3.1259 \(\int \frac {(a+b \tan (e+f x))^4}{(c+d \tan (e+f x))^{5/2}} \, dx\)

Optimal. Leaf size=290 \[ -\frac {2 b^2 \left (a d (2 b c-a d)-b^2 \left (4 c^2+3 d^2\right )\right ) \sqrt {c+d \tan (e+f x)}}{3 d^3 f \left (c^2+d^2\right )}-\frac {2 (b c-a d)^2 (a+b \tan (e+f x))^2}{3 d f \left (c^2+d^2\right ) (c+d \tan (e+f x))^{3/2}}+\frac {4 (b c-a d)^3 \left (3 a c d+2 b c^2+5 b d^2\right )}{3 d^3 f \left (c^2+d^2\right )^2 \sqrt {c+d \tan (e+f x)}}-\frac {i (a-i b)^4 \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{f (c-i d)^{5/2}}+\frac {i (a+i b)^4 \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{f (c+i d)^{5/2}} \]

[Out]

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

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Rubi [A]  time = 1.01, antiderivative size = 290, normalized size of antiderivative = 1.00, number of steps used = 10, number of rules used = 7, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.259, Rules used = {3565, 3635, 3630, 3539, 3537, 63, 208} \[ -\frac {2 b^2 \left (a d (2 b c-a d)-b^2 \left (4 c^2+3 d^2\right )\right ) \sqrt {c+d \tan (e+f x)}}{3 d^3 f \left (c^2+d^2\right )}+\frac {4 (b c-a d)^3 \left (3 a c d+2 b c^2+5 b d^2\right )}{3 d^3 f \left (c^2+d^2\right )^2 \sqrt {c+d \tan (e+f x)}}-\frac {2 (b c-a d)^2 (a+b \tan (e+f x))^2}{3 d f \left (c^2+d^2\right ) (c+d \tan (e+f x))^{3/2}}-\frac {i (a-i b)^4 \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{f (c-i d)^{5/2}}+\frac {i (a+i b)^4 \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{f (c+i d)^{5/2}} \]

Antiderivative was successfully verified.

[In]

Int[(a + b*Tan[e + f*x])^4/(c + d*Tan[e + f*x])^(5/2),x]

[Out]

((-I)*(a - I*b)^4*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(5/2)*f) + (I*(a + I*b)^4*ArcTan
h[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(5/2)*f) - (2*(b*c - a*d)^2*(a + b*Tan[e + f*x])^2)/(3*d
*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) + (4*(b*c - a*d)^3*(2*b*c^2 + 3*a*c*d + 5*b*d^2))/(3*d^3*(c^2 + d^2
)^2*f*Sqrt[c + d*Tan[e + f*x]]) - (2*b^2*(a*d*(2*b*c - a*d) - b^2*(4*c^2 + 3*d^2))*Sqrt[c + d*Tan[e + f*x]])/(
3*d^3*(c^2 + 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 3565

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

Rule 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))^4}{(c+d \tan (e+f x))^{5/2}} \, dx &=-\frac {2 (b c-a d)^2 (a+b \tan (e+f x))^2}{3 d \left (c^2+d^2\right ) f (c+d \tan (e+f x))^{3/2}}+\frac {2 \int \frac {(a+b \tan (e+f x)) \left (\frac {1}{2} \left (4 b^3 c^2+3 a^3 c d-11 a b^2 c d+10 a^2 b d^2\right )+\frac {3}{2} d \left (3 a^2 b c-b^3 c-a^3 d+3 a b^2 d\right ) \tan (e+f x)-\frac {1}{2} b \left (a d (2 b c-a d)-b^2 \left (4 c^2+3 d^2\right )\right ) \tan ^2(e+f x)\right )}{(c+d \tan (e+f x))^{3/2}} \, dx}{3 d \left (c^2+d^2\right )}\\ &=-\frac {2 (b c-a d)^2 (a+b \tan (e+f x))^2}{3 d \left (c^2+d^2\right ) f (c+d \tan (e+f x))^{3/2}}+\frac {4 (b c-a d)^3 \left (2 b c^2+3 a c d+5 b d^2\right )}{3 d^3 \left (c^2+d^2\right )^2 f \sqrt {c+d \tan (e+f x)}}+\frac {2 \int \frac {\frac {1}{2} \left (24 a^3 b c d^3-a^2 b^2 d^2 \left (17 c^2-19 d^2\right )+3 a^4 d^2 \left (c^2-d^2\right )-2 a b^3 c d \left (c^2+13 d^2\right )+2 b^4 \left (2 c^4+5 c^2 d^2\right )\right )+3 d^2 \left (a^2 c-b^2 c+2 a b d\right ) \left (2 a b c-a^2 d+b^2 d\right ) \tan (e+f x)-\frac {1}{2} b^2 \left (c^2+d^2\right ) \left (a d (2 b c-a d)-b^2 \left (4 c^2+3 d^2\right )\right ) \tan ^2(e+f x)}{\sqrt {c+d \tan (e+f x)}} \, dx}{3 d^2 \left (c^2+d^2\right )^2}\\ &=-\frac {2 (b c-a d)^2 (a+b \tan (e+f x))^2}{3 d \left (c^2+d^2\right ) f (c+d \tan (e+f x))^{3/2}}+\frac {4 (b c-a d)^3 \left (2 b c^2+3 a c d+5 b d^2\right )}{3 d^3 \left (c^2+d^2\right )^2 f \sqrt {c+d \tan (e+f x)}}-\frac {2 b^2 \left (a d (2 b c-a d)-b^2 \left (4 c^2+3 d^2\right )\right ) \sqrt {c+d \tan (e+f x)}}{3 d^3 \left (c^2+d^2\right ) f}+\frac {2 \int \frac {\frac {3}{2} d^2 \left (8 a^3 b c d-8 a b^3 c d+a^4 \left (c^2-d^2\right )-6 a^2 b^2 \left (c^2-d^2\right )+b^4 \left (c^2-d^2\right )\right )+3 d^2 \left (a^2 c-b^2 c+2 a b d\right ) \left (2 a b c-a^2 d+b^2 d\right ) \tan (e+f x)}{\sqrt {c+d \tan (e+f x)}} \, dx}{3 d^2 \left (c^2+d^2\right )^2}\\ &=-\frac {2 (b c-a d)^2 (a+b \tan (e+f x))^2}{3 d \left (c^2+d^2\right ) f (c+d \tan (e+f x))^{3/2}}+\frac {4 (b c-a d)^3 \left (2 b c^2+3 a c d+5 b d^2\right )}{3 d^3 \left (c^2+d^2\right )^2 f \sqrt {c+d \tan (e+f x)}}-\frac {2 b^2 \left (a d (2 b c-a d)-b^2 \left (4 c^2+3 d^2\right )\right ) \sqrt {c+d \tan (e+f x)}}{3 d^3 \left (c^2+d^2\right ) f}+\frac {(a-i b)^4 \int \frac {1+i \tan (e+f x)}{\sqrt {c+d \tan (e+f x)}} \, dx}{2 (c-i d)^2}+\frac {(a+i b)^4 \int \frac {1-i \tan (e+f x)}{\sqrt {c+d \tan (e+f x)}} \, dx}{2 (c+i d)^2}\\ &=-\frac {2 (b c-a d)^2 (a+b \tan (e+f x))^2}{3 d \left (c^2+d^2\right ) f (c+d \tan (e+f x))^{3/2}}+\frac {4 (b c-a d)^3 \left (2 b c^2+3 a c d+5 b d^2\right )}{3 d^3 \left (c^2+d^2\right )^2 f \sqrt {c+d \tan (e+f x)}}-\frac {2 b^2 \left (a d (2 b c-a d)-b^2 \left (4 c^2+3 d^2\right )\right ) \sqrt {c+d \tan (e+f x)}}{3 d^3 \left (c^2+d^2\right ) f}+\frac {\left (i (a-i b)^4\right ) \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)^2 f}-\frac {\left (i (a+i b)^4\right ) \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)^2 f}\\ &=-\frac {2 (b c-a d)^2 (a+b \tan (e+f x))^2}{3 d \left (c^2+d^2\right ) f (c+d \tan (e+f x))^{3/2}}+\frac {4 (b c-a d)^3 \left (2 b c^2+3 a c d+5 b d^2\right )}{3 d^3 \left (c^2+d^2\right )^2 f \sqrt {c+d \tan (e+f x)}}-\frac {2 b^2 \left (a d (2 b c-a d)-b^2 \left (4 c^2+3 d^2\right )\right ) \sqrt {c+d \tan (e+f x)}}{3 d^3 \left (c^2+d^2\right ) f}-\frac {(a-i b)^4 \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)^2 d f}-\frac {(a+i b)^4 \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)^2 d f}\\ &=-\frac {i (a-i b)^4 \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c-i d}}\right )}{(c-i d)^{5/2} f}+\frac {i (a+i b)^4 \tanh ^{-1}\left (\frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {c+i d}}\right )}{(c+i d)^{5/2} f}-\frac {2 (b c-a d)^2 (a+b \tan (e+f x))^2}{3 d \left (c^2+d^2\right ) f (c+d \tan (e+f x))^{3/2}}+\frac {4 (b c-a d)^3 \left (2 b c^2+3 a c d+5 b d^2\right )}{3 d^3 \left (c^2+d^2\right )^2 f \sqrt {c+d \tan (e+f x)}}-\frac {2 b^2 \left (a d (2 b c-a d)-b^2 \left (4 c^2+3 d^2\right )\right ) \sqrt {c+d \tan (e+f x)}}{3 d^3 \left (c^2+d^2\right ) f}\\ \end {align*}

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Mathematica [C]  time = 3.62, size = 368, normalized size = 1.27 \[ -\frac {-2 b^2 (c-i d) (c+i d) \left (9 a^2 d^2-20 a b c d+b^2 \left (8 c^2+d^2\right )\right )-12 a b d^2 \left (a^2-b^2\right ) (c+d \tan (e+f x)) \left (i (c+i d) \, _2F_1\left (-\frac {1}{2},1;\frac {1}{2};\frac {c+d \tan (e+f x)}{c-i d}\right )-(d+i c) \, _2F_1\left (-\frac {1}{2},1;\frac {1}{2};\frac {c+d \tan (e+f x)}{c+i d}\right )\right )+d^2 \left (a^4 d-4 a^3 b c-6 a^2 b^2 d+4 a b^3 c+b^4 d\right ) \left ((d-i c) \, _2F_1\left (-\frac {3}{2},1;-\frac {1}{2};\frac {c+d \tan (e+f x)}{c-i d}\right )+(d+i c) \, _2F_1\left (-\frac {3}{2},1;-\frac {1}{2};\frac {c+d \tan (e+f x)}{c+i d}\right )\right )-6 b^2 d^2 (c-i d) (c+i d) (a+b \tan (e+f x))^2-12 b^2 d (c-i d) (c+i d) (2 b c-3 a d) (a+b \tan (e+f x))}{3 d^3 f \left (c^2+d^2\right ) (c+d \tan (e+f x))^{3/2}} \]

Antiderivative was successfully verified.

[In]

Integrate[(a + b*Tan[e + f*x])^4/(c + d*Tan[e + f*x])^(5/2),x]

[Out]

-1/3*(-2*b^2*(c - I*d)*(c + I*d)*(-20*a*b*c*d + 9*a^2*d^2 + b^2*(8*c^2 + d^2)) + d^2*(-4*a^3*b*c + 4*a*b^3*c +
a^4*d - 6*a^2*b^2*d + b^4*d)*(((-I)*c + d)*Hypergeometric2F1[-3/2, 1, -1/2, (c + d*Tan[e + f*x])/(c - I*d)] +
(I*c + d)*Hypergeometric2F1[-3/2, 1, -1/2, (c + d*Tan[e + f*x])/(c + I*d)]) - 12*b^2*(c - I*d)*(c + I*d)*d*(2
*b*c - 3*a*d)*(a + b*Tan[e + f*x]) - 6*b^2*(c - I*d)*(c + I*d)*d^2*(a + b*Tan[e + f*x])^2 - 12*a*b*(a^2 - b^2)
*d^2*(I*(c + I*d)*Hypergeometric2F1[-1/2, 1, 1/2, (c + d*Tan[e + f*x])/(c - I*d)] - (I*c + d)*Hypergeometric2F
1[-1/2, 1, 1/2, (c + d*Tan[e + f*x])/(c + I*d)])*(c + d*Tan[e + f*x]))/(d^3*(c^2 + d^2)*f*(c + d*Tan[e + f*x])
^(3/2))

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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))^4/(c+d*tan(f*x+e))^(5/2),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))^4/(c+d*tan(f*x+e))^(5/2),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.43, size = 33851, normalized size = 116.73 \[ \text {output too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^(5/2),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))^4/(c+d*tan(f*x+e))^(5/2),x, algorithm="maxima")

[Out]

Timed out

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mupad [B]  time = 35.67, size = 43980, normalized size = 151.66 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + b*tan(e + f*x))^4/(c + d*tan(e + f*x))^(5/2),x)

[Out]

