\(\int \frac {1}{(3+b \sin (e+f x)) (c+d \sin (e+f x))^3} \, dx\) [705]

Optimal result

Integrand size = 25, antiderivative size = 271 \[ \int \frac {1}{(3+b \sin (e+f x)) (c+d \sin (e+f x))^3} \, dx=\frac {2 b^3 \arctan \left (\frac {b+3 \tan \left (\frac {1}{2} (e+f x)\right )}{\sqrt {9-b^2}}\right )}{\sqrt {9-b^2} (b c-3 d)^3 f}+\frac {d \left (18 b c^3 d-9 d^2 \left (2 c^2+d^2\right )-b^2 \left (6 c^4-5 c^2 d^2+2 d^4\right )\right ) \arctan \left (\frac {d+c \tan \left (\frac {1}{2} (e+f x)\right )}{\sqrt {c^2-d^2}}\right )}{(b c-3 d)^3 \left (c^2-d^2\right )^{5/2} f}-\frac {d^2 \cos (e+f x)}{2 (b c-3 d) \left (c^2-d^2\right ) f (c+d \sin (e+f x))^2}-\frac {d^2 \left (5 b c^2-9 c d-2 b d^2\right ) \cos (e+f x)}{2 (b c-3 d)^2 \left (c^2-d^2\right )^2 f (c+d \sin (e+f x))} \]

[Out]

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

Rubi [A] (verified)

Time = 0.71 (sec) , antiderivative size = 284, normalized size of antiderivative = 1.05, number of steps used = 9, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.240, Rules used = {2881, 3134, 3080, 2739, 632, 210} \[ \int \frac {1}{(3+b \sin (e+f x)) (c+d \sin (e+f x))^3} \, dx=\frac {d \left (-a^2 d^2 \left (2 c^2+d^2\right )+6 a b c^3 d-b^2 \left (6 c^4-5 c^2 d^2+2 d^4\right )\right ) \arctan \left (\frac {c \tan \left (\frac {1}{2} (e+f x)\right )+d}{\sqrt {c^2-d^2}}\right )}{f \left (c^2-d^2\right )^{5/2} (b c-a d)^3}+\frac {2 b^3 \arctan \left (\frac {a \tan \left (\frac {1}{2} (e+f x)\right )+b}{\sqrt {a^2-b^2}}\right )}{f \sqrt {a^2-b^2} (b c-a d)^3}-\frac {d^2 \left (-3 a c d+5 b c^2-2 b d^2\right ) \cos (e+f x)}{2 f \left (c^2-d^2\right )^2 (b c-a d)^2 (c+d \sin (e+f x))}-\frac {d^2 \cos (e+f x)}{2 f \left (c^2-d^2\right ) (b c-a d) (c+d \sin (e+f x))^2} \]

[In]

Int[1/((a + b*Sin[e + f*x])*(c + d*Sin[e + f*x])^3),x]

[Out]

(2*b^3*ArcTan[(b + a*Tan[(e + f*x)/2])/Sqrt[a^2 - b^2]])/(Sqrt[a^2 - b^2]*(b*c - a*d)^3*f) + (d*(6*a*b*c^3*d -
a^2*d^2*(2*c^2 + d^2) - b^2*(6*c^4 - 5*c^2*d^2 + 2*d^4))*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/((
b*c - a*d)^3*(c^2 - d^2)^(5/2)*f) - (d^2*Cos[e + f*x])/(2*(b*c - a*d)*(c^2 - d^2)*f*(c + d*Sin[e + f*x])^2) -
(d^2*(5*b*c^2 - 3*a*c*d - 2*b*d^2)*Cos[e + f*x])/(2*(b*c - a*d)^2*(c^2 - d^2)^2*f*(c + d*Sin[e + f*x]))

Rule 210

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

Rule 632

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

Rule 2739

Int[((a_) + (b_.)*sin[(c_.) + (d_.)*(x_)])^(-1), x_Symbol] :> With[{e = FreeFactors[Tan[(c + d*x)/2], x]}, Dis
t[2*(e/d), Subst[Int[1/(a + 2*b*e*x + a*e^2*x^2), x], x, Tan[(c + d*x)/2]/e], x]] /; FreeQ[{a, b, c, d}, x] &&
NeQ[a^2 - b^2, 0]

Rule 2881

Int[((a_.) + (b_.)*sin[(e_.) + (f_.)*(x_)])^(m_)*((c_.) + (d_.)*sin[(e_.) + (f_.)*(x_)])^(n_), x_Symbol] :> Si
mp[(-b^2)*Cos[e + f*x]*(a + b*Sin[e + f*x])^(m + 1)*((c + d*Sin[e + f*x])^(n + 1)/(f*(m + 1)*(b*c - a*d)*(a^2
- b^2))), x] + Dist[1/((m + 1)*(b*c - a*d)*(a^2 - b^2)), Int[(a + b*Sin[e + f*x])^(m + 1)*(c + d*Sin[e + f*x])
^n*Simp[a*(b*c - a*d)*(m + 1) + b^2*d*(m + n + 2) - (b^2*c + b*(b*c - a*d)*(m + 1))*Sin[e + f*x] - b^2*d*(m +
n + 3)*Sin[e + f*x]^2, x], x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && NeQ[a^2 - b^2, 0]
&& NeQ[c^2 - d^2, 0] && LtQ[m, -1] && IntegersQ[2*m, 2*n] && ((EqQ[a, 0] && IntegerQ[m] &&  !IntegerQ[n]) ||
!(IntegerQ[2*n] && LtQ[n, -1] && ((IntegerQ[n] &&  !IntegerQ[m]) || EqQ[a, 0])))

Rule 3080

Int[((A_.) + (B_.)*sin[(e_.) + (f_.)*(x_)])/(((a_.) + (b_.)*sin[(e_.) + (f_.)*(x_)])*((c_.) + (d_.)*sin[(e_.)
+ (f_.)*(x_)])), x_Symbol] :> Dist[(A*b - a*B)/(b*c - a*d), Int[1/(a + b*Sin[e + f*x]), x], x] + Dist[(B*c - A
*d)/(b*c - a*d), Int[1/(c + d*Sin[e + f*x]), x], x] /; FreeQ[{a, b, c, d, e, f, A, B}, x] && NeQ[b*c - a*d, 0]
&& NeQ[a^2 - b^2, 0] && NeQ[c^2 - d^2, 0]

Rule 3134

Int[((a_.) + (b_.)*sin[(e_.) + (f_.)*(x_)])^(m_)*((c_.) + (d_.)*sin[(e_.) + (f_.)*(x_)])^(n_)*((A_.) + (B_.)*s
in[(e_.) + (f_.)*(x_)] + (C_.)*sin[(e_.) + (f_.)*(x_)]^2), x_Symbol] :> Simp[(-(A*b^2 - a*b*B + a^2*C))*Cos[e
+ f*x]*(a + b*Sin[e + f*x])^(m + 1)*((c + d*Sin[e + f*x])^(n + 1)/(f*(m + 1)*(b*c - a*d)*(a^2 - b^2))), x] + D
ist[1/((m + 1)*(b*c - a*d)*(a^2 - b^2)), Int[(a + b*Sin[e + f*x])^(m + 1)*(c + d*Sin[e + f*x])^n*Simp[(m + 1)*
(b*c - a*d)*(a*A - b*B + a*C) + d*(A*b^2 - a*b*B + a^2*C)*(m + n + 2) - (c*(A*b^2 - a*b*B + a^2*C) + (m + 1)*(
b*c - a*d)*(A*b - a*B + b*C))*Sin[e + f*x] - d*(A*b^2 - a*b*B + a^2*C)*(m + n + 3)*Sin[e + f*x]^2, x], x], x]
/; FreeQ[{a, b, c, d, e, f, A, B, C, n}, x] && NeQ[b*c - a*d, 0] && NeQ[a^2 - b^2, 0] && NeQ[c^2 - d^2, 0] &&
LtQ[m, -1] && ((EqQ[a, 0] && IntegerQ[m] &&  !IntegerQ[n]) ||  !(IntegerQ[2*n] && LtQ[n, -1] && ((IntegerQ[n]
&&  !IntegerQ[m]) || EqQ[a, 0])))

Rubi steps \begin{align*} \text {integral}& = -\frac {d^2 \cos (e+f x)}{2 (b c-a d) \left (c^2-d^2\right ) f (c+d \sin (e+f x))^2}+\frac {\int \frac {-2 \left (a c d-b \left (c^2-d^2\right )\right )-d (2 b c-a d) \sin (e+f x)+b d^2 \sin ^2(e+f x)}{(a+b \sin (e+f x)) (c+d \sin (e+f x))^2} \, dx}{2 (b c-a d) \left (c^2-d^2\right )} \\ & = -\frac {d^2 \cos (e+f x)}{2 (b c-a d) \left (c^2-d^2\right ) f (c+d \sin (e+f x))^2}-\frac {d^2 \left (5 b c^2-3 a c d-2 b d^2\right ) \cos (e+f x)}{2 (b c-a d)^2 \left (c^2-d^2\right )^2 f (c+d \sin (e+f x))}+\frac {\int \frac {2 b^2 \left (c^2-d^2\right )^2-a b c d \left (4 c^2-d^2\right )+a^2 d^2 \left (2 c^2+d^2\right )-b d \left (4 b c^3-2 a c^2 d-b c d^2-a d^3\right ) \sin (e+f x)}{(a+b \sin (e+f x)) (c+d \sin (e+f x))} \, dx}{2 (b c-a d)^2 \left (c^2-d^2\right )^2} \\ & = -\frac {d^2 \cos (e+f x)}{2 (b c-a d) \left (c^2-d^2\right ) f (c+d \sin (e+f x))^2}-\frac {d^2 \left (5 b c^2-3 a c d-2 b d^2\right ) \cos (e+f x)}{2 (b c-a d)^2 \left (c^2-d^2\right )^2 f (c+d \sin (e+f x))}+\frac {b^3 \int \frac {1}{a+b \sin (e+f x)} \, dx}{(b c-a d)^3}+\frac {\left (d \left (6 a b c^3 d-a^2 d^2 \left (2 c^2+d^2\right )-b^2 \left (6 c^4-5 c^2 d^2+2 d^4\right )\right )\right ) \int \frac {1}{c+d \sin (e+f x)} \, dx}{2 (b c-a d)^3 \left (c^2-d^2\right )^2} \\ & = -\frac {d^2 \cos (e+f x)}{2 (b c-a d) \left (c^2-d^2\right ) f (c+d \sin (e+f x))^2}-\frac {d^2 \left (5 b c^2-3 a c d-2 b d^2\right ) \cos (e+f x)}{2 (b c-a d)^2 \left (c^2-d^2\right )^2 f (c+d \sin (e+f x))}+\frac {\left (2 b^3\right ) \text {Subst}\left (\int \frac {1}{a+2 b x+a x^2} \, dx,x,\tan \left (\frac {1}{2} (e+f x)\right )\right )}{(b c-a d)^3 f}+\frac {\left (d \left (6 a b c^3 d-a^2 d^2 \left (2 c^2+d^2\right )-b^2 \left (6 c^4-5 c^2 d^2+2 d^4\right )\right )\right ) \text {Subst}\left (\int \frac {1}{c+2 d x+c x^2} \, dx,x,\tan \left (\frac {1}{2} (e+f x)\right )\right )}{(b c-a d)^3 \left (c^2-d^2\right )^2 f} \\ & = -\frac {d^2 \cos (e+f x)}{2 (b c-a d) \left (c^2-d^2\right ) f (c+d \sin (e+f x))^2}-\frac {d^2 \left (5 b c^2-3 a c d-2 b d^2\right ) \cos (e+f x)}{2 (b c-a d)^2 \left (c^2-d^2\right )^2 f (c+d \sin (e+f x))}-\frac {\left (4 b^3\right ) \text {Subst}\left (\int \frac {1}{-4 \left (a^2-b^2\right )-x^2} \, dx,x,2 b+2 a \tan \left (\frac {1}{2} (e+f x)\right )\right )}{(b c-a d)^3 f}-\frac {\left (2 d \left (6 a b c^3 d-a^2 d^2 \left (2 c^2+d^2\right )-b^2 \left (6 c^4-5 c^2 d^2+2 d^4\right )\right )\right ) \text {Subst}\left (\int \frac {1}{-4 \left (c^2-d^2\right )-x^2} \, dx,x,2 d+2 c \tan \left (\frac {1}{2} (e+f x)\right )\right )}{(b c-a d)^3 \left (c^2-d^2\right )^2 f} \\ & = \frac {2 b^3 \arctan \left (\frac {b+a \tan \left (\frac {1}{2} (e+f x)\right )}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2} (b c-a d)^3 f}+\frac {d \left (6 a b c^3 d-a^2 d^2 \left (2 c^2+d^2\right )-b^2 \left (6 c^4-5 c^2 d^2+2 d^4\right )\right ) \arctan \left (\frac {d+c \tan \left (\frac {1}{2} (e+f x)\right )}{\sqrt {c^2-d^2}}\right )}{(b c-a d)^3 \left (c^2-d^2\right )^{5/2} f}-\frac {d^2 \cos (e+f x)}{2 (b c-a d) \left (c^2-d^2\right ) f (c+d \sin (e+f x))^2}-\frac {d^2 \left (5 b c^2-3 a c d-2 b d^2\right ) \cos (e+f x)}{2 (b c-a d)^2 \left (c^2-d^2\right )^2 f (c+d \sin (e+f x))} \\ \end{align*}

Mathematica [A] (verified)

Time = 1.73 (sec) , antiderivative size = 251, normalized size of antiderivative = 0.93 \[ \int \frac {1}{(3+b \sin (e+f x)) (c+d \sin (e+f x))^3} \, dx=-\frac {-\frac {4 b^3 \arctan \left (\frac {b+3 \tan \left (\frac {1}{2} (e+f x)\right )}{\sqrt {9-b^2}}\right )}{\sqrt {9-b^2}}+\frac {2 d \left (-18 b c^3 d+9 \left (2 c^2 d^2+d^4\right )+b^2 \left (6 c^4-5 c^2 d^2+2 d^4\right )\right ) \arctan \left (\frac {d+c \tan \left (\frac {1}{2} (e+f x)\right )}{\sqrt {c^2-d^2}}\right )}{\left (c^2-d^2\right )^{5/2}}+\frac {(b c-3 d)^2 d^2 \cos (e+f x)}{(c-d) (c+d) (c+d \sin (e+f x))^2}+\frac {(b c-3 d) d^2 \left (5 b c^2-9 c d-2 b d^2\right ) \cos (e+f x)}{(c-d)^2 (c+d)^2 (c+d \sin (e+f x))}}{2 (b c-3 d)^3 f} \]

[In]

Integrate[1/((3 + b*Sin[e + f*x])*(c + d*Sin[e + f*x])^3),x]

[Out]

-1/2*((-4*b^3*ArcTan[(b + 3*Tan[(e + f*x)/2])/Sqrt[9 - b^2]])/Sqrt[9 - b^2] + (2*d*(-18*b*c^3*d + 9*(2*c^2*d^2
+ d^4) + b^2*(6*c^4 - 5*c^2*d^2 + 2*d^4))*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(c^2 - d^2)^(5/2)
+ ((b*c - 3*d)^2*d^2*Cos[e + f*x])/((c - d)*(c + d)*(c + d*Sin[e + f*x])^2) + ((b*c - 3*d)*d^2*(5*b*c^2 - 9*c
*d - 2*b*d^2)*Cos[e + f*x])/((c - d)^2*(c + d)^2*(c + d*Sin[e + f*x])))/((b*c - 3*d)^3*f)

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(624\) vs. \(2(270)=540\).

Time = 6.01 (sec) , antiderivative size = 625, normalized size of antiderivative = 2.31

method	result	size
derivativedivides	\(\frac {\frac {2 d \left (\frac {\frac {d^{2} \left (5 a^{2} c^{2} d^{2}-2 a^{2} d^{4}-12 a b \,c^{3} d +6 d^{3} a b c +7 b^{2} c^{4}-4 b^{2} c^{2} d^{2}\right ) \left (\tan ^{3}\left (\frac {f x}{2}+\frac {e}{2}\right )\right )}{2 \left (c^{4}-2 c^{2} d^{2}+d^{4}\right ) c}+\frac {d \left (4 a^{2} c^{4} d^{2}+7 a^{2} c^{2} d^{4}-2 a^{2} d^{6}-10 a b \,c^{5} d -16 a b \,c^{3} d^{3}+8 a b c \,d^{5}+6 b^{2} c^{6}+9 b^{2} c^{4} d^{2}-6 b^{2} c^{2} d^{4}\right ) \left (\tan ^{2}\left (\frac {f x}{2}+\frac {e}{2}\right )\right )}{2 \left (c^{4}-2 c^{2} d^{2}+d^{4}\right ) c^{2}}+\frac {d^{2} \left (11 a^{2} c^{2} d^{2}-2 a^{2} d^{4}-28 a b \,c^{3} d +10 d^{3} a b c +17 b^{2} c^{4}-8 b^{2} c^{2} d^{2}\right ) \tan \left (\frac {f x}{2}+\frac {e}{2}\right )}{2 c \left (c^{4}-2 c^{2} d^{2}+d^{4}\right )}+\frac {d \left (4 a^{2} c^{2} d^{2}-a^{2} d^{4}-10 a b \,c^{3} d +4 d^{3} a b c +6 b^{2} c^{4}-3 b^{2} c^{2} d^{2}\right )}{2 c^{4}-4 c^{2} d^{2}+2 d^{4}}}{{\left (\left (\tan ^{2}\left (\frac {f x}{2}+\frac {e}{2}\right )\right ) c +2 d \tan \left (\frac {f x}{2}+\frac {e}{2}\right )+c \right )}^{2}}+\frac {\left (2 a^{2} c^{2} d^{2}+a^{2} d^{4}-6 a b \,c^{3} d +6 b^{2} c^{4}-5 b^{2} c^{2} d^{2}+2 b^{2} d^{4}\right ) \arctan \left (\frac {2 c \tan \left (\frac {f x}{2}+\frac {e}{2}\right )+2 d}{2 \sqrt {c^{2}-d^{2}}}\right )}{2 \left (c^{4}-2 c^{2} d^{2}+d^{4}\right ) \sqrt {c^{2}-d^{2}}}\right )}{\left (d a -c b \right )^{3}}-\frac {2 b^{3} \arctan \left (\frac {2 a \tan \left (\frac {f x}{2}+\frac {e}{2}\right )+2 b}{2 \sqrt {a^{2}-b^{2}}}\right )}{\left (d^{3} a^{3}-3 c \,d^{2} a^{2} b +3 a \,b^{2} c^{2} d -b^{3} c^{3}\right ) \sqrt {a^{2}-b^{2}}}}{f}\)	\(625\)
default	\(\frac {\frac {2 d \left (\frac {\frac {d^{2} \left (5 a^{2} c^{2} d^{2}-2 a^{2} d^{4}-12 a b \,c^{3} d +6 d^{3} a b c +7 b^{2} c^{4}-4 b^{2} c^{2} d^{2}\right ) \left (\tan ^{3}\left (\frac {f x}{2}+\frac {e}{2}\right )\right )}{2 \left (c^{4}-2 c^{2} d^{2}+d^{4}\right ) c}+\frac {d \left (4 a^{2} c^{4} d^{2}+7 a^{2} c^{2} d^{4}-2 a^{2} d^{6}-10 a b \,c^{5} d -16 a b \,c^{3} d^{3}+8 a b c \,d^{5}+6 b^{2} c^{6}+9 b^{2} c^{4} d^{2}-6 b^{2} c^{2} d^{4}\right ) \left (\tan ^{2}\left (\frac {f x}{2}+\frac {e}{2}\right )\right )}{2 \left (c^{4}-2 c^{2} d^{2}+d^{4}\right ) c^{2}}+\frac {d^{2} \left (11 a^{2} c^{2} d^{2}-2 a^{2} d^{4}-28 a b \,c^{3} d +10 d^{3} a b c +17 b^{2} c^{4}-8 b^{2} c^{2} d^{2}\right ) \tan \left (\frac {f x}{2}+\frac {e}{2}\right )}{2 c \left (c^{4}-2 c^{2} d^{2}+d^{4}\right )}+\frac {d \left (4 a^{2} c^{2} d^{2}-a^{2} d^{4}-10 a b \,c^{3} d +4 d^{3} a b c +6 b^{2} c^{4}-3 b^{2} c^{2} d^{2}\right )}{2 c^{4}-4 c^{2} d^{2}+2 d^{4}}}{{\left (\left (\tan ^{2}\left (\frac {f x}{2}+\frac {e}{2}\right )\right ) c +2 d \tan \left (\frac {f x}{2}+\frac {e}{2}\right )+c \right )}^{2}}+\frac {\left (2 a^{2} c^{2} d^{2}+a^{2} d^{4}-6 a b \,c^{3} d +6 b^{2} c^{4}-5 b^{2} c^{2} d^{2}+2 b^{2} d^{4}\right ) \arctan \left (\frac {2 c \tan \left (\frac {f x}{2}+\frac {e}{2}\right )+2 d}{2 \sqrt {c^{2}-d^{2}}}\right )}{2 \left (c^{4}-2 c^{2} d^{2}+d^{4}\right ) \sqrt {c^{2}-d^{2}}}\right )}{\left (d a -c b \right )^{3}}-\frac {2 b^{3} \arctan \left (\frac {2 a \tan \left (\frac {f x}{2}+\frac {e}{2}\right )+2 b}{2 \sqrt {a^{2}-b^{2}}}\right )}{\left (d^{3} a^{3}-3 c \,d^{2} a^{2} b +3 a \,b^{2} c^{2} d -b^{3} c^{3}\right ) \sqrt {a^{2}-b^{2}}}}{f}\)	\(625\)
risch	\(\text {Expression too large to display}\)	\(1603\)

