3.356 \(\int \frac {\cot ^3(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx\)

Optimal. Leaf size=285 \[ \frac {(5 A b-4 a B) \cot (c+d x)}{4 a^2 d \sqrt {a+b \tan (c+d x)}}+\frac {\left (8 a^2 A+12 a b B-15 A b^2\right ) \tanh ^{-1}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{4 a^{7/2} d}+\frac {b \left (-4 a^3 B+7 a^2 A b-12 a b^2 B+15 A b^3\right )}{4 a^3 d \left (a^2+b^2\right ) \sqrt {a+b \tan (c+d x)}}-\frac {(A-i B) \tanh ^{-1}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{d (a-i b)^{3/2}}-\frac {(A+i B) \tanh ^{-1}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{d (a+i b)^{3/2}}-\frac {A \cot ^2(c+d x)}{2 a d \sqrt {a+b \tan (c+d x)}} \]

[Out]

1/4*(8*A*a^2-15*A*b^2+12*B*a*b)*arctanh((a+b*tan(d*x+c))^(1/2)/a^(1/2))/a^(7/2)/d-(A-I*B)*arctanh((a+b*tan(d*x
+c))^(1/2)/(a-I*b)^(1/2))/(a-I*b)^(3/2)/d-(A+I*B)*arctanh((a+b*tan(d*x+c))^(1/2)/(a+I*b)^(1/2))/(a+I*b)^(3/2)/
d+1/4*b*(7*A*a^2*b+15*A*b^3-4*B*a^3-12*B*a*b^2)/a^3/(a^2+b^2)/d/(a+b*tan(d*x+c))^(1/2)+1/4*(5*A*b-4*B*a)*cot(d
*x+c)/a^2/d/(a+b*tan(d*x+c))^(1/2)-1/2*A*cot(d*x+c)^2/a/d/(a+b*tan(d*x+c))^(1/2)

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Rubi [A]  time = 1.21, antiderivative size = 285, normalized size of antiderivative = 1.00, number of steps used = 14, number of rules used = 8, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.242, Rules used = {3609, 3649, 3653, 3539, 3537, 63, 208, 3634} \[ \frac {b \left (7 a^2 A b-4 a^3 B-12 a b^2 B+15 A b^3\right )}{4 a^3 d \left (a^2+b^2\right ) \sqrt {a+b \tan (c+d x)}}+\frac {\left (8 a^2 A+12 a b B-15 A b^2\right ) \tanh ^{-1}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{4 a^{7/2} d}+\frac {(5 A b-4 a B) \cot (c+d x)}{4 a^2 d \sqrt {a+b \tan (c+d x)}}-\frac {(A-i B) \tanh ^{-1}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{d (a-i b)^{3/2}}-\frac {(A+i B) \tanh ^{-1}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{d (a+i b)^{3/2}}-\frac {A \cot ^2(c+d x)}{2 a d \sqrt {a+b \tan (c+d x)}} \]

Antiderivative was successfully verified.

[In]

Int[(Cot[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]

[Out]

((8*a^2*A - 15*A*b^2 + 12*a*b*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(4*a^(7/2)*d) - ((A - I*B)*ArcTanh
[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(3/2)*d) - ((A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sq
rt[a + I*b]])/((a + I*b)^(3/2)*d) + (b*(7*a^2*A*b + 15*A*b^3 - 4*a^3*B - 12*a*b^2*B))/(4*a^3*(a^2 + b^2)*d*Sqr
t[a + b*Tan[c + d*x]]) + ((5*A*b - 4*a*B)*Cot[c + d*x])/(4*a^2*d*Sqrt[a + b*Tan[c + d*x]]) - (A*Cot[c + d*x]^2
)/(2*a*d*Sqrt[a + b*Tan[c + d*x]])

Rule 63

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> With[{p = Denominator[m]}, Dist[p/b, Sub
st[Int[x^(p*(m + 1) - 1)*(c - (a*d)/b + (d*x^p)/b)^n, x], x, (a + b*x)^(1/p)], x]] /; FreeQ[{a, b, c, d}, x] &
& NeQ[b*c - a*d, 0] && LtQ[-1, m, 0] && LeQ[-1, n, 0] && LeQ[Denominator[n], Denominator[m]] && IntLinearQ[a,
b, c, d, m, n, x]

Rule 208

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

Rule 3537

Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_)*((c_) + (d_.)*tan[(e_.) + (f_.)*(x_)]), x_Symbol] :> Dist[(c*
d)/f, Subst[Int[(a + (b*x)/d)^m/(d^2 + c*x), x], x, d*Tan[e + f*x]], x] /; FreeQ[{a, b, c, d, e, f, m}, x] &&
NeQ[b*c - a*d, 0] && NeQ[a^2 + b^2, 0] && EqQ[c^2 + d^2, 0]

Rule 3539

Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_)*((c_.) + (d_.)*tan[(e_.) + (f_.)*(x_)]), x_Symbol] :> Dist[(c
+ I*d)/2, Int[(a + b*Tan[e + f*x])^m*(1 - I*Tan[e + f*x]), x], x] + Dist[(c - I*d)/2, Int[(a + b*Tan[e + f*x]
)^m*(1 + I*Tan[e + f*x]), x], x] /; FreeQ[{a, b, c, d, e, f, m}, x] && NeQ[b*c - a*d, 0] && NeQ[a^2 + b^2, 0]
&& NeQ[c^2 + d^2, 0] &&  !IntegerQ[m]

Rule 3609

Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_)*((A_.) + (B_.)*tan[(e_.) + (f_.)*(x_)])*((c_.) + (d_.)*tan[(e
_.) + (f_.)*(x_)])^(n_), x_Symbol] :> Simp[(b*(A*b - a*B)*(a + b*Tan[e + f*x])^(m + 1)*(c + d*Tan[e + f*x])^(n
+ 1))/(f*(m + 1)*(b*c - a*d)*(a^2 + b^2)), x] + Dist[1/((m + 1)*(b*c - a*d)*(a^2 + b^2)), Int[(a + b*Tan[e +
f*x])^(m + 1)*(c + d*Tan[e + f*x])^n*Simp[b*B*(b*c*(m + 1) + a*d*(n + 1)) + A*(a*(b*c - a*d)*(m + 1) - b^2*d*(
m + n + 2)) - (A*b - a*B)*(b*c - a*d)*(m + 1)*Tan[e + f*x] - b*d*(A*b - a*B)*(m + n + 2)*Tan[e + f*x]^2, x], x
], x] /; FreeQ[{a, b, c, d, e, f, A, B, n}, x] && NeQ[b*c - a*d, 0] && NeQ[a^2 + b^2, 0] && NeQ[c^2 + d^2, 0]
&& LtQ[m, -1] && (IntegerQ[m] || IntegersQ[2*m, 2*n]) &&  !(ILtQ[n, -1] && ( !IntegerQ[m] || (EqQ[c, 0] && NeQ
[a, 0])))

Rule 3634

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

Rule 3649

Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_)*((c_.) + (d_.)*tan[(e_.) + (f_.)*(x_)])^(n_)*((A_.) + (B_.)*t
an[(e_.) + (f_.)*(x_)] + (C_.)*tan[(e_.) + (f_.)*(x_)]^2), x_Symbol] :> Simp[((A*b^2 - a*(b*B - a*C))*(a + b*T
an[e + f*x])^(m + 1)*(c + d*Tan[e + f*x])^(n + 1))/(f*(m + 1)*(b*c - a*d)*(a^2 + b^2)), x] + Dist[1/((m + 1)*(
b*c - a*d)*(a^2 + b^2)), Int[(a + b*Tan[e + f*x])^(m + 1)*(c + d*Tan[e + f*x])^n*Simp[A*(a*(b*c - a*d)*(m + 1)
- b^2*d*(m + n + 2)) + (b*B - a*C)*(b*c*(m + 1) + a*d*(n + 1)) - (m + 1)*(b*c - a*d)*(A*b - a*B - b*C)*Tan[e
+ f*x] - d*(A*b^2 - a*(b*B - a*C))*(m + n + 2)*Tan[e + f*x]^2, x], x], x] /; FreeQ[{a, b, c, d, e, f, A, B, C,
n}, x] && NeQ[b*c - a*d, 0] && NeQ[a^2 + b^2, 0] && NeQ[c^2 + d^2, 0] && LtQ[m, -1] &&  !(ILtQ[n, -1] && ( !I
ntegerQ[m] || (EqQ[c, 0] && NeQ[a, 0])))

Rule 3653

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

Rubi steps

\begin {align*} \int \frac {\cot ^3(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx &=-\frac {A \cot ^2(c+d x)}{2 a d \sqrt {a+b \tan (c+d x)}}-\frac {\int \frac {\cot ^2(c+d x) \left (\frac {1}{2} (5 A b-4 a B)+2 a A \tan (c+d x)+\frac {5}{2} A b \tan ^2(c+d x)\right )}{(a+b \tan (c+d x))^{3/2}} \, dx}{2 a}\\ &=\frac {(5 A b-4 a B) \cot (c+d x)}{4 a^2 d \sqrt {a+b \tan (c+d x)}}-\frac {A \cot ^2(c+d x)}{2 a d \sqrt {a+b \tan (c+d x)}}+\frac {\int \frac {\cot (c+d x) \left (\frac {1}{4} \left (-8 a^2 A+15 A b^2-12 a b B\right )-2 a^2 B \tan (c+d x)+\frac {3}{4} b (5 A b-4 a B) \tan ^2(c+d x)\right )}{(a+b \tan (c+d x))^{3/2}} \, dx}{2 a^2}\\ &=\frac {b \left (7 a^2 A b+15 A b^3-4 a^3 B-12 a b^2 B\right )}{4 a^3 \left (a^2+b^2\right ) d \sqrt {a+b \tan (c+d x)}}+\frac {(5 A b-4 a B) \cot (c+d x)}{4 a^2 d \sqrt {a+b \tan (c+d x)}}-\frac {A \cot ^2(c+d x)}{2 a d \sqrt {a+b \tan (c+d x)}}+\frac {\int \frac {\cot (c+d x) \left (-\frac {1}{8} \left (a^2+b^2\right ) \left (8 a^2 A-15 A b^2+12 a b B\right )+a^3 (A b-a B) \tan (c+d x)+\frac {1}{8} b \left (7 a^2 A b+15 A b^3-4 a^3 B-12 a b^2 B\right ) \tan ^2(c+d x)\right )}{\sqrt {a+b \tan (c+d x)}} \, dx}{a^3 \left (a^2+b^2\right )}\\ &=\frac {b \left (7 a^2 A b+15 A b^3-4 a^3 B-12 a b^2 B\right )}{4 a^3 \left (a^2+b^2\right ) d \sqrt {a+b \tan (c+d x)}}+\frac {(5 A b-4 a B) \cot (c+d x)}{4 a^2 d \sqrt {a+b \tan (c+d x)}}-\frac {A \cot ^2(c+d x)}{2 a d \sqrt {a+b \tan (c+d x)}}+\frac {\int \frac {a^3 (A b-a B)+a^3 (a A+b B) \tan (c+d x)}{\sqrt {a+b \tan (c+d x)}} \, dx}{a^3 \left (a^2+b^2\right )}-\frac {\left (8 a^2 A-15 A b^2+12 a b B\right ) \int \frac {\cot (c+d x) \left (1+\tan ^2(c+d x)\right )}{\sqrt {a+b \tan (c+d x)}} \, dx}{8 a^3}\\ &=\frac {b \left (7 a^2 A b+15 A b^3-4 a^3 B-12 a b^2 B\right )}{4 a^3 \left (a^2+b^2\right ) d \sqrt {a+b \tan (c+d x)}}+\frac {(5 A b-4 a B) \cot (c+d x)}{4 a^2 d \sqrt {a+b \tan (c+d x)}}-\frac {A \cot ^2(c+d x)}{2 a d \sqrt {a+b \tan (c+d x)}}+\frac {(A-i B) \int \frac {1+i \tan (c+d x)}{\sqrt {a+b \tan (c+d x)}} \, dx}{2 (i a+b)}+\frac {((i a+b) (A+i B)) \int \frac {1-i \tan (c+d x)}{\sqrt {a+b \tan (c+d x)}} \, dx}{2 \left (a^2+b^2\right )}-\frac {\left (8 a^2 A-15 A b^2+12 a b B\right ) \operatorname {Subst}\left (\int \frac {1}{x \sqrt {a+b x}} \, dx,x,\tan (c+d x)\right )}{8 a^3 d}\\ &=\frac {b \left (7 a^2 A b+15 A b^3-4 a^3 B-12 a b^2 B\right )}{4 a^3 \left (a^2+b^2\right ) d \sqrt {a+b \tan (c+d x)}}+\frac {(5 A b-4 a B) \cot (c+d x)}{4 a^2 d \sqrt {a+b \tan (c+d x)}}-\frac {A \cot ^2(c+d x)}{2 a d \sqrt {a+b \tan (c+d x)}}+\frac {(A-i B) \operatorname {Subst}\left (\int \frac {1}{(-1+x) \sqrt {a-i b x}} \, dx,x,i \tan (c+d x)\right )}{2 (a-i b) d}+\frac {(A+i B) \operatorname {Subst}\left (\int \frac {1}{(-1+x) \sqrt {a+i b x}} \, dx,x,-i \tan (c+d x)\right )}{2 (a+i b) d}-\frac {\left (8 a^2 A-15 A b^2+12 a b B\right ) \operatorname {Subst}\left (\int \frac {1}{-\frac {a}{b}+\frac {x^2}{b}} \, dx,x,\sqrt {a+b \tan (c+d x)}\right )}{4 a^3 b d}\\ &=\frac {\left (8 a^2 A-15 A b^2+12 a b B\right ) \tanh ^{-1}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{4 a^{7/2} d}+\frac {b \left (7 a^2 A b+15 A b^3-4 a^3 B-12 a b^2 B\right )}{4 a^3 \left (a^2+b^2\right ) d \sqrt {a+b \tan (c+d x)}}+\frac {(5 A b-4 a B) \cot (c+d x)}{4 a^2 d \sqrt {a+b \tan (c+d x)}}-\frac {A \cot ^2(c+d x)}{2 a d \sqrt {a+b \tan (c+d x)}}-\frac {(i (A+i B)) \operatorname {Subst}\left (\int \frac {1}{-1+\frac {i a}{b}-\frac {i x^2}{b}} \, dx,x,\sqrt {a+b \tan (c+d x)}\right )}{(a+i b) b d}+\frac {(i A+B) \operatorname {Subst}\left (\int \frac {1}{-1-\frac {i a}{b}+\frac {i x^2}{b}} \, dx,x,\sqrt {a+b \tan (c+d x)}\right )}{(a-i b) b d}\\ &=\frac {\left (8 a^2 A-15 A b^2+12 a b B\right ) \tanh ^{-1}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{4 a^{7/2} d}-\frac {(A-i B) \tanh ^{-1}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{(a-i b)^{3/2} d}-\frac {(A+i B) \tanh ^{-1}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{(a+i b)^{3/2} d}+\frac {b \left (7 a^2 A b+15 A b^3-4 a^3 B-12 a b^2 B\right )}{4 a^3 \left (a^2+b^2\right ) d \sqrt {a+b \tan (c+d x)}}+\frac {(5 A b-4 a B) \cot (c+d x)}{4 a^2 d \sqrt {a+b \tan (c+d x)}}-\frac {A \cot ^2(c+d x)}{2 a d \sqrt {a+b \tan (c+d x)}}\\ \end {align*}

