3.118 \(\int \frac {(a+b \tan (e+f x)) (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{3/2}} \, dx\)
Optimal. Leaf size=201 \[ \frac {2 (b c-a d) \left (A d^2-B c d+c^2 C\right )}{d^2 f \left (c^2+d^2\right ) \sqrt {c+d \tan (e+f x)}}-\frac {(b+i a) (A-i B-C) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{f (c-i d)^{3/2}}+\frac {(-b+i a) (A+i B-C) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{f (c+i d)^{3/2}}+\frac {2 b C \sqrt {c+d \tan (e+f x)}}{d^2 f} \]
[Out]
-(I*a+b)*(A-I*B-C)*arctanh((c+d*tan(f*x+e))^(1/2)/(c-I*d)^(1/2))/(c-I*d)^(3/2)/f+(I*a-b)*(A+I*B-C)*arctanh((c+
d*tan(f*x+e))^(1/2)/(c+I*d)^(1/2))/(c+I*d)^(3/2)/f+2*(-a*d+b*c)*(A*d^2-B*c*d+C*c^2)/d^2/(c^2+d^2)/f/(c+d*tan(f
*x+e))^(1/2)+2*b*C*(c+d*tan(f*x+e))^(1/2)/d^2/f
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Rubi [A] time = 0.55, antiderivative size = 201, normalized size of antiderivative = 1.00,
number of steps used = 9, number of rules used = 6, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used =
{3635, 3630, 3539, 3537, 63, 208} \[ \frac {2 (b c-a d) \left (A d^2-B c d+c^2 C\right )}{d^2 f \left (c^2+d^2\right ) \sqrt {c+d \tan (e+f x)}}-\frac {(b+i a) (A-i B-C) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{f (c-i d)^{3/2}}+\frac {(-b+i a) (A+i B-C) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{f (c+i d)^{3/2}}+\frac {2 b C \sqrt {c+d \tan (e+f x)}}{d^2 f} \]
Antiderivative was successfully verified.
[In]
Int[((a + b*Tan[e + f*x])*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^(3/2),x]
[Out]
-(((I*a + b)*(A - I*B - C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(3/2)*f)) + ((I*a - b)*
(A + I*B - C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(3/2)*f) + (2*(b*c - a*d)*(c^2*C - B
*c*d + A*d^2))/(d^2*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]]) + (2*b*C*Sqrt[c + d*Tan[e + f*x]])/(d^2*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 3630
Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_.)*((A_.) + (B_.)*tan[(e_.) + (f_.)*(x_)] + (C_.)*tan[(e_.) + (
f_.)*(x_)]^2), x_Symbol] :> Simp[(C*(a + b*Tan[e + f*x])^(m + 1))/(b*f*(m + 1)), x] + Int[(a + b*Tan[e + f*x])
^m*Simp[A - C + B*Tan[e + f*x], x], x] /; FreeQ[{a, b, e, f, A, B, C, m}, x] && NeQ[A*b^2 - a*b*B + a^2*C, 0]
&& !LeQ[m, -1]
Rule 3635
Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])*((c_.) + (d_.)*tan[(e_.) + (f_.)*(x_)])^(n_)*((A_.) + (B_.)*tan[(e
_.) + (f_.)*(x_)] + (C_.)*tan[(e_.) + (f_.)*(x_)]^2), x_Symbol] :> -Simp[((b*c - a*d)*(c^2*C - B*c*d + A*d^2)*
(c + d*Tan[e + f*x])^(n + 1))/(d^2*f*(n + 1)*(c^2 + d^2)), x] + Dist[1/(d*(c^2 + d^2)), Int[(c + d*Tan[e + f*x
])^(n + 1)*Simp[a*d*(A*c - c*C + B*d) + b*(c^2*C - B*c*d + A*d^2) + d*(A*b*c + a*B*c - b*c*C - a*A*d + b*B*d +
a*C*d)*Tan[e + f*x] + b*C*(c^2 + d^2)*Tan[e + f*x]^2, x], x], x] /; FreeQ[{a, b, c, d, e, f, A, B, C}, x] &&
NeQ[b*c - a*d, 0] && NeQ[c^2 + d^2, 0] && LtQ[n, -1]
Rubi steps
\begin {align*} \int \frac {(a+b \tan (e+f x)) \left (A+B \tan (e+f x)+C \tan ^2(e+f x)\right )}{(c+d \tan (e+f x))^{3/2}} \, dx &=\frac {2 (b c-a d) \left (c^2 C-B c d+A d^2\right )}{d^2 \left (c^2+d^2\right ) f \sqrt {c+d \tan (e+f x)}}+\frac {\int \frac {a d (A c-c C+B d)+b \left (c^2 C-B c d+A d^2\right )+d (A b c+a B c-b c C-a A d+b B d+a C d) \tan (e+f x)+b C \left (c^2+d^2\right ) \tan ^2(e+f x)}{\sqrt {c+d \tan (e+f x)}} \, dx}{d \left (c^2+d^2\right )}\\ &=\frac {2 (b c-a d) \left (c^2 C-B c d+A d^2\right )}{d^2 \left (c^2+d^2\right ) f \sqrt {c+d \tan (e+f x)}}+\frac {2 b C \sqrt {c+d \tan (e+f x)}}{d^2 f}+\frac {\int \frac {d (a (A c-c C+B d)-b (B c-(A-C) d))+d (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}{d \left (c^2+d^2\right )}\\ &=\frac {2 (b c-a d) \left (c^2 C-B c d+A d^2\right )}{d^2 \left (c^2+d^2\right ) f \sqrt {c+d \tan (e+f x)}}+\frac {2 b C \sqrt {c+d \tan (e+f x)}}{d^2 f}+\frac {((a-i b) (A-i B-C)) \int \frac {1+i \tan (e+f x)}{\sqrt {c+d \tan (e+f x)}} \, dx}{2 (c-i d)}+\frac {((a+i b) (A+i B-C)) \int \frac {1-i \tan (e+f x)}{\sqrt {c+d \tan (e+f x)}} \, dx}{2 (c+i d)}\\ &=\frac {2 (b c-a d) \left (c^2 C-B c d+A d^2\right )}{d^2 \left (c^2+d^2\right ) f \sqrt {c+d \tan (e+f x)}}+\frac {2 b C \sqrt {c+d \tan (e+f x)}}{d^2 f}+\frac {(i (a-i b) (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 (c-i d) f}-\frac {((i a-b) (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 (c+i d) f}\\ &=\frac {2 (b c-a d) \left (c^2 C-B c d+A d^2\right )}{d^2 \left (c^2+d^2\right ) f \sqrt {c+d \tan (e+f x)}}+\frac {2 b C \sqrt {c+d \tan (e+f x)}}{d^2 f}-\frac {((a-i b) (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 )}{(c-i d) d f}-\frac {((a+i b) (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 )}{(c+i d) d f}\\ &=-\frac {(i a+b) (A-i B-C) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{(c-i d)^{3/2} f}+\frac {(i a-b) (A+i B-C) \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{(c+i d)^{3/2} f}+\frac {2 (b c-a d) \left (c^2 C-B c d+A d^2\right )}{d^2 \left (c^2+d^2\right ) f \sqrt {c+d \tan (e+f x)}}+\frac {2 b C \sqrt {c+d \tan (e+f x)}}{d^2 f}\\ \end {align*}
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Mathematica [C] time = 2.59, size = 290, normalized size = 1.44 \[ \frac {\frac {(-a A d+a B c+a C d+A b c+b B d-b c C) \left ((d-i c) \, _2F_1\left (-\frac {1}{2},1;\frac {1}{2};\frac {c+d \tan (e+f x)}{c-i d}\right )+(d+i c) \, _2F_1\left (-\frac {1}{2},1;\frac {1}{2};\frac {c+d \tan (e+f x)}{c+i d}\right )\right )}{\left (c^2+d^2\right ) \sqrt {c+d \tan (e+f x)}}+(a B+A b-b C) \left (\frac {i \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{\sqrt {c+i d}}-\frac {i \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{\sqrt {c-i d}}\right )-\frac {2 (2 a C d+b B d-2 b c C)}{d \sqrt {c+d \tan (e+f x)}}+\frac {2 C (a+b \tan (e+f x))}{\sqrt {c+d \tan (e+f x)}}}{d f} \]
Antiderivative was successfully verified.
[In]
Integrate[((a + b*Tan[e + f*x])*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^(3/2),x]
[Out]
((A*b + a*B - b*C)*(((-I)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/Sqrt[c - I*d] + (I*ArcTanh[Sqrt[c +
d*Tan[e + f*x]]/Sqrt[c + I*d]])/Sqrt[c + I*d]) - (2*(-2*b*c*C + b*B*d + 2*a*C*d))/(d*Sqrt[c + d*Tan[e + f*x]]
) + ((A*b*c + a*B*c - b*c*C - a*A*d + b*B*d + a*C*d)*(((-I)*c + d)*Hypergeometric2F1[-1/2, 1, 1/2, (c + d*Tan[
e + f*x])/(c - I*d)] + (I*c + d)*Hypergeometric2F1[-1/2, 1, 1/2, (c + d*Tan[e + f*x])/(c + I*d)]))/((c^2 + d^2
)*Sqrt[c + d*Tan[e + f*x]]) + (2*C*(a + b*Tan[e + f*x]))/Sqrt[c + d*Tan[e + f*x]])/(d*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((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),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))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x, algorithm="giac")
[Out]
Timed out
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maple [B] time = 0.44, size = 23472, normalized size = 116.78 \[ \text {output too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x)
[Out]
result too large to display
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maxima [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))*(A+B*tan(f*x+e)+C*tan(f*x+e)^2)/(c+d*tan(f*x+e))^(3/2),x, algorithm="maxima")
[Out]
Timed out
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mupad [B] time = 41.07, size = 40542, normalized size = 201.70 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((a + b*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)^2))/(c + d*tan(e + f*x))^(3/2),x)
[Out]
atan((((c + d*tan(e + f*x))^(1/2)*(16*A^2*a^2*d^10*f^3 - 16*B^2*a^2*d^10*f^3 + 16*C^2*a^2*d^10*f^3 + 32*A^2*a^
2*c^2*d^8*f^3 - 32*A^2*a^2*c^6*d^4*f^3 - 16*A^2*a^2*c^8*d^2*f^3 - 32*B^2*a^2*c^2*d^8*f^3 + 32*B^2*a^2*c^6*d^4*
