3.461 \(\int \frac {\cot ^3(e+f x)}{a+b \sec ^3(e+f x)} \, dx\)

Optimal. Leaf size=393 \[ -\frac {b^2 \left (2 a^2+b^2\right ) \log \left (a \cos ^3(e+f x)+b\right )}{3 a f \left (a^2-b^2\right )^2}+\frac {b^{4/3} \left (3 a^{2/3} b^{4/3}+a^2+2 b^2\right ) \log \left (a^{2/3} \cos ^2(e+f x)-\sqrt [3]{a} \sqrt [3]{b} \cos (e+f x)+b^{2/3}\right )}{6 \sqrt [3]{a} f \left (a^2-b^2\right )^2}-\frac {b^{4/3} \left (3 a^{2/3} b^{4/3}+a^2+2 b^2\right ) \log \left (\sqrt [3]{a} \cos (e+f x)+\sqrt [3]{b}\right )}{3 \sqrt [3]{a} f \left (a^2-b^2\right )^2}+\frac {b^{4/3} \left (-3 a^{2/3} b^{4/3}+a^2+2 b^2\right ) \tan ^{-1}\left (\frac {\sqrt [3]{b}-2 \sqrt [3]{a} \cos (e+f x)}{\sqrt {3} \sqrt [3]{b}}\right )}{\sqrt {3} \sqrt [3]{a} f \left (a^2-b^2\right )^2}-\frac {1}{4 f (a+b) (1-\cos (e+f x))}-\frac {1}{4 f (a-b) (\cos (e+f x)+1)}-\frac {(2 a+5 b) \log (1-\cos (e+f x))}{4 f (a+b)^2}-\frac {(2 a-5 b) \log (\cos (e+f x)+1)}{4 f (a-b)^2} \]

[Out]

-1/4/(a+b)/f/(1-cos(f*x+e))-1/4/(a-b)/f/(1+cos(f*x+e))-1/4*(2*a+5*b)*ln(1-cos(f*x+e))/(a+b)^2/f-1/4*(2*a-5*b)*
ln(1+cos(f*x+e))/(a-b)^2/f-1/3*b^(4/3)*(a^2+3*a^(2/3)*b^(4/3)+2*b^2)*ln(b^(1/3)+a^(1/3)*cos(f*x+e))/a^(1/3)/(a
^2-b^2)^2/f+1/6*b^(4/3)*(a^2+3*a^(2/3)*b^(4/3)+2*b^2)*ln(b^(2/3)-a^(1/3)*b^(1/3)*cos(f*x+e)+a^(2/3)*cos(f*x+e)
^2)/a^(1/3)/(a^2-b^2)^2/f-1/3*b^2*(2*a^2+b^2)*ln(b+a*cos(f*x+e)^3)/a/(a^2-b^2)^2/f+1/3*b^(4/3)*(a^2-3*a^(2/3)*
b^(4/3)+2*b^2)*arctan(1/3*(b^(1/3)-2*a^(1/3)*cos(f*x+e))/b^(1/3)*3^(1/2))/a^(1/3)/(a^2-b^2)^2/f*3^(1/2)

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Rubi [A]  time = 0.63, antiderivative size = 393, normalized size of antiderivative = 1.00, number of steps used = 11, number of rules used = 10, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.435, Rules used = {4138, 6725, 1871, 1860, 31, 634, 617, 204, 628, 260} \[ -\frac {b^2 \left (2 a^2+b^2\right ) \log \left (a \cos ^3(e+f x)+b\right )}{3 a f \left (a^2-b^2\right )^2}+\frac {b^{4/3} \left (3 a^{2/3} b^{4/3}+a^2+2 b^2\right ) \log \left (a^{2/3} \cos ^2(e+f x)-\sqrt [3]{a} \sqrt [3]{b} \cos (e+f x)+b^{2/3}\right )}{6 \sqrt [3]{a} f \left (a^2-b^2\right )^2}-\frac {b^{4/3} \left (3 a^{2/3} b^{4/3}+a^2+2 b^2\right ) \log \left (\sqrt [3]{a} \cos (e+f x)+\sqrt [3]{b}\right )}{3 \sqrt [3]{a} f \left (a^2-b^2\right )^2}+\frac {b^{4/3} \left (-3 a^{2/3} b^{4/3}+a^2+2 b^2\right ) \tan ^{-1}\left (\frac {\sqrt [3]{b}-2 \sqrt [3]{a} \cos (e+f x)}{\sqrt {3} \sqrt [3]{b}}\right )}{\sqrt {3} \sqrt [3]{a} f \left (a^2-b^2\right )^2}-\frac {1}{4 f (a+b) (1-\cos (e+f x))}-\frac {1}{4 f (a-b) (\cos (e+f x)+1)}-\frac {(2 a+5 b) \log (1-\cos (e+f x))}{4 f (a+b)^2}-\frac {(2 a-5 b) \log (\cos (e+f x)+1)}{4 f (a-b)^2} \]

Antiderivative was successfully verified.

[In]

Int[Cot[e + f*x]^3/(a + b*Sec[e + f*x]^3),x]

[Out]

(b^(4/3)*(a^2 - 3*a^(2/3)*b^(4/3) + 2*b^2)*ArcTan[(b^(1/3) - 2*a^(1/3)*Cos[e + f*x])/(Sqrt[3]*b^(1/3))])/(Sqrt
[3]*a^(1/3)*(a^2 - b^2)^2*f) - 1/(4*(a + b)*f*(1 - Cos[e + f*x])) - 1/(4*(a - b)*f*(1 + Cos[e + f*x])) - ((2*a
+ 5*b)*Log[1 - Cos[e + f*x]])/(4*(a + b)^2*f) - ((2*a - 5*b)*Log[1 + Cos[e + f*x]])/(4*(a - b)^2*f) - (b^(4/3
)*(a^2 + 3*a^(2/3)*b^(4/3) + 2*b^2)*Log[b^(1/3) + a^(1/3)*Cos[e + f*x]])/(3*a^(1/3)*(a^2 - b^2)^2*f) + (b^(4/3
)*(a^2 + 3*a^(2/3)*b^(4/3) + 2*b^2)*Log[b^(2/3) - a^(1/3)*b^(1/3)*Cos[e + f*x] + a^(2/3)*Cos[e + f*x]^2])/(6*a
^(1/3)*(a^2 - b^2)^2*f) - (b^2*(2*a^2 + b^2)*Log[b + a*Cos[e + f*x]^3])/(3*a*(a^2 - b^2)^2*f)

Rule 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rule 204

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

Rule 260

Int[(x_)^(m_.)/((a_) + (b_.)*(x_)^(n_)), x_Symbol] :> Simp[Log[RemoveContent[a + b*x^n, x]]/(b*n), x] /; FreeQ
[{a, b, m, n}, x] && EqQ[m, n - 1]

Rule 617

Int[((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> With[{q = 1 - 4*Simplify[(a*c)/b^2]}, Dist[-2/b, Sub
st[Int[1/(q - x^2), x], x, 1 + (2*c*x)/b], x] /; RationalQ[q] && (EqQ[q^2, 1] ||  !RationalQ[b^2 - 4*a*c])] /;
FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]

Rule 628

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

Rule 634

Int[((d_.) + (e_.)*(x_))/((a_) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Dist[(2*c*d - b*e)/(2*c), Int[1/(a +
b*x + c*x^2), x], x] + Dist[e/(2*c), Int[(b + 2*c*x)/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c, d, e}, x] &
& NeQ[2*c*d - b*e, 0] && NeQ[b^2 - 4*a*c, 0] &&  !NiceSqrtQ[b^2 - 4*a*c]

Rule 1860

Int[((A_) + (B_.)*(x_))/((a_) + (b_.)*(x_)^3), x_Symbol] :> With[{r = Numerator[Rt[a/b, 3]], s = Denominator[R
t[a/b, 3]]}, -Dist[(r*(B*r - A*s))/(3*a*s), Int[1/(r + s*x), x], x] + Dist[r/(3*a*s), Int[(r*(B*r + 2*A*s) + s
*(B*r - A*s)*x)/(r^2 - r*s*x + s^2*x^2), x], x]] /; FreeQ[{a, b, A, B}, x] && NeQ[a*B^3 - b*A^3, 0] && PosQ[a/
b]

Rule 1871

Int[(P2_)/((a_) + (b_.)*(x_)^3), x_Symbol] :> With[{A = Coeff[P2, x, 0], B = Coeff[P2, x, 1], C = Coeff[P2, x,
2]}, Int[(A + B*x)/(a + b*x^3), x] + Dist[C, Int[x^2/(a + b*x^3), x], x] /; EqQ[a*B^3 - b*A^3, 0] ||  !Ration
alQ[a/b]] /; FreeQ[{a, b}, x] && PolyQ[P2, x, 2]

Rule 4138

Int[((a_) + (b_.)*sec[(e_.) + (f_.)*(x_)]^(n_))^(p_.)*tan[(e_.) + (f_.)*(x_)]^(m_.), x_Symbol] :> Module[{ff =
FreeFactors[Cos[e + f*x], x]}, -Dist[(f*ff^(m + n*p - 1))^(-1), Subst[Int[((1 - ff^2*x^2)^((m - 1)/2)*(b + a*
(ff*x)^n)^p)/x^(m + n*p), x], x, Cos[e + f*x]/ff], x]] /; FreeQ[{a, b, e, f, n}, x] && IntegerQ[(m - 1)/2] &&
IntegerQ[n] && IntegerQ[p]

Rule 6725

Int[(u_)/((a_) + (b_.)*(x_)^(n_)), x_Symbol] :> With[{v = RationalFunctionExpand[u/(a + b*x^n), x]}, Int[v, x]
/; SumQ[v]] /; FreeQ[{a, b}, x] && IGtQ[n, 0]

Rubi steps

\begin {align*} \int \frac {\cot ^3(e+f x)}{a+b \sec ^3(e+f x)} \, dx &=-\frac {\operatorname {Subst}\left (\int \frac {x^6}{\left (1-x^2\right )^2 \left (b+a x^3\right )} \, dx,x,\cos (e+f x)\right )}{f}\\ &=-\frac {\operatorname {Subst}\left (\int \left (\frac {1}{4 (a+b) (-1+x)^2}+\frac {2 a+5 b}{4 (a+b)^2 (-1+x)}-\frac {1}{4 (a-b) (1+x)^2}+\frac {2 a-5 b}{4 (a-b)^2 (1+x)}+\frac {b^2 \left (a^2+2 b^2-3 a b x+\left (2 a^2+b^2\right ) x^2\right )}{\left (a^2-b^2\right )^2 \left (b+a x^3\right )}\right ) \, dx,x,\cos (e+f x)\right )}{f}\\ &=-\frac {1}{4 (a+b) f (1-\cos (e+f x))}-\frac {1}{4 (a-b) f (1+\cos (e+f x))}-\frac {(2 a+5 b) \log (1-\cos (e+f x))}{4 (a+b)^2 f}-\frac {(2 a-5 b) \log (1+\cos (e+f x))}{4 (a-b)^2 f}-\frac {b^2 \operatorname {Subst}\left (\int \frac {a^2+2 b^2-3 a b x+\left (2 a^2+b^2\right ) x^2}{b+a x^3} \, dx,x,\cos (e+f x)\right )}{\left (a^2-b^2\right )^2 f}\\ &=-\frac {1}{4 (a+b) f (1-\cos (e+f x))}-\frac {1}{4 (a-b) f (1+\cos (e+f x))}-\frac {(2 a+5 b) \log (1-\cos (e+f x))}{4 (a+b)^2 f}-\frac {(2 a-5 b) \log (1+\cos (e+f x))}{4 (a-b)^2 f}-\frac {b^2 \operatorname {Subst}\left (\int \frac {a^2+2 b^2-3 a b x}{b+a x^3} \, dx,x,\cos (e+f x)\right )}{\left (a^2-b^2\right )^2 f}-\frac {\left (b^2 \left (2 a^2+b^2\right )\right ) \operatorname {Subst}\left (\int \frac {x^2}{b+a x^3} \, dx,x,\cos (e+f x)\right )}{\left (a^2-b^2\right )^2 f}\\ &=-\frac {1}{4 (a+b) f (1-\cos (e+f x))}-\frac {1}{4 (a-b) f (1+\cos (e+f x))}-\frac {(2 a+5 b) \log (1-\cos (e+f x))}{4 (a+b)^2 f}-\frac {(2 a-5 b) \log (1+\cos (e+f x))}{4 (a-b)^2 f}-\frac {b^2 \left (2 a^2+b^2\right ) \log \left (b+a \cos ^3(e+f x)\right )}{3 a \left (a^2-b^2\right )^2 f}-\frac {b^{4/3} \operatorname {Subst}\left (\int \frac {\sqrt [3]{b} \left (-3 a b^{4/3}+2 \sqrt [3]{a} \left (a^2+2 b^2\right )\right )+\sqrt [3]{a} \left (-3 a b^{4/3}-\sqrt [3]{a} \left (a^2+2 b^2\right )\right ) x}{b^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+a^{2/3} x^2} \, dx,x,\cos (e+f x)\right )}{3 \sqrt [3]{a} \left (a^2-b^2\right )^2 f}-\frac {\left (b^{4/3} \left (a^2+3 a^{2/3} b^{4/3}+2 b^2\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt [3]{b}+\sqrt [3]{a} x} \, dx,x,\cos (e+f x)\right )}{3 \left (a^2-b^2\right )^2 f}\\ &=-\frac {1}{4 (a+b) f (1-\cos (e+f x))}-\frac {1}{4 (a-b) f (1+\cos (e+f x))}-\frac {(2 a+5 b) \log (1-\cos (e+f x))}{4 (a+b)^2 f}-\frac {(2 a-5 b) \log (1+\cos (e+f x))}{4 (a-b)^2 f}-\frac {b^{4/3} \left (a^2+3 a^{2/3} b^{4/3}+2 b^2\right ) \log \left (\sqrt [3]{b}+\sqrt [3]{a} \cos (e+f x)\right )}{3 \sqrt [3]{a} \left (a^2-b^2\right )^2 f}-\frac {b^2 \left (2 a^2+b^2\right ) \log \left (b+a \cos ^3(e+f x)\right )}{3 a \left (a^2-b^2\right )^2 f}-\frac {\left (b^{5/3} \left (a^2-3 a^{2/3} b^{4/3}+2 b^2\right )\right ) \operatorname {Subst}\left (\int \frac {1}{b^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+a^{2/3} x^2} \, dx,x,\cos (e+f x)\right )}{2 \left (a^2-b^2\right )^2 f}+\frac {\left (b^{4/3} \left (a^2+3 a^{2/3} b^{4/3}+2 b^2\right )\right ) \operatorname {Subst}\left (\int \frac {-\sqrt [3]{a} \sqrt [3]{b}+2 a^{2/3} x}{b^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+a^{2/3} x^2} \, dx,x,\cos (e+f x)\right )}{6 \sqrt [3]{a} \left (a^2-b^2\right )^2 f}\\ &=-\frac {1}{4 (a+b) f (1-\cos (e+f x))}-\frac {1}{4 (a-b) f (1+\cos (e+f x))}-\frac {(2 a+5 b) \log (1-\cos (e+f x))}{4 (a+b)^2 f}-\frac {(2 a-5 b) \log (1+\cos (e+f x))}{4 (a-b)^2 f}-\frac {b^{4/3} \left (a^2+3 a^{2/3} b^{4/3}+2 b^2\right ) \log \left (\sqrt [3]{b}+\sqrt [3]{a} \cos (e+f x)\right )}{3 \sqrt [3]{a} \left (a^2-b^2\right )^2 f}+\frac {b^{4/3} \left (a^2+3 a^{2/3} b^{4/3}+2 b^2\right ) \log \left (b^{2/3}-\sqrt [3]{a} \sqrt [3]{b} \cos (e+f x)+a^{2/3} \cos ^2(e+f x)\right )}{6 \sqrt [3]{a} \left (a^2-b^2\right )^2 f}-\frac {b^2 \left (2 a^2+b^2\right ) \log \left (b+a \cos ^3(e+f x)\right )}{3 a \left (a^2-b^2\right )^2 f}-\frac {\left (b^{4/3} \left (a^2-3 a^{2/3} b^{4/3}+2 b^2\right )\right ) \operatorname {Subst}\left (\int \frac {1}{-3-x^2} \, dx,x,1-\frac {2 \sqrt [3]{a} \cos (e+f x)}{\sqrt [3]{b}}\right )}{\sqrt [3]{a} \left (a^2-b^2\right )^2 f}\\ &=\frac {b^{4/3} \left (a^2-3 a^{2/3} b^{4/3}+2 b^2\right ) \tan ^{-1}\left (\frac {1-\frac {2 \sqrt [3]{a} \cos (e+f x)}{\sqrt [3]{b}}}{\sqrt {3}}\right )}{\sqrt {3} \sqrt [3]{a} \left (a^2-b^2\right )^2 f}-\frac {1}{4 (a+b) f (1-\cos (e+f x))}-\frac {1}{4 (a-b) f (1+\cos (e+f x))}-\frac {(2 a+5 b) \log (1-\cos (e+f x))}{4 (a+b)^2 f}-\frac {(2 a-5 b) \log (1+\cos (e+f x))}{4 (a-b)^2 f}-\frac {b^{4/3} \left (a^2+3 a^{2/3} b^{4/3}+2 b^2\right ) \log \left (\sqrt [3]{b}+\sqrt [3]{a} \cos (e+f x)\right )}{3 \sqrt [3]{a} \left (a^2-b^2\right )^2 f}+\frac {b^{4/3} \left (a^2+3 a^{2/3} b^{4/3}+2 b^2\right ) \log \left (b^{2/3}-\sqrt [3]{a} \sqrt [3]{b} \cos (e+f x)+a^{2/3} \cos ^2(e+f x)\right )}{6 \sqrt [3]{a} \left (a^2-b^2\right )^2 f}-\frac {b^2 \left (2 a^2+b^2\right ) \log \left (b+a \cos ^3(e+f x)\right )}{3 a \left (a^2-b^2\right )^2 f}\\ \end {align*}