(2*b^4*(c + d*tan(e + f*x))^(1/2))/(d^3*f) - atan((((-(((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64
*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2
*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*
c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^
3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*
a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d
^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4
)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2)
)^(1/2) + 4*a^8*c^5*f^2 + 4*b^8*c^5*f^2 - 32*a*b^7*d^5*f^2 + 32*a^7*b*d^5*f^2 + 20*a^8*c*d^4*f^2 + 20*b^8*c*d^
4*f^2 - 112*a^2*b^6*c^5*f^2 + 280*a^4*b^4*c^5*f^2 - 112*a^6*b^2*c^5*f^2 + 224*a^3*b^5*d^5*f^2 - 224*a^5*b^3*d^
5*f^2 - 40*a^8*c^3*d^2*f^2 - 40*b^8*c^3*d^2*f^2 + 1120*a^2*b^6*c^3*d^2*f^2 - 2240*a^3*b^5*c^2*d^3*f^2 - 2800*a
^4*b^4*c^3*d^2*f^2 + 2240*a^5*b^3*c^2*d^3*f^2 + 1120*a^6*b^2*c^3*d^2*f^2 - 160*a*b^7*c^4*d*f^2 + 160*a^7*b*c^4
*d*f^2 + 320*a*b^7*c^2*d^3*f^2 - 560*a^2*b^6*c*d^4*f^2 + 1120*a^3*b^5*c^4*d*f^2 + 1400*a^4*b^4*c*d^4*f^2 - 112
0*a^5*b^3*c^4*d*f^2 - 560*a^6*b^2*c*d^4*f^2 - 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4
+ 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*((c + d*tan(e + f*x))^(1/2)*(-(((8*a^8*c^5*f^2 + 8*
b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2
+ 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 -
80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^
5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f
^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*
a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4
+ 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a
^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^(1/2) + 4*a^8*c^5*f^2 + 4*b^8*c^5*f^2 - 32*a*b^7*d^5*f^2 + 32*a^7*b*d^5*f
^2 + 20*a^8*c*d^4*f^2 + 20*b^8*c*d^4*f^2 - 112*a^2*b^6*c^5*f^2 + 280*a^4*b^4*c^5*f^2 - 112*a^6*b^2*c^5*f^2 + 2
24*a^3*b^5*d^5*f^2 - 224*a^5*b^3*d^5*f^2 - 40*a^8*c^3*d^2*f^2 - 40*b^8*c^3*d^2*f^2 + 1120*a^2*b^6*c^3*d^2*f^2
- 2240*a^3*b^5*c^2*d^3*f^2 - 2800*a^4*b^4*c^3*d^2*f^2 + 2240*a^5*b^3*c^2*d^3*f^2 + 1120*a^6*b^2*c^3*d^2*f^2 -
160*a*b^7*c^4*d*f^2 + 160*a^7*b*c^4*d*f^2 + 320*a*b^7*c^2*d^3*f^2 - 560*a^2*b^6*c*d^4*f^2 + 1120*a^3*b^5*c^4*d
*f^2 + 1400*a^4*b^4*c*d^4*f^2 - 1120*a^5*b^3*c^4*d*f^2 - 560*a^6*b^2*c*d^4*f^2 - 320*a^7*b*c^2*d^3*f^2)/(16*(c
^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*(64*c*d^22*f^5 +
640*c^3*d^20*f^5 + 2880*c^5*d^18*f^5 + 7680*c^7*d^16*f^5 + 13440*c^9*d^14*f^5 + 16128*c^11*d^12*f^5 + 13440*c
^13*d^10*f^5 + 7680*c^15*d^8*f^5 + 2880*c^17*d^6*f^5 + 640*c^19*d^4*f^5 + 64*c^21*d^2*f^5) - 32*a^4*d^21*f^4 -
32*b^4*d^21*f^4 + 192*a^2*b^2*d^21*f^4 - 160*a^4*c^2*d^19*f^4 - 128*a^4*c^4*d^17*f^4 + 896*a^4*c^6*d^15*f^4 +
3136*a^4*c^8*d^13*f^4 + 4928*a^4*c^10*d^11*f^4 + 4480*a^4*c^12*d^9*f^4 + 2432*a^4*c^14*d^7*f^4 + 736*a^4*c^16
*d^5*f^4 + 96*a^4*c^18*d^3*f^4 - 160*b^4*c^2*d^19*f^4 - 128*b^4*c^4*d^17*f^4 + 896*b^4*c^6*d^15*f^4 + 3136*b^4
*c^8*d^13*f^4 + 4928*b^4*c^10*d^11*f^4 + 4480*b^4*c^12*d^9*f^4 + 2432*b^4*c^14*d^7*f^4 + 736*b^4*c^16*d^5*f^4
+ 96*b^4*c^18*d^3*f^4 + 960*a^2*b^2*c^2*d^19*f^4 + 768*a^2*b^2*c^4*d^17*f^4 - 5376*a^2*b^2*c^6*d^15*f^4 - 1881
6*a^2*b^2*c^8*d^13*f^4 - 29568*a^2*b^2*c^10*d^11*f^4 - 26880*a^2*b^2*c^12*d^9*f^4 - 14592*a^2*b^2*c^14*d^7*f^4
- 4416*a^2*b^2*c^16*d^5*f^4 - 576*a^2*b^2*c^18*d^3*f^4 - 384*a*b^3*c*d^20*f^4 + 384*a^3*b*c*d^20*f^4 - 2944*a
*b^3*c^3*d^18*f^4 - 9728*a*b^3*c^5*d^16*f^4 - 17920*a*b^3*c^7*d^14*f^4 - 19712*a*b^3*c^9*d^12*f^4 - 12544*a*b^
3*c^11*d^10*f^4 - 3584*a*b^3*c^13*d^8*f^4 + 512*a*b^3*c^15*d^6*f^4 + 640*a*b^3*c^17*d^4*f^4 + 128*a*b^3*c^19*d
^2*f^4 + 2944*a^3*b*c^3*d^18*f^4 + 9728*a^3*b*c^5*d^16*f^4 + 17920*a^3*b*c^7*d^14*f^4 + 19712*a^3*b*c^9*d^12*f
^4 + 12544*a^3*b*c^11*d^10*f^4 + 3584*a^3*b*c^13*d^8*f^4 - 512*a^3*b*c^15*d^6*f^4 - 640*a^3*b*c^17*d^4*f^4 - 1
28*a^3*b*c^19*d^2*f^4) - (c + d*tan(e + f*x))^(1/2)*(448*a^2*b^6*d^18*f^3 - 16*b^8*d^18*f^3 - 16*a^8*d^18*f^3
- 1120*a^4*b^4*d^18*f^3 + 448*a^6*b^2*d^18*f^3 + 320*a^8*c^4*d^14*f^3 + 1024*a^8*c^6*d^12*f^3 + 1440*a^8*c^8*d
^10*f^3 + 1024*a^8*c^10*d^8*f^3 + 320*a^8*c^12*d^6*f^3 - 16*a^8*c^16*d^2*f^3 + 320*b^8*c^4*d^14*f^3 + 1024*b^8
*c^6*d^12*f^3 + 1440*b^8*c^8*d^10*f^3 + 1024*b^8*c^10*d^8*f^3 + 320*b^8*c^12*d^6*f^3 - 16*b^8*c^16*d^2*f^3 - 8
960*a^2*b^6*c^4*d^14*f^3 - 28672*a^2*b^6*c^6*d^12*f^3 - 40320*a^2*b^6*c^8*d^10*f^3 - 28672*a^2*b^6*c^10*d^8*f^
3 - 8960*a^2*b^6*c^12*d^6*f^3 + 448*a^2*b^6*c^16*d^2*f^3 + 17920*a^3*b^5*c^3*d^15*f^3 + 32256*a^3*b^5*c^5*d^13
*f^3 + 17920*a^3*b^5*c^7*d^11*f^3 - 17920*a^3*b^5*c^9*d^9*f^3 - 32256*a^3*b^5*c^11*d^7*f^3 - 17920*a^3*b^5*c^1
3*d^5*f^3 - 3584*a^3*b^5*c^15*d^3*f^3 + 22400*a^4*b^4*c^4*d^14*f^3 + 71680*a^4*b^4*c^6*d^12*f^3 + 100800*a^4*b
^4*c^8*d^10*f^3 + 71680*a^4*b^4*c^10*d^8*f^3 + 22400*a^4*b^4*c^12*d^6*f^3 - 1120*a^4*b^4*c^16*d^2*f^3 - 17920*
a^5*b^3*c^3*d^15*f^3 - 32256*a^5*b^3*c^5*d^13*f^3 - 17920*a^5*b^3*c^7*d^11*f^3 + 17920*a^5*b^3*c^9*d^9*f^3 + 3
2256*a^5*b^3*c^11*d^7*f^3 + 17920*a^5*b^3*c^13*d^5*f^3 + 3584*a^5*b^3*c^15*d^3*f^3 - 8960*a^6*b^2*c^4*d^14*f^3
- 28672*a^6*b^2*c^6*d^12*f^3 - 40320*a^6*b^2*c^8*d^10*f^3 - 28672*a^6*b^2*c^10*d^8*f^3 - 8960*a^6*b^2*c^12*d^
6*f^3 + 448*a^6*b^2*c^16*d^2*f^3 - 512*a*b^7*c*d^17*f^3 + 512*a^7*b*c*d^17*f^3 - 2560*a*b^7*c^3*d^15*f^3 - 460
8*a*b^7*c^5*d^13*f^3 - 2560*a*b^7*c^7*d^11*f^3 + 2560*a*b^7*c^9*d^9*f^3 + 4608*a*b^7*c^11*d^7*f^3 + 2560*a*b^7
*c^13*d^5*f^3 + 512*a*b^7*c^15*d^3*f^3 + 3584*a^3*b^5*c*d^17*f^3 - 3584*a^5*b^3*c*d^17*f^3 + 2560*a^7*b*c^3*d^
15*f^3 + 4608*a^7*b*c^5*d^13*f^3 + 2560*a^7*b*c^7*d^11*f^3 - 2560*a^7*b*c^9*d^9*f^3 - 4608*a^7*b*c^11*d^7*f^3
- 2560*a^7*b*c^13*d^5*f^3 - 512*a^7*b*c^15*d^3*f^3))*(-(((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 6
4*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^
2*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6
*c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c
^3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240
*a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*
d^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^
4)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2
))^(1/2) + 4*a^8*c^5*f^2 + 4*b^8*c^5*f^2 - 32*a*b^7*d^5*f^2 + 32*a^7*b*d^5*f^2 + 20*a^8*c*d^4*f^2 + 20*b^8*c*d
^4*f^2 - 112*a^2*b^6*c^5*f^2 + 280*a^4*b^4*c^5*f^2 - 112*a^6*b^2*c^5*f^2 + 224*a^3*b^5*d^5*f^2 - 224*a^5*b^3*d
^5*f^2 - 40*a^8*c^3*d^2*f^2 - 40*b^8*c^3*d^2*f^2 + 1120*a^2*b^6*c^3*d^2*f^2 - 2240*a^3*b^5*c^2*d^3*f^2 - 2800*
a^4*b^4*c^3*d^2*f^2 + 2240*a^5*b^3*c^2*d^3*f^2 + 1120*a^6*b^2*c^3*d^2*f^2 - 160*a*b^7*c^4*d*f^2 + 160*a^7*b*c^
4*d*f^2 + 320*a*b^7*c^2*d^3*f^2 - 560*a^2*b^6*c*d^4*f^2 + 1120*a^3*b^5*c^4*d*f^2 + 1400*a^4*b^4*c*d^4*f^2 - 11
20*a^5*b^3*c^4*d*f^2 - 560*a^6*b^2*c*d^4*f^2 - 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4
+ 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*1i - ((-(((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^
7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2
- 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 +
2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2
240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d
^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 6
40*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 +
80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4
+ 8*a^14*b^2))^(1/2) + 4*a^8*c^5*f^2 + 4*b^8*c^5*f^2 - 32*a*b^7*d^5*f^2 + 32*a^7*b*d^5*f^2 + 20*a^8*c*d^4*f^2
+ 20*b^8*c*d^4*f^2 - 112*a^2*b^6*c^5*f^2 + 280*a^4*b^4*c^5*f^2 - 112*a^6*b^2*c^5*f^2 + 224*a^3*b^5*d^5*f^2 -
224*a^5*b^3*d^5*f^2 - 40*a^8*c^3*d^2*f^2 - 40*b^8*c^3*d^2*f^2 + 1120*a^2*b^6*c^3*d^2*f^2 - 2240*a^3*b^5*c^2*d^
3*f^2 - 2800*a^4*b^4*c^3*d^2*f^2 + 2240*a^5*b^3*c^2*d^3*f^2 + 1120*a^6*b^2*c^3*d^2*f^2 - 160*a*b^7*c^4*d*f^2 +
160*a^7*b*c^4*d*f^2 + 320*a*b^7*c^2*d^3*f^2 - 560*a^2*b^6*c*d^4*f^2 + 1120*a^3*b^5*c^4*d*f^2 + 1400*a^4*b^4*c
*d^4*f^2 - 1120*a^5*b^3*c^4*d*f^2 - 560*a^6*b^2*c*d^4*f^2 - 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 +
5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*(192*a^2*b^2*d^21*f^4 - 32*a^4*d^21*f
^4 - 32*b^4*d^21*f^4 - (c + d*tan(e + f*x))^(1/2)*(-(((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a
^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c
^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^
3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*
d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^
3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3
*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*
(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^
(1/2) + 4*a^8*c^5*f^2 + 4*b^8*c^5*f^2 - 32*a*b^7*d^5*f^2 + 32*a^7*b*d^5*f^2 + 20*a^8*c*d^4*f^2 + 20*b^8*c*d^4*
f^2 - 112*a^2*b^6*c^5*f^2 + 280*a^4*b^4*c^5*f^2 - 112*a^6*b^2*c^5*f^2 + 224*a^3*b^5*d^5*f^2 - 224*a^5*b^3*d^5*
f^2 - 40*a^8*c^3*d^2*f^2 - 40*b^8*c^3*d^2*f^2 + 1120*a^2*b^6*c^3*d^2*f^2 - 2240*a^3*b^5*c^2*d^3*f^2 - 2800*a^4
*b^4*c^3*d^2*f^2 + 2240*a^5*b^3*c^2*d^3*f^2 + 1120*a^6*b^2*c^3*d^2*f^2 - 160*a*b^7*c^4*d*f^2 + 160*a^7*b*c^4*d