f^3 + 16*B^2*a^2*c^8*d^2*f^3 + 32*C^2*a^2*c^2*d^8*f^3 - 32*C^2*a^2*c^6*d^4*f^3 - 16*C^2*a^2*c^8*d^2*f^3 - 32*A
*C*a^2*d^10*f^3 - 64*A*B*a^2*c*d^9*f^3 + 64*B*C*a^2*c*d^9*f^3 - 192*A*B*a^2*c^3*d^7*f^3 - 192*A*B*a^2*c^5*d^5*
f^3 - 64*A*B*a^2*c^7*d^3*f^3 - 64*A*C*a^2*c^2*d^8*f^3 + 64*A*C*a^2*c^6*d^4*f^3 + 32*A*C*a^2*c^8*d^2*f^3 + 192*
B*C*a^2*c^3*d^7*f^3 + 192*B*C*a^2*c^5*d^5*f^3 + 64*B*C*a^2*c^7*d^3*f^3) - ((((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^
3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^
2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2
*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C
^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) - 4*A^2*a^2*c^3*f
^2 + 4*B^2*a^2*c^3*f^2 - 4*C^2*a^2*c^3*f^2 + 8*A*B*a^2*d^3*f^2 + 8*A*C*a^2*c^3*f^2 - 8*B*C*a^2*d^3*f^2 + 12*A^
2*a^2*c*d^2*f^2 - 12*B^2*a^2*c*d^2*f^2 + 12*C^2*a^2*c*d^2*f^2 - 24*A*B*a^2*c^2*d*f^2 - 24*A*C*a^2*c*d^2*f^2 +
24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*((c + d*tan(e + f*x))^(1
/2)*((((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 +
16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2
+ 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f
^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 -
4*A*B^2*C*a^4))^(1/2) - 4*A^2*a^2*c^3*f^2 + 4*B^2*a^2*c^3*f^2 - 4*C^2*a^2*c^3*f^2 + 8*A*B*a^2*d^3*f^2 + 8*A*C
*a^2*c^3*f^2 - 8*B*C*a^2*d^3*f^2 + 12*A^2*a^2*c*d^2*f^2 - 12*B^2*a^2*c*d^2*f^2 + 12*C^2*a^2*c*d^2*f^2 - 24*A*B
*a^2*c^2*d*f^2 - 24*A*C*a^2*c*d^2*f^2 + 24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d
^2*f^4)))^(1/2)*(64*c*d^12*f^5 + 320*c^3*d^10*f^5 + 640*c^5*d^8*f^5 + 640*c^7*d^6*f^5 + 320*c^9*d^4*f^5 + 64*c
^11*d^2*f^5) - 32*B*a*d^12*f^4 - 256*A*a*c^3*d^9*f^4 - 384*A*a*c^5*d^7*f^4 - 256*A*a*c^7*d^5*f^4 - 64*A*a*c^9*
d^3*f^4 - 96*B*a*c^2*d^10*f^4 - 64*B*a*c^4*d^8*f^4 + 64*B*a*c^6*d^6*f^4 + 96*B*a*c^8*d^4*f^4 + 32*B*a*c^10*d^2
*f^4 + 256*C*a*c^3*d^9*f^4 + 384*C*a*c^5*d^7*f^4 + 256*C*a*c^7*d^5*f^4 + 64*C*a*c^9*d^3*f^4 - 64*A*a*c*d^11*f^
4 + 64*C*a*c*d^11*f^4))*((((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 1
6*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 +
48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^
4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a
^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) - 4*A^2*a^2*c^3*f^2 + 4*B^2*a^2*c^3*f^2 - 4*C^2*a^2*c^3*f^2 + 8*A*B
*a^2*d^3*f^2 + 8*A*C*a^2*c^3*f^2 - 8*B*C*a^2*d^3*f^2 + 12*A^2*a^2*c*d^2*f^2 - 12*B^2*a^2*c*d^2*f^2 + 12*C^2*a^
2*c*d^2*f^2 - 24*A*B*a^2*c^2*d*f^2 - 24*A*C*a^2*c*d^2*f^2 + 24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c
^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*1i + ((c + d*tan(e + f*x))^(1/2)*(16*A^2*a^2*d^10*f^3 - 16*B^2*a^2*d^10*f^
3 + 16*C^2*a^2*d^10*f^3 + 32*A^2*a^2*c^2*d^8*f^3 - 32*A^2*a^2*c^6*d^4*f^3 - 16*A^2*a^2*c^8*d^2*f^3 - 32*B^2*a^
2*c^2*d^8*f^3 + 32*B^2*a^2*c^6*d^4*f^3 + 16*B^2*a^2*c^8*d^2*f^3 + 32*C^2*a^2*c^2*d^8*f^3 - 32*C^2*a^2*c^6*d^4*
f^3 - 16*C^2*a^2*c^8*d^2*f^3 - 32*A*C*a^2*d^10*f^3 - 64*A*B*a^2*c*d^9*f^3 + 64*B*C*a^2*c*d^9*f^3 - 192*A*B*a^2
*c^3*d^7*f^3 - 192*A*B*a^2*c^5*d^5*f^3 - 64*A*B*a^2*c^7*d^3*f^3 - 64*A*C*a^2*c^2*d^8*f^3 + 64*A*C*a^2*c^6*d^4*
f^3 + 32*A*C*a^2*c^8*d^2*f^3 + 192*B*C*a^2*c^3*d^7*f^3 + 192*B*C*a^2*c^5*d^5*f^3 + 64*B*C*a^2*c^7*d^3*f^3) - (
(((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*
C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48
*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(
A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*
B^2*C*a^4))^(1/2) - 4*A^2*a^2*c^3*f^2 + 4*B^2*a^2*c^3*f^2 - 4*C^2*a^2*c^3*f^2 + 8*A*B*a^2*d^3*f^2 + 8*A*C*a^2*
c^3*f^2 - 8*B*C*a^2*d^3*f^2 + 12*A^2*a^2*c*d^2*f^2 - 12*B^2*a^2*c*d^2*f^2 + 12*C^2*a^2*c*d^2*f^2 - 24*A*B*a^2*
c^2*d*f^2 - 24*A*C*a^2*c*d^2*f^2 + 24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^
4)))^(1/2)*((c + d*tan(e + f*x))^(1/2)*((((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*
a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a
^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*
f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^
4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) - 4*A^2*a^2*c^3*f^2 + 4*B^2*a^2*c^3*f^2 - 4*C^2*a^2*
c^3*f^2 + 8*A*B*a^2*d^3*f^2 + 8*A*C*a^2*c^3*f^2 - 8*B*C*a^2*d^3*f^2 + 12*A^2*a^2*c*d^2*f^2 - 12*B^2*a^2*c*d^2*
f^2 + 12*C^2*a^2*c*d^2*f^2 - 24*A*B*a^2*c^2*d*f^2 - 24*A*C*a^2*c*d^2*f^2 + 24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4
+ d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*(64*c*d^12*f^5 + 320*c^3*d^10*f^5 + 640*c^5*d^8*f^5 + 640*c
^7*d^6*f^5 + 320*c^9*d^4*f^5 + 64*c^11*d^2*f^5) + 32*B*a*d^12*f^4 + 256*A*a*c^3*d^9*f^4 + 384*A*a*c^5*d^7*f^4
+ 256*A*a*c^7*d^5*f^4 + 64*A*a*c^9*d^3*f^4 + 96*B*a*c^2*d^10*f^4 + 64*B*a*c^4*d^8*f^4 - 64*B*a*c^6*d^6*f^4 - 9
6*B*a*c^8*d^4*f^4 - 32*B*a*c^10*d^2*f^4 - 256*C*a*c^3*d^9*f^4 - 384*C*a*c^5*d^7*f^4 - 256*C*a*c^7*d^5*f^4 - 64
*C*a*c^9*d^3*f^4 + 64*A*a*c*d^11*f^4 - 64*C*a*c*d^11*f^4))*((((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a
^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*
c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (
16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*
C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) - 4*A^2*a^2*c^3*f^2 + 4*B^2*a^2*
c^3*f^2 - 4*C^2*a^2*c^3*f^2 + 8*A*B*a^2*d^3*f^2 + 8*A*C*a^2*c^3*f^2 - 8*B*C*a^2*d^3*f^2 + 12*A^2*a^2*c*d^2*f^2
- 12*B^2*a^2*c*d^2*f^2 + 12*C^2*a^2*c*d^2*f^2 - 24*A*B*a^2*c^2*d*f^2 - 24*A*C*a^2*c*d^2*f^2 + 24*B*C*a^2*c^2*
d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*1i)/(((c + d*tan(e + f*x))^(1/2)*(16*A^
2*a^2*d^10*f^3 - 16*B^2*a^2*d^10*f^3 + 16*C^2*a^2*d^10*f^3 + 32*A^2*a^2*c^2*d^8*f^3 - 32*A^2*a^2*c^6*d^4*f^3 -
16*A^2*a^2*c^8*d^2*f^3 - 32*B^2*a^2*c^2*d^8*f^3 + 32*B^2*a^2*c^6*d^4*f^3 + 16*B^2*a^2*c^8*d^2*f^3 + 32*C^2*a^
2*c^2*d^8*f^3 - 32*C^2*a^2*c^6*d^4*f^3 - 16*C^2*a^2*c^8*d^2*f^3 - 32*A*C*a^2*d^10*f^3 - 64*A*B*a^2*c*d^9*f^3 +
64*B*C*a^2*c*d^9*f^3 - 192*A*B*a^2*c^3*d^7*f^3 - 192*A*B*a^2*c^5*d^5*f^3 - 64*A*B*a^2*c^7*d^3*f^3 - 64*A*C*a^
2*c^2*d^8*f^3 + 64*A*C*a^2*c^6*d^4*f^3 + 32*A*C*a^2*c^8*d^2*f^3 + 192*B*C*a^2*c^3*d^7*f^3 + 192*B*C*a^2*c^5*d^
5*f^3 + 64*B*C*a^2*c^7*d^3*f^3) - ((((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d
^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*
d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 +
48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6
*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) - 4*A^2*a^2*c^3*f^2 + 4*B^2*a^2*c^3*f^2 - 4*C^2*a^2*c^3*f
^2 + 8*A*B*a^2*d^3*f^2 + 8*A*C*a^2*c^3*f^2 - 8*B*C*a^2*d^3*f^2 + 12*A^2*a^2*c*d^2*f^2 - 12*B^2*a^2*c*d^2*f^2 +
12*C^2*a^2*c*d^2*f^2 - 24*A*B*a^2*c^2*d*f^2 - 24*A*C*a^2*c*d^2*f^2 + 24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6
*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*((c + d*tan(e + f*x))^(1/2)*((((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^
3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^
2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2
*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C
^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) - 4*A^2*a^2*c^3*f
^2 + 4*B^2*a^2*c^3*f^2 - 4*C^2*a^2*c^3*f^2 + 8*A*B*a^2*d^3*f^2 + 8*A*C*a^2*c^3*f^2 - 8*B*C*a^2*d^3*f^2 + 12*A^
2*a^2*c*d^2*f^2 - 12*B^2*a^2*c*d^2*f^2 + 12*C^2*a^2*c*d^2*f^2 - 24*A*B*a^2*c^2*d*f^2 - 24*A*C*a^2*c*d^2*f^2 +
24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*(64*c*d^12*f^5 + 320*c^3
*d^10*f^5 + 640*c^5*d^8*f^5 + 640*c^7*d^6*f^5 + 320*c^9*d^4*f^5 + 64*c^11*d^2*f^5) - 32*B*a*d^12*f^4 - 256*A*a
*c^3*d^9*f^4 - 384*A*a*c^5*d^7*f^4 - 256*A*a*c^7*d^5*f^4 - 64*A*a*c^9*d^3*f^4 - 96*B*a*c^2*d^10*f^4 - 64*B*a*c