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Mathematica [C]  time = 1.97, size = 336, normalized size = 0.85 \[ \frac {\frac {8 b^2 \left ((b-a) \text {RootSum}\left [\text {$\#$1}^3 a-\text {$\#$1}^3 b-6 \text {$\#$1}^2 a+12 \text {$\#$1} a-8 a\& ,\frac {2 \text {$\#$1}^2 a^2 \log \left (-\text {$\#$1}+\tan ^2\left (\frac {1}{2} (e+f x)\right )+1\right )+\text {$\#$1}^2 b^2 \log \left (-\text {$\#$1}+\tan ^2\left (\frac {1}{2} (e+f x)\right )+1\right )+8 a^2 \log \left (-\text {$\#$1}+\tan ^2\left (\frac {1}{2} (e+f x)\right )+1\right )-6 \text {$\#$1} a^2 \log \left (-\text {$\#$1}+\tan ^2\left (\frac {1}{2} (e+f x)\right )+1\right )-4 a b \log \left (-\text {$\#$1}+\tan ^2\left (\frac {1}{2} (e+f x)\right )+1\right )}{\text {$\#$1}^2 a-\text {$\#$1}^2 b-4 \text {$\#$1} a+4 a}\& \right ]+3 \left (2 a^2+b^2\right ) \log \left (\sec ^2\left (\frac {1}{2} (e+f x)\right )\right )\right )}{a \left (a^2-b^2\right )^2}-\frac {3 \csc ^2\left (\frac {1}{2} (e+f x)\right )}{a+b}-\frac {3 \sec ^2\left (\frac {1}{2} (e+f x)\right )}{a-b}-\frac {12 (2 a+5 b) \log \left (\sin \left (\frac {1}{2} (e+f x)\right )\right )}{(a+b)^2}+\frac {12 (5 b-2 a) \log \left (\cos \left (\frac {1}{2} (e+f x)\right )\right )}{(a-b)^2}}{24 f} \]

Antiderivative was successfully verified.

[In]

Integrate[Cot[e + f*x]^3/(a + b*Sec[e + f*x]^3),x]

[Out]

((-3*Csc[(e + f*x)/2]^2)/(a + b) + (12*(-2*a + 5*b)*Log[Cos[(e + f*x)/2]])/(a - b)^2 - (12*(2*a + 5*b)*Log[Sin
[(e + f*x)/2]])/(a + b)^2 + (8*b^2*(3*(2*a^2 + b^2)*Log[Sec[(e + f*x)/2]^2] + (-a + b)*RootSum[-8*a + 12*a*#1
- 6*a*#1^2 + a*#1^3 - b*#1^3 & , (8*a^2*Log[1 - #1 + Tan[(e + f*x)/2]^2] - 4*a*b*Log[1 - #1 + Tan[(e + f*x)/2]
^2] - 6*a^2*Log[1 - #1 + Tan[(e + f*x)/2]^2]*#1 + 2*a^2*Log[1 - #1 + Tan[(e + f*x)/2]^2]*#1^2 + b^2*Log[1 - #1
+ Tan[(e + f*x)/2]^2]*#1^2)/(4*a - 4*a*#1 + a*#1^2 - b*#1^2) & ]))/(a*(a^2 - b^2)^2) - (3*Sec[(e + f*x)/2]^2)
/(a - b))/(24*f)

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fricas [C]  time = 3.84, size = 10746, normalized size = 27.34 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cot(f*x+e)^3/(a+b*sec(f*x+e)^3),x, algorithm="fricas")

[Out]

1/36*(18*a^4 - 18*a^2*b^2 + 2*((a^5 - 2*a^3*b^2 + a*b^4)*f*cos(f*x + e)^2 - (a^5 - 2*a^3*b^2 + a*b^4)*f)*((b^4
/(a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^2)*(-I*sqrt(3)
+ 1)/(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2
+ a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3
+ 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) +
1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(
2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3)*(I*
sqrt(3) + 1) - 6*(2*a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))*log(1/12*(a^6 - 2*a^4*b^2 + a^2*b^4)*((b^4
/(a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^2)*(-I*sqrt(3)
+ 1)/(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2
+ a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3
+ 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) +
1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(
2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3)*(I*
sqrt(3) + 1) - 6*(2*a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))^2*f^2 + 2*a^2*b^2 + 7*b^4 + 1/6*(a^5 + 16*
a^3*b^2 + 10*a*b^4)*((b^4/(a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f +
a*b^4*f)^2)*(-I*sqrt(3) + 1)/(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/
((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f -
2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5
*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b
^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 -
b^2)^4*a*f^3))^(1/3)*(I*sqrt(3) + 1) - 6*(2*a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))*f - (a^3*b + 8*a*
b^3)*cos(f*x + e)) - 18*(a^3*b - a*b^3)*cos(f*x + e) + (36*a^2*b^2 + 18*b^4 - 18*(2*a^2*b^2 + b^4)*cos(f*x + e
)^2 - ((a^5 - 2*a^3*b^2 + a*b^4)*f*cos(f*x + e)^2 - (a^5 - 2*a^3*b^2 + a*b^4)*f)*((b^4/(a^6*f^2 - 2*a^4*b^2*f^
2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^2)*(-I*sqrt(3) + 1)/(-1/54*b^4/(a^7*f^3
- 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f -
2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4
/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*
b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*
f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3)*(I*sqrt(3) + 1) - 6*(2*a^2*
b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f)) + 3*sqrt(1/3)*((a^5 - 2*a^3*b^2 + a*b^4)*f*cos(f*x + e)^2 - (a^5 -
2*a^3*b^2 + a*b^4)*f)*sqrt((288*a^4*b^4 + 720*a^2*b^6 - 36*b^8 - (a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 +
a^2*b^8)*((b^4/(a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^2
)*(-I*sqrt(3) + 1)/(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 -
2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f
+ a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 +
a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^
4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f
^3))^(1/3)*(I*sqrt(3) + 1) - 6*(2*a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))^2*f^2 - 12*(2*a^7*b^2 - 3*a^
5*b^4 + a*b^8)*((b^4/(a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^
4*f)^2)*(-I*sqrt(3) + 1)/(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6
*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3
*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*
f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f
+ a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)
^4*a*f^3))^(1/3)*(I*sqrt(3) + 1) - 6*(2*a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))*f)/((a^10 - 4*a^8*b^2
+ 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8)*f^2)))*log(1/12*(a^6 - 2*a^4*b^2 + a^2*b^4)*((b^4/(a^6*f^2 - 2*a^4*b^2*f^2
+ a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^2)*(-I*sqrt(3) + 1)/(-1/54*b^4/(a^7*f^3 -
2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2
*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/(
(a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^
4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f
- 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3)*(I*sqrt(3) + 1) - 6*(2*a^2*b^
2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))^2*f^2 + 2*a^2*b^2 + 7*b^4 + 1/6*(a^5 + 16*a^3*b^2 + 10*a*b^4)*((b^4/
(a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^2)*(-I*sqrt(3) +
1)/(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2
+ a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 +
1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) +
1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2
*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3)*(I*s
qrt(3) + 1) - 6*(2*a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))*f + 1/4*sqrt(1/3)*((a^6 - 2*a^4*b^2 + a^2*b
^4)*((b^4/(a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^2)*(-I
*sqrt(3) + 1)/(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^
4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*
b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b
^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f))
- 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^
(1/3)*(I*sqrt(3) + 1) - 6*(2*a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))*f^2 - 2*(a^5 - 2*a^3*b^2 + a*b^4)
*f)*sqrt((288*a^4*b^4 + 720*a^2*b^6 - 36*b^8 - (a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8)*((b^4/(a^6
*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^2)*(-I*sqrt(3) + 1)/
(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^
2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/5
4*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18
*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2
*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3)*(I*sqrt(
3) + 1) - 6*(2*a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))^2*f^2 - 12*(2*a^7*b^2 - 3*a^5*b^4 + a*b^8)*((b^
4/(a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^2)*(-I*sqrt(3)
+ 1)/(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^
2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3
+ 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3)
+ 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*
(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3)*(I
*sqrt(3) + 1) - 6*(2*a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))*f)/((a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4
*b^6 + a^2*b^8)*f^2)) + 2*(a^3*b + 8*a*b^3)*cos(f*x + e)) + (36*a^2*b^2 + 18*b^4 - 18*(2*a^2*b^2 + b^4)*cos(f*
x + e)^2 - ((a^5 - 2*a^3*b^2 + a*b^4)*f*cos(f*x + e)^2 - (a^5 - 2*a^3*b^2 + a*b^4)*f)*((b^4/(a^6*f^2 - 2*a^4*b
^2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^2)*(-I*sqrt(3) + 1)/(-1/54*b^4/(a^
7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^
5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2
)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 +
b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/
(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3)*(I*sqrt(3) + 1) - 6*(2
*a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 3*sqrt(1/3)*((a^5 - 2*a^3*b^2 + a*b^4)*f*cos(f*x + e)^2 - (
a^5 - 2*a^3*b^2 + a*b^4)*f)*sqrt((288*a^4*b^4 + 720*a^2*b^6 - 36*b^8 - (a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b
^6 + a^2*b^8)*((b^4/(a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^4
*f)^2)*(-I*sqrt(3) + 1)/(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*
f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*
b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f
^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f +
a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^
4*a*f^3))^(1/3)*(I*sqrt(3) + 1) - 6*(2*a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))^2*f^2 - 12*(2*a^7*b^2 -
3*a^5*b^4 + a*b^8)*((b^4/(a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f +
a*b^4*f)^2)*(-I*sqrt(3) + 1)/(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/
((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f -
2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5
*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b
^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 -
b^2)^4*a*f^3))^(1/3)*(I*sqrt(3) + 1) - 6*(2*a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))*f)/((a^10 - 4*a^8
*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8)*f^2)))*log(-1/12*(a^6 - 2*a^4*b^2 + a^2*b^4)*((b^4/(a^6*f^2 - 2*a^4*b^
2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^2)*(-I*sqrt(3) + 1)/(-1/54*b^4/(a^7
*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5
*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)
*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b
^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(
a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3)*(I*sqrt(3) + 1) - 6*(2*
a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))^2*f^2 - 2*a^2*b^2 - 7*b^4 - 1/6*(a^5 + 16*a^3*b^2 + 10*a*b^4)*
((b^4/(a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^2)*(-I*sqr
t(3) + 1)/(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^
2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*
f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f
^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1
/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3
)*(I*sqrt(3) + 1) - 6*(2*a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))*f + 1/4*sqrt(1/3)*((a^6 - 2*a^4*b^2 +
a^2*b^4)*((b^4/(a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^
2)*(-I*sqrt(3) + 1)/(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2
- 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*
f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 +
a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b
^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*
f^3))^(1/3)*(I*sqrt(3) + 1) - 6*(2*a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))*f^2 - 2*(a^5 - 2*a^3*b^2 +
a*b^4)*f)*sqrt((288*a^4*b^4 + 720*a^2*b^6 - 36*b^8 - (a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8)*((b^
4/(a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^2)*(-I*sqrt(3)
+ 1)/(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^
2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3
+ 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3)
+ 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*
(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3)*(I
*sqrt(3) + 1) - 6*(2*a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))^2*f^2 - 12*(2*a^7*b^2 - 3*a^5*b^4 + a*b^8
)*((b^4/(a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2) - (2*a^2*b^2 + b^4)^2/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^2)*(-I*s
qrt(3) + 1)/(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*
b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) - 1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^
4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1/3) - 9*(-1/54*b^4/(a^7*f^3 - 2*a^5*b^2*f^3 + a^3*b^4
*f^3) + 1/18*(2*a^2*b^2 + b^4)*b^4/((a^6*f^2 - 2*a^4*b^2*f^2 + a^2*b^4*f^2)*(a^5*f - 2*a^3*b^2*f + a*b^4*f)) -
1/27*(2*a^2*b^2 + b^4)^3/(a^5*f - 2*a^3*b^2*f + a*b^4*f)^3 + 1/54*(a^2 + 8*b^2)*b^4/((a^2 - b^2)^4*a*f^3))^(1
/3)*(I*sqrt(3) + 1) - 6*(2*a^2*b^2 + b^4)/(a^5*f - 2*a^3*b^2*f + a*b^4*f))*f)/((a^10 - 4*a^8*b^2 + 6*a^6*b^4 -
4*a^4*b^6 + a^2*b^8)*f^2)) - 2*(a^3*b + 8*a*b^3)*cos(f*x + e)) + 9*(2*a^4 - a^3*b - 8*a^2*b^2 - 5*a*b^3 - (2*
a^4 - a^3*b - 8*a^2*b^2 - 5*a*b^3)*cos(f*x + e)^2)*log(1/2*cos(f*x + e) + 1/2) + 9*(2*a^4 + a^3*b - 8*a^2*b^2
+ 5*a*b^3 - (2*a^4 + a^3*b - 8*a^2*b^2 + 5*a*b^3)*cos(f*x + e)^2)*log(-1/2*cos(f*x + e) + 1/2))/((a^5 - 2*a^3*
b^2 + a*b^4)*f*cos(f*x + e)^2 - (a^5 - 2*a^3*b^2 + a*b^4)*f)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cot \left (f x + e\right )^{3}}{b \sec \left (f x + e\right )^{3} + a}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cot(f*x+e)^3/(a+b*sec(f*x+e)^3),x, algorithm="giac")

