∫ ∘ __________ c+d tan(e+fx) (A+B tan(e+fx)+C tan2(e+fx)) ___________________________________________________________________

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

Optimal. Leaf size=234 \[ -\frac {2 \sqrt {b c-a d} \left (A b^2-a (b B-a C)\right ) \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {c+d \tan (e+f x)}}{\sqrt {b c-a d}}\right )}{b^{3/2} f \left (a^2+b^2\right )}-\frac {\sqrt {c-i d} (i A+B-i C) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{f (a-i b)}+\frac {\sqrt {c+i d} (i A-B-i C) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{f (a+i b)}+\frac {2 C \sqrt {c+d \tan (e+f x)}}{b f} \]

[Out]

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

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

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

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Rubi [A] time = 1.09, antiderivative size = 234, 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 = {3647, 3653, 3539, 3537, 63, 208, 3634} \[ -\frac {2 \sqrt {b c-a d} \left (A b^2-a (b B-a C)\right ) \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {c+d \tan (e+f x)}}{\sqrt {b c-a d}}\right )}{b^{3/2} f \left (a^2+b^2\right )}-\frac {\sqrt {c-i d} (i A+B-i C) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{f (a-i b)}+\frac {\sqrt {c+i d} (i A-B-i C) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{f (a+i b)}+\frac {2 C \sqrt {c+d \tan (e+f x)}}{b f} \]

Antiderivative was successfully veriﬁed.

[In]

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

[Out]

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

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

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

Sqrt[c + d*Tan[e + f*x]])/(b*f)

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 3647

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

tan[(e_.) + (f_.)*(x_)] + (C_.)*tan[(e_.) + (f_.)*(x_)]^2), x_Symbol] :> Simp[(C*(a + b*Tan[e + f*x])^m*(c + d

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

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

*x] - (C*m*(b*c - a*d) - b*B*d*(m + n + 1))*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] && GtQ[m, 0] && !(IGtQ[n, 0] && ( !Intege

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

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Mathematica [A] time = 0.69, size = 233, normalized size = 1.00 \[ \frac {2 \sqrt {b} C \left (a^2+b^2\right ) \sqrt {c+d \tan (e+f x)}+b^{3/2} (b-i a) \sqrt {c-i d} (A-i B-C) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )+b^{3/2} (b+i a) \sqrt {c+i d} (A+i B-C) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )-2 \sqrt {b c-a d} \left (a (a C-b B)+A b^2\right ) \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {c+d \tan (e+f x)}}{\sqrt {b c-a d}}\right )}{b^{3/2} f \left (a^2+b^2\right )} \]

Antiderivative was successfully veriﬁed.

[In]

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

[Out]

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

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

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

t[c + d*Tan[e + f*x]])/(b^(3/2)*(a^2 + b^2)*f)

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

[Out]

Timed out

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maple [B] time = 0.75, size = 3576, normalized size = 15.28 \[ \text {output too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

)/((a*d-b*c)*b)^(1/2)*arctan((c+d*tan(f*x+e))^(1/2)*b/((a*d-b*c)*b)^(1/2))*a^3*C*d+1/4/f/(a^2+b^2)/d*ln((c+d*t

an(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)

*(c^2+d^2)^(1/2)*a+1/4/f/(a^2+b^2)/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c

^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b-1/4/f/(a^2+b^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))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b+1/4/f/(a^2+b^2)/d

*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+

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

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

2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2

)-2*c)^(1/2))*C*(c^2+d^2)^(1/2)*b-1/f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^

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

)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/

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

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

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

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

f/(a^2+b^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(

c^2+d^2)^(1/2)-2*c)^(1/2))*A*b*c+1/f/(a^2+b^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*(c^2+d^2)^(1/2)*b+1/f/(a^2+b^2)*d/(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*a-1/f/(a^2+b^2)*d/(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*a-1/f/(a^2+b^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*(c^2+d^2)^(1/2)*a+1/f/(a^2+b^2)*d/(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*b-1/f/(a^2+b^2)*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan

(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*A*a-1/f/(a^2+b^2)*d/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan(((2*(c

^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*b-1/f/(a^2+b^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-1/4/f/(a^2+b^2)/d*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))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*b+1/4/f/(a^2+b^2)/d*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))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c+1/4/f/(a^2+b^2)/d*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))*B*(2*(c^2+d^2)^(1/2)+2*c)

^(1/2)*b*c+1/4/f/(a^2+b^2)/d*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))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a-1/4/f/(a^2+b^2)/d*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))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c-2/f*b/(a^2+b^2)/((a*d

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

)^(1/2)*arctan(((2*(c^2+d^2)^(1/2)+2*c)^(1/2)-2*(c+d*tan(f*x+e))^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))*B*a*c+1

/f/(a^2+b^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*b*c+1/f/(a^2+b^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*a*c-1/f/(a^2+b^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*(c^2+d^2)^

(1/2)*b-1/4/f/(a^2+b^2)/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/

2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b*c-1/4/f/(a^2+b^2)/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1

/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*C*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*(c^2+d^2)^(1/2)*a-1/4/f/(a^2+b^2)/d*ln(d*t

an(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))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1

/2)*(c^2+d^2)^(1/2)*a-1/4/f/(a^2+b^2)/d*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c

-(c^2+d^2)^(1/2))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a*c-1/4/f/(a^2+b^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))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a+1/4/f/(a^2+b^2)*ln((c+d*tan(

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

1/4/f/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+e)-c-(c^2+d^2)^(1/2))*A*(2*(

c^2+d^2)^(1/2)+2*c)^(1/2)*b+1/4/f/(a^2+b^2)*ln((c+d*tan(f*x+e))^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)-d*tan(f*x+

e)-c-(c^2+d^2)^(1/2))*B*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*a+1/4/f/(a^2+b^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))*A*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)*b

________________________________________________________________________________________

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((c+d*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(a+b*tan(f*x+e)),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 = 36.22, size = 62245, normalized size = 266.00 \[ \text {result too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

atan(((((((32*(4*C*a*b^8*d^11*f^4 - 4*C*b^9*c*d^10*f^4 + 8*C*a^3*b^6*d^11*f^4 + 4*C*a^5*b^4*d^11*f^4 - 4*C*b^9

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

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

+ f*x))^(1/2)*((((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4

+ 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^

4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*(16*b^10*d^10*f^4 + 16*a^2*b^8*d^10*f^4 - 16*a^4*b^6*d^10*f^4 - 16*a^6*b^4*d^10

*f^4 + 24*b^10*c^2*d^8*f^4 + 40*a^2*b^8*c^2*d^8*f^4 + 8*a^4*b^6*c^2*d^8*f^4 - 8*a^6*b^4*c^2*d^8*f^4 + 8*a*b^9*

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

8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/

2) - 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (3

2*(c + d*tan(e + f*x))^(1/2)*(14*C^2*a*b^7*d^11*f^2 - 2*C^2*a^5*b^3*d^11*f^2 - 10*C^2*b^8*c^3*d^8*f^2 - 4*C^2*

a^3*b^5*d^11*f^2 - 16*C^2*a^7*b*d^11*f^2 + 8*C^2*a^8*c*d^10*f^2 - 6*C^2*b^8*c*d^10*f^2 + 18*C^2*a*b^7*c^2*d^9*

f^2 + 12*C^2*a^2*b^6*c*d^10*f^2 + 2*C^2*a^4*b^4*c*d^10*f^2 + 24*C^2*a^6*b^2*c*d^10*f^2 - 16*C^2*a^7*b*c^2*d^9*

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

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

(C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*

C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(15*C^3*a^4*b^3*d^12*f^2 - C^3*a^2*b^5*d^

12*f^2 + C^3*b^7*c^2*d^10*f^2 + C^3*b^7*c^4*d^8*f^2 - 12*C^3*a^6*b*d^12*f^2 - 24*C^3*a^3*b^4*c*d^11*f^2 + 24*C

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

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

^2))/(b*f^5))*((((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4

+ 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^

4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))^(1/2)*(C^4*b^6*d^12 - 2*C^4*a^6*d^12 + 2*C^4*a^6*c^2

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

d^11 - 4*C^4*a^5*b*c^3*d^9))/(b*f^4))*((((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2

+ C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*C^2*a*b*

d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*1i - (((((32*(4*C*a*b^8*d^11*f^4 - 4*C*b^9*c*d^10*f^4 +

8*C*a^3*b^6*d^11*f^4 + 4*C*a^5*b^4*d^11*f^4 - 4*C*b^9*c^3*d^8*f^4 + 4*C*a*b^8*c^2*d^9*f^4 - 8*C*a^2*b^7*c*d^1