^4*d^8*f^4 + 64*B*a*c^6*d^6*f^4 + 96*B*a*c^8*d^4*f^4 + 32*B*a*c^10*d^2*f^4 + 256*C*a*c^3*d^9*f^4 + 384*C*a*c^5
*d^7*f^4 + 256*C*a*c^7*d^5*f^4 + 64*C*a*c^9*d^3*f^4 - 64*A*a*c*d^11*f^4 + 64*C*a*c*d^11*f^4))*((((8*A^2*a^2*c^
3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 -
24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*
f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a
^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/
2) - 4*A^2*a^2*c^3*f^2 + 4*B^2*a^2*c^3*f^2 - 4*C^2*a^2*c^3*f^2 + 8*A*B*a^2*d^3*f^2 + 8*A*C*a^2*c^3*f^2 - 8*B*C
*a^2*d^3*f^2 + 12*A^2*a^2*c*d^2*f^2 - 12*B^2*a^2*c*d^2*f^2 + 12*C^2*a^2*c*d^2*f^2 - 24*A*B*a^2*c^2*d*f^2 - 24*
A*C*a^2*c*d^2*f^2 + 24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2) - ((
c + d*tan(e + f*x))^(1/2)*(16*A^2*a^2*d^10*f^3 - 16*B^2*a^2*d^10*f^3 + 16*C^2*a^2*d^10*f^3 + 32*A^2*a^2*c^2*d^
8*f^3 - 32*A^2*a^2*c^6*d^4*f^3 - 16*A^2*a^2*c^8*d^2*f^3 - 32*B^2*a^2*c^2*d^8*f^3 + 32*B^2*a^2*c^6*d^4*f^3 + 16
*B^2*a^2*c^8*d^2*f^3 + 32*C^2*a^2*c^2*d^8*f^3 - 32*C^2*a^2*c^6*d^4*f^3 - 16*C^2*a^2*c^8*d^2*f^3 - 32*A*C*a^2*d
^10*f^3 - 64*A*B*a^2*c*d^9*f^3 + 64*B*C*a^2*c*d^9*f^3 - 192*A*B*a^2*c^3*d^7*f^3 - 192*A*B*a^2*c^5*d^5*f^3 - 64
*A*B*a^2*c^7*d^3*f^3 - 64*A*C*a^2*c^2*d^8*f^3 + 64*A*C*a^2*c^6*d^4*f^3 + 32*A*C*a^2*c^8*d^2*f^3 + 192*B*C*a^2*
c^3*d^7*f^3 + 192*B*C*a^2*c^5*d^5*f^3 + 64*B*C*a^2*c^7*d^3*f^3) - ((((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 +
8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B
^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^
2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 -
4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) - 4*A^2*a^2*c^3*f^2 + 4*B
^2*a^2*c^3*f^2 - 4*C^2*a^2*c^3*f^2 + 8*A*B*a^2*d^3*f^2 + 8*A*C*a^2*c^3*f^2 - 8*B*C*a^2*d^3*f^2 + 12*A^2*a^2*c*
d^2*f^2 - 12*B^2*a^2*c*d^2*f^2 + 12*C^2*a^2*c*d^2*f^2 - 24*A*B*a^2*c^2*d*f^2 - 24*A*C*a^2*c*d^2*f^2 + 24*B*C*a
^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*((c + d*tan(e + f*x))^(1/2)*((((
8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a
^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*
C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4
*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2
*C*a^4))^(1/2) - 4*A^2*a^2*c^3*f^2 + 4*B^2*a^2*c^3*f^2 - 4*C^2*a^2*c^3*f^2 + 8*A*B*a^2*d^3*f^2 + 8*A*C*a^2*c^3
*f^2 - 8*B*C*a^2*d^3*f^2 + 12*A^2*a^2*c*d^2*f^2 - 12*B^2*a^2*c*d^2*f^2 + 12*C^2*a^2*c*d^2*f^2 - 24*A*B*a^2*c^2
*d*f^2 - 24*A*C*a^2*c*d^2*f^2 + 24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4))
)^(1/2)*(64*c*d^12*f^5 + 320*c^3*d^10*f^5 + 640*c^5*d^8*f^5 + 640*c^7*d^6*f^5 + 320*c^9*d^4*f^5 + 64*c^11*d^2*
f^5) + 32*B*a*d^12*f^4 + 256*A*a*c^3*d^9*f^4 + 384*A*a*c^5*d^7*f^4 + 256*A*a*c^7*d^5*f^4 + 64*A*a*c^9*d^3*f^4
+ 96*B*a*c^2*d^10*f^4 + 64*B*a*c^4*d^8*f^4 - 64*B*a*c^6*d^6*f^4 - 96*B*a*c^8*d^4*f^4 - 32*B*a*c^10*d^2*f^4 - 2
56*C*a*c^3*d^9*f^4 - 384*C*a*c^5*d^7*f^4 - 256*C*a*c^7*d^5*f^4 - 64*C*a*c^9*d^3*f^4 + 64*A*a*c*d^11*f^4 - 64*C
*a*c*d^11*f^4))*((((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^
2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a
^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 +
48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B
^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) - 4*A^2*a^2*c^3*f^2 + 4*B^2*a^2*c^3*f^2 - 4*C^2*a^2*c^3*f^2 + 8*A*B*a^2*d^3
*f^2 + 8*A*C*a^2*c^3*f^2 - 8*B*C*a^2*d^3*f^2 + 12*A^2*a^2*c*d^2*f^2 - 12*B^2*a^2*c*d^2*f^2 + 12*C^2*a^2*c*d^2*
f^2 - 24*A*B*a^2*c^2*d*f^2 - 24*A*C*a^2*c*d^2*f^2 + 24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f
^4 + 3*c^4*d^2*f^4)))^(1/2) - 16*A^3*a^3*d^9*f^2 + 16*C^3*a^3*d^9*f^2 - 48*A^3*a^3*c^2*d^7*f^2 - 48*A^3*a^3*c^
4*d^5*f^2 - 16*A^3*a^3*c^6*d^3*f^2 + 48*B^3*a^3*c^3*d^6*f^2 + 48*B^3*a^3*c^5*d^4*f^2 + 16*B^3*a^3*c^7*d^2*f^2
+ 48*C^3*a^3*c^2*d^7*f^2 + 48*C^3*a^3*c^4*d^5*f^2 + 16*C^3*a^3*c^6*d^3*f^2 - 16*A*B^2*a^3*d^9*f^2 - 48*A*C^2*a
^3*d^9*f^2 + 48*A^2*C*a^3*d^9*f^2 + 16*B^2*C*a^3*d^9*f^2 + 16*B^3*a^3*c*d^8*f^2 - 48*A*B^2*a^3*c^2*d^7*f^2 - 4
8*A*B^2*a^3*c^4*d^5*f^2 - 16*A*B^2*a^3*c^6*d^3*f^2 + 48*A^2*B*a^3*c^3*d^6*f^2 + 48*A^2*B*a^3*c^5*d^4*f^2 + 16*
A^2*B*a^3*c^7*d^2*f^2 - 144*A*C^2*a^3*c^2*d^7*f^2 - 144*A*C^2*a^3*c^4*d^5*f^2 - 48*A*C^2*a^3*c^6*d^3*f^2 + 144
*A^2*C*a^3*c^2*d^7*f^2 + 144*A^2*C*a^3*c^4*d^5*f^2 + 48*A^2*C*a^3*c^6*d^3*f^2 + 48*B*C^2*a^3*c^3*d^6*f^2 + 48*
B*C^2*a^3*c^5*d^4*f^2 + 16*B*C^2*a^3*c^7*d^2*f^2 + 48*B^2*C*a^3*c^2*d^7*f^2 + 48*B^2*C*a^3*c^4*d^5*f^2 + 16*B^
2*C*a^3*c^6*d^3*f^2 + 16*A^2*B*a^3*c*d^8*f^2 + 16*B*C^2*a^3*c*d^8*f^2 - 96*A*B*C*a^3*c^3*d^6*f^2 - 96*A*B*C*a^
3*c^5*d^4*f^2 - 32*A*B*C*a^3*c^7*d^2*f^2 - 32*A*B*C*a^3*c*d^8*f^2))*((((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2
+ 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24
*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2
)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4
- 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) - 4*A^2*a^2*c^3*f^2 + 4
*B^2*a^2*c^3*f^2 - 4*C^2*a^2*c^3*f^2 + 8*A*B*a^2*d^3*f^2 + 8*A*C*a^2*c^3*f^2 - 8*B*C*a^2*d^3*f^2 + 12*A^2*a^2*
c*d^2*f^2 - 12*B^2*a^2*c*d^2*f^2 + 12*C^2*a^2*c*d^2*f^2 - 24*A*B*a^2*c^2*d*f^2 - 24*A*C*a^2*c*d^2*f^2 + 24*B*C
*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*2i - atan(((((((8*A^2*b^2*c^3*
f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 2
4*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^
2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4
+ C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2)
+ 4*A^2*b^2*c^3*f^2 - 4*B^2*b^2*c^3*f^2 + 4*C^2*b^2*c^3*f^2 - 8*A*B*b^2*d^3*f^2 - 8*A*C*b^2*c^3*f^2 + 8*B*C*b
^2*d^3*f^2 - 12*A^2*b^2*c*d^2*f^2 + 12*B^2*b^2*c*d^2*f^2 - 12*C^2*b^2*c*d^2*f^2 + 24*A*B*b^2*c^2*d*f^2 + 24*A*
C*b^2*c*d^2*f^2 - 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*((c +
d*tan(e + f*x))^(1/2)*((((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*
A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48
*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*
f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4
+ 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) + 4*A^2*b^2*c^3*f^2 - 4*B^2*b^2*c^3*f^2 + 4*C^2*b^2*c^3*f^2 - 8*A*B*b
^2*d^3*f^2 - 8*A*C*b^2*c^3*f^2 + 8*B*C*b^2*d^3*f^2 - 12*A^2*b^2*c*d^2*f^2 + 12*B^2*b^2*c*d^2*f^2 - 12*C^2*b^2*
c*d^2*f^2 + 24*A*B*b^2*c^2*d*f^2 + 24*A*C*b^2*c*d^2*f^2 - 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2
*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*(64*c*d^12*f^5 + 320*c^3*d^10*f^5 + 640*c^5*d^8*f^5 + 640*c^7*d^6*f^5 + 320*
c^9*d^4*f^5 + 64*c^11*d^2*f^5) - 32*A*b*d^12*f^4 + 32*C*b*d^12*f^4 - 96*A*b*c^2*d^10*f^4 - 64*A*b*c^4*d^8*f^4
+ 64*A*b*c^6*d^6*f^4 + 96*A*b*c^8*d^4*f^4 + 32*A*b*c^10*d^2*f^4 + 256*B*b*c^3*d^9*f^4 + 384*B*b*c^5*d^7*f^4 +
256*B*b*c^7*d^5*f^4 + 64*B*b*c^9*d^3*f^4 + 96*C*b*c^2*d^10*f^4 + 64*C*b*c^4*d^8*f^4 - 64*C*b*c^6*d^6*f^4 - 96*
C*b*c^8*d^4*f^4 - 32*C*b*c^10*d^2*f^4 + 64*B*b*c*d^11*f^4) + (c + d*tan(e + f*x))^(1/2)*(16*A^2*b^2*d^10*f^3 -
16*B^2*b^2*d^10*f^3 + 16*C^2*b^2*d^10*f^3 + 32*A^2*b^2*c^2*d^8*f^3 - 32*A^2*b^2*c^6*d^4*f^3 - 16*A^2*b^2*c^8*
d^2*f^3 - 32*B^2*b^2*c^2*d^8*f^3 + 32*B^2*b^2*c^6*d^4*f^3 + 16*B^2*b^2*c^8*d^2*f^3 + 32*C^2*b^2*c^2*d^8*f^3 -
32*C^2*b^2*c^6*d^4*f^3 - 16*C^2*b^2*c^8*d^2*f^3 - 32*A*C*b^2*d^10*f^3 - 64*A*B*b^2*c*d^9*f^3 + 64*B*C*b^2*c*d^
9*f^3 - 192*A*B*b^2*c^3*d^7*f^3 - 192*A*B*b^2*c^5*d^5*f^3 - 64*A*B*b^2*c^7*d^3*f^3 - 64*A*C*b^2*c^2*d^8*f^3 +
64*A*C*b^2*c^6*d^4*f^3 + 32*A*C*b^2*c^8*d^2*f^3 + 192*B*C*b^2*c^3*d^7*f^3 + 192*B*C*b^2*c^5*d^5*f^3 + 64*B*C*b
^2*c^7*d^3*f^3))*((((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b
