + 720*B*C*a^7*b^5*c^4*d^4*f^2 - 480*B*C*a^5*b^7*c^6*d^2*f^2 - 408*B*C*a^5*b^7*c^2
*d^6*f^2 + 384*B*C*a^7*b^5*c^2*d^6*f^2 - 336*B*C*a^8*b^4*c^5*d^3*f^2 + 324*B*C*a^4*b^8*c^3*d^5*f^2 + 312*B*C*a
^7*b^5*c^6*d^2*f^2 - 248*B*C*a^3*b^9*c^6*d^2*f^2 + 216*B*C*a^9*b^3*c^2*d^6*f^2 - 196*B*C*a^3*b^9*c^4*d^4*f^2 +
132*B*C*a^9*b^3*c^4*d^4*f^2 + 80*B*C*a^6*b^6*c^3*d^5*f^2 - 64*B*C*a^6*b^6*c^5*d^3*f^2 - 36*B*C*a^2*b^10*c^3*d
^5*f^2 - 28*B*C*a^3*b^9*c^2*d^6*f^2 + 12*B*C*a^10*b^2*c^5*d^3*f^2 - 12*B*C*a^10*b^2*c^3*d^5*f^2 - 12*B*C*a^2*b
^10*c^5*d^3*f^2 - 4*B*C*a^9*b^3*c^6*d^2*f^2 - 1468*A*C*a^6*b^6*c^4*d^4*f^2 + 996*A*C*a^7*b^5*c^3*d^5*f^2 + 900
*A*C*a^5*b^7*c^5*d^3*f^2 - 676*A*C*a^6*b^6*c^6*d^2*f^2 - 660*A*C*a^6*b^6*c^2*d^6*f^2 + 636*A*C*a^5*b^7*c^3*d^5
*f^2 + 540*A*C*a^7*b^5*c^5*d^3*f^2 - 236*A*C*a^3*b^9*c^5*d^3*f^2 - 204*A*C*a^9*b^3*c^3*d^5*f^2 + 156*A*C*a^10*
b^2*c^2*d^6*f^2 + 132*A*C*a^2*b^10*c^6*d^2*f^2 - 72*A*C*a^9*b^3*c^5*d^3*f^2 - 72*A*C*a^4*b^8*c^6*d^2*f^2 + 66*
A*C*a^4*b^8*c^2*d^6*f^2 + 54*A*C*a^10*b^2*c^4*d^4*f^2 + 54*A*C*a^2*b^10*c^4*d^4*f^2 - 48*A*C*a^8*b^4*c^2*d^6*f
^2 - 48*A*C*a^4*b^8*c^4*d^4*f^2 + 42*A*C*a^8*b^4*c^6*d^2*f^2 - 40*A*C*a^3*b^9*c^3*d^5*f^2 - 36*A*C*a^8*b^4*c^4
*d^4*f^2 + 24*A*C*a^2*b^10*c^2*d^6*f^2 + 960*A*B*a^5*b^7*c^4*d^4*f^2 - 864*A*B*a^4*b^8*c^5*d^3*f^2 + 756*A*B*a
^8*b^4*c^3*d^5*f^2 - 744*A*B*a^7*b^5*c^4*d^4*f^2 - 528*A*B*a^4*b^8*c^3*d^5*f^2 + 504*A*B*a^5*b^7*c^6*d^2*f^2 -
432*A*B*a^7*b^5*c^2*d^6*f^2 + 432*A*B*a^5*b^7*c^2*d^6*f^2 + 348*A*B*a^8*b^4*c^5*d^3*f^2 - 312*A*B*a^7*b^5*c^6
*d^2*f^2 - 284*A*B*a^9*b^3*c^2*d^6*f^2 + 280*A*B*a^3*b^9*c^6*d^2*f^2 + 264*A*B*a^3*b^9*c^4*d^4*f^2 - 240*A*B*a
^6*b^6*c^3*d^5*f^2 - 172*A*B*a^9*b^3*c^4*d^4*f^2 + 68*A*B*a^3*b^9*c^2*d^6*f^2 - 60*A*B*a^2*b^10*c^3*d^5*f^2 +
24*A*B*a^6*b^6*c^5*d^3*f^2 - 24*A*B*a^2*b^10*c^5*d^3*f^2 + 12*A*B*a^10*b^2*c^3*d^5*f^2 + 360*B*C*a^4*b^8*c^7*d
*f^2 - 336*B*C*a^8*b^4*c*d^7*f^2 + 168*B*C*a^6*b^6*c*d^7*f^2 - 136*B*C*a^6*b^6*c^7*d*f^2 - 36*B*C*a^11*b*c^2*d
^6*f^2 + 36*B*C*a*b^11*c^6*d^2*f^2 + 24*B*C*a^10*b^2*c*d^7*f^2 - 24*B*C*a^2*b^10*c^7*d*f^2 - 12*B*C*a^11*b*c^4
*d^4*f^2 + 12*B*C*a^4*b^8*c*d^7*f^2 + 12*B*C*a*b^11*c^4*d^4*f^2 + 444*A*C*a^7*b^5*c*d^7*f^2 + 348*A*C*a^5*b^7*
c^7*d*f^2 - 164*A*C*a^3*b^9*c^7*d*f^2 - 132*A*C*a^9*b^3*c*d^7*f^2 + 84*A*C*a^5*b^7*c*d^7*f^2 + 32*A*C*a^3*b^9*
c*d^7*f^2 - 12*A*C*a^11*b*c^3*d^5*f^2 - 12*A*C*a^7*b^5*c^7*d*f^2 - 12*A*C*a*b^11*c^5*d^3*f^2 - 360*A*B*a^4*b^8
*c^7*d*f^2 + 288*A*B*a^8*b^4*c*d^7*f^2 - 288*A*B*a^6*b^6*c*d^7*f^2 - 144*A*B*a^4*b^8*c*d^7*f^2 + 136*A*B*a^6*b
^6*c^7*d*f^2 - 60*A*B*a^2*b^10*c*d^7*f^2 - 36*A*B*a^10*b^2*c*d^7*f^2 + 24*A*B*a^2*b^10*c^7*d*f^2 - 24*A*B*a*b^
11*c^6*d^2*f^2 + 12*A*B*a^11*b*c^2*d^6*f^2 + 12*A*B*a*b^11*c^4*d^4*f^2 + 12*A*B*a*b^11*c^2*d^6*f^2 - 8*B*C*b^1
2*c^5*d^3*f^2 - 8*B*C*b^12*c^3*d^5*f^2 + 8*A*C*b^12*c^2*d^6*f^2 - 4*B*C*a^12*c^3*d^5*f^2 + 4*A*C*b^12*c^4*d^4*
f^2 - 2*A*C*b^12*c^6*d^2*f^2 + 80*B*C*a^9*b^3*d^8*f^2 - 24*B*C*a^7*b^5*d^8*f^2 + 6*A*C*a^12*c^2*d^6*f^2 + 4*A*
B*b^12*c^5*d^3*f^2 - 4*A*B*b^12*c^3*d^5*f^2 - 90*A*C*a^8*b^4*d^8*f^2 - 80*B*C*a^3*b^9*c^8*f^2 + 54*A*C*a^10*b^
2*d^8*f^2 - 30*A*C*a^6*b^6*d^8*f^2 + 24*B*C*a^5*b^7*c^8*f^2 - 12*A*C*a^4*b^8*d^8*f^2 - 112*A*B*a^9*b^3*d^8*f^2
- 66*A*C*a^4*b^8*c^8*f^2 + 54*A*C*a^2*b^10*c^8*f^2 + 4*A*B*a^3*b^9*d^8*f^2 + 2*A*C*a^6*b^6*c^8*f^2 + 80*A*B*a
^3*b^9*c^8*f^2 - 24*A*B*a^5*b^7*c^8*f^2 + 726*C^2*a^6*b^6*c^4*d^4*f^2 - 402*C^2*a^7*b^5*c^3*d^5*f^2 - 402*C^2*
a^5*b^7*c^5*d^3*f^2 + 322*C^2*a^6*b^6*c^6*d^2*f^2 + 322*C^2*a^6*b^6*c^2*d^6*f^2 - 222*C^2*a^7*b^5*c^5*d^3*f^2
- 222*C^2*a^5*b^7*c^3*d^5*f^2 + 134*C^2*a^9*b^3*c^3*d^5*f^2 + 134*C^2*a^3*b^9*c^5*d^3*f^2 - 66*C^2*a^10*b^2*c^
2*d^6*f^2 - 66*C^2*a^2*b^10*c^6*d^2*f^2 + 52*C^2*a^9*b^3*c^5*d^3*f^2 + 52*C^2*a^3*b^9*c^3*d^5*f^2 - 27*C^2*a^8
*b^4*c^6*d^2*f^2 - 27*C^2*a^4*b^8*c^2*d^6*f^2 + 24*C^2*a^8*b^4*c^4*d^4*f^2 + 24*C^2*a^8*b^4*c^2*d^6*f^2 + 24*C
^2*a^4*b^8*c^6*d^2*f^2 + 24*C^2*a^4*b^8*c^4*d^4*f^2 - 15*C^2*a^10*b^2*c^4*d^4*f^2 - 15*C^2*a^2*b^10*c^4*d^4*f^
2 - 570*B^2*a^6*b^6*c^4*d^4*f^2 + 366*B^2*a^7*b^5*c^3*d^5*f^2 + 318*B^2*a^5*b^7*c^5*d^3*f^2 - 262*B^2*a^6*b^6*
c^6*d^2*f^2 - 222*B^2*a^6*b^6*c^2*d^6*f^2 - 210*B^2*a^3*b^9*c^5*d^3*f^2 + 186*B^2*a^7*b^5*c^5*d^3*f^2 + 162*B^
2*a^5*b^7*c^3*d^5*f^2 - 142*B^2*a^9*b^3*c^3*d^5*f^2 + 132*B^2*a^4*b^8*c^4*d^4*f^2 + 117*B^2*a^4*b^8*c^2*d^6*f^
2 + 102*B^2*a^2*b^10*c^6*d^2*f^2 - 96*B^2*a^3*b^9*c^3*d^5*f^2 + 90*B^2*a^10*b^2*c^2*d^6*f^2 + 81*B^2*a^2*b^10*
c^4*d^4*f^2 - 56*B^2*a^9*b^3*c^5*d^3*f^2 + 48*B^2*a^8*b^4*c^4*d^4*f^2 + 48*B^2*a^4*b^8*c^6*d^2*f^2 + 45*B^2*a^
8*b^4*c^6*d^2*f^2 + 36*B^2*a^8*b^4*c^2*d^6*f^2 + 36*B^2*a^2*b^10*c^2*d^6*f^2 + 33*B^2*a^10*b^2*c^4*d^4*f^2 + 8
22*A^2*a^6*b^6*c^4*d^4*f^2 - 594*A^2*a^7*b^5*c^3*d^5*f^2 + 498*A^2*a^6*b^6*c^2*d^6*f^2 - 498*A^2*a^5*b^7*c^5*d
^3*f^2 - 414*A^2*a^5*b^7*c^3*d^5*f^2 + 354*A^2*a^6*b^6*c^6*d^2*f^2 - 318*A^2*a^7*b^5*c^5*d^3*f^2 + 144*A^2*a^8
*b^4*c^2*d^6*f^2 + 102*A^2*a^3*b^9*c^5*d^3*f^2 + 84*A^2*a^4*b^8*c^4*d^4*f^2 + 81*A^2*a^4*b^8*c^2*d^6*f^2 + 72*
A^2*a^8*b^4*c^4*d^4*f^2 + 70*A^2*a^9*b^3*c^3*d^5*f^2 - 66*A^2*a^2*b^10*c^6*d^2*f^2 + 48*A^2*a^4*b^8*c^6*d^2*f^
2 - 42*A^2*a^10*b^2*c^2*d^6*f^2 + 24*A^2*a^2*b^10*c^2*d^6*f^2 + 20*A^2*a^9*b^3*c^5*d^3*f^2 - 15*A^2*a^10*b^2*c
^4*d^4*f^2 - 15*A^2*a^8*b^4*c^6*d^2*f^2 - 15*A^2*a^2*b^10*c^4*d^4*f^2 - 12*A^2*a^3*b^9*c^3*d^5*f^2 - 8*B*C*b^1
2*c^7*d*f^2 + 4*B*C*a^12*c*d^7*f^2 - 24*B*C*a^11*b*d^8*f^2 + 8*A*B*b^12*c^7*d*f^2 - 8*A*B*b^12*c*d^7*f^2 + 24*
B*C*a*b^11*c^8*f^2 - 8*A*B*a^12*c*d^7*f^2 + 12*A*B*a^11*b*d^8*f^2 - 24*A*B*a*b^11*c^8*f^2 - 174*C^2*a^7*b^5*c*
d^7*f^2 - 174*C^2*a^5*b^7*c^7*d*f^2 + 82*C^2*a^9*b^3*c*d^7*f^2 + 82*C^2*a^3*b^9*c^7*d*f^2 + 6*C^2*a^11*b*c^3*d
^5*f^2 + 6*C^2*a^7*b^5*c^7*d*f^2 + 6*C^2*a^5*b^7*c*d^7*f^2 + 6*C^2*a*b^11*c^5*d^3*f^2 + 162*B^2*a^7*b^5*c*d^7*
f^2 + 138*B^2*a^5*b^7*c^7*d*f^2 - 118*B^2*a^3*b^9*c^7*d*f^2 - 86*B^2*a^9*b^3*c*d^7*f^2 - 30*B^2*a*b^11*c^5*d^3
*f^2 - 18*B^2*a^7*b^5*c^7*d*f^2 - 18*B^2*a^5*b^7*c*d^7*f^2 - 12*B^2*a*b^11*c^3*d^5*f^2 - 6*B^2*a^11*b*c^3*d^5*
f^2 - 4*B^2*a^3*b^9*c*d^7*f^2 - 270*A^2*a^7*b^5*c*d^7*f^2 - 174*A^2*a^5*b^7*c^7*d*f^2 - 90*A^2*a^5*b^7*c*d^7*f
^2 + 82*A^2*a^3*b^9*c^7*d*f^2 + 50*A^2*a^9*b^3*c*d^7*f^2 - 32*A^2*a^3*b^9*c*d^7*f^2 + 6*A^2*a^11*b*c^3*d^5*f^2
+ 6*A^2*a^7*b^5*c^7*d*f^2 + 6*A^2*a*b^11*c^5*d^3*f^2 + 6*C^2*a^11*b*c*d^7*f^2 + 6*C^2*a*b^11*c^7*d*f^2 - 18*B
^2*a*b^11*c^7*d*f^2 - 6*B^2*a^11*b*c*d^7*f^2 + 6*A^2*a^11*b*c*d^7*f^2 + 6*A^2*a*b^11*c^7*d*f^2 - 6*A*C*b^12*c^
8*f^2 - 2*A*C*a^12*d^8*f^2 + 4*C^2*b^12*c^4*d^4*f^2 + 3*C^2*b^12*c^6*d^2*f^2 + 4*C^2*a^12*c^4*d^4*f^2 + 4*B^2*
b^12*c^4*d^4*f^2 + 4*B^2*b^12*c^2*d^6*f^2 + 3*C^2*a^12*c^2*d^6*f^2 + 3*B^2*b^12*c^6*d^2*f^2 + 33*C^2*a^8*b^4*d
^8*f^2 - 27*C^2*a^10*b^2*d^8*f^2 - 4*A^2*b^12*c^4*d^4*f^2 + 3*B^2*a^12*c^2*d^6*f^2 - C^2*a^6*b^6*d^8*f^2 - A^2
*b^12*c^6*d^2*f^2 + 33*C^2*a^4*b^8*c^8*f^2 + 33*B^2*a^10*b^2*d^8*f^2 - 27*C^2*a^2*b^10*c^8*f^2 - 27*B^2*a^8*b^
4*d^8*f^2 + 3*B^2*a^6*b^6*d^8*f^2 - C^2*a^6*b^6*c^8*f^2 - A^2*a^12*c^2*d^6*f^2 + 117*A^2*a^8*b^4*d^8*f^2 + 111
*A^2*a^6*b^6*d^8*f^2 + 72*A^2*a^4*b^8*d^8*f^2 + 33*B^2*a^2*b^10*c^8*f^2 - 27*B^2*a^4*b^8*c^8*f^2 + 24*A^2*a^2*
b^10*d^8*f^2 + 3*B^2*a^6*b^6*c^8*f^2 - 3*A^2*a^10*b^2*d^8*f^2 + 33*A^2*a^4*b^8*c^8*f^2 - 27*A^2*a^2*b^10*c^8*f
^2 - A^2*a^6*b^6*c^8*f^2 + 3*C^2*b^12*c^8*f^2 + 3*C^2*a^12*d^8*f^2 + 4*A^2*b^12*d^8*f^2 - B^2*b^12*c^8*f^2 - B
^2*a^12*d^8*f^2 + 3*A^2*b^12*c^8*f^2 + 3*A^2*a^12*d^8*f^2 - 24*A*B*C*a*b^8*c*d^6*f + 342*A*B*C*a^4*b^5*c^2*d^5
*f - 186*A*B*C*a^5*b^4*c^3*d^4*f - 66*A*B*C*a^2*b^7*c^4*d^3*f + 48*A*B*C*a^2*b^7*c^2*d^5*f + 42*A*B*C*a^6*b^3*
c^2*d^5*f + 26*A*B*C*a^3*b^6*c^5*d^2*f + 24*A*B*C*a^6*b^3*c^4*d^3*f - 18*A*B*C*a^7*b^2*c^3*d^4*f - 18*A*B*C*a^
4*b^5*c^4*d^3*f - 8*A*B*C*a^3*b^6*c^3*d^4*f + 6*A*B*C*a^5*b^4*c^5*d^2*f - 128*A*B*C*a^3*b^6*c*d^6*f + 126*A*B*
C*a^7*b^2*c*d^6*f + 72*A*B*C*a*b^8*c^3*d^4*f - 36*A*B*C*a^8*b*c^2*d^5*f - 36*A*B*C*a*b^8*c^5*d^2*f + 30*A*B*C*
a^2*b^7*c^6*d*f - 12*A*B*C*a^5*b^4*c*d^6*f - 12*A*B*C*a^4*b^5*c^6*d*f - 21*B^2*C*a^8*b*c*d^6*f - 3*B^2*C*a*b^8
*c^6*d*f + 21*A^2*C*a^8*b*c*d^6*f - 21*A*C^2*a^8*b*c*d^6*f - 9*A^2*C*a*b^8*c^6*d*f + 9*A*C^2*a*b^8*c^6*d*f + 3
6*A^2*B*a*b^8*c*d^6*f + 21*A*B^2*a^8*b*c*d^6*f + 3*A*B^2*a*b^8*c^6*d*f + 16*A*B*C*b^9*c^4*d^3*f - 16*A*B*C*b^9
*c^2*d^5*f - 78*A*B*C*a^6*b^3*d^7*f + 24*A*B*C*a^4*b^5*d^7*f + 2*A*B*C*a^3*b^6*c^7*f - 237*B^2*C*a^4*b^5*c^3*d
^4*f + 165*B*C^2*a^5*b^4*c^3*d^4*f + 92*B^2*C*a^3*b^6*c^2*d^5*f - 81*B^2*C*a^7*b^2*c^2*d^5*f + 77*B^2*C*a^3*b^
6*c^4*d^3*f - 75*B*C^2*a^4*b^5*c^2*d^5*f + 69*B^2*C*a^5*b^4*c^4*d^3*f + 69*B*C^2*a^4*b^5*c^4*d^3*f - 68*B*C^2*
a^3*b^6*c^3*d^4*f - 63*B^2*C*a^4*b^5*c^5*d^2*f - 61*B*C^2*a^6*b^3*c^2*d^5*f + 57*B*C^2*a^2*b^7*c^4*d^3*f - 53*
B*C^2*a^3*b^6*c^5*d^2*f - 44*B*C^2*a^6*b^3*c^4*d^3*f - 36*B^2*C*a^2*b^7*c^3*d^4*f + 35*B^2*C*a^6*b^3*c^3*d^4*f
- 33*B^2*C*a^5*b^4*c^2*d^5*f + 33*B^2*C*a^2*b^7*c^5*d^2*f + 33*B*C^2*a^7*b^2*c^3*d^4*f - 12*B^2*C*a^7*b^2*c^4
*d^3*f + 9*B*C^2*a^5*b^4*c^5*d^2*f + 4*B^2*C*a^6*b^3*c^5*d^2*f + 225*A^2*C*a^5*b^4*c^2*d^5*f - 105*A*C^2*a^5*b
^4*c^2*d^5*f - 99*A^2*C*a^4*b^5*c^3*d^4*f - 81*A^2*C*a^4*b^5*c^5*d^2*f + 67*A^2*C*a^3*b^6*c^4*d^3*f - 59*A*C^2
*a^3*b^6*c^4*d^3*f - 57*A*C^2*a^7*b^2*c^2*d^5*f + 57*A*C^2*a^2*b^7*c^5*d^2*f + 51*A^2*C*a^5*b^4*c^4*d^3*f + 48
*A^2*C*a^2*b^7*c^3*d^4*f + 45*A*C^2*a^4*b^5*c^5*d^2*f - 35*A^2*C*a^6*b^3*c^3*d^4*f + 33*A^2*C*a^7*b^2*c^2*d^5*
f - 33*A^2*C*a^2*b^7*c^5*d^2*f + 33*A*C^2*a^5*b^4*c^4*d^3*f + 27*A*C^2*a^6*b^3*c^3*d^4*f + 24*A*C^2*a^3*b^6*c^
2*d^5*f - 24*A*C^2*a^2*b^7*c^3*d^4*f - 21*A*C^2*a^4*b^5*c^3*d^4*f - 16*A^2*C*a^3*b^6*c^2*d^5*f - 243*A^2*B*a^4
*b^5*c^2*d^5*f - 156*A*B^2*a^3*b^6*c^2*d^5*f + 141*A*B^2*a^4*b^5*c^3*d^4*f + 108*A^2*B*a^3*b^6*c^3*d^4*f - 105
*A*B^2*a^3*b^6*c^4*d^3*f + 84*A*B^2*a^2*b^7*c^3*d^4*f + 81*A*B^2*a^5*b^4*c^2*d^5*f + 51*A^2*B*a^6*b^3*c^2*d^5*
f - 51*A^2*B*a^4*b^5*c^4*d^3*f - 48*A^2*B*a^2*b^7*c^2*d^5*f + 45*A^2*B*a^5*b^4*c^3*d^4*f + 39*A*B^2*a^4*b^5*c^
5*d^2*f - 35*A*B^2*a^6*b^3*c^3*d^4*f + 33*A*B^2*a^7*b^2*c^2*d^5*f + 27*A^2*B*a^3*b^6*c^5*d^2*f - 21*A*B^2*a^5*
b^4*c^4*d^3*f + 20*A^2*B*a^6*b^3*c^4*d^3*f - 15*A^2*B*a^7*b^2*c^3*d^4*f - 15*A^2*B*a^5*b^4*c^5*d^2*f + 9*A^2*B
*a^2*b^7*c^4*d^3*f + 3*A*B^2*a^2*b^7*c^5*d^2*f + 2*A*B*C*b^9*c^6*d*f - 6*A*B*C*a^9*c*d^6*f + 18*A*B*C*a^8*b*d^
7*f - 6*A*B*C*a*b^8*c^7*f + 63*B^2*C*a^6*b^3*c*d^6*f - 48*B^2*C*a*b^8*c^4*d^3*f + 42*B*C^2*a^8*b*c^2*d^5*f + 4
2*B*C^2*a^5*b^4*c*d^6*f - 39*B*C^2*a^7*b^2*c*d^6*f + 30*B*C^2*a*b^8*c^5*d^2*f - 24*B^2*C*a^4*b^5*c*d^6*f - 24*
B*C^2*a*b^8*c^3*d^4*f + 17*B^2*C*a^3*b^6*c^6*d*f - 15*B*C^2*a^2*b^7*c^6*d*f + 12*B^2*C*a^8*b*c^3*d^4*f + 12*B^
2*C*a*b^8*c^2*d^5*f + 6*B*C^2*a^4*b^5*c^6*d*f - 192*A^2*C*a^4*b^5*c*d^6*f - 99*A^2*C*a^6*b^3*c*d^6*f + 84*A*C^
2*a^4*b^5*c*d^6*f + 59*A*C^2*a^6*b^3*c*d^6*f + 51*A^2*C*a^3*b^6*c^6*d*f - 51*A*C^2*a^3*b^6*c^6*d*f - 36*A^2*C*
a*b^8*c^2*d^5*f - 24*A*C^2*a*b^8*c^4*d^3*f + 24*A*C^2*a*b^8*c^2*d^5*f + 12*A^2*C*a*b^8*c^4*d^3*f + 12*A*C^2*a^
8*b*c^3*d^4*f + 160*A^2*B*a^3*b^6*c*d^6*f - 99*A*B^2*a^6*b^3*c*d^6*f - 87*A^2*B*a^7*b^2*c*d^6*f - 72*A*B^2*a^4
*b^5*c*d^6*f - 48*A*B^2*a*b^8*c^2*d^5*f - 36*A^2*B*a*b^8*c^3*d^4*f + 24*A*B^2*a*b^8*c^4*d^3*f - 17*A*B^2*a^3*b
^6*c^6*d*f - 15*A^2*B*a^2*b^7*c^6*d*f + 12*A*B^2*a^2*b^7*c*d^6*f + 6*A^2*B*a^8*b*c^2*d^5*f - 6*A^2*B*a^5*b^4*c
*d^6*f + 6*A^2*B*a^4*b^5*c^6*d*f + 6*A^2*B*a*b^8*c^5*d^2*f + 12*B^2*C*b^9*c^3*d^4*f - 12*B*C^2*b^9*c^4*d^3*f -
12*A^2*C*b^9*c^3*d^4*f - 8*A*C^2*b^9*c^5*d^2*f + 8*A*C^2*b^9*c^3*d^4*f + 4*B^2*C*a^9*c^2*d^5*f + 4*A^2*C*b^9*
c^5*d^2*f - 4*B*C^2*a^9*c^3*d^4*f + 12*A^2*B*b^9*c^2*d^5*f - 8*A*B^2*b^9*c^3*d^4*f - 4*A^2*B*b^9*c^4*d^3*f + 4
*A*C^2*a^9*c^2*d^5*f + 3*B^2*C*a^7*b^2*d^7*f - B*C^2*a^6*b^3*d^7*f + 96*A^2*C*a^5*b^4*d^7*f - 39*A^2*C*a^7*b^2
*d^7*f - 36*A*C^2*a^5*b^4*d^7*f + 32*A^2*C*a^3*b^6*d^7*f + 15*A*C^2*a^7*b^2*d^7*f - 3*B^2*C*a^2*b^7*c^7*f - B*
C^2*a^3*b^6*c^7*f + 111*A^2*B*a^6*b^3*d^7*f - 39*A*B^2*a^7*b^2*d^7*f + 24*A*B^2*a^5*b^4*d^7*f - 9*A^2*C*a^2*b^
7*c^7*f + 9*A*C^2*a^2*b^7*c^7*f - 4*A*B^2*a^3*b^6*d^7*f + 3*A*B^2*a^2*b^7*c^7*f - A^2*B*a^3*b^6*c^7*f + 3*C^3*
a^8*b*c*d^6*f - 3*C^3*a*b^8*c^6*d*f - 3*A^3*a^8*b*c*d^6*f + 3*A^3*a*b^8*c^6*d*f - B*C^2*b^9*c^6*d*f + 4*A^2*C*