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

4*C*a^5*b^4*c^2*d^9*f^4))/(b*f^5) + (32*(c + d*tan(e + f*x))^(1/2)*((((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16

*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*C^2*a^2*c*f^2

+ 4*C^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*(16*b^10*d^10*f^4 + 16*a^

2*b^8*d^10*f^4 - 16*a^4*b^6*d^10*f^4 - 16*a^6*b^4*d^10*f^4 + 24*b^10*c^2*d^8*f^4 + 40*a^2*b^8*c^2*d^8*f^4 + 8*

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

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

4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2

)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(c + d*tan(e + f*x))^(1/2)*(14*C^2*a*b^7*d^11*f^2 - 2*

C^2*a^5*b^3*d^11*f^2 - 10*C^2*b^8*c^3*d^8*f^2 - 4*C^2*a^3*b^5*d^11*f^2 - 16*C^2*a^7*b*d^11*f^2 + 8*C^2*a^8*c*d

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

^2 + 24*C^2*a^6*b^2*c*d^10*f^2 - 16*C^2*a^7*b*c^2*d^9*f^2 + 4*C^2*a^2*b^6*c^3*d^8*f^2 + 4*C^2*a^3*b^5*c^2*d^9*

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

a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^

2*f^4))^(1/2) - 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))

^(1/2) + (32*(15*C^3*a^4*b^3*d^12*f^2 - C^3*a^2*b^5*d^12*f^2 + C^3*b^7*c^2*d^10*f^2 + C^3*b^7*c^4*d^8*f^2 - 12

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

3*a^2*b^5*c^2*d^10*f^2 + 9*C^3*a^2*b^5*c^4*d^8*f^2 - 24*C^3*a^3*b^4*c^3*d^9*f^2 + 3*C^3*a^4*b^3*c^2*d^10*f^2 -

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

*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*C^2*a^2*c*f^2

+ 4*C^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(c + d*tan(e + f*x)

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

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

2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^

(1/2) - 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*1

i)/((((((32*(4*C*a*b^8*d^11*f^4 - 4*C*b^9*c*d^10*f^4 + 8*C*a^3*b^6*d^11*f^4 + 4*C*a^5*b^4*d^11*f^4 - 4*C*b^9*c

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

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

f*x))^(1/2)*((((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 +

16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*

f^4 + 2*a^2*b^2*f^4)))^(1/2)*(16*b^10*d^10*f^4 + 16*a^2*b^8*d^10*f^4 - 16*a^4*b^6*d^10*f^4 - 16*a^6*b^4*d^10*f

^4 + 24*b^10*c^2*d^8*f^4 + 40*a^2*b^8*c^2*d^8*f^4 + 8*a^4*b^6*c^2*d^8*f^4 - 8*a^6*b^4*c^2*d^8*f^4 + 8*a*b^9*c*

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

*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2)

- 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*

(c + d*tan(e + f*x))^(1/2)*(14*C^2*a*b^7*d^11*f^2 - 2*C^2*a^5*b^3*d^11*f^2 - 10*C^2*b^8*c^3*d^8*f^2 - 4*C^2*a^

3*b^5*d^11*f^2 - 16*C^2*a^7*b*d^11*f^2 + 8*C^2*a^8*c*d^10*f^2 - 6*C^2*b^8*c*d^10*f^2 + 18*C^2*a*b^7*c^2*d^9*f^

2 + 12*C^2*a^2*b^6*c*d^10*f^2 + 2*C^2*a^4*b^4*c*d^10*f^2 + 24*C^2*a^6*b^2*c*d^10*f^2 - 16*C^2*a^7*b*c^2*d^9*f^

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

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

^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*C^

2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(15*C^3*a^4*b^3*d^12*f^2 - C^3*a^2*b^5*d^12

*f^2 + C^3*b^7*c^2*d^10*f^2 + C^3*b^7*c^4*d^8*f^2 - 12*C^3*a^6*b*d^12*f^2 - 24*C^3*a^3*b^4*c*d^11*f^2 + 24*C^3

*a^5*b^2*c*d^11*f^2 - 12*C^3*a^6*b*c^2*d^10*f^2 + 8*C^3*a^2*b^5*c^2*d^10*f^2 + 9*C^3*a^2*b^5*c^4*d^8*f^2 - 24*

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

))/(b*f^5))*((((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 +

16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*

f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))^(1/2)*(C^4*b^6*d^12 - 2*C^4*a^6*d^12 + 2*C^4*a^6*c^2*d

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

11 - 4*C^4*a^5*b*c^3*d^9))/(b*f^4))*((((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 +

C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*C^2*a*b*d*

f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (((((32*(4*C*a*b^8*d^11*f^4 - 4*C*b^9*c*d^10*f^4 + 8*C*

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

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

a^5*b^4*c^2*d^9*f^4))/(b*f^5) + (32*(c + d*tan(e + f*x))^(1/2)*((((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*

a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*C^2*a^2*c*f^2 + 4*C

^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*(16*b^10*d^10*f^4 + 16*a^2*b^8

*d^10*f^4 - 16*a^4*b^6*d^10*f^4 - 16*a^6*b^4*d^10*f^4 + 24*b^10*c^2*d^8*f^4 + 40*a^2*b^8*c^2*d^8*f^4 + 8*a^4*b

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

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

)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2)/(16

*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(c + d*tan(e + f*x))^(1/2)*(14*C^2*a*b^7*d^11*f^2 - 2*C^2*a

^5*b^3*d^11*f^2 - 10*C^2*b^8*c^3*d^8*f^2 - 4*C^2*a^3*b^5*d^11*f^2 - 16*C^2*a^7*b*d^11*f^2 + 8*C^2*a^8*c*d^10*f

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

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

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

*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4

))^(1/2) - 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2

) + (32*(15*C^3*a^4*b^3*d^12*f^2 - C^3*a^2*b^5*d^12*f^2 + C^3*b^7*c^2*d^10*f^2 + C^3*b^7*c^4*d^8*f^2 - 12*C^3*

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

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

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

a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*C^2*a^2*c*f^2 + 4*C

^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(c + d*tan(e + f*x))^(1/

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

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

*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2)

- 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (64*

(C^5*a^5*d^13 - C^5*a^3*b^2*d^13 + C^5*a^5*c^2*d^11 + 2*C^5*a^2*b^3*c^3*d^10 + C^5*a^2*b^3*c^5*d^8 - 2*C^5*a^3

*b^2*c^2*d^11 - C^5*a^3*b^2*c^4*d^9 - C^5*a^4*b*c*d^12 + C^5*a^2*b^3*c*d^12 - C^5*a^4*b*c^3*d^10))/(b*f^5)))*(

(((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 +

32*a^2*b^2*f^4))^(1/2) - 4*C^2*a^2*c*f^2 + 4*C^2*b^2*c*f^2 - 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b

^2*f^4)))^(1/2)*2i - atan(((((32*(15*B^3*a^3*b^3*d^12*f^2 + B^3*b^6*c^3*d^9*f^2 - B^3*a*b^5*d^12*f^2 - 4*B^3*a

^5*b*d^12*f^2 + B^3*b^6*c*d^11*f^2 + 6*B^3*a*b^5*c^2*d^10*f^2 + 7*B^3*a*b^5*c^4*d^8*f^2 - 22*B^3*a^2*b^4*c*d^1

1*f^2 + 9*B^3*a^4*b^2*c*d^11*f^2 - 4*B^3*a^5*b*c^2*d^10*f^2 - 22*B^3*a^2*b^4*c^3*d^9*f^2 + 10*B^3*a^3*b^3*c^2*

d^10*f^2 - 5*B^3*a^3*b^3*c^4*d^8*f^2 + 9*B^3*a^4*b^2*c^3*d^9*f^2))/f^5 - (((32*(4*B*a^2*b^6*d^11*f^4 + 8*B*a^4

*b^4*d^11*f^4 + 4*B*a^6*b^2*d^11*f^4 - 4*B*a*b^7*c^3*d^8*f^4 - 8*B*a^3*b^5*c*d^10*f^4 - 4*B*a^5*b^3*c*d^10*f^4

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

*a^6*b^2*c^2*d^9*f^4 - 4*B*a*b^7*c*d^10*f^4))/f^5 - (32*(c + d*tan(e + f*x))^(1/2)*((((8*B^2*a^2*c*f^2 - 8*B^2

*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4

*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^2 + 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*(16*b^9*d^

10*f^4 + 16*a^2*b^7*d^10*f^4 - 16*a^4*b^5*d^10*f^4 - 16*a^6*b^3*d^10*f^4 + 24*b^9*c^2*d^8*f^4 + 40*a^2*b^7*c^2

