∫ A+B tan(e+fx)+C tan2(e+fx)_ (a+b tan(e+fx))2∘ _________

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

Optimal. Leaf size=327 \[ -\frac {\left (A b^2-a (b B-a C)\right ) \sqrt {c+d \tan (e+f x)}}{f \left (a^2+b^2\right ) (b c-a d) (a+b \tan (e+f x))}-\frac {\left (a^4 (-C) d+3 a^3 b B d-a^2 b^2 (5 A d+2 B c-3 C d)+a b^3 (4 A c-B d-4 c C)+b^4 (2 B c-A d)\right ) \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {c+d \tan (e+f x)}}{\sqrt {b c-a d}}\right )}{\sqrt {b} f \left (a^2+b^2\right )^2 (b c-a d)^{3/2}}-\frac {(i A+B-i C) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{f (a-i b)^2 \sqrt {c-i d}}-\frac {(B-i (A-C)) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{f (a+i b)^2 \sqrt {c+i d}} \]

[Out]

-(3*a^3*b*B*d-a^4*C*d+b^4*(-A*d+2*B*c)+a*b^3*(4*A*c-B*d-4*C*c)-a^2*b^2*(5*A*d+2*B*c-3*C*d))*arctanh(b^(1/2)*(c

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

+e))^(1/2)/(c-I*d)^(1/2))/(a-I*b)^2/f/(c-I*d)^(1/2)-(B-I*(A-C))*arctanh((c+d*tan(f*x+e))^(1/2)/(c+I*d)^(1/2))/

(a+I*b)^2/f/(c+I*d)^(1/2)-(A*b^2-a*(B*b-C*a))*(c+d*tan(f*x+e))^(1/2)/(a^2+b^2)/(-a*d+b*c)/f/(a+b*tan(f*x+e))

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Rubi [A] time = 1.38, antiderivative size = 327, normalized size of antiderivative = 1.00, number of steps used = 12, number of rules used = 7, integrand size = 47, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.149, Rules used = {3649, 3653, 3539, 3537, 63, 208, 3634} \[ -\frac {\left (A b^2-a (b B-a C)\right ) \sqrt {c+d \tan (e+f x)}}{f \left (a^2+b^2\right ) (b c-a d) (a+b \tan (e+f x))}-\frac {\left (-a^2 b^2 (5 A d+2 B c-3 C d)+3 a^3 b B d+a^4 (-C) d+a b^3 (4 A c-B d-4 c C)+b^4 (2 B c-A d)\right ) \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {c+d \tan (e+f x)}}{\sqrt {b c-a d}}\right )}{\sqrt {b} f \left (a^2+b^2\right )^2 (b c-a d)^{3/2}}-\frac {(i A+B-i C) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{f (a-i b)^2 \sqrt {c-i d}}-\frac {(B-i (A-C)) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{f (a+i b)^2 \sqrt {c+i d}} \]

Antiderivative was successfully veriﬁed.

[In]

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

[Out]

-(((I*A + B - I*C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)^2*Sqrt[c - I*d]*f)) - ((B - I*(

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

*d + b^4*(2*B*c - A*d) + a*b^3*(4*A*c - 4*c*C - B*d) - a^2*b^2*(2*B*c + 5*A*d - 3*C*d))*ArcTanh[(Sqrt[b]*Sqrt[

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

Sqrt[c + d*Tan[e + f*x]])/((a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x]))

Rule 63

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 208

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(Rt[-(a/b), 2]*ArcTanh[x/Rt[-(a/b), 2]])/a, x] /; FreeQ[{a,

b}, x] && NegQ[a/b]

Rule 3537

Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_)*((c_) + (d_.)*tan[(e_.) + (f_.)*(x_)]), x_Symbol] :> Dist[(c*

d)/f, Subst[Int[(a + (b*x)/d)^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 3539

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 3634

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 3649

Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_)*((c_.) + (d_.)*tan[(e_.) + (f_.)*(x_)])^(n_)*((A_.) + (B_.)*t

an[(e_.) + (f_.)*(x_)] + (C_.)*tan[(e_.) + (f_.)*(x_)]^2), x_Symbol] :> Simp[((A*b^2 - a*(b*B - a*C))*(a + b*T

an[e + f*x])^(m + 1)*(c + d*Tan[e + f*x])^(n + 1))/(f*(m + 1)*(b*c - a*d)*(a^2 + b^2)), x] + Dist[1/((m + 1)*(

b*c - a*d)*(a^2 + b^2)), Int[(a + b*Tan[e + f*x])^(m + 1)*(c + d*Tan[e + f*x])^n*Simp[A*(a*(b*c - a*d)*(m + 1)

- b^2*d*(m + n + 2)) + (b*B - a*C)*(b*c*(m + 1) + a*d*(n + 1)) - (m + 1)*(b*c - a*d)*(A*b - a*B - b*C)*Tan[e

+ f*x] - d*(A*b^2 - a*(b*B - a*C))*(m + n + 2)*Tan[e + f*x]^2, x], x], x] /; FreeQ[{a, b, c, d, e, f, A, B, C,

n}, x] && NeQ[b*c - a*d, 0] && NeQ[a^2 + b^2, 0] && NeQ[c^2 + d^2, 0] && LtQ[m, -1] && !(ILtQ[n, -1] && ( !I

ntegerQ[m] || (EqQ[c, 0] && NeQ[a, 0])))

Rule 3653

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, -

Rubi steps

\begin {align*} \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 \sqrt {c+d \tan (e+f x)}} \, dx &=-\frac {\left (A b^2-a (b B-a C)\right ) \sqrt {c+d \tan (e+f x)}}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x))}-\frac {\int \frac {\frac {1}{2} \left (A b^2 d-2 a A (b c-a d)-2 (b B-a C) \left (b c-\frac {a d}{2}\right )\right )+(A b-a B-b C) (b c-a d) \tan (e+f x)+\frac {1}{2} \left (A b^2-a (b B-a C)\right ) d \tan ^2(e+f x)}{(a+b \tan (e+f x)) \sqrt {c+d \tan (e+f x)}} \, dx}{\left (a^2+b^2\right ) (b c-a d)}\\ &=-\frac {\left (A b^2-a (b B-a C)\right ) \sqrt {c+d \tan (e+f x)}}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x))}-\frac {\int \frac {-\left (2 a b B+a^2 (A-C)-b^2 (A-C)\right ) (b c-a d)-\left (a^2 B-b^2 B-2 a b (A-C)\right ) (b c-a d) \tan (e+f x)}{\sqrt {c+d \tan (e+f x)}} \, dx}{\left (a^2+b^2\right )^2 (b c-a d)}+\frac {\left (3 a^3 b B d-a^4 C d+b^4 (2 B c-A d)+a b^3 (4 A c-4 c C-B d)-a^2 b^2 (2 B c+5 A d-3 C d)\right ) \int \frac {1+\tan ^2(e+f x)}{(a+b \tan (e+f x)) \sqrt {c+d \tan (e+f x)}} \, dx}{2 \left (a^2+b^2\right )^2 (b c-a d)}\\ &=-\frac {\left (A b^2-a (b B-a C)\right ) \sqrt {c+d \tan (e+f x)}}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x))}+\frac {(A-i B-C) \int \frac {1+i \tan (e+f x)}{\sqrt {c+d \tan (e+f x)}} \, dx}{2 (a-i b)^2}+\frac {(A+i B-C) \int \frac {1-i \tan (e+f x)}{\sqrt {c+d \tan (e+f x)}} \, dx}{2 (a+i b)^2}+\frac {\left (3 a^3 b B d-a^4 C d+b^4 (2 B c-A d)+a b^3 (4 A c-4 c C-B d)-a^2 b^2 (2 B c+5 A d-3 C d)\right ) \operatorname {Subst}\left (\int \frac {1}{(a+b x) \sqrt {c+d x}} \, dx,x,\tan (e+f x)\right )}{2 \left (a^2+b^2\right )^2 (b c-a d) f}\\ &=-\frac {\left (A b^2-a (b B-a C)\right ) \sqrt {c+d \tan (e+f x)}}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x))}-\frac {(i (A+i B-C)) \operatorname {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 A+B-i C) \operatorname {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 (3 a^3 b B d-a^4 C d+b^4 (2 B c-A d)+a b^3 (4 A c-4 c C-B d)-a^2 b^2 (2 B c+5 A d-3 C d)\right ) \operatorname {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 )}{\left (a^2+b^2\right )^2 d (b c-a d) f}\\ &=-\frac {\left (3 a^3 b B d-a^4 C d+b^4 (2 B c-A d)+a b^3 (4 A c-4 c C-B d)-a^2 b^2 (2 B c+5 A d-3 C d)\right ) \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {c+d \tan (e+f x)}}{\sqrt {b c-a d}}\right )}{\sqrt {b} \left (a^2+b^2\right )^2 (b c-a d)^{3/2} f}-\frac {\left (A b^2-a (b B-a C)\right ) \sqrt {c+d \tan (e+f x)}}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x))}-\frac {(A-i B-C) \operatorname {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 {(A+i B-C) \operatorname {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 A+B-i C) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{(a-i b)^2 \sqrt {c-i d} f}-\frac {(B-i (A-C)) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{(a+i b)^2 \sqrt {c+i d} f}-\frac {\left (3 a^3 b B d-a^4 C d+b^4 (2 B c-A d)+a b^3 (4 A c-4 c C-B d)-a^2 b^2 (2 B c+5 A d-3 C d)\right ) \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {c+d \tan (e+f x)}}{\sqrt {b c-a d}}\right )}{\sqrt {b} \left (a^2+b^2\right )^2 (b c-a d)^{3/2} f}-\frac {\left (A b^2-a (b B-a C)\right ) \sqrt {c+d \tan (e+f x)}}{\left (a^2+b^2\right ) (b c-a d) f (a+b \tan (e+f x))}\\ \end {align*}

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Mathematica [A] time = 6.22, size = 521, normalized size = 1.59 \[ -\frac {\left (A b^2-a (b B-a C)\right ) \sqrt {c+d \tan (e+f x)}}{f \left (a^2+b^2\right ) (b c-a d) (a+b \tan (e+f x))}-\frac {\frac {2 \sqrt {b c-a d} \left (\frac {1}{2} a^2 d \left (A b^2-a (b B-a C)\right )+\frac {1}{2} b^2 \left (-2 a A (b c-a d)-2 (b B-a C) \left (b c-\frac {a d}{2}\right )+A b^2 d\right )-a b (b c-a d) (-a B+A b-b C)\right ) \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {c+d \tan (e+f x)}}{\sqrt {b c-a d}}\right )}{\sqrt {b} f \left (a^2+b^2\right ) (a d-b c)}+\frac {\frac {i \sqrt {c-i d} \left (-(b c-a d) \left (a^2 (A-C)+2 a b B-b^2 (A-C)\right )+i (b c-a d) \left (a^2 B-2 a b (A-C)-b^2 B\right )\right ) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{f (-c+i d)}-\frac {i \sqrt {c+i d} \left (-(b c-a d) \left (a^2 (A-C)+2 a b B-b^2 (A-C)\right )-i (b c-a d) \left (a^2 B-2 a b (A-C)-b^2 B\right )\right ) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{f (-c-i d)}}{a^2+b^2}}{\left (a^2+b^2\right ) (b c-a d)} \]

Antiderivative was successfully veriﬁed.

