\(\int \frac {1}{(a+i a \tan (e+f x))^3 \sqrt {c+d \tan (e+f x)}} \, dx\) [1124]
Optimal result
Integrand size = 30, antiderivative size = 298 \[
\int \frac {1}{(a+i a \tan (e+f x))^3 \sqrt {c+d \tan (e+f x)}} \, dx=-\frac {i \text {arctanh}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{8 a^3 \sqrt {c-i d} f}+\frac {\left (2 i c^3-8 c^2 d-13 i c d^2+12 d^3\right ) \text {arctanh}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{16 a^3 (c+i d)^{7/2} f}-\frac {\sqrt {c+d \tan (e+f x)}}{6 (i c-d) f (a+i a \tan (e+f x))^3}+\frac {(3 i c-8 d) \sqrt {c+d \tan (e+f x)}}{24 a (c+i d)^2 f (a+i a \tan (e+f x))^2}+\frac {\left (2 c^2+7 i c d-10 d^2\right ) \sqrt {c+d \tan (e+f x)}}{16 (i c-d)^3 f \left (a^3+i a^3 \tan (e+f x)\right )}
\]
[Out]
1/16*(2*I*c^3-8*c^2*d-13*I*c*d^2+12*d^3)*arctanh((c+d*tan(f*x+e))^(1/2)/(c+I*d)^(1/2))/a^3/(c+I*d)^(7/2)/f-1/8
*I*arctanh((c+d*tan(f*x+e))^(1/2)/(c-I*d)^(1/2))/a^3/f/(c-I*d)^(1/2)-1/6*(c+d*tan(f*x+e))^(1/2)/(I*c-d)/f/(a+I
*a*tan(f*x+e))^3+1/24*(3*I*c-8*d)*(c+d*tan(f*x+e))^(1/2)/a/(c+I*d)^2/f/(a+I*a*tan(f*x+e))^2+1/16*(2*c^2+7*I*c*
d-10*d^2)*(c+d*tan(f*x+e))^(1/2)/(I*c-d)^3/f/(a^3+I*a^3*tan(f*x+e))
Rubi [A] (verified)
Time = 1.13 (sec) , antiderivative size = 298, normalized size of antiderivative = 1.00, number of
steps used = 10, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {3640, 3677, 3620, 3618, 65,
214} \[
\int \frac {1}{(a+i a \tan (e+f x))^3 \sqrt {c+d \tan (e+f x)}} \, dx=\frac {\left (2 i c^3-8 c^2 d-13 i c d^2+12 d^3\right ) \text {arctanh}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{16 a^3 f (c+i d)^{7/2}}-\frac {i \text {arctanh}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{8 a^3 f \sqrt {c-i d}}+\frac {\left (2 c^2+7 i c d-10 d^2\right ) \sqrt {c+d \tan (e+f x)}}{16 f (-d+i c)^3 \left (a^3+i a^3 \tan (e+f x)\right )}+\frac {(-8 d+3 i c) \sqrt {c+d \tan (e+f x)}}{24 a f (c+i d)^2 (a+i a \tan (e+f x))^2}-\frac {\sqrt {c+d \tan (e+f x)}}{6 f (-d+i c) (a+i a \tan (e+f x))^3}
\]
[In]
Int[1/((a + I*a*Tan[e + f*x])^3*Sqrt[c + d*Tan[e + f*x]]),x]
[Out]
((-1/8*I)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a^3*Sqrt[c - I*d]*f) + (((2*I)*c^3 - 8*c^2*d - (13
*I)*c*d^2 + 12*d^3)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(16*a^3*(c + I*d)^(7/2)*f) - Sqrt[c + d*T
an[e + f*x]]/(6*(I*c - d)*f*(a + I*a*Tan[e + f*x])^3) + (((3*I)*c - 8*d)*Sqrt[c + d*Tan[e + f*x]])/(24*a*(c +
I*d)^2*f*(a + I*a*Tan[e + f*x])^2) + ((2*c^2 + (7*I)*c*d - 10*d^2)*Sqrt[c + d*Tan[e + f*x]])/(16*(I*c - d)^3*f
*(a^3 + I*a^3*Tan[e + f*x]))
Rule 65
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> With[{p = Denominator[m]}, Dist[p/b, Sub
st[Int[x^(p*(m + 1) - 1)*(c - a*(d/b) + d*(x^p/b))^n, x], x, (a + b*x)^(1/p)], x]] /; FreeQ[{a, b, c, d}, x] &
& NeQ[b*c - a*d, 0] && LtQ[-1, m, 0] && LeQ[-1, n, 0] && LeQ[Denominator[n], Denominator[m]] && IntLinearQ[a,
b, c, d, m, n, x]
Rule 214
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(Rt[-a/b, 2]/a)*ArcTanh[x/Rt[-a/b, 2]], x] /; FreeQ[{a, b},
x] && NegQ[a/b]
Rule 3618
Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_)*((c_) + (d_.)*tan[(e_.) + (f_.)*(x_)]), x_Symbol] :> Dist[c*(
d/f), Subst[Int[(a + (b/d)*x)^m/(d^2 + c*x), x], x, d*Tan[e + f*x]], x] /; FreeQ[{a, b, c, d, e, f, m}, x] &&
NeQ[b*c - a*d, 0] && NeQ[a^2 + b^2, 0] && EqQ[c^2 + d^2, 0]
Rule 3620
Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_)*((c_.) + (d_.)*tan[(e_.) + (f_.)*(x_)]), x_Symbol] :> Dist[(c
+ I*d)/2, Int[(a + b*Tan[e + f*x])^m*(1 - I*Tan[e + f*x]), x], x] + Dist[(c - I*d)/2, Int[(a + b*Tan[e + f*x]
)^m*(1 + I*Tan[e + f*x]), x], x] /; FreeQ[{a, b, c, d, e, f, m}, x] && NeQ[b*c - a*d, 0] && NeQ[a^2 + b^2, 0]
&& NeQ[c^2 + d^2, 0] && !IntegerQ[m]
Rule 3640
Int[((a_) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_)*((c_.) + (d_.)*tan[(e_.) + (f_.)*(x_)])^(n_), x_Symbol] :> Sim
p[a*(a + b*Tan[e + f*x])^m*((c + d*Tan[e + f*x])^(n + 1)/(2*f*m*(b*c - a*d))), x] + Dist[1/(2*a*m*(b*c - a*d))
, Int[(a + b*Tan[e + f*x])^(m + 1)*(c + d*Tan[e + f*x])^n*Simp[b*c*m - a*d*(2*m + n + 1) + b*d*(m + n + 1)*Tan
[e + f*x], x], x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && EqQ[a^2 + b^2, 0] && NeQ[c^2
+ d^2, 0] && LtQ[m, 0] && (IntegerQ[m] || IntegersQ[2*m, 2*n])
Rule 3677
Int[((a_) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_)*((A_.) + (B_.)*tan[(e_.) + (f_.)*(x_)])*((c_.) + (d_.)*tan[(e_
.) + (f_.)*(x_)])^(n_), x_Symbol] :> Simp[(a*A + b*B)*(a + b*Tan[e + f*x])^m*((c + d*Tan[e + f*x])^(n + 1)/(2*
f*m*(b*c - a*d))), x] + Dist[1/(2*a*m*(b*c - a*d)), Int[(a + b*Tan[e + f*x])^(m + 1)*(c + d*Tan[e + f*x])^n*Si
mp[A*(b*c*m - a*d*(2*m + n + 1)) + B*(a*c*m - b*d*(n + 1)) + d*(A*b - a*B)*(m + n + 1)*Tan[e + f*x], x], x], x
] /; FreeQ[{a, b, c, d, e, f, A, B, n}, x] && NeQ[b*c - a*d, 0] && EqQ[a^2 + b^2, 0] && LtQ[m, 0] && !GtQ[n,
0]
Rubi steps \begin{align*}
\text {integral}& = -\frac {\sqrt {c+d \tan (e+f x)}}{6 (i c-d) f (a+i a \tan (e+f x))^3}-\frac {\int \frac {-\frac {1}{2} a (6 i c-11 d)-\frac {5}{2} i a d \tan (e+f x)}{(a+i a \tan (e+f x))^2 \sqrt {c+d \tan (e+f x)}} \, dx}{6 a^2 (i c-d)} \\ & = -\frac {\sqrt {c+d \tan (e+f x)}}{6 (i c-d) f (a+i a \tan (e+f x))^3}+\frac {(3 i c-8 d) \sqrt {c+d \tan (e+f x)}}{24 a (c+i d)^2 f (a+i a \tan (e+f x))^2}-\frac {\int \frac {-\frac {3}{2} a^2 \left (4 c^2+11 i c d-12 d^2\right )-\frac {3}{2} a^2 (3 c+8 i d) d \tan (e+f x)}{(a+i a \tan (e+f x)) \sqrt {c+d \tan (e+f x)}} \, dx}{24 a^4 (c+i d)^2} \\ & = -\frac {\sqrt {c+d \tan (e+f x)}}{6 (i c-d) f (a+i a \tan (e+f x))^3}+\frac {(3 i c-8 d) \sqrt {c+d \tan (e+f x)}}{24 a (c+i d)^2 f (a+i a \tan (e+f x))^2}+\frac {\left (2 c^2+7 i c d-10 d^2\right ) \sqrt {c+d \tan (e+f x)}}{16 (i c-d)^3 f \left (a^3+i a^3 \tan (e+f x)\right )}-\frac {\int \frac {\frac {3}{2} a^3 (i c-2 d) \left (4 c^2+6 i c d-7 d^2\right )+\frac {3}{2} a^3 d \left (2 i c^2-7 c d-10 i d^2\right ) \tan (e+f x)}{\sqrt {c+d \tan (e+f x)}} \, dx}{48 a^6 (i c-d)^3} \\ & = -\frac {\sqrt {c+d \tan (e+f x)}}{6 (i c-d) f (a+i a \tan (e+f x))^3}+\frac {(3 i c-8 d) \sqrt {c+d \tan (e+f x)}}{24 a (c+i d)^2 f (a+i a \tan (e+f x))^2}+\frac {\left (2 c^2+7 i c d-10 d^2\right ) \sqrt {c+d \tan (e+f x)}}{16 (i c-d)^3 f \left (a^3+i a^3 \tan (e+f x)\right )}+\frac {\int \frac {1+i \tan (e+f x)}{\sqrt {c+d \tan (e+f x)}} \, dx}{16 a^3}+\frac {\left (2 c^3+8 i c^2 d-13 c d^2-12 i d^3\right ) \int \frac {1-i \tan (e+f x)}{\sqrt {c+d \tan (e+f x)}} \, dx}{32 a^3 (c+i d)^3} \\ & = -\frac {\sqrt {c+d \tan (e+f x)}}{6 (i c-d) f (a+i a \tan (e+f x))^3}+\frac {(3 i c-8 d) \sqrt {c+d \tan (e+f x)}}{24 a (c+i d)^2 f (a+i a \tan (e+f x))^2}+\frac {\left (2 c^2+7 i c d-10 d^2\right ) \sqrt {c+d \tan (e+f x)}}{16 (i c-d)^3 f \left (a^3+i a^3 \tan (e+f x)\right )}+\frac {i \text {Subst}\left (\int \frac {1}{(-1+x) \sqrt {c-i d x}} \, dx,x,i \tan (e+f x)\right )}{16 a^3 f}-\frac {\left (2 i c^3-8 c^2 d-13 i c d^2+12 d^3\right ) \text {Subst}\left (\int \frac {1}{(-1+x) \sqrt {c+i d x}} \, dx,x,-i \tan (e+f x)\right )}{32 a^3 (c+i d)^3 f} \\ & = -\frac {\sqrt {c+d \tan (e+f x)}}{6 (i c-d) f (a+i a \tan (e+f x))^3}+\frac {(3 i c-8 d) \sqrt {c+d \tan (e+f x)}}{24 a (c+i d)^2 f (a+i a \tan (e+f x))^2}+\frac {\left (2 c^2+7 i c d-10 d^2\right ) \sqrt {c+d \tan (e+f x)}}{16 (i c-d)^3 f \left (a^3+i a^3 \tan (e+f x)\right )}-\frac {\text {Subst}\left (\int \frac {1}{-1-\frac {i c}{d}+\frac {i x^2}{d}} \, dx,x,\sqrt {c+d \tan (e+f x)}\right )}{8 a^3 d f}-\frac {\left (2 c^3+8 i c^2 d-13 c d^2-12 i d^3\right ) \text {Subst}\left (\int \frac {1}{-1+\frac {i c}{d}-\frac {i x^2}{d}} \, dx,x,\sqrt {c+d \tan (e+f x)}\right )}{16 a^3 (c+i d)^3 d f} \\ & = -\frac {i \text {arctanh}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{8 a^3 \sqrt {c-i d} f}+\frac {\left (2 i c^3-8 c^2 d-13 i c d^2+12 d^3\right ) \text {arctanh}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{16 a^3 (c+i d)^{7/2} f}-\frac {\sqrt {c+d \tan (e+f x)}}{6 (i c-d) f (a+i a \tan (e+f x))^3}+\frac {(3 i c-8 d) \sqrt {c+d \tan (e+f x)}}{24 a (c+i d)^2 f (a+i a \tan (e+f x))^2}+\frac {\left (2 c^2+7 i c d-10 d^2\right ) \sqrt {c+d \tan (e+f x)}}{16 (i c-d)^3 f \left (a^3+i a^3 \tan (e+f x)\right )} \\
\end{align*}
Mathematica [A] (verified)
Time = 3.67 (sec) , antiderivative size = 266, normalized size of antiderivative = 0.89
\[
\int \frac {1}{(a+i a \tan (e+f x))^3 \sqrt {c+d \tan (e+f x)}} \, dx=-\frac {\frac {6 i (c+i d)^2 \text {arctanh}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{\sqrt {c-i d}}+\frac {3 \left (-2 i c^3+8 c^2 d+13 i c d^2-12 d^3\right ) \text {arctanh}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{(c+i d)^{3/2}}+\frac {8 (c+i d) \sqrt {c+d \tan (e+f x)}}{(-i+\tan (e+f x))^3}+\frac {2 i (3 c+8 i d) \sqrt {c+d \tan (e+f x)}}{(-i+\tan (e+f x))^2}-\frac {3 \left (2 c^2+7 i c d-10 d^2\right ) \sqrt {c+d \tan (e+f x)}}{(c+i d) (-i+\tan (e+f x))}}{48 a^3 (c+i d)^2 f}
\]
[In]
Integrate[1/((a + I*a*Tan[e + f*x])^3*Sqrt[c + d*Tan[e + f*x]]),x]
[Out]
-1/48*(((6*I)*(c + I*d)^2*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/Sqrt[c - I*d] + (3*((-2*I)*c^3 + 8*
c^2*d + (13*I)*c*d^2 - 12*d^3)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(c + I*d)^(3/2) + (8*(c + I*d)
*Sqrt[c + d*Tan[e + f*x]])/(-I + Tan[e + f*x])^3 + ((2*I)*(3*c + (8*I)*d)*Sqrt[c + d*Tan[e + f*x]])/(-I + Tan[
e + f*x])^2 - (3*(2*c^2 + (7*I)*c*d - 10*d^2)*Sqrt[c + d*Tan[e + f*x]])/((c + I*d)*(-I + Tan[e + f*x])))/(a^3*
(c + I*d)^2*f)
Maple [A] (verified)
Time = 0.73 (sec) , antiderivative size = 357, normalized size of antiderivative = 1.20
| | |
method | result | size |
| | |
derivativedivides |
\(\frac {2 d^{4} \left (\frac {i \arctan \left (\frac {\sqrt {c +d \tan \left (f x +e \right )}}{\sqrt {i d -c}}\right )}{16 d^{4} \sqrt {i d -c}}+\frac {\frac {-\frac {d \left (7 i c d +2 c^{2}-10 d^{2}\right ) \left (c +d \tan \left (f x +e \right )\right )^{\frac {5}{2}}}{2 \left (3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right )}+\frac {2 d \left (15 i c^{2} d -19 i d^{3}+3 c^{3}-31 c \,d^{2}\right ) \left (c +d \tan \left (f x +e \right )\right )^{\frac {3}{2}}}{3 \left (3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right )}-\frac {d \left (13 i c^{3} d -45 i c \,d^{3}+2 c^{4}-38 c^{2} d^{2}+18 d^{4}\right ) \sqrt {c +d \tan \left (f x +e \right )}}{2 \left (3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right )}}{\left (-d \tan \left (f x +e \right )+i d \right )^{3}}-\frac {\left (2 i c^{3}-13 i c \,d^{2}-8 c^{2} d +12 d^{3}\right ) \arctan \left (\frac {\sqrt {c +d \tan \left (f x +e \right )}}{\sqrt {-i d -c}}\right )}{2 \left (3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right ) \sqrt {-i d -c}}}{16 d^{4}}\right )}{f \,a^{3}}\) |
\(357\) |
default |
\(\frac {2 d^{4} \left (\frac {i \arctan \left (\frac {\sqrt {c +d \tan \left (f x +e \right )}}{\sqrt {i d -c}}\right )}{16 d^{4} \sqrt {i d -c}}+\frac {\frac {-\frac {d \left (7 i c d +2 c^{2}-10 d^{2}\right ) \left (c +d \tan \left (f x +e \right )\right )^{\frac {5}{2}}}{2 \left (3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right )}+\frac {2 d \left (15 i c^{2} d -19 i d^{3}+3 c^{3}-31 c \,d^{2}\right ) \left (c +d \tan \left (f x +e \right )\right )^{\frac {3}{2}}}{3 \left (3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right )}-\frac {d \left (13 i c^{3} d -45 i c \,d^{3}+2 c^{4}-38 c^{2} d^{2}+18 d^{4}\right ) \sqrt {c +d \tan \left (f x +e \right )}}{2 \left (3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right )}}{\left (-d \tan \left (f x +e \right )+i d \right )^{3}}-\frac {\left (2 i c^{3}-13 i c \,d^{2}-8 c^{2} d +12 d^{3}\right ) \arctan \left (\frac {\sqrt {c +d \tan \left (f x +e \right )}}{\sqrt {-i d -c}}\right )}{2 \left (3 i c^{2} d -i d^{3}+c^{3}-3 c \,d^{2}\right ) \sqrt {-i d -c}}}{16 d^{4}}\right )}{f \,a^{3}}\) |
\(357\) |
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[In]
int(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x,method=_RETURNVERBOSE)
[Out]
2/f/a^3*d^4*(1/16*I/d^4/(I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(I*d-c)^(1/2))+1/16/d^4*((-1/2*d*(2*c^2+7*
I*c*d-10*d^2)/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(5/2)+2/3*d*(-31*c*d^2+15*I*c^2*d-19*I*d^3+3*c^3)
/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(3/2)-1/2*d*(13*I*c^3*d-45*I*c*d^3+2*c^4-38*c^2*d^2+18*d^4)/(3
*I*c^2*d-I*d^3+c^3-3*c*d^2)*(c+d*tan(f*x+e))^(1/2))/(-d*tan(f*x+e)+I*d)^3-1/2*(2*I*c^3-8*c^2*d-13*I*c*d^2+12*d
^3)/(3*I*c^2*d-I*d^3+c^3-3*c*d^2)/(-I*d-c)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)/(-I*d-c)^(1/2))))
Fricas [B] (verification not implemented)
Both result and optimal contain complex but leaf count of result is larger than twice the leaf
count of optimal. 1747 vs. \(2 (240) = 480\).