*f^2 + 320*a*b^7*c^2*d^3*f^2 - 560*a^2*b^6*c*d^4*f^2 + 1120*a^3*b^5*c^4*d*f^2 + 1400*a^4*b^4*c*d^4*f^2 - 1120*
a^5*b^3*c^4*d*f^2 - 560*a^6*b^2*c*d^4*f^2 - 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 +
10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*(64*c*d^22*f^5 + 640*c^3*d^20*f^5 + 2880*c^5*d^18*f^5
+ 7680*c^7*d^16*f^5 + 13440*c^9*d^14*f^5 + 16128*c^11*d^12*f^5 + 13440*c^13*d^10*f^5 + 7680*c^15*d^8*f^5 + 28
80*c^17*d^6*f^5 + 640*c^19*d^4*f^5 + 64*c^21*d^2*f^5) - 160*a^4*c^2*d^19*f^4 - 128*a^4*c^4*d^17*f^4 + 896*a^4*
c^6*d^15*f^4 + 3136*a^4*c^8*d^13*f^4 + 4928*a^4*c^10*d^11*f^4 + 4480*a^4*c^12*d^9*f^4 + 2432*a^4*c^14*d^7*f^4
+ 736*a^4*c^16*d^5*f^4 + 96*a^4*c^18*d^3*f^4 - 160*b^4*c^2*d^19*f^4 - 128*b^4*c^4*d^17*f^4 + 896*b^4*c^6*d^15*
f^4 + 3136*b^4*c^8*d^13*f^4 + 4928*b^4*c^10*d^11*f^4 + 4480*b^4*c^12*d^9*f^4 + 2432*b^4*c^14*d^7*f^4 + 736*b^4
*c^16*d^5*f^4 + 96*b^4*c^18*d^3*f^4 + 960*a^2*b^2*c^2*d^19*f^4 + 768*a^2*b^2*c^4*d^17*f^4 - 5376*a^2*b^2*c^6*d
^15*f^4 - 18816*a^2*b^2*c^8*d^13*f^4 - 29568*a^2*b^2*c^10*d^11*f^4 - 26880*a^2*b^2*c^12*d^9*f^4 - 14592*a^2*b^
2*c^14*d^7*f^4 - 4416*a^2*b^2*c^16*d^5*f^4 - 576*a^2*b^2*c^18*d^3*f^4 - 384*a*b^3*c*d^20*f^4 + 384*a^3*b*c*d^2
0*f^4 - 2944*a*b^3*c^3*d^18*f^4 - 9728*a*b^3*c^5*d^16*f^4 - 17920*a*b^3*c^7*d^14*f^4 - 19712*a*b^3*c^9*d^12*f^
4 - 12544*a*b^3*c^11*d^10*f^4 - 3584*a*b^3*c^13*d^8*f^4 + 512*a*b^3*c^15*d^6*f^4 + 640*a*b^3*c^17*d^4*f^4 + 12
8*a*b^3*c^19*d^2*f^4 + 2944*a^3*b*c^3*d^18*f^4 + 9728*a^3*b*c^5*d^16*f^4 + 17920*a^3*b*c^7*d^14*f^4 + 19712*a^
3*b*c^9*d^12*f^4 + 12544*a^3*b*c^11*d^10*f^4 + 3584*a^3*b*c^13*d^8*f^4 - 512*a^3*b*c^15*d^6*f^4 - 640*a^3*b*c^
17*d^4*f^4 - 128*a^3*b*c^19*d^2*f^4) + (c + d*tan(e + f*x))^(1/2)*(448*a^2*b^6*d^18*f^3 - 16*b^8*d^18*f^3 - 16
*a^8*d^18*f^3 - 1120*a^4*b^4*d^18*f^3 + 448*a^6*b^2*d^18*f^3 + 320*a^8*c^4*d^14*f^3 + 1024*a^8*c^6*d^12*f^3 +
1440*a^8*c^8*d^10*f^3 + 1024*a^8*c^10*d^8*f^3 + 320*a^8*c^12*d^6*f^3 - 16*a^8*c^16*d^2*f^3 + 320*b^8*c^4*d^14*
f^3 + 1024*b^8*c^6*d^12*f^3 + 1440*b^8*c^8*d^10*f^3 + 1024*b^8*c^10*d^8*f^3 + 320*b^8*c^12*d^6*f^3 - 16*b^8*c^
16*d^2*f^3 - 8960*a^2*b^6*c^4*d^14*f^3 - 28672*a^2*b^6*c^6*d^12*f^3 - 40320*a^2*b^6*c^8*d^10*f^3 - 28672*a^2*b
^6*c^10*d^8*f^3 - 8960*a^2*b^6*c^12*d^6*f^3 + 448*a^2*b^6*c^16*d^2*f^3 + 17920*a^3*b^5*c^3*d^15*f^3 + 32256*a^
3*b^5*c^5*d^13*f^3 + 17920*a^3*b^5*c^7*d^11*f^3 - 17920*a^3*b^5*c^9*d^9*f^3 - 32256*a^3*b^5*c^11*d^7*f^3 - 179
20*a^3*b^5*c^13*d^5*f^3 - 3584*a^3*b^5*c^15*d^3*f^3 + 22400*a^4*b^4*c^4*d^14*f^3 + 71680*a^4*b^4*c^6*d^12*f^3
+ 100800*a^4*b^4*c^8*d^10*f^3 + 71680*a^4*b^4*c^10*d^8*f^3 + 22400*a^4*b^4*c^12*d^6*f^3 - 1120*a^4*b^4*c^16*d^
2*f^3 - 17920*a^5*b^3*c^3*d^15*f^3 - 32256*a^5*b^3*c^5*d^13*f^3 - 17920*a^5*b^3*c^7*d^11*f^3 + 17920*a^5*b^3*c
^9*d^9*f^3 + 32256*a^5*b^3*c^11*d^7*f^3 + 17920*a^5*b^3*c^13*d^5*f^3 + 3584*a^5*b^3*c^15*d^3*f^3 - 8960*a^6*b^
2*c^4*d^14*f^3 - 28672*a^6*b^2*c^6*d^12*f^3 - 40320*a^6*b^2*c^8*d^10*f^3 - 28672*a^6*b^2*c^10*d^8*f^3 - 8960*a
^6*b^2*c^12*d^6*f^3 + 448*a^6*b^2*c^16*d^2*f^3 - 512*a*b^7*c*d^17*f^3 + 512*a^7*b*c*d^17*f^3 - 2560*a*b^7*c^3*
d^15*f^3 - 4608*a*b^7*c^5*d^13*f^3 - 2560*a*b^7*c^7*d^11*f^3 + 2560*a*b^7*c^9*d^9*f^3 + 4608*a*b^7*c^11*d^7*f^
3 + 2560*a*b^7*c^13*d^5*f^3 + 512*a*b^7*c^15*d^3*f^3 + 3584*a^3*b^5*c*d^17*f^3 - 3584*a^5*b^3*c*d^17*f^3 + 256
0*a^7*b*c^3*d^15*f^3 + 4608*a^7*b*c^5*d^13*f^3 + 2560*a^7*b*c^7*d^11*f^3 - 2560*a^7*b*c^9*d^9*f^3 - 4608*a^7*b
*c^11*d^7*f^3 - 2560*a^7*b*c^13*d^5*f^3 - 512*a^7*b*c^15*d^3*f^3))*(-(((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b
^7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^
2 - 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2
+ 2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 +
2240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*
d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 -
640*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 +
80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^
4 + 8*a^14*b^2))^(1/2) + 4*a^8*c^5*f^2 + 4*b^8*c^5*f^2 - 32*a*b^7*d^5*f^2 + 32*a^7*b*d^5*f^2 + 20*a^8*c*d^4*f^
2 + 20*b^8*c*d^4*f^2 - 112*a^2*b^6*c^5*f^2 + 280*a^4*b^4*c^5*f^2 - 112*a^6*b^2*c^5*f^2 + 224*a^3*b^5*d^5*f^2 -
224*a^5*b^3*d^5*f^2 - 40*a^8*c^3*d^2*f^2 - 40*b^8*c^3*d^2*f^2 + 1120*a^2*b^6*c^3*d^2*f^2 - 2240*a^3*b^5*c^2*d
^3*f^2 - 2800*a^4*b^4*c^3*d^2*f^2 + 2240*a^5*b^3*c^2*d^3*f^2 + 1120*a^6*b^2*c^3*d^2*f^2 - 160*a*b^7*c^4*d*f^2
+ 160*a^7*b*c^4*d*f^2 + 320*a*b^7*c^2*d^3*f^2 - 560*a^2*b^6*c*d^4*f^2 + 1120*a^3*b^5*c^4*d*f^2 + 1400*a^4*b^4*
c*d^4*f^2 - 1120*a^5*b^3*c^4*d*f^2 - 560*a^6*b^2*c*d^4*f^2 - 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 +
5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*1i)/(((-(((8*a^8*c^5*f^2 + 8*b^8*c^5
*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a
^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8
*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c
^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 11
20*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2
*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*
c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6
+ 28*a^12*b^4 + 8*a^14*b^2))^(1/2) + 4*a^8*c^5*f^2 + 4*b^8*c^5*f^2 - 32*a*b^7*d^5*f^2 + 32*a^7*b*d^5*f^2 + 20
*a^8*c*d^4*f^2 + 20*b^8*c*d^4*f^2 - 112*a^2*b^6*c^5*f^2 + 280*a^4*b^4*c^5*f^2 - 112*a^6*b^2*c^5*f^2 + 224*a^3*
b^5*d^5*f^2 - 224*a^5*b^3*d^5*f^2 - 40*a^8*c^3*d^2*f^2 - 40*b^8*c^3*d^2*f^2 + 1120*a^2*b^6*c^3*d^2*f^2 - 2240*
a^3*b^5*c^2*d^3*f^2 - 2800*a^4*b^4*c^3*d^2*f^2 + 2240*a^5*b^3*c^2*d^3*f^2 + 1120*a^6*b^2*c^3*d^2*f^2 - 160*a*b
^7*c^4*d*f^2 + 160*a^7*b*c^4*d*f^2 + 320*a*b^7*c^2*d^3*f^2 - 560*a^2*b^6*c*d^4*f^2 + 1120*a^3*b^5*c^4*d*f^2 +
1400*a^4*b^4*c*d^4*f^2 - 1120*a^5*b^3*c^4*d*f^2 - 560*a^6*b^2*c*d^4*f^2 - 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4
+ d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*((c + d*tan(e + f*x))^(
1/2)*(-(((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^
4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^
5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a
^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4
*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 22
40*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c
^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*
a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^(1/2) + 4*a^8*c^5*f^2 + 4*b^8*c^5*f^2 - 32*a*
b^7*d^5*f^2 + 32*a^7*b*d^5*f^2 + 20*a^8*c*d^4*f^2 + 20*b^8*c*d^4*f^2 - 112*a^2*b^6*c^5*f^2 + 280*a^4*b^4*c^5*f
^2 - 112*a^6*b^2*c^5*f^2 + 224*a^3*b^5*d^5*f^2 - 224*a^5*b^3*d^5*f^2 - 40*a^8*c^3*d^2*f^2 - 40*b^8*c^3*d^2*f^2
+ 1120*a^2*b^6*c^3*d^2*f^2 - 2240*a^3*b^5*c^2*d^3*f^2 - 2800*a^4*b^4*c^3*d^2*f^2 + 2240*a^5*b^3*c^2*d^3*f^2 +
1120*a^6*b^2*c^3*d^2*f^2 - 160*a*b^7*c^4*d*f^2 + 160*a^7*b*c^4*d*f^2 + 320*a*b^7*c^2*d^3*f^2 - 560*a^2*b^6*c*
d^4*f^2 + 1120*a^3*b^5*c^4*d*f^2 + 1400*a^4*b^4*c*d^4*f^2 - 1120*a^5*b^3*c^4*d*f^2 - 560*a^6*b^2*c*d^4*f^2 - 3
20*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f
^4)))^(1/2)*(64*c*d^22*f^5 + 640*c^3*d^20*f^5 + 2880*c^5*d^18*f^5 + 7680*c^7*d^16*f^5 + 13440*c^9*d^14*f^5 + 1
6128*c^11*d^12*f^5 + 13440*c^13*d^10*f^5 + 7680*c^15*d^8*f^5 + 2880*c^17*d^6*f^5 + 640*c^19*d^4*f^5 + 64*c^21*
d^2*f^5) - 32*a^4*d^21*f^4 - 32*b^4*d^21*f^4 + 192*a^2*b^2*d^21*f^4 - 160*a^4*c^2*d^19*f^4 - 128*a^4*c^4*d^17*
f^4 + 896*a^4*c^6*d^15*f^4 + 3136*a^4*c^8*d^13*f^4 + 4928*a^4*c^10*d^11*f^4 + 4480*a^4*c^12*d^9*f^4 + 2432*a^4
*c^14*d^7*f^4 + 736*a^4*c^16*d^5*f^4 + 96*a^4*c^18*d^3*f^4 - 160*b^4*c^2*d^19*f^4 - 128*b^4*c^4*d^17*f^4 + 896
*b^4*c^6*d^15*f^4 + 3136*b^4*c^8*d^13*f^4 + 4928*b^4*c^10*d^11*f^4 + 4480*b^4*c^12*d^9*f^4 + 2432*b^4*c^14*d^7
*f^4 + 736*b^4*c^16*d^5*f^4 + 96*b^4*c^18*d^3*f^4 + 960*a^2*b^2*c^2*d^19*f^4 + 768*a^2*b^2*c^4*d^17*f^4 - 5376
*a^2*b^2*c^6*d^15*f^4 - 18816*a^2*b^2*c^8*d^13*f^4 - 29568*a^2*b^2*c^10*d^11*f^4 - 26880*a^2*b^2*c^12*d^9*f^4
- 14592*a^2*b^2*c^14*d^7*f^4 - 4416*a^2*b^2*c^16*d^5*f^4 - 576*a^2*b^2*c^18*d^3*f^4 - 384*a*b^3*c*d^20*f^4 + 3
84*a^3*b*c*d^20*f^4 - 2944*a*b^3*c^3*d^18*f^4 - 9728*a*b^3*c^5*d^16*f^4 - 17920*a*b^3*c^7*d^14*f^4 - 19712*a*b
^3*c^9*d^12*f^4 - 12544*a*b^3*c^11*d^10*f^4 - 3584*a*b^3*c^13*d^8*f^4 + 512*a*b^3*c^15*d^6*f^4 + 640*a*b^3*c^1
7*d^4*f^4 + 128*a*b^3*c^19*d^2*f^4 + 2944*a^3*b*c^3*d^18*f^4 + 9728*a^3*b*c^5*d^16*f^4 + 17920*a^3*b*c^7*d^14*
f^4 + 19712*a^3*b*c^9*d^12*f^4 + 12544*a^3*b*c^11*d^10*f^4 + 3584*a^3*b*c^13*d^8*f^4 - 512*a^3*b*c^15*d^6*f^4
- 640*a^3*b*c^17*d^4*f^4 - 128*a^3*b*c^19*d^2*f^4) - (c + d*tan(e + f*x))^(1/2)*(448*a^2*b^6*d^18*f^3 - 16*b^8
*d^18*f^3 - 16*a^8*d^18*f^3 - 1120*a^4*b^4*d^18*f^3 + 448*a^6*b^2*d^18*f^3 + 320*a^8*c^4*d^14*f^3 + 1024*a^8*c
^6*d^12*f^3 + 1440*a^8*c^8*d^10*f^3 + 1024*a^8*c^10*d^8*f^3 + 320*a^8*c^12*d^6*f^3 - 16*a^8*c^16*d^2*f^3 + 320
*b^8*c^4*d^14*f^3 + 1024*b^8*c^6*d^12*f^3 + 1440*b^8*c^8*d^10*f^3 + 1024*b^8*c^10*d^8*f^3 + 320*b^8*c^12*d^6*f
^3 - 16*b^8*c^16*d^2*f^3 - 8960*a^2*b^6*c^4*d^14*f^3 - 28672*a^2*b^6*c^6*d^12*f^3 - 40320*a^2*b^6*c^8*d^10*f^3
- 28672*a^2*b^6*c^10*d^8*f^3 - 8960*a^2*b^6*c^12*d^6*f^3 + 448*a^2*b^6*c^16*d^2*f^3 + 17920*a^3*b^5*c^3*d^15*