[In]

int(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^3,x,method=_RETURNVERBOSE)

[Out]

1/f*(2*d/(a*d-b*c)^3*((1/2*d^2*(5*a^2*c^2*d^2-2*a^2*d^4-12*a*b*c^3*d+6*a*b*c*d^3+7*b^2*c^4-4*b^2*c^2*d^2)/(c^4
-2*c^2*d^2+d^4)/c*tan(1/2*f*x+1/2*e)^3+1/2*d*(4*a^2*c^4*d^2+7*a^2*c^2*d^4-2*a^2*d^6-10*a*b*c^5*d-16*a*b*c^3*d^
3+8*a*b*c*d^5+6*b^2*c^6+9*b^2*c^4*d^2-6*b^2*c^2*d^4)/(c^4-2*c^2*d^2+d^4)/c^2*tan(1/2*f*x+1/2*e)^2+1/2*d^2*(11*
a^2*c^2*d^2-2*a^2*d^4-28*a*b*c^3*d+10*a*b*c*d^3+17*b^2*c^4-8*b^2*c^2*d^2)/c/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/
2*e)+1/2*d*(4*a^2*c^2*d^2-a^2*d^4-10*a*b*c^3*d+4*a*b*c*d^3+6*b^2*c^4-3*b^2*c^2*d^2)/(c^4-2*c^2*d^2+d^4))/(tan(
1/2*f*x+1/2*e)^2*c+2*d*tan(1/2*f*x+1/2*e)+c)^2+1/2*(2*a^2*c^2*d^2+a^2*d^4-6*a*b*c^3*d+6*b^2*c^4-5*b^2*c^2*d^2+
2*b^2*d^4)/(c^4-2*c^2*d^2+d^4)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2)))-2*b^3
/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^
2)^(1/2)))

Fricas [F(-1)]

Timed out. \[ \int \frac {1}{(3+b \sin (e+f x)) (c+d \sin (e+f x))^3} \, dx=\text {Timed out} \]

[In]

integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm="fricas")

[Out]

Timed out

Sympy [F(-1)]

Timed out. \[ \int \frac {1}{(3+b \sin (e+f x)) (c+d \sin (e+f x))^3} \, dx=\text {Timed out} \]

[In]

integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))**3,x)

[Out]

Timed out

Maxima [F(-2)]

Exception generated. \[ \int \frac {1}{(3+b \sin (e+f x)) (c+d \sin (e+f x))^3} \, dx=\text {Exception raised: ValueError} \]

[In]

integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm="maxima")

[Out]

Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'a
ssume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?`
for more de

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 766 vs. \(2 (270) = 540\).

Time = 0.35 (sec) , antiderivative size = 766, normalized size of antiderivative = 2.83 \[ \int \frac {1}{(3+b \sin (e+f x)) (c+d \sin (e+f x))^3} \, dx=\frac {\frac {2 \, {\left (\pi \left \lfloor \frac {f x + e}{2 \, \pi } + \frac {1}{2} \right \rfloor \mathrm {sgn}\left (a\right ) + \arctan \left (\frac {a \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right ) + b}{\sqrt {a^{2} - b^{2}}}\right )\right )} b^{3}}{{\left (b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right )} \sqrt {a^{2} - b^{2}}} - \frac {{\left (6 \, b^{2} c^{4} d - 6 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3} - 5 \, b^{2} c^{2} d^{3} + a^{2} d^{5} + 2 \, b^{2} d^{5}\right )} {\left (\pi \left \lfloor \frac {f x + e}{2 \, \pi } + \frac {1}{2} \right \rfloor \mathrm {sgn}\left (c\right ) + \arctan \left (\frac {c \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right ) + d}{\sqrt {c^{2} - d^{2}}}\right )\right )}}{{\left (b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c^{5} d^{2} - 2 \, b^{3} c^{5} d^{2} - a^{3} c^{4} d^{3} + 6 \, a b^{2} c^{4} d^{3} - 6 \, a^{2} b c^{3} d^{4} + b^{3} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{5} - 3 \, a b^{2} c^{2} d^{5} + 3 \, a^{2} b c d^{6} - a^{3} d^{7}\right )} \sqrt {c^{2} - d^{2}}} - \frac {7 \, b c^{4} d^{3} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{3} - 5 \, a c^{3} d^{4} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{3} - 4 \, b c^{2} d^{5} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{3} + 2 \, a c d^{6} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{3} + 6 \, b c^{5} d^{2} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{2} - 4 \, a c^{4} d^{3} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{2} + 9 \, b c^{3} d^{4} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{2} - 7 \, a c^{2} d^{5} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{2} - 6 \, b c d^{6} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{2} + 2 \, a d^{7} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{2} + 17 \, b c^{4} d^{3} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right ) - 11 \, a c^{3} d^{4} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right ) - 8 \, b c^{2} d^{5} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right ) + 2 \, a c d^{6} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right ) + 6 \, b c^{5} d^{2} - 4 \, a c^{4} d^{3} - 3 \, b c^{3} d^{4} + a c^{2} d^{5}}{{\left (b^{2} c^{8} - 2 \, a b c^{7} d + a^{2} c^{6} d^{2} - 2 \, b^{2} c^{6} d^{2} + 4 \, a b c^{5} d^{3} - 2 \, a^{2} c^{4} d^{4} + b^{2} c^{4} d^{4} - 2 \, a b c^{3} d^{5} + a^{2} c^{2} d^{6}\right )} {\left (c \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{2} + 2 \, d \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right ) + c\right )}^{2}}}{f} \]

[In]

integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm="giac")

[Out]

(2*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))*b^3/((b^3*
c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(a^2 - b^2)) - (6*b^2*c^4*d - 6*a*b*c^3*d^2 + 2*a^2*c^2*d^3
- 5*b^2*c^2*d^3 + a^2*d^5 + 2*b^2*d^5)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2
*e) + d)/sqrt(c^2 - d^2)))/((b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c^5*d^2 - 2*b^3*c^5*d^2 - a^3*c^4*d^3 + 6*a*b^2
*c^4*d^3 - 6*a^2*b*c^3*d^4 + b^3*c^3*d^4 + 2*a^3*c^2*d^5 - 3*a*b^2*c^2*d^5 + 3*a^2*b*c*d^6 - a^3*d^7)*sqrt(c^2
- d^2)) - (7*b*c^4*d^3*tan(1/2*f*x + 1/2*e)^3 - 5*a*c^3*d^4*tan(1/2*f*x + 1/2*e)^3 - 4*b*c^2*d^5*tan(1/2*f*x
+ 1/2*e)^3 + 2*a*c*d^6*tan(1/2*f*x + 1/2*e)^3 + 6*b*c^5*d^2*tan(1/2*f*x + 1/2*e)^2 - 4*a*c^4*d^3*tan(1/2*f*x +
1/2*e)^2 + 9*b*c^3*d^4*tan(1/2*f*x + 1/2*e)^2 - 7*a*c^2*d^5*tan(1/2*f*x + 1/2*e)^2 - 6*b*c*d^6*tan(1/2*f*x +
1/2*e)^2 + 2*a*d^7*tan(1/2*f*x + 1/2*e)^2 + 17*b*c^4*d^3*tan(1/2*f*x + 1/2*e) - 11*a*c^3*d^4*tan(1/2*f*x + 1/2
*e) - 8*b*c^2*d^5*tan(1/2*f*x + 1/2*e) + 2*a*c*d^6*tan(1/2*f*x + 1/2*e) + 6*b*c^5*d^2 - 4*a*c^4*d^3 - 3*b*c^3*
d^4 + a*c^2*d^5)/((b^2*c^8 - 2*a*b*c^7*d + a^2*c^6*d^2 - 2*b^2*c^6*d^2 + 4*a*b*c^5*d^3 - 2*a^2*c^4*d^4 + b^2*c
^4*d^4 - 2*a*b*c^3*d^5 + a^2*c^2*d^6)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^2))/f

Mupad [B] (verification not implemented)

Time = 33.29 (sec) , antiderivative size = 62873, normalized size of antiderivative = 232.00 \[ \int \frac {1}{(3+b \sin (e+f x)) (c+d \sin (e+f x))^3} \, dx=\text {Too large to display} \]

[In]

int(1/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^3),x)

[Out]

