\(\int \frac {(c+d \tan (e+f x))^{5/2}}{(a+b \tan (e+f x))^2} \, dx\) [1245]

Optimal result

Integrand size = 27, antiderivative size = 243 \[ \int \frac {(c+d \tan (e+f x))^{5/2}}{(a+b \tan (e+f x))^2} \, dx=-\frac {i (c-i d)^{5/2} \text {arctanh}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{(a-i b)^2 f}+\frac {i (c+i d)^{5/2} \text {arctanh}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{(a+i b)^2 f}-\frac {(b c-a d)^{3/2} \left (4 a b c+a^2 d+5 b^2 d\right ) \text {arctanh}\left (\frac {\sqrt {b} \sqrt {c+d \tan (e+f x)}}{\sqrt {b c-a d}}\right )}{b^{3/2} \left (a^2+b^2\right )^2 f}-\frac {(b c-a d)^2 \sqrt {c+d \tan (e+f x)}}{b \left (a^2+b^2\right ) f (a+b \tan (e+f x))} \]

[Out]

-I*(c-I*d)^(5/2)*arctanh((c+d*tan(f*x+e))^(1/2)/(c-I*d)^(1/2))/(a-I*b)^2/f+I*(c+I*d)^(5/2)*arctanh((c+d*tan(f*
x+e))^(1/2)/(c+I*d)^(1/2))/(a+I*b)^2/f-(-a*d+b*c)^(3/2)*(a^2*d+4*a*b*c+5*b^2*d)*arctanh(b^(1/2)*(c+d*tan(f*x+e
))^(1/2)/(-a*d+b*c)^(1/2))/b^(3/2)/(a^2+b^2)^2/f-(-a*d+b*c)^2*(c+d*tan(f*x+e))^(1/2)/b/(a^2+b^2)/f/(a+b*tan(f*
x+e))

Rubi [A] (verified)

Time = 1.26 (sec) , antiderivative size = 243, normalized size of antiderivative = 1.00, number of steps used = 12, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.259, Rules used = {3646, 3734, 3620, 3618, 65, 214, 3715} \[ \int \frac {(c+d \tan (e+f x))^{5/2}}{(a+b \tan (e+f x))^2} \, dx=-\frac {(b c-a d)^{3/2} \left (a^2 d+4 a b c+5 b^2 d\right ) \text {arctanh}\left (\frac {\sqrt {b} \sqrt {c+d \tan (e+f x)}}{\sqrt {b c-a d}}\right )}{b^{3/2} f \left (a^2+b^2\right )^2}-\frac {(b c-a d)^2 \sqrt {c+d \tan (e+f x)}}{b f \left (a^2+b^2\right ) (a+b \tan (e+f x))}-\frac {i (c-i d)^{5/2} \text {arctanh}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{f (a-i b)^2}+\frac {i (c+i d)^{5/2} \text {arctanh}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{f (a+i b)^2} \]

[In]

Int[(c + d*Tan[e + f*x])^(5/2)/(a + b*Tan[e + f*x])^2,x]

[Out]

((-I)*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)^2*f) + (I*(c + I*d)^(5/2)*Ar
cTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)^2*f) - ((b*c - a*d)^(3/2)*(4*a*b*c + a^2*d + 5*b^2*d
)*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(b^(3/2)*(a^2 + b^2)^2*f) - ((b*c - a*d)^2*Sqrt
[c + d*Tan[e + f*x]])/(b*(a^2 + b^2)*f*(a + b*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 3646

Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_)*((c_.) + (d_.)*tan[(e_.) + (f_.)*(x_)])^(n_), x_Symbol] :> Si
mp[(b*c - a*d)^2*(a + b*Tan[e + f*x])^(m - 2)*((c + d*Tan[e + f*x])^(n + 1)/(d*f*(n + 1)*(c^2 + d^2))), x] - D
ist[1/(d*(n + 1)*(c^2 + d^2)), Int[(a + b*Tan[e + f*x])^(m - 3)*(c + d*Tan[e + f*x])^(n + 1)*Simp[a^2*d*(b*d*(
m - 2) - a*c*(n + 1)) + b*(b*c - 2*a*d)*(b*c*(m - 2) + a*d*(n + 1)) - d*(n + 1)*(3*a^2*b*c - b^3*c - a^3*d + 3
*a*b^2*d)*Tan[e + f*x] - b*(a*d*(2*b*c - a*d)*(m + n - 1) - b^2*(c^2*(m - 2) - d^2*(n + 1)))*Tan[e + f*x]^2, x
], x], x] /; FreeQ[{a, b, c, d, e, f}, x] && NeQ[b*c - a*d, 0] && NeQ[a^2 + b^2, 0] && NeQ[c^2 + d^2, 0] && Gt
Q[m, 2] && LtQ[n, -1] && IntegerQ[2*m]

Rule 3715

Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_.)*((c_.) + (d_.)*tan[(e_.) + (f_.)*(x_)])^(n_.)*((A_) + (C_.)*
tan[(e_.) + (f_.)*(x_)]^2), x_Symbol] :> Dist[A/f, Subst[Int[(a + b*x)^m*(c + d*x)^n, x], x, Tan[e + f*x]], x]
/; FreeQ[{a, b, c, d, e, f, A, C, m, n}, x] && EqQ[A, C]

Rule 3734

Int[(((c_.) + (d_.)*tan[(e_.) + (f_.)*(x_)])^(n_)*((A_.) + (B_.)*tan[(e_.) + (f_.)*(x_)] + (C_.)*tan[(e_.) + (
f_.)*(x_)]^2))/((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)]), x_Symbol] :> Dist[1/(a^2 + b^2), Int[(c + d*Tan[e + f*
x])^n*Simp[b*B + a*(A - C) + (a*B - b*(A - C))*Tan[e + f*x], x], x], x] + Dist[(A*b^2 - a*b*B + a^2*C)/(a^2 +
b^2), Int[(c + d*Tan[e + f*x])^n*((1 + Tan[e + f*x]^2)/(a + b*Tan[e + f*x])), x], x] /; FreeQ[{a, b, c, d, e,
f, A, B, C, n}, x] && NeQ[b*c - a*d, 0] && NeQ[a^2 + b^2, 0] && NeQ[c^2 + d^2, 0] &&  !GtQ[n, 0] &&  !LeQ[n, -
1]

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

Mathematica [A] (verified)

Time = 5.24 (sec) , antiderivative size = 333, normalized size of antiderivative = 1.37 \[ \int \frac {(c+d \tan (e+f x))^{5/2}}{(a+b \tan (e+f x))^2} \, dx=\frac {-\frac {i (a+i b)^2 b^{3/2} (c-i d)^{5/2} (b c-a d) \text {arctanh}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )+i b^{3/2} (i a+b)^2 (c+i d)^{5/2} (b c-a d) \text {arctanh}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )+(b c-a d)^{5/2} \left (4 a b c+a^2 d+5 b^2 d\right ) \text {arctanh}\left (\frac {\sqrt {b} \sqrt {c+d \tan (e+f x)}}{\sqrt {b c-a d}}\right )}{b^{3/2} \left (a^2+b^2\right )}+\frac {d (b c-a d)^2 \sqrt {c+d \tan (e+f x)}}{b}+d (b c-a d) (c+d \tan (e+f x))^{3/2}+b d (c+d \tan (e+f x))^{5/2}-\frac {b^2 (c+d \tan (e+f x))^{7/2}}{a+b \tan (e+f x)}}{\left (a^2+b^2\right ) (b c-a d) f} \]

[In]

Integrate[(c + d*Tan[e + f*x])^(5/2)/(a + b*Tan[e + f*x])^2,x]

[Out]

(-((I*(a + I*b)^2*b^(3/2)*(c - I*d)^(5/2)*(b*c - a*d)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]] + I*b^(3
/2)*(I*a + b)^2*(c + I*d)^(5/2)*(b*c - a*d)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]] + (b*c - a*d)^(5/2
)*(4*a*b*c + a^2*d + 5*b^2*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(b^(3/2)*(a^2 + b^2
))) + (d*(b*c - a*d)^2*Sqrt[c + d*Tan[e + f*x]])/b + d*(b*c - a*d)*(c + d*Tan[e + f*x])^(3/2) + b*d*(c + d*Tan
[e + f*x])^(5/2) - (b^2*(c + d*Tan[e + f*x])^(7/2))/(a + b*Tan[e + f*x]))/((a^2 + b^2)*(b*c - a*d)*f)

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(4576\) vs. \(2(211)=422\).

Time = 0.90 (sec) , antiderivative size = 4577, normalized size of antiderivative = 18.84

method	result	size
derivativedivides	\(\text {Expression too large to display}\)	\(4577\)
default	\(\text {Expression too large to display}\)	\(4577\)

[In]

int((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^2,x,method=_RETURNVERBOSE)

[Out]

1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2
*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2*c^2-2/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*
(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2*c-7/f
*d/(a^2+b^2)^2*b/((a*d-b*c)*b)^(1/2)*arctan(b*(c+d*tan(f*x+e))^(1/2)/((a*d-b*c)*b)^(1/2))*a^2*c^2-10/f*d^2/(a^
2+b^2)^2*b^2/((a*d-b*c)*b)^(1/2)*arctan(b*(c+d*tan(f*x+e))^(1/2)/((a*d-b*c)*b)^(1/2))*a*c+1/4/f/d/(a^2+b^2)^2*
ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c
)^(1/2)*(c^2+d^2)^(1/2)*a^2*c^2-1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2
)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2*c^2+2/f/(a^2+b^2)^2/(2*(c^2+d^
2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1
/2))*(c^2+d^2)^(1/2)*a*b*c^2+1/f/(a^2+b^2)^2*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^
(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b*c+2/f/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-
2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2
+d^2)^(1/2)*a*b*c^2-1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)
+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2*c^2+6/f*d^2/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)
-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b
*c+2/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1
/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^2*c+6/f*d^2/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*ar
ctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c+2/f*d/(a^2+
b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d
^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*b^2*c-1/f*d/(a^2+b^2)^2*b*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+a*d)*a^
2*c^2+2/f*d^2/(a^2+b^2)^2*b^2*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+a*d)*a*c-2/f*d^2/(a^2+b^2)^2/(2*(c^2+d^2)
^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2
))*(c^2+d^2)^(1/2)*a*b-2/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^
2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*(c^2+d^2)^(1/2)*a^2*c-2/f*d^2/(a^2+b^2)^2/(2*(c^2+d^2)
^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2
))*(c^2+d^2)^(1/2)*a*b-1/f/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+
(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a*b*c+3/2/f/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*
tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b*c^2-2/f/(a^
2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2
+d^2)^(1/2)-2*c)^(1/2))*a*b*c^3+4/f/(a^2+b^2)^2/((a*d-b*c)*b)^(1/2)*arctan(b*(c+d*tan(f*x+e))^(1/2)/((a*d-b*c)
*b)^(1/2))*a*c^3*b^2-2/f/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^
2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a*b*c^3-1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x
+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c^3+3/f*d/(a^2+b^2
)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)
^(1/2)-2*c)^(1/2))*a^2*c^2-1/f*d^3/(a^2+b^2)^2*b*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+a*d)*a^2-1/f*d/(a^2+b^
2)^2*b^3*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+a*d)*c^2-3/2/f/(a^2+b^2)^2*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^
(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*b*c^2-1/f*d^3/(a^2+b^2)^2
/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1
/2)-2*c)^(1/2))*a^2+1/f*d^3/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2
+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2-1/f*d^3/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*a
rctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2+1/f*d^3/(a^2
+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+
d^2)^(1/2)-2*c)^(1/2))*b^2+2/f*d^2/(a^2+b^2)^2*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+a*d)*a^3*c+1/4/f/d/(a^2+
b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1
/2)+2*c)^(1/2)*a^2*c^3+3/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^
2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*a^2*c^2+1/4/f*d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan
(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^
2-1/4/f*d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*
(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2-3/4/f*d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)
*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c-1/2/f*d^2/(a^2+b^2)^2*ln(d
*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1
/2)*a*b+3/4/f*d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c+(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(
1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c+1/f*d^3/(a^2+b^2)^2/b/((a*d-b*c)*b)^(1/2)*arctan(b*(c+d*tan(f*x+e))^
(1/2)/((a*d-b*c)*b)^(1/2))*a^4+2/f*d^2/(a^2+b^2)^2/((a*d-b*c)*b)^(1/2)*arctan(b*(c+d*tan(f*x+e))^(1/2)/((a*d-b
*c)*b)^(1/2))*a^3*c-3/f*d/(a^2+b^2)^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)-(2*(c^2+d
^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*b^2*c^2-1/4/f*d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c-(c+d*tan(f*
x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a^2-3
/4/f*d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*
(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c+5/f*d^3/(a^2+b^2)^2*b/((a*d-b*c)*b)^(1/2)*arctan(b*(c+d*tan(f*x+e))^(1/2)/((a
*d-b*c)*b)^(1/2))*a^2+5/f*d/(a^2+b^2)^2*b^3/((a*d-b*c)*b)^(1/2)*arctan(b*(c+d*tan(f*x+e))^(1/2)/((a*d-b*c)*b)^
(1/2))*c^2-1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2
)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c^3+1/4/f/d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2
*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b^2*c^3+1/2/f*d^2/(a^2+b^2)^2*ln(d*
tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/
2)*a*b+1/4/f*d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1
/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b^2+3/4/f*d/(a^2+b^2)^2*ln(d*tan(f*x+e)+c-(c+d*tan(f*x+e))^
(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a^2*c-3/f*d/(a^2+b^2)^2/(2*
(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(c+d*tan(f*x+e))^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-
2*c)^(1/2))*b^2*c^2-1/f*d^3/(a^2+b^2)^2/b*(c+d*tan(f*x+e))^(1/2)/(tan(f*x+e)*b*d+a*d)*a^4

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 9974 vs. \(2 (203) = 406\).

Time = 123.10 (sec) , antiderivative size = 19967, normalized size of antiderivative = 82.17 \[ \int \frac {(c+d \tan (e+f x))^{5/2}}{(a+b \tan (e+f x))^2} \, dx=\text {Too large to display} \]

[In]

integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^2,x, algorithm="fricas")

[Out]

Too large to include

Sympy [F]

\[ \int \frac {(c+d \tan (e+f x))^{5/2}}{(a+b \tan (e+f x))^2} \, dx=\int \frac {\left (c + d \tan {\left (e + f x \right )}\right )^{\frac {5}{2}}}{\left (a + b \tan {\left (e + f x \right )}\right )^{2}}\, dx \]

[In]

integrate((c+d*tan(f*x+e))**(5/2)/(a+b*tan(f*x+e))**2,x)

[Out]

Integral((c + d*tan(e + f*x))**(5/2)/(a + b*tan(e + f*x))**2, x)

Maxima [F(-2)]

Exception generated. \[ \int \frac {(c+d \tan (e+f x))^{5/2}}{(a+b \tan (e+f x))^2} \, dx=\text {Exception raised: ValueError} \]

[In]

integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^2,x, algorithm="maxima")

[Out]

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

Giac [F(-1)]

Timed out. \[ \int \frac {(c+d \tan (e+f x))^{5/2}}{(a+b \tan (e+f x))^2} \, dx=\text {Timed out} \]

[In]

integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^2,x, algorithm="giac")

[Out]

Timed out

Mupad [B] (verification not implemented)

Time = 19.12 (sec) , antiderivative size = 78132, normalized size of antiderivative = 321.53 \[ \int \frac {(c+d \tan (e+f x))^{5/2}}{(a+b \tan (e+f x))^2} \, dx=\text {Too large to display} \]

[In]

int((c + d*tan(e + f*x))^(5/2)/(a + b*tan(e + f*x))^2,x)

[Out]