^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*
b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 +
48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*
B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) + 4*A^2*b^2*c^3*f^2 - 4*B^2*b^2*c^3*f^2 + 4*C^2*b^2*c^3*f^2 - 8*A*B*b^2*d^
3*f^2 - 8*A*C*b^2*c^3*f^2 + 8*B*C*b^2*d^3*f^2 - 12*A^2*b^2*c*d^2*f^2 + 12*B^2*b^2*c*d^2*f^2 - 12*C^2*b^2*c*d^2
*f^2 + 24*A*B*b^2*c^2*d*f^2 + 24*A*C*b^2*c*d^2*f^2 - 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*
f^4 + 3*c^4*d^2*f^4)))^(1/2)*1i - (((((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*
d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c
*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4
+ 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 +
6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) + 4*A^2*b^2*c^3*f^2 - 4*B^2*b^2*c^3*f^2 + 4*C^2*b^2*c^3*
f^2 - 8*A*B*b^2*d^3*f^2 - 8*A*C*b^2*c^3*f^2 + 8*B*C*b^2*d^3*f^2 - 12*A^2*b^2*c*d^2*f^2 + 12*B^2*b^2*c*d^2*f^2
- 12*C^2*b^2*c*d^2*f^2 + 24*A*B*b^2*c^2*d*f^2 + 24*A*C*b^2*c*d^2*f^2 - 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^
6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*(32*C*b*d^12*f^4 - 32*A*b*d^12*f^4 - (c + d*tan(e + f*x))^(1/2)
*((((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*
B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 +
48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)
*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*
A*B^2*C*b^4))^(1/2) + 4*A^2*b^2*c^3*f^2 - 4*B^2*b^2*c^3*f^2 + 4*C^2*b^2*c^3*f^2 - 8*A*B*b^2*d^3*f^2 - 8*A*C*b^
2*c^3*f^2 + 8*B*C*b^2*d^3*f^2 - 12*A^2*b^2*c*d^2*f^2 + 12*B^2*b^2*c*d^2*f^2 - 12*C^2*b^2*c*d^2*f^2 + 24*A*B*b^
2*c^2*d*f^2 + 24*A*C*b^2*c*d^2*f^2 - 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*
f^4)))^(1/2)*(64*c*d^12*f^5 + 320*c^3*d^10*f^5 + 640*c^5*d^8*f^5 + 640*c^7*d^6*f^5 + 320*c^9*d^4*f^5 + 64*c^11
*d^2*f^5) - 96*A*b*c^2*d^10*f^4 - 64*A*b*c^4*d^8*f^4 + 64*A*b*c^6*d^6*f^4 + 96*A*b*c^8*d^4*f^4 + 32*A*b*c^10*d
^2*f^4 + 256*B*b*c^3*d^9*f^4 + 384*B*b*c^5*d^7*f^4 + 256*B*b*c^7*d^5*f^4 + 64*B*b*c^9*d^3*f^4 + 96*C*b*c^2*d^1
0*f^4 + 64*C*b*c^4*d^8*f^4 - 64*C*b*c^6*d^6*f^4 - 96*C*b*c^8*d^4*f^4 - 32*C*b*c^10*d^2*f^4 + 64*B*b*c*d^11*f^4
) - (c + d*tan(e + f*x))^(1/2)*(16*A^2*b^2*d^10*f^3 - 16*B^2*b^2*d^10*f^3 + 16*C^2*b^2*d^10*f^3 + 32*A^2*b^2*c
^2*d^8*f^3 - 32*A^2*b^2*c^6*d^4*f^3 - 16*A^2*b^2*c^8*d^2*f^3 - 32*B^2*b^2*c^2*d^8*f^3 + 32*B^2*b^2*c^6*d^4*f^3
+ 16*B^2*b^2*c^8*d^2*f^3 + 32*C^2*b^2*c^2*d^8*f^3 - 32*C^2*b^2*c^6*d^4*f^3 - 16*C^2*b^2*c^8*d^2*f^3 - 32*A*C*
b^2*d^10*f^3 - 64*A*B*b^2*c*d^9*f^3 + 64*B*C*b^2*c*d^9*f^3 - 192*A*B*b^2*c^3*d^7*f^3 - 192*A*B*b^2*c^5*d^5*f^3
- 64*A*B*b^2*c^7*d^3*f^3 - 64*A*C*b^2*c^2*d^8*f^3 + 64*A*C*b^2*c^6*d^4*f^3 + 32*A*C*b^2*c^8*d^2*f^3 + 192*B*C
*b^2*c^3*d^7*f^3 + 192*B*C*b^2*c^5*d^5*f^3 + 64*B*C*b^2*c^7*d^3*f^3))*((((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^
2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 +
24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f
^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b
^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) + 4*A^2*b^2*c^3*f^2 -
4*B^2*b^2*c^3*f^2 + 4*C^2*b^2*c^3*f^2 - 8*A*B*b^2*d^3*f^2 - 8*A*C*b^2*c^3*f^2 + 8*B*C*b^2*d^3*f^2 - 12*A^2*b^
2*c*d^2*f^2 + 12*B^2*b^2*c*d^2*f^2 - 12*C^2*b^2*c*d^2*f^2 + 24*A*B*b^2*c^2*d*f^2 + 24*A*C*b^2*c*d^2*f^2 - 24*B
*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*1i)/(16*B^3*b^3*d^9*f^2 - ((
(((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*
C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48
*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(
A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*
B^2*C*b^4))^(1/2) + 4*A^2*b^2*c^3*f^2 - 4*B^2*b^2*c^3*f^2 + 4*C^2*b^2*c^3*f^2 - 8*A*B*b^2*d^3*f^2 - 8*A*C*b^2*
c^3*f^2 + 8*B*C*b^2*d^3*f^2 - 12*A^2*b^2*c*d^2*f^2 + 12*B^2*b^2*c*d^2*f^2 - 12*C^2*b^2*c*d^2*f^2 + 24*A*B*b^2*
c^2*d*f^2 + 24*A*C*b^2*c*d^2*f^2 - 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^
4)))^(1/2)*(32*C*b*d^12*f^4 - 32*A*b*d^12*f^4 - (c + d*tan(e + f*x))^(1/2)*((((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c
^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f
^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^
2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*
C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) + 4*A^2*b^2*c^3*
f^2 - 4*B^2*b^2*c^3*f^2 + 4*C^2*b^2*c^3*f^2 - 8*A*B*b^2*d^3*f^2 - 8*A*C*b^2*c^3*f^2 + 8*B*C*b^2*d^3*f^2 - 12*A
^2*b^2*c*d^2*f^2 + 12*B^2*b^2*c*d^2*f^2 - 12*C^2*b^2*c*d^2*f^2 + 24*A*B*b^2*c^2*d*f^2 + 24*A*C*b^2*c*d^2*f^2 -
24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*(64*c*d^12*f^5 + 320*c^
3*d^10*f^5 + 640*c^5*d^8*f^5 + 640*c^7*d^6*f^5 + 320*c^9*d^4*f^5 + 64*c^11*d^2*f^5) - 96*A*b*c^2*d^10*f^4 - 64
*A*b*c^4*d^8*f^4 + 64*A*b*c^6*d^6*f^4 + 96*A*b*c^8*d^4*f^4 + 32*A*b*c^10*d^2*f^4 + 256*B*b*c^3*d^9*f^4 + 384*B
*b*c^5*d^7*f^4 + 256*B*b*c^7*d^5*f^4 + 64*B*b*c^9*d^3*f^4 + 96*C*b*c^2*d^10*f^4 + 64*C*b*c^4*d^8*f^4 - 64*C*b*
c^6*d^6*f^4 - 96*C*b*c^8*d^4*f^4 - 32*C*b*c^10*d^2*f^4 + 64*B*b*c*d^11*f^4) - (c + d*tan(e + f*x))^(1/2)*(16*A
^2*b^2*d^10*f^3 - 16*B^2*b^2*d^10*f^3 + 16*C^2*b^2*d^10*f^3 + 32*A^2*b^2*c^2*d^8*f^3 - 32*A^2*b^2*c^6*d^4*f^3
- 16*A^2*b^2*c^8*d^2*f^3 - 32*B^2*b^2*c^2*d^8*f^3 + 32*B^2*b^2*c^6*d^4*f^3 + 16*B^2*b^2*c^8*d^2*f^3 + 32*C^2*b
^2*c^2*d^8*f^3 - 32*C^2*b^2*c^6*d^4*f^3 - 16*C^2*b^2*c^8*d^2*f^3 - 32*A*C*b^2*d^10*f^3 - 64*A*B*b^2*c*d^9*f^3
+ 64*B*C*b^2*c*d^9*f^3 - 192*A*B*b^2*c^3*d^7*f^3 - 192*A*B*b^2*c^5*d^5*f^3 - 64*A*B*b^2*c^7*d^3*f^3 - 64*A*C*b
^2*c^2*d^8*f^3 + 64*A*C*b^2*c^6*d^4*f^3 + 32*A*C*b^2*c^8*d^2*f^3 + 192*B*C*b^2*c^3*d^7*f^3 + 192*B*C*b^2*c^5*d
^5*f^3 + 64*B*C*b^2*c^7*d^3*f^3))*((((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d
^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*
d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 +
48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6
*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) + 4*A^2*b^2*c^3*f^2 - 4*B^2*b^2*c^3*f^2 + 4*C^2*b^2*c^3*f
^2 - 8*A*B*b^2*d^3*f^2 - 8*A*C*b^2*c^3*f^2 + 8*B*C*b^2*d^3*f^2 - 12*A^2*b^2*c*d^2*f^2 + 12*B^2*b^2*c*d^2*f^2 -
12*C^2*b^2*c*d^2*f^2 + 24*A*B*b^2*c^2*d*f^2 + 24*A*C*b^2*c*d^2*f^2 - 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6
*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2) - (((((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2
- 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2
- 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4
+ 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*
A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) + 4*A^2*b^2*c^3*f^2 - 4*B^2*b^2*c^3*f^2 +
4*C^2*b^2*c^3*f^2 - 8*A*B*b^2*d^3*f^2 - 8*A*C*b^2*c^3*f^2 + 8*B*C*b^2*d^3*f^2 - 12*A^2*b^2*c*d^2*f^2 + 12*B^2*
b^2*c*d^2*f^2 - 12*C^2*b^2*c*d^2*f^2 + 24*A*B*b^2*c^2*d*f^2 + 24*A*C*b^2*c*d^2*f^2 - 24*B*C*b^2*c^2*d*f^2)/(16
*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*((c + d*tan(e + f*x))^(1/2)*((((8*A^2*b^2*c^3*f^2
- 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A
^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 -
48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 +
C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) +
4*A^2*b^2*c^3*f^2 - 4*B^2*b^2*c^3*f^2 + 4*C^2*b^2*c^3*f^2 - 8*A*B*b^2*d^3*f^2 - 8*A*C*b^2*c^3*f^2 + 8*B*C*b^2*
d^3*f^2 - 12*A^2*b^2*c*d^2*f^2 + 12*B^2*b^2*c*d^2*f^2 - 12*C^2*b^2*c*d^2*f^2 + 24*A*B*b^2*c^2*d*f^2 + 24*A*C*b
^2*c*d^2*f^2 - 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*(64*c*d^1
2*f^5 + 320*c^3*d^10*f^5 + 640*c^5*d^8*f^5 + 640*c^7*d^6*f^5 + 320*c^9*d^4*f^5 + 64*c^11*d^2*f^5) - 32*A*b*d^1