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Mathematica [A]  time = 6.25, size = 409, normalized size = 1.44 \[ -\frac {A \cot ^2(c+d x)}{2 a d \sqrt {a+b \tan (c+d x)}}-\frac {-\frac {(5 A b-4 a B) \cot (c+d x)}{2 a d \sqrt {a+b \tan (c+d x)}}-\frac {\frac {2 \left (\frac {1}{4} b^2 \left (-8 a^2 A-12 a b B+15 A b^2\right )-a \left (-2 a^2 b B-\frac {3}{4} a b (5 A b-4 a B)\right )\right )}{a d \left (a^2+b^2\right ) \sqrt {a+b \tan (c+d x)}}+\frac {2 \left (\frac {i \sqrt {a-i b} \left (a^3 (A b-a B)-i a^3 (a A+b B)\right ) \tanh ^{-1}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{d (-a+i b)}-\frac {i \sqrt {a+i b} \left (a^3 (A b-a B)+i a^3 (a A+b B)\right ) \tanh ^{-1}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{d (-a-i b)}+\frac {\left (a^2+b^2\right ) \left (8 a^2 A+12 a b B-15 A b^2\right ) \tanh ^{-1}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{4 \sqrt {a} d}\right )}{a \left (a^2+b^2\right )}}{a}}{2 a} \]

Antiderivative was successfully verified.

[In]

Integrate[(Cot[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]

[Out]

-1/2*(A*Cot[c + d*x]^2)/(a*d*Sqrt[a + b*Tan[c + d*x]]) - (-1/2*((5*A*b - 4*a*B)*Cot[c + d*x])/(a*d*Sqrt[a + b*
Tan[c + d*x]]) - ((2*(((a^2 + b^2)*(8*a^2*A - 15*A*b^2 + 12*a*b*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/
(4*Sqrt[a]*d) + (I*Sqrt[a - I*b]*(a^3*(A*b - a*B) - I*a^3*(a*A + b*B))*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a
- I*b]])/((-a + I*b)*d) - (I*Sqrt[a + I*b]*(a^3*(A*b - a*B) + I*a^3*(a*A + b*B))*ArcTanh[Sqrt[a + b*Tan[c + d
*x]]/Sqrt[a + I*b]])/((-a - I*b)*d)))/(a*(a^2 + b^2)) + (2*((b^2*(-8*a^2*A + 15*A*b^2 - 12*a*b*B))/4 - a*(-2*a
^2*b*B - (3*a*b*(5*A*b - 4*a*B))/4)))/(a*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]]))/a)/(2*a)

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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(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm="fricas")

[Out]

Timed out

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unab
le to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*p
i/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warn
ing, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was
done assuming [d]=[-4,-46]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argumen
t ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The
choice was done assuming [d]=[-14,53]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error:
Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Values
ym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const
gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const inde
x_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecte
ur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad
Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2p
oly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen
& e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m
& i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur &
l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argu
ment ValueWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is r
eal):Check [abs(t_nostep^2-1)]Discontinuities at zeroes of t_nostep^2-1 were not checkedEvaluation time: 81.83
Done

________________________________________________________________________________________

maple [C]  time = 6.31, size = 174426, normalized size = 612.02 \[ \text {output too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x)

[Out]

result too large to display

________________________________________________________________________________________

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(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm="maxima")

[Out]

Timed out

________________________________________________________________________________________

mupad [B]  time = 10.28, size = 42371, normalized size = 148.67 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((cot(c + d*x)^3*(A + B*tan(c + d*x)))/(a + b*tan(c + d*x))^(3/2),x)

[Out]