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

^4*c*d^9*f^4 + 8*a^7*b^2*c*d^9*f^4))/f^4)*((((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4

*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^2 + 8*B^2*

a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(c + d*tan(e + f*x))^(1/2)*(14*B^2*a^5*b^2*d^

11*f^2 - 4*B^2*a^3*b^4*d^11*f^2 - 10*B^2*b^7*c^3*d^8*f^2 + 14*B^2*a*b^6*d^11*f^2 - 6*B^2*b^7*c*d^10*f^2 - 8*B^

2*a^6*b*c*d^10*f^2 + 18*B^2*a*b^6*c^2*d^9*f^2 + 12*B^2*a^2*b^5*c*d^10*f^2 - 22*B^2*a^4*b^3*c*d^10*f^2 + 12*B^2

*a^2*b^5*c^3*d^8*f^2 + 4*B^2*a^3*b^4*c^2*d^9*f^2 - 10*B^2*a^4*b^3*c^3*d^8*f^2 + 18*B^2*a^5*b^2*c^2*d^9*f^2))/f

^4)*((((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f

^4 + 32*a^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^2 + 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*

a^2*b^2*f^4)))^(1/2))*((((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*

a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^2 + 8*B^2*a*b*d*f^2)/(16*(a^4*

f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(c + d*tan(e + f*x))^(1/2)*(B^4*b^5*d^12 + 2*B^4*b^5*c^2*d^10 + B

^4*b^5*c^4*d^8 + 2*B^4*a^4*b*d^12 + 2*B^4*a^2*b^3*c^2*d^10 - 2*B^4*a^2*b^3*c^4*d^8 + 4*B^4*a^3*b^2*c^3*d^9 - 4

*B^4*a^3*b^2*c*d^11 - 2*B^4*a^4*b*c^2*d^10))/f^4)*((((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/

4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^2

+ 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*1i - (((32*(15*B^3*a^3*b^3*d^12*f^2 + B^3*b

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

*B^3*a*b^5*c^4*d^8*f^2 - 22*B^3*a^2*b^4*c*d^11*f^2 + 9*B^3*a^4*b^2*c*d^11*f^2 - 4*B^3*a^5*b*c^2*d^10*f^2 - 22*

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

)/f^5 - (((32*(4*B*a^2*b^6*d^11*f^4 + 8*B*a^4*b^4*d^11*f^4 + 4*B*a^6*b^2*d^11*f^4 - 4*B*a*b^7*c^3*d^8*f^4 - 8*

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

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

n(e + f*x))^(1/2)*((((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*

f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^2 + 8*B^2*a*b*d*f^2)/(16*(a^4*f^4

+ b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*(16*b^9*d^10*f^4 + 16*a^2*b^7*d^10*f^4 - 16*a^4*b^5*d^10*f^4 - 16*a^6*b^3*d

^10*f^4 + 24*b^9*c^2*d^8*f^4 + 40*a^2*b^7*c^2*d^8*f^4 + 8*a^4*b^5*c^2*d^8*f^4 - 8*a^6*b^3*c^2*d^8*f^4 + 8*a*b^

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

*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2)

+ 4*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^2 + 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*

(c + d*tan(e + f*x))^(1/2)*(14*B^2*a^5*b^2*d^11*f^2 - 4*B^2*a^3*b^4*d^11*f^2 - 10*B^2*b^7*c^3*d^8*f^2 + 14*B^2

*a*b^6*d^11*f^2 - 6*B^2*b^7*c*d^10*f^2 - 8*B^2*a^6*b*c*d^10*f^2 + 18*B^2*a*b^6*c^2*d^9*f^2 + 12*B^2*a^2*b^5*c*

d^10*f^2 - 22*B^2*a^4*b^3*c*d^10*f^2 + 12*B^2*a^2*b^5*c^3*d^8*f^2 + 4*B^2*a^3*b^4*c^2*d^9*f^2 - 10*B^2*a^4*b^3

*c^3*d^8*f^2 + 18*B^2*a^5*b^2*c^2*d^9*f^2))/f^4)*((((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4

- (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^2 +

8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2))*((((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*

B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*f^2 -

4*B^2*b^2*c*f^2 + 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))

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

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

*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4

))^(1/2) + 4*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^2 + 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2

)*1i)/((((32*(15*B^3*a^3*b^3*d^12*f^2 + B^3*b^6*c^3*d^9*f^2 - B^3*a*b^5*d^12*f^2 - 4*B^3*a^5*b*d^12*f^2 + B^3*

b^6*c*d^11*f^2 + 6*B^3*a*b^5*c^2*d^10*f^2 + 7*B^3*a*b^5*c^4*d^8*f^2 - 22*B^3*a^2*b^4*c*d^11*f^2 + 9*B^3*a^4*b^

2*c*d^11*f^2 - 4*B^3*a^5*b*c^2*d^10*f^2 - 22*B^3*a^2*b^4*c^3*d^9*f^2 + 10*B^3*a^3*b^3*c^2*d^10*f^2 - 5*B^3*a^3

*b^3*c^4*d^8*f^2 + 9*B^3*a^4*b^2*c^3*d^9*f^2))/f^5 - (((32*(4*B*a^2*b^6*d^11*f^4 + 8*B*a^4*b^4*d^11*f^4 + 4*B*

a^6*b^2*d^11*f^4 - 4*B*a*b^7*c^3*d^8*f^4 - 8*B*a^3*b^5*c*d^10*f^4 - 4*B*a^5*b^3*c*d^10*f^4 + 4*B*a^2*b^6*c^2*d

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

- 4*B*a*b^7*c*d^10*f^4))/f^5 - (32*(c + d*tan(e + f*x))^(1/2)*((((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*

a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*f^2 - 4*B

^2*b^2*c*f^2 + 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*(16*b^9*d^10*f^4 + 16*a^2*b^7*

d^10*f^4 - 16*a^4*b^5*d^10*f^4 - 16*a^6*b^3*d^10*f^4 + 24*b^9*c^2*d^8*f^4 + 40*a^2*b^7*c^2*d^8*f^4 + 8*a^4*b^5

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

*b^2*c*d^9*f^4))/f^4)*((((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*

a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^2 + 8*B^2*a*b*d*f^2)/(16*(a^4*

f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(c + d*tan(e + f*x))^(1/2)*(14*B^2*a^5*b^2*d^11*f^2 - 4*B^2*a^3*b

^4*d^11*f^2 - 10*B^2*b^7*c^3*d^8*f^2 + 14*B^2*a*b^6*d^11*f^2 - 6*B^2*b^7*c*d^10*f^2 - 8*B^2*a^6*b*c*d^10*f^2 +

18*B^2*a*b^6*c^2*d^9*f^2 + 12*B^2*a^2*b^5*c*d^10*f^2 - 22*B^2*a^4*b^3*c*d^10*f^2 + 12*B^2*a^2*b^5*c^3*d^8*f^2

+ 4*B^2*a^3*b^4*c^2*d^9*f^2 - 10*B^2*a^4*b^3*c^3*d^8*f^2 + 18*B^2*a^5*b^2*c^2*d^9*f^2))/f^4)*((((8*B^2*a^2*c*

f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4)

)^(1/2) + 4*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^2 + 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)

)*((((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4

+ 32*a^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^2 + 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^

2*b^2*f^4)))^(1/2) + (32*(c + d*tan(e + f*x))^(1/2)*(B^4*b^5*d^12 + 2*B^4*b^5*c^2*d^10 + B^4*b^5*c^4*d^8 + 2*B

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

- 2*B^4*a^4*b*c^2*d^10))/f^4)*((((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d

^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^2 + 8*B^2*a*b*d*f^2)/(

16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (((32*(15*B^3*a^3*b^3*d^12*f^2 + B^3*b^6*c^3*d^9*f^2 - B^3*a*

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

- 22*B^3*a^2*b^4*c*d^11*f^2 + 9*B^3*a^4*b^2*c*d^11*f^2 - 4*B^3*a^5*b*c^2*d^10*f^2 - 22*B^3*a^2*b^4*c^3*d^9*f^2

+ 10*B^3*a^3*b^3*c^2*d^10*f^2 - 5*B^3*a^3*b^3*c^4*d^8*f^2 + 9*B^3*a^4*b^2*c^3*d^9*f^2))/f^5 - (((32*(4*B*a^2*

b^6*d^11*f^4 + 8*B*a^4*b^4*d^11*f^4 + 4*B*a^6*b^2*d^11*f^4 - 4*B*a*b^7*c^3*d^8*f^4 - 8*B*a^3*b^5*c*d^10*f^4 -