Time = 0.59 (sec) , antiderivative size = 1747, normalized size of antiderivative = 5.86
\[
\int \frac {1}{(a+i a \tan (e+f x))^3 \sqrt {c+d \tan (e+f x)}} \, dx=\text {Too large to display}
\]
[In]
integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm="fricas")
[Out]
1/192*(48*(I*a^3*c^3 - 3*a^3*c^2*d - 3*I*a^3*c*d^2 + a^3*d^3)*f*sqrt(1/64*I/((-I*a^6*c - a^6*d)*f^2))*e^(6*I*f
*x + 6*I*e)*log(-2*(8*((I*a^3*c + a^3*d)*f*e^(2*I*f*x + 2*I*e) + (I*a^3*c + a^3*d)*f)*sqrt(((c - I*d)*e^(2*I*f
*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/64*I/((-I*a^6*c - a^6*d)*f^2)) - (c - I*d)*e^(2*I*f*x
+ 2*I*e) - c)*e^(-2*I*f*x - 2*I*e)) + 48*(-I*a^3*c^3 + 3*a^3*c^2*d + 3*I*a^3*c*d^2 - a^3*d^3)*f*sqrt(1/64*I/(
(-I*a^6*c - a^6*d)*f^2))*e^(6*I*f*x + 6*I*e)*log(-2*(8*((-I*a^3*c - a^3*d)*f*e^(2*I*f*x + 2*I*e) + (-I*a^3*c -
a^3*d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/64*I/((-I*a^6*c -
a^6*d)*f^2)) - (c - I*d)*e^(2*I*f*x + 2*I*e) - c)*e^(-2*I*f*x - 2*I*e)) + 3*(-I*a^3*c^3 + 3*a^3*c^2*d + 3*I*a^
3*c*d^2 - a^3*d^3)*f*sqrt(-(-4*I*c^6 + 32*c^5*d + 116*I*c^4*d^2 - 256*c^3*d^3 - 361*I*c^2*d^4 + 312*c*d^5 + 14
4*I*d^6)/((-I*a^6*c^7 + 7*a^6*c^6*d + 21*I*a^6*c^5*d^2 - 35*a^6*c^4*d^3 - 35*I*a^6*c^3*d^4 + 21*a^6*c^2*d^5 +
7*I*a^6*c*d^6 - a^6*d^7)*f^2))*e^(6*I*f*x + 6*I*e)*log(1/16*(2*I*c^4 - 10*c^3*d - 21*I*c^2*d^2 + 25*c*d^3 + 12
*I*d^4 + ((a^3*c^4 + 4*I*a^3*c^3*d - 6*a^3*c^2*d^2 - 4*I*a^3*c*d^3 + a^3*d^4)*f*e^(2*I*f*x + 2*I*e) + (a^3*c^4
+ 4*I*a^3*c^3*d - 6*a^3*c^2*d^2 - 4*I*a^3*c*d^3 + a^3*d^4)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/
(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(-4*I*c^6 + 32*c^5*d + 116*I*c^4*d^2 - 256*c^3*d^3 - 361*I*c^2*d^4 + 312*c*d^
5 + 144*I*d^6)/((-I*a^6*c^7 + 7*a^6*c^6*d + 21*I*a^6*c^5*d^2 - 35*a^6*c^4*d^3 - 35*I*a^6*c^3*d^4 + 21*a^6*c^2*
d^5 + 7*I*a^6*c*d^6 - a^6*d^7)*f^2)) + (2*I*c^4 - 8*c^3*d - 13*I*c^2*d^2 + 12*c*d^3)*e^(2*I*f*x + 2*I*e))*e^(-
2*I*f*x - 2*I*e)/((a^3*c^4 + 4*I*a^3*c^3*d - 6*a^3*c^2*d^2 - 4*I*a^3*c*d^3 + a^3*d^4)*f)) + 3*(I*a^3*c^3 - 3*a
^3*c^2*d - 3*I*a^3*c*d^2 + a^3*d^3)*f*sqrt(-(-4*I*c^6 + 32*c^5*d + 116*I*c^4*d^2 - 256*c^3*d^3 - 361*I*c^2*d^4
+ 312*c*d^5 + 144*I*d^6)/((-I*a^6*c^7 + 7*a^6*c^6*d + 21*I*a^6*c^5*d^2 - 35*a^6*c^4*d^3 - 35*I*a^6*c^3*d^4 +
21*a^6*c^2*d^5 + 7*I*a^6*c*d^6 - a^6*d^7)*f^2))*e^(6*I*f*x + 6*I*e)*log(1/16*(2*I*c^4 - 10*c^3*d - 21*I*c^2*d^
2 + 25*c*d^3 + 12*I*d^4 - ((a^3*c^4 + 4*I*a^3*c^3*d - 6*a^3*c^2*d^2 - 4*I*a^3*c*d^3 + a^3*d^4)*f*e^(2*I*f*x +
2*I*e) + (a^3*c^4 + 4*I*a^3*c^3*d - 6*a^3*c^2*d^2 - 4*I*a^3*c*d^3 + a^3*d^4)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2
*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(-4*I*c^6 + 32*c^5*d + 116*I*c^4*d^2 - 256*c^3*d^3 - 361*I*c
^2*d^4 + 312*c*d^5 + 144*I*d^6)/((-I*a^6*c^7 + 7*a^6*c^6*d + 21*I*a^6*c^5*d^2 - 35*a^6*c^4*d^3 - 35*I*a^6*c^3*
d^4 + 21*a^6*c^2*d^5 + 7*I*a^6*c*d^6 - a^6*d^7)*f^2)) + (2*I*c^4 - 8*c^3*d - 13*I*c^2*d^2 + 12*c*d^3)*e^(2*I*f
*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((a^3*c^4 + 4*I*a^3*c^3*d - 6*a^3*c^2*d^2 - 4*I*a^3*c*d^3 + a^3*d^4)*f)) + 2
*(2*c^2 + 4*I*c*d - 2*d^2 + (11*c^2 + 36*I*c*d - 40*d^2)*e^(6*I*f*x + 6*I*e) + (18*c^2 + 55*I*c*d - 52*d^2)*e^
(4*I*f*x + 4*I*e) + (9*c^2 + 23*I*c*d - 14*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c +
I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-6*I*f*x - 6*I*e)/((-I*a^3*c^3 + 3*a^3*c^2*d + 3*I*a^3*c*d^2 - a^3*d^3)*f
)
Sympy [F]
\[
\int \frac {1}{(a+i a \tan (e+f x))^3 \sqrt {c+d \tan (e+f x)}} \, dx=\frac {i \int \frac {1}{\sqrt {c + d \tan {\left (e + f x \right )}} \tan ^{3}{\left (e + f x \right )} - 3 i \sqrt {c + d \tan {\left (e + f x \right )}} \tan ^{2}{\left (e + f x \right )} - 3 \sqrt {c + d \tan {\left (e + f x \right )}} \tan {\left (e + f x \right )} + i \sqrt {c + d \tan {\left (e + f x \right )}}}\, dx}{a^{3}}
\]
[In]
integrate(1/(c+d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**3,x)
[Out]
I*Integral(1/(sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3 - 3*I*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2 - 3*sqrt
(c + d*tan(e + f*x))*tan(e + f*x) + I*sqrt(c + d*tan(e + f*x))), x)/a**3
Maxima [F(-2)]
Exception generated. \[
\int \frac {1}{(a+i a \tan (e+f x))^3 \sqrt {c+d \tan (e+f x)}} \, dx=\text {Exception raised: RuntimeError}
\]
[In]
integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm="maxima")
[Out]
Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negative exponent.
Giac [B] (verification not implemented)
Both result and optimal contain complex but leaf count of result is larger than twice the leaf
count of optimal. 661 vs. \(2 (240) = 480\).