((2*(A*b^4 - B*a*b^3))/(a*(a^2 + b^2)) + ((a + b*tan(c + d*x))^2*(15*A*b^4 + 7*A*a^2*b^2 - 12*B*a*b^3 - 4*B*a^
3*b))/(4*a^3*(a^2 + b^2)) - ((a + b*tan(c + d*x))*(25*A*b^4 + 9*A*a^2*b^2 - 20*B*a*b^3 - 4*B*a^3*b))/(4*a^2*(a
^2 + b^2)))/(d*(a + b*tan(c + d*x))^(5/2) - 2*a*d*(a + b*tan(c + d*x))^(3/2) + a^2*d*(a + b*tan(c + d*x))^(1/2
)) + atan((((a + b*tan(c + d*x))^(1/2)*(704643072*A^4*a^29*b^20*d^5 - 290979840*A^4*a^23*b^26*d^5 - 465043456*
A^4*a^25*b^24*d^5 - 37224448*A^4*a^27*b^22*d^5 - 58982400*A^4*a^21*b^28*d^5 + 767033344*A^4*a^31*b^18*d^5 + 23
8551040*A^4*a^33*b^16*d^5 + 1572864*A^4*a^35*b^14*d^5 + 92536832*A^4*a^37*b^12*d^5 + 96468992*A^4*a^39*b^10*d^
5 + 25165824*A^4*a^41*b^8*d^5 + 37748736*B^4*a^23*b^26*d^5 + 226492416*B^4*a^25*b^24*d^5 + 536870912*B^4*a^27*
b^22*d^5 + 587202560*B^4*a^29*b^20*d^5 + 176160768*B^4*a^31*b^18*d^5 - 234881024*B^4*a^33*b^16*d^5 - 234881024
*B^4*a^35*b^14*d^5 - 50331648*B^4*a^37*b^12*d^5 + 20971520*B^4*a^39*b^10*d^5 + 8388608*B^4*a^41*b^8*d^5 - 9437
1840*A*B^3*a^22*b^27*d^5 - 364904448*A*B^3*a^24*b^25*d^5 + 37748736*A*B^3*a^26*b^23*d^5 + 2554331136*A*B^3*a^2
8*b^21*d^5 + 5989466112*A*B^3*a^30*b^19*d^5 + 6606028800*A*B^3*a^32*b^17*d^5 + 3787456512*A*B^3*a^34*b^15*d^5
+ 918552576*A*B^3*a^36*b^13*d^5 - 56623104*A*B^3*a^38*b^11*d^5 - 50331648*A*B^3*a^40*b^9*d^5 + 330301440*A^3*B
*a^22*b^27*d^5 + 1915748352*A^3*B*a^24*b^25*d^5 + 4279238656*A^3*B*a^26*b^23*d^5 + 4059037696*A^3*B*a^28*b^21*
d^5 + 154140672*A^3*B*a^30*b^19*d^5 - 2825912320*A^3*B*a^32*b^17*d^5 - 1901068288*A^3*B*a^34*b^15*d^5 + 220200
96*A^3*B*a^36*b^13*d^5 + 425721856*A^3*B*a^38*b^11*d^5 + 117440512*A^3*B*a^40*b^9*d^5 + 58982400*A^2*B^2*a^21*
b^28*d^5 - 124256256*A^2*B^2*a^23*b^26*d^5 - 2202533888*A^2*B^2*a^25*b^24*d^5 - 6984040448*A^2*B^2*a^27*b^22*d
^5 - 10041163776*A^2*B^2*a^29*b^20*d^5 - 6404177920*A^2*B^2*a^31*b^18*d^5 + 289931264*A^2*B^2*a^33*b^16*d^5 +
2993160192*A^2*B^2*a^35*b^14*d^5 + 1694236672*A^2*B^2*a^37*b^12*d^5 + 318767104*A^2*B^2*a^39*b^10*d^5) + (-(((
8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 -
(A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 +
4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4
+ 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(773849088*A^3*a^35*b^16*d^6 - 117964800*A^3*a^21*b^30*d^6 - 6999244
80*A^3*a^23*b^28*d^6 - 1889533952*A^3*a^25*b^26*d^6 - 3336568832*A^3*a^27*b^24*d^6 - 4495245312*A^3*a^29*b^22*
d^6 - 4279238656*A^3*a^31*b^20*d^6 - 1923088384*A^3*a^33*b^18*d^6 - ((a + b*tan(c + d*x))^(1/2)*(235929600*A^2
*a^22*b^30*d^7 + 1871708160*A^2*a^24*b^28*d^7 + 6295650304*A^2*a^26*b^26*d^7 + 11144265728*A^2*a^28*b^24*d^7 +
9560915968*A^2*a^30*b^22*d^7 - 337641472*A^2*a^32*b^20*d^7 - 9307160576*A^2*a^34*b^18*d^7 - 8887730176*A^2*a^
36*b^16*d^7 - 2943352832*A^2*a^38*b^14*d^7 + 621805568*A^2*a^40*b^12*d^7 + 721420288*A^2*a^42*b^10*d^7 + 15099
4944*A^2*a^44*b^8*d^7 + 150994944*B^2*a^24*b^28*d^7 + 1358954496*B^2*a^26*b^26*d^7 + 5653921792*B^2*a^28*b^24*
d^7 + 14126415872*B^2*a^30*b^22*d^7 + 23018340352*B^2*a^32*b^20*d^7 + 24897388544*B^2*a^34*b^18*d^7 + 17381195
776*B^2*a^36*b^16*d^7 + 7079985152*B^2*a^38*b^14*d^7 + 1124073472*B^2*a^40*b^12*d^7 - 218103808*B^2*a^42*b^10*
d^7 - 83886080*B^2*a^44*b^8*d^7 - 377487360*A*B*a^23*b^29*d^7 - 3196059648*A*B*a^25*b^27*d^7 - 11911823360*A*B
*a^27*b^25*d^7 - 24930942976*A*B*a^29*b^23*d^7 - 30182211584*A*B*a^31*b^21*d^7 - 17028874240*A*B*a^33*b^19*d^7
+ 5402263552*A*B*a^35*b^17*d^7 + 16944988160*A*B*a^37*b^15*d^7 + 12775849984*A*B*a^39*b^13*d^7 + 4588568576*A
*B*a^41*b^11*d^7 + 671088640*A*B*a^43*b^9*d^7) - (-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*
a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a
^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^
2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*((a + b*tan(c
+ d*x))^(1/2)*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A
*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)
- 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16
*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(134217728*a^27*b^28*d^9 + 1409286144*a^29*b^26*d
^9 + 6643777536*a^31*b^24*d^9 + 18522046464*a^33*b^22*d^9 + 33822867456*a^35*b^20*d^9 + 42278584320*a^37*b^18*
d^9 + 36641439744*a^39*b^16*d^9 + 21743271936*a^41*b^14*d^9 + 8455716864*a^43*b^12*d^9 + 1946157056*a^45*b^10*
d^9 + 201326592*a^47*b^8*d^9) - 251658240*A*a^24*b^30*d^8 - 2382364672*A*a^26*b^28*d^8 - 9948889088*A*a^28*b^2
6*d^8 - 23924310016*A*a^30*b^24*d^8 - 36071014400*A*a^32*b^22*d^8 - 34292629504*A*a^34*b^20*d^8 - 18555600896*
A*a^36*b^18*d^8 - 2483027968*A*a^38*b^16*d^8 + 3841982464*A*a^40*b^14*d^8 + 2852126720*A*a^42*b^12*d^8 + 85563
8016*A*a^44*b^10*d^8 + 100663296*A*a^46*b^8*d^8 + 201326592*B*a^25*b^29*d^8 + 2013265920*B*a^27*b^27*d^8 + 899
2587776*B*a^29*b^25*d^8 + 23622320128*B*a^31*b^23*d^8 + 40399536128*B*a^33*b^21*d^8 + 46976204800*B*a^35*b^19*
d^8 + 37580963840*B*a^37*b^17*d^8 + 20401094656*B*a^39*b^15*d^8 + 7180648448*B*a^41*b^13*d^8 + 1476395008*B*a^
43*b^11*d^8 + 134217728*B*a^45*b^9*d^8))*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^
2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d
^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*
d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) + 1421344768*A^3*a^37*
b^14*d^6 + 587726848*A^3*a^39*b^12*d^6 + 25165824*A^3*a^41*b^10*d^6 - 25165824*A^3*a^43*b^8*d^6 + 150994944*B^
3*a^24*b^27*d^6 + 905969664*B^3*a^26*b^25*d^6 + 2222981120*B^3*a^28*b^23*d^6 + 2877292544*B^3*a^30*b^21*d^6 +
2290089984*B^3*a^32*b^19*d^6 + 1702887424*B^3*a^34*b^17*d^6 + 1702887424*B^3*a^36*b^15*d^6 + 1384120320*B^3*a^
38*b^13*d^6 + 612368384*B^3*a^40*b^11*d^6 + 109051904*B^3*a^42*b^9*d^6 - 452984832*A*B^2*a^23*b^28*d^6 - 27682
40640*A*B^2*a^25*b^26*d^6 - 7348420608*A*B^2*a^27*b^24*d^6 - 11903434752*A*B^2*a^29*b^22*d^6 - 14973665280*A*B
^2*a^31*b^20*d^6 - 16735272960*A*B^2*a^33*b^18*d^6 - 14973665280*A*B^2*a^35*b^16*d^6 - 8732540928*A*B^2*a^37*b
^14*d^6 - 2592079872*A*B^2*a^39*b^12*d^6 - 125829120*A*B^2*a^41*b^10*d^6 + 75497472*A*B^2*a^43*b^8*d^6 + 42467
3280*A^2*B*a^22*b^29*d^6 + 2604662784*A^2*B*a^24*b^27*d^6 + 7159676928*A^2*B*a^26*b^25*d^6 + 12532580352*A^2*B
*a^28*b^23*d^6 + 16867393536*A^2*B*a^30*b^21*d^6 + 17792237568*A^2*B*a^32*b^19*d^6 + 12419334144*A^2*B*a^34*b^
17*d^6 + 3573547008*A^2*B*a^36*b^15*d^6 - 1513095168*A^2*B*a^38*b^13*d^6 - 1472200704*A^2*B*a^40*b^11*d^6 - 32
7155712*A^2*B*a^42*b^9*d^6))*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a
*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*
b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B
*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*1i + ((a + b*tan(c + d*x))^(1/2)*(
704643072*A^4*a^29*b^20*d^5 - 290979840*A^4*a^23*b^26*d^5 - 465043456*A^4*a^25*b^24*d^5 - 37224448*A^4*a^27*b^
22*d^5 - 58982400*A^4*a^21*b^28*d^5 + 767033344*A^4*a^31*b^18*d^5 + 238551040*A^4*a^33*b^16*d^5 + 1572864*A^4*
a^35*b^14*d^5 + 92536832*A^4*a^37*b^12*d^5 + 96468992*A^4*a^39*b^10*d^5 + 25165824*A^4*a^41*b^8*d^5 + 37748736
*B^4*a^23*b^26*d^5 + 226492416*B^4*a^25*b^24*d^5 + 536870912*B^4*a^27*b^22*d^5 + 587202560*B^4*a^29*b^20*d^5 +
176160768*B^4*a^31*b^18*d^5 - 234881024*B^4*a^33*b^16*d^5 - 234881024*B^4*a^35*b^14*d^5 - 50331648*B^4*a^37*b
^12*d^5 + 20971520*B^4*a^39*b^10*d^5 + 8388608*B^4*a^41*b^8*d^5 - 94371840*A*B^3*a^22*b^27*d^5 - 364904448*A*B
^3*a^24*b^25*d^5 + 37748736*A*B^3*a^26*b^23*d^5 + 2554331136*A*B^3*a^28*b^21*d^5 + 5989466112*A*B^3*a^30*b^19*
d^5 + 6606028800*A*B^3*a^32*b^17*d^5 + 3787456512*A*B^3*a^34*b^15*d^5 + 918552576*A*B^3*a^36*b^13*d^5 - 566231
04*A*B^3*a^38*b^11*d^5 - 50331648*A*B^3*a^40*b^9*d^5 + 330301440*A^3*B*a^22*b^27*d^5 + 1915748352*A^3*B*a^24*b
^25*d^5 + 4279238656*A^3*B*a^26*b^23*d^5 + 4059037696*A^3*B*a^28*b^21*d^5 + 154140672*A^3*B*a^30*b^19*d^5 - 28
25912320*A^3*B*a^32*b^17*d^5 - 1901068288*A^3*B*a^34*b^15*d^5 + 22020096*A^3*B*a^36*b^13*d^5 + 425721856*A^3*B
*a^38*b^11*d^5 + 117440512*A^3*B*a^40*b^9*d^5 + 58982400*A^2*B^2*a^21*b^28*d^5 - 124256256*A^2*B^2*a^23*b^26*d
^5 - 2202533888*A^2*B^2*a^25*b^24*d^5 - 6984040448*A^2*B^2*a^27*b^22*d^5 - 10041163776*A^2*B^2*a^29*b^20*d^5 -
6404177920*A^2*B^2*a^31*b^18*d^5 + 289931264*A^2*B^2*a^33*b^16*d^5 + 2993160192*A^2*B^2*a^35*b^14*d^5 + 16942
36672*A^2*B^2*a^37*b^12*d^5 + 318767104*A^2*B^2*a^39*b^10*d^5) - (-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b
^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 1
6*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a
*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2
)*(((a + b*tan(c + d*x))^(1/2)*(235929600*A^2*a^22*b^30*d^7 + 1871708160*A^2*a^24*b^28*d^7 + 6295650304*A^2*a^
26*b^26*d^7 + 11144265728*A^2*a^28*b^24*d^7 + 9560915968*A^2*a^30*b^22*d^7 - 337641472*A^2*a^32*b^20*d^7 - 930
7160576*A^2*a^34*b^18*d^7 - 8887730176*A^2*a^36*b^16*d^7 - 2943352832*A^2*a^38*b^14*d^7 + 621805568*A^2*a^40*b
^12*d^7 + 721420288*A^2*a^42*b^10*d^7 + 150994944*A^2*a^44*b^8*d^7 + 150994944*B^2*a^24*b^28*d^7 + 1358954496*
B^2*a^26*b^26*d^7 + 5653921792*B^2*a^28*b^24*d^7 + 14126415872*B^2*a^30*b^22*d^7 + 23018340352*B^2*a^32*b^20*d
^7 + 24897388544*B^2*a^34*b^18*d^7 + 17381195776*B^2*a^36*b^16*d^7 + 7079985152*B^2*a^38*b^14*d^7 + 1124073472
*B^2*a^40*b^12*d^7 - 218103808*B^2*a^42*b^10*d^7 - 83886080*B^2*a^44*b^8*d^7 - 377487360*A*B*a^23*b^29*d^7 - 3
196059648*A*B*a^25*b^27*d^7 - 11911823360*A*B*a^27*b^25*d^7 - 24930942976*A*B*a^29*b^23*d^7 - 30182211584*A*B*
a^31*b^21*d^7 - 17028874240*A*B*a^33*b^19*d^7 + 5402263552*A*B*a^35*b^17*d^7 + 16944988160*A*B*a^37*b^15*d^7 +
12775849984*A*B*a^39*b^13*d^7 + 4588568576*A*B*a^41*b^11*d^7 + 671088640*A*B*a^43*b^9*d^7) + (-(((8*A^2*a^3*d
^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A