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

*b^3*c^3*d^8*f^4 + 4*B*a^6*b^2*c^2*d^9*f^4 - 4*B*a*b^7*c*d^10*f^4))/f^5 + (32*(c + d*tan(e + f*x))^(1/2)*((((8

*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a

^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^2 + 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f

^4)))^(1/2)*(16*b^9*d^10*f^4 + 16*a^2*b^7*d^10*f^4 - 16*a^4*b^5*d^10*f^4 - 16*a^6*b^3*d^10*f^4 + 24*b^9*c^2*d^

8*f^4 + 40*a^2*b^7*c^2*d^8*f^4 + 8*a^4*b^5*c^2*d^8*f^4 - 8*a^6*b^3*c^2*d^8*f^4 + 8*a*b^8*c*d^9*f^4 + 24*a^3*b^

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

*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*f^2 - 4*

B^2*b^2*c*f^2 + 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))^(1

/2)*(14*B^2*a^5*b^2*d^11*f^2 - 4*B^2*a^3*b^4*d^11*f^2 - 10*B^2*b^7*c^3*d^8*f^2 + 14*B^2*a*b^6*d^11*f^2 - 6*B^2

*b^7*c*d^10*f^2 - 8*B^2*a^6*b*c*d^10*f^2 + 18*B^2*a*b^6*c^2*d^9*f^2 + 12*B^2*a^2*b^5*c*d^10*f^2 - 22*B^2*a^4*b

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

^5*b^2*c^2*d^9*f^2))/f^4)*((((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*

(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^2 + 8*B^2*a*b*d*f^2)/(16*(

a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2))*((((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B

^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^2 + 8*B^

2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))^(1/2)*(B^4*b^5*d^12 +

2*B^4*b^5*c^2*d^10 + B^4*b^5*c^4*d^8 + 2*B^4*a^4*b*d^12 + 2*B^4*a^2*b^3*c^2*d^10 - 2*B^4*a^2*b^3*c^4*d^8 + 4*B

^4*a^3*b^2*c^3*d^9 - 4*B^4*a^3*b^2*c*d^11 - 2*B^4*a^4*b*c^2*d^10))/f^4)*((((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2

+ 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*

f^2 - 4*B^2*b^2*c*f^2 + 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (64*(B^5*a*b^3*c*d^

12 - 3*B^5*a^2*b^2*c^2*d^11 - 2*B^5*a^2*b^2*c^4*d^9 - B^5*a^2*b^2*d^13 + B^5*a^3*b*c*d^12 + 2*B^5*a*b^3*c^3*d^

10 + B^5*a*b^3*c^5*d^8 + B^5*a^3*b*c^3*d^10))/f^5))*((((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^

2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*B^2*a^2*c*f^2 - 4*B^2*b^2*c*f^

2 + 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*2i - atan(((((32*(15*B^3*a^3*b^3*d^12*f^2

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

*f^2 + 7*B^3*a*b^5*c^4*d^8*f^2 - 22*B^3*a^2*b^4*c*d^11*f^2 + 9*B^3*a^4*b^2*c*d^11*f^2 - 4*B^3*a^5*b*c^2*d^10*f

^2 - 22*B^3*a^2*b^4*c^3*d^9*f^2 + 10*B^3*a^3*b^3*c^2*d^10*f^2 - 5*B^3*a^3*b^3*c^4*d^8*f^2 + 9*B^3*a^4*b^2*c^3*

d^9*f^2))/f^5 - (((32*(4*B*a^2*b^6*d^11*f^4 + 8*B*a^4*b^4*d^11*f^4 + 4*B*a^6*b^2*d^11*f^4 - 4*B*a*b^7*c^3*d^8*

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

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

c + d*tan(e + f*x))^(1/2)*(-(((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)

*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*

(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*(16*b^9*d^10*f^4 + 16*a^2*b^7*d^10*f^4 - 16*a^4*b^5*d^10*f^4 - 16*

a^6*b^3*d^10*f^4 + 24*b^9*c^2*d^8*f^4 + 40*a^2*b^7*c^2*d^8*f^4 + 8*a^4*b^5*c^2*d^8*f^4 - 8*a^6*b^3*c^2*d^8*f^4

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

*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f

^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1

/2) + (32*(c + d*tan(e + f*x))^(1/2)*(14*B^2*a^5*b^2*d^11*f^2 - 4*B^2*a^3*b^4*d^11*f^2 - 10*B^2*b^7*c^3*d^8*f^

2 + 14*B^2*a*b^6*d^11*f^2 - 6*B^2*b^7*c*d^10*f^2 - 8*B^2*a^6*b*c*d^10*f^2 + 18*B^2*a*b^6*c^2*d^9*f^2 + 12*B^2*

a^2*b^5*c*d^10*f^2 - 22*B^2*a^4*b^3*c*d^10*f^2 + 12*B^2*a^2*b^5*c^3*d^8*f^2 + 4*B^2*a^3*b^4*c^2*d^9*f^2 - 10*B

^2*a^4*b^3*c^3*d^8*f^2 + 18*B^2*a^5*b^2*c^2*d^9*f^2))/f^4)*(-(((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b

*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*B^2*

b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2))*(-(((8*B^2*a^2*c*f^2 - 8*B^2*b^2

*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*B^2

*a^2*c*f^2 + 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(c + d*t

an(e + f*x))^(1/2)*(B^4*b^5*d^12 + 2*B^4*b^5*c^2*d^10 + B^4*b^5*c^4*d^8 + 2*B^4*a^4*b*d^12 + 2*B^4*a^2*b^3*c^2

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

((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 3

2*a^2*b^2*f^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^

2*f^4)))^(1/2)*1i - (((32*(15*B^3*a^3*b^3*d^12*f^2 + B^3*b^6*c^3*d^9*f^2 - B^3*a*b^5*d^12*f^2 - 4*B^3*a^5*b*d^

12*f^2 + B^3*b^6*c*d^11*f^2 + 6*B^3*a*b^5*c^2*d^10*f^2 + 7*B^3*a*b^5*c^4*d^8*f^2 - 22*B^3*a^2*b^4*c*d^11*f^2 +

9*B^3*a^4*b^2*c*d^11*f^2 - 4*B^3*a^5*b*c^2*d^10*f^2 - 22*B^3*a^2*b^4*c^3*d^9*f^2 + 10*B^3*a^3*b^3*c^2*d^10*f^

2 - 5*B^3*a^3*b^3*c^4*d^8*f^2 + 9*B^3*a^4*b^2*c^3*d^9*f^2))/f^5 - (((32*(4*B*a^2*b^6*d^11*f^4 + 8*B*a^4*b^4*d^

11*f^4 + 4*B*a^6*b^2*d^11*f^4 - 4*B*a*b^7*c^3*d^8*f^4 - 8*B*a^3*b^5*c*d^10*f^4 - 4*B*a^5*b^3*c*d^10*f^4 + 4*B*

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

2*c^2*d^9*f^4 - 4*B*a*b^7*c*d^10*f^4))/f^5 + (32*(c + d*tan(e + f*x))^(1/2)*(-(((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c

*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*B^2*a

^2*c*f^2 + 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*(16*b^9*d^10*f^4

+ 16*a^2*b^7*d^10*f^4 - 16*a^4*b^5*d^10*f^4 - 16*a^6*b^3*d^10*f^4 + 24*b^9*c^2*d^8*f^4 + 40*a^2*b^7*c^2*d^8*f

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

^9*f^4 + 8*a^7*b^2*c*d^9*f^4))/f^4)*(-(((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2

+ B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d

*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))^(1/2)*(14*B^2*a^5*b^2*d^11*f^

2 - 4*B^2*a^3*b^4*d^11*f^2 - 10*B^2*b^7*c^3*d^8*f^2 + 14*B^2*a*b^6*d^11*f^2 - 6*B^2*b^7*c*d^10*f^2 - 8*B^2*a^6

*b*c*d^10*f^2 + 18*B^2*a*b^6*c^2*d^9*f^2 + 12*B^2*a^2*b^5*c*d^10*f^2 - 22*B^2*a^4*b^3*c*d^10*f^2 + 12*B^2*a^2*

b^5*c^3*d^8*f^2 + 4*B^2*a^3*b^4*c^2*d^9*f^2 - 10*B^2*a^4*b^3*c^3*d^8*f^2 + 18*B^2*a^5*b^2*c^2*d^9*f^2))/f^4)*(