[In]

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

[Out]

-((((I*Sqrt[c - I*d]*(I*(a^2*B - b^2*B - 2*a*b*(A - C))*(b*c - a*d) - (2*a*b*B + a^2*(A - C) - b^2*(A - C))*(b

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

^2*B - 2*a*b*(A - C))*(b*c - a*d) - (2*a*b*B + a^2*(A - C) - b^2*(A - C))*(b*c - a*d))*ArcTanh[Sqrt[c + d*Tan[

e + f*x]]/Sqrt[c + I*d]])/((-c - I*d)*f))/(a^2 + b^2) + (2*Sqrt[b*c - a*d]*((a^2*(A*b^2 - a*(b*B - a*C))*d)/2

- a*b*(A*b - a*B - b*C)*(b*c - a*d) + (b^2*(A*b^2*d - 2*a*A*(b*c - a*d) - 2*(b*B - a*C)*(b*c - (a*d)/2)))/2)*A

rcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(Sqrt[b]*(a^2 + b^2)*(-(b*c) + a*d)*f))/((a^2 + b^

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

+ f*x]))

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fricas [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x, algorithm="fricas")

[Out]

Timed out

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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x, algorithm="giac")

[Out]

Timed out

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maple [B] time = 0.64, size = 20870, normalized size = 63.82 \[ \text {output too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x)

[Out]

result too large to display

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(1/2)/(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 details)Is a*d-b*c positive or negative?

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mupad [B] time = 57.65, size = 225004, normalized size = 688.09 \[ \text {result too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((A + B*tan(e + f*x) + C*tan(e + f*x)^2)/((a + b*tan(e + f*x))^2*(c + d*tan(e + f*x))^(1/2)),x)

[Out]

(atan(((((((16*(8*C^3*a^6*b^7*d^11*f^2 - 78*C^3*a^4*b^9*d^11*f^2 + 60*C^3*a^8*b^5*d^11*f^2 - 24*C^3*a^10*b^3*d

^11*f^2 + 2*C^3*a^12*b*d^11*f^2 - 32*C^3*a*b^12*c^3*d^8*f^2 + 152*C^3*a^3*b^10*c*d^10*f^2 + 128*C^3*a^5*b^8*c*

d^10*f^2 - 64*C^3*a^7*b^6*c*d^10*f^2 - 32*C^3*a^9*b^4*c*d^10*f^2 + 8*C^3*a^11*b^2*c*d^10*f^2 - 40*C^3*a^2*b^11

*c^2*d^9*f^2 + 64*C^3*a^3*b^10*c^3*d^8*f^2 - 216*C^3*a^4*b^9*c^2*d^9*f^2 + 96*C^3*a^5*b^8*c^3*d^8*f^2 - 120*C^

3*a^6*b^7*c^2*d^9*f^2 + 56*C^3*a^8*b^5*c^2*d^9*f^2))/(a^10*d^2*f^5 + b^10*c^2*f^5 + 4*a^2*b^8*c^2*f^5 + 6*a^4*

b^6*c^2*f^5 + 4*a^6*b^4*c^2*f^5 + a^8*b^2*c^2*f^5 + a^2*b^8*d^2*f^5 + 4*a^4*b^6*d^2*f^5 + 6*a^6*b^4*d^2*f^5 +

4*a^8*b^2*d^2*f^5 - 2*a*b^9*c*d*f^5 - 2*a^9*b*c*d*f^5 - 8*a^3*b^7*c*d*f^5 - 12*a^5*b^5*c*d*f^5 - 8*a^7*b^3*c*d

*f^5) - (((((16*(40*C*a^3*b^14*d^12*f^4 + 192*C*a^5*b^12*d^12*f^4 + 360*C*a^7*b^10*d^12*f^4 + 320*C*a^9*b^8*d^

12*f^4 + 120*C*a^11*b^6*d^12*f^4 - 8*C*a^15*b^2*d^12*f^4 + 8*C*b^17*c^3*d^9*f^4 + 40*C*a*b^16*c^2*d^10*f^4 + 3

2*C*a*b^16*c^4*d^8*f^4 - 88*C*a^2*b^15*c*d^11*f^4 - 448*C*a^4*b^13*c*d^11*f^4 - 920*C*a^6*b^11*c*d^11*f^4 - 96

0*C*a^8*b^9*c*d^11*f^4 - 520*C*a^10*b^7*c*d^11*f^4 - 128*C*a^12*b^5*c*d^11*f^4 - 8*C*a^14*b^3*c*d^11*f^4 - 32*

C*a^2*b^15*c^3*d^9*f^4 + 256*C*a^3*b^14*c^2*d^10*f^4 + 160*C*a^3*b^14*c^4*d^8*f^4 - 280*C*a^4*b^13*c^3*d^9*f^4

+ 680*C*a^5*b^12*c^2*d^10*f^4 + 320*C*a^5*b^12*c^4*d^8*f^4 - 640*C*a^6*b^11*c^3*d^9*f^4 + 960*C*a^7*b^10*c^2*

d^10*f^4 + 320*C*a^7*b^10*c^4*d^8*f^4 - 680*C*a^8*b^9*c^3*d^9*f^4 + 760*C*a^9*b^8*c^2*d^10*f^4 + 160*C*a^9*b^8

*c^4*d^8*f^4 - 352*C*a^10*b^7*c^3*d^9*f^4 + 320*C*a^11*b^6*c^2*d^10*f^4 + 32*C*a^11*b^6*c^4*d^8*f^4 - 72*C*a^1

2*b^5*c^3*d^9*f^4 + 56*C*a^13*b^4*c^2*d^10*f^4))/(a^10*d^2*f^5 + b^10*c^2*f^5 + 4*a^2*b^8*c^2*f^5 + 6*a^4*b^6*

c^2*f^5 + 4*a^6*b^4*c^2*f^5 + a^8*b^2*c^2*f^5 + a^2*b^8*d^2*f^5 + 4*a^4*b^6*d^2*f^5 + 6*a^6*b^4*d^2*f^5 + 4*a^

8*b^2*d^2*f^5 - 2*a*b^9*c*d*f^5 - 2*a^9*b*c*d*f^5 - 8*a^3*b^7*c*d*f^5 - 12*a^5*b^5*c*d*f^5 - 8*a^7*b^3*c*d*f^5

) - (16*((C^2*a^8*d^2 + 16*C^2*a^2*b^6*c^2 + 9*C^2*a^4*b^4*d^2 - 6*C^2*a^6*b^2*d^2 - 24*C^2*a^3*b^5*c*d + 8*C^

2*a^5*b^3*c*d)*(b^12*c^3*f^2 - a^11*b*d^3*f^2 + 4*a^2*b^10*c^3*f^2 + 6*a^4*b^8*c^3*f^2 + 4*a^6*b^6*c^3*f^2 + a

^8*b^4*c^3*f^2 - a^3*b^9*d^3*f^2 - 4*a^5*b^7*d^3*f^2 - 6*a^7*b^5*d^3*f^2 - 4*a^9*b^3*d^3*f^2 - 3*a*b^11*c^2*d*

f^2 + 3*a^2*b^10*c*d^2*f^2 - 12*a^3*b^9*c^2*d*f^2 + 12*a^4*b^8*c*d^2*f^2 - 18*a^5*b^7*c^2*d*f^2 + 18*a^6*b^6*c

*d^2*f^2 - 12*a^7*b^5*c^2*d*f^2 + 12*a^8*b^4*c*d^2*f^2 - 3*a^9*b^3*c^2*d*f^2 + 3*a^10*b^2*c*d^2*f^2))^(1/2)*(c

+ d*tan(e + f*x))^(1/2)*(32*a^2*b^17*d^12*f^4 + 160*a^4*b^15*d^12*f^4 + 288*a^6*b^13*d^12*f^4 + 160*a^8*b^11*

d^12*f^4 - 160*a^10*b^9*d^12*f^4 - 288*a^12*b^7*d^12*f^4 - 160*a^14*b^5*d^12*f^4 - 32*a^16*b^3*d^12*f^4 + 32*b

^19*c^2*d^10*f^4 + 48*b^19*c^4*d^8*f^4 + 176*a^2*b^17*c^2*d^10*f^4 + 272*a^2*b^17*c^4*d^8*f^4 - 432*a^3*b^16*c

^3*d^9*f^4 + 336*a^4*b^15*c^2*d^10*f^4 + 624*a^4*b^15*c^4*d^8*f^4 - 912*a^5*b^14*c^3*d^9*f^4 + 112*a^6*b^13*c^

2*d^10*f^4 + 720*a^6*b^13*c^4*d^8*f^4 - 880*a^7*b^12*c^3*d^9*f^4 - 560*a^8*b^11*c^2*d^10*f^4 + 400*a^8*b^11*c^

4*d^8*f^4 - 240*a^9*b^10*c^3*d^9*f^4 - 1008*a^10*b^9*c^2*d^10*f^4 + 48*a^10*b^9*c^4*d^8*f^4 + 240*a^11*b^8*c^3

*d^9*f^4 - 784*a^12*b^7*c^2*d^10*f^4 - 48*a^12*b^7*c^4*d^8*f^4 + 208*a^13*b^6*c^3*d^9*f^4 - 304*a^14*b^5*c^2*d

^10*f^4 - 16*a^14*b^5*c^4*d^8*f^4 + 48*a^15*b^4*c^3*d^9*f^4 - 48*a^16*b^3*c^2*d^10*f^4 - 64*a*b^18*c*d^11*f^4

- 80*a*b^18*c^3*d^9*f^4 - 304*a^3*b^16*c*d^11*f^4 - 464*a^5*b^14*c*d^11*f^4 + 16*a^7*b^12*c*d^11*f^4 + 880*a^9

*b^10*c*d^11*f^4 + 1136*a^11*b^8*c*d^11*f^4 + 656*a^13*b^6*c*d^11*f^4 + 176*a^15*b^4*c*d^11*f^4 + 16*a^17*b^2*

c*d^11*f^4))/((b^10*(8*a^2*c^3*f^2 + 6*a^2*c*d^2*f^2) + b^4*(2*a^8*c^3*f^2 + 24*a^8*c*d^2*f^2) + b^8*(12*a^4*c

^3*f^2 + 24*a^4*c*d^2*f^2) + b^6*(8*a^6*c^3*f^2 + 36*a^6*c*d^2*f^2) - b^3*(8*a^9*d^3*f^2 + 6*a^9*c^2*d*f^2) -

b^9*(2*a^3*d^3*f^2 + 24*a^3*c^2*d*f^2) - b^5*(12*a^7*d^3*f^2 + 24*a^7*c^2*d*f^2) - b^7*(8*a^5*d^3*f^2 + 36*a^5

*c^2*d*f^2) + 2*b^12*c^3*f^2 - 2*a^11*b*d^3*f^2 - 6*a*b^11*c^2*d*f^2 + 6*a^10*b^2*c*d^2*f^2)*(a^10*d^2*f^4 + b

^10*c^2*f^4 + 4*a^2*b^8*c^2*f^4 + 6*a^4*b^6*c^2*f^4 + 4*a^6*b^4*c^2*f^4 + a^8*b^2*c^2*f^4 + a^2*b^8*d^2*f^4 +

4*a^4*b^6*d^2*f^4 + 6*a^6*b^4*d^2*f^4 + 4*a^8*b^2*d^2*f^4 - 2*a*b^9*c*d*f^4 - 2*a^9*b*c*d*f^4 - 8*a^3*b^7*c*d*

f^4 - 12*a^5*b^5*c*d*f^4 - 8*a^7*b^3*c*d*f^4)))*((C^2*a^8*d^2 + 16*C^2*a^2*b^6*c^2 + 9*C^2*a^4*b^4*d^2 - 6*C^2

*a^6*b^2*d^2 - 24*C^2*a^3*b^5*c*d + 8*C^2*a^5*b^3*c*d)*(b^12*c^3*f^2 - a^11*b*d^3*f^2 + 4*a^2*b^10*c^3*f^2 + 6

*a^4*b^8*c^3*f^2 + 4*a^6*b^6*c^3*f^2 + a^8*b^4*c^3*f^2 - a^3*b^9*d^3*f^2 - 4*a^5*b^7*d^3*f^2 - 6*a^7*b^5*d^3*f

^2 - 4*a^9*b^3*d^3*f^2 - 3*a*b^11*c^2*d*f^2 + 3*a^2*b^10*c*d^2*f^2 - 12*a^3*b^9*c^2*d*f^2 + 12*a^4*b^8*c*d^2*f

^2 - 18*a^5*b^7*c^2*d*f^2 + 18*a^6*b^6*c*d^2*f^2 - 12*a^7*b^5*c^2*d*f^2 + 12*a^8*b^4*c*d^2*f^2 - 3*a^9*b^3*c^2