b^9*c*d^6*f + 3*B*C^2*a^9*c*d^6*f + 8*A*B^2*b^9*c*d^6*f + 3*B*C^2*a^8*b*d^7*f - A^2*B*b^9*c^6*d*f + 12*A^2*C*a
*b^8*d^7*f + 3*B*C^2*a*b^8*c^7*f - A^2*B*a^9*c*d^6*f - 9*A^2*B*a^8*b*d^7*f + 3*A^2*B*a*b^8*c^7*f - 39*C^3*a^5*
b^4*c^4*d^3*f + 39*C^3*a^4*b^5*c^3*d^4*f + 27*C^3*a^7*b^2*c^2*d^5*f - 27*C^3*a^2*b^7*c^5*d^2*f - 17*C^3*a^6*b^
3*c^3*d^4*f + 17*C^3*a^3*b^6*c^4*d^3*f + 3*C^3*a^5*b^4*c^2*d^5*f - 3*C^3*a^4*b^5*c^5*d^2*f - 63*B^3*a^5*b^4*c^
3*d^4*f + 57*B^3*a^4*b^5*c^2*d^5*f - 51*B^3*a^2*b^7*c^4*d^3*f + 48*B^3*a^3*b^6*c^3*d^4*f + 31*B^3*a^6*b^3*c^2*
d^5*f + 27*B^3*a^3*b^6*c^5*d^2*f + 16*B^3*a^6*b^3*c^4*d^3*f - 15*B^3*a^5*b^4*c^5*d^2*f - 12*B^3*a^2*b^7*c^2*d^
5*f + 9*B^3*a^4*b^5*c^4*d^3*f - 3*B^3*a^7*b^2*c^3*d^4*f - 123*A^3*a^5*b^4*c^2*d^5*f + 81*A^3*a^4*b^5*c^3*d^4*f
- 45*A^3*a^5*b^4*c^4*d^3*f + 39*A^3*a^4*b^5*c^5*d^2*f + 25*A^3*a^6*b^3*c^3*d^4*f - 25*A^3*a^3*b^6*c^4*d^3*f -
24*A^3*a^2*b^7*c^3*d^4*f - 8*A^3*a^3*b^6*c^2*d^5*f - 3*A^3*a^7*b^2*c^2*d^5*f + 3*A^3*a^2*b^7*c^5*d^2*f - 17*C
^3*a^6*b^3*c*d^6*f + 17*C^3*a^3*b^6*c^6*d*f - 12*C^3*a^8*b*c^3*d^4*f + 12*C^3*a*b^8*c^4*d^3*f + 24*B^3*a*b^8*c
^3*d^4*f + 21*B^3*a^7*b^2*c*d^6*f - 18*B^3*a^5*b^4*c*d^6*f - 15*B^3*a^2*b^7*c^6*d*f - 6*B^3*a^8*b*c^2*d^5*f +
6*B^3*a^4*b^5*c^6*d*f + 6*B^3*a*b^8*c^5*d^2*f + 4*B^3*a^3*b^6*c*d^6*f + 108*A^3*a^4*b^5*c*d^6*f + 57*A^3*a^6*b
^3*c*d^6*f - 17*A^3*a^3*b^6*c^6*d*f + 12*A^3*a*b^8*c^2*d^5*f + 4*C^3*b^9*c^5*d^2*f - 4*C^3*a^9*c^2*d^5*f - 4*B
^3*b^9*c^2*d^5*f + 4*A^3*b^9*c^3*d^4*f + 3*C^3*a^7*b^2*d^7*f - 3*C^3*a^2*b^7*c^7*f - B^3*a^6*b^3*d^7*f - 60*A^
3*a^5*b^4*d^7*f - 32*A^3*a^3*b^6*d^7*f + 21*A^3*a^7*b^2*d^7*f - B^3*a^3*b^6*c^7*f + 3*A^3*a^2*b^7*c^7*f - B^3*
b^9*c^6*d*f - 4*A^3*b^9*c*d^6*f - B^3*a^9*c*d^6*f + 3*B^3*a^8*b*d^7*f - 12*A^3*a*b^8*d^7*f + 3*B^3*a*b^8*c^7*f
- B^2*C*a^9*d^7*f - 4*A^2*B*b^9*d^7*f + 3*A^2*C*b^9*c^7*f - 3*A*C^2*b^9*c^7*f - A*C^2*a^9*d^7*f - A*B^2*b^9*c
^7*f - C^3*a^9*d^7*f - A^3*b^9*c^7*f + B^2*C*b^9*c^7*f + A^2*C*a^9*d^7*f + A*B^2*a^9*d^7*f + C^3*b^9*c^7*f + A
^3*a^9*d^7*f - 6*A*B^2*C*a^5*b*c*d^5 - 21*A^2*B*C*a^3*b^3*c^2*d^4 + 21*A*B*C^2*a^3*b^3*c^2*d^4 + 12*A*B^2*C*a^
4*b^2*c^2*d^4 - 12*A*B^2*C*a^2*b^4*c^2*d^4 - 10*A*B^2*C*a^3*b^3*c^3*d^3 - 6*A*B*C^2*a^4*b^2*c^3*d^3 + 3*A^2*B*
C*a^4*b^2*c^3*d^3 + 3*A^2*B*C*a^2*b^4*c^3*d^3 + 3*A*B^2*C*a^2*b^4*c^4*d^2 + 3*A*B*C^2*a^2*b^4*c^3*d^3 + 2*A*B*
C^2*a^3*b^3*c^4*d^2 - A^2*B*C*a^3*b^3*c^4*d^2 + 18*A^2*B*C*a^2*b^4*c*d^5 + 10*A*B^2*C*a^3*b^3*c*d^5 + 9*A^2*B*
C*a^4*b^2*c*d^5 - 9*A*B*C^2*a^4*b^2*c*d^5 - 9*A*B*C^2*a^2*b^4*c*d^5 - 6*A^2*B*C*a*b^5*c^2*d^4 + 6*A*B^2*C*a*b^
5*c^3*d^3 + 6*A*B*C^2*a^5*b*c^2*d^4 - 6*A*B*C^2*a*b^5*c^4*d^2 - 3*A^2*B*C*a^5*b*c^2*d^4 + 3*A^2*B*C*a*b^5*c^4*
d^2 + 3*A*B*C^2*a*b^5*c^2*d^4 - 3*B^3*C*a^5*b*c^2*d^4 + 3*B^3*C*a^4*b^2*c*d^5 + 3*B^3*C*a*b^5*c^4*d^2 + 3*B^2*
C^2*a^5*b*c*d^5 - 3*B*C^3*a^5*b*c^2*d^4 + 3*B*C^3*a^4*b^2*c*d^5 + 3*B*C^3*a*b^5*c^4*d^2 + 24*A^3*C*a^3*b^3*c*d
^5 + 8*A*C^3*a^3*b^3*c*d^5 - 9*A^3*B*a^2*b^4*c*d^5 - 9*A*B^3*a^2*b^4*c*d^5 - 3*A^3*B*a^4*b^2*c*d^5 + 3*A^3*B*a
*b^5*c^2*d^4 + 3*A^2*B^2*a^5*b*c*d^5 - 3*A*B^3*a^4*b^2*c*d^5 + 3*A*B^3*a*b^5*c^2*d^4 + 5*A*B*C^2*b^6*c^3*d^3 -
4*A^2*B*C*b^6*c^3*d^3 - A*B^2*C*b^6*c^4*d^2 - 3*A*B^2*C*a^4*b^2*d^6 - 2*A^2*B*C*a^3*b^3*d^6 + 9*B^2*C^2*a^3*b
^3*c^3*d^3 - 6*B^2*C^2*a^4*b^2*c^2*d^4 + 6*B^2*C^2*a^2*b^4*c^2*d^4 - 3*B^2*C^2*a^2*b^4*c^4*d^2 + 24*A^2*C^2*a^
3*b^3*c^3*d^3 - 15*A^2*C^2*a^4*b^2*c^2*d^4 - 9*A^2*C^2*a^2*b^4*c^4*d^2 + 3*A^2*C^2*a^2*b^4*c^2*d^4 + 9*A^2*B^2
*a^2*b^4*c^2*d^4 - 3*A^2*B^2*a^4*b^2*c^2*d^4 + 4*A^2*B*C*b^6*c*d^5 - 2*A*B*C^2*b^6*c*d^5 + 2*A*B*C^2*a^6*c*d^5
- A^2*B*C*a^6*c*d^5 + 6*A^2*B*C*a^5*b*d^6 - 3*A*B*C^2*a^5*b*d^6 - 7*B^3*C*a^3*b^3*c^2*d^4 - 7*B*C^3*a^3*b^3*c
^2*d^4 + 3*B^3*C*a^4*b^2*c^3*d^3 - 3*B^3*C*a^2*b^4*c^3*d^3 - 3*B^2*C^2*a*b^5*c^3*d^3 + 3*B*C^3*a^4*b^2*c^3*d^3
- 3*B*C^3*a^2*b^4*c^3*d^3 - B^3*C*a^3*b^3*c^4*d^2 - B^2*C^2*a^3*b^3*c*d^5 - B*C^3*a^3*b^3*c^4*d^2 - 24*A^2*C^
2*a^3*b^3*c*d^5 - 24*A*C^3*a^3*b^3*c^3*d^3 + 12*A*C^3*a^4*b^2*c^2*d^4 + 9*A*C^3*a^2*b^4*c^4*d^2 - 8*A^3*C*a^3*
b^3*c^3*d^3 + 6*A^3*C*a^4*b^2*c^2*d^4 - 6*A^3*C*a^2*b^4*c^2*d^4 + 3*A^3*C*a^2*b^4*c^4*d^2 - 9*A^2*B^2*a^3*b^3*
c*d^5 + 7*A^3*B*a^3*b^3*c^2*d^4 + 7*A*B^3*a^3*b^3*c^2*d^4 - 3*A^3*B*a^2*b^4*c^3*d^3 - 3*A^2*B^2*a*b^5*c^3*d^3
- 3*A*B^3*a^2*b^4*c^3*d^3 - 5*A^2*C^2*b^6*c^2*d^4 + 3*A^2*C^2*b^6*c^4*d^2 + 12*A^2*C^2*a^4*b^2*d^6 + 3*A^2*C^2
*a^2*b^4*d^6 + 6*A^2*B^2*a^4*b^2*d^6 + 3*A^2*B^2*a^2*b^4*d^6 + A*B*C^2*a^3*b^3*d^6 - 3*B^4*a*b^5*c^3*d^3 - B^4
*a^3*b^3*c*d^5 + A^2*B^2*a^3*b^3*c^3*d^3 - 8*A^4*a^3*b^3*c*d^5 - 2*B^3*C*b^6*c^3*d^3 - 2*B*C^3*b^6*c^3*d^3 + 4
*A^3*C*b^6*c^2*d^4 - 3*A*C^3*b^6*c^4*d^2 + 2*A*C^3*b^6*c^2*d^4 - A^3*C*b^6*c^4*d^2 - 2*A*C^3*a^6*c^2*d^4 - 15*
A^3*C*a^4*b^2*d^6 - 6*A^3*C*a^2*b^4*d^6 - 3*A*C^3*a^4*b^2*d^6 + 3*B^4*a^5*b*c*d^5 - B^3*C*a^6*c*d^5 - B*C^3*a^
6*c*d^5 - 2*A^3*B*b^6*c*d^5 - 2*A*B^3*b^6*c*d^5 - 3*A^3*B*a^5*b*d^6 - 3*A*B^3*a^5*b*d^6 + 8*C^4*a^3*b^3*c^3*d^
3 - 3*C^4*a^4*b^2*c^2*d^4 - 3*C^4*a^2*b^4*c^4*d^2 + 6*B^4*a^2*b^4*c^2*d^4 - 3*B^4*a^4*b^2*c^2*d^4 + 3*A^4*a^2*
b^4*c^2*d^4 + B^2*C^2*b^6*c^4*d^2 + B^2*C^2*b^6*c^2*d^4 + B^2*C^2*a^6*c^2*d^4 + A^2*C^2*a^6*c^2*d^4 - 2*A^3*C*
b^6*d^6 + A^3*B*b^6*c^3*d^3 + A*B^3*b^6*c^3*d^3 + A^3*B*a^3*b^3*d^6 + A*B^3*a^3*b^3*d^6 - A^4*b^6*c^2*d^4 + 6*
A^4*a^4*b^2*d^6 + 3*A^4*a^2*b^4*d^6 - 2*A^2*C^2*a^6*d^6 + A*B^2*C*a^6*d^6 + B^4*a^3*b^3*c^3*d^3 + A^3*C*a^6*d^
6 + A*C^3*a^6*d^6 + C^4*b^6*c^4*d^2 + C^4*a^6*c^2*d^4 + B^4*b^6*c^2*d^4 + A^2*C^2*b^6*d^6 + A^2*B^2*b^6*d^6 +
A^4*b^6*d^6, f, k)*(root(480*a^11*b^7*c*d^9*f^4 + 480*a^7*b^11*c^9*d*f^4 + 360*a^13*b^5*c*d^9*f^4 + 360*a^9*b^
9*c^9*d*f^4 + 360*a^9*b^9*c*d^9*f^4 + 360*a^5*b^13*c^9*d*f^4 + 144*a^15*b^3*c*d^9*f^4 + 144*a^11*b^7*c^9*d*f^4
+ 144*a^7*b^11*c*d^9*f^4 + 144*a^3*b^15*c^9*d*f^4 + 48*a^17*b*c^3*d^7*f^4 + 48*a*b^17*c^7*d^3*f^4 + 24*a^17*b
*c^5*d^5*f^4 + 24*a^13*b^5*c^9*d*f^4 + 24*a^5*b^13*c*d^9*f^4 + 24*a*b^17*c^5*d^5*f^4 + 24*a^17*b*c*d^9*f^4 + 2
4*a*b^17*c^9*d*f^4 + 3920*a^9*b^9*c^5*d^5*f^4 - 3360*a^10*b^8*c^4*d^6*f^4 - 3360*a^8*b^10*c^6*d^4*f^4 + 3024*a
^11*b^7*c^5*d^5*f^4 - 3024*a^10*b^8*c^6*d^4*f^4 - 3024*a^8*b^10*c^4*d^6*f^4 + 3024*a^7*b^11*c^5*d^5*f^4 + 2320
*a^9*b^9*c^7*d^3*f^4 + 2320*a^9*b^9*c^3*d^7*f^4 - 2240*a^12*b^6*c^4*d^6*f^4 - 2240*a^6*b^12*c^6*d^4*f^4 + 2160
*a^11*b^7*c^3*d^7*f^4 + 2160*a^7*b^11*c^7*d^3*f^4 - 1624*a^12*b^6*c^6*d^4*f^4 - 1624*a^6*b^12*c^4*d^6*f^4 + 14
88*a^11*b^7*c^7*d^3*f^4 + 1488*a^7*b^11*c^3*d^7*f^4 + 1344*a^13*b^5*c^5*d^5*f^4 + 1344*a^5*b^13*c^5*d^5*f^4 -
1320*a^10*b^8*c^2*d^8*f^4 - 1320*a^8*b^10*c^8*d^2*f^4 + 1200*a^13*b^5*c^3*d^7*f^4 + 1200*a^5*b^13*c^7*d^3*f^4
- 1060*a^12*b^6*c^2*d^8*f^4 - 1060*a^6*b^12*c^8*d^2*f^4 - 948*a^10*b^8*c^8*d^2*f^4 - 948*a^8*b^10*c^2*d^8*f^4
- 840*a^14*b^4*c^4*d^6*f^4 - 840*a^4*b^14*c^6*d^4*f^4 + 528*a^13*b^5*c^7*d^3*f^4 + 528*a^5*b^13*c^3*d^7*f^4 -
480*a^14*b^4*c^6*d^4*f^4 - 480*a^14*b^4*c^2*d^8*f^4 - 480*a^4*b^14*c^8*d^2*f^4 - 480*a^4*b^14*c^4*d^6*f^4 + 36
8*a^15*b^3*c^3*d^7*f^4 - 368*a^12*b^6*c^8*d^2*f^4 - 368*a^6*b^12*c^2*d^8*f^4 + 368*a^3*b^15*c^7*d^3*f^4 + 304*
a^15*b^3*c^5*d^5*f^4 + 304*a^3*b^15*c^5*d^5*f^4 - 144*a^16*b^2*c^4*d^6*f^4 - 144*a^2*b^16*c^6*d^4*f^4 - 108*a^
16*b^2*c^2*d^8*f^4 - 108*a^2*b^16*c^8*d^2*f^4 + 80*a^15*b^3*c^7*d^3*f^4 + 80*a^3*b^15*c^3*d^7*f^4 - 60*a^16*b^
2*c^6*d^4*f^4 - 60*a^14*b^4*c^8*d^2*f^4 - 60*a^4*b^14*c^2*d^8*f^4 - 60*a^2*b^16*c^4*d^6*f^4 - 8*b^18*c^8*d^2*f
^4 - 4*b^18*c^6*d^4*f^4 - 8*a^18*c^2*d^8*f^4 - 4*a^18*c^4*d^6*f^4 - 80*a^12*b^6*d^10*f^4 - 60*a^14*b^4*d^10*f^
4 - 60*a^10*b^8*d^10*f^4 - 24*a^16*b^2*d^10*f^4 - 24*a^8*b^10*d^10*f^4 - 4*a^6*b^12*d^10*f^4 - 80*a^6*b^12*c^1
0*f^4 - 60*a^8*b^10*c^10*f^4 - 60*a^4*b^14*c^10*f^4 - 24*a^10*b^8*c^10*f^4 - 24*a^2*b^16*c^10*f^4 - 4*a^12*b^6
*c^10*f^4 - 4*b^18*c^10*f^4 - 4*a^18*d^10*f^4 - 12*A*C*a^11*b*c*d^7*f^2 - 12*A*C*a*b^11*c^7*d*f^2 - 912*B*C*a^
5*b^7*c^4*d^4*f^2 - 792*B*C*a^8*b^4*c^3*d^5*f^2 + 792*B*C*a^4*b^8*c^5*d^3*f^2 + 720*B*C*a^7*b^5*c^4*d^4*f^2 -
480*B*C*a^5*b^7*c^6*d^2*f^2 - 408*B*C*a^5*b^7*c^2*d^6*f^2 + 384*B*C*a^7*b^5*c^2*d^6*f^2 - 336*B*C*a^8*b^4*c^5*
d^3*f^2 + 324*B*C*a^4*b^8*c^3*d^5*f^2 + 312*B*C*a^7*b^5*c^6*d^2*f^2 - 248*B*C*a^3*b^9*c^6*d^2*f^2 + 216*B*C*a^
9*b^3*c^2*d^6*f^2 - 196*B*C*a^3*b^9*c^4*d^4*f^2 + 132*B*C*a^9*b^3*c^4*d^4*f^2 + 80*B*C*a^6*b^6*c^3*d^5*f^2 - 6
4*B*C*a^6*b^6*c^5*d^3*f^2 - 36*B*C*a^2*b^10*c^3*d^5*f^2 - 28*B*C*a^3*b^9*c^2*d^6*f^2 + 12*B*C*a^10*b^2*c^5*d^3
*f^2 - 12*B*C*a^10*b^2*c^3*d^5*f^2 - 12*B*C*a^2*b^10*c^5*d^3*f^2 - 4*B*C*a^9*b^3*c^6*d^2*f^2 - 1468*A*C*a^6*b^
6*c^4*d^4*f^2 + 996*A*C*a^7*b^5*c^3*d^5*f^2 + 900*A*C*a^5*b^7*c^5*d^3*f^2 - 676*A*C*a^6*b^6*c^6*d^2*f^2 - 660*
A*C*a^6*b^6*c^2*d^6*f^2 + 636*A*C*a^5*b^7*c^3*d^5*f^2 + 540*A*C*a^7*b^5*c^5*d^3*f^2 - 236*A*C*a^3*b^9*c^5*d^3*
f^2 - 204*A*C*a^9*b^3*c^3*d^5*f^2 + 156*A*C*a^10*b^2*c^2*d^6*f^2 + 132*A*C*a^2*b^10*c^6*d^2*f^2 - 72*A*C*a^9*b
^3*c^5*d^3*f^2 - 72*A*C*a^4*b^8*c^6*d^2*f^2 + 66*A*C*a^4*b^8*c^2*d^6*f^2 + 54*A*C*a^10*b^2*c^4*d^4*f^2 + 54*A*
C*a^2*b^10*c^4*d^4*f^2 - 48*A*C*a^8*b^4*c^2*d^6*f^2 - 48*A*C*a^4*b^8*c^4*d^4*f^2 + 42*A*C*a^8*b^4*c^6*d^2*f^2
- 40*A*C*a^3*b^9*c^3*d^5*f^2 - 36*A*C*a^8*b^4*c^4*d^4*f^2 + 24*A*C*a^2*b^10*c^2*d^6*f^2 + 960*A*B*a^5*b^7*c^4*
d^4*f^2 - 864*A*B*a^4*b^8*c^5*d^3*f^2 + 756*A*B*a^8*b^4*c^3*d^5*f^2 - 744*A*B*a^7*b^5*c^4*d^4*f^2 - 528*A*B*a^
4*b^8*c^3*d^5*f^2 + 504*A*B*a^5*b^7*c^6*d^2*f^2 - 432*A*B*a^7*b^5*c^2*d^6*f^2 + 432*A*B*a^5*b^7*c^2*d^6*f^2 +
348*A*B*a^8*b^4*c^5*d^3*f^2 - 312*A*B*a^7*b^5*c^6*d^2*f^2 - 284*A*B*a^9*b^3*c^2*d^6*f^2 + 280*A*B*a^3*b^9*c^6*
d^2*f^2 + 264*A*B*a^3*b^9*c^4*d^4*f^2 - 240*A*B*a^6*b^6*c^3*d^5*f^2 - 172*A*B*a^9*b^3*c^4*d^4*f^2 + 68*A*B*a^3
*b^9*c^2*d^6*f^2 - 60*A*B*a^2*b^10*c^3*d^5*f^2 + 24*A*B*a^6*b^6*c^5*d^3*f^2 - 24*A*B*a^2*b^10*c^5*d^3*f^2 + 12
*A*B*a^10*b^2*c^3*d^5*f^2 + 360*B*C*a^4*b^8*c^7*d*f^2 - 336*B*C*a^8*b^4*c*d^7*f^2 + 168*B*C*a^6*b^6*c*d^7*f^2
- 136*B*C*a^6*b^6*c^7*d*f^2 - 36*B*C*a^11*b*c^2*d^6*f^2 + 36*B*C*a*b^11*c^6*d^2*f^2 + 24*B*C*a^10*b^2*c*d^7*f^
2 - 24*B*C*a^2*b^10*c^7*d*f^2 - 12*B*C*a^11*b*c^4*d^4*f^2 + 12*B*C*a^4*b^8*c*d^7*f^2 + 12*B*C*a*b^11*c^4*d^4*f
^2 + 444*A*C*a^7*b^5*c*d^7*f^2 + 348*A*C*a^5*b^7*c^7*d*f^2 - 164*A*C*a^3*b^9*c^7*d*f^2 - 132*A*C*a^9*b^3*c*d^7
*f^2 + 84*A*C*a^5*b^7*c*d^7*f^2 + 32*A*C*a^3*b^9*c*d^7*f^2 - 12*A*C*a^11*b*c^3*d^5*f^2 - 12*A*C*a^7*b^5*c^7*d*
f^2 - 12*A*C*a*b^11*c^5*d^3*f^2 - 360*A*B*a^4*b^8*c^7*d*f^2 + 288*A*B*a^8*b^4*c*d^7*f^2 - 288*A*B*a^6*b^6*c*d^
7*f^2 - 144*A*B*a^4*b^8*c*d^7*f^2 + 136*A*B*a^6*b^6*c^7*d*f^2 - 60*A*B*a^2*b^10*c*d^7*f^2 - 36*A*B*a^10*b^2*c*
d^7*f^2 + 24*A*B*a^2*b^10*c^7*d*f^2 - 24*A*B*a*b^11*c^6*d^2*f^2 + 12*A*B*a^11*b*c^2*d^6*f^2 + 12*A*B*a*b^11*c^
4*d^4*f^2 + 12*A*B*a*b^11*c^2*d^6*f^2 - 8*B*C*b^12*c^5*d^3*f^2 - 8*B*C*b^12*c^3*d^5*f^2 + 8*A*C*b^12*c^2*d^6*f
^2 - 4*B*C*a^12*c^3*d^5*f^2 + 4*A*C*b^12*c^4*d^4*f^2 - 2*A*C*b^12*c^6*d^2*f^2 + 80*B*C*a^9*b^3*d^8*f^2 - 24*B*
C*a^7*b^5*d^8*f^2 + 6*A*C*a^12*c^2*d^6*f^2 + 4*A*B*b^12*c^5*d^3*f^2 - 4*A*B*b^12*c^3*d^5*f^2 - 90*A*C*a^8*b^4*
d^8*f^2 - 80*B*C*a^3*b^9*c^8*f^2 + 54*A*C*a^10*b^2*d^8*f^2 - 30*A*C*a^6*b^6*d^8*f^2 + 24*B*C*a^5*b^7*c^8*f^2 -
12*A*C*a^4*b^8*d^8*f^2 - 112*A*B*a^9*b^3*d^8*f^2 - 66*A*C*a^4*b^8*c^8*f^2 + 54*A*C*a^2*b^10*c^8*f^2 + 4*A*B*a
^3*b^9*d^8*f^2 + 2*A*C*a^6*b^6*c^8*f^2 + 80*A*B*a^3*b^9*c^8*f^2 - 24*A*B*a^5*b^7*c^8*f^2 + 726*C^2*a^6*b^6*c^4
*d^4*f^2 - 402*C^2*a^7*b^5*c^3*d^5*f^2 - 402*C^2*a^5*b^7*c^5*d^3*f^2 + 322*C^2*a^6*b^6*c^6*d^2*f^2 + 322*C^2*a
^6*b^6*c^2*d^6*f^2 - 222*C^2*a^7*b^5*c^5*d^3*f^2 - 222*C^2*a^5*b^7*c^3*d^5*f^2 + 134*C^2*a^9*b^3*c^3*d^5*f^2 +
134*C^2*a^3*b^9*c^5*d^3*f^2 - 66*C^2*a^10*b^2*c^2*d^6*f^2 - 66*C^2*a^2*b^10*c^6*d^2*f^2 + 52*C^2*a^9*b^3*c^5*
d^3*f^2 + 52*C^2*a^3*b^9*c^3*d^5*f^2 - 27*C^2*a^8*b^4*c^6*d^2*f^2 - 27*C^2*a^4*b^8*c^2*d^6*f^2 + 24*C^2*a^8*b^
4*c^4*d^4*f^2 + 24*C^2*a^8*b^4*c^2*d^6*f^2 + 24*C^2*a^4*b^8*c^6*d^2*f^2 + 24*C^2*a^4*b^8*c^4*d^4*f^2 - 15*C^2*
a^10*b^2*c^4*d^4*f^2 - 15*C^2*a^2*b^10*c^4*d^4*f^2 - 570*B^2*a^6*b^6*c^4*d^4*f^2 + 366*B^2*a^7*b^5*c^3*d^5*f^2
+ 318*B^2*a^5*b^7*c^5*d^3*f^2 - 262*B^2*a^6*b^6*c^6*d^2*f^2 - 222*B^2*a^6*b^6*c^2*d^6*f^2 - 210*B^2*a^3*b^9*c
^5*d^3*f^2 + 186*B^2*a^7*b^5*c^5*d^3*f^2 + 162*B^2*a^5*b^7*c^3*d^5*f^2 - 142*B^2*a^9*b^3*c^3*d^5*f^2 + 132*B^2