- atan(((((8*(4*b^12*c*d^17*f^2 - 16*a^11*b*d^18*f^2 - 8*a^12*c*d^17*f^2 - 4*a*b^11*d^18*f^2 + 304*a^3*b^9*d^1
8*f^2 + 120*a^5*b^7*d^18*f^2 - 320*a^7*b^5*d^18*f^2 - 148*a^9*b^3*d^18*f^2 - 8*a^12*c^3*d^15*f^2 - 400*b^12*c^
3*d^15*f^2 + 176*b^12*c^5*d^13*f^2 + 488*b^12*c^7*d^11*f^2 - 92*b^12*c^9*d^9*f^2 + 6576*a^2*b^10*c^3*d^15*f^2
+ 400*a^2*b^10*c^5*d^13*f^2 - 6144*a^2*b^10*c^7*d^11*f^2 + 1056*a^2*b^10*c^9*d^9*f^2 - 5408*a^3*b^9*c^2*d^16*f
^2 + 3888*a^3*b^9*c^4*d^14*f^2 + 6400*a^3*b^9*c^6*d^12*f^2 - 3072*a^3*b^9*c^8*d^10*f^2 + 128*a^3*b^9*c^10*d^8*
f^2 - 648*a^4*b^8*c^3*d^15*f^2 - 1952*a^4*b^8*c^5*d^13*f^2 + 208*a^4*b^8*c^7*d^11*f^2 + 200*a^4*b^8*c^9*d^9*f^
2 - 4288*a^5*b^7*c^2*d^16*f^2 + 4112*a^5*b^7*c^4*d^14*f^2 + 5120*a^5*b^7*c^6*d^12*f^2 - 3208*a^5*b^7*c^8*d^10*
f^2 + 192*a^5*b^7*c^10*d^8*f^2 - 6688*a^6*b^6*c^3*d^15*f^2 - 2464*a^6*b^6*c^5*d^13*f^2 + 5952*a^6*b^6*c^7*d^11
*f^2 - 960*a^6*b^6*c^9*d^9*f^2 + 2624*a^7*b^5*c^2*d^16*f^2 - 2016*a^7*b^5*c^4*d^14*f^2 - 3456*a^7*b^5*c^6*d^12
*f^2 + 1504*a^7*b^5*c^8*d^10*f^2 + 992*a^8*b^4*c^3*d^15*f^2 - 144*a^8*b^4*c^5*d^13*f^2 - 888*a^8*b^4*c^7*d^11*
f^2 - 12*a^8*b^4*c^9*d^9*f^2 + 352*a^9*b^3*c^2*d^16*f^2 + 520*a^9*b^3*c^4*d^14*f^2 + 32*a^9*b^3*c^6*d^12*f^2 +
12*a^9*b^3*c^8*d^10*f^2 + 48*a^10*b^2*c^3*d^15*f^2 + 144*a^10*b^2*c^5*d^13*f^2 + 1120*a*b^11*c^2*d^16*f^2 - 2
776*a*b^11*c^4*d^14*f^2 - 2208*a*b^11*c^6*d^12*f^2 + 1628*a*b^11*c^8*d^10*f^2 - 64*a*b^11*c^10*d^8*f^2 - 1024*
a^2*b^10*c*d^17*f^2 + 1312*a^4*b^8*c*d^17*f^2 + 2688*a^6*b^6*c*d^17*f^2 + 260*a^8*b^4*c*d^17*f^2 - 96*a^10*b^2
*c*d^17*f^2 - 32*a^11*b*c^2*d^16*f^2 - 16*a^11*b*c^4*d^14*f^2))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b
^5*f^5 + 4*a^6*b^3*f^5) - (((8*(96*a^2*b^14*d^13*f^4 + 480*a^4*b^12*d^13*f^4 + 960*a^6*b^10*d^13*f^4 + 960*a^8
*b^8*d^13*f^4 + 480*a^10*b^6*d^13*f^4 + 96*a^12*b^4*d^13*f^4 + 128*b^16*c^2*d^11*f^4 + 128*b^16*c^4*d^9*f^4 +
640*a^2*b^14*c^2*d^11*f^4 + 544*a^2*b^14*c^4*d^9*f^4 - 768*a^3*b^13*c^3*d^10*f^4 + 320*a^3*b^13*c^5*d^8*f^4 +
1280*a^4*b^12*c^2*d^11*f^4 + 800*a^4*b^12*c^4*d^9*f^4 - 1440*a^5*b^11*c^3*d^10*f^4 + 640*a^5*b^11*c^5*d^8*f^4
+ 1280*a^6*b^10*c^2*d^11*f^4 + 320*a^6*b^10*c^4*d^9*f^4 - 1280*a^7*b^9*c^3*d^10*f^4 + 640*a^7*b^9*c^5*d^8*f^4
+ 640*a^8*b^8*c^2*d^11*f^4 - 320*a^8*b^8*c^4*d^9*f^4 - 480*a^9*b^7*c^3*d^10*f^4 + 320*a^9*b^7*c^5*d^8*f^4 + 12
8*a^10*b^6*c^2*d^11*f^4 - 352*a^10*b^6*c^4*d^9*f^4 + 64*a^11*b^5*c^5*d^8*f^4 - 96*a^12*b^4*c^4*d^9*f^4 + 32*a^
13*b^3*c^3*d^10*f^4 - 224*a*b^15*c*d^12*f^4 - 160*a*b^15*c^3*d^10*f^4 + 64*a*b^15*c^5*d^8*f^4 - 1088*a^3*b^13*
c*d^12*f^4 - 2080*a^5*b^11*c*d^12*f^4 - 1920*a^7*b^9*c*d^12*f^4 - 800*a^9*b^7*c*d^12*f^4 - 64*a^11*b^5*c*d^12*
f^4 + 32*a^13*b^3*c*d^12*f^4))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5) - (16*(c
+ d*tan(e + f*x))^(1/2)*((((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4
*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f
^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2
*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*
c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) - 4*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*
a^3*b*d^5*f^2 - 20*a^4*c*d^4*f^2 - 20*b^4*c*d^4*f^2 + 24*a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2
*f^2 - 240*a^2*b^2*c^3*d^2*f^2 + 80*a*b^3*c^4*d*f^2 - 80*a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2
*c*d^4*f^2 + 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^
(1/2)*(32*b^18*d^10*f^4 + 160*a^2*b^16*d^10*f^4 + 288*a^4*b^14*d^10*f^4 + 160*a^6*b^12*d^10*f^4 - 160*a^8*b^10
*d^10*f^4 - 288*a^10*b^8*d^10*f^4 - 160*a^12*b^6*d^10*f^4 - 32*a^14*b^4*d^10*f^4 + 48*b^18*c^2*d^8*f^4 + 272*a
^2*b^16*c^2*d^8*f^4 + 624*a^4*b^14*c^2*d^8*f^4 + 720*a^6*b^12*c^2*d^8*f^4 + 400*a^8*b^10*c^2*d^8*f^4 + 48*a^10
*b^8*c^2*d^8*f^4 - 48*a^12*b^6*c^2*d^8*f^4 - 16*a^14*b^4*c^2*d^8*f^4 + 16*a*b^17*c*d^9*f^4 + 112*a^3*b^15*c*d^
9*f^4 + 336*a^5*b^13*c*d^9*f^4 + 560*a^7*b^11*c*d^9*f^4 + 560*a^9*b^9*c*d^9*f^4 + 336*a^11*b^7*c*d^9*f^4 + 112
*a^13*b^5*c*d^9*f^4 + 16*a^15*b^3*c*d^9*f^4))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3
*f^4))*((((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d
^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^
4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (
16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*
d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) - 4*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 2
0*a^4*c*d^4*f^2 - 20*b^4*c*d^4*f^2 + 24*a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^
2*c^3*d^2*f^2 + 80*a*b^3*c^4*d*f^2 - 80*a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*
a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2) - (16*(c +
d*tan(e + f*x))^(1/2)*(4*a^14*c*d^14*f^2 - 8*a^13*b*d^15*f^2 - 60*a*b^13*d^15*f^2 + 76*b^14*c*d^14*f^2 - 52*a^
3*b^11*d^15*f^2 - 128*a^5*b^9*d^15*f^2 - 424*a^7*b^7*d^15*f^2 - 380*a^9*b^5*d^15*f^2 - 100*a^11*b^3*d^15*f^2 -
20*b^14*c^3*d^12*f^2 - 304*b^14*c^5*d^10*f^2 + 20*b^14*c^7*d^8*f^2 + 540*a^2*b^12*c^3*d^12*f^2 + 624*a^2*b^12
*c^5*d^10*f^2 - 116*a^2*b^12*c^7*d^8*f^2 - 596*a^3*b^11*c^2*d^13*f^2 + 1540*a^3*b^11*c^4*d^11*f^2 - 588*a^3*b^
11*c^6*d^9*f^2 + 80*a^4*b^10*c^3*d^12*f^2 + 1760*a^4*b^10*c^5*d^10*f^2 - 216*a^4*b^10*c^7*d^8*f^2 - 2184*a^5*b
^9*c^2*d^13*f^2 + 1320*a^5*b^9*c^4*d^11*f^2 + 152*a^5*b^9*c^6*d^9*f^2 - 1960*a^6*b^8*c^3*d^12*f^2 + 800*a^6*b^
8*c^5*d^10*f^2 - 8*a^6*b^8*c^7*d^8*f^2 - 584*a^7*b^7*c^2*d^13*f^2 + 840*a^7*b^7*c^4*d^11*f^2 - 56*a^7*b^7*c^6*
d^9*f^2 - 1940*a^8*b^6*c^3*d^12*f^2 + 336*a^8*b^6*c^5*d^10*f^2 + 68*a^8*b^6*c^7*d^8*f^2 + 676*a^9*b^5*c^2*d^13
*f^2 + 180*a^9*b^5*c^4*d^11*f^2 - 260*a^9*b^5*c^6*d^9*f^2 - 500*a^10*b^4*c^3*d^12*f^2 + 368*a^10*b^4*c^5*d^10*
f^2 - 4*a^10*b^4*c^7*d^8*f^2 + 156*a^11*b^3*c^2*d^13*f^2 - 140*a^11*b^3*c^4*d^11*f^2 + 4*a^11*b^3*c^6*d^9*f^2
- 40*a^12*b^2*c^3*d^12*f^2 + 468*a*b^13*c^2*d^13*f^2 + 740*a*b^13*c^4*d^11*f^2 - 532*a*b^13*c^6*d^9*f^2 - 284*
a^2*b^12*c*d^14*f^2 + 84*a^4*b^10*c*d^14*f^2 + 1436*a^6*b^8*c*d^14*f^2 + 1108*a^8*b^6*c*d^14*f^2 + 124*a^10*b^
4*c*d^14*f^2 + 12*a^12*b^2*c*d^14*f^2 + 16*a^13*b*c^2*d^13*f^2))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*
b^5*f^4 + 4*a^6*b^3*f^4))*((((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d
^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2
*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c
^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 +
5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) - 4*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 1
6*a^3*b*d^5*f^2 - 20*a^4*c*d^4*f^2 - 20*b^4*c*d^4*f^2 + 24*a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d
^2*f^2 - 240*a^2*b^2*c^3*d^2*f^2 + 80*a*b^3*c^4*d*f^2 - 80*a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b
^2*c*d^4*f^2 + 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4))
)^(1/2))*((((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c
*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*
c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 -
(16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^
4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) - 4*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 -
20*a^4*c*d^4*f^2 - 20*b^4*c*d^4*f^2 + 24*a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*
b^2*c^3*d^2*f^2 + 80*a*b^3*c^4*d*f^2 - 80*a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 16
0*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2) + (16*(c
+ d*tan(e + f*x))^(1/2)*(2*b^10*d^20 - a^10*d^20 + 4*a^2*b^8*d^20 + 27*a^4*b^6*d^20 - 15*a^6*b^4*d^20 - 9*a^8*
b^2*d^20 + 15*a^10*c^2*d^18 - 15*a^10*c^4*d^16 + a^10*c^6*d^14 + 12*b^10*c^2*d^18 + 55*b^10*c^4*d^16 - 335*b^1
0*c^6*d^14 + 405*b^10*c^8*d^12 - 13*b^10*c^10*d^10 + 2*b^10*c^12*d^8 - 100*a*b^9*c^3*d^17 + 1840*a*b^9*c^5*d^1
5 - 3100*a*b^9*c^7*d^13 + 1000*a*b^9*c^9*d^11 - 40*a*b^9*c^11*d^9 - 100*a^3*b^7*c*d^19 + 400*a^5*b^5*c*d^19 +
124*a^7*b^3*c*d^19 + 20*a^9*b*c^3*d^17 - 48*a^9*b*c^5*d^15 + 4*a^9*b*c^7*d^13 + 174*a^2*b^8*c^2*d^18 - 3565*a^
2*b^8*c^4*d^16 + 9451*a^2*b^8*c^6*d^14 - 5755*a^2*b^8*c^8*d^12 + 919*a^2*b^8*c^10*d^10 - 12*a^2*b^8*c^12*d^8 +
3600*a^3*b^7*c^3*d^17 - 13896*a^3*b^7*c^5*d^15 + 14032*a^3*b^7*c^7*d^13 - 4180*a^3*b^7*c^9*d^11 + 288*a^3*b^7
*c^11*d^9 - 1813*a^4*b^6*c^2*d^18 + 10770*a^4*b^6*c^4*d^16 - 16848*a^4*b^6*c^6*d^14 + 8385*a^4*b^6*c^8*d^12 -
1115*a^4*b^6*c^10*d^10 + 18*a^4*b^6*c^12*d^8 - 3920*a^5*b^5*c^3*d^17 + 9936*a^5*b^5*c^5*d^15 - 8040*a^5*b^5*c^
7*d^13 + 1840*a^5*b^5*c^9*d^11 - 56*a^5*b^5*c^11*d^9 + 315*a^6*b^4*c^2*d^18 - 1880*a^6*b^4*c^4*d^16 + 3140*a^6
*b^4*c^6*d^14 - 1305*a^6*b^4*c^8*d^12 + 65*a^6*b^4*c^10*d^10 - 560*a^7*b^3*c^3*d^17 + 280*a^7*b^3*c^5*d^15 + 1
76*a^7*b^3*c^7*d^13 - 20*a^7*b^3*c^9*d^11 + 193*a^8*b^2*c^2*d^18 - 445*a^8*b^2*c^4*d^16 + 207*a^8*b^2*c^6*d^14
- 10*a^8*b^2*c^8*d^12 + 8*a^9*b*c*d^19))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4
))*((((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f
^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*
f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a
^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6
+ 10*c^6*d^4 + 5*c^8*d^2))^(1/2) - 4*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 20*a^
4*c*d^4*f^2 - 20*b^4*c*d^4*f^2 + 24*a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^2*c^
3*d^2*f^2 + 80*a*b^3*c^4*d*f^2 - 80*a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*a^3*
b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2)*1i - (((8*(4*b^
12*c*d^17*f^2 - 16*a^11*b*d^18*f^2 - 8*a^12*c*d^17*f^2 - 4*a*b^11*d^18*f^2 + 304*a^3*b^9*d^18*f^2 + 120*a^5*b^
7*d^18*f^2 - 320*a^7*b^5*d^18*f^2 - 148*a^9*b^3*d^18*f^2 - 8*a^12*c^3*d^15*f^2 - 400*b^12*c^3*d^15*f^2 + 176*b
^12*c^5*d^13*f^2 + 488*b^12*c^7*d^11*f^2 - 92*b^12*c^9*d^9*f^2 + 6576*a^2*b^10*c^3*d^15*f^2 + 400*a^2*b^10*c^5
*d^13*f^2 - 6144*a^2*b^10*c^7*d^11*f^2 + 1056*a^2*b^10*c^9*d^9*f^2 - 5408*a^3*b^9*c^2*d^16*f^2 + 3888*a^3*b^9*
c^4*d^14*f^2 + 6400*a^3*b^9*c^6*d^12*f^2 - 3072*a^3*b^9*c^8*d^10*f^2 + 128*a^3*b^9*c^10*d^8*f^2 - 648*a^4*b^8*
c^3*d^15*f^2 - 1952*a^4*b^8*c^5*d^13*f^2 + 208*a^4*b^8*c^7*d^11*f^2 + 200*a^4*b^8*c^9*d^9*f^2 - 4288*a^5*b^7*c
^2*d^16*f^2 + 4112*a^5*b^7*c^4*d^14*f^2 + 5120*a^5*b^7*c^6*d^12*f^2 - 3208*a^5*b^7*c^8*d^10*f^2 + 192*a^5*b^7*
c^10*d^8*f^2 - 6688*a^6*b^6*c^3*d^15*f^2 - 2464*a^6*b^6*c^5*d^13*f^2 + 5952*a^6*b^6*c^7*d^11*f^2 - 960*a^6*b^6
*c^9*d^9*f^2 + 2624*a^7*b^5*c^2*d^16*f^2 - 2016*a^7*b^5*c^4*d^14*f^2 - 3456*a^7*b^5*c^6*d^12*f^2 + 1504*a^7*b^
5*c^8*d^10*f^2 + 992*a^8*b^4*c^3*d^15*f^2 - 144*a^8*b^4*c^5*d^13*f^2 - 888*a^8*b^4*c^7*d^11*f^2 - 12*a^8*b^4*c
^9*d^9*f^2 + 352*a^9*b^3*c^2*d^16*f^2 + 520*a^9*b^3*c^4*d^14*f^2 + 32*a^9*b^3*c^6*d^12*f^2 + 12*a^9*b^3*c^8*d^
10*f^2 + 48*a^10*b^2*c^3*d^15*f^2 + 144*a^10*b^2*c^5*d^13*f^2 + 1120*a*b^11*c^2*d^16*f^2 - 2776*a*b^11*c^4*d^1
4*f^2 - 2208*a*b^11*c^6*d^12*f^2 + 1628*a*b^11*c^8*d^10*f^2 - 64*a*b^11*c^10*d^8*f^2 - 1024*a^2*b^10*c*d^17*f^
2 + 1312*a^4*b^8*c*d^17*f^2 + 2688*a^6*b^6*c*d^17*f^2 + 260*a^8*b^4*c*d^17*f^2 - 96*a^10*b^2*c*d^17*f^2 - 32*a
^11*b*c^2*d^16*f^2 - 16*a^11*b*c^4*d^14*f^2))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3
*f^5) - (((8*(96*a^2*b^14*d^13*f^4 + 480*a^4*b^12*d^13*f^4 + 960*a^6*b^10*d^13*f^4 + 960*a^8*b^8*d^13*f^4 + 48
0*a^10*b^6*d^13*f^4 + 96*a^12*b^4*d^13*f^4 + 128*b^16*c^2*d^11*f^4 + 128*b^16*c^4*d^9*f^4 + 640*a^2*b^14*c^2*d
^11*f^4 + 544*a^2*b^14*c^4*d^9*f^4 - 768*a^3*b^13*c^3*d^10*f^4 + 320*a^3*b^13*c^5*d^8*f^4 + 1280*a^4*b^12*c^2*
d^11*f^4 + 800*a^4*b^12*c^4*d^9*f^4 - 1440*a^5*b^11*c^3*d^10*f^4 + 640*a^5*b^11*c^5*d^8*f^4 + 1280*a^6*b^10*c^
2*d^11*f^4 + 320*a^6*b^10*c^4*d^9*f^4 - 1280*a^7*b^9*c^3*d^10*f^4 + 640*a^7*b^9*c^5*d^8*f^4 + 640*a^8*b^8*c^2*
d^11*f^4 - 320*a^8*b^8*c^4*d^9*f^4 - 480*a^9*b^7*c^3*d^10*f^4 + 320*a^9*b^7*c^5*d^8*f^4 + 128*a^10*b^6*c^2*d^1
1*f^4 - 352*a^10*b^6*c^4*d^9*f^4 + 64*a^11*b^5*c^5*d^8*f^4 - 96*a^12*b^4*c^4*d^9*f^4 + 32*a^13*b^3*c^3*d^10*f^
4 - 224*a*b^15*c*d^12*f^4 - 160*a*b^15*c^3*d^10*f^4 + 64*a*b^15*c^5*d^8*f^4 - 1088*a^3*b^13*c*d^12*f^4 - 2080*
a^5*b^11*c*d^12*f^4 - 1920*a^7*b^9*c*d^12*f^4 - 800*a^9*b^7*c*d^12*f^4 - 64*a^11*b^5*c*d^12*f^4 + 32*a^13*b^3*
c*d^12*f^4))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5) + (16*(c + d*tan(e + f*x))^
(1/2)*((((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^
4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4
*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (1
6*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d
^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) - 4*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 20
*a^4*c*d^4*f^2 - 20*b^4*c*d^4*f^2 + 24*a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^2
*c^3*d^2*f^2 + 80*a*b^3*c^4*d*f^2 - 80*a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*a
^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2)*(32*b^18*d^1
0*f^4 + 160*a^2*b^16*d^10*f^4 + 288*a^4*b^14*d^10*f^4 + 160*a^6*b^12*d^10*f^4 - 160*a^8*b^10*d^10*f^4 - 288*a^
10*b^8*d^10*f^4 - 160*a^12*b^6*d^10*f^4 - 32*a^14*b^4*d^10*f^4 + 48*b^18*c^2*d^8*f^4 + 272*a^2*b^16*c^2*d^8*f^
4 + 624*a^4*b^14*c^2*d^8*f^4 + 720*a^6*b^12*c^2*d^8*f^4 + 400*a^8*b^10*c^2*d^8*f^4 + 48*a^10*b^8*c^2*d^8*f^4 -
48*a^12*b^6*c^2*d^8*f^4 - 16*a^14*b^4*c^2*d^8*f^4 + 16*a*b^17*c*d^9*f^4 + 112*a^3*b^15*c*d^9*f^4 + 336*a^5*b^
13*c*d^9*f^4 + 560*a^7*b^11*c*d^9*f^4 + 560*a^9*b^9*c*d^9*f^4 + 336*a^11*b^7*c*d^9*f^4 + 112*a^13*b^5*c*d^9*f^
4 + 16*a^15*b^3*c*d^9*f^4))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4))*((((8*a^4*c
^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^
2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*
b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^
8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 +
5*c^8*d^2))^(1/2) - 4*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 20*a^4*c*d^4*f^2 -
20*b^4*c*d^4*f^2 + 24*a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^2*c^3*d^2*f^2 + 80
*a*b^3*c^4*d*f^2 - 80*a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*a^3*b*c^2*d^3*f^2)
/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2) + (16*(c + d*tan(e + f*x))^(1
/2)*(4*a^14*c*d^14*f^2 - 8*a^13*b*d^15*f^2 - 60*a*b^13*d^15*f^2 + 76*b^14*c*d^14*f^2 - 52*a^3*b^11*d^15*f^2 -
128*a^5*b^9*d^15*f^2 - 424*a^7*b^7*d^15*f^2 - 380*a^9*b^5*d^15*f^2 - 100*a^11*b^3*d^15*f^2 - 20*b^14*c^3*d^12*
f^2 - 304*b^14*c^5*d^10*f^2 + 20*b^14*c^7*d^8*f^2 + 540*a^2*b^12*c^3*d^12*f^2 + 624*a^2*b^12*c^5*d^10*f^2 - 11
6*a^2*b^12*c^7*d^8*f^2 - 596*a^3*b^11*c^2*d^13*f^2 + 1540*a^3*b^11*c^4*d^11*f^2 - 588*a^3*b^11*c^6*d^9*f^2 + 8
0*a^4*b^10*c^3*d^12*f^2 + 1760*a^4*b^10*c^5*d^10*f^2 - 216*a^4*b^10*c^7*d^8*f^2 - 2184*a^5*b^9*c^2*d^13*f^2 +
1320*a^5*b^9*c^4*d^11*f^2 + 152*a^5*b^9*c^6*d^9*f^2 - 1960*a^6*b^8*c^3*d^12*f^2 + 800*a^6*b^8*c^5*d^10*f^2 - 8
*a^6*b^8*c^7*d^8*f^2 - 584*a^7*b^7*c^2*d^13*f^2 + 840*a^7*b^7*c^4*d^11*f^2 - 56*a^7*b^7*c^6*d^9*f^2 - 1940*a^8
*b^6*c^3*d^12*f^2 + 336*a^8*b^6*c^5*d^10*f^2 + 68*a^8*b^6*c^7*d^8*f^2 + 676*a^9*b^5*c^2*d^13*f^2 + 180*a^9*b^5
*c^4*d^11*f^2 - 260*a^9*b^5*c^6*d^9*f^2 - 500*a^10*b^4*c^3*d^12*f^2 + 368*a^10*b^4*c^5*d^10*f^2 - 4*a^10*b^4*c
^7*d^8*f^2 + 156*a^11*b^3*c^2*d^13*f^2 - 140*a^11*b^3*c^4*d^11*f^2 + 4*a^11*b^3*c^6*d^9*f^2 - 40*a^12*b^2*c^3*
d^12*f^2 + 468*a*b^13*c^2*d^13*f^2 + 740*a*b^13*c^4*d^11*f^2 - 532*a*b^13*c^6*d^9*f^2 - 284*a^2*b^12*c*d^14*f^
2 + 84*a^4*b^10*c*d^14*f^2 + 1436*a^6*b^8*c*d^14*f^2 + 1108*a^8*b^6*c*d^14*f^2 + 124*a^10*b^4*c*d^14*f^2 + 12*
a^12*b^2*c*d^14*f^2 + 16*a^13*b*c^2*d^13*f^2))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^
3*f^4))*((((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*
d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c
^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 -
(16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4
*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) - 4*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 -
20*a^4*c*d^4*f^2 - 20*b^4*c*d^4*f^2 + 24*a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b
^2*c^3*d^2*f^2 + 80*a*b^3*c^4*d*f^2 - 80*a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160
*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2))*((((8*a^4
*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*
b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^
3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*
b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4