-(((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 +

32*a^2*b^2*f^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*

b^2*f^4)))^(1/2))*(-(((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4

*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*(a^4*f^4

+ b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))^(1/2)*(B^4*b^5*d^12 + 2*B^4*b^5*c^2*d^10 + B^4*

b^5*c^4*d^8 + 2*B^4*a^4*b*d^12 + 2*B^4*a^2*b^3*c^2*d^10 - 2*B^4*a^2*b^3*c^4*d^8 + 4*B^4*a^3*b^2*c^3*d^9 - 4*B^

4*a^3*b^2*c*d^11 - 2*B^4*a^4*b*c^2*d^10))/f^4)*(-(((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4

- (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*B^2*b^2*c*f^2 -

8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*1i)/((((32*(15*B^3*a^3*b^3*d^12*f^2 + B^3*b^6

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

^3*a*b^5*c^4*d^8*f^2 - 22*B^3*a^2*b^4*c*d^11*f^2 + 9*B^3*a^4*b^2*c*d^11*f^2 - 4*B^3*a^5*b*c^2*d^10*f^2 - 22*B^

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

f^5 - (((32*(4*B*a^2*b^6*d^11*f^4 + 8*B*a^4*b^4*d^11*f^4 + 4*B*a^6*b^2*d^11*f^4 - 4*B*a*b^7*c^3*d^8*f^4 - 8*B*

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

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

e + f*x))^(1/2)*(-(((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f

^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 +

b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*(16*b^9*d^10*f^4 + 16*a^2*b^7*d^10*f^4 - 16*a^4*b^5*d^10*f^4 - 16*a^6*b^3*d^

10*f^4 + 24*b^9*c^2*d^8*f^4 + 40*a^2*b^7*c^2*d^8*f^4 + 8*a^4*b^5*c^2*d^8*f^4 - 8*a^6*b^3*c^2*d^8*f^4 + 8*a*b^8

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

*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2)

- 4*B^2*a^2*c*f^2 + 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*

(c + d*tan(e + f*x))^(1/2)*(14*B^2*a^5*b^2*d^11*f^2 - 4*B^2*a^3*b^4*d^11*f^2 - 10*B^2*b^7*c^3*d^8*f^2 + 14*B^2

*a*b^6*d^11*f^2 - 6*B^2*b^7*c*d^10*f^2 - 8*B^2*a^6*b*c*d^10*f^2 + 18*B^2*a*b^6*c^2*d^9*f^2 + 12*B^2*a^2*b^5*c*

d^10*f^2 - 22*B^2*a^4*b^3*c*d^10*f^2 + 12*B^2*a^2*b^5*c^3*d^8*f^2 + 4*B^2*a^3*b^4*c^2*d^9*f^2 - 10*B^2*a^4*b^3

*c^3*d^8*f^2 + 18*B^2*a^5*b^2*c^2*d^9*f^2))/f^4)*(-(((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/

4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*B^2*b^2*c*f^2

- 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2))*(-(((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 1

6*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*B^2*a^2*c*f^2

+ 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(c + d*tan(e + f*x

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

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

2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*

f^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(

1/2) + (((32*(15*B^3*a^3*b^3*d^12*f^2 + B^3*b^6*c^3*d^9*f^2 - B^3*a*b^5*d^12*f^2 - 4*B^3*a^5*b*d^12*f^2 + B^3*

b^6*c*d^11*f^2 + 6*B^3*a*b^5*c^2*d^10*f^2 + 7*B^3*a*b^5*c^4*d^8*f^2 - 22*B^3*a^2*b^4*c*d^11*f^2 + 9*B^3*a^4*b^

2*c*d^11*f^2 - 4*B^3*a^5*b*c^2*d^10*f^2 - 22*B^3*a^2*b^4*c^3*d^9*f^2 + 10*B^3*a^3*b^3*c^2*d^10*f^2 - 5*B^3*a^3

*b^3*c^4*d^8*f^2 + 9*B^3*a^4*b^2*c^3*d^9*f^2))/f^5 - (((32*(4*B*a^2*b^6*d^11*f^4 + 8*B*a^4*b^4*d^11*f^4 + 4*B*

a^6*b^2*d^11*f^4 - 4*B*a*b^7*c^3*d^8*f^4 - 8*B*a^3*b^5*c*d^10*f^4 - 4*B*a^5*b^3*c*d^10*f^4 + 4*B*a^2*b^6*c^2*d

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

- 4*B*a*b^7*c*d^10*f^4))/f^5 + (32*(c + d*tan(e + f*x))^(1/2)*(-(((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2

*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*

B^2*b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*(16*b^9*d^10*f^4 + 16*a^2*b^7

*d^10*f^4 - 16*a^4*b^5*d^10*f^4 - 16*a^6*b^3*d^10*f^4 + 24*b^9*c^2*d^8*f^4 + 40*a^2*b^7*c^2*d^8*f^4 + 8*a^4*b^

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

7*b^2*c*d^9*f^4))/f^4)*(-(((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(1

6*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*(a^

4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))^(1/2)*(14*B^2*a^5*b^2*d^11*f^2 - 4*B^2*a^3

*b^4*d^11*f^2 - 10*B^2*b^7*c^3*d^8*f^2 + 14*B^2*a*b^6*d^11*f^2 - 6*B^2*b^7*c*d^10*f^2 - 8*B^2*a^6*b*c*d^10*f^2

+ 18*B^2*a*b^6*c^2*d^9*f^2 + 12*B^2*a^2*b^5*c*d^10*f^2 - 22*B^2*a^4*b^3*c*d^10*f^2 + 12*B^2*a^2*b^5*c^3*d^8*f

^2 + 4*B^2*a^3*b^4*c^2*d^9*f^2 - 10*B^2*a^4*b^3*c^3*d^8*f^2 + 18*B^2*a^5*b^2*c^2*d^9*f^2))/f^4)*(-(((8*B^2*a^2

*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f

^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1

/2))*(-(((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^4 + 16*b^4

*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 +

2*a^2*b^2*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))^(1/2)*(B^4*b^5*d^12 + 2*B^4*b^5*c^2*d^10 + B^4*b^5*c^4*d^8 +

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

^11 - 2*B^4*a^4*b*c^2*d^10))/f^4)*(-(((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 +

B^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d*f

^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (64*(B^5*a*b^3*c*d^12 - 3*B^5*a^2*b^2*c^2*d^11 - 2*B^5*a

^2*b^2*c^4*d^9 - B^5*a^2*b^2*d^13 + B^5*a^3*b*c*d^12 + 2*B^5*a*b^3*c^3*d^10 + B^5*a*b^3*c^5*d^8 + B^5*a^3*b*c^

3*d^10))/f^5))*(-(((8*B^2*a^2*c*f^2 - 8*B^2*b^2*c*f^2 + 16*B^2*a*b*d*f^2)^2/4 - (B^4*c^2 + B^4*d^2)*(16*a^4*f^

4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*B^2*a^2*c*f^2 + 4*B^2*b^2*c*f^2 - 8*B^2*a*b*d*f^2)/(16*(a^4*f^4 +

b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*2i + atan(((((((32*(4*C*a*b^8*d^11*f^4 - 4*C*b^9*c*d^10*f^4 + 8*C*a^3*b^6*d^1

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

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

*d^9*f^4))/(b*f^5) - (32*(c + d*tan(e + f*x))^(1/2)*(-(((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)

^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*C^2*a^2*c*f^2 - 4*C^2*b^2*c*f

^2 + 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*(16*b^10*d^10*f^4 + 16*a^2*b^8*d^10*f^4

- 16*a^4*b^6*d^10*f^4 - 16*a^6*b^4*d^10*f^4 + 24*b^10*c^2*d^8*f^4 + 40*a^2*b^8*c^2*d^8*f^4 + 8*a^4*b^6*c^2*d^8

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

^9*f^4))/(b*f^4))*(-(((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4

*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*C^2*a^2*c*f^2 - 4*C^2*b^2*c*f^2 + 8*C^2*a*b*d*f^2)/(16*(a^4*f^4

+ b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))^(1/2)*(14*C^2*a*b^7*d^11*f^2 - 2*C^2*a^5*b^3*d^

11*f^2 - 10*C^2*b^8*c^3*d^8*f^2 - 4*C^2*a^3*b^5*d^11*f^2 - 16*C^2*a^7*b*d^11*f^2 + 8*C^2*a^8*c*d^10*f^2 - 6*C^

2*b^8*c*d^10*f^2 + 18*C^2*a*b^7*c^2*d^9*f^2 + 12*C^2*a^2*b^6*c*d^10*f^2 + 2*C^2*a^4*b^4*c*d^10*f^2 + 24*C^2*a^

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

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

*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2)

+ 4*C^2*a^2*c*f^2 - 4*C^2*b^2*c*f^2 + 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*