*a^4*b^8*c^4*d^4*f^2 + 117*B^2*a^4*b^8*c^2*d^6*f^2 + 102*B^2*a^2*b^10*c^6*d^2*f^2 - 96*B^2*a^3*b^9*c^3*d^5*f^2
+ 90*B^2*a^10*b^2*c^2*d^6*f^2 + 81*B^2*a^2*b^10*c^4*d^4*f^2 - 56*B^2*a^9*b^3*c^5*d^3*f^2 + 48*B^2*a^8*b^4*c^4
*d^4*f^2 + 48*B^2*a^4*b^8*c^6*d^2*f^2 + 45*B^2*a^8*b^4*c^6*d^2*f^2 + 36*B^2*a^8*b^4*c^2*d^6*f^2 + 36*B^2*a^2*b
^10*c^2*d^6*f^2 + 33*B^2*a^10*b^2*c^4*d^4*f^2 + 822*A^2*a^6*b^6*c^4*d^4*f^2 - 594*A^2*a^7*b^5*c^3*d^5*f^2 + 49
8*A^2*a^6*b^6*c^2*d^6*f^2 - 498*A^2*a^5*b^7*c^5*d^3*f^2 - 414*A^2*a^5*b^7*c^3*d^5*f^2 + 354*A^2*a^6*b^6*c^6*d^
2*f^2 - 318*A^2*a^7*b^5*c^5*d^3*f^2 + 144*A^2*a^8*b^4*c^2*d^6*f^2 + 102*A^2*a^3*b^9*c^5*d^3*f^2 + 84*A^2*a^4*b
^8*c^4*d^4*f^2 + 81*A^2*a^4*b^8*c^2*d^6*f^2 + 72*A^2*a^8*b^4*c^4*d^4*f^2 + 70*A^2*a^9*b^3*c^3*d^5*f^2 - 66*A^2
*a^2*b^10*c^6*d^2*f^2 + 48*A^2*a^4*b^8*c^6*d^2*f^2 - 42*A^2*a^10*b^2*c^2*d^6*f^2 + 24*A^2*a^2*b^10*c^2*d^6*f^2
+ 20*A^2*a^9*b^3*c^5*d^3*f^2 - 15*A^2*a^10*b^2*c^4*d^4*f^2 - 15*A^2*a^8*b^4*c^6*d^2*f^2 - 15*A^2*a^2*b^10*c^4
*d^4*f^2 - 12*A^2*a^3*b^9*c^3*d^5*f^2 - 8*B*C*b^12*c^7*d*f^2 + 4*B*C*a^12*c*d^7*f^2 - 24*B*C*a^11*b*d^8*f^2 +
8*A*B*b^12*c^7*d*f^2 - 8*A*B*b^12*c*d^7*f^2 + 24*B*C*a*b^11*c^8*f^2 - 8*A*B*a^12*c*d^7*f^2 + 12*A*B*a^11*b*d^8
*f^2 - 24*A*B*a*b^11*c^8*f^2 - 174*C^2*a^7*b^5*c*d^7*f^2 - 174*C^2*a^5*b^7*c^7*d*f^2 + 82*C^2*a^9*b^3*c*d^7*f^
2 + 82*C^2*a^3*b^9*c^7*d*f^2 + 6*C^2*a^11*b*c^3*d^5*f^2 + 6*C^2*a^7*b^5*c^7*d*f^2 + 6*C^2*a^5*b^7*c*d^7*f^2 +
6*C^2*a*b^11*c^5*d^3*f^2 + 162*B^2*a^7*b^5*c*d^7*f^2 + 138*B^2*a^5*b^7*c^7*d*f^2 - 118*B^2*a^3*b^9*c^7*d*f^2 -
86*B^2*a^9*b^3*c*d^7*f^2 - 30*B^2*a*b^11*c^5*d^3*f^2 - 18*B^2*a^7*b^5*c^7*d*f^2 - 18*B^2*a^5*b^7*c*d^7*f^2 -
12*B^2*a*b^11*c^3*d^5*f^2 - 6*B^2*a^11*b*c^3*d^5*f^2 - 4*B^2*a^3*b^9*c*d^7*f^2 - 270*A^2*a^7*b^5*c*d^7*f^2 - 1
74*A^2*a^5*b^7*c^7*d*f^2 - 90*A^2*a^5*b^7*c*d^7*f^2 + 82*A^2*a^3*b^9*c^7*d*f^2 + 50*A^2*a^9*b^3*c*d^7*f^2 - 32
*A^2*a^3*b^9*c*d^7*f^2 + 6*A^2*a^11*b*c^3*d^5*f^2 + 6*A^2*a^7*b^5*c^7*d*f^2 + 6*A^2*a*b^11*c^5*d^3*f^2 + 6*C^2
*a^11*b*c*d^7*f^2 + 6*C^2*a*b^11*c^7*d*f^2 - 18*B^2*a*b^11*c^7*d*f^2 - 6*B^2*a^11*b*c*d^7*f^2 + 6*A^2*a^11*b*c
*d^7*f^2 + 6*A^2*a*b^11*c^7*d*f^2 - 6*A*C*b^12*c^8*f^2 - 2*A*C*a^12*d^8*f^2 + 4*C^2*b^12*c^4*d^4*f^2 + 3*C^2*b
^12*c^6*d^2*f^2 + 4*C^2*a^12*c^4*d^4*f^2 + 4*B^2*b^12*c^4*d^4*f^2 + 4*B^2*b^12*c^2*d^6*f^2 + 3*C^2*a^12*c^2*d^
6*f^2 + 3*B^2*b^12*c^6*d^2*f^2 + 33*C^2*a^8*b^4*d^8*f^2 - 27*C^2*a^10*b^2*d^8*f^2 - 4*A^2*b^12*c^4*d^4*f^2 + 3
*B^2*a^12*c^2*d^6*f^2 - C^2*a^6*b^6*d^8*f^2 - A^2*b^12*c^6*d^2*f^2 + 33*C^2*a^4*b^8*c^8*f^2 + 33*B^2*a^10*b^2*
d^8*f^2 - 27*C^2*a^2*b^10*c^8*f^2 - 27*B^2*a^8*b^4*d^8*f^2 + 3*B^2*a^6*b^6*d^8*f^2 - C^2*a^6*b^6*c^8*f^2 - A^2
*a^12*c^2*d^6*f^2 + 117*A^2*a^8*b^4*d^8*f^2 + 111*A^2*a^6*b^6*d^8*f^2 + 72*A^2*a^4*b^8*d^8*f^2 + 33*B^2*a^2*b^
10*c^8*f^2 - 27*B^2*a^4*b^8*c^8*f^2 + 24*A^2*a^2*b^10*d^8*f^2 + 3*B^2*a^6*b^6*c^8*f^2 - 3*A^2*a^10*b^2*d^8*f^2
+ 33*A^2*a^4*b^8*c^8*f^2 - 27*A^2*a^2*b^10*c^8*f^2 - A^2*a^6*b^6*c^8*f^2 + 3*C^2*b^12*c^8*f^2 + 3*C^2*a^12*d^
8*f^2 + 4*A^2*b^12*d^8*f^2 - B^2*b^12*c^8*f^2 - B^2*a^12*d^8*f^2 + 3*A^2*b^12*c^8*f^2 + 3*A^2*a^12*d^8*f^2 - 2
4*A*B*C*a*b^8*c*d^6*f + 342*A*B*C*a^4*b^5*c^2*d^5*f - 186*A*B*C*a^5*b^4*c^3*d^4*f - 66*A*B*C*a^2*b^7*c^4*d^3*f
+ 48*A*B*C*a^2*b^7*c^2*d^5*f + 42*A*B*C*a^6*b^3*c^2*d^5*f + 26*A*B*C*a^3*b^6*c^5*d^2*f + 24*A*B*C*a^6*b^3*c^4
*d^3*f - 18*A*B*C*a^7*b^2*c^3*d^4*f - 18*A*B*C*a^4*b^5*c^4*d^3*f - 8*A*B*C*a^3*b^6*c^3*d^4*f + 6*A*B*C*a^5*b^4
*c^5*d^2*f - 128*A*B*C*a^3*b^6*c*d^6*f + 126*A*B*C*a^7*b^2*c*d^6*f + 72*A*B*C*a*b^8*c^3*d^4*f - 36*A*B*C*a^8*b
*c^2*d^5*f - 36*A*B*C*a*b^8*c^5*d^2*f + 30*A*B*C*a^2*b^7*c^6*d*f - 12*A*B*C*a^5*b^4*c*d^6*f - 12*A*B*C*a^4*b^5
*c^6*d*f - 21*B^2*C*a^8*b*c*d^6*f - 3*B^2*C*a*b^8*c^6*d*f + 21*A^2*C*a^8*b*c*d^6*f - 21*A*C^2*a^8*b*c*d^6*f -
9*A^2*C*a*b^8*c^6*d*f + 9*A*C^2*a*b^8*c^6*d*f + 36*A^2*B*a*b^8*c*d^6*f + 21*A*B^2*a^8*b*c*d^6*f + 3*A*B^2*a*b^
8*c^6*d*f + 16*A*B*C*b^9*c^4*d^3*f - 16*A*B*C*b^9*c^2*d^5*f - 78*A*B*C*a^6*b^3*d^7*f + 24*A*B*C*a^4*b^5*d^7*f
+ 2*A*B*C*a^3*b^6*c^7*f - 237*B^2*C*a^4*b^5*c^3*d^4*f + 165*B*C^2*a^5*b^4*c^3*d^4*f + 92*B^2*C*a^3*b^6*c^2*d^5
*f - 81*B^2*C*a^7*b^2*c^2*d^5*f + 77*B^2*C*a^3*b^6*c^4*d^3*f - 75*B*C^2*a^4*b^5*c^2*d^5*f + 69*B^2*C*a^5*b^4*c
^4*d^3*f + 69*B*C^2*a^4*b^5*c^4*d^3*f - 68*B*C^2*a^3*b^6*c^3*d^4*f - 63*B^2*C*a^4*b^5*c^5*d^2*f - 61*B*C^2*a^6
*b^3*c^2*d^5*f + 57*B*C^2*a^2*b^7*c^4*d^3*f - 53*B*C^2*a^3*b^6*c^5*d^2*f - 44*B*C^2*a^6*b^3*c^4*d^3*f - 36*B^2
*C*a^2*b^7*c^3*d^4*f + 35*B^2*C*a^6*b^3*c^3*d^4*f - 33*B^2*C*a^5*b^4*c^2*d^5*f + 33*B^2*C*a^2*b^7*c^5*d^2*f +
33*B*C^2*a^7*b^2*c^3*d^4*f - 12*B^2*C*a^7*b^2*c^4*d^3*f + 9*B*C^2*a^5*b^4*c^5*d^2*f + 4*B^2*C*a^6*b^3*c^5*d^2*
f + 225*A^2*C*a^5*b^4*c^2*d^5*f - 105*A*C^2*a^5*b^4*c^2*d^5*f - 99*A^2*C*a^4*b^5*c^3*d^4*f - 81*A^2*C*a^4*b^5*
c^5*d^2*f + 67*A^2*C*a^3*b^6*c^4*d^3*f - 59*A*C^2*a^3*b^6*c^4*d^3*f - 57*A*C^2*a^7*b^2*c^2*d^5*f + 57*A*C^2*a^
2*b^7*c^5*d^2*f + 51*A^2*C*a^5*b^4*c^4*d^3*f + 48*A^2*C*a^2*b^7*c^3*d^4*f + 45*A*C^2*a^4*b^5*c^5*d^2*f - 35*A^
2*C*a^6*b^3*c^3*d^4*f + 33*A^2*C*a^7*b^2*c^2*d^5*f - 33*A^2*C*a^2*b^7*c^5*d^2*f + 33*A*C^2*a^5*b^4*c^4*d^3*f +
27*A*C^2*a^6*b^3*c^3*d^4*f + 24*A*C^2*a^3*b^6*c^2*d^5*f - 24*A*C^2*a^2*b^7*c^3*d^4*f - 21*A*C^2*a^4*b^5*c^3*d
^4*f - 16*A^2*C*a^3*b^6*c^2*d^5*f - 243*A^2*B*a^4*b^5*c^2*d^5*f - 156*A*B^2*a^3*b^6*c^2*d^5*f + 141*A*B^2*a^4*
b^5*c^3*d^4*f + 108*A^2*B*a^3*b^6*c^3*d^4*f - 105*A*B^2*a^3*b^6*c^4*d^3*f + 84*A*B^2*a^2*b^7*c^3*d^4*f + 81*A*
B^2*a^5*b^4*c^2*d^5*f + 51*A^2*B*a^6*b^3*c^2*d^5*f - 51*A^2*B*a^4*b^5*c^4*d^3*f - 48*A^2*B*a^2*b^7*c^2*d^5*f +
45*A^2*B*a^5*b^4*c^3*d^4*f + 39*A*B^2*a^4*b^5*c^5*d^2*f - 35*A*B^2*a^6*b^3*c^3*d^4*f + 33*A*B^2*a^7*b^2*c^2*d
^5*f + 27*A^2*B*a^3*b^6*c^5*d^2*f - 21*A*B^2*a^5*b^4*c^4*d^3*f + 20*A^2*B*a^6*b^3*c^4*d^3*f - 15*A^2*B*a^7*b^2
*c^3*d^4*f - 15*A^2*B*a^5*b^4*c^5*d^2*f + 9*A^2*B*a^2*b^7*c^4*d^3*f + 3*A*B^2*a^2*b^7*c^5*d^2*f + 2*A*B*C*b^9*
c^6*d*f - 6*A*B*C*a^9*c*d^6*f + 18*A*B*C*a^8*b*d^7*f - 6*A*B*C*a*b^8*c^7*f + 63*B^2*C*a^6*b^3*c*d^6*f - 48*B^2
*C*a*b^8*c^4*d^3*f + 42*B*C^2*a^8*b*c^2*d^5*f + 42*B*C^2*a^5*b^4*c*d^6*f - 39*B*C^2*a^7*b^2*c*d^6*f + 30*B*C^2
*a*b^8*c^5*d^2*f - 24*B^2*C*a^4*b^5*c*d^6*f - 24*B*C^2*a*b^8*c^3*d^4*f + 17*B^2*C*a^3*b^6*c^6*d*f - 15*B*C^2*a
^2*b^7*c^6*d*f + 12*B^2*C*a^8*b*c^3*d^4*f + 12*B^2*C*a*b^8*c^2*d^5*f + 6*B*C^2*a^4*b^5*c^6*d*f - 192*A^2*C*a^4
*b^5*c*d^6*f - 99*A^2*C*a^6*b^3*c*d^6*f + 84*A*C^2*a^4*b^5*c*d^6*f + 59*A*C^2*a^6*b^3*c*d^6*f + 51*A^2*C*a^3*b
^6*c^6*d*f - 51*A*C^2*a^3*b^6*c^6*d*f - 36*A^2*C*a*b^8*c^2*d^5*f - 24*A*C^2*a*b^8*c^4*d^3*f + 24*A*C^2*a*b^8*c
^2*d^5*f + 12*A^2*C*a*b^8*c^4*d^3*f + 12*A*C^2*a^8*b*c^3*d^4*f + 160*A^2*B*a^3*b^6*c*d^6*f - 99*A*B^2*a^6*b^3*
c*d^6*f - 87*A^2*B*a^7*b^2*c*d^6*f - 72*A*B^2*a^4*b^5*c*d^6*f - 48*A*B^2*a*b^8*c^2*d^5*f - 36*A^2*B*a*b^8*c^3*
d^4*f + 24*A*B^2*a*b^8*c^4*d^3*f - 17*A*B^2*a^3*b^6*c^6*d*f - 15*A^2*B*a^2*b^7*c^6*d*f + 12*A*B^2*a^2*b^7*c*d^
6*f + 6*A^2*B*a^8*b*c^2*d^5*f - 6*A^2*B*a^5*b^4*c*d^6*f + 6*A^2*B*a^4*b^5*c^6*d*f + 6*A^2*B*a*b^8*c^5*d^2*f +
12*B^2*C*b^9*c^3*d^4*f - 12*B*C^2*b^9*c^4*d^3*f - 12*A^2*C*b^9*c^3*d^4*f - 8*A*C^2*b^9*c^5*d^2*f + 8*A*C^2*b^9
*c^3*d^4*f + 4*B^2*C*a^9*c^2*d^5*f + 4*A^2*C*b^9*c^5*d^2*f - 4*B*C^2*a^9*c^3*d^4*f + 12*A^2*B*b^9*c^2*d^5*f -
8*A*B^2*b^9*c^3*d^4*f - 4*A^2*B*b^9*c^4*d^3*f + 4*A*C^2*a^9*c^2*d^5*f + 3*B^2*C*a^7*b^2*d^7*f - B*C^2*a^6*b^3*
d^7*f + 96*A^2*C*a^5*b^4*d^7*f - 39*A^2*C*a^7*b^2*d^7*f - 36*A*C^2*a^5*b^4*d^7*f + 32*A^2*C*a^3*b^6*d^7*f + 15
*A*C^2*a^7*b^2*d^7*f - 3*B^2*C*a^2*b^7*c^7*f - B*C^2*a^3*b^6*c^7*f + 111*A^2*B*a^6*b^3*d^7*f - 39*A*B^2*a^7*b^
2*d^7*f + 24*A*B^2*a^5*b^4*d^7*f - 9*A^2*C*a^2*b^7*c^7*f + 9*A*C^2*a^2*b^7*c^7*f - 4*A*B^2*a^3*b^6*d^7*f + 3*A
*B^2*a^2*b^7*c^7*f - A^2*B*a^3*b^6*c^7*f + 3*C^3*a^8*b*c*d^6*f - 3*C^3*a*b^8*c^6*d*f - 3*A^3*a^8*b*c*d^6*f + 3
*A^3*a*b^8*c^6*d*f - B*C^2*b^9*c^6*d*f + 4*A^2*C*b^9*c*d^6*f + 3*B*C^2*a^9*c*d^6*f + 8*A*B^2*b^9*c*d^6*f + 3*B
*C^2*a^8*b*d^7*f - A^2*B*b^9*c^6*d*f + 12*A^2*C*a*b^8*d^7*f + 3*B*C^2*a*b^8*c^7*f - A^2*B*a^9*c*d^6*f - 9*A^2*
B*a^8*b*d^7*f + 3*A^2*B*a*b^8*c^7*f - 39*C^3*a^5*b^4*c^4*d^3*f + 39*C^3*a^4*b^5*c^3*d^4*f + 27*C^3*a^7*b^2*c^2
*d^5*f - 27*C^3*a^2*b^7*c^5*d^2*f - 17*C^3*a^6*b^3*c^3*d^4*f + 17*C^3*a^3*b^6*c^4*d^3*f + 3*C^3*a^5*b^4*c^2*d^
5*f - 3*C^3*a^4*b^5*c^5*d^2*f - 63*B^3*a^5*b^4*c^3*d^4*f + 57*B^3*a^4*b^5*c^2*d^5*f - 51*B^3*a^2*b^7*c^4*d^3*f
+ 48*B^3*a^3*b^6*c^3*d^4*f + 31*B^3*a^6*b^3*c^2*d^5*f + 27*B^3*a^3*b^6*c^5*d^2*f + 16*B^3*a^6*b^3*c^4*d^3*f -
15*B^3*a^5*b^4*c^5*d^2*f - 12*B^3*a^2*b^7*c^2*d^5*f + 9*B^3*a^4*b^5*c^4*d^3*f - 3*B^3*a^7*b^2*c^3*d^4*f - 123
*A^3*a^5*b^4*c^2*d^5*f + 81*A^3*a^4*b^5*c^3*d^4*f - 45*A^3*a^5*b^4*c^4*d^3*f + 39*A^3*a^4*b^5*c^5*d^2*f + 25*A
^3*a^6*b^3*c^3*d^4*f - 25*A^3*a^3*b^6*c^4*d^3*f - 24*A^3*a^2*b^7*c^3*d^4*f - 8*A^3*a^3*b^6*c^2*d^5*f - 3*A^3*a
^7*b^2*c^2*d^5*f + 3*A^3*a^2*b^7*c^5*d^2*f - 17*C^3*a^6*b^3*c*d^6*f + 17*C^3*a^3*b^6*c^6*d*f - 12*C^3*a^8*b*c^
3*d^4*f + 12*C^3*a*b^8*c^4*d^3*f + 24*B^3*a*b^8*c^3*d^4*f + 21*B^3*a^7*b^2*c*d^6*f - 18*B^3*a^5*b^4*c*d^6*f -
15*B^3*a^2*b^7*c^6*d*f - 6*B^3*a^8*b*c^2*d^5*f + 6*B^3*a^4*b^5*c^6*d*f + 6*B^3*a*b^8*c^5*d^2*f + 4*B^3*a^3*b^6
*c*d^6*f + 108*A^3*a^4*b^5*c*d^6*f + 57*A^3*a^6*b^3*c*d^6*f - 17*A^3*a^3*b^6*c^6*d*f + 12*A^3*a*b^8*c^2*d^5*f
+ 4*C^3*b^9*c^5*d^2*f - 4*C^3*a^9*c^2*d^5*f - 4*B^3*b^9*c^2*d^5*f + 4*A^3*b^9*c^3*d^4*f + 3*C^3*a^7*b^2*d^7*f
- 3*C^3*a^2*b^7*c^7*f - B^3*a^6*b^3*d^7*f - 60*A^3*a^5*b^4*d^7*f - 32*A^3*a^3*b^6*d^7*f + 21*A^3*a^7*b^2*d^7*f
- B^3*a^3*b^6*c^7*f + 3*A^3*a^2*b^7*c^7*f - B^3*b^9*c^6*d*f - 4*A^3*b^9*c*d^6*f - B^3*a^9*c*d^6*f + 3*B^3*a^8
*b*d^7*f - 12*A^3*a*b^8*d^7*f + 3*B^3*a*b^8*c^7*f - B^2*C*a^9*d^7*f - 4*A^2*B*b^9*d^7*f + 3*A^2*C*b^9*c^7*f -
3*A*C^2*b^9*c^7*f - A*C^2*a^9*d^7*f - A*B^2*b^9*c^7*f - C^3*a^9*d^7*f - A^3*b^9*c^7*f + B^2*C*b^9*c^7*f + A^2*
C*a^9*d^7*f + A*B^2*a^9*d^7*f + C^3*b^9*c^7*f + A^3*a^9*d^7*f - 6*A*B^2*C*a^5*b*c*d^5 - 21*A^2*B*C*a^3*b^3*c^2
*d^4 + 21*A*B*C^2*a^3*b^3*c^2*d^4 + 12*A*B^2*C*a^4*b^2*c^2*d^4 - 12*A*B^2*C*a^2*b^4*c^2*d^4 - 10*A*B^2*C*a^3*b
^3*c^3*d^3 - 6*A*B*C^2*a^4*b^2*c^3*d^3 + 3*A^2*B*C*a^4*b^2*c^3*d^3 + 3*A^2*B*C*a^2*b^4*c^3*d^3 + 3*A*B^2*C*a^2
*b^4*c^4*d^2 + 3*A*B*C^2*a^2*b^4*c^3*d^3 + 2*A*B*C^2*a^3*b^3*c^4*d^2 - A^2*B*C*a^3*b^3*c^4*d^2 + 18*A^2*B*C*a^
2*b^4*c*d^5 + 10*A*B^2*C*a^3*b^3*c*d^5 + 9*A^2*B*C*a^4*b^2*c*d^5 - 9*A*B*C^2*a^4*b^2*c*d^5 - 9*A*B*C^2*a^2*b^4
*c*d^5 - 6*A^2*B*C*a*b^5*c^2*d^4 + 6*A*B^2*C*a*b^5*c^3*d^3 + 6*A*B*C^2*a^5*b*c^2*d^4 - 6*A*B*C^2*a*b^5*c^4*d^2
- 3*A^2*B*C*a^5*b*c^2*d^4 + 3*A^2*B*C*a*b^5*c^4*d^2 + 3*A*B*C^2*a*b^5*c^2*d^4 - 3*B^3*C*a^5*b*c^2*d^4 + 3*B^3
*C*a^4*b^2*c*d^5 + 3*B^3*C*a*b^5*c^4*d^2 + 3*B^2*C^2*a^5*b*c*d^5 - 3*B*C^3*a^5*b*c^2*d^4 + 3*B*C^3*a^4*b^2*c*d
^5 + 3*B*C^3*a*b^5*c^4*d^2 + 24*A^3*C*a^3*b^3*c*d^5 + 8*A*C^3*a^3*b^3*c*d^5 - 9*A^3*B*a^2*b^4*c*d^5 - 9*A*B^3*
a^2*b^4*c*d^5 - 3*A^3*B*a^4*b^2*c*d^5 + 3*A^3*B*a*b^5*c^2*d^4 + 3*A^2*B^2*a^5*b*c*d^5 - 3*A*B^3*a^4*b^2*c*d^5
+ 3*A*B^3*a*b^5*c^2*d^4 + 5*A*B*C^2*b^6*c^3*d^3 - 4*A^2*B*C*b^6*c^3*d^3 - A*B^2*C*b^6*c^4*d^2 - 3*A*B^2*C*a^4*
b^2*d^6 - 2*A^2*B*C*a^3*b^3*d^6 + 9*B^2*C^2*a^3*b^3*c^3*d^3 - 6*B^2*C^2*a^4*b^2*c^2*d^4 + 6*B^2*C^2*a^2*b^4*c^
2*d^4 - 3*B^2*C^2*a^2*b^4*c^4*d^2 + 24*A^2*C^2*a^3*b^3*c^3*d^3 - 15*A^2*C^2*a^4*b^2*c^2*d^4 - 9*A^2*C^2*a^2*b^
4*c^4*d^2 + 3*A^2*C^2*a^2*b^4*c^2*d^4 + 9*A^2*B^2*a^2*b^4*c^2*d^4 - 3*A^2*B^2*a^4*b^2*c^2*d^4 + 4*A^2*B*C*b^6*
c*d^5 - 2*A*B*C^2*b^6*c*d^5 + 2*A*B*C^2*a^6*c*d^5 - A^2*B*C*a^6*c*d^5 + 6*A^2*B*C*a^5*b*d^6 - 3*A*B*C^2*a^5*b*
d^6 - 7*B^3*C*a^3*b^3*c^2*d^4 - 7*B*C^3*a^3*b^3*c^2*d^4 + 3*B^3*C*a^4*b^2*c^3*d^3 - 3*B^3*C*a^2*b^4*c^3*d^3 -
3*B^2*C^2*a*b^5*c^3*d^3 + 3*B*C^3*a^4*b^2*c^3*d^3 - 3*B*C^3*a^2*b^4*c^3*d^3 - B^3*C*a^3*b^3*c^4*d^2 - B^2*C^2*
a^3*b^3*c*d^5 - B*C^3*a^3*b^3*c^4*d^2 - 24*A^2*C^2*a^3*b^3*c*d^5 - 24*A*C^3*a^3*b^3*c^3*d^3 + 12*A*C^3*a^4*b^2
*c^2*d^4 + 9*A*C^3*a^2*b^4*c^4*d^2 - 8*A^3*C*a^3*b^3*c^3*d^3 + 6*A^3*C*a^4*b^2*c^2*d^4 - 6*A^3*C*a^2*b^4*c^2*d
^4 + 3*A^3*C*a^2*b^4*c^4*d^2 - 9*A^2*B^2*a^3*b^3*c*d^5 + 7*A^3*B*a^3*b^3*c^2*d^4 + 7*A*B^3*a^3*b^3*c^2*d^4 - 3
*A^3*B*a^2*b^4*c^3*d^3 - 3*A^2*B^2*a*b^5*c^3*d^3 - 3*A*B^3*a^2*b^4*c^3*d^3 - 5*A^2*C^2*b^6*c^2*d^4 + 3*A^2*C^2