^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d
^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^
4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(3841982464*A*a^40*b^14*d^8 - 251658240*A*a^24*b^30*d^8 - 2382364672*A*a^26*b^2
8*d^8 - 9948889088*A*a^28*b^26*d^8 - 23924310016*A*a^30*b^24*d^8 - 36071014400*A*a^32*b^22*d^8 - 34292629504*A
*a^34*b^20*d^8 - 18555600896*A*a^36*b^18*d^8 - 2483027968*A*a^38*b^16*d^8 - (a + b*tan(c + d*x))^(1/2)*(-(((8*
A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (
A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*
B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 +
3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(134217728*a^27*b^28*d^9 + 1409286144*a^29*b^26*d^9 + 6643777536*a^31*
b^24*d^9 + 18522046464*a^33*b^22*d^9 + 33822867456*a^35*b^20*d^9 + 42278584320*a^37*b^18*d^9 + 36641439744*a^3
9*b^16*d^9 + 21743271936*a^41*b^14*d^9 + 8455716864*a^43*b^12*d^9 + 1946157056*a^45*b^10*d^9 + 201326592*a^47*
b^8*d^9) + 2852126720*A*a^42*b^12*d^8 + 855638016*A*a^44*b^10*d^8 + 100663296*A*a^46*b^8*d^8 + 201326592*B*a^2
5*b^29*d^8 + 2013265920*B*a^27*b^27*d^8 + 8992587776*B*a^29*b^25*d^8 + 23622320128*B*a^31*b^23*d^8 + 403995361
28*B*a^33*b^21*d^8 + 46976204800*B*a^35*b^19*d^8 + 37580963840*B*a^37*b^17*d^8 + 20401094656*B*a^39*b^15*d^8 +
7180648448*B*a^41*b^13*d^8 + 1476395008*B*a^43*b^11*d^8 + 134217728*B*a^45*b^9*d^8))*(-(((8*A^2*a^3*d^2 - 8*B
^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 +
B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A
*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 +
3*a^4*b^2*d^4)))^(1/2) - 117964800*A^3*a^21*b^30*d^6 - 699924480*A^3*a^23*b^28*d^6 - 1889533952*A^3*a^25*b^26*
d^6 - 3336568832*A^3*a^27*b^24*d^6 - 4495245312*A^3*a^29*b^22*d^6 - 4279238656*A^3*a^31*b^20*d^6 - 1923088384*
A^3*a^33*b^18*d^6 + 773849088*A^3*a^35*b^16*d^6 + 1421344768*A^3*a^37*b^14*d^6 + 587726848*A^3*a^39*b^12*d^6 +
25165824*A^3*a^41*b^10*d^6 - 25165824*A^3*a^43*b^8*d^6 + 150994944*B^3*a^24*b^27*d^6 + 905969664*B^3*a^26*b^2
5*d^6 + 2222981120*B^3*a^28*b^23*d^6 + 2877292544*B^3*a^30*b^21*d^6 + 2290089984*B^3*a^32*b^19*d^6 + 170288742
4*B^3*a^34*b^17*d^6 + 1702887424*B^3*a^36*b^15*d^6 + 1384120320*B^3*a^38*b^13*d^6 + 612368384*B^3*a^40*b^11*d^
6 + 109051904*B^3*a^42*b^9*d^6 - 452984832*A*B^2*a^23*b^28*d^6 - 2768240640*A*B^2*a^25*b^26*d^6 - 7348420608*A
*B^2*a^27*b^24*d^6 - 11903434752*A*B^2*a^29*b^22*d^6 - 14973665280*A*B^2*a^31*b^20*d^6 - 16735272960*A*B^2*a^3
3*b^18*d^6 - 14973665280*A*B^2*a^35*b^16*d^6 - 8732540928*A*B^2*a^37*b^14*d^6 - 2592079872*A*B^2*a^39*b^12*d^6
- 125829120*A*B^2*a^41*b^10*d^6 + 75497472*A*B^2*a^43*b^8*d^6 + 424673280*A^2*B*a^22*b^29*d^6 + 2604662784*A^
2*B*a^24*b^27*d^6 + 7159676928*A^2*B*a^26*b^25*d^6 + 12532580352*A^2*B*a^28*b^23*d^6 + 16867393536*A^2*B*a^30*
b^21*d^6 + 17792237568*A^2*B*a^32*b^19*d^6 + 12419334144*A^2*B*a^34*b^17*d^6 + 3573547008*A^2*B*a^36*b^15*d^6
- 1513095168*A^2*B*a^38*b^13*d^6 - 1472200704*A^2*B*a^40*b^11*d^6 - 327155712*A^2*B*a^42*b^9*d^6))*(-(((8*A^2*
a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4
+ 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*
a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a
^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*1i)/(((a + b*tan(c + d*x))^(1/2)*(704643072*A^4*a^29*b^20*d^5 - 290979840*
A^4*a^23*b^26*d^5 - 465043456*A^4*a^25*b^24*d^5 - 37224448*A^4*a^27*b^22*d^5 - 58982400*A^4*a^21*b^28*d^5 + 76
7033344*A^4*a^31*b^18*d^5 + 238551040*A^4*a^33*b^16*d^5 + 1572864*A^4*a^35*b^14*d^5 + 92536832*A^4*a^37*b^12*d
^5 + 96468992*A^4*a^39*b^10*d^5 + 25165824*A^4*a^41*b^8*d^5 + 37748736*B^4*a^23*b^26*d^5 + 226492416*B^4*a^25*
b^24*d^5 + 536870912*B^4*a^27*b^22*d^5 + 587202560*B^4*a^29*b^20*d^5 + 176160768*B^4*a^31*b^18*d^5 - 234881024
*B^4*a^33*b^16*d^5 - 234881024*B^4*a^35*b^14*d^5 - 50331648*B^4*a^37*b^12*d^5 + 20971520*B^4*a^39*b^10*d^5 + 8
388608*B^4*a^41*b^8*d^5 - 94371840*A*B^3*a^22*b^27*d^5 - 364904448*A*B^3*a^24*b^25*d^5 + 37748736*A*B^3*a^26*b
^23*d^5 + 2554331136*A*B^3*a^28*b^21*d^5 + 5989466112*A*B^3*a^30*b^19*d^5 + 6606028800*A*B^3*a^32*b^17*d^5 + 3
787456512*A*B^3*a^34*b^15*d^5 + 918552576*A*B^3*a^36*b^13*d^5 - 56623104*A*B^3*a^38*b^11*d^5 - 50331648*A*B^3*
a^40*b^9*d^5 + 330301440*A^3*B*a^22*b^27*d^5 + 1915748352*A^3*B*a^24*b^25*d^5 + 4279238656*A^3*B*a^26*b^23*d^5
+ 4059037696*A^3*B*a^28*b^21*d^5 + 154140672*A^3*B*a^30*b^19*d^5 - 2825912320*A^3*B*a^32*b^17*d^5 - 190106828
8*A^3*B*a^34*b^15*d^5 + 22020096*A^3*B*a^36*b^13*d^5 + 425721856*A^3*B*a^38*b^11*d^5 + 117440512*A^3*B*a^40*b^
9*d^5 + 58982400*A^2*B^2*a^21*b^28*d^5 - 124256256*A^2*B^2*a^23*b^26*d^5 - 2202533888*A^2*B^2*a^25*b^24*d^5 -
6984040448*A^2*B^2*a^27*b^22*d^5 - 10041163776*A^2*B^2*a^29*b^20*d^5 - 6404177920*A^2*B^2*a^31*b^18*d^5 + 2899
31264*A^2*B^2*a^33*b^16*d^5 + 2993160192*A^2*B^2*a^35*b^14*d^5 + 1694236672*A^2*B^2*a^37*b^12*d^5 + 318767104*
A^2*B^2*a^39*b^10*d^5) - (-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2
*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*
d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2
*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(((a + b*tan(c + d*x))^(1/2)*(23592960
0*A^2*a^22*b^30*d^7 + 1871708160*A^2*a^24*b^28*d^7 + 6295650304*A^2*a^26*b^26*d^7 + 11144265728*A^2*a^28*b^24*
d^7 + 9560915968*A^2*a^30*b^22*d^7 - 337641472*A^2*a^32*b^20*d^7 - 9307160576*A^2*a^34*b^18*d^7 - 8887730176*A
^2*a^36*b^16*d^7 - 2943352832*A^2*a^38*b^14*d^7 + 621805568*A^2*a^40*b^12*d^7 + 721420288*A^2*a^42*b^10*d^7 +
150994944*A^2*a^44*b^8*d^7 + 150994944*B^2*a^24*b^28*d^7 + 1358954496*B^2*a^26*b^26*d^7 + 5653921792*B^2*a^28*
b^24*d^7 + 14126415872*B^2*a^30*b^22*d^7 + 23018340352*B^2*a^32*b^20*d^7 + 24897388544*B^2*a^34*b^18*d^7 + 173
81195776*B^2*a^36*b^16*d^7 + 7079985152*B^2*a^38*b^14*d^7 + 1124073472*B^2*a^40*b^12*d^7 - 218103808*B^2*a^42*
b^10*d^7 - 83886080*B^2*a^44*b^8*d^7 - 377487360*A*B*a^23*b^29*d^7 - 3196059648*A*B*a^25*b^27*d^7 - 1191182336
0*A*B*a^27*b^25*d^7 - 24930942976*A*B*a^29*b^23*d^7 - 30182211584*A*B*a^31*b^21*d^7 - 17028874240*A*B*a^33*b^1
9*d^7 + 5402263552*A*B*a^35*b^17*d^7 + 16944988160*A*B*a^37*b^15*d^7 + 12775849984*A*B*a^39*b^13*d^7 + 4588568
576*A*B*a^41*b^11*d^7 + 671088640*A*B*a^43*b^9*d^7) + (-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24
*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 +
48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 -
12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(38419824
64*A*a^40*b^14*d^8 - 251658240*A*a^24*b^30*d^8 - 2382364672*A*a^26*b^28*d^8 - 9948889088*A*a^28*b^26*d^8 - 239
24310016*A*a^30*b^24*d^8 - 36071014400*A*a^32*b^22*d^8 - 34292629504*A*a^34*b^20*d^8 - 18555600896*A*a^36*b^18
*d^8 - 2483027968*A*a^38*b^16*d^8 - (a + b*tan(c + d*x))^(1/2)*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3
*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*
b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b
^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*
(134217728*a^27*b^28*d^9 + 1409286144*a^29*b^26*d^9 + 6643777536*a^31*b^24*d^9 + 18522046464*a^33*b^22*d^9 + 3
3822867456*a^35*b^20*d^9 + 42278584320*a^37*b^18*d^9 + 36641439744*a^39*b^16*d^9 + 21743271936*a^41*b^14*d^9 +
8455716864*a^43*b^12*d^9 + 1946157056*a^45*b^10*d^9 + 201326592*a^47*b^8*d^9) + 2852126720*A*a^42*b^12*d^8 +
855638016*A*a^44*b^10*d^8 + 100663296*A*a^46*b^8*d^8 + 201326592*B*a^25*b^29*d^8 + 2013265920*B*a^27*b^27*d^8
+ 8992587776*B*a^29*b^25*d^8 + 23622320128*B*a^31*b^23*d^8 + 40399536128*B*a^33*b^21*d^8 + 46976204800*B*a^35*
b^19*d^8 + 37580963840*B*a^37*b^17*d^8 + 20401094656*B*a^39*b^15*d^8 + 7180648448*B*a^41*b^13*d^8 + 1476395008
*B*a^43*b^11*d^8 + 134217728*B*a^45*b^9*d^8))*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b
^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*
b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a
*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) - 117964800*A^3*a
^21*b^30*d^6 - 699924480*A^3*a^23*b^28*d^6 - 1889533952*A^3*a^25*b^26*d^6 - 3336568832*A^3*a^27*b^24*d^6 - 449
5245312*A^3*a^29*b^22*d^6 - 4279238656*A^3*a^31*b^20*d^6 - 1923088384*A^3*a^33*b^18*d^6 + 773849088*A^3*a^35*b
^16*d^6 + 1421344768*A^3*a^37*b^14*d^6 + 587726848*A^3*a^39*b^12*d^6 + 25165824*A^3*a^41*b^10*d^6 - 25165824*A
^3*a^43*b^8*d^6 + 150994944*B^3*a^24*b^27*d^6 + 905969664*B^3*a^26*b^25*d^6 + 2222981120*B^3*a^28*b^23*d^6 + 2
877292544*B^3*a^30*b^21*d^6 + 2290089984*B^3*a^32*b^19*d^6 + 1702887424*B^3*a^34*b^17*d^6 + 1702887424*B^3*a^3
6*b^15*d^6 + 1384120320*B^3*a^38*b^13*d^6 + 612368384*B^3*a^40*b^11*d^6 + 109051904*B^3*a^42*b^9*d^6 - 4529848
32*A*B^2*a^23*b^28*d^6 - 2768240640*A*B^2*a^25*b^26*d^6 - 7348420608*A*B^2*a^27*b^24*d^6 - 11903434752*A*B^2*a
^29*b^22*d^6 - 14973665280*A*B^2*a^31*b^20*d^6 - 16735272960*A*B^2*a^33*b^18*d^6 - 14973665280*A*B^2*a^35*b^16
*d^6 - 8732540928*A*B^2*a^37*b^14*d^6 - 2592079872*A*B^2*a^39*b^12*d^6 - 125829120*A*B^2*a^41*b^10*d^6 + 75497
472*A*B^2*a^43*b^8*d^6 + 424673280*A^2*B*a^22*b^29*d^6 + 2604662784*A^2*B*a^24*b^27*d^6 + 7159676928*A^2*B*a^2
6*b^25*d^6 + 12532580352*A^2*B*a^28*b^23*d^6 + 16867393536*A^2*B*a^30*b^21*d^6 + 17792237568*A^2*B*a^32*b^19*d
^6 + 12419334144*A^2*B*a^34*b^17*d^6 + 3573547008*A^2*B*a^36*b^15*d^6 - 1513095168*A^2*B*a^38*b^13*d^6 - 14722
00704*A^2*B*a^40*b^11*d^6 - 327155712*A^2*B*a^42*b^9*d^6))*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2
- 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*
d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d
^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) - ((
a + b*tan(c + d*x))^(1/2)*(704643072*A^4*a^29*b^20*d^5 - 290979840*A^4*a^23*b^26*d^5 - 465043456*A^4*a^25*b^24