(b^3*atan(((b^3*(b^2 - a^2)^(1/2)*((8*(4*a*b^8*c^4*d^9 - 16*a*b^8*c^6*d^7 + 24*a*b^8*c^8*d^5 - 16*a*b^8*c^10*d
^3 + 4*a^4*b^5*c*d^12 + 4*a^6*b^3*c*d^12 + 4*a^8*b*c^3*d^10 + 4*a^8*b*c^5*d^8 - 4*a^2*b^7*c^3*d^10 + 12*a^2*b^
7*c^5*d^8 + a^2*b^7*c^7*d^6 - 28*a^2*b^7*c^9*d^4 + 28*a^2*b^7*c^11*d^2 - 4*a^3*b^6*c^2*d^11 + 24*a^3*b^6*c^4*d
^9 - 98*a^3*b^6*c^6*d^7 + 164*a^3*b^6*c^8*d^5 - 140*a^3*b^6*c^10*d^3 - 16*a^4*b^5*c^3*d^10 + 95*a^4*b^5*c^5*d^
8 - 188*a^4*b^5*c^7*d^6 + 240*a^4*b^5*c^9*d^4 - 8*a^5*b^4*c^2*d^11 - 20*a^5*b^4*c^4*d^9 + 64*a^5*b^4*c^6*d^7 -
216*a^5*b^4*c^8*d^5 - a^6*b^3*c^3*d^10 + 20*a^6*b^3*c^5*d^8 + 112*a^6*b^3*c^7*d^6 - 2*a^7*b^2*c^2*d^11 - 20*a
^7*b^2*c^4*d^9 - 32*a^7*b^2*c^6*d^7 + 4*a*b^8*c^12*d + a^8*b*c*d^12))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 +
6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 -
6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*
d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*
a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a
^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4
*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(4*a*b^8*c^13 +
a^9*c*d^12 + 4*a^9*c^3*d^10 + 4*a^9*c^5*d^8 - 16*a*b^8*c^3*d^10 + 76*a*b^8*c^5*d^8 - 162*a*b^8*c^7*d^6 + 176*a
*b^8*c^9*d^4 - 96*a*b^8*c^11*d^2 - 8*a^2*b^7*c^12*d - 16*a^3*b^6*c*d^12 - 4*a^5*b^4*c*d^12 + 2*a^7*b^2*c*d^12
- 2*a^8*b*c^2*d^11 - 20*a^8*b*c^4*d^9 - 32*a^8*b*c^6*d^7 + 32*a^2*b^7*c^2*d^11 - 152*a^2*b^7*c^4*d^9 + 372*a^2
*b^7*c^6*d^7 - 472*a^2*b^7*c^8*d^5 + 336*a^2*b^7*c^10*d^3 + 72*a^3*b^6*c^3*d^10 - 274*a^3*b^6*c^5*d^8 + 481*a^
3*b^6*c^7*d^6 - 564*a^3*b^6*c^9*d^4 + 40*a^3*b^6*c^11*d^2 + 8*a^4*b^5*c^2*d^11 + 80*a^4*b^5*c^4*d^9 - 250*a^4*
b^5*c^6*d^7 + 612*a^4*b^5*c^8*d^5 - 144*a^4*b^5*c^10*d^3 - 14*a^5*b^4*c^3*d^10 + 55*a^5*b^4*c^5*d^8 - 412*a^5*
b^4*c^7*d^6 + 240*a^5*b^4*c^9*d^4 - 4*a^6*b^3*c^2*d^11 + 20*a^6*b^3*c^4*d^9 + 128*a^6*b^3*c^6*d^7 - 216*a^6*b^
3*c^8*d^5 - 9*a^7*b^2*c^3*d^10 + 12*a^7*b^2*c^5*d^8 + 112*a^7*b^2*c^7*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d
^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12
*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*
b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6
- 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7
+ 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 -
60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (b^3*(b^2 - a^2)^(1/2)*((8*(4*a^
2*b^8*c^16 + 2*a^10*c^2*d^14 - 6*a^10*c^6*d^10 + 4*a^10*c^8*d^8 + 4*a*b^9*c^7*d^9 - 18*a*b^9*c^9*d^7 + 36*a*b^
9*c^11*d^5 - 34*a*b^9*c^13*d^3 - 32*a^3*b^7*c^15*d + 4*a^7*b^3*c*d^15 - 10*a^9*b*c^3*d^13 - 12*a^9*b*c^5*d^11
+ 54*a^9*b*c^7*d^9 - 32*a^9*b*c^9*d^7 - 24*a^2*b^8*c^6*d^10 + 110*a^2*b^8*c^8*d^8 - 232*a^2*b^8*c^10*d^6 + 234
*a^2*b^8*c^12*d^4 - 92*a^2*b^8*c^14*d^2 + 60*a^3*b^7*c^5*d^11 - 282*a^3*b^7*c^7*d^9 + 638*a^3*b^7*c^9*d^7 - 70
2*a^3*b^7*c^11*d^5 + 318*a^3*b^7*c^13*d^3 - 80*a^4*b^6*c^4*d^12 + 390*a^4*b^6*c^6*d^10 - 970*a^4*b^6*c^8*d^8 +
1202*a^4*b^6*c^10*d^6 - 654*a^4*b^6*c^12*d^4 + 112*a^4*b^6*c^14*d^2 + 60*a^5*b^5*c^3*d^13 - 310*a^5*b^5*c^5*d
^11 + 878*a^5*b^5*c^7*d^9 - 1290*a^5*b^5*c^9*d^7 + 886*a^5*b^5*c^11*d^5 - 224*a^5*b^5*c^13*d^3 - 24*a^6*b^4*c^
2*d^14 + 138*a^6*b^4*c^4*d^12 - 466*a^6*b^4*c^6*d^10 + 894*a^6*b^4*c^8*d^8 - 822*a^6*b^4*c^10*d^6 + 280*a^6*b^
4*c^12*d^4 - 30*a^7*b^3*c^3*d^13 + 122*a^7*b^3*c^5*d^11 - 394*a^7*b^3*c^7*d^9 + 522*a^7*b^3*c^9*d^7 - 224*a^7*
b^3*c^11*d^5 + 2*a^8*b^2*c^2*d^14 + 2*a^8*b^2*c^4*d^12 + 102*a^8*b^2*c^6*d^10 - 218*a^8*b^2*c^8*d^8 + 112*a^8*
b^2*c^10*d^6 + 12*a*b^9*c^15*d))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*
c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 -
36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*
d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^
2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3
+ 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 -
6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^16 + 4*a^10*c*d^15 - 12*a^10*c^5*d^11 + 8*
a^10*c^7*d^9 + 4*a*b^9*c^8*d^8 - 8*a*b^9*c^10*d^6 + 12*a*b^9*c^12*d^4 - 16*a*b^9*c^14*d^2 - 40*a^2*b^8*c^15*d
+ 4*a^8*b^2*c*d^15 - 20*a^9*b*c^2*d^14 - 24*a^9*b*c^4*d^12 + 108*a^9*b*c^6*d^10 - 64*a^9*b*c^8*d^8 - 20*a^2*b^
8*c^7*d^9 + 16*a^2*b^8*c^9*d^7 - 12*a^2*b^8*c^11*d^5 + 56*a^2*b^8*c^13*d^3 + 36*a^3*b^7*c^6*d^10 + 76*a^3*b^7*
c^8*d^8 - 204*a^3*b^7*c^10*d^6 + 36*a^3*b^7*c^12*d^4 + 56*a^3*b^7*c^14*d^2 - 20*a^4*b^6*c^5*d^11 - 340*a^4*b^6
*c^7*d^9 + 804*a^4*b^6*c^9*d^7 - 508*a^4*b^6*c^11*d^5 + 64*a^4*b^6*c^13*d^3 - 20*a^5*b^5*c^4*d^12 + 556*a^5*b^
5*c^6*d^10 - 1380*a^5*b^5*c^8*d^8 + 1172*a^5*b^5*c^10*d^6 - 328*a^5*b^5*c^12*d^4 + 36*a^6*b^4*c^3*d^13 - 452*a
^6*b^4*c^5*d^11 + 1308*a^6*b^4*c^7*d^9 - 1404*a^6*b^4*c^9*d^7 + 512*a^6*b^4*c^11*d^5 - 20*a^7*b^3*c^2*d^14 + 1
64*a^7*b^3*c^4*d^12 - 708*a^7*b^3*c^6*d^10 + 1004*a^7*b^3*c^8*d^8 - 440*a^7*b^3*c^10*d^6 + 4*a^8*b^2*c^3*d^13
+ 204*a^8*b^2*c^5*d^11 - 436*a^8*b^2*c^7*d^9 + 224*a^8*b^2*c^9*d^7))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6
*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 -
6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d
^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a
^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^
3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*
b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (b^3*(b^2 - a^2)^(1/2)*((8*(4*a^2*b^9*c
^19 + 4*a^11*c^2*d^17 - 16*a^11*c^4*d^15 + 24*a^11*c^6*d^13 - 16*a^11*c^8*d^11 + 4*a^11*c^10*d^9 - 4*a*b^10*c^
10*d^9 + 16*a*b^10*c^12*d^7 - 24*a*b^10*c^14*d^5 + 16*a*b^10*c^16*d^3 - 28*a^3*b^8*c^18*d - 12*a^10*b*c^3*d^16
+ 88*a^10*b*c^5*d^14 - 152*a^10*b*c^7*d^12 + 108*a^10*b*c^9*d^10 - 28*a^10*b*c^11*d^8 + 28*a^2*b^9*c^9*d^10 -
108*a^2*b^9*c^11*d^8 + 152*a^2*b^9*c^13*d^6 - 88*a^2*b^9*c^15*d^4 + 12*a^2*b^9*c^17*d^2 - 80*a^3*b^8*c^8*d^11
+ 292*a^3*b^8*c^10*d^9 - 368*a^3*b^8*c^12*d^7 + 152*a^3*b^8*c^14*d^5 + 32*a^3*b^8*c^16*d^3 + 112*a^4*b^7*c^7*
d^12 - 368*a^4*b^7*c^9*d^10 + 352*a^4*b^7*c^11*d^8 + 32*a^4*b^7*c^13*d^6 - 208*a^4*b^7*c^15*d^4 + 80*a^4*b^7*c
^17*d^2 - 56*a^5*b^6*c^6*d^13 + 112*a^5*b^6*c^8*d^11 + 112*a^5*b^6*c^10*d^9 - 448*a^5*b^6*c^12*d^7 + 392*a^5*b
^6*c^14*d^5 - 112*a^5*b^6*c^16*d^3 - 56*a^6*b^5*c^5*d^14 + 280*a^6*b^5*c^7*d^12 - 560*a^6*b^5*c^9*d^10 + 560*a
^6*b^5*c^11*d^8 - 280*a^6*b^5*c^13*d^6 + 56*a^6*b^5*c^15*d^4 + 112*a^7*b^4*c^4*d^15 - 392*a^7*b^4*c^6*d^13 + 4
48*a^7*b^4*c^8*d^11 - 112*a^7*b^4*c^10*d^9 - 112*a^7*b^4*c^12*d^7 + 56*a^7*b^4*c^14*d^5 - 80*a^8*b^3*c^3*d^16
+ 208*a^8*b^3*c^5*d^14 - 32*a^8*b^3*c^7*d^12 - 352*a^8*b^3*c^9*d^10 + 368*a^8*b^3*c^11*d^8 - 112*a^8*b^3*c^13*
d^6 + 28*a^9*b^2*c^2*d^17 - 32*a^9*b^2*c^4*d^15 - 152*a^9*b^2*c^6*d^13 + 368*a^9*b^2*c^8*d^11 - 292*a^9*b^2*c^
10*d^9 + 80*a^9*b^2*c^12*d^7 - 4*a*b^10*c^18*d - 4*a^10*b*c*d^18))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a
^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*
a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9
+ 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2
*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*
b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^
2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(8*a^3*b^8*c^19 - 1
2*a^11*c*d^18 - 12*a*b^10*c^19 + 56*a^11*c^3*d^16 - 104*a^11*c^5*d^14 + 96*a^11*c^7*d^12 - 44*a^11*c^9*d^10 +
8*a^11*c^11*d^8 + 16*a*b^10*c^9*d^10 - 76*a*b^10*c^11*d^8 + 144*a*b^10*c^13*d^6 - 136*a*b^10*c^15*d^4 + 64*a*b
^10*c^17*d^2 + 96*a^2*b^9*c^18*d - 64*a^4*b^7*c^18*d + 16*a^9*b^2*c*d^18 + 96*a^10*b*c^2*d^17 - 448*a^10*b*c^4
*d^15 + 832*a^10*b*c^6*d^13 - 768*a^10*b*c^8*d^11 + 352*a^10*b*c^10*d^9 - 64*a^10*b*c^12*d^7 - 128*a^2*b^9*c^8
*d^11 + 608*a^2*b^9*c^10*d^9 - 1152*a^2*b^9*c^12*d^7 + 1088*a^2*b^9*c^14*d^5 - 512*a^2*b^9*c^16*d^3 + 448*a^3*
b^8*c^7*d^12 - 2140*a^3*b^8*c^9*d^10 + 4088*a^3*b^8*c^11*d^8 - 3912*a^3*b^8*c^13*d^6 + 1888*a^3*b^8*c^15*d^4 -
380*a^3*b^8*c^17*d^2 - 896*a^4*b^7*c^6*d^13 + 4352*a^4*b^7*c^8*d^11 - 8512*a^4*b^7*c^10*d^9 + 8448*a^4*b^7*c^
12*d^7 - 4352*a^4*b^7*c^14*d^5 + 1024*a^4*b^7*c^16*d^3 + 1120*a^5*b^6*c^5*d^14 - 5656*a^5*b^6*c^7*d^12 + 11648
*a^5*b^6*c^9*d^10 - 12432*a^5*b^6*c^11*d^8 + 7168*a^5*b^6*c^13*d^6 - 2072*a^5*b^6*c^15*d^4 + 224*a^5*b^6*c^17*
d^2 - 896*a^6*b^5*c^4*d^15 + 4928*a^6*b^5*c^6*d^13 - 11200*a^6*b^5*c^8*d^11 + 13440*a^6*b^5*c^10*d^9 - 8960*a^
6*b^5*c^12*d^7 + 3136*a^6*b^5*c^14*d^5 - 448*a^6*b^5*c^16*d^3 + 448*a^7*b^4*c^3*d^16 - 2968*a^7*b^4*c^5*d^14 +
7952*a^7*b^4*c^7*d^12 - 11088*a^7*b^4*c^9*d^10 + 8512*a^7*b^4*c^11*d^8 - 3416*a^7*b^4*c^13*d^6 + 560*a^7*b^4*
c^15*d^4 - 128*a^8*b^3*c^2*d^17 + 1280*a^8*b^3*c^4*d^15 - 4288*a^8*b^3*c^6*d^13 + 6912*a^8*b^3*c^8*d^11 - 5888
*a^8*b^3*c^10*d^9 + 2560*a^8*b^3*c^12*d^7 - 448*a^8*b^3*c^14*d^5 - 412*a^9*b^2*c^3*d^16 + 1712*a^9*b^2*c^5*d^1
4 - 3048*a^9*b^2*c^7*d^12 + 2752*a^9*b^2*c^9*d^10 - 1244*a^9*b^2*c^11*d^8 + 224*a^9*b^2*c^13*d^6))/(a^6*d^14 +
b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^
6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a
^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d
^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9
- 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10
+ 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13)))/(a^5*d^3
+ b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2)))/(
a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*
d^2))*1i)/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d -
3*a^4*b*c*d^2) - (b^3*(b^2 - a^2)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a*b^8*c^13 + a^9*c*d^12 + 4*a^9*c^3*d^10 +
4*a^9*c^5*d^8 - 16*a*b^8*c^3*d^10 + 76*a*b^8*c^5*d^8 - 162*a*b^8*c^7*d^6 + 176*a*b^8*c^9*d^4 - 96*a*b^8*c^11*d
^2 - 8*a^2*b^7*c^12*d - 16*a^3*b^6*c*d^12 - 4*a^5*b^4*c*d^12 + 2*a^7*b^2*c*d^12 - 2*a^8*b*c^2*d^11 - 20*a^8*b*
c^4*d^9 - 32*a^8*b*c^6*d^7 + 32*a^2*b^7*c^2*d^11 - 152*a^2*b^7*c^4*d^9 + 372*a^2*b^7*c^6*d^7 - 472*a^2*b^7*c^8
*d^5 + 336*a^2*b^7*c^10*d^3 + 72*a^3*b^6*c^3*d^10 - 274*a^3*b^6*c^5*d^8 + 481*a^3*b^6*c^7*d^6 - 564*a^3*b^6*c^
9*d^4 + 40*a^3*b^6*c^11*d^2 + 8*a^4*b^5*c^2*d^11 + 80*a^4*b^5*c^4*d^9 - 250*a^4*b^5*c^6*d^7 + 612*a^4*b^5*c^8*
d^5 - 144*a^4*b^5*c^10*d^3 - 14*a^5*b^4*c^3*d^10 + 55*a^5*b^4*c^5*d^8 - 412*a^5*b^4*c^7*d^6 + 240*a^5*b^4*c^9*
d^4 - 4*a^6*b^3*c^2*d^11 + 20*a^6*b^3*c^4*d^9 + 128*a^6*b^3*c^6*d^7 - 216*a^6*b^3*c^8*d^5 - 9*a^7*b^2*c^3*d^10
+ 12*a^7*b^2*c^5*d^8 + 112*a^7*b^2*c^7*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c
^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*
b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 -
6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^
2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*
b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^
2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*(4*a*b^8*c^4*d^9 - 16*a*b^8*c^6*d^7 + 24*a*b^8*c^8*d^5 - 16
*a*b^8*c^10*d^3 + 4*a^4*b^5*c*d^12 + 4*a^6*b^3*c*d^12 + 4*a^8*b*c^3*d^10 + 4*a^8*b*c^5*d^8 - 4*a^2*b^7*c^3*d^1
0 + 12*a^2*b^7*c^5*d^8 + a^2*b^7*c^7*d^6 - 28*a^2*b^7*c^9*d^4 + 28*a^2*b^7*c^11*d^2 - 4*a^3*b^6*c^2*d^11 + 24*
a^3*b^6*c^4*d^9 - 98*a^3*b^6*c^6*d^7 + 164*a^3*b^6*c^8*d^5 - 140*a^3*b^6*c^10*d^3 - 16*a^4*b^5*c^3*d^10 + 95*a
^4*b^5*c^5*d^8 - 188*a^4*b^5*c^7*d^6 + 240*a^4*b^5*c^9*d^4 - 8*a^5*b^4*c^2*d^11 - 20*a^5*b^4*c^4*d^9 + 64*a^5*
b^4*c^6*d^7 - 216*a^5*b^4*c^8*d^5 - a^6*b^3*c^3*d^10 + 20*a^6*b^3*c^5*d^8 + 112*a^6*b^3*c^7*d^6 - 2*a^7*b^2*c^
2*d^11 - 20*a^7*b^2*c^4*d^9 - 32*a^7*b^2*c^6*d^7 + 4*a*b^8*c^12*d + a^8*b*c*d^12))/(a^6*d^14 + b^6*c^14 - 4*a^
6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b
^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 -
36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*
c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c
^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6
*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (b^3*(b^2 - a^2)^(1/2)*((
8*(4*a^2*b^8*c^16 + 2*a^10*c^2*d^14 - 6*a^10*c^6*d^10 + 4*a^10*c^8*d^8 + 4*a*b^9*c^7*d^9 - 18*a*b^9*c^9*d^7 +
36*a*b^9*c^11*d^5 - 34*a*b^9*c^13*d^3 - 32*a^3*b^7*c^15*d + 4*a^7*b^3*c*d^15 - 10*a^9*b*c^3*d^13 - 12*a^9*b*c^
5*d^11 + 54*a^9*b*c^7*d^9 - 32*a^9*b*c^9*d^7 - 24*a^2*b^8*c^6*d^10 + 110*a^2*b^8*c^8*d^8 - 232*a^2*b^8*c^10*d^
6 + 234*a^2*b^8*c^12*d^4 - 92*a^2*b^8*c^14*d^2 + 60*a^3*b^7*c^5*d^11 - 282*a^3*b^7*c^7*d^9 + 638*a^3*b^7*c^9*d
^7 - 702*a^3*b^7*c^11*d^5 + 318*a^3*b^7*c^13*d^3 - 80*a^4*b^6*c^4*d^12 + 390*a^4*b^6*c^6*d^10 - 970*a^4*b^6*c^
8*d^8 + 1202*a^4*b^6*c^10*d^6 - 654*a^4*b^6*c^12*d^4 + 112*a^4*b^6*c^14*d^2 + 60*a^5*b^5*c^3*d^13 - 310*a^5*b^
5*c^5*d^11 + 878*a^5*b^5*c^7*d^9 - 1290*a^5*b^5*c^9*d^7 + 886*a^5*b^5*c^11*d^5 - 224*a^5*b^5*c^13*d^3 - 24*a^6
*b^4*c^2*d^14 + 138*a^6*b^4*c^4*d^12 - 466*a^6*b^4*c^6*d^10 + 894*a^6*b^4*c^8*d^8 - 822*a^6*b^4*c^10*d^6 + 280
*a^6*b^4*c^12*d^4 - 30*a^7*b^3*c^3*d^13 + 122*a^7*b^3*c^5*d^11 - 394*a^7*b^3*c^7*d^9 + 522*a^7*b^3*c^9*d^7 - 2
24*a^7*b^3*c^11*d^5 + 2*a^8*b^2*c^2*d^14 + 2*a^8*b^2*c^4*d^12 + 102*a^8*b^2*c^6*d^10 - 218*a^8*b^2*c^8*d^8 + 1
12*a^8*b^2*c^10*d^6 + 12*a*b^9*c^15*d))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8
+ a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^
7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5
*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*
c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^
11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10
*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^16 + 4*a^10*c*d^15 - 12*a^10*c^5*d^
11 + 8*a^10*c^7*d^9 + 4*a*b^9*c^8*d^8 - 8*a*b^9*c^10*d^6 + 12*a*b^9*c^12*d^4 - 16*a*b^9*c^14*d^2 - 40*a^2*b^8*
c^15*d + 4*a^8*b^2*c*d^15 - 20*a^9*b*c^2*d^14 - 24*a^9*b*c^4*d^12 + 108*a^9*b*c^6*d^10 - 64*a^9*b*c^8*d^8 - 20
*a^2*b^8*c^7*d^9 + 16*a^2*b^8*c^9*d^7 - 12*a^2*b^8*c^11*d^5 + 56*a^2*b^8*c^13*d^3 + 36*a^3*b^7*c^6*d^10 + 76*a