*b^6*c^4*d^2 + 12*A^2*C^2*a^4*b^2*d^6 + 3*A^2*C^2*a^2*b^4*d^6 + 6*A^2*B^2*a^4*b^2*d^6 + 3*A^2*B^2*a^2*b^4*d^6
+ A*B*C^2*a^3*b^3*d^6 - 3*B^4*a*b^5*c^3*d^3 - B^4*a^3*b^3*c*d^5 + A^2*B^2*a^3*b^3*c^3*d^3 - 8*A^4*a^3*b^3*c*d^
5 - 2*B^3*C*b^6*c^3*d^3 - 2*B*C^3*b^6*c^3*d^3 + 4*A^3*C*b^6*c^2*d^4 - 3*A*C^3*b^6*c^4*d^2 + 2*A*C^3*b^6*c^2*d^
4 - A^3*C*b^6*c^4*d^2 - 2*A*C^3*a^6*c^2*d^4 - 15*A^3*C*a^4*b^2*d^6 - 6*A^3*C*a^2*b^4*d^6 - 3*A*C^3*a^4*b^2*d^6
+ 3*B^4*a^5*b*c*d^5 - B^3*C*a^6*c*d^5 - B*C^3*a^6*c*d^5 - 2*A^3*B*b^6*c*d^5 - 2*A*B^3*b^6*c*d^5 - 3*A^3*B*a^5
*b*d^6 - 3*A*B^3*a^5*b*d^6 + 8*C^4*a^3*b^3*c^3*d^3 - 3*C^4*a^4*b^2*c^2*d^4 - 3*C^4*a^2*b^4*c^4*d^2 + 6*B^4*a^2
*b^4*c^2*d^4 - 3*B^4*a^4*b^2*c^2*d^4 + 3*A^4*a^2*b^4*c^2*d^4 + B^2*C^2*b^6*c^4*d^2 + B^2*C^2*b^6*c^2*d^4 + B^2
*C^2*a^6*c^2*d^4 + A^2*C^2*a^6*c^2*d^4 - 2*A^3*C*b^6*d^6 + A^3*B*b^6*c^3*d^3 + A*B^3*b^6*c^3*d^3 + A^3*B*a^3*b
^3*d^6 + A*B^3*a^3*b^3*d^6 - A^4*b^6*c^2*d^4 + 6*A^4*a^4*b^2*d^6 + 3*A^4*a^2*b^4*d^6 - 2*A^2*C^2*a^6*d^6 + A*B
^2*C*a^6*d^6 + B^4*a^3*b^3*c^3*d^3 + A^3*C*a^6*d^6 + A*C^3*a^6*d^6 + C^4*b^6*c^4*d^2 + C^4*a^6*c^2*d^4 + B^4*b
^6*c^2*d^4 + A^2*C^2*b^6*d^6 + A^2*B^2*b^6*d^6 + A^4*b^6*d^6, f, k)*((B*b^14*c^7*d - B*a^13*b*d^8 - 4*A*a^2*b^
12*d^8 - 16*A*a^4*b^10*d^8 - 35*A*a^6*b^8*d^8 - 33*A*a^8*b^6*d^8 - 5*A*a^10*b^4*d^8 + 5*A*a^12*b^2*d^8 - 4*B*a
^5*b^9*d^8 + 3*B*a^7*b^7*d^8 + 17*B*a^9*b^5*d^8 + 9*B*a^11*b^3*d^8 - 4*A*b^14*c^2*d^6 + 4*A*b^14*c^4*d^4 - 3*A
*b^14*c^6*d^2 + 11*C*a^6*b^8*d^8 + 17*C*a^8*b^6*d^8 + C*a^10*b^4*d^8 - 5*C*a^12*b^2*d^8 + 4*B*b^14*c^3*d^5 - 4
*B*b^14*c^5*d^3 - 4*C*b^14*c^4*d^4 + 3*C*b^14*c^6*d^2 - 6*A*a*b^13*c^5*d^3 + 40*A*a^3*b^11*c*d^7 + 3*A*a^3*b^1
1*c^7*d + 122*A*a^5*b^9*c*d^7 + 3*A*a^5*b^9*c^7*d + 175*A*a^7*b^7*c*d^7 + A*a^7*b^7*c^7*d + 105*A*a^9*b^5*c*d^
7 + 21*A*a^11*b^3*c*d^7 - 8*B*a*b^13*c^2*d^6 - 4*B*a*b^13*c^4*d^4 + 5*B*a*b^13*c^6*d^2 + 4*B*a^2*b^12*c*d^7 +
3*B*a^2*b^12*c^7*d + 32*B*a^4*b^10*c*d^7 + 3*B*a^4*b^10*c^7*d + 31*B*a^6*b^8*c*d^7 + B*a^6*b^8*c^7*d - 27*B*a^
8*b^6*c*d^7 - 39*B*a^10*b^4*c*d^7 - 9*B*a^12*b^2*c*d^7 + 8*C*a*b^13*c^3*d^5 + 10*C*a*b^13*c^5*d^3 - 3*C*a^3*b^
11*c^7*d - 38*C*a^5*b^9*c*d^7 - 3*C*a^5*b^9*c^7*d - 79*C*a^7*b^7*c*d^7 - C*a^7*b^7*c^7*d - 41*C*a^9*b^5*c*d^7
+ 3*C*a^11*b^3*c*d^7 - 28*A*a^2*b^12*c^2*d^6 + 43*A*a^2*b^12*c^4*d^4 + A*a^2*b^12*c^6*d^2 - 4*A*a^3*b^11*c^3*d
^5 - 35*A*a^3*b^11*c^5*d^3 - 117*A*a^4*b^10*c^2*d^6 + 69*A*a^4*b^10*c^4*d^4 + 5*A*a^4*b^10*c^6*d^2 + 67*A*a^5*
b^9*c^3*d^5 - 37*A*a^5*b^9*c^5*d^3 - 245*A*a^6*b^8*c^2*d^6 + 5*A*a^6*b^8*c^4*d^4 - 5*A*a^6*b^8*c^6*d^2 + 161*A
*a^7*b^7*c^3*d^5 + 7*A*a^7*b^7*c^5*d^3 - 237*A*a^8*b^6*c^2*d^6 - 45*A*a^8*b^6*c^4*d^4 - 6*A*a^8*b^6*c^6*d^2 +
105*A*a^9*b^5*c^3*d^5 + 15*A*a^9*b^5*c^5*d^3 - 91*A*a^10*b^4*c^2*d^6 - 20*A*a^10*b^4*c^4*d^4 + 15*A*a^11*b^3*c
^3*d^5 - 6*A*a^12*b^2*c^2*d^6 + 44*B*a^2*b^12*c^3*d^5 - 11*B*a^2*b^12*c^5*d^3 - 64*B*a^3*b^11*c^2*d^6 - 71*B*a
^3*b^11*c^4*d^4 - B*a^3*b^11*c^6*d^2 + 187*B*a^4*b^10*c^3*d^5 + 23*B*a^4*b^10*c^5*d^3 - 145*B*a^5*b^9*c^2*d^6
- 173*B*a^5*b^9*c^4*d^4 - 17*B*a^5*b^9*c^6*d^2 + 273*B*a^6*b^8*c^3*d^5 + 63*B*a^6*b^8*c^5*d^3 - 115*B*a^7*b^7*
c^2*d^6 - 149*B*a^7*b^7*c^4*d^4 - 11*B*a^7*b^7*c^6*d^2 + 141*B*a^8*b^6*c^3*d^5 + 33*B*a^8*b^6*c^5*d^3 - 11*B*a
^9*b^5*c^2*d^6 - 43*B*a^9*b^5*c^4*d^4 + 15*B*a^10*b^4*c^3*d^5 + 15*B*a^11*b^3*c^2*d^6 - 4*C*a^2*b^12*c^2*d^6 -
47*C*a^2*b^12*c^4*d^4 - C*a^2*b^12*c^6*d^2 + 36*C*a^3*b^11*c^3*d^5 + 51*C*a^3*b^11*c^5*d^3 + 25*C*a^4*b^10*c^
2*d^6 - 85*C*a^4*b^10*c^4*d^4 - 5*C*a^4*b^10*c^6*d^2 - 19*C*a^5*b^9*c^3*d^5 + 61*C*a^5*b^9*c^5*d^3 + 117*C*a^6
*b^8*c^2*d^6 - 29*C*a^6*b^8*c^4*d^4 + 5*C*a^6*b^8*c^6*d^2 - 129*C*a^7*b^7*c^3*d^5 + 9*C*a^7*b^7*c^5*d^3 + 145*
C*a^8*b^6*c^2*d^6 + 29*C*a^8*b^6*c^4*d^4 + 6*C*a^8*b^6*c^6*d^2 - 97*C*a^9*b^5*c^3*d^5 - 11*C*a^9*b^5*c^5*d^3 +
59*C*a^10*b^4*c^2*d^6 + 16*C*a^10*b^4*c^4*d^4 - 15*C*a^11*b^3*c^3*d^5 + 2*C*a^12*b^2*c^2*d^6 + 8*A*a*b^13*c*d
^7 + A*a*b^13*c^7*d + A*a^13*b*c*d^7 - C*a*b^13*c^7*d + 3*C*a^13*b*c*d^7)/(a^12*d^4 + b^12*c^4 + 4*a^2*b^10*c^
4 + 6*a^4*b^8*c^4 + 4*a^6*b^6*c^4 + a^8*b^4*c^4 + a^4*b^8*d^4 + 4*a^6*b^6*d^4 + 6*a^8*b^4*d^4 + 4*a^10*b^2*d^4
- 4*a^3*b^9*c*d^3 - 16*a^3*b^9*c^3*d - 16*a^5*b^7*c*d^3 - 24*a^5*b^7*c^3*d - 24*a^7*b^5*c*d^3 - 16*a^7*b^5*c^
3*d - 16*a^9*b^3*c*d^3 - 4*a^9*b^3*c^3*d + 6*a^2*b^10*c^2*d^2 + 24*a^4*b^8*c^2*d^2 + 36*a^6*b^6*c^2*d^2 + 24*a
^8*b^4*c^2*d^2 + 6*a^10*b^2*c^2*d^2 - 4*a*b^11*c^3*d - 4*a^11*b*c*d^3) + root(480*a^11*b^7*c*d^9*f^4 + 480*a^7
*b^11*c^9*d*f^4 + 360*a^13*b^5*c*d^9*f^4 + 360*a^9*b^9*c^9*d*f^4 + 360*a^9*b^9*c*d^9*f^4 + 360*a^5*b^13*c^9*d*
f^4 + 144*a^15*b^3*c*d^9*f^4 + 144*a^11*b^7*c^9*d*f^4 + 144*a^7*b^11*c*d^9*f^4 + 144*a^3*b^15*c^9*d*f^4 + 48*a
^17*b*c^3*d^7*f^4 + 48*a*b^17*c^7*d^3*f^4 + 24*a^17*b*c^5*d^5*f^4 + 24*a^13*b^5*c^9*d*f^4 + 24*a^5*b^13*c*d^9*
f^4 + 24*a*b^17*c^5*d^5*f^4 + 24*a^17*b*c*d^9*f^4 + 24*a*b^17*c^9*d*f^4 + 3920*a^9*b^9*c^5*d^5*f^4 - 3360*a^10
*b^8*c^4*d^6*f^4 - 3360*a^8*b^10*c^6*d^4*f^4 + 3024*a^11*b^7*c^5*d^5*f^4 - 3024*a^10*b^8*c^6*d^4*f^4 - 3024*a^
8*b^10*c^4*d^6*f^4 + 3024*a^7*b^11*c^5*d^5*f^4 + 2320*a^9*b^9*c^7*d^3*f^4 + 2320*a^9*b^9*c^3*d^7*f^4 - 2240*a^
12*b^6*c^4*d^6*f^4 - 2240*a^6*b^12*c^6*d^4*f^4 + 2160*a^11*b^7*c^3*d^7*f^4 + 2160*a^7*b^11*c^7*d^3*f^4 - 1624*
a^12*b^6*c^6*d^4*f^4 - 1624*a^6*b^12*c^4*d^6*f^4 + 1488*a^11*b^7*c^7*d^3*f^4 + 1488*a^7*b^11*c^3*d^7*f^4 + 134
4*a^13*b^5*c^5*d^5*f^4 + 1344*a^5*b^13*c^5*d^5*f^4 - 1320*a^10*b^8*c^2*d^8*f^4 - 1320*a^8*b^10*c^8*d^2*f^4 + 1
200*a^13*b^5*c^3*d^7*f^4 + 1200*a^5*b^13*c^7*d^3*f^4 - 1060*a^12*b^6*c^2*d^8*f^4 - 1060*a^6*b^12*c^8*d^2*f^4 -
948*a^10*b^8*c^8*d^2*f^4 - 948*a^8*b^10*c^2*d^8*f^4 - 840*a^14*b^4*c^4*d^6*f^4 - 840*a^4*b^14*c^6*d^4*f^4 + 5
28*a^13*b^5*c^7*d^3*f^4 + 528*a^5*b^13*c^3*d^7*f^4 - 480*a^14*b^4*c^6*d^4*f^4 - 480*a^14*b^4*c^2*d^8*f^4 - 480
*a^4*b^14*c^8*d^2*f^4 - 480*a^4*b^14*c^4*d^6*f^4 + 368*a^15*b^3*c^3*d^7*f^4 - 368*a^12*b^6*c^8*d^2*f^4 - 368*a
^6*b^12*c^2*d^8*f^4 + 368*a^3*b^15*c^7*d^3*f^4 + 304*a^15*b^3*c^5*d^5*f^4 + 304*a^3*b^15*c^5*d^5*f^4 - 144*a^1
6*b^2*c^4*d^6*f^4 - 144*a^2*b^16*c^6*d^4*f^4 - 108*a^16*b^2*c^2*d^8*f^4 - 108*a^2*b^16*c^8*d^2*f^4 + 80*a^15*b
^3*c^7*d^3*f^4 + 80*a^3*b^15*c^3*d^7*f^4 - 60*a^16*b^2*c^6*d^4*f^4 - 60*a^14*b^4*c^8*d^2*f^4 - 60*a^4*b^14*c^2
*d^8*f^4 - 60*a^2*b^16*c^4*d^6*f^4 - 8*b^18*c^8*d^2*f^4 - 4*b^18*c^6*d^4*f^4 - 8*a^18*c^2*d^8*f^4 - 4*a^18*c^4
*d^6*f^4 - 80*a^12*b^6*d^10*f^4 - 60*a^14*b^4*d^10*f^4 - 60*a^10*b^8*d^10*f^4 - 24*a^16*b^2*d^10*f^4 - 24*a^8*
b^10*d^10*f^4 - 4*a^6*b^12*d^10*f^4 - 80*a^6*b^12*c^10*f^4 - 60*a^8*b^10*c^10*f^4 - 60*a^4*b^14*c^10*f^4 - 24*
a^10*b^8*c^10*f^4 - 24*a^2*b^16*c^10*f^4 - 4*a^12*b^6*c^10*f^4 - 4*b^18*c^10*f^4 - 4*a^18*d^10*f^4 - 12*A*C*a^
11*b*c*d^7*f^2 - 12*A*C*a*b^11*c^7*d*f^2 - 912*B*C*a^5*b^7*c^4*d^4*f^2 - 792*B*C*a^8*b^4*c^3*d^5*f^2 + 792*B*C
*a^4*b^8*c^5*d^3*f^2 + 720*B*C*a^7*b^5*c^4*d^4*f^2 - 480*B*C*a^5*b^7*c^6*d^2*f^2 - 408*B*C*a^5*b^7*c^2*d^6*f^2
+ 384*B*C*a^7*b^5*c^2*d^6*f^2 - 336*B*C*a^8*b^4*c^5*d^3*f^2 + 324*B*C*a^4*b^8*c^3*d^5*f^2 + 312*B*C*a^7*b^5*c
^6*d^2*f^2 - 248*B*C*a^3*b^9*c^6*d^2*f^2 + 216*B*C*a^9*b^3*c^2*d^6*f^2 - 196*B*C*a^3*b^9*c^4*d^4*f^2 + 132*B*C
*a^9*b^3*c^4*d^4*f^2 + 80*B*C*a^6*b^6*c^3*d^5*f^2 - 64*B*C*a^6*b^6*c^5*d^3*f^2 - 36*B*C*a^2*b^10*c^3*d^5*f^2 -
28*B*C*a^3*b^9*c^2*d^6*f^2 + 12*B*C*a^10*b^2*c^5*d^3*f^2 - 12*B*C*a^10*b^2*c^3*d^5*f^2 - 12*B*C*a^2*b^10*c^5*
d^3*f^2 - 4*B*C*a^9*b^3*c^6*d^2*f^2 - 1468*A*C*a^6*b^6*c^4*d^4*f^2 + 996*A*C*a^7*b^5*c^3*d^5*f^2 + 900*A*C*a^5
*b^7*c^5*d^3*f^2 - 676*A*C*a^6*b^6*c^6*d^2*f^2 - 660*A*C*a^6*b^6*c^2*d^6*f^2 + 636*A*C*a^5*b^7*c^3*d^5*f^2 + 5
40*A*C*a^7*b^5*c^5*d^3*f^2 - 236*A*C*a^3*b^9*c^5*d^3*f^2 - 204*A*C*a^9*b^3*c^3*d^5*f^2 + 156*A*C*a^10*b^2*c^2*
d^6*f^2 + 132*A*C*a^2*b^10*c^6*d^2*f^2 - 72*A*C*a^9*b^3*c^5*d^3*f^2 - 72*A*C*a^4*b^8*c^6*d^2*f^2 + 66*A*C*a^4*
b^8*c^2*d^6*f^2 + 54*A*C*a^10*b^2*c^4*d^4*f^2 + 54*A*C*a^2*b^10*c^4*d^4*f^2 - 48*A*C*a^8*b^4*c^2*d^6*f^2 - 48*
A*C*a^4*b^8*c^4*d^4*f^2 + 42*A*C*a^8*b^4*c^6*d^2*f^2 - 40*A*C*a^3*b^9*c^3*d^5*f^2 - 36*A*C*a^8*b^4*c^4*d^4*f^2
+ 24*A*C*a^2*b^10*c^2*d^6*f^2 + 960*A*B*a^5*b^7*c^4*d^4*f^2 - 864*A*B*a^4*b^8*c^5*d^3*f^2 + 756*A*B*a^8*b^4*c
^3*d^5*f^2 - 744*A*B*a^7*b^5*c^4*d^4*f^2 - 528*A*B*a^4*b^8*c^3*d^5*f^2 + 504*A*B*a^5*b^7*c^6*d^2*f^2 - 432*A*B
*a^7*b^5*c^2*d^6*f^2 + 432*A*B*a^5*b^7*c^2*d^6*f^2 + 348*A*B*a^8*b^4*c^5*d^3*f^2 - 312*A*B*a^7*b^5*c^6*d^2*f^2
- 284*A*B*a^9*b^3*c^2*d^6*f^2 + 280*A*B*a^3*b^9*c^6*d^2*f^2 + 264*A*B*a^3*b^9*c^4*d^4*f^2 - 240*A*B*a^6*b^6*c
^3*d^5*f^2 - 172*A*B*a^9*b^3*c^4*d^4*f^2 + 68*A*B*a^3*b^9*c^2*d^6*f^2 - 60*A*B*a^2*b^10*c^3*d^5*f^2 + 24*A*B*a
^6*b^6*c^5*d^3*f^2 - 24*A*B*a^2*b^10*c^5*d^3*f^2 + 12*A*B*a^10*b^2*c^3*d^5*f^2 + 360*B*C*a^4*b^8*c^7*d*f^2 - 3
36*B*C*a^8*b^4*c*d^7*f^2 + 168*B*C*a^6*b^6*c*d^7*f^2 - 136*B*C*a^6*b^6*c^7*d*f^2 - 36*B*C*a^11*b*c^2*d^6*f^2 +
36*B*C*a*b^11*c^6*d^2*f^2 + 24*B*C*a^10*b^2*c*d^7*f^2 - 24*B*C*a^2*b^10*c^7*d*f^2 - 12*B*C*a^11*b*c^4*d^4*f^2
+ 12*B*C*a^4*b^8*c*d^7*f^2 + 12*B*C*a*b^11*c^4*d^4*f^2 + 444*A*C*a^7*b^5*c*d^7*f^2 + 348*A*C*a^5*b^7*c^7*d*f^
2 - 164*A*C*a^3*b^9*c^7*d*f^2 - 132*A*C*a^9*b^3*c*d^7*f^2 + 84*A*C*a^5*b^7*c*d^7*f^2 + 32*A*C*a^3*b^9*c*d^7*f^
2 - 12*A*C*a^11*b*c^3*d^5*f^2 - 12*A*C*a^7*b^5*c^7*d*f^2 - 12*A*C*a*b^11*c^5*d^3*f^2 - 360*A*B*a^4*b^8*c^7*d*f
^2 + 288*A*B*a^8*b^4*c*d^7*f^2 - 288*A*B*a^6*b^6*c*d^7*f^2 - 144*A*B*a^4*b^8*c*d^7*f^2 + 136*A*B*a^6*b^6*c^7*d
*f^2 - 60*A*B*a^2*b^10*c*d^7*f^2 - 36*A*B*a^10*b^2*c*d^7*f^2 + 24*A*B*a^2*b^10*c^7*d*f^2 - 24*A*B*a*b^11*c^6*d
^2*f^2 + 12*A*B*a^11*b*c^2*d^6*f^2 + 12*A*B*a*b^11*c^4*d^4*f^2 + 12*A*B*a*b^11*c^2*d^6*f^2 - 8*B*C*b^12*c^5*d^
3*f^2 - 8*B*C*b^12*c^3*d^5*f^2 + 8*A*C*b^12*c^2*d^6*f^2 - 4*B*C*a^12*c^3*d^5*f^2 + 4*A*C*b^12*c^4*d^4*f^2 - 2*
A*C*b^12*c^6*d^2*f^2 + 80*B*C*a^9*b^3*d^8*f^2 - 24*B*C*a^7*b^5*d^8*f^2 + 6*A*C*a^12*c^2*d^6*f^2 + 4*A*B*b^12*c
^5*d^3*f^2 - 4*A*B*b^12*c^3*d^5*f^2 - 90*A*C*a^8*b^4*d^8*f^2 - 80*B*C*a^3*b^9*c^8*f^2 + 54*A*C*a^10*b^2*d^8*f^
2 - 30*A*C*a^6*b^6*d^8*f^2 + 24*B*C*a^5*b^7*c^8*f^2 - 12*A*C*a^4*b^8*d^8*f^2 - 112*A*B*a^9*b^3*d^8*f^2 - 66*A*
C*a^4*b^8*c^8*f^2 + 54*A*C*a^2*b^10*c^8*f^2 + 4*A*B*a^3*b^9*d^8*f^2 + 2*A*C*a^6*b^6*c^8*f^2 + 80*A*B*a^3*b^9*c
^8*f^2 - 24*A*B*a^5*b^7*c^8*f^2 + 726*C^2*a^6*b^6*c^4*d^4*f^2 - 402*C^2*a^7*b^5*c^3*d^5*f^2 - 402*C^2*a^5*b^7*
c^5*d^3*f^2 + 322*C^2*a^6*b^6*c^6*d^2*f^2 + 322*C^2*a^6*b^6*c^2*d^6*f^2 - 222*C^2*a^7*b^5*c^5*d^3*f^2 - 222*C^
2*a^5*b^7*c^3*d^5*f^2 + 134*C^2*a^9*b^3*c^3*d^5*f^2 + 134*C^2*a^3*b^9*c^5*d^3*f^2 - 66*C^2*a^10*b^2*c^2*d^6*f^
2 - 66*C^2*a^2*b^10*c^6*d^2*f^2 + 52*C^2*a^9*b^3*c^5*d^3*f^2 + 52*C^2*a^3*b^9*c^3*d^5*f^2 - 27*C^2*a^8*b^4*c^6
*d^2*f^2 - 27*C^2*a^4*b^8*c^2*d^6*f^2 + 24*C^2*a^8*b^4*c^4*d^4*f^2 + 24*C^2*a^8*b^4*c^2*d^6*f^2 + 24*C^2*a^4*b
^8*c^6*d^2*f^2 + 24*C^2*a^4*b^8*c^4*d^4*f^2 - 15*C^2*a^10*b^2*c^4*d^4*f^2 - 15*C^2*a^2*b^10*c^4*d^4*f^2 - 570*
B^2*a^6*b^6*c^4*d^4*f^2 + 366*B^2*a^7*b^5*c^3*d^5*f^2 + 318*B^2*a^5*b^7*c^5*d^3*f^2 - 262*B^2*a^6*b^6*c^6*d^2*
f^2 - 222*B^2*a^6*b^6*c^2*d^6*f^2 - 210*B^2*a^3*b^9*c^5*d^3*f^2 + 186*B^2*a^7*b^5*c^5*d^3*f^2 + 162*B^2*a^5*b^
7*c^3*d^5*f^2 - 142*B^2*a^9*b^3*c^3*d^5*f^2 + 132*B^2*a^4*b^8*c^4*d^4*f^2 + 117*B^2*a^4*b^8*c^2*d^6*f^2 + 102*
B^2*a^2*b^10*c^6*d^2*f^2 - 96*B^2*a^3*b^9*c^3*d^5*f^2 + 90*B^2*a^10*b^2*c^2*d^6*f^2 + 81*B^2*a^2*b^10*c^4*d^4*
f^2 - 56*B^2*a^9*b^3*c^5*d^3*f^2 + 48*B^2*a^8*b^4*c^4*d^4*f^2 + 48*B^2*a^4*b^8*c^6*d^2*f^2 + 45*B^2*a^8*b^4*c^
6*d^2*f^2 + 36*B^2*a^8*b^4*c^2*d^6*f^2 + 36*B^2*a^2*b^10*c^2*d^6*f^2 + 33*B^2*a^10*b^2*c^4*d^4*f^2 + 822*A^2*a
^6*b^6*c^4*d^4*f^2 - 594*A^2*a^7*b^5*c^3*d^5*f^2 + 498*A^2*a^6*b^6*c^2*d^6*f^2 - 498*A^2*a^5*b^7*c^5*d^3*f^2 -
414*A^2*a^5*b^7*c^3*d^5*f^2 + 354*A^2*a^6*b^6*c^6*d^2*f^2 - 318*A^2*a^7*b^5*c^5*d^3*f^2 + 144*A^2*a^8*b^4*c^2
*d^6*f^2 + 102*A^2*a^3*b^9*c^5*d^3*f^2 + 84*A^2*a^4*b^8*c^4*d^4*f^2 + 81*A^2*a^4*b^8*c^2*d^6*f^2 + 72*A^2*a^8*
b^4*c^4*d^4*f^2 + 70*A^2*a^9*b^3*c^3*d^5*f^2 - 66*A^2*a^2*b^10*c^6*d^2*f^2 + 48*A^2*a^4*b^8*c^6*d^2*f^2 - 42*A
^2*a^10*b^2*c^2*d^6*f^2 + 24*A^2*a^2*b^10*c^2*d^6*f^2 + 20*A^2*a^9*b^3*c^5*d^3*f^2 - 15*A^2*a^10*b^2*c^4*d^4*f
^2 - 15*A^2*a^8*b^4*c^6*d^2*f^2 - 15*A^2*a^2*b^10*c^4*d^4*f^2 - 12*A^2*a^3*b^9*c^3*d^5*f^2 - 8*B*C*b^12*c^7*d*