[Out]

integrate(cot(f*x + e)^3/(b*sec(f*x + e)^3 + a), x)

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maple [B]  time = 1.33, size = 676, normalized size = 1.72 \[ -\frac {b^{2} a \ln \left (\cos \left (f x +e \right )+\left (\frac {b}{a}\right )^{\frac {1}{3}}\right )}{3 f \left (a -b \right )^{2} \left (a +b \right )^{2} \left (\frac {b}{a}\right )^{\frac {2}{3}}}-\frac {2 b^{4} \ln \left (\cos \left (f x +e \right )+\left (\frac {b}{a}\right )^{\frac {1}{3}}\right )}{3 f \left (a -b \right )^{2} \left (a +b \right )^{2} a \left (\frac {b}{a}\right )^{\frac {2}{3}}}+\frac {b^{2} a \ln \left (\cos ^{2}\left (f x +e \right )-\left (\frac {b}{a}\right )^{\frac {1}{3}} \cos \left (f x +e \right )+\left (\frac {b}{a}\right )^{\frac {2}{3}}\right )}{6 f \left (a -b \right )^{2} \left (a +b \right )^{2} \left (\frac {b}{a}\right )^{\frac {2}{3}}}+\frac {b^{4} \ln \left (\cos ^{2}\left (f x +e \right )-\left (\frac {b}{a}\right )^{\frac {1}{3}} \cos \left (f x +e \right )+\left (\frac {b}{a}\right )^{\frac {2}{3}}\right )}{3 f \left (a -b \right )^{2} \left (a +b \right )^{2} a \left (\frac {b}{a}\right )^{\frac {2}{3}}}-\frac {b^{2} a \sqrt {3}\, \arctan \left (\frac {\sqrt {3}\, \left (\frac {2 \cos \left (f x +e \right )}{\left (\frac {b}{a}\right )^{\frac {1}{3}}}-1\right )}{3}\right )}{3 f \left (a -b \right )^{2} \left (a +b \right )^{2} \left (\frac {b}{a}\right )^{\frac {2}{3}}}-\frac {2 b^{4} \sqrt {3}\, \arctan \left (\frac {\sqrt {3}\, \left (\frac {2 \cos \left (f x +e \right )}{\left (\frac {b}{a}\right )^{\frac {1}{3}}}-1\right )}{3}\right )}{3 f \left (a -b \right )^{2} \left (a +b \right )^{2} a \left (\frac {b}{a}\right )^{\frac {2}{3}}}-\frac {b^{3} \ln \left (\cos \left (f x +e \right )+\left (\frac {b}{a}\right )^{\frac {1}{3}}\right )}{f \left (a -b \right )^{2} \left (a +b \right )^{2} \left (\frac {b}{a}\right )^{\frac {1}{3}}}+\frac {b^{3} \ln \left (\cos ^{2}\left (f x +e \right )-\left (\frac {b}{a}\right )^{\frac {1}{3}} \cos \left (f x +e \right )+\left (\frac {b}{a}\right )^{\frac {2}{3}}\right )}{2 f \left (a -b \right )^{2} \left (a +b \right )^{2} \left (\frac {b}{a}\right )^{\frac {1}{3}}}+\frac {b^{3} \sqrt {3}\, \arctan \left (\frac {\sqrt {3}\, \left (\frac {2 \cos \left (f x +e \right )}{\left (\frac {b}{a}\right )^{\frac {1}{3}}}-1\right )}{3}\right )}{f \left (a -b \right )^{2} \left (a +b \right )^{2} \left (\frac {b}{a}\right )^{\frac {1}{3}}}-\frac {2 b^{2} a \ln \left (b +a \left (\cos ^{3}\left (f x +e \right )\right )\right )}{3 f \left (a -b \right )^{2} \left (a +b \right )^{2}}-\frac {b^{4} \ln \left (b +a \left (\cos ^{3}\left (f x +e \right )\right )\right )}{3 f \left (a -b \right )^{2} \left (a +b \right )^{2} a}+\frac {1}{f \left (4 a +4 b \right ) \left (-1+\cos \left (f x +e \right )\right )}-\frac {\ln \left (-1+\cos \left (f x +e \right )\right ) a}{2 f \left (a +b \right )^{2}}-\frac {5 \ln \left (-1+\cos \left (f x +e \right )\right ) b}{4 f \left (a +b \right )^{2}}-\frac {1}{f \left (4 a -4 b \right ) \left (1+\cos \left (f x +e \right )\right )}-\frac {\ln \left (1+\cos \left (f x +e \right )\right ) a}{2 f \left (a -b \right )^{2}}+\frac {5 \ln \left (1+\cos \left (f x +e \right )\right ) b}{4 f \left (a -b \right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cot(f*x+e)^3/(a+b*sec(f*x+e)^3),x)

[Out]

-1/3/f*b^2/(a-b)^2/(a+b)^2*a/(1/a*b)^(2/3)*ln(cos(f*x+e)+(1/a*b)^(1/3))-2/3/f*b^4/(a-b)^2/(a+b)^2/a/(1/a*b)^(2
/3)*ln(cos(f*x+e)+(1/a*b)^(1/3))+1/6/f*b^2/(a-b)^2/(a+b)^2*a/(1/a*b)^(2/3)*ln(cos(f*x+e)^2-(1/a*b)^(1/3)*cos(f
*x+e)+(1/a*b)^(2/3))+1/3/f*b^4/(a-b)^2/(a+b)^2/a/(1/a*b)^(2/3)*ln(cos(f*x+e)^2-(1/a*b)^(1/3)*cos(f*x+e)+(1/a*b
)^(2/3))-1/3/f*b^2/(a-b)^2/(a+b)^2*a/(1/a*b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/a*b)^(1/3)*cos(f*x+e)-1))-
2/3/f*b^4/(a-b)^2/(a+b)^2/a/(1/a*b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/a*b)^(1/3)*cos(f*x+e)-1))-1/f*b^3/(
a-b)^2/(a+b)^2/(1/a*b)^(1/3)*ln(cos(f*x+e)+(1/a*b)^(1/3))+1/2/f*b^3/(a-b)^2/(a+b)^2/(1/a*b)^(1/3)*ln(cos(f*x+e
)^2-(1/a*b)^(1/3)*cos(f*x+e)+(1/a*b)^(2/3))+1/f*b^3/(a-b)^2/(a+b)^2*3^(1/2)/(1/a*b)^(1/3)*arctan(1/3*3^(1/2)*(
2/(1/a*b)^(1/3)*cos(f*x+e)-1))-2/3/f*b^2/(a-b)^2/(a+b)^2*a*ln(b+a*cos(f*x+e)^3)-1/3/f*b^4/(a-b)^2/(a+b)^2/a*ln
(b+a*cos(f*x+e)^3)+1/f/(4*a+4*b)/(-1+cos(f*x+e))-1/2/f/(a+b)^2*ln(-1+cos(f*x+e))*a-5/4/f/(a+b)^2*ln(-1+cos(f*x
+e))*b-1/f/(4*a-4*b)/(1+cos(f*x+e))-1/2/f/(a-b)^2*ln(1+cos(f*x+e))*a+5/4/f/(a-b)^2*ln(1+cos(f*x+e))*b

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maxima [A]  time = 0.43, size = 488, normalized size = 1.24 \[ \frac {\frac {4 \, \sqrt {3} {\left (a^{2} b^{3} {\left (9 \, \left (\frac {b}{a}\right )^{\frac {2}{3}} + 4\right )} - a^{3} b^{2} {\left (3 \, \left (\frac {b}{a}\right )^{\frac {1}{3}} + \frac {4 \, b}{a}\right )} - 2 \, a b^{4} {\left (3 \, \left (\frac {b}{a}\right )^{\frac {1}{3}} + \frac {b}{a}\right )} + 2 \, b^{5}\right )} \arctan \left (-\frac {\sqrt {3} {\left (\left (\frac {b}{a}\right )^{\frac {1}{3}} - 2 \, \cos \left (f x + e\right )\right )}}{3 \, \left (\frac {b}{a}\right )^{\frac {1}{3}}}\right )}{{\left (a^{6} \left (\frac {b}{a}\right )^{\frac {2}{3}} - 2 \, a^{4} b^{2} \left (\frac {b}{a}\right )^{\frac {2}{3}} + a^{2} b^{4} \left (\frac {b}{a}\right )^{\frac {2}{3}}\right )} \left (\frac {b}{a}\right )^{\frac {1}{3}}} - \frac {6 \, {\left (a^{2} b^{2} {\left (4 \, \left (\frac {b}{a}\right )^{\frac {2}{3}} - 1\right )} + 2 \, b^{4} {\left (\left (\frac {b}{a}\right )^{\frac {2}{3}} - 1\right )} - 3 \, a b^{3} \left (\frac {b}{a}\right )^{\frac {1}{3}}\right )} \log \left (\cos \left (f x + e\right )^{2} - \left (\frac {b}{a}\right )^{\frac {1}{3}} \cos \left (f x + e\right ) + \left (\frac {b}{a}\right )^{\frac {2}{3}}\right )}{a^{5} \left (\frac {b}{a}\right )^{\frac {2}{3}} - 2 \, a^{3} b^{2} \left (\frac {b}{a}\right )^{\frac {2}{3}} + a b^{4} \left (\frac {b}{a}\right )^{\frac {2}{3}}} - \frac {12 \, {\left (a^{2} b^{2} {\left (2 \, \left (\frac {b}{a}\right )^{\frac {2}{3}} + 1\right )} + b^{4} {\left (\left (\frac {b}{a}\right )^{\frac {2}{3}} + 2\right )} + 3 \, a b^{3} \left (\frac {b}{a}\right )^{\frac {1}{3}}\right )} \log \left (\left (\frac {b}{a}\right )^{\frac {1}{3}} + \cos \left (f x + e\right )\right )}{a^{5} \left (\frac {b}{a}\right )^{\frac {2}{3}} - 2 \, a^{3} b^{2} \left (\frac {b}{a}\right )^{\frac {2}{3}} + a b^{4} \left (\frac {b}{a}\right )^{\frac {2}{3}}} - \frac {9 \, {\left (2 \, a - 5 \, b\right )} \log \left (\cos \left (f x + e\right ) + 1\right )}{a^{2} - 2 \, a b + b^{2}} - \frac {9 \, {\left (2 \, a + 5 \, b\right )} \log \left (\cos \left (f x + e\right ) - 1\right )}{a^{2} + 2 \, a b + b^{2}} - \frac {18 \, {\left (b \cos \left (f x + e\right ) - a\right )}}{{\left (a^{2} - b^{2}\right )} \cos \left (f x + e\right )^{2} - a^{2} + b^{2}}}{36 \, f} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cot(f*x+e)^3/(a+b*sec(f*x+e)^3),x, algorithm="maxima")

[Out]

1/36*(4*sqrt(3)*(a^2*b^3*(9*(b/a)^(2/3) + 4) - a^3*b^2*(3*(b/a)^(1/3) + 4*b/a) - 2*a*b^4*(3*(b/a)^(1/3) + b/a)
+ 2*b^5)*arctan(-1/3*sqrt(3)*((b/a)^(1/3) - 2*cos(f*x + e))/(b/a)^(1/3))/((a^6*(b/a)^(2/3) - 2*a^4*b^2*(b/a)^
(2/3) + a^2*b^4*(b/a)^(2/3))*(b/a)^(1/3)) - 6*(a^2*b^2*(4*(b/a)^(2/3) - 1) + 2*b^4*((b/a)^(2/3) - 1) - 3*a*b^3
*(b/a)^(1/3))*log(cos(f*x + e)^2 - (b/a)^(1/3)*cos(f*x + e) + (b/a)^(2/3))/(a^5*(b/a)^(2/3) - 2*a^3*b^2*(b/a)^
(2/3) + a*b^4*(b/a)^(2/3)) - 12*(a^2*b^2*(2*(b/a)^(2/3) + 1) + b^4*((b/a)^(2/3) + 2) + 3*a*b^3*(b/a)^(1/3))*lo
g((b/a)^(1/3) + cos(f*x + e))/(a^5*(b/a)^(2/3) - 2*a^3*b^2*(b/a)^(2/3) + a*b^4*(b/a)^(2/3)) - 9*(2*a - 5*b)*lo
g(cos(f*x + e) + 1)/(a^2 - 2*a*b + b^2) - 9*(2*a + 5*b)*log(cos(f*x + e) - 1)/(a^2 + 2*a*b + b^2) - 18*(b*cos(
f*x + e) - a)/((a^2 - b^2)*cos(f*x + e)^2 - a^2 + b^2))/f

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mupad [B]  time = 19.52, size = 58699, normalized size = 149.36 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cot(e + f*x)^3/(a + b/cos(e + f*x)^3),x)

[Out]

