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

Optimal. Leaf size=487 \[ -\frac {x \left (a \left (-A \left (c^3-3 c d^2\right )-3 B c^2 d+B d^3+c^3 C-3 c C d^2\right )+b \left (d (A-C) \left (3 c^2-d^2\right )-B \left (c^3-3 c d^2\right )\right )\right )}{\left (a^2+b^2\right ) \left (c^2+d^2\right )^3}-\frac {\left (a^2 d^3 \left (d (A-C) \left (3 c^2-d^2\right )-B \left (c^3-3 c d^2\right )\right )-a b d^2 \left (8 c^3 d (A-C)-B \left (3 c^4-6 c^2 d^2-d^4\right )\right )+b^2 \left (3 c^4 d^2 (2 A-C)+3 A c^2 d^4+A d^6-3 B c^5 d+B c^3 d^3+c^6 C\right )\right ) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left (c^2+d^2\right )^3 (b c-a d)^3}+\frac {b^2 \left (A b^2-a (b B-a C)\right ) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left (a^2+b^2\right ) (b c-a d)^3}+\frac {A d^2-B c d+c^2 C}{2 f \left (c^2+d^2\right ) (b c-a d) (c+d \tan (e+f x))^2}+\frac {b \left (c^2 d^2 (3 A-C)+A d^4-2 B c^3 d+c^4 C\right )-a d^2 \left (2 c d (A-C)-B \left (c^2-d^2\right )\right )}{f \left (c^2+d^2\right )^2 (b c-a d)^2 (c+d \tan (e+f x))} \]

[Out]

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

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Rubi [A]  time = 1.83, antiderivative size = 487, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {3649, 3651, 3530} \[ -\frac {\left (a^2 d^3 \left (d (A-C) \left (3 c^2-d^2\right )-B \left (c^3-3 c d^2\right )\right )-a b d^2 \left (8 c^3 d (A-C)-B \left (-6 c^2 d^2+3 c^4-d^4\right )\right )+b^2 \left (3 c^4 d^2 (2 A-C)+3 A c^2 d^4+A d^6+B c^3 d^3-3 B c^5 d+c^6 C\right )\right ) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left (c^2+d^2\right )^3 (b c-a d)^3}-\frac {x \left (a \left (-A \left (c^3-3 c d^2\right )-3 B c^2 d+B d^3+c^3 C-3 c C d^2\right )+b \left (d (A-C) \left (3 c^2-d^2\right )-B \left (c^3-3 c d^2\right )\right )\right )}{\left (a^2+b^2\right ) \left (c^2+d^2\right )^3}+\frac {b^2 \left (A b^2-a (b B-a C)\right ) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left (a^2+b^2\right ) (b c-a d)^3}+\frac {b \left (c^2 d^2 (3 A-C)+A d^4-2 B c^3 d+c^4 C\right )-a d^2 \left (2 c d (A-C)-B \left (c^2-d^2\right )\right )}{f \left (c^2+d^2\right )^2 (b c-a d)^2 (c+d \tan (e+f x))}+\frac {A d^2-B c d+c^2 C}{2 f \left (c^2+d^2\right ) (b c-a d) (c+d \tan (e+f x))^2} \]

Antiderivative was successfully verified.

[In]

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

[Out]

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

Rule 3530

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

Rule 3649

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

Rule 3651

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

Rubi steps

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

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Mathematica [A]  time = 9.24, size = 912, normalized size = 1.87 \[ -\frac {A d^2-c (B d-c C)}{2 (a d-b c) \left (c^2+d^2\right ) f (c+d \tan (e+f x))^2}-\frac {-\frac {-2 \left (a A c d-a (c C-B d) d-A b \left (c^2+d^2\right )\right ) d^2-c \left (2 d (b c-a d) (B c-(A-C) d)-2 b c \left (C c^2-B d c+A d^2\right )\right )}{(a d-b c) \left (c^2+d^2\right ) f (c+d \tan (e+f x))}-\frac {\frac {2 \left (A b^2-a (b B-a C)\right ) \left (c^2+d^2\right )^2 \log (a+b \tan (e+f x)) b^3}{\left (a^2+b^2\right ) (b c-a d)}-\frac {(b c-a d)^2 \left (A b c^3-a B c^3-b C c^3+3 a A d c^2+3 b B d c^2-3 a C d c^2-3 A b d^2 c+3 a B d^2 c+3 b C d^2 c-a A d^3-b B d^3+a C d^3-\frac {\sqrt {-b^2} \left (a \left (C c^3-3 B d c^2-3 C d^2 c+B d^3-A \left (c^3-3 c d^2\right )\right )+b \left ((A-C) d \left (3 c^2-d^2\right )-B \left (c^3-3 c d^2\right )\right )\right )}{b}\right ) \log \left (\sqrt {-b^2}-b \tan (e+f x)\right ) b}{\left (a^2+b^2\right ) \left (c^2+d^2\right )}-\frac {(b c-a d)^2 \left (A b c^3-a B c^3-b C c^3+3 a A d c^2+3 b B d c^2-3 a C d c^2-3 A b d^2 c+3 a B d^2 c+3 b C d^2 c-a A d^3-b B d^3+a C d^3+\frac {\sqrt {-b^2} \left (b (A-C) d \left (3 c^2-d^2\right )-b B \left (c^3-3 c d^2\right )-a \left (A c^3-C c^3+3 B d c^2-3 A d^2 c+3 C d^2 c-B d^3\right )\right )}{b}\right ) \log \left (b \tan (e+f x)+\sqrt {-b^2}\right ) b}{\left (a^2+b^2\right ) \left (c^2+d^2\right )}-\frac {2 \left (a^2 \left ((A-C) d \left (3 c^2-d^2\right )-B \left (c^3-3 c d^2\right )\right ) d^3-a b \left (8 c^3 (A-C) d-B \left (3 c^4-6 d^2 c^2-d^4\right )\right ) d^2+b^2 \left (C c^6-3 B d c^5+3 (2 A-C) d^2 c^4+B d^3 c^3+3 A d^4 c^2+A d^6\right )\right ) \log (c+d \tan (e+f x)) b}{(b c-a d) \left (c^2+d^2\right )}}{b (a d-b c) \left (c^2+d^2\right ) f}}{2 (a d-b c) \left (c^2+d^2\right )} \]

Antiderivative was successfully verified.

[In]

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

[Out]

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

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fricas [B]  time = 6.77, size = 3496, normalized size = 7.18 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [B]  time = 17.82, size = 2125, normalized size = 4.36 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [B]  time = 0.53, size = 2298, normalized size = 4.72 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [B]  time = 0.56, size = 1078, normalized size = 2.21 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [B]  time = 24.61, size = 65817, normalized size = 135.15 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: NotImplementedError

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