*d^5 - 37224448*A^4*a^27*b^22*d^5 - 58982400*A^4*a^21*b^28*d^5 + 767033344*A^4*a^31*b^18*d^5 + 238551040*A^4*a
^33*b^16*d^5 + 1572864*A^4*a^35*b^14*d^5 + 92536832*A^4*a^37*b^12*d^5 + 96468992*A^4*a^39*b^10*d^5 + 25165824*
A^4*a^41*b^8*d^5 + 37748736*B^4*a^23*b^26*d^5 + 226492416*B^4*a^25*b^24*d^5 + 536870912*B^4*a^27*b^22*d^5 + 58
7202560*B^4*a^29*b^20*d^5 + 176160768*B^4*a^31*b^18*d^5 - 234881024*B^4*a^33*b^16*d^5 - 234881024*B^4*a^35*b^1
4*d^5 - 50331648*B^4*a^37*b^12*d^5 + 20971520*B^4*a^39*b^10*d^5 + 8388608*B^4*a^41*b^8*d^5 - 94371840*A*B^3*a^
22*b^27*d^5 - 364904448*A*B^3*a^24*b^25*d^5 + 37748736*A*B^3*a^26*b^23*d^5 + 2554331136*A*B^3*a^28*b^21*d^5 +
5989466112*A*B^3*a^30*b^19*d^5 + 6606028800*A*B^3*a^32*b^17*d^5 + 3787456512*A*B^3*a^34*b^15*d^5 + 918552576*A
*B^3*a^36*b^13*d^5 - 56623104*A*B^3*a^38*b^11*d^5 - 50331648*A*B^3*a^40*b^9*d^5 + 330301440*A^3*B*a^22*b^27*d^
5 + 1915748352*A^3*B*a^24*b^25*d^5 + 4279238656*A^3*B*a^26*b^23*d^5 + 4059037696*A^3*B*a^28*b^21*d^5 + 1541406
72*A^3*B*a^30*b^19*d^5 - 2825912320*A^3*B*a^32*b^17*d^5 - 1901068288*A^3*B*a^34*b^15*d^5 + 22020096*A^3*B*a^36
*b^13*d^5 + 425721856*A^3*B*a^38*b^11*d^5 + 117440512*A^3*B*a^40*b^9*d^5 + 58982400*A^2*B^2*a^21*b^28*d^5 - 12
4256256*A^2*B^2*a^23*b^26*d^5 - 2202533888*A^2*B^2*a^25*b^24*d^5 - 6984040448*A^2*B^2*a^27*b^22*d^5 - 10041163
776*A^2*B^2*a^29*b^20*d^5 - 6404177920*A^2*B^2*a^31*b^18*d^5 + 289931264*A^2*B^2*a^33*b^16*d^5 + 2993160192*A^
2*B^2*a^35*b^14*d^5 + 1694236672*A^2*B^2*a^37*b^12*d^5 + 318767104*A^2*B^2*a^39*b^10*d^5) + (-(((8*A^2*a^3*d^2
- 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2
*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2
+ 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*
d^4 + 3*a^4*b^2*d^4)))^(1/2)*(773849088*A^3*a^35*b^16*d^6 - 117964800*A^3*a^21*b^30*d^6 - 699924480*A^3*a^23*b
^28*d^6 - 1889533952*A^3*a^25*b^26*d^6 - 3336568832*A^3*a^27*b^24*d^6 - 4495245312*A^3*a^29*b^22*d^6 - 4279238
656*A^3*a^31*b^20*d^6 - 1923088384*A^3*a^33*b^18*d^6 - ((a + b*tan(c + d*x))^(1/2)*(235929600*A^2*a^22*b^30*d^
7 + 1871708160*A^2*a^24*b^28*d^7 + 6295650304*A^2*a^26*b^26*d^7 + 11144265728*A^2*a^28*b^24*d^7 + 9560915968*A
^2*a^30*b^22*d^7 - 337641472*A^2*a^32*b^20*d^7 - 9307160576*A^2*a^34*b^18*d^7 - 8887730176*A^2*a^36*b^16*d^7 -
2943352832*A^2*a^38*b^14*d^7 + 621805568*A^2*a^40*b^12*d^7 + 721420288*A^2*a^42*b^10*d^7 + 150994944*A^2*a^44
*b^8*d^7 + 150994944*B^2*a^24*b^28*d^7 + 1358954496*B^2*a^26*b^26*d^7 + 5653921792*B^2*a^28*b^24*d^7 + 1412641
5872*B^2*a^30*b^22*d^7 + 23018340352*B^2*a^32*b^20*d^7 + 24897388544*B^2*a^34*b^18*d^7 + 17381195776*B^2*a^36*
b^16*d^7 + 7079985152*B^2*a^38*b^14*d^7 + 1124073472*B^2*a^40*b^12*d^7 - 218103808*B^2*a^42*b^10*d^7 - 8388608
0*B^2*a^44*b^8*d^7 - 377487360*A*B*a^23*b^29*d^7 - 3196059648*A*B*a^25*b^27*d^7 - 11911823360*A*B*a^27*b^25*d^
7 - 24930942976*A*B*a^29*b^23*d^7 - 30182211584*A*B*a^31*b^21*d^7 - 17028874240*A*B*a^33*b^19*d^7 + 5402263552
*A*B*a^35*b^17*d^7 + 16944988160*A*B*a^37*b^15*d^7 + 12775849984*A*B*a^39*b^13*d^7 + 4588568576*A*B*a^41*b^11*
d^7 + 671088640*A*B*a^43*b^9*d^7) - (-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 2
4*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 +
48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 -
24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*((a + b*tan(c + d*x))^(1/2)
*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)
^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*
d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b
^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(134217728*a^27*b^28*d^9 + 1409286144*a^29*b^26*d^9 + 66437775
36*a^31*b^24*d^9 + 18522046464*a^33*b^22*d^9 + 33822867456*a^35*b^20*d^9 + 42278584320*a^37*b^18*d^9 + 3664143
9744*a^39*b^16*d^9 + 21743271936*a^41*b^14*d^9 + 8455716864*a^43*b^12*d^9 + 1946157056*a^45*b^10*d^9 + 2013265
92*a^47*b^8*d^9) - 251658240*A*a^24*b^30*d^8 - 2382364672*A*a^26*b^28*d^8 - 9948889088*A*a^28*b^26*d^8 - 23924
310016*A*a^30*b^24*d^8 - 36071014400*A*a^32*b^22*d^8 - 34292629504*A*a^34*b^20*d^8 - 18555600896*A*a^36*b^18*d
^8 - 2483027968*A*a^38*b^16*d^8 + 3841982464*A*a^40*b^14*d^8 + 2852126720*A*a^42*b^12*d^8 + 855638016*A*a^44*b
^10*d^8 + 100663296*A*a^46*b^8*d^8 + 201326592*B*a^25*b^29*d^8 + 2013265920*B*a^27*b^27*d^8 + 8992587776*B*a^2
9*b^25*d^8 + 23622320128*B*a^31*b^23*d^8 + 40399536128*B*a^33*b^21*d^8 + 46976204800*B*a^35*b^19*d^8 + 3758096
3840*B*a^37*b^17*d^8 + 20401094656*B*a^39*b^15*d^8 + 7180648448*B*a^41*b^13*d^8 + 1476395008*B*a^43*b^11*d^8 +
134217728*B*a^45*b^9*d^8))*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*
b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b
^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*
a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) + 1421344768*A^3*a^37*b^14*d^6 + 58
7726848*A^3*a^39*b^12*d^6 + 25165824*A^3*a^41*b^10*d^6 - 25165824*A^3*a^43*b^8*d^6 + 150994944*B^3*a^24*b^27*d
^6 + 905969664*B^3*a^26*b^25*d^6 + 2222981120*B^3*a^28*b^23*d^6 + 2877292544*B^3*a^30*b^21*d^6 + 2290089984*B^
3*a^32*b^19*d^6 + 1702887424*B^3*a^34*b^17*d^6 + 1702887424*B^3*a^36*b^15*d^6 + 1384120320*B^3*a^38*b^13*d^6 +
612368384*B^3*a^40*b^11*d^6 + 109051904*B^3*a^42*b^9*d^6 - 452984832*A*B^2*a^23*b^28*d^6 - 2768240640*A*B^2*a
^25*b^26*d^6 - 7348420608*A*B^2*a^27*b^24*d^6 - 11903434752*A*B^2*a^29*b^22*d^6 - 14973665280*A*B^2*a^31*b^20*
d^6 - 16735272960*A*B^2*a^33*b^18*d^6 - 14973665280*A*B^2*a^35*b^16*d^6 - 8732540928*A*B^2*a^37*b^14*d^6 - 259
2079872*A*B^2*a^39*b^12*d^6 - 125829120*A*B^2*a^41*b^10*d^6 + 75497472*A*B^2*a^43*b^8*d^6 + 424673280*A^2*B*a^
22*b^29*d^6 + 2604662784*A^2*B*a^24*b^27*d^6 + 7159676928*A^2*B*a^26*b^25*d^6 + 12532580352*A^2*B*a^28*b^23*d^
6 + 16867393536*A^2*B*a^30*b^21*d^6 + 17792237568*A^2*B*a^32*b^19*d^6 + 12419334144*A^2*B*a^34*b^17*d^6 + 3573
547008*A^2*B*a^36*b^15*d^6 - 1513095168*A^2*B*a^38*b^13*d^6 - 1472200704*A^2*B*a^40*b^11*d^6 - 327155712*A^2*B
*a^42*b^9*d^6))*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48
*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/
2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(
16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) + 58982400*A^5*a^22*b^26*d^4 + 381419520*A^5*a^
24*b^24*d^4 + 1018429440*A^5*a^26*b^22*d^4 + 1403781120*A^5*a^28*b^20*d^4 + 963379200*A^5*a^30*b^18*d^4 + 1376
25600*A^5*a^32*b^16*d^4 - 247726080*A^5*a^34*b^14*d^4 - 161218560*A^5*a^36*b^12*d^4 - 31457280*A^5*a^38*b^10*d
^4 + 37748736*B^5*a^23*b^25*d^4 + 239075328*B^5*a^25*b^23*d^4 + 616562688*B^5*a^27*b^21*d^4 + 792723456*B^5*a^
29*b^19*d^4 + 440401920*B^5*a^31*b^17*d^4 - 88080384*B^5*a^33*b^15*d^4 - 264241152*B^5*a^35*b^13*d^4 - 1384120
32*B^5*a^37*b^11*d^4 - 25165824*B^5*a^39*b^9*d^4 - 94371840*A*B^4*a^22*b^26*d^4 - 541065216*A*B^4*a^24*b^24*d^
4 - 1161822208*A*B^4*a^26*b^22*d^4 - 910163968*A*B^4*a^28*b^20*d^4 + 528482304*A*B^4*a^30*b^18*d^4 + 161480704
0*A*B^4*a^32*b^16*d^4 + 1262485504*A*B^4*a^34*b^14*d^4 + 390070272*A*B^4*a^36*b^12*d^4 + 2097152*A*B^4*a^38*b^
10*d^4 - 16777216*A*B^4*a^40*b^8*d^4 + 58982400*A^4*B*a^21*b^27*d^4 + 255590400*A^4*B*a^23*b^25*d^4 + 17956864
0*A^4*B*a^25*b^23*d^4 - 945029120*A^4*B*a^27*b^21*d^4 - 2559836160*A^4*B*a^29*b^19*d^4 - 2798387200*A^4*B*a^31
*b^17*d^4 - 1422131200*A^4*B*a^33*b^15*d^4 - 161218560*A^4*B*a^35*b^13*d^4 + 136314880*A^4*B*a^37*b^11*d^4 + 4
1943040*A^4*B*a^39*b^9*d^4 + 58982400*A^2*B^3*a^21*b^27*d^4 + 293339136*A^2*B^3*a^23*b^25*d^4 + 418643968*A^2*
B^3*a^25*b^23*d^4 - 328466432*A^2*B^3*a^27*b^21*d^4 - 1767112704*A^2*B^3*a^29*b^19*d^4 - 2357985280*A^2*B^3*a^
31*b^17*d^4 - 1510211584*A^2*B^3*a^33*b^15*d^4 - 425459712*A^2*B^3*a^35*b^13*d^4 - 2097152*A^2*B^3*a^37*b^11*d
^4 + 16777216*A^2*B^3*a^39*b^9*d^4 - 35389440*A^3*B^2*a^22*b^26*d^4 - 159645696*A^3*B^2*a^24*b^24*d^4 - 143392
768*A^3*B^2*a^26*b^22*d^4 + 493617152*A^3*B^2*a^28*b^20*d^4 + 1491861504*A^3*B^2*a^30*b^18*d^4 + 1752432640*A^
3*B^2*a^32*b^16*d^4 + 1014759424*A^3*B^2*a^34*b^14*d^4 + 228851712*A^3*B^2*a^36*b^12*d^4 - 29360128*A^3*B^2*a^
38*b^10*d^4 - 16777216*A^3*B^2*a^40*b^8*d^4))*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b
^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*
b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a
*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*2i + atan((((a +
b*tan(c + d*x))^(1/2)*(704643072*A^4*a^29*b^20*d^5 - 290979840*A^4*a^23*b^26*d^5 - 465043456*A^4*a^25*b^24*d^5
- 37224448*A^4*a^27*b^22*d^5 - 58982400*A^4*a^21*b^28*d^5 + 767033344*A^4*a^31*b^18*d^5 + 238551040*A^4*a^33*
b^16*d^5 + 1572864*A^4*a^35*b^14*d^5 + 92536832*A^4*a^37*b^12*d^5 + 96468992*A^4*a^39*b^10*d^5 + 25165824*A^4*
a^41*b^8*d^5 + 37748736*B^4*a^23*b^26*d^5 + 226492416*B^4*a^25*b^24*d^5 + 536870912*B^4*a^27*b^22*d^5 + 587202
560*B^4*a^29*b^20*d^5 + 176160768*B^4*a^31*b^18*d^5 - 234881024*B^4*a^33*b^16*d^5 - 234881024*B^4*a^35*b^14*d^
5 - 50331648*B^4*a^37*b^12*d^5 + 20971520*B^4*a^39*b^10*d^5 + 8388608*B^4*a^41*b^8*d^5 - 94371840*A*B^3*a^22*b
^27*d^5 - 364904448*A*B^3*a^24*b^25*d^5 + 37748736*A*B^3*a^26*b^23*d^5 + 2554331136*A*B^3*a^28*b^21*d^5 + 5989
466112*A*B^3*a^30*b^19*d^5 + 6606028800*A*B^3*a^32*b^17*d^5 + 3787456512*A*B^3*a^34*b^15*d^5 + 918552576*A*B^3
*a^36*b^13*d^5 - 56623104*A*B^3*a^38*b^11*d^5 - 50331648*A*B^3*a^40*b^9*d^5 + 330301440*A^3*B*a^22*b^27*d^5 +
1915748352*A^3*B*a^24*b^25*d^5 + 4279238656*A^3*B*a^26*b^23*d^5 + 4059037696*A^3*B*a^28*b^21*d^5 + 154140672*A
^3*B*a^30*b^19*d^5 - 2825912320*A^3*B*a^32*b^17*d^5 - 1901068288*A^3*B*a^34*b^15*d^5 + 22020096*A^3*B*a^36*b^1
3*d^5 + 425721856*A^3*B*a^38*b^11*d^5 + 117440512*A^3*B*a^40*b^9*d^5 + 58982400*A^2*B^2*a^21*b^28*d^5 - 124256
256*A^2*B^2*a^23*b^26*d^5 - 2202533888*A^2*B^2*a^25*b^24*d^5 - 6984040448*A^2*B^2*a^27*b^22*d^5 - 10041163776*