^3*b^7*c^8*d^8 - 204*a^3*b^7*c^10*d^6 + 36*a^3*b^7*c^12*d^4 + 56*a^3*b^7*c^14*d^2 - 20*a^4*b^6*c^5*d^11 - 340*
a^4*b^6*c^7*d^9 + 804*a^4*b^6*c^9*d^7 - 508*a^4*b^6*c^11*d^5 + 64*a^4*b^6*c^13*d^3 - 20*a^5*b^5*c^4*d^12 + 556
*a^5*b^5*c^6*d^10 - 1380*a^5*b^5*c^8*d^8 + 1172*a^5*b^5*c^10*d^6 - 328*a^5*b^5*c^12*d^4 + 36*a^6*b^4*c^3*d^13
- 452*a^6*b^4*c^5*d^11 + 1308*a^6*b^4*c^7*d^9 - 1404*a^6*b^4*c^9*d^7 + 512*a^6*b^4*c^11*d^5 - 20*a^7*b^3*c^2*d
^14 + 164*a^7*b^3*c^4*d^12 - 708*a^7*b^3*c^6*d^10 + 1004*a^7*b^3*c^8*d^8 - 440*a^7*b^3*c^10*d^6 + 4*a^8*b^2*c^
3*d^13 + 204*a^8*b^2*c^5*d^11 - 436*a^8*b^2*c^7*d^9 + 224*a^8*b^2*c^9*d^7))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d
^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12
*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*
b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6
- 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7
+ 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 -
60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (b^3*(b^2 - a^2)^(1/2)*((8*(4*a^
2*b^9*c^19 + 4*a^11*c^2*d^17 - 16*a^11*c^4*d^15 + 24*a^11*c^6*d^13 - 16*a^11*c^8*d^11 + 4*a^11*c^10*d^9 - 4*a*
b^10*c^10*d^9 + 16*a*b^10*c^12*d^7 - 24*a*b^10*c^14*d^5 + 16*a*b^10*c^16*d^3 - 28*a^3*b^8*c^18*d - 12*a^10*b*c
^3*d^16 + 88*a^10*b*c^5*d^14 - 152*a^10*b*c^7*d^12 + 108*a^10*b*c^9*d^10 - 28*a^10*b*c^11*d^8 + 28*a^2*b^9*c^9
*d^10 - 108*a^2*b^9*c^11*d^8 + 152*a^2*b^9*c^13*d^6 - 88*a^2*b^9*c^15*d^4 + 12*a^2*b^9*c^17*d^2 - 80*a^3*b^8*c
^8*d^11 + 292*a^3*b^8*c^10*d^9 - 368*a^3*b^8*c^12*d^7 + 152*a^3*b^8*c^14*d^5 + 32*a^3*b^8*c^16*d^3 + 112*a^4*b
^7*c^7*d^12 - 368*a^4*b^7*c^9*d^10 + 352*a^4*b^7*c^11*d^8 + 32*a^4*b^7*c^13*d^6 - 208*a^4*b^7*c^15*d^4 + 80*a^
4*b^7*c^17*d^2 - 56*a^5*b^6*c^6*d^13 + 112*a^5*b^6*c^8*d^11 + 112*a^5*b^6*c^10*d^9 - 448*a^5*b^6*c^12*d^7 + 39
2*a^5*b^6*c^14*d^5 - 112*a^5*b^6*c^16*d^3 - 56*a^6*b^5*c^5*d^14 + 280*a^6*b^5*c^7*d^12 - 560*a^6*b^5*c^9*d^10
+ 560*a^6*b^5*c^11*d^8 - 280*a^6*b^5*c^13*d^6 + 56*a^6*b^5*c^15*d^4 + 112*a^7*b^4*c^4*d^15 - 392*a^7*b^4*c^6*d
^13 + 448*a^7*b^4*c^8*d^11 - 112*a^7*b^4*c^10*d^9 - 112*a^7*b^4*c^12*d^7 + 56*a^7*b^4*c^14*d^5 - 80*a^8*b^3*c^
3*d^16 + 208*a^8*b^3*c^5*d^14 - 32*a^8*b^3*c^7*d^12 - 352*a^8*b^3*c^9*d^10 + 368*a^8*b^3*c^11*d^8 - 112*a^8*b^
3*c^13*d^6 + 28*a^9*b^2*c^2*d^17 - 32*a^9*b^2*c^4*d^15 - 152*a^9*b^2*c^6*d^13 + 368*a^9*b^2*c^8*d^11 - 292*a^9
*b^2*c^10*d^9 + 80*a^9*b^2*c^12*d^7 - 4*a*b^10*c^18*d - 4*a^10*b*c*d^18))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^1
2 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d
^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*
c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 -
60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 +
80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60
*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(8*a^3*b^8*c
^19 - 12*a^11*c*d^18 - 12*a*b^10*c^19 + 56*a^11*c^3*d^16 - 104*a^11*c^5*d^14 + 96*a^11*c^7*d^12 - 44*a^11*c^9*
d^10 + 8*a^11*c^11*d^8 + 16*a*b^10*c^9*d^10 - 76*a*b^10*c^11*d^8 + 144*a*b^10*c^13*d^6 - 136*a*b^10*c^15*d^4 +
64*a*b^10*c^17*d^2 + 96*a^2*b^9*c^18*d - 64*a^4*b^7*c^18*d + 16*a^9*b^2*c*d^18 + 96*a^10*b*c^2*d^17 - 448*a^1
0*b*c^4*d^15 + 832*a^10*b*c^6*d^13 - 768*a^10*b*c^8*d^11 + 352*a^10*b*c^10*d^9 - 64*a^10*b*c^12*d^7 - 128*a^2*
b^9*c^8*d^11 + 608*a^2*b^9*c^10*d^9 - 1152*a^2*b^9*c^12*d^7 + 1088*a^2*b^9*c^14*d^5 - 512*a^2*b^9*c^16*d^3 + 4
48*a^3*b^8*c^7*d^12 - 2140*a^3*b^8*c^9*d^10 + 4088*a^3*b^8*c^11*d^8 - 3912*a^3*b^8*c^13*d^6 + 1888*a^3*b^8*c^1
5*d^4 - 380*a^3*b^8*c^17*d^2 - 896*a^4*b^7*c^6*d^13 + 4352*a^4*b^7*c^8*d^11 - 8512*a^4*b^7*c^10*d^9 + 8448*a^4
*b^7*c^12*d^7 - 4352*a^4*b^7*c^14*d^5 + 1024*a^4*b^7*c^16*d^3 + 1120*a^5*b^6*c^5*d^14 - 5656*a^5*b^6*c^7*d^12
+ 11648*a^5*b^6*c^9*d^10 - 12432*a^5*b^6*c^11*d^8 + 7168*a^5*b^6*c^13*d^6 - 2072*a^5*b^6*c^15*d^4 + 224*a^5*b^
6*c^17*d^2 - 896*a^6*b^5*c^4*d^15 + 4928*a^6*b^5*c^6*d^13 - 11200*a^6*b^5*c^8*d^11 + 13440*a^6*b^5*c^10*d^9 -
8960*a^6*b^5*c^12*d^7 + 3136*a^6*b^5*c^14*d^5 - 448*a^6*b^5*c^16*d^3 + 448*a^7*b^4*c^3*d^16 - 2968*a^7*b^4*c^5
*d^14 + 7952*a^7*b^4*c^7*d^12 - 11088*a^7*b^4*c^9*d^10 + 8512*a^7*b^4*c^11*d^8 - 3416*a^7*b^4*c^13*d^6 + 560*a
^7*b^4*c^15*d^4 - 128*a^8*b^3*c^2*d^17 + 1280*a^8*b^3*c^4*d^15 - 4288*a^8*b^3*c^6*d^13 + 6912*a^8*b^3*c^8*d^11
- 5888*a^8*b^3*c^10*d^9 + 2560*a^8*b^3*c^12*d^7 - 448*a^8*b^3*c^14*d^5 - 412*a^9*b^2*c^3*d^16 + 1712*a^9*b^2*
c^5*d^14 - 3048*a^9*b^2*c^7*d^12 + 2752*a^9*b^2*c^9*d^10 - 1244*a^9*b^2*c^11*d^8 + 224*a^9*b^2*c^13*d^6))/(a^6
*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6
+ 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3
+ 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^
4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*
c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^
4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13)))/(a
^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d
^2)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a
^4*b*c*d^2))*1i)/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*
c^2*d - 3*a^4*b*c*d^2))/((16*(36*a*b^7*c^5*d^5 - 18*a*b^7*c^3*d^7 - 34*a*b^7*c^7*d^3 + 4*a^3*b^5*c*d^9 + a^5*b
^3*c*d^9 + 2*a^2*b^6*c^2*d^8 - 25*a^2*b^6*c^4*d^6 + 50*a^2*b^6*c^6*d^4 - 36*a^2*b^6*c^8*d^2 - a^3*b^5*c^3*d^7
- 16*a^3*b^5*c^5*d^5 + 40*a^3*b^5*c^7*d^3 + a^4*b^4*c^2*d^8 - 8*a^4*b^4*c^4*d^6 - 20*a^4*b^4*c^6*d^4 + 4*a^5*b
^3*c^3*d^7 + 4*a^5*b^3*c^5*d^5 + 4*a*b^7*c*d^9 + 12*a*b^7*c^9*d))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^
6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a
*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9
+ 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*
b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b
^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2
*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (16*tan(e/2 + (f*x)/2)*(4*a*b^7*c^2*d^8 -
26*a*b^7*c^4*d^6 + 52*a*b^7*c^6*d^4 - 48*a*b^7*c^8*d^2 + 4*a^2*b^6*c*d^9 + 2*a^4*b^4*c*d^9 - 2*a^2*b^6*c^3*d^7
- 20*a^2*b^6*c^5*d^5 + 72*a^2*b^6*c^7*d^3 + 2*a^3*b^5*c^2*d^8 - 16*a^3*b^5*c^4*d^6 - 40*a^3*b^5*c^6*d^4 + 8*a
^4*b^4*c^3*d^7 + 8*a^4*b^4*c^5*d^5))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 +
a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d
^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*
c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^1
2*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*
d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^
4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (b^3*(b^2 - a^2)^(1/2)*((8*(4*a*b^8*c^4*d^9 - 16*a*b^8*c^6*d^7 + 24*a*b
^8*c^8*d^5 - 16*a*b^8*c^10*d^3 + 4*a^4*b^5*c*d^12 + 4*a^6*b^3*c*d^12 + 4*a^8*b*c^3*d^10 + 4*a^8*b*c^5*d^8 - 4*
a^2*b^7*c^3*d^10 + 12*a^2*b^7*c^5*d^8 + a^2*b^7*c^7*d^6 - 28*a^2*b^7*c^9*d^4 + 28*a^2*b^7*c^11*d^2 - 4*a^3*b^6
*c^2*d^11 + 24*a^3*b^6*c^4*d^9 - 98*a^3*b^6*c^6*d^7 + 164*a^3*b^6*c^8*d^5 - 140*a^3*b^6*c^10*d^3 - 16*a^4*b^5*
c^3*d^10 + 95*a^4*b^5*c^5*d^8 - 188*a^4*b^5*c^7*d^6 + 240*a^4*b^5*c^9*d^4 - 8*a^5*b^4*c^2*d^11 - 20*a^5*b^4*c^
4*d^9 + 64*a^5*b^4*c^6*d^7 - 216*a^5*b^4*c^8*d^5 - a^6*b^3*c^3*d^10 + 20*a^6*b^3*c^5*d^8 + 112*a^6*b^3*c^7*d^6
- 2*a^7*b^2*c^2*d^11 - 20*a^7*b^2*c^4*d^9 - 32*a^7*b^2*c^6*d^7 + 4*a*b^8*c^12*d + a^8*b*c*d^12))/(a^6*d^14 +
b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6
*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^
5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^
8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9
- 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 +
90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2
+ (f*x)/2)*(4*a*b^8*c^13 + a^9*c*d^12 + 4*a^9*c^3*d^10 + 4*a^9*c^5*d^8 - 16*a*b^8*c^3*d^10 + 76*a*b^8*c^5*d^8
- 162*a*b^8*c^7*d^6 + 176*a*b^8*c^9*d^4 - 96*a*b^8*c^11*d^2 - 8*a^2*b^7*c^12*d - 16*a^3*b^6*c*d^12 - 4*a^5*b^
4*c*d^12 + 2*a^7*b^2*c*d^12 - 2*a^8*b*c^2*d^11 - 20*a^8*b*c^4*d^9 - 32*a^8*b*c^6*d^7 + 32*a^2*b^7*c^2*d^11 - 1
52*a^2*b^7*c^4*d^9 + 372*a^2*b^7*c^6*d^7 - 472*a^2*b^7*c^8*d^5 + 336*a^2*b^7*c^10*d^3 + 72*a^3*b^6*c^3*d^10 -
274*a^3*b^6*c^5*d^8 + 481*a^3*b^6*c^7*d^6 - 564*a^3*b^6*c^9*d^4 + 40*a^3*b^6*c^11*d^2 + 8*a^4*b^5*c^2*d^11 + 8
0*a^4*b^5*c^4*d^9 - 250*a^4*b^5*c^6*d^7 + 612*a^4*b^5*c^8*d^5 - 144*a^4*b^5*c^10*d^3 - 14*a^5*b^4*c^3*d^10 + 5
5*a^5*b^4*c^5*d^8 - 412*a^5*b^4*c^7*d^6 + 240*a^5*b^4*c^9*d^4 - 4*a^6*b^3*c^2*d^11 + 20*a^6*b^3*c^4*d^9 + 128*
a^6*b^3*c^6*d^7 - 216*a^6*b^3*c^8*d^5 - 9*a^7*b^2*c^3*d^10 + 12*a^7*b^2*c^5*d^8 + 112*a^7*b^2*c^7*d^6))/(a^6*d
^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 +
6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 +
24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*
c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^
5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*
d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (b^3
*(b^2 - a^2)^(1/2)*((8*(4*a^2*b^8*c^16 + 2*a^10*c^2*d^14 - 6*a^10*c^6*d^10 + 4*a^10*c^8*d^8 + 4*a*b^9*c^7*d^9
- 18*a*b^9*c^9*d^7 + 36*a*b^9*c^11*d^5 - 34*a*b^9*c^13*d^3 - 32*a^3*b^7*c^15*d + 4*a^7*b^3*c*d^15 - 10*a^9*b*c
^3*d^13 - 12*a^9*b*c^5*d^11 + 54*a^9*b*c^7*d^9 - 32*a^9*b*c^9*d^7 - 24*a^2*b^8*c^6*d^10 + 110*a^2*b^8*c^8*d^8
- 232*a^2*b^8*c^10*d^6 + 234*a^2*b^8*c^12*d^4 - 92*a^2*b^8*c^14*d^2 + 60*a^3*b^7*c^5*d^11 - 282*a^3*b^7*c^7*d^
9 + 638*a^3*b^7*c^9*d^7 - 702*a^3*b^7*c^11*d^5 + 318*a^3*b^7*c^13*d^3 - 80*a^4*b^6*c^4*d^12 + 390*a^4*b^6*c^6*
d^10 - 970*a^4*b^6*c^8*d^8 + 1202*a^4*b^6*c^10*d^6 - 654*a^4*b^6*c^12*d^4 + 112*a^4*b^6*c^14*d^2 + 60*a^5*b^5*
c^3*d^13 - 310*a^5*b^5*c^5*d^11 + 878*a^5*b^5*c^7*d^9 - 1290*a^5*b^5*c^9*d^7 + 886*a^5*b^5*c^11*d^5 - 224*a^5*
b^5*c^13*d^3 - 24*a^6*b^4*c^2*d^14 + 138*a^6*b^4*c^4*d^12 - 466*a^6*b^4*c^6*d^10 + 894*a^6*b^4*c^8*d^8 - 822*a
^6*b^4*c^10*d^6 + 280*a^6*b^4*c^12*d^4 - 30*a^7*b^3*c^3*d^13 + 122*a^7*b^3*c^5*d^11 - 394*a^7*b^3*c^7*d^9 + 52
2*a^7*b^3*c^9*d^7 - 224*a^7*b^3*c^11*d^5 + 2*a^8*b^2*c^2*d^14 + 2*a^8*b^2*c^4*d^12 + 102*a^8*b^2*c^6*d^10 - 21
8*a^8*b^2*c^8*d^8 + 112*a^8*b^2*c^10*d^6 + 12*a*b^9*c^15*d))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4
*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*
c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*
a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c
^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^
9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*
d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^16 + 4*a^10*c*
d^15 - 12*a^10*c^5*d^11 + 8*a^10*c^7*d^9 + 4*a*b^9*c^8*d^8 - 8*a*b^9*c^10*d^6 + 12*a*b^9*c^12*d^4 - 16*a*b^9*c
^14*d^2 - 40*a^2*b^8*c^15*d + 4*a^8*b^2*c*d^15 - 20*a^9*b*c^2*d^14 - 24*a^9*b*c^4*d^12 + 108*a^9*b*c^6*d^10 -
64*a^9*b*c^8*d^8 - 20*a^2*b^8*c^7*d^9 + 16*a^2*b^8*c^9*d^7 - 12*a^2*b^8*c^11*d^5 + 56*a^2*b^8*c^13*d^3 + 36*a^
3*b^7*c^6*d^10 + 76*a^3*b^7*c^8*d^8 - 204*a^3*b^7*c^10*d^6 + 36*a^3*b^7*c^12*d^4 + 56*a^3*b^7*c^14*d^2 - 20*a^
4*b^6*c^5*d^11 - 340*a^4*b^6*c^7*d^9 + 804*a^4*b^6*c^9*d^7 - 508*a^4*b^6*c^11*d^5 + 64*a^4*b^6*c^13*d^3 - 20*a
^5*b^5*c^4*d^12 + 556*a^5*b^5*c^6*d^10 - 1380*a^5*b^5*c^8*d^8 + 1172*a^5*b^5*c^10*d^6 - 328*a^5*b^5*c^12*d^4 +
36*a^6*b^4*c^3*d^13 - 452*a^6*b^4*c^5*d^11 + 1308*a^6*b^4*c^7*d^9 - 1404*a^6*b^4*c^9*d^7 + 512*a^6*b^4*c^11*d
^5 - 20*a^7*b^3*c^2*d^14 + 164*a^7*b^3*c^4*d^12 - 708*a^7*b^3*c^6*d^10 + 1004*a^7*b^3*c^8*d^8 - 440*a^7*b^3*c^
10*d^6 + 4*a^8*b^2*c^3*d^13 + 204*a^8*b^2*c^5*d^11 - 436*a^8*b^2*c^7*d^9 + 224*a^8*b^2*c^9*d^7))/(a^6*d^14 + b
^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*
c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5
*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8
+ 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 -
120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 +
90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (b^3*(b^2 -
a^2)^(1/2)*((8*(4*a^2*b^9*c^19 + 4*a^11*c^2*d^17 - 16*a^11*c^4*d^15 + 24*a^11*c^6*d^13 - 16*a^11*c^8*d^11 + 4
*a^11*c^10*d^9 - 4*a*b^10*c^10*d^9 + 16*a*b^10*c^12*d^7 - 24*a*b^10*c^14*d^5 + 16*a*b^10*c^16*d^3 - 28*a^3*b^8
*c^18*d - 12*a^10*b*c^3*d^16 + 88*a^10*b*c^5*d^14 - 152*a^10*b*c^7*d^12 + 108*a^10*b*c^9*d^10 - 28*a^10*b*c^11
*d^8 + 28*a^2*b^9*c^9*d^10 - 108*a^2*b^9*c^11*d^8 + 152*a^2*b^9*c^13*d^6 - 88*a^2*b^9*c^15*d^4 + 12*a^2*b^9*c^
17*d^2 - 80*a^3*b^8*c^8*d^11 + 292*a^3*b^8*c^10*d^9 - 368*a^3*b^8*c^12*d^7 + 152*a^3*b^8*c^14*d^5 + 32*a^3*b^8
*c^16*d^3 + 112*a^4*b^7*c^7*d^12 - 368*a^4*b^7*c^9*d^10 + 352*a^4*b^7*c^11*d^8 + 32*a^4*b^7*c^13*d^6 - 208*a^4
*b^7*c^15*d^4 + 80*a^4*b^7*c^17*d^2 - 56*a^5*b^6*c^6*d^13 + 112*a^5*b^6*c^8*d^11 + 112*a^5*b^6*c^10*d^9 - 448*
a^5*b^6*c^12*d^7 + 392*a^5*b^6*c^14*d^5 - 112*a^5*b^6*c^16*d^3 - 56*a^6*b^5*c^5*d^14 + 280*a^6*b^5*c^7*d^12 -
560*a^6*b^5*c^9*d^10 + 560*a^6*b^5*c^11*d^8 - 280*a^6*b^5*c^13*d^6 + 56*a^6*b^5*c^15*d^4 + 112*a^7*b^4*c^4*d^1
5 - 392*a^7*b^4*c^6*d^13 + 448*a^7*b^4*c^8*d^11 - 112*a^7*b^4*c^10*d^9 - 112*a^7*b^4*c^12*d^7 + 56*a^7*b^4*c^1
4*d^5 - 80*a^8*b^3*c^3*d^16 + 208*a^8*b^3*c^5*d^14 - 32*a^8*b^3*c^7*d^12 - 352*a^8*b^3*c^9*d^10 + 368*a^8*b^3*
c^11*d^8 - 112*a^8*b^3*c^13*d^6 + 28*a^9*b^2*c^2*d^17 - 32*a^9*b^2*c^4*d^15 - 152*a^9*b^2*c^6*d^13 + 368*a^9*b
^2*c^8*d^11 - 292*a^9*b^2*c^10*d^9 + 80*a^9*b^2*c^12*d^7 - 4*a*b^10*c^18*d - 4*a^10*b*c*d^18))/(a^6*d^14 + b^6
*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^
10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b
*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 +
90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 1
20*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90
*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 +
(f*x)/2)*(8*a^3*b^8*c^19 - 12*a^11*c*d^18 - 12*a*b^10*c^19 + 56*a^11*c^3*d^16 - 104*a^11*c^5*d^14 + 96*a^11*c^