Time = 1.01 (sec) , antiderivative size = 661, normalized size of antiderivative = 2.22
\[
\int \frac {1}{(a+i a \tan (e+f x))^3 \sqrt {c+d \tan (e+f x)}} \, dx=-\frac {1}{4} \, d^{4} {\left (\frac {8 \, {\left (2 \, c^{3} + 8 i \, c^{2} d - 13 \, c d^{2} - 12 i \, d^{3}\right )} \arctan \left (\frac {2 \, {\left (\sqrt {d \tan \left (f x + e\right ) + c} c - \sqrt {c^{2} + d^{2}} \sqrt {d \tan \left (f x + e\right ) + c}\right )}}{c \sqrt {-2 \, c + 2 \, \sqrt {c^{2} + d^{2}}} + i \, \sqrt {-2 \, c + 2 \, \sqrt {c^{2} + d^{2}}} d - \sqrt {c^{2} + d^{2}} \sqrt {-2 \, c + 2 \, \sqrt {c^{2} + d^{2}}}}\right )}{-16 \, {\left (i \, a^{3} c^{3} d^{4} f - 3 \, a^{3} c^{2} d^{5} f - 3 i \, a^{3} c d^{6} f + a^{3} d^{7} f\right )} \sqrt {-2 \, c + 2 \, \sqrt {c^{2} + d^{2}}} {\left (\frac {i \, d}{c - \sqrt {c^{2} + d^{2}}} + 1\right )}} - \frac {8 \, {\left (-6 i \, {\left (d \tan \left (f x + e\right ) + c\right )}^{\frac {5}{2}} c^{2} + 12 i \, {\left (d \tan \left (f x + e\right ) + c\right )}^{\frac {3}{2}} c^{3} - 6 i \, \sqrt {d \tan \left (f x + e\right ) + c} c^{4} + 21 \, {\left (d \tan \left (f x + e\right ) + c\right )}^{\frac {5}{2}} c d - 60 \, {\left (d \tan \left (f x + e\right ) + c\right )}^{\frac {3}{2}} c^{2} d + 39 \, \sqrt {d \tan \left (f x + e\right ) + c} c^{3} d + 30 i \, {\left (d \tan \left (f x + e\right ) + c\right )}^{\frac {5}{2}} d^{2} - 124 i \, {\left (d \tan \left (f x + e\right ) + c\right )}^{\frac {3}{2}} c d^{2} + 114 i \, \sqrt {d \tan \left (f x + e\right ) + c} c^{2} d^{2} + 76 \, {\left (d \tan \left (f x + e\right ) + c\right )}^{\frac {3}{2}} d^{3} - 135 \, \sqrt {d \tan \left (f x + e\right ) + c} c d^{3} - 54 i \, \sqrt {d \tan \left (f x + e\right ) + c} d^{4}\right )}}{-96 \, {\left (i \, a^{3} c^{3} d^{3} f - 3 \, a^{3} c^{2} d^{4} f - 3 i \, a^{3} c d^{5} f + a^{3} d^{6} f\right )} {\left (d \tan \left (f x + e\right ) - i \, d\right )}^{3}} - \frac {i \, \arctan \left (\frac {2 \, {\left (\sqrt {d \tan \left (f x + e\right ) + c} c - \sqrt {c^{2} + d^{2}} \sqrt {d \tan \left (f x + e\right ) + c}\right )}}{c \sqrt {-2 \, c + 2 \, \sqrt {c^{2} + d^{2}}} - i \, \sqrt {-2 \, c + 2 \, \sqrt {c^{2} + d^{2}}} d - \sqrt {c^{2} + d^{2}} \sqrt {-2 \, c + 2 \, \sqrt {c^{2} + d^{2}}}}\right )}{a^{3} \sqrt {-2 \, c + 2 \, \sqrt {c^{2} + d^{2}}} d^{4} f {\left (-\frac {i \, d}{c - \sqrt {c^{2} + d^{2}}} + 1\right )}}\right )}
\]
[In]
integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm="giac")
[Out]
-1/4*d^4*(8*(2*c^3 + 8*I*c^2*d - 13*c*d^2 - 12*I*d^3)*arctan(2*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*s
qrt(d*tan(f*x + e) + c))/(c*sqrt(-2*c + 2*sqrt(c^2 + d^2)) + I*sqrt(-2*c + 2*sqrt(c^2 + d^2))*d - sqrt(c^2 + d
^2)*sqrt(-2*c + 2*sqrt(c^2 + d^2))))/((-16*I*a^3*c^3*d^4*f + 48*a^3*c^2*d^5*f + 48*I*a^3*c*d^6*f - 16*a^3*d^7*
f)*sqrt(-2*c + 2*sqrt(c^2 + d^2))*(I*d/(c - sqrt(c^2 + d^2)) + 1)) - 8*(-6*I*(d*tan(f*x + e) + c)^(5/2)*c^2 +
12*I*(d*tan(f*x + e) + c)^(3/2)*c^3 - 6*I*sqrt(d*tan(f*x + e) + c)*c^4 + 21*(d*tan(f*x + e) + c)^(5/2)*c*d - 6
0*(d*tan(f*x + e) + c)^(3/2)*c^2*d + 39*sqrt(d*tan(f*x + e) + c)*c^3*d + 30*I*(d*tan(f*x + e) + c)^(5/2)*d^2 -
124*I*(d*tan(f*x + e) + c)^(3/2)*c*d^2 + 114*I*sqrt(d*tan(f*x + e) + c)*c^2*d^2 + 76*(d*tan(f*x + e) + c)^(3/
2)*d^3 - 135*sqrt(d*tan(f*x + e) + c)*c*d^3 - 54*I*sqrt(d*tan(f*x + e) + c)*d^4)/((-96*I*a^3*c^3*d^3*f + 288*a
^3*c^2*d^4*f + 288*I*a^3*c*d^5*f - 96*a^3*d^6*f)*(d*tan(f*x + e) - I*d)^3) - I*arctan(2*(sqrt(d*tan(f*x + e) +
c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-2*c + 2*sqrt(c^2 + d^2)) - I*sqrt(-2*c + 2*sqrt(c^2
+ d^2))*d - sqrt(c^2 + d^2)*sqrt(-2*c + 2*sqrt(c^2 + d^2))))/(a^3*sqrt(-2*c + 2*sqrt(c^2 + d^2))*d^4*f*(-I*d/
(c - sqrt(c^2 + d^2)) + 1)))
Mupad [B] (verification not implemented)
Time = 12.62 (sec) , antiderivative size = 60949, normalized size of antiderivative = 204.53
\[
\int \frac {1}{(a+i a \tan (e+f x))^3 \sqrt {c+d \tan (e+f x)}} \, dx=\text {Too large to display}
\]
[In]
int(1/((a + a*tan(e + f*x)*1i)^3*(c + d*tan(e + f*x))^(1/2)),x)
[Out]
log(a^3*d^14*f*240i - ((-(140*d^11 - c*d^10*140i + 35*c^2*d^9 - c^3*d^8*245i - 280*c^4*d^7 + c^5*d^6*168i + 56
*c^6*d^5 - c^7*d^4*8i - a^6*c^6*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d
^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^
12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d
^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^
11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*
f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^
6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2
+ 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*
d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*
d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*
f^2))^2)^(1/2)*4i + a^6*d^6*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)
/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f
^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f
^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d
^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4
+ 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^
11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15
*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14
)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12
*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2)
)^2)^(1/2)*4i + 24*a^6*c*d^5*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12
)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*
f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*
f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*
d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4
+ 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d
^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 1
5*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^1
4)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^1
2*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2
))^2)^(1/2) + 24*a^6*c^5*d*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/
1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^
4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^
4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^
5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 +
15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^1
1)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*
a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)
/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*
f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))
^2)^(1/2) - a^6*c^2*d^4*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/102
4 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 +
6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)
- (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/
128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15
*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/
4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6
*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4
+ (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2
+ 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)
^(1/2)*60i - 80*a^6*c^3*d^3*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)
/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f
^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f
^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d
^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4
+ 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^
11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15
*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14
)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12
*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2)
)^2)^(1/2) + a^6*c^4*d^2*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/10
24 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4
+ 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)
- (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)
/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 1
5*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)
/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^
6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4
+ (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^
2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2
)^(1/2)*60i)/(2048*(d^6 + c^2*d^4)*(a^6*d^6*f^2*1i - a^6*c^6*f^2*1i + 6*a^6*c*d^5*f^2 + 6*a^6*c^5*d*f^2 - a^6*
c^2*d^4*f^2*15i - 20*a^6*c^3*d^3*f^2 + a^6*c^4*d^2*f^2*15i)))^(1/2)*((c + d*tan(e + f*x))^(1/2)*(-(140*d^11 -
c*d^10*140i + 35*c^2*d^9 - c^3*d^8*245i - 280*c^4*d^7 + c^5*d^6*168i + 56*c^6*d^5 - c^7*d^4*8i - a^6*c^6*f^2*(
4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15
*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^1
2*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3
*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^1
2*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^
10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10
*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6
*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*
d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^
6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*4i + a^6*d^6*f^2*(4*(2
56*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8
*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^
4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^1
3)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^
12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d
^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7
+ 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2
+ 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10
)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^
4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*4i + 24*a^6*c*d^5*f^2*(4*(
256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^
8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c
^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^
13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d
^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*
d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^
7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^
2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^1
0)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c
^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2) + 24*a^6*c^5*d*f^2*(4*(25
6*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*
d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4
*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13
)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^1
2*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^
2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7
+ 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2
+ 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)
/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4
*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2) - a^6*c^2*d^4*f^2*(4*(256*d
^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8
)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^
8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/5
12 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f
^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f
^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2
*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 1
5*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4
+ (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^
8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*60i - 80*a^6*c^3*d^3*f^2*(4*(2
56*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8
*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^
4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^1
3)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^
12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d
^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7
+ 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2
+ 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10
)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^
4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2) + a^6*c^4*d^2*f^2*(4*(256*
d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^
8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d
^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/
512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*
f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*
f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 +
2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 +
15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4
+ (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d
^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*60i)/(2048*(d^6 + c^2*d^4)*(a
^6*d^6*f^2*1i - a^6*c^6*f^2*1i + 6*a^6*c*d^5*f^2 + 6*a^6*c^5*d*f^2 - a^6*c^2*d^4*f^2*15i - 20*a^6*c^3*d^3*f^2
+ a^6*c^4*d^2*f^2*15i)))^(1/2)*(65536*a^12*c*d^14*f^4 + 393216*a^12*c^3*d^12*f^4 + 983040*a^12*c^5*d^10*f^4 +
1310720*a^12*c^7*d^8*f^4 + 983040*a^12*c^9*d^6*f^4 + 393216*a^12*c^11*d^4*f^4 + 65536*a^12*c^13*d^2*f^4) + 143
36*a^9*d^15*f^3 + a^9*c*d^14*f^3*33792i + 20480*a^9*c^2*d^13*f^3 + a^9*c^3*d^12*f^3*95232i - 18432*a^9*c^4*d^1
1*f^3 + a^9*c^5*d^10*f^3*83968i - 32768*a^9*c^6*d^9*f^3 + a^9*c^7*d^8*f^3*18432i + 2048*a^9*c^8*d^7*f^3 - a^9*
c^9*d^6*f^3*3072i + 12288*a^9*c^10*d^5*f^3 + a^9*c^11*d^4*f^3*1024i + 2048*a^9*c^12*d^3*f^3) + (c + d*tan(e +
f*x))^(1/2)*(4736*a^6*d^14*f^2 + a^6*c*d^13*f^2*17664i - 20000*a^6*c^2*d^12*f^2 - a^6*c^3*d^11*f^2*3520i - 800
*a^6*c^4*d^10*f^2 + a^6*c^5*d^9*f^2*7296i - 1248*a^6*c^6*d^8*f^2 + a^6*c^7*d^7*f^2*3904i + 1440*a^6*c^8*d^6*f^
2 + a^6*c^9*d^5*f^2*1280i + 1280*a^6*c^10*d^4*f^2 + a^6*c^11*d^3*f^2*256i + 256*a^6*c^12*d^2*f^2))*(-(140*d^11
- c*d^10*140i + 35*c^2*d^9 - c^3*d^8*245i - 280*c^4*d^7 + c^5*d^6*168i + 56*c^6*d^5 - c^7*d^4*8i - a^6*c^6*f^
2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 +
(15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*
a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*
c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 +
a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12
*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c
^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*