-(a^3*cos(e/2 + (f*x)/2)^4 + a^3*sin(e/2 + (f*x)/2)^4 - a*b^2*cos(e/2 + (f*x)/2)^4 + a*b^2*sin(e/2 + (f*x)/2)^
4 + 2*a^2*b*sin(e/2 + (f*x)/2)^4 - 8*a^3*log((cos(e/2 + (f*x)/2)^2 + sin(e/2 + (f*x)/2)^2)/cos(e/2 + (f*x)/2)^
2)*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^2 + 8*b^3*log((cos(e/2 + (f*x)/2)^2 + sin(e/2 + (f*x)/2)^2)/cos(e/2
+ (f*x)/2)^2)*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^2 + 8*a^3*cos(e/2 + (f*x)/2)^2*log(sin(e/2 + (f*x)/2)/c
os(e/2 + (f*x)/2))*sin(e/2 + (f*x)/2)^2 - 8*a^4*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^2*symsum(log((131072*(
980*b^11*cos(e/2 + (f*x)/2)^2 + 336*b^11*sin(e/2 + (f*x)/2)^2 + 1764*a^2*b^9*cos(e/2 + (f*x)/2)^2 + 392*a^3*b^
8*cos(e/2 + (f*x)/2)^2 + 640*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z
^2 - 9*a*b^4*z - b^4, z, k)^2*b^13*sin(e/2 + (f*x)/2)^2 + 32*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3
- 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*b^14*sin(e/2 + (f*x)/2)^2 - 1176*a^2*b^9*sin(e/2
+ (f*x)/2)^2 - 784*a^3*b^8*sin(e/2 + (f*x)/2)^2 + 952*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*
a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*b^12*cos(e/2 + (f*x)/2)^2 + 2352*a*b^10*cos(e/2 + (f*x)/
2)^2 + 1944*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z -
b^4, z, k)*b^12*sin(e/2 + (f*x)/2)^2 - 56*a*b^10*sin(e/2 + (f*x)/2)^2 + 304*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z
^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*b^13*cos(e/2 + (f*x)/2)^2 + 32*ro
ot(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*b
^14*cos(e/2 + (f*x)/2)^2 + 1032*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^
4*z^2 - 9*a*b^4*z - b^4, z, k)*a*b^11*sin(e/2 + (f*x)/2)^2 + 39032*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a
^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^2*b^10*cos(e/2 + (f*x)/2)^2 + 30296*root(5
4*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^3*b^9
*cos(e/2 + (f*x)/2)^2 + 7420*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z
^2 - 9*a*b^4*z - b^4, z, k)*a^4*b^8*cos(e/2 + (f*x)/2)^2 - 252*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z
^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^5*b^7*cos(e/2 + (f*x)/2)^2 - 168*root(54*a^5*b
^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^6*b^6*cos(e/
2 + (f*x)/2)^2 + 14240*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9
*a*b^4*z - b^4, z, k)^2*a*b^12*cos(e/2 + (f*x)/2)^2 + 4064*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a*b^13*cos(e/2 + (f*x)/2)^2 + 384*root(54*a^5*b^2*
z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a*b^14*cos(e/2
+ (f*x)/2)^2 - 27888*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a
*b^4*z - b^4, z, k)*a^2*b^10*sin(e/2 + (f*x)/2)^2 - 55576*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^3*b^9*sin(e/2 + (f*x)/2)^2 - 32174*root(54*a^5*b^2*
z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^4*b^8*sin(e/2 +
(f*x)/2)^2 - 3318*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b
^4*z - b^4, z, k)*a^5*b^7*sin(e/2 + (f*x)/2)^2 + 252*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^
4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^6*b^6*sin(e/2 + (f*x)/2)^2 + 24840*root(54*a^5*b^2*z^3 -
27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a*b^12*sin(e/2 + (f*
x)/2)^2 + 7856*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z
- b^4, z, k)^3*a*b^13*sin(e/2 + (f*x)/2)^2 + 384*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b
^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a*b^14*sin(e/2 + (f*x)/2)^2 + 107772*root(54*a^5*b^2*z^3 -
27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^2*b^11*cos(e/2 + (f
*x)/2)^2 + 156216*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^
4*z - b^4, z, k)^2*a^3*b^10*cos(e/2 + (f*x)/2)^2 + 55448*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 5
4*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^4*b^9*cos(e/2 + (f*x)/2)^2 + 21772*root(54*a^5*b^2
*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^5*b^8*cos(e/
2 + (f*x)/2)^2 + 35364*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9
*a*b^4*z - b^4, z, k)^2*a^6*b^7*cos(e/2 + (f*x)/2)^2 + 3588*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3
- 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^7*b^6*cos(e/2 + (f*x)/2)^2 - 3051*root(54*a^5*b
^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^8*b^5*cos(
e/2 + (f*x)/2)^2 + 18*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*
a*b^4*z - b^4, z, k)^2*a^9*b^4*cos(e/2 + (f*x)/2)^2 + 73528*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3
- 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^2*b^12*cos(e/2 + (f*x)/2)^2 + 222176*root(54*a^
5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^3*b^11*
cos(e/2 + (f*x)/2)^2 - 101192*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*
z^2 - 9*a*b^4*z - b^4, z, k)^3*a^4*b^10*cos(e/2 + (f*x)/2)^2 - 567064*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 2
7*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^5*b^9*cos(e/2 + (f*x)/2)^2 - 125428*r
oot(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*
a^6*b^8*cos(e/2 + (f*x)/2)^2 + 278436*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*
a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^7*b^7*cos(e/2 + (f*x)/2)^2 + 66894*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z
^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^8*b^6*cos(e/2 + (f*x)/2)^2 - 26
928*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z,
k)^3*a^9*b^5*cos(e/2 + (f*x)/2)^2 - 3042*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 -
27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^10*b^4*cos(e/2 + (f*x)/2)^2 + 648*root(54*a^5*b^2*z^3 - 27*a^3*b^4
*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^11*b^3*cos(e/2 + (f*x)/2)^2 +
19104*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4,
z, k)^4*a^2*b^13*cos(e/2 + (f*x)/2)^2 + 128832*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*
z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^3*b^12*cos(e/2 + (f*x)/2)^2 - 191988*root(54*a^5*b^2*z^3 - 2
7*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^4*b^11*cos(e/2 + (f*
x)/2)^2 - 899856*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4
*z - b^4, z, k)^4*a^5*b^10*cos(e/2 + (f*x)/2)^2 + 183204*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 5
4*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^6*b^9*cos(e/2 + (f*x)/2)^2 + 1173036*root(54*a^5*b
^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^7*b^8*cos(
e/2 + (f*x)/2)^2 - 519612*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2
- 9*a*b^4*z - b^4, z, k)^4*a^8*b^7*cos(e/2 + (f*x)/2)^2 - 666384*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7
*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^9*b^6*cos(e/2 + (f*x)/2)^2 + 368028*root(5
4*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^10*
b^5*cos(e/2 + (f*x)/2)^2 + 46260*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b
^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^11*b^4*cos(e/2 + (f*x)/2)^2 - 46332*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 -
27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^12*b^3*cos(e/2 + (f*x)/2)^2 + 5832*
root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4
*a^13*b^2*cos(e/2 + (f*x)/2)^2 + 1728*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*
a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^2*b^14*cos(e/2 + (f*x)/2)^2 + 34560*root(54*a^5*b^2*z^3 - 27*a^3*b^4*
z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^3*b^13*cos(e/2 + (f*x)/2)^2 -
51480*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z
, k)^5*a^4*b^12*cos(e/2 + (f*x)/2)^2 - 677880*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z
^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^5*b^11*cos(e/2 + (f*x)/2)^2 + 773640*root(54*a^5*b^2*z^3 - 27
*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^6*b^10*cos(e/2 + (f*x
)/2)^2 + 1207440*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4
*z - b^4, z, k)^5*a^7*b^9*cos(e/2 + (f*x)/2)^2 - 1363176*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 5
4*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^8*b^8*cos(e/2 + (f*x)/2)^2 - 82728*root(54*a^5*b^2
*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^9*b^7*cos(e/
2 + (f*x)/2)^2 + 738792*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 -
9*a*b^4*z - b^4, z, k)^5*a^10*b^6*cos(e/2 + (f*x)/2)^2 - 412704*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*
z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^11*b^5*cos(e/2 + (f*x)/2)^2 + 11304*root(54
*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^12*b
^4*cos(e/2 + (f*x)/2)^2 + 36288*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^
4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^13*b^3*cos(e/2 + (f*x)/2)^2 - 5832*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 2
7*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^14*b^2*cos(e/2 + (f*x)/2)^2 + 3456*ro
ot(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a
^3*b^14*cos(e/2 + (f*x)/2)^2 + 7344*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^
2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^4*b^13*cos(e/2 + (f*x)/2)^2 - 225504*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z
^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^5*b^12*cos(e/2 + (f*x)/2)^2 + 4
50468*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z
, k)^6*a^6*b^11*cos(e/2 + (f*x)/2)^2 + 360072*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z
^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^7*b^10*cos(e/2 + (f*x)/2)^2 - 879984*root(54*a^5*b^2*z^3 - 27
*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^8*b^9*cos(e/2 + (f*x)
/2)^2 - 183600*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z
- b^4, z, k)^6*a^9*b^8*cos(e/2 + (f*x)/2)^2 + 431352*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a
^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^10*b^7*cos(e/2 + (f*x)/2)^2 + 165888*root(54*a^5*b^2*
z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^11*b^6*cos(e/
2 + (f*x)/2)^2 - 61344*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9
*a*b^4*z - b^4, z, k)^6*a^12*b^5*cos(e/2 + (f*x)/2)^2 - 114480*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z
^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^13*b^4*cos(e/2 + (f*x)/2)^2 + 52164*root(54*
a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^14*b^
3*cos(e/2 + (f*x)/2)^2 - 5832*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*
z^2 - 9*a*b^4*z - b^4, z, k)^6*a^15*b^2*cos(e/2 + (f*x)/2)^2 + 2592*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*
a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^4*b^14*cos(e/2 + (f*x)/2)^2 - 28512*roo
t(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^
5*b^13*cos(e/2 + (f*x)/2)^2 + 75816*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^
2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^6*b^12*cos(e/2 + (f*x)/2)^2 + 71280*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^
3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^7*b^11*cos(e/2 + (f*x)/2)^2 - 32
3352*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z,
k)^7*a^8*b^10*cos(e/2 + (f*x)/2)^2 + 483408*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^
2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^10*b^8*cos(e/2 + (f*x)/2)^2 - 142560*root(54*a^5*b^2*z^3 - 27*
a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^11*b^7*cos(e/2 + (f*x)
/2)^2 - 307152*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z
- b^4, z, k)^7*a^12*b^6*cos(e/2 + (f*x)/2)^2 + 142560*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*
a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^13*b^5*cos(e/2 + (f*x)/2)^2 + 62856*root(54*a^5*b^2*
z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^14*b^4*cos(e/
2 + (f*x)/2)^2 - 42768*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9
*a*b^4*z - b^4, z, k)^7*a^15*b^3*cos(e/2 + (f*x)/2)^2 + 5832*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3
- 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^16*b^2*cos(e/2 + (f*x)/2)^2 - 43760*root(54*a^
5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^2*b^11*
sin(e/2 + (f*x)/2)^2 - 401720*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*
z^2 - 9*a*b^4*z - b^4, z, k)^2*a^3*b^10*sin(e/2 + (f*x)/2)^2 - 563860*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 2
7*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^4*b^9*sin(e/2 + (f*x)/2)^2 - 249110*r
oot(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*
a^5*b^8*sin(e/2 + (f*x)/2)^2 - 59988*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a
^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^6*b^7*sin(e/2 + (f*x)/2)^2 - 35586*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^
3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^7*b^6*sin(e/2 + (f*x)/2)^2 + 575
1*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)
^2*a^8*b^5*sin(e/2 + (f*x)/2)^2 - 18*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a
^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^9*b^4*sin(e/2 + (f*x)/2)^2 + 95632*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^
3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^2*b^12*sin(e/2 + (f*x)/2)^2 - 43
9696*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z,
k)^3*a^3*b^11*sin(e/2 + (f*x)/2)^2 - 1471448*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z
^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^4*b^10*sin(e/2 + (f*x)/2)^2 - 606964*root(54*a^5*b^2*z^3 - 27
*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^5*b^9*sin(e/2 + (f*x)
/2)^2 + 521558*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z
- b^4, z, k)^3*a^6*b^8*sin(e/2 + (f*x)/2)^2 - 415182*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a
^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^7*b^7*sin(e/2 + (f*x)/2)^2 - 598284*root(54*a^5*b^2*z
^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^8*b^6*sin(e/2
+ (f*x)/2)^2 + 24606*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a
*b^4*z - b^4, z, k)^3*a^9*b^5*sin(e/2 + (f*x)/2)^2 + 20592*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^10*b^4*sin(e/2 + (f*x)/2)^2 - 756*root(54*a^5*b^
2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^11*b^3*sin(
e/2 + (f*x)/2)^2 + 33984*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 -
9*a*b^4*z - b^4, z, k)^4*a^2*b^13*sin(e/2 + (f*x)/2)^2 + 32784*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*
z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^3*b^12*sin(e/2 + (f*x)/2)^2 - 1159584*root(
54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^4*
b^11*sin(e/2 + (f*x)/2)^2 + 567024*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2
*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^5*b^10*sin(e/2 + (f*x)/2)^2 + 6779964*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z
^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^6*b^9*sin(e/2 + (f*x)/2)^2 + 44
75790*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z
, k)^4*a^7*b^8*sin(e/2 + (f*x)/2)^2 - 2069340*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z
^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^8*b^7*sin(e/2 + (f*x)/2)^2 - 421956*root(54*a^5*b^2*z^3 - 27*
a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^9*b^6*sin(e/2 + (f*x)/
2)^2 + 382248*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z
- b^4, z, k)^4*a^10*b^5*sin(e/2 + (f*x)/2)^2 - 554778*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a
^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^11*b^4*sin(e/2 + (f*x)/2)^2 + 146880*root(54*a^5*b^2*
z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^12*b^3*sin(e/
2 + (f*x)/2)^2 - 7776*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*
a*b^4*z - b^4, z, k)^4*a^13*b^2*sin(e/2 + (f*x)/2)^2 + 1728*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3
- 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^2*b^14*sin(e/2 + (f*x)/2)^2 + 54432*root(54*a^5
*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^3*b^13*s
in(e/2 + (f*x)/2)^2 - 422856*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z
^2 - 9*a*b^4*z - b^4, z, k)^5*a^4*b^12*sin(e/2 + (f*x)/2)^2 + 625176*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27
*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^5*b^11*sin(e/2 + (f*x)/2)^2 + 6126696*
root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5
*a^6*b^10*sin(e/2 + (f*x)/2)^2 - 2480004*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 -
27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^7*b^9*sin(e/2 + (f*x)/2)^2 - 15505344*root(54*a^5*b^2*z^3 - 27*a^3