f^3 + 32256*a^3*b^5*c^5*d^13*f^3 + 17920*a^3*b^5*c^7*d^11*f^3 - 17920*a^3*b^5*c^9*d^9*f^3 - 32256*a^3*b^5*c^11
*d^7*f^3 - 17920*a^3*b^5*c^13*d^5*f^3 - 3584*a^3*b^5*c^15*d^3*f^3 + 22400*a^4*b^4*c^4*d^14*f^3 + 71680*a^4*b^4
*c^6*d^12*f^3 + 100800*a^4*b^4*c^8*d^10*f^3 + 71680*a^4*b^4*c^10*d^8*f^3 + 22400*a^4*b^4*c^12*d^6*f^3 - 1120*a
^4*b^4*c^16*d^2*f^3 - 17920*a^5*b^3*c^3*d^15*f^3 - 32256*a^5*b^3*c^5*d^13*f^3 - 17920*a^5*b^3*c^7*d^11*f^3 + 1
7920*a^5*b^3*c^9*d^9*f^3 + 32256*a^5*b^3*c^11*d^7*f^3 + 17920*a^5*b^3*c^13*d^5*f^3 + 3584*a^5*b^3*c^15*d^3*f^3
- 8960*a^6*b^2*c^4*d^14*f^3 - 28672*a^6*b^2*c^6*d^12*f^3 - 40320*a^6*b^2*c^8*d^10*f^3 - 28672*a^6*b^2*c^10*d^
8*f^3 - 8960*a^6*b^2*c^12*d^6*f^3 + 448*a^6*b^2*c^16*d^2*f^3 - 512*a*b^7*c*d^17*f^3 + 512*a^7*b*c*d^17*f^3 - 2
560*a*b^7*c^3*d^15*f^3 - 4608*a*b^7*c^5*d^13*f^3 - 2560*a*b^7*c^7*d^11*f^3 + 2560*a*b^7*c^9*d^9*f^3 + 4608*a*b
^7*c^11*d^7*f^3 + 2560*a*b^7*c^13*d^5*f^3 + 512*a*b^7*c^15*d^3*f^3 + 3584*a^3*b^5*c*d^17*f^3 - 3584*a^5*b^3*c*
d^17*f^3 + 2560*a^7*b*c^3*d^15*f^3 + 4608*a^7*b*c^5*d^13*f^3 + 2560*a^7*b*c^7*d^11*f^3 - 2560*a^7*b*c^9*d^9*f^
3 - 4608*a^7*b*c^11*d^7*f^3 - 2560*a^7*b*c^13*d^5*f^3 - 512*a^7*b*c^15*d^3*f^3))*(-(((8*a^8*c^5*f^2 + 8*b^8*c^
5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*
a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^
8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*
c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1
120*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^
2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160
*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^
6 + 28*a^12*b^4 + 8*a^14*b^2))^(1/2) + 4*a^8*c^5*f^2 + 4*b^8*c^5*f^2 - 32*a*b^7*d^5*f^2 + 32*a^7*b*d^5*f^2 + 2
0*a^8*c*d^4*f^2 + 20*b^8*c*d^4*f^2 - 112*a^2*b^6*c^5*f^2 + 280*a^4*b^4*c^5*f^2 - 112*a^6*b^2*c^5*f^2 + 224*a^3
*b^5*d^5*f^2 - 224*a^5*b^3*d^5*f^2 - 40*a^8*c^3*d^2*f^2 - 40*b^8*c^3*d^2*f^2 + 1120*a^2*b^6*c^3*d^2*f^2 - 2240
*a^3*b^5*c^2*d^3*f^2 - 2800*a^4*b^4*c^3*d^2*f^2 + 2240*a^5*b^3*c^2*d^3*f^2 + 1120*a^6*b^2*c^3*d^2*f^2 - 160*a*
b^7*c^4*d*f^2 + 160*a^7*b*c^4*d*f^2 + 320*a*b^7*c^2*d^3*f^2 - 560*a^2*b^6*c*d^4*f^2 + 1120*a^3*b^5*c^4*d*f^2 +
1400*a^4*b^4*c*d^4*f^2 - 1120*a^5*b^3*c^4*d*f^2 - 560*a^6*b^2*c*d^4*f^2 - 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^
4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2) + ((-(((8*a^8*c^5*f^2
+ 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*
f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f
^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 448
0*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d
^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1
120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6
*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 +
56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^(1/2) + 4*a^8*c^5*f^2 + 4*b^8*c^5*f^2 - 32*a*b^7*d^5*f^2 + 32*a^7*b*d
^5*f^2 + 20*a^8*c*d^4*f^2 + 20*b^8*c*d^4*f^2 - 112*a^2*b^6*c^5*f^2 + 280*a^4*b^4*c^5*f^2 - 112*a^6*b^2*c^5*f^2
+ 224*a^3*b^5*d^5*f^2 - 224*a^5*b^3*d^5*f^2 - 40*a^8*c^3*d^2*f^2 - 40*b^8*c^3*d^2*f^2 + 1120*a^2*b^6*c^3*d^2*
f^2 - 2240*a^3*b^5*c^2*d^3*f^2 - 2800*a^4*b^4*c^3*d^2*f^2 + 2240*a^5*b^3*c^2*d^3*f^2 + 1120*a^6*b^2*c^3*d^2*f^
2 - 160*a*b^7*c^4*d*f^2 + 160*a^7*b*c^4*d*f^2 + 320*a*b^7*c^2*d^3*f^2 - 560*a^2*b^6*c*d^4*f^2 + 1120*a^3*b^5*c
^4*d*f^2 + 1400*a^4*b^4*c*d^4*f^2 - 1120*a^5*b^3*c^4*d*f^2 - 560*a^6*b^2*c*d^4*f^2 - 320*a^7*b*c^2*d^3*f^2)/(1
6*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*(192*a^2*b^2
*d^21*f^4 - 32*a^4*d^21*f^4 - 32*b^4*d^21*f^4 - (c + d*tan(e + f*x))^(1/2)*(-(((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2
- 64*a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^
4*c^5*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*
d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^
3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^
2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^
4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d
^4*f^4 + 80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28
*a^12*b^4 + 8*a^14*b^2))^(1/2) + 4*a^8*c^5*f^2 + 4*b^8*c^5*f^2 - 32*a*b^7*d^5*f^2 + 32*a^7*b*d^5*f^2 + 20*a^8*
c*d^4*f^2 + 20*b^8*c*d^4*f^2 - 112*a^2*b^6*c^5*f^2 + 280*a^4*b^4*c^5*f^2 - 112*a^6*b^2*c^5*f^2 + 224*a^3*b^5*d
^5*f^2 - 224*a^5*b^3*d^5*f^2 - 40*a^8*c^3*d^2*f^2 - 40*b^8*c^3*d^2*f^2 + 1120*a^2*b^6*c^3*d^2*f^2 - 2240*a^3*b
^5*c^2*d^3*f^2 - 2800*a^4*b^4*c^3*d^2*f^2 + 2240*a^5*b^3*c^2*d^3*f^2 + 1120*a^6*b^2*c^3*d^2*f^2 - 160*a*b^7*c^
4*d*f^2 + 160*a^7*b*c^4*d*f^2 + 320*a*b^7*c^2*d^3*f^2 - 560*a^2*b^6*c*d^4*f^2 + 1120*a^3*b^5*c^4*d*f^2 + 1400*
a^4*b^4*c*d^4*f^2 - 1120*a^5*b^3*c^4*d*f^2 - 560*a^6*b^2*c*d^4*f^2 - 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^
10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*(64*c*d^22*f^5 + 640*c^3*d^2
0*f^5 + 2880*c^5*d^18*f^5 + 7680*c^7*d^16*f^5 + 13440*c^9*d^14*f^5 + 16128*c^11*d^12*f^5 + 13440*c^13*d^10*f^5
+ 7680*c^15*d^8*f^5 + 2880*c^17*d^6*f^5 + 640*c^19*d^4*f^5 + 64*c^21*d^2*f^5) - 160*a^4*c^2*d^19*f^4 - 128*a^
4*c^4*d^17*f^4 + 896*a^4*c^6*d^15*f^4 + 3136*a^4*c^8*d^13*f^4 + 4928*a^4*c^10*d^11*f^4 + 4480*a^4*c^12*d^9*f^4
+ 2432*a^4*c^14*d^7*f^4 + 736*a^4*c^16*d^5*f^4 + 96*a^4*c^18*d^3*f^4 - 160*b^4*c^2*d^19*f^4 - 128*b^4*c^4*d^1
7*f^4 + 896*b^4*c^6*d^15*f^4 + 3136*b^4*c^8*d^13*f^4 + 4928*b^4*c^10*d^11*f^4 + 4480*b^4*c^12*d^9*f^4 + 2432*b
^4*c^14*d^7*f^4 + 736*b^4*c^16*d^5*f^4 + 96*b^4*c^18*d^3*f^4 + 960*a^2*b^2*c^2*d^19*f^4 + 768*a^2*b^2*c^4*d^17
*f^4 - 5376*a^2*b^2*c^6*d^15*f^4 - 18816*a^2*b^2*c^8*d^13*f^4 - 29568*a^2*b^2*c^10*d^11*f^4 - 26880*a^2*b^2*c^
12*d^9*f^4 - 14592*a^2*b^2*c^14*d^7*f^4 - 4416*a^2*b^2*c^16*d^5*f^4 - 576*a^2*b^2*c^18*d^3*f^4 - 384*a*b^3*c*d
^20*f^4 + 384*a^3*b*c*d^20*f^4 - 2944*a*b^3*c^3*d^18*f^4 - 9728*a*b^3*c^5*d^16*f^4 - 17920*a*b^3*c^7*d^14*f^4
- 19712*a*b^3*c^9*d^12*f^4 - 12544*a*b^3*c^11*d^10*f^4 - 3584*a*b^3*c^13*d^8*f^4 + 512*a*b^3*c^15*d^6*f^4 + 64
0*a*b^3*c^17*d^4*f^4 + 128*a*b^3*c^19*d^2*f^4 + 2944*a^3*b*c^3*d^18*f^4 + 9728*a^3*b*c^5*d^16*f^4 + 17920*a^3*
b*c^7*d^14*f^4 + 19712*a^3*b*c^9*d^12*f^4 + 12544*a^3*b*c^11*d^10*f^4 + 3584*a^3*b*c^13*d^8*f^4 - 512*a^3*b*c^
15*d^6*f^4 - 640*a^3*b*c^17*d^4*f^4 - 128*a^3*b*c^19*d^2*f^4) + (c + d*tan(e + f*x))^(1/2)*(448*a^2*b^6*d^18*f
^3 - 16*b^8*d^18*f^3 - 16*a^8*d^18*f^3 - 1120*a^4*b^4*d^18*f^3 + 448*a^6*b^2*d^18*f^3 + 320*a^8*c^4*d^14*f^3 +
1024*a^8*c^6*d^12*f^3 + 1440*a^8*c^8*d^10*f^3 + 1024*a^8*c^10*d^8*f^3 + 320*a^8*c^12*d^6*f^3 - 16*a^8*c^16*d^
2*f^3 + 320*b^8*c^4*d^14*f^3 + 1024*b^8*c^6*d^12*f^3 + 1440*b^8*c^8*d^10*f^3 + 1024*b^8*c^10*d^8*f^3 + 320*b^8
*c^12*d^6*f^3 - 16*b^8*c^16*d^2*f^3 - 8960*a^2*b^6*c^4*d^14*f^3 - 28672*a^2*b^6*c^6*d^12*f^3 - 40320*a^2*b^6*c
^8*d^10*f^3 - 28672*a^2*b^6*c^10*d^8*f^3 - 8960*a^2*b^6*c^12*d^6*f^3 + 448*a^2*b^6*c^16*d^2*f^3 + 17920*a^3*b^
5*c^3*d^15*f^3 + 32256*a^3*b^5*c^5*d^13*f^3 + 17920*a^3*b^5*c^7*d^11*f^3 - 17920*a^3*b^5*c^9*d^9*f^3 - 32256*a
^3*b^5*c^11*d^7*f^3 - 17920*a^3*b^5*c^13*d^5*f^3 - 3584*a^3*b^5*c^15*d^3*f^3 + 22400*a^4*b^4*c^4*d^14*f^3 + 71
680*a^4*b^4*c^6*d^12*f^3 + 100800*a^4*b^4*c^8*d^10*f^3 + 71680*a^4*b^4*c^10*d^8*f^3 + 22400*a^4*b^4*c^12*d^6*f
^3 - 1120*a^4*b^4*c^16*d^2*f^3 - 17920*a^5*b^3*c^3*d^15*f^3 - 32256*a^5*b^3*c^5*d^13*f^3 - 17920*a^5*b^3*c^7*d
^11*f^3 + 17920*a^5*b^3*c^9*d^9*f^3 + 32256*a^5*b^3*c^11*d^7*f^3 + 17920*a^5*b^3*c^13*d^5*f^3 + 3584*a^5*b^3*c
^15*d^3*f^3 - 8960*a^6*b^2*c^4*d^14*f^3 - 28672*a^6*b^2*c^6*d^12*f^3 - 40320*a^6*b^2*c^8*d^10*f^3 - 28672*a^6*
b^2*c^10*d^8*f^3 - 8960*a^6*b^2*c^12*d^6*f^3 + 448*a^6*b^2*c^16*d^2*f^3 - 512*a*b^7*c*d^17*f^3 + 512*a^7*b*c*d
^17*f^3 - 2560*a*b^7*c^3*d^15*f^3 - 4608*a*b^7*c^5*d^13*f^3 - 2560*a*b^7*c^7*d^11*f^3 + 2560*a*b^7*c^9*d^9*f^3
+ 4608*a*b^7*c^11*d^7*f^3 + 2560*a*b^7*c^13*d^5*f^3 + 512*a*b^7*c^15*d^3*f^3 + 3584*a^3*b^5*c*d^17*f^3 - 3584
*a^5*b^3*c*d^17*f^3 + 2560*a^7*b*c^3*d^15*f^3 + 4608*a^7*b*c^5*d^13*f^3 + 2560*a^7*b*c^7*d^11*f^3 - 2560*a^7*b
*c^9*d^9*f^3 - 4608*a^7*b*c^11*d^7*f^3 - 2560*a^7*b*c^13*d^5*f^3 - 512*a^7*b*c^15*d^3*f^3))*(-(((8*a^8*c^5*f^2
+ 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5
*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*
f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 44
80*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*
d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 -
1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^
6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 +
56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^(1/2) + 4*a^8*c^5*f^2 + 4*b^8*c^5*f^2 - 32*a*b^7*d^5*f^2 + 32*a^7*b*
d^5*f^2 + 20*a^8*c*d^4*f^2 + 20*b^8*c*d^4*f^2 - 112*a^2*b^6*c^5*f^2 + 280*a^4*b^4*c^5*f^2 - 112*a^6*b^2*c^5*f^
2 + 224*a^3*b^5*d^5*f^2 - 224*a^5*b^3*d^5*f^2 - 40*a^8*c^3*d^2*f^2 - 40*b^8*c^3*d^2*f^2 + 1120*a^2*b^6*c^3*d^2
*f^2 - 2240*a^3*b^5*c^2*d^3*f^2 - 2800*a^4*b^4*c^3*d^2*f^2 + 2240*a^5*b^3*c^2*d^3*f^2 + 1120*a^6*b^2*c^3*d^2*f
^2 - 160*a*b^7*c^4*d*f^2 + 160*a^7*b*c^4*d*f^2 + 320*a*b^7*c^2*d^3*f^2 - 560*a^2*b^6*c*d^4*f^2 + 1120*a^3*b^5*