2*f^4 + 32*C*b*d^12*f^4 - 96*A*b*c^2*d^10*f^4 - 64*A*b*c^4*d^8*f^4 + 64*A*b*c^6*d^6*f^4 + 96*A*b*c^8*d^4*f^4 +
32*A*b*c^10*d^2*f^4 + 256*B*b*c^3*d^9*f^4 + 384*B*b*c^5*d^7*f^4 + 256*B*b*c^7*d^5*f^4 + 64*B*b*c^9*d^3*f^4 +
96*C*b*c^2*d^10*f^4 + 64*C*b*c^4*d^8*f^4 - 64*C*b*c^6*d^6*f^4 - 96*C*b*c^8*d^4*f^4 - 32*C*b*c^10*d^2*f^4 + 64*
B*b*c*d^11*f^4) + (c + d*tan(e + f*x))^(1/2)*(16*A^2*b^2*d^10*f^3 - 16*B^2*b^2*d^10*f^3 + 16*C^2*b^2*d^10*f^3
+ 32*A^2*b^2*c^2*d^8*f^3 - 32*A^2*b^2*c^6*d^4*f^3 - 16*A^2*b^2*c^8*d^2*f^3 - 32*B^2*b^2*c^2*d^8*f^3 + 32*B^2*b
^2*c^6*d^4*f^3 + 16*B^2*b^2*c^8*d^2*f^3 + 32*C^2*b^2*c^2*d^8*f^3 - 32*C^2*b^2*c^6*d^4*f^3 - 16*C^2*b^2*c^8*d^2
*f^3 - 32*A*C*b^2*d^10*f^3 - 64*A*B*b^2*c*d^9*f^3 + 64*B*C*b^2*c*d^9*f^3 - 192*A*B*b^2*c^3*d^7*f^3 - 192*A*B*b
^2*c^5*d^5*f^3 - 64*A*B*b^2*c^7*d^3*f^3 - 64*A*C*b^2*c^2*d^8*f^3 + 64*A*C*b^2*c^6*d^4*f^3 + 32*A*C*b^2*c^8*d^2
*f^3 + 192*B*C*b^2*c^3*d^7*f^3 + 192*B*C*b^2*c^5*d^5*f^3 + 64*B*C*b^2*c^7*d^3*f^3))*((((8*A^2*b^2*c^3*f^2 - 8*
B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^
2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B
*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b
^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) + 4*A^2
*b^2*c^3*f^2 - 4*B^2*b^2*c^3*f^2 + 4*C^2*b^2*c^3*f^2 - 8*A*B*b^2*d^3*f^2 - 8*A*C*b^2*c^3*f^2 + 8*B*C*b^2*d^3*f
^2 - 12*A^2*b^2*c*d^2*f^2 + 12*B^2*b^2*c*d^2*f^2 - 12*C^2*b^2*c*d^2*f^2 + 24*A*B*b^2*c^2*d*f^2 + 24*A*C*b^2*c*
d^2*f^2 - 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2) + 48*A^3*b^3*c
^3*d^6*f^2 + 48*A^3*b^3*c^5*d^4*f^2 + 16*A^3*b^3*c^7*d^2*f^2 + 48*B^3*b^3*c^2*d^7*f^2 + 48*B^3*b^3*c^4*d^5*f^2
+ 16*B^3*b^3*c^6*d^3*f^2 - 48*C^3*b^3*c^3*d^6*f^2 - 48*C^3*b^3*c^5*d^4*f^2 - 16*C^3*b^3*c^7*d^2*f^2 + 16*A^2*
B*b^3*d^9*f^2 + 16*B*C^2*b^3*d^9*f^2 + 16*A^3*b^3*c*d^8*f^2 - 16*C^3*b^3*c*d^8*f^2 + 48*A*B^2*b^3*c^3*d^6*f^2
+ 48*A*B^2*b^3*c^5*d^4*f^2 + 16*A*B^2*b^3*c^7*d^2*f^2 + 48*A^2*B*b^3*c^2*d^7*f^2 + 48*A^2*B*b^3*c^4*d^5*f^2 +
16*A^2*B*b^3*c^6*d^3*f^2 + 144*A*C^2*b^3*c^3*d^6*f^2 + 144*A*C^2*b^3*c^5*d^4*f^2 + 48*A*C^2*b^3*c^7*d^2*f^2 -
144*A^2*C*b^3*c^3*d^6*f^2 - 144*A^2*C*b^3*c^5*d^4*f^2 - 48*A^2*C*b^3*c^7*d^2*f^2 + 48*B*C^2*b^3*c^2*d^7*f^2 +
48*B*C^2*b^3*c^4*d^5*f^2 + 16*B*C^2*b^3*c^6*d^3*f^2 - 48*B^2*C*b^3*c^3*d^6*f^2 - 48*B^2*C*b^3*c^5*d^4*f^2 - 16
*B^2*C*b^3*c^7*d^2*f^2 - 32*A*B*C*b^3*d^9*f^2 + 16*A*B^2*b^3*c*d^8*f^2 + 48*A*C^2*b^3*c*d^8*f^2 - 48*A^2*C*b^3
*c*d^8*f^2 - 16*B^2*C*b^3*c*d^8*f^2 - 96*A*B*C*b^3*c^2*d^7*f^2 - 96*A*B*C*b^3*c^4*d^5*f^2 - 32*A*B*C*b^3*c^6*d
^3*f^2))*((((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f
^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*
d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*
d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*
b^4 - 4*A*B^2*C*b^4))^(1/2) + 4*A^2*b^2*c^3*f^2 - 4*B^2*b^2*c^3*f^2 + 4*C^2*b^2*c^3*f^2 - 8*A*B*b^2*d^3*f^2 -
8*A*C*b^2*c^3*f^2 + 8*B*C*b^2*d^3*f^2 - 12*A^2*b^2*c*d^2*f^2 + 12*B^2*b^2*c*d^2*f^2 - 12*C^2*b^2*c*d^2*f^2 + 2
4*A*B*b^2*c^2*d*f^2 + 24*A*C*b^2*c*d^2*f^2 - 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*
c^4*d^2*f^4)))^(1/2)*2i - atan((((-(((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d
^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*
d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 +
48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6
*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) - 4*A^2*b^2*c^3*f^2 + 4*B^2*b^2*c^3*f^2 - 4*C^2*b^2*c^3*f
^2 + 8*A*B*b^2*d^3*f^2 + 8*A*C*b^2*c^3*f^2 - 8*B*C*b^2*d^3*f^2 + 12*A^2*b^2*c*d^2*f^2 - 12*B^2*b^2*c*d^2*f^2 +
12*C^2*b^2*c*d^2*f^2 - 24*A*B*b^2*c^2*d*f^2 - 24*A*C*b^2*c*d^2*f^2 + 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6
*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*((c + d*tan(e + f*x))^(1/2)*(-(((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c
^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f
^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^
2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*
C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) - 4*A^2*b^2*c^3*
f^2 + 4*B^2*b^2*c^3*f^2 - 4*C^2*b^2*c^3*f^2 + 8*A*B*b^2*d^3*f^2 + 8*A*C*b^2*c^3*f^2 - 8*B*C*b^2*d^3*f^2 + 12*A
^2*b^2*c*d^2*f^2 - 12*B^2*b^2*c*d^2*f^2 + 12*C^2*b^2*c*d^2*f^2 - 24*A*B*b^2*c^2*d*f^2 - 24*A*C*b^2*c*d^2*f^2 +
24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*(64*c*d^12*f^5 + 320*c^
3*d^10*f^5 + 640*c^5*d^8*f^5 + 640*c^7*d^6*f^5 + 320*c^9*d^4*f^5 + 64*c^11*d^2*f^5) - 32*A*b*d^12*f^4 + 32*C*b
*d^12*f^4 - 96*A*b*c^2*d^10*f^4 - 64*A*b*c^4*d^8*f^4 + 64*A*b*c^6*d^6*f^4 + 96*A*b*c^8*d^4*f^4 + 32*A*b*c^10*d
^2*f^4 + 256*B*b*c^3*d^9*f^4 + 384*B*b*c^5*d^7*f^4 + 256*B*b*c^7*d^5*f^4 + 64*B*b*c^9*d^3*f^4 + 96*C*b*c^2*d^1
0*f^4 + 64*C*b*c^4*d^8*f^4 - 64*C*b*c^6*d^6*f^4 - 96*C*b*c^8*d^4*f^4 - 32*C*b*c^10*d^2*f^4 + 64*B*b*c*d^11*f^4
) + (c + d*tan(e + f*x))^(1/2)*(16*A^2*b^2*d^10*f^3 - 16*B^2*b^2*d^10*f^3 + 16*C^2*b^2*d^10*f^3 + 32*A^2*b^2*c
^2*d^8*f^3 - 32*A^2*b^2*c^6*d^4*f^3 - 16*A^2*b^2*c^8*d^2*f^3 - 32*B^2*b^2*c^2*d^8*f^3 + 32*B^2*b^2*c^6*d^4*f^3
+ 16*B^2*b^2*c^8*d^2*f^3 + 32*C^2*b^2*c^2*d^8*f^3 - 32*C^2*b^2*c^6*d^4*f^3 - 16*C^2*b^2*c^8*d^2*f^3 - 32*A*C*
b^2*d^10*f^3 - 64*A*B*b^2*c*d^9*f^3 + 64*B*C*b^2*c*d^9*f^3 - 192*A*B*b^2*c^3*d^7*f^3 - 192*A*B*b^2*c^5*d^5*f^3
- 64*A*B*b^2*c^7*d^3*f^3 - 64*A*C*b^2*c^2*d^8*f^3 + 64*A*C*b^2*c^6*d^4*f^3 + 32*A*C*b^2*c^8*d^2*f^3 + 192*B*C
*b^2*c^3*d^7*f^3 + 192*B*C*b^2*c^5*d^5*f^3 + 64*B*C*b^2*c^7*d^3*f^3))*(-(((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f
^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 +
24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*
f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*
b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) - 4*A^2*b^2*c^3*f^2
+ 4*B^2*b^2*c^3*f^2 - 4*C^2*b^2*c^3*f^2 + 8*A*B*b^2*d^3*f^2 + 8*A*C*b^2*c^3*f^2 - 8*B*C*b^2*d^3*f^2 + 12*A^2*b
^2*c*d^2*f^2 - 12*B^2*b^2*c*d^2*f^2 + 12*C^2*b^2*c*d^2*f^2 - 24*A*B*b^2*c^2*d*f^2 - 24*A*C*b^2*c*d^2*f^2 + 24*
B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*1i - ((-(((8*A^2*b^2*c^3*f^
2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*
A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2
- 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 +
C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) -
4*A^2*b^2*c^3*f^2 + 4*B^2*b^2*c^3*f^2 - 4*C^2*b^2*c^3*f^2 + 8*A*B*b^2*d^3*f^2 + 8*A*C*b^2*c^3*f^2 - 8*B*C*b^2
*d^3*f^2 + 12*A^2*b^2*c*d^2*f^2 - 12*B^2*b^2*c*d^2*f^2 + 12*C^2*b^2*c*d^2*f^2 - 24*A*B*b^2*c^2*d*f^2 - 24*A*C*
b^2*c*d^2*f^2 + 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*(32*C*b*
d^12*f^4 - 32*A*b*d^12*f^4 - (c + d*tan(e + f*x))^(1/2)*(-(((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2
*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*
d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16
*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*
b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) - 4*A^2*b^2*c^3*f^2 + 4*B^2*b^2*c^
3*f^2 - 4*C^2*b^2*c^3*f^2 + 8*A*B*b^2*d^3*f^2 + 8*A*C*b^2*c^3*f^2 - 8*B*C*b^2*d^3*f^2 + 12*A^2*b^2*c*d^2*f^2 -
12*B^2*b^2*c*d^2*f^2 + 12*C^2*b^2*c*d^2*f^2 - 24*A*B*b^2*c^2*d*f^2 - 24*A*C*b^2*c*d^2*f^2 + 24*B*C*b^2*c^2*d*
f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*(64*c*d^12*f^5 + 320*c^3*d^10*f^5 + 640*c
^5*d^8*f^5 + 640*c^7*d^6*f^5 + 320*c^9*d^4*f^5 + 64*c^11*d^2*f^5) - 96*A*b*c^2*d^10*f^4 - 64*A*b*c^4*d^8*f^4 +
64*A*b*c^6*d^6*f^4 + 96*A*b*c^8*d^4*f^4 + 32*A*b*c^10*d^2*f^4 + 256*B*b*c^3*d^9*f^4 + 384*B*b*c^5*d^7*f^4 + 2
56*B*b*c^7*d^5*f^4 + 64*B*b*c^9*d^3*f^4 + 96*C*b*c^2*d^10*f^4 + 64*C*b*c^4*d^8*f^4 - 64*C*b*c^6*d^6*f^4 - 96*C