*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^8*b^8*sin(e/2 + (f*x)/2)^
2 - 346572*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b
^4, z, k)^5*a^9*b^7*sin(e/2 + (f*x)/2)^2 + 9474120*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*
b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^10*b^6*sin(e/2 + (f*x)/2)^2 + 24660*root(54*a^5*b^2*z^3
- 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^11*b^5*sin(e/2 +
(f*x)/2)^2 - 1571688*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a
*b^4*z - b^4, z, k)^5*a^12*b^4*sin(e/2 + (f*x)/2)^2 + 232740*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3
- 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^13*b^3*sin(e/2 + (f*x)/2)^2 + 7776*root(54*a^5
*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^14*b^2*s
in(e/2 + (f*x)/2)^2 + 3456*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2
- 9*a*b^4*z - b^4, z, k)^6*a^3*b^14*sin(e/2 + (f*x)/2)^2 - 1728*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7
*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^4*b^13*sin(e/2 + (f*x)/2)^2 - 319896*root(
54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^5*
b^12*sin(e/2 + (f*x)/2)^2 + 3246912*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^
2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^6*b^11*sin(e/2 + (f*x)/2)^2 - 5322240*root(54*a^5*b^2*z^3 - 27*a^3*b^4*
z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^7*b^10*sin(e/2 + (f*x)/2)^2 -
9560160*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4,
z, k)^6*a^8*b^9*sin(e/2 + (f*x)/2)^2 + 16055280*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^
2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^9*b^8*sin(e/2 + (f*x)/2)^2 + 8485344*root(54*a^5*b^2*z^3 -
27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^10*b^7*sin(e/2 + (
f*x)/2)^2 - 14873760*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a
*b^4*z - b^4, z, k)^6*a^11*b^6*sin(e/2 + (f*x)/2)^2 - 1269216*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^
3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^12*b^5*sin(e/2 + (f*x)/2)^2 + 4449384*root(54
*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^13*b
^4*sin(e/2 + (f*x)/2)^2 - 901152*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b
^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^14*b^3*sin(e/2 + (f*x)/2)^2 + 7776*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 -
27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^15*b^2*sin(e/2 + (f*x)/2)^2 + 2592*r
oot(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*
a^4*b^14*sin(e/2 + (f*x)/2)^2 - 58320*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*
a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^5*b^13*sin(e/2 + (f*x)/2)^2 + 603936*root(54*a^5*b^2*z^3 - 27*a^3*b^4
*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^6*b^12*sin(e/2 + (f*x)/2)^2 -
2230416*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4
, z, k)^7*a^7*b^11*sin(e/2 + (f*x)/2)^2 + 536544*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^
2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^8*b^10*sin(e/2 + (f*x)/2)^2 + 6518880*root(54*a^5*b^2*z^3
- 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^9*b^9*sin(e/2 + (
f*x)/2)^2 - 5251392*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*
b^4*z - b^4, z, k)^7*a^10*b^8*sin(e/2 + (f*x)/2)^2 - 5590944*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3
- 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^11*b^7*sin(e/2 + (f*x)/2)^2 + 6456672*root(54*
a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^12*b^
6*sin(e/2 + (f*x)/2)^2 + 838512*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^
4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^13*b^5*sin(e/2 + (f*x)/2)^2 - 2340576*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3
- 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^14*b^4*sin(e/2 + (f*x)/2)^2 + 5222
88*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k
)^7*a^15*b^3*sin(e/2 + (f*x)/2)^2 - 7776*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 -
27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^16*b^2*sin(e/2 + (f*x)/2)^2 + 17192*root(54*a^5*b^2*z^3 - 27*a^3*b
^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a*b^11*cos(e/2 + (f*x)/2)^2))/(
cos(e/2 + (f*x)/2)^2*(a + b)^3*(a^2 - 2*a*b + b^2)))*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^
4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k), k, 1, 3) + 8*a^2*b^2*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)
/2)^2*symsum(log((131072*(980*b^11*cos(e/2 + (f*x)/2)^2 + 336*b^11*sin(e/2 + (f*x)/2)^2 + 1764*a^2*b^9*cos(e/2
+ (f*x)/2)^2 + 392*a^3*b^8*cos(e/2 + (f*x)/2)^2 + 640*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*
a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*b^13*sin(e/2 + (f*x)/2)^2 + 32*root(54*a^5*b^2*z^3 - 2
7*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*b^14*sin(e/2 + (f*x)/2
)^2 - 1176*a^2*b^9*sin(e/2 + (f*x)/2)^2 - 784*a^3*b^8*sin(e/2 + (f*x)/2)^2 + 952*root(54*a^5*b^2*z^3 - 27*a^3*
b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*b^12*cos(e/2 + (f*x)/2)^2 + 23
52*a*b^10*cos(e/2 + (f*x)/2)^2 + 1944*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*
a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*b^12*sin(e/2 + (f*x)/2)^2 - 56*a*b^10*sin(e/2 + (f*x)/2)^2 + 304*root(54*
a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*b^13*co
s(e/2 + (f*x)/2)^2 + 32*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 -
9*a*b^4*z - b^4, z, k)^3*b^14*cos(e/2 + (f*x)/2)^2 + 1032*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a*b^11*sin(e/2 + (f*x)/2)^2 + 39032*root(54*a^5*b^2*z
^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^2*b^10*cos(e/2 +
(f*x)/2)^2 + 30296*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*
b^4*z - b^4, z, k)*a^3*b^9*cos(e/2 + (f*x)/2)^2 + 7420*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*
a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^4*b^8*cos(e/2 + (f*x)/2)^2 - 252*root(54*a^5*b^2*z^3 -
27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^5*b^7*cos(e/2 + (f*x
)/2)^2 - 168*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z -
b^4, z, k)*a^6*b^6*cos(e/2 + (f*x)/2)^2 + 14240*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^
2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a*b^12*cos(e/2 + (f*x)/2)^2 + 4064*root(54*a^5*b^2*z^3 - 27*
a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a*b^13*cos(e/2 + (f*x)/2
)^2 + 384*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^
4, z, k)^4*a*b^14*cos(e/2 + (f*x)/2)^2 - 27888*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*
z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^2*b^10*sin(e/2 + (f*x)/2)^2 - 55576*root(54*a^5*b^2*z^3 - 27*a
^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^3*b^9*sin(e/2 + (f*x)/2)^
2 - 32174*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^
4, z, k)*a^4*b^8*sin(e/2 + (f*x)/2)^2 - 3318*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^
2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^5*b^7*sin(e/2 + (f*x)/2)^2 + 252*root(54*a^5*b^2*z^3 - 27*a^3*b^
4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^6*b^6*sin(e/2 + (f*x)/2)^2 + 2
4840*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z,
k)^2*a*b^12*sin(e/2 + (f*x)/2)^2 + 7856*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 -
27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a*b^13*sin(e/2 + (f*x)/2)^2 + 384*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z
^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a*b^14*sin(e/2 + (f*x)/2)^2 + 107
772*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z,
k)^2*a^2*b^11*cos(e/2 + (f*x)/2)^2 + 156216*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2
- 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^3*b^10*cos(e/2 + (f*x)/2)^2 + 55448*root(54*a^5*b^2*z^3 - 27*a^
3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^4*b^9*cos(e/2 + (f*x)/2)
^2 + 21772*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b
^4, z, k)^2*a^5*b^8*cos(e/2 + (f*x)/2)^2 + 35364*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^
2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^6*b^7*cos(e/2 + (f*x)/2)^2 + 3588*root(54*a^5*b^2*z^3 - 27
*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^7*b^6*cos(e/2 + (f*x)
/2)^2 - 3051*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z -
b^4, z, k)^2*a^8*b^5*cos(e/2 + (f*x)/2)^2 + 18*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2
*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^9*b^4*cos(e/2 + (f*x)/2)^2 + 73528*root(54*a^5*b^2*z^3 - 27
*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^2*b^12*cos(e/2 + (f*x
)/2)^2 + 222176*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*
z - b^4, z, k)^3*a^3*b^11*cos(e/2 + (f*x)/2)^2 - 101192*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54
*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^4*b^10*cos(e/2 + (f*x)/2)^2 - 567064*root(54*a^5*b^
2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^5*b^9*cos(e
/2 + (f*x)/2)^2 - 125428*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 -
9*a*b^4*z - b^4, z, k)^3*a^6*b^8*cos(e/2 + (f*x)/2)^2 + 278436*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*
z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^7*b^7*cos(e/2 + (f*x)/2)^2 + 66894*root(54*
a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^8*b^6
*cos(e/2 + (f*x)/2)^2 - 26928*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*
z^2 - 9*a*b^4*z - b^4, z, k)^3*a^9*b^5*cos(e/2 + (f*x)/2)^2 - 3042*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a
^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^10*b^4*cos(e/2 + (f*x)/2)^2 + 648*root(5
4*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^11*
b^3*cos(e/2 + (f*x)/2)^2 + 19104*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b
^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^2*b^13*cos(e/2 + (f*x)/2)^2 + 128832*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3
- 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^3*b^12*cos(e/2 + (f*x)/2)^2 - 1919
88*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k
)^4*a^4*b^11*cos(e/2 + (f*x)/2)^2 - 899856*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2
- 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^5*b^10*cos(e/2 + (f*x)/2)^2 + 183204*root(54*a^5*b^2*z^3 - 27*a^
3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^6*b^9*cos(e/2 + (f*x)/2)
^2 + 1173036*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z -
b^4, z, k)^4*a^7*b^8*cos(e/2 + (f*x)/2)^2 - 519612*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4
*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^8*b^7*cos(e/2 + (f*x)/2)^2 - 666384*root(54*a^5*b^2*z^3
- 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^9*b^6*cos(e/2 +
(f*x)/2)^2 + 368028*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*
b^4*z - b^4, z, k)^4*a^10*b^5*cos(e/2 + (f*x)/2)^2 + 46260*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^11*b^4*cos(e/2 + (f*x)/2)^2 - 46332*root(54*a^5*
b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^12*b^3*co
s(e/2 + (f*x)/2)^2 + 5832*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2
- 9*a*b^4*z - b^4, z, k)^4*a^13*b^2*cos(e/2 + (f*x)/2)^2 + 1728*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*
z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^2*b^14*cos(e/2 + (f*x)/2)^2 + 34560*root(54
*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^3*b^
13*cos(e/2 + (f*x)/2)^2 - 51480*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^
4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^4*b^12*cos(e/2 + (f*x)/2)^2 - 677880*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 -
27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^5*b^11*cos(e/2 + (f*x)/2)^2 + 77364
0*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)
^5*a^6*b^10*cos(e/2 + (f*x)/2)^2 + 1207440*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2
- 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^7*b^9*cos(e/2 + (f*x)/2)^2 - 1363176*root(54*a^5*b^2*z^3 - 27*a^
3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^8*b^8*cos(e/2 + (f*x)/2)
^2 - 82728*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b
^4, z, k)^5*a^9*b^7*cos(e/2 + (f*x)/2)^2 + 738792*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b
^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^10*b^6*cos(e/2 + (f*x)/2)^2 - 412704*root(54*a^5*b^2*z^3
- 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^11*b^5*cos(e/2 +
(f*x)/2)^2 + 11304*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b
^4*z - b^4, z, k)^5*a^12*b^4*cos(e/2 + (f*x)/2)^2 + 36288*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^13*b^3*cos(e/2 + (f*x)/2)^2 - 5832*root(54*a^5*b^
2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^14*b^2*cos(
e/2 + (f*x)/2)^2 + 3456*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 -
9*a*b^4*z - b^4, z, k)^6*a^3*b^14*cos(e/2 + (f*x)/2)^2 + 7344*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^
3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^4*b^13*cos(e/2 + (f*x)/2)^2 - 225504*root(54*
a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^5*b^1
2*cos(e/2 + (f*x)/2)^2 + 450468*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^
4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^6*b^11*cos(e/2 + (f*x)/2)^2 + 360072*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 -
27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^7*b^10*cos(e/2 + (f*x)/2)^2 - 87998
4*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)
^6*a^8*b^9*cos(e/2 + (f*x)/2)^2 - 183600*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 -
27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^9*b^8*cos(e/2 + (f*x)/2)^2 + 431352*root(54*a^5*b^2*z^3 - 27*a^3*b
^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^10*b^7*cos(e/2 + (f*x)/2)^2
+ 165888*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^
4, z, k)^6*a^11*b^6*cos(e/2 + (f*x)/2)^2 - 61344*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^
2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^12*b^5*cos(e/2 + (f*x)/2)^2 - 114480*root(54*a^5*b^2*z^3 -
27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^13*b^4*cos(e/2 + (
f*x)/2)^2 + 52164*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^
4*z - b^4, z, k)^6*a^14*b^3*cos(e/2 + (f*x)/2)^2 - 5832*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54
*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^15*b^2*cos(e/2 + (f*x)/2)^2 + 2592*root(54*a^5*b^2*
z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^4*b^14*cos(e/
2 + (f*x)/2)^2 - 28512*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9
*a*b^4*z - b^4, z, k)^7*a^5*b^13*cos(e/2 + (f*x)/2)^2 + 75816*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^
3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^6*b^12*cos(e/2 + (f*x)/2)^2 + 71280*root(54*a
^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^7*b^11
*cos(e/2 + (f*x)/2)^2 - 323352*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4
*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^8*b^10*cos(e/2 + (f*x)/2)^2 + 483408*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 -
27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^10*b^8*cos(e/2 + (f*x)/2)^2 - 142560
*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^
7*a^11*b^7*cos(e/2 + (f*x)/2)^2 - 307152*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 -
27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^12*b^6*cos(e/2 + (f*x)/2)^2 + 142560*root(54*a^5*b^2*z^3 - 27*a^3*
b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^13*b^5*cos(e/2 + (f*x)/2)^
2 + 62856*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^
4, z, k)^7*a^14*b^4*cos(e/2 + (f*x)/2)^2 - 42768*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^
2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^15*b^3*cos(e/2 + (f*x)/2)^2 + 5832*root(54*a^5*b^2*z^3 - 2
7*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^16*b^2*cos(e/2 + (f*
x)/2)^2 - 43760*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*
z - b^4, z, k)^2*a^2*b^11*sin(e/2 + (f*x)/2)^2 - 401720*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54
*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^3*b^10*sin(e/2 + (f*x)/2)^2 - 563860*root(54*a^5*b^
2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^4*b^9*sin(e
/2 + (f*x)/2)^2 - 249110*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 -
9*a*b^4*z - b^4, z, k)^2*a^5*b^8*sin(e/2 + (f*x)/2)^2 - 59988*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z
^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^6*b^7*sin(e/2 + (f*x)/2)^2 - 35586*root(54*a
^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^7*b^6*