c^4*d*f^2 + 1400*a^4*b^4*c*d^4*f^2 - 1120*a^5*b^3*c^4*d*f^2 - 560*a^6*b^2*c*d^4*f^2 - 320*a^7*b*c^2*d^3*f^2)/(
16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2) + 64*a*b^11
*d^16*f^2 - 64*a^11*b*d^16*f^2 - 32*a^12*c*d^15*f^2 - 32*b^12*c*d^15*f^2 + 192*a^3*b^9*d^16*f^2 + 128*a^5*b^7*
d^16*f^2 - 128*a^7*b^5*d^16*f^2 - 192*a^9*b^3*d^16*f^2 - 192*a^12*c^3*d^13*f^2 - 480*a^12*c^5*d^11*f^2 - 640*a
^12*c^7*d^9*f^2 - 480*a^12*c^9*d^7*f^2 - 192*a^12*c^11*d^5*f^2 - 32*a^12*c^13*d^3*f^2 - 192*b^12*c^3*d^13*f^2
- 480*b^12*c^5*d^11*f^2 - 640*b^12*c^7*d^9*f^2 - 480*b^12*c^9*d^7*f^2 - 192*b^12*c^11*d^5*f^2 - 32*b^12*c^13*d
^3*f^2 + 384*a^2*b^10*c^3*d^13*f^2 + 960*a^2*b^10*c^5*d^11*f^2 + 1280*a^2*b^10*c^7*d^9*f^2 + 960*a^2*b^10*c^9*
d^7*f^2 + 384*a^2*b^10*c^11*d^5*f^2 + 64*a^2*b^10*c^13*d^3*f^2 + 960*a^3*b^9*c^2*d^14*f^2 + 1728*a^3*b^9*c^4*d
^12*f^2 + 960*a^3*b^9*c^6*d^10*f^2 - 960*a^3*b^9*c^8*d^8*f^2 - 1728*a^3*b^9*c^10*d^6*f^2 - 960*a^3*b^9*c^12*d^
4*f^2 - 192*a^3*b^9*c^14*d^2*f^2 + 3264*a^4*b^8*c^3*d^13*f^2 + 8160*a^4*b^8*c^5*d^11*f^2 + 10880*a^4*b^8*c^7*d
^9*f^2 + 8160*a^4*b^8*c^9*d^7*f^2 + 3264*a^4*b^8*c^11*d^5*f^2 + 544*a^4*b^8*c^13*d^3*f^2 + 640*a^5*b^7*c^2*d^1
4*f^2 + 1152*a^5*b^7*c^4*d^12*f^2 + 640*a^5*b^7*c^6*d^10*f^2 - 640*a^5*b^7*c^8*d^8*f^2 - 1152*a^5*b^7*c^10*d^6
*f^2 - 640*a^5*b^7*c^12*d^4*f^2 - 128*a^5*b^7*c^14*d^2*f^2 + 5376*a^6*b^6*c^3*d^13*f^2 + 13440*a^6*b^6*c^5*d^1
1*f^2 + 17920*a^6*b^6*c^7*d^9*f^2 + 13440*a^6*b^6*c^9*d^7*f^2 + 5376*a^6*b^6*c^11*d^5*f^2 + 896*a^6*b^6*c^13*d
^3*f^2 - 640*a^7*b^5*c^2*d^14*f^2 - 1152*a^7*b^5*c^4*d^12*f^2 - 640*a^7*b^5*c^6*d^10*f^2 + 640*a^7*b^5*c^8*d^8
*f^2 + 1152*a^7*b^5*c^10*d^6*f^2 + 640*a^7*b^5*c^12*d^4*f^2 + 128*a^7*b^5*c^14*d^2*f^2 + 3264*a^8*b^4*c^3*d^13
*f^2 + 8160*a^8*b^4*c^5*d^11*f^2 + 10880*a^8*b^4*c^7*d^9*f^2 + 8160*a^8*b^4*c^9*d^7*f^2 + 3264*a^8*b^4*c^11*d^
5*f^2 + 544*a^8*b^4*c^13*d^3*f^2 - 960*a^9*b^3*c^2*d^14*f^2 - 1728*a^9*b^3*c^4*d^12*f^2 - 960*a^9*b^3*c^6*d^10
*f^2 + 960*a^9*b^3*c^8*d^8*f^2 + 1728*a^9*b^3*c^10*d^6*f^2 + 960*a^9*b^3*c^12*d^4*f^2 + 192*a^9*b^3*c^14*d^2*f
^2 + 384*a^10*b^2*c^3*d^13*f^2 + 960*a^10*b^2*c^5*d^11*f^2 + 1280*a^10*b^2*c^7*d^9*f^2 + 960*a^10*b^2*c^9*d^7*
f^2 + 384*a^10*b^2*c^11*d^5*f^2 + 64*a^10*b^2*c^13*d^3*f^2 + 320*a*b^11*c^2*d^14*f^2 + 576*a*b^11*c^4*d^12*f^2
+ 320*a*b^11*c^6*d^10*f^2 - 320*a*b^11*c^8*d^8*f^2 - 576*a*b^11*c^10*d^6*f^2 - 320*a*b^11*c^12*d^4*f^2 - 64*a
*b^11*c^14*d^2*f^2 + 64*a^2*b^10*c*d^15*f^2 + 544*a^4*b^8*c*d^15*f^2 + 896*a^6*b^6*c*d^15*f^2 + 544*a^8*b^4*c*
d^15*f^2 + 64*a^10*b^2*c*d^15*f^2 - 320*a^11*b*c^2*d^14*f^2 - 576*a^11*b*c^4*d^12*f^2 - 320*a^11*b*c^6*d^10*f^
2 + 320*a^11*b*c^8*d^8*f^2 + 576*a^11*b*c^10*d^6*f^2 + 320*a^11*b*c^12*d^4*f^2 + 64*a^11*b*c^14*d^2*f^2))*(-((
(8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 2
24*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 8
0*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^
3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 +
640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^
3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^
4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10
+ 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^(1/2) + 4*a^8*c^5*f^2 + 4*b^8*c^5*f^2 - 32*a*b^7*d^5*f
^2 + 32*a^7*b*d^5*f^2 + 20*a^8*c*d^4*f^2 + 20*b^8*c*d^4*f^2 - 112*a^2*b^6*c^5*f^2 + 280*a^4*b^4*c^5*f^2 - 112*
a^6*b^2*c^5*f^2 + 224*a^3*b^5*d^5*f^2 - 224*a^5*b^3*d^5*f^2 - 40*a^8*c^3*d^2*f^2 - 40*b^8*c^3*d^2*f^2 + 1120*a
^2*b^6*c^3*d^2*f^2 - 2240*a^3*b^5*c^2*d^3*f^2 - 2800*a^4*b^4*c^3*d^2*f^2 + 2240*a^5*b^3*c^2*d^3*f^2 + 1120*a^6
*b^2*c^3*d^2*f^2 - 160*a*b^7*c^4*d*f^2 + 160*a^7*b*c^4*d*f^2 + 320*a*b^7*c^2*d^3*f^2 - 560*a^2*b^6*c*d^4*f^2 +
1120*a^3*b^5*c^4*d*f^2 + 1400*a^4*b^4*c*d^4*f^2 - 1120*a^5*b^3*c^4*d*f^2 - 560*a^6*b^2*c*d^4*f^2 - 320*a^7*b*
c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/
2)*2i - atan(((((((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40
*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a
^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2
- 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*
a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4
*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f
^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b
^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^(1/2) - 4*a^8*c^5*f^2 - 4*b^8*c^5*f^
2 + 32*a*b^7*d^5*f^2 - 32*a^7*b*d^5*f^2 - 20*a^8*c*d^4*f^2 - 20*b^8*c*d^4*f^2 + 112*a^2*b^6*c^5*f^2 - 280*a^4*
b^4*c^5*f^2 + 112*a^6*b^2*c^5*f^2 - 224*a^3*b^5*d^5*f^2 + 224*a^5*b^3*d^5*f^2 + 40*a^8*c^3*d^2*f^2 + 40*b^8*c^
3*d^2*f^2 - 1120*a^2*b^6*c^3*d^2*f^2 + 2240*a^3*b^5*c^2*d^3*f^2 + 2800*a^4*b^4*c^3*d^2*f^2 - 2240*a^5*b^3*c^2*
d^3*f^2 - 1120*a^6*b^2*c^3*d^2*f^2 + 160*a*b^7*c^4*d*f^2 - 160*a^7*b*c^4*d*f^2 - 320*a*b^7*c^2*d^3*f^2 + 560*a
^2*b^6*c*d^4*f^2 - 1120*a^3*b^5*c^4*d*f^2 - 1400*a^4*b^4*c*d^4*f^2 + 1120*a^5*b^3*c^4*d*f^2 + 560*a^6*b^2*c*d^
4*f^2 + 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*
c^8*d^2*f^4)))^(1/2)*((c + d*tan(e + f*x))^(1/2)*((((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7
*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5
*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*
d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^
2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^3*
b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f
^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a
^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^(1
/2) - 4*a^8*c^5*f^2 - 4*b^8*c^5*f^2 + 32*a*b^7*d^5*f^2 - 32*a^7*b*d^5*f^2 - 20*a^8*c*d^4*f^2 - 20*b^8*c*d^4*f^
2 + 112*a^2*b^6*c^5*f^2 - 280*a^4*b^4*c^5*f^2 + 112*a^6*b^2*c^5*f^2 - 224*a^3*b^5*d^5*f^2 + 224*a^5*b^3*d^5*f^
2 + 40*a^8*c^3*d^2*f^2 + 40*b^8*c^3*d^2*f^2 - 1120*a^2*b^6*c^3*d^2*f^2 + 2240*a^3*b^5*c^2*d^3*f^2 + 2800*a^4*b
^4*c^3*d^2*f^2 - 2240*a^5*b^3*c^2*d^3*f^2 - 1120*a^6*b^2*c^3*d^2*f^2 + 160*a*b^7*c^4*d*f^2 - 160*a^7*b*c^4*d*f
^2 - 320*a*b^7*c^2*d^3*f^2 + 560*a^2*b^6*c*d^4*f^2 - 1120*a^3*b^5*c^4*d*f^2 - 1400*a^4*b^4*c*d^4*f^2 + 1120*a^
5*b^3*c^4*d*f^2 + 560*a^6*b^2*c*d^4*f^2 + 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10
*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*(64*c*d^22*f^5 + 640*c^3*d^20*f^5 + 2880*c^5*d^18*f^5 +
7680*c^7*d^16*f^5 + 13440*c^9*d^14*f^5 + 16128*c^11*d^12*f^5 + 13440*c^13*d^10*f^5 + 7680*c^15*d^8*f^5 + 2880
*c^17*d^6*f^5 + 640*c^19*d^4*f^5 + 64*c^21*d^2*f^5) - 32*a^4*d^21*f^4 - 32*b^4*d^21*f^4 + 192*a^2*b^2*d^21*f^4
- 160*a^4*c^2*d^19*f^4 - 128*a^4*c^4*d^17*f^4 + 896*a^4*c^6*d^15*f^4 + 3136*a^4*c^8*d^13*f^4 + 4928*a^4*c^10*
d^11*f^4 + 4480*a^4*c^12*d^9*f^4 + 2432*a^4*c^14*d^7*f^4 + 736*a^4*c^16*d^5*f^4 + 96*a^4*c^18*d^3*f^4 - 160*b^
4*c^2*d^19*f^4 - 128*b^4*c^4*d^17*f^4 + 896*b^4*c^6*d^15*f^4 + 3136*b^4*c^8*d^13*f^4 + 4928*b^4*c^10*d^11*f^4
+ 4480*b^4*c^12*d^9*f^4 + 2432*b^4*c^14*d^7*f^4 + 736*b^4*c^16*d^5*f^4 + 96*b^4*c^18*d^3*f^4 + 960*a^2*b^2*c^2
*d^19*f^4 + 768*a^2*b^2*c^4*d^17*f^4 - 5376*a^2*b^2*c^6*d^15*f^4 - 18816*a^2*b^2*c^8*d^13*f^4 - 29568*a^2*b^2*
c^10*d^11*f^4 - 26880*a^2*b^2*c^12*d^9*f^4 - 14592*a^2*b^2*c^14*d^7*f^4 - 4416*a^2*b^2*c^16*d^5*f^4 - 576*a^2*
b^2*c^18*d^3*f^4 - 384*a*b^3*c*d^20*f^4 + 384*a^3*b*c*d^20*f^4 - 2944*a*b^3*c^3*d^18*f^4 - 9728*a*b^3*c^5*d^16
*f^4 - 17920*a*b^3*c^7*d^14*f^4 - 19712*a*b^3*c^9*d^12*f^4 - 12544*a*b^3*c^11*d^10*f^4 - 3584*a*b^3*c^13*d^8*f
^4 + 512*a*b^3*c^15*d^6*f^4 + 640*a*b^3*c^17*d^4*f^4 + 128*a*b^3*c^19*d^2*f^4 + 2944*a^3*b*c^3*d^18*f^4 + 9728
*a^3*b*c^5*d^16*f^4 + 17920*a^3*b*c^7*d^14*f^4 + 19712*a^3*b*c^9*d^12*f^4 + 12544*a^3*b*c^11*d^10*f^4 + 3584*a
^3*b*c^13*d^8*f^4 - 512*a^3*b*c^15*d^6*f^4 - 640*a^3*b*c^17*d^4*f^4 - 128*a^3*b*c^19*d^2*f^4) - (c + d*tan(e +
f*x))^(1/2)*(448*a^2*b^6*d^18*f^3 - 16*b^8*d^18*f^3 - 16*a^8*d^18*f^3 - 1120*a^4*b^4*d^18*f^3 + 448*a^6*b^2*d
^18*f^3 + 320*a^8*c^4*d^14*f^3 + 1024*a^8*c^6*d^12*f^3 + 1440*a^8*c^8*d^10*f^3 + 1024*a^8*c^10*d^8*f^3 + 320*a
^8*c^12*d^6*f^3 - 16*a^8*c^16*d^2*f^3 + 320*b^8*c^4*d^14*f^3 + 1024*b^8*c^6*d^12*f^3 + 1440*b^8*c^8*d^10*f^3 +
1024*b^8*c^10*d^8*f^3 + 320*b^8*c^12*d^6*f^3 - 16*b^8*c^16*d^2*f^3 - 8960*a^2*b^6*c^4*d^14*f^3 - 28672*a^2*b^
6*c^6*d^12*f^3 - 40320*a^2*b^6*c^8*d^10*f^3 - 28672*a^2*b^6*c^10*d^8*f^3 - 8960*a^2*b^6*c^12*d^6*f^3 + 448*a^2
*b^6*c^16*d^2*f^3 + 17920*a^3*b^5*c^3*d^15*f^3 + 32256*a^3*b^5*c^5*d^13*f^3 + 17920*a^3*b^5*c^7*d^11*f^3 - 179
20*a^3*b^5*c^9*d^9*f^3 - 32256*a^3*b^5*c^11*d^7*f^3 - 17920*a^3*b^5*c^13*d^5*f^3 - 3584*a^3*b^5*c^15*d^3*f^3 +
22400*a^4*b^4*c^4*d^14*f^3 + 71680*a^4*b^4*c^6*d^12*f^3 + 100800*a^4*b^4*c^8*d^10*f^3 + 71680*a^4*b^4*c^10*d^
8*f^3 + 22400*a^4*b^4*c^12*d^6*f^3 - 1120*a^4*b^4*c^16*d^2*f^3 - 17920*a^5*b^3*c^3*d^15*f^3 - 32256*a^5*b^3*c^
5*d^13*f^3 - 17920*a^5*b^3*c^7*d^11*f^3 + 17920*a^5*b^3*c^9*d^9*f^3 + 32256*a^5*b^3*c^11*d^7*f^3 + 17920*a^5*b
^3*c^13*d^5*f^3 + 3584*a^5*b^3*c^15*d^3*f^3 - 8960*a^6*b^2*c^4*d^14*f^3 - 28672*a^6*b^2*c^6*d^12*f^3 - 40320*a
^6*b^2*c^8*d^10*f^3 - 28672*a^6*b^2*c^10*d^8*f^3 - 8960*a^6*b^2*c^12*d^6*f^3 + 448*a^6*b^2*c^16*d^2*f^3 - 512*