d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c
^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15
*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*4i + a^6*d^6*f^2*(4
*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*
c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12
*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*
d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12
*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^1
0*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*
d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*
f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d
^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6
*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*4i + 24*a^6*c*d^5*f^2*(
4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15
*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^1
2*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3
*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^1
2*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^
10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10
*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6
*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*
d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^
6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2) + 24*a^6*c^5*d*f^2*(4*
(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c
^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*
c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d
^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*
d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10
*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d
^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f
^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^
10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*
c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2) - a^6*c^2*d^4*f^2*(4*(25
6*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*
d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4
*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13
)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^1
2*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^
2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7
+ 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2
+ 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)
/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4
*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*60i - 80*a^6*c^3*d^3*f^2*(4
*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*
c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12
*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*
d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12
*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^1
0*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*
d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*
f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d
^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6
*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2) + a^6*c^4*d^2*f^2*(4*(2
56*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8
*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^
4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^1
3)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^
12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d
^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7
+ 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2
+ 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10
)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^
4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*60i)/(2048*(d^6 + c^2*d^4)
*(a^6*d^6*f^2*1i - a^6*c^6*f^2*1i + 6*a^6*c*d^5*f^2 + 6*a^6*c^5*d*f^2 - a^6*c^2*d^4*f^2*15i - 20*a^6*c^3*d^3*f
^2 + a^6*c^4*d^2*f^2*15i)))^(1/2) - a^3*c^2*d^12*f*1422i + 516*a^3*c^3*d^11*f - a^3*c^4*d^10*f*274i - 112*a^3*
c^5*d^9*f - a^3*c^6*d^8*f*294i - 68*a^3*c^7*d^7*f - a^3*c^8*d^6*f*94i - 36*a^3*c^9*d^5*f - a^3*c^10*d^4*f*12i
- 8*a^3*c^11*d^3*f - 1012*a^3*c*d^13*f)*(-(140*d^11 - c*d^10*140i + 35*c^2*d^9 - c^3*d^8*245i - 280*c^4*d^7 +
c^5*d^6*168i + 56*c^6*d^5 - c^7*d^4*8i - a^6*c^6*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^1
6)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c
^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^
4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c
^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 +
20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*
d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*
a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c
*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^
6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2
+ 6*a^6*c^10*d^2*f^2))^2)^(1/2)*4i + a^6*d^6*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/6
4 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*
f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 +
6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d
^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*
a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13
)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*
c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^1
6 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^
12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*
a^6*c^10*d^2*f^2))^2)^(1/2)*4i + 24*a^6*c*d^5*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/
64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12
*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 +
6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*
d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20
*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^1
3)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6
*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^
16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c
^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6
*a^6*c^10*d^2*f^2))^2)^(1/2) + 24*a^6*c^5*d*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64
+ (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f
^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6
*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^
7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a
^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)
/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c
^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16
- (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^1
2*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a
^6*c^10*d^2*f^2))^2)^(1/2) - a^6*c^2*d^4*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 +
(85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4
+ a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^
12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/
128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12
*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4
+ (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*
d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 -
(735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f
^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*
c^10*d^2*f^2))^2)^(1/2)*60i - 80*a^6*c^3*d^3*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/6
4 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*
f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 +
6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d
^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*
a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13
)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*
c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^1
6 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^
12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*
a^6*c^10*d^2*f^2))^2)^(1/2) + a^6*c^4*d^2*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 +
(85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4
+ a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a
^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)
/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^1
2*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4
+ (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2
*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 -
(735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*
f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6
*c^10*d^2*f^2))^2)^(1/2)*60i)/(2048*(d^6 + c^2*d^4)*(a^6*d^6*f^2*1i - a^6*c^6*f^2*1i + 6*a^6*c*d^5*f^2 + 6*a^6
*c^5*d*f^2 - a^6*c^2*d^4*f^2*15i - 20*a^6*c^3*d^3*f^2 + a^6*c^4*d^2*f^2*15i)))^(1/2) + log(a^3*d^14*f*240i - (
((c*d^10*140i - 140*d^11 - 35*c^2*d^9 + c^3*d^8*245i + 280*c^4*d^7 - c^5*d^6*168i - 56*c^6*d^5 + c^7*d^4*8i -
a^6*c^6*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^1
0)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10
*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/
128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c
^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^
4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9
)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 2
0*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)
/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^1
0*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*4i + a^6*
d^6*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1
024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4
+ 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128
- (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*
f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 +
6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4
+ 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^
6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 +
(83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^
2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*4i + 24*a^6*c
*d^5*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/
1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^
4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128
- (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12
*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 +
6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4
+ 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a
^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4
+ (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f
^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2) + 24*a^6*c^5
*d*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/10
24 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4
+ 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 -
(55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f
^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6
*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 +
12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6
*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 +
(83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2
+ 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2) - a^6*c^2*d^4*
f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024
+ (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 1
5*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (5
5*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4
+ a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^
12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12
*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^
6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83
*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 +
15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*60i - 80*a^6*c^3*
d^3*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1
024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4
+ 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128
- (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*
f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 +
6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4
+ 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^
6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 +
(83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^
2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2) + a^6*c^4*d^2
*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024
+ (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 +
15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (
55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4
+ a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a
^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 1
2*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c
^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (8
3*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 +
15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*60i)/(2048*(d^6
+ c^2*d^4)*(a^6*d^6*f^2*1i - a^6*c^6*f^2*1i + 6*a^6*c*d^5*f^2 + 6*a^6*c^5*d*f^2 - a^6*c^2*d^4*f^2*15i - 20*a^6
*c^3*d^3*f^2 + a^6*c^4*d^2*f^2*15i)))^(1/2)*((c + d*tan(e + f*x))^(1/2)*((c*d^10*140i - 140*d^11 - 35*c^2*d^9
+ c^3*d^8*245i + 280*c^4*d^7 - c^5*d^6*168i - 56*c^6*d^5 + c^7*d^4*8i - a^6*c^6*f^2*(4*(256*d^6 + 256*c^2*d^4)
*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^
6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c
^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11
)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d
^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c
^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a
^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2
+ 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4
+ 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^
6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*4i + a^6*d^6*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((
649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/6
4 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d
^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/25
6 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*
f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d
^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c
^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6