(15*C^3*a^4*b^3*d^12*f^2 - C^3*a^2*b^5*d^12*f^2 + C^3*b^7*c^2*d^10*f^2 + C^3*b^7*c^4*d^8*f^2 - 12*C^3*a^6*b*d^

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

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

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

^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*C^2*a^2*c*f^2 - 4*C^2*b^2*

c*f^2 + 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))^(1/2)*(C^4

*b^6*d^12 - 2*C^4*a^6*d^12 + 2*C^4*a^6*c^2*d^10 + 2*C^4*b^6*c^2*d^10 + C^4*b^6*c^4*d^8 - 2*C^4*a^4*b^2*c^2*d^1

0 + 2*C^4*a^4*b^2*c^4*d^8 + 4*C^4*a^5*b*c*d^11 - 4*C^4*a^5*b*c^3*d^9))/(b*f^4))*(-(((8*C^2*a^2*c*f^2 - 8*C^2*b

^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*C

^2*a^2*c*f^2 - 4*C^2*b^2*c*f^2 + 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*1i - (((((32

*(4*C*a*b^8*d^11*f^4 - 4*C*b^9*c*d^10*f^4 + 8*C*a^3*b^6*d^11*f^4 + 4*C*a^5*b^4*d^11*f^4 - 4*C*b^9*c^3*d^8*f^4

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

b^6*c^2*d^9*f^4 - 4*C*a^4*b^5*c^3*d^8*f^4 + 4*C*a^5*b^4*c^2*d^9*f^4))/(b*f^5) + (32*(c + d*tan(e + f*x))^(1/2)

*(-(((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4

+ 32*a^2*b^2*f^4))^(1/2) + 4*C^2*a^2*c*f^2 - 4*C^2*b^2*c*f^2 + 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^

2*b^2*f^4)))^(1/2)*(16*b^10*d^10*f^4 + 16*a^2*b^8*d^10*f^4 - 16*a^4*b^6*d^10*f^4 - 16*a^6*b^4*d^10*f^4 + 24*b^

10*c^2*d^8*f^4 + 40*a^2*b^8*c^2*d^8*f^4 + 8*a^4*b^6*c^2*d^8*f^4 - 8*a^6*b^4*c^2*d^8*f^4 + 8*a*b^9*c*d^9*f^4 +

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

c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*C^2*

a^2*c*f^2 - 4*C^2*b^2*c*f^2 + 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(c + d*ta

n(e + f*x))^(1/2)*(14*C^2*a*b^7*d^11*f^2 - 2*C^2*a^5*b^3*d^11*f^2 - 10*C^2*b^8*c^3*d^8*f^2 - 4*C^2*a^3*b^5*d^1

1*f^2 - 16*C^2*a^7*b*d^11*f^2 + 8*C^2*a^8*c*d^10*f^2 - 6*C^2*b^8*c*d^10*f^2 + 18*C^2*a*b^7*c^2*d^9*f^2 + 12*C^

2*a^2*b^6*c*d^10*f^2 + 2*C^2*a^4*b^4*c*d^10*f^2 + 24*C^2*a^6*b^2*c*d^10*f^2 - 16*C^2*a^7*b*c^2*d^9*f^2 + 4*C^2

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

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

C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*C^2*a^2*c*f^2 - 4*C^2*b^2*c*f^2 + 8*C^2*a*b*d*

f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(15*C^3*a^4*b^3*d^12*f^2 - C^3*a^2*b^5*d^12*f^2 + C

^3*b^7*c^2*d^10*f^2 + C^3*b^7*c^4*d^8*f^2 - 12*C^3*a^6*b*d^12*f^2 - 24*C^3*a^3*b^4*c*d^11*f^2 + 24*C^3*a^5*b^2

*c*d^11*f^2 - 12*C^3*a^6*b*c^2*d^10*f^2 + 8*C^3*a^2*b^5*c^2*d^10*f^2 + 9*C^3*a^2*b^5*c^4*d^8*f^2 - 24*C^3*a^3*

b^4*c^3*d^9*f^2 + 3*C^3*a^4*b^3*c^2*d^10*f^2 - 12*C^3*a^4*b^3*c^4*d^8*f^2 + 24*C^3*a^5*b^2*c^3*d^9*f^2))/(b*f^

5))*(-(((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*

f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*C^2*a^2*c*f^2 - 4*C^2*b^2*c*f^2 + 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2

*a^2*b^2*f^4)))^(1/2) + (32*(c + d*tan(e + f*x))^(1/2)*(C^4*b^6*d^12 - 2*C^4*a^6*d^12 + 2*C^4*a^6*c^2*d^10 + 2

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

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

^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*C^2*a^2*c*f^2 - 4*C^2*b^2*c*f^2 + 8*C^2*a*b*d*f^2)/(

16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*1i)/((((((32*(4*C*a*b^8*d^11*f^4 - 4*C*b^9*c*d^10*f^4 + 8*C*a^3

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

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

*b^4*c^2*d^9*f^4))/(b*f^5) - (32*(c + d*tan(e + f*x))^(1/2)*(-(((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*

b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*C^2*a^2*c*f^2 - 4*C^2

*b^2*c*f^2 + 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*(16*b^10*d^10*f^4 + 16*a^2*b^8*d

^10*f^4 - 16*a^4*b^6*d^10*f^4 - 16*a^6*b^4*d^10*f^4 + 24*b^10*c^2*d^8*f^4 + 40*a^2*b^8*c^2*d^8*f^4 + 8*a^4*b^6

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

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

*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*C^2*a^2*c*f^2 - 4*C^2*b^2*c*f^2 + 8*C^2*a*b*d*f^2)/(16*

(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))^(1/2)*(14*C^2*a*b^7*d^11*f^2 - 2*C^2*a^

5*b^3*d^11*f^2 - 10*C^2*b^8*c^3*d^8*f^2 - 4*C^2*a^3*b^5*d^11*f^2 - 16*C^2*a^7*b*d^11*f^2 + 8*C^2*a^8*c*d^10*f^

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

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

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

*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4

))^(1/2) + 4*C^2*a^2*c*f^2 - 4*C^2*b^2*c*f^2 + 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2

) + (32*(15*C^3*a^4*b^3*d^12*f^2 - C^3*a^2*b^5*d^12*f^2 + C^3*b^7*c^2*d^10*f^2 + C^3*b^7*c^4*d^8*f^2 - 12*C^3*

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

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

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

*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*C^2*a^2*c*f^2 - 4*

C^2*b^2*c*f^2 + 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))^(1

/2)*(C^4*b^6*d^12 - 2*C^4*a^6*d^12 + 2*C^4*a^6*c^2*d^10 + 2*C^4*b^6*c^2*d^10 + C^4*b^6*c^4*d^8 - 2*C^4*a^4*b^2

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

8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/

2) + 4*C^2*a^2*c*f^2 - 4*C^2*b^2*c*f^2 + 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + ((

(((32*(4*C*a*b^8*d^11*f^4 - 4*C*b^9*c*d^10*f^4 + 8*C*a^3*b^6*d^11*f^4 + 4*C*a^5*b^4*d^11*f^4 - 4*C*b^9*c^3*d^8

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

*a^3*b^6*c^2*d^9*f^4 - 4*C*a^4*b^5*c^3*d^8*f^4 + 4*C*a^5*b^4*c^2*d^9*f^4))/(b*f^5) + (32*(c + d*tan(e + f*x))^

(1/2)*(-(((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^

4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*C^2*a^2*c*f^2 - 4*C^2*b^2*c*f^2 + 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 +

2*a^2*b^2*f^4)))^(1/2)*(16*b^10*d^10*f^4 + 16*a^2*b^8*d^10*f^4 - 16*a^4*b^6*d^10*f^4 - 16*a^6*b^4*d^10*f^4 +

24*b^10*c^2*d^8*f^4 + 40*a^2*b^8*c^2*d^8*f^4 + 8*a^4*b^6*c^2*d^8*f^4 - 8*a^6*b^4*c^2*d^8*f^4 + 8*a*b^9*c*d^9*f

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

*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4

*C^2*a^2*c*f^2 - 4*C^2*b^2*c*f^2 + 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(c +

d*tan(e + f*x))^(1/2)*(14*C^2*a*b^7*d^11*f^2 - 2*C^2*a^5*b^3*d^11*f^2 - 10*C^2*b^8*c^3*d^8*f^2 - 4*C^2*a^3*b^

5*d^11*f^2 - 16*C^2*a^7*b*d^11*f^2 + 8*C^2*a^8*c*d^10*f^2 - 6*C^2*b^8*c*d^10*f^2 + 18*C^2*a*b^7*c^2*d^9*f^2 +