a*b^7*c*d^17*f^3 + 512*a^7*b*c*d^17*f^3 - 2560*a*b^7*c^3*d^15*f^3 - 4608*a*b^7*c^5*d^13*f^3 - 2560*a*b^7*c^7*d
^11*f^3 + 2560*a*b^7*c^9*d^9*f^3 + 4608*a*b^7*c^11*d^7*f^3 + 2560*a*b^7*c^13*d^5*f^3 + 512*a*b^7*c^15*d^3*f^3
+ 3584*a^3*b^5*c*d^17*f^3 - 3584*a^5*b^3*c*d^17*f^3 + 2560*a^7*b*c^3*d^15*f^3 + 4608*a^7*b*c^5*d^13*f^3 + 2560
*a^7*b*c^7*d^11*f^3 - 2560*a^7*b*c^9*d^9*f^3 - 4608*a^7*b*c^11*d^7*f^3 - 2560*a^7*b*c^13*d^5*f^3 - 512*a^7*b*c
^15*d^3*f^3))*((((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*
b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^
5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2
- 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a
^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*
f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^
4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^
12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^(1/2) - 4*a^8*c^5*f^2 - 4*b^8*c^5*f^2
+ 32*a*b^7*d^5*f^2 - 32*a^7*b*d^5*f^2 - 20*a^8*c*d^4*f^2 - 20*b^8*c*d^4*f^2 + 112*a^2*b^6*c^5*f^2 - 280*a^4*b
^4*c^5*f^2 + 112*a^6*b^2*c^5*f^2 - 224*a^3*b^5*d^5*f^2 + 224*a^5*b^3*d^5*f^2 + 40*a^8*c^3*d^2*f^2 + 40*b^8*c^3
*d^2*f^2 - 1120*a^2*b^6*c^3*d^2*f^2 + 2240*a^3*b^5*c^2*d^3*f^2 + 2800*a^4*b^4*c^3*d^2*f^2 - 2240*a^5*b^3*c^2*d
^3*f^2 - 1120*a^6*b^2*c^3*d^2*f^2 + 160*a*b^7*c^4*d*f^2 - 160*a^7*b*c^4*d*f^2 - 320*a*b^7*c^2*d^3*f^2 + 560*a^
2*b^6*c*d^4*f^2 - 1120*a^3*b^5*c^4*d*f^2 - 1400*a^4*b^4*c*d^4*f^2 + 1120*a^5*b^3*c^4*d*f^2 + 560*a^6*b^2*c*d^4
*f^2 + 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c
^8*d^2*f^4)))^(1/2)*1i - (((((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c*d
^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^5*
f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^5*
c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4*d
*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*a^
4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^4
+ 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^14
+ 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^(1/2) - 4*a^8*c^5*f^2 - 4
*b^8*c^5*f^2 + 32*a*b^7*d^5*f^2 - 32*a^7*b*d^5*f^2 - 20*a^8*c*d^4*f^2 - 20*b^8*c*d^4*f^2 + 112*a^2*b^6*c^5*f^2
- 280*a^4*b^4*c^5*f^2 + 112*a^6*b^2*c^5*f^2 - 224*a^3*b^5*d^5*f^2 + 224*a^5*b^3*d^5*f^2 + 40*a^8*c^3*d^2*f^2
+ 40*b^8*c^3*d^2*f^2 - 1120*a^2*b^6*c^3*d^2*f^2 + 2240*a^3*b^5*c^2*d^3*f^2 + 2800*a^4*b^4*c^3*d^2*f^2 - 2240*a
^5*b^3*c^2*d^3*f^2 - 1120*a^6*b^2*c^3*d^2*f^2 + 160*a*b^7*c^4*d*f^2 - 160*a^7*b*c^4*d*f^2 - 320*a*b^7*c^2*d^3*
f^2 + 560*a^2*b^6*c*d^4*f^2 - 1120*a^3*b^5*c^4*d*f^2 - 1400*a^4*b^4*c*d^4*f^2 + 1120*a^5*b^3*c^4*d*f^2 + 560*a
^6*b^2*c*d^4*f^2 + 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6*d
^4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*(192*a^2*b^2*d^21*f^4 - 32*a^4*d^21*f^4 - 32*b^4*d^21*f^4 - (c + d*tan(e + f*x
))^(1/2)*((((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c
*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3
*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 560
0*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*
c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 -
2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 8
0*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 +
56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^(1/2) - 4*a^8*c^5*f^2 - 4*b^8*c^5*f^2 + 32
*a*b^7*d^5*f^2 - 32*a^7*b*d^5*f^2 - 20*a^8*c*d^4*f^2 - 20*b^8*c*d^4*f^2 + 112*a^2*b^6*c^5*f^2 - 280*a^4*b^4*c^
5*f^2 + 112*a^6*b^2*c^5*f^2 - 224*a^3*b^5*d^5*f^2 + 224*a^5*b^3*d^5*f^2 + 40*a^8*c^3*d^2*f^2 + 40*b^8*c^3*d^2*
f^2 - 1120*a^2*b^6*c^3*d^2*f^2 + 2240*a^3*b^5*c^2*d^3*f^2 + 2800*a^4*b^4*c^3*d^2*f^2 - 2240*a^5*b^3*c^2*d^3*f^
2 - 1120*a^6*b^2*c^3*d^2*f^2 + 160*a*b^7*c^4*d*f^2 - 160*a^7*b*c^4*d*f^2 - 320*a*b^7*c^2*d^3*f^2 + 560*a^2*b^6
*c*d^4*f^2 - 1120*a^3*b^5*c^4*d*f^2 - 1400*a^4*b^4*c*d^4*f^2 + 1120*a^5*b^3*c^4*d*f^2 + 560*a^6*b^2*c*d^4*f^2
+ 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^
2*f^4)))^(1/2)*(64*c*d^22*f^5 + 640*c^3*d^20*f^5 + 2880*c^5*d^18*f^5 + 7680*c^7*d^16*f^5 + 13440*c^9*d^14*f^5
+ 16128*c^11*d^12*f^5 + 13440*c^13*d^10*f^5 + 7680*c^15*d^8*f^5 + 2880*c^17*d^6*f^5 + 640*c^19*d^4*f^5 + 64*c^
21*d^2*f^5) - 160*a^4*c^2*d^19*f^4 - 128*a^4*c^4*d^17*f^4 + 896*a^4*c^6*d^15*f^4 + 3136*a^4*c^8*d^13*f^4 + 492
8*a^4*c^10*d^11*f^4 + 4480*a^4*c^12*d^9*f^4 + 2432*a^4*c^14*d^7*f^4 + 736*a^4*c^16*d^5*f^4 + 96*a^4*c^18*d^3*f
^4 - 160*b^4*c^2*d^19*f^4 - 128*b^4*c^4*d^17*f^4 + 896*b^4*c^6*d^15*f^4 + 3136*b^4*c^8*d^13*f^4 + 4928*b^4*c^1
0*d^11*f^4 + 4480*b^4*c^12*d^9*f^4 + 2432*b^4*c^14*d^7*f^4 + 736*b^4*c^16*d^5*f^4 + 96*b^4*c^18*d^3*f^4 + 960*
a^2*b^2*c^2*d^19*f^4 + 768*a^2*b^2*c^4*d^17*f^4 - 5376*a^2*b^2*c^6*d^15*f^4 - 18816*a^2*b^2*c^8*d^13*f^4 - 295
68*a^2*b^2*c^10*d^11*f^4 - 26880*a^2*b^2*c^12*d^9*f^4 - 14592*a^2*b^2*c^14*d^7*f^4 - 4416*a^2*b^2*c^16*d^5*f^4
- 576*a^2*b^2*c^18*d^3*f^4 - 384*a*b^3*c*d^20*f^4 + 384*a^3*b*c*d^20*f^4 - 2944*a*b^3*c^3*d^18*f^4 - 9728*a*b
^3*c^5*d^16*f^4 - 17920*a*b^3*c^7*d^14*f^4 - 19712*a*b^3*c^9*d^12*f^4 - 12544*a*b^3*c^11*d^10*f^4 - 3584*a*b^3
*c^13*d^8*f^4 + 512*a*b^3*c^15*d^6*f^4 + 640*a*b^3*c^17*d^4*f^4 + 128*a*b^3*c^19*d^2*f^4 + 2944*a^3*b*c^3*d^18
*f^4 + 9728*a^3*b*c^5*d^16*f^4 + 17920*a^3*b*c^7*d^14*f^4 + 19712*a^3*b*c^9*d^12*f^4 + 12544*a^3*b*c^11*d^10*f
^4 + 3584*a^3*b*c^13*d^8*f^4 - 512*a^3*b*c^15*d^6*f^4 - 640*a^3*b*c^17*d^4*f^4 - 128*a^3*b*c^19*d^2*f^4) + (c
+ d*tan(e + f*x))^(1/2)*(448*a^2*b^6*d^18*f^3 - 16*b^8*d^18*f^3 - 16*a^8*d^18*f^3 - 1120*a^4*b^4*d^18*f^3 + 44
8*a^6*b^2*d^18*f^3 + 320*a^8*c^4*d^14*f^3 + 1024*a^8*c^6*d^12*f^3 + 1440*a^8*c^8*d^10*f^3 + 1024*a^8*c^10*d^8*
f^3 + 320*a^8*c^12*d^6*f^3 - 16*a^8*c^16*d^2*f^3 + 320*b^8*c^4*d^14*f^3 + 1024*b^8*c^6*d^12*f^3 + 1440*b^8*c^8
*d^10*f^3 + 1024*b^8*c^10*d^8*f^3 + 320*b^8*c^12*d^6*f^3 - 16*b^8*c^16*d^2*f^3 - 8960*a^2*b^6*c^4*d^14*f^3 - 2
8672*a^2*b^6*c^6*d^12*f^3 - 40320*a^2*b^6*c^8*d^10*f^3 - 28672*a^2*b^6*c^10*d^8*f^3 - 8960*a^2*b^6*c^12*d^6*f^
3 + 448*a^2*b^6*c^16*d^2*f^3 + 17920*a^3*b^5*c^3*d^15*f^3 + 32256*a^3*b^5*c^5*d^13*f^3 + 17920*a^3*b^5*c^7*d^1
1*f^3 - 17920*a^3*b^5*c^9*d^9*f^3 - 32256*a^3*b^5*c^11*d^7*f^3 - 17920*a^3*b^5*c^13*d^5*f^3 - 3584*a^3*b^5*c^1
5*d^3*f^3 + 22400*a^4*b^4*c^4*d^14*f^3 + 71680*a^4*b^4*c^6*d^12*f^3 + 100800*a^4*b^4*c^8*d^10*f^3 + 71680*a^4*
b^4*c^10*d^8*f^3 + 22400*a^4*b^4*c^12*d^6*f^3 - 1120*a^4*b^4*c^16*d^2*f^3 - 17920*a^5*b^3*c^3*d^15*f^3 - 32256
*a^5*b^3*c^5*d^13*f^3 - 17920*a^5*b^3*c^7*d^11*f^3 + 17920*a^5*b^3*c^9*d^9*f^3 + 32256*a^5*b^3*c^11*d^7*f^3 +
17920*a^5*b^3*c^13*d^5*f^3 + 3584*a^5*b^3*c^15*d^3*f^3 - 8960*a^6*b^2*c^4*d^14*f^3 - 28672*a^6*b^2*c^6*d^12*f^
3 - 40320*a^6*b^2*c^8*d^10*f^3 - 28672*a^6*b^2*c^10*d^8*f^3 - 8960*a^6*b^2*c^12*d^6*f^3 + 448*a^6*b^2*c^16*d^2
*f^3 - 512*a*b^7*c*d^17*f^3 + 512*a^7*b*c*d^17*f^3 - 2560*a*b^7*c^3*d^15*f^3 - 4608*a*b^7*c^5*d^13*f^3 - 2560*
a*b^7*c^7*d^11*f^3 + 2560*a*b^7*c^9*d^9*f^3 + 4608*a*b^7*c^11*d^7*f^3 + 2560*a*b^7*c^13*d^5*f^3 + 512*a*b^7*c^
15*d^3*f^3 + 3584*a^3*b^5*c*d^17*f^3 - 3584*a^5*b^3*c*d^17*f^3 + 2560*a^7*b*c^3*d^15*f^3 + 4608*a^7*b*c^5*d^13
*f^3 + 2560*a^7*b*c^7*d^11*f^3 - 2560*a^7*b*c^9*d^9*f^3 - 4608*a^7*b*c^11*d^7*f^3 - 2560*a^7*b*c^13*d^5*f^3 -
512*a^7*b*c^15*d^3*f^3))*((((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c*d^
4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^5*f
^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^5*c
^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4*d*
f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*a^4
*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^4 +
16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^14
+ 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^(1/2) - 4*a^8*c^5*f^2 - 4*
b^8*c^5*f^2 + 32*a*b^7*d^5*f^2 - 32*a^7*b*d^5*f^2 - 20*a^8*c*d^4*f^2 - 20*b^8*c*d^4*f^2 + 112*a^2*b^6*c^5*f^2
- 280*a^4*b^4*c^5*f^2 + 112*a^6*b^2*c^5*f^2 - 224*a^3*b^5*d^5*f^2 + 224*a^5*b^3*d^5*f^2 + 40*a^8*c^3*d^2*f^2 +
40*b^8*c^3*d^2*f^2 - 1120*a^2*b^6*c^3*d^2*f^2 + 2240*a^3*b^5*c^2*d^3*f^2 + 2800*a^4*b^4*c^3*d^2*f^2 - 2240*a^
5*b^3*c^2*d^3*f^2 - 1120*a^6*b^2*c^3*d^2*f^2 + 160*a*b^7*c^4*d*f^2 - 160*a^7*b*c^4*d*f^2 - 320*a*b^7*c^2*d^3*f
^2 + 560*a^2*b^6*c*d^4*f^2 - 1120*a^3*b^5*c^4*d*f^2 - 1400*a^4*b^4*c*d^4*f^2 + 1120*a^5*b^3*c^4*d*f^2 + 560*a^
6*b^2*c*d^4*f^2 + 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6*d^
4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*1i)/((((((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 +
40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a
^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 44
80*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2 - 320*
a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^
2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2/4 - (1
6*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16 + b^16 +
8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^(1/2) - 4*a^8*
c^5*f^2 - 4*b^8*c^5*f^2 + 32*a*b^7*d^5*f^2 - 32*a^7*b*d^5*f^2 - 20*a^8*c*d^4*f^2 - 20*b^8*c*d^4*f^2 + 112*a^2*
b^6*c^5*f^2 - 280*a^4*b^4*c^5*f^2 + 112*a^6*b^2*c^5*f^2 - 224*a^3*b^5*d^5*f^2 + 224*a^5*b^3*d^5*f^2 + 40*a^8*c