*b*c^8*d^4*f^4 - 32*C*b*c^10*d^2*f^4 + 64*B*b*c*d^11*f^4) - (c + d*tan(e + f*x))^(1/2)*(16*A^2*b^2*d^10*f^3 -
16*B^2*b^2*d^10*f^3 + 16*C^2*b^2*d^10*f^3 + 32*A^2*b^2*c^2*d^8*f^3 - 32*A^2*b^2*c^6*d^4*f^3 - 16*A^2*b^2*c^8*d
^2*f^3 - 32*B^2*b^2*c^2*d^8*f^3 + 32*B^2*b^2*c^6*d^4*f^3 + 16*B^2*b^2*c^8*d^2*f^3 + 32*C^2*b^2*c^2*d^8*f^3 - 3
2*C^2*b^2*c^6*d^4*f^3 - 16*C^2*b^2*c^8*d^2*f^3 - 32*A*C*b^2*d^10*f^3 - 64*A*B*b^2*c*d^9*f^3 + 64*B*C*b^2*c*d^9
*f^3 - 192*A*B*b^2*c^3*d^7*f^3 - 192*A*B*b^2*c^5*d^5*f^3 - 64*A*B*b^2*c^7*d^3*f^3 - 64*A*C*b^2*c^2*d^8*f^3 + 6
4*A*C*b^2*c^6*d^4*f^3 + 32*A*C*b^2*c^8*d^2*f^3 + 192*B*C*b^2*c^3*d^7*f^3 + 192*B*C*b^2*c^5*d^5*f^3 + 64*B*C*b^
2*c^7*d^3*f^3))*(-(((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b
^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*
b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 +
48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*
B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) - 4*A^2*b^2*c^3*f^2 + 4*B^2*b^2*c^3*f^2 - 4*C^2*b^2*c^3*f^2 + 8*A*B*b^2*d^
3*f^2 + 8*A*C*b^2*c^3*f^2 - 8*B*C*b^2*d^3*f^2 + 12*A^2*b^2*c*d^2*f^2 - 12*B^2*b^2*c*d^2*f^2 + 12*C^2*b^2*c*d^2
*f^2 - 24*A*B*b^2*c^2*d*f^2 - 24*A*C*b^2*c*d^2*f^2 + 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*
f^4 + 3*c^4*d^2*f^4)))^(1/2)*1i)/(16*B^3*b^3*d^9*f^2 - ((-(((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2
*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*
d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16
*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*
b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) - 4*A^2*b^2*c^3*f^2 + 4*B^2*b^2*c^
3*f^2 - 4*C^2*b^2*c^3*f^2 + 8*A*B*b^2*d^3*f^2 + 8*A*C*b^2*c^3*f^2 - 8*B*C*b^2*d^3*f^2 + 12*A^2*b^2*c*d^2*f^2 -
12*B^2*b^2*c*d^2*f^2 + 12*C^2*b^2*c*d^2*f^2 - 24*A*B*b^2*c^2*d*f^2 - 24*A*C*b^2*c*d^2*f^2 + 24*B*C*b^2*c^2*d*
f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*(32*C*b*d^12*f^4 - 32*A*b*d^12*f^4 - (c +
d*tan(e + f*x))^(1/2)*(-(((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 1
6*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 +
48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^
4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b
^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) - 4*A^2*b^2*c^3*f^2 + 4*B^2*b^2*c^3*f^2 - 4*C^2*b^2*c^3*f^2 + 8*A*B
*b^2*d^3*f^2 + 8*A*C*b^2*c^3*f^2 - 8*B*C*b^2*d^3*f^2 + 12*A^2*b^2*c*d^2*f^2 - 12*B^2*b^2*c*d^2*f^2 + 12*C^2*b^
2*c*d^2*f^2 - 24*A*B*b^2*c^2*d*f^2 - 24*A*C*b^2*c*d^2*f^2 + 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c
^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*(64*c*d^12*f^5 + 320*c^3*d^10*f^5 + 640*c^5*d^8*f^5 + 640*c^7*d^6*f^5 + 32
0*c^9*d^4*f^5 + 64*c^11*d^2*f^5) - 96*A*b*c^2*d^10*f^4 - 64*A*b*c^4*d^8*f^4 + 64*A*b*c^6*d^6*f^4 + 96*A*b*c^8*
d^4*f^4 + 32*A*b*c^10*d^2*f^4 + 256*B*b*c^3*d^9*f^4 + 384*B*b*c^5*d^7*f^4 + 256*B*b*c^7*d^5*f^4 + 64*B*b*c^9*d
^3*f^4 + 96*C*b*c^2*d^10*f^4 + 64*C*b*c^4*d^8*f^4 - 64*C*b*c^6*d^6*f^4 - 96*C*b*c^8*d^4*f^4 - 32*C*b*c^10*d^2*
f^4 + 64*B*b*c*d^11*f^4) - (c + d*tan(e + f*x))^(1/2)*(16*A^2*b^2*d^10*f^3 - 16*B^2*b^2*d^10*f^3 + 16*C^2*b^2*
d^10*f^3 + 32*A^2*b^2*c^2*d^8*f^3 - 32*A^2*b^2*c^6*d^4*f^3 - 16*A^2*b^2*c^8*d^2*f^3 - 32*B^2*b^2*c^2*d^8*f^3 +
32*B^2*b^2*c^6*d^4*f^3 + 16*B^2*b^2*c^8*d^2*f^3 + 32*C^2*b^2*c^2*d^8*f^3 - 32*C^2*b^2*c^6*d^4*f^3 - 16*C^2*b^
2*c^8*d^2*f^3 - 32*A*C*b^2*d^10*f^3 - 64*A*B*b^2*c*d^9*f^3 + 64*B*C*b^2*c*d^9*f^3 - 192*A*B*b^2*c^3*d^7*f^3 -
192*A*B*b^2*c^5*d^5*f^3 - 64*A*B*b^2*c^7*d^3*f^3 - 64*A*C*b^2*c^2*d^8*f^3 + 64*A*C*b^2*c^6*d^4*f^3 + 32*A*C*b^
2*c^8*d^2*f^3 + 192*B*C*b^2*c^3*d^7*f^3 + 192*B*C*b^2*c^5*d^5*f^3 + 64*B*C*b^2*c^7*d^3*f^3))*(-(((8*A^2*b^2*c^
3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 -
24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*
f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b
^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/
2) - 4*A^2*b^2*c^3*f^2 + 4*B^2*b^2*c^3*f^2 - 4*C^2*b^2*c^3*f^2 + 8*A*B*b^2*d^3*f^2 + 8*A*C*b^2*c^3*f^2 - 8*B*C
*b^2*d^3*f^2 + 12*A^2*b^2*c*d^2*f^2 - 12*B^2*b^2*c*d^2*f^2 + 12*C^2*b^2*c*d^2*f^2 - 24*A*B*b^2*c^2*d*f^2 - 24*
A*C*b^2*c*d^2*f^2 + 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2) - ((
-(((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B
*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 4
8*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*
(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A
*B^2*C*b^4))^(1/2) - 4*A^2*b^2*c^3*f^2 + 4*B^2*b^2*c^3*f^2 - 4*C^2*b^2*c^3*f^2 + 8*A*B*b^2*d^3*f^2 + 8*A*C*b^2
*c^3*f^2 - 8*B*C*b^2*d^3*f^2 + 12*A^2*b^2*c*d^2*f^2 - 12*B^2*b^2*c*d^2*f^2 + 12*C^2*b^2*c*d^2*f^2 - 24*A*B*b^2
*c^2*d*f^2 - 24*A*C*b^2*c*d^2*f^2 + 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f
^4)))^(1/2)*((c + d*tan(e + f*x))^(1/2)*(-(((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*
B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2
*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^
6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*
b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) - 4*A^2*b^2*c^3*f^2 + 4*B^2*b^2*c^3*f^2 - 4*C^2*b^
2*c^3*f^2 + 8*A*B*b^2*d^3*f^2 + 8*A*C*b^2*c^3*f^2 - 8*B*C*b^2*d^3*f^2 + 12*A^2*b^2*c*d^2*f^2 - 12*B^2*b^2*c*d^
2*f^2 + 12*C^2*b^2*c*d^2*f^2 - 24*A*B*b^2*c^2*d*f^2 - 24*A*C*b^2*c*d^2*f^2 + 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^
4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*(64*c*d^12*f^5 + 320*c^3*d^10*f^5 + 640*c^5*d^8*f^5 + 640
*c^7*d^6*f^5 + 320*c^9*d^4*f^5 + 64*c^11*d^2*f^5) - 32*A*b*d^12*f^4 + 32*C*b*d^12*f^4 - 96*A*b*c^2*d^10*f^4 -
64*A*b*c^4*d^8*f^4 + 64*A*b*c^6*d^6*f^4 + 96*A*b*c^8*d^4*f^4 + 32*A*b*c^10*d^2*f^4 + 256*B*b*c^3*d^9*f^4 + 384
*B*b*c^5*d^7*f^4 + 256*B*b*c^7*d^5*f^4 + 64*B*b*c^9*d^3*f^4 + 96*C*b*c^2*d^10*f^4 + 64*C*b*c^4*d^8*f^4 - 64*C*
b*c^6*d^6*f^4 - 96*C*b*c^8*d^4*f^4 - 32*C*b*c^10*d^2*f^4 + 64*B*b*c*d^11*f^4) + (c + d*tan(e + f*x))^(1/2)*(16
*A^2*b^2*d^10*f^3 - 16*B^2*b^2*d^10*f^3 + 16*C^2*b^2*d^10*f^3 + 32*A^2*b^2*c^2*d^8*f^3 - 32*A^2*b^2*c^6*d^4*f^
3 - 16*A^2*b^2*c^8*d^2*f^3 - 32*B^2*b^2*c^2*d^8*f^3 + 32*B^2*b^2*c^6*d^4*f^3 + 16*B^2*b^2*c^8*d^2*f^3 + 32*C^2
*b^2*c^2*d^8*f^3 - 32*C^2*b^2*c^6*d^4*f^3 - 16*C^2*b^2*c^8*d^2*f^3 - 32*A*C*b^2*d^10*f^3 - 64*A*B*b^2*c*d^9*f^
3 + 64*B*C*b^2*c*d^9*f^3 - 192*A*B*b^2*c^3*d^7*f^3 - 192*A*B*b^2*c^5*d^5*f^3 - 64*A*B*b^2*c^7*d^3*f^3 - 64*A*C
*b^2*c^2*d^8*f^3 + 64*A*C*b^2*c^6*d^4*f^3 + 32*A*C*b^2*c^8*d^2*f^3 + 192*B*C*b^2*c^3*d^7*f^3 + 192*B*C*b^2*c^5
*d^5*f^3 + 64*B*C*b^2*c^7*d^3*f^3))*(-(((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^
2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2 + 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2
*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^
4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4
+ 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) - 4*A^2*b^2*c^3*f^2 + 4*B^2*b^2*c^3*f^2 - 4*C^2*b^2*c^
3*f^2 + 8*A*B*b^2*d^3*f^2 + 8*A*C*b^2*c^3*f^2 - 8*B*C*b^2*d^3*f^2 + 12*A^2*b^2*c*d^2*f^2 - 12*B^2*b^2*c*d^2*f^
2 + 12*C^2*b^2*c*d^2*f^2 - 24*A*B*b^2*c^2*d*f^2 - 24*A*C*b^2*c*d^2*f^2 + 24*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 +
d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2) + 48*A^3*b^3*c^3*d^6*f^2 + 48*A^3*b^3*c^5*d^4*f^2 + 16*A^3*b^
3*c^7*d^2*f^2 + 48*B^3*b^3*c^2*d^7*f^2 + 48*B^3*b^3*c^4*d^5*f^2 + 16*B^3*b^3*c^6*d^3*f^2 - 48*C^3*b^3*c^3*d^6*
f^2 - 48*C^3*b^3*c^5*d^4*f^2 - 16*C^3*b^3*c^7*d^2*f^2 + 16*A^2*B*b^3*d^9*f^2 + 16*B*C^2*b^3*d^9*f^2 + 16*A^3*b
^3*c*d^8*f^2 - 16*C^3*b^3*c*d^8*f^2 + 48*A*B^2*b^3*c^3*d^6*f^2 + 48*A*B^2*b^3*c^5*d^4*f^2 + 16*A*B^2*b^3*c^7*d
^2*f^2 + 48*A^2*B*b^3*c^2*d^7*f^2 + 48*A^2*B*b^3*c^4*d^5*f^2 + 16*A^2*B*b^3*c^6*d^3*f^2 + 144*A*C^2*b^3*c^3*d^