7*d^12 - 44*a^11*c^9*d^10 + 8*a^11*c^11*d^8 + 16*a*b^10*c^9*d^10 - 76*a*b^10*c^11*d^8 + 144*a*b^10*c^13*d^6 -
136*a*b^10*c^15*d^4 + 64*a*b^10*c^17*d^2 + 96*a^2*b^9*c^18*d - 64*a^4*b^7*c^18*d + 16*a^9*b^2*c*d^18 + 96*a^10
*b*c^2*d^17 - 448*a^10*b*c^4*d^15 + 832*a^10*b*c^6*d^13 - 768*a^10*b*c^8*d^11 + 352*a^10*b*c^10*d^9 - 64*a^10*
b*c^12*d^7 - 128*a^2*b^9*c^8*d^11 + 608*a^2*b^9*c^10*d^9 - 1152*a^2*b^9*c^12*d^7 + 1088*a^2*b^9*c^14*d^5 - 512
*a^2*b^9*c^16*d^3 + 448*a^3*b^8*c^7*d^12 - 2140*a^3*b^8*c^9*d^10 + 4088*a^3*b^8*c^11*d^8 - 3912*a^3*b^8*c^13*d
^6 + 1888*a^3*b^8*c^15*d^4 - 380*a^3*b^8*c^17*d^2 - 896*a^4*b^7*c^6*d^13 + 4352*a^4*b^7*c^8*d^11 - 8512*a^4*b^
7*c^10*d^9 + 8448*a^4*b^7*c^12*d^7 - 4352*a^4*b^7*c^14*d^5 + 1024*a^4*b^7*c^16*d^3 + 1120*a^5*b^6*c^5*d^14 - 5
656*a^5*b^6*c^7*d^12 + 11648*a^5*b^6*c^9*d^10 - 12432*a^5*b^6*c^11*d^8 + 7168*a^5*b^6*c^13*d^6 - 2072*a^5*b^6*
c^15*d^4 + 224*a^5*b^6*c^17*d^2 - 896*a^6*b^5*c^4*d^15 + 4928*a^6*b^5*c^6*d^13 - 11200*a^6*b^5*c^8*d^11 + 1344
0*a^6*b^5*c^10*d^9 - 8960*a^6*b^5*c^12*d^7 + 3136*a^6*b^5*c^14*d^5 - 448*a^6*b^5*c^16*d^3 + 448*a^7*b^4*c^3*d^
16 - 2968*a^7*b^4*c^5*d^14 + 7952*a^7*b^4*c^7*d^12 - 11088*a^7*b^4*c^9*d^10 + 8512*a^7*b^4*c^11*d^8 - 3416*a^7
*b^4*c^13*d^6 + 560*a^7*b^4*c^15*d^4 - 128*a^8*b^3*c^2*d^17 + 1280*a^8*b^3*c^4*d^15 - 4288*a^8*b^3*c^6*d^13 +
6912*a^8*b^3*c^8*d^11 - 5888*a^8*b^3*c^10*d^9 + 2560*a^8*b^3*c^12*d^7 - 448*a^8*b^3*c^14*d^5 - 412*a^9*b^2*c^3
*d^16 + 1712*a^9*b^2*c^5*d^14 - 3048*a^9*b^2*c^7*d^12 + 2752*a^9*b^2*c^9*d^10 - 1244*a^9*b^2*c^11*d^8 + 224*a^
9*b^2*c^13*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^
6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^
5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4
*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c
^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2
*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d -
6*a^5*b*c*d^13)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^
4*c^2*d - 3*a^4*b*c*d^2)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d
- 3*a*b^4*c^2*d - 3*a^4*b*c*d^2)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^
2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2) - (b^3*(b^2 - a^2)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a*b^8*c^13 + a^9*c
*d^12 + 4*a^9*c^3*d^10 + 4*a^9*c^5*d^8 - 16*a*b^8*c^3*d^10 + 76*a*b^8*c^5*d^8 - 162*a*b^8*c^7*d^6 + 176*a*b^8*
c^9*d^4 - 96*a*b^8*c^11*d^2 - 8*a^2*b^7*c^12*d - 16*a^3*b^6*c*d^12 - 4*a^5*b^4*c*d^12 + 2*a^7*b^2*c*d^12 - 2*a
^8*b*c^2*d^11 - 20*a^8*b*c^4*d^9 - 32*a^8*b*c^6*d^7 + 32*a^2*b^7*c^2*d^11 - 152*a^2*b^7*c^4*d^9 + 372*a^2*b^7*
c^6*d^7 - 472*a^2*b^7*c^8*d^5 + 336*a^2*b^7*c^10*d^3 + 72*a^3*b^6*c^3*d^10 - 274*a^3*b^6*c^5*d^8 + 481*a^3*b^6
*c^7*d^6 - 564*a^3*b^6*c^9*d^4 + 40*a^3*b^6*c^11*d^2 + 8*a^4*b^5*c^2*d^11 + 80*a^4*b^5*c^4*d^9 - 250*a^4*b^5*c
^6*d^7 + 612*a^4*b^5*c^8*d^5 - 144*a^4*b^5*c^10*d^3 - 14*a^5*b^4*c^3*d^10 + 55*a^5*b^4*c^5*d^8 - 412*a^5*b^4*c
^7*d^6 + 240*a^5*b^4*c^9*d^4 - 4*a^6*b^3*c^2*d^11 + 20*a^6*b^3*c^4*d^9 + 128*a^6*b^3*c^6*d^7 - 216*a^6*b^3*c^8
*d^5 - 9*a^7*b^2*c^3*d^10 + 12*a^7*b^2*c^5*d^8 + 112*a^7*b^2*c^7*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 +
6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2
- 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5
*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60
*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*
a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^
4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*(4*a*b^8*c^4*d^9 - 16*a*b^8*c^6*d^
7 + 24*a*b^8*c^8*d^5 - 16*a*b^8*c^10*d^3 + 4*a^4*b^5*c*d^12 + 4*a^6*b^3*c*d^12 + 4*a^8*b*c^3*d^10 + 4*a^8*b*c^
5*d^8 - 4*a^2*b^7*c^3*d^10 + 12*a^2*b^7*c^5*d^8 + a^2*b^7*c^7*d^6 - 28*a^2*b^7*c^9*d^4 + 28*a^2*b^7*c^11*d^2 -
4*a^3*b^6*c^2*d^11 + 24*a^3*b^6*c^4*d^9 - 98*a^3*b^6*c^6*d^7 + 164*a^3*b^6*c^8*d^5 - 140*a^3*b^6*c^10*d^3 - 1
6*a^4*b^5*c^3*d^10 + 95*a^4*b^5*c^5*d^8 - 188*a^4*b^5*c^7*d^6 + 240*a^4*b^5*c^9*d^4 - 8*a^5*b^4*c^2*d^11 - 20*
a^5*b^4*c^4*d^9 + 64*a^5*b^4*c^6*d^7 - 216*a^5*b^4*c^8*d^5 - a^6*b^3*c^3*d^10 + 20*a^6*b^3*c^5*d^8 + 112*a^6*b
^3*c^7*d^6 - 2*a^7*b^2*c^2*d^11 - 20*a^7*b^2*c^4*d^9 - 32*a^7*b^2*c^6*d^7 + 4*a*b^8*c^12*d + a^8*b*c*d^12))/(a
^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d
^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d
^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*
b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^
3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*
c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) +
(b^3*(b^2 - a^2)^(1/2)*((8*(4*a^2*b^8*c^16 + 2*a^10*c^2*d^14 - 6*a^10*c^6*d^10 + 4*a^10*c^8*d^8 + 4*a*b^9*c^7*
d^9 - 18*a*b^9*c^9*d^7 + 36*a*b^9*c^11*d^5 - 34*a*b^9*c^13*d^3 - 32*a^3*b^7*c^15*d + 4*a^7*b^3*c*d^15 - 10*a^9
*b*c^3*d^13 - 12*a^9*b*c^5*d^11 + 54*a^9*b*c^7*d^9 - 32*a^9*b*c^9*d^7 - 24*a^2*b^8*c^6*d^10 + 110*a^2*b^8*c^8*
d^8 - 232*a^2*b^8*c^10*d^6 + 234*a^2*b^8*c^12*d^4 - 92*a^2*b^8*c^14*d^2 + 60*a^3*b^7*c^5*d^11 - 282*a^3*b^7*c^
7*d^9 + 638*a^3*b^7*c^9*d^7 - 702*a^3*b^7*c^11*d^5 + 318*a^3*b^7*c^13*d^3 - 80*a^4*b^6*c^4*d^12 + 390*a^4*b^6*
c^6*d^10 - 970*a^4*b^6*c^8*d^8 + 1202*a^4*b^6*c^10*d^6 - 654*a^4*b^6*c^12*d^4 + 112*a^4*b^6*c^14*d^2 + 60*a^5*
b^5*c^3*d^13 - 310*a^5*b^5*c^5*d^11 + 878*a^5*b^5*c^7*d^9 - 1290*a^5*b^5*c^9*d^7 + 886*a^5*b^5*c^11*d^5 - 224*
a^5*b^5*c^13*d^3 - 24*a^6*b^4*c^2*d^14 + 138*a^6*b^4*c^4*d^12 - 466*a^6*b^4*c^6*d^10 + 894*a^6*b^4*c^8*d^8 - 8
22*a^6*b^4*c^10*d^6 + 280*a^6*b^4*c^12*d^4 - 30*a^7*b^3*c^3*d^13 + 122*a^7*b^3*c^5*d^11 - 394*a^7*b^3*c^7*d^9
+ 522*a^7*b^3*c^9*d^7 - 224*a^7*b^3*c^11*d^5 + 2*a^8*b^2*c^2*d^14 + 2*a^8*b^2*c^4*d^12 + 102*a^8*b^2*c^6*d^10
- 218*a^8*b^2*c^8*d^8 + 112*a^8*b^2*c^10*d^6 + 12*a*b^9*c^15*d))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6
*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*
b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 +
24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b
^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^
3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*
c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^16 + 4*a^1
0*c*d^15 - 12*a^10*c^5*d^11 + 8*a^10*c^7*d^9 + 4*a*b^9*c^8*d^8 - 8*a*b^9*c^10*d^6 + 12*a*b^9*c^12*d^4 - 16*a*b
^9*c^14*d^2 - 40*a^2*b^8*c^15*d + 4*a^8*b^2*c*d^15 - 20*a^9*b*c^2*d^14 - 24*a^9*b*c^4*d^12 + 108*a^9*b*c^6*d^1
0 - 64*a^9*b*c^8*d^8 - 20*a^2*b^8*c^7*d^9 + 16*a^2*b^8*c^9*d^7 - 12*a^2*b^8*c^11*d^5 + 56*a^2*b^8*c^13*d^3 + 3
6*a^3*b^7*c^6*d^10 + 76*a^3*b^7*c^8*d^8 - 204*a^3*b^7*c^10*d^6 + 36*a^3*b^7*c^12*d^4 + 56*a^3*b^7*c^14*d^2 - 2
0*a^4*b^6*c^5*d^11 - 340*a^4*b^6*c^7*d^9 + 804*a^4*b^6*c^9*d^7 - 508*a^4*b^6*c^11*d^5 + 64*a^4*b^6*c^13*d^3 -
20*a^5*b^5*c^4*d^12 + 556*a^5*b^5*c^6*d^10 - 1380*a^5*b^5*c^8*d^8 + 1172*a^5*b^5*c^10*d^6 - 328*a^5*b^5*c^12*d
^4 + 36*a^6*b^4*c^3*d^13 - 452*a^6*b^4*c^5*d^11 + 1308*a^6*b^4*c^7*d^9 - 1404*a^6*b^4*c^9*d^7 + 512*a^6*b^4*c^
11*d^5 - 20*a^7*b^3*c^2*d^14 + 164*a^7*b^3*c^4*d^12 - 708*a^7*b^3*c^6*d^10 + 1004*a^7*b^3*c^8*d^8 - 440*a^7*b^
3*c^10*d^6 + 4*a^8*b^2*c^3*d^13 + 204*a^8*b^2*c^5*d^11 - 436*a^8*b^2*c^7*d^9 + 224*a^8*b^2*c^9*d^7))/(a^6*d^14
+ b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*
b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24
*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6
*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d
^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^1
0 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (b^3*(b
^2 - a^2)^(1/2)*((8*(4*a^2*b^9*c^19 + 4*a^11*c^2*d^17 - 16*a^11*c^4*d^15 + 24*a^11*c^6*d^13 - 16*a^11*c^8*d^11
+ 4*a^11*c^10*d^9 - 4*a*b^10*c^10*d^9 + 16*a*b^10*c^12*d^7 - 24*a*b^10*c^14*d^5 + 16*a*b^10*c^16*d^3 - 28*a^3
*b^8*c^18*d - 12*a^10*b*c^3*d^16 + 88*a^10*b*c^5*d^14 - 152*a^10*b*c^7*d^12 + 108*a^10*b*c^9*d^10 - 28*a^10*b*
c^11*d^8 + 28*a^2*b^9*c^9*d^10 - 108*a^2*b^9*c^11*d^8 + 152*a^2*b^9*c^13*d^6 - 88*a^2*b^9*c^15*d^4 + 12*a^2*b^
9*c^17*d^2 - 80*a^3*b^8*c^8*d^11 + 292*a^3*b^8*c^10*d^9 - 368*a^3*b^8*c^12*d^7 + 152*a^3*b^8*c^14*d^5 + 32*a^3
*b^8*c^16*d^3 + 112*a^4*b^7*c^7*d^12 - 368*a^4*b^7*c^9*d^10 + 352*a^4*b^7*c^11*d^8 + 32*a^4*b^7*c^13*d^6 - 208
*a^4*b^7*c^15*d^4 + 80*a^4*b^7*c^17*d^2 - 56*a^5*b^6*c^6*d^13 + 112*a^5*b^6*c^8*d^11 + 112*a^5*b^6*c^10*d^9 -
448*a^5*b^6*c^12*d^7 + 392*a^5*b^6*c^14*d^5 - 112*a^5*b^6*c^16*d^3 - 56*a^6*b^5*c^5*d^14 + 280*a^6*b^5*c^7*d^1
2 - 560*a^6*b^5*c^9*d^10 + 560*a^6*b^5*c^11*d^8 - 280*a^6*b^5*c^13*d^6 + 56*a^6*b^5*c^15*d^4 + 112*a^7*b^4*c^4
*d^15 - 392*a^7*b^4*c^6*d^13 + 448*a^7*b^4*c^8*d^11 - 112*a^7*b^4*c^10*d^9 - 112*a^7*b^4*c^12*d^7 + 56*a^7*b^4
*c^14*d^5 - 80*a^8*b^3*c^3*d^16 + 208*a^8*b^3*c^5*d^14 - 32*a^8*b^3*c^7*d^12 - 352*a^8*b^3*c^9*d^10 + 368*a^8*
b^3*c^11*d^8 - 112*a^8*b^3*c^13*d^6 + 28*a^9*b^2*c^2*d^17 - 32*a^9*b^2*c^4*d^15 - 152*a^9*b^2*c^6*d^13 + 368*a
^9*b^2*c^8*d^11 - 292*a^9*b^2*c^10*d^9 + 80*a^9*b^2*c^12*d^7 - 4*a*b^10*c^18*d - 4*a^10*b*c*d^18))/(a^6*d^14 +
b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^
6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a
^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d
^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9
- 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10
+ 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/
2 + (f*x)/2)*(8*a^3*b^8*c^19 - 12*a^11*c*d^18 - 12*a*b^10*c^19 + 56*a^11*c^3*d^16 - 104*a^11*c^5*d^14 + 96*a^1
1*c^7*d^12 - 44*a^11*c^9*d^10 + 8*a^11*c^11*d^8 + 16*a*b^10*c^9*d^10 - 76*a*b^10*c^11*d^8 + 144*a*b^10*c^13*d^
6 - 136*a*b^10*c^15*d^4 + 64*a*b^10*c^17*d^2 + 96*a^2*b^9*c^18*d - 64*a^4*b^7*c^18*d + 16*a^9*b^2*c*d^18 + 96*
a^10*b*c^2*d^17 - 448*a^10*b*c^4*d^15 + 832*a^10*b*c^6*d^13 - 768*a^10*b*c^8*d^11 + 352*a^10*b*c^10*d^9 - 64*a
^10*b*c^12*d^7 - 128*a^2*b^9*c^8*d^11 + 608*a^2*b^9*c^10*d^9 - 1152*a^2*b^9*c^12*d^7 + 1088*a^2*b^9*c^14*d^5 -
512*a^2*b^9*c^16*d^3 + 448*a^3*b^8*c^7*d^12 - 2140*a^3*b^8*c^9*d^10 + 4088*a^3*b^8*c^11*d^8 - 3912*a^3*b^8*c^
13*d^6 + 1888*a^3*b^8*c^15*d^4 - 380*a^3*b^8*c^17*d^2 - 896*a^4*b^7*c^6*d^13 + 4352*a^4*b^7*c^8*d^11 - 8512*a^
4*b^7*c^10*d^9 + 8448*a^4*b^7*c^12*d^7 - 4352*a^4*b^7*c^14*d^5 + 1024*a^4*b^7*c^16*d^3 + 1120*a^5*b^6*c^5*d^14
- 5656*a^5*b^6*c^7*d^12 + 11648*a^5*b^6*c^9*d^10 - 12432*a^5*b^6*c^11*d^8 + 7168*a^5*b^6*c^13*d^6 - 2072*a^5*
b^6*c^15*d^4 + 224*a^5*b^6*c^17*d^2 - 896*a^6*b^5*c^4*d^15 + 4928*a^6*b^5*c^6*d^13 - 11200*a^6*b^5*c^8*d^11 +
13440*a^6*b^5*c^10*d^9 - 8960*a^6*b^5*c^12*d^7 + 3136*a^6*b^5*c^14*d^5 - 448*a^6*b^5*c^16*d^3 + 448*a^7*b^4*c^
3*d^16 - 2968*a^7*b^4*c^5*d^14 + 7952*a^7*b^4*c^7*d^12 - 11088*a^7*b^4*c^9*d^10 + 8512*a^7*b^4*c^11*d^8 - 3416
*a^7*b^4*c^13*d^6 + 560*a^7*b^4*c^15*d^4 - 128*a^8*b^3*c^2*d^17 + 1280*a^8*b^3*c^4*d^15 - 4288*a^8*b^3*c^6*d^1
3 + 6912*a^8*b^3*c^8*d^11 - 5888*a^8*b^3*c^10*d^9 + 2560*a^8*b^3*c^12*d^7 - 448*a^8*b^3*c^14*d^5 - 412*a^9*b^2
*c^3*d^16 + 1712*a^9*b^2*c^5*d^14 - 3048*a^9*b^2*c^7*d^12 + 2752*a^9*b^2*c^9*d^10 - 1244*a^9*b^2*c^11*d^8 + 22
4*a^9*b^2*c^13*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^
6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^
9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2
*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b
^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2
*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13
*d - 6*a^5*b*c*d^13)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*
a*b^4*c^2*d - 3*a^4*b*c*d^2)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^
2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^
3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2)))*(b^2 - a^2)^(1/2)*2i)/(f*(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3
*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2)) - ((a*d^5 - 4*a*c^2*d^3 + 6*b*c
^3*d^2 - 3*b*c*d^4)/((a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(c^4 + d^4 - 2*c^2*d^2)) + (d*tan(e/2 + (f*x)/2)*(2*a*d^5
- 11*a*c^2*d^3 + 17*b*c^3*d^2 - 8*b*c*d^4))/(c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(c^4 + d^4 - 2*c^2*d^2)) + (ta
n(e/2 + (f*x)/2)^2*(c^2 + 2*d^2)*(a*d^5 - 4*a*c^2*d^3 + 6*b*c^3*d^2 - 3*b*c*d^4))/(c^2*(a^2*d^2 + b^2*c^2 - 2*
a*b*c*d)*(c^4 + d^4 - 2*c^2*d^2)) + (d*tan(e/2 + (f*x)/2)^3*(2*a*d^5 - 5*a*c^2*d^3 + 7*b*c^3*d^2 - 4*b*c*d^4))
/(c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(c^4 + d^4 - 2*c^2*d^2)))/(f*(tan(e/2 + (f*x)/2)^2*(2*c^2 + 4*d^2) + c^2*t
an(e/2 + (f*x)/2)^4 + c^2 + 4*c*d*tan(e/2 + (f*x)/2)^3 + 4*c*d*tan(e/2 + (f*x)/2))) - (d*atan(((d*(-(c + d)^5*
(c - d)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a*b^8*c^13 + a^9*c*d^12 + 4*a^9*c^3*d^10 + 4*a^9*c^5*d^8 - 16*a*b^8
*c^3*d^10 + 76*a*b^8*c^5*d^8 - 162*a*b^8*c^7*d^6 + 176*a*b^8*c^9*d^4 - 96*a*b^8*c^11*d^2 - 8*a^2*b^7*c^12*d -
16*a^3*b^6*c*d^12 - 4*a^5*b^4*c*d^12 + 2*a^7*b^2*c*d^12 - 2*a^8*b*c^2*d^11 - 20*a^8*b*c^4*d^9 - 32*a^8*b*c^6*d
^7 + 32*a^2*b^7*c^2*d^11 - 152*a^2*b^7*c^4*d^9 + 372*a^2*b^7*c^6*d^7 - 472*a^2*b^7*c^8*d^5 + 336*a^2*b^7*c^10*
d^3 + 72*a^3*b^6*c^3*d^10 - 274*a^3*b^6*c^5*d^8 + 481*a^3*b^6*c^7*d^6 - 564*a^3*b^6*c^9*d^4 + 40*a^3*b^6*c^11*
d^2 + 8*a^4*b^5*c^2*d^11 + 80*a^4*b^5*c^4*d^9 - 250*a^4*b^5*c^6*d^7 + 612*a^4*b^5*c^8*d^5 - 144*a^4*b^5*c^10*d
^3 - 14*a^5*b^4*c^3*d^10 + 55*a^5*b^4*c^5*d^8 - 412*a^5*b^4*c^7*d^6 + 240*a^5*b^4*c^9*d^4 - 4*a^6*b^3*c^2*d^11
+ 20*a^6*b^3*c^4*d^9 + 128*a^6*b^3*c^6*d^7 - 216*a^6*b^3*c^8*d^5 - 9*a^7*b^2*c^3*d^10 + 12*a^7*b^2*c^5*d^8 +
112*a^7*b^2*c^7*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b
^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c
^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^
2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*
b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^