^3*d^2*f^2 + 40*b^8*c^3*d^2*f^2 - 1120*a^2*b^6*c^3*d^2*f^2 + 2240*a^3*b^5*c^2*d^3*f^2 + 2800*a^4*b^4*c^3*d^2*f
^2 - 2240*a^5*b^3*c^2*d^3*f^2 - 1120*a^6*b^2*c^3*d^2*f^2 + 160*a*b^7*c^4*d*f^2 - 160*a^7*b*c^4*d*f^2 - 320*a*b
^7*c^2*d^3*f^2 + 560*a^2*b^6*c*d^4*f^2 - 1120*a^3*b^5*c^4*d*f^2 - 1400*a^4*b^4*c*d^4*f^2 + 1120*a^5*b^3*c^4*d*
f^2 + 560*a^6*b^2*c*d^4*f^2 + 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4
+ 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*((c + d*tan(e + f*x))^(1/2)*((((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*
a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5
*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f
^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2
+ 2240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6
*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2
- 640*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^
4 + 80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12
*b^4 + 8*a^14*b^2))^(1/2) - 4*a^8*c^5*f^2 - 4*b^8*c^5*f^2 + 32*a*b^7*d^5*f^2 - 32*a^7*b*d^5*f^2 - 20*a^8*c*d^4
*f^2 - 20*b^8*c*d^4*f^2 + 112*a^2*b^6*c^5*f^2 - 280*a^4*b^4*c^5*f^2 + 112*a^6*b^2*c^5*f^2 - 224*a^3*b^5*d^5*f^
2 + 224*a^5*b^3*d^5*f^2 + 40*a^8*c^3*d^2*f^2 + 40*b^8*c^3*d^2*f^2 - 1120*a^2*b^6*c^3*d^2*f^2 + 2240*a^3*b^5*c^
2*d^3*f^2 + 2800*a^4*b^4*c^3*d^2*f^2 - 2240*a^5*b^3*c^2*d^3*f^2 - 1120*a^6*b^2*c^3*d^2*f^2 + 160*a*b^7*c^4*d*f
^2 - 160*a^7*b*c^4*d*f^2 - 320*a*b^7*c^2*d^3*f^2 + 560*a^2*b^6*c*d^4*f^2 - 1120*a^3*b^5*c^4*d*f^2 - 1400*a^4*b
^4*c*d^4*f^2 + 1120*a^5*b^3*c^4*d*f^2 + 560*a^6*b^2*c*d^4*f^2 + 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^
4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*(64*c*d^22*f^5 + 640*c^3*d^20*f^5
+ 2880*c^5*d^18*f^5 + 7680*c^7*d^16*f^5 + 13440*c^9*d^14*f^5 + 16128*c^11*d^12*f^5 + 13440*c^13*d^10*f^5 + 76
80*c^15*d^8*f^5 + 2880*c^17*d^6*f^5 + 640*c^19*d^4*f^5 + 64*c^21*d^2*f^5) - 32*a^4*d^21*f^4 - 32*b^4*d^21*f^4
+ 192*a^2*b^2*d^21*f^4 - 160*a^4*c^2*d^19*f^4 - 128*a^4*c^4*d^17*f^4 + 896*a^4*c^6*d^15*f^4 + 3136*a^4*c^8*d^1
3*f^4 + 4928*a^4*c^10*d^11*f^4 + 4480*a^4*c^12*d^9*f^4 + 2432*a^4*c^14*d^7*f^4 + 736*a^4*c^16*d^5*f^4 + 96*a^4
*c^18*d^3*f^4 - 160*b^4*c^2*d^19*f^4 - 128*b^4*c^4*d^17*f^4 + 896*b^4*c^6*d^15*f^4 + 3136*b^4*c^8*d^13*f^4 + 4
928*b^4*c^10*d^11*f^4 + 4480*b^4*c^12*d^9*f^4 + 2432*b^4*c^14*d^7*f^4 + 736*b^4*c^16*d^5*f^4 + 96*b^4*c^18*d^3
*f^4 + 960*a^2*b^2*c^2*d^19*f^4 + 768*a^2*b^2*c^4*d^17*f^4 - 5376*a^2*b^2*c^6*d^15*f^4 - 18816*a^2*b^2*c^8*d^1
3*f^4 - 29568*a^2*b^2*c^10*d^11*f^4 - 26880*a^2*b^2*c^12*d^9*f^4 - 14592*a^2*b^2*c^14*d^7*f^4 - 4416*a^2*b^2*c
^16*d^5*f^4 - 576*a^2*b^2*c^18*d^3*f^4 - 384*a*b^3*c*d^20*f^4 + 384*a^3*b*c*d^20*f^4 - 2944*a*b^3*c^3*d^18*f^4
- 9728*a*b^3*c^5*d^16*f^4 - 17920*a*b^3*c^7*d^14*f^4 - 19712*a*b^3*c^9*d^12*f^4 - 12544*a*b^3*c^11*d^10*f^4 -
3584*a*b^3*c^13*d^8*f^4 + 512*a*b^3*c^15*d^6*f^4 + 640*a*b^3*c^17*d^4*f^4 + 128*a*b^3*c^19*d^2*f^4 + 2944*a^3
*b*c^3*d^18*f^4 + 9728*a^3*b*c^5*d^16*f^4 + 17920*a^3*b*c^7*d^14*f^4 + 19712*a^3*b*c^9*d^12*f^4 + 12544*a^3*b*
c^11*d^10*f^4 + 3584*a^3*b*c^13*d^8*f^4 - 512*a^3*b*c^15*d^6*f^4 - 640*a^3*b*c^17*d^4*f^4 - 128*a^3*b*c^19*d^2
*f^4) - (c + d*tan(e + f*x))^(1/2)*(448*a^2*b^6*d^18*f^3 - 16*b^8*d^18*f^3 - 16*a^8*d^18*f^3 - 1120*a^4*b^4*d^
18*f^3 + 448*a^6*b^2*d^18*f^3 + 320*a^8*c^4*d^14*f^3 + 1024*a^8*c^6*d^12*f^3 + 1440*a^8*c^8*d^10*f^3 + 1024*a^
8*c^10*d^8*f^3 + 320*a^8*c^12*d^6*f^3 - 16*a^8*c^16*d^2*f^3 + 320*b^8*c^4*d^14*f^3 + 1024*b^8*c^6*d^12*f^3 + 1
440*b^8*c^8*d^10*f^3 + 1024*b^8*c^10*d^8*f^3 + 320*b^8*c^12*d^6*f^3 - 16*b^8*c^16*d^2*f^3 - 8960*a^2*b^6*c^4*d
^14*f^3 - 28672*a^2*b^6*c^6*d^12*f^3 - 40320*a^2*b^6*c^8*d^10*f^3 - 28672*a^2*b^6*c^10*d^8*f^3 - 8960*a^2*b^6*
c^12*d^6*f^3 + 448*a^2*b^6*c^16*d^2*f^3 + 17920*a^3*b^5*c^3*d^15*f^3 + 32256*a^3*b^5*c^5*d^13*f^3 + 17920*a^3*
b^5*c^7*d^11*f^3 - 17920*a^3*b^5*c^9*d^9*f^3 - 32256*a^3*b^5*c^11*d^7*f^3 - 17920*a^3*b^5*c^13*d^5*f^3 - 3584*
a^3*b^5*c^15*d^3*f^3 + 22400*a^4*b^4*c^4*d^14*f^3 + 71680*a^4*b^4*c^6*d^12*f^3 + 100800*a^4*b^4*c^8*d^10*f^3 +
71680*a^4*b^4*c^10*d^8*f^3 + 22400*a^4*b^4*c^12*d^6*f^3 - 1120*a^4*b^4*c^16*d^2*f^3 - 17920*a^5*b^3*c^3*d^15*
f^3 - 32256*a^5*b^3*c^5*d^13*f^3 - 17920*a^5*b^3*c^7*d^11*f^3 + 17920*a^5*b^3*c^9*d^9*f^3 + 32256*a^5*b^3*c^11
*d^7*f^3 + 17920*a^5*b^3*c^13*d^5*f^3 + 3584*a^5*b^3*c^15*d^3*f^3 - 8960*a^6*b^2*c^4*d^14*f^3 - 28672*a^6*b^2*
c^6*d^12*f^3 - 40320*a^6*b^2*c^8*d^10*f^3 - 28672*a^6*b^2*c^10*d^8*f^3 - 8960*a^6*b^2*c^12*d^6*f^3 + 448*a^6*b
^2*c^16*d^2*f^3 - 512*a*b^7*c*d^17*f^3 + 512*a^7*b*c*d^17*f^3 - 2560*a*b^7*c^3*d^15*f^3 - 4608*a*b^7*c^5*d^13*
f^3 - 2560*a*b^7*c^7*d^11*f^3 + 2560*a*b^7*c^9*d^9*f^3 + 4608*a*b^7*c^11*d^7*f^3 + 2560*a*b^7*c^13*d^5*f^3 + 5
12*a*b^7*c^15*d^3*f^3 + 3584*a^3*b^5*c*d^17*f^3 - 3584*a^5*b^3*c*d^17*f^3 + 2560*a^7*b*c^3*d^15*f^3 + 4608*a^7
*b*c^5*d^13*f^3 + 2560*a^7*b*c^7*d^11*f^3 - 2560*a^7*b*c^9*d^9*f^3 - 4608*a^7*b*c^11*d^7*f^3 - 2560*a^7*b*c^13
*d^5*f^3 - 512*a^7*b*c^15*d^3*f^3))*((((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 +
40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a^
3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 448
0*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2 - 320*a
*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2
+ 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2/4 - (16
*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16 + b^16 +
8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^(1/2) - 4*a^8*c
^5*f^2 - 4*b^8*c^5*f^2 + 32*a*b^7*d^5*f^2 - 32*a^7*b*d^5*f^2 - 20*a^8*c*d^4*f^2 - 20*b^8*c*d^4*f^2 + 112*a^2*b
^6*c^5*f^2 - 280*a^4*b^4*c^5*f^2 + 112*a^6*b^2*c^5*f^2 - 224*a^3*b^5*d^5*f^2 + 224*a^5*b^3*d^5*f^2 + 40*a^8*c^
3*d^2*f^2 + 40*b^8*c^3*d^2*f^2 - 1120*a^2*b^6*c^3*d^2*f^2 + 2240*a^3*b^5*c^2*d^3*f^2 + 2800*a^4*b^4*c^3*d^2*f^
2 - 2240*a^5*b^3*c^2*d^3*f^2 - 1120*a^6*b^2*c^3*d^2*f^2 + 160*a*b^7*c^4*d*f^2 - 160*a^7*b*c^4*d*f^2 - 320*a*b^
7*c^2*d^3*f^2 + 560*a^2*b^6*c*d^4*f^2 - 1120*a^3*b^5*c^4*d*f^2 - 1400*a^4*b^4*c*d^4*f^2 + 1120*a^5*b^3*c^4*d*f
^2 + 560*a^6*b^2*c*d^4*f^2 + 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4
+ 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2) + (((((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d
^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2
+ 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*
f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^
2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*
c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^
2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16
+ b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^(1/2)
- 4*a^8*c^5*f^2 - 4*b^8*c^5*f^2 + 32*a*b^7*d^5*f^2 - 32*a^7*b*d^5*f^2 - 20*a^8*c*d^4*f^2 - 20*b^8*c*d^4*f^2 +
112*a^2*b^6*c^5*f^2 - 280*a^4*b^4*c^5*f^2 + 112*a^6*b^2*c^5*f^2 - 224*a^3*b^5*d^5*f^2 + 224*a^5*b^3*d^5*f^2 +
40*a^8*c^3*d^2*f^2 + 40*b^8*c^3*d^2*f^2 - 1120*a^2*b^6*c^3*d^2*f^2 + 2240*a^3*b^5*c^2*d^3*f^2 + 2800*a^4*b^4*c
^3*d^2*f^2 - 2240*a^5*b^3*c^2*d^3*f^2 - 1120*a^6*b^2*c^3*d^2*f^2 + 160*a*b^7*c^4*d*f^2 - 160*a^7*b*c^4*d*f^2 -
320*a*b^7*c^2*d^3*f^2 + 560*a^2*b^6*c*d^4*f^2 - 1120*a^3*b^5*c^4*d*f^2 - 1400*a^4*b^4*c*d^4*f^2 + 1120*a^5*b^
3*c^4*d*f^2 + 560*a^6*b^2*c*d^4*f^2 + 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4
*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*(192*a^2*b^2*d^21*f^4 - 32*a^4*d^21*f^4 - 32*b^4*d^21*f^4 -
(c + d*tan(e + f*x))^(1/2)*((((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d^5*f^2 + 40*a^8*c
*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2 + 448*a^3*b^5*d^
5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f^2 - 4480*a^3*b^
5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2 - 320*a*b^7*c^4
*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c^4*d*f^2 + 2800*
a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2/4 - (16*c^10*f^
4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16 + b^16 + 8*a^2*b^
14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^(1/2) - 4*a^8*c^5*f^2 -
4*b^8*c^5*f^2 + 32*a*b^7*d^5*f^2 - 32*a^7*b*d^5*f^2 - 20*a^8*c*d^4*f^2 - 20*b^8*c*d^4*f^2 + 112*a^2*b^6*c^5*f
^2 - 280*a^4*b^4*c^5*f^2 + 112*a^6*b^2*c^5*f^2 - 224*a^3*b^5*d^5*f^2 + 224*a^5*b^3*d^5*f^2 + 40*a^8*c^3*d^2*f^
2 + 40*b^8*c^3*d^2*f^2 - 1120*a^2*b^6*c^3*d^2*f^2 + 2240*a^3*b^5*c^2*d^3*f^2 + 2800*a^4*b^4*c^3*d^2*f^2 - 2240
*a^5*b^3*c^2*d^3*f^2 - 1120*a^6*b^2*c^3*d^2*f^2 + 160*a*b^7*c^4*d*f^2 - 160*a^7*b*c^4*d*f^2 - 320*a*b^7*c^2*d^
3*f^2 + 560*a^2*b^6*c*d^4*f^2 - 1120*a^3*b^5*c^4*d*f^2 - 1400*a^4*b^4*c*d^4*f^2 + 1120*a^5*b^3*c^4*d*f^2 + 560
*a^6*b^2*c*d^4*f^2 + 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*d^6*f^4 + 10*c^6
*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*(64*c*d^22*f^5 + 640*c^3*d^20*f^5 + 2880*c^5*d^18*f^5 + 7680*c^7*d^16*f^5 +
13440*c^9*d^14*f^5 + 16128*c^11*d^12*f^5 + 13440*c^13*d^10*f^5 + 7680*c^15*d^8*f^5 + 2880*c^17*d^6*f^5 + 640*c
^19*d^4*f^5 + 64*c^21*d^2*f^5) - 160*a^4*c^2*d^19*f^4 - 128*a^4*c^4*d^17*f^4 + 896*a^4*c^6*d^15*f^4 + 3136*a^4