*d*f^2 + 3*a^10*b^2*c*d^2*f^2))^(1/2))/(b^10*(8*a^2*c^3*f^2 + 6*a^2*c*d^2*f^2) + b^4*(2*a^8*c^3*f^2 + 24*a^8*c

*d^2*f^2) + b^8*(12*a^4*c^3*f^2 + 24*a^4*c*d^2*f^2) + b^6*(8*a^6*c^3*f^2 + 36*a^6*c*d^2*f^2) - b^3*(8*a^9*d^3*

f^2 + 6*a^9*c^2*d*f^2) - b^9*(2*a^3*d^3*f^2 + 24*a^3*c^2*d*f^2) - b^5*(12*a^7*d^3*f^2 + 24*a^7*c^2*d*f^2) - b^

7*(8*a^5*d^3*f^2 + 36*a^5*c^2*d*f^2) + 2*b^12*c^3*f^2 - 2*a^11*b*d^3*f^2 - 6*a*b^11*c^2*d*f^2 + 6*a^10*b^2*c*d

^2*f^2) + (16*(c + d*tan(e + f*x))^(1/2)*(20*C^2*a^5*b^10*d^11*f^2 - 60*C^2*a^3*b^12*d^11*f^2 + 168*C^2*a^7*b^

8*d^11*f^2 + 40*C^2*a^9*b^6*d^11*f^2 - 44*C^2*a^11*b^4*d^11*f^2 + 4*C^2*a^13*b^2*d^11*f^2 - 20*C^2*b^15*c^3*d^

8*f^2 - 4*C^2*a^14*b*c*d^10*f^2 - 20*C^2*a*b^14*c^2*d^9*f^2 + 100*C^2*a^2*b^13*c*d^10*f^2 - 300*C^2*a^6*b^9*c*

d^10*f^2 - 160*C^2*a^8*b^7*c*d^10*f^2 + 76*C^2*a^10*b^5*c*d^10*f^2 + 32*C^2*a^12*b^3*c*d^10*f^2 + 116*C^2*a^2*

b^13*c^3*d^8*f^2 - 124*C^2*a^3*b^12*c^2*d^9*f^2 + 216*C^2*a^4*b^11*c^3*d^8*f^2 - 40*C^2*a^5*b^10*c^2*d^9*f^2 +

8*C^2*a^6*b^9*c^3*d^8*f^2 + 168*C^2*a^7*b^8*c^2*d^9*f^2 - 68*C^2*a^8*b^7*c^3*d^8*f^2 + 60*C^2*a^9*b^6*c^2*d^9

*f^2 + 4*C^2*a^10*b^5*c^3*d^8*f^2 - 44*C^2*a^11*b^4*c^2*d^9*f^2))/(a^10*d^2*f^4 + b^10*c^2*f^4 + 4*a^2*b^8*c^2

*f^4 + 6*a^4*b^6*c^2*f^4 + 4*a^6*b^4*c^2*f^4 + a^8*b^2*c^2*f^4 + a^2*b^8*d^2*f^4 + 4*a^4*b^6*d^2*f^4 + 6*a^6*b

^4*d^2*f^4 + 4*a^8*b^2*d^2*f^4 - 2*a*b^9*c*d*f^4 - 2*a^9*b*c*d*f^4 - 8*a^3*b^7*c*d*f^4 - 12*a^5*b^5*c*d*f^4 -

8*a^7*b^3*c*d*f^4))*((C^2*a^8*d^2 + 16*C^2*a^2*b^6*c^2 + 9*C^2*a^4*b^4*d^2 - 6*C^2*a^6*b^2*d^2 - 24*C^2*a^3*b^

5*c*d + 8*C^2*a^5*b^3*c*d)*(b^12*c^3*f^2 - a^11*b*d^3*f^2 + 4*a^2*b^10*c^3*f^2 + 6*a^4*b^8*c^3*f^2 + 4*a^6*b^6

*c^3*f^2 + a^8*b^4*c^3*f^2 - a^3*b^9*d^3*f^2 - 4*a^5*b^7*d^3*f^2 - 6*a^7*b^5*d^3*f^2 - 4*a^9*b^3*d^3*f^2 - 3*a

*b^11*c^2*d*f^2 + 3*a^2*b^10*c*d^2*f^2 - 12*a^3*b^9*c^2*d*f^2 + 12*a^4*b^8*c*d^2*f^2 - 18*a^5*b^7*c^2*d*f^2 +

18*a^6*b^6*c*d^2*f^2 - 12*a^7*b^5*c^2*d*f^2 + 12*a^8*b^4*c*d^2*f^2 - 3*a^9*b^3*c^2*d*f^2 + 3*a^10*b^2*c*d^2*f^

2))^(1/2))/(b^10*(8*a^2*c^3*f^2 + 6*a^2*c*d^2*f^2) + b^4*(2*a^8*c^3*f^2 + 24*a^8*c*d^2*f^2) + b^8*(12*a^4*c^3*

f^2 + 24*a^4*c*d^2*f^2) + b^6*(8*a^6*c^3*f^2 + 36*a^6*c*d^2*f^2) - b^3*(8*a^9*d^3*f^2 + 6*a^9*c^2*d*f^2) - b^9

*(2*a^3*d^3*f^2 + 24*a^3*c^2*d*f^2) - b^5*(12*a^7*d^3*f^2 + 24*a^7*c^2*d*f^2) - b^7*(8*a^5*d^3*f^2 + 36*a^5*c^

2*d*f^2) + 2*b^12*c^3*f^2 - 2*a^11*b*d^3*f^2 - 6*a*b^11*c^2*d*f^2 + 6*a^10*b^2*c*d^2*f^2))*((C^2*a^8*d^2 + 16*

C^2*a^2*b^6*c^2 + 9*C^2*a^4*b^4*d^2 - 6*C^2*a^6*b^2*d^2 - 24*C^2*a^3*b^5*c*d + 8*C^2*a^5*b^3*c*d)*(b^12*c^3*f^

2 - a^11*b*d^3*f^2 + 4*a^2*b^10*c^3*f^2 + 6*a^4*b^8*c^3*f^2 + 4*a^6*b^6*c^3*f^2 + a^8*b^4*c^3*f^2 - a^3*b^9*d^

3*f^2 - 4*a^5*b^7*d^3*f^2 - 6*a^7*b^5*d^3*f^2 - 4*a^9*b^3*d^3*f^2 - 3*a*b^11*c^2*d*f^2 + 3*a^2*b^10*c*d^2*f^2

- 12*a^3*b^9*c^2*d*f^2 + 12*a^4*b^8*c*d^2*f^2 - 18*a^5*b^7*c^2*d*f^2 + 18*a^6*b^6*c*d^2*f^2 - 12*a^7*b^5*c^2*d

*f^2 + 12*a^8*b^4*c*d^2*f^2 - 3*a^9*b^3*c^2*d*f^2 + 3*a^10*b^2*c*d^2*f^2))^(1/2))/(b^10*(8*a^2*c^3*f^2 + 6*a^2

*c*d^2*f^2) + b^4*(2*a^8*c^3*f^2 + 24*a^8*c*d^2*f^2) + b^8*(12*a^4*c^3*f^2 + 24*a^4*c*d^2*f^2) + b^6*(8*a^6*c^

3*f^2 + 36*a^6*c*d^2*f^2) - b^3*(8*a^9*d^3*f^2 + 6*a^9*c^2*d*f^2) - b^9*(2*a^3*d^3*f^2 + 24*a^3*c^2*d*f^2) - b

^5*(12*a^7*d^3*f^2 + 24*a^7*c^2*d*f^2) - b^7*(8*a^5*d^3*f^2 + 36*a^5*c^2*d*f^2) + 2*b^12*c^3*f^2 - 2*a^11*b*d^

3*f^2 - 6*a*b^11*c^2*d*f^2 + 6*a^10*b^2*c*d^2*f^2) + (16*(c + d*tan(e + f*x))^(1/2)*(2*C^4*a^2*b^9*d^10 - 5*C^

4*a^4*b^7*d^10 + 17*C^4*a^6*b^5*d^10 - 7*C^4*a^8*b^3*d^10 + 2*C^4*b^11*c^2*d^8 + C^4*a^10*b*d^10 - 12*C^4*a^2*

b^9*c^2*d^8 + 18*C^4*a^4*b^7*c^2*d^8 - 4*C^4*a*b^10*c*d^9 + 16*C^4*a^3*b^8*c*d^9 - 36*C^4*a^5*b^6*c*d^9 + 8*C^

4*a^7*b^4*c*d^9))/(a^10*d^2*f^4 + b^10*c^2*f^4 + 4*a^2*b^8*c^2*f^4 + 6*a^4*b^6*c^2*f^4 + 4*a^6*b^4*c^2*f^4 + a

^8*b^2*c^2*f^4 + a^2*b^8*d^2*f^4 + 4*a^4*b^6*d^2*f^4 + 6*a^6*b^4*d^2*f^4 + 4*a^8*b^2*d^2*f^4 - 2*a*b^9*c*d*f^4

- 2*a^9*b*c*d*f^4 - 8*a^3*b^7*c*d*f^4 - 12*a^5*b^5*c*d*f^4 - 8*a^7*b^3*c*d*f^4))*((C^2*a^8*d^2 + 16*C^2*a^2*b

^6*c^2 + 9*C^2*a^4*b^4*d^2 - 6*C^2*a^6*b^2*d^2 - 24*C^2*a^3*b^5*c*d + 8*C^2*a^5*b^3*c*d)*(b^12*c^3*f^2 - a^11*

b*d^3*f^2 + 4*a^2*b^10*c^3*f^2 + 6*a^4*b^8*c^3*f^2 + 4*a^6*b^6*c^3*f^2 + a^8*b^4*c^3*f^2 - a^3*b^9*d^3*f^2 - 4

*a^5*b^7*d^3*f^2 - 6*a^7*b^5*d^3*f^2 - 4*a^9*b^3*d^3*f^2 - 3*a*b^11*c^2*d*f^2 + 3*a^2*b^10*c*d^2*f^2 - 12*a^3*

b^9*c^2*d*f^2 + 12*a^4*b^8*c*d^2*f^2 - 18*a^5*b^7*c^2*d*f^2 + 18*a^6*b^6*c*d^2*f^2 - 12*a^7*b^5*c^2*d*f^2 + 12

*a^8*b^4*c*d^2*f^2 - 3*a^9*b^3*c^2*d*f^2 + 3*a^10*b^2*c*d^2*f^2))^(1/2)*1i)/(b^10*(8*a^2*c^3*f^2 + 6*a^2*c*d^2

*f^2) + b^4*(2*a^8*c^3*f^2 + 24*a^8*c*d^2*f^2) + b^8*(12*a^4*c^3*f^2 + 24*a^4*c*d^2*f^2) + b^6*(8*a^6*c^3*f^2

+ 36*a^6*c*d^2*f^2) - b^3*(8*a^9*d^3*f^2 + 6*a^9*c^2*d*f^2) - b^9*(2*a^3*d^3*f^2 + 24*a^3*c^2*d*f^2) - b^5*(12

*a^7*d^3*f^2 + 24*a^7*c^2*d*f^2) - b^7*(8*a^5*d^3*f^2 + 36*a^5*c^2*d*f^2) + 2*b^12*c^3*f^2 - 2*a^11*b*d^3*f^2

- 6*a*b^11*c^2*d*f^2 + 6*a^10*b^2*c*d^2*f^2) - (((((16*(8*C^3*a^6*b^7*d^11*f^2 - 78*C^3*a^4*b^9*d^11*f^2 + 60*

C^3*a^8*b^5*d^11*f^2 - 24*C^3*a^10*b^3*d^11*f^2 + 2*C^3*a^12*b*d^11*f^2 - 32*C^3*a*b^12*c^3*d^8*f^2 + 152*C^3*

a^3*b^10*c*d^10*f^2 + 128*C^3*a^5*b^8*c*d^10*f^2 - 64*C^3*a^7*b^6*c*d^10*f^2 - 32*C^3*a^9*b^4*c*d^10*f^2 + 8*C