f^2 + 4*B*C*a^12*c*d^7*f^2 - 24*B*C*a^11*b*d^8*f^2 + 8*A*B*b^12*c^7*d*f^2 - 8*A*B*b^12*c*d^7*f^2 + 24*B*C*a*b^
11*c^8*f^2 - 8*A*B*a^12*c*d^7*f^2 + 12*A*B*a^11*b*d^8*f^2 - 24*A*B*a*b^11*c^8*f^2 - 174*C^2*a^7*b^5*c*d^7*f^2
- 174*C^2*a^5*b^7*c^7*d*f^2 + 82*C^2*a^9*b^3*c*d^7*f^2 + 82*C^2*a^3*b^9*c^7*d*f^2 + 6*C^2*a^11*b*c^3*d^5*f^2 +
6*C^2*a^7*b^5*c^7*d*f^2 + 6*C^2*a^5*b^7*c*d^7*f^2 + 6*C^2*a*b^11*c^5*d^3*f^2 + 162*B^2*a^7*b^5*c*d^7*f^2 + 13
8*B^2*a^5*b^7*c^7*d*f^2 - 118*B^2*a^3*b^9*c^7*d*f^2 - 86*B^2*a^9*b^3*c*d^7*f^2 - 30*B^2*a*b^11*c^5*d^3*f^2 - 1
8*B^2*a^7*b^5*c^7*d*f^2 - 18*B^2*a^5*b^7*c*d^7*f^2 - 12*B^2*a*b^11*c^3*d^5*f^2 - 6*B^2*a^11*b*c^3*d^5*f^2 - 4*
B^2*a^3*b^9*c*d^7*f^2 - 270*A^2*a^7*b^5*c*d^7*f^2 - 174*A^2*a^5*b^7*c^7*d*f^2 - 90*A^2*a^5*b^7*c*d^7*f^2 + 82*
A^2*a^3*b^9*c^7*d*f^2 + 50*A^2*a^9*b^3*c*d^7*f^2 - 32*A^2*a^3*b^9*c*d^7*f^2 + 6*A^2*a^11*b*c^3*d^5*f^2 + 6*A^2
*a^7*b^5*c^7*d*f^2 + 6*A^2*a*b^11*c^5*d^3*f^2 + 6*C^2*a^11*b*c*d^7*f^2 + 6*C^2*a*b^11*c^7*d*f^2 - 18*B^2*a*b^1
1*c^7*d*f^2 - 6*B^2*a^11*b*c*d^7*f^2 + 6*A^2*a^11*b*c*d^7*f^2 + 6*A^2*a*b^11*c^7*d*f^2 - 6*A*C*b^12*c^8*f^2 -
2*A*C*a^12*d^8*f^2 + 4*C^2*b^12*c^4*d^4*f^2 + 3*C^2*b^12*c^6*d^2*f^2 + 4*C^2*a^12*c^4*d^4*f^2 + 4*B^2*b^12*c^4
*d^4*f^2 + 4*B^2*b^12*c^2*d^6*f^2 + 3*C^2*a^12*c^2*d^6*f^2 + 3*B^2*b^12*c^6*d^2*f^2 + 33*C^2*a^8*b^4*d^8*f^2 -
27*C^2*a^10*b^2*d^8*f^2 - 4*A^2*b^12*c^4*d^4*f^2 + 3*B^2*a^12*c^2*d^6*f^2 - C^2*a^6*b^6*d^8*f^2 - A^2*b^12*c^
6*d^2*f^2 + 33*C^2*a^4*b^8*c^8*f^2 + 33*B^2*a^10*b^2*d^8*f^2 - 27*C^2*a^2*b^10*c^8*f^2 - 27*B^2*a^8*b^4*d^8*f^
2 + 3*B^2*a^6*b^6*d^8*f^2 - C^2*a^6*b^6*c^8*f^2 - A^2*a^12*c^2*d^6*f^2 + 117*A^2*a^8*b^4*d^8*f^2 + 111*A^2*a^6
*b^6*d^8*f^2 + 72*A^2*a^4*b^8*d^8*f^2 + 33*B^2*a^2*b^10*c^8*f^2 - 27*B^2*a^4*b^8*c^8*f^2 + 24*A^2*a^2*b^10*d^8
*f^2 + 3*B^2*a^6*b^6*c^8*f^2 - 3*A^2*a^10*b^2*d^8*f^2 + 33*A^2*a^4*b^8*c^8*f^2 - 27*A^2*a^2*b^10*c^8*f^2 - A^2
*a^6*b^6*c^8*f^2 + 3*C^2*b^12*c^8*f^2 + 3*C^2*a^12*d^8*f^2 + 4*A^2*b^12*d^8*f^2 - B^2*b^12*c^8*f^2 - B^2*a^12*
d^8*f^2 + 3*A^2*b^12*c^8*f^2 + 3*A^2*a^12*d^8*f^2 - 24*A*B*C*a*b^8*c*d^6*f + 342*A*B*C*a^4*b^5*c^2*d^5*f - 186
*A*B*C*a^5*b^4*c^3*d^4*f - 66*A*B*C*a^2*b^7*c^4*d^3*f + 48*A*B*C*a^2*b^7*c^2*d^5*f + 42*A*B*C*a^6*b^3*c^2*d^5*
f + 26*A*B*C*a^3*b^6*c^5*d^2*f + 24*A*B*C*a^6*b^3*c^4*d^3*f - 18*A*B*C*a^7*b^2*c^3*d^4*f - 18*A*B*C*a^4*b^5*c^
4*d^3*f - 8*A*B*C*a^3*b^6*c^3*d^4*f + 6*A*B*C*a^5*b^4*c^5*d^2*f - 128*A*B*C*a^3*b^6*c*d^6*f + 126*A*B*C*a^7*b^
2*c*d^6*f + 72*A*B*C*a*b^8*c^3*d^4*f - 36*A*B*C*a^8*b*c^2*d^5*f - 36*A*B*C*a*b^8*c^5*d^2*f + 30*A*B*C*a^2*b^7*
c^6*d*f - 12*A*B*C*a^5*b^4*c*d^6*f - 12*A*B*C*a^4*b^5*c^6*d*f - 21*B^2*C*a^8*b*c*d^6*f - 3*B^2*C*a*b^8*c^6*d*f
+ 21*A^2*C*a^8*b*c*d^6*f - 21*A*C^2*a^8*b*c*d^6*f - 9*A^2*C*a*b^8*c^6*d*f + 9*A*C^2*a*b^8*c^6*d*f + 36*A^2*B*
a*b^8*c*d^6*f + 21*A*B^2*a^8*b*c*d^6*f + 3*A*B^2*a*b^8*c^6*d*f + 16*A*B*C*b^9*c^4*d^3*f - 16*A*B*C*b^9*c^2*d^5
*f - 78*A*B*C*a^6*b^3*d^7*f + 24*A*B*C*a^4*b^5*d^7*f + 2*A*B*C*a^3*b^6*c^7*f - 237*B^2*C*a^4*b^5*c^3*d^4*f + 1
65*B*C^2*a^5*b^4*c^3*d^4*f + 92*B^2*C*a^3*b^6*c^2*d^5*f - 81*B^2*C*a^7*b^2*c^2*d^5*f + 77*B^2*C*a^3*b^6*c^4*d^
3*f - 75*B*C^2*a^4*b^5*c^2*d^5*f + 69*B^2*C*a^5*b^4*c^4*d^3*f + 69*B*C^2*a^4*b^5*c^4*d^3*f - 68*B*C^2*a^3*b^6*
c^3*d^4*f - 63*B^2*C*a^4*b^5*c^5*d^2*f - 61*B*C^2*a^6*b^3*c^2*d^5*f + 57*B*C^2*a^2*b^7*c^4*d^3*f - 53*B*C^2*a^
3*b^6*c^5*d^2*f - 44*B*C^2*a^6*b^3*c^4*d^3*f - 36*B^2*C*a^2*b^7*c^3*d^4*f + 35*B^2*C*a^6*b^3*c^3*d^4*f - 33*B^
2*C*a^5*b^4*c^2*d^5*f + 33*B^2*C*a^2*b^7*c^5*d^2*f + 33*B*C^2*a^7*b^2*c^3*d^4*f - 12*B^2*C*a^7*b^2*c^4*d^3*f +
9*B*C^2*a^5*b^4*c^5*d^2*f + 4*B^2*C*a^6*b^3*c^5*d^2*f + 225*A^2*C*a^5*b^4*c^2*d^5*f - 105*A*C^2*a^5*b^4*c^2*d
^5*f - 99*A^2*C*a^4*b^5*c^3*d^4*f - 81*A^2*C*a^4*b^5*c^5*d^2*f + 67*A^2*C*a^3*b^6*c^4*d^3*f - 59*A*C^2*a^3*b^6
*c^4*d^3*f - 57*A*C^2*a^7*b^2*c^2*d^5*f + 57*A*C^2*a^2*b^7*c^5*d^2*f + 51*A^2*C*a^5*b^4*c^4*d^3*f + 48*A^2*C*a
^2*b^7*c^3*d^4*f + 45*A*C^2*a^4*b^5*c^5*d^2*f - 35*A^2*C*a^6*b^3*c^3*d^4*f + 33*A^2*C*a^7*b^2*c^2*d^5*f - 33*A
^2*C*a^2*b^7*c^5*d^2*f + 33*A*C^2*a^5*b^4*c^4*d^3*f + 27*A*C^2*a^6*b^3*c^3*d^4*f + 24*A*C^2*a^3*b^6*c^2*d^5*f
- 24*A*C^2*a^2*b^7*c^3*d^4*f - 21*A*C^2*a^4*b^5*c^3*d^4*f - 16*A^2*C*a^3*b^6*c^2*d^5*f - 243*A^2*B*a^4*b^5*c^2
*d^5*f - 156*A*B^2*a^3*b^6*c^2*d^5*f + 141*A*B^2*a^4*b^5*c^3*d^4*f + 108*A^2*B*a^3*b^6*c^3*d^4*f - 105*A*B^2*a
^3*b^6*c^4*d^3*f + 84*A*B^2*a^2*b^7*c^3*d^4*f + 81*A*B^2*a^5*b^4*c^2*d^5*f + 51*A^2*B*a^6*b^3*c^2*d^5*f - 51*A
^2*B*a^4*b^5*c^4*d^3*f - 48*A^2*B*a^2*b^7*c^2*d^5*f + 45*A^2*B*a^5*b^4*c^3*d^4*f + 39*A*B^2*a^4*b^5*c^5*d^2*f
- 35*A*B^2*a^6*b^3*c^3*d^4*f + 33*A*B^2*a^7*b^2*c^2*d^5*f + 27*A^2*B*a^3*b^6*c^5*d^2*f - 21*A*B^2*a^5*b^4*c^4*
d^3*f + 20*A^2*B*a^6*b^3*c^4*d^3*f - 15*A^2*B*a^7*b^2*c^3*d^4*f - 15*A^2*B*a^5*b^4*c^5*d^2*f + 9*A^2*B*a^2*b^7
*c^4*d^3*f + 3*A*B^2*a^2*b^7*c^5*d^2*f + 2*A*B*C*b^9*c^6*d*f - 6*A*B*C*a^9*c*d^6*f + 18*A*B*C*a^8*b*d^7*f - 6*
A*B*C*a*b^8*c^7*f + 63*B^2*C*a^6*b^3*c*d^6*f - 48*B^2*C*a*b^8*c^4*d^3*f + 42*B*C^2*a^8*b*c^2*d^5*f + 42*B*C^2*
a^5*b^4*c*d^6*f - 39*B*C^2*a^7*b^2*c*d^6*f + 30*B*C^2*a*b^8*c^5*d^2*f - 24*B^2*C*a^4*b^5*c*d^6*f - 24*B*C^2*a*
b^8*c^3*d^4*f + 17*B^2*C*a^3*b^6*c^6*d*f - 15*B*C^2*a^2*b^7*c^6*d*f + 12*B^2*C*a^8*b*c^3*d^4*f + 12*B^2*C*a*b^
8*c^2*d^5*f + 6*B*C^2*a^4*b^5*c^6*d*f - 192*A^2*C*a^4*b^5*c*d^6*f - 99*A^2*C*a^6*b^3*c*d^6*f + 84*A*C^2*a^4*b^
5*c*d^6*f + 59*A*C^2*a^6*b^3*c*d^6*f + 51*A^2*C*a^3*b^6*c^6*d*f - 51*A*C^2*a^3*b^6*c^6*d*f - 36*A^2*C*a*b^8*c^
2*d^5*f - 24*A*C^2*a*b^8*c^4*d^3*f + 24*A*C^2*a*b^8*c^2*d^5*f + 12*A^2*C*a*b^8*c^4*d^3*f + 12*A*C^2*a^8*b*c^3*
d^4*f + 160*A^2*B*a^3*b^6*c*d^6*f - 99*A*B^2*a^6*b^3*c*d^6*f - 87*A^2*B*a^7*b^2*c*d^6*f - 72*A*B^2*a^4*b^5*c*d
^6*f - 48*A*B^2*a*b^8*c^2*d^5*f - 36*A^2*B*a*b^8*c^3*d^4*f + 24*A*B^2*a*b^8*c^4*d^3*f - 17*A*B^2*a^3*b^6*c^6*d
*f - 15*A^2*B*a^2*b^7*c^6*d*f + 12*A*B^2*a^2*b^7*c*d^6*f + 6*A^2*B*a^8*b*c^2*d^5*f - 6*A^2*B*a^5*b^4*c*d^6*f +
6*A^2*B*a^4*b^5*c^6*d*f + 6*A^2*B*a*b^8*c^5*d^2*f + 12*B^2*C*b^9*c^3*d^4*f - 12*B*C^2*b^9*c^4*d^3*f - 12*A^2*
C*b^9*c^3*d^4*f - 8*A*C^2*b^9*c^5*d^2*f + 8*A*C^2*b^9*c^3*d^4*f + 4*B^2*C*a^9*c^2*d^5*f + 4*A^2*C*b^9*c^5*d^2*
f - 4*B*C^2*a^9*c^3*d^4*f + 12*A^2*B*b^9*c^2*d^5*f - 8*A*B^2*b^9*c^3*d^4*f - 4*A^2*B*b^9*c^4*d^3*f + 4*A*C^2*a
^9*c^2*d^5*f + 3*B^2*C*a^7*b^2*d^7*f - B*C^2*a^6*b^3*d^7*f + 96*A^2*C*a^5*b^4*d^7*f - 39*A^2*C*a^7*b^2*d^7*f -
36*A*C^2*a^5*b^4*d^7*f + 32*A^2*C*a^3*b^6*d^7*f + 15*A*C^2*a^7*b^2*d^7*f - 3*B^2*C*a^2*b^7*c^7*f - B*C^2*a^3*
b^6*c^7*f + 111*A^2*B*a^6*b^3*d^7*f - 39*A*B^2*a^7*b^2*d^7*f + 24*A*B^2*a^5*b^4*d^7*f - 9*A^2*C*a^2*b^7*c^7*f
+ 9*A*C^2*a^2*b^7*c^7*f - 4*A*B^2*a^3*b^6*d^7*f + 3*A*B^2*a^2*b^7*c^7*f - A^2*B*a^3*b^6*c^7*f + 3*C^3*a^8*b*c*
d^6*f - 3*C^3*a*b^8*c^6*d*f - 3*A^3*a^8*b*c*d^6*f + 3*A^3*a*b^8*c^6*d*f - B*C^2*b^9*c^6*d*f + 4*A^2*C*b^9*c*d^
6*f + 3*B*C^2*a^9*c*d^6*f + 8*A*B^2*b^9*c*d^6*f + 3*B*C^2*a^8*b*d^7*f - A^2*B*b^9*c^6*d*f + 12*A^2*C*a*b^8*d^7
*f + 3*B*C^2*a*b^8*c^7*f - A^2*B*a^9*c*d^6*f - 9*A^2*B*a^8*b*d^7*f + 3*A^2*B*a*b^8*c^7*f - 39*C^3*a^5*b^4*c^4*
d^3*f + 39*C^3*a^4*b^5*c^3*d^4*f + 27*C^3*a^7*b^2*c^2*d^5*f - 27*C^3*a^2*b^7*c^5*d^2*f - 17*C^3*a^6*b^3*c^3*d^
4*f + 17*C^3*a^3*b^6*c^4*d^3*f + 3*C^3*a^5*b^4*c^2*d^5*f - 3*C^3*a^4*b^5*c^5*d^2*f - 63*B^3*a^5*b^4*c^3*d^4*f
+ 57*B^3*a^4*b^5*c^2*d^5*f - 51*B^3*a^2*b^7*c^4*d^3*f + 48*B^3*a^3*b^6*c^3*d^4*f + 31*B^3*a^6*b^3*c^2*d^5*f +
27*B^3*a^3*b^6*c^5*d^2*f + 16*B^3*a^6*b^3*c^4*d^3*f - 15*B^3*a^5*b^4*c^5*d^2*f - 12*B^3*a^2*b^7*c^2*d^5*f + 9*
B^3*a^4*b^5*c^4*d^3*f - 3*B^3*a^7*b^2*c^3*d^4*f - 123*A^3*a^5*b^4*c^2*d^5*f + 81*A^3*a^4*b^5*c^3*d^4*f - 45*A^
3*a^5*b^4*c^4*d^3*f + 39*A^3*a^4*b^5*c^5*d^2*f + 25*A^3*a^6*b^3*c^3*d^4*f - 25*A^3*a^3*b^6*c^4*d^3*f - 24*A^3*
a^2*b^7*c^3*d^4*f - 8*A^3*a^3*b^6*c^2*d^5*f - 3*A^3*a^7*b^2*c^2*d^5*f + 3*A^3*a^2*b^7*c^5*d^2*f - 17*C^3*a^6*b
^3*c*d^6*f + 17*C^3*a^3*b^6*c^6*d*f - 12*C^3*a^8*b*c^3*d^4*f + 12*C^3*a*b^8*c^4*d^3*f + 24*B^3*a*b^8*c^3*d^4*f
+ 21*B^3*a^7*b^2*c*d^6*f - 18*B^3*a^5*b^4*c*d^6*f - 15*B^3*a^2*b^7*c^6*d*f - 6*B^3*a^8*b*c^2*d^5*f + 6*B^3*a^
4*b^5*c^6*d*f + 6*B^3*a*b^8*c^5*d^2*f + 4*B^3*a^3*b^6*c*d^6*f + 108*A^3*a^4*b^5*c*d^6*f + 57*A^3*a^6*b^3*c*d^6
*f - 17*A^3*a^3*b^6*c^6*d*f + 12*A^3*a*b^8*c^2*d^5*f + 4*C^3*b^9*c^5*d^2*f - 4*C^3*a^9*c^2*d^5*f - 4*B^3*b^9*c
^2*d^5*f + 4*A^3*b^9*c^3*d^4*f + 3*C^3*a^7*b^2*d^7*f - 3*C^3*a^2*b^7*c^7*f - B^3*a^6*b^3*d^7*f - 60*A^3*a^5*b^
4*d^7*f - 32*A^3*a^3*b^6*d^7*f + 21*A^3*a^7*b^2*d^7*f - B^3*a^3*b^6*c^7*f + 3*A^3*a^2*b^7*c^7*f - B^3*b^9*c^6*
d*f - 4*A^3*b^9*c*d^6*f - B^3*a^9*c*d^6*f + 3*B^3*a^8*b*d^7*f - 12*A^3*a*b^8*d^7*f + 3*B^3*a*b^8*c^7*f - B^2*C
*a^9*d^7*f - 4*A^2*B*b^9*d^7*f + 3*A^2*C*b^9*c^7*f - 3*A*C^2*b^9*c^7*f - A*C^2*a^9*d^7*f - A*B^2*b^9*c^7*f - C
^3*a^9*d^7*f - A^3*b^9*c^7*f + B^2*C*b^9*c^7*f + A^2*C*a^9*d^7*f + A*B^2*a^9*d^7*f + C^3*b^9*c^7*f + A^3*a^9*d
^7*f - 6*A*B^2*C*a^5*b*c*d^5 - 21*A^2*B*C*a^3*b^3*c^2*d^4 + 21*A*B*C^2*a^3*b^3*c^2*d^4 + 12*A*B^2*C*a^4*b^2*c^
2*d^4 - 12*A*B^2*C*a^2*b^4*c^2*d^4 - 10*A*B^2*C*a^3*b^3*c^3*d^3 - 6*A*B*C^2*a^4*b^2*c^3*d^3 + 3*A^2*B*C*a^4*b^
2*c^3*d^3 + 3*A^2*B*C*a^2*b^4*c^3*d^3 + 3*A*B^2*C*a^2*b^4*c^4*d^2 + 3*A*B*C^2*a^2*b^4*c^3*d^3 + 2*A*B*C^2*a^3*
b^3*c^4*d^2 - A^2*B*C*a^3*b^3*c^4*d^2 + 18*A^2*B*C*a^2*b^4*c*d^5 + 10*A*B^2*C*a^3*b^3*c*d^5 + 9*A^2*B*C*a^4*b^
2*c*d^5 - 9*A*B*C^2*a^4*b^2*c*d^5 - 9*A*B*C^2*a^2*b^4*c*d^5 - 6*A^2*B*C*a*b^5*c^2*d^4 + 6*A*B^2*C*a*b^5*c^3*d^
3 + 6*A*B*C^2*a^5*b*c^2*d^4 - 6*A*B*C^2*a*b^5*c^4*d^2 - 3*A^2*B*C*a^5*b*c^2*d^4 + 3*A^2*B*C*a*b^5*c^4*d^2 + 3*
A*B*C^2*a*b^5*c^2*d^4 - 3*B^3*C*a^5*b*c^2*d^4 + 3*B^3*C*a^4*b^2*c*d^5 + 3*B^3*C*a*b^5*c^4*d^2 + 3*B^2*C^2*a^5*
b*c*d^5 - 3*B*C^3*a^5*b*c^2*d^4 + 3*B*C^3*a^4*b^2*c*d^5 + 3*B*C^3*a*b^5*c^4*d^2 + 24*A^3*C*a^3*b^3*c*d^5 + 8*A
*C^3*a^3*b^3*c*d^5 - 9*A^3*B*a^2*b^4*c*d^5 - 9*A*B^3*a^2*b^4*c*d^5 - 3*A^3*B*a^4*b^2*c*d^5 + 3*A^3*B*a*b^5*c^2
*d^4 + 3*A^2*B^2*a^5*b*c*d^5 - 3*A*B^3*a^4*b^2*c*d^5 + 3*A*B^3*a*b^5*c^2*d^4 + 5*A*B*C^2*b^6*c^3*d^3 - 4*A^2*B
*C*b^6*c^3*d^3 - A*B^2*C*b^6*c^4*d^2 - 3*A*B^2*C*a^4*b^2*d^6 - 2*A^2*B*C*a^3*b^3*d^6 + 9*B^2*C^2*a^3*b^3*c^3*d
^3 - 6*B^2*C^2*a^4*b^2*c^2*d^4 + 6*B^2*C^2*a^2*b^4*c^2*d^4 - 3*B^2*C^2*a^2*b^4*c^4*d^2 + 24*A^2*C^2*a^3*b^3*c^
3*d^3 - 15*A^2*C^2*a^4*b^2*c^2*d^4 - 9*A^2*C^2*a^2*b^4*c^4*d^2 + 3*A^2*C^2*a^2*b^4*c^2*d^4 + 9*A^2*B^2*a^2*b^4
*c^2*d^4 - 3*A^2*B^2*a^4*b^2*c^2*d^4 + 4*A^2*B*C*b^6*c*d^5 - 2*A*B*C^2*b^6*c*d^5 + 2*A*B*C^2*a^6*c*d^5 - A^2*B
*C*a^6*c*d^5 + 6*A^2*B*C*a^5*b*d^6 - 3*A*B*C^2*a^5*b*d^6 - 7*B^3*C*a^3*b^3*c^2*d^4 - 7*B*C^3*a^3*b^3*c^2*d^4 +
3*B^3*C*a^4*b^2*c^3*d^3 - 3*B^3*C*a^2*b^4*c^3*d^3 - 3*B^2*C^2*a*b^5*c^3*d^3 + 3*B*C^3*a^4*b^2*c^3*d^3 - 3*B*C
^3*a^2*b^4*c^3*d^3 - B^3*C*a^3*b^3*c^4*d^2 - B^2*C^2*a^3*b^3*c*d^5 - B*C^3*a^3*b^3*c^4*d^2 - 24*A^2*C^2*a^3*b^
3*c*d^5 - 24*A*C^3*a^3*b^3*c^3*d^3 + 12*A*C^3*a^4*b^2*c^2*d^4 + 9*A*C^3*a^2*b^4*c^4*d^2 - 8*A^3*C*a^3*b^3*c^3*
d^3 + 6*A^3*C*a^4*b^2*c^2*d^4 - 6*A^3*C*a^2*b^4*c^2*d^4 + 3*A^3*C*a^2*b^4*c^4*d^2 - 9*A^2*B^2*a^3*b^3*c*d^5 +
7*A^3*B*a^3*b^3*c^2*d^4 + 7*A*B^3*a^3*b^3*c^2*d^4 - 3*A^3*B*a^2*b^4*c^3*d^3 - 3*A^2*B^2*a*b^5*c^3*d^3 - 3*A*B^
3*a^2*b^4*c^3*d^3 - 5*A^2*C^2*b^6*c^2*d^4 + 3*A^2*C^2*b^6*c^4*d^2 + 12*A^2*C^2*a^4*b^2*d^6 + 3*A^2*C^2*a^2*b^4
*d^6 + 6*A^2*B^2*a^4*b^2*d^6 + 3*A^2*B^2*a^2*b^4*d^6 + A*B*C^2*a^3*b^3*d^6 - 3*B^4*a*b^5*c^3*d^3 - B^4*a^3*b^3
*c*d^5 + A^2*B^2*a^3*b^3*c^3*d^3 - 8*A^4*a^3*b^3*c*d^5 - 2*B^3*C*b^6*c^3*d^3 - 2*B*C^3*b^6*c^3*d^3 + 4*A^3*C*b
^6*c^2*d^4 - 3*A*C^3*b^6*c^4*d^2 + 2*A*C^3*b^6*c^2*d^4 - A^3*C*b^6*c^4*d^2 - 2*A*C^3*a^6*c^2*d^4 - 15*A^3*C*a^
4*b^2*d^6 - 6*A^3*C*a^2*b^4*d^6 - 3*A*C^3*a^4*b^2*d^6 + 3*B^4*a^5*b*c*d^5 - B^3*C*a^6*c*d^5 - B*C^3*a^6*c*d^5
- 2*A^3*B*b^6*c*d^5 - 2*A*B^3*b^6*c*d^5 - 3*A^3*B*a^5*b*d^6 - 3*A*B^3*a^5*b*d^6 + 8*C^4*a^3*b^3*c^3*d^3 - 3*C^
4*a^4*b^2*c^2*d^4 - 3*C^4*a^2*b^4*c^4*d^2 + 6*B^4*a^2*b^4*c^2*d^4 - 3*B^4*a^4*b^2*c^2*d^4 + 3*A^4*a^2*b^4*c^2*
d^4 + B^2*C^2*b^6*c^4*d^2 + B^2*C^2*b^6*c^2*d^4 + B^2*C^2*a^6*c^2*d^4 + A^2*C^2*a^6*c^2*d^4 - 2*A^3*C*b^6*d^6
+ A^3*B*b^6*c^3*d^3 + A*B^3*b^6*c^3*d^3 + A^3*B*a^3*b^3*d^6 + A*B^3*a^3*b^3*d^6 - A^4*b^6*c^2*d^4 + 6*A^4*a^4*
b^2*d^6 + 3*A^4*a^2*b^4*d^6 - 2*A^2*C^2*a^6*d^6 + A*B^2*C*a^6*d^6 + B^4*a^3*b^3*c^3*d^3 + A^3*C*a^6*d^6 + A*C^