*c^8*d^13*f^4 + 4928*a^4*c^10*d^11*f^4 + 4480*a^4*c^12*d^9*f^4 + 2432*a^4*c^14*d^7*f^4 + 736*a^4*c^16*d^5*f^4
+ 96*a^4*c^18*d^3*f^4 - 160*b^4*c^2*d^19*f^4 - 128*b^4*c^4*d^17*f^4 + 896*b^4*c^6*d^15*f^4 + 3136*b^4*c^8*d^13
*f^4 + 4928*b^4*c^10*d^11*f^4 + 4480*b^4*c^12*d^9*f^4 + 2432*b^4*c^14*d^7*f^4 + 736*b^4*c^16*d^5*f^4 + 96*b^4*
c^18*d^3*f^4 + 960*a^2*b^2*c^2*d^19*f^4 + 768*a^2*b^2*c^4*d^17*f^4 - 5376*a^2*b^2*c^6*d^15*f^4 - 18816*a^2*b^2
*c^8*d^13*f^4 - 29568*a^2*b^2*c^10*d^11*f^4 - 26880*a^2*b^2*c^12*d^9*f^4 - 14592*a^2*b^2*c^14*d^7*f^4 - 4416*a
^2*b^2*c^16*d^5*f^4 - 576*a^2*b^2*c^18*d^3*f^4 - 384*a*b^3*c*d^20*f^4 + 384*a^3*b*c*d^20*f^4 - 2944*a*b^3*c^3*
d^18*f^4 - 9728*a*b^3*c^5*d^16*f^4 - 17920*a*b^3*c^7*d^14*f^4 - 19712*a*b^3*c^9*d^12*f^4 - 12544*a*b^3*c^11*d^
10*f^4 - 3584*a*b^3*c^13*d^8*f^4 + 512*a*b^3*c^15*d^6*f^4 + 640*a*b^3*c^17*d^4*f^4 + 128*a*b^3*c^19*d^2*f^4 +
2944*a^3*b*c^3*d^18*f^4 + 9728*a^3*b*c^5*d^16*f^4 + 17920*a^3*b*c^7*d^14*f^4 + 19712*a^3*b*c^9*d^12*f^4 + 1254
4*a^3*b*c^11*d^10*f^4 + 3584*a^3*b*c^13*d^8*f^4 - 512*a^3*b*c^15*d^6*f^4 - 640*a^3*b*c^17*d^4*f^4 - 128*a^3*b*
c^19*d^2*f^4) + (c + d*tan(e + f*x))^(1/2)*(448*a^2*b^6*d^18*f^3 - 16*b^8*d^18*f^3 - 16*a^8*d^18*f^3 - 1120*a^
4*b^4*d^18*f^3 + 448*a^6*b^2*d^18*f^3 + 320*a^8*c^4*d^14*f^3 + 1024*a^8*c^6*d^12*f^3 + 1440*a^8*c^8*d^10*f^3 +
1024*a^8*c^10*d^8*f^3 + 320*a^8*c^12*d^6*f^3 - 16*a^8*c^16*d^2*f^3 + 320*b^8*c^4*d^14*f^3 + 1024*b^8*c^6*d^12
*f^3 + 1440*b^8*c^8*d^10*f^3 + 1024*b^8*c^10*d^8*f^3 + 320*b^8*c^12*d^6*f^3 - 16*b^8*c^16*d^2*f^3 - 8960*a^2*b
^6*c^4*d^14*f^3 - 28672*a^2*b^6*c^6*d^12*f^3 - 40320*a^2*b^6*c^8*d^10*f^3 - 28672*a^2*b^6*c^10*d^8*f^3 - 8960*
a^2*b^6*c^12*d^6*f^3 + 448*a^2*b^6*c^16*d^2*f^3 + 17920*a^3*b^5*c^3*d^15*f^3 + 32256*a^3*b^5*c^5*d^13*f^3 + 17
920*a^3*b^5*c^7*d^11*f^3 - 17920*a^3*b^5*c^9*d^9*f^3 - 32256*a^3*b^5*c^11*d^7*f^3 - 17920*a^3*b^5*c^13*d^5*f^3
- 3584*a^3*b^5*c^15*d^3*f^3 + 22400*a^4*b^4*c^4*d^14*f^3 + 71680*a^4*b^4*c^6*d^12*f^3 + 100800*a^4*b^4*c^8*d^
10*f^3 + 71680*a^4*b^4*c^10*d^8*f^3 + 22400*a^4*b^4*c^12*d^6*f^3 - 1120*a^4*b^4*c^16*d^2*f^3 - 17920*a^5*b^3*c
^3*d^15*f^3 - 32256*a^5*b^3*c^5*d^13*f^3 - 17920*a^5*b^3*c^7*d^11*f^3 + 17920*a^5*b^3*c^9*d^9*f^3 + 32256*a^5*
b^3*c^11*d^7*f^3 + 17920*a^5*b^3*c^13*d^5*f^3 + 3584*a^5*b^3*c^15*d^3*f^3 - 8960*a^6*b^2*c^4*d^14*f^3 - 28672*
a^6*b^2*c^6*d^12*f^3 - 40320*a^6*b^2*c^8*d^10*f^3 - 28672*a^6*b^2*c^10*d^8*f^3 - 8960*a^6*b^2*c^12*d^6*f^3 + 4
48*a^6*b^2*c^16*d^2*f^3 - 512*a*b^7*c*d^17*f^3 + 512*a^7*b*c*d^17*f^3 - 2560*a*b^7*c^3*d^15*f^3 - 4608*a*b^7*c
^5*d^13*f^3 - 2560*a*b^7*c^7*d^11*f^3 + 2560*a*b^7*c^9*d^9*f^3 + 4608*a*b^7*c^11*d^7*f^3 + 2560*a*b^7*c^13*d^5
*f^3 + 512*a*b^7*c^15*d^3*f^3 + 3584*a^3*b^5*c*d^17*f^3 - 3584*a^5*b^3*c*d^17*f^3 + 2560*a^7*b*c^3*d^15*f^3 +
4608*a^7*b*c^5*d^13*f^3 + 2560*a^7*b*c^7*d^11*f^3 - 2560*a^7*b*c^9*d^9*f^3 - 4608*a^7*b*c^11*d^7*f^3 - 2560*a^
7*b*c^13*d^5*f^3 - 512*a^7*b*c^15*d^3*f^3))*((((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2 + 64*a^7*b*d^
5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6*b^2*c^5*f^2
+ 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*b^6*c^3*d^2*f
^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^2*c^3*d^2*f^2
- 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2240*a^3*b^5*c
^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c^2*d^3*f^2)^2
/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2*f^4)*(a^16 +
b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))^(1/2) -
4*a^8*c^5*f^2 - 4*b^8*c^5*f^2 + 32*a*b^7*d^5*f^2 - 32*a^7*b*d^5*f^2 - 20*a^8*c*d^4*f^2 - 20*b^8*c*d^4*f^2 + 1
12*a^2*b^6*c^5*f^2 - 280*a^4*b^4*c^5*f^2 + 112*a^6*b^2*c^5*f^2 - 224*a^3*b^5*d^5*f^2 + 224*a^5*b^3*d^5*f^2 + 4
0*a^8*c^3*d^2*f^2 + 40*b^8*c^3*d^2*f^2 - 1120*a^2*b^6*c^3*d^2*f^2 + 2240*a^3*b^5*c^2*d^3*f^2 + 2800*a^4*b^4*c^
3*d^2*f^2 - 2240*a^5*b^3*c^2*d^3*f^2 - 1120*a^6*b^2*c^3*d^2*f^2 + 160*a*b^7*c^4*d*f^2 - 160*a^7*b*c^4*d*f^2 -
320*a*b^7*c^2*d^3*f^2 + 560*a^2*b^6*c*d^4*f^2 - 1120*a^3*b^5*c^4*d*f^2 - 1400*a^4*b^4*c*d^4*f^2 + 1120*a^5*b^3
*c^4*d*f^2 + 560*a^6*b^2*c*d^4*f^2 + 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*f^4 + 10*c^4*
d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2) + 64*a*b^11*d^16*f^2 - 64*a^11*b*d^16*f^2 - 32*a^12*c*d^15*f
^2 - 32*b^12*c*d^15*f^2 + 192*a^3*b^9*d^16*f^2 + 128*a^5*b^7*d^16*f^2 - 128*a^7*b^5*d^16*f^2 - 192*a^9*b^3*d^1
6*f^2 - 192*a^12*c^3*d^13*f^2 - 480*a^12*c^5*d^11*f^2 - 640*a^12*c^7*d^9*f^2 - 480*a^12*c^9*d^7*f^2 - 192*a^12
*c^11*d^5*f^2 - 32*a^12*c^13*d^3*f^2 - 192*b^12*c^3*d^13*f^2 - 480*b^12*c^5*d^11*f^2 - 640*b^12*c^7*d^9*f^2 -
480*b^12*c^9*d^7*f^2 - 192*b^12*c^11*d^5*f^2 - 32*b^12*c^13*d^3*f^2 + 384*a^2*b^10*c^3*d^13*f^2 + 960*a^2*b^10
*c^5*d^11*f^2 + 1280*a^2*b^10*c^7*d^9*f^2 + 960*a^2*b^10*c^9*d^7*f^2 + 384*a^2*b^10*c^11*d^5*f^2 + 64*a^2*b^10
*c^13*d^3*f^2 + 960*a^3*b^9*c^2*d^14*f^2 + 1728*a^3*b^9*c^4*d^12*f^2 + 960*a^3*b^9*c^6*d^10*f^2 - 960*a^3*b^9*
c^8*d^8*f^2 - 1728*a^3*b^9*c^10*d^6*f^2 - 960*a^3*b^9*c^12*d^4*f^2 - 192*a^3*b^9*c^14*d^2*f^2 + 3264*a^4*b^8*c
^3*d^13*f^2 + 8160*a^4*b^8*c^5*d^11*f^2 + 10880*a^4*b^8*c^7*d^9*f^2 + 8160*a^4*b^8*c^9*d^7*f^2 + 3264*a^4*b^8*
c^11*d^5*f^2 + 544*a^4*b^8*c^13*d^3*f^2 + 640*a^5*b^7*c^2*d^14*f^2 + 1152*a^5*b^7*c^4*d^12*f^2 + 640*a^5*b^7*c
^6*d^10*f^2 - 640*a^5*b^7*c^8*d^8*f^2 - 1152*a^5*b^7*c^10*d^6*f^2 - 640*a^5*b^7*c^12*d^4*f^2 - 128*a^5*b^7*c^1
4*d^2*f^2 + 5376*a^6*b^6*c^3*d^13*f^2 + 13440*a^6*b^6*c^5*d^11*f^2 + 17920*a^6*b^6*c^7*d^9*f^2 + 13440*a^6*b^6
*c^9*d^7*f^2 + 5376*a^6*b^6*c^11*d^5*f^2 + 896*a^6*b^6*c^13*d^3*f^2 - 640*a^7*b^5*c^2*d^14*f^2 - 1152*a^7*b^5*
c^4*d^12*f^2 - 640*a^7*b^5*c^6*d^10*f^2 + 640*a^7*b^5*c^8*d^8*f^2 + 1152*a^7*b^5*c^10*d^6*f^2 + 640*a^7*b^5*c^
12*d^4*f^2 + 128*a^7*b^5*c^14*d^2*f^2 + 3264*a^8*b^4*c^3*d^13*f^2 + 8160*a^8*b^4*c^5*d^11*f^2 + 10880*a^8*b^4*
c^7*d^9*f^2 + 8160*a^8*b^4*c^9*d^7*f^2 + 3264*a^8*b^4*c^11*d^5*f^2 + 544*a^8*b^4*c^13*d^3*f^2 - 960*a^9*b^3*c^
2*d^14*f^2 - 1728*a^9*b^3*c^4*d^12*f^2 - 960*a^9*b^3*c^6*d^10*f^2 + 960*a^9*b^3*c^8*d^8*f^2 + 1728*a^9*b^3*c^1
0*d^6*f^2 + 960*a^9*b^3*c^12*d^4*f^2 + 192*a^9*b^3*c^14*d^2*f^2 + 384*a^10*b^2*c^3*d^13*f^2 + 960*a^10*b^2*c^5
*d^11*f^2 + 1280*a^10*b^2*c^7*d^9*f^2 + 960*a^10*b^2*c^9*d^7*f^2 + 384*a^10*b^2*c^11*d^5*f^2 + 64*a^10*b^2*c^1
3*d^3*f^2 + 320*a*b^11*c^2*d^14*f^2 + 576*a*b^11*c^4*d^12*f^2 + 320*a*b^11*c^6*d^10*f^2 - 320*a*b^11*c^8*d^8*f
^2 - 576*a*b^11*c^10*d^6*f^2 - 320*a*b^11*c^12*d^4*f^2 - 64*a*b^11*c^14*d^2*f^2 + 64*a^2*b^10*c*d^15*f^2 + 544
*a^4*b^8*c*d^15*f^2 + 896*a^6*b^6*c*d^15*f^2 + 544*a^8*b^4*c*d^15*f^2 + 64*a^10*b^2*c*d^15*f^2 - 320*a^11*b*c^
2*d^14*f^2 - 576*a^11*b*c^4*d^12*f^2 - 320*a^11*b*c^6*d^10*f^2 + 320*a^11*b*c^8*d^8*f^2 + 576*a^11*b*c^10*d^6*
f^2 + 320*a^11*b*c^12*d^4*f^2 + 64*a^11*b*c^14*d^2*f^2))*((((8*a^8*c^5*f^2 + 8*b^8*c^5*f^2 - 64*a*b^7*d^5*f^2
+ 64*a^7*b*d^5*f^2 + 40*a^8*c*d^4*f^2 + 40*b^8*c*d^4*f^2 - 224*a^2*b^6*c^5*f^2 + 560*a^4*b^4*c^5*f^2 - 224*a^6
*b^2*c^5*f^2 + 448*a^3*b^5*d^5*f^2 - 448*a^5*b^3*d^5*f^2 - 80*a^8*c^3*d^2*f^2 - 80*b^8*c^3*d^2*f^2 + 2240*a^2*
b^6*c^3*d^2*f^2 - 4480*a^3*b^5*c^2*d^3*f^2 - 5600*a^4*b^4*c^3*d^2*f^2 + 4480*a^5*b^3*c^2*d^3*f^2 + 2240*a^6*b^
2*c^3*d^2*f^2 - 320*a*b^7*c^4*d*f^2 + 320*a^7*b*c^4*d*f^2 + 640*a*b^7*c^2*d^3*f^2 - 1120*a^2*b^6*c*d^4*f^2 + 2
240*a^3*b^5*c^4*d*f^2 + 2800*a^4*b^4*c*d^4*f^2 - 2240*a^5*b^3*c^4*d*f^2 - 1120*a^6*b^2*c*d^4*f^2 - 640*a^7*b*c
^2*d^3*f^2)^2/4 - (16*c^10*f^4 + 16*d^10*f^4 + 80*c^2*d^8*f^4 + 160*c^4*d^6*f^4 + 160*c^6*d^4*f^4 + 80*c^8*d^2
*f^4)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*
b^2))^(1/2) - 4*a^8*c^5*f^2 - 4*b^8*c^5*f^2 + 32*a*b^7*d^5*f^2 - 32*a^7*b*d^5*f^2 - 20*a^8*c*d^4*f^2 - 20*b^8*
c*d^4*f^2 + 112*a^2*b^6*c^5*f^2 - 280*a^4*b^4*c^5*f^2 + 112*a^6*b^2*c^5*f^2 - 224*a^3*b^5*d^5*f^2 + 224*a^5*b^
3*d^5*f^2 + 40*a^8*c^3*d^2*f^2 + 40*b^8*c^3*d^2*f^2 - 1120*a^2*b^6*c^3*d^2*f^2 + 2240*a^3*b^5*c^2*d^3*f^2 + 28
00*a^4*b^4*c^3*d^2*f^2 - 2240*a^5*b^3*c^2*d^3*f^2 - 1120*a^6*b^2*c^3*d^2*f^2 + 160*a*b^7*c^4*d*f^2 - 160*a^7*b
*c^4*d*f^2 - 320*a*b^7*c^2*d^3*f^2 + 560*a^2*b^6*c*d^4*f^2 - 1120*a^3*b^5*c^4*d*f^2 - 1400*a^4*b^4*c*d^4*f^2 +
1120*a^5*b^3*c^4*d*f^2 + 560*a^6*b^2*c*d^4*f^2 + 320*a^7*b*c^2*d^3*f^2)/(16*(c^10*f^4 + d^10*f^4 + 5*c^2*d^8*
f^4 + 10*c^4*d^6*f^4 + 10*c^6*d^4*f^4 + 5*c^8*d^2*f^4)))^(1/2)*2i - ((2*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2
- 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/(3*(c^2 + d^2)) - (4*(c + d*tan(e + f*x))*(b^4*c^5 - 2*a^3*b*d^5 - a^4*c*d^
4 + 2*b^4*c^3*d^2 - 6*a*b^3*c^2*d^3 + 6*a^2*b^2*c*d^4 + 2*a^3*b*c^2*d^3 - 2*a*b^3*c^4*d))/(c^2 + d^2)^2)/(d^3*
f*(c + d*tan(e + f*x))^(3/2))

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sympy [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (a + b \tan {\left (e + f x \right )}\right )^{4}}{\left (c + d \tan {\left (e + f x \right )}\right )^{\frac {5}{2}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*tan(f*x+e))**4/(c+d*tan(f*x+e))**(5/2),x)

[Out]

Integral((a + b*tan(e + f*x))**4/(c + d*tan(e + f*x))**(5/2), x)

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