^3*a^11*b^2*c*d^10*f^2 - 40*C^3*a^2*b^11*c^2*d^9*f^2 + 64*C^3*a^3*b^10*c^3*d^8*f^2 - 216*C^3*a^4*b^9*c^2*d^9*f

^2 + 96*C^3*a^5*b^8*c^3*d^8*f^2 - 120*C^3*a^6*b^7*c^2*d^9*f^2 + 56*C^3*a^8*b^5*c^2*d^9*f^2))/(a^10*d^2*f^5 + b

^10*c^2*f^5 + 4*a^2*b^8*c^2*f^5 + 6*a^4*b^6*c^2*f^5 + 4*a^6*b^4*c^2*f^5 + a^8*b^2*c^2*f^5 + a^2*b^8*d^2*f^5 +

4*a^4*b^6*d^2*f^5 + 6*a^6*b^4*d^2*f^5 + 4*a^8*b^2*d^2*f^5 - 2*a*b^9*c*d*f^5 - 2*a^9*b*c*d*f^5 - 8*a^3*b^7*c*d*

f^5 - 12*a^5*b^5*c*d*f^5 - 8*a^7*b^3*c*d*f^5) - (((((16*(40*C*a^3*b^14*d^12*f^4 + 192*C*a^5*b^12*d^12*f^4 + 36

0*C*a^7*b^10*d^12*f^4 + 320*C*a^9*b^8*d^12*f^4 + 120*C*a^11*b^6*d^12*f^4 - 8*C*a^15*b^2*d^12*f^4 + 8*C*b^17*c^

3*d^9*f^4 + 40*C*a*b^16*c^2*d^10*f^4 + 32*C*a*b^16*c^4*d^8*f^4 - 88*C*a^2*b^15*c*d^11*f^4 - 448*C*a^4*b^13*c*d

^11*f^4 - 920*C*a^6*b^11*c*d^11*f^4 - 960*C*a^8*b^9*c*d^11*f^4 - 520*C*a^10*b^7*c*d^11*f^4 - 128*C*a^12*b^5*c*

d^11*f^4 - 8*C*a^14*b^3*c*d^11*f^4 - 32*C*a^2*b^15*c^3*d^9*f^4 + 256*C*a^3*b^14*c^2*d^10*f^4 + 160*C*a^3*b^14*

c^4*d^8*f^4 - 280*C*a^4*b^13*c^3*d^9*f^4 + 680*C*a^5*b^12*c^2*d^10*f^4 + 320*C*a^5*b^12*c^4*d^8*f^4 - 640*C*a^

6*b^11*c^3*d^9*f^4 + 960*C*a^7*b^10*c^2*d^10*f^4 + 320*C*a^7*b^10*c^4*d^8*f^4 - 680*C*a^8*b^9*c^3*d^9*f^4 + 76

0*C*a^9*b^8*c^2*d^10*f^4 + 160*C*a^9*b^8*c^4*d^8*f^4 - 352*C*a^10*b^7*c^3*d^9*f^4 + 320*C*a^11*b^6*c^2*d^10*f^

4 + 32*C*a^11*b^6*c^4*d^8*f^4 - 72*C*a^12*b^5*c^3*d^9*f^4 + 56*C*a^13*b^4*c^2*d^10*f^4))/(a^10*d^2*f^5 + b^10*

c^2*f^5 + 4*a^2*b^8*c^2*f^5 + 6*a^4*b^6*c^2*f^5 + 4*a^6*b^4*c^2*f^5 + a^8*b^2*c^2*f^5 + a^2*b^8*d^2*f^5 + 4*a^

4*b^6*d^2*f^5 + 6*a^6*b^4*d^2*f^5 + 4*a^8*b^2*d^2*f^5 - 2*a*b^9*c*d*f^5 - 2*a^9*b*c*d*f^5 - 8*a^3*b^7*c*d*f^5

- 12*a^5*b^5*c*d*f^5 - 8*a^7*b^3*c*d*f^5) + (16*((C^2*a^8*d^2 + 16*C^2*a^2*b^6*c^2 + 9*C^2*a^4*b^4*d^2 - 6*C^2

*a^6*b^2*d^2 - 24*C^2*a^3*b^5*c*d + 8*C^2*a^5*b^3*c*d)*(b^12*c^3*f^2 - a^11*b*d^3*f^2 + 4*a^2*b^10*c^3*f^2 + 6

*a^4*b^8*c^3*f^2 + 4*a^6*b^6*c^3*f^2 + a^8*b^4*c^3*f^2 - a^3*b^9*d^3*f^2 - 4*a^5*b^7*d^3*f^2 - 6*a^7*b^5*d^3*f

^2 - 4*a^9*b^3*d^3*f^2 - 3*a*b^11*c^2*d*f^2 + 3*a^2*b^10*c*d^2*f^2 - 12*a^3*b^9*c^2*d*f^2 + 12*a^4*b^8*c*d^2*f

^2 - 18*a^5*b^7*c^2*d*f^2 + 18*a^6*b^6*c*d^2*f^2 - 12*a^7*b^5*c^2*d*f^2 + 12*a^8*b^4*c*d^2*f^2 - 3*a^9*b^3*c^2

*d*f^2 + 3*a^10*b^2*c*d^2*f^2))^(1/2)*(c + d*tan(e + f*x))^(1/2)*(32*a^2*b^17*d^12*f^4 + 160*a^4*b^15*d^12*f^4

+ 288*a^6*b^13*d^12*f^4 + 160*a^8*b^11*d^12*f^4 - 160*a^10*b^9*d^12*f^4 - 288*a^12*b^7*d^12*f^4 - 160*a^14*b^

5*d^12*f^4 - 32*a^16*b^3*d^12*f^4 + 32*b^19*c^2*d^10*f^4 + 48*b^19*c^4*d^8*f^4 + 176*a^2*b^17*c^2*d^10*f^4 + 2

72*a^2*b^17*c^4*d^8*f^4 - 432*a^3*b^16*c^3*d^9*f^4 + 336*a^4*b^15*c^2*d^10*f^4 + 624*a^4*b^15*c^4*d^8*f^4 - 91

2*a^5*b^14*c^3*d^9*f^4 + 112*a^6*b^13*c^2*d^10*f^4 + 720*a^6*b^13*c^4*d^8*f^4 - 880*a^7*b^12*c^3*d^9*f^4 - 560

*a^8*b^11*c^2*d^10*f^4 + 400*a^8*b^11*c^4*d^8*f^4 - 240*a^9*b^10*c^3*d^9*f^4 - 1008*a^10*b^9*c^2*d^10*f^4 + 48

*a^10*b^9*c^4*d^8*f^4 + 240*a^11*b^8*c^3*d^9*f^4 - 784*a^12*b^7*c^2*d^10*f^4 - 48*a^12*b^7*c^4*d^8*f^4 + 208*a

^13*b^6*c^3*d^9*f^4 - 304*a^14*b^5*c^2*d^10*f^4 - 16*a^14*b^5*c^4*d^8*f^4 + 48*a^15*b^4*c^3*d^9*f^4 - 48*a^16*

b^3*c^2*d^10*f^4 - 64*a*b^18*c*d^11*f^4 - 80*a*b^18*c^3*d^9*f^4 - 304*a^3*b^16*c*d^11*f^4 - 464*a^5*b^14*c*d^1

1*f^4 + 16*a^7*b^12*c*d^11*f^4 + 880*a^9*b^10*c*d^11*f^4 + 1136*a^11*b^8*c*d^11*f^4 + 656*a^13*b^6*c*d^11*f^4

+ 176*a^15*b^4*c*d^11*f^4 + 16*a^17*b^2*c*d^11*f^4))/((b^10*(8*a^2*c^3*f^2 + 6*a^2*c*d^2*f^2) + b^4*(2*a^8*c^3

*f^2 + 24*a^8*c*d^2*f^2) + b^8*(12*a^4*c^3*f^2 + 24*a^4*c*d^2*f^2) + b^6*(8*a^6*c^3*f^2 + 36*a^6*c*d^2*f^2) -

b^3*(8*a^9*d^3*f^2 + 6*a^9*c^2*d*f^2) - b^9*(2*a^3*d^3*f^2 + 24*a^3*c^2*d*f^2) - b^5*(12*a^7*d^3*f^2 + 24*a^7*

c^2*d*f^2) - b^7*(8*a^5*d^3*f^2 + 36*a^5*c^2*d*f^2) + 2*b^12*c^3*f^2 - 2*a^11*b*d^3*f^2 - 6*a*b^11*c^2*d*f^2 +

6*a^10*b^2*c*d^2*f^2)*(a^10*d^2*f^4 + b^10*c^2*f^4 + 4*a^2*b^8*c^2*f^4 + 6*a^4*b^6*c^2*f^4 + 4*a^6*b^4*c^2*f^

4 + a^8*b^2*c^2*f^4 + a^2*b^8*d^2*f^4 + 4*a^4*b^6*d^2*f^4 + 6*a^6*b^4*d^2*f^4 + 4*a^8*b^2*d^2*f^4 - 2*a*b^9*c*

d*f^4 - 2*a^9*b*c*d*f^4 - 8*a^3*b^7*c*d*f^4 - 12*a^5*b^5*c*d*f^4 - 8*a^7*b^3*c*d*f^4)))*((C^2*a^8*d^2 + 16*C^2

*a^2*b^6*c^2 + 9*C^2*a^4*b^4*d^2 - 6*C^2*a^6*b^2*d^2 - 24*C^2*a^3*b^5*c*d + 8*C^2*a^5*b^3*c*d)*(b^12*c^3*f^2 -

a^11*b*d^3*f^2 + 4*a^2*b^10*c^3*f^2 + 6*a^4*b^8*c^3*f^2 + 4*a^6*b^6*c^3*f^2 + a^8*b^4*c^3*f^2 - a^3*b^9*d^3*f

^2 - 4*a^5*b^7*d^3*f^2 - 6*a^7*b^5*d^3*f^2 - 4*a^9*b^3*d^3*f^2 - 3*a*b^11*c^2*d*f^2 + 3*a^2*b^10*c*d^2*f^2 - 1

2*a^3*b^9*c^2*d*f^2 + 12*a^4*b^8*c*d^2*f^2 - 18*a^5*b^7*c^2*d*f^2 + 18*a^6*b^6*c*d^2*f^2 - 12*a^7*b^5*c^2*d*f^

2 + 12*a^8*b^4*c*d^2*f^2 - 3*a^9*b^3*c^2*d*f^2 + 3*a^10*b^2*c*d^2*f^2))^(1/2))/(b^10*(8*a^2*c^3*f^2 + 6*a^2*c*

d^2*f^2) + b^4*(2*a^8*c^3*f^2 + 24*a^8*c*d^2*f^2) + b^8*(12*a^4*c^3*f^2 + 24*a^4*c*d^2*f^2) + b^6*(8*a^6*c^3*f

^2 + 36*a^6*c*d^2*f^2) - b^3*(8*a^9*d^3*f^2 + 6*a^9*c^2*d*f^2) - b^9*(2*a^3*d^3*f^2 + 24*a^3*c^2*d*f^2) - b^5*

(12*a^7*d^3*f^2 + 24*a^7*c^2*d*f^2) - b^7*(8*a^5*d^3*f^2 + 36*a^5*c^2*d*f^2) + 2*b^12*c^3*f^2 - 2*a^11*b*d^3*f

^2 - 6*a*b^11*c^2*d*f^2 + 6*a^10*b^2*c*d^2*f^2) - (16*(c + d*tan(e + f*x))^(1/2)*(20*C^2*a^5*b^10*d^11*f^2 - 6

0*C^2*a^3*b^12*d^11*f^2 + 168*C^2*a^7*b^8*d^11*f^2 + 40*C^2*a^9*b^6*d^11*f^2 - 44*C^2*a^11*b^4*d^11*f^2 + 4*C^