2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^1
3*d - 6*a^5*b*c*d^13) - (8*(4*a*b^8*c^4*d^9 - 16*a*b^8*c^6*d^7 + 24*a*b^8*c^8*d^5 - 16*a*b^8*c^10*d^3 + 4*a^4*
b^5*c*d^12 + 4*a^6*b^3*c*d^12 + 4*a^8*b*c^3*d^10 + 4*a^8*b*c^5*d^8 - 4*a^2*b^7*c^3*d^10 + 12*a^2*b^7*c^5*d^8 +
a^2*b^7*c^7*d^6 - 28*a^2*b^7*c^9*d^4 + 28*a^2*b^7*c^11*d^2 - 4*a^3*b^6*c^2*d^11 + 24*a^3*b^6*c^4*d^9 - 98*a^3
*b^6*c^6*d^7 + 164*a^3*b^6*c^8*d^5 - 140*a^3*b^6*c^10*d^3 - 16*a^4*b^5*c^3*d^10 + 95*a^4*b^5*c^5*d^8 - 188*a^4
*b^5*c^7*d^6 + 240*a^4*b^5*c^9*d^4 - 8*a^5*b^4*c^2*d^11 - 20*a^5*b^4*c^4*d^9 + 64*a^5*b^4*c^6*d^7 - 216*a^5*b^
4*c^8*d^5 - a^6*b^3*c^3*d^10 + 20*a^6*b^3*c^5*d^8 + 112*a^6*b^3*c^7*d^6 - 2*a^7*b^2*c^2*d^11 - 20*a^7*b^2*c^4*
d^9 - 32*a^7*b^2*c^6*d^7 + 4*a*b^8*c^12*d + a^8*b*c*d^12))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d
^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^
5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^
5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^1
0*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*
d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^
6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (d*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*a^2*b^8*c^
16 + 2*a^10*c^2*d^14 - 6*a^10*c^6*d^10 + 4*a^10*c^8*d^8 + 4*a*b^9*c^7*d^9 - 18*a*b^9*c^9*d^7 + 36*a*b^9*c^11*d
^5 - 34*a*b^9*c^13*d^3 - 32*a^3*b^7*c^15*d + 4*a^7*b^3*c*d^15 - 10*a^9*b*c^3*d^13 - 12*a^9*b*c^5*d^11 + 54*a^9
*b*c^7*d^9 - 32*a^9*b*c^9*d^7 - 24*a^2*b^8*c^6*d^10 + 110*a^2*b^8*c^8*d^8 - 232*a^2*b^8*c^10*d^6 + 234*a^2*b^8
*c^12*d^4 - 92*a^2*b^8*c^14*d^2 + 60*a^3*b^7*c^5*d^11 - 282*a^3*b^7*c^7*d^9 + 638*a^3*b^7*c^9*d^7 - 702*a^3*b^
7*c^11*d^5 + 318*a^3*b^7*c^13*d^3 - 80*a^4*b^6*c^4*d^12 + 390*a^4*b^6*c^6*d^10 - 970*a^4*b^6*c^8*d^8 + 1202*a^
4*b^6*c^10*d^6 - 654*a^4*b^6*c^12*d^4 + 112*a^4*b^6*c^14*d^2 + 60*a^5*b^5*c^3*d^13 - 310*a^5*b^5*c^5*d^11 + 87
8*a^5*b^5*c^7*d^9 - 1290*a^5*b^5*c^9*d^7 + 886*a^5*b^5*c^11*d^5 - 224*a^5*b^5*c^13*d^3 - 24*a^6*b^4*c^2*d^14 +
138*a^6*b^4*c^4*d^12 - 466*a^6*b^4*c^6*d^10 + 894*a^6*b^4*c^8*d^8 - 822*a^6*b^4*c^10*d^6 + 280*a^6*b^4*c^12*d
^4 - 30*a^7*b^3*c^3*d^13 + 122*a^7*b^3*c^5*d^11 - 394*a^7*b^3*c^7*d^9 + 522*a^7*b^3*c^9*d^7 - 224*a^7*b^3*c^11
*d^5 + 2*a^8*b^2*c^2*d^14 + 2*a^8*b^2*c^4*d^12 + 102*a^8*b^2*c^6*d^10 - 218*a^8*b^2*c^8*d^8 + 112*a^8*b^2*c^10
*d^6 + 12*a*b^9*c^15*d))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6
+ b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^
5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15
*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a
^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4
*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*
c^13*d - 6*a^5*b*c*d^13) + (8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^16 + 4*a^10*c*d^15 - 12*a^10*c^5*d^11 + 8*a^10*c^7
*d^9 + 4*a*b^9*c^8*d^8 - 8*a*b^9*c^10*d^6 + 12*a*b^9*c^12*d^4 - 16*a*b^9*c^14*d^2 - 40*a^2*b^8*c^15*d + 4*a^8*
b^2*c*d^15 - 20*a^9*b*c^2*d^14 - 24*a^9*b*c^4*d^12 + 108*a^9*b*c^6*d^10 - 64*a^9*b*c^8*d^8 - 20*a^2*b^8*c^7*d^
9 + 16*a^2*b^8*c^9*d^7 - 12*a^2*b^8*c^11*d^5 + 56*a^2*b^8*c^13*d^3 + 36*a^3*b^7*c^6*d^10 + 76*a^3*b^7*c^8*d^8
- 204*a^3*b^7*c^10*d^6 + 36*a^3*b^7*c^12*d^4 + 56*a^3*b^7*c^14*d^2 - 20*a^4*b^6*c^5*d^11 - 340*a^4*b^6*c^7*d^9
+ 804*a^4*b^6*c^9*d^7 - 508*a^4*b^6*c^11*d^5 + 64*a^4*b^6*c^13*d^3 - 20*a^5*b^5*c^4*d^12 + 556*a^5*b^5*c^6*d^
10 - 1380*a^5*b^5*c^8*d^8 + 1172*a^5*b^5*c^10*d^6 - 328*a^5*b^5*c^12*d^4 + 36*a^6*b^4*c^3*d^13 - 452*a^6*b^4*c
^5*d^11 + 1308*a^6*b^4*c^7*d^9 - 1404*a^6*b^4*c^9*d^7 + 512*a^6*b^4*c^11*d^5 - 20*a^7*b^3*c^2*d^14 + 164*a^7*b
^3*c^4*d^12 - 708*a^7*b^3*c^6*d^10 + 1004*a^7*b^3*c^8*d^8 - 440*a^7*b^3*c^10*d^6 + 4*a^8*b^2*c^3*d^13 + 204*a^
8*b^2*c^5*d^11 - 436*a^8*b^2*c^7*d^9 + 224*a^8*b^2*c^9*d^7))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4
*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*
c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*
a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c
^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^
9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*
d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (d*((8*(4*a^2*b^9*c^19 + 4*a^11*c^2*d^17 - 16*a
^11*c^4*d^15 + 24*a^11*c^6*d^13 - 16*a^11*c^8*d^11 + 4*a^11*c^10*d^9 - 4*a*b^10*c^10*d^9 + 16*a*b^10*c^12*d^7
- 24*a*b^10*c^14*d^5 + 16*a*b^10*c^16*d^3 - 28*a^3*b^8*c^18*d - 12*a^10*b*c^3*d^16 + 88*a^10*b*c^5*d^14 - 152*
a^10*b*c^7*d^12 + 108*a^10*b*c^9*d^10 - 28*a^10*b*c^11*d^8 + 28*a^2*b^9*c^9*d^10 - 108*a^2*b^9*c^11*d^8 + 152*
a^2*b^9*c^13*d^6 - 88*a^2*b^9*c^15*d^4 + 12*a^2*b^9*c^17*d^2 - 80*a^3*b^8*c^8*d^11 + 292*a^3*b^8*c^10*d^9 - 36
8*a^3*b^8*c^12*d^7 + 152*a^3*b^8*c^14*d^5 + 32*a^3*b^8*c^16*d^3 + 112*a^4*b^7*c^7*d^12 - 368*a^4*b^7*c^9*d^10
+ 352*a^4*b^7*c^11*d^8 + 32*a^4*b^7*c^13*d^6 - 208*a^4*b^7*c^15*d^4 + 80*a^4*b^7*c^17*d^2 - 56*a^5*b^6*c^6*d^1
3 + 112*a^5*b^6*c^8*d^11 + 112*a^5*b^6*c^10*d^9 - 448*a^5*b^6*c^12*d^7 + 392*a^5*b^6*c^14*d^5 - 112*a^5*b^6*c^
16*d^3 - 56*a^6*b^5*c^5*d^14 + 280*a^6*b^5*c^7*d^12 - 560*a^6*b^5*c^9*d^10 + 560*a^6*b^5*c^11*d^8 - 280*a^6*b^
5*c^13*d^6 + 56*a^6*b^5*c^15*d^4 + 112*a^7*b^4*c^4*d^15 - 392*a^7*b^4*c^6*d^13 + 448*a^7*b^4*c^8*d^11 - 112*a^
7*b^4*c^10*d^9 - 112*a^7*b^4*c^12*d^7 + 56*a^7*b^4*c^14*d^5 - 80*a^8*b^3*c^3*d^16 + 208*a^8*b^3*c^5*d^14 - 32*
a^8*b^3*c^7*d^12 - 352*a^8*b^3*c^9*d^10 + 368*a^8*b^3*c^11*d^8 - 112*a^8*b^3*c^13*d^6 + 28*a^9*b^2*c^2*d^17 -
32*a^9*b^2*c^4*d^15 - 152*a^9*b^2*c^6*d^13 + 368*a^9*b^2*c^8*d^11 - 292*a^9*b^2*c^10*d^9 + 80*a^9*b^2*c^12*d^7
- 4*a*b^10*c^18*d - 4*a^10*b*c*d^18))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8
+ a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7
*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*
b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c
^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^1
1*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*
d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(8*a^3*b^8*c^19 - 12*a^11*c*d^18 - 12*a*b^10*c^
19 + 56*a^11*c^3*d^16 - 104*a^11*c^5*d^14 + 96*a^11*c^7*d^12 - 44*a^11*c^9*d^10 + 8*a^11*c^11*d^8 + 16*a*b^10*
c^9*d^10 - 76*a*b^10*c^11*d^8 + 144*a*b^10*c^13*d^6 - 136*a*b^10*c^15*d^4 + 64*a*b^10*c^17*d^2 + 96*a^2*b^9*c^
18*d - 64*a^4*b^7*c^18*d + 16*a^9*b^2*c*d^18 + 96*a^10*b*c^2*d^17 - 448*a^10*b*c^4*d^15 + 832*a^10*b*c^6*d^13
- 768*a^10*b*c^8*d^11 + 352*a^10*b*c^10*d^9 - 64*a^10*b*c^12*d^7 - 128*a^2*b^9*c^8*d^11 + 608*a^2*b^9*c^10*d^9
- 1152*a^2*b^9*c^12*d^7 + 1088*a^2*b^9*c^14*d^5 - 512*a^2*b^9*c^16*d^3 + 448*a^3*b^8*c^7*d^12 - 2140*a^3*b^8*
c^9*d^10 + 4088*a^3*b^8*c^11*d^8 - 3912*a^3*b^8*c^13*d^6 + 1888*a^3*b^8*c^15*d^4 - 380*a^3*b^8*c^17*d^2 - 896*
a^4*b^7*c^6*d^13 + 4352*a^4*b^7*c^8*d^11 - 8512*a^4*b^7*c^10*d^9 + 8448*a^4*b^7*c^12*d^7 - 4352*a^4*b^7*c^14*d
^5 + 1024*a^4*b^7*c^16*d^3 + 1120*a^5*b^6*c^5*d^14 - 5656*a^5*b^6*c^7*d^12 + 11648*a^5*b^6*c^9*d^10 - 12432*a^
5*b^6*c^11*d^8 + 7168*a^5*b^6*c^13*d^6 - 2072*a^5*b^6*c^15*d^4 + 224*a^5*b^6*c^17*d^2 - 896*a^6*b^5*c^4*d^15 +
4928*a^6*b^5*c^6*d^13 - 11200*a^6*b^5*c^8*d^11 + 13440*a^6*b^5*c^10*d^9 - 8960*a^6*b^5*c^12*d^7 + 3136*a^6*b^
5*c^14*d^5 - 448*a^6*b^5*c^16*d^3 + 448*a^7*b^4*c^3*d^16 - 2968*a^7*b^4*c^5*d^14 + 7952*a^7*b^4*c^7*d^12 - 110
88*a^7*b^4*c^9*d^10 + 8512*a^7*b^4*c^11*d^8 - 3416*a^7*b^4*c^13*d^6 + 560*a^7*b^4*c^15*d^4 - 128*a^8*b^3*c^2*d
^17 + 1280*a^8*b^3*c^4*d^15 - 4288*a^8*b^3*c^6*d^13 + 6912*a^8*b^3*c^8*d^11 - 5888*a^8*b^3*c^10*d^9 + 2560*a^8
*b^3*c^12*d^7 - 448*a^8*b^3*c^14*d^5 - 412*a^9*b^2*c^3*d^16 + 1712*a^9*b^2*c^5*d^14 - 3048*a^9*b^2*c^7*d^12 +
2752*a^9*b^2*c^9*d^10 - 1244*a^9*b^2*c^11*d^8 + 224*a^9*b^2*c^13*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 +
6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2
- 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5
*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60
*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*
a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^
4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13))*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4
+ 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^
11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^
7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^
8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2
*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)))*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*
d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5
- a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^
2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a
^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)))*(a^
2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d)*1i)/(2*(a^3*d^13 + b^3*c^13 - 5*a
^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 -
10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30
*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^
4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)) - (d*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*a*b^8*c^4*d^
9 - 16*a*b^8*c^6*d^7 + 24*a*b^8*c^8*d^5 - 16*a*b^8*c^10*d^3 + 4*a^4*b^5*c*d^12 + 4*a^6*b^3*c*d^12 + 4*a^8*b*c^
3*d^10 + 4*a^8*b*c^5*d^8 - 4*a^2*b^7*c^3*d^10 + 12*a^2*b^7*c^5*d^8 + a^2*b^7*c^7*d^6 - 28*a^2*b^7*c^9*d^4 + 28
*a^2*b^7*c^11*d^2 - 4*a^3*b^6*c^2*d^11 + 24*a^3*b^6*c^4*d^9 - 98*a^3*b^6*c^6*d^7 + 164*a^3*b^6*c^8*d^5 - 140*a
^3*b^6*c^10*d^3 - 16*a^4*b^5*c^3*d^10 + 95*a^4*b^5*c^5*d^8 - 188*a^4*b^5*c^7*d^6 + 240*a^4*b^5*c^9*d^4 - 8*a^5
*b^4*c^2*d^11 - 20*a^5*b^4*c^4*d^9 + 64*a^5*b^4*c^6*d^7 - 216*a^5*b^4*c^8*d^5 - a^6*b^3*c^3*d^10 + 20*a^6*b^3*
c^5*d^8 + 112*a^6*b^3*c^7*d^6 - 2*a^7*b^2*c^2*d^11 - 20*a^7*b^2*c^4*d^9 - 32*a^7*b^2*c^6*d^7 + 4*a*b^8*c^12*d
+ a^8*b*c*d^12))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^
6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^
5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4
*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c
^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2
*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d -
6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(4*a*b^8*c^13 + a^9*c*d^12 + 4*a^9*c^3*d^10 + 4*a^9*c^5*d^8 - 16*a*b^
8*c^3*d^10 + 76*a*b^8*c^5*d^8 - 162*a*b^8*c^7*d^6 + 176*a*b^8*c^9*d^4 - 96*a*b^8*c^11*d^2 - 8*a^2*b^7*c^12*d -
16*a^3*b^6*c*d^12 - 4*a^5*b^4*c*d^12 + 2*a^7*b^2*c*d^12 - 2*a^8*b*c^2*d^11 - 20*a^8*b*c^4*d^9 - 32*a^8*b*c^6*
d^7 + 32*a^2*b^7*c^2*d^11 - 152*a^2*b^7*c^4*d^9 + 372*a^2*b^7*c^6*d^7 - 472*a^2*b^7*c^8*d^5 + 336*a^2*b^7*c^10
*d^3 + 72*a^3*b^6*c^3*d^10 - 274*a^3*b^6*c^5*d^8 + 481*a^3*b^6*c^7*d^6 - 564*a^3*b^6*c^9*d^4 + 40*a^3*b^6*c^11
*d^2 + 8*a^4*b^5*c^2*d^11 + 80*a^4*b^5*c^4*d^9 - 250*a^4*b^5*c^6*d^7 + 612*a^4*b^5*c^8*d^5 - 144*a^4*b^5*c^10*
d^3 - 14*a^5*b^4*c^3*d^10 + 55*a^5*b^4*c^5*d^8 - 412*a^5*b^4*c^7*d^6 + 240*a^5*b^4*c^9*d^4 - 4*a^6*b^3*c^2*d^1
1 + 20*a^6*b^3*c^4*d^9 + 128*a^6*b^3*c^6*d^7 - 216*a^6*b^3*c^8*d^5 - 9*a^7*b^2*c^3*d^10 + 12*a^7*b^2*c^5*d^8 +
112*a^7*b^2*c^7*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 +
b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*
c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a
^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3
*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b
^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^
13*d - 6*a^5*b*c*d^13) + (d*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*a^2*b^8*c^16 + 2*a^10*c^2*d^14 - 6*a^10*c^6*d^
10 + 4*a^10*c^8*d^8 + 4*a*b^9*c^7*d^9 - 18*a*b^9*c^9*d^7 + 36*a*b^9*c^11*d^5 - 34*a*b^9*c^13*d^3 - 32*a^3*b^7*
c^15*d + 4*a^7*b^3*c*d^15 - 10*a^9*b*c^3*d^13 - 12*a^9*b*c^5*d^11 + 54*a^9*b*c^7*d^9 - 32*a^9*b*c^9*d^7 - 24*a
^2*b^8*c^6*d^10 + 110*a^2*b^8*c^8*d^8 - 232*a^2*b^8*c^10*d^6 + 234*a^2*b^8*c^12*d^4 - 92*a^2*b^8*c^14*d^2 + 60
*a^3*b^7*c^5*d^11 - 282*a^3*b^7*c^7*d^9 + 638*a^3*b^7*c^9*d^7 - 702*a^3*b^7*c^11*d^5 + 318*a^3*b^7*c^13*d^3 -
80*a^4*b^6*c^4*d^12 + 390*a^4*b^6*c^6*d^10 - 970*a^4*b^6*c^8*d^8 + 1202*a^4*b^6*c^10*d^6 - 654*a^4*b^6*c^12*d^
4 + 112*a^4*b^6*c^14*d^2 + 60*a^5*b^5*c^3*d^13 - 310*a^5*b^5*c^5*d^11 + 878*a^5*b^5*c^7*d^9 - 1290*a^5*b^5*c^9
*d^7 + 886*a^5*b^5*c^11*d^5 - 224*a^5*b^5*c^13*d^3 - 24*a^6*b^4*c^2*d^14 + 138*a^6*b^4*c^4*d^12 - 466*a^6*b^4*
c^6*d^10 + 894*a^6*b^4*c^8*d^8 - 822*a^6*b^4*c^10*d^6 + 280*a^6*b^4*c^12*d^4 - 30*a^7*b^3*c^3*d^13 + 122*a^7*b
^3*c^5*d^11 - 394*a^7*b^3*c^7*d^9 + 522*a^7*b^3*c^9*d^7 - 224*a^7*b^3*c^11*d^5 + 2*a^8*b^2*c^2*d^14 + 2*a^8*b^
2*c^4*d^12 + 102*a^8*b^2*c^6*d^10 - 218*a^8*b^2*c^8*d^8 + 112*a^8*b^2*c^10*d^6 + 12*a*b^9*c^15*d))/(a^6*d^14 +
b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^
6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a
^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d
^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9
- 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10
+ 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (8*tan(e/
2 + (f*x)/2)*(8*a*b^9*c^16 + 4*a^10*c*d^15 - 12*a^10*c^5*d^11 + 8*a^10*c^7*d^9 + 4*a*b^9*c^8*d^8 - 8*a*b^9*c^1
0*d^6 + 12*a*b^9*c^12*d^4 - 16*a*b^9*c^14*d^2 - 40*a^2*b^8*c^15*d + 4*a^8*b^2*c*d^15 - 20*a^9*b*c^2*d^14 - 24*
a^9*b*c^4*d^12 + 108*a^9*b*c^6*d^10 - 64*a^9*b*c^8*d^8 - 20*a^2*b^8*c^7*d^9 + 16*a^2*b^8*c^9*d^7 - 12*a^2*b^8*
c^11*d^5 + 56*a^2*b^8*c^13*d^3 + 36*a^3*b^7*c^6*d^10 + 76*a^3*b^7*c^8*d^8 - 204*a^3*b^7*c^10*d^6 + 36*a^3*b^7*
c^12*d^4 + 56*a^3*b^7*c^14*d^2 - 20*a^4*b^6*c^5*d^11 - 340*a^4*b^6*c^7*d^9 + 804*a^4*b^6*c^9*d^7 - 508*a^4*b^6
*c^11*d^5 + 64*a^4*b^6*c^13*d^3 - 20*a^5*b^5*c^4*d^12 + 556*a^5*b^5*c^6*d^10 - 1380*a^5*b^5*c^8*d^8 + 1172*a^5
*b^5*c^10*d^6 - 328*a^5*b^5*c^12*d^4 + 36*a^6*b^4*c^3*d^13 - 452*a^6*b^4*c^5*d^11 + 1308*a^6*b^4*c^7*d^9 - 140