12*C^2*a^2*b^6*c*d^10*f^2 + 2*C^2*a^4*b^4*c*d^10*f^2 + 24*C^2*a^6*b^2*c*d^10*f^2 - 16*C^2*a^7*b*c^2*d^9*f^2 +

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

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

c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*C^2*a^2*c*f^2 - 4*C^2*b^2*c*f^2 + 8*C^2*a

*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(15*C^3*a^4*b^3*d^12*f^2 - C^3*a^2*b^5*d^12*f^

2 + C^3*b^7*c^2*d^10*f^2 + C^3*b^7*c^4*d^8*f^2 - 12*C^3*a^6*b*d^12*f^2 - 24*C^3*a^3*b^4*c*d^11*f^2 + 24*C^3*a^

5*b^2*c*d^11*f^2 - 12*C^3*a^6*b*c^2*d^10*f^2 + 8*C^3*a^2*b^5*c^2*d^10*f^2 + 9*C^3*a^2*b^5*c^4*d^8*f^2 - 24*C^3

*a^3*b^4*c^3*d^9*f^2 + 3*C^3*a^4*b^3*c^2*d^10*f^2 - 12*C^3*a^4*b^3*c^4*d^8*f^2 + 24*C^3*a^5*b^2*c^3*d^9*f^2))/

(b*f^5))*(-(((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16

*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*C^2*a^2*c*f^2 - 4*C^2*b^2*c*f^2 + 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^

4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(c + d*tan(e + f*x))^(1/2)*(C^4*b^6*d^12 - 2*C^4*a^6*d^12 + 2*C^4*a^6*c^2*d^1

0 + 2*C^4*b^6*c^2*d^10 + C^4*b^6*c^4*d^8 - 2*C^4*a^4*b^2*c^2*d^10 + 2*C^4*a^4*b^2*c^4*d^8 + 4*C^4*a^5*b*c*d^11

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

C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*C^2*a^2*c*f^2 - 4*C^2*b^2*c*f^2 + 8*C^2*a*b*d*f

^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (64*(C^5*a^5*d^13 - C^5*a^3*b^2*d^13 + C^5*a^5*c^2*d^11

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

12 + C^5*a^2*b^3*c*d^12 - C^5*a^4*b*c^3*d^10))/(b*f^5)))*(-(((8*C^2*a^2*c*f^2 - 8*C^2*b^2*c*f^2 + 16*C^2*a*b*d

*f^2)^2/4 - (C^4*c^2 + C^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) + 4*C^2*a^2*c*f^2 - 4*C^2*b^

2*c*f^2 + 8*C^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*2i + atan(((((((32*(12*A*a*b^7*d^11

*f^4 - 12*A*b^8*c*d^10*f^4 + 24*A*a^3*b^5*d^11*f^4 + 12*A*a^5*b^3*d^11*f^4 - 12*A*b^8*c^3*d^8*f^4 + 12*A*a*b^7

*c^2*d^9*f^4 - 24*A*a^2*b^6*c*d^10*f^4 - 12*A*a^4*b^4*c*d^10*f^4 - 24*A*a^2*b^6*c^3*d^8*f^4 + 24*A*a^3*b^5*c^2

*d^9*f^4 - 12*A*a^4*b^4*c^3*d^8*f^4 + 12*A*a^5*b^3*c^2*d^9*f^4))/f^5 - (32*(c + d*tan(e + f*x))^(1/2)*((((8*A^

2*a^2*c*f^2 - 8*A^2*b^2*c*f^2 + 16*A^2*a*b*d*f^2)^2/4 - (A^4*c^2 + A^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*

b^2*f^4))^(1/2) - 4*A^2*a^2*c*f^2 + 4*A^2*b^2*c*f^2 - 8*A^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)

))^(1/2)*(16*b^9*d^10*f^4 + 16*a^2*b^7*d^10*f^4 - 16*a^4*b^5*d^10*f^4 - 16*a^6*b^3*d^10*f^4 + 24*b^9*c^2*d^8*f

^4 + 40*a^2*b^7*c^2*d^8*f^4 + 8*a^4*b^5*c^2*d^8*f^4 - 8*a^6*b^3*c^2*d^8*f^4 + 8*a*b^8*c*d^9*f^4 + 24*a^3*b^6*c

*d^9*f^4 + 24*a^5*b^4*c*d^9*f^4 + 8*a^7*b^2*c*d^9*f^4))/f^4)*((((8*A^2*a^2*c*f^2 - 8*A^2*b^2*c*f^2 + 16*A^2*a*

b*d*f^2)^2/4 - (A^4*c^2 + A^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*A^2*a^2*c*f^2 + 4*A^2

*b^2*c*f^2 - 8*A^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(c + d*tan(e + f*x))^(1/2)

*(20*A^2*a^3*b^4*d^11*f^2 + 2*A^2*a^5*b^2*d^11*f^2 + 18*A^2*b^7*c^3*d^8*f^2 - 14*A^2*a*b^6*d^11*f^2 + 6*A^2*b^

7*c*d^10*f^2 - 18*A^2*a*b^6*c^2*d^9*f^2 - 36*A^2*a^2*b^5*c*d^10*f^2 - 10*A^2*a^4*b^3*c*d^10*f^2 - 12*A^2*a^2*b

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

(8*A^2*a^2*c*f^2 - 8*A^2*b^2*c*f^2 + 16*A^2*a*b*d*f^2)^2/4 - (A^4*c^2 + A^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32

*a^2*b^2*f^4))^(1/2) - 4*A^2*a^2*c*f^2 + 4*A^2*b^2*c*f^2 - 8*A^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2

*f^4)))^(1/2) + (32*(13*A^3*a^2*b^4*d^12*f^2 + A^3*a^4*b^2*d^12*f^2 + 3*A^3*b^6*c^2*d^10*f^2 + 3*A^3*b^6*c^4*d

^8*f^2 - 16*A^3*a*b^5*c*d^11*f^2 - 16*A^3*a*b^5*c^3*d^9*f^2 + 12*A^3*a^2*b^4*c^2*d^10*f^2 - A^3*a^2*b^4*c^4*d^

8*f^2 + A^3*a^4*b^2*c^2*d^10*f^2))/f^5)*((((8*A^2*a^2*c*f^2 - 8*A^2*b^2*c*f^2 + 16*A^2*a*b*d*f^2)^2/4 - (A^4*c

^2 + A^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*A^2*a^2*c*f^2 + 4*A^2*b^2*c*f^2 - 8*A^2*a*

b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))^(1/2)*(A^4*b^5*d^12 - 2*A^

4*a^2*b^3*d^12 + 3*A^4*b^5*c^4*d^8 + 2*A^4*a^2*b^3*c^2*d^10 + 4*A^4*a*b^4*c*d^11 - 4*A^4*a*b^4*c^3*d^9))/f^4)*

((((8*A^2*a^2*c*f^2 - 8*A^2*b^2*c*f^2 + 16*A^2*a*b*d*f^2)^2/4 - (A^4*c^2 + A^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 +

32*a^2*b^2*f^4))^(1/2) - 4*A^2*a^2*c*f^2 + 4*A^2*b^2*c*f^2 - 8*A^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*

b^2*f^4)))^(1/2)*1i - (((((32*(12*A*a*b^7*d^11*f^4 - 12*A*b^8*c*d^10*f^4 + 24*A*a^3*b^5*d^11*f^4 + 12*A*a^5*b^

3*d^11*f^4 - 12*A*b^8*c^3*d^8*f^4 + 12*A*a*b^7*c^2*d^9*f^4 - 24*A*a^2*b^6*c*d^10*f^4 - 12*A*a^4*b^4*c*d^10*f^4

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

/f^5 + (32*(c + d*tan(e + f*x))^(1/2)*((((8*A^2*a^2*c*f^2 - 8*A^2*b^2*c*f^2 + 16*A^2*a*b*d*f^2)^2/4 - (A^4*c^2

+ A^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*A^2*a^2*c*f^2 + 4*A^2*b^2*c*f^2 - 8*A^2*a*b*

d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*(16*b^9*d^10*f^4 + 16*a^2*b^7*d^10*f^4 - 16*a^4*b^5*d^1

0*f^4 - 16*a^6*b^3*d^10*f^4 + 24*b^9*c^2*d^8*f^4 + 40*a^2*b^7*c^2*d^8*f^4 + 8*a^4*b^5*c^2*d^8*f^4 - 8*a^6*b^3*

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

(8*A^2*a^2*c*f^2 - 8*A^2*b^2*c*f^2 + 16*A^2*a*b*d*f^2)^2/4 - (A^4*c^2 + A^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32