*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12
*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^
6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*4i + 24*a^6*c*d^5*f^2*(4*(256*d^6 + 256*c^2*d^4)*((
(649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/
64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*
d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/2
56 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10
*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*
d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*
c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 +
6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 1
2*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d
^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2) + 24*a^6*c^5*d*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((6
49*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64
- (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^
6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256
+ (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f
^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^
15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^
12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*
a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*
c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6
*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2) - a^6*c^2*d^4*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*
c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 -
(c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f
^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 +
(61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4
+ 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)
/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*
f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6
*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^1
1*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^
2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*60i - 80*a^6*c^3*d^3*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((
649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/6
4 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d
^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/25
6 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*
f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d
^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c
^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6
*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12
*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^
6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2) + a^6*c^4*d^2*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649
*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 -
(c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*
f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 +
(61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4
+ 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15
)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12
*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^
6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^
11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f
^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*60i)/(2048*(d^6 + c^2*d^4)*(a^6*d^6*f^2*1i - a^6*c^6*f
^2*1i + 6*a^6*c*d^5*f^2 + 6*a^6*c^5*d*f^2 - a^6*c^2*d^4*f^2*15i - 20*a^6*c^3*d^3*f^2 + a^6*c^4*d^2*f^2*15i)))^
(1/2)*(65536*a^12*c*d^14*f^4 + 393216*a^12*c^3*d^12*f^4 + 983040*a^12*c^5*d^10*f^4 + 1310720*a^12*c^7*d^8*f^4
+ 983040*a^12*c^9*d^6*f^4 + 393216*a^12*c^11*d^4*f^4 + 65536*a^12*c^13*d^2*f^4) + 14336*a^9*d^15*f^3 + a^9*c*d
^14*f^3*33792i + 20480*a^9*c^2*d^13*f^3 + a^9*c^3*d^12*f^3*95232i - 18432*a^9*c^4*d^11*f^3 + a^9*c^5*d^10*f^3*
83968i - 32768*a^9*c^6*d^9*f^3 + a^9*c^7*d^8*f^3*18432i + 2048*a^9*c^8*d^7*f^3 - a^9*c^9*d^6*f^3*3072i + 12288
*a^9*c^10*d^5*f^3 + a^9*c^11*d^4*f^3*1024i + 2048*a^9*c^12*d^3*f^3) + (c + d*tan(e + f*x))^(1/2)*(4736*a^6*d^1
4*f^2 + a^6*c*d^13*f^2*17664i - 20000*a^6*c^2*d^12*f^2 - a^6*c^3*d^11*f^2*3520i - 800*a^6*c^4*d^10*f^2 + a^6*c
^5*d^9*f^2*7296i - 1248*a^6*c^6*d^8*f^2 + a^6*c^7*d^7*f^2*3904i + 1440*a^6*c^8*d^6*f^2 + a^6*c^9*d^5*f^2*1280i
+ 1280*a^6*c^10*d^4*f^2 + a^6*c^11*d^3*f^2*256i + 256*a^6*c^12*d^2*f^2))*((c*d^10*140i - 140*d^11 - 35*c^2*d^
9 + c^3*d^8*245i + 280*c^4*d^7 - c^5*d^6*168i - 56*c^6*d^5 + c^7*d^4*8i - a^6*c^6*f^2*(4*(256*d^6 + 256*c^2*d^
4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*
d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12
*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^
11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2
*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225
*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/
(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f
^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/
4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*
c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*4i + a^6*d^6*f^2*(4*(256*d^6 + 256*c^2*d^4)*(
((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)
/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6
*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/
256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^1
0*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2
*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6
*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 +
6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 +
12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*
d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*4i + 24*a^6*c*d^5*f^2*(4*(256*d^6 + 256*c^2*d^4)*
(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6
)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^
6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)
/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^
10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^
2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^
6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2
+ 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 +
12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6
*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2) + 24*a^6*c^5*d*f^2*(4*(256*d^6 + 256*c^2*d^4)*((
(649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/
64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*
d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/2
56 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10
*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*
d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*
c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 +
6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 1
2*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d
^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2) - a^6*c^2*d^4*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((64
9*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64
- (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6
*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256
+ (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^
4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^1
5)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^1
2*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a
^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c
^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*
f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*60i - 80*a^6*c^3*d^3*f^2*(4*(256*d^6 + 256*c^2*d^4)*(
((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)
/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6
*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/
256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^1
0*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2
*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6
*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 +
6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 +
12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*
d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2) + a^6*c^4*d^2*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((6
49*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64
- (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^
6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256
+ (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f
^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^
15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^
12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*
a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*
c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6
*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*60i)/(2048*(d^6 + c^2*d^4)*(a^6*d^6*f^2*1i - a^6*c^6
*f^2*1i + 6*a^6*c*d^5*f^2 + 6*a^6*c^5*d*f^2 - a^6*c^2*d^4*f^2*15i - 20*a^6*c^3*d^3*f^2 + a^6*c^4*d^2*f^2*15i))
)^(1/2) - a^3*c^2*d^12*f*1422i + 516*a^3*c^3*d^11*f - a^3*c^4*d^10*f*274i - 112*a^3*c^5*d^9*f - a^3*c^6*d^8*f*
294i - 68*a^3*c^7*d^7*f - a^3*c^8*d^6*f*94i - 36*a^3*c^9*d^5*f - a^3*c^10*d^4*f*12i - 8*a^3*c^11*d^3*f - 1012*
a^3*c*d^13*f)*((c*d^10*140i - 140*d^11 - 35*c^2*d^9 + c^3*d^8*245i + 280*c^4*d^7 - c^5*d^6*168i - 56*c^6*d^5 +
c^7*d^4*8i - a^6*c^6*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024
+ (119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6
*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) -
(((69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/12
8)*1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a
^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4
+ (197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c
^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 +
(203*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 +
6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(
1/2)*4i + a^6*d^6*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (1
19*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^1
2*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((6
9*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1
i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*
c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (1
97*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d
^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203
*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a
^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)
*4i + 24*a^6*c*d^5*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (
119*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^
12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((
69*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*
1i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12
*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (
197*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*
d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (20
3*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*
a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2
) + 24*a^6*c^5*d*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (11
9*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12
*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69
*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i
)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c
^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (19
7*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^
8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*
c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^
6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)
- a^6*c^2*d^4*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*c
^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^
2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c*
d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/(
a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*
d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*c
^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f
^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^5
*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c
^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*60i
- 80*a^6*c^3*d^3*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (1
19*c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^1
2*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((6
9*c*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1
i)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*
c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (1
97*c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d
^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203
*c^5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a
^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)
+ a^6*c^4*d^2*f^2*(4*(256*d^6 + 256*c^2*d^4)*(((649*c^2*d^14)/1024 - (9*d^16)/64 + (85*c^4*d^12)/1024 + (119*
c^6*d^10)/1024 + (15*c^8*d^8)/1024 - (c^10*d^6)/64 - (c^12*d^4)/256)/(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c
^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8*d^4*f^4 + 6*a^12*c^10*d^2*f^4) - (((69*c
*d^15)/128 - (55*c^3*d^13)/512 + (57*c^5*d^11)/256 + (61*c^7*d^9)/512 + (5*c^9*d^7)/128 + (c^11*d^5)/128)*1i)/
(a^12*c^12*f^4 + a^12*d^12*f^4 + 6*a^12*c^2*d^10*f^4 + 15*a^12*c^4*d^8*f^4 + 20*a^12*c^6*d^6*f^4 + 15*a^12*c^8
*d^4*f^4 + 6*a^12*c^10*d^2*f^4)) + ((((1225*c^2*d^15)/4 - 35*d^17 + (35*c^4*d^13)/4 + (427*c^6*d^11)/4 + (197*
c^8*d^9)/4 + 12*c^10*d^7 + 2*c^12*d^5)*1i)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*c^2*d^10*f^2 + 15*a^6*c^4*d^8*
f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2) + (175*c*d^16 - (735*c^3*d^14)/4 + (203*c^
5*d^12)/4 + (83*c^7*d^10)/4 + (85*c^9*d^8)/4 + 12*c^11*d^6 + 2*c^13*d^4)/(a^6*c^12*f^2 + a^6*d^12*f^2 + 6*a^6*
c^2*d^10*f^2 + 15*a^6*c^4*d^8*f^2 + 20*a^6*c^6*d^6*f^2 + 15*a^6*c^8*d^4*f^2 + 6*a^6*c^10*d^2*f^2))^2)^(1/2)*60
i)/(2048*(d^6 + c^2*d^4)*(a^6*d^6*f^2*1i - a^6*c^6*f^2*1i + 6*a^6*c*d^5*f^2 + 6*a^6*c^5*d*f^2 - a^6*c^2*d^4*f^
2*15i - 20*a^6*c^3*d^3*f^2 + a^6*c^4*d^2*f^2*15i)))^(1/2) - log(((c + d*tan(e + f*x))^(1/2)*(4736*a^6*d^14*f^2
+ a^6*c*d^13*f^2*17664i - 20000*a^6*c^2*d^12*f^2 - a^6*c^3*d^11*f^2*3520i - 800*a^6*c^4*d^10*f^2 + a^6*c^5*d^