2*a^13*b^2*d^11*f^2 - 20*C^2*b^15*c^3*d^8*f^2 - 4*C^2*a^14*b*c*d^10*f^2 - 20*C^2*a*b^14*c^2*d^9*f^2 + 100*C^2*

a^2*b^13*c*d^10*f^2 - 300*C^2*a^6*b^9*c*d^10*f^2 - 160*C^2*a^8*b^7*c*d^10*f^2 + 76*C^2*a^10*b^5*c*d^10*f^2 + 3

2*C^2*a^12*b^3*c*d^10*f^2 + 116*C^2*a^2*b^13*c^3*d^8*f^2 - 124*C^2*a^3*b^12*c^2*d^9*f^2 + 216*C^2*a^4*b^11*c^3

*d^8*f^2 - 40*C^2*a^5*b^10*c^2*d^9*f^2 + 8*C^2*a^6*b^9*c^3*d^8*f^2 + 168*C^2*a^7*b^8*c^2*d^9*f^2 - 68*C^2*a^8*

b^7*c^3*d^8*f^2 + 60*C^2*a^9*b^6*c^2*d^9*f^2 + 4*C^2*a^10*b^5*c^3*d^8*f^2 - 44*C^2*a^11*b^4*c^2*d^9*f^2))/(a^1

0*d^2*f^4 + b^10*c^2*f^4 + 4*a^2*b^8*c^2*f^4 + 6*a^4*b^6*c^2*f^4 + 4*a^6*b^4*c^2*f^4 + a^8*b^2*c^2*f^4 + a^2*b

^8*d^2*f^4 + 4*a^4*b^6*d^2*f^4 + 6*a^6*b^4*d^2*f^4 + 4*a^8*b^2*d^2*f^4 - 2*a*b^9*c*d*f^4 - 2*a^9*b*c*d*f^4 - 8

*a^3*b^7*c*d*f^4 - 12*a^5*b^5*c*d*f^4 - 8*a^7*b^3*c*d*f^4))*((C^2*a^8*d^2 + 16*C^2*a^2*b^6*c^2 + 9*C^2*a^4*b^4

*d^2 - 6*C^2*a^6*b^2*d^2 - 24*C^2*a^3*b^5*c*d + 8*C^2*a^5*b^3*c*d)*(b^12*c^3*f^2 - a^11*b*d^3*f^2 + 4*a^2*b^10

*c^3*f^2 + 6*a^4*b^8*c^3*f^2 + 4*a^6*b^6*c^3*f^2 + a^8*b^4*c^3*f^2 - a^3*b^9*d^3*f^2 - 4*a^5*b^7*d^3*f^2 - 6*a

^7*b^5*d^3*f^2 - 4*a^9*b^3*d^3*f^2 - 3*a*b^11*c^2*d*f^2 + 3*a^2*b^10*c*d^2*f^2 - 12*a^3*b^9*c^2*d*f^2 + 12*a^4

*b^8*c*d^2*f^2 - 18*a^5*b^7*c^2*d*f^2 + 18*a^6*b^6*c*d^2*f^2 - 12*a^7*b^5*c^2*d*f^2 + 12*a^8*b^4*c*d^2*f^2 - 3

*a^9*b^3*c^2*d*f^2 + 3*a^10*b^2*c*d^2*f^2))^(1/2))/(b^10*(8*a^2*c^3*f^2 + 6*a^2*c*d^2*f^2) + b^4*(2*a^8*c^3*f^

2 + 24*a^8*c*d^2*f^2) + b^8*(12*a^4*c^3*f^2 + 24*a^4*c*d^2*f^2) + b^6*(8*a^6*c^3*f^2 + 36*a^6*c*d^2*f^2) - b^3

*(8*a^9*d^3*f^2 + 6*a^9*c^2*d*f^2) - b^9*(2*a^3*d^3*f^2 + 24*a^3*c^2*d*f^2) - b^5*(12*a^7*d^3*f^2 + 24*a^7*c^2

*d*f^2) - b^7*(8*a^5*d^3*f^2 + 36*a^5*c^2*d*f^2) + 2*b^12*c^3*f^2 - 2*a^11*b*d^3*f^2 - 6*a*b^11*c^2*d*f^2 + 6*

a^10*b^2*c*d^2*f^2))*((C^2*a^8*d^2 + 16*C^2*a^2*b^6*c^2 + 9*C^2*a^4*b^4*d^2 - 6*C^2*a^6*b^2*d^2 - 24*C^2*a^3*b

^5*c*d + 8*C^2*a^5*b^3*c*d)*(b^12*c^3*f^2 - a^11*b*d^3*f^2 + 4*a^2*b^10*c^3*f^2 + 6*a^4*b^8*c^3*f^2 + 4*a^6*b^

6*c^3*f^2 + a^8*b^4*c^3*f^2 - a^3*b^9*d^3*f^2 - 4*a^5*b^7*d^3*f^2 - 6*a^7*b^5*d^3*f^2 - 4*a^9*b^3*d^3*f^2 - 3*

a*b^11*c^2*d*f^2 + 3*a^2*b^10*c*d^2*f^2 - 12*a^3*b^9*c^2*d*f^2 + 12*a^4*b^8*c*d^2*f^2 - 18*a^5*b^7*c^2*d*f^2 +

18*a^6*b^6*c*d^2*f^2 - 12*a^7*b^5*c^2*d*f^2 + 12*a^8*b^4*c*d^2*f^2 - 3*a^9*b^3*c^2*d*f^2 + 3*a^10*b^2*c*d^2*f

^2))^(1/2))/(b^10*(8*a^2*c^3*f^2 + 6*a^2*c*d^2*f^2) + b^4*(2*a^8*c^3*f^2 + 24*a^8*c*d^2*f^2) + b^8*(12*a^4*c^3

*f^2 + 24*a^4*c*d^2*f^2) + b^6*(8*a^6*c^3*f^2 + 36*a^6*c*d^2*f^2) - b^3*(8*a^9*d^3*f^2 + 6*a^9*c^2*d*f^2) - b^

9*(2*a^3*d^3*f^2 + 24*a^3*c^2*d*f^2) - b^5*(12*a^7*d^3*f^2 + 24*a^7*c^2*d*f^2) - b^7*(8*a^5*d^3*f^2 + 36*a^5*c

^2*d*f^2) + 2*b^12*c^3*f^2 - 2*a^11*b*d^3*f^2 - 6*a*b^11*c^2*d*f^2 + 6*a^10*b^2*c*d^2*f^2) - (16*(c + d*tan(e

+ f*x))^(1/2)*(2*C^4*a^2*b^9*d^10 - 5*C^4*a^4*b^7*d^10 + 17*C^4*a^6*b^5*d^10 - 7*C^4*a^8*b^3*d^10 + 2*C^4*b^11

*c^2*d^8 + C^4*a^10*b*d^10 - 12*C^4*a^2*b^9*c^2*d^8 + 18*C^4*a^4*b^7*c^2*d^8 - 4*C^4*a*b^10*c*d^9 + 16*C^4*a^3

*b^8*c*d^9 - 36*C^4*a^5*b^6*c*d^9 + 8*C^4*a^7*b^4*c*d^9))/(a^10*d^2*f^4 + b^10*c^2*f^4 + 4*a^2*b^8*c^2*f^4 + 6

*a^4*b^6*c^2*f^4 + 4*a^6*b^4*c^2*f^4 + a^8*b^2*c^2*f^4 + a^2*b^8*d^2*f^4 + 4*a^4*b^6*d^2*f^4 + 6*a^6*b^4*d^2*f

^4 + 4*a^8*b^2*d^2*f^4 - 2*a*b^9*c*d*f^4 - 2*a^9*b*c*d*f^4 - 8*a^3*b^7*c*d*f^4 - 12*a^5*b^5*c*d*f^4 - 8*a^7*b^

3*c*d*f^4))*((C^2*a^8*d^2 + 16*C^2*a^2*b^6*c^2 + 9*C^2*a^4*b^4*d^2 - 6*C^2*a^6*b^2*d^2 - 24*C^2*a^3*b^5*c*d +

8*C^2*a^5*b^3*c*d)*(b^12*c^3*f^2 - a^11*b*d^3*f^2 + 4*a^2*b^10*c^3*f^2 + 6*a^4*b^8*c^3*f^2 + 4*a^6*b^6*c^3*f^2

+ a^8*b^4*c^3*f^2 - a^3*b^9*d^3*f^2 - 4*a^5*b^7*d^3*f^2 - 6*a^7*b^5*d^3*f^2 - 4*a^9*b^3*d^3*f^2 - 3*a*b^11*c^

2*d*f^2 + 3*a^2*b^10*c*d^2*f^2 - 12*a^3*b^9*c^2*d*f^2 + 12*a^4*b^8*c*d^2*f^2 - 18*a^5*b^7*c^2*d*f^2 + 18*a^6*b

^6*c*d^2*f^2 - 12*a^7*b^5*c^2*d*f^2 + 12*a^8*b^4*c*d^2*f^2 - 3*a^9*b^3*c^2*d*f^2 + 3*a^10*b^2*c*d^2*f^2))^(1/2

)*1i)/(b^10*(8*a^2*c^3*f^2 + 6*a^2*c*d^2*f^2) + b^4*(2*a^8*c^3*f^2 + 24*a^8*c*d^2*f^2) + b^8*(12*a^4*c^3*f^2 +

24*a^4*c*d^2*f^2) + b^6*(8*a^6*c^3*f^2 + 36*a^6*c*d^2*f^2) - b^3*(8*a^9*d^3*f^2 + 6*a^9*c^2*d*f^2) - b^9*(2*a

^3*d^3*f^2 + 24*a^3*c^2*d*f^2) - b^5*(12*a^7*d^3*f^2 + 24*a^7*c^2*d*f^2) - b^7*(8*a^5*d^3*f^2 + 36*a^5*c^2*d*f

^2) + 2*b^12*c^3*f^2 - 2*a^11*b*d^3*f^2 - 6*a*b^11*c^2*d*f^2 + 6*a^10*b^2*c*d^2*f^2))/((((((16*(8*C^3*a^6*b^7*

d^11*f^2 - 78*C^3*a^4*b^9*d^11*f^2 + 60*C^3*a^8*b^5*d^11*f^2 - 24*C^3*a^10*b^3*d^11*f^2 + 2*C^3*a^12*b*d^11*f^

2 - 32*C^3*a*b^12*c^3*d^8*f^2 + 152*C^3*a^3*b^10*c*d^10*f^2 + 128*C^3*a^5*b^8*c*d^10*f^2 - 64*C^3*a^7*b^6*c*d^

10*f^2 - 32*C^3*a^9*b^4*c*d^10*f^2 + 8*C^3*a^11*b^2*c*d^10*f^2 - 40*C^3*a^2*b^11*c^2*d^9*f^2 + 64*C^3*a^3*b^10

*c^3*d^8*f^2 - 216*C^3*a^4*b^9*c^2*d^9*f^2 + 96*C^3*a^5*b^8*c^3*d^8*f^2 - 120*C^3*a^6*b^7*c^2*d^9*f^2 + 56*C^3

*a^8*b^5*c^2*d^9*f^2))/(a^10*d^2*f^5 + b^10*c^2*f^5 + 4*a^2*b^8*c^2*f^5 + 6*a^4*b^6*c^2*f^5 + 4*a^6*b^4*c^2*f^

5 + a^8*b^2*c^2*f^5 + a^2*b^8*d^2*f^5 + 4*a^4*b^6*d^2*f^5 + 6*a^6*b^4*d^2*f^5 + 4*a^8*b^2*d^2*f^5 - 2*a*b^9*c*

d*f^5 - 2*a^9*b*c*d*f^5 - 8*a^3*b^7*c*d*f^5 - 12*a^5*b^5*c*d*f^5 - 8*a^7*b^3*c*d*f^5) - (((((16*(40*C*a^3*b^14