6*f^2 + 144*A*C^2*b^3*c^5*d^4*f^2 + 48*A*C^2*b^3*c^7*d^2*f^2 - 144*A^2*C*b^3*c^3*d^6*f^2 - 144*A^2*C*b^3*c^5*d
^4*f^2 - 48*A^2*C*b^3*c^7*d^2*f^2 + 48*B*C^2*b^3*c^2*d^7*f^2 + 48*B*C^2*b^3*c^4*d^5*f^2 + 16*B*C^2*b^3*c^6*d^3
*f^2 - 48*B^2*C*b^3*c^3*d^6*f^2 - 48*B^2*C*b^3*c^5*d^4*f^2 - 16*B^2*C*b^3*c^7*d^2*f^2 - 32*A*B*C*b^3*d^9*f^2 +
16*A*B^2*b^3*c*d^8*f^2 + 48*A*C^2*b^3*c*d^8*f^2 - 48*A^2*C*b^3*c*d^8*f^2 - 16*B^2*C*b^3*c*d^8*f^2 - 96*A*B*C*
b^3*c^2*d^7*f^2 - 96*A*B*C*b^3*c^4*d^5*f^2 - 32*A*B*C*b^3*c^6*d^3*f^2))*(-(((8*A^2*b^2*c^3*f^2 - 8*B^2*b^2*c^3
*f^2 + 8*C^2*b^2*c^3*f^2 - 16*A*B*b^2*d^3*f^2 - 16*A*C*b^2*c^3*f^2 + 16*B*C*b^2*d^3*f^2 - 24*A^2*b^2*c*d^2*f^2
+ 24*B^2*b^2*c*d^2*f^2 - 24*C^2*b^2*c*d^2*f^2 + 48*A*B*b^2*c^2*d*f^2 + 48*A*C*b^2*c*d^2*f^2 - 48*B*C*b^2*c^2*
d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*b^4 + B^4*b^4 + C^4*b^4 - 4*A*C^
3*b^4 - 4*A^3*C*b^4 + 2*A^2*B^2*b^4 + 6*A^2*C^2*b^4 + 2*B^2*C^2*b^4 - 4*A*B^2*C*b^4))^(1/2) - 4*A^2*b^2*c^3*f^
2 + 4*B^2*b^2*c^3*f^2 - 4*C^2*b^2*c^3*f^2 + 8*A*B*b^2*d^3*f^2 + 8*A*C*b^2*c^3*f^2 - 8*B*C*b^2*d^3*f^2 + 12*A^2
*b^2*c*d^2*f^2 - 12*B^2*b^2*c*d^2*f^2 + 12*C^2*b^2*c*d^2*f^2 - 24*A*B*b^2*c^2*d*f^2 - 24*A*C*b^2*c*d^2*f^2 + 2
4*B*C*b^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*2i + atan((((c + d*tan(e
+ f*x))^(1/2)*(16*A^2*a^2*d^10*f^3 - 16*B^2*a^2*d^10*f^3 + 16*C^2*a^2*d^10*f^3 + 32*A^2*a^2*c^2*d^8*f^3 - 32*A
^2*a^2*c^6*d^4*f^3 - 16*A^2*a^2*c^8*d^2*f^3 - 32*B^2*a^2*c^2*d^8*f^3 + 32*B^2*a^2*c^6*d^4*f^3 + 16*B^2*a^2*c^8
*d^2*f^3 + 32*C^2*a^2*c^2*d^8*f^3 - 32*C^2*a^2*c^6*d^4*f^3 - 16*C^2*a^2*c^8*d^2*f^3 - 32*A*C*a^2*d^10*f^3 - 64
*A*B*a^2*c*d^9*f^3 + 64*B*C*a^2*c*d^9*f^3 - 192*A*B*a^2*c^3*d^7*f^3 - 192*A*B*a^2*c^5*d^5*f^3 - 64*A*B*a^2*c^7
*d^3*f^3 - 64*A*C*a^2*c^2*d^8*f^3 + 64*A*C*a^2*c^6*d^4*f^3 + 32*A*C*a^2*c^8*d^2*f^3 + 192*B*C*a^2*c^3*d^7*f^3
+ 192*B*C*a^2*c^5*d^5*f^3 + 64*B*C*a^2*c^7*d^3*f^3) - (-(((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c
^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^
2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c
^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^
4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) + 4*A^2*a^2*c^3*f^2 - 4*B^2*a^2*c^3*
f^2 + 4*C^2*a^2*c^3*f^2 - 8*A*B*a^2*d^3*f^2 - 8*A*C*a^2*c^3*f^2 + 8*B*C*a^2*d^3*f^2 - 12*A^2*a^2*c*d^2*f^2 + 1
2*B^2*a^2*c*d^2*f^2 - 12*C^2*a^2*c*d^2*f^2 + 24*A*B*a^2*c^2*d*f^2 + 24*A*C*a^2*c*d^2*f^2 - 24*B*C*a^2*c^2*d*f^
2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*((c + d*tan(e + f*x))^(1/2)*(-(((8*A^2*a^2*
c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2
- 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^
2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4
*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(
1/2) + 4*A^2*a^2*c^3*f^2 - 4*B^2*a^2*c^3*f^2 + 4*C^2*a^2*c^3*f^2 - 8*A*B*a^2*d^3*f^2 - 8*A*C*a^2*c^3*f^2 + 8*B
*C*a^2*d^3*f^2 - 12*A^2*a^2*c*d^2*f^2 + 12*B^2*a^2*c*d^2*f^2 - 12*C^2*a^2*c*d^2*f^2 + 24*A*B*a^2*c^2*d*f^2 + 2
4*A*C*a^2*c*d^2*f^2 - 24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*(6
4*c*d^12*f^5 + 320*c^3*d^10*f^5 + 640*c^5*d^8*f^5 + 640*c^7*d^6*f^5 + 320*c^9*d^4*f^5 + 64*c^11*d^2*f^5) - 32*
B*a*d^12*f^4 - 256*A*a*c^3*d^9*f^4 - 384*A*a*c^5*d^7*f^4 - 256*A*a*c^7*d^5*f^4 - 64*A*a*c^9*d^3*f^4 - 96*B*a*c
^2*d^10*f^4 - 64*B*a*c^4*d^8*f^4 + 64*B*a*c^6*d^6*f^4 + 96*B*a*c^8*d^4*f^4 + 32*B*a*c^10*d^2*f^4 + 256*C*a*c^3
*d^9*f^4 + 384*C*a*c^5*d^7*f^4 + 256*C*a*c^7*d^5*f^4 + 64*C*a*c^9*d^3*f^4 - 64*A*a*c*d^11*f^4 + 64*C*a*c*d^11*
f^4))*(-(((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2
+ 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*
f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^
2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^
4 - 4*A*B^2*C*a^4))^(1/2) + 4*A^2*a^2*c^3*f^2 - 4*B^2*a^2*c^3*f^2 + 4*C^2*a^2*c^3*f^2 - 8*A*B*a^2*d^3*f^2 - 8*
A*C*a^2*c^3*f^2 + 8*B*C*a^2*d^3*f^2 - 12*A^2*a^2*c*d^2*f^2 + 12*B^2*a^2*c*d^2*f^2 - 12*C^2*a^2*c*d^2*f^2 + 24*
A*B*a^2*c^2*d*f^2 + 24*A*C*a^2*c*d^2*f^2 - 24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^
4*d^2*f^4)))^(1/2)*1i + ((c + d*tan(e + f*x))^(1/2)*(16*A^2*a^2*d^10*f^3 - 16*B^2*a^2*d^10*f^3 + 16*C^2*a^2*d^
10*f^3 + 32*A^2*a^2*c^2*d^8*f^3 - 32*A^2*a^2*c^6*d^4*f^3 - 16*A^2*a^2*c^8*d^2*f^3 - 32*B^2*a^2*c^2*d^8*f^3 + 3
2*B^2*a^2*c^6*d^4*f^3 + 16*B^2*a^2*c^8*d^2*f^3 + 32*C^2*a^2*c^2*d^8*f^3 - 32*C^2*a^2*c^6*d^4*f^3 - 16*C^2*a^2*
c^8*d^2*f^3 - 32*A*C*a^2*d^10*f^3 - 64*A*B*a^2*c*d^9*f^3 + 64*B*C*a^2*c*d^9*f^3 - 192*A*B*a^2*c^3*d^7*f^3 - 19
2*A*B*a^2*c^5*d^5*f^3 - 64*A*B*a^2*c^7*d^3*f^3 - 64*A*C*a^2*c^2*d^8*f^3 + 64*A*C*a^2*c^6*d^4*f^3 + 32*A*C*a^2*
c^8*d^2*f^3 + 192*B*C*a^2*c^3*d^7*f^3 + 192*B*C*a^2*c^5*d^5*f^3 + 64*B*C*a^2*c^7*d^3*f^3) - (-(((8*A^2*a^2*c^3
*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 -
24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f
^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^
4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2
) + 4*A^2*a^2*c^3*f^2 - 4*B^2*a^2*c^3*f^2 + 4*C^2*a^2*c^3*f^2 - 8*A*B*a^2*d^3*f^2 - 8*A*C*a^2*c^3*f^2 + 8*B*C*
a^2*d^3*f^2 - 12*A^2*a^2*c*d^2*f^2 + 12*B^2*a^2*c*d^2*f^2 - 12*C^2*a^2*c*d^2*f^2 + 24*A*B*a^2*c^2*d*f^2 + 24*A
*C*a^2*c*d^2*f^2 - 24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*((c +
d*tan(e + f*x))^(1/2)*(-(((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 1
6*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 +
48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^
4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a
^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) + 4*A^2*a^2*c^3*f^2 - 4*B^2*a^2*c^3*f^2 + 4*C^2*a^2*c^3*f^2 - 8*A*B
*a^2*d^3*f^2 - 8*A*C*a^2*c^3*f^2 + 8*B*C*a^2*d^3*f^2 - 12*A^2*a^2*c*d^2*f^2 + 12*B^2*a^2*c*d^2*f^2 - 12*C^2*a^
2*c*d^2*f^2 + 24*A*B*a^2*c^2*d*f^2 + 24*A*C*a^2*c*d^2*f^2 - 24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c
^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*(64*c*d^12*f^5 + 320*c^3*d^10*f^5 + 640*c^5*d^8*f^5 + 640*c^7*d^6*f^5 + 32
0*c^9*d^4*f^5 + 64*c^11*d^2*f^5) + 32*B*a*d^12*f^4 + 256*A*a*c^3*d^9*f^4 + 384*A*a*c^5*d^7*f^4 + 256*A*a*c^7*d
^5*f^4 + 64*A*a*c^9*d^3*f^4 + 96*B*a*c^2*d^10*f^4 + 64*B*a*c^4*d^8*f^4 - 64*B*a*c^6*d^6*f^4 - 96*B*a*c^8*d^4*f
^4 - 32*B*a*c^10*d^2*f^4 - 256*C*a*c^3*d^9*f^4 - 384*C*a*c^5*d^7*f^4 - 256*C*a*c^7*d^5*f^4 - 64*C*a*c^9*d^3*f^
4 + 64*A*a*c*d^11*f^4 - 64*C*a*c*d^11*f^4))*(-(((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 1
6*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24
*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 1
6*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*
B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) + 4*A^2*a^2*c^3*f^2 - 4*B^2*a^2*c^3*f^2 + 4*C^
2*a^2*c^3*f^2 - 8*A*B*a^2*d^3*f^2 - 8*A*C*a^2*c^3*f^2 + 8*B*C*a^2*d^3*f^2 - 12*A^2*a^2*c*d^2*f^2 + 12*B^2*a^2*
c*d^2*f^2 - 12*C^2*a^2*c*d^2*f^2 + 24*A*B*a^2*c^2*d*f^2 + 24*A*C*a^2*c*d^2*f^2 - 24*B*C*a^2*c^2*d*f^2)/(16*(c^
6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*1i)/(((c + d*tan(e + f*x))^(1/2)*(16*A^2*a^2*d^10*f^3
- 16*B^2*a^2*d^10*f^3 + 16*C^2*a^2*d^10*f^3 + 32*A^2*a^2*c^2*d^8*f^3 - 32*A^2*a^2*c^6*d^4*f^3 - 16*A^2*a^2*c^
8*d^2*f^3 - 32*B^2*a^2*c^2*d^8*f^3 + 32*B^2*a^2*c^6*d^4*f^3 + 16*B^2*a^2*c^8*d^2*f^3 + 32*C^2*a^2*c^2*d^8*f^3
- 32*C^2*a^2*c^6*d^4*f^3 - 16*C^2*a^2*c^8*d^2*f^3 - 32*A*C*a^2*d^10*f^3 - 64*A*B*a^2*c*d^9*f^3 + 64*B*C*a^2*c*
d^9*f^3 - 192*A*B*a^2*c^3*d^7*f^3 - 192*A*B*a^2*c^5*d^5*f^3 - 64*A*B*a^2*c^7*d^3*f^3 - 64*A*C*a^2*c^2*d^8*f^3
+ 64*A*C*a^2*c^6*d^4*f^3 + 32*A*C*a^2*c^8*d^2*f^3 + 192*B*C*a^2*c^3*d^7*f^3 + 192*B*C*a^2*c^5*d^5*f^3 + 64*B*C