A^2*B^2*a^29*b^20*d^5 - 6404177920*A^2*B^2*a^31*b^18*d^5 + 289931264*A^2*B^2*a^33*b^16*d^5 + 2993160192*A^2*B^
2*a^35*b^14*d^5 + 1694236672*A^2*B^2*a^37*b^12*d^5 + 318767104*A^2*B^2*a^39*b^10*d^5) + ((((8*A^2*a^3*d^2 - 8*
B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2
+ B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*
A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 +
3*a^4*b^2*d^4)))^(1/2)*(773849088*A^3*a^35*b^16*d^6 - 117964800*A^3*a^21*b^30*d^6 - 699924480*A^3*a^23*b^28*d
^6 - 1889533952*A^3*a^25*b^26*d^6 - 3336568832*A^3*a^27*b^24*d^6 - 4495245312*A^3*a^29*b^22*d^6 - 4279238656*A
^3*a^31*b^20*d^6 - 1923088384*A^3*a^33*b^18*d^6 - ((a + b*tan(c + d*x))^(1/2)*(235929600*A^2*a^22*b^30*d^7 + 1
871708160*A^2*a^24*b^28*d^7 + 6295650304*A^2*a^26*b^26*d^7 + 11144265728*A^2*a^28*b^24*d^7 + 9560915968*A^2*a^
30*b^22*d^7 - 337641472*A^2*a^32*b^20*d^7 - 9307160576*A^2*a^34*b^18*d^7 - 8887730176*A^2*a^36*b^16*d^7 - 2943
352832*A^2*a^38*b^14*d^7 + 621805568*A^2*a^40*b^12*d^7 + 721420288*A^2*a^42*b^10*d^7 + 150994944*A^2*a^44*b^8*
d^7 + 150994944*B^2*a^24*b^28*d^7 + 1358954496*B^2*a^26*b^26*d^7 + 5653921792*B^2*a^28*b^24*d^7 + 14126415872*
B^2*a^30*b^22*d^7 + 23018340352*B^2*a^32*b^20*d^7 + 24897388544*B^2*a^34*b^18*d^7 + 17381195776*B^2*a^36*b^16*
d^7 + 7079985152*B^2*a^38*b^14*d^7 + 1124073472*B^2*a^40*b^12*d^7 - 218103808*B^2*a^42*b^10*d^7 - 83886080*B^2
*a^44*b^8*d^7 - 377487360*A*B*a^23*b^29*d^7 - 3196059648*A*B*a^25*b^27*d^7 - 11911823360*A*B*a^27*b^25*d^7 - 2
4930942976*A*B*a^29*b^23*d^7 - 30182211584*A*B*a^31*b^21*d^7 - 17028874240*A*B*a^33*b^19*d^7 + 5402263552*A*B*
a^35*b^17*d^7 + 16944988160*A*B*a^37*b^15*d^7 + 12775849984*A*B*a^39*b^13*d^7 + 4588568576*A*B*a^41*b^11*d^7 +
671088640*A*B*a^43*b^9*d^7) - ((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*
a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4
*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*
B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*((a + b*tan(c + d*x))^(1/2)*((((8
*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 -
(A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4
*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4
+ 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(134217728*a^27*b^28*d^9 + 1409286144*a^29*b^26*d^9 + 6643777536*a^31
*b^24*d^9 + 18522046464*a^33*b^22*d^9 + 33822867456*a^35*b^20*d^9 + 42278584320*a^37*b^18*d^9 + 36641439744*a^
39*b^16*d^9 + 21743271936*a^41*b^14*d^9 + 8455716864*a^43*b^12*d^9 + 1946157056*a^45*b^10*d^9 + 201326592*a^47
*b^8*d^9) - 251658240*A*a^24*b^30*d^8 - 2382364672*A*a^26*b^28*d^8 - 9948889088*A*a^28*b^26*d^8 - 23924310016*
A*a^30*b^24*d^8 - 36071014400*A*a^32*b^22*d^8 - 34292629504*A*a^34*b^20*d^8 - 18555600896*A*a^36*b^18*d^8 - 24
83027968*A*a^38*b^16*d^8 + 3841982464*A*a^40*b^14*d^8 + 2852126720*A*a^42*b^12*d^8 + 855638016*A*a^44*b^10*d^8
+ 100663296*A*a^46*b^8*d^8 + 201326592*B*a^25*b^29*d^8 + 2013265920*B*a^27*b^27*d^8 + 8992587776*B*a^29*b^25*
d^8 + 23622320128*B*a^31*b^23*d^8 + 40399536128*B*a^33*b^21*d^8 + 46976204800*B*a^35*b^19*d^8 + 37580963840*B*
a^37*b^17*d^8 + 20401094656*B*a^39*b^15*d^8 + 7180648448*B*a^41*b^13*d^8 + 1476395008*B*a^43*b^11*d^8 + 134217
728*B*a^45*b^9*d^8))*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2
+ 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))
^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^
2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) + 1421344768*A^3*a^37*b^14*d^6 + 587726848*
A^3*a^39*b^12*d^6 + 25165824*A^3*a^41*b^10*d^6 - 25165824*A^3*a^43*b^8*d^6 + 150994944*B^3*a^24*b^27*d^6 + 905
969664*B^3*a^26*b^25*d^6 + 2222981120*B^3*a^28*b^23*d^6 + 2877292544*B^3*a^30*b^21*d^6 + 2290089984*B^3*a^32*b
^19*d^6 + 1702887424*B^3*a^34*b^17*d^6 + 1702887424*B^3*a^36*b^15*d^6 + 1384120320*B^3*a^38*b^13*d^6 + 6123683
84*B^3*a^40*b^11*d^6 + 109051904*B^3*a^42*b^9*d^6 - 452984832*A*B^2*a^23*b^28*d^6 - 2768240640*A*B^2*a^25*b^26
*d^6 - 7348420608*A*B^2*a^27*b^24*d^6 - 11903434752*A*B^2*a^29*b^22*d^6 - 14973665280*A*B^2*a^31*b^20*d^6 - 16
735272960*A*B^2*a^33*b^18*d^6 - 14973665280*A*B^2*a^35*b^16*d^6 - 8732540928*A*B^2*a^37*b^14*d^6 - 2592079872*
A*B^2*a^39*b^12*d^6 - 125829120*A*B^2*a^41*b^10*d^6 + 75497472*A*B^2*a^43*b^8*d^6 + 424673280*A^2*B*a^22*b^29*
d^6 + 2604662784*A^2*B*a^24*b^27*d^6 + 7159676928*A^2*B*a^26*b^25*d^6 + 12532580352*A^2*B*a^28*b^23*d^6 + 1686
7393536*A^2*B*a^30*b^21*d^6 + 17792237568*A^2*B*a^32*b^19*d^6 + 12419334144*A^2*B*a^34*b^17*d^6 + 3573547008*A
^2*B*a^36*b^15*d^6 - 1513095168*A^2*B*a^38*b^13*d^6 - 1472200704*A^2*B*a^40*b^11*d^6 - 327155712*A^2*B*a^42*b^
9*d^6))*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*
b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^
2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d
^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*1i + ((a + b*tan(c + d*x))^(1/2)*(704643072*A^4*a^29*b^2
0*d^5 - 290979840*A^4*a^23*b^26*d^5 - 465043456*A^4*a^25*b^24*d^5 - 37224448*A^4*a^27*b^22*d^5 - 58982400*A^4*
a^21*b^28*d^5 + 767033344*A^4*a^31*b^18*d^5 + 238551040*A^4*a^33*b^16*d^5 + 1572864*A^4*a^35*b^14*d^5 + 925368
32*A^4*a^37*b^12*d^5 + 96468992*A^4*a^39*b^10*d^5 + 25165824*A^4*a^41*b^8*d^5 + 37748736*B^4*a^23*b^26*d^5 + 2
26492416*B^4*a^25*b^24*d^5 + 536870912*B^4*a^27*b^22*d^5 + 587202560*B^4*a^29*b^20*d^5 + 176160768*B^4*a^31*b^
18*d^5 - 234881024*B^4*a^33*b^16*d^5 - 234881024*B^4*a^35*b^14*d^5 - 50331648*B^4*a^37*b^12*d^5 + 20971520*B^4
*a^39*b^10*d^5 + 8388608*B^4*a^41*b^8*d^5 - 94371840*A*B^3*a^22*b^27*d^5 - 364904448*A*B^3*a^24*b^25*d^5 + 377
48736*A*B^3*a^26*b^23*d^5 + 2554331136*A*B^3*a^28*b^21*d^5 + 5989466112*A*B^3*a^30*b^19*d^5 + 6606028800*A*B^3
*a^32*b^17*d^5 + 3787456512*A*B^3*a^34*b^15*d^5 + 918552576*A*B^3*a^36*b^13*d^5 - 56623104*A*B^3*a^38*b^11*d^5
- 50331648*A*B^3*a^40*b^9*d^5 + 330301440*A^3*B*a^22*b^27*d^5 + 1915748352*A^3*B*a^24*b^25*d^5 + 4279238656*A
^3*B*a^26*b^23*d^5 + 4059037696*A^3*B*a^28*b^21*d^5 + 154140672*A^3*B*a^30*b^19*d^5 - 2825912320*A^3*B*a^32*b^
17*d^5 - 1901068288*A^3*B*a^34*b^15*d^5 + 22020096*A^3*B*a^36*b^13*d^5 + 425721856*A^3*B*a^38*b^11*d^5 + 11744
0512*A^3*B*a^40*b^9*d^5 + 58982400*A^2*B^2*a^21*b^28*d^5 - 124256256*A^2*B^2*a^23*b^26*d^5 - 2202533888*A^2*B^
2*a^25*b^24*d^5 - 6984040448*A^2*B^2*a^27*b^22*d^5 - 10041163776*A^2*B^2*a^29*b^20*d^5 - 6404177920*A^2*B^2*a^
31*b^18*d^5 + 289931264*A^2*B^2*a^33*b^16*d^5 + 2993160192*A^2*B^2*a^35*b^14*d^5 + 1694236672*A^2*B^2*a^37*b^1
2*d^5 + 318767104*A^2*B^2*a^39*b^10*d^5) - ((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d
^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*
d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2
*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(((a + b*tan(c + d*x)
)^(1/2)*(235929600*A^2*a^22*b^30*d^7 + 1871708160*A^2*a^24*b^28*d^7 + 6295650304*A^2*a^26*b^26*d^7 + 111442657
28*A^2*a^28*b^24*d^7 + 9560915968*A^2*a^30*b^22*d^7 - 337641472*A^2*a^32*b^20*d^7 - 9307160576*A^2*a^34*b^18*d
^7 - 8887730176*A^2*a^36*b^16*d^7 - 2943352832*A^2*a^38*b^14*d^7 + 621805568*A^2*a^40*b^12*d^7 + 721420288*A^2
*a^42*b^10*d^7 + 150994944*A^2*a^44*b^8*d^7 + 150994944*B^2*a^24*b^28*d^7 + 1358954496*B^2*a^26*b^26*d^7 + 565
3921792*B^2*a^28*b^24*d^7 + 14126415872*B^2*a^30*b^22*d^7 + 23018340352*B^2*a^32*b^20*d^7 + 24897388544*B^2*a^
34*b^18*d^7 + 17381195776*B^2*a^36*b^16*d^7 + 7079985152*B^2*a^38*b^14*d^7 + 1124073472*B^2*a^40*b^12*d^7 - 21
8103808*B^2*a^42*b^10*d^7 - 83886080*B^2*a^44*b^8*d^7 - 377487360*A*B*a^23*b^29*d^7 - 3196059648*A*B*a^25*b^27
*d^7 - 11911823360*A*B*a^27*b^25*d^7 - 24930942976*A*B*a^29*b^23*d^7 - 30182211584*A*B*a^31*b^21*d^7 - 1702887
4240*A*B*a^33*b^19*d^7 + 5402263552*A*B*a^35*b^17*d^7 + 16944988160*A*B*a^37*b^15*d^7 + 12775849984*A*B*a^39*b
^13*d^7 + 4588568576*A*B*a^41*b^11*d^7 + 671088640*A*B*a^43*b^9*d^7) + ((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*
A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^
4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*
A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))
^(1/2)*(3841982464*A*a^40*b^14*d^8 - 251658240*A*a^24*b^30*d^8 - 2382364672*A*a^26*b^28*d^8 - 9948889088*A*a^2
8*b^26*d^8 - 23924310016*A*a^30*b^24*d^8 - 36071014400*A*a^32*b^22*d^8 - 34292629504*A*a^34*b^20*d^8 - 1855560
0896*A*a^36*b^18*d^8 - 2483027968*A*a^38*b^16*d^8 - (a + b*tan(c + d*x))^(1/2)*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d
^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(1
6*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d
^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^
2*d^4)))^(1/2)*(134217728*a^27*b^28*d^9 + 1409286144*a^29*b^26*d^9 + 6643777536*a^31*b^24*d^9 + 18522046464*a^
33*b^22*d^9 + 33822867456*a^35*b^20*d^9 + 42278584320*a^37*b^18*d^9 + 36641439744*a^39*b^16*d^9 + 21743271936*
a^41*b^14*d^9 + 8455716864*a^43*b^12*d^9 + 1946157056*a^45*b^10*d^9 + 201326592*a^47*b^8*d^9) + 2852126720*A*a
^42*b^12*d^8 + 855638016*A*a^44*b^10*d^8 + 100663296*A*a^46*b^8*d^8 + 201326592*B*a^25*b^29*d^8 + 2013265920*B
*a^27*b^27*d^8 + 8992587776*B*a^29*b^25*d^8 + 23622320128*B*a^31*b^23*d^8 + 40399536128*B*a^33*b^21*d^8 + 4697
6204800*B*a^35*b^19*d^8 + 37580963840*B*a^37*b^17*d^8 + 20401094656*B*a^39*b^15*d^8 + 7180648448*B*a^41*b^13*d
^8 + 1476395008*B*a^43*b^11*d^8 + 134217728*B*a^45*b^9*d^8))*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^
2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6
*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*
d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) - 1
17964800*A^3*a^21*b^30*d^6 - 699924480*A^3*a^23*b^28*d^6 - 1889533952*A^3*a^25*b^26*d^6 - 3336568832*A^3*a^27*
b^24*d^6 - 4495245312*A^3*a^29*b^22*d^6 - 4279238656*A^3*a^31*b^20*d^6 - 1923088384*A^3*a^33*b^18*d^6 + 773849