+ 5*c^8*d^2))^(1/2) - 4*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 20*a^4*c*d^4*f^2
- 20*b^4*c*d^4*f^2 + 24*a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^2*c^3*d^2*f^2 +
80*a*b^3*c^4*d*f^2 - 80*a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*a^3*b*c^2*d^3*f^
2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2) - (16*(c + d*tan(e + f*x))^
(1/2)*(2*b^10*d^20 - a^10*d^20 + 4*a^2*b^8*d^20 + 27*a^4*b^6*d^20 - 15*a^6*b^4*d^20 - 9*a^8*b^2*d^20 + 15*a^10
*c^2*d^18 - 15*a^10*c^4*d^16 + a^10*c^6*d^14 + 12*b^10*c^2*d^18 + 55*b^10*c^4*d^16 - 335*b^10*c^6*d^14 + 405*b
^10*c^8*d^12 - 13*b^10*c^10*d^10 + 2*b^10*c^12*d^8 - 100*a*b^9*c^3*d^17 + 1840*a*b^9*c^5*d^15 - 3100*a*b^9*c^7
*d^13 + 1000*a*b^9*c^9*d^11 - 40*a*b^9*c^11*d^9 - 100*a^3*b^7*c*d^19 + 400*a^5*b^5*c*d^19 + 124*a^7*b^3*c*d^19
+ 20*a^9*b*c^3*d^17 - 48*a^9*b*c^5*d^15 + 4*a^9*b*c^7*d^13 + 174*a^2*b^8*c^2*d^18 - 3565*a^2*b^8*c^4*d^16 + 9
451*a^2*b^8*c^6*d^14 - 5755*a^2*b^8*c^8*d^12 + 919*a^2*b^8*c^10*d^10 - 12*a^2*b^8*c^12*d^8 + 3600*a^3*b^7*c^3*
d^17 - 13896*a^3*b^7*c^5*d^15 + 14032*a^3*b^7*c^7*d^13 - 4180*a^3*b^7*c^9*d^11 + 288*a^3*b^7*c^11*d^9 - 1813*a
^4*b^6*c^2*d^18 + 10770*a^4*b^6*c^4*d^16 - 16848*a^4*b^6*c^6*d^14 + 8385*a^4*b^6*c^8*d^12 - 1115*a^4*b^6*c^10*
d^10 + 18*a^4*b^6*c^12*d^8 - 3920*a^5*b^5*c^3*d^17 + 9936*a^5*b^5*c^5*d^15 - 8040*a^5*b^5*c^7*d^13 + 1840*a^5*
b^5*c^9*d^11 - 56*a^5*b^5*c^11*d^9 + 315*a^6*b^4*c^2*d^18 - 1880*a^6*b^4*c^4*d^16 + 3140*a^6*b^4*c^6*d^14 - 13
05*a^6*b^4*c^8*d^12 + 65*a^6*b^4*c^10*d^10 - 560*a^7*b^3*c^3*d^17 + 280*a^7*b^3*c^5*d^15 + 176*a^7*b^3*c^7*d^1
3 - 20*a^7*b^3*c^9*d^11 + 193*a^8*b^2*c^2*d^18 - 445*a^8*b^2*c^4*d^16 + 207*a^8*b^2*c^6*d^14 - 10*a^8*b^2*c^8*
d^12 + 8*a^9*b*c*d^19))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4))*((((8*a^4*c^5*f
^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^
5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^
4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^
4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c
^8*d^2))^(1/2) - 4*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 20*a^4*c*d^4*f^2 - 20*b
^4*c*d^4*f^2 + 24*a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^2*c^3*d^2*f^2 + 80*a*b
^3*c^4*d*f^2 - 80*a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*a^3*b*c^2*d^3*f^2)/(16
*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2)*1i)/((((8*(4*b^12*c*d^17*f^2 - 16
*a^11*b*d^18*f^2 - 8*a^12*c*d^17*f^2 - 4*a*b^11*d^18*f^2 + 304*a^3*b^9*d^18*f^2 + 120*a^5*b^7*d^18*f^2 - 320*a
^7*b^5*d^18*f^2 - 148*a^9*b^3*d^18*f^2 - 8*a^12*c^3*d^15*f^2 - 400*b^12*c^3*d^15*f^2 + 176*b^12*c^5*d^13*f^2 +
488*b^12*c^7*d^11*f^2 - 92*b^12*c^9*d^9*f^2 + 6576*a^2*b^10*c^3*d^15*f^2 + 400*a^2*b^10*c^5*d^13*f^2 - 6144*a
^2*b^10*c^7*d^11*f^2 + 1056*a^2*b^10*c^9*d^9*f^2 - 5408*a^3*b^9*c^2*d^16*f^2 + 3888*a^3*b^9*c^4*d^14*f^2 + 640
0*a^3*b^9*c^6*d^12*f^2 - 3072*a^3*b^9*c^8*d^10*f^2 + 128*a^3*b^9*c^10*d^8*f^2 - 648*a^4*b^8*c^3*d^15*f^2 - 195
2*a^4*b^8*c^5*d^13*f^2 + 208*a^4*b^8*c^7*d^11*f^2 + 200*a^4*b^8*c^9*d^9*f^2 - 4288*a^5*b^7*c^2*d^16*f^2 + 4112
*a^5*b^7*c^4*d^14*f^2 + 5120*a^5*b^7*c^6*d^12*f^2 - 3208*a^5*b^7*c^8*d^10*f^2 + 192*a^5*b^7*c^10*d^8*f^2 - 668
8*a^6*b^6*c^3*d^15*f^2 - 2464*a^6*b^6*c^5*d^13*f^2 + 5952*a^6*b^6*c^7*d^11*f^2 - 960*a^6*b^6*c^9*d^9*f^2 + 262
4*a^7*b^5*c^2*d^16*f^2 - 2016*a^7*b^5*c^4*d^14*f^2 - 3456*a^7*b^5*c^6*d^12*f^2 + 1504*a^7*b^5*c^8*d^10*f^2 + 9
92*a^8*b^4*c^3*d^15*f^2 - 144*a^8*b^4*c^5*d^13*f^2 - 888*a^8*b^4*c^7*d^11*f^2 - 12*a^8*b^4*c^9*d^9*f^2 + 352*a
^9*b^3*c^2*d^16*f^2 + 520*a^9*b^3*c^4*d^14*f^2 + 32*a^9*b^3*c^6*d^12*f^2 + 12*a^9*b^3*c^8*d^10*f^2 + 48*a^10*b
^2*c^3*d^15*f^2 + 144*a^10*b^2*c^5*d^13*f^2 + 1120*a*b^11*c^2*d^16*f^2 - 2776*a*b^11*c^4*d^14*f^2 - 2208*a*b^1
1*c^6*d^12*f^2 + 1628*a*b^11*c^8*d^10*f^2 - 64*a*b^11*c^10*d^8*f^2 - 1024*a^2*b^10*c*d^17*f^2 + 1312*a^4*b^8*c
*d^17*f^2 + 2688*a^6*b^6*c*d^17*f^2 + 260*a^8*b^4*c*d^17*f^2 - 96*a^10*b^2*c*d^17*f^2 - 32*a^11*b*c^2*d^16*f^2
- 16*a^11*b*c^4*d^14*f^2))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5) - (((8*(96*a
^2*b^14*d^13*f^4 + 480*a^4*b^12*d^13*f^4 + 960*a^6*b^10*d^13*f^4 + 960*a^8*b^8*d^13*f^4 + 480*a^10*b^6*d^13*f^
4 + 96*a^12*b^4*d^13*f^4 + 128*b^16*c^2*d^11*f^4 + 128*b^16*c^4*d^9*f^4 + 640*a^2*b^14*c^2*d^11*f^4 + 544*a^2*
b^14*c^4*d^9*f^4 - 768*a^3*b^13*c^3*d^10*f^4 + 320*a^3*b^13*c^5*d^8*f^4 + 1280*a^4*b^12*c^2*d^11*f^4 + 800*a^4
*b^12*c^4*d^9*f^4 - 1440*a^5*b^11*c^3*d^10*f^4 + 640*a^5*b^11*c^5*d^8*f^4 + 1280*a^6*b^10*c^2*d^11*f^4 + 320*a
^6*b^10*c^4*d^9*f^4 - 1280*a^7*b^9*c^3*d^10*f^4 + 640*a^7*b^9*c^5*d^8*f^4 + 640*a^8*b^8*c^2*d^11*f^4 - 320*a^8
*b^8*c^4*d^9*f^4 - 480*a^9*b^7*c^3*d^10*f^4 + 320*a^9*b^7*c^5*d^8*f^4 + 128*a^10*b^6*c^2*d^11*f^4 - 352*a^10*b
^6*c^4*d^9*f^4 + 64*a^11*b^5*c^5*d^8*f^4 - 96*a^12*b^4*c^4*d^9*f^4 + 32*a^13*b^3*c^3*d^10*f^4 - 224*a*b^15*c*d
^12*f^4 - 160*a*b^15*c^3*d^10*f^4 + 64*a*b^15*c^5*d^8*f^4 - 1088*a^3*b^13*c*d^12*f^4 - 2080*a^5*b^11*c*d^12*f^
4 - 1920*a^7*b^9*c*d^12*f^4 - 800*a^9*b^7*c*d^12*f^4 - 64*a^11*b^5*c*d^12*f^4 + 32*a^13*b^3*c*d^12*f^4))/(b^9*
f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5) - (16*(c + d*tan(e + f*x))^(1/2)*((((8*a^4*c^
5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2
*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b
*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8
*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 +
5*c^8*d^2))^(1/2) - 4*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 20*a^4*c*d^4*f^2 - 2
0*b^4*c*d^4*f^2 + 24*a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^2*c^3*d^2*f^2 + 80*
a*b^3*c^4*d*f^2 - 80*a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*a^3*b*c^2*d^3*f^2)/
(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2)*(32*b^18*d^10*f^4 + 160*a^2*b^
16*d^10*f^4 + 288*a^4*b^14*d^10*f^4 + 160*a^6*b^12*d^10*f^4 - 160*a^8*b^10*d^10*f^4 - 288*a^10*b^8*d^10*f^4 -
160*a^12*b^6*d^10*f^4 - 32*a^14*b^4*d^10*f^4 + 48*b^18*c^2*d^8*f^4 + 272*a^2*b^16*c^2*d^8*f^4 + 624*a^4*b^14*c
^2*d^8*f^4 + 720*a^6*b^12*c^2*d^8*f^4 + 400*a^8*b^10*c^2*d^8*f^4 + 48*a^10*b^8*c^2*d^8*f^4 - 48*a^12*b^6*c^2*d
^8*f^4 - 16*a^14*b^4*c^2*d^8*f^4 + 16*a*b^17*c*d^9*f^4 + 112*a^3*b^15*c*d^9*f^4 + 336*a^5*b^13*c*d^9*f^4 + 560
*a^7*b^11*c*d^9*f^4 + 560*a^9*b^9*c*d^9*f^4 + 336*a^11*b^7*c*d^9*f^4 + 112*a^13*b^5*c*d^9*f^4 + 16*a^15*b^3*c*
d^9*f^4))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4))*((((8*a^4*c^5*f^2 + 8*b^4*c^5
*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4
*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*
a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6
*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2)
- 4*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 20*a^4*c*d^4*f^2 - 20*b^4*c*d^4*f^2 +
24*a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^2*c^3*d^2*f^2 + 80*a*b^3*c^4*d*f^2 -
80*a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^
8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2) - (16*(c + d*tan(e + f*x))^(1/2)*(4*a^14*c*d^14
*f^2 - 8*a^13*b*d^15*f^2 - 60*a*b^13*d^15*f^2 + 76*b^14*c*d^14*f^2 - 52*a^3*b^11*d^15*f^2 - 128*a^5*b^9*d^15*f
^2 - 424*a^7*b^7*d^15*f^2 - 380*a^9*b^5*d^15*f^2 - 100*a^11*b^3*d^15*f^2 - 20*b^14*c^3*d^12*f^2 - 304*b^14*c^5
*d^10*f^2 + 20*b^14*c^7*d^8*f^2 + 540*a^2*b^12*c^3*d^12*f^2 + 624*a^2*b^12*c^5*d^10*f^2 - 116*a^2*b^12*c^7*d^8
*f^2 - 596*a^3*b^11*c^2*d^13*f^2 + 1540*a^3*b^11*c^4*d^11*f^2 - 588*a^3*b^11*c^6*d^9*f^2 + 80*a^4*b^10*c^3*d^1
2*f^2 + 1760*a^4*b^10*c^5*d^10*f^2 - 216*a^4*b^10*c^7*d^8*f^2 - 2184*a^5*b^9*c^2*d^13*f^2 + 1320*a^5*b^9*c^4*d
^11*f^2 + 152*a^5*b^9*c^6*d^9*f^2 - 1960*a^6*b^8*c^3*d^12*f^2 + 800*a^6*b^8*c^5*d^10*f^2 - 8*a^6*b^8*c^7*d^8*f
^2 - 584*a^7*b^7*c^2*d^13*f^2 + 840*a^7*b^7*c^4*d^11*f^2 - 56*a^7*b^7*c^6*d^9*f^2 - 1940*a^8*b^6*c^3*d^12*f^2
+ 336*a^8*b^6*c^5*d^10*f^2 + 68*a^8*b^6*c^7*d^8*f^2 + 676*a^9*b^5*c^2*d^13*f^2 + 180*a^9*b^5*c^4*d^11*f^2 - 26
0*a^9*b^5*c^6*d^9*f^2 - 500*a^10*b^4*c^3*d^12*f^2 + 368*a^10*b^4*c^5*d^10*f^2 - 4*a^10*b^4*c^7*d^8*f^2 + 156*a
^11*b^3*c^2*d^13*f^2 - 140*a^11*b^3*c^4*d^11*f^2 + 4*a^11*b^3*c^6*d^9*f^2 - 40*a^12*b^2*c^3*d^12*f^2 + 468*a*b
^13*c^2*d^13*f^2 + 740*a*b^13*c^4*d^11*f^2 - 532*a*b^13*c^6*d^9*f^2 - 284*a^2*b^12*c*d^14*f^2 + 84*a^4*b^10*c*
d^14*f^2 + 1436*a^6*b^8*c*d^14*f^2 + 1108*a^8*b^6*c*d^14*f^2 + 124*a^10*b^4*c*d^14*f^2 + 12*a^12*b^2*c*d^14*f^
2 + 16*a^13*b*c^2*d^13*f^2))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4))*((((8*a^4*
c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b
^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3
*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b
^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4
+ 5*c^8*d^2))^(1/2) - 4*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 20*a^4*c*d^4*f^2 -
20*b^4*c*d^4*f^2 + 24*a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^2*c^3*d^2*f^2 + 8
0*a*b^3*c^4*d*f^2 - 80*a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*a^3*b*c^2*d^3*f^2
)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2))*((((8*a^4*c^5*f^2 + 8*b^4*c
^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a
^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 32
0*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b
^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/
2) - 4*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 20*a^4*c*d^4*f^2 - 20*b^4*c*d^4*f^2
+ 24*a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^2*c^3*d^2*f^2 + 80*a*b^3*c^4*d*f^2
- 80*a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 +
b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2) + (16*(c + d*tan(e + f*x))^(1/2)*(2*b^10*d^20
- a^10*d^20 + 4*a^2*b^8*d^20 + 27*a^4*b^6*d^20 - 15*a^6*b^4*d^20 - 9*a^8*b^2*d^20 + 15*a^10*c^2*d^18 - 15*a^1
0*c^4*d^16 + a^10*c^6*d^14 + 12*b^10*c^2*d^18 + 55*b^10*c^4*d^16 - 335*b^10*c^6*d^14 + 405*b^10*c^8*d^12 - 13*
b^10*c^10*d^10 + 2*b^10*c^12*d^8 - 100*a*b^9*c^3*d^17 + 1840*a*b^9*c^5*d^15 - 3100*a*b^9*c^7*d^13 + 1000*a*b^9
*c^9*d^11 - 40*a*b^9*c^11*d^9 - 100*a^3*b^7*c*d^19 + 400*a^5*b^5*c*d^19 + 124*a^7*b^3*c*d^19 + 20*a^9*b*c^3*d^
17 - 48*a^9*b*c^5*d^15 + 4*a^9*b*c^7*d^13 + 174*a^2*b^8*c^2*d^18 - 3565*a^2*b^8*c^4*d^16 + 9451*a^2*b^8*c^6*d^
14 - 5755*a^2*b^8*c^8*d^12 + 919*a^2*b^8*c^10*d^10 - 12*a^2*b^8*c^12*d^8 + 3600*a^3*b^7*c^3*d^17 - 13896*a^3*b
^7*c^5*d^15 + 14032*a^3*b^7*c^7*d^13 - 4180*a^3*b^7*c^9*d^11 + 288*a^3*b^7*c^11*d^9 - 1813*a^4*b^6*c^2*d^18 +
10770*a^4*b^6*c^4*d^16 - 16848*a^4*b^6*c^6*d^14 + 8385*a^4*b^6*c^8*d^12 - 1115*a^4*b^6*c^10*d^10 + 18*a^4*b^6*
c^12*d^8 - 3920*a^5*b^5*c^3*d^17 + 9936*a^5*b^5*c^5*d^15 - 8040*a^5*b^5*c^7*d^13 + 1840*a^5*b^5*c^9*d^11 - 56*
a^5*b^5*c^11*d^9 + 315*a^6*b^4*c^2*d^18 - 1880*a^6*b^4*c^4*d^16 + 3140*a^6*b^4*c^6*d^14 - 1305*a^6*b^4*c^8*d^1
2 + 65*a^6*b^4*c^10*d^10 - 560*a^7*b^3*c^3*d^17 + 280*a^7*b^3*c^5*d^15 + 176*a^7*b^3*c^7*d^13 - 20*a^7*b^3*c^9
*d^11 + 193*a^8*b^2*c^2*d^18 - 445*a^8*b^2*c^4*d^16 + 207*a^8*b^2*c^6*d^14 - 10*a^8*b^2*c^8*d^12 + 8*a^9*b*c*d
^19))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4))*((((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2
- 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3
*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^
3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4
+ 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) - 4
*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 20*a^4*c*d^4*f^2 - 20*b^4*c*d^4*f^2 + 24*
a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^2*c^3*d^2*f^2 + 80*a*b^3*c^4*d*f^2 - 80*
a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^
4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2) + (((8*(4*b^12*c*d^17*f^2 - 16*a^11*b*d^18*f^2 - 8*
a^12*c*d^17*f^2 - 4*a*b^11*d^18*f^2 + 304*a^3*b^9*d^18*f^2 + 120*a^5*b^7*d^18*f^2 - 320*a^7*b^5*d^18*f^2 - 148
*a^9*b^3*d^18*f^2 - 8*a^12*c^3*d^15*f^2 - 400*b^12*c^3*d^15*f^2 + 176*b^12*c^5*d^13*f^2 + 488*b^12*c^7*d^11*f^
2 - 92*b^12*c^9*d^9*f^2 + 6576*a^2*b^10*c^3*d^15*f^2 + 400*a^2*b^10*c^5*d^13*f^2 - 6144*a^2*b^10*c^7*d^11*f^2
+ 1056*a^2*b^10*c^9*d^9*f^2 - 5408*a^3*b^9*c^2*d^16*f^2 + 3888*a^3*b^9*c^4*d^14*f^2 + 6400*a^3*b^9*c^6*d^12*f^
2 - 3072*a^3*b^9*c^8*d^10*f^2 + 128*a^3*b^9*c^10*d^8*f^2 - 648*a^4*b^8*c^3*d^15*f^2 - 1952*a^4*b^8*c^5*d^13*f^
2 + 208*a^4*b^8*c^7*d^11*f^2 + 200*a^4*b^8*c^9*d^9*f^2 - 4288*a^5*b^7*c^2*d^16*f^2 + 4112*a^5*b^7*c^4*d^14*f^2
+ 5120*a^5*b^7*c^6*d^12*f^2 - 3208*a^5*b^7*c^8*d^10*f^2 + 192*a^5*b^7*c^10*d^8*f^2 - 6688*a^6*b^6*c^3*d^15*f^
2 - 2464*a^6*b^6*c^5*d^13*f^2 + 5952*a^6*b^6*c^7*d^11*f^2 - 960*a^6*b^6*c^9*d^9*f^2 + 2624*a^7*b^5*c^2*d^16*f^
2 - 2016*a^7*b^5*c^4*d^14*f^2 - 3456*a^7*b^5*c^6*d^12*f^2 + 1504*a^7*b^5*c^8*d^10*f^2 + 992*a^8*b^4*c^3*d^15*f
^2 - 144*a^8*b^4*c^5*d^13*f^2 - 888*a^8*b^4*c^7*d^11*f^2 - 12*a^8*b^4*c^9*d^9*f^2 + 352*a^9*b^3*c^2*d^16*f^2 +
520*a^9*b^3*c^4*d^14*f^2 + 32*a^9*b^3*c^6*d^12*f^2 + 12*a^9*b^3*c^8*d^10*f^2 + 48*a^10*b^2*c^3*d^15*f^2 + 144
*a^10*b^2*c^5*d^13*f^2 + 1120*a*b^11*c^2*d^16*f^2 - 2776*a*b^11*c^4*d^14*f^2 - 2208*a*b^11*c^6*d^12*f^2 + 1628
*a*b^11*c^8*d^10*f^2 - 64*a*b^11*c^10*d^8*f^2 - 1024*a^2*b^10*c*d^17*f^2 + 1312*a^4*b^8*c*d^17*f^2 + 2688*a^6*
b^6*c*d^17*f^2 + 260*a^8*b^4*c*d^17*f^2 - 96*a^10*b^2*c*d^17*f^2 - 32*a^11*b*c^2*d^16*f^2 - 16*a^11*b*c^4*d^14
*f^2))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5) - (((8*(96*a^2*b^14*d^13*f^4 + 48
0*a^4*b^12*d^13*f^4 + 960*a^6*b^10*d^13*f^4 + 960*a^8*b^8*d^13*f^4 + 480*a^10*b^6*d^13*f^4 + 96*a^12*b^4*d^13*
f^4 + 128*b^16*c^2*d^11*f^4 + 128*b^16*c^4*d^9*f^4 + 640*a^2*b^14*c^2*d^11*f^4 + 544*a^2*b^14*c^4*d^9*f^4 - 76
8*a^3*b^13*c^3*d^10*f^4 + 320*a^3*b^13*c^5*d^8*f^4 + 1280*a^4*b^12*c^2*d^11*f^4 + 800*a^4*b^12*c^4*d^9*f^4 - 1
440*a^5*b^11*c^3*d^10*f^4 + 640*a^5*b^11*c^5*d^8*f^4 + 1280*a^6*b^10*c^2*d^11*f^4 + 320*a^6*b^10*c^4*d^9*f^4 -
1280*a^7*b^9*c^3*d^10*f^4 + 640*a^7*b^9*c^5*d^8*f^4 + 640*a^8*b^8*c^2*d^11*f^4 - 320*a^8*b^8*c^4*d^9*f^4 - 48
0*a^9*b^7*c^3*d^10*f^4 + 320*a^9*b^7*c^5*d^8*f^4 + 128*a^10*b^6*c^2*d^11*f^4 - 352*a^10*b^6*c^4*d^9*f^4 + 64*a
^11*b^5*c^5*d^8*f^4 - 96*a^12*b^4*c^4*d^9*f^4 + 32*a^13*b^3*c^3*d^10*f^4 - 224*a*b^15*c*d^12*f^4 - 160*a*b^15*
c^3*d^10*f^4 + 64*a*b^15*c^5*d^8*f^4 - 1088*a^3*b^13*c*d^12*f^4 - 2080*a^5*b^11*c*d^12*f^4 - 1920*a^7*b^9*c*d^
12*f^4 - 800*a^9*b^7*c*d^12*f^4 - 64*a^11*b^5*c*d^12*f^4 + 32*a^13*b^3*c*d^12*f^4))/(b^9*f^5 + a^8*b*f^5 + 4*a
^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5) + (16*(c + d*tan(e + f*x))^(1/2)*((((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2
- 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3
*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^
3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4
+ 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) - 4
*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 20*a^4*c*d^4*f^2 - 20*b^4*c*d^4*f^2 + 24*
a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^2*c^3*d^2*f^2 + 80*a*b^3*c^4*d*f^2 - 80*
a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^
4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2)*(32*b^18*d^10*f^4 + 160*a^2*b^16*d^10*f^4 + 288*a^4
*b^14*d^10*f^4 + 160*a^6*b^12*d^10*f^4 - 160*a^8*b^10*d^10*f^4 - 288*a^10*b^8*d^10*f^4 - 160*a^12*b^6*d^10*f^4
- 32*a^14*b^4*d^10*f^4 + 48*b^18*c^2*d^8*f^4 + 272*a^2*b^16*c^2*d^8*f^4 + 624*a^4*b^14*c^2*d^8*f^4 + 720*a^6*
b^12*c^2*d^8*f^4 + 400*a^8*b^10*c^2*d^8*f^4 + 48*a^10*b^8*c^2*d^8*f^4 - 48*a^12*b^6*c^2*d^8*f^4 - 16*a^14*b^4*
c^2*d^8*f^4 + 16*a*b^17*c*d^9*f^4 + 112*a^3*b^15*c*d^9*f^4 + 336*a^5*b^13*c*d^9*f^4 + 560*a^7*b^11*c*d^9*f^4 +
560*a^9*b^9*c*d^9*f^4 + 336*a^11*b^7*c*d^9*f^4 + 112*a^13*b^5*c*d^9*f^4 + 16*a^15*b^3*c*d^9*f^4))/(b^9*f^4 +
a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4))*((((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f
^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4
*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 2
40*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4
+ 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) - 4*a^4*c^5*f^2 - 4*
b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 20*a^4*c*d^4*f^2 - 20*b^4*c*d^4*f^2 + 24*a^2*b^2*c^5*f^2 +
40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^2*c^3*d^2*f^2 + 80*a*b^3*c^4*d*f^2 - 80*a^3*b*c^4*d*f^2 -
160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4
+ 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2) + (16*(c + d*tan(e + f*x))^(1/2)*(4*a^14*c*d^14*f^2 - 8*a^13*b*d^15*