sin(e/2 + (f*x)/2)^2 + 5751*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^
2 - 9*a*b^4*z - b^4, z, k)^2*a^8*b^5*sin(e/2 + (f*x)/2)^2 - 18*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z
^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^9*b^4*sin(e/2 + (f*x)/2)^2 + 95632*root(54*a
^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^2*b^12
*sin(e/2 + (f*x)/2)^2 - 439696*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4
*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^3*b^11*sin(e/2 + (f*x)/2)^2 - 1471448*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 -
27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^4*b^10*sin(e/2 + (f*x)/2)^2 - 60696
4*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)
^3*a^5*b^9*sin(e/2 + (f*x)/2)^2 + 521558*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 -
27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^6*b^8*sin(e/2 + (f*x)/2)^2 - 415182*root(54*a^5*b^2*z^3 - 27*a^3*b
^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^7*b^7*sin(e/2 + (f*x)/2)^2
- 598284*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4
, z, k)^3*a^8*b^6*sin(e/2 + (f*x)/2)^2 + 24606*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*
z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^9*b^5*sin(e/2 + (f*x)/2)^2 + 20592*root(54*a^5*b^2*z^3 - 27*
a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^10*b^4*sin(e/2 + (f*x)
/2)^2 - 756*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z -
b^4, z, k)^3*a^11*b^3*sin(e/2 + (f*x)/2)^2 + 33984*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*
b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^2*b^13*sin(e/2 + (f*x)/2)^2 + 32784*root(54*a^5*b^2*z^3
- 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^3*b^12*sin(e/2 +
(f*x)/2)^2 - 1159584*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a
*b^4*z - b^4, z, k)^4*a^4*b^11*sin(e/2 + (f*x)/2)^2 + 567024*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3
- 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^5*b^10*sin(e/2 + (f*x)/2)^2 + 6779964*root(54*
a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^6*b^9
*sin(e/2 + (f*x)/2)^2 + 4475790*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^
4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^7*b^8*sin(e/2 + (f*x)/2)^2 - 2069340*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 -
27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^8*b^7*sin(e/2 + (f*x)/2)^2 - 421956
*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^
4*a^9*b^6*sin(e/2 + (f*x)/2)^2 + 382248*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 2
7*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^10*b^5*sin(e/2 + (f*x)/2)^2 - 554778*root(54*a^5*b^2*z^3 - 27*a^3*b
^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^11*b^4*sin(e/2 + (f*x)/2)^2
+ 146880*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^
4, z, k)^4*a^12*b^3*sin(e/2 + (f*x)/2)^2 - 7776*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2
*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^13*b^2*sin(e/2 + (f*x)/2)^2 + 1728*root(54*a^5*b^2*z^3 - 27
*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^2*b^14*sin(e/2 + (f*x
)/2)^2 + 54432*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z
- b^4, z, k)^5*a^3*b^13*sin(e/2 + (f*x)/2)^2 - 422856*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*
a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^4*b^12*sin(e/2 + (f*x)/2)^2 + 625176*root(54*a^5*b^2
*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^5*b^11*sin(e
/2 + (f*x)/2)^2 + 6126696*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2
- 9*a*b^4*z - b^4, z, k)^5*a^6*b^10*sin(e/2 + (f*x)/2)^2 - 2480004*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a
^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^7*b^9*sin(e/2 + (f*x)/2)^2 - 15505344*ro
ot(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a
^8*b^8*sin(e/2 + (f*x)/2)^2 - 346572*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a
^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^9*b^7*sin(e/2 + (f*x)/2)^2 + 9474120*root(54*a^5*b^2*z^3 - 27*a^3*b^4*
z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^10*b^6*sin(e/2 + (f*x)/2)^2 +
24660*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z
, k)^5*a^11*b^5*sin(e/2 + (f*x)/2)^2 - 1571688*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*
z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^12*b^4*sin(e/2 + (f*x)/2)^2 + 232740*root(54*a^5*b^2*z^3 - 2
7*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^13*b^3*sin(e/2 + (f*
x)/2)^2 + 7776*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z
- b^4, z, k)^5*a^14*b^2*sin(e/2 + (f*x)/2)^2 + 3456*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^
4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^3*b^14*sin(e/2 + (f*x)/2)^2 - 1728*root(54*a^5*b^2*z^3
- 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^4*b^13*sin(e/2 +
(f*x)/2)^2 - 319896*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a
*b^4*z - b^4, z, k)^6*a^5*b^12*sin(e/2 + (f*x)/2)^2 + 3246912*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^
3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^6*b^11*sin(e/2 + (f*x)/2)^2 - 5322240*root(54
*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^7*b^
10*sin(e/2 + (f*x)/2)^2 - 9560160*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*
b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^8*b^9*sin(e/2 + (f*x)/2)^2 + 16055280*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^
3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^9*b^8*sin(e/2 + (f*x)/2)^2 + 848
5344*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z,
k)^6*a^10*b^7*sin(e/2 + (f*x)/2)^2 - 14873760*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*
z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^11*b^6*sin(e/2 + (f*x)/2)^2 - 1269216*root(54*a^5*b^2*z^3 -
27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^12*b^5*sin(e/2 + (f
*x)/2)^2 + 4449384*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b
^4*z - b^4, z, k)^6*a^13*b^4*sin(e/2 + (f*x)/2)^2 - 901152*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^14*b^3*sin(e/2 + (f*x)/2)^2 + 7776*root(54*a^5*b
^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^15*b^2*sin
(e/2 + (f*x)/2)^2 + 2592*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 -
9*a*b^4*z - b^4, z, k)^7*a^4*b^14*sin(e/2 + (f*x)/2)^2 - 58320*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*
z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^5*b^13*sin(e/2 + (f*x)/2)^2 + 603936*root(5
4*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^6*b
^12*sin(e/2 + (f*x)/2)^2 - 2230416*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2
*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^7*b^11*sin(e/2 + (f*x)/2)^2 + 536544*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^
3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^8*b^10*sin(e/2 + (f*x)/2)^2 + 65
18880*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z
, k)^7*a^9*b^9*sin(e/2 + (f*x)/2)^2 - 5251392*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z
^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^10*b^8*sin(e/2 + (f*x)/2)^2 - 5590944*root(54*a^5*b^2*z^3 - 2
7*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^11*b^7*sin(e/2 + (f*
x)/2)^2 + 6456672*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^
4*z - b^4, z, k)^7*a^12*b^6*sin(e/2 + (f*x)/2)^2 + 838512*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^13*b^5*sin(e/2 + (f*x)/2)^2 - 2340576*root(54*a^5
*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^14*b^4*s
in(e/2 + (f*x)/2)^2 + 522288*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z
^2 - 9*a*b^4*z - b^4, z, k)^7*a^15*b^3*sin(e/2 + (f*x)/2)^2 - 7776*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a
^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^16*b^2*sin(e/2 + (f*x)/2)^2 + 17192*root
(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a*b^1
1*cos(e/2 + (f*x)/2)^2))/(cos(e/2 + (f*x)/2)^2*(a + b)^3*(a^2 - 2*a*b + b^2)))*root(54*a^5*b^2*z^3 - 27*a^3*b^
4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k), k, 1, 3) + 8*a*b^2*log((cos(e/2
+ (f*x)/2)^2 + sin(e/2 + (f*x)/2)^2)/cos(e/2 + (f*x)/2)^2)*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^2 - 8*a^2*
b*log((cos(e/2 + (f*x)/2)^2 + sin(e/2 + (f*x)/2)^2)/cos(e/2 + (f*x)/2)^2)*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)
/2)^2 - 20*a*b^2*cos(e/2 + (f*x)/2)^2*log(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2))*sin(e/2 + (f*x)/2)^2 + 12*a^2
*b*cos(e/2 + (f*x)/2)^2*log(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2))*sin(e/2 + (f*x)/2)^2 + 8*a*b^3*cos(e/2 + (f
*x)/2)^2*sin(e/2 + (f*x)/2)^2*symsum(log((131072*(980*b^11*cos(e/2 + (f*x)/2)^2 + 336*b^11*sin(e/2 + (f*x)/2)^
2 + 1764*a^2*b^9*cos(e/2 + (f*x)/2)^2 + 392*a^3*b^8*cos(e/2 + (f*x)/2)^2 + 640*root(54*a^5*b^2*z^3 - 27*a^3*b^
4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*b^13*sin(e/2 + (f*x)/2)^2 + 32
*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^
3*b^14*sin(e/2 + (f*x)/2)^2 - 1176*a^2*b^9*sin(e/2 + (f*x)/2)^2 - 784*a^3*b^8*sin(e/2 + (f*x)/2)^2 + 952*root(
54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*b^12*c
os(e/2 + (f*x)/2)^2 + 2352*a*b^10*cos(e/2 + (f*x)/2)^2 + 1944*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^
3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*b^12*sin(e/2 + (f*x)/2)^2 - 56*a*b^10*sin(e/2 + (
f*x)/2)^2 + 304*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*
z - b^4, z, k)^2*b^13*cos(e/2 + (f*x)/2)^2 + 32*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2
*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*b^14*cos(e/2 + (f*x)/2)^2 + 1032*root(54*a^5*b^2*z^3 - 27*a^3
*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a*b^11*sin(e/2 + (f*x)/2)^2 +
39032*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4,
z, k)*a^2*b^10*cos(e/2 + (f*x)/2)^2 + 30296*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2
- 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^3*b^9*cos(e/2 + (f*x)/2)^2 + 7420*root(54*a^5*b^2*z^3 - 27*a^3*b^
4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^4*b^8*cos(e/2 + (f*x)/2)^2 - 2
52*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k
)*a^5*b^7*cos(e/2 + (f*x)/2)^2 - 168*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a
^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^6*b^6*cos(e/2 + (f*x)/2)^2 + 14240*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3
- 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a*b^12*cos(e/2 + (f*x)/2)^2 + 4064*r
oot(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*
a*b^13*cos(e/2 + (f*x)/2)^2 + 384*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*
b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a*b^14*cos(e/2 + (f*x)/2)^2 - 27888*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 -
27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^2*b^10*sin(e/2 + (f*x)/2)^2 - 55576*ro
ot(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^3
*b^9*sin(e/2 + (f*x)/2)^2 - 32174*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*
b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^4*b^8*sin(e/2 + (f*x)/2)^2 - 3318*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27
*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^5*b^7*sin(e/2 + (f*x)/2)^2 + 252*root(54
*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^6*b^6*
sin(e/2 + (f*x)/2)^2 + 24840*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z
^2 - 9*a*b^4*z - b^4, z, k)^2*a*b^12*sin(e/2 + (f*x)/2)^2 + 7856*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7
*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a*b^13*sin(e/2 + (f*x)/2)^2 + 384*root(54*a^
5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a*b^14*si
n(e/2 + (f*x)/2)^2 + 107772*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^
2 - 9*a*b^4*z - b^4, z, k)^2*a^2*b^11*cos(e/2 + (f*x)/2)^2 + 156216*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*
a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^3*b^10*cos(e/2 + (f*x)/2)^2 + 55448*roo
t(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^
4*b^9*cos(e/2 + (f*x)/2)^2 + 21772*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2
*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^5*b^8*cos(e/2 + (f*x)/2)^2 + 35364*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3
- 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^6*b^7*cos(e/2 + (f*x)/2)^2 + 3588*
root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2
*a^7*b^6*cos(e/2 + (f*x)/2)^2 - 3051*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a
^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^8*b^5*cos(e/2 + (f*x)/2)^2 + 18*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 -
27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^9*b^4*cos(e/2 + (f*x)/2)^2 + 73528*
root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3
*a^2*b^12*cos(e/2 + (f*x)/2)^2 + 222176*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 2
7*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^3*b^11*cos(e/2 + (f*x)/2)^2 - 101192*root(54*a^5*b^2*z^3 - 27*a^3*b
^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^4*b^10*cos(e/2 + (f*x)/2)^2
- 567064*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^
4, z, k)^3*a^5*b^9*cos(e/2 + (f*x)/2)^2 - 125428*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^
2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^6*b^8*cos(e/2 + (f*x)/2)^2 + 278436*root(54*a^5*b^2*z^3 -
27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^7*b^7*cos(e/2 + (f*
x)/2)^2 + 66894*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*
z - b^4, z, k)^3*a^8*b^6*cos(e/2 + (f*x)/2)^2 - 26928*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a
^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^9*b^5*cos(e/2 + (f*x)/2)^2 - 3042*root(54*a^5*b^2*z^3
- 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^10*b^4*cos(e/2 +
(f*x)/2)^2 + 648*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^
4*z - b^4, z, k)^3*a^11*b^3*cos(e/2 + (f*x)/2)^2 + 19104*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 5
4*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^2*b^13*cos(e/2 + (f*x)/2)^2 + 128832*root(54*a^5*b
^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^3*b^12*cos
(e/2 + (f*x)/2)^2 - 191988*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2
- 9*a*b^4*z - b^4, z, k)^4*a^4*b^11*cos(e/2 + (f*x)/2)^2 - 899856*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a
^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^5*b^10*cos(e/2 + (f*x)/2)^2 + 183204*roo
t(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^
6*b^9*cos(e/2 + (f*x)/2)^2 + 1173036*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a
^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^7*b^8*cos(e/2 + (f*x)/2)^2 - 519612*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z
^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^8*b^7*cos(e/2 + (f*x)/2)^2 - 66
6384*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z,
k)^4*a^9*b^6*cos(e/2 + (f*x)/2)^2 + 368028*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2
- 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^10*b^5*cos(e/2 + (f*x)/2)^2 + 46260*root(54*a^5*b^2*z^3 - 27*a^
3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^11*b^4*cos(e/2 + (f*x)/2
)^2 - 46332*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z -
b^4, z, k)^4*a^12*b^3*cos(e/2 + (f*x)/2)^2 + 5832*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b
^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^13*b^2*cos(e/2 + (f*x)/2)^2 + 1728*root(54*a^5*b^2*z^3 -
27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^2*b^14*cos(e/2 + (f
*x)/2)^2 + 34560*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4
*z - b^4, z, k)^5*a^3*b^13*cos(e/2 + (f*x)/2)^2 - 51480*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54
*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^4*b^12*cos(e/2 + (f*x)/2)^2 - 677880*root(54*a^5*b^
2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^5*b^11*cos(
e/2 + (f*x)/2)^2 + 773640*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2
- 9*a*b^4*z - b^4, z, k)^5*a^6*b^10*cos(e/2 + (f*x)/2)^2 + 1207440*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a
^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^7*b^9*cos(e/2 + (f*x)/2)^2 - 1363176*roo
t(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^
8*b^8*cos(e/2 + (f*x)/2)^2 - 82728*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2
*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^9*b^7*cos(e/2 + (f*x)/2)^2 + 738792*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3