088*A^3*a^35*b^16*d^6 + 1421344768*A^3*a^37*b^14*d^6 + 587726848*A^3*a^39*b^12*d^6 + 25165824*A^3*a^41*b^10*d^
6 - 25165824*A^3*a^43*b^8*d^6 + 150994944*B^3*a^24*b^27*d^6 + 905969664*B^3*a^26*b^25*d^6 + 2222981120*B^3*a^2
8*b^23*d^6 + 2877292544*B^3*a^30*b^21*d^6 + 2290089984*B^3*a^32*b^19*d^6 + 1702887424*B^3*a^34*b^17*d^6 + 1702
887424*B^3*a^36*b^15*d^6 + 1384120320*B^3*a^38*b^13*d^6 + 612368384*B^3*a^40*b^11*d^6 + 109051904*B^3*a^42*b^9
*d^6 - 452984832*A*B^2*a^23*b^28*d^6 - 2768240640*A*B^2*a^25*b^26*d^6 - 7348420608*A*B^2*a^27*b^24*d^6 - 11903
434752*A*B^2*a^29*b^22*d^6 - 14973665280*A*B^2*a^31*b^20*d^6 - 16735272960*A*B^2*a^33*b^18*d^6 - 14973665280*A
*B^2*a^35*b^16*d^6 - 8732540928*A*B^2*a^37*b^14*d^6 - 2592079872*A*B^2*a^39*b^12*d^6 - 125829120*A*B^2*a^41*b^
10*d^6 + 75497472*A*B^2*a^43*b^8*d^6 + 424673280*A^2*B*a^22*b^29*d^6 + 2604662784*A^2*B*a^24*b^27*d^6 + 715967
6928*A^2*B*a^26*b^25*d^6 + 12532580352*A^2*B*a^28*b^23*d^6 + 16867393536*A^2*B*a^30*b^21*d^6 + 17792237568*A^2
*B*a^32*b^19*d^6 + 12419334144*A^2*B*a^34*b^17*d^6 + 3573547008*A^2*B*a^36*b^15*d^6 - 1513095168*A^2*B*a^38*b^
13*d^6 - 1472200704*A^2*B*a^40*b^11*d^6 - 327155712*A^2*B*a^42*b^9*d^6))*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 1
6*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*
d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 1
2*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)
))^(1/2)*1i)/(((a + b*tan(c + d*x))^(1/2)*(704643072*A^4*a^29*b^20*d^5 - 290979840*A^4*a^23*b^26*d^5 - 4650434
56*A^4*a^25*b^24*d^5 - 37224448*A^4*a^27*b^22*d^5 - 58982400*A^4*a^21*b^28*d^5 + 767033344*A^4*a^31*b^18*d^5 +
238551040*A^4*a^33*b^16*d^5 + 1572864*A^4*a^35*b^14*d^5 + 92536832*A^4*a^37*b^12*d^5 + 96468992*A^4*a^39*b^10
*d^5 + 25165824*A^4*a^41*b^8*d^5 + 37748736*B^4*a^23*b^26*d^5 + 226492416*B^4*a^25*b^24*d^5 + 536870912*B^4*a^
27*b^22*d^5 + 587202560*B^4*a^29*b^20*d^5 + 176160768*B^4*a^31*b^18*d^5 - 234881024*B^4*a^33*b^16*d^5 - 234881
024*B^4*a^35*b^14*d^5 - 50331648*B^4*a^37*b^12*d^5 + 20971520*B^4*a^39*b^10*d^5 + 8388608*B^4*a^41*b^8*d^5 - 9
4371840*A*B^3*a^22*b^27*d^5 - 364904448*A*B^3*a^24*b^25*d^5 + 37748736*A*B^3*a^26*b^23*d^5 + 2554331136*A*B^3*
a^28*b^21*d^5 + 5989466112*A*B^3*a^30*b^19*d^5 + 6606028800*A*B^3*a^32*b^17*d^5 + 3787456512*A*B^3*a^34*b^15*d
^5 + 918552576*A*B^3*a^36*b^13*d^5 - 56623104*A*B^3*a^38*b^11*d^5 - 50331648*A*B^3*a^40*b^9*d^5 + 330301440*A^
3*B*a^22*b^27*d^5 + 1915748352*A^3*B*a^24*b^25*d^5 + 4279238656*A^3*B*a^26*b^23*d^5 + 4059037696*A^3*B*a^28*b^
21*d^5 + 154140672*A^3*B*a^30*b^19*d^5 - 2825912320*A^3*B*a^32*b^17*d^5 - 1901068288*A^3*B*a^34*b^15*d^5 + 220
20096*A^3*B*a^36*b^13*d^5 + 425721856*A^3*B*a^38*b^11*d^5 + 117440512*A^3*B*a^40*b^9*d^5 + 58982400*A^2*B^2*a^
21*b^28*d^5 - 124256256*A^2*B^2*a^23*b^26*d^5 - 2202533888*A^2*B^2*a^25*b^24*d^5 - 6984040448*A^2*B^2*a^27*b^2
2*d^5 - 10041163776*A^2*B^2*a^29*b^20*d^5 - 6404177920*A^2*B^2*a^31*b^18*d^5 + 289931264*A^2*B^2*a^33*b^16*d^5
+ 2993160192*A^2*B^2*a^35*b^14*d^5 + 1694236672*A^2*B^2*a^37*b^12*d^5 + 318767104*A^2*B^2*a^39*b^10*d^5) - ((
((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4
- (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2
- 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d
^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(((a + b*tan(c + d*x))^(1/2)*(235929600*A^2*a^22*b^30*d^7 + 187170
8160*A^2*a^24*b^28*d^7 + 6295650304*A^2*a^26*b^26*d^7 + 11144265728*A^2*a^28*b^24*d^7 + 9560915968*A^2*a^30*b^
22*d^7 - 337641472*A^2*a^32*b^20*d^7 - 9307160576*A^2*a^34*b^18*d^7 - 8887730176*A^2*a^36*b^16*d^7 - 294335283
2*A^2*a^38*b^14*d^7 + 621805568*A^2*a^40*b^12*d^7 + 721420288*A^2*a^42*b^10*d^7 + 150994944*A^2*a^44*b^8*d^7 +
150994944*B^2*a^24*b^28*d^7 + 1358954496*B^2*a^26*b^26*d^7 + 5653921792*B^2*a^28*b^24*d^7 + 14126415872*B^2*a
^30*b^22*d^7 + 23018340352*B^2*a^32*b^20*d^7 + 24897388544*B^2*a^34*b^18*d^7 + 17381195776*B^2*a^36*b^16*d^7 +
7079985152*B^2*a^38*b^14*d^7 + 1124073472*B^2*a^40*b^12*d^7 - 218103808*B^2*a^42*b^10*d^7 - 83886080*B^2*a^44
*b^8*d^7 - 377487360*A*B*a^23*b^29*d^7 - 3196059648*A*B*a^25*b^27*d^7 - 11911823360*A*B*a^27*b^25*d^7 - 249309
42976*A*B*a^29*b^23*d^7 - 30182211584*A*B*a^31*b^21*d^7 - 17028874240*A*B*a^33*b^19*d^7 + 5402263552*A*B*a^35*
b^17*d^7 + 16944988160*A*B*a^37*b^15*d^7 + 12775849984*A*B*a^39*b^13*d^7 + 4588568576*A*B*a^41*b^11*d^7 + 6710
88640*A*B*a^43*b^9*d^7) + ((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2
*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*
d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2
*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(3841982464*A*a^40*b^14*d^8 - 25165824
0*A*a^24*b^30*d^8 - 2382364672*A*a^26*b^28*d^8 - 9948889088*A*a^28*b^26*d^8 - 23924310016*A*a^30*b^24*d^8 - 36
071014400*A*a^32*b^22*d^8 - 34292629504*A*a^34*b^20*d^8 - 18555600896*A*a^36*b^18*d^8 - 2483027968*A*a^38*b^16
*d^8 - (a + b*tan(c + d*x))^(1/2)*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B
^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*
a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24
*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(134217728*a^27*b^28*d^9 + 140
9286144*a^29*b^26*d^9 + 6643777536*a^31*b^24*d^9 + 18522046464*a^33*b^22*d^9 + 33822867456*a^35*b^20*d^9 + 422
78584320*a^37*b^18*d^9 + 36641439744*a^39*b^16*d^9 + 21743271936*a^41*b^14*d^9 + 8455716864*a^43*b^12*d^9 + 19
46157056*a^45*b^10*d^9 + 201326592*a^47*b^8*d^9) + 2852126720*A*a^42*b^12*d^8 + 855638016*A*a^44*b^10*d^8 + 10
0663296*A*a^46*b^8*d^8 + 201326592*B*a^25*b^29*d^8 + 2013265920*B*a^27*b^27*d^8 + 8992587776*B*a^29*b^25*d^8 +
23622320128*B*a^31*b^23*d^8 + 40399536128*B*a^33*b^21*d^8 + 46976204800*B*a^35*b^19*d^8 + 37580963840*B*a^37*
b^17*d^8 + 20401094656*B*a^39*b^15*d^8 + 7180648448*B*a^41*b^13*d^8 + 1476395008*B*a^43*b^11*d^8 + 134217728*B
*a^45*b^9*d^8))*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*
A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2
) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(1
6*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) - 117964800*A^3*a^21*b^30*d^6 - 699924480*A^3*a^
23*b^28*d^6 - 1889533952*A^3*a^25*b^26*d^6 - 3336568832*A^3*a^27*b^24*d^6 - 4495245312*A^3*a^29*b^22*d^6 - 427
9238656*A^3*a^31*b^20*d^6 - 1923088384*A^3*a^33*b^18*d^6 + 773849088*A^3*a^35*b^16*d^6 + 1421344768*A^3*a^37*b
^14*d^6 + 587726848*A^3*a^39*b^12*d^6 + 25165824*A^3*a^41*b^10*d^6 - 25165824*A^3*a^43*b^8*d^6 + 150994944*B^3
*a^24*b^27*d^6 + 905969664*B^3*a^26*b^25*d^6 + 2222981120*B^3*a^28*b^23*d^6 + 2877292544*B^3*a^30*b^21*d^6 + 2
290089984*B^3*a^32*b^19*d^6 + 1702887424*B^3*a^34*b^17*d^6 + 1702887424*B^3*a^36*b^15*d^6 + 1384120320*B^3*a^3
8*b^13*d^6 + 612368384*B^3*a^40*b^11*d^6 + 109051904*B^3*a^42*b^9*d^6 - 452984832*A*B^2*a^23*b^28*d^6 - 276824
0640*A*B^2*a^25*b^26*d^6 - 7348420608*A*B^2*a^27*b^24*d^6 - 11903434752*A*B^2*a^29*b^22*d^6 - 14973665280*A*B^
2*a^31*b^20*d^6 - 16735272960*A*B^2*a^33*b^18*d^6 - 14973665280*A*B^2*a^35*b^16*d^6 - 8732540928*A*B^2*a^37*b^
14*d^6 - 2592079872*A*B^2*a^39*b^12*d^6 - 125829120*A*B^2*a^41*b^10*d^6 + 75497472*A*B^2*a^43*b^8*d^6 + 424673
280*A^2*B*a^22*b^29*d^6 + 2604662784*A^2*B*a^24*b^27*d^6 + 7159676928*A^2*B*a^26*b^25*d^6 + 12532580352*A^2*B*
a^28*b^23*d^6 + 16867393536*A^2*B*a^30*b^21*d^6 + 17792237568*A^2*B*a^32*b^19*d^6 + 12419334144*A^2*B*a^34*b^1
7*d^6 + 3573547008*A^2*B*a^36*b^15*d^6 - 1513095168*A^2*B*a^38*b^13*d^6 - 1472200704*A^2*B*a^40*b^11*d^6 - 327
155712*A^2*B*a^42*b^9*d^6))*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b
^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^
2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a
^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) - ((a + b*tan(c + d*x))^(1/2)*(70464
3072*A^4*a^29*b^20*d^5 - 290979840*A^4*a^23*b^26*d^5 - 465043456*A^4*a^25*b^24*d^5 - 37224448*A^4*a^27*b^22*d^
5 - 58982400*A^4*a^21*b^28*d^5 + 767033344*A^4*a^31*b^18*d^5 + 238551040*A^4*a^33*b^16*d^5 + 1572864*A^4*a^35*
b^14*d^5 + 92536832*A^4*a^37*b^12*d^5 + 96468992*A^4*a^39*b^10*d^5 + 25165824*A^4*a^41*b^8*d^5 + 37748736*B^4*
a^23*b^26*d^5 + 226492416*B^4*a^25*b^24*d^5 + 536870912*B^4*a^27*b^22*d^5 + 587202560*B^4*a^29*b^20*d^5 + 1761
60768*B^4*a^31*b^18*d^5 - 234881024*B^4*a^33*b^16*d^5 - 234881024*B^4*a^35*b^14*d^5 - 50331648*B^4*a^37*b^12*d
^5 + 20971520*B^4*a^39*b^10*d^5 + 8388608*B^4*a^41*b^8*d^5 - 94371840*A*B^3*a^22*b^27*d^5 - 364904448*A*B^3*a^
24*b^25*d^5 + 37748736*A*B^3*a^26*b^23*d^5 + 2554331136*A*B^3*a^28*b^21*d^5 + 5989466112*A*B^3*a^30*b^19*d^5 +
6606028800*A*B^3*a^32*b^17*d^5 + 3787456512*A*B^3*a^34*b^15*d^5 + 918552576*A*B^3*a^36*b^13*d^5 - 56623104*A*
B^3*a^38*b^11*d^5 - 50331648*A*B^3*a^40*b^9*d^5 + 330301440*A^3*B*a^22*b^27*d^5 + 1915748352*A^3*B*a^24*b^25*d
^5 + 4279238656*A^3*B*a^26*b^23*d^5 + 4059037696*A^3*B*a^28*b^21*d^5 + 154140672*A^3*B*a^30*b^19*d^5 - 2825912
320*A^3*B*a^32*b^17*d^5 - 1901068288*A^3*B*a^34*b^15*d^5 + 22020096*A^3*B*a^36*b^13*d^5 + 425721856*A^3*B*a^38
*b^11*d^5 + 117440512*A^3*B*a^40*b^9*d^5 + 58982400*A^2*B^2*a^21*b^28*d^5 - 124256256*A^2*B^2*a^23*b^26*d^5 -
2202533888*A^2*B^2*a^25*b^24*d^5 - 6984040448*A^2*B^2*a^27*b^22*d^5 - 10041163776*A^2*B^2*a^29*b^20*d^5 - 6404
177920*A^2*B^2*a^31*b^18*d^5 + 289931264*A^2*B^2*a^33*b^16*d^5 + 2993160192*A^2*B^2*a^35*b^14*d^5 + 1694236672
*A^2*B^2*a^37*b^12*d^5 + 318767104*A^2*B^2*a^39*b^10*d^5) + ((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2
- 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*
d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d
^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(773
849088*A^3*a^35*b^16*d^6 - 117964800*A^3*a^21*b^30*d^6 - 699924480*A^3*a^23*b^28*d^6 - 1889533952*A^3*a^25*b^2