f^2 - 60*a*b^13*d^15*f^2 + 76*b^14*c*d^14*f^2 - 52*a^3*b^11*d^15*f^2 - 128*a^5*b^9*d^15*f^2 - 424*a^7*b^7*d^15
*f^2 - 380*a^9*b^5*d^15*f^2 - 100*a^11*b^3*d^15*f^2 - 20*b^14*c^3*d^12*f^2 - 304*b^14*c^5*d^10*f^2 + 20*b^14*c
^7*d^8*f^2 + 540*a^2*b^12*c^3*d^12*f^2 + 624*a^2*b^12*c^5*d^10*f^2 - 116*a^2*b^12*c^7*d^8*f^2 - 596*a^3*b^11*c
^2*d^13*f^2 + 1540*a^3*b^11*c^4*d^11*f^2 - 588*a^3*b^11*c^6*d^9*f^2 + 80*a^4*b^10*c^3*d^12*f^2 + 1760*a^4*b^10
*c^5*d^10*f^2 - 216*a^4*b^10*c^7*d^8*f^2 - 2184*a^5*b^9*c^2*d^13*f^2 + 1320*a^5*b^9*c^4*d^11*f^2 + 152*a^5*b^9
*c^6*d^9*f^2 - 1960*a^6*b^8*c^3*d^12*f^2 + 800*a^6*b^8*c^5*d^10*f^2 - 8*a^6*b^8*c^7*d^8*f^2 - 584*a^7*b^7*c^2*
d^13*f^2 + 840*a^7*b^7*c^4*d^11*f^2 - 56*a^7*b^7*c^6*d^9*f^2 - 1940*a^8*b^6*c^3*d^12*f^2 + 336*a^8*b^6*c^5*d^1
0*f^2 + 68*a^8*b^6*c^7*d^8*f^2 + 676*a^9*b^5*c^2*d^13*f^2 + 180*a^9*b^5*c^4*d^11*f^2 - 260*a^9*b^5*c^6*d^9*f^2
- 500*a^10*b^4*c^3*d^12*f^2 + 368*a^10*b^4*c^5*d^10*f^2 - 4*a^10*b^4*c^7*d^8*f^2 + 156*a^11*b^3*c^2*d^13*f^2
- 140*a^11*b^3*c^4*d^11*f^2 + 4*a^11*b^3*c^6*d^9*f^2 - 40*a^12*b^2*c^3*d^12*f^2 + 468*a*b^13*c^2*d^13*f^2 + 74
0*a*b^13*c^4*d^11*f^2 - 532*a*b^13*c^6*d^9*f^2 - 284*a^2*b^12*c*d^14*f^2 + 84*a^4*b^10*c*d^14*f^2 + 1436*a^6*b
^8*c*d^14*f^2 + 1108*a^8*b^6*c*d^14*f^2 + 124*a^10*b^4*c*d^14*f^2 + 12*a^12*b^2*c*d^14*f^2 + 16*a^13*b*c^2*d^1
3*f^2))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4))*((((8*a^4*c^5*f^2 + 8*b^4*c^5*f
^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c
^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*
b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f
^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) -
4*a^4*c^5*f^2 - 4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 20*a^4*c*d^4*f^2 - 20*b^4*c*d^4*f^2 + 2
4*a^2*b^2*c^5*f^2 + 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^2*c^3*d^2*f^2 + 80*a*b^3*c^4*d*f^2 - 8
0*a^3*b*c^4*d*f^2 - 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*
f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2))*((((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5
*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b
^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 -
240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f
^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) - 4*a^4*c^5*f^2 -
4*b^4*c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 20*a^4*c*d^4*f^2 - 20*b^4*c*d^4*f^2 + 24*a^2*b^2*c^5*f^2
+ 40*a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^2*c^3*d^2*f^2 + 80*a*b^3*c^4*d*f^2 - 80*a^3*b*c^4*d*f^2
- 160*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f
^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2) - (16*(c + d*tan(e + f*x))^(1/2)*(2*b^10*d^20 - a^10*d^20 + 4*a^2*
b^8*d^20 + 27*a^4*b^6*d^20 - 15*a^6*b^4*d^20 - 9*a^8*b^2*d^20 + 15*a^10*c^2*d^18 - 15*a^10*c^4*d^16 + a^10*c^6
*d^14 + 12*b^10*c^2*d^18 + 55*b^10*c^4*d^16 - 335*b^10*c^6*d^14 + 405*b^10*c^8*d^12 - 13*b^10*c^10*d^10 + 2*b^
10*c^12*d^8 - 100*a*b^9*c^3*d^17 + 1840*a*b^9*c^5*d^15 - 3100*a*b^9*c^7*d^13 + 1000*a*b^9*c^9*d^11 - 40*a*b^9*
c^11*d^9 - 100*a^3*b^7*c*d^19 + 400*a^5*b^5*c*d^19 + 124*a^7*b^3*c*d^19 + 20*a^9*b*c^3*d^17 - 48*a^9*b*c^5*d^1
5 + 4*a^9*b*c^7*d^13 + 174*a^2*b^8*c^2*d^18 - 3565*a^2*b^8*c^4*d^16 + 9451*a^2*b^8*c^6*d^14 - 5755*a^2*b^8*c^8
*d^12 + 919*a^2*b^8*c^10*d^10 - 12*a^2*b^8*c^12*d^8 + 3600*a^3*b^7*c^3*d^17 - 13896*a^3*b^7*c^5*d^15 + 14032*a
^3*b^7*c^7*d^13 - 4180*a^3*b^7*c^9*d^11 + 288*a^3*b^7*c^11*d^9 - 1813*a^4*b^6*c^2*d^18 + 10770*a^4*b^6*c^4*d^1
6 - 16848*a^4*b^6*c^6*d^14 + 8385*a^4*b^6*c^8*d^12 - 1115*a^4*b^6*c^10*d^10 + 18*a^4*b^6*c^12*d^8 - 3920*a^5*b
^5*c^3*d^17 + 9936*a^5*b^5*c^5*d^15 - 8040*a^5*b^5*c^7*d^13 + 1840*a^5*b^5*c^9*d^11 - 56*a^5*b^5*c^11*d^9 + 31
5*a^6*b^4*c^2*d^18 - 1880*a^6*b^4*c^4*d^16 + 3140*a^6*b^4*c^6*d^14 - 1305*a^6*b^4*c^8*d^12 + 65*a^6*b^4*c^10*d
^10 - 560*a^7*b^3*c^3*d^17 + 280*a^7*b^3*c^5*d^15 + 176*a^7*b^3*c^7*d^13 - 20*a^7*b^3*c^9*d^11 + 193*a^8*b^2*c
^2*d^18 - 445*a^8*b^2*c^4*d^16 + 207*a^8*b^2*c^6*d^14 - 10*a^8*b^2*c^8*d^12 + 8*a^9*b*c*d^19))/(b^9*f^4 + a^8*
b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4))*((((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 +
32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3
*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a
^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 6
4*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) - 4*a^4*c^5*f^2 - 4*b^4*
c^5*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 20*a^4*c*d^4*f^2 - 20*b^4*c*d^4*f^2 + 24*a^2*b^2*c^5*f^2 + 40*
a^4*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^2*c^3*d^2*f^2 + 80*a*b^3*c^4*d*f^2 - 80*a^3*b*c^4*d*f^2 - 160
*a*b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6
*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2) + (16*(6*a^8*c^4*d^19 - 10*a^2*b^6*d^23 - 27*a^4*b^4*d^23 - 10*a^6*b^2*d
^23 - a^8*d^23 + 8*a^8*c^6*d^17 + 3*a^8*c^8*d^15 - 10*b^8*c^2*d^21 - 85*b^8*c^4*d^19 - 150*b^8*c^6*d^17 - 50*b
^8*c^8*d^15 + 50*b^8*c^10*d^13 + 15*b^8*c^12*d^11 - 10*b^8*c^14*d^9 + 212*a*b^7*c^3*d^20 + 212*a*b^7*c^5*d^18
- 320*a*b^7*c^7*d^16 - 420*a*b^7*c^9*d^14 + 20*a*b^7*c^11*d^12 + 92*a*b^7*c^13*d^10 - 8*a*b^7*c^15*d^8 + 96*a^
3*b^5*c*d^22 + 24*a^7*b*c^5*d^18 + 32*a^7*b*c^7*d^16 + 12*a^7*b*c^9*d^14 - 196*a^2*b^6*c^2*d^21 + 84*a^2*b^6*c
^4*d^19 + 894*a^2*b^6*c^6*d^17 + 430*a^2*b^6*c^8*d^15 - 504*a^2*b^6*c^10*d^13 - 248*a^2*b^6*c^12*d^11 + 62*a^2
*b^6*c^14*d^9 - 224*a^3*b^5*c^3*d^20 - 604*a^3*b^5*c^5*d^18 + 320*a^3*b^5*c^7*d^16 + 904*a^3*b^5*c^9*d^14 + 12
8*a^3*b^5*c^11*d^12 - 172*a^3*b^5*c^13*d^10 + 88*a^4*b^4*c^2*d^21 + 55*a^4*b^4*c^4*d^19 - 440*a^4*b^4*c^6*d^17
- 365*a^4*b^4*c^8*d^15 + 208*a^4*b^4*c^10*d^13 + 193*a^4*b^4*c^12*d^11 + 20*a^5*b^3*c^3*d^20 - 120*a^5*b^3*c^
7*d^16 - 160*a^5*b^3*c^9*d^14 - 60*a^5*b^3*c^11*d^12 + 10*a^6*b^2*c^2*d^21 + 60*a^6*b^2*c^4*d^19 + 20*a^6*b^2*
c^6*d^17 - 50*a^6*b^2*c^8*d^15 - 30*a^6*b^2*c^10*d^13 + 20*a*b^7*c*d^22 - 4*a^7*b*c*d^22))/(b^9*f^5 + a^8*b*f^
5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5)))*((((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32
*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^
2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*
b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a
^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) - 4*a^4*c^5*f^2 - 4*b^4*c^5
*f^2 + 16*a*b^3*d^5*f^2 - 16*a^3*b*d^5*f^2 - 20*a^4*c*d^4*f^2 - 20*b^4*c*d^4*f^2 + 24*a^2*b^2*c^5*f^2 + 40*a^4
*c^3*d^2*f^2 + 40*b^4*c^3*d^2*f^2 - 240*a^2*b^2*c^3*d^2*f^2 + 80*a*b^3*c^4*d*f^2 - 80*a^3*b*c^4*d*f^2 - 160*a*
b^3*c^2*d^3*f^2 + 120*a^2*b^2*c*d^4*f^2 + 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^
4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2)*2i - atan(((((8*(4*b^12*c*d^17*f^2 - 16*a^11*b*d^18*f^2 - 8*a^12*c*d^17*f^2
- 4*a*b^11*d^18*f^2 + 304*a^3*b^9*d^18*f^2 + 120*a^5*b^7*d^18*f^2 - 320*a^7*b^5*d^18*f^2 - 148*a^9*b^3*d^18*f
^2 - 8*a^12*c^3*d^15*f^2 - 400*b^12*c^3*d^15*f^2 + 176*b^12*c^5*d^13*f^2 + 488*b^12*c^7*d^11*f^2 - 92*b^12*c^9
*d^9*f^2 + 6576*a^2*b^10*c^3*d^15*f^2 + 400*a^2*b^10*c^5*d^13*f^2 - 6144*a^2*b^10*c^7*d^11*f^2 + 1056*a^2*b^10
*c^9*d^9*f^2 - 5408*a^3*b^9*c^2*d^16*f^2 + 3888*a^3*b^9*c^4*d^14*f^2 + 6400*a^3*b^9*c^6*d^12*f^2 - 3072*a^3*b^
9*c^8*d^10*f^2 + 128*a^3*b^9*c^10*d^8*f^2 - 648*a^4*b^8*c^3*d^15*f^2 - 1952*a^4*b^8*c^5*d^13*f^2 + 208*a^4*b^8
*c^7*d^11*f^2 + 200*a^4*b^8*c^9*d^9*f^2 - 4288*a^5*b^7*c^2*d^16*f^2 + 4112*a^5*b^7*c^4*d^14*f^2 + 5120*a^5*b^7
*c^6*d^12*f^2 - 3208*a^5*b^7*c^8*d^10*f^2 + 192*a^5*b^7*c^10*d^8*f^2 - 6688*a^6*b^6*c^3*d^15*f^2 - 2464*a^6*b^
6*c^5*d^13*f^2 + 5952*a^6*b^6*c^7*d^11*f^2 - 960*a^6*b^6*c^9*d^9*f^2 + 2624*a^7*b^5*c^2*d^16*f^2 - 2016*a^7*b^
5*c^4*d^14*f^2 - 3456*a^7*b^5*c^6*d^12*f^2 + 1504*a^7*b^5*c^8*d^10*f^2 + 992*a^8*b^4*c^3*d^15*f^2 - 144*a^8*b^
4*c^5*d^13*f^2 - 888*a^8*b^4*c^7*d^11*f^2 - 12*a^8*b^4*c^9*d^9*f^2 + 352*a^9*b^3*c^2*d^16*f^2 + 520*a^9*b^3*c^
4*d^14*f^2 + 32*a^9*b^3*c^6*d^12*f^2 + 12*a^9*b^3*c^8*d^10*f^2 + 48*a^10*b^2*c^3*d^15*f^2 + 144*a^10*b^2*c^5*d
^13*f^2 + 1120*a*b^11*c^2*d^16*f^2 - 2776*a*b^11*c^4*d^14*f^2 - 2208*a*b^11*c^6*d^12*f^2 + 1628*a*b^11*c^8*d^1
0*f^2 - 64*a*b^11*c^10*d^8*f^2 - 1024*a^2*b^10*c*d^17*f^2 + 1312*a^4*b^8*c*d^17*f^2 + 2688*a^6*b^6*c*d^17*f^2
+ 260*a^8*b^4*c*d^17*f^2 - 96*a^10*b^2*c*d^17*f^2 - 32*a^11*b*c^2*d^16*f^2 - 16*a^11*b*c^4*d^14*f^2))/(b^9*f^5
+ a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5) - (((8*(96*a^2*b^14*d^13*f^4 + 480*a^4*b^12*d^13
*f^4 + 960*a^6*b^10*d^13*f^4 + 960*a^8*b^8*d^13*f^4 + 480*a^10*b^6*d^13*f^4 + 96*a^12*b^4*d^13*f^4 + 128*b^16*
c^2*d^11*f^4 + 128*b^16*c^4*d^9*f^4 + 640*a^2*b^14*c^2*d^11*f^4 + 544*a^2*b^14*c^4*d^9*f^4 - 768*a^3*b^13*c^3*
d^10*f^4 + 320*a^3*b^13*c^5*d^8*f^4 + 1280*a^4*b^12*c^2*d^11*f^4 + 800*a^4*b^12*c^4*d^9*f^4 - 1440*a^5*b^11*c^
3*d^10*f^4 + 640*a^5*b^11*c^5*d^8*f^4 + 1280*a^6*b^10*c^2*d^11*f^4 + 320*a^6*b^10*c^4*d^9*f^4 - 1280*a^7*b^9*c
^3*d^10*f^4 + 640*a^7*b^9*c^5*d^8*f^4 + 640*a^8*b^8*c^2*d^11*f^4 - 320*a^8*b^8*c^4*d^9*f^4 - 480*a^9*b^7*c^3*d
^10*f^4 + 320*a^9*b^7*c^5*d^8*f^4 + 128*a^10*b^6*c^2*d^11*f^4 - 352*a^10*b^6*c^4*d^9*f^4 + 64*a^11*b^5*c^5*d^8
*f^4 - 96*a^12*b^4*c^4*d^9*f^4 + 32*a^13*b^3*c^3*d^10*f^4 - 224*a*b^15*c*d^12*f^4 - 160*a*b^15*c^3*d^10*f^4 +
64*a*b^15*c^5*d^8*f^4 - 1088*a^3*b^13*c*d^12*f^4 - 2080*a^5*b^11*c*d^12*f^4 - 1920*a^7*b^9*c*d^12*f^4 - 800*a^
9*b^7*c*d^12*f^4 - 64*a^11*b^5*c*d^12*f^4 + 32*a^13*b^3*c*d^12*f^4))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*
a^4*b^5*f^5 + 4*a^6*b^3*f^5) - (16*(c + d*tan(e + f*x))^(1/2)*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^
5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*
b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2
- 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*
f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 +
4*b^4*c^5*f^2 - 16*a*b^3*d^5*f^2 + 16*a^3*b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^
2 - 40*a^4*c^3*d^2*f^2 - 40*b^4*c^3*d^2*f^2 + 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^
2 + 160*a*b^3*c^2*d^3*f^2 - 120*a^2*b^2*c*d^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*
f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2)*(32*b^18*d^10*f^4 + 160*a^2*b^16*d^10*f^4 + 288*a^4*b^14*d^10*f^4
+ 160*a^6*b^12*d^10*f^4 - 160*a^8*b^10*d^10*f^4 - 288*a^10*b^8*d^10*f^4 - 160*a^12*b^6*d^10*f^4 - 32*a^14*b^4
*d^10*f^4 + 48*b^18*c^2*d^8*f^4 + 272*a^2*b^16*c^2*d^8*f^4 + 624*a^4*b^14*c^2*d^8*f^4 + 720*a^6*b^12*c^2*d^8*f
^4 + 400*a^8*b^10*c^2*d^8*f^4 + 48*a^10*b^8*c^2*d^8*f^4 - 48*a^12*b^6*c^2*d^8*f^4 - 16*a^14*b^4*c^2*d^8*f^4 +
16*a*b^17*c*d^9*f^4 + 112*a^3*b^15*c*d^9*f^4 + 336*a^5*b^13*c*d^9*f^4 + 560*a^7*b^11*c*d^9*f^4 + 560*a^9*b^9*c
*d^9*f^4 + 336*a^11*b^7*c*d^9*f^4 + 112*a^13*b^5*c*d^9*f^4 + 16*a^15*b^3*c*d^9*f^4))/(b^9*f^4 + a^8*b*f^4 + 4*
a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4))*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b
*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2
+ 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*
d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2
*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^2 -
16*a*b^3*d^5*f^2 + 16*a^3*b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^3*d
^2*f^2 - 40*b^4*c^3*d^2*f^2 + 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3*c^
2*d^3*f^2 - 120*a^2*b^2*c*d^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*
f^4 + 4*a^6*b^2*f^4)))^(1/2) - (16*(c + d*tan(e + f*x))^(1/2)*(4*a^14*c*d^14*f^2 - 8*a^13*b*d^15*f^2 - 60*a*b^
13*d^15*f^2 + 76*b^14*c*d^14*f^2 - 52*a^3*b^11*d^15*f^2 - 128*a^5*b^9*d^15*f^2 - 424*a^7*b^7*d^15*f^2 - 380*a^
9*b^5*d^15*f^2 - 100*a^11*b^3*d^15*f^2 - 20*b^14*c^3*d^12*f^2 - 304*b^14*c^5*d^10*f^2 + 20*b^14*c^7*d^8*f^2 +
540*a^2*b^12*c^3*d^12*f^2 + 624*a^2*b^12*c^5*d^10*f^2 - 116*a^2*b^12*c^7*d^8*f^2 - 596*a^3*b^11*c^2*d^13*f^2 +
1540*a^3*b^11*c^4*d^11*f^2 - 588*a^3*b^11*c^6*d^9*f^2 + 80*a^4*b^10*c^3*d^12*f^2 + 1760*a^4*b^10*c^5*d^10*f^2
- 216*a^4*b^10*c^7*d^8*f^2 - 2184*a^5*b^9*c^2*d^13*f^2 + 1320*a^5*b^9*c^4*d^11*f^2 + 152*a^5*b^9*c^6*d^9*f^2
- 1960*a^6*b^8*c^3*d^12*f^2 + 800*a^6*b^8*c^5*d^10*f^2 - 8*a^6*b^8*c^7*d^8*f^2 - 584*a^7*b^7*c^2*d^13*f^2 + 84
0*a^7*b^7*c^4*d^11*f^2 - 56*a^7*b^7*c^6*d^9*f^2 - 1940*a^8*b^6*c^3*d^12*f^2 + 336*a^8*b^6*c^5*d^10*f^2 + 68*a^
8*b^6*c^7*d^8*f^2 + 676*a^9*b^5*c^2*d^13*f^2 + 180*a^9*b^5*c^4*d^11*f^2 - 260*a^9*b^5*c^6*d^9*f^2 - 500*a^10*b
^4*c^3*d^12*f^2 + 368*a^10*b^4*c^5*d^10*f^2 - 4*a^10*b^4*c^7*d^8*f^2 + 156*a^11*b^3*c^2*d^13*f^2 - 140*a^11*b^
3*c^4*d^11*f^2 + 4*a^11*b^3*c^6*d^9*f^2 - 40*a^12*b^2*c^3*d^12*f^2 + 468*a*b^13*c^2*d^13*f^2 + 740*a*b^13*c^4*
d^11*f^2 - 532*a*b^13*c^6*d^9*f^2 - 284*a^2*b^12*c*d^14*f^2 + 84*a^4*b^10*c*d^14*f^2 + 1436*a^6*b^8*c*d^14*f^2
+ 1108*a^8*b^6*c*d^14*f^2 + 124*a^10*b^4*c*d^14*f^2 + 12*a^12*b^2*c*d^14*f^2 + 16*a^13*b*c^2*d^13*f^2))/(b^9*
f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4))*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^
3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 -
80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*
f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*
b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f
^2 + 4*b^4*c^5*f^2 - 16*a*b^3*d^5*f^2 + 16*a^3*b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^
5*f^2 - 40*a^4*c^3*d^2*f^2 - 40*b^4*c^3*d^2*f^2 + 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*
d*f^2 + 160*a*b^3*c^2*d^3*f^2 - 120*a^2*b^2*c*d^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*
b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2))*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a
^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*
f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^
2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6
*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f
^2 - 16*a*b^3*d^5*f^2 + 16*a^3*b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c
^3*d^2*f^2 - 40*b^4*c^3*d^2*f^2 + 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^
3*c^2*d^3*f^2 - 120*a^2*b^2*c*d^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*
b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2) + (16*(c + d*tan(e + f*x))^(1/2)*(2*b^10*d^20 - a^10*d^20 + 4*a^2*b^8*d^20 +
27*a^4*b^6*d^20 - 15*a^6*b^4*d^20 - 9*a^8*b^2*d^20 + 15*a^10*c^2*d^18 - 15*a^10*c^4*d^16 + a^10*c^6*d^14 + 12*
b^10*c^2*d^18 + 55*b^10*c^4*d^16 - 335*b^10*c^6*d^14 + 405*b^10*c^8*d^12 - 13*b^10*c^10*d^10 + 2*b^10*c^12*d^8
- 100*a*b^9*c^3*d^17 + 1840*a*b^9*c^5*d^15 - 3100*a*b^9*c^7*d^13 + 1000*a*b^9*c^9*d^11 - 40*a*b^9*c^11*d^9 -
100*a^3*b^7*c*d^19 + 400*a^5*b^5*c*d^19 + 124*a^7*b^3*c*d^19 + 20*a^9*b*c^3*d^17 - 48*a^9*b*c^5*d^15 + 4*a^9*b
*c^7*d^13 + 174*a^2*b^8*c^2*d^18 - 3565*a^2*b^8*c^4*d^16 + 9451*a^2*b^8*c^6*d^14 - 5755*a^2*b^8*c^8*d^12 + 919
*a^2*b^8*c^10*d^10 - 12*a^2*b^8*c^12*d^8 + 3600*a^3*b^7*c^3*d^17 - 13896*a^3*b^7*c^5*d^15 + 14032*a^3*b^7*c^7*
d^13 - 4180*a^3*b^7*c^9*d^11 + 288*a^3*b^7*c^11*d^9 - 1813*a^4*b^6*c^2*d^18 + 10770*a^4*b^6*c^4*d^16 - 16848*a
^4*b^6*c^6*d^14 + 8385*a^4*b^6*c^8*d^12 - 1115*a^4*b^6*c^10*d^10 + 18*a^4*b^6*c^12*d^8 - 3920*a^5*b^5*c^3*d^17
+ 9936*a^5*b^5*c^5*d^15 - 8040*a^5*b^5*c^7*d^13 + 1840*a^5*b^5*c^9*d^11 - 56*a^5*b^5*c^11*d^9 + 315*a^6*b^4*c
^2*d^18 - 1880*a^6*b^4*c^4*d^16 + 3140*a^6*b^4*c^6*d^14 - 1305*a^6*b^4*c^8*d^12 + 65*a^6*b^4*c^10*d^10 - 560*a
^7*b^3*c^3*d^17 + 280*a^7*b^3*c^5*d^15 + 176*a^7*b^3*c^7*d^13 - 20*a^7*b^3*c^9*d^11 + 193*a^8*b^2*c^2*d^18 - 4
45*a^8*b^2*c^4*d^16 + 207*a^8*b^2*c^6*d^14 - 10*a^8*b^2*c^8*d^12 + 8*a^9*b*c*d^19))/(b^9*f^4 + a^8*b*f^4 + 4*a
^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4))*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*
d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 +
480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d
^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*
f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^2 -
16*a*b^3*d^5*f^2 + 16*a^3*b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^3*d^
2*f^2 - 40*b^4*c^3*d^2*f^2 + 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3*c^2
*d^3*f^2 - 120*a^2*b^2*c*d^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f
^4 + 4*a^6*b^2*f^4)))^(1/2)*1i - (((8*(4*b^12*c*d^17*f^2 - 16*a^11*b*d^18*f^2 - 8*a^12*c*d^17*f^2 - 4*a*b^11*d