3*a^6*d^6 + C^4*b^6*c^4*d^2 + C^4*a^6*c^2*d^4 + B^4*b^6*c^2*d^4 + A^2*C^2*b^6*d^6 + A^2*B^2*b^6*d^6 + A^4*b^6*
d^6, f, k)*((4*a^5*b^12*d^9 + 12*a^7*b^10*d^9 + 8*a^9*b^8*d^9 - 8*a^11*b^6*d^9 - 12*a^13*b^4*d^9 - 4*a^15*b^2*
d^9 + 4*b^17*c^5*d^4 - 4*b^17*c^7*d^2 - 12*a*b^16*c^4*d^5 + 28*a*b^16*c^6*d^3 + 32*a^3*b^14*c^8*d - 12*a^4*b^1
3*c*d^8 + 48*a^5*b^12*c^8*d - 20*a^6*b^11*c*d^8 + 32*a^7*b^10*c^8*d + 48*a^8*b^9*c*d^8 + 8*a^9*b^8*c^8*d + 152
*a^10*b^7*c*d^8 + 148*a^12*b^5*c*d^8 + 60*a^14*b^3*c*d^8 + 8*a^2*b^15*c^3*d^6 - 44*a^2*b^15*c^5*d^4 - 52*a^2*b
^15*c^7*d^2 + 8*a^3*b^14*c^2*d^7 - 12*a^3*b^14*c^4*d^5 + 172*a^3*b^14*c^6*d^3 + 68*a^4*b^13*c^3*d^6 - 248*a^4*
b^13*c^5*d^4 - 168*a^4*b^13*c^7*d^2 - 28*a^5*b^12*c^2*d^7 + 40*a^5*b^12*c^4*d^5 + 408*a^5*b^12*c^6*d^3 + 252*a
^6*b^11*c^3*d^6 - 472*a^6*b^11*c^5*d^4 - 232*a^6*b^11*c^7*d^2 - 228*a^7*b^10*c^2*d^7 + 40*a^7*b^10*c^4*d^5 + 4
72*a^7*b^10*c^6*d^3 + 488*a^8*b^9*c^3*d^6 - 428*a^8*b^9*c^5*d^4 - 148*a^8*b^9*c^7*d^2 - 472*a^9*b^8*c^2*d^7 -
60*a^9*b^8*c^4*d^5 + 268*a^9*b^8*c^6*d^3 + 512*a^10*b^7*c^3*d^6 - 188*a^10*b^7*c^5*d^4 - 36*a^10*b^7*c^7*d^2 -
448*a^11*b^6*c^2*d^7 - 92*a^11*b^6*c^4*d^5 + 60*a^11*b^6*c^6*d^3 + 276*a^12*b^5*c^3*d^6 - 32*a^12*b^5*c^5*d^4
- 204*a^13*b^4*c^2*d^7 - 32*a^13*b^4*c^4*d^5 + 60*a^14*b^3*c^3*d^6 - 36*a^15*b^2*c^2*d^7 + 8*a*b^16*c^8*d + 8
*a^16*b*c*d^8)/(a^12*d^4 + b^12*c^4 + 4*a^2*b^10*c^4 + 6*a^4*b^8*c^4 + 4*a^6*b^6*c^4 + a^8*b^4*c^4 + a^4*b^8*d
^4 + 4*a^6*b^6*d^4 + 6*a^8*b^4*d^4 + 4*a^10*b^2*d^4 - 4*a^3*b^9*c*d^3 - 16*a^3*b^9*c^3*d - 16*a^5*b^7*c*d^3 -
24*a^5*b^7*c^3*d - 24*a^7*b^5*c*d^3 - 16*a^7*b^5*c^3*d - 16*a^9*b^3*c*d^3 - 4*a^9*b^3*c^3*d + 6*a^2*b^10*c^2*d
^2 + 24*a^4*b^8*c^2*d^2 + 36*a^6*b^6*c^2*d^2 + 24*a^8*b^4*c^2*d^2 + 6*a^10*b^2*c^2*d^2 - 4*a*b^11*c^3*d - 4*a^
11*b*c*d^3) + (tan(e + f*x)*(6*a^16*b*d^9 + 6*b^17*c^8*d + 8*a^4*b^13*d^9 + 38*a^6*b^11*d^9 + 78*a^8*b^9*d^9 +
92*a^10*b^7*d^9 + 68*a^12*b^5*d^9 + 30*a^14*b^3*d^9 + 8*b^17*c^4*d^5 + 6*b^17*c^6*d^3 - 32*a*b^16*c^3*d^6 - 2
0*a*b^16*c^5*d^4 - 20*a*b^16*c^7*d^2 + 22*a^2*b^15*c^8*d - 32*a^3*b^14*c*d^8 + 28*a^4*b^13*c^8*d - 148*a^5*b^1
2*c*d^8 + 12*a^6*b^11*c^8*d - 292*a^7*b^10*c*d^8 - 2*a^8*b^9*c^8*d - 328*a^9*b^8*c*d^8 - 2*a^10*b^7*c^8*d - 23
2*a^11*b^6*c*d^8 - 100*a^13*b^4*c*d^8 - 20*a^15*b^2*c*d^8 - 2*a^16*b*c^2*d^7 + 48*a^2*b^15*c^2*d^7 + 58*a^2*b^
15*c^4*d^5 + 32*a^2*b^15*c^6*d^3 - 152*a^3*b^14*c^3*d^6 - 28*a^3*b^14*c^5*d^4 - 68*a^3*b^14*c^7*d^2 + 218*a^4*
b^13*c^2*d^7 + 60*a^4*b^13*c^4*d^5 + 38*a^4*b^13*c^6*d^3 - 236*a^5*b^12*c^3*d^6 + 128*a^5*b^12*c^5*d^4 - 72*a^
5*b^12*c^7*d^2 + 400*a^6*b^11*c^2*d^7 - 210*a^6*b^11*c^4*d^5 - 48*a^6*b^11*c^6*d^3 - 52*a^7*b^10*c^3*d^6 + 392
*a^7*b^10*c^5*d^4 - 8*a^7*b^10*c^7*d^2 + 378*a^8*b^9*c^2*d^7 - 560*a^8*b^9*c^4*d^5 - 142*a^8*b^9*c^6*d^3 + 232
*a^9*b^8*c^3*d^6 + 428*a^9*b^8*c^5*d^4 + 28*a^9*b^8*c^7*d^2 + 192*a^10*b^7*c^2*d^7 - 522*a^10*b^7*c^4*d^5 - 11
2*a^10*b^7*c^6*d^3 + 256*a^11*b^6*c^3*d^6 + 212*a^11*b^6*c^5*d^4 + 12*a^11*b^6*c^7*d^2 + 46*a^12*b^5*c^2*d^7 -
212*a^12*b^5*c^4*d^5 - 30*a^12*b^5*c^6*d^3 + 100*a^13*b^4*c^3*d^6 + 40*a^13*b^4*c^5*d^4 - 30*a^14*b^3*c^4*d^5
+ 12*a^15*b^2*c^3*d^6))/(a^12*d^4 + b^12*c^4 + 4*a^2*b^10*c^4 + 6*a^4*b^8*c^4 + 4*a^6*b^6*c^4 + a^8*b^4*c^4 +
a^4*b^8*d^4 + 4*a^6*b^6*d^4 + 6*a^8*b^4*d^4 + 4*a^10*b^2*d^4 - 4*a^3*b^9*c*d^3 - 16*a^3*b^9*c^3*d - 16*a^5*b^
7*c*d^3 - 24*a^5*b^7*c^3*d - 24*a^7*b^5*c*d^3 - 16*a^7*b^5*c^3*d - 16*a^9*b^3*c*d^3 - 4*a^9*b^3*c^3*d + 6*a^2*
b^10*c^2*d^2 + 24*a^4*b^8*c^2*d^2 + 36*a^6*b^6*c^2*d^2 + 24*a^8*b^4*c^2*d^2 + 6*a^10*b^2*c^2*d^2 - 4*a*b^11*c^
3*d - 4*a^11*b*c*d^3)) + (tan(e + f*x)*(3*A*a^13*b*d^8 - 3*A*b^14*c^7*d + C*a^13*b*d^8 + 3*C*b^14*c^7*d + 8*A*
a^3*b^11*d^8 + 24*A*a^5*b^9*d^8 + 51*A*a^7*b^7*d^8 + 65*A*a^9*b^5*d^8 + 33*A*a^11*b^3*d^8 - 4*B*a^4*b^10*d^8 +
7*B*a^6*b^8*d^8 + 21*B*a^8*b^6*d^8 + 5*B*a^10*b^4*d^8 - 5*B*a^12*b^2*d^8 + 8*A*b^14*c^3*d^5 - 8*A*b^14*c^5*d^
3 + 12*C*a^5*b^9*d^8 + 13*C*a^7*b^7*d^8 - 9*C*a^9*b^5*d^8 - 9*C*a^11*b^3*d^8 - 12*B*b^14*c^4*d^4 - B*b^14*c^6*
d^2 + 12*C*b^14*c^5*d^3 - 8*A*a*b^13*c^2*d^6 + 8*A*a*b^13*c^4*d^4 + 13*A*a*b^13*c^6*d^2 - 8*A*a^2*b^12*c*d^7 -
A*a^2*b^12*c^7*d + 8*A*a^4*b^10*c*d^7 + 7*A*a^4*b^10*c^7*d + 3*A*a^6*b^8*c*d^7 + 5*A*a^6*b^8*c^7*d - 63*A*a^8
*b^6*c*d^7 - 63*A*a^10*b^4*c*d^7 - 13*A*a^12*b^2*c*d^7 + 24*B*a*b^13*c^3*d^5 + 30*B*a*b^13*c^5*d^3 + 8*B*a^3*b
^11*c*d^7 + 13*B*a^3*b^11*c^7*d - 50*B*a^5*b^9*c*d^7 + 5*B*a^5*b^9*c^7*d - 143*B*a^7*b^7*c*d^7 - B*a^7*b^7*c^7
*d - 105*B*a^9*b^5*c*d^7 - 21*B*a^11*b^3*c*d^7 - 12*C*a*b^13*c^4*d^4 - 13*C*a*b^13*c^6*d^2 + C*a^2*b^12*c^7*d
- 44*C*a^4*b^10*c*d^7 - 7*C*a^4*b^10*c^7*d - 67*C*a^6*b^8*c*d^7 - 5*C*a^6*b^8*c^7*d + 7*C*a^8*b^6*c*d^7 + 39*C
*a^10*b^4*c*d^7 + 9*C*a^12*b^2*c*d^7 + 64*A*a^2*b^12*c^3*d^5 - 7*A*a^2*b^12*c^5*d^3 - 96*A*a^3*b^11*c^2*d^6 -
87*A*a^3*b^11*c^4*d^4 - A*a^3*b^11*c^6*d^2 + 263*A*a^4*b^10*c^3*d^5 + 67*A*a^4*b^10*c^5*d^3 - 233*A*a^5*b^9*c^
2*d^6 - 253*A*a^5*b^9*c^4*d^4 - 41*A*a^5*b^9*c^6*d^2 + 381*A*a^6*b^8*c^3*d^5 + 123*A*a^6*b^8*c^5*d^3 - 195*A*a
^7*b^7*c^2*d^6 - 213*A*a^7*b^7*c^4*d^4 - 27*A*a^7*b^7*c^6*d^2 + 189*A*a^8*b^6*c^3*d^5 + 57*A*a^8*b^6*c^5*d^3 -
35*A*a^9*b^5*c^2*d^6 - 55*A*a^9*b^5*c^4*d^4 + 15*A*a^10*b^4*c^3*d^5 + 15*A*a^11*b^3*c^2*d^6 - 16*B*a^2*b^12*c
^2*d^6 - 119*B*a^2*b^12*c^4*d^4 - 37*B*a^2*b^12*c^6*d^2 + 116*B*a^3*b^11*c^3*d^5 + 115*B*a^3*b^11*c^5*d^3 + 17
*B*a^4*b^10*c^2*d^6 - 209*B*a^4*b^10*c^4*d^4 - 65*B*a^4*b^10*c^6*d^2 + 85*B*a^5*b^9*c^3*d^5 + 125*B*a^5*b^9*c^
5*d^3 + 161*B*a^6*b^8*c^2*d^6 - 89*B*a^6*b^8*c^4*d^4 - 23*B*a^6*b^8*c^6*d^2 - 97*B*a^7*b^7*c^3*d^5 + 25*B*a^7*
b^7*c^5*d^3 + 213*B*a^8*b^6*c^2*d^6 + 33*B*a^8*b^6*c^4*d^4 + 6*B*a^8*b^6*c^6*d^2 - 105*B*a^9*b^5*c^3*d^5 - 15*
B*a^9*b^5*c^5*d^3 + 91*B*a^10*b^4*c^2*d^6 + 20*B*a^10*b^4*c^4*d^4 - 15*B*a^11*b^3*c^3*d^5 + 6*B*a^12*b^2*c^2*d
^6 - 32*C*a^2*b^12*c^3*d^5 + 23*C*a^2*b^12*c^5*d^3 + 64*C*a^3*b^11*c^2*d^6 + 71*C*a^3*b^11*c^4*d^4 + C*a^3*b^1
1*c^6*d^2 - 215*C*a^4*b^10*c^3*d^5 - 43*C*a^4*b^10*c^5*d^3 + 185*C*a^5*b^9*c^2*d^6 + 229*C*a^5*b^9*c^4*d^4 + 4
1*C*a^5*b^9*c^6*d^2 - 349*C*a^6*b^8*c^3*d^5 - 107*C*a^6*b^8*c^5*d^3 + 163*C*a^7*b^7*c^2*d^6 + 197*C*a^7*b^7*c^
4*d^4 + 27*C*a^7*b^7*c^6*d^2 - 181*C*a^8*b^6*c^3*d^5 - 53*C*a^8*b^6*c^5*d^3 + 27*C*a^9*b^5*c^2*d^6 + 51*C*a^9*
b^5*c^4*d^4 - 15*C*a^10*b^4*c^3*d^5 - 15*C*a^11*b^3*c^2*d^6 + 7*B*a*b^13*c^7*d - B*a^13*b*c*d^7))/(a^12*d^4 +
b^12*c^4 + 4*a^2*b^10*c^4 + 6*a^4*b^8*c^4 + 4*a^6*b^6*c^4 + a^8*b^4*c^4 + a^4*b^8*d^4 + 4*a^6*b^6*d^4 + 6*a^8*
b^4*d^4 + 4*a^10*b^2*d^4 - 4*a^3*b^9*c*d^3 - 16*a^3*b^9*c^3*d - 16*a^5*b^7*c*d^3 - 24*a^5*b^7*c^3*d - 24*a^7*b
^5*c*d^3 - 16*a^7*b^5*c^3*d - 16*a^9*b^3*c*d^3 - 4*a^9*b^3*c^3*d + 6*a^2*b^10*c^2*d^2 + 24*a^4*b^8*c^2*d^2 + 3
6*a^6*b^6*c^2*d^2 + 24*a^8*b^4*c^2*d^2 + 6*a^10*b^2*c^2*d^2 - 4*a*b^11*c^3*d - 4*a^11*b*c*d^3)) - (A^2*a^9*b^2
*d^7 - 45*A^2*a^5*b^6*d^7 - 24*A^2*a^7*b^4*d^7 - 28*A^2*a^3*b^8*d^7 - B^2*a^5*b^6*d^7 - 3*B^2*a^9*b^2*d^7 + 4*
A^2*b^11*c^3*d^4 - A^2*b^11*c^5*d^2 - C^2*a^5*b^6*d^7 - 4*C^2*a^7*b^4*d^7 + C^2*a^9*b^2*d^7 - B^2*b^11*c^5*d^2
- C^2*b^11*c^5*d^2 - 4*A^2*a*b^10*d^7 - 4*A^2*b^11*c*d^6 - 26*A^2*a^2*b^9*c^3*d^4 + 10*A^2*a^2*b^9*c^5*d^2 +
14*A^2*a^3*b^8*c^2*d^5 - 24*A^2*a^3*b^8*c^4*d^3 + 72*A^2*a^4*b^7*c^3*d^4 - 13*A^2*a^4*b^7*c^5*d^2 - 154*A^2*a^
5*b^6*c^2*d^5 + 33*A^2*a^5*b^6*c^4*d^3 - 42*A^2*a^6*b^5*c^3*d^4 + 28*A^2*a^7*b^4*c^2*d^5 + 34*B^2*a^2*b^9*c^3*
d^4 - 14*B^2*a^2*b^9*c^5*d^2 - 46*B^2*a^3*b^8*c^2*d^5 + 36*B^2*a^3*b^8*c^4*d^3 - 68*B^2*a^4*b^7*c^3*d^4 + 11*B
^2*a^4*b^7*c^5*d^2 + 102*B^2*a^5*b^6*c^2*d^5 - 27*B^2*a^5*b^6*c^4*d^3 + 42*B^2*a^6*b^5*c^3*d^4 - 52*B^2*a^7*b^
4*c^2*d^5 - 22*C^2*a^2*b^9*c^3*d^4 + 10*C^2*a^2*b^9*c^5*d^2 + 10*C^2*a^3*b^8*c^2*d^5 - 24*C^2*a^3*b^8*c^4*d^3
+ 92*C^2*a^4*b^7*c^3*d^4 - 13*C^2*a^4*b^7*c^5*d^2 - 134*C^2*a^5*b^6*c^2*d^5 + 33*C^2*a^5*b^6*c^4*d^3 - 30*C^2*
a^6*b^5*c^3*d^4 + 48*C^2*a^7*b^4*c^2*d^5 + 4*C^2*a^9*b^2*c^2*d^5 - 4*A*B*a^2*b^9*d^7 + 4*A*B*a^4*b^7*d^7 + 19*
A*B*a^6*b^5*d^7 + 18*A*B*a^8*b^3*d^7 + 12*A*C*a^3*b^8*d^7 + 22*A*C*a^5*b^6*d^7 + 12*A*C*a^7*b^4*d^7 - 6*A*C*a^
9*b^2*d^7 + 4*A*B*b^11*c^2*d^5 + B*C*a^6*b^5*d^7 - 6*B*C*a^8*b^3*d^7 - 4*A*C*b^11*c^3*d^4 + 2*A*C*b^11*c^5*d^2
- 2*A^2*a*b^10*c^6*d + 2*B^2*a*b^10*c^6*d - 2*C^2*a*b^10*c^6*d + 4*C^2*a^10*b*c*d^6 + 8*A^2*a*b^10*c^2*d^5 +
3*A^2*a*b^10*c^4*d^3 + 8*A^2*a^2*b^9*c*d^6 + 2*A^2*a^3*b^8*c^6*d + 63*A^2*a^4*b^7*c*d^6 + 130*A^2*a^6*b^5*c*d^
6 - 9*A^2*a^8*b^3*c*d^6 - 12*B^2*a*b^10*c^2*d^5 + 3*B^2*a*b^10*c^4*d^3 + 4*B^2*a^2*b^9*c*d^6 - 2*B^2*a^3*b^8*c
^6*d + 3*B^2*a^4*b^7*c*d^6 - 50*B^2*a^6*b^5*c*d^6 + 39*B^2*a^8*b^3*c*d^6 + 3*C^2*a*b^10*c^4*d^3 + 2*C^2*a^3*b^
8*c^6*d + 3*C^2*a^4*b^7*c*d^6 + 54*C^2*a^6*b^5*c*d^6 - 33*C^2*a^8*b^3*c*d^6 - A*B*a^10*b*d^7 - A*B*b^11*c^6*d
+ B*C*a^10*b*d^7 + B*C*b^11*c^6*d + 16*A*B*a*b^10*c*d^6 + 4*A*C*a*b^10*c^6*d - 24*A*B*a*b^10*c^3*d^4 + 6*A*B*a
*b^10*c^5*d^2 + 6*A*B*a^2*b^9*c^6*d + 56*A*B*a^3*b^8*c*d^6 - A*B*a^4*b^7*c^6*d + 70*A*B*a^5*b^6*c*d^6 - 140*A*
B*a^7*b^4*c*d^6 + 6*A*B*a^9*b^2*c*d^6 - 4*A*C*a*b^10*c^2*d^5 - 6*A*C*a*b^10*c^4*d^3 - 20*A*C*a^2*b^9*c*d^6 - 4
*A*C*a^3*b^8*c^6*d - 74*A*C*a^4*b^7*c*d^6 - 176*A*C*a^6*b^5*c*d^6 + 54*A*C*a^8*b^3*c*d^6 + 12*B*C*a*b^10*c^3*d
^4 - 6*B*C*a*b^10*c^5*d^2 - 6*B*C*a^2*b^9*c^6*d - 12*B*C*a^3*b^8*c*d^6 + B*C*a^4*b^7*c^6*d - 50*B*C*a^5*b^6*c*
d^6 + 112*B*C*a^7*b^4*c*d^6 - 26*B*C*a^9*b^2*c*d^6 - 20*A*B*a^2*b^9*c^2*d^5 - 15*A*B*a^2*b^9*c^4*d^3 + 100*A*B
*a^3*b^8*c^3*d^4 - 36*A*B*a^3*b^8*c^5*d^2 - 195*A*B*a^4*b^7*c^2*d^5 + 90*A*B*a^4*b^7*c^4*d^3 - 144*A*B*a^5*b^6
*c^3*d^4 + 6*A*B*a^5*b^6*c^5*d^2 + 190*A*B*a^6*b^5*c^2*d^5 - 15*A*B*a^6*b^5*c^4*d^3 + 20*A*B*a^7*b^4*c^3*d^4 -
15*A*B*a^8*b^3*c^2*d^5 + 48*A*C*a^2*b^9*c^3*d^4 - 20*A*C*a^2*b^9*c^5*d^2 - 8*A*C*a^3*b^8*c^2*d^5 + 48*A*C*a^3
*b^8*c^4*d^3 - 164*A*C*a^4*b^7*c^3*d^4 + 26*A*C*a^4*b^7*c^5*d^2 + 312*A*C*a^5*b^6*c^2*d^5 - 66*A*C*a^5*b^6*c^4
*d^3 + 72*A*C*a^6*b^5*c^3*d^4 - 60*A*C*a^7*b^4*c^2*d^5 + 16*B*C*a^2*b^9*c^2*d^5 + 15*B*C*a^2*b^9*c^4*d^3 - 120
*B*C*a^3*b^8*c^3*d^4 + 36*B*C*a^3*b^8*c^5*d^2 + 175*B*C*a^4*b^7*c^2*d^5 - 90*B*C*a^4*b^7*c^4*d^3 + 140*B*C*a^5
*b^6*c^3*d^4 - 6*B*C*a^5*b^6*c^5*d^2 - 202*B*C*a^6*b^5*c^2*d^5 + 15*B*C*a^6*b^5*c^4*d^3 - 16*B*C*a^7*b^4*c^3*d
^4 + 15*B*C*a^8*b^3*c^2*d^5)/(a^12*d^4 + b^12*c^4 + 4*a^2*b^10*c^4 + 6*a^4*b^8*c^4 + 4*a^6*b^6*c^4 + a^8*b^4*c
^4 + a^4*b^8*d^4 + 4*a^6*b^6*d^4 + 6*a^8*b^4*d^4 + 4*a^10*b^2*d^4 - 4*a^3*b^9*c*d^3 - 16*a^3*b^9*c^3*d - 16*a^
5*b^7*c*d^3 - 24*a^5*b^7*c^3*d - 24*a^7*b^5*c*d^3 - 16*a^7*b^5*c^3*d - 16*a^9*b^3*c*d^3 - 4*a^9*b^3*c^3*d + 6*
a^2*b^10*c^2*d^2 + 24*a^4*b^8*c^2*d^2 + 36*a^6*b^6*c^2*d^2 + 24*a^8*b^4*c^2*d^2 + 6*a^10*b^2*c^2*d^2 - 4*a*b^1
1*c^3*d - 4*a^11*b*c*d^3) + (tan(e + f*x)*(2*A^2*b^11*d^7 + 6*A^2*a^2*b^9*d^7 - 12*A^2*a^4*b^7*d^7 - 66*A^2*a^
6*b^5*d^7 + 18*A^2*a^8*b^3*d^7 - 2*B^2*a^4*b^7*d^7 + 29*B^2*a^6*b^5*d^7 - 36*B^2*a^8*b^3*d^7 - 6*A^2*b^11*c^2*
d^5 + 2*A^2*b^11*c^4*d^3 + 2*C^2*a^4*b^7*d^7 - 32*C^2*a^6*b^5*d^7 + 30*C^2*a^8*b^3*d^7 + 2*B^2*b^11*c^2*d^5 +
2*B^2*b^11*c^4*d^3 + 4*C^2*b^11*c^4*d^3 + B^2*a^10*b*d^7 - 4*C^2*a^10*b*d^7 + B^2*b^11*c^6*d + 38*A^2*a^2*b^9*
c^2*d^5 + 4*A^2*a^2*b^9*c^4*d^3 - 16*A^2*a^3*b^8*c^3*d^4 - 24*A^2*a^3*b^8*c^5*d^2 - 2*A^2*a^4*b^7*c^2*d^5 + 62
*A^2*a^4*b^7*c^4*d^3 - 88*A^2*a^5*b^6*c^3*d^4 + 78*A^2*a^6*b^5*c^2*d^5 - 8*B^2*a^2*b^9*c^2*d^5 + 19*B^2*a^2*b^
9*c^4*d^3 - 46*B^2*a^3*b^8*c^3*d^4 + 12*B^2*a^3*b^8*c^5*d^2 + 83*B^2*a^4*b^7*c^2*d^5 - 28*B^2*a^4*b^7*c^4*d^3
+ 30*B^2*a^5*b^6*c^3*d^4 - 6*B^2*a^5*b^6*c^5*d^2 - 22*B^2*a^6*b^5*c^2*d^5 + 15*B^2*a^6*b^5*c^4*d^3 - 18*B^2*a^
7*b^4*c^3*d^4 + 9*B^2*a^8*b^3*c^2*d^5 + 12*C^2*a^2*b^9*c^2*d^5 + 2*C^2*a^2*b^9*c^4*d^3 - 24*C^2*a^3*b^8*c^5*d^
2 - 82*C^2*a^4*b^7*c^2*d^5 + 52*C^2*a^4*b^7*c^4*d^3 - 56*C^2*a^5*b^6*c^3*d^4 + 22*C^2*a^6*b^5*c^2*d^5 - 6*C^2*
a^6*b^5*c^4*d^3 + 16*C^2*a^7*b^4*c^3*d^4 - 6*C^2*a^8*b^3*c^2*d^5 - 6*A*B*a^3*b^8*d^7 - 18*A*B*a^5*b^6*d^7 + 11
4*A*B*a^7*b^4*d^7 - 10*A*B*a^9*b^2*d^7 + 14*A*C*a^4*b^7*d^7 + 94*A*C*a^6*b^5*d^7 - 54*A*C*a^8*b^3*d^7 + 2*A*B*
b^11*c^3*d^4 + 24*B*C*a^5*b^6*d^7 - 84*B*C*a^7*b^4*d^7 + 28*B*C*a^9*b^2*d^7 + 4*A*C*b^11*c^2*d^5 - 6*A*C*b^11*
c^4*d^3 - 4*B*C*b^11*c^3*d^4 - 8*A^2*a*b^10*c*d^6 - 8*A^2*a*b^10*c^3*d^4 + 4*A^2*a^2*b^9*c^6*d - 40*A^2*a^3*b^