- 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^10*b^6*cos(e/2 + (f*x)/2)^2 - 412
704*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z,
k)^5*a^11*b^5*cos(e/2 + (f*x)/2)^2 + 11304*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2
- 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^12*b^4*cos(e/2 + (f*x)/2)^2 + 36288*root(54*a^5*b^2*z^3 - 27*a^3
*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^13*b^3*cos(e/2 + (f*x)/2)
^2 - 5832*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^
4, z, k)^5*a^14*b^2*cos(e/2 + (f*x)/2)^2 + 3456*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2
*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^3*b^14*cos(e/2 + (f*x)/2)^2 + 7344*root(54*a^5*b^2*z^3 - 27
*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^4*b^13*cos(e/2 + (f*x
)/2)^2 - 225504*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*
z - b^4, z, k)^6*a^5*b^12*cos(e/2 + (f*x)/2)^2 + 450468*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54
*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^6*b^11*cos(e/2 + (f*x)/2)^2 + 360072*root(54*a^5*b^
2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^7*b^10*cos(
e/2 + (f*x)/2)^2 - 879984*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2
- 9*a*b^4*z - b^4, z, k)^6*a^8*b^9*cos(e/2 + (f*x)/2)^2 - 183600*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7
*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^9*b^8*cos(e/2 + (f*x)/2)^2 + 431352*root(5
4*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^10*
b^7*cos(e/2 + (f*x)/2)^2 + 165888*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*
b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^11*b^6*cos(e/2 + (f*x)/2)^2 - 61344*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3
- 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^12*b^5*cos(e/2 + (f*x)/2)^2 - 1144
80*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k
)^6*a^13*b^4*cos(e/2 + (f*x)/2)^2 + 52164*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 -
27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^14*b^3*cos(e/2 + (f*x)/2)^2 - 5832*root(54*a^5*b^2*z^3 - 27*a^3*b
^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^15*b^2*cos(e/2 + (f*x)/2)^2
+ 2592*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4,
z, k)^7*a^4*b^14*cos(e/2 + (f*x)/2)^2 - 28512*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*
z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^5*b^13*cos(e/2 + (f*x)/2)^2 + 75816*root(54*a^5*b^2*z^3 - 27
*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^6*b^12*cos(e/2 + (f*x
)/2)^2 + 71280*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z
- b^4, z, k)^7*a^7*b^11*cos(e/2 + (f*x)/2)^2 - 323352*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*
a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^8*b^10*cos(e/2 + (f*x)/2)^2 + 483408*root(54*a^5*b^2
*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^10*b^8*cos(e
/2 + (f*x)/2)^2 - 142560*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 -
9*a*b^4*z - b^4, z, k)^7*a^11*b^7*cos(e/2 + (f*x)/2)^2 - 307152*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7
*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^12*b^6*cos(e/2 + (f*x)/2)^2 + 142560*root(
54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^13
*b^5*cos(e/2 + (f*x)/2)^2 + 62856*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*
b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^14*b^4*cos(e/2 + (f*x)/2)^2 - 42768*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3
- 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^15*b^3*cos(e/2 + (f*x)/2)^2 + 5832
*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^
7*a^16*b^2*cos(e/2 + (f*x)/2)^2 - 43760*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 2
7*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^2*b^11*sin(e/2 + (f*x)/2)^2 - 401720*root(54*a^5*b^2*z^3 - 27*a^3*b
^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^3*b^10*sin(e/2 + (f*x)/2)^2
- 563860*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^
4, z, k)^2*a^4*b^9*sin(e/2 + (f*x)/2)^2 - 249110*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^
2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^5*b^8*sin(e/2 + (f*x)/2)^2 - 59988*root(54*a^5*b^2*z^3 - 2
7*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^6*b^7*sin(e/2 + (f*x
)/2)^2 - 35586*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z
- b^4, z, k)^2*a^7*b^6*sin(e/2 + (f*x)/2)^2 + 5751*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4
*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^8*b^5*sin(e/2 + (f*x)/2)^2 - 18*root(54*a^5*b^2*z^3 - 2
7*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^9*b^4*sin(e/2 + (f*x
)/2)^2 + 95632*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z
- b^4, z, k)^3*a^2*b^12*sin(e/2 + (f*x)/2)^2 - 439696*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*
a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^3*b^11*sin(e/2 + (f*x)/2)^2 - 1471448*root(54*a^5*b^
2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^4*b^10*sin(
e/2 + (f*x)/2)^2 - 606964*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2
- 9*a*b^4*z - b^4, z, k)^3*a^5*b^9*sin(e/2 + (f*x)/2)^2 + 521558*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7
*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^6*b^8*sin(e/2 + (f*x)/2)^2 - 415182*root(5
4*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^7*b
^7*sin(e/2 + (f*x)/2)^2 - 598284*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b
^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^8*b^6*sin(e/2 + (f*x)/2)^2 + 24606*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 -
27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^9*b^5*sin(e/2 + (f*x)/2)^2 + 20592*r
oot(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*
a^10*b^4*sin(e/2 + (f*x)/2)^2 - 756*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^
2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^11*b^3*sin(e/2 + (f*x)/2)^2 + 33984*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^
3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^2*b^13*sin(e/2 + (f*x)/2)^2 + 32
784*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z,
k)^4*a^3*b^12*sin(e/2 + (f*x)/2)^2 - 1159584*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^
2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^4*b^11*sin(e/2 + (f*x)/2)^2 + 567024*root(54*a^5*b^2*z^3 - 27*
a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^5*b^10*sin(e/2 + (f*x)
/2)^2 + 6779964*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*
z - b^4, z, k)^4*a^6*b^9*sin(e/2 + (f*x)/2)^2 + 4475790*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54
*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^7*b^8*sin(e/2 + (f*x)/2)^2 - 2069340*root(54*a^5*b^
2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^8*b^7*sin(e
/2 + (f*x)/2)^2 - 421956*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 -
9*a*b^4*z - b^4, z, k)^4*a^9*b^6*sin(e/2 + (f*x)/2)^2 + 382248*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*
z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^10*b^5*sin(e/2 + (f*x)/2)^2 - 554778*root(5
4*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^11*
b^4*sin(e/2 + (f*x)/2)^2 + 146880*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*
b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^12*b^3*sin(e/2 + (f*x)/2)^2 - 7776*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 -
27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^13*b^2*sin(e/2 + (f*x)/2)^2 + 1728*
root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5
*a^2*b^14*sin(e/2 + (f*x)/2)^2 + 54432*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27
*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^3*b^13*sin(e/2 + (f*x)/2)^2 - 422856*root(54*a^5*b^2*z^3 - 27*a^3*b^
4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^4*b^12*sin(e/2 + (f*x)/2)^2
+ 625176*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4
, z, k)^5*a^5*b^11*sin(e/2 + (f*x)/2)^2 + 6126696*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b
^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^6*b^10*sin(e/2 + (f*x)/2)^2 - 2480004*root(54*a^5*b^2*z^3
- 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^7*b^9*sin(e/2 +
(f*x)/2)^2 - 15505344*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*
a*b^4*z - b^4, z, k)^5*a^8*b^8*sin(e/2 + (f*x)/2)^2 - 346572*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3
- 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^9*b^7*sin(e/2 + (f*x)/2)^2 + 9474120*root(54*a
^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^10*b^6
*sin(e/2 + (f*x)/2)^2 + 24660*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*
z^2 - 9*a*b^4*z - b^4, z, k)^5*a^11*b^5*sin(e/2 + (f*x)/2)^2 - 1571688*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 -
27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^12*b^4*sin(e/2 + (f*x)/2)^2 + 232740
*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^
5*a^13*b^3*sin(e/2 + (f*x)/2)^2 + 7776*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27
*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^14*b^2*sin(e/2 + (f*x)/2)^2 + 3456*root(54*a^5*b^2*z^3 - 27*a^3*b^4*
z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^3*b^14*sin(e/2 + (f*x)/2)^2 -
1728*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z,
k)^6*a^4*b^13*sin(e/2 + (f*x)/2)^2 - 319896*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^
2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^5*b^12*sin(e/2 + (f*x)/2)^2 + 3246912*root(54*a^5*b^2*z^3 - 27
*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^6*b^11*sin(e/2 + (f*x
)/2)^2 - 5322240*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4
*z - b^4, z, k)^6*a^7*b^10*sin(e/2 + (f*x)/2)^2 - 9560160*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^8*b^9*sin(e/2 + (f*x)/2)^2 + 16055280*root(54*a^5
*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^9*b^8*si
n(e/2 + (f*x)/2)^2 + 8485344*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z
^2 - 9*a*b^4*z - b^4, z, k)^6*a^10*b^7*sin(e/2 + (f*x)/2)^2 - 14873760*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 -
27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^11*b^6*sin(e/2 + (f*x)/2)^2 - 126921
6*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)
^6*a^12*b^5*sin(e/2 + (f*x)/2)^2 + 4449384*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2
- 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^13*b^4*sin(e/2 + (f*x)/2)^2 - 901152*root(54*a^5*b^2*z^3 - 27*a^
3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^14*b^3*sin(e/2 + (f*x)/2
)^2 + 7776*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b
^4, z, k)^6*a^15*b^2*sin(e/2 + (f*x)/2)^2 + 2592*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^
2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^4*b^14*sin(e/2 + (f*x)/2)^2 - 58320*root(54*a^5*b^2*z^3 -
27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^5*b^13*sin(e/2 + (f
*x)/2)^2 + 603936*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^
4*z - b^4, z, k)^7*a^6*b^12*sin(e/2 + (f*x)/2)^2 - 2230416*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^7*b^11*sin(e/2 + (f*x)/2)^2 + 536544*root(54*a^5
*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^8*b^10*s
in(e/2 + (f*x)/2)^2 + 6518880*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*
z^2 - 9*a*b^4*z - b^4, z, k)^7*a^9*b^9*sin(e/2 + (f*x)/2)^2 - 5251392*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 2
7*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^10*b^8*sin(e/2 + (f*x)/2)^2 - 5590944
*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^
7*a^11*b^7*sin(e/2 + (f*x)/2)^2 + 6456672*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 -
27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^12*b^6*sin(e/2 + (f*x)/2)^2 + 838512*root(54*a^5*b^2*z^3 - 27*a^3
*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^13*b^5*sin(e/2 + (f*x)/2)
^2 - 2340576*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z -
b^4, z, k)^7*a^14*b^4*sin(e/2 + (f*x)/2)^2 + 522288*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^
4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^15*b^3*sin(e/2 + (f*x)/2)^2 - 7776*root(54*a^5*b^2*z^3
- 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^16*b^2*sin(e/2 +
(f*x)/2)^2 + 17192*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*
b^4*z - b^4, z, k)*a*b^11*cos(e/2 + (f*x)/2)^2))/(cos(e/2 + (f*x)/2)^2*(a + b)^3*(a^2 - 2*a*b + b^2)))*root(54
*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k), k, 1, 3
) - 8*a^3*b*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^2*symsum(log((131072*(980*b^11*cos(e/2 + (f*x)/2)^2 + 336*
b^11*sin(e/2 + (f*x)/2)^2 + 1764*a^2*b^9*cos(e/2 + (f*x)/2)^2 + 392*a^3*b^8*cos(e/2 + (f*x)/2)^2 + 640*root(54
*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*b^13*s
in(e/2 + (f*x)/2)^2 + 32*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 -
9*a*b^4*z - b^4, z, k)^3*b^14*sin(e/2 + (f*x)/2)^2 - 1176*a^2*b^9*sin(e/2 + (f*x)/2)^2 - 784*a^3*b^8*sin(e/2
+ (f*x)/2)^2 + 952*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b
^4*z - b^4, z, k)*b^12*cos(e/2 + (f*x)/2)^2 + 2352*a*b^10*cos(e/2 + (f*x)/2)^2 + 1944*root(54*a^5*b^2*z^3 - 27
*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*b^12*sin(e/2 + (f*x)/2)^2
- 56*a*b^10*sin(e/2 + (f*x)/2)^2 + 304*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 2
7*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*b^13*cos(e/2 + (f*x)/2)^2 + 32*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 -
27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*b^14*cos(e/2 + (f*x)/2)^2 + 1032*root
(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a*b^1
1*sin(e/2 + (f*x)/2)^2 + 39032*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4
*z^2 - 9*a*b^4*z - b^4, z, k)*a^2*b^10*cos(e/2 + (f*x)/2)^2 + 30296*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*
a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^3*b^9*cos(e/2 + (f*x)/2)^2 + 7420*root(54
*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^4*b^8*
cos(e/2 + (f*x)/2)^2 - 252*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2
- 9*a*b^4*z - b^4, z, k)*a^5*b^7*cos(e/2 + (f*x)/2)^2 - 168*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3
- 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^6*b^6*cos(e/2 + (f*x)/2)^2 + 14240*root(54*a^5*b
^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a*b^12*cos(e
/2 + (f*x)/2)^2 + 4064*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9
*a*b^4*z - b^4, z, k)^3*a*b^13*cos(e/2 + (f*x)/2)^2 + 384*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a*b^14*cos(e/2 + (f*x)/2)^2 - 27888*root(54*a^5*b^2
*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^2*b^10*sin(e/2
+ (f*x)/2)^2 - 55576*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*
a*b^4*z - b^4, z, k)*a^3*b^9*sin(e/2 + (f*x)/2)^2 - 32174*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^4*b^8*sin(e/2 + (f*x)/2)^2 - 3318*root(54*a^5*b^2*z
^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a^5*b^7*sin(e/2 +
(f*x)/2)^2 + 252*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4
*z - b^4, z, k)*a^6*b^6*sin(e/2 + (f*x)/2)^2 + 24840*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^
4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a*b^12*sin(e/2 + (f*x)/2)^2 + 7856*root(54*a^5*b^2*z^3 -
27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a*b^13*sin(e/2 + (f*
x)/2)^2 + 384*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z
- b^4, z, k)^4*a*b^14*sin(e/2 + (f*x)/2)^2 + 107772*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4
*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^2*b^11*cos(e/2 + (f*x)/2)^2 + 156216*root(54*a^5*b^2*z^
3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^3*b^10*cos(e/2
+ (f*x)/2)^2 + 55448*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a
*b^4*z - b^4, z, k)^2*a^4*b^9*cos(e/2 + (f*x)/2)^2 + 21772*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^5*b^8*cos(e/2 + (f*x)/2)^2 + 35364*root(54*a^5*b
^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^6*b^7*cos(
e/2 + (f*x)/2)^2 + 3588*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 -
9*a*b^4*z - b^4, z, k)^2*a^7*b^6*cos(e/2 + (f*x)/2)^2 - 3051*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3
- 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^8*b^5*cos(e/2 + (f*x)/2)^2 + 18*root(54*a^5*b^
2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^9*b^4*cos(e
/2 + (f*x)/2)^2 + 73528*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 -
9*a*b^4*z - b^4, z, k)^3*a^2*b^12*cos(e/2 + (f*x)/2)^2 + 222176*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*