^18*f^2 + 304*a^3*b^9*d^18*f^2 + 120*a^5*b^7*d^18*f^2 - 320*a^7*b^5*d^18*f^2 - 148*a^9*b^3*d^18*f^2 - 8*a^12*c
^3*d^15*f^2 - 400*b^12*c^3*d^15*f^2 + 176*b^12*c^5*d^13*f^2 + 488*b^12*c^7*d^11*f^2 - 92*b^12*c^9*d^9*f^2 + 65
76*a^2*b^10*c^3*d^15*f^2 + 400*a^2*b^10*c^5*d^13*f^2 - 6144*a^2*b^10*c^7*d^11*f^2 + 1056*a^2*b^10*c^9*d^9*f^2
- 5408*a^3*b^9*c^2*d^16*f^2 + 3888*a^3*b^9*c^4*d^14*f^2 + 6400*a^3*b^9*c^6*d^12*f^2 - 3072*a^3*b^9*c^8*d^10*f^
2 + 128*a^3*b^9*c^10*d^8*f^2 - 648*a^4*b^8*c^3*d^15*f^2 - 1952*a^4*b^8*c^5*d^13*f^2 + 208*a^4*b^8*c^7*d^11*f^2
+ 200*a^4*b^8*c^9*d^9*f^2 - 4288*a^5*b^7*c^2*d^16*f^2 + 4112*a^5*b^7*c^4*d^14*f^2 + 5120*a^5*b^7*c^6*d^12*f^2
- 3208*a^5*b^7*c^8*d^10*f^2 + 192*a^5*b^7*c^10*d^8*f^2 - 6688*a^6*b^6*c^3*d^15*f^2 - 2464*a^6*b^6*c^5*d^13*f^
2 + 5952*a^6*b^6*c^7*d^11*f^2 - 960*a^6*b^6*c^9*d^9*f^2 + 2624*a^7*b^5*c^2*d^16*f^2 - 2016*a^7*b^5*c^4*d^14*f^
2 - 3456*a^7*b^5*c^6*d^12*f^2 + 1504*a^7*b^5*c^8*d^10*f^2 + 992*a^8*b^4*c^3*d^15*f^2 - 144*a^8*b^4*c^5*d^13*f^
2 - 888*a^8*b^4*c^7*d^11*f^2 - 12*a^8*b^4*c^9*d^9*f^2 + 352*a^9*b^3*c^2*d^16*f^2 + 520*a^9*b^3*c^4*d^14*f^2 +
32*a^9*b^3*c^6*d^12*f^2 + 12*a^9*b^3*c^8*d^10*f^2 + 48*a^10*b^2*c^3*d^15*f^2 + 144*a^10*b^2*c^5*d^13*f^2 + 112
0*a*b^11*c^2*d^16*f^2 - 2776*a*b^11*c^4*d^14*f^2 - 2208*a*b^11*c^6*d^12*f^2 + 1628*a*b^11*c^8*d^10*f^2 - 64*a*
b^11*c^10*d^8*f^2 - 1024*a^2*b^10*c*d^17*f^2 + 1312*a^4*b^8*c*d^17*f^2 + 2688*a^6*b^6*c*d^17*f^2 + 260*a^8*b^4
*c*d^17*f^2 - 96*a^10*b^2*c*d^17*f^2 - 32*a^11*b*c^2*d^16*f^2 - 16*a^11*b*c^4*d^14*f^2))/(b^9*f^5 + a^8*b*f^5
+ 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5) - (((8*(96*a^2*b^14*d^13*f^4 + 480*a^4*b^12*d^13*f^4 + 960*a^
6*b^10*d^13*f^4 + 960*a^8*b^8*d^13*f^4 + 480*a^10*b^6*d^13*f^4 + 96*a^12*b^4*d^13*f^4 + 128*b^16*c^2*d^11*f^4
+ 128*b^16*c^4*d^9*f^4 + 640*a^2*b^14*c^2*d^11*f^4 + 544*a^2*b^14*c^4*d^9*f^4 - 768*a^3*b^13*c^3*d^10*f^4 + 32
0*a^3*b^13*c^5*d^8*f^4 + 1280*a^4*b^12*c^2*d^11*f^4 + 800*a^4*b^12*c^4*d^9*f^4 - 1440*a^5*b^11*c^3*d^10*f^4 +
640*a^5*b^11*c^5*d^8*f^4 + 1280*a^6*b^10*c^2*d^11*f^4 + 320*a^6*b^10*c^4*d^9*f^4 - 1280*a^7*b^9*c^3*d^10*f^4 +
640*a^7*b^9*c^5*d^8*f^4 + 640*a^8*b^8*c^2*d^11*f^4 - 320*a^8*b^8*c^4*d^9*f^4 - 480*a^9*b^7*c^3*d^10*f^4 + 320
*a^9*b^7*c^5*d^8*f^4 + 128*a^10*b^6*c^2*d^11*f^4 - 352*a^10*b^6*c^4*d^9*f^4 + 64*a^11*b^5*c^5*d^8*f^4 - 96*a^1
2*b^4*c^4*d^9*f^4 + 32*a^13*b^3*c^3*d^10*f^4 - 224*a*b^15*c*d^12*f^4 - 160*a*b^15*c^3*d^10*f^4 + 64*a*b^15*c^5
*d^8*f^4 - 1088*a^3*b^13*c*d^12*f^4 - 2080*a^5*b^11*c*d^12*f^4 - 1920*a^7*b^9*c*d^12*f^4 - 800*a^9*b^7*c*d^12*
f^4 - 64*a^11*b^5*c*d^12*f^4 + 32*a^13*b^3*c*d^12*f^4))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 +
4*a^6*b^3*f^5) + (16*(c + d*tan(e + f*x))^(1/2)*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^
3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f
^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2
*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*
b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^
2 - 16*a*b^3*d^5*f^2 + 16*a^3*b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^
3*d^2*f^2 - 40*b^4*c^3*d^2*f^2 + 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3
*c^2*d^3*f^2 - 120*a^2*b^2*c*d^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b
^4*f^4 + 4*a^6*b^2*f^4)))^(1/2)*(32*b^18*d^10*f^4 + 160*a^2*b^16*d^10*f^4 + 288*a^4*b^14*d^10*f^4 + 160*a^6*b^
12*d^10*f^4 - 160*a^8*b^10*d^10*f^4 - 288*a^10*b^8*d^10*f^4 - 160*a^12*b^6*d^10*f^4 - 32*a^14*b^4*d^10*f^4 + 4
8*b^18*c^2*d^8*f^4 + 272*a^2*b^16*c^2*d^8*f^4 + 624*a^4*b^14*c^2*d^8*f^4 + 720*a^6*b^12*c^2*d^8*f^4 + 400*a^8*
b^10*c^2*d^8*f^4 + 48*a^10*b^8*c^2*d^8*f^4 - 48*a^12*b^6*c^2*d^8*f^4 - 16*a^14*b^4*c^2*d^8*f^4 + 16*a*b^17*c*d
^9*f^4 + 112*a^3*b^15*c*d^9*f^4 + 336*a^5*b^13*c*d^9*f^4 + 560*a^7*b^11*c*d^9*f^4 + 560*a^9*b^9*c*d^9*f^4 + 33
6*a^11*b^7*c*d^9*f^4 + 112*a^13*b^5*c*d^9*f^4 + 16*a^15*b^3*c*d^9*f^4))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 +
6*a^4*b^5*f^4 + 4*a^6*b^3*f^4))*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40
*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2
*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320
*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 +
d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^2 - 16*a*b^3*d^5
*f^2 + 16*a^3*b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^3*d^2*f^2 - 40*b
^4*c^3*d^2*f^2 + 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3*c^2*d^3*f^2 - 1
20*a^2*b^2*c*d^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b
^2*f^4)))^(1/2) + (16*(c + d*tan(e + f*x))^(1/2)*(4*a^14*c*d^14*f^2 - 8*a^13*b*d^15*f^2 - 60*a*b^13*d^15*f^2 +
76*b^14*c*d^14*f^2 - 52*a^3*b^11*d^15*f^2 - 128*a^5*b^9*d^15*f^2 - 424*a^7*b^7*d^15*f^2 - 380*a^9*b^5*d^15*f^
2 - 100*a^11*b^3*d^15*f^2 - 20*b^14*c^3*d^12*f^2 - 304*b^14*c^5*d^10*f^2 + 20*b^14*c^7*d^8*f^2 + 540*a^2*b^12*
c^3*d^12*f^2 + 624*a^2*b^12*c^5*d^10*f^2 - 116*a^2*b^12*c^7*d^8*f^2 - 596*a^3*b^11*c^2*d^13*f^2 + 1540*a^3*b^1
1*c^4*d^11*f^2 - 588*a^3*b^11*c^6*d^9*f^2 + 80*a^4*b^10*c^3*d^12*f^2 + 1760*a^4*b^10*c^5*d^10*f^2 - 216*a^4*b^
10*c^7*d^8*f^2 - 2184*a^5*b^9*c^2*d^13*f^2 + 1320*a^5*b^9*c^4*d^11*f^2 + 152*a^5*b^9*c^6*d^9*f^2 - 1960*a^6*b^
8*c^3*d^12*f^2 + 800*a^6*b^8*c^5*d^10*f^2 - 8*a^6*b^8*c^7*d^8*f^2 - 584*a^7*b^7*c^2*d^13*f^2 + 840*a^7*b^7*c^4
*d^11*f^2 - 56*a^7*b^7*c^6*d^9*f^2 - 1940*a^8*b^6*c^3*d^12*f^2 + 336*a^8*b^6*c^5*d^10*f^2 + 68*a^8*b^6*c^7*d^8
*f^2 + 676*a^9*b^5*c^2*d^13*f^2 + 180*a^9*b^5*c^4*d^11*f^2 - 260*a^9*b^5*c^6*d^9*f^2 - 500*a^10*b^4*c^3*d^12*f
^2 + 368*a^10*b^4*c^5*d^10*f^2 - 4*a^10*b^4*c^7*d^8*f^2 + 156*a^11*b^3*c^2*d^13*f^2 - 140*a^11*b^3*c^4*d^11*f^
2 + 4*a^11*b^3*c^6*d^9*f^2 - 40*a^12*b^2*c^3*d^12*f^2 + 468*a*b^13*c^2*d^13*f^2 + 740*a*b^13*c^4*d^11*f^2 - 53
2*a*b^13*c^6*d^9*f^2 - 284*a^2*b^12*c*d^14*f^2 + 84*a^4*b^10*c*d^14*f^2 + 1436*a^6*b^8*c*d^14*f^2 + 1108*a^8*b
^6*c*d^14*f^2 + 124*a^10*b^4*c*d^14*f^2 + 12*a^12*b^2*c*d^14*f^2 + 16*a^13*b*c^2*d^13*f^2))/(b^9*f^4 + a^8*b*f
^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4))*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 3
2*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d
^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2
*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*
a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^
5*f^2 - 16*a*b^3*d^5*f^2 + 16*a^3*b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^
4*c^3*d^2*f^2 - 40*b^4*c^3*d^2*f^2 + 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a
*b^3*c^2*d^3*f^2 - 120*a^2*b^2*c*d^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a
^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2))*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2
+ 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2
*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 -
320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^
10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^2 - 16*a*b^3
*d^5*f^2 + 16*a^3*b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^3*d^2*f^2 -
40*b^4*c^3*d^2*f^2 + 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3*c^2*d^3*f^2
- 120*a^2*b^2*c*d^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a
^6*b^2*f^4)))^(1/2) - (16*(c + d*tan(e + f*x))^(1/2)*(2*b^10*d^20 - a^10*d^20 + 4*a^2*b^8*d^20 + 27*a^4*b^6*d^
20 - 15*a^6*b^4*d^20 - 9*a^8*b^2*d^20 + 15*a^10*c^2*d^18 - 15*a^10*c^4*d^16 + a^10*c^6*d^14 + 12*b^10*c^2*d^18
+ 55*b^10*c^4*d^16 - 335*b^10*c^6*d^14 + 405*b^10*c^8*d^12 - 13*b^10*c^10*d^10 + 2*b^10*c^12*d^8 - 100*a*b^9*
c^3*d^17 + 1840*a*b^9*c^5*d^15 - 3100*a*b^9*c^7*d^13 + 1000*a*b^9*c^9*d^11 - 40*a*b^9*c^11*d^9 - 100*a^3*b^7*c
*d^19 + 400*a^5*b^5*c*d^19 + 124*a^7*b^3*c*d^19 + 20*a^9*b*c^3*d^17 - 48*a^9*b*c^5*d^15 + 4*a^9*b*c^7*d^13 + 1
74*a^2*b^8*c^2*d^18 - 3565*a^2*b^8*c^4*d^16 + 9451*a^2*b^8*c^6*d^14 - 5755*a^2*b^8*c^8*d^12 + 919*a^2*b^8*c^10
*d^10 - 12*a^2*b^8*c^12*d^8 + 3600*a^3*b^7*c^3*d^17 - 13896*a^3*b^7*c^5*d^15 + 14032*a^3*b^7*c^7*d^13 - 4180*a
^3*b^7*c^9*d^11 + 288*a^3*b^7*c^11*d^9 - 1813*a^4*b^6*c^2*d^18 + 10770*a^4*b^6*c^4*d^16 - 16848*a^4*b^6*c^6*d^
14 + 8385*a^4*b^6*c^8*d^12 - 1115*a^4*b^6*c^10*d^10 + 18*a^4*b^6*c^12*d^8 - 3920*a^5*b^5*c^3*d^17 + 9936*a^5*b
^5*c^5*d^15 - 8040*a^5*b^5*c^7*d^13 + 1840*a^5*b^5*c^9*d^11 - 56*a^5*b^5*c^11*d^9 + 315*a^6*b^4*c^2*d^18 - 188
0*a^6*b^4*c^4*d^16 + 3140*a^6*b^4*c^6*d^14 - 1305*a^6*b^4*c^8*d^12 + 65*a^6*b^4*c^10*d^10 - 560*a^7*b^3*c^3*d^
17 + 280*a^7*b^3*c^5*d^15 + 176*a^7*b^3*c^7*d^13 - 20*a^7*b^3*c^9*d^11 + 193*a^8*b^2*c^2*d^18 - 445*a^8*b^2*c^
4*d^16 + 207*a^8*b^2*c^6*d^14 - 10*a^8*b^2*c^8*d^12 + 8*a^9*b*c*d^19))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 +
6*a^4*b^5*f^4 + 4*a^6*b^3*f^4))*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*
a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*
c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*
a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 +
d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^2 - 16*a*b^3*d^5*
f^2 + 16*a^3*b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^3*d^2*f^2 - 40*b^
4*c^3*d^2*f^2 + 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3*c^2*d^3*f^2 - 12
0*a^2*b^2*c*d^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^
2*f^4)))^(1/2)*1i)/((((8*(4*b^12*c*d^17*f^2 - 16*a^11*b*d^18*f^2 - 8*a^12*c*d^17*f^2 - 4*a*b^11*d^18*f^2 + 304
*a^3*b^9*d^18*f^2 + 120*a^5*b^7*d^18*f^2 - 320*a^7*b^5*d^18*f^2 - 148*a^9*b^3*d^18*f^2 - 8*a^12*c^3*d^15*f^2 -
400*b^12*c^3*d^15*f^2 + 176*b^12*c^5*d^13*f^2 + 488*b^12*c^7*d^11*f^2 - 92*b^12*c^9*d^9*f^2 + 6576*a^2*b^10*c
^3*d^15*f^2 + 400*a^2*b^10*c^5*d^13*f^2 - 6144*a^2*b^10*c^7*d^11*f^2 + 1056*a^2*b^10*c^9*d^9*f^2 - 5408*a^3*b^
9*c^2*d^16*f^2 + 3888*a^3*b^9*c^4*d^14*f^2 + 6400*a^3*b^9*c^6*d^12*f^2 - 3072*a^3*b^9*c^8*d^10*f^2 + 128*a^3*b
^9*c^10*d^8*f^2 - 648*a^4*b^8*c^3*d^15*f^2 - 1952*a^4*b^8*c^5*d^13*f^2 + 208*a^4*b^8*c^7*d^11*f^2 + 200*a^4*b^
8*c^9*d^9*f^2 - 4288*a^5*b^7*c^2*d^16*f^2 + 4112*a^5*b^7*c^4*d^14*f^2 + 5120*a^5*b^7*c^6*d^12*f^2 - 3208*a^5*b
^7*c^8*d^10*f^2 + 192*a^5*b^7*c^10*d^8*f^2 - 6688*a^6*b^6*c^3*d^15*f^2 - 2464*a^6*b^6*c^5*d^13*f^2 + 5952*a^6*
b^6*c^7*d^11*f^2 - 960*a^6*b^6*c^9*d^9*f^2 + 2624*a^7*b^5*c^2*d^16*f^2 - 2016*a^7*b^5*c^4*d^14*f^2 - 3456*a^7*
b^5*c^6*d^12*f^2 + 1504*a^7*b^5*c^8*d^10*f^2 + 992*a^8*b^4*c^3*d^15*f^2 - 144*a^8*b^4*c^5*d^13*f^2 - 888*a^8*b
^4*c^7*d^11*f^2 - 12*a^8*b^4*c^9*d^9*f^2 + 352*a^9*b^3*c^2*d^16*f^2 + 520*a^9*b^3*c^4*d^14*f^2 + 32*a^9*b^3*c^
6*d^12*f^2 + 12*a^9*b^3*c^8*d^10*f^2 + 48*a^10*b^2*c^3*d^15*f^2 + 144*a^10*b^2*c^5*d^13*f^2 + 1120*a*b^11*c^2*
d^16*f^2 - 2776*a*b^11*c^4*d^14*f^2 - 2208*a*b^11*c^6*d^12*f^2 + 1628*a*b^11*c^8*d^10*f^2 - 64*a*b^11*c^10*d^8
*f^2 - 1024*a^2*b^10*c*d^17*f^2 + 1312*a^4*b^8*c*d^17*f^2 + 2688*a^6*b^6*c*d^17*f^2 + 260*a^8*b^4*c*d^17*f^2 -
96*a^10*b^2*c*d^17*f^2 - 32*a^11*b*c^2*d^16*f^2 - 16*a^11*b*c^4*d^14*f^2))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f
^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5) - (((8*(96*a^2*b^14*d^13*f^4 + 480*a^4*b^12*d^13*f^4 + 960*a^6*b^10*d^13*f
^4 + 960*a^8*b^8*d^13*f^4 + 480*a^10*b^6*d^13*f^4 + 96*a^12*b^4*d^13*f^4 + 128*b^16*c^2*d^11*f^4 + 128*b^16*c^
4*d^9*f^4 + 640*a^2*b^14*c^2*d^11*f^4 + 544*a^2*b^14*c^4*d^9*f^4 - 768*a^3*b^13*c^3*d^10*f^4 + 320*a^3*b^13*c^
5*d^8*f^4 + 1280*a^4*b^12*c^2*d^11*f^4 + 800*a^4*b^12*c^4*d^9*f^4 - 1440*a^5*b^11*c^3*d^10*f^4 + 640*a^5*b^11*
c^5*d^8*f^4 + 1280*a^6*b^10*c^2*d^11*f^4 + 320*a^6*b^10*c^4*d^9*f^4 - 1280*a^7*b^9*c^3*d^10*f^4 + 640*a^7*b^9*
c^5*d^8*f^4 + 640*a^8*b^8*c^2*d^11*f^4 - 320*a^8*b^8*c^4*d^9*f^4 - 480*a^9*b^7*c^3*d^10*f^4 + 320*a^9*b^7*c^5*
d^8*f^4 + 128*a^10*b^6*c^2*d^11*f^4 - 352*a^10*b^6*c^4*d^9*f^4 + 64*a^11*b^5*c^5*d^8*f^4 - 96*a^12*b^4*c^4*d^9
*f^4 + 32*a^13*b^3*c^3*d^10*f^4 - 224*a*b^15*c*d^12*f^4 - 160*a*b^15*c^3*d^10*f^4 + 64*a*b^15*c^5*d^8*f^4 - 10
88*a^3*b^13*c*d^12*f^4 - 2080*a^5*b^11*c*d^12*f^4 - 1920*a^7*b^9*c*d^12*f^4 - 800*a^9*b^7*c*d^12*f^4 - 64*a^11
*b^5*c*d^12*f^4 + 32*a^13*b^3*c*d^12*f^4))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^
5) - (16*(c + d*tan(e + f*x))^(1/2)*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 +
40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*
b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 -
320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^1
0 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^2 - 16*a*b^3*
d^5*f^2 + 16*a^3*b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^3*d^2*f^2 - 4
0*b^4*c^3*d^2*f^2 + 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3*c^2*d^3*f^2
- 120*a^2*b^2*c*d^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^
6*b^2*f^4)))^(1/2)*(32*b^18*d^10*f^4 + 160*a^2*b^16*d^10*f^4 + 288*a^4*b^14*d^10*f^4 + 160*a^6*b^12*d^10*f^4 -
160*a^8*b^10*d^10*f^4 - 288*a^10*b^8*d^10*f^4 - 160*a^12*b^6*d^10*f^4 - 32*a^14*b^4*d^10*f^4 + 48*b^18*c^2*d^
8*f^4 + 272*a^2*b^16*c^2*d^8*f^4 + 624*a^4*b^14*c^2*d^8*f^4 + 720*a^6*b^12*c^2*d^8*f^4 + 400*a^8*b^10*c^2*d^8*
f^4 + 48*a^10*b^8*c^2*d^8*f^4 - 48*a^12*b^6*c^2*d^8*f^4 - 16*a^14*b^4*c^2*d^8*f^4 + 16*a*b^17*c*d^9*f^4 + 112*
a^3*b^15*c*d^9*f^4 + 336*a^5*b^13*c*d^9*f^4 + 560*a^7*b^11*c*d^9*f^4 + 560*a^9*b^9*c*d^9*f^4 + 336*a^11*b^7*c*
d^9*f^4 + 112*a^13*b^5*c*d^9*f^4 + 16*a^15*b^3*c*d^9*f^4))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^
4 + 4*a^6*b^3*f^4))*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^
2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2
- 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^
3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2
*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^2 - 16*a*b^3*d^5*f^2 + 16*a^3
*b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^3*d^2*f^2 - 40*b^4*c^3*d^2*f^
2 + 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3*c^2*d^3*f^2 - 120*a^2*b^2*c*
d^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/
2) - (16*(c + d*tan(e + f*x))^(1/2)*(4*a^14*c*d^14*f^2 - 8*a^13*b*d^15*f^2 - 60*a*b^13*d^15*f^2 + 76*b^14*c*d^
14*f^2 - 52*a^3*b^11*d^15*f^2 - 128*a^5*b^9*d^15*f^2 - 424*a^7*b^7*d^15*f^2 - 380*a^9*b^5*d^15*f^2 - 100*a^11*
b^3*d^15*f^2 - 20*b^14*c^3*d^12*f^2 - 304*b^14*c^5*d^10*f^2 + 20*b^14*c^7*d^8*f^2 + 540*a^2*b^12*c^3*d^12*f^2
+ 624*a^2*b^12*c^5*d^10*f^2 - 116*a^2*b^12*c^7*d^8*f^2 - 596*a^3*b^11*c^2*d^13*f^2 + 1540*a^3*b^11*c^4*d^11*f^
2 - 588*a^3*b^11*c^6*d^9*f^2 + 80*a^4*b^10*c^3*d^12*f^2 + 1760*a^4*b^10*c^5*d^10*f^2 - 216*a^4*b^10*c^7*d^8*f^
2 - 2184*a^5*b^9*c^2*d^13*f^2 + 1320*a^5*b^9*c^4*d^11*f^2 + 152*a^5*b^9*c^6*d^9*f^2 - 1960*a^6*b^8*c^3*d^12*f^
2 + 800*a^6*b^8*c^5*d^10*f^2 - 8*a^6*b^8*c^7*d^8*f^2 - 584*a^7*b^7*c^2*d^13*f^2 + 840*a^7*b^7*c^4*d^11*f^2 - 5
6*a^7*b^7*c^6*d^9*f^2 - 1940*a^8*b^6*c^3*d^12*f^2 + 336*a^8*b^6*c^5*d^10*f^2 + 68*a^8*b^6*c^7*d^8*f^2 + 676*a^
9*b^5*c^2*d^13*f^2 + 180*a^9*b^5*c^4*d^11*f^2 - 260*a^9*b^5*c^6*d^9*f^2 - 500*a^10*b^4*c^3*d^12*f^2 + 368*a^10
*b^4*c^5*d^10*f^2 - 4*a^10*b^4*c^7*d^8*f^2 + 156*a^11*b^3*c^2*d^13*f^2 - 140*a^11*b^3*c^4*d^11*f^2 + 4*a^11*b^
3*c^6*d^9*f^2 - 40*a^12*b^2*c^3*d^12*f^2 + 468*a*b^13*c^2*d^13*f^2 + 740*a*b^13*c^4*d^11*f^2 - 532*a*b^13*c^6*
d^9*f^2 - 284*a^2*b^12*c*d^14*f^2 + 84*a^4*b^10*c*d^14*f^2 + 1436*a^6*b^8*c*d^14*f^2 + 1108*a^8*b^6*c*d^14*f^2
+ 124*a^10*b^4*c*d^14*f^2 + 12*a^12*b^2*c*d^14*f^2 + 16*a^13*b*c^2*d^13*f^2))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^
7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4))*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f
^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*
a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^
2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*
(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^2 - 16*a*
b^3*d^5*f^2 + 16*a^3*b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^3*d^2*f^2
- 40*b^4*c^3*d^2*f^2 + 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3*c^2*d^3*
f^2 - 120*a^2*b^2*c*d^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 +
4*a^6*b^2*f^4)))^(1/2))*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^
4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*
f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^
2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5
*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^2 - 16*a*b^3*d^5*f^2 + 16
*a^3*b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^3*d^2*f^2 - 40*b^4*c^3*d^
2*f^2 + 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3*c^2*d^3*f^2 - 120*a^2*b^