*d^12*f^4 + 192*C*a^5*b^12*d^12*f^4 + 360*C*a^7*b^10*d^12*f^4 + 320*C*a^9*b^8*d^12*f^4 + 120*C*a^11*b^6*d^12*f

^4 - 8*C*a^15*b^2*d^12*f^4 + 8*C*b^17*c^3*d^9*f^4 + 40*C*a*b^16*c^2*d^10*f^4 + 32*C*a*b^16*c^4*d^8*f^4 - 88*C*

a^2*b^15*c*d^11*f^4 - 448*C*a^4*b^13*c*d^11*f^4 - 920*C*a^6*b^11*c*d^11*f^4 - 960*C*a^8*b^9*c*d^11*f^4 - 520*C

*a^10*b^7*c*d^11*f^4 - 128*C*a^12*b^5*c*d^11*f^4 - 8*C*a^14*b^3*c*d^11*f^4 - 32*C*a^2*b^15*c^3*d^9*f^4 + 256*C

*a^3*b^14*c^2*d^10*f^4 + 160*C*a^3*b^14*c^4*d^8*f^4 - 280*C*a^4*b^13*c^3*d^9*f^4 + 680*C*a^5*b^12*c^2*d^10*f^4

+ 320*C*a^5*b^12*c^4*d^8*f^4 - 640*C*a^6*b^11*c^3*d^9*f^4 + 960*C*a^7*b^10*c^2*d^10*f^4 + 320*C*a^7*b^10*c^4*

d^8*f^4 - 680*C*a^8*b^9*c^3*d^9*f^4 + 760*C*a^9*b^8*c^2*d^10*f^4 + 160*C*a^9*b^8*c^4*d^8*f^4 - 352*C*a^10*b^7*

c^3*d^9*f^4 + 320*C*a^11*b^6*c^2*d^10*f^4 + 32*C*a^11*b^6*c^4*d^8*f^4 - 72*C*a^12*b^5*c^3*d^9*f^4 + 56*C*a^13*

b^4*c^2*d^10*f^4))/(a^10*d^2*f^5 + b^10*c^2*f^5 + 4*a^2*b^8*c^2*f^5 + 6*a^4*b^6*c^2*f^5 + 4*a^6*b^4*c^2*f^5 +

a^8*b^2*c^2*f^5 + a^2*b^8*d^2*f^5 + 4*a^4*b^6*d^2*f^5 + 6*a^6*b^4*d^2*f^5 + 4*a^8*b^2*d^2*f^5 - 2*a*b^9*c*d*f^

5 - 2*a^9*b*c*d*f^5 - 8*a^3*b^7*c*d*f^5 - 12*a^5*b^5*c*d*f^5 - 8*a^7*b^3*c*d*f^5) - (16*((C^2*a^8*d^2 + 16*C^2

*a^2*b^6*c^2 + 9*C^2*a^4*b^4*d^2 - 6*C^2*a^6*b^2*d^2 - 24*C^2*a^3*b^5*c*d + 8*C^2*a^5*b^3*c*d)*(b^12*c^3*f^2 -

a^11*b*d^3*f^2 + 4*a^2*b^10*c^3*f^2 + 6*a^4*b^8*c^3*f^2 + 4*a^6*b^6*c^3*f^2 + a^8*b^4*c^3*f^2 - a^3*b^9*d^3*f

^2 - 4*a^5*b^7*d^3*f^2 - 6*a^7*b^5*d^3*f^2 - 4*a^9*b^3*d^3*f^2 - 3*a*b^11*c^2*d*f^2 + 3*a^2*b^10*c*d^2*f^2 - 1

2*a^3*b^9*c^2*d*f^2 + 12*a^4*b^8*c*d^2*f^2 - 18*a^5*b^7*c^2*d*f^2 + 18*a^6*b^6*c*d^2*f^2 - 12*a^7*b^5*c^2*d*f^

2 + 12*a^8*b^4*c*d^2*f^2 - 3*a^9*b^3*c^2*d*f^2 + 3*a^10*b^2*c*d^2*f^2))^(1/2)*(c + d*tan(e + f*x))^(1/2)*(32*a

^2*b^17*d^12*f^4 + 160*a^4*b^15*d^12*f^4 + 288*a^6*b^13*d^12*f^4 + 160*a^8*b^11*d^12*f^4 - 160*a^10*b^9*d^12*f

^4 - 288*a^12*b^7*d^12*f^4 - 160*a^14*b^5*d^12*f^4 - 32*a^16*b^3*d^12*f^4 + 32*b^19*c^2*d^10*f^4 + 48*b^19*c^4

*d^8*f^4 + 176*a^2*b^17*c^2*d^10*f^4 + 272*a^2*b^17*c^4*d^8*f^4 - 432*a^3*b^16*c^3*d^9*f^4 + 336*a^4*b^15*c^2*

d^10*f^4 + 624*a^4*b^15*c^4*d^8*f^4 - 912*a^5*b^14*c^3*d^9*f^4 + 112*a^6*b^13*c^2*d^10*f^4 + 720*a^6*b^13*c^4*

d^8*f^4 - 880*a^7*b^12*c^3*d^9*f^4 - 560*a^8*b^11*c^2*d^10*f^4 + 400*a^8*b^11*c^4*d^8*f^4 - 240*a^9*b^10*c^3*d

^9*f^4 - 1008*a^10*b^9*c^2*d^10*f^4 + 48*a^10*b^9*c^4*d^8*f^4 + 240*a^11*b^8*c^3*d^9*f^4 - 784*a^12*b^7*c^2*d^

10*f^4 - 48*a^12*b^7*c^4*d^8*f^4 + 208*a^13*b^6*c^3*d^9*f^4 - 304*a^14*b^5*c^2*d^10*f^4 - 16*a^14*b^5*c^4*d^8*

f^4 + 48*a^15*b^4*c^3*d^9*f^4 - 48*a^16*b^3*c^2*d^10*f^4 - 64*a*b^18*c*d^11*f^4 - 80*a*b^18*c^3*d^9*f^4 - 304*

a^3*b^16*c*d^11*f^4 - 464*a^5*b^14*c*d^11*f^4 + 16*a^7*b^12*c*d^11*f^4 + 880*a^9*b^10*c*d^11*f^4 + 1136*a^11*b

^8*c*d^11*f^4 + 656*a^13*b^6*c*d^11*f^4 + 176*a^15*b^4*c*d^11*f^4 + 16*a^17*b^2*c*d^11*f^4))/((b^10*(8*a^2*c^3

*f^2 + 6*a^2*c*d^2*f^2) + b^4*(2*a^8*c^3*f^2 + 24*a^8*c*d^2*f^2) + b^8*(12*a^4*c^3*f^2 + 24*a^4*c*d^2*f^2) + b

^6*(8*a^6*c^3*f^2 + 36*a^6*c*d^2*f^2) - b^3*(8*a^9*d^3*f^2 + 6*a^9*c^2*d*f^2) - b^9*(2*a^3*d^3*f^2 + 24*a^3*c^

2*d*f^2) - b^5*(12*a^7*d^3*f^2 + 24*a^7*c^2*d*f^2) - b^7*(8*a^5*d^3*f^2 + 36*a^5*c^2*d*f^2) + 2*b^12*c^3*f^2 -

2*a^11*b*d^3*f^2 - 6*a*b^11*c^2*d*f^2 + 6*a^10*b^2*c*d^2*f^2)*(a^10*d^2*f^4 + b^10*c^2*f^4 + 4*a^2*b^8*c^2*f^

4 + 6*a^4*b^6*c^2*f^4 + 4*a^6*b^4*c^2*f^4 + a^8*b^2*c^2*f^4 + a^2*b^8*d^2*f^4 + 4*a^4*b^6*d^2*f^4 + 6*a^6*b^4*

d^2*f^4 + 4*a^8*b^2*d^2*f^4 - 2*a*b^9*c*d*f^4 - 2*a^9*b*c*d*f^4 - 8*a^3*b^7*c*d*f^4 - 12*a^5*b^5*c*d*f^4 - 8*a

^7*b^3*c*d*f^4)))*((C^2*a^8*d^2 + 16*C^2*a^2*b^6*c^2 + 9*C^2*a^4*b^4*d^2 - 6*C^2*a^6*b^2*d^2 - 24*C^2*a^3*b^5*

c*d + 8*C^2*a^5*b^3*c*d)*(b^12*c^3*f^2 - a^11*b*d^3*f^2 + 4*a^2*b^10*c^3*f^2 + 6*a^4*b^8*c^3*f^2 + 4*a^6*b^6*c

^3*f^2 + a^8*b^4*c^3*f^2 - a^3*b^9*d^3*f^2 - 4*a^5*b^7*d^3*f^2 - 6*a^7*b^5*d^3*f^2 - 4*a^9*b^3*d^3*f^2 - 3*a*b

^11*c^2*d*f^2 + 3*a^2*b^10*c*d^2*f^2 - 12*a^3*b^9*c^2*d*f^2 + 12*a^4*b^8*c*d^2*f^2 - 18*a^5*b^7*c^2*d*f^2 + 18

*a^6*b^6*c*d^2*f^2 - 12*a^7*b^5*c^2*d*f^2 + 12*a^8*b^4*c*d^2*f^2 - 3*a^9*b^3*c^2*d*f^2 + 3*a^10*b^2*c*d^2*f^2)

)^(1/2))/(b^10*(8*a^2*c^3*f^2 + 6*a^2*c*d^2*f^2) + b^4*(2*a^8*c^3*f^2 + 24*a^8*c*d^2*f^2) + b^8*(12*a^4*c^3*f^

2 + 24*a^4*c*d^2*f^2) + b^6*(8*a^6*c^3*f^2 + 36*a^6*c*d^2*f^2) - b^3*(8*a^9*d^3*f^2 + 6*a^9*c^2*d*f^2) - b^9*(

2*a^3*d^3*f^2 + 24*a^3*c^2*d*f^2) - b^5*(12*a^7*d^3*f^2 + 24*a^7*c^2*d*f^2) - b^7*(8*a^5*d^3*f^2 + 36*a^5*c^2*

d*f^2) + 2*b^12*c^3*f^2 - 2*a^11*b*d^3*f^2 - 6*a*b^11*c^2*d*f^2 + 6*a^10*b^2*c*d^2*f^2) + (16*(c + d*tan(e + f

*x))^(1/2)*(20*C^2*a^5*b^10*d^11*f^2 - 60*C^2*a^3*b^12*d^11*f^2 + 168*C^2*a^7*b^8*d^11*f^2 + 40*C^2*a^9*b^6*d^

11*f^2 - 44*C^2*a^11*b^4*d^11*f^2 + 4*C^2*a^13*b^2*d^11*f^2 - 20*C^2*b^15*c^3*d^8*f^2 - 4*C^2*a^14*b*c*d^10*f^

2 - 20*C^2*a*b^14*c^2*d^9*f^2 + 100*C^2*a^2*b^13*c*d^10*f^2 - 300*C^2*a^6*b^9*c*d^10*f^2 - 160*C^2*a^8*b^7*c*d

^10*f^2 + 76*C^2*a^10*b^5*c*d^10*f^2 + 32*C^2*a^12*b^3*c*d^10*f^2 + 116*C^2*a^2*b^13*c^3*d^8*f^2 - 124*C^2*a^3

*b^12*c^2*d^9*f^2 + 216*C^2*a^4*b^11*c^3*d^8*f^2 - 40*C^2*a^5*b^10*c^2*d^9*f^2 + 8*C^2*a^6*b^9*c^3*d^8*f^2 + 1

68*C^2*a^7*b^8*c^2*d^9*f^2 - 68*C^2*a^8*b^7*c^3*d^8*f^2 + 60*C^2*a^9*b^6*c^2*d^9*f^2 + 4*C^2*a^10*b^5*c^3*d^8*

f^2 - 44*C^2*a^11*b^4*c^2*d^9*f^2))/(a^10*d^2*f^4 + b^10*c^2*f^4 + 4*a^2*b^8*c^2*f^4 + 6*a^4*b^6*c^2*f^4 + 4*a