z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^3*b^11*cos(e/2 + (f*x)/2)^2 - 101192*root(5
4*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^4*b
^10*cos(e/2 + (f*x)/2)^2 - 567064*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*
b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^5*b^9*cos(e/2 + (f*x)/2)^2 - 125428*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3
- 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^6*b^8*cos(e/2 + (f*x)/2)^2 + 27843
6*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)
^3*a^7*b^7*cos(e/2 + (f*x)/2)^2 + 66894*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 2
7*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^8*b^6*cos(e/2 + (f*x)/2)^2 - 26928*root(54*a^5*b^2*z^3 - 27*a^3*b^4
*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^9*b^5*cos(e/2 + (f*x)/2)^2 -
3042*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z,
k)^3*a^10*b^4*cos(e/2 + (f*x)/2)^2 + 648*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 -
27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^11*b^3*cos(e/2 + (f*x)/2)^2 + 19104*root(54*a^5*b^2*z^3 - 27*a^3*
b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^2*b^13*cos(e/2 + (f*x)/2)^
2 + 128832*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b
^4, z, k)^4*a^3*b^12*cos(e/2 + (f*x)/2)^2 - 191988*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*
b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^4*b^11*cos(e/2 + (f*x)/2)^2 - 899856*root(54*a^5*b^2*z^3
- 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^5*b^10*cos(e/2 +
(f*x)/2)^2 + 183204*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a
*b^4*z - b^4, z, k)^4*a^6*b^9*cos(e/2 + (f*x)/2)^2 + 1173036*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3
- 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^7*b^8*cos(e/2 + (f*x)/2)^2 - 519612*root(54*a^
5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^8*b^7*c
os(e/2 + (f*x)/2)^2 - 666384*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z
^2 - 9*a*b^4*z - b^4, z, k)^4*a^9*b^6*cos(e/2 + (f*x)/2)^2 + 368028*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*
a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^10*b^5*cos(e/2 + (f*x)/2)^2 + 46260*roo
t(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^
11*b^4*cos(e/2 + (f*x)/2)^2 - 46332*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^
2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^12*b^3*cos(e/2 + (f*x)/2)^2 + 5832*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3
- 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^13*b^2*cos(e/2 + (f*x)/2)^2 + 172
8*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)
^5*a^2*b^14*cos(e/2 + (f*x)/2)^2 + 34560*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 -
27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^3*b^13*cos(e/2 + (f*x)/2)^2 - 51480*root(54*a^5*b^2*z^3 - 27*a^3*b
^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^4*b^12*cos(e/2 + (f*x)/2)^2
- 677880*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^
4, z, k)^5*a^5*b^11*cos(e/2 + (f*x)/2)^2 + 773640*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b
^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^6*b^10*cos(e/2 + (f*x)/2)^2 + 1207440*root(54*a^5*b^2*z^3
- 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^7*b^9*cos(e/2 +
(f*x)/2)^2 - 1363176*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a
*b^4*z - b^4, z, k)^5*a^8*b^8*cos(e/2 + (f*x)/2)^2 - 82728*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^9*b^7*cos(e/2 + (f*x)/2)^2 + 738792*root(54*a^5*
b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^10*b^6*co
s(e/2 + (f*x)/2)^2 - 412704*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^
2 - 9*a*b^4*z - b^4, z, k)^5*a^11*b^5*cos(e/2 + (f*x)/2)^2 + 11304*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a
^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^12*b^4*cos(e/2 + (f*x)/2)^2 + 36288*root
(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^1
3*b^3*cos(e/2 + (f*x)/2)^2 - 5832*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*
b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^14*b^2*cos(e/2 + (f*x)/2)^2 + 3456*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 -
27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^3*b^14*cos(e/2 + (f*x)/2)^2 + 7344*
root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6
*a^4*b^13*cos(e/2 + (f*x)/2)^2 - 225504*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 2
7*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^5*b^12*cos(e/2 + (f*x)/2)^2 + 450468*root(54*a^5*b^2*z^3 - 27*a^3*b
^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^6*b^11*cos(e/2 + (f*x)/2)^2
+ 360072*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^
4, z, k)^6*a^7*b^10*cos(e/2 + (f*x)/2)^2 - 879984*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b
^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^8*b^9*cos(e/2 + (f*x)/2)^2 - 183600*root(54*a^5*b^2*z^3 -
27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^9*b^8*cos(e/2 + (f
*x)/2)^2 + 431352*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^
4*z - b^4, z, k)^6*a^10*b^7*cos(e/2 + (f*x)/2)^2 + 165888*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^11*b^6*cos(e/2 + (f*x)/2)^2 - 61344*root(54*a^5*b
^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^12*b^5*cos
(e/2 + (f*x)/2)^2 - 114480*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2
- 9*a*b^4*z - b^4, z, k)^6*a^13*b^4*cos(e/2 + (f*x)/2)^2 + 52164*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^
7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^14*b^3*cos(e/2 + (f*x)/2)^2 - 5832*root(5
4*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^15*
b^2*cos(e/2 + (f*x)/2)^2 + 2592*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^
4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^4*b^14*cos(e/2 + (f*x)/2)^2 - 28512*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 -
27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^5*b^13*cos(e/2 + (f*x)/2)^2 + 75816*
root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7
*a^6*b^12*cos(e/2 + (f*x)/2)^2 + 71280*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27
*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^7*b^11*cos(e/2 + (f*x)/2)^2 - 323352*root(54*a^5*b^2*z^3 - 27*a^3*b^
4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^8*b^10*cos(e/2 + (f*x)/2)^2
+ 483408*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4
, z, k)^7*a^10*b^8*cos(e/2 + (f*x)/2)^2 - 142560*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^
2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^11*b^7*cos(e/2 + (f*x)/2)^2 - 307152*root(54*a^5*b^2*z^3 -
27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^12*b^6*cos(e/2 + (
f*x)/2)^2 + 142560*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b
^4*z - b^4, z, k)^7*a^13*b^5*cos(e/2 + (f*x)/2)^2 + 62856*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^14*b^4*cos(e/2 + (f*x)/2)^2 - 42768*root(54*a^5*b
^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^15*b^3*cos
(e/2 + (f*x)/2)^2 + 5832*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 -
9*a*b^4*z - b^4, z, k)^7*a^16*b^2*cos(e/2 + (f*x)/2)^2 - 43760*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*
z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^2*b^11*sin(e/2 + (f*x)/2)^2 - 401720*root(5
4*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^3*b
^10*sin(e/2 + (f*x)/2)^2 - 563860*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*
b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^4*b^9*sin(e/2 + (f*x)/2)^2 - 249110*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3
- 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^5*b^8*sin(e/2 + (f*x)/2)^2 - 59988
*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^
2*a^6*b^7*sin(e/2 + (f*x)/2)^2 - 35586*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27
*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^7*b^6*sin(e/2 + (f*x)/2)^2 + 5751*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z
^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^2*a^8*b^5*sin(e/2 + (f*x)/2)^2 - 18
*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^
2*a^9*b^4*sin(e/2 + (f*x)/2)^2 + 95632*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27
*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^2*b^12*sin(e/2 + (f*x)/2)^2 - 439696*root(54*a^5*b^2*z^3 - 27*a^3*b^
4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^3*b^11*sin(e/2 + (f*x)/2)^2
- 1471448*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^
4, z, k)^3*a^4*b^10*sin(e/2 + (f*x)/2)^2 - 606964*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b
^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^5*b^9*sin(e/2 + (f*x)/2)^2 + 521558*root(54*a^5*b^2*z^3 -
27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^6*b^8*sin(e/2 + (f
*x)/2)^2 - 415182*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^
4*z - b^4, z, k)^3*a^7*b^7*sin(e/2 + (f*x)/2)^2 - 598284*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 5
4*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^8*b^6*sin(e/2 + (f*x)/2)^2 + 24606*root(54*a^5*b^2
*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^9*b^5*sin(e/
2 + (f*x)/2)^2 + 20592*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9
*a*b^4*z - b^4, z, k)^3*a^10*b^4*sin(e/2 + (f*x)/2)^2 - 756*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3
- 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^3*a^11*b^3*sin(e/2 + (f*x)/2)^2 + 33984*root(54*a^5
*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^2*b^13*s
in(e/2 + (f*x)/2)^2 + 32784*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^
2 - 9*a*b^4*z - b^4, z, k)^4*a^3*b^12*sin(e/2 + (f*x)/2)^2 - 1159584*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27
*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^4*b^11*sin(e/2 + (f*x)/2)^2 + 567024*r
oot(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*
a^5*b^10*sin(e/2 + (f*x)/2)^2 + 6779964*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 2
7*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^6*b^9*sin(e/2 + (f*x)/2)^2 + 4475790*root(54*a^5*b^2*z^3 - 27*a^3*b
^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^7*b^8*sin(e/2 + (f*x)/2)^2
- 2069340*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^
4, z, k)^4*a^8*b^7*sin(e/2 + (f*x)/2)^2 - 421956*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^
2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^9*b^6*sin(e/2 + (f*x)/2)^2 + 382248*root(54*a^5*b^2*z^3 -
27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^10*b^5*sin(e/2 + (f
*x)/2)^2 - 554778*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^
4*z - b^4, z, k)^4*a^11*b^4*sin(e/2 + (f*x)/2)^2 + 146880*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 -
54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^12*b^3*sin(e/2 + (f*x)/2)^2 - 7776*root(54*a^5*b^
2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^4*a^13*b^2*sin(
e/2 + (f*x)/2)^2 + 1728*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 -
9*a*b^4*z - b^4, z, k)^5*a^2*b^14*sin(e/2 + (f*x)/2)^2 + 54432*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z
^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^3*b^13*sin(e/2 + (f*x)/2)^2 - 422856*root(54
*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^4*b^
12*sin(e/2 + (f*x)/2)^2 + 625176*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b
^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^5*b^11*sin(e/2 + (f*x)/2)^2 + 6126696*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3
- 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^6*b^10*sin(e/2 + (f*x)/2)^2 - 248
0004*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z,
k)^5*a^7*b^9*sin(e/2 + (f*x)/2)^2 - 15505344*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z
^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^8*b^8*sin(e/2 + (f*x)/2)^2 - 346572*root(54*a^5*b^2*z^3 - 27*
a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^9*b^7*sin(e/2 + (f*x)/
2)^2 + 9474120*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z
- b^4, z, k)^5*a^10*b^6*sin(e/2 + (f*x)/2)^2 + 24660*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a
^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^11*b^5*sin(e/2 + (f*x)/2)^2 - 1571688*root(54*a^5*b^2
*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^12*b^4*sin(e
/2 + (f*x)/2)^2 + 232740*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 -
9*a*b^4*z - b^4, z, k)^5*a^13*b^3*sin(e/2 + (f*x)/2)^2 + 7776*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z
^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^5*a^14*b^2*sin(e/2 + (f*x)/2)^2 + 3456*root(54*a
^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^3*b^14
*sin(e/2 + (f*x)/2)^2 - 1728*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z
^2 - 9*a*b^4*z - b^4, z, k)^6*a^4*b^13*sin(e/2 + (f*x)/2)^2 - 319896*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27
*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^5*b^12*sin(e/2 + (f*x)/2)^2 + 3246912*
root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6
*a^6*b^11*sin(e/2 + (f*x)/2)^2 - 5322240*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 -
27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^7*b^10*sin(e/2 + (f*x)/2)^2 - 9560160*root(54*a^5*b^2*z^3 - 27*a^3
*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^8*b^9*sin(e/2 + (f*x)/2)^
2 + 16055280*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z -
b^4, z, k)^6*a^9*b^8*sin(e/2 + (f*x)/2)^2 + 8485344*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^
4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^10*b^7*sin(e/2 + (f*x)/2)^2 - 14873760*root(54*a^5*b^2
*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^11*b^6*sin(e
/2 + (f*x)/2)^2 - 1269216*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2
- 9*a*b^4*z - b^4, z, k)^6*a^12*b^5*sin(e/2 + (f*x)/2)^2 + 4449384*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a
^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^13*b^4*sin(e/2 + (f*x)/2)^2 - 901152*roo
t(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^
14*b^3*sin(e/2 + (f*x)/2)^2 + 7776*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2
*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^6*a^15*b^2*sin(e/2 + (f*x)/2)^2 + 2592*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3
- 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^4*b^14*sin(e/2 + (f*x)/2)^2 - 5832
0*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)
^7*a^5*b^13*sin(e/2 + (f*x)/2)^2 + 603936*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 -
27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^6*b^12*sin(e/2 + (f*x)/2)^2 - 2230416*root(54*a^5*b^2*z^3 - 27*a^
3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^7*b^11*sin(e/2 + (f*x)/2
)^2 + 536544*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z -
b^4, z, k)^7*a^8*b^10*sin(e/2 + (f*x)/2)^2 + 6518880*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a
^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^9*b^9*sin(e/2 + (f*x)/2)^2 - 5251392*root(54*a^5*b^2*
z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^10*b^8*sin(e/
2 + (f*x)/2)^2 - 5590944*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 -
9*a*b^4*z - b^4, z, k)^7*a^11*b^7*sin(e/2 + (f*x)/2)^2 + 6456672*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^
7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^12*b^6*sin(e/2 + (f*x)/2)^2 + 838512*root
(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^1
3*b^5*sin(e/2 + (f*x)/2)^2 - 2340576*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a
^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^14*b^4*sin(e/2 + (f*x)/2)^2 + 522288*root(54*a^5*b^2*z^3 - 27*a^3*b^4*
z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)^7*a^15*b^3*sin(e/2 + (f*x)/2)^2 -
7776*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z,
k)^7*a^16*b^2*sin(e/2 + (f*x)/2)^2 + 17192*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2
- 27*a^2*b^4*z^2 - 9*a*b^4*z - b^4, z, k)*a*b^11*cos(e/2 + (f*x)/2)^2))/(cos(e/2 + (f*x)/2)^2*(a + b)^3*(a^2
- 2*a*b + b^2)))*root(54*a^5*b^2*z^3 - 27*a^3*b^4*z^3 - 27*a^7*z^3 - 54*a^4*b^2*z^2 - 27*a^2*b^4*z^2 - 9*a*b^4
*z - b^4, z, k), k, 1, 3))/(8*a*f*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^2*(a + b)^2*(a - b))

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sympy [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cot ^{3}{\left (e + f x \right )}}{a + b \sec ^{3}{\left (e + f x \right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cot(f*x+e)**3/(a+b*sec(f*x+e)**3),x)

[Out]

Integral(cot(e + f*x)**3/(a + b*sec(e + f*x)**3), x)

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