*a^2*c^7*d^3*f^3) - (-(((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A
*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*
A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f
^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4
+ 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) + 4*A^2*a^2*c^3*f^2 - 4*B^2*a^2*c^3*f^2 + 4*C^2*a^2*c^3*f^2 - 8*A*B*a^
2*d^3*f^2 - 8*A*C*a^2*c^3*f^2 + 8*B*C*a^2*d^3*f^2 - 12*A^2*a^2*c*d^2*f^2 + 12*B^2*a^2*c*d^2*f^2 - 12*C^2*a^2*c
*d^2*f^2 + 24*A*B*a^2*c^2*d*f^2 + 24*A*C*a^2*c*d^2*f^2 - 24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*
d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*((c + d*tan(e + f*x))^(1/2)*(-(((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^
2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a
^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4
- (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A
^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) + 4*A^2*a^2*c^3*f^2 - 4*B^2*a
^2*c^3*f^2 + 4*C^2*a^2*c^3*f^2 - 8*A*B*a^2*d^3*f^2 - 8*A*C*a^2*c^3*f^2 + 8*B*C*a^2*d^3*f^2 - 12*A^2*a^2*c*d^2*
f^2 + 12*B^2*a^2*c*d^2*f^2 - 12*C^2*a^2*c*d^2*f^2 + 24*A*B*a^2*c^2*d*f^2 + 24*A*C*a^2*c*d^2*f^2 - 24*B*C*a^2*c
^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*(64*c*d^12*f^5 + 320*c^3*d^10*f^5 +
640*c^5*d^8*f^5 + 640*c^7*d^6*f^5 + 320*c^9*d^4*f^5 + 64*c^11*d^2*f^5) - 32*B*a*d^12*f^4 - 256*A*a*c^3*d^9*f^4
- 384*A*a*c^5*d^7*f^4 - 256*A*a*c^7*d^5*f^4 - 64*A*a*c^9*d^3*f^4 - 96*B*a*c^2*d^10*f^4 - 64*B*a*c^4*d^8*f^4 +
64*B*a*c^6*d^6*f^4 + 96*B*a*c^8*d^4*f^4 + 32*B*a*c^10*d^2*f^4 + 256*C*a*c^3*d^9*f^4 + 384*C*a*c^5*d^7*f^4 + 2
56*C*a*c^7*d^5*f^4 + 64*C*a*c^9*d^3*f^4 - 64*A*a*c*d^11*f^4 + 64*C*a*c*d^11*f^4))*(-(((8*A^2*a^2*c^3*f^2 - 8*B
^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2
*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*
C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^
4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) + 4*A^2*
a^2*c^3*f^2 - 4*B^2*a^2*c^3*f^2 + 4*C^2*a^2*c^3*f^2 - 8*A*B*a^2*d^3*f^2 - 8*A*C*a^2*c^3*f^2 + 8*B*C*a^2*d^3*f^
2 - 12*A^2*a^2*c*d^2*f^2 + 12*B^2*a^2*c*d^2*f^2 - 12*C^2*a^2*c*d^2*f^2 + 24*A*B*a^2*c^2*d*f^2 + 24*A*C*a^2*c*d
^2*f^2 - 24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2) - ((c + d*tan(e
+ f*x))^(1/2)*(16*A^2*a^2*d^10*f^3 - 16*B^2*a^2*d^10*f^3 + 16*C^2*a^2*d^10*f^3 + 32*A^2*a^2*c^2*d^8*f^3 - 32*
A^2*a^2*c^6*d^4*f^3 - 16*A^2*a^2*c^8*d^2*f^3 - 32*B^2*a^2*c^2*d^8*f^3 + 32*B^2*a^2*c^6*d^4*f^3 + 16*B^2*a^2*c^
8*d^2*f^3 + 32*C^2*a^2*c^2*d^8*f^3 - 32*C^2*a^2*c^6*d^4*f^3 - 16*C^2*a^2*c^8*d^2*f^3 - 32*A*C*a^2*d^10*f^3 - 6
4*A*B*a^2*c*d^9*f^3 + 64*B*C*a^2*c*d^9*f^3 - 192*A*B*a^2*c^3*d^7*f^3 - 192*A*B*a^2*c^5*d^5*f^3 - 64*A*B*a^2*c^
7*d^3*f^3 - 64*A*C*a^2*c^2*d^8*f^3 + 64*A*C*a^2*c^6*d^4*f^3 + 32*A*C*a^2*c^8*d^2*f^3 + 192*B*C*a^2*c^3*d^7*f^3
+ 192*B*C*a^2*c^5*d^5*f^3 + 64*B*C*a^2*c^7*d^3*f^3) - (-(((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*
c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d
^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*
c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a
^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) + 4*A^2*a^2*c^3*f^2 - 4*B^2*a^2*c^3
*f^2 + 4*C^2*a^2*c^3*f^2 - 8*A*B*a^2*d^3*f^2 - 8*A*C*a^2*c^3*f^2 + 8*B*C*a^2*d^3*f^2 - 12*A^2*a^2*c*d^2*f^2 +
12*B^2*a^2*c*d^2*f^2 - 12*C^2*a^2*c*d^2*f^2 + 24*A*B*a^2*c^2*d*f^2 + 24*A*C*a^2*c*d^2*f^2 - 24*B*C*a^2*c^2*d*f
^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*((c + d*tan(e + f*x))^(1/2)*(-(((8*A^2*a^2
*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^
2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d
^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^
4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^
(1/2) + 4*A^2*a^2*c^3*f^2 - 4*B^2*a^2*c^3*f^2 + 4*C^2*a^2*c^3*f^2 - 8*A*B*a^2*d^3*f^2 - 8*A*C*a^2*c^3*f^2 + 8*
B*C*a^2*d^3*f^2 - 12*A^2*a^2*c*d^2*f^2 + 12*B^2*a^2*c*d^2*f^2 - 12*C^2*a^2*c*d^2*f^2 + 24*A*B*a^2*c^2*d*f^2 +
24*A*C*a^2*c*d^2*f^2 - 24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*(
64*c*d^12*f^5 + 320*c^3*d^10*f^5 + 640*c^5*d^8*f^5 + 640*c^7*d^6*f^5 + 320*c^9*d^4*f^5 + 64*c^11*d^2*f^5) + 32
*B*a*d^12*f^4 + 256*A*a*c^3*d^9*f^4 + 384*A*a*c^5*d^7*f^4 + 256*A*a*c^7*d^5*f^4 + 64*A*a*c^9*d^3*f^4 + 96*B*a*
c^2*d^10*f^4 + 64*B*a*c^4*d^8*f^4 - 64*B*a*c^6*d^6*f^4 - 96*B*a*c^8*d^4*f^4 - 32*B*a*c^10*d^2*f^4 - 256*C*a*c^
3*d^9*f^4 - 384*C*a*c^5*d^7*f^4 - 256*C*a*c^7*d^5*f^4 - 64*C*a*c^9*d^3*f^4 + 64*A*a*c*d^11*f^4 - 64*C*a*c*d^11
*f^4))*(-(((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^
2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d
*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 - (16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d
^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a
^4 - 4*A*B^2*C*a^4))^(1/2) + 4*A^2*a^2*c^3*f^2 - 4*B^2*a^2*c^3*f^2 + 4*C^2*a^2*c^3*f^2 - 8*A*B*a^2*d^3*f^2 - 8
*A*C*a^2*c^3*f^2 + 8*B*C*a^2*d^3*f^2 - 12*A^2*a^2*c*d^2*f^2 + 12*B^2*a^2*c*d^2*f^2 - 12*C^2*a^2*c*d^2*f^2 + 24
*A*B*a^2*c^2*d*f^2 + 24*A*C*a^2*c*d^2*f^2 - 24*B*C*a^2*c^2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c
^4*d^2*f^4)))^(1/2) - 16*A^3*a^3*d^9*f^2 + 16*C^3*a^3*d^9*f^2 - 48*A^3*a^3*c^2*d^7*f^2 - 48*A^3*a^3*c^4*d^5*f^
2 - 16*A^3*a^3*c^6*d^3*f^2 + 48*B^3*a^3*c^3*d^6*f^2 + 48*B^3*a^3*c^5*d^4*f^2 + 16*B^3*a^3*c^7*d^2*f^2 + 48*C^3
*a^3*c^2*d^7*f^2 + 48*C^3*a^3*c^4*d^5*f^2 + 16*C^3*a^3*c^6*d^3*f^2 - 16*A*B^2*a^3*d^9*f^2 - 48*A*C^2*a^3*d^9*f
^2 + 48*A^2*C*a^3*d^9*f^2 + 16*B^2*C*a^3*d^9*f^2 + 16*B^3*a^3*c*d^8*f^2 - 48*A*B^2*a^3*c^2*d^7*f^2 - 48*A*B^2*
a^3*c^4*d^5*f^2 - 16*A*B^2*a^3*c^6*d^3*f^2 + 48*A^2*B*a^3*c^3*d^6*f^2 + 48*A^2*B*a^3*c^5*d^4*f^2 + 16*A^2*B*a^
3*c^7*d^2*f^2 - 144*A*C^2*a^3*c^2*d^7*f^2 - 144*A*C^2*a^3*c^4*d^5*f^2 - 48*A*C^2*a^3*c^6*d^3*f^2 + 144*A^2*C*a
^3*c^2*d^7*f^2 + 144*A^2*C*a^3*c^4*d^5*f^2 + 48*A^2*C*a^3*c^6*d^3*f^2 + 48*B*C^2*a^3*c^3*d^6*f^2 + 48*B*C^2*a^
3*c^5*d^4*f^2 + 16*B*C^2*a^3*c^7*d^2*f^2 + 48*B^2*C*a^3*c^2*d^7*f^2 + 48*B^2*C*a^3*c^4*d^5*f^2 + 16*B^2*C*a^3*
c^6*d^3*f^2 + 16*A^2*B*a^3*c*d^8*f^2 + 16*B*C^2*a^3*c*d^8*f^2 - 96*A*B*C*a^3*c^3*d^6*f^2 - 96*A*B*C*a^3*c^5*d^
4*f^2 - 32*A*B*C*a^3*c^7*d^2*f^2 - 32*A*B*C*a^3*c*d^8*f^2))*(-(((8*A^2*a^2*c^3*f^2 - 8*B^2*a^2*c^3*f^2 + 8*C^2
*a^2*c^3*f^2 - 16*A*B*a^2*d^3*f^2 - 16*A*C*a^2*c^3*f^2 + 16*B*C*a^2*d^3*f^2 - 24*A^2*a^2*c*d^2*f^2 + 24*B^2*a^
2*c*d^2*f^2 - 24*C^2*a^2*c*d^2*f^2 + 48*A*B*a^2*c^2*d*f^2 + 48*A*C*a^2*c*d^2*f^2 - 48*B*C*a^2*c^2*d*f^2)^2/4 -
(16*c^6*f^4 + 16*d^6*f^4 + 48*c^2*d^4*f^4 + 48*c^4*d^2*f^4)*(A^4*a^4 + B^4*a^4 + C^4*a^4 - 4*A*C^3*a^4 - 4*A^
3*C*a^4 + 2*A^2*B^2*a^4 + 6*A^2*C^2*a^4 + 2*B^2*C^2*a^4 - 4*A*B^2*C*a^4))^(1/2) + 4*A^2*a^2*c^3*f^2 - 4*B^2*a^
2*c^3*f^2 + 4*C^2*a^2*c^3*f^2 - 8*A*B*a^2*d^3*f^2 - 8*A*C*a^2*c^3*f^2 + 8*B*C*a^2*d^3*f^2 - 12*A^2*a^2*c*d^2*f
^2 + 12*B^2*a^2*c*d^2*f^2 - 12*C^2*a^2*c*d^2*f^2 + 24*A*B*a^2*c^2*d*f^2 + 24*A*C*a^2*c*d^2*f^2 - 24*B*C*a^2*c^
2*d*f^2)/(16*(c^6*f^4 + d^6*f^4 + 3*c^2*d^4*f^4 + 3*c^4*d^2*f^4)))^(1/2)*2i + (2*(C*b*c^3 + A*b*c*d^2 - B*b*c^
2*d))/(d^2*f*(c^2 + d^2)*(c + d*tan(e + f*x))^(1/2)) - (2*(A*a*d^2 + C*a*c^2 - B*a*c*d))/(d*f*(c^2 + d^2)*(c +
d*tan(e + f*x))^(1/2)) + (2*C*b*(c + d*tan(e + f*x))^(1/2))/(d^2*f)
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (a + b \tan {\left (e + f x \right )}\right ) \left (A + B \tan {\left (e + f x \right )} + C \tan ^{2}{\left (e + f x \right )}\right )}{\left (c + d \tan {\left (e + f x \right )}\right )^{\frac {3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(3/2),x)
[Out]
Integral((a + b*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(c + d*tan(e + f*x))**(3/2), x)
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