9*f^2*7296i - 1248*a^6*c^6*d^8*f^2 + a^6*c^7*d^7*f^2*3904i + 1440*a^6*c^8*d^6*f^2 + a^6*c^9*d^5*f^2*1280i + 12
80*a^6*c^10*d^4*f^2 + a^6*c^11*d^3*f^2*256i + 256*a^6*c^12*d^2*f^2) - (-(700*c*d^16 - d^17*140i + c^2*d^15*122
5i - 735*c^3*d^14 + c^4*d^13*35i + 203*c^5*d^12 + c^6*d^11*427i + 83*c^7*d^10 + c^8*d^9*197i + 85*c^9*d^8 + c^
10*d^7*48i + 48*c^11*d^6 + c^12*d^5*8i + 8*c^13*d^4 - 4*a^6*c^12*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c
^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849
497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 4
0999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a
^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^
4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 +
3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) - 4*a^6*d^12*f^2*(-(c*d^33*204
832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d
^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12
*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^
16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18
*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4
+ 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) -
24*a^6*c^2*d^10*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 +
c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24
+ c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18
+ c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*
c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^
12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 +
192*a^12*c^22*d^2*f^4))^(1/2) - 60*a^6*c^4*d^8*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^3
1*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^
9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 +
c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 19
2*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^
10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^
6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) - 80*a^6*c^6*d^6*f^2*(-(c*d^33*204832i + 21904*
d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^2
7*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*
d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*
c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a
^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*
c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) - 60*a^6*c^8*d^
4*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*19853
90i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*1
45560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5
390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 +
3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672
*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22
*d^2*f^4))^(1/2) - 24*a^6*c^10*d^2*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i +
2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562
i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*305
48i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^
22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 +
14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*
a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2))/(2048*a^6*d^18*f^2 + 14336*a^6*c^2*d^16*f^2 + 43008*a^6*c^4
*d^14*f^2 + 71680*a^6*c^6*d^12*f^2 + 71680*a^6*c^8*d^10*f^2 + 43008*a^6*c^10*d^8*f^2 + 14336*a^6*c^12*d^6*f^2
+ 2048*a^6*c^14*d^4*f^2))^(1/2)*(14336*a^9*d^15*f^3 - (-(700*c*d^16 - d^17*140i + c^2*d^15*1225i - 735*c^3*d^1
4 + c^4*d^13*35i + 203*c^5*d^12 + c^6*d^11*427i + 83*c^7*d^10 + c^8*d^9*197i + 85*c^9*d^8 + c^10*d^7*48i + 48*
c^11*d^6 + c^12*d^5*8i + 8*c^13*d^4 - 4*a^6*c^12*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^
31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c
^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 +
c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 1
92*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c
^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d
^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) - 4*a^6*d^12*f^2*(-(c*d^33*204832i + 21904*d^3
4 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*7
20812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^2
1*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^2
4*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12
*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^1
6*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) - 24*a^6*c^2*d^10*
f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390
i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145
560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*539
0i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3
520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a
^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d
^2*f^4))^(1/2) - 60*a^6*c^4*d^8*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 249
4161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i +
56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i
+ 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*
f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14
784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^1
2*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) - 80*a^6*c^6*d^6*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^
2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 8494
97*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40
999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^
12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4
+ 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3
520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) - 60*a^6*c^8*d^4*f^2*(-(c*d^33*
204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^
6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c
^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18
*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d
^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*
f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2)
- 24*a^6*c^10*d^2*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30
+ c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d
^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d
^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^
12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12
*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^
4 + 192*a^12*c^22*d^2*f^4))^(1/2))/(2048*a^6*d^18*f^2 + 14336*a^6*c^2*d^16*f^2 + 43008*a^6*c^4*d^14*f^2 + 7168
0*a^6*c^6*d^12*f^2 + 71680*a^6*c^8*d^10*f^2 + 43008*a^6*c^10*d^8*f^2 + 14336*a^6*c^12*d^6*f^2 + 2048*a^6*c^14*
d^4*f^2))^(1/2)*(c + d*tan(e + f*x))^(1/2)*(65536*a^12*c*d^14*f^4 + 393216*a^12*c^3*d^12*f^4 + 983040*a^12*c^5
*d^10*f^4 + 1310720*a^12*c^7*d^8*f^4 + 983040*a^12*c^9*d^6*f^4 + 393216*a^12*c^11*d^4*f^4 + 65536*a^12*c^13*d^
2*f^4) + a^9*c*d^14*f^3*33792i + 20480*a^9*c^2*d^13*f^3 + a^9*c^3*d^12*f^3*95232i - 18432*a^9*c^4*d^11*f^3 + a
^9*c^5*d^10*f^3*83968i - 32768*a^9*c^6*d^9*f^3 + a^9*c^7*d^8*f^3*18432i + 2048*a^9*c^8*d^7*f^3 - a^9*c^9*d^6*f
^3*3072i + 12288*a^9*c^10*d^5*f^3 + a^9*c^11*d^4*f^3*1024i + 2048*a^9*c^12*d^3*f^3))*(-(700*c*d^16 - d^17*140i
+ c^2*d^15*1225i - 735*c^3*d^14 + c^4*d^13*35i + 203*c^5*d^12 + c^6*d^11*427i + 83*c^7*d^10 + c^8*d^9*197i +
85*c^9*d^8 + c^10*d^7*48i + 48*c^11*d^6 + c^12*d^5*8i + 8*c^13*d^4 - 4*a^6*c^12*f^2*(-(c*d^33*204832i + 21904*
d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^2
7*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*
d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*
c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a
^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*
c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) - 4*a^6*d^12*f^
2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i
- 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*14556
0i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i
- 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 352
0*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^1
2*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2
*f^4))^(1/2) - 24*a^6*c^2*d^10*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494
161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i +
56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i
+ 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f
^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 147
84*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12
*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) - 60*a^6*c^4*d^8*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2
*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 84949
7*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 409
99*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^1
2*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4
+ 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 35
20*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) - 80*a^6*c^6*d^6*f^2*(-(c*d^33*2
04832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6
*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^
12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*
d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^
18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f
^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2)
- 60*a^6*c^8*d^4*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 +
c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^2
4 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^1
8 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12
*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d
^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4
+ 192*a^12*c^22*d^2*f^4))^(1/2) - 24*a^6*c^10*d^2*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d
^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 +
c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20
+ c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 +
192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*
c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*
d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2))/(2048*a^6*d^18*f^2 + 14336*a^6*c^2*d^16*f^2
+ 43008*a^6*c^4*d^14*f^2 + 71680*a^6*c^6*d^12*f^2 + 71680*a^6*c^8*d^10*f^2 + 43008*a^6*c^10*d^8*f^2 + 14336*a^
6*c^12*d^6*f^2 + 2048*a^6*c^14*d^4*f^2))^(1/2) + a^3*d^14*f*240i - a^3*c^2*d^12*f*1422i + 516*a^3*c^3*d^11*f -
a^3*c^4*d^10*f*274i - 112*a^3*c^5*d^9*f - a^3*c^6*d^8*f*294i - 68*a^3*c^7*d^7*f - a^3*c^8*d^6*f*94i - 36*a^3*
c^9*d^5*f - a^3*c^10*d^4*f*12i - 8*a^3*c^11*d^3*f - 1012*a^3*c*d^13*f)*(-(700*c*d^16 - d^17*140i + c^2*d^15*12
25i - 735*c^3*d^14 + c^4*d^13*35i + 203*c^5*d^12 + c^6*d^11*427i + 83*c^7*d^10 + c^8*d^9*197i + 85*c^9*d^8 + c
^10*d^7*48i + 48*c^11*d^6 + c^12*d^5*8i + 8*c^13*d^4 - 4*a^6*c^12*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*
c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 84
9497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i +
40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*
a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f
^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 +
3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) - 4*a^6*d^12*f^2*(-(c*d^33*20
4832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*
d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^1
2*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d
^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^1
8*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^
4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) -
24*a^6*c^2*d^10*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 +
c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^2
4 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^1
8 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12
*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d
^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4
+ 192*a^12*c^22*d^2*f^4))^(1/2) - 60*a^6*c^4*d^8*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^
31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c
^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 +
c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 1
92*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c
^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d
^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) - 80*a^6*c^6*d^6*f^2*(-(c*d^33*204832i + 21904
*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^
27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13
*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12
*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*
a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12
*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) - 60*a^6*c^8*d
^4*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985
390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*
145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*
5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4
+ 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 1267
2*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^2
2*d^2*f^4))^(1/2) - 24*a^6*c^10*d^2*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i +
2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*49656
2i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30
548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d
^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4
+ 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056
*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2))/(2048*a^6*d^18*f^2 + 14336*a^6*c^2*d^16*f^2 + 43008*a^6*c^
4*d^14*f^2 + 71680*a^6*c^6*d^12*f^2 + 71680*a^6*c^8*d^10*f^2 + 43008*a^6*c^10*d^8*f^2 + 14336*a^6*c^12*d^6*f^2
+ 2048*a^6*c^14*d^4*f^2))^(1/2) - log(((c + d*tan(e + f*x))^(1/2)*(4736*a^6*d^14*f^2 + a^6*c*d^13*f^2*17664i
- 20000*a^6*c^2*d^12*f^2 - a^6*c^3*d^11*f^2*3520i - 800*a^6*c^4*d^10*f^2 + a^6*c^5*d^9*f^2*7296i - 1248*a^6*c^
6*d^8*f^2 + a^6*c^7*d^7*f^2*3904i + 1440*a^6*c^8*d^6*f^2 + a^6*c^9*d^5*f^2*1280i + 1280*a^6*c^10*d^4*f^2 + a^6
*c^11*d^3*f^2*256i + 256*a^6*c^12*d^2*f^2) - (-(700*c*d^16 - d^17*140i + c^2*d^15*1225i - 735*c^3*d^14 + c^4*d
^13*35i + 203*c^5*d^12 + c^6*d^11*427i + 83*c^7*d^10 + c^8*d^9*197i + 85*c^9*d^8 + c^10*d^7*48i + 48*c^11*d^6