8*c*d^6 + 72*A^2*a^5*b^6*c*d^6 - 48*A^2*a^7*b^4*c*d^6 - 14*B^2*a*b^10*c^3*d^4 - 6*B^2*a*b^10*c^5*d^2 - 2*B^2*a
^2*b^9*c^6*d + 14*B^2*a^3*b^8*c*d^6 + B^2*a^4*b^7*c^6*d - 100*B^2*a^5*b^6*c*d^6 + 38*B^2*a^7*b^4*c*d^6 - 8*C^2
*a*b^10*c^3*d^4 + 4*C^2*a^2*b^9*c^6*d - 8*C^2*a^3*b^8*c*d^6 + 104*C^2*a^5*b^6*c*d^6 - 48*C^2*a^7*b^4*c*d^6 - 8
*C^2*a^9*b^2*c*d^6 + 2*C^2*a^10*b*c^2*d^5 + 2*A*C*a^10*b*d^7 - 4*A*B*b^11*c*d^6 + 4*A*B*a*b^10*c^6*d - 4*B*C*a
*b^10*c^6*d - 2*B*C*a^10*b*c*d^6 + 30*A*B*a*b^10*c^2*d^5 - 10*A*B*a^2*b^9*c*d^6 - 4*A*B*a^3*b^8*c^6*d + 114*A*
B*a^4*b^7*c*d^6 - 166*A*B*a^6*b^5*c*d^6 + 18*A*B*a^8*b^3*c*d^6 + 16*A*C*a*b^10*c^3*d^4 - 8*A*C*a^2*b^9*c^6*d +
16*A*C*a^3*b^8*c*d^6 - 224*A*C*a^5*b^6*c*d^6 + 64*A*C*a^7*b^4*c*d^6 + 6*B*C*a*b^10*c^4*d^3 + 4*B*C*a^3*b^8*c^
6*d - 106*B*C*a^4*b^7*c*d^6 + 194*B*C*a^6*b^5*c*d^6 - 6*B*C*a^8*b^3*c*d^6 - 2*A*B*a^2*b^9*c^3*d^4 - 24*A*B*a^2
*b^9*c^5*d^2 - 54*A*B*a^3*b^8*c^2*d^5 + 60*A*B*a^3*b^8*c^4*d^3 - 90*A*B*a^4*b^7*c^3*d^4 + 24*A*B*a^4*b^7*c^5*d
^2 + 118*A*B*a^5*b^6*c^2*d^5 - 60*A*B*a^5*b^6*c^4*d^3 + 74*A*B*a^6*b^5*c^3*d^4 - 46*A*B*a^7*b^4*c^2*d^5 - 56*A
*C*a^2*b^9*c^2*d^5 - 6*A*C*a^2*b^9*c^4*d^3 + 16*A*C*a^3*b^8*c^3*d^4 + 48*A*C*a^3*b^8*c^5*d^2 + 80*A*C*a^4*b^7*
c^2*d^5 - 114*A*C*a^4*b^7*c^4*d^3 + 144*A*C*a^5*b^6*c^3*d^4 - 96*A*C*a^6*b^5*c^2*d^5 + 6*A*C*a^6*b^5*c^4*d^3 -
16*A*C*a^7*b^4*c^3*d^4 + 12*A*C*a^8*b^3*c^2*d^5 - 14*B*C*a^2*b^9*c^3*d^4 + 24*B*C*a^2*b^9*c^5*d^2 + 106*B*C*a
^3*b^8*c^2*d^5 - 50*B*C*a^3*b^8*c^4*d^3 + 70*B*C*a^4*b^7*c^3*d^4 - 24*B*C*a^4*b^7*c^5*d^2 - 110*B*C*a^5*b^6*c^
2*d^5 + 62*B*C*a^5*b^6*c^4*d^3 - 74*B*C*a^6*b^5*c^3*d^4 + 26*B*C*a^7*b^4*c^2*d^5 - 2*B*C*a^7*b^4*c^4*d^3 + 6*B
*C*a^8*b^3*c^3*d^4 - 6*B*C*a^9*b^2*c^2*d^5))/(a^12*d^4 + b^12*c^4 + 4*a^2*b^10*c^4 + 6*a^4*b^8*c^4 + 4*a^6*b^6
*c^4 + a^8*b^4*c^4 + a^4*b^8*d^4 + 4*a^6*b^6*d^4 + 6*a^8*b^4*d^4 + 4*a^10*b^2*d^4 - 4*a^3*b^9*c*d^3 - 16*a^3*b
^9*c^3*d - 16*a^5*b^7*c*d^3 - 24*a^5*b^7*c^3*d - 24*a^7*b^5*c*d^3 - 16*a^7*b^5*c^3*d - 16*a^9*b^3*c*d^3 - 4*a^
9*b^3*c^3*d + 6*a^2*b^10*c^2*d^2 + 24*a^4*b^8*c^2*d^2 + 36*a^6*b^6*c^2*d^2 + 24*a^8*b^4*c^2*d^2 + 6*a^10*b^2*c
^2*d^2 - 4*a*b^11*c^3*d - 4*a^11*b*c*d^3)) - (tan(e + f*x)*(B^3*a^4*b^4*d^6 - A^3*a^3*b^5*d^6 - 3*B^3*a^6*b^2*
d^6 - 3*C^3*a^5*b^3*d^6 - B^3*b^8*c^2*d^4 - A^2*B*b^8*d^6 - A^3*a*b^7*d^6 + A^3*b^8*c*d^5 + C^3*a^7*b*d^6 + 2*
B^3*a^2*b^6*c^2*d^4 - B^3*a^4*b^4*c^2*d^4 + 4*C^3*a^2*b^6*c^3*d^3 - 12*C^3*a^3*b^5*c^2*d^4 - A*C^2*a^7*b*d^6 +
A^2*C*a*b^7*d^6 + 2*A*B^2*b^8*c*d^5 + B^2*C*a^7*b*d^6 - A^2*C*b^8*c*d^5 + A*B^2*a^3*b^5*d^6 + 9*A*B^2*a^5*b^3
*d^6 - 3*A^2*B*a^2*b^6*d^6 - 6*A^2*B*a^4*b^4*d^6 + 2*A*C^2*a^3*b^5*d^6 + 9*A*C^2*a^5*b^3*d^6 - A^2*C*a^3*b^5*d
^6 - 6*A^2*C*a^5*b^3*d^6 + B*C^2*a^4*b^4*d^6 - 3*B*C^2*a^6*b^2*d^6 - 3*B^2*C*a^5*b^3*d^6 + B^2*C*b^8*c^3*d^3 +
A^3*a^2*b^6*c*d^5 - 5*B^3*a^3*b^5*c*d^5 + 3*B^3*a^5*b^3*c*d^5 + 11*C^3*a^4*b^4*c*d^5 - C^3*a^6*b^2*c*d^5 + 4*
A*B^2*a^3*b^5*c^2*d^4 - 4*A^2*B*a^2*b^6*c^2*d^4 - 8*A*C^2*a^2*b^6*c^3*d^3 + 24*A*C^2*a^3*b^5*c^2*d^4 + 4*A^2*C
*a^2*b^6*c^3*d^3 - 12*A^2*C*a^3*b^5*c^2*d^4 + 8*B*C^2*a^2*b^6*c^2*d^4 + 4*B*C^2*a^3*b^5*c^3*d^3 - 12*B*C^2*a^4
*b^4*c^2*d^4 - 2*B^2*C*a^2*b^6*c^3*d^3 + 2*B^2*C*a^3*b^5*c^2*d^4 + B^2*C*a^4*b^4*c^3*d^3 - 3*B^2*C*a^5*b^3*c^2
*d^4 + 2*A*B*C*a^4*b^4*d^6 + 2*A*B*C*a^6*b^2*d^6 + A^2*B*a*b^7*c*d^5 - B*C^2*a^7*b*c*d^5 - 4*A*B^2*a*b^7*c^2*d
^4 + 7*A*B^2*a^2*b^6*c*d^5 - 11*A*B^2*a^4*b^4*c*d^5 + 9*A^2*B*a^3*b^5*c*d^5 - 2*A*C^2*a^2*b^6*c*d^5 - 25*A*C^2
*a^4*b^4*c*d^5 + A*C^2*a^6*b^2*c*d^5 + A^2*C*a^2*b^6*c*d^5 + 14*A^2*C*a^4*b^4*c*d^5 - 4*B*C^2*a*b^7*c^3*d^3 -
6*B*C^2*a^3*b^5*c*d^5 + 9*B*C^2*a^5*b^3*c*d^5 + B^2*C*a*b^7*c^2*d^4 + 7*B^2*C*a^4*b^4*c*d^5 + 3*B^2*C*a^6*b^2*
c*d^5 - 4*A*B*C*a^2*b^6*c^2*d^4 - 4*A*B*C*a^3*b^5*c^3*d^3 + 12*A*B*C*a^4*b^4*c^2*d^4 - 2*A*B*C*a*b^7*c*d^5 + 4
*A*B*C*a*b^7*c^3*d^3 - 6*A*B*C*a^3*b^5*c*d^5 - 12*A*B*C*a^5*b^3*c*d^5))/(a^12*d^4 + b^12*c^4 + 4*a^2*b^10*c^4
+ 6*a^4*b^8*c^4 + 4*a^6*b^6*c^4 + a^8*b^4*c^4 + a^4*b^8*d^4 + 4*a^6*b^6*d^4 + 6*a^8*b^4*d^4 + 4*a^10*b^2*d^4 -
4*a^3*b^9*c*d^3 - 16*a^3*b^9*c^3*d - 16*a^5*b^7*c*d^3 - 24*a^5*b^7*c^3*d - 24*a^7*b^5*c*d^3 - 16*a^7*b^5*c^3*
d - 16*a^9*b^3*c*d^3 - 4*a^9*b^3*c^3*d + 6*a^2*b^10*c^2*d^2 + 24*a^4*b^8*c^2*d^2 + 36*a^6*b^6*c^2*d^2 + 24*a^8
*b^4*c^2*d^2 + 6*a^10*b^2*c^2*d^2 - 4*a*b^11*c^3*d - 4*a^11*b*c*d^3))*root(480*a^11*b^7*c*d^9*f^4 + 480*a^7*b^
11*c^9*d*f^4 + 360*a^13*b^5*c*d^9*f^4 + 360*a^9*b^9*c^9*d*f^4 + 360*a^9*b^9*c*d^9*f^4 + 360*a^5*b^13*c^9*d*f^4
+ 144*a^15*b^3*c*d^9*f^4 + 144*a^11*b^7*c^9*d*f^4 + 144*a^7*b^11*c*d^9*f^4 + 144*a^3*b^15*c^9*d*f^4 + 48*a^17
*b*c^3*d^7*f^4 + 48*a*b^17*c^7*d^3*f^4 + 24*a^17*b*c^5*d^5*f^4 + 24*a^13*b^5*c^9*d*f^4 + 24*a^5*b^13*c*d^9*f^4
+ 24*a*b^17*c^5*d^5*f^4 + 24*a^17*b*c*d^9*f^4 + 24*a*b^17*c^9*d*f^4 + 3920*a^9*b^9*c^5*d^5*f^4 - 3360*a^10*b^
8*c^4*d^6*f^4 - 3360*a^8*b^10*c^6*d^4*f^4 + 3024*a^11*b^7*c^5*d^5*f^4 - 3024*a^10*b^8*c^6*d^4*f^4 - 3024*a^8*b
^10*c^4*d^6*f^4 + 3024*a^7*b^11*c^5*d^5*f^4 + 2320*a^9*b^9*c^7*d^3*f^4 + 2320*a^9*b^9*c^3*d^7*f^4 - 2240*a^12*
b^6*c^4*d^6*f^4 - 2240*a^6*b^12*c^6*d^4*f^4 + 2160*a^11*b^7*c^3*d^7*f^4 + 2160*a^7*b^11*c^7*d^3*f^4 - 1624*a^1
2*b^6*c^6*d^4*f^4 - 1624*a^6*b^12*c^4*d^6*f^4 + 1488*a^11*b^7*c^7*d^3*f^4 + 1488*a^7*b^11*c^3*d^7*f^4 + 1344*a
^13*b^5*c^5*d^5*f^4 + 1344*a^5*b^13*c^5*d^5*f^4 - 1320*a^10*b^8*c^2*d^8*f^4 - 1320*a^8*b^10*c^8*d^2*f^4 + 1200
*a^13*b^5*c^3*d^7*f^4 + 1200*a^5*b^13*c^7*d^3*f^4 - 1060*a^12*b^6*c^2*d^8*f^4 - 1060*a^6*b^12*c^8*d^2*f^4 - 94
8*a^10*b^8*c^8*d^2*f^4 - 948*a^8*b^10*c^2*d^8*f^4 - 840*a^14*b^4*c^4*d^6*f^4 - 840*a^4*b^14*c^6*d^4*f^4 + 528*
a^13*b^5*c^7*d^3*f^4 + 528*a^5*b^13*c^3*d^7*f^4 - 480*a^14*b^4*c^6*d^4*f^4 - 480*a^14*b^4*c^2*d^8*f^4 - 480*a^
4*b^14*c^8*d^2*f^4 - 480*a^4*b^14*c^4*d^6*f^4 + 368*a^15*b^3*c^3*d^7*f^4 - 368*a^12*b^6*c^8*d^2*f^4 - 368*a^6*
b^12*c^2*d^8*f^4 + 368*a^3*b^15*c^7*d^3*f^4 + 304*a^15*b^3*c^5*d^5*f^4 + 304*a^3*b^15*c^5*d^5*f^4 - 144*a^16*b
^2*c^4*d^6*f^4 - 144*a^2*b^16*c^6*d^4*f^4 - 108*a^16*b^2*c^2*d^8*f^4 - 108*a^2*b^16*c^8*d^2*f^4 + 80*a^15*b^3*
c^7*d^3*f^4 + 80*a^3*b^15*c^3*d^7*f^4 - 60*a^16*b^2*c^6*d^4*f^4 - 60*a^14*b^4*c^8*d^2*f^4 - 60*a^4*b^14*c^2*d^
8*f^4 - 60*a^2*b^16*c^4*d^6*f^4 - 8*b^18*c^8*d^2*f^4 - 4*b^18*c^6*d^4*f^4 - 8*a^18*c^2*d^8*f^4 - 4*a^18*c^4*d^
6*f^4 - 80*a^12*b^6*d^10*f^4 - 60*a^14*b^4*d^10*f^4 - 60*a^10*b^8*d^10*f^4 - 24*a^16*b^2*d^10*f^4 - 24*a^8*b^1
0*d^10*f^4 - 4*a^6*b^12*d^10*f^4 - 80*a^6*b^12*c^10*f^4 - 60*a^8*b^10*c^10*f^4 - 60*a^4*b^14*c^10*f^4 - 24*a^1
0*b^8*c^10*f^4 - 24*a^2*b^16*c^10*f^4 - 4*a^12*b^6*c^10*f^4 - 4*b^18*c^10*f^4 - 4*a^18*d^10*f^4 - 12*A*C*a^11*
b*c*d^7*f^2 - 12*A*C*a*b^11*c^7*d*f^2 - 912*B*C*a^5*b^7*c^4*d^4*f^2 - 792*B*C*a^8*b^4*c^3*d^5*f^2 + 792*B*C*a^
4*b^8*c^5*d^3*f^2 + 720*B*C*a^7*b^5*c^4*d^4*f^2 - 480*B*C*a^5*b^7*c^6*d^2*f^2 - 408*B*C*a^5*b^7*c^2*d^6*f^2 +
384*B*C*a^7*b^5*c^2*d^6*f^2 - 336*B*C*a^8*b^4*c^5*d^3*f^2 + 324*B*C*a^4*b^8*c^3*d^5*f^2 + 312*B*C*a^7*b^5*c^6*
d^2*f^2 - 248*B*C*a^3*b^9*c^6*d^2*f^2 + 216*B*C*a^9*b^3*c^2*d^6*f^2 - 196*B*C*a^3*b^9*c^4*d^4*f^2 + 132*B*C*a^
9*b^3*c^4*d^4*f^2 + 80*B*C*a^6*b^6*c^3*d^5*f^2 - 64*B*C*a^6*b^6*c^5*d^3*f^2 - 36*B*C*a^2*b^10*c^3*d^5*f^2 - 28
*B*C*a^3*b^9*c^2*d^6*f^2 + 12*B*C*a^10*b^2*c^5*d^3*f^2 - 12*B*C*a^10*b^2*c^3*d^5*f^2 - 12*B*C*a^2*b^10*c^5*d^3
*f^2 - 4*B*C*a^9*b^3*c^6*d^2*f^2 - 1468*A*C*a^6*b^6*c^4*d^4*f^2 + 996*A*C*a^7*b^5*c^3*d^5*f^2 + 900*A*C*a^5*b^
7*c^5*d^3*f^2 - 676*A*C*a^6*b^6*c^6*d^2*f^2 - 660*A*C*a^6*b^6*c^2*d^6*f^2 + 636*A*C*a^5*b^7*c^3*d^5*f^2 + 540*
A*C*a^7*b^5*c^5*d^3*f^2 - 236*A*C*a^3*b^9*c^5*d^3*f^2 - 204*A*C*a^9*b^3*c^3*d^5*f^2 + 156*A*C*a^10*b^2*c^2*d^6
*f^2 + 132*A*C*a^2*b^10*c^6*d^2*f^2 - 72*A*C*a^9*b^3*c^5*d^3*f^2 - 72*A*C*a^4*b^8*c^6*d^2*f^2 + 66*A*C*a^4*b^8
*c^2*d^6*f^2 + 54*A*C*a^10*b^2*c^4*d^4*f^2 + 54*A*C*a^2*b^10*c^4*d^4*f^2 - 48*A*C*a^8*b^4*c^2*d^6*f^2 - 48*A*C
*a^4*b^8*c^4*d^4*f^2 + 42*A*C*a^8*b^4*c^6*d^2*f^2 - 40*A*C*a^3*b^9*c^3*d^5*f^2 - 36*A*C*a^8*b^4*c^4*d^4*f^2 +
24*A*C*a^2*b^10*c^2*d^6*f^2 + 960*A*B*a^5*b^7*c^4*d^4*f^2 - 864*A*B*a^4*b^8*c^5*d^3*f^2 + 756*A*B*a^8*b^4*c^3*
d^5*f^2 - 744*A*B*a^7*b^5*c^4*d^4*f^2 - 528*A*B*a^4*b^8*c^3*d^5*f^2 + 504*A*B*a^5*b^7*c^6*d^2*f^2 - 432*A*B*a^
7*b^5*c^2*d^6*f^2 + 432*A*B*a^5*b^7*c^2*d^6*f^2 + 348*A*B*a^8*b^4*c^5*d^3*f^2 - 312*A*B*a^7*b^5*c^6*d^2*f^2 -
284*A*B*a^9*b^3*c^2*d^6*f^2 + 280*A*B*a^3*b^9*c^6*d^2*f^2 + 264*A*B*a^3*b^9*c^4*d^4*f^2 - 240*A*B*a^6*b^6*c^3*
d^5*f^2 - 172*A*B*a^9*b^3*c^4*d^4*f^2 + 68*A*B*a^3*b^9*c^2*d^6*f^2 - 60*A*B*a^2*b^10*c^3*d^5*f^2 + 24*A*B*a^6*
b^6*c^5*d^3*f^2 - 24*A*B*a^2*b^10*c^5*d^3*f^2 + 12*A*B*a^10*b^2*c^3*d^5*f^2 + 360*B*C*a^4*b^8*c^7*d*f^2 - 336*
B*C*a^8*b^4*c*d^7*f^2 + 168*B*C*a^6*b^6*c*d^7*f^2 - 136*B*C*a^6*b^6*c^7*d*f^2 - 36*B*C*a^11*b*c^2*d^6*f^2 + 36
*B*C*a*b^11*c^6*d^2*f^2 + 24*B*C*a^10*b^2*c*d^7*f^2 - 24*B*C*a^2*b^10*c^7*d*f^2 - 12*B*C*a^11*b*c^4*d^4*f^2 +
12*B*C*a^4*b^8*c*d^7*f^2 + 12*B*C*a*b^11*c^4*d^4*f^2 + 444*A*C*a^7*b^5*c*d^7*f^2 + 348*A*C*a^5*b^7*c^7*d*f^2 -
164*A*C*a^3*b^9*c^7*d*f^2 - 132*A*C*a^9*b^3*c*d^7*f^2 + 84*A*C*a^5*b^7*c*d^7*f^2 + 32*A*C*a^3*b^9*c*d^7*f^2 -
12*A*C*a^11*b*c^3*d^5*f^2 - 12*A*C*a^7*b^5*c^7*d*f^2 - 12*A*C*a*b^11*c^5*d^3*f^2 - 360*A*B*a^4*b^8*c^7*d*f^2
+ 288*A*B*a^8*b^4*c*d^7*f^2 - 288*A*B*a^6*b^6*c*d^7*f^2 - 144*A*B*a^4*b^8*c*d^7*f^2 + 136*A*B*a^6*b^6*c^7*d*f^
2 - 60*A*B*a^2*b^10*c*d^7*f^2 - 36*A*B*a^10*b^2*c*d^7*f^2 + 24*A*B*a^2*b^10*c^7*d*f^2 - 24*A*B*a*b^11*c^6*d^2*
f^2 + 12*A*B*a^11*b*c^2*d^6*f^2 + 12*A*B*a*b^11*c^4*d^4*f^2 + 12*A*B*a*b^11*c^2*d^6*f^2 - 8*B*C*b^12*c^5*d^3*f
^2 - 8*B*C*b^12*c^3*d^5*f^2 + 8*A*C*b^12*c^2*d^6*f^2 - 4*B*C*a^12*c^3*d^5*f^2 + 4*A*C*b^12*c^4*d^4*f^2 - 2*A*C
*b^12*c^6*d^2*f^2 + 80*B*C*a^9*b^3*d^8*f^2 - 24*B*C*a^7*b^5*d^8*f^2 + 6*A*C*a^12*c^2*d^6*f^2 + 4*A*B*b^12*c^5*
d^3*f^2 - 4*A*B*b^12*c^3*d^5*f^2 - 90*A*C*a^8*b^4*d^8*f^2 - 80*B*C*a^3*b^9*c^8*f^2 + 54*A*C*a^10*b^2*d^8*f^2 -
30*A*C*a^6*b^6*d^8*f^2 + 24*B*C*a^5*b^7*c^8*f^2 - 12*A*C*a^4*b^8*d^8*f^2 - 112*A*B*a^9*b^3*d^8*f^2 - 66*A*C*a
^4*b^8*c^8*f^2 + 54*A*C*a^2*b^10*c^8*f^2 + 4*A*B*a^3*b^9*d^8*f^2 + 2*A*C*a^6*b^6*c^8*f^2 + 80*A*B*a^3*b^9*c^8*
f^2 - 24*A*B*a^5*b^7*c^8*f^2 + 726*C^2*a^6*b^6*c^4*d^4*f^2 - 402*C^2*a^7*b^5*c^3*d^5*f^2 - 402*C^2*a^5*b^7*c^5
*d^3*f^2 + 322*C^2*a^6*b^6*c^6*d^2*f^2 + 322*C^2*a^6*b^6*c^2*d^6*f^2 - 222*C^2*a^7*b^5*c^5*d^3*f^2 - 222*C^2*a
^5*b^7*c^3*d^5*f^2 + 134*C^2*a^9*b^3*c^3*d^5*f^2 + 134*C^2*a^3*b^9*c^5*d^3*f^2 - 66*C^2*a^10*b^2*c^2*d^6*f^2 -
66*C^2*a^2*b^10*c^6*d^2*f^2 + 52*C^2*a^9*b^3*c^5*d^3*f^2 + 52*C^2*a^3*b^9*c^3*d^5*f^2 - 27*C^2*a^8*b^4*c^6*d^
2*f^2 - 27*C^2*a^4*b^8*c^2*d^6*f^2 + 24*C^2*a^8*b^4*c^4*d^4*f^2 + 24*C^2*a^8*b^4*c^2*d^6*f^2 + 24*C^2*a^4*b^8*
c^6*d^2*f^2 + 24*C^2*a^4*b^8*c^4*d^4*f^2 - 15*C^2*a^10*b^2*c^4*d^4*f^2 - 15*C^2*a^2*b^10*c^4*d^4*f^2 - 570*B^2
*a^6*b^6*c^4*d^4*f^2 + 366*B^2*a^7*b^5*c^3*d^5*f^2 + 318*B^2*a^5*b^7*c^5*d^3*f^2 - 262*B^2*a^6*b^6*c^6*d^2*f^2
- 222*B^2*a^6*b^6*c^2*d^6*f^2 - 210*B^2*a^3*b^9*c^5*d^3*f^2 + 186*B^2*a^7*b^5*c^5*d^3*f^2 + 162*B^2*a^5*b^7*c
^3*d^5*f^2 - 142*B^2*a^9*b^3*c^3*d^5*f^2 + 132*B^2*a^4*b^8*c^4*d^4*f^2 + 117*B^2*a^4*b^8*c^2*d^6*f^2 + 102*B^2
*a^2*b^10*c^6*d^2*f^2 - 96*B^2*a^3*b^9*c^3*d^5*f^2 + 90*B^2*a^10*b^2*c^2*d^6*f^2 + 81*B^2*a^2*b^10*c^4*d^4*f^2
- 56*B^2*a^9*b^3*c^5*d^3*f^2 + 48*B^2*a^8*b^4*c^4*d^4*f^2 + 48*B^2*a^4*b^8*c^6*d^2*f^2 + 45*B^2*a^8*b^4*c^6*d
^2*f^2 + 36*B^2*a^8*b^4*c^2*d^6*f^2 + 36*B^2*a^2*b^10*c^2*d^6*f^2 + 33*B^2*a^10*b^2*c^4*d^4*f^2 + 822*A^2*a^6*
b^6*c^4*d^4*f^2 - 594*A^2*a^7*b^5*c^3*d^5*f^2 + 498*A^2*a^6*b^6*c^2*d^6*f^2 - 498*A^2*a^5*b^7*c^5*d^3*f^2 - 41
4*A^2*a^5*b^7*c^3*d^5*f^2 + 354*A^2*a^6*b^6*c^6*d^2*f^2 - 318*A^2*a^7*b^5*c^5*d^3*f^2 + 144*A^2*a^8*b^4*c^2*d^
6*f^2 + 102*A^2*a^3*b^9*c^5*d^3*f^2 + 84*A^2*a^4*b^8*c^4*d^4*f^2 + 81*A^2*a^4*b^8*c^2*d^6*f^2 + 72*A^2*a^8*b^4
*c^4*d^4*f^2 + 70*A^2*a^9*b^3*c^3*d^5*f^2 - 66*A^2*a^2*b^10*c^6*d^2*f^2 + 48*A^2*a^4*b^8*c^6*d^2*f^2 - 42*A^2*
a^10*b^2*c^2*d^6*f^2 + 24*A^2*a^2*b^10*c^2*d^6*f^2 + 20*A^2*a^9*b^3*c^5*d^3*f^2 - 15*A^2*a^10*b^2*c^4*d^4*f^2
- 15*A^2*a^8*b^4*c^6*d^2*f^2 - 15*A^2*a^2*b^10*c^4*d^4*f^2 - 12*A^2*a^3*b^9*c^3*d^5*f^2 - 8*B*C*b^12*c^7*d*f^2
+ 4*B*C*a^12*c*d^7*f^2 - 24*B*C*a^11*b*d^8*f^2 + 8*A*B*b^12*c^7*d*f^2 - 8*A*B*b^12*c*d^7*f^2 + 24*B*C*a*b^11*