4*a^6*b^4*c^9*d^7 + 512*a^6*b^4*c^11*d^5 - 20*a^7*b^3*c^2*d^14 + 164*a^7*b^3*c^4*d^12 - 708*a^7*b^3*c^6*d^10 +
1004*a^7*b^3*c^8*d^8 - 440*a^7*b^3*c^10*d^6 + 4*a^8*b^2*c^3*d^13 + 204*a^8*b^2*c^5*d^11 - 436*a^8*b^2*c^7*d^9
+ 224*a^8*b^2*c^9*d^7))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6
+ b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^
5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15
*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a
^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4
*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*
c^13*d - 6*a^5*b*c*d^13) + (d*((8*(4*a^2*b^9*c^19 + 4*a^11*c^2*d^17 - 16*a^11*c^4*d^15 + 24*a^11*c^6*d^13 - 16
*a^11*c^8*d^11 + 4*a^11*c^10*d^9 - 4*a*b^10*c^10*d^9 + 16*a*b^10*c^12*d^7 - 24*a*b^10*c^14*d^5 + 16*a*b^10*c^1
6*d^3 - 28*a^3*b^8*c^18*d - 12*a^10*b*c^3*d^16 + 88*a^10*b*c^5*d^14 - 152*a^10*b*c^7*d^12 + 108*a^10*b*c^9*d^1
0 - 28*a^10*b*c^11*d^8 + 28*a^2*b^9*c^9*d^10 - 108*a^2*b^9*c^11*d^8 + 152*a^2*b^9*c^13*d^6 - 88*a^2*b^9*c^15*d
^4 + 12*a^2*b^9*c^17*d^2 - 80*a^3*b^8*c^8*d^11 + 292*a^3*b^8*c^10*d^9 - 368*a^3*b^8*c^12*d^7 + 152*a^3*b^8*c^1
4*d^5 + 32*a^3*b^8*c^16*d^3 + 112*a^4*b^7*c^7*d^12 - 368*a^4*b^7*c^9*d^10 + 352*a^4*b^7*c^11*d^8 + 32*a^4*b^7*
c^13*d^6 - 208*a^4*b^7*c^15*d^4 + 80*a^4*b^7*c^17*d^2 - 56*a^5*b^6*c^6*d^13 + 112*a^5*b^6*c^8*d^11 + 112*a^5*b
^6*c^10*d^9 - 448*a^5*b^6*c^12*d^7 + 392*a^5*b^6*c^14*d^5 - 112*a^5*b^6*c^16*d^3 - 56*a^6*b^5*c^5*d^14 + 280*a
^6*b^5*c^7*d^12 - 560*a^6*b^5*c^9*d^10 + 560*a^6*b^5*c^11*d^8 - 280*a^6*b^5*c^13*d^6 + 56*a^6*b^5*c^15*d^4 + 1
12*a^7*b^4*c^4*d^15 - 392*a^7*b^4*c^6*d^13 + 448*a^7*b^4*c^8*d^11 - 112*a^7*b^4*c^10*d^9 - 112*a^7*b^4*c^12*d^
7 + 56*a^7*b^4*c^14*d^5 - 80*a^8*b^3*c^3*d^16 + 208*a^8*b^3*c^5*d^14 - 32*a^8*b^3*c^7*d^12 - 352*a^8*b^3*c^9*d
^10 + 368*a^8*b^3*c^11*d^8 - 112*a^8*b^3*c^13*d^6 + 28*a^9*b^2*c^2*d^17 - 32*a^9*b^2*c^4*d^15 - 152*a^9*b^2*c^
6*d^13 + 368*a^9*b^2*c^8*d^11 - 292*a^9*b^2*c^10*d^9 + 80*a^9*b^2*c^12*d^7 - 4*a*b^10*c^18*d - 4*a^10*b*c*d^18
))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*
c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c
^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60
*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a
^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4
*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^1
3) - (8*tan(e/2 + (f*x)/2)*(8*a^3*b^8*c^19 - 12*a^11*c*d^18 - 12*a*b^10*c^19 + 56*a^11*c^3*d^16 - 104*a^11*c^5
*d^14 + 96*a^11*c^7*d^12 - 44*a^11*c^9*d^10 + 8*a^11*c^11*d^8 + 16*a*b^10*c^9*d^10 - 76*a*b^10*c^11*d^8 + 144*
a*b^10*c^13*d^6 - 136*a*b^10*c^15*d^4 + 64*a*b^10*c^17*d^2 + 96*a^2*b^9*c^18*d - 64*a^4*b^7*c^18*d + 16*a^9*b^
2*c*d^18 + 96*a^10*b*c^2*d^17 - 448*a^10*b*c^4*d^15 + 832*a^10*b*c^6*d^13 - 768*a^10*b*c^8*d^11 + 352*a^10*b*c
^10*d^9 - 64*a^10*b*c^12*d^7 - 128*a^2*b^9*c^8*d^11 + 608*a^2*b^9*c^10*d^9 - 1152*a^2*b^9*c^12*d^7 + 1088*a^2*
b^9*c^14*d^5 - 512*a^2*b^9*c^16*d^3 + 448*a^3*b^8*c^7*d^12 - 2140*a^3*b^8*c^9*d^10 + 4088*a^3*b^8*c^11*d^8 - 3
912*a^3*b^8*c^13*d^6 + 1888*a^3*b^8*c^15*d^4 - 380*a^3*b^8*c^17*d^2 - 896*a^4*b^7*c^6*d^13 + 4352*a^4*b^7*c^8*
d^11 - 8512*a^4*b^7*c^10*d^9 + 8448*a^4*b^7*c^12*d^7 - 4352*a^4*b^7*c^14*d^5 + 1024*a^4*b^7*c^16*d^3 + 1120*a^
5*b^6*c^5*d^14 - 5656*a^5*b^6*c^7*d^12 + 11648*a^5*b^6*c^9*d^10 - 12432*a^5*b^6*c^11*d^8 + 7168*a^5*b^6*c^13*d
^6 - 2072*a^5*b^6*c^15*d^4 + 224*a^5*b^6*c^17*d^2 - 896*a^6*b^5*c^4*d^15 + 4928*a^6*b^5*c^6*d^13 - 11200*a^6*b
^5*c^8*d^11 + 13440*a^6*b^5*c^10*d^9 - 8960*a^6*b^5*c^12*d^7 + 3136*a^6*b^5*c^14*d^5 - 448*a^6*b^5*c^16*d^3 +
448*a^7*b^4*c^3*d^16 - 2968*a^7*b^4*c^5*d^14 + 7952*a^7*b^4*c^7*d^12 - 11088*a^7*b^4*c^9*d^10 + 8512*a^7*b^4*c
^11*d^8 - 3416*a^7*b^4*c^13*d^6 + 560*a^7*b^4*c^15*d^4 - 128*a^8*b^3*c^2*d^17 + 1280*a^8*b^3*c^4*d^15 - 4288*a
^8*b^3*c^6*d^13 + 6912*a^8*b^3*c^8*d^11 - 5888*a^8*b^3*c^10*d^9 + 2560*a^8*b^3*c^12*d^7 - 448*a^8*b^3*c^14*d^5
- 412*a^9*b^2*c^3*d^16 + 1712*a^9*b^2*c^5*d^14 - 3048*a^9*b^2*c^7*d^12 + 2752*a^9*b^2*c^9*d^10 - 1244*a^9*b^2
*c^11*d^8 + 224*a^9*b^2*c^13*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^
6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7
- 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^
9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*
d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^
3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4
- 6*a*b^5*c^13*d - 6*a^5*b*c*d^13))*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*
d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7
+ 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*
d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b
*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2
*b*c*d^12)))*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b
^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b
^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2
*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15
*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)))*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^
2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d)*1i)/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^
3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*
b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 +
15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*
d - 3*a^2*b*c*d^12)))/((16*(36*a*b^7*c^5*d^5 - 18*a*b^7*c^3*d^7 - 34*a*b^7*c^7*d^3 + 4*a^3*b^5*c*d^9 + a^5*b^3
*c*d^9 + 2*a^2*b^6*c^2*d^8 - 25*a^2*b^6*c^4*d^6 + 50*a^2*b^6*c^6*d^4 - 36*a^2*b^6*c^8*d^2 - a^3*b^5*c^3*d^7 -
16*a^3*b^5*c^5*d^5 + 40*a^3*b^5*c^7*d^3 + a^4*b^4*c^2*d^8 - 8*a^4*b^4*c^4*d^6 - 20*a^4*b^4*c^6*d^4 + 4*a^5*b^3
*c^3*d^7 + 4*a^5*b^3*c^5*d^5 + 4*a*b^7*c*d^9 + 12*a*b^7*c^9*d))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*
c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b
^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 +
24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^
4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3
*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c
^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (16*tan(e/2 + (f*x)/2)*(4*a*b^7*c^2*d^8 - 26
*a*b^7*c^4*d^6 + 52*a*b^7*c^6*d^4 - 48*a*b^7*c^8*d^2 + 4*a^2*b^6*c*d^9 + 2*a^4*b^4*c*d^9 - 2*a^2*b^6*c^3*d^7 -
20*a^2*b^6*c^5*d^5 + 72*a^2*b^6*c^7*d^3 + 2*a^3*b^5*c^2*d^8 - 16*a^3*b^5*c^4*d^6 - 40*a^3*b^5*c^6*d^4 + 8*a^4
*b^4*c^3*d^7 + 8*a^4*b^4*c^5*d^5))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^
6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7
- 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^
9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*
d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^
3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4
- 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (d*(-(c + d)^5*(c - d)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a*b^8*c^13 + a^
9*c*d^12 + 4*a^9*c^3*d^10 + 4*a^9*c^5*d^8 - 16*a*b^8*c^3*d^10 + 76*a*b^8*c^5*d^8 - 162*a*b^8*c^7*d^6 + 176*a*b
^8*c^9*d^4 - 96*a*b^8*c^11*d^2 - 8*a^2*b^7*c^12*d - 16*a^3*b^6*c*d^12 - 4*a^5*b^4*c*d^12 + 2*a^7*b^2*c*d^12 -
2*a^8*b*c^2*d^11 - 20*a^8*b*c^4*d^9 - 32*a^8*b*c^6*d^7 + 32*a^2*b^7*c^2*d^11 - 152*a^2*b^7*c^4*d^9 + 372*a^2*b
^7*c^6*d^7 - 472*a^2*b^7*c^8*d^5 + 336*a^2*b^7*c^10*d^3 + 72*a^3*b^6*c^3*d^10 - 274*a^3*b^6*c^5*d^8 + 481*a^3*
b^6*c^7*d^6 - 564*a^3*b^6*c^9*d^4 + 40*a^3*b^6*c^11*d^2 + 8*a^4*b^5*c^2*d^11 + 80*a^4*b^5*c^4*d^9 - 250*a^4*b^
5*c^6*d^7 + 612*a^4*b^5*c^8*d^5 - 144*a^4*b^5*c^10*d^3 - 14*a^5*b^4*c^3*d^10 + 55*a^5*b^4*c^5*d^8 - 412*a^5*b^
4*c^7*d^6 + 240*a^5*b^4*c^9*d^4 - 4*a^6*b^3*c^2*d^11 + 20*a^6*b^3*c^4*d^9 + 128*a^6*b^3*c^6*d^7 - 216*a^6*b^3*
c^8*d^5 - 9*a^7*b^2*c^3*d^10 + 12*a^7*b^2*c^5*d^8 + 112*a^7*b^2*c^7*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^1
2 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d
^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*
c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 -
60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 +
80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60
*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*(4*a*b^8*c^4*d^9 - 16*a*b^8*c^6
*d^7 + 24*a*b^8*c^8*d^5 - 16*a*b^8*c^10*d^3 + 4*a^4*b^5*c*d^12 + 4*a^6*b^3*c*d^12 + 4*a^8*b*c^3*d^10 + 4*a^8*b
*c^5*d^8 - 4*a^2*b^7*c^3*d^10 + 12*a^2*b^7*c^5*d^8 + a^2*b^7*c^7*d^6 - 28*a^2*b^7*c^9*d^4 + 28*a^2*b^7*c^11*d^
2 - 4*a^3*b^6*c^2*d^11 + 24*a^3*b^6*c^4*d^9 - 98*a^3*b^6*c^6*d^7 + 164*a^3*b^6*c^8*d^5 - 140*a^3*b^6*c^10*d^3
- 16*a^4*b^5*c^3*d^10 + 95*a^4*b^5*c^5*d^8 - 188*a^4*b^5*c^7*d^6 + 240*a^4*b^5*c^9*d^4 - 8*a^5*b^4*c^2*d^11 -
20*a^5*b^4*c^4*d^9 + 64*a^5*b^4*c^6*d^7 - 216*a^5*b^4*c^8*d^5 - a^6*b^3*c^3*d^10 + 20*a^6*b^3*c^5*d^8 + 112*a^
6*b^3*c^7*d^6 - 2*a^7*b^2*c^2*d^11 - 20*a^7*b^2*c^4*d^9 - 32*a^7*b^2*c^6*d^7 + 4*a*b^8*c^12*d + a^8*b*c*d^12))
/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^
8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^1
1*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a
^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3
*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b
^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13)
+ (d*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*a^2*b^8*c^16 + 2*a^10*c^2*d^14 - 6*a^10*c^6*d^10 + 4*a^10*c^8*d^8 +
4*a*b^9*c^7*d^9 - 18*a*b^9*c^9*d^7 + 36*a*b^9*c^11*d^5 - 34*a*b^9*c^13*d^3 - 32*a^3*b^7*c^15*d + 4*a^7*b^3*c*d
^15 - 10*a^9*b*c^3*d^13 - 12*a^9*b*c^5*d^11 + 54*a^9*b*c^7*d^9 - 32*a^9*b*c^9*d^7 - 24*a^2*b^8*c^6*d^10 + 110*
a^2*b^8*c^8*d^8 - 232*a^2*b^8*c^10*d^6 + 234*a^2*b^8*c^12*d^4 - 92*a^2*b^8*c^14*d^2 + 60*a^3*b^7*c^5*d^11 - 28
2*a^3*b^7*c^7*d^9 + 638*a^3*b^7*c^9*d^7 - 702*a^3*b^7*c^11*d^5 + 318*a^3*b^7*c^13*d^3 - 80*a^4*b^6*c^4*d^12 +
390*a^4*b^6*c^6*d^10 - 970*a^4*b^6*c^8*d^8 + 1202*a^4*b^6*c^10*d^6 - 654*a^4*b^6*c^12*d^4 + 112*a^4*b^6*c^14*d
^2 + 60*a^5*b^5*c^3*d^13 - 310*a^5*b^5*c^5*d^11 + 878*a^5*b^5*c^7*d^9 - 1290*a^5*b^5*c^9*d^7 + 886*a^5*b^5*c^1
1*d^5 - 224*a^5*b^5*c^13*d^3 - 24*a^6*b^4*c^2*d^14 + 138*a^6*b^4*c^4*d^12 - 466*a^6*b^4*c^6*d^10 + 894*a^6*b^4
*c^8*d^8 - 822*a^6*b^4*c^10*d^6 + 280*a^6*b^4*c^12*d^4 - 30*a^7*b^3*c^3*d^13 + 122*a^7*b^3*c^5*d^11 - 394*a^7*
b^3*c^7*d^9 + 522*a^7*b^3*c^9*d^7 - 224*a^7*b^3*c^11*d^5 + 2*a^8*b^2*c^2*d^14 + 2*a^8*b^2*c^4*d^12 + 102*a^8*b
^2*c^6*d^10 - 218*a^8*b^2*c^8*d^8 + 112*a^8*b^2*c^10*d^6 + 12*a*b^9*c^15*d))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*
d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^1
2*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5
*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^
6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7
+ 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 -
60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (8*tan(e/2 + (f*x)/2)*(8*a*b^9*
c^16 + 4*a^10*c*d^15 - 12*a^10*c^5*d^11 + 8*a^10*c^7*d^9 + 4*a*b^9*c^8*d^8 - 8*a*b^9*c^10*d^6 + 12*a*b^9*c^12*
d^4 - 16*a*b^9*c^14*d^2 - 40*a^2*b^8*c^15*d + 4*a^8*b^2*c*d^15 - 20*a^9*b*c^2*d^14 - 24*a^9*b*c^4*d^12 + 108*a
^9*b*c^6*d^10 - 64*a^9*b*c^8*d^8 - 20*a^2*b^8*c^7*d^9 + 16*a^2*b^8*c^9*d^7 - 12*a^2*b^8*c^11*d^5 + 56*a^2*b^8*
c^13*d^3 + 36*a^3*b^7*c^6*d^10 + 76*a^3*b^7*c^8*d^8 - 204*a^3*b^7*c^10*d^6 + 36*a^3*b^7*c^12*d^4 + 56*a^3*b^7*
c^14*d^2 - 20*a^4*b^6*c^5*d^11 - 340*a^4*b^6*c^7*d^9 + 804*a^4*b^6*c^9*d^7 - 508*a^4*b^6*c^11*d^5 + 64*a^4*b^6
*c^13*d^3 - 20*a^5*b^5*c^4*d^12 + 556*a^5*b^5*c^6*d^10 - 1380*a^5*b^5*c^8*d^8 + 1172*a^5*b^5*c^10*d^6 - 328*a^
5*b^5*c^12*d^4 + 36*a^6*b^4*c^3*d^13 - 452*a^6*b^4*c^5*d^11 + 1308*a^6*b^4*c^7*d^9 - 1404*a^6*b^4*c^9*d^7 + 51
2*a^6*b^4*c^11*d^5 - 20*a^7*b^3*c^2*d^14 + 164*a^7*b^3*c^4*d^12 - 708*a^7*b^3*c^6*d^10 + 1004*a^7*b^3*c^8*d^8
- 440*a^7*b^3*c^10*d^6 + 4*a^8*b^2*c^3*d^13 + 204*a^8*b^2*c^5*d^11 - 436*a^8*b^2*c^7*d^9 + 224*a^8*b^2*c^9*d^7
))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*
c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c
^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60
*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a
^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4
*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^1
3) - (d*((8*(4*a^2*b^9*c^19 + 4*a^11*c^2*d^17 - 16*a^11*c^4*d^15 + 24*a^11*c^6*d^13 - 16*a^11*c^8*d^11 + 4*a^1
1*c^10*d^9 - 4*a*b^10*c^10*d^9 + 16*a*b^10*c^12*d^7 - 24*a*b^10*c^14*d^5 + 16*a*b^10*c^16*d^3 - 28*a^3*b^8*c^1
8*d - 12*a^10*b*c^3*d^16 + 88*a^10*b*c^5*d^14 - 152*a^10*b*c^7*d^12 + 108*a^10*b*c^9*d^10 - 28*a^10*b*c^11*d^8
+ 28*a^2*b^9*c^9*d^10 - 108*a^2*b^9*c^11*d^8 + 152*a^2*b^9*c^13*d^6 - 88*a^2*b^9*c^15*d^4 + 12*a^2*b^9*c^17*d
^2 - 80*a^3*b^8*c^8*d^11 + 292*a^3*b^8*c^10*d^9 - 368*a^3*b^8*c^12*d^7 + 152*a^3*b^8*c^14*d^5 + 32*a^3*b^8*c^1
6*d^3 + 112*a^4*b^7*c^7*d^12 - 368*a^4*b^7*c^9*d^10 + 352*a^4*b^7*c^11*d^8 + 32*a^4*b^7*c^13*d^6 - 208*a^4*b^7
*c^15*d^4 + 80*a^4*b^7*c^17*d^2 - 56*a^5*b^6*c^6*d^13 + 112*a^5*b^6*c^8*d^11 + 112*a^5*b^6*c^10*d^9 - 448*a^5*
b^6*c^12*d^7 + 392*a^5*b^6*c^14*d^5 - 112*a^5*b^6*c^16*d^3 - 56*a^6*b^5*c^5*d^14 + 280*a^6*b^5*c^7*d^12 - 560*
a^6*b^5*c^9*d^10 + 560*a^6*b^5*c^11*d^8 - 280*a^6*b^5*c^13*d^6 + 56*a^6*b^5*c^15*d^4 + 112*a^7*b^4*c^4*d^15 -
392*a^7*b^4*c^6*d^13 + 448*a^7*b^4*c^8*d^11 - 112*a^7*b^4*c^10*d^9 - 112*a^7*b^4*c^12*d^7 + 56*a^7*b^4*c^14*d^
5 - 80*a^8*b^3*c^3*d^16 + 208*a^8*b^3*c^5*d^14 - 32*a^8*b^3*c^7*d^12 - 352*a^8*b^3*c^9*d^10 + 368*a^8*b^3*c^11
*d^8 - 112*a^8*b^3*c^13*d^6 + 28*a^9*b^2*c^2*d^17 - 32*a^9*b^2*c^4*d^15 - 152*a^9*b^2*c^6*d^13 + 368*a^9*b^2*c
^8*d^11 - 292*a^9*b^2*c^10*d^9 + 80*a^9*b^2*c^12*d^7 - 4*a*b^10*c^18*d - 4*a^10*b*c*d^18))/(a^6*d^14 + b^6*c^1
4 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d