+ c^12*d^5*8i + 8*c^13*d^4 + 4*a^6*c^12*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*186073
6i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*4
96562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^1
9*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c
^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*
f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 +
1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 4*a^6*d^12*f^2*(-(c*d^33*204832i + 21904*d^34 - 82725
6*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i +
849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i
+ 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 1
6*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16
*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4
+ 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 24*a^6*c^2*d^10*f^2*(-(c*
d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 10070
83*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16
171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225
*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*
c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*
d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^
(1/2) + 60*a^6*c^4*d^8*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*
d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^
10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^
16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 105
6*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*
c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^
4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 80*a^6*c^6*d^6*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 -
c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^
26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*
d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f
^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*
a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*
c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 60*a^6*c^8*d^4*f^2*(-(c*d^33*204832i +
21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 -
c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22
+ c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(1
6*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 +
7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 792
0*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 24*a^6
*c^10*d^2*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^
29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^1
1*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^1
7*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^
20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4
+ 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a
^12*c^22*d^2*f^4))^(1/2))/(2048*a^6*d^18*f^2 + 14336*a^6*c^2*d^16*f^2 + 43008*a^6*c^4*d^14*f^2 + 71680*a^6*c^6
*d^12*f^2 + 71680*a^6*c^8*d^10*f^2 + 43008*a^6*c^10*d^8*f^2 + 14336*a^6*c^12*d^6*f^2 + 2048*a^6*c^14*d^4*f^2))
^(1/2)*(14336*a^9*d^15*f^3 - (-(700*c*d^16 - d^17*140i + c^2*d^15*1225i - 735*c^3*d^14 + c^4*d^13*35i + 203*c^
5*d^12 + c^6*d^11*427i + 83*c^7*d^10 + c^8*d^9*197i + 85*c^9*d^8 + c^10*d^7*48i + 48*c^11*d^6 + c^12*d^5*8i +
8*c^13*d^4 + 4*a^6*c^12*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4
*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c
^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c
^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 10
56*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12
*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d
^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 4*a^6*d^12*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3
*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26
+ c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^2
0 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4
+ 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^1
2*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^1
8*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 24*a^6*c^2*d^10*f^2*(-(c*d^33*204832i + 2
1904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^
7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 +
c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*
a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7
920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*
a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 60*a^6*c
^4*d^8*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*
1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d
^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d
^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*
f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 +
12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12
*c^22*d^2*f^4))^(1/2) + 80*a^6*c^6*d^6*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736
i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*49
6562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19
*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^
2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f
^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1
056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 60*a^6*c^8*d^4*f^2*(-(c*d^33*204832i + 21904*d^34 - 82
7256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i
+ 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*2238
6i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4
+ 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d
^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*
f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 24*a^6*c^10*d^2*f^2*(-
(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 10
07083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i +
16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1
225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^
12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^
14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4
))^(1/2))/(2048*a^6*d^18*f^2 + 14336*a^6*c^2*d^16*f^2 + 43008*a^6*c^4*d^14*f^2 + 71680*a^6*c^6*d^12*f^2 + 7168
0*a^6*c^8*d^10*f^2 + 43008*a^6*c^10*d^8*f^2 + 14336*a^6*c^12*d^6*f^2 + 2048*a^6*c^14*d^4*f^2))^(1/2)*(c + d*ta
n(e + f*x))^(1/2)*(65536*a^12*c*d^14*f^4 + 393216*a^12*c^3*d^12*f^4 + 983040*a^12*c^5*d^10*f^4 + 1310720*a^12*
c^7*d^8*f^4 + 983040*a^12*c^9*d^6*f^4 + 393216*a^12*c^11*d^4*f^4 + 65536*a^12*c^13*d^2*f^4) + a^9*c*d^14*f^3*3
3792i + 20480*a^9*c^2*d^13*f^3 + a^9*c^3*d^12*f^3*95232i - 18432*a^9*c^4*d^11*f^3 + a^9*c^5*d^10*f^3*83968i -
32768*a^9*c^6*d^9*f^3 + a^9*c^7*d^8*f^3*18432i + 2048*a^9*c^8*d^7*f^3 - a^9*c^9*d^6*f^3*3072i + 12288*a^9*c^10
*d^5*f^3 + a^9*c^11*d^4*f^3*1024i + 2048*a^9*c^12*d^3*f^3))*(-(700*c*d^16 - d^17*140i + c^2*d^15*1225i - 735*c
^3*d^14 + c^4*d^13*35i + 203*c^5*d^12 + c^6*d^11*427i + 83*c^7*d^10 + c^8*d^9*197i + 85*c^9*d^8 + c^10*d^7*48i
+ 48*c^11*d^6 + c^12*d^5*8i + 8*c^13*d^4 + 4*a^6*c^12*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 -
c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^
26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*
d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f
^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*
a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*
c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 4*a^6*d^12*f^2*(-(c*d^33*204832i + 219
04*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*
d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^
13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^
12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 792
0*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^
12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 24*a^6*c^2
*d^10*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1
985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^
23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^
17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f
^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 1
2672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*
c^22*d^2*f^4))^(1/2) + 60*a^6*c^4*d^8*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i
+ 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496
562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*
30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2
*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^
4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 10
56*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 80*a^6*c^6*d^6*f^2*(-(c*d^33*204832i + 21904*d^34 - 827
256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i
+ 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386
i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 +
16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^
16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f
^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 60*a^6*c^8*d^4*f^2*(-(c
*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007
083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 1
6171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 122
5*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12
*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14
*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))
^(1/2) + 24*a^6*c^10*d^2*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^
4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*
c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*
c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1
056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^1
2*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*
d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2))/(2048*a^6*d^18*f^2 + 14336*a^6*c^2*d^16*f^2 + 43008*a^6*c^4*d^14*f^2
+ 71680*a^6*c^6*d^12*f^2 + 71680*a^6*c^8*d^10*f^2 + 43008*a^6*c^10*d^8*f^2 + 14336*a^6*c^12*d^6*f^2 + 2048*a^6
*c^14*d^4*f^2))^(1/2) + a^3*d^14*f*240i - a^3*c^2*d^12*f*1422i + 516*a^3*c^3*d^11*f - a^3*c^4*d^10*f*274i - 11
2*a^3*c^5*d^9*f - a^3*c^6*d^8*f*294i - 68*a^3*c^7*d^7*f - a^3*c^8*d^6*f*94i - 36*a^3*c^9*d^5*f - a^3*c^10*d^4*
f*12i - 8*a^3*c^11*d^3*f - 1012*a^3*c*d^13*f)*(-(700*c*d^16 - d^17*140i + c^2*d^15*1225i - 735*c^3*d^14 + c^4*
d^13*35i + 203*c^5*d^12 + c^6*d^11*427i + 83*c^7*d^10 + c^8*d^9*197i + 85*c^9*d^8 + c^10*d^7*48i + 48*c^11*d^6
+ c^12*d^5*8i + 8*c^13*d^4 + 4*a^6*c^12*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*18607
36i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*
496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^
19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*
c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14
*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 +
1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 4*a^6*d^12*f^2*(-(c*d^33*204832i + 21904*d^34 - 8272
56*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i +
849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i
+ 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 +
16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^1
6*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^
4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 24*a^6*c^2*d^10*f^2*(-(c
*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007
083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 1
6171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 122
5*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12
*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14
*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))
^(1/2) + 60*a^6*c^4*d^8*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4
*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c
^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c
^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 10
56*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12
*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d
^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 80*a^6*c^6*d^6*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 -
c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d
^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14
*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*
f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672
*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12
*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 60*a^6*c^8*d^4*f^2*(-(c*d^33*204832i
+ 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d^29*1985390i - 1007083*c^6*d^28 -
c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^11*d^23*145560i + 16171*c^12*d^22
+ c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^17*d^17*5390i - 1225*c^18*d^16)/(
16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d^20*f^4 + 3520*a^12*c^6*d^18*f^4
+ 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^4 + 12672*a^12*c^14*d^10*f^4 + 79
20*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*a^12*c^22*d^2*f^4))^(1/2) + 24*a^
6*c^10*d^2*f^2*(-(c*d^33*204832i + 21904*d^34 - 827256*c^2*d^32 - c^3*d^31*1860736i + 2494161*c^4*d^30 + c^5*d
^29*1985390i - 1007083*c^6*d^28 - c^7*d^27*720812i + 849497*c^8*d^26 + c^9*d^25*496562i + 56837*c^10*d^24 + c^
11*d^23*145560i + 16171*c^12*d^22 + c^13*d^21*22386i + 40999*c^14*d^20 + c^15*d^19*30548i + 539*c^16*d^18 + c^
17*d^17*5390i - 1225*c^18*d^16)/(16*a^12*c^24*f^4 + 16*a^12*d^24*f^4 + 192*a^12*c^2*d^22*f^4 + 1056*a^12*c^4*d
^20*f^4 + 3520*a^12*c^6*d^18*f^4 + 7920*a^12*c^8*d^16*f^4 + 12672*a^12*c^10*d^14*f^4 + 14784*a^12*c^12*d^12*f^
4 + 12672*a^12*c^14*d^10*f^4 + 7920*a^12*c^16*d^8*f^4 + 3520*a^12*c^18*d^6*f^4 + 1056*a^12*c^20*d^4*f^4 + 192*
a^12*c^22*d^2*f^4))^(1/2))/(2048*a^6*d^18*f^2 + 14336*a^6*c^2*d^16*f^2 + 43008*a^6*c^4*d^14*f^2 + 71680*a^6*c^
6*d^12*f^2 + 71680*a^6*c^8*d^10*f^2 + 43008*a^6*c^10*d^8*f^2 + 14336*a^6*c^12*d^6*f^2 + 2048*a^6*c^14*d^4*f^2)
)^(1/2) + (((c + d*tan(e + f*x))^(3/2)*(c*d^2*48i + 12*c^2*d - 76*d^3)*1i)/(48*a^3*f*(2*c*d - c^2*1i + d^2*1i)
) - ((c + d*tan(e + f*x))^(1/2)*(45*c*d^2 - c^2*d*10i + d^3*90i))/(80*a^3*f*(c*1i - d)) + (d*(c + d*tan(e + f*
x))^(5/2)*(c*d*7i + 2*c^2 - 10*d^2))/(16*a^3*f*(c*1i - d)*(2*c*d - c^2*1i + d^2*1i)))/((c + d*tan(e + f*x))*(c
*d*6i + 3*c^2 - 3*d^2) + (c + d*tan(e + f*x))^3 + 3*c*d^2 - c^2*d*3i - (3*c + d*3i)*(c + d*tan(e + f*x))^2 - c
^3 + d^3*1i)