c^8*f^2 - 8*A*B*a^12*c*d^7*f^2 + 12*A*B*a^11*b*d^8*f^2 - 24*A*B*a*b^11*c^8*f^2 - 174*C^2*a^7*b^5*c*d^7*f^2 - 1
74*C^2*a^5*b^7*c^7*d*f^2 + 82*C^2*a^9*b^3*c*d^7*f^2 + 82*C^2*a^3*b^9*c^7*d*f^2 + 6*C^2*a^11*b*c^3*d^5*f^2 + 6*
C^2*a^7*b^5*c^7*d*f^2 + 6*C^2*a^5*b^7*c*d^7*f^2 + 6*C^2*a*b^11*c^5*d^3*f^2 + 162*B^2*a^7*b^5*c*d^7*f^2 + 138*B
^2*a^5*b^7*c^7*d*f^2 - 118*B^2*a^3*b^9*c^7*d*f^2 - 86*B^2*a^9*b^3*c*d^7*f^2 - 30*B^2*a*b^11*c^5*d^3*f^2 - 18*B
^2*a^7*b^5*c^7*d*f^2 - 18*B^2*a^5*b^7*c*d^7*f^2 - 12*B^2*a*b^11*c^3*d^5*f^2 - 6*B^2*a^11*b*c^3*d^5*f^2 - 4*B^2
*a^3*b^9*c*d^7*f^2 - 270*A^2*a^7*b^5*c*d^7*f^2 - 174*A^2*a^5*b^7*c^7*d*f^2 - 90*A^2*a^5*b^7*c*d^7*f^2 + 82*A^2
*a^3*b^9*c^7*d*f^2 + 50*A^2*a^9*b^3*c*d^7*f^2 - 32*A^2*a^3*b^9*c*d^7*f^2 + 6*A^2*a^11*b*c^3*d^5*f^2 + 6*A^2*a^
7*b^5*c^7*d*f^2 + 6*A^2*a*b^11*c^5*d^3*f^2 + 6*C^2*a^11*b*c*d^7*f^2 + 6*C^2*a*b^11*c^7*d*f^2 - 18*B^2*a*b^11*c
^7*d*f^2 - 6*B^2*a^11*b*c*d^7*f^2 + 6*A^2*a^11*b*c*d^7*f^2 + 6*A^2*a*b^11*c^7*d*f^2 - 6*A*C*b^12*c^8*f^2 - 2*A
*C*a^12*d^8*f^2 + 4*C^2*b^12*c^4*d^4*f^2 + 3*C^2*b^12*c^6*d^2*f^2 + 4*C^2*a^12*c^4*d^4*f^2 + 4*B^2*b^12*c^4*d^
4*f^2 + 4*B^2*b^12*c^2*d^6*f^2 + 3*C^2*a^12*c^2*d^6*f^2 + 3*B^2*b^12*c^6*d^2*f^2 + 33*C^2*a^8*b^4*d^8*f^2 - 27
*C^2*a^10*b^2*d^8*f^2 - 4*A^2*b^12*c^4*d^4*f^2 + 3*B^2*a^12*c^2*d^6*f^2 - C^2*a^6*b^6*d^8*f^2 - A^2*b^12*c^6*d
^2*f^2 + 33*C^2*a^4*b^8*c^8*f^2 + 33*B^2*a^10*b^2*d^8*f^2 - 27*C^2*a^2*b^10*c^8*f^2 - 27*B^2*a^8*b^4*d^8*f^2 +
3*B^2*a^6*b^6*d^8*f^2 - C^2*a^6*b^6*c^8*f^2 - A^2*a^12*c^2*d^6*f^2 + 117*A^2*a^8*b^4*d^8*f^2 + 111*A^2*a^6*b^
6*d^8*f^2 + 72*A^2*a^4*b^8*d^8*f^2 + 33*B^2*a^2*b^10*c^8*f^2 - 27*B^2*a^4*b^8*c^8*f^2 + 24*A^2*a^2*b^10*d^8*f^
2 + 3*B^2*a^6*b^6*c^8*f^2 - 3*A^2*a^10*b^2*d^8*f^2 + 33*A^2*a^4*b^8*c^8*f^2 - 27*A^2*a^2*b^10*c^8*f^2 - A^2*a^
6*b^6*c^8*f^2 + 3*C^2*b^12*c^8*f^2 + 3*C^2*a^12*d^8*f^2 + 4*A^2*b^12*d^8*f^2 - B^2*b^12*c^8*f^2 - B^2*a^12*d^8
*f^2 + 3*A^2*b^12*c^8*f^2 + 3*A^2*a^12*d^8*f^2 - 24*A*B*C*a*b^8*c*d^6*f + 342*A*B*C*a^4*b^5*c^2*d^5*f - 186*A*
B*C*a^5*b^4*c^3*d^4*f - 66*A*B*C*a^2*b^7*c^4*d^3*f + 48*A*B*C*a^2*b^7*c^2*d^5*f + 42*A*B*C*a^6*b^3*c^2*d^5*f +
26*A*B*C*a^3*b^6*c^5*d^2*f + 24*A*B*C*a^6*b^3*c^4*d^3*f - 18*A*B*C*a^7*b^2*c^3*d^4*f - 18*A*B*C*a^4*b^5*c^4*d
^3*f - 8*A*B*C*a^3*b^6*c^3*d^4*f + 6*A*B*C*a^5*b^4*c^5*d^2*f - 128*A*B*C*a^3*b^6*c*d^6*f + 126*A*B*C*a^7*b^2*c
*d^6*f + 72*A*B*C*a*b^8*c^3*d^4*f - 36*A*B*C*a^8*b*c^2*d^5*f - 36*A*B*C*a*b^8*c^5*d^2*f + 30*A*B*C*a^2*b^7*c^6
*d*f - 12*A*B*C*a^5*b^4*c*d^6*f - 12*A*B*C*a^4*b^5*c^6*d*f - 21*B^2*C*a^8*b*c*d^6*f - 3*B^2*C*a*b^8*c^6*d*f +
21*A^2*C*a^8*b*c*d^6*f - 21*A*C^2*a^8*b*c*d^6*f - 9*A^2*C*a*b^8*c^6*d*f + 9*A*C^2*a*b^8*c^6*d*f + 36*A^2*B*a*b
^8*c*d^6*f + 21*A*B^2*a^8*b*c*d^6*f + 3*A*B^2*a*b^8*c^6*d*f + 16*A*B*C*b^9*c^4*d^3*f - 16*A*B*C*b^9*c^2*d^5*f
- 78*A*B*C*a^6*b^3*d^7*f + 24*A*B*C*a^4*b^5*d^7*f + 2*A*B*C*a^3*b^6*c^7*f - 237*B^2*C*a^4*b^5*c^3*d^4*f + 165*
B*C^2*a^5*b^4*c^3*d^4*f + 92*B^2*C*a^3*b^6*c^2*d^5*f - 81*B^2*C*a^7*b^2*c^2*d^5*f + 77*B^2*C*a^3*b^6*c^4*d^3*f
- 75*B*C^2*a^4*b^5*c^2*d^5*f + 69*B^2*C*a^5*b^4*c^4*d^3*f + 69*B*C^2*a^4*b^5*c^4*d^3*f - 68*B*C^2*a^3*b^6*c^3
*d^4*f - 63*B^2*C*a^4*b^5*c^5*d^2*f - 61*B*C^2*a^6*b^3*c^2*d^5*f + 57*B*C^2*a^2*b^7*c^4*d^3*f - 53*B*C^2*a^3*b
^6*c^5*d^2*f - 44*B*C^2*a^6*b^3*c^4*d^3*f - 36*B^2*C*a^2*b^7*c^3*d^4*f + 35*B^2*C*a^6*b^3*c^3*d^4*f - 33*B^2*C
*a^5*b^4*c^2*d^5*f + 33*B^2*C*a^2*b^7*c^5*d^2*f + 33*B*C^2*a^7*b^2*c^3*d^4*f - 12*B^2*C*a^7*b^2*c^4*d^3*f + 9*
B*C^2*a^5*b^4*c^5*d^2*f + 4*B^2*C*a^6*b^3*c^5*d^2*f + 225*A^2*C*a^5*b^4*c^2*d^5*f - 105*A*C^2*a^5*b^4*c^2*d^5*
f - 99*A^2*C*a^4*b^5*c^3*d^4*f - 81*A^2*C*a^4*b^5*c^5*d^2*f + 67*A^2*C*a^3*b^6*c^4*d^3*f - 59*A*C^2*a^3*b^6*c^
4*d^3*f - 57*A*C^2*a^7*b^2*c^2*d^5*f + 57*A*C^2*a^2*b^7*c^5*d^2*f + 51*A^2*C*a^5*b^4*c^4*d^3*f + 48*A^2*C*a^2*
b^7*c^3*d^4*f + 45*A*C^2*a^4*b^5*c^5*d^2*f - 35*A^2*C*a^6*b^3*c^3*d^4*f + 33*A^2*C*a^7*b^2*c^2*d^5*f - 33*A^2*
C*a^2*b^7*c^5*d^2*f + 33*A*C^2*a^5*b^4*c^4*d^3*f + 27*A*C^2*a^6*b^3*c^3*d^4*f + 24*A*C^2*a^3*b^6*c^2*d^5*f - 2
4*A*C^2*a^2*b^7*c^3*d^4*f - 21*A*C^2*a^4*b^5*c^3*d^4*f - 16*A^2*C*a^3*b^6*c^2*d^5*f - 243*A^2*B*a^4*b^5*c^2*d^
5*f - 156*A*B^2*a^3*b^6*c^2*d^5*f + 141*A*B^2*a^4*b^5*c^3*d^4*f + 108*A^2*B*a^3*b^6*c^3*d^4*f - 105*A*B^2*a^3*
b^6*c^4*d^3*f + 84*A*B^2*a^2*b^7*c^3*d^4*f + 81*A*B^2*a^5*b^4*c^2*d^5*f + 51*A^2*B*a^6*b^3*c^2*d^5*f - 51*A^2*
B*a^4*b^5*c^4*d^3*f - 48*A^2*B*a^2*b^7*c^2*d^5*f + 45*A^2*B*a^5*b^4*c^3*d^4*f + 39*A*B^2*a^4*b^5*c^5*d^2*f - 3
5*A*B^2*a^6*b^3*c^3*d^4*f + 33*A*B^2*a^7*b^2*c^2*d^5*f + 27*A^2*B*a^3*b^6*c^5*d^2*f - 21*A*B^2*a^5*b^4*c^4*d^3
*f + 20*A^2*B*a^6*b^3*c^4*d^3*f - 15*A^2*B*a^7*b^2*c^3*d^4*f - 15*A^2*B*a^5*b^4*c^5*d^2*f + 9*A^2*B*a^2*b^7*c^
4*d^3*f + 3*A*B^2*a^2*b^7*c^5*d^2*f + 2*A*B*C*b^9*c^6*d*f - 6*A*B*C*a^9*c*d^6*f + 18*A*B*C*a^8*b*d^7*f - 6*A*B
*C*a*b^8*c^7*f + 63*B^2*C*a^6*b^3*c*d^6*f - 48*B^2*C*a*b^8*c^4*d^3*f + 42*B*C^2*a^8*b*c^2*d^5*f + 42*B*C^2*a^5
*b^4*c*d^6*f - 39*B*C^2*a^7*b^2*c*d^6*f + 30*B*C^2*a*b^8*c^5*d^2*f - 24*B^2*C*a^4*b^5*c*d^6*f - 24*B*C^2*a*b^8
*c^3*d^4*f + 17*B^2*C*a^3*b^6*c^6*d*f - 15*B*C^2*a^2*b^7*c^6*d*f + 12*B^2*C*a^8*b*c^3*d^4*f + 12*B^2*C*a*b^8*c
^2*d^5*f + 6*B*C^2*a^4*b^5*c^6*d*f - 192*A^2*C*a^4*b^5*c*d^6*f - 99*A^2*C*a^6*b^3*c*d^6*f + 84*A*C^2*a^4*b^5*c
*d^6*f + 59*A*C^2*a^6*b^3*c*d^6*f + 51*A^2*C*a^3*b^6*c^6*d*f - 51*A*C^2*a^3*b^6*c^6*d*f - 36*A^2*C*a*b^8*c^2*d
^5*f - 24*A*C^2*a*b^8*c^4*d^3*f + 24*A*C^2*a*b^8*c^2*d^5*f + 12*A^2*C*a*b^8*c^4*d^3*f + 12*A*C^2*a^8*b*c^3*d^4
*f + 160*A^2*B*a^3*b^6*c*d^6*f - 99*A*B^2*a^6*b^3*c*d^6*f - 87*A^2*B*a^7*b^2*c*d^6*f - 72*A*B^2*a^4*b^5*c*d^6*
f - 48*A*B^2*a*b^8*c^2*d^5*f - 36*A^2*B*a*b^8*c^3*d^4*f + 24*A*B^2*a*b^8*c^4*d^3*f - 17*A*B^2*a^3*b^6*c^6*d*f
- 15*A^2*B*a^2*b^7*c^6*d*f + 12*A*B^2*a^2*b^7*c*d^6*f + 6*A^2*B*a^8*b*c^2*d^5*f - 6*A^2*B*a^5*b^4*c*d^6*f + 6*
A^2*B*a^4*b^5*c^6*d*f + 6*A^2*B*a*b^8*c^5*d^2*f + 12*B^2*C*b^9*c^3*d^4*f - 12*B*C^2*b^9*c^4*d^3*f - 12*A^2*C*b
^9*c^3*d^4*f - 8*A*C^2*b^9*c^5*d^2*f + 8*A*C^2*b^9*c^3*d^4*f + 4*B^2*C*a^9*c^2*d^5*f + 4*A^2*C*b^9*c^5*d^2*f -
4*B*C^2*a^9*c^3*d^4*f + 12*A^2*B*b^9*c^2*d^5*f - 8*A*B^2*b^9*c^3*d^4*f - 4*A^2*B*b^9*c^4*d^3*f + 4*A*C^2*a^9*
c^2*d^5*f + 3*B^2*C*a^7*b^2*d^7*f - B*C^2*a^6*b^3*d^7*f + 96*A^2*C*a^5*b^4*d^7*f - 39*A^2*C*a^7*b^2*d^7*f - 36
*A*C^2*a^5*b^4*d^7*f + 32*A^2*C*a^3*b^6*d^7*f + 15*A*C^2*a^7*b^2*d^7*f - 3*B^2*C*a^2*b^7*c^7*f - B*C^2*a^3*b^6
*c^7*f + 111*A^2*B*a^6*b^3*d^7*f - 39*A*B^2*a^7*b^2*d^7*f + 24*A*B^2*a^5*b^4*d^7*f - 9*A^2*C*a^2*b^7*c^7*f + 9
*A*C^2*a^2*b^7*c^7*f - 4*A*B^2*a^3*b^6*d^7*f + 3*A*B^2*a^2*b^7*c^7*f - A^2*B*a^3*b^6*c^7*f + 3*C^3*a^8*b*c*d^6
*f - 3*C^3*a*b^8*c^6*d*f - 3*A^3*a^8*b*c*d^6*f + 3*A^3*a*b^8*c^6*d*f - B*C^2*b^9*c^6*d*f + 4*A^2*C*b^9*c*d^6*f
+ 3*B*C^2*a^9*c*d^6*f + 8*A*B^2*b^9*c*d^6*f + 3*B*C^2*a^8*b*d^7*f - A^2*B*b^9*c^6*d*f + 12*A^2*C*a*b^8*d^7*f
+ 3*B*C^2*a*b^8*c^7*f - A^2*B*a^9*c*d^6*f - 9*A^2*B*a^8*b*d^7*f + 3*A^2*B*a*b^8*c^7*f - 39*C^3*a^5*b^4*c^4*d^3
*f + 39*C^3*a^4*b^5*c^3*d^4*f + 27*C^3*a^7*b^2*c^2*d^5*f - 27*C^3*a^2*b^7*c^5*d^2*f - 17*C^3*a^6*b^3*c^3*d^4*f
+ 17*C^3*a^3*b^6*c^4*d^3*f + 3*C^3*a^5*b^4*c^2*d^5*f - 3*C^3*a^4*b^5*c^5*d^2*f - 63*B^3*a^5*b^4*c^3*d^4*f + 5
7*B^3*a^4*b^5*c^2*d^5*f - 51*B^3*a^2*b^7*c^4*d^3*f + 48*B^3*a^3*b^6*c^3*d^4*f + 31*B^3*a^6*b^3*c^2*d^5*f + 27*
B^3*a^3*b^6*c^5*d^2*f + 16*B^3*a^6*b^3*c^4*d^3*f - 15*B^3*a^5*b^4*c^5*d^2*f - 12*B^3*a^2*b^7*c^2*d^5*f + 9*B^3
*a^4*b^5*c^4*d^3*f - 3*B^3*a^7*b^2*c^3*d^4*f - 123*A^3*a^5*b^4*c^2*d^5*f + 81*A^3*a^4*b^5*c^3*d^4*f - 45*A^3*a
^5*b^4*c^4*d^3*f + 39*A^3*a^4*b^5*c^5*d^2*f + 25*A^3*a^6*b^3*c^3*d^4*f - 25*A^3*a^3*b^6*c^4*d^3*f - 24*A^3*a^2
*b^7*c^3*d^4*f - 8*A^3*a^3*b^6*c^2*d^5*f - 3*A^3*a^7*b^2*c^2*d^5*f + 3*A^3*a^2*b^7*c^5*d^2*f - 17*C^3*a^6*b^3*
c*d^6*f + 17*C^3*a^3*b^6*c^6*d*f - 12*C^3*a^8*b*c^3*d^4*f + 12*C^3*a*b^8*c^4*d^3*f + 24*B^3*a*b^8*c^3*d^4*f +
21*B^3*a^7*b^2*c*d^6*f - 18*B^3*a^5*b^4*c*d^6*f - 15*B^3*a^2*b^7*c^6*d*f - 6*B^3*a^8*b*c^2*d^5*f + 6*B^3*a^4*b
^5*c^6*d*f + 6*B^3*a*b^8*c^5*d^2*f + 4*B^3*a^3*b^6*c*d^6*f + 108*A^3*a^4*b^5*c*d^6*f + 57*A^3*a^6*b^3*c*d^6*f
- 17*A^3*a^3*b^6*c^6*d*f + 12*A^3*a*b^8*c^2*d^5*f + 4*C^3*b^9*c^5*d^2*f - 4*C^3*a^9*c^2*d^5*f - 4*B^3*b^9*c^2*
d^5*f + 4*A^3*b^9*c^3*d^4*f + 3*C^3*a^7*b^2*d^7*f - 3*C^3*a^2*b^7*c^7*f - B^3*a^6*b^3*d^7*f - 60*A^3*a^5*b^4*d
^7*f - 32*A^3*a^3*b^6*d^7*f + 21*A^3*a^7*b^2*d^7*f - B^3*a^3*b^6*c^7*f + 3*A^3*a^2*b^7*c^7*f - B^3*b^9*c^6*d*f
- 4*A^3*b^9*c*d^6*f - B^3*a^9*c*d^6*f + 3*B^3*a^8*b*d^7*f - 12*A^3*a*b^8*d^7*f + 3*B^3*a*b^8*c^7*f - B^2*C*a^
9*d^7*f - 4*A^2*B*b^9*d^7*f + 3*A^2*C*b^9*c^7*f - 3*A*C^2*b^9*c^7*f - A*C^2*a^9*d^7*f - A*B^2*b^9*c^7*f - C^3*
a^9*d^7*f - A^3*b^9*c^7*f + B^2*C*b^9*c^7*f + A^2*C*a^9*d^7*f + A*B^2*a^9*d^7*f + C^3*b^9*c^7*f + A^3*a^9*d^7*
f - 6*A*B^2*C*a^5*b*c*d^5 - 21*A^2*B*C*a^3*b^3*c^2*d^4 + 21*A*B*C^2*a^3*b^3*c^2*d^4 + 12*A*B^2*C*a^4*b^2*c^2*d
^4 - 12*A*B^2*C*a^2*b^4*c^2*d^4 - 10*A*B^2*C*a^3*b^3*c^3*d^3 - 6*A*B*C^2*a^4*b^2*c^3*d^3 + 3*A^2*B*C*a^4*b^2*c
^3*d^3 + 3*A^2*B*C*a^2*b^4*c^3*d^3 + 3*A*B^2*C*a^2*b^4*c^4*d^2 + 3*A*B*C^2*a^2*b^4*c^3*d^3 + 2*A*B*C^2*a^3*b^3
*c^4*d^2 - A^2*B*C*a^3*b^3*c^4*d^2 + 18*A^2*B*C*a^2*b^4*c*d^5 + 10*A*B^2*C*a^3*b^3*c*d^5 + 9*A^2*B*C*a^4*b^2*c
*d^5 - 9*A*B*C^2*a^4*b^2*c*d^5 - 9*A*B*C^2*a^2*b^4*c*d^5 - 6*A^2*B*C*a*b^5*c^2*d^4 + 6*A*B^2*C*a*b^5*c^3*d^3 +
6*A*B*C^2*a^5*b*c^2*d^4 - 6*A*B*C^2*a*b^5*c^4*d^2 - 3*A^2*B*C*a^5*b*c^2*d^4 + 3*A^2*B*C*a*b^5*c^4*d^2 + 3*A*B
*C^2*a*b^5*c^2*d^4 - 3*B^3*C*a^5*b*c^2*d^4 + 3*B^3*C*a^4*b^2*c*d^5 + 3*B^3*C*a*b^5*c^4*d^2 + 3*B^2*C^2*a^5*b*c
*d^5 - 3*B*C^3*a^5*b*c^2*d^4 + 3*B*C^3*a^4*b^2*c*d^5 + 3*B*C^3*a*b^5*c^4*d^2 + 24*A^3*C*a^3*b^3*c*d^5 + 8*A*C^
3*a^3*b^3*c*d^5 - 9*A^3*B*a^2*b^4*c*d^5 - 9*A*B^3*a^2*b^4*c*d^5 - 3*A^3*B*a^4*b^2*c*d^5 + 3*A^3*B*a*b^5*c^2*d^
4 + 3*A^2*B^2*a^5*b*c*d^5 - 3*A*B^3*a^4*b^2*c*d^5 + 3*A*B^3*a*b^5*c^2*d^4 + 5*A*B*C^2*b^6*c^3*d^3 - 4*A^2*B*C*
b^6*c^3*d^3 - A*B^2*C*b^6*c^4*d^2 - 3*A*B^2*C*a^4*b^2*d^6 - 2*A^2*B*C*a^3*b^3*d^6 + 9*B^2*C^2*a^3*b^3*c^3*d^3
- 6*B^2*C^2*a^4*b^2*c^2*d^4 + 6*B^2*C^2*a^2*b^4*c^2*d^4 - 3*B^2*C^2*a^2*b^4*c^4*d^2 + 24*A^2*C^2*a^3*b^3*c^3*d
^3 - 15*A^2*C^2*a^4*b^2*c^2*d^4 - 9*A^2*C^2*a^2*b^4*c^4*d^2 + 3*A^2*C^2*a^2*b^4*c^2*d^4 + 9*A^2*B^2*a^2*b^4*c^
2*d^4 - 3*A^2*B^2*a^4*b^2*c^2*d^4 + 4*A^2*B*C*b^6*c*d^5 - 2*A*B*C^2*b^6*c*d^5 + 2*A*B*C^2*a^6*c*d^5 - A^2*B*C*
a^6*c*d^5 + 6*A^2*B*C*a^5*b*d^6 - 3*A*B*C^2*a^5*b*d^6 - 7*B^3*C*a^3*b^3*c^2*d^4 - 7*B*C^3*a^3*b^3*c^2*d^4 + 3*
B^3*C*a^4*b^2*c^3*d^3 - 3*B^3*C*a^2*b^4*c^3*d^3 - 3*B^2*C^2*a*b^5*c^3*d^3 + 3*B*C^3*a^4*b^2*c^3*d^3 - 3*B*C^3*
a^2*b^4*c^3*d^3 - B^3*C*a^3*b^3*c^4*d^2 - B^2*C^2*a^3*b^3*c*d^5 - B*C^3*a^3*b^3*c^4*d^2 - 24*A^2*C^2*a^3*b^3*c
*d^5 - 24*A*C^3*a^3*b^3*c^3*d^3 + 12*A*C^3*a^4*b^2*c^2*d^4 + 9*A*C^3*a^2*b^4*c^4*d^2 - 8*A^3*C*a^3*b^3*c^3*d^3
+ 6*A^3*C*a^4*b^2*c^2*d^4 - 6*A^3*C*a^2*b^4*c^2*d^4 + 3*A^3*C*a^2*b^4*c^4*d^2 - 9*A^2*B^2*a^3*b^3*c*d^5 + 7*A
^3*B*a^3*b^3*c^2*d^4 + 7*A*B^3*a^3*b^3*c^2*d^4 - 3*A^3*B*a^2*b^4*c^3*d^3 - 3*A^2*B^2*a*b^5*c^3*d^3 - 3*A*B^3*a
^2*b^4*c^3*d^3 - 5*A^2*C^2*b^6*c^2*d^4 + 3*A^2*C^2*b^6*c^4*d^2 + 12*A^2*C^2*a^4*b^2*d^6 + 3*A^2*C^2*a^2*b^4*d^
6 + 6*A^2*B^2*a^4*b^2*d^6 + 3*A^2*B^2*a^2*b^4*d^6 + A*B*C^2*a^3*b^3*d^6 - 3*B^4*a*b^5*c^3*d^3 - B^4*a^3*b^3*c*
d^5 + A^2*B^2*a^3*b^3*c^3*d^3 - 8*A^4*a^3*b^3*c*d^5 - 2*B^3*C*b^6*c^3*d^3 - 2*B*C^3*b^6*c^3*d^3 + 4*A^3*C*b^6*
c^2*d^4 - 3*A*C^3*b^6*c^4*d^2 + 2*A*C^3*b^6*c^2*d^4 - A^3*C*b^6*c^4*d^2 - 2*A*C^3*a^6*c^2*d^4 - 15*A^3*C*a^4*b
^2*d^6 - 6*A^3*C*a^2*b^4*d^6 - 3*A*C^3*a^4*b^2*d^6 + 3*B^4*a^5*b*c*d^5 - B^3*C*a^6*c*d^5 - B*C^3*a^6*c*d^5 - 2
*A^3*B*b^6*c*d^5 - 2*A*B^3*b^6*c*d^5 - 3*A^3*B*a^5*b*d^6 - 3*A*B^3*a^5*b*d^6 + 8*C^4*a^3*b^3*c^3*d^3 - 3*C^4*a
^4*b^2*c^2*d^4 - 3*C^4*a^2*b^4*c^4*d^2 + 6*B^4*a^2*b^4*c^2*d^4 - 3*B^4*a^4*b^2*c^2*d^4 + 3*A^4*a^2*b^4*c^2*d^4
+ B^2*C^2*b^6*c^4*d^2 + B^2*C^2*b^6*c^2*d^4 + B^2*C^2*a^6*c^2*d^4 + A^2*C^2*a^6*c^2*d^4 - 2*A^3*C*b^6*d^6 + A
^3*B*b^6*c^3*d^3 + A*B^3*b^6*c^3*d^3 + A^3*B*a^3*b^3*d^6 + A*B^3*a^3*b^3*d^6 - A^4*b^6*c^2*d^4 + 6*A^4*a^4*b^2
*d^6 + 3*A^4*a^2*b^4*d^6 - 2*A^2*C^2*a^6*d^6 + A*B^2*C*a^6*d^6 + B^4*a^3*b^3*c^3*d^3 + A^3*C*a^6*d^6 + A*C^3*a
^6*d^6 + C^4*b^6*c^4*d^2 + C^4*a^6*c^2*d^4 + B^4*b^6*c^2*d^4 + A^2*C^2*b^6*d^6 + A^2*B^2*b^6*d^6 + A^4*b^6*d^6
, f, k), k, 1, 4))/f