^6*b^4*c^2*f^4 + a^8*b^2*c^2*f^4 + a^2*b^8*d^2*f^4 + 4*a^4*b^6*d^2*f^4 + 6*a^6*b^4*d^2*f^4 + 4*a^8*b^2*d^2*f^4

- 2*a*b^9*c*d*f^4 - 2*a^9*b*c*d*f^4 - 8*a^3*b^7*c*d*f^4 - 12*a^5*b^5*c*d*f^4 - 8*a^7*b^3*c*d*f^4))*((C^2*a^8*

d^2 + 16*C^2*a^2*b^6*c^2 + 9*C^2*a^4*b^4*d^2 - 6*C^2*a^6*b^2*d^2 - 24*C^2*a^3*b^5*c*d + 8*C^2*a^5*b^3*c*d)*(b^

12*c^3*f^2 - a^11*b*d^3*f^2 + 4*a^2*b^10*c^3*f^2 + 6*a^4*b^8*c^3*f^2 + 4*a^6*b^6*c^3*f^2 + a^8*b^4*c^3*f^2 - a

^3*b^9*d^3*f^2 - 4*a^5*b^7*d^3*f^2 - 6*a^7*b^5*d^3*f^2 - 4*a^9*b^3*d^3*f^2 - 3*a*b^11*c^2*d*f^2 + 3*a^2*b^10*c

*d^2*f^2 - 12*a^3*b^9*c^2*d*f^2 + 12*a^4*b^8*c*d^2*f^2 - 18*a^5*b^7*c^2*d*f^2 + 18*a^6*b^6*c*d^2*f^2 - 12*a^7*

b^5*c^2*d*f^2 + 12*a^8*b^4*c*d^2*f^2 - 3*a^9*b^3*c^2*d*f^2 + 3*a^10*b^2*c*d^2*f^2))^(1/2))/(b^10*(8*a^2*c^3*f^

2 + 6*a^2*c*d^2*f^2) + b^4*(2*a^8*c^3*f^2 + 24*a^8*c*d^2*f^2) + b^8*(12*a^4*c^3*f^2 + 24*a^4*c*d^2*f^2) + b^6*

(8*a^6*c^3*f^2 + 36*a^6*c*d^2*f^2) - b^3*(8*a^9*d^3*f^2 + 6*a^9*c^2*d*f^2) - b^9*(2*a^3*d^3*f^2 + 24*a^3*c^2*d

*f^2) - b^5*(12*a^7*d^3*f^2 + 24*a^7*c^2*d*f^2) - b^7*(8*a^5*d^3*f^2 + 36*a^5*c^2*d*f^2) + 2*b^12*c^3*f^2 - 2*

a^11*b*d^3*f^2 - 6*a*b^11*c^2*d*f^2 + 6*a^10*b^2*c*d^2*f^2))*((C^2*a^8*d^2 + 16*C^2*a^2*b^6*c^2 + 9*C^2*a^4*b^

4*d^2 - 6*C^2*a^6*b^2*d^2 - 24*C^2*a^3*b^5*c*d + 8*C^2*a^5*b^3*c*d)*(b^12*c^3*f^2 - a^11*b*d^3*f^2 + 4*a^2*b^1

0*c^3*f^2 + 6*a^4*b^8*c^3*f^2 + 4*a^6*b^6*c^3*f^2 + a^8*b^4*c^3*f^2 - a^3*b^9*d^3*f^2 - 4*a^5*b^7*d^3*f^2 - 6*

a^7*b^5*d^3*f^2 - 4*a^9*b^3*d^3*f^2 - 3*a*b^11*c^2*d*f^2 + 3*a^2*b^10*c*d^2*f^2 - 12*a^3*b^9*c^2*d*f^2 + 12*a^

4*b^8*c*d^2*f^2 - 18*a^5*b^7*c^2*d*f^2 + 18*a^6*b^6*c*d^2*f^2 - 12*a^7*b^5*c^2*d*f^2 + 12*a^8*b^4*c*d^2*f^2 -

3*a^9*b^3*c^2*d*f^2 + 3*a^10*b^2*c*d^2*f^2))^(1/2))/(b^10*(8*a^2*c^3*f^2 + 6*a^2*c*d^2*f^2) + b^4*(2*a^8*c^3*f

^2 + 24*a^8*c*d^2*f^2) + b^8*(12*a^4*c^3*f^2 + 24*a^4*c*d^2*f^2) + b^6*(8*a^6*c^3*f^2 + 36*a^6*c*d^2*f^2) - b^

3*(8*a^9*d^3*f^2 + 6*a^9*c^2*d*f^2) - b^9*(2*a^3*d^3*f^2 + 24*a^3*c^2*d*f^2) - b^5*(12*a^7*d^3*f^2 + 24*a^7*c^

2*d*f^2) - b^7*(8*a^5*d^3*f^2 + 36*a^5*c^2*d*f^2) + 2*b^12*c^3*f^2 - 2*a^11*b*d^3*f^2 - 6*a*b^11*c^2*d*f^2 + 6

*a^10*b^2*c*d^2*f^2) + (16*(c + d*tan(e + f*x))^(1/2)*(2*C^4*a^2*b^9*d^10 - 5*C^4*a^4*b^7*d^10 + 17*C^4*a^6*b^

5*d^10 - 7*C^4*a^8*b^3*d^10 + 2*C^4*b^11*c^2*d^8 + C^4*a^10*b*d^10 - 12*C^4*a^2*b^9*c^2*d^8 + 18*C^4*a^4*b^7*c

^2*d^8 - 4*C^4*a*b^10*c*d^9 + 16*C^4*a^3*b^8*c*d^9 - 36*C^4*a^5*b^6*c*d^9 + 8*C^4*a^7*b^4*c*d^9))/(a^10*d^2*f^

4 + b^10*c^2*f^4 + 4*a^2*b^8*c^2*f^4 + 6*a^4*b^6*c^2*f^4 + 4*a^6*b^4*c^2*f^4 + a^8*b^2*c^2*f^4 + a^2*b^8*d^2*f

^4 + 4*a^4*b^6*d^2*f^4 + 6*a^6*b^4*d^2*f^4 + 4*a^8*b^2*d^2*f^4 - 2*a*b^9*c*d*f^4 - 2*a^9*b*c*d*f^4 - 8*a^3*b^7

*c*d*f^4 - 12*a^5*b^5*c*d*f^4 - 8*a^7*b^3*c*d*f^4))*((C^2*a^8*d^2 + 16*C^2*a^2*b^6*c^2 + 9*C^2*a^4*b^4*d^2 - 6

*C^2*a^6*b^2*d^2 - 24*C^2*a^3*b^5*c*d + 8*C^2*a^5*b^3*c*d)*(b^12*c^3*f^2 - a^11*b*d^3*f^2 + 4*a^2*b^10*c^3*f^2

+ 6*a^4*b^8*c^3*f^2 + 4*a^6*b^6*c^3*f^2 + a^8*b^4*c^3*f^2 - a^3*b^9*d^3*f^2 - 4*a^5*b^7*d^3*f^2 - 6*a^7*b^5*d

^3*f^2 - 4*a^9*b^3*d^3*f^2 - 3*a*b^11*c^2*d*f^2 + 3*a^2*b^10*c*d^2*f^2 - 12*a^3*b^9*c^2*d*f^2 + 12*a^4*b^8*c*d

^2*f^2 - 18*a^5*b^7*c^2*d*f^2 + 18*a^6*b^6*c*d^2*f^2 - 12*a^7*b^5*c^2*d*f^2 + 12*a^8*b^4*c*d^2*f^2 - 3*a^9*b^3

*c^2*d*f^2 + 3*a^10*b^2*c*d^2*f^2))^(1/2))/(b^10*(8*a^2*c^3*f^2 + 6*a^2*c*d^2*f^2) + b^4*(2*a^8*c^3*f^2 + 24*a

^8*c*d^2*f^2) + b^8*(12*a^4*c^3*f^2 + 24*a^4*c*d^2*f^2) + b^6*(8*a^6*c^3*f^2 + 36*a^6*c*d^2*f^2) - b^3*(8*a^9*

d^3*f^2 + 6*a^9*c^2*d*f^2) - b^9*(2*a^3*d^3*f^2 + 24*a^3*c^2*d*f^2) - b^5*(12*a^7*d^3*f^2 + 24*a^7*c^2*d*f^2)

- b^7*(8*a^5*d^3*f^2 + 36*a^5*c^2*d*f^2) + 2*b^12*c^3*f^2 - 2*a^11*b*d^3*f^2 - 6*a*b^11*c^2*d*f^2 + 6*a^10*b^2

*c*d^2*f^2) - (32*(3*C^5*a^3*b^6*d^10 - C^5*a^5*b^4*d^10 + 4*C^5*a*b^8*c^2*d^8 - 7*C^5*a^2*b^7*c*d^9 + C^5*a^4

*b^5*c*d^9))/(a^10*d^2*f^5 + b^10*c^2*f^5 + 4*a^2*b^8*c^2*f^5 + 6*a^4*b^6*c^2*f^5 + 4*a^6*b^4*c^2*f^5 + a^8*b^

2*c^2*f^5 + a^2*b^8*d^2*f^5 + 4*a^4*b^6*d^2*f^5 + 6*a^6*b^4*d^2*f^5 + 4*a^8*b^2*d^2*f^5 - 2*a*b^9*c*d*f^5 - 2*

a^9*b*c*d*f^5 - 8*a^3*b^7*c*d*f^5 - 12*a^5*b^5*c*d*f^5 - 8*a^7*b^3*c*d*f^5) + (((((16*(8*C^3*a^6*b^7*d^11*f^2

- 78*C^3*a^4*b^9*d^11*f^2 + 60*C^3*a^8*b^5*d^11*f^2 - 24*C^3*a^10*b^3*d^11*f^2 + 2*C^3*a^12*b*d^11*f^2 - 32*C^

3*a*b^12*c^3*d^8*f^2 + 152*C^3*a^3*b^10*c*d^10*f^2 + 128*C^3*a^5*b^8*c*d^10*f^2 - 64*C^3*a^7*b^6*c*d^10*f^2 -

32*C^3*a^9*b^4*c*d^10*f^2 + 8*C^3*a^11*b^2*c*d^10*f^2 - 40*C^3*a^2*b^11*c^2*d^9*f^2 + 64*C^3*a^3*b^10*c^3*d^8*

f^2 - 216*C^3*a^4*b^9*c^2*d^9*f^2 + 96*C^3*a^5*b^8*c^3*d^8*f^2 - 120*C^3*a^6*b^7*c^2*d^9*f^2 + 56*C^3*a^8*b^5*

c^2*d^9*f^2))/(a^10*d^2*f^5 + b^10*c^2*f^5 + 4*a^2*b^8*c^2*f^5 + 6*a^4*b^6*c^2*f^5 + 4*a^6*b^4*c^2*f^5 + a^8*b

^2*c^2*f^5 + a^2*b^8*d^2*f^5 + 4*a^4*b^6*d^2*f^5 + 6*a^6*b^4*d^2*f^5 + 4*a^8*b^2*d^2*f^5 - 2*a*b^9*c*d*f^5 - 2

*a^9*b*c*d*f^5 - 8*a^3*b^7*c*d*f^5 - 12*a^5*b^5*c*d*f^5 - 8*a^7*b^3*c*d*f^5) - (((((16*(40*C*a^3*b^14*d^12*f^4

+ 192*C*a^5*b^12*d^12*f^4 + 360*C*a^7*b^10*d^12*f^4 + 320*C*a^9*b^8*d^12*f^4 + 120*C*a^11*b^6*d^12*f^4 - 8*C*

a^15*b^2*d^12*f^4 + 8*C*b^17*c^3*d^9*f^4 + 40*C*a*b^16*c^2*d^10*f^4 + 32*C*a*b^16*c^4*d^8*f^4 - 88*C*a^2*b^15*

c*d^11*f^4 - 448*C*a^4*b^13*c*d^11*f^4 - 920*C*a^6*b^11*c*d^11*f^4 - 960*C*a^8*b^9*c*d^11*f^4 - 520*C*a^10*b^7