2*c*d^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))
^(1/2) + (16*(c + d*tan(e + f*x))^(1/2)*(2*b^10*d^20 - a^10*d^20 + 4*a^2*b^8*d^20 + 27*a^4*b^6*d^20 - 15*a^6*b
^4*d^20 - 9*a^8*b^2*d^20 + 15*a^10*c^2*d^18 - 15*a^10*c^4*d^16 + a^10*c^6*d^14 + 12*b^10*c^2*d^18 + 55*b^10*c^
4*d^16 - 335*b^10*c^6*d^14 + 405*b^10*c^8*d^12 - 13*b^10*c^10*d^10 + 2*b^10*c^12*d^8 - 100*a*b^9*c^3*d^17 + 18
40*a*b^9*c^5*d^15 - 3100*a*b^9*c^7*d^13 + 1000*a*b^9*c^9*d^11 - 40*a*b^9*c^11*d^9 - 100*a^3*b^7*c*d^19 + 400*a
^5*b^5*c*d^19 + 124*a^7*b^3*c*d^19 + 20*a^9*b*c^3*d^17 - 48*a^9*b*c^5*d^15 + 4*a^9*b*c^7*d^13 + 174*a^2*b^8*c^
2*d^18 - 3565*a^2*b^8*c^4*d^16 + 9451*a^2*b^8*c^6*d^14 - 5755*a^2*b^8*c^8*d^12 + 919*a^2*b^8*c^10*d^10 - 12*a^
2*b^8*c^12*d^8 + 3600*a^3*b^7*c^3*d^17 - 13896*a^3*b^7*c^5*d^15 + 14032*a^3*b^7*c^7*d^13 - 4180*a^3*b^7*c^9*d^
11 + 288*a^3*b^7*c^11*d^9 - 1813*a^4*b^6*c^2*d^18 + 10770*a^4*b^6*c^4*d^16 - 16848*a^4*b^6*c^6*d^14 + 8385*a^4
*b^6*c^8*d^12 - 1115*a^4*b^6*c^10*d^10 + 18*a^4*b^6*c^12*d^8 - 3920*a^5*b^5*c^3*d^17 + 9936*a^5*b^5*c^5*d^15 -
8040*a^5*b^5*c^7*d^13 + 1840*a^5*b^5*c^9*d^11 - 56*a^5*b^5*c^11*d^9 + 315*a^6*b^4*c^2*d^18 - 1880*a^6*b^4*c^4
*d^16 + 3140*a^6*b^4*c^6*d^14 - 1305*a^6*b^4*c^8*d^12 + 65*a^6*b^4*c^10*d^10 - 560*a^7*b^3*c^3*d^17 + 280*a^7*
b^3*c^5*d^15 + 176*a^7*b^3*c^7*d^13 - 20*a^7*b^3*c^9*d^11 + 193*a^8*b^2*c^2*d^18 - 445*a^8*b^2*c^4*d^16 + 207*
a^8*b^2*c^6*d^14 - 10*a^8*b^2*c^8*d^12 + 8*a^9*b*c*d^19))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4
+ 4*a^6*b^3*f^4))*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2
+ 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 -
160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3
*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*
d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^2 - 16*a*b^3*d^5*f^2 + 16*a^3*
b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^3*d^2*f^2 - 40*b^4*c^3*d^2*f^2
+ 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3*c^2*d^3*f^2 - 120*a^2*b^2*c*d
^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2
) + (((8*(4*b^12*c*d^17*f^2 - 16*a^11*b*d^18*f^2 - 8*a^12*c*d^17*f^2 - 4*a*b^11*d^18*f^2 + 304*a^3*b^9*d^18*f^
2 + 120*a^5*b^7*d^18*f^2 - 320*a^7*b^5*d^18*f^2 - 148*a^9*b^3*d^18*f^2 - 8*a^12*c^3*d^15*f^2 - 400*b^12*c^3*d^
15*f^2 + 176*b^12*c^5*d^13*f^2 + 488*b^12*c^7*d^11*f^2 - 92*b^12*c^9*d^9*f^2 + 6576*a^2*b^10*c^3*d^15*f^2 + 40
0*a^2*b^10*c^5*d^13*f^2 - 6144*a^2*b^10*c^7*d^11*f^2 + 1056*a^2*b^10*c^9*d^9*f^2 - 5408*a^3*b^9*c^2*d^16*f^2 +
3888*a^3*b^9*c^4*d^14*f^2 + 6400*a^3*b^9*c^6*d^12*f^2 - 3072*a^3*b^9*c^8*d^10*f^2 + 128*a^3*b^9*c^10*d^8*f^2
- 648*a^4*b^8*c^3*d^15*f^2 - 1952*a^4*b^8*c^5*d^13*f^2 + 208*a^4*b^8*c^7*d^11*f^2 + 200*a^4*b^8*c^9*d^9*f^2 -
4288*a^5*b^7*c^2*d^16*f^2 + 4112*a^5*b^7*c^4*d^14*f^2 + 5120*a^5*b^7*c^6*d^12*f^2 - 3208*a^5*b^7*c^8*d^10*f^2
+ 192*a^5*b^7*c^10*d^8*f^2 - 6688*a^6*b^6*c^3*d^15*f^2 - 2464*a^6*b^6*c^5*d^13*f^2 + 5952*a^6*b^6*c^7*d^11*f^2
- 960*a^6*b^6*c^9*d^9*f^2 + 2624*a^7*b^5*c^2*d^16*f^2 - 2016*a^7*b^5*c^4*d^14*f^2 - 3456*a^7*b^5*c^6*d^12*f^2
+ 1504*a^7*b^5*c^8*d^10*f^2 + 992*a^8*b^4*c^3*d^15*f^2 - 144*a^8*b^4*c^5*d^13*f^2 - 888*a^8*b^4*c^7*d^11*f^2
- 12*a^8*b^4*c^9*d^9*f^2 + 352*a^9*b^3*c^2*d^16*f^2 + 520*a^9*b^3*c^4*d^14*f^2 + 32*a^9*b^3*c^6*d^12*f^2 + 12*
a^9*b^3*c^8*d^10*f^2 + 48*a^10*b^2*c^3*d^15*f^2 + 144*a^10*b^2*c^5*d^13*f^2 + 1120*a*b^11*c^2*d^16*f^2 - 2776*
a*b^11*c^4*d^14*f^2 - 2208*a*b^11*c^6*d^12*f^2 + 1628*a*b^11*c^8*d^10*f^2 - 64*a*b^11*c^10*d^8*f^2 - 1024*a^2*
b^10*c*d^17*f^2 + 1312*a^4*b^8*c*d^17*f^2 + 2688*a^6*b^6*c*d^17*f^2 + 260*a^8*b^4*c*d^17*f^2 - 96*a^10*b^2*c*d
^17*f^2 - 32*a^11*b*c^2*d^16*f^2 - 16*a^11*b*c^4*d^14*f^2))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f
^5 + 4*a^6*b^3*f^5) - (((8*(96*a^2*b^14*d^13*f^4 + 480*a^4*b^12*d^13*f^4 + 960*a^6*b^10*d^13*f^4 + 960*a^8*b^8
*d^13*f^4 + 480*a^10*b^6*d^13*f^4 + 96*a^12*b^4*d^13*f^4 + 128*b^16*c^2*d^11*f^4 + 128*b^16*c^4*d^9*f^4 + 640*
a^2*b^14*c^2*d^11*f^4 + 544*a^2*b^14*c^4*d^9*f^4 - 768*a^3*b^13*c^3*d^10*f^4 + 320*a^3*b^13*c^5*d^8*f^4 + 1280
*a^4*b^12*c^2*d^11*f^4 + 800*a^4*b^12*c^4*d^9*f^4 - 1440*a^5*b^11*c^3*d^10*f^4 + 640*a^5*b^11*c^5*d^8*f^4 + 12
80*a^6*b^10*c^2*d^11*f^4 + 320*a^6*b^10*c^4*d^9*f^4 - 1280*a^7*b^9*c^3*d^10*f^4 + 640*a^7*b^9*c^5*d^8*f^4 + 64
0*a^8*b^8*c^2*d^11*f^4 - 320*a^8*b^8*c^4*d^9*f^4 - 480*a^9*b^7*c^3*d^10*f^4 + 320*a^9*b^7*c^5*d^8*f^4 + 128*a^
10*b^6*c^2*d^11*f^4 - 352*a^10*b^6*c^4*d^9*f^4 + 64*a^11*b^5*c^5*d^8*f^4 - 96*a^12*b^4*c^4*d^9*f^4 + 32*a^13*b
^3*c^3*d^10*f^4 - 224*a*b^15*c*d^12*f^4 - 160*a*b^15*c^3*d^10*f^4 + 64*a*b^15*c^5*d^8*f^4 - 1088*a^3*b^13*c*d^
12*f^4 - 2080*a^5*b^11*c*d^12*f^4 - 1920*a^7*b^9*c*d^12*f^4 - 800*a^9*b^7*c*d^12*f^4 - 64*a^11*b^5*c*d^12*f^4
+ 32*a^13*b^3*c*d^12*f^4))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5) + (16*(c + d*
tan(e + f*x))^(1/2)*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^
2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2
- 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^
3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2
*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^2 - 16*a*b^3*d^5*f^2 + 16*a^3
*b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^3*d^2*f^2 - 40*b^4*c^3*d^2*f^
2 + 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3*c^2*d^3*f^2 - 120*a^2*b^2*c*
d^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/
2)*(32*b^18*d^10*f^4 + 160*a^2*b^16*d^10*f^4 + 288*a^4*b^14*d^10*f^4 + 160*a^6*b^12*d^10*f^4 - 160*a^8*b^10*d^
10*f^4 - 288*a^10*b^8*d^10*f^4 - 160*a^12*b^6*d^10*f^4 - 32*a^14*b^4*d^10*f^4 + 48*b^18*c^2*d^8*f^4 + 272*a^2*
b^16*c^2*d^8*f^4 + 624*a^4*b^14*c^2*d^8*f^4 + 720*a^6*b^12*c^2*d^8*f^4 + 400*a^8*b^10*c^2*d^8*f^4 + 48*a^10*b^
8*c^2*d^8*f^4 - 48*a^12*b^6*c^2*d^8*f^4 - 16*a^14*b^4*c^2*d^8*f^4 + 16*a*b^17*c*d^9*f^4 + 112*a^3*b^15*c*d^9*f
^4 + 336*a^5*b^13*c*d^9*f^4 + 560*a^7*b^11*c*d^9*f^4 + 560*a^9*b^9*c*d^9*f^4 + 336*a^11*b^7*c*d^9*f^4 + 112*a^
13*b^5*c*d^9*f^4 + 16*a^15*b^3*c*d^9*f^4))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^
4))*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4
*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*
d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16
*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^
6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^2 - 16*a*b^3*d^5*f^2 + 16*a^3*b*d^5*f^2 + 20*
a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^3*d^2*f^2 - 40*b^4*c^3*d^2*f^2 + 240*a^2*b^2*
c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3*c^2*d^3*f^2 - 120*a^2*b^2*c*d^4*f^2 - 160*a^
3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2) + (16*(c + d*
tan(e + f*x))^(1/2)*(4*a^14*c*d^14*f^2 - 8*a^13*b*d^15*f^2 - 60*a*b^13*d^15*f^2 + 76*b^14*c*d^14*f^2 - 52*a^3*
b^11*d^15*f^2 - 128*a^5*b^9*d^15*f^2 - 424*a^7*b^7*d^15*f^2 - 380*a^9*b^5*d^15*f^2 - 100*a^11*b^3*d^15*f^2 - 2
0*b^14*c^3*d^12*f^2 - 304*b^14*c^5*d^10*f^2 + 20*b^14*c^7*d^8*f^2 + 540*a^2*b^12*c^3*d^12*f^2 + 624*a^2*b^12*c
^5*d^10*f^2 - 116*a^2*b^12*c^7*d^8*f^2 - 596*a^3*b^11*c^2*d^13*f^2 + 1540*a^3*b^11*c^4*d^11*f^2 - 588*a^3*b^11
*c^6*d^9*f^2 + 80*a^4*b^10*c^3*d^12*f^2 + 1760*a^4*b^10*c^5*d^10*f^2 - 216*a^4*b^10*c^7*d^8*f^2 - 2184*a^5*b^9
*c^2*d^13*f^2 + 1320*a^5*b^9*c^4*d^11*f^2 + 152*a^5*b^9*c^6*d^9*f^2 - 1960*a^6*b^8*c^3*d^12*f^2 + 800*a^6*b^8*
c^5*d^10*f^2 - 8*a^6*b^8*c^7*d^8*f^2 - 584*a^7*b^7*c^2*d^13*f^2 + 840*a^7*b^7*c^4*d^11*f^2 - 56*a^7*b^7*c^6*d^
9*f^2 - 1940*a^8*b^6*c^3*d^12*f^2 + 336*a^8*b^6*c^5*d^10*f^2 + 68*a^8*b^6*c^7*d^8*f^2 + 676*a^9*b^5*c^2*d^13*f
^2 + 180*a^9*b^5*c^4*d^11*f^2 - 260*a^9*b^5*c^6*d^9*f^2 - 500*a^10*b^4*c^3*d^12*f^2 + 368*a^10*b^4*c^5*d^10*f^
2 - 4*a^10*b^4*c^7*d^8*f^2 + 156*a^11*b^3*c^2*d^13*f^2 - 140*a^11*b^3*c^4*d^11*f^2 + 4*a^11*b^3*c^6*d^9*f^2 -
40*a^12*b^2*c^3*d^12*f^2 + 468*a*b^13*c^2*d^13*f^2 + 740*a*b^13*c^4*d^11*f^2 - 532*a*b^13*c^6*d^9*f^2 - 284*a^
2*b^12*c*d^14*f^2 + 84*a^4*b^10*c*d^14*f^2 + 1436*a^6*b^8*c*d^14*f^2 + 1108*a^8*b^6*c*d^14*f^2 + 124*a^10*b^4*
c*d^14*f^2 + 12*a^12*b^2*c*d^14*f^2 + 16*a^13*b*c^2*d^13*f^2))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^
5*f^4 + 4*a^6*b^3*f^4))*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^
4*f^2 + 40*b^4*c*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*
f^2 - 160*a*b^3*c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^
2*d^3*f^2)^2/4 - (16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5
*c^2*d^8 + 10*c^4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^2 - 16*a*b^3*d^5*f^2 + 16
*a^3*b*d^5*f^2 + 20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^3*d^2*f^2 - 40*b^4*c^3*d^
2*f^2 + 240*a^2*b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3*c^2*d^3*f^2 - 120*a^2*b^
2*c*d^4*f^2 - 160*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))
^(1/2))*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c
*d^4*f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*
c^4*d*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 -
(16*a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^
4*d^6 + 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^2 - 16*a*b^3*d^5*f^2 + 16*a^3*b*d^5*f^2 +
20*a^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^3*d^2*f^2 - 40*b^4*c^3*d^2*f^2 + 240*a^2*
b^2*c^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3*c^2*d^3*f^2 - 120*a^2*b^2*c*d^4*f^2 - 16
0*a^3*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2) - (16*(c
+ d*tan(e + f*x))^(1/2)*(2*b^10*d^20 - a^10*d^20 + 4*a^2*b^8*d^20 + 27*a^4*b^6*d^20 - 15*a^6*b^4*d^20 - 9*a^8*
b^2*d^20 + 15*a^10*c^2*d^18 - 15*a^10*c^4*d^16 + a^10*c^6*d^14 + 12*b^10*c^2*d^18 + 55*b^10*c^4*d^16 - 335*b^1
0*c^6*d^14 + 405*b^10*c^8*d^12 - 13*b^10*c^10*d^10 + 2*b^10*c^12*d^8 - 100*a*b^9*c^3*d^17 + 1840*a*b^9*c^5*d^1
5 - 3100*a*b^9*c^7*d^13 + 1000*a*b^9*c^9*d^11 - 40*a*b^9*c^11*d^9 - 100*a^3*b^7*c*d^19 + 400*a^5*b^5*c*d^19 +
124*a^7*b^3*c*d^19 + 20*a^9*b*c^3*d^17 - 48*a^9*b*c^5*d^15 + 4*a^9*b*c^7*d^13 + 174*a^2*b^8*c^2*d^18 - 3565*a^
2*b^8*c^4*d^16 + 9451*a^2*b^8*c^6*d^14 - 5755*a^2*b^8*c^8*d^12 + 919*a^2*b^8*c^10*d^10 - 12*a^2*b^8*c^12*d^8 +
3600*a^3*b^7*c^3*d^17 - 13896*a^3*b^7*c^5*d^15 + 14032*a^3*b^7*c^7*d^13 - 4180*a^3*b^7*c^9*d^11 + 288*a^3*b^7
*c^11*d^9 - 1813*a^4*b^6*c^2*d^18 + 10770*a^4*b^6*c^4*d^16 - 16848*a^4*b^6*c^6*d^14 + 8385*a^4*b^6*c^8*d^12 -
1115*a^4*b^6*c^10*d^10 + 18*a^4*b^6*c^12*d^8 - 3920*a^5*b^5*c^3*d^17 + 9936*a^5*b^5*c^5*d^15 - 8040*a^5*b^5*c^
7*d^13 + 1840*a^5*b^5*c^9*d^11 - 56*a^5*b^5*c^11*d^9 + 315*a^6*b^4*c^2*d^18 - 1880*a^6*b^4*c^4*d^16 + 3140*a^6
*b^4*c^6*d^14 - 1305*a^6*b^4*c^8*d^12 + 65*a^6*b^4*c^10*d^10 - 560*a^7*b^3*c^3*d^17 + 280*a^7*b^3*c^5*d^15 + 1
76*a^7*b^3*c^7*d^13 - 20*a^7*b^3*c^9*d^11 + 193*a^8*b^2*c^2*d^18 - 445*a^8*b^2*c^4*d^16 + 207*a^8*b^2*c^6*d^14
- 10*a^8*b^2*c^8*d^12 + 8*a^9*b*c*d^19))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4
))*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*
f^2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d
*f^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*
a^8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6
+ 10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^2 - 16*a*b^3*d^5*f^2 + 16*a^3*b*d^5*f^2 + 20*a
^4*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^3*d^2*f^2 - 40*b^4*c^3*d^2*f^2 + 240*a^2*b^2*c
^3*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3*c^2*d^3*f^2 - 120*a^2*b^2*c*d^4*f^2 - 160*a^3
*b*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2) + (16*(6*a^8*c
^4*d^19 - 10*a^2*b^6*d^23 - 27*a^4*b^4*d^23 - 10*a^6*b^2*d^23 - a^8*d^23 + 8*a^8*c^6*d^17 + 3*a^8*c^8*d^15 - 1
0*b^8*c^2*d^21 - 85*b^8*c^4*d^19 - 150*b^8*c^6*d^17 - 50*b^8*c^8*d^15 + 50*b^8*c^10*d^13 + 15*b^8*c^12*d^11 -
10*b^8*c^14*d^9 + 212*a*b^7*c^3*d^20 + 212*a*b^7*c^5*d^18 - 320*a*b^7*c^7*d^16 - 420*a*b^7*c^9*d^14 + 20*a*b^7
*c^11*d^12 + 92*a*b^7*c^13*d^10 - 8*a*b^7*c^15*d^8 + 96*a^3*b^5*c*d^22 + 24*a^7*b*c^5*d^18 + 32*a^7*b*c^7*d^16
+ 12*a^7*b*c^9*d^14 - 196*a^2*b^6*c^2*d^21 + 84*a^2*b^6*c^4*d^19 + 894*a^2*b^6*c^6*d^17 + 430*a^2*b^6*c^8*d^1
5 - 504*a^2*b^6*c^10*d^13 - 248*a^2*b^6*c^12*d^11 + 62*a^2*b^6*c^14*d^9 - 224*a^3*b^5*c^3*d^20 - 604*a^3*b^5*c
^5*d^18 + 320*a^3*b^5*c^7*d^16 + 904*a^3*b^5*c^9*d^14 + 128*a^3*b^5*c^11*d^12 - 172*a^3*b^5*c^13*d^10 + 88*a^4
*b^4*c^2*d^21 + 55*a^4*b^4*c^4*d^19 - 440*a^4*b^4*c^6*d^17 - 365*a^4*b^4*c^8*d^15 + 208*a^4*b^4*c^10*d^13 + 19
3*a^4*b^4*c^12*d^11 + 20*a^5*b^3*c^3*d^20 - 120*a^5*b^3*c^7*d^16 - 160*a^5*b^3*c^9*d^14 - 60*a^5*b^3*c^11*d^12
+ 10*a^6*b^2*c^2*d^21 + 60*a^6*b^2*c^4*d^19 + 20*a^6*b^2*c^6*d^17 - 50*a^6*b^2*c^8*d^15 - 30*a^6*b^2*c^10*d^1
3 + 20*a*b^7*c*d^22 - 4*a^7*b*c*d^22))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5)))
*(-(((8*a^4*c^5*f^2 + 8*b^4*c^5*f^2 - 32*a*b^3*d^5*f^2 + 32*a^3*b*d^5*f^2 + 40*a^4*c*d^4*f^2 + 40*b^4*c*d^4*f^
2 - 48*a^2*b^2*c^5*f^2 - 80*a^4*c^3*d^2*f^2 - 80*b^4*c^3*d^2*f^2 + 480*a^2*b^2*c^3*d^2*f^2 - 160*a*b^3*c^4*d*f
^2 + 160*a^3*b*c^4*d*f^2 + 320*a*b^3*c^2*d^3*f^2 - 240*a^2*b^2*c*d^4*f^2 - 320*a^3*b*c^2*d^3*f^2)^2/4 - (16*a^
8*f^4 + 16*b^8*f^4 + 64*a^2*b^6*f^4 + 96*a^4*b^4*f^4 + 64*a^6*b^2*f^4)*(c^10 + d^10 + 5*c^2*d^8 + 10*c^4*d^6 +
10*c^6*d^4 + 5*c^8*d^2))^(1/2) + 4*a^4*c^5*f^2 + 4*b^4*c^5*f^2 - 16*a*b^3*d^5*f^2 + 16*a^3*b*d^5*f^2 + 20*a^4
*c*d^4*f^2 + 20*b^4*c*d^4*f^2 - 24*a^2*b^2*c^5*f^2 - 40*a^4*c^3*d^2*f^2 - 40*b^4*c^3*d^2*f^2 + 240*a^2*b^2*c^3
*d^2*f^2 - 80*a*b^3*c^4*d*f^2 + 80*a^3*b*c^4*d*f^2 + 160*a*b^3*c^2*d^3*f^2 - 120*a^2*b^2*c*d^4*f^2 - 160*a^3*b
*c^2*d^3*f^2)/(16*(a^8*f^4 + b^8*f^4 + 4*a^2*b^6*f^4 + 6*a^4*b^4*f^4 + 4*a^6*b^2*f^4)))^(1/2)*2i - (atan(((((1
6*(c + d*tan(e + f*x))^(1/2)*(2*b^10*d^20 - a^10*d^20 + 4*a^2*b^8*d^20 + 27*a^4*b^6*d^20 - 15*a^6*b^4*d^20 - 9
*a^8*b^2*d^20 + 15*a^10*c^2*d^18 - 15*a^10*c^4*d^16 + a^10*c^6*d^14 + 12*b^10*c^2*d^18 + 55*b^10*c^4*d^16 - 33
5*b^10*c^6*d^14 + 405*b^10*c^8*d^12 - 13*b^10*c^10*d^10 + 2*b^10*c^12*d^8 - 100*a*b^9*c^3*d^17 + 1840*a*b^9*c^
5*d^15 - 3100*a*b^9*c^7*d^13 + 1000*a*b^9*c^9*d^11 - 40*a*b^9*c^11*d^9 - 100*a^3*b^7*c*d^19 + 400*a^5*b^5*c*d^
19 + 124*a^7*b^3*c*d^19 + 20*a^9*b*c^3*d^17 - 48*a^9*b*c^5*d^15 + 4*a^9*b*c^7*d^13 + 174*a^2*b^8*c^2*d^18 - 35
65*a^2*b^8*c^4*d^16 + 9451*a^2*b^8*c^6*d^14 - 5755*a^2*b^8*c^8*d^12 + 919*a^2*b^8*c^10*d^10 - 12*a^2*b^8*c^12*
d^8 + 3600*a^3*b^7*c^3*d^17 - 13896*a^3*b^7*c^5*d^15 + 14032*a^3*b^7*c^7*d^13 - 4180*a^3*b^7*c^9*d^11 + 288*a^
3*b^7*c^11*d^9 - 1813*a^4*b^6*c^2*d^18 + 10770*a^4*b^6*c^4*d^16 - 16848*a^4*b^6*c^6*d^14 + 8385*a^4*b^6*c^8*d^
12 - 1115*a^4*b^6*c^10*d^10 + 18*a^4*b^6*c^12*d^8 - 3920*a^5*b^5*c^3*d^17 + 9936*a^5*b^5*c^5*d^15 - 8040*a^5*b
^5*c^7*d^13 + 1840*a^5*b^5*c^9*d^11 - 56*a^5*b^5*c^11*d^9 + 315*a^6*b^4*c^2*d^18 - 1880*a^6*b^4*c^4*d^16 + 314
0*a^6*b^4*c^6*d^14 - 1305*a^6*b^4*c^8*d^12 + 65*a^6*b^4*c^10*d^10 - 560*a^7*b^3*c^3*d^17 + 280*a^7*b^3*c^5*d^1
5 + 176*a^7*b^3*c^7*d^13 - 20*a^7*b^3*c^9*d^11 + 193*a^8*b^2*c^2*d^18 - 445*a^8*b^2*c^4*d^16 + 207*a^8*b^2*c^6
*d^14 - 10*a^8*b^2*c^8*d^12 + 8*a^9*b*c*d^19))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^
3*f^4) + (((8*(4*b^12*c*d^17*f^2 - 16*a^11*b*d^18*f^2 - 8*a^12*c*d^17*f^2 - 4*a*b^11*d^18*f^2 + 304*a^3*b^9*d^
18*f^2 + 120*a^5*b^7*d^18*f^2 - 320*a^7*b^5*d^18*f^2 - 148*a^9*b^3*d^18*f^2 - 8*a^12*c^3*d^15*f^2 - 400*b^12*c
^3*d^15*f^2 + 176*b^12*c^5*d^13*f^2 + 488*b^12*c^7*d^11*f^2 - 92*b^12*c^9*d^9*f^2 + 6576*a^2*b^10*c^3*d^15*f^2
+ 400*a^2*b^10*c^5*d^13*f^2 - 6144*a^2*b^10*c^7*d^11*f^2 + 1056*a^2*b^10*c^9*d^9*f^2 - 5408*a^3*b^9*c^2*d^16*
f^2 + 3888*a^3*b^9*c^4*d^14*f^2 + 6400*a^3*b^9*c^6*d^12*f^2 - 3072*a^3*b^9*c^8*d^10*f^2 + 128*a^3*b^9*c^10*d^8
*f^2 - 648*a^4*b^8*c^3*d^15*f^2 - 1952*a^4*b^8*c^5*d^13*f^2 + 208*a^4*b^8*c^7*d^11*f^2 + 200*a^4*b^8*c^9*d^9*f
^2 - 4288*a^5*b^7*c^2*d^16*f^2 + 4112*a^5*b^7*c^4*d^14*f^2 + 5120*a^5*b^7*c^6*d^12*f^2 - 3208*a^5*b^7*c^8*d^10
*f^2 + 192*a^5*b^7*c^10*d^8*f^2 - 6688*a^6*b^6*c^3*d^15*f^2 - 2464*a^6*b^6*c^5*d^13*f^2 + 5952*a^6*b^6*c^7*d^1
1*f^2 - 960*a^6*b^6*c^9*d^9*f^2 + 2624*a^7*b^5*c^2*d^16*f^2 - 2016*a^7*b^5*c^4*d^14*f^2 - 3456*a^7*b^5*c^6*d^1
2*f^2 + 1504*a^7*b^5*c^8*d^10*f^2 + 992*a^8*b^4*c^3*d^15*f^2 - 144*a^8*b^4*c^5*d^13*f^2 - 888*a^8*b^4*c^7*d^11
*f^2 - 12*a^8*b^4*c^9*d^9*f^2 + 352*a^9*b^3*c^2*d^16*f^2 + 520*a^9*b^3*c^4*d^14*f^2 + 32*a^9*b^3*c^6*d^12*f^2
+ 12*a^9*b^3*c^8*d^10*f^2 + 48*a^10*b^2*c^3*d^15*f^2 + 144*a^10*b^2*c^5*d^13*f^2 + 1120*a*b^11*c^2*d^16*f^2 -