*a^2*b^2*f^4))^(1/2) - 4*A^2*a^2*c*f^2 + 4*A^2*b^2*c*f^2 - 8*A^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2

*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))^(1/2)*(20*A^2*a^3*b^4*d^11*f^2 + 2*A^2*a^5*b^2*d^11*f^2 + 18*A^2*b^7*

c^3*d^8*f^2 - 14*A^2*a*b^6*d^11*f^2 + 6*A^2*b^7*c*d^10*f^2 - 18*A^2*a*b^6*c^2*d^9*f^2 - 36*A^2*a^2*b^5*c*d^10*

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

d^8*f^2 - 2*A^2*a^5*b^2*c^2*d^9*f^2))/f^4)*((((8*A^2*a^2*c*f^2 - 8*A^2*b^2*c*f^2 + 16*A^2*a*b*d*f^2)^2/4 - (A^

4*c^2 + A^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*A^2*a^2*c*f^2 + 4*A^2*b^2*c*f^2 - 8*A^2

*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(13*A^3*a^2*b^4*d^12*f^2 + A^3*a^4*b^2*d^12*

f^2 + 3*A^3*b^6*c^2*d^10*f^2 + 3*A^3*b^6*c^4*d^8*f^2 - 16*A^3*a*b^5*c*d^11*f^2 - 16*A^3*a*b^5*c^3*d^9*f^2 + 12

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

A^2*b^2*c*f^2 + 16*A^2*a*b*d*f^2)^2/4 - (A^4*c^2 + A^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2)

- 4*A^2*a^2*c*f^2 + 4*A^2*b^2*c*f^2 - 8*A^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(

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

A^4*a*b^4*c*d^11 - 4*A^4*a*b^4*c^3*d^9))/f^4)*((((8*A^2*a^2*c*f^2 - 8*A^2*b^2*c*f^2 + 16*A^2*a*b*d*f^2)^2/4 -

(A^4*c^2 + A^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*A^2*a^2*c*f^2 + 4*A^2*b^2*c*f^2 - 8*

A^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*1i)/((((((32*(12*A*a*b^7*d^11*f^4 - 12*A*b^8*c*

d^10*f^4 + 24*A*a^3*b^5*d^11*f^4 + 12*A*a^5*b^3*d^11*f^4 - 12*A*b^8*c^3*d^8*f^4 + 12*A*a*b^7*c^2*d^9*f^4 - 24*

A*a^2*b^6*c*d^10*f^4 - 12*A*a^4*b^4*c*d^10*f^4 - 24*A*a^2*b^6*c^3*d^8*f^4 + 24*A*a^3*b^5*c^2*d^9*f^4 - 12*A*a^

4*b^4*c^3*d^8*f^4 + 12*A*a^5*b^3*c^2*d^9*f^4))/f^5 - (32*(c + d*tan(e + f*x))^(1/2)*((((8*A^2*a^2*c*f^2 - 8*A^

2*b^2*c*f^2 + 16*A^2*a*b*d*f^2)^2/4 - (A^4*c^2 + A^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) -

4*A^2*a^2*c*f^2 + 4*A^2*b^2*c*f^2 - 8*A^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2)*(16*b^9*d

^10*f^4 + 16*a^2*b^7*d^10*f^4 - 16*a^4*b^5*d^10*f^4 - 16*a^6*b^3*d^10*f^4 + 24*b^9*c^2*d^8*f^4 + 40*a^2*b^7*c^

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

b^4*c*d^9*f^4 + 8*a^7*b^2*c*d^9*f^4))/f^4)*((((8*A^2*a^2*c*f^2 - 8*A^2*b^2*c*f^2 + 16*A^2*a*b*d*f^2)^2/4 - (A^

4*c^2 + A^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*A^2*a^2*c*f^2 + 4*A^2*b^2*c*f^2 - 8*A^2

*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (32*(c + d*tan(e + f*x))^(1/2)*(20*A^2*a^3*b^4*d

^11*f^2 + 2*A^2*a^5*b^2*d^11*f^2 + 18*A^2*b^7*c^3*d^8*f^2 - 14*A^2*a*b^6*d^11*f^2 + 6*A^2*b^7*c*d^10*f^2 - 18*

A^2*a*b^6*c^2*d^9*f^2 - 36*A^2*a^2*b^5*c*d^10*f^2 - 10*A^2*a^4*b^3*c*d^10*f^2 - 12*A^2*a^2*b^5*c^3*d^8*f^2 + 1

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

8*A^2*b^2*c*f^2 + 16*A^2*a*b*d*f^2)^2/4 - (A^4*c^2 + A^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/

2) - 4*A^2*a^2*c*f^2 + 4*A^2*b^2*c*f^2 - 8*A^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) + (3

2*(13*A^3*a^2*b^4*d^12*f^2 + A^3*a^4*b^2*d^12*f^2 + 3*A^3*b^6*c^2*d^10*f^2 + 3*A^3*b^6*c^4*d^8*f^2 - 16*A^3*a*

b^5*c*d^11*f^2 - 16*A^3*a*b^5*c^3*d^9*f^2 + 12*A^3*a^2*b^4*c^2*d^10*f^2 - A^3*a^2*b^4*c^4*d^8*f^2 + A^3*a^4*b^

2*c^2*d^10*f^2))/f^5)*((((8*A^2*a^2*c*f^2 - 8*A^2*b^2*c*f^2 + 16*A^2*a*b*d*f^2)^2/4 - (A^4*c^2 + A^4*d^2)*(16*

a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*A^2*a^2*c*f^2 + 4*A^2*b^2*c*f^2 - 8*A^2*a*b*d*f^2)/(16*(a^4*

f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))^(1/2)*(A^4*b^5*d^12 - 2*A^4*a^2*b^3*d^12 + 3

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

2 - 8*A^2*b^2*c*f^2 + 16*A^2*a*b*d*f^2)^2/4 - (A^4*c^2 + A^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^

(1/2) - 4*A^2*a^2*c*f^2 + 4*A^2*b^2*c*f^2 - 8*A^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) -

(64*(A^5*b^4*c^3*d^10 - A^5*a*b^3*d^13 + A^5*b^4*c*d^12 - A^5*a*b^3*c^2*d^11))/f^5 + (((((32*(12*A*a*b^7*d^11

*f^4 - 12*A*b^8*c*d^10*f^4 + 24*A*a^3*b^5*d^11*f^4 + 12*A*a^5*b^3*d^11*f^4 - 12*A*b^8*c^3*d^8*f^4 + 12*A*a*b^7

*c^2*d^9*f^4 - 24*A*a^2*b^6*c*d^10*f^4 - 12*A*a^4*b^4*c*d^10*f^4 - 24*A*a^2*b^6*c^3*d^8*f^4 + 24*A*a^3*b^5*c^2

*d^9*f^4 - 12*A*a^4*b^4*c^3*d^8*f^4 + 12*A*a^5*b^3*c^2*d^9*f^4))/f^5 + (32*(c + d*tan(e + f*x))^(1/2)*((((8*A^

2*a^2*c*f^2 - 8*A^2*b^2*c*f^2 + 16*A^2*a*b*d*f^2)^2/4 - (A^4*c^2 + A^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*

b^2*f^4))^(1/2) - 4*A^2*a^2*c*f^2 + 4*A^2*b^2*c*f^2 - 8*A^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)

))^(1/2)*(16*b^9*d^10*f^4 + 16*a^2*b^7*d^10*f^4 - 16*a^4*b^5*d^10*f^4 - 16*a^6*b^3*d^10*f^4 + 24*b^9*c^2*d^8*f

^4 + 40*a^2*b^7*c^2*d^8*f^4 + 8*a^4*b^5*c^2*d^8*f^4 - 8*a^6*b^3*c^2*d^8*f^4 + 8*a*b^8*c*d^9*f^4 + 24*a^3*b^6*c

*d^9*f^4 + 24*a^5*b^4*c*d^9*f^4 + 8*a^7*b^2*c*d^9*f^4))/f^4)*((((8*A^2*a^2*c*f^2 - 8*A^2*b^2*c*f^2 + 16*A^2*a*

b*d*f^2)^2/4 - (A^4*c^2 + A^4*d^2)*(16*a^4*f^4 + 16*b^4*f^4 + 32*a^2*b^2*f^4))^(1/2) - 4*A^2*a^2*c*f^2 + 4*A^2

*b^2*c*f^2 - 8*A^2*a*b*d*f^2)/(16*(a^4*f^4 + b^4*f^4 + 2*a^2*b^2*f^4)))^(1/2) - (32*(c + d*tan(e + f*x))^(1/2)