*c*d^11*f^4 - 128*C*a^12*b^5*c*d^11*f^4 - 8*C*a^14*b^3*c*d^11*f^4 - 32*C*a^2*b^15*c^3*d^9*f^4 + 256*C*a^3*b^14

*c^2*d^10*f^4 + 160*C*a^3*b^14*c^4*d^8*f^4 - 280*C*a^4*b^13*c^3*d^9*f^4 + 680*C*a^5*b^12*c^2*d^10*f^4 + 320*C*

a^5*b^12*c^4*d^8*f^4 - 640*C*a^6*b^11*c^3*d^9*f^4 + 960*C*a^7*b^10*c^2*d^10*f^4 + 320*C*a^7*b^10*c^4*d^8*f^4 -

680*C*a^8*b^9*c^3*d^9*f^4 + 760*C*a^9*b^8*c^2*d^10*f^4 + 160*C*a^9*b^8*c^4*d^8*f^4 - 352*C*a^10*b^7*c^3*d^9*f

^4 + 320*C*a^11*b^6*c^2*d^10*f^4 + 32*C*a^11*b^6*c^4*d^8*f^4 - 72*C*a^12*b^5*c^3*d^9*f^4 + 56*C*a^13*b^4*c^2*d

^10*f^4))/(a^10*d^2*f^5 + b^10*c^2*f^5 + 4*a^2*b^8*c^2*f^5 + 6*a^4*b^6*c^2*f^5 + 4*a^6*b^4*c^2*f^5 + a^8*b^2*c

^2*f^5 + a^2*b^8*d^2*f^5 + 4*a^4*b^6*d^2*f^5 + 6*a^6*b^4*d^2*f^5 + 4*a^8*b^2*d^2*f^5 - 2*a*b^9*c*d*f^5 - 2*a^9

*b*c*d*f^5 - 8*a^3*b^7*c*d*f^5 - 12*a^5*b^5*c*d*f^5 - 8*a^7*b^3*c*d*f^5) + (16*((C^2*a^8*d^2 + 16*C^2*a^2*b^6*

c^2 + 9*C^2*a^4*b^4*d^2 - 6*C^2*a^6*b^2*d^2 - 24*C^2*a^3*b^5*c*d + 8*C^2*a^5*b^3*c*d)*(b^12*c^3*f^2 - a^11*b*d

^3*f^2 + 4*a^2*b^10*c^3*f^2 + 6*a^4*b^8*c^3*f^2 + 4*a^6*b^6*c^3*f^2 + a^8*b^4*c^3*f^2 - a^3*b^9*d^3*f^2 - 4*a^

5*b^7*d^3*f^2 - 6*a^7*b^5*d^3*f^2 - 4*a^9*b^3*d^3*f^2 - 3*a*b^11*c^2*d*f^2 + 3*a^2*b^10*c*d^2*f^2 - 12*a^3*b^9

*c^2*d*f^2 + 12*a^4*b^8*c*d^2*f^2 - 18*a^5*b^7*c^2*d*f^2 + 18*a^6*b^6*c*d^2*f^2 - 12*a^7*b^5*c^2*d*f^2 + 12*a^

8*b^4*c*d^2*f^2 - 3*a^9*b^3*c^2*d*f^2 + 3*a^10*b^2*c*d^2*f^2))^(1/2)*(c + d*tan(e + f*x))^(1/2)*(32*a^2*b^17*d

^12*f^4 + 160*a^4*b^15*d^12*f^4 + 288*a^6*b^13*d^12*f^4 + 160*a^8*b^11*d^12*f^4 - 160*a^10*b^9*d^12*f^4 - 288*

a^12*b^7*d^12*f^4 - 160*a^14*b^5*d^12*f^4 - 32*a^16*b^3*d^12*f^4 + 32*b^19*c^2*d^10*f^4 + 48*b^19*c^4*d^8*f^4

+ 176*a^2*b^17*c^2*d^10*f^4 + 272*a^2*b^17*c^4*d^8*f^4 - 432*a^3*b^16*c^3*d^9*f^4 + 336*a^4*b^15*c^2*d^10*f^4

+ 624*a^4*b^15*c^4*d^8*f^4 - 912*a^5*b^14*c^3*d^9*f^4 + 112*a^6*b^13*c^2*d^10*f^4 + 720*a^6*b^13*c^4*d^8*f^4 -

880*a^7*b^12*c^3*d^9*f^4 - 560*a^8*b^11*c^2*d^10*f^4 + 400*a^8*b^11*c^4*d^8*f^4 - 240*a^9*b^10*c^3*d^9*f^4 -

1008*a^10*b^9*c^2*d^10*f^4 + 48*a^10*b^9*c^4*d^8*f^4 + 240*a^11*b^8*c^3*d^9*f^4 - 784*a^12*b^7*c^2*d^10*f^4 -

48*a^12*b^7*c^4*d^8*f^4 + 208*a^13*b^6*c^3*d^9*f^4 - 304*a^14*b^5*c^2*d^10*f^4 - 16*a^14*b^5*c^4*d^8*f^4 + 48*

a^15*b^4*c^3*d^9*f^4 - 48*a^16*b^3*c^2*d^10*f^4 - 64*a*b^18*c*d^11*f^4 - 80*a*b^18*c^3*d^9*f^4 - 304*a^3*b^16*

c*d^11*f^4 - 464*a^5*b^14*c*d^11*f^4 + 16*a^7*b^12*c*d^11*f^4 + 880*a^9*b^10*c*d^11*f^4 + 1136*a^11*b^8*c*d^11

*f^4 + 656*a^13*b^6*c*d^11*f^4 + 176*a^15*b^4*c*d^11*f^4 + 16*a^17*b^2*c*d^11*f^4))/((b^10*(8*a^2*c^3*f^2 + 6*

a^2*c*d^2*f^2) + b^4*(2*a^8*c^3*f^2 + 24*a^8*c*d^2*f^2) + b^8*(12*a^4*c^3*f^2 + 24*a^4*c*d^2*f^2) + b^6*(8*a^6

*c^3*f^2 + 36*a^6*c*d^2*f^2) - b^3*(8*a^9*d^3*f^2 + 6*a^9*c^2*d*f^2) - b^9*(2*a^3*d^3*f^2 + 24*a^3*c^2*d*f^2)

- b^5*(12*a^7*d^3*f^2 + 24*a^7*c^2*d*f^2) - b^7*(8*a^5*d^3*f^2 + 36*a^5*c^2*d*f^2) + 2*b^12*c^3*f^2 - 2*a^11*b

*d^3*f^2 - 6*a*b^11*c^2*d*f^2 + 6*a^10*b^2*c*d^2*f^2)*(a^10*d^2*f^4 + b^10*c^2*f^4 + 4*a^2*b^8*c^2*f^4 + 6*a^4

*b^6*c^2*f^4 + 4*a^6*b^4*c^2*f^4 + a^8*b^2*c^2*f^4 + a^2*b^8*d^2*f^4 + 4*a^4*b^6*d^2*f^4 + 6*a^6*b^4*d^2*f^4 +

4*a^8*b^2*d^2*f^4 - 2*a*b^9*c*d*f^4 - 2*a^9*b*c*d*f^4 - 8*a^3*b^7*c*d*f^4 - 12*a^5*b^5*c*d*f^4 - 8*a^7*b^3*c*

d*f^4)))*((C^2*a^8*d^2 + 16*C^2*a^2*b^6*c^2 + 9*C^2*a^4*b^4*d^2 - 6*C^2*a^6*b^2*d^2 - 24*C^2*a^3*b^5*c*d + 8*C

^2*a^5*b^3*c*d)*(b^12*c^3*f^2 - a^11*b*d^3*f^2 + 4*a^2*b^10*c^3*f^2 + 6*a^4*b^8*c^3*f^2 + 4*a^6*b^6*c^3*f^2 +

a^8*b^4*c^3*f^2 - a^3*b^9*d^3*f^2 - 4*a^5*b^7*d^3*f^2 - 6*a^7*b^5*d^3*f^2 - 4*a^9*b^3*d^3*f^2 - 3*a*b^11*c^2*d

*f^2 + 3*a^2*b^10*c*d^2*f^2 - 12*a^3*b^9*c^2*d*f^2 + 12*a^4*b^8*c*d^2*f^2 - 18*a^5*b^7*c^2*d*f^2 + 18*a^6*b^6*

c*d^2*f^2 - 12*a^7*b^5*c^2*d*f^2 + 12*a^8*b^4*c*d^2*f^2 - 3*a^9*b^3*c^2*d*f^2 + 3*a^10*b^2*c*d^2*f^2))^(1/2))/

(b^10*(8*a^2*c^3*f^2 + 6*a^2*c*d^2*f^2) + b^4*(2*a^8*c^3*f^2 + 24*a^8*c*d^2*f^2) + b^8*(12*a^4*c^3*f^2 + 24*a^

4*c*d^2*f^2) + b^6*(8*a^6*c^3*f^2 + 36*a^6*c*d^2*f^2) - b^3*(8*a^9*d^3*f^2 + 6*a^9*c^2*d*f^2) - b^9*(2*a^3*d^3

*f^2 + 24*a^3*c^2*d*f^2) - b^5*(12*a^7*d^3*f^2 + 24*a^7*c^2*d*f^2) - b^7*(8*a^5*d^3*f^2 + 36*a^5*c^2*d*f^2) +

2*b^12*c^3*f^2 - 2*a^11*b*d^3*f^2 - 6*a*b^11*c^2*d*f^2 + 6*a^10*b^2*c*d^2*f^2) - (16*(c + d*tan(e + f*x))^(1/2

)*(20*C^2*a^5*b^10*d^11*f^2 - 60*C^2*a^3*b^12*d^11*f^2 + 168*C^2*a^7*b^8*d^11*f^2 + 40*C^2*a^9*b^6*d^11*f^2 -

44*C^2*a^11*b^4*d^11*f^2 + 4*C^2*a^13*b^2*d^11*f^2 - 20*C^2*b^15*c^3*d^8*f^2 - 4*C^2*a^14*b*c*d^10*f^2 - 20*C^

2*a*b^14*c^2*d^9*f^2 + 100*C^2*a^2*b^13*c*d^10*f^2 - 300*C^2*a^6*b^9*c*d^10*f^2 - 160*C^2*a^8*b^7*c*d^10*f^2 +

76*C^2*a^10*b^5*c*d^10*f^2 + 32*C^2*a^12*b^3*c*d^10*f^2 + 116*C^2*a^2*b^13*c^3*d^8*f^2 - 124*C^2*a^3*b^12*c^2

*d^9*f^2 + 216*C^2*a^4*b^11*c^3*d^8*f^2 - 40*C^2*a^5*b^10*c^2*d^9*f^2 + 8*C^2*a^6*b^9*c^3*d^8*f^2 + 168*C^2*a^

7*b^8*c^2*d^9*f^2 - 68*C^2*a^8*b^7*c^3*d^8*f^2 + 60*C^2*a^9*b^6*c^2*d^9*f^2 + 4*C^2*a^10*b^5*c^3*d^8*f^2 - 44*

C^2*a^11*b^4*c^2*d^9*f^2))/(a^10*d^2*f^4 + b^10*c^2*f^4 + 4*a^2*b^8*c^2*f^4 + 6*a^4*b^6*c^2*f^4 + 4*a^6*b^4*c^

2*f^4 + a^8*b^2*c^2*f^4 + a^2*b^8*d^2*f^4 + 4*a^4*b^6*d^2*f^4 + 6*a^6*b^4*d^2*f^4 + 4*a^8*b^2*d^2*f^4 - 2*a*b^

9*c*d*f^4 - 2*a^9*b*c*d*f^4 - 8*a^3*b^7*c*d*f^4 - 12*a^5*b^5*c*d*f^4 - 8*a^7*b^3*c*d*f^4))*((C^2*a^8*d^2 + 16*