2776*a*b^11*c^4*d^14*f^2 - 2208*a*b^11*c^6*d^12*f^2 + 1628*a*b^11*c^8*d^10*f^2 - 64*a*b^11*c^10*d^8*f^2 - 1024
*a^2*b^10*c*d^17*f^2 + 1312*a^4*b^8*c*d^17*f^2 + 2688*a^6*b^6*c*d^17*f^2 + 260*a^8*b^4*c*d^17*f^2 - 96*a^10*b^
2*c*d^17*f^2 - 32*a^11*b*c^2*d^16*f^2 - 16*a^11*b*c^4*d^14*f^2))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*
b^5*f^5 + 4*a^6*b^3*f^5) + (((16*(c + d*tan(e + f*x))^(1/2)*(4*a^14*c*d^14*f^2 - 8*a^13*b*d^15*f^2 - 60*a*b^13
*d^15*f^2 + 76*b^14*c*d^14*f^2 - 52*a^3*b^11*d^15*f^2 - 128*a^5*b^9*d^15*f^2 - 424*a^7*b^7*d^15*f^2 - 380*a^9*
b^5*d^15*f^2 - 100*a^11*b^3*d^15*f^2 - 20*b^14*c^3*d^12*f^2 - 304*b^14*c^5*d^10*f^2 + 20*b^14*c^7*d^8*f^2 + 54
0*a^2*b^12*c^3*d^12*f^2 + 624*a^2*b^12*c^5*d^10*f^2 - 116*a^2*b^12*c^7*d^8*f^2 - 596*a^3*b^11*c^2*d^13*f^2 + 1
540*a^3*b^11*c^4*d^11*f^2 - 588*a^3*b^11*c^6*d^9*f^2 + 80*a^4*b^10*c^3*d^12*f^2 + 1760*a^4*b^10*c^5*d^10*f^2 -
216*a^4*b^10*c^7*d^8*f^2 - 2184*a^5*b^9*c^2*d^13*f^2 + 1320*a^5*b^9*c^4*d^11*f^2 + 152*a^5*b^9*c^6*d^9*f^2 -
1960*a^6*b^8*c^3*d^12*f^2 + 800*a^6*b^8*c^5*d^10*f^2 - 8*a^6*b^8*c^7*d^8*f^2 - 584*a^7*b^7*c^2*d^13*f^2 + 840*
a^7*b^7*c^4*d^11*f^2 - 56*a^7*b^7*c^6*d^9*f^2 - 1940*a^8*b^6*c^3*d^12*f^2 + 336*a^8*b^6*c^5*d^10*f^2 + 68*a^8*
b^6*c^7*d^8*f^2 + 676*a^9*b^5*c^2*d^13*f^2 + 180*a^9*b^5*c^4*d^11*f^2 - 260*a^9*b^5*c^6*d^9*f^2 - 500*a^10*b^4
*c^3*d^12*f^2 + 368*a^10*b^4*c^5*d^10*f^2 - 4*a^10*b^4*c^7*d^8*f^2 + 156*a^11*b^3*c^2*d^13*f^2 - 140*a^11*b^3*
c^4*d^11*f^2 + 4*a^11*b^3*c^6*d^9*f^2 - 40*a^12*b^2*c^3*d^12*f^2 + 468*a*b^13*c^2*d^13*f^2 + 740*a*b^13*c^4*d^
11*f^2 - 532*a*b^13*c^6*d^9*f^2 - 284*a^2*b^12*c*d^14*f^2 + 84*a^4*b^10*c*d^14*f^2 + 1436*a^6*b^8*c*d^14*f^2 +
1108*a^8*b^6*c*d^14*f^2 + 124*a^10*b^4*c*d^14*f^2 + 12*a^12*b^2*c*d^14*f^2 + 16*a^13*b*c^2*d^13*f^2))/(b^9*f^
4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4) - (((8*(96*a^2*b^14*d^13*f^4 + 480*a^4*b^12*d^1
3*f^4 + 960*a^6*b^10*d^13*f^4 + 960*a^8*b^8*d^13*f^4 + 480*a^10*b^6*d^13*f^4 + 96*a^12*b^4*d^13*f^4 + 128*b^16
*c^2*d^11*f^4 + 128*b^16*c^4*d^9*f^4 + 640*a^2*b^14*c^2*d^11*f^4 + 544*a^2*b^14*c^4*d^9*f^4 - 768*a^3*b^13*c^3
*d^10*f^4 + 320*a^3*b^13*c^5*d^8*f^4 + 1280*a^4*b^12*c^2*d^11*f^4 + 800*a^4*b^12*c^4*d^9*f^4 - 1440*a^5*b^11*c
^3*d^10*f^4 + 640*a^5*b^11*c^5*d^8*f^4 + 1280*a^6*b^10*c^2*d^11*f^4 + 320*a^6*b^10*c^4*d^9*f^4 - 1280*a^7*b^9*
c^3*d^10*f^4 + 640*a^7*b^9*c^5*d^8*f^4 + 640*a^8*b^8*c^2*d^11*f^4 - 320*a^8*b^8*c^4*d^9*f^4 - 480*a^9*b^7*c^3*
d^10*f^4 + 320*a^9*b^7*c^5*d^8*f^4 + 128*a^10*b^6*c^2*d^11*f^4 - 352*a^10*b^6*c^4*d^9*f^4 + 64*a^11*b^5*c^5*d^
8*f^4 - 96*a^12*b^4*c^4*d^9*f^4 + 32*a^13*b^3*c^3*d^10*f^4 - 224*a*b^15*c*d^12*f^4 - 160*a*b^15*c^3*d^10*f^4 +
64*a*b^15*c^5*d^8*f^4 - 1088*a^3*b^13*c*d^12*f^4 - 2080*a^5*b^11*c*d^12*f^4 - 1920*a^7*b^9*c*d^12*f^4 - 800*a
^9*b^7*c*d^12*f^4 - 64*a^11*b^5*c*d^12*f^4 + 32*a^13*b^3*c*d^12*f^4))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6
*a^4*b^5*f^5 + 4*a^6*b^3*f^5) - (4*(c + d*tan(e + f*x))^(1/2)*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 +
4*a^6*b^5*f^2 + a^8*b^3*f^2)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c^3*d^2 + 75
*a*b^6*c^2*d^3 - 75*a^2*b^5*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*a^3*b^4*c^2
*d^3 - 25*a^4*b^3*c^3*d^2 - 5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2)*(32*b^18*d^10*f^4 + 160
*a^2*b^16*d^10*f^4 + 288*a^4*b^14*d^10*f^4 + 160*a^6*b^12*d^10*f^4 - 160*a^8*b^10*d^10*f^4 - 288*a^10*b^8*d^10
*f^4 - 160*a^12*b^6*d^10*f^4 - 32*a^14*b^4*d^10*f^4 + 48*b^18*c^2*d^8*f^4 + 272*a^2*b^16*c^2*d^8*f^4 + 624*a^4
*b^14*c^2*d^8*f^4 + 720*a^6*b^12*c^2*d^8*f^4 + 400*a^8*b^10*c^2*d^8*f^4 + 48*a^10*b^8*c^2*d^8*f^4 - 48*a^12*b^
6*c^2*d^8*f^4 - 16*a^14*b^4*c^2*d^8*f^4 + 16*a*b^17*c*d^9*f^4 + 112*a^3*b^15*c*d^9*f^4 + 336*a^5*b^13*c*d^9*f^
4 + 560*a^7*b^11*c*d^9*f^4 + 560*a^9*b^9*c*d^9*f^4 + 336*a^11*b^7*c*d^9*f^4 + 112*a^13*b^5*c*d^9*f^4 + 16*a^15
*b^3*c*d^9*f^4))/((b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4)*(b^11*f^2 + 4*a^2*b^9*
f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)))*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5
*f^2 + a^8*b^3*f^2)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c^3*d^2 + 75*a*b^6*c^
2*d^3 - 75*a^2*b^5*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*a^3*b^4*c^2*d^3 - 25
*a^4*b^3*c^3*d^2 - 5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2))/(4*(b^11*f^2 + 4*a^2*b^9*f^2 +
6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)))*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 +
a^8*b^3*f^2)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c^3*d^2 + 75*a*b^6*c^2*d^3
- 75*a^2*b^5*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*a^3*b^4*c^2*d^3 - 25*a^4*b
^3*c^3*d^2 - 5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2))/(4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*
b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)))*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b
^3*f^2)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c^3*d^2 + 75*a*b^6*c^2*d^3 - 75*a
^2*b^5*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*a^3*b^4*c^2*d^3 - 25*a^4*b^3*c^3
*d^2 - 5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2))/(4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^
2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)))*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2
)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c^3*d^2 + 75*a*b^6*c^2*d^3 - 75*a^2*b^5
*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*a^3*b^4*c^2*d^3 - 25*a^4*b^3*c^3*d^2 -
5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2)*1i)/(4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 +
4*a^6*b^5*f^2 + a^8*b^3*f^2)) + (((16*(c + d*tan(e + f*x))^(1/2)*(2*b^10*d^20 - a^10*d^20 + 4*a^2*b^8*d^20 +
27*a^4*b^6*d^20 - 15*a^6*b^4*d^20 - 9*a^8*b^2*d^20 + 15*a^10*c^2*d^18 - 15*a^10*c^4*d^16 + a^10*c^6*d^14 + 12*
b^10*c^2*d^18 + 55*b^10*c^4*d^16 - 335*b^10*c^6*d^14 + 405*b^10*c^8*d^12 - 13*b^10*c^10*d^10 + 2*b^10*c^12*d^8
- 100*a*b^9*c^3*d^17 + 1840*a*b^9*c^5*d^15 - 3100*a*b^9*c^7*d^13 + 1000*a*b^9*c^9*d^11 - 40*a*b^9*c^11*d^9 -
100*a^3*b^7*c*d^19 + 400*a^5*b^5*c*d^19 + 124*a^7*b^3*c*d^19 + 20*a^9*b*c^3*d^17 - 48*a^9*b*c^5*d^15 + 4*a^9*b
*c^7*d^13 + 174*a^2*b^8*c^2*d^18 - 3565*a^2*b^8*c^4*d^16 + 9451*a^2*b^8*c^6*d^14 - 5755*a^2*b^8*c^8*d^12 + 919
*a^2*b^8*c^10*d^10 - 12*a^2*b^8*c^12*d^8 + 3600*a^3*b^7*c^3*d^17 - 13896*a^3*b^7*c^5*d^15 + 14032*a^3*b^7*c^7*
d^13 - 4180*a^3*b^7*c^9*d^11 + 288*a^3*b^7*c^11*d^9 - 1813*a^4*b^6*c^2*d^18 + 10770*a^4*b^6*c^4*d^16 - 16848*a
^4*b^6*c^6*d^14 + 8385*a^4*b^6*c^8*d^12 - 1115*a^4*b^6*c^10*d^10 + 18*a^4*b^6*c^12*d^8 - 3920*a^5*b^5*c^3*d^17
+ 9936*a^5*b^5*c^5*d^15 - 8040*a^5*b^5*c^7*d^13 + 1840*a^5*b^5*c^9*d^11 - 56*a^5*b^5*c^11*d^9 + 315*a^6*b^4*c
^2*d^18 - 1880*a^6*b^4*c^4*d^16 + 3140*a^6*b^4*c^6*d^14 - 1305*a^6*b^4*c^8*d^12 + 65*a^6*b^4*c^10*d^10 - 560*a
^7*b^3*c^3*d^17 + 280*a^7*b^3*c^5*d^15 + 176*a^7*b^3*c^7*d^13 - 20*a^7*b^3*c^9*d^11 + 193*a^8*b^2*c^2*d^18 - 4
45*a^8*b^2*c^4*d^16 + 207*a^8*b^2*c^6*d^14 - 10*a^8*b^2*c^8*d^12 + 8*a^9*b*c*d^19))/(b^9*f^4 + a^8*b*f^4 + 4*a
^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4) - (((8*(4*b^12*c*d^17*f^2 - 16*a^11*b*d^18*f^2 - 8*a^12*c*d^17*f^2
- 4*a*b^11*d^18*f^2 + 304*a^3*b^9*d^18*f^2 + 120*a^5*b^7*d^18*f^2 - 320*a^7*b^5*d^18*f^2 - 148*a^9*b^3*d^18*f
^2 - 8*a^12*c^3*d^15*f^2 - 400*b^12*c^3*d^15*f^2 + 176*b^12*c^5*d^13*f^2 + 488*b^12*c^7*d^11*f^2 - 92*b^12*c^9
*d^9*f^2 + 6576*a^2*b^10*c^3*d^15*f^2 + 400*a^2*b^10*c^5*d^13*f^2 - 6144*a^2*b^10*c^7*d^11*f^2 + 1056*a^2*b^10
*c^9*d^9*f^2 - 5408*a^3*b^9*c^2*d^16*f^2 + 3888*a^3*b^9*c^4*d^14*f^2 + 6400*a^3*b^9*c^6*d^12*f^2 - 3072*a^3*b^
9*c^8*d^10*f^2 + 128*a^3*b^9*c^10*d^8*f^2 - 648*a^4*b^8*c^3*d^15*f^2 - 1952*a^4*b^8*c^5*d^13*f^2 + 208*a^4*b^8
*c^7*d^11*f^2 + 200*a^4*b^8*c^9*d^9*f^2 - 4288*a^5*b^7*c^2*d^16*f^2 + 4112*a^5*b^7*c^4*d^14*f^2 + 5120*a^5*b^7
*c^6*d^12*f^2 - 3208*a^5*b^7*c^8*d^10*f^2 + 192*a^5*b^7*c^10*d^8*f^2 - 6688*a^6*b^6*c^3*d^15*f^2 - 2464*a^6*b^
6*c^5*d^13*f^2 + 5952*a^6*b^6*c^7*d^11*f^2 - 960*a^6*b^6*c^9*d^9*f^2 + 2624*a^7*b^5*c^2*d^16*f^2 - 2016*a^7*b^
5*c^4*d^14*f^2 - 3456*a^7*b^5*c^6*d^12*f^2 + 1504*a^7*b^5*c^8*d^10*f^2 + 992*a^8*b^4*c^3*d^15*f^2 - 144*a^8*b^
4*c^5*d^13*f^2 - 888*a^8*b^4*c^7*d^11*f^2 - 12*a^8*b^4*c^9*d^9*f^2 + 352*a^9*b^3*c^2*d^16*f^2 + 520*a^9*b^3*c^
4*d^14*f^2 + 32*a^9*b^3*c^6*d^12*f^2 + 12*a^9*b^3*c^8*d^10*f^2 + 48*a^10*b^2*c^3*d^15*f^2 + 144*a^10*b^2*c^5*d
^13*f^2 + 1120*a*b^11*c^2*d^16*f^2 - 2776*a*b^11*c^4*d^14*f^2 - 2208*a*b^11*c^6*d^12*f^2 + 1628*a*b^11*c^8*d^1
0*f^2 - 64*a*b^11*c^10*d^8*f^2 - 1024*a^2*b^10*c*d^17*f^2 + 1312*a^4*b^8*c*d^17*f^2 + 2688*a^6*b^6*c*d^17*f^2
+ 260*a^8*b^4*c*d^17*f^2 - 96*a^10*b^2*c*d^17*f^2 - 32*a^11*b*c^2*d^16*f^2 - 16*a^11*b*c^4*d^14*f^2))/(b^9*f^5
+ a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5) - (((16*(c + d*tan(e + f*x))^(1/2)*(4*a^14*c*d^1
4*f^2 - 8*a^13*b*d^15*f^2 - 60*a*b^13*d^15*f^2 + 76*b^14*c*d^14*f^2 - 52*a^3*b^11*d^15*f^2 - 128*a^5*b^9*d^15*
f^2 - 424*a^7*b^7*d^15*f^2 - 380*a^9*b^5*d^15*f^2 - 100*a^11*b^3*d^15*f^2 - 20*b^14*c^3*d^12*f^2 - 304*b^14*c^
5*d^10*f^2 + 20*b^14*c^7*d^8*f^2 + 540*a^2*b^12*c^3*d^12*f^2 + 624*a^2*b^12*c^5*d^10*f^2 - 116*a^2*b^12*c^7*d^
8*f^2 - 596*a^3*b^11*c^2*d^13*f^2 + 1540*a^3*b^11*c^4*d^11*f^2 - 588*a^3*b^11*c^6*d^9*f^2 + 80*a^4*b^10*c^3*d^
12*f^2 + 1760*a^4*b^10*c^5*d^10*f^2 - 216*a^4*b^10*c^7*d^8*f^2 - 2184*a^5*b^9*c^2*d^13*f^2 + 1320*a^5*b^9*c^4*
d^11*f^2 + 152*a^5*b^9*c^6*d^9*f^2 - 1960*a^6*b^8*c^3*d^12*f^2 + 800*a^6*b^8*c^5*d^10*f^2 - 8*a^6*b^8*c^7*d^8*
f^2 - 584*a^7*b^7*c^2*d^13*f^2 + 840*a^7*b^7*c^4*d^11*f^2 - 56*a^7*b^7*c^6*d^9*f^2 - 1940*a^8*b^6*c^3*d^12*f^2
+ 336*a^8*b^6*c^5*d^10*f^2 + 68*a^8*b^6*c^7*d^8*f^2 + 676*a^9*b^5*c^2*d^13*f^2 + 180*a^9*b^5*c^4*d^11*f^2 - 2
60*a^9*b^5*c^6*d^9*f^2 - 500*a^10*b^4*c^3*d^12*f^2 + 368*a^10*b^4*c^5*d^10*f^2 - 4*a^10*b^4*c^7*d^8*f^2 + 156*
a^11*b^3*c^2*d^13*f^2 - 140*a^11*b^3*c^4*d^11*f^2 + 4*a^11*b^3*c^6*d^9*f^2 - 40*a^12*b^2*c^3*d^12*f^2 + 468*a*
b^13*c^2*d^13*f^2 + 740*a*b^13*c^4*d^11*f^2 - 532*a*b^13*c^6*d^9*f^2 - 284*a^2*b^12*c*d^14*f^2 + 84*a^4*b^10*c
*d^14*f^2 + 1436*a^6*b^8*c*d^14*f^2 + 1108*a^8*b^6*c*d^14*f^2 + 124*a^10*b^4*c*d^14*f^2 + 12*a^12*b^2*c*d^14*f
^2 + 16*a^13*b*c^2*d^13*f^2))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4) + (((8*(96
*a^2*b^14*d^13*f^4 + 480*a^4*b^12*d^13*f^4 + 960*a^6*b^10*d^13*f^4 + 960*a^8*b^8*d^13*f^4 + 480*a^10*b^6*d^13*
f^4 + 96*a^12*b^4*d^13*f^4 + 128*b^16*c^2*d^11*f^4 + 128*b^16*c^4*d^9*f^4 + 640*a^2*b^14*c^2*d^11*f^4 + 544*a^
2*b^14*c^4*d^9*f^4 - 768*a^3*b^13*c^3*d^10*f^4 + 320*a^3*b^13*c^5*d^8*f^4 + 1280*a^4*b^12*c^2*d^11*f^4 + 800*a
^4*b^12*c^4*d^9*f^4 - 1440*a^5*b^11*c^3*d^10*f^4 + 640*a^5*b^11*c^5*d^8*f^4 + 1280*a^6*b^10*c^2*d^11*f^4 + 320
*a^6*b^10*c^4*d^9*f^4 - 1280*a^7*b^9*c^3*d^10*f^4 + 640*a^7*b^9*c^5*d^8*f^4 + 640*a^8*b^8*c^2*d^11*f^4 - 320*a
^8*b^8*c^4*d^9*f^4 - 480*a^9*b^7*c^3*d^10*f^4 + 320*a^9*b^7*c^5*d^8*f^4 + 128*a^10*b^6*c^2*d^11*f^4 - 352*a^10
*b^6*c^4*d^9*f^4 + 64*a^11*b^5*c^5*d^8*f^4 - 96*a^12*b^4*c^4*d^9*f^4 + 32*a^13*b^3*c^3*d^10*f^4 - 224*a*b^15*c
*d^12*f^4 - 160*a*b^15*c^3*d^10*f^4 + 64*a*b^15*c^5*d^8*f^4 - 1088*a^3*b^13*c*d^12*f^4 - 2080*a^5*b^11*c*d^12*
f^4 - 1920*a^7*b^9*c*d^12*f^4 - 800*a^9*b^7*c*d^12*f^4 - 64*a^11*b^5*c*d^12*f^4 + 32*a^13*b^3*c*d^12*f^4))/(b^
9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5) + (4*(c + d*tan(e + f*x))^(1/2)*(-4*(b^11*f
^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 +
10*a^5*b^2*d^5 - 25*b^7*c^3*d^2 + 75*a*b^6*c^2*d^3 - 75*a^2*b^5*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 +
110*a^2*b^5*c^3*d^2 - 90*a^3*b^4*c^2*d^3 - 25*a^4*b^3*c^3*d^2 - 5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*
c*d^4))^(1/2)*(32*b^18*d^10*f^4 + 160*a^2*b^16*d^10*f^4 + 288*a^4*b^14*d^10*f^4 + 160*a^6*b^12*d^10*f^4 - 160*
a^8*b^10*d^10*f^4 - 288*a^10*b^8*d^10*f^4 - 160*a^12*b^6*d^10*f^4 - 32*a^14*b^4*d^10*f^4 + 48*b^18*c^2*d^8*f^4
+ 272*a^2*b^16*c^2*d^8*f^4 + 624*a^4*b^14*c^2*d^8*f^4 + 720*a^6*b^12*c^2*d^8*f^4 + 400*a^8*b^10*c^2*d^8*f^4 +
48*a^10*b^8*c^2*d^8*f^4 - 48*a^12*b^6*c^2*d^8*f^4 - 16*a^14*b^4*c^2*d^8*f^4 + 16*a*b^17*c*d^9*f^4 + 112*a^3*b
^15*c*d^9*f^4 + 336*a^5*b^13*c*d^9*f^4 + 560*a^7*b^11*c*d^9*f^4 + 560*a^9*b^9*c*d^9*f^4 + 336*a^11*b^7*c*d^9*f
^4 + 112*a^13*b^5*c*d^9*f^4 + 16*a^15*b^3*c*d^9*f^4))/((b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 +
4*a^6*b^3*f^4)*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)))*(-4*(b^11*f^2 + 4*a^
2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b
^2*d^5 - 25*b^7*c^3*d^2 + 75*a*b^6*c^2*d^3 - 75*a^2*b^5*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*
b^5*c^3*d^2 - 90*a^3*b^4*c^2*d^3 - 25*a^4*b^3*c^3*d^2 - 5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(
1/2))/(4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)))*(-4*(b^11*f^2 + 4*a^2*b^9*
f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5
- 25*b^7*c^3*d^2 + 75*a*b^6*c^2*d^3 - 75*a^2*b^5*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^
3*d^2 - 90*a^3*b^4*c^2*d^3 - 25*a^4*b^3*c^3*d^2 - 5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2))/
(4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)))*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 +
6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*
b^7*c^3*d^2 + 75*a*b^6*c^2*d^3 - 75*a^2*b^5*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2
- 90*a^3*b^4*c^2*d^3 - 25*a^4*b^3*c^3*d^2 - 5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2))/(4*(b^
11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)))*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*
b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c^
3*d^2 + 75*a*b^6*c^2*d^3 - 75*a^2*b^5*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*a
^3*b^4*c^2*d^3 - 25*a^4*b^3*c^3*d^2 - 5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2)*1i)/(4*(b^11*
f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)))/((16*(6*a^8*c^4*d^19 - 10*a^2*b^6*d^23 -
27*a^4*b^4*d^23 - 10*a^6*b^2*d^23 - a^8*d^23 + 8*a^8*c^6*d^17 + 3*a^8*c^8*d^15 - 10*b^8*c^2*d^21 - 85*b^8*c^4*
d^19 - 150*b^8*c^6*d^17 - 50*b^8*c^8*d^15 + 50*b^8*c^10*d^13 + 15*b^8*c^12*d^11 - 10*b^8*c^14*d^9 + 212*a*b^7*
c^3*d^20 + 212*a*b^7*c^5*d^18 - 320*a*b^7*c^7*d^16 - 420*a*b^7*c^9*d^14 + 20*a*b^7*c^11*d^12 + 92*a*b^7*c^13*d
^10 - 8*a*b^7*c^15*d^8 + 96*a^3*b^5*c*d^22 + 24*a^7*b*c^5*d^18 + 32*a^7*b*c^7*d^16 + 12*a^7*b*c^9*d^14 - 196*a
^2*b^6*c^2*d^21 + 84*a^2*b^6*c^4*d^19 + 894*a^2*b^6*c^6*d^17 + 430*a^2*b^6*c^8*d^15 - 504*a^2*b^6*c^10*d^13 -
248*a^2*b^6*c^12*d^11 + 62*a^2*b^6*c^14*d^9 - 224*a^3*b^5*c^3*d^20 - 604*a^3*b^5*c^5*d^18 + 320*a^3*b^5*c^7*d^
16 + 904*a^3*b^5*c^9*d^14 + 128*a^3*b^5*c^11*d^12 - 172*a^3*b^5*c^13*d^10 + 88*a^4*b^4*c^2*d^21 + 55*a^4*b^4*c
^4*d^19 - 440*a^4*b^4*c^6*d^17 - 365*a^4*b^4*c^8*d^15 + 208*a^4*b^4*c^10*d^13 + 193*a^4*b^4*c^12*d^11 + 20*a^5
*b^3*c^3*d^20 - 120*a^5*b^3*c^7*d^16 - 160*a^5*b^3*c^9*d^14 - 60*a^5*b^3*c^11*d^12 + 10*a^6*b^2*c^2*d^21 + 60*
a^6*b^2*c^4*d^19 + 20*a^6*b^2*c^6*d^17 - 50*a^6*b^2*c^8*d^15 - 30*a^6*b^2*c^10*d^13 + 20*a*b^7*c*d^22 - 4*a^7*
b*c*d^22))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5) + (((16*(c + d*tan(e + f*x))^
(1/2)*(2*b^10*d^20 - a^10*d^20 + 4*a^2*b^8*d^20 + 27*a^4*b^6*d^20 - 15*a^6*b^4*d^20 - 9*a^8*b^2*d^20 + 15*a^10
*c^2*d^18 - 15*a^10*c^4*d^16 + a^10*c^6*d^14 + 12*b^10*c^2*d^18 + 55*b^10*c^4*d^16 - 335*b^10*c^6*d^14 + 405*b
^10*c^8*d^12 - 13*b^10*c^10*d^10 + 2*b^10*c^12*d^8 - 100*a*b^9*c^3*d^17 + 1840*a*b^9*c^5*d^15 - 3100*a*b^9*c^7
*d^13 + 1000*a*b^9*c^9*d^11 - 40*a*b^9*c^11*d^9 - 100*a^3*b^7*c*d^19 + 400*a^5*b^5*c*d^19 + 124*a^7*b^3*c*d^19
+ 20*a^9*b*c^3*d^17 - 48*a^9*b*c^5*d^15 + 4*a^9*b*c^7*d^13 + 174*a^2*b^8*c^2*d^18 - 3565*a^2*b^8*c^4*d^16 + 9
451*a^2*b^8*c^6*d^14 - 5755*a^2*b^8*c^8*d^12 + 919*a^2*b^8*c^10*d^10 - 12*a^2*b^8*c^12*d^8 + 3600*a^3*b^7*c^3*
d^17 - 13896*a^3*b^7*c^5*d^15 + 14032*a^3*b^7*c^7*d^13 - 4180*a^3*b^7*c^9*d^11 + 288*a^3*b^7*c^11*d^9 - 1813*a
^4*b^6*c^2*d^18 + 10770*a^4*b^6*c^4*d^16 - 16848*a^4*b^6*c^6*d^14 + 8385*a^4*b^6*c^8*d^12 - 1115*a^4*b^6*c^10*
d^10 + 18*a^4*b^6*c^12*d^8 - 3920*a^5*b^5*c^3*d^17 + 9936*a^5*b^5*c^5*d^15 - 8040*a^5*b^5*c^7*d^13 + 1840*a^5*
b^5*c^9*d^11 - 56*a^5*b^5*c^11*d^9 + 315*a^6*b^4*c^2*d^18 - 1880*a^6*b^4*c^4*d^16 + 3140*a^6*b^4*c^6*d^14 - 13
05*a^6*b^4*c^8*d^12 + 65*a^6*b^4*c^10*d^10 - 560*a^7*b^3*c^3*d^17 + 280*a^7*b^3*c^5*d^15 + 176*a^7*b^3*c^7*d^1