^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3
*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*
a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a
^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4
*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x
)/2)*(8*a^3*b^8*c^19 - 12*a^11*c*d^18 - 12*a*b^10*c^19 + 56*a^11*c^3*d^16 - 104*a^11*c^5*d^14 + 96*a^11*c^7*d^
12 - 44*a^11*c^9*d^10 + 8*a^11*c^11*d^8 + 16*a*b^10*c^9*d^10 - 76*a*b^10*c^11*d^8 + 144*a*b^10*c^13*d^6 - 136*
a*b^10*c^15*d^4 + 64*a*b^10*c^17*d^2 + 96*a^2*b^9*c^18*d - 64*a^4*b^7*c^18*d + 16*a^9*b^2*c*d^18 + 96*a^10*b*c
^2*d^17 - 448*a^10*b*c^4*d^15 + 832*a^10*b*c^6*d^13 - 768*a^10*b*c^8*d^11 + 352*a^10*b*c^10*d^9 - 64*a^10*b*c^
12*d^7 - 128*a^2*b^9*c^8*d^11 + 608*a^2*b^9*c^10*d^9 - 1152*a^2*b^9*c^12*d^7 + 1088*a^2*b^9*c^14*d^5 - 512*a^2
*b^9*c^16*d^3 + 448*a^3*b^8*c^7*d^12 - 2140*a^3*b^8*c^9*d^10 + 4088*a^3*b^8*c^11*d^8 - 3912*a^3*b^8*c^13*d^6 +
1888*a^3*b^8*c^15*d^4 - 380*a^3*b^8*c^17*d^2 - 896*a^4*b^7*c^6*d^13 + 4352*a^4*b^7*c^8*d^11 - 8512*a^4*b^7*c^
10*d^9 + 8448*a^4*b^7*c^12*d^7 - 4352*a^4*b^7*c^14*d^5 + 1024*a^4*b^7*c^16*d^3 + 1120*a^5*b^6*c^5*d^14 - 5656*
a^5*b^6*c^7*d^12 + 11648*a^5*b^6*c^9*d^10 - 12432*a^5*b^6*c^11*d^8 + 7168*a^5*b^6*c^13*d^6 - 2072*a^5*b^6*c^15
*d^4 + 224*a^5*b^6*c^17*d^2 - 896*a^6*b^5*c^4*d^15 + 4928*a^6*b^5*c^6*d^13 - 11200*a^6*b^5*c^8*d^11 + 13440*a^
6*b^5*c^10*d^9 - 8960*a^6*b^5*c^12*d^7 + 3136*a^6*b^5*c^14*d^5 - 448*a^6*b^5*c^16*d^3 + 448*a^7*b^4*c^3*d^16 -
2968*a^7*b^4*c^5*d^14 + 7952*a^7*b^4*c^7*d^12 - 11088*a^7*b^4*c^9*d^10 + 8512*a^7*b^4*c^11*d^8 - 3416*a^7*b^4
*c^13*d^6 + 560*a^7*b^4*c^15*d^4 - 128*a^8*b^3*c^2*d^17 + 1280*a^8*b^3*c^4*d^15 - 4288*a^8*b^3*c^6*d^13 + 6912
*a^8*b^3*c^8*d^11 - 5888*a^8*b^3*c^10*d^9 + 2560*a^8*b^3*c^12*d^7 - 448*a^8*b^3*c^14*d^5 - 412*a^9*b^2*c^3*d^1
6 + 1712*a^9*b^2*c^5*d^14 - 3048*a^9*b^2*c^7*d^12 + 2752*a^9*b^2*c^9*d^10 - 1244*a^9*b^2*c^11*d^8 + 224*a^9*b^
2*c^13*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^
8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 +
24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4
*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d
^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^1
2 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a
^5*b*c*d^13))*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 -
6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3
*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11
- 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c
^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)))*(a^2*d^4
+ 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^
11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^
7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^
8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2
*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)))*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*
d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5
- a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^
2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a
^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)) - (d
*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*a*b^8*c^4*d^9 - 16*a*b^8*c^6*d^7 + 24*a*b^8*c^8*d^5 - 16*a*b^8*c^10*d^3 +
4*a^4*b^5*c*d^12 + 4*a^6*b^3*c*d^12 + 4*a^8*b*c^3*d^10 + 4*a^8*b*c^5*d^8 - 4*a^2*b^7*c^3*d^10 + 12*a^2*b^7*c^
5*d^8 + a^2*b^7*c^7*d^6 - 28*a^2*b^7*c^9*d^4 + 28*a^2*b^7*c^11*d^2 - 4*a^3*b^6*c^2*d^11 + 24*a^3*b^6*c^4*d^9 -
98*a^3*b^6*c^6*d^7 + 164*a^3*b^6*c^8*d^5 - 140*a^3*b^6*c^10*d^3 - 16*a^4*b^5*c^3*d^10 + 95*a^4*b^5*c^5*d^8 -
188*a^4*b^5*c^7*d^6 + 240*a^4*b^5*c^9*d^4 - 8*a^5*b^4*c^2*d^11 - 20*a^5*b^4*c^4*d^9 + 64*a^5*b^4*c^6*d^7 - 216
*a^5*b^4*c^8*d^5 - a^6*b^3*c^3*d^10 + 20*a^6*b^3*c^5*d^8 + 112*a^6*b^3*c^7*d^6 - 2*a^7*b^2*c^2*d^11 - 20*a^7*b
^2*c^4*d^9 - 32*a^7*b^2*c^6*d^7 + 4*a*b^8*c^12*d + a^8*b*c*d^12))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^
6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a
*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9
+ 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*
b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b
^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2
*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(4*a*b^8*c^13 + a^9*
c*d^12 + 4*a^9*c^3*d^10 + 4*a^9*c^5*d^8 - 16*a*b^8*c^3*d^10 + 76*a*b^8*c^5*d^8 - 162*a*b^8*c^7*d^6 + 176*a*b^8
*c^9*d^4 - 96*a*b^8*c^11*d^2 - 8*a^2*b^7*c^12*d - 16*a^3*b^6*c*d^12 - 4*a^5*b^4*c*d^12 + 2*a^7*b^2*c*d^12 - 2*
a^8*b*c^2*d^11 - 20*a^8*b*c^4*d^9 - 32*a^8*b*c^6*d^7 + 32*a^2*b^7*c^2*d^11 - 152*a^2*b^7*c^4*d^9 + 372*a^2*b^7
*c^6*d^7 - 472*a^2*b^7*c^8*d^5 + 336*a^2*b^7*c^10*d^3 + 72*a^3*b^6*c^3*d^10 - 274*a^3*b^6*c^5*d^8 + 481*a^3*b^
6*c^7*d^6 - 564*a^3*b^6*c^9*d^4 + 40*a^3*b^6*c^11*d^2 + 8*a^4*b^5*c^2*d^11 + 80*a^4*b^5*c^4*d^9 - 250*a^4*b^5*
c^6*d^7 + 612*a^4*b^5*c^8*d^5 - 144*a^4*b^5*c^10*d^3 - 14*a^5*b^4*c^3*d^10 + 55*a^5*b^4*c^5*d^8 - 412*a^5*b^4*
c^7*d^6 + 240*a^5*b^4*c^9*d^4 - 4*a^6*b^3*c^2*d^11 + 20*a^6*b^3*c^4*d^9 + 128*a^6*b^3*c^6*d^7 - 216*a^6*b^3*c^
8*d^5 - 9*a^7*b^2*c^3*d^10 + 12*a^7*b^2*c^5*d^8 + 112*a^7*b^2*c^7*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12
+ 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2
- 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^
5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 6
0*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80
*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a
^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (d*(-(c + d)^5*(c - d)^5)^(1/2)*((8*
(4*a^2*b^8*c^16 + 2*a^10*c^2*d^14 - 6*a^10*c^6*d^10 + 4*a^10*c^8*d^8 + 4*a*b^9*c^7*d^9 - 18*a*b^9*c^9*d^7 + 36
*a*b^9*c^11*d^5 - 34*a*b^9*c^13*d^3 - 32*a^3*b^7*c^15*d + 4*a^7*b^3*c*d^15 - 10*a^9*b*c^3*d^13 - 12*a^9*b*c^5*
d^11 + 54*a^9*b*c^7*d^9 - 32*a^9*b*c^9*d^7 - 24*a^2*b^8*c^6*d^10 + 110*a^2*b^8*c^8*d^8 - 232*a^2*b^8*c^10*d^6
+ 234*a^2*b^8*c^12*d^4 - 92*a^2*b^8*c^14*d^2 + 60*a^3*b^7*c^5*d^11 - 282*a^3*b^7*c^7*d^9 + 638*a^3*b^7*c^9*d^7
- 702*a^3*b^7*c^11*d^5 + 318*a^3*b^7*c^13*d^3 - 80*a^4*b^6*c^4*d^12 + 390*a^4*b^6*c^6*d^10 - 970*a^4*b^6*c^8*
d^8 + 1202*a^4*b^6*c^10*d^6 - 654*a^4*b^6*c^12*d^4 + 112*a^4*b^6*c^14*d^2 + 60*a^5*b^5*c^3*d^13 - 310*a^5*b^5*
c^5*d^11 + 878*a^5*b^5*c^7*d^9 - 1290*a^5*b^5*c^9*d^7 + 886*a^5*b^5*c^11*d^5 - 224*a^5*b^5*c^13*d^3 - 24*a^6*b
^4*c^2*d^14 + 138*a^6*b^4*c^4*d^12 - 466*a^6*b^4*c^6*d^10 + 894*a^6*b^4*c^8*d^8 - 822*a^6*b^4*c^10*d^6 + 280*a
^6*b^4*c^12*d^4 - 30*a^7*b^3*c^3*d^13 + 122*a^7*b^3*c^5*d^11 - 394*a^7*b^3*c^7*d^9 + 522*a^7*b^3*c^9*d^7 - 224
*a^7*b^3*c^11*d^5 + 2*a^8*b^2*c^2*d^14 + 2*a^8*b^2*c^4*d^12 + 102*a^8*b^2*c^6*d^10 - 218*a^8*b^2*c^8*d^8 + 112
*a^8*b^2*c^10*d^6 + 12*a*b^9*c^15*d))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 +
a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*
d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b
*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^
12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11
*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d
^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^16 + 4*a^10*c*d^15 - 12*a^10*c^5*d^11
+ 8*a^10*c^7*d^9 + 4*a*b^9*c^8*d^8 - 8*a*b^9*c^10*d^6 + 12*a*b^9*c^12*d^4 - 16*a*b^9*c^14*d^2 - 40*a^2*b^8*c^
15*d + 4*a^8*b^2*c*d^15 - 20*a^9*b*c^2*d^14 - 24*a^9*b*c^4*d^12 + 108*a^9*b*c^6*d^10 - 64*a^9*b*c^8*d^8 - 20*a
^2*b^8*c^7*d^9 + 16*a^2*b^8*c^9*d^7 - 12*a^2*b^8*c^11*d^5 + 56*a^2*b^8*c^13*d^3 + 36*a^3*b^7*c^6*d^10 + 76*a^3
*b^7*c^8*d^8 - 204*a^3*b^7*c^10*d^6 + 36*a^3*b^7*c^12*d^4 + 56*a^3*b^7*c^14*d^2 - 20*a^4*b^6*c^5*d^11 - 340*a^
4*b^6*c^7*d^9 + 804*a^4*b^6*c^9*d^7 - 508*a^4*b^6*c^11*d^5 + 64*a^4*b^6*c^13*d^3 - 20*a^5*b^5*c^4*d^12 + 556*a
^5*b^5*c^6*d^10 - 1380*a^5*b^5*c^8*d^8 + 1172*a^5*b^5*c^10*d^6 - 328*a^5*b^5*c^12*d^4 + 36*a^6*b^4*c^3*d^13 -
452*a^6*b^4*c^5*d^11 + 1308*a^6*b^4*c^7*d^9 - 1404*a^6*b^4*c^9*d^7 + 512*a^6*b^4*c^11*d^5 - 20*a^7*b^3*c^2*d^1
4 + 164*a^7*b^3*c^4*d^12 - 708*a^7*b^3*c^6*d^10 + 1004*a^7*b^3*c^8*d^8 - 440*a^7*b^3*c^10*d^6 + 4*a^8*b^2*c^3*
d^13 + 204*a^8*b^2*c^5*d^11 - 436*a^8*b^2*c^7*d^9 + 224*a^8*b^2*c^9*d^7))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^1
2 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d
^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*
c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 -
60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 +
80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60
*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (d*((8*(4*a^2*b^9*c^19 + 4*a^11*c^
2*d^17 - 16*a^11*c^4*d^15 + 24*a^11*c^6*d^13 - 16*a^11*c^8*d^11 + 4*a^11*c^10*d^9 - 4*a*b^10*c^10*d^9 + 16*a*b
^10*c^12*d^7 - 24*a*b^10*c^14*d^5 + 16*a*b^10*c^16*d^3 - 28*a^3*b^8*c^18*d - 12*a^10*b*c^3*d^16 + 88*a^10*b*c^
5*d^14 - 152*a^10*b*c^7*d^12 + 108*a^10*b*c^9*d^10 - 28*a^10*b*c^11*d^8 + 28*a^2*b^9*c^9*d^10 - 108*a^2*b^9*c^
11*d^8 + 152*a^2*b^9*c^13*d^6 - 88*a^2*b^9*c^15*d^4 + 12*a^2*b^9*c^17*d^2 - 80*a^3*b^8*c^8*d^11 + 292*a^3*b^8*
c^10*d^9 - 368*a^3*b^8*c^12*d^7 + 152*a^3*b^8*c^14*d^5 + 32*a^3*b^8*c^16*d^3 + 112*a^4*b^7*c^7*d^12 - 368*a^4*
b^7*c^9*d^10 + 352*a^4*b^7*c^11*d^8 + 32*a^4*b^7*c^13*d^6 - 208*a^4*b^7*c^15*d^4 + 80*a^4*b^7*c^17*d^2 - 56*a^
5*b^6*c^6*d^13 + 112*a^5*b^6*c^8*d^11 + 112*a^5*b^6*c^10*d^9 - 448*a^5*b^6*c^12*d^7 + 392*a^5*b^6*c^14*d^5 - 1
12*a^5*b^6*c^16*d^3 - 56*a^6*b^5*c^5*d^14 + 280*a^6*b^5*c^7*d^12 - 560*a^6*b^5*c^9*d^10 + 560*a^6*b^5*c^11*d^8
- 280*a^6*b^5*c^13*d^6 + 56*a^6*b^5*c^15*d^4 + 112*a^7*b^4*c^4*d^15 - 392*a^7*b^4*c^6*d^13 + 448*a^7*b^4*c^8*
d^11 - 112*a^7*b^4*c^10*d^9 - 112*a^7*b^4*c^12*d^7 + 56*a^7*b^4*c^14*d^5 - 80*a^8*b^3*c^3*d^16 + 208*a^8*b^3*c
^5*d^14 - 32*a^8*b^3*c^7*d^12 - 352*a^8*b^3*c^9*d^10 + 368*a^8*b^3*c^11*d^8 - 112*a^8*b^3*c^13*d^6 + 28*a^9*b^
2*c^2*d^17 - 32*a^9*b^2*c^4*d^15 - 152*a^9*b^2*c^6*d^13 + 368*a^9*b^2*c^8*d^11 - 292*a^9*b^2*c^10*d^9 + 80*a^9
*b^2*c^12*d^7 - 4*a*b^10*c^18*d - 4*a^10*b*c*d^18))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4
*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 +
24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7
*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 +
15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 2
0*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*
a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(8*a^3*b^8*c^19 - 12*a^11*c*d^18 -
12*a*b^10*c^19 + 56*a^11*c^3*d^16 - 104*a^11*c^5*d^14 + 96*a^11*c^7*d^12 - 44*a^11*c^9*d^10 + 8*a^11*c^11*d^8
+ 16*a*b^10*c^9*d^10 - 76*a*b^10*c^11*d^8 + 144*a*b^10*c^13*d^6 - 136*a*b^10*c^15*d^4 + 64*a*b^10*c^17*d^2 +
96*a^2*b^9*c^18*d - 64*a^4*b^7*c^18*d + 16*a^9*b^2*c*d^18 + 96*a^10*b*c^2*d^17 - 448*a^10*b*c^4*d^15 + 832*a^1
0*b*c^6*d^13 - 768*a^10*b*c^8*d^11 + 352*a^10*b*c^10*d^9 - 64*a^10*b*c^12*d^7 - 128*a^2*b^9*c^8*d^11 + 608*a^2
*b^9*c^10*d^9 - 1152*a^2*b^9*c^12*d^7 + 1088*a^2*b^9*c^14*d^5 - 512*a^2*b^9*c^16*d^3 + 448*a^3*b^8*c^7*d^12 -
2140*a^3*b^8*c^9*d^10 + 4088*a^3*b^8*c^11*d^8 - 3912*a^3*b^8*c^13*d^6 + 1888*a^3*b^8*c^15*d^4 - 380*a^3*b^8*c^
17*d^2 - 896*a^4*b^7*c^6*d^13 + 4352*a^4*b^7*c^8*d^11 - 8512*a^4*b^7*c^10*d^9 + 8448*a^4*b^7*c^12*d^7 - 4352*a
^4*b^7*c^14*d^5 + 1024*a^4*b^7*c^16*d^3 + 1120*a^5*b^6*c^5*d^14 - 5656*a^5*b^6*c^7*d^12 + 11648*a^5*b^6*c^9*d^
10 - 12432*a^5*b^6*c^11*d^8 + 7168*a^5*b^6*c^13*d^6 - 2072*a^5*b^6*c^15*d^4 + 224*a^5*b^6*c^17*d^2 - 896*a^6*b
^5*c^4*d^15 + 4928*a^6*b^5*c^6*d^13 - 11200*a^6*b^5*c^8*d^11 + 13440*a^6*b^5*c^10*d^9 - 8960*a^6*b^5*c^12*d^7
+ 3136*a^6*b^5*c^14*d^5 - 448*a^6*b^5*c^16*d^3 + 448*a^7*b^4*c^3*d^16 - 2968*a^7*b^4*c^5*d^14 + 7952*a^7*b^4*c
^7*d^12 - 11088*a^7*b^4*c^9*d^10 + 8512*a^7*b^4*c^11*d^8 - 3416*a^7*b^4*c^13*d^6 + 560*a^7*b^4*c^15*d^4 - 128*
a^8*b^3*c^2*d^17 + 1280*a^8*b^3*c^4*d^15 - 4288*a^8*b^3*c^6*d^13 + 6912*a^8*b^3*c^8*d^11 - 5888*a^8*b^3*c^10*d
^9 + 2560*a^8*b^3*c^12*d^7 - 448*a^8*b^3*c^14*d^5 - 412*a^9*b^2*c^3*d^16 + 1712*a^9*b^2*c^5*d^14 - 3048*a^9*b^
2*c^7*d^12 + 2752*a^9*b^2*c^9*d^10 - 1244*a^9*b^2*c^11*d^8 + 224*a^9*b^2*c^13*d^6))/(a^6*d^14 + b^6*c^14 - 4*a
^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*
b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 -
36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4
*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*
c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^
6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13))*(-(c + d)^5*(c - d)^5)^(1
/2)*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 -
5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^
8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7
- 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^
9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)))*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2
- 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 +
5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2
+ 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^
3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*
c*d^12)))*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*
c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*
c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^
6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^
2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12))))*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 6
*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d)*1i)/(f*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^
11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^
7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^
8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2
*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12))