3 - 20*a^7*b^3*c^9*d^11 + 193*a^8*b^2*c^2*d^18 - 445*a^8*b^2*c^4*d^16 + 207*a^8*b^2*c^6*d^14 - 10*a^8*b^2*c^8*
d^12 + 8*a^9*b*c*d^19))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4) + (((8*(4*b^12*c
*d^17*f^2 - 16*a^11*b*d^18*f^2 - 8*a^12*c*d^17*f^2 - 4*a*b^11*d^18*f^2 + 304*a^3*b^9*d^18*f^2 + 120*a^5*b^7*d^
18*f^2 - 320*a^7*b^5*d^18*f^2 - 148*a^9*b^3*d^18*f^2 - 8*a^12*c^3*d^15*f^2 - 400*b^12*c^3*d^15*f^2 + 176*b^12*
c^5*d^13*f^2 + 488*b^12*c^7*d^11*f^2 - 92*b^12*c^9*d^9*f^2 + 6576*a^2*b^10*c^3*d^15*f^2 + 400*a^2*b^10*c^5*d^1
3*f^2 - 6144*a^2*b^10*c^7*d^11*f^2 + 1056*a^2*b^10*c^9*d^9*f^2 - 5408*a^3*b^9*c^2*d^16*f^2 + 3888*a^3*b^9*c^4*
d^14*f^2 + 6400*a^3*b^9*c^6*d^12*f^2 - 3072*a^3*b^9*c^8*d^10*f^2 + 128*a^3*b^9*c^10*d^8*f^2 - 648*a^4*b^8*c^3*
d^15*f^2 - 1952*a^4*b^8*c^5*d^13*f^2 + 208*a^4*b^8*c^7*d^11*f^2 + 200*a^4*b^8*c^9*d^9*f^2 - 4288*a^5*b^7*c^2*d
^16*f^2 + 4112*a^5*b^7*c^4*d^14*f^2 + 5120*a^5*b^7*c^6*d^12*f^2 - 3208*a^5*b^7*c^8*d^10*f^2 + 192*a^5*b^7*c^10
*d^8*f^2 - 6688*a^6*b^6*c^3*d^15*f^2 - 2464*a^6*b^6*c^5*d^13*f^2 + 5952*a^6*b^6*c^7*d^11*f^2 - 960*a^6*b^6*c^9
*d^9*f^2 + 2624*a^7*b^5*c^2*d^16*f^2 - 2016*a^7*b^5*c^4*d^14*f^2 - 3456*a^7*b^5*c^6*d^12*f^2 + 1504*a^7*b^5*c^
8*d^10*f^2 + 992*a^8*b^4*c^3*d^15*f^2 - 144*a^8*b^4*c^5*d^13*f^2 - 888*a^8*b^4*c^7*d^11*f^2 - 12*a^8*b^4*c^9*d
^9*f^2 + 352*a^9*b^3*c^2*d^16*f^2 + 520*a^9*b^3*c^4*d^14*f^2 + 32*a^9*b^3*c^6*d^12*f^2 + 12*a^9*b^3*c^8*d^10*f
^2 + 48*a^10*b^2*c^3*d^15*f^2 + 144*a^10*b^2*c^5*d^13*f^2 + 1120*a*b^11*c^2*d^16*f^2 - 2776*a*b^11*c^4*d^14*f^
2 - 2208*a*b^11*c^6*d^12*f^2 + 1628*a*b^11*c^8*d^10*f^2 - 64*a*b^11*c^10*d^8*f^2 - 1024*a^2*b^10*c*d^17*f^2 +
1312*a^4*b^8*c*d^17*f^2 + 2688*a^6*b^6*c*d^17*f^2 + 260*a^8*b^4*c*d^17*f^2 - 96*a^10*b^2*c*d^17*f^2 - 32*a^11*
b*c^2*d^16*f^2 - 16*a^11*b*c^4*d^14*f^2))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5
) + (((16*(c + d*tan(e + f*x))^(1/2)*(4*a^14*c*d^14*f^2 - 8*a^13*b*d^15*f^2 - 60*a*b^13*d^15*f^2 + 76*b^14*c*d
^14*f^2 - 52*a^3*b^11*d^15*f^2 - 128*a^5*b^9*d^15*f^2 - 424*a^7*b^7*d^15*f^2 - 380*a^9*b^5*d^15*f^2 - 100*a^11
*b^3*d^15*f^2 - 20*b^14*c^3*d^12*f^2 - 304*b^14*c^5*d^10*f^2 + 20*b^14*c^7*d^8*f^2 + 540*a^2*b^12*c^3*d^12*f^2
+ 624*a^2*b^12*c^5*d^10*f^2 - 116*a^2*b^12*c^7*d^8*f^2 - 596*a^3*b^11*c^2*d^13*f^2 + 1540*a^3*b^11*c^4*d^11*f
^2 - 588*a^3*b^11*c^6*d^9*f^2 + 80*a^4*b^10*c^3*d^12*f^2 + 1760*a^4*b^10*c^5*d^10*f^2 - 216*a^4*b^10*c^7*d^8*f
^2 - 2184*a^5*b^9*c^2*d^13*f^2 + 1320*a^5*b^9*c^4*d^11*f^2 + 152*a^5*b^9*c^6*d^9*f^2 - 1960*a^6*b^8*c^3*d^12*f
^2 + 800*a^6*b^8*c^5*d^10*f^2 - 8*a^6*b^8*c^7*d^8*f^2 - 584*a^7*b^7*c^2*d^13*f^2 + 840*a^7*b^7*c^4*d^11*f^2 -
56*a^7*b^7*c^6*d^9*f^2 - 1940*a^8*b^6*c^3*d^12*f^2 + 336*a^8*b^6*c^5*d^10*f^2 + 68*a^8*b^6*c^7*d^8*f^2 + 676*a
^9*b^5*c^2*d^13*f^2 + 180*a^9*b^5*c^4*d^11*f^2 - 260*a^9*b^5*c^6*d^9*f^2 - 500*a^10*b^4*c^3*d^12*f^2 + 368*a^1
0*b^4*c^5*d^10*f^2 - 4*a^10*b^4*c^7*d^8*f^2 + 156*a^11*b^3*c^2*d^13*f^2 - 140*a^11*b^3*c^4*d^11*f^2 + 4*a^11*b
^3*c^6*d^9*f^2 - 40*a^12*b^2*c^3*d^12*f^2 + 468*a*b^13*c^2*d^13*f^2 + 740*a*b^13*c^4*d^11*f^2 - 532*a*b^13*c^6
*d^9*f^2 - 284*a^2*b^12*c*d^14*f^2 + 84*a^4*b^10*c*d^14*f^2 + 1436*a^6*b^8*c*d^14*f^2 + 1108*a^8*b^6*c*d^14*f^
2 + 124*a^10*b^4*c*d^14*f^2 + 12*a^12*b^2*c*d^14*f^2 + 16*a^13*b*c^2*d^13*f^2))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b
^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4) - (((8*(96*a^2*b^14*d^13*f^4 + 480*a^4*b^12*d^13*f^4 + 960*a^6*b^10*d^
13*f^4 + 960*a^8*b^8*d^13*f^4 + 480*a^10*b^6*d^13*f^4 + 96*a^12*b^4*d^13*f^4 + 128*b^16*c^2*d^11*f^4 + 128*b^1
6*c^4*d^9*f^4 + 640*a^2*b^14*c^2*d^11*f^4 + 544*a^2*b^14*c^4*d^9*f^4 - 768*a^3*b^13*c^3*d^10*f^4 + 320*a^3*b^1
3*c^5*d^8*f^4 + 1280*a^4*b^12*c^2*d^11*f^4 + 800*a^4*b^12*c^4*d^9*f^4 - 1440*a^5*b^11*c^3*d^10*f^4 + 640*a^5*b
^11*c^5*d^8*f^4 + 1280*a^6*b^10*c^2*d^11*f^4 + 320*a^6*b^10*c^4*d^9*f^4 - 1280*a^7*b^9*c^3*d^10*f^4 + 640*a^7*
b^9*c^5*d^8*f^4 + 640*a^8*b^8*c^2*d^11*f^4 - 320*a^8*b^8*c^4*d^9*f^4 - 480*a^9*b^7*c^3*d^10*f^4 + 320*a^9*b^7*
c^5*d^8*f^4 + 128*a^10*b^6*c^2*d^11*f^4 - 352*a^10*b^6*c^4*d^9*f^4 + 64*a^11*b^5*c^5*d^8*f^4 - 96*a^12*b^4*c^4
*d^9*f^4 + 32*a^13*b^3*c^3*d^10*f^4 - 224*a*b^15*c*d^12*f^4 - 160*a*b^15*c^3*d^10*f^4 + 64*a*b^15*c^5*d^8*f^4
- 1088*a^3*b^13*c*d^12*f^4 - 2080*a^5*b^11*c*d^12*f^4 - 1920*a^7*b^9*c*d^12*f^4 - 800*a^9*b^7*c*d^12*f^4 - 64*
a^11*b^5*c*d^12*f^4 + 32*a^13*b^3*c*d^12*f^4))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^
3*f^5) - (4*(c + d*tan(e + f*x))^(1/2)*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3
*f^2)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c^3*d^2 + 75*a*b^6*c^2*d^3 - 75*a^2
*b^5*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*a^3*b^4*c^2*d^3 - 25*a^4*b^3*c^3*d
^2 - 5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2)*(32*b^18*d^10*f^4 + 160*a^2*b^16*d^10*f^4 + 28
8*a^4*b^14*d^10*f^4 + 160*a^6*b^12*d^10*f^4 - 160*a^8*b^10*d^10*f^4 - 288*a^10*b^8*d^10*f^4 - 160*a^12*b^6*d^1
0*f^4 - 32*a^14*b^4*d^10*f^4 + 48*b^18*c^2*d^8*f^4 + 272*a^2*b^16*c^2*d^8*f^4 + 624*a^4*b^14*c^2*d^8*f^4 + 720
*a^6*b^12*c^2*d^8*f^4 + 400*a^8*b^10*c^2*d^8*f^4 + 48*a^10*b^8*c^2*d^8*f^4 - 48*a^12*b^6*c^2*d^8*f^4 - 16*a^14
*b^4*c^2*d^8*f^4 + 16*a*b^17*c*d^9*f^4 + 112*a^3*b^15*c*d^9*f^4 + 336*a^5*b^13*c*d^9*f^4 + 560*a^7*b^11*c*d^9*
f^4 + 560*a^9*b^9*c*d^9*f^4 + 336*a^11*b^7*c*d^9*f^4 + 112*a^13*b^5*c*d^9*f^4 + 16*a^15*b^3*c*d^9*f^4))/((b^9*
f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4)*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4
*a^6*b^5*f^2 + a^8*b^3*f^2)))*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)*(a^
7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c^3*d^2 + 75*a*b^6*c^2*d^3 - 75*a^2*b^5*c*d^
4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*a^3*b^4*c^2*d^3 - 25*a^4*b^3*c^3*d^2 - 5*a^
5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2))/(4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b
^5*f^2 + a^8*b^3*f^2)))*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)*(a^7*d^5
- 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c^3*d^2 + 75*a*b^6*c^2*d^3 - 75*a^2*b^5*c*d^4 + 40
*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*a^3*b^4*c^2*d^3 - 25*a^4*b^3*c^3*d^2 - 5*a^5*b^2*
c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2))/(4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2
+ a^8*b^3*f^2)))*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)*(a^7*d^5 - 16*a
^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c^3*d^2 + 75*a*b^6*c^2*d^3 - 75*a^2*b^5*c*d^4 + 40*a^3*b
^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*a^3*b^4*c^2*d^3 - 25*a^4*b^3*c^3*d^2 - 5*a^5*b^2*c^2*d^
3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2))/(4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8
*b^3*f^2)))*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)*(a^7*d^5 - 16*a^2*b^5
*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c^3*d^2 + 75*a*b^6*c^2*d^3 - 75*a^2*b^5*c*d^4 + 40*a^3*b^4*c^4
*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*a^3*b^4*c^2*d^3 - 25*a^4*b^3*c^3*d^2 - 5*a^5*b^2*c^2*d^3 - 40
*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2))/(4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f
^2)) - (((16*(c + d*tan(e + f*x))^(1/2)*(2*b^10*d^20 - a^10*d^20 + 4*a^2*b^8*d^20 + 27*a^4*b^6*d^20 - 15*a^6*b
^4*d^20 - 9*a^8*b^2*d^20 + 15*a^10*c^2*d^18 - 15*a^10*c^4*d^16 + a^10*c^6*d^14 + 12*b^10*c^2*d^18 + 55*b^10*c^
4*d^16 - 335*b^10*c^6*d^14 + 405*b^10*c^8*d^12 - 13*b^10*c^10*d^10 + 2*b^10*c^12*d^8 - 100*a*b^9*c^3*d^17 + 18
40*a*b^9*c^5*d^15 - 3100*a*b^9*c^7*d^13 + 1000*a*b^9*c^9*d^11 - 40*a*b^9*c^11*d^9 - 100*a^3*b^7*c*d^19 + 400*a
^5*b^5*c*d^19 + 124*a^7*b^3*c*d^19 + 20*a^9*b*c^3*d^17 - 48*a^9*b*c^5*d^15 + 4*a^9*b*c^7*d^13 + 174*a^2*b^8*c^
2*d^18 - 3565*a^2*b^8*c^4*d^16 + 9451*a^2*b^8*c^6*d^14 - 5755*a^2*b^8*c^8*d^12 + 919*a^2*b^8*c^10*d^10 - 12*a^
2*b^8*c^12*d^8 + 3600*a^3*b^7*c^3*d^17 - 13896*a^3*b^7*c^5*d^15 + 14032*a^3*b^7*c^7*d^13 - 4180*a^3*b^7*c^9*d^
11 + 288*a^3*b^7*c^11*d^9 - 1813*a^4*b^6*c^2*d^18 + 10770*a^4*b^6*c^4*d^16 - 16848*a^4*b^6*c^6*d^14 + 8385*a^4
*b^6*c^8*d^12 - 1115*a^4*b^6*c^10*d^10 + 18*a^4*b^6*c^12*d^8 - 3920*a^5*b^5*c^3*d^17 + 9936*a^5*b^5*c^5*d^15 -
8040*a^5*b^5*c^7*d^13 + 1840*a^5*b^5*c^9*d^11 - 56*a^5*b^5*c^11*d^9 + 315*a^6*b^4*c^2*d^18 - 1880*a^6*b^4*c^4
*d^16 + 3140*a^6*b^4*c^6*d^14 - 1305*a^6*b^4*c^8*d^12 + 65*a^6*b^4*c^10*d^10 - 560*a^7*b^3*c^3*d^17 + 280*a^7*
b^3*c^5*d^15 + 176*a^7*b^3*c^7*d^13 - 20*a^7*b^3*c^9*d^11 + 193*a^8*b^2*c^2*d^18 - 445*a^8*b^2*c^4*d^16 + 207*
a^8*b^2*c^6*d^14 - 10*a^8*b^2*c^8*d^12 + 8*a^9*b*c*d^19))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4
+ 4*a^6*b^3*f^4) - (((8*(4*b^12*c*d^17*f^2 - 16*a^11*b*d^18*f^2 - 8*a^12*c*d^17*f^2 - 4*a*b^11*d^18*f^2 + 304
*a^3*b^9*d^18*f^2 + 120*a^5*b^7*d^18*f^2 - 320*a^7*b^5*d^18*f^2 - 148*a^9*b^3*d^18*f^2 - 8*a^12*c^3*d^15*f^2 -
400*b^12*c^3*d^15*f^2 + 176*b^12*c^5*d^13*f^2 + 488*b^12*c^7*d^11*f^2 - 92*b^12*c^9*d^9*f^2 + 6576*a^2*b^10*c
^3*d^15*f^2 + 400*a^2*b^10*c^5*d^13*f^2 - 6144*a^2*b^10*c^7*d^11*f^2 + 1056*a^2*b^10*c^9*d^9*f^2 - 5408*a^3*b^
9*c^2*d^16*f^2 + 3888*a^3*b^9*c^4*d^14*f^2 + 6400*a^3*b^9*c^6*d^12*f^2 - 3072*a^3*b^9*c^8*d^10*f^2 + 128*a^3*b
^9*c^10*d^8*f^2 - 648*a^4*b^8*c^3*d^15*f^2 - 1952*a^4*b^8*c^5*d^13*f^2 + 208*a^4*b^8*c^7*d^11*f^2 + 200*a^4*b^
8*c^9*d^9*f^2 - 4288*a^5*b^7*c^2*d^16*f^2 + 4112*a^5*b^7*c^4*d^14*f^2 + 5120*a^5*b^7*c^6*d^12*f^2 - 3208*a^5*b
^7*c^8*d^10*f^2 + 192*a^5*b^7*c^10*d^8*f^2 - 6688*a^6*b^6*c^3*d^15*f^2 - 2464*a^6*b^6*c^5*d^13*f^2 + 5952*a^6*
b^6*c^7*d^11*f^2 - 960*a^6*b^6*c^9*d^9*f^2 + 2624*a^7*b^5*c^2*d^16*f^2 - 2016*a^7*b^5*c^4*d^14*f^2 - 3456*a^7*
b^5*c^6*d^12*f^2 + 1504*a^7*b^5*c^8*d^10*f^2 + 992*a^8*b^4*c^3*d^15*f^2 - 144*a^8*b^4*c^5*d^13*f^2 - 888*a^8*b
^4*c^7*d^11*f^2 - 12*a^8*b^4*c^9*d^9*f^2 + 352*a^9*b^3*c^2*d^16*f^2 + 520*a^9*b^3*c^4*d^14*f^2 + 32*a^9*b^3*c^
6*d^12*f^2 + 12*a^9*b^3*c^8*d^10*f^2 + 48*a^10*b^2*c^3*d^15*f^2 + 144*a^10*b^2*c^5*d^13*f^2 + 1120*a*b^11*c^2*
d^16*f^2 - 2776*a*b^11*c^4*d^14*f^2 - 2208*a*b^11*c^6*d^12*f^2 + 1628*a*b^11*c^8*d^10*f^2 - 64*a*b^11*c^10*d^8
*f^2 - 1024*a^2*b^10*c*d^17*f^2 + 1312*a^4*b^8*c*d^17*f^2 + 2688*a^6*b^6*c*d^17*f^2 + 260*a^8*b^4*c*d^17*f^2 -
96*a^10*b^2*c*d^17*f^2 - 32*a^11*b*c^2*d^16*f^2 - 16*a^11*b*c^4*d^14*f^2))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*b^7*f
^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5) - (((16*(c + d*tan(e + f*x))^(1/2)*(4*a^14*c*d^14*f^2 - 8*a^13*b*d^15*f^2
- 60*a*b^13*d^15*f^2 + 76*b^14*c*d^14*f^2 - 52*a^3*b^11*d^15*f^2 - 128*a^5*b^9*d^15*f^2 - 424*a^7*b^7*d^15*f^2
- 380*a^9*b^5*d^15*f^2 - 100*a^11*b^3*d^15*f^2 - 20*b^14*c^3*d^12*f^2 - 304*b^14*c^5*d^10*f^2 + 20*b^14*c^7*d
^8*f^2 + 540*a^2*b^12*c^3*d^12*f^2 + 624*a^2*b^12*c^5*d^10*f^2 - 116*a^2*b^12*c^7*d^8*f^2 - 596*a^3*b^11*c^2*d
^13*f^2 + 1540*a^3*b^11*c^4*d^11*f^2 - 588*a^3*b^11*c^6*d^9*f^2 + 80*a^4*b^10*c^3*d^12*f^2 + 1760*a^4*b^10*c^5
*d^10*f^2 - 216*a^4*b^10*c^7*d^8*f^2 - 2184*a^5*b^9*c^2*d^13*f^2 + 1320*a^5*b^9*c^4*d^11*f^2 + 152*a^5*b^9*c^6
*d^9*f^2 - 1960*a^6*b^8*c^3*d^12*f^2 + 800*a^6*b^8*c^5*d^10*f^2 - 8*a^6*b^8*c^7*d^8*f^2 - 584*a^7*b^7*c^2*d^13
*f^2 + 840*a^7*b^7*c^4*d^11*f^2 - 56*a^7*b^7*c^6*d^9*f^2 - 1940*a^8*b^6*c^3*d^12*f^2 + 336*a^8*b^6*c^5*d^10*f^
2 + 68*a^8*b^6*c^7*d^8*f^2 + 676*a^9*b^5*c^2*d^13*f^2 + 180*a^9*b^5*c^4*d^11*f^2 - 260*a^9*b^5*c^6*d^9*f^2 - 5
00*a^10*b^4*c^3*d^12*f^2 + 368*a^10*b^4*c^5*d^10*f^2 - 4*a^10*b^4*c^7*d^8*f^2 + 156*a^11*b^3*c^2*d^13*f^2 - 14
0*a^11*b^3*c^4*d^11*f^2 + 4*a^11*b^3*c^6*d^9*f^2 - 40*a^12*b^2*c^3*d^12*f^2 + 468*a*b^13*c^2*d^13*f^2 + 740*a*
b^13*c^4*d^11*f^2 - 532*a*b^13*c^6*d^9*f^2 - 284*a^2*b^12*c*d^14*f^2 + 84*a^4*b^10*c*d^14*f^2 + 1436*a^6*b^8*c
*d^14*f^2 + 1108*a^8*b^6*c*d^14*f^2 + 124*a^10*b^4*c*d^14*f^2 + 12*a^12*b^2*c*d^14*f^2 + 16*a^13*b*c^2*d^13*f^
2))/(b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4) + (((8*(96*a^2*b^14*d^13*f^4 + 480*a
^4*b^12*d^13*f^4 + 960*a^6*b^10*d^13*f^4 + 960*a^8*b^8*d^13*f^4 + 480*a^10*b^6*d^13*f^4 + 96*a^12*b^4*d^13*f^4
+ 128*b^16*c^2*d^11*f^4 + 128*b^16*c^4*d^9*f^4 + 640*a^2*b^14*c^2*d^11*f^4 + 544*a^2*b^14*c^4*d^9*f^4 - 768*a
^3*b^13*c^3*d^10*f^4 + 320*a^3*b^13*c^5*d^8*f^4 + 1280*a^4*b^12*c^2*d^11*f^4 + 800*a^4*b^12*c^4*d^9*f^4 - 1440
*a^5*b^11*c^3*d^10*f^4 + 640*a^5*b^11*c^5*d^8*f^4 + 1280*a^6*b^10*c^2*d^11*f^4 + 320*a^6*b^10*c^4*d^9*f^4 - 12
80*a^7*b^9*c^3*d^10*f^4 + 640*a^7*b^9*c^5*d^8*f^4 + 640*a^8*b^8*c^2*d^11*f^4 - 320*a^8*b^8*c^4*d^9*f^4 - 480*a
^9*b^7*c^3*d^10*f^4 + 320*a^9*b^7*c^5*d^8*f^4 + 128*a^10*b^6*c^2*d^11*f^4 - 352*a^10*b^6*c^4*d^9*f^4 + 64*a^11
*b^5*c^5*d^8*f^4 - 96*a^12*b^4*c^4*d^9*f^4 + 32*a^13*b^3*c^3*d^10*f^4 - 224*a*b^15*c*d^12*f^4 - 160*a*b^15*c^3
*d^10*f^4 + 64*a*b^15*c^5*d^8*f^4 - 1088*a^3*b^13*c*d^12*f^4 - 2080*a^5*b^11*c*d^12*f^4 - 1920*a^7*b^9*c*d^12*
f^4 - 800*a^9*b^7*c*d^12*f^4 - 64*a^11*b^5*c*d^12*f^4 + 32*a^13*b^3*c*d^12*f^4))/(b^9*f^5 + a^8*b*f^5 + 4*a^2*
b^7*f^5 + 6*a^4*b^5*f^5 + 4*a^6*b^3*f^5) + (4*(c + d*tan(e + f*x))^(1/2)*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4
*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c
^3*d^2 + 75*a*b^6*c^2*d^3 - 75*a^2*b^5*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*
a^3*b^4*c^2*d^3 - 25*a^4*b^3*c^3*d^2 - 5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2)*(32*b^18*d^1
0*f^4 + 160*a^2*b^16*d^10*f^4 + 288*a^4*b^14*d^10*f^4 + 160*a^6*b^12*d^10*f^4 - 160*a^8*b^10*d^10*f^4 - 288*a^
10*b^8*d^10*f^4 - 160*a^12*b^6*d^10*f^4 - 32*a^14*b^4*d^10*f^4 + 48*b^18*c^2*d^8*f^4 + 272*a^2*b^16*c^2*d^8*f^
4 + 624*a^4*b^14*c^2*d^8*f^4 + 720*a^6*b^12*c^2*d^8*f^4 + 400*a^8*b^10*c^2*d^8*f^4 + 48*a^10*b^8*c^2*d^8*f^4 -
48*a^12*b^6*c^2*d^8*f^4 - 16*a^14*b^4*c^2*d^8*f^4 + 16*a*b^17*c*d^9*f^4 + 112*a^3*b^15*c*d^9*f^4 + 336*a^5*b^
13*c*d^9*f^4 + 560*a^7*b^11*c*d^9*f^4 + 560*a^9*b^9*c*d^9*f^4 + 336*a^11*b^7*c*d^9*f^4 + 112*a^13*b^5*c*d^9*f^
4 + 16*a^15*b^3*c*d^9*f^4))/((b^9*f^4 + a^8*b*f^4 + 4*a^2*b^7*f^4 + 6*a^4*b^5*f^4 + 4*a^6*b^3*f^4)*(b^11*f^2 +
4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)))*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2
+ 4*a^6*b^5*f^2 + a^8*b^3*f^2)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c^3*d^2 +
75*a*b^6*c^2*d^3 - 75*a^2*b^5*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*a^3*b^4*c
^2*d^3 - 25*a^4*b^3*c^3*d^2 - 5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2))/(4*(b^11*f^2 + 4*a^2
*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)))*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^
6*b^5*f^2 + a^8*b^3*f^2)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c^3*d^2 + 75*a*b
^6*c^2*d^3 - 75*a^2*b^5*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*a^3*b^4*c^2*d^3
- 25*a^4*b^3*c^3*d^2 - 5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2))/(4*(b^11*f^2 + 4*a^2*b^9*f
^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)))*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*
f^2 + a^8*b^3*f^2)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c^3*d^2 + 75*a*b^6*c^2
*d^3 - 75*a^2*b^5*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*a^3*b^4*c^2*d^3 - 25*
a^4*b^3*c^3*d^2 - 5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2))/(4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6
*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)))*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 +
a^8*b^3*f^2)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c^3*d^2 + 75*a*b^6*c^2*d^3 -
75*a^2*b^5*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*a^3*b^4*c^2*d^3 - 25*a^4*b^
3*c^3*d^2 - 5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2))/(4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b
^7*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2))))*(-4*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7*f^2 + 4*a^6*b^5*f^2 + a^8*b
^3*f^2)*(a^7*d^5 - 16*a^2*b^5*c^5 + 25*a^3*b^4*d^5 + 10*a^5*b^2*d^5 - 25*b^7*c^3*d^2 + 75*a*b^6*c^2*d^3 - 75*a
^2*b^5*c*d^4 + 40*a^3*b^4*c^4*d + 10*a^4*b^3*c*d^4 + 110*a^2*b^5*c^3*d^2 - 90*a^3*b^4*c^2*d^3 - 25*a^4*b^3*c^3
*d^2 - 5*a^5*b^2*c^2*d^3 - 40*a*b^6*c^4*d + 5*a^6*b*c*d^4))^(1/2)*1i)/(2*(b^11*f^2 + 4*a^2*b^9*f^2 + 6*a^4*b^7
*f^2 + 4*a^6*b^5*f^2 + a^8*b^3*f^2)) - (d*(c + d*tan(e + f*x))^(1/2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(b*(a^2
+ b^2)*(b*f*(c + d*tan(e + f*x)) + a*d*f - b*c*f))