6*d^6 - 3336568832*A^3*a^27*b^24*d^6 - 4495245312*A^3*a^29*b^22*d^6 - 4279238656*A^3*a^31*b^20*d^6 - 192308838
4*A^3*a^33*b^18*d^6 - ((a + b*tan(c + d*x))^(1/2)*(235929600*A^2*a^22*b^30*d^7 + 1871708160*A^2*a^24*b^28*d^7
+ 6295650304*A^2*a^26*b^26*d^7 + 11144265728*A^2*a^28*b^24*d^7 + 9560915968*A^2*a^30*b^22*d^7 - 337641472*A^2*
a^32*b^20*d^7 - 9307160576*A^2*a^34*b^18*d^7 - 8887730176*A^2*a^36*b^16*d^7 - 2943352832*A^2*a^38*b^14*d^7 + 6
21805568*A^2*a^40*b^12*d^7 + 721420288*A^2*a^42*b^10*d^7 + 150994944*A^2*a^44*b^8*d^7 + 150994944*B^2*a^24*b^2
8*d^7 + 1358954496*B^2*a^26*b^26*d^7 + 5653921792*B^2*a^28*b^24*d^7 + 14126415872*B^2*a^30*b^22*d^7 + 23018340
352*B^2*a^32*b^20*d^7 + 24897388544*B^2*a^34*b^18*d^7 + 17381195776*B^2*a^36*b^16*d^7 + 7079985152*B^2*a^38*b^
14*d^7 + 1124073472*B^2*a^40*b^12*d^7 - 218103808*B^2*a^42*b^10*d^7 - 83886080*B^2*a^44*b^8*d^7 - 377487360*A*
B*a^23*b^29*d^7 - 3196059648*A*B*a^25*b^27*d^7 - 11911823360*A*B*a^27*b^25*d^7 - 24930942976*A*B*a^29*b^23*d^7
- 30182211584*A*B*a^31*b^21*d^7 - 17028874240*A*B*a^33*b^19*d^7 + 5402263552*A*B*a^35*b^17*d^7 + 16944988160*
A*B*a^37*b^15*d^7 + 12775849984*A*B*a^39*b^13*d^7 + 4588568576*A*B*a^41*b^11*d^7 + 671088640*A*B*a^43*b^9*d^7)
- ((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2
)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3
*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 +
b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*((a + b*tan(c + d*x))^(1/2)*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2
- 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*
a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2
- 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*
d^4)))^(1/2)*(134217728*a^27*b^28*d^9 + 1409286144*a^29*b^26*d^9 + 6643777536*a^31*b^24*d^9 + 18522046464*a^33
*b^22*d^9 + 33822867456*a^35*b^20*d^9 + 42278584320*a^37*b^18*d^9 + 36641439744*a^39*b^16*d^9 + 21743271936*a^
41*b^14*d^9 + 8455716864*a^43*b^12*d^9 + 1946157056*a^45*b^10*d^9 + 201326592*a^47*b^8*d^9) - 251658240*A*a^24
*b^30*d^8 - 2382364672*A*a^26*b^28*d^8 - 9948889088*A*a^28*b^26*d^8 - 23924310016*A*a^30*b^24*d^8 - 3607101440
0*A*a^32*b^22*d^8 - 34292629504*A*a^34*b^20*d^8 - 18555600896*A*a^36*b^18*d^8 - 2483027968*A*a^38*b^16*d^8 + 3
841982464*A*a^40*b^14*d^8 + 2852126720*A*a^42*b^12*d^8 + 855638016*A*a^44*b^10*d^8 + 100663296*A*a^46*b^8*d^8
+ 201326592*B*a^25*b^29*d^8 + 2013265920*B*a^27*b^27*d^8 + 8992587776*B*a^29*b^25*d^8 + 23622320128*B*a^31*b^2
3*d^8 + 40399536128*B*a^33*b^21*d^8 + 46976204800*B*a^35*b^19*d^8 + 37580963840*B*a^37*b^17*d^8 + 20401094656*
B*a^39*b^15*d^8 + 7180648448*B*a^41*b^13*d^8 + 1476395008*B*a^43*b^11*d^8 + 134217728*B*a^45*b^9*d^8))*((((8*A
^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A
^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B
^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 +
3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) + 1421344768*A^3*a^37*b^14*d^6 + 587726848*A^3*a^39*b^12*d^6 + 25165824
*A^3*a^41*b^10*d^6 - 25165824*A^3*a^43*b^8*d^6 + 150994944*B^3*a^24*b^27*d^6 + 905969664*B^3*a^26*b^25*d^6 + 2
222981120*B^3*a^28*b^23*d^6 + 2877292544*B^3*a^30*b^21*d^6 + 2290089984*B^3*a^32*b^19*d^6 + 1702887424*B^3*a^3
4*b^17*d^6 + 1702887424*B^3*a^36*b^15*d^6 + 1384120320*B^3*a^38*b^13*d^6 + 612368384*B^3*a^40*b^11*d^6 + 10905
1904*B^3*a^42*b^9*d^6 - 452984832*A*B^2*a^23*b^28*d^6 - 2768240640*A*B^2*a^25*b^26*d^6 - 7348420608*A*B^2*a^27
*b^24*d^6 - 11903434752*A*B^2*a^29*b^22*d^6 - 14973665280*A*B^2*a^31*b^20*d^6 - 16735272960*A*B^2*a^33*b^18*d^
6 - 14973665280*A*B^2*a^35*b^16*d^6 - 8732540928*A*B^2*a^37*b^14*d^6 - 2592079872*A*B^2*a^39*b^12*d^6 - 125829
120*A*B^2*a^41*b^10*d^6 + 75497472*A*B^2*a^43*b^8*d^6 + 424673280*A^2*B*a^22*b^29*d^6 + 2604662784*A^2*B*a^24*
b^27*d^6 + 7159676928*A^2*B*a^26*b^25*d^6 + 12532580352*A^2*B*a^28*b^23*d^6 + 16867393536*A^2*B*a^30*b^21*d^6
+ 17792237568*A^2*B*a^32*b^19*d^6 + 12419334144*A^2*B*a^34*b^17*d^6 + 3573547008*A^2*B*a^36*b^15*d^6 - 1513095
168*A^2*B*a^38*b^13*d^6 - 1472200704*A^2*B*a^40*b^11*d^6 - 327155712*A^2*B*a^42*b^9*d^6))*((((8*A^2*a^3*d^2 -
8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^
2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 -
8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4
+ 3*a^4*b^2*d^4)))^(1/2) + 58982400*A^5*a^22*b^26*d^4 + 381419520*A^5*a^24*b^24*d^4 + 1018429440*A^5*a^26*b^2
2*d^4 + 1403781120*A^5*a^28*b^20*d^4 + 963379200*A^5*a^30*b^18*d^4 + 137625600*A^5*a^32*b^16*d^4 - 247726080*A
^5*a^34*b^14*d^4 - 161218560*A^5*a^36*b^12*d^4 - 31457280*A^5*a^38*b^10*d^4 + 37748736*B^5*a^23*b^25*d^4 + 239
075328*B^5*a^25*b^23*d^4 + 616562688*B^5*a^27*b^21*d^4 + 792723456*B^5*a^29*b^19*d^4 + 440401920*B^5*a^31*b^17
*d^4 - 88080384*B^5*a^33*b^15*d^4 - 264241152*B^5*a^35*b^13*d^4 - 138412032*B^5*a^37*b^11*d^4 - 25165824*B^5*a
^39*b^9*d^4 - 94371840*A*B^4*a^22*b^26*d^4 - 541065216*A*B^4*a^24*b^24*d^4 - 1161822208*A*B^4*a^26*b^22*d^4 -
910163968*A*B^4*a^28*b^20*d^4 + 528482304*A*B^4*a^30*b^18*d^4 + 1614807040*A*B^4*a^32*b^16*d^4 + 1262485504*A*
B^4*a^34*b^14*d^4 + 390070272*A*B^4*a^36*b^12*d^4 + 2097152*A*B^4*a^38*b^10*d^4 - 16777216*A*B^4*a^40*b^8*d^4
+ 58982400*A^4*B*a^21*b^27*d^4 + 255590400*A^4*B*a^23*b^25*d^4 + 179568640*A^4*B*a^25*b^23*d^4 - 945029120*A^4
*B*a^27*b^21*d^4 - 2559836160*A^4*B*a^29*b^19*d^4 - 2798387200*A^4*B*a^31*b^17*d^4 - 1422131200*A^4*B*a^33*b^1
5*d^4 - 161218560*A^4*B*a^35*b^13*d^4 + 136314880*A^4*B*a^37*b^11*d^4 + 41943040*A^4*B*a^39*b^9*d^4 + 58982400
*A^2*B^3*a^21*b^27*d^4 + 293339136*A^2*B^3*a^23*b^25*d^4 + 418643968*A^2*B^3*a^25*b^23*d^4 - 328466432*A^2*B^3
*a^27*b^21*d^4 - 1767112704*A^2*B^3*a^29*b^19*d^4 - 2357985280*A^2*B^3*a^31*b^17*d^4 - 1510211584*A^2*B^3*a^33
*b^15*d^4 - 425459712*A^2*B^3*a^35*b^13*d^4 - 2097152*A^2*B^3*a^37*b^11*d^4 + 16777216*A^2*B^3*a^39*b^9*d^4 -
35389440*A^3*B^2*a^22*b^26*d^4 - 159645696*A^3*B^2*a^24*b^24*d^4 - 143392768*A^3*B^2*a^26*b^22*d^4 + 493617152
*A^3*B^2*a^28*b^20*d^4 + 1491861504*A^3*B^2*a^30*b^18*d^4 + 1752432640*A^3*B^2*a^32*b^16*d^4 + 1014759424*A^3*
B^2*a^34*b^14*d^4 + 228851712*A^3*B^2*a^36*b^12*d^4 - 29360128*A^3*B^2*a^38*b^10*d^4 - 16777216*A^3*B^2*a^40*b
^8*d^4))*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2
*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A
^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*
d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*2i + (atan((((((a + b*tan(c + d*x))^(1/2)*(704643072*A^
4*a^29*b^20*d^5 - 290979840*A^4*a^23*b^26*d^5 - 465043456*A^4*a^25*b^24*d^5 - 37224448*A^4*a^27*b^22*d^5 - 589
82400*A^4*a^21*b^28*d^5 + 767033344*A^4*a^31*b^18*d^5 + 238551040*A^4*a^33*b^16*d^5 + 1572864*A^4*a^35*b^14*d^
5 + 92536832*A^4*a^37*b^12*d^5 + 96468992*A^4*a^39*b^10*d^5 + 25165824*A^4*a^41*b^8*d^5 + 37748736*B^4*a^23*b^
26*d^5 + 226492416*B^4*a^25*b^24*d^5 + 536870912*B^4*a^27*b^22*d^5 + 587202560*B^4*a^29*b^20*d^5 + 176160768*B
^4*a^31*b^18*d^5 - 234881024*B^4*a^33*b^16*d^5 - 234881024*B^4*a^35*b^14*d^5 - 50331648*B^4*a^37*b^12*d^5 + 20
971520*B^4*a^39*b^10*d^5 + 8388608*B^4*a^41*b^8*d^5 - 94371840*A*B^3*a^22*b^27*d^5 - 364904448*A*B^3*a^24*b^25
*d^5 + 37748736*A*B^3*a^26*b^23*d^5 + 2554331136*A*B^3*a^28*b^21*d^5 + 5989466112*A*B^3*a^30*b^19*d^5 + 660602
8800*A*B^3*a^32*b^17*d^5 + 3787456512*A*B^3*a^34*b^15*d^5 + 918552576*A*B^3*a^36*b^13*d^5 - 56623104*A*B^3*a^3
8*b^11*d^5 - 50331648*A*B^3*a^40*b^9*d^5 + 330301440*A^3*B*a^22*b^27*d^5 + 1915748352*A^3*B*a^24*b^25*d^5 + 42
79238656*A^3*B*a^26*b^23*d^5 + 4059037696*A^3*B*a^28*b^21*d^5 + 154140672*A^3*B*a^30*b^19*d^5 - 2825912320*A^3
*B*a^32*b^17*d^5 - 1901068288*A^3*B*a^34*b^15*d^5 + 22020096*A^3*B*a^36*b^13*d^5 + 425721856*A^3*B*a^38*b^11*d
^5 + 117440512*A^3*B*a^40*b^9*d^5 + 58982400*A^2*B^2*a^21*b^28*d^5 - 124256256*A^2*B^2*a^23*b^26*d^5 - 2202533
888*A^2*B^2*a^25*b^24*d^5 - 6984040448*A^2*B^2*a^27*b^22*d^5 - 10041163776*A^2*B^2*a^29*b^20*d^5 - 6404177920*
A^2*B^2*a^31*b^18*d^5 + 289931264*A^2*B^2*a^33*b^16*d^5 + 2993160192*A^2*B^2*a^35*b^14*d^5 + 1694236672*A^2*B^
2*a^37*b^12*d^5 + 318767104*A^2*B^2*a^39*b^10*d^5))/8 - ((64*A^2*a^11 + 225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 14
4*B^2*a^9*b^2 + 192*A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2)*(96731136*A^3*a^35*b^16*d^6 - 87490560*A^3*a^23*b^28*d
^6 - 236191744*A^3*a^25*b^26*d^6 - 417071104*A^3*a^27*b^24*d^6 - 561905664*A^3*a^29*b^22*d^6 - 534904832*A^3*a
^31*b^20*d^6 - 240386048*A^3*a^33*b^18*d^6 - 14745600*A^3*a^21*b^30*d^6 + 177668096*A^3*a^37*b^14*d^6 + 734658
56*A^3*a^39*b^12*d^6 + 3145728*A^3*a^41*b^10*d^6 - 3145728*A^3*a^43*b^8*d^6 + 18874368*B^3*a^24*b^27*d^6 + 113
246208*B^3*a^26*b^25*d^6 + 277872640*B^3*a^28*b^23*d^6 + 359661568*B^3*a^30*b^21*d^6 + 286261248*B^3*a^32*b^19
*d^6 + 212860928*B^3*a^34*b^17*d^6 + 212860928*B^3*a^36*b^15*d^6 + 173015040*B^3*a^38*b^13*d^6 + 76546048*B^3*
a^40*b^11*d^6 + 13631488*B^3*a^42*b^9*d^6 + ((((a + b*tan(c + d*x))^(1/2)*(235929600*A^2*a^22*b^30*d^7 + 18717
08160*A^2*a^24*b^28*d^7 + 6295650304*A^2*a^26*b^26*d^7 + 11144265728*A^2*a^28*b^24*d^7 + 9560915968*A^2*a^30*b
^22*d^7 - 337641472*A^2*a^32*b^20*d^7 - 9307160576*A^2*a^34*b^18*d^7 - 8887730176*A^2*a^36*b^16*d^7 - 29433528
32*A^2*a^38*b^14*d^7 + 621805568*A^2*a^40*b^12*d^7 + 721420288*A^2*a^42*b^10*d^7 + 150994944*A^2*a^44*b^8*d^7
+ 150994944*B^2*a^24*b^28*d^7 + 1358954496*B^2*a^26*b^26*d^7 + 5653921792*B^2*a^28*b^24*d^7 + 14126415872*B^2*
a^30*b^22*d^7 + 23018340352*B^2*a^32*b^20*d^7 + 24897388544*B^2*a^34*b^18*d^7 + 17381195776*B^2*a^36*b^16*d^7
+ 7079985152*B^2*a^38*b^14*d^7 + 1124073472*B^2*a^40*b^12*d^7 - 218103808*B^2*a^42*b^10*d^7 - 83886080*B^2*a^4
4*b^8*d^7 - 377487360*A*B*a^23*b^29*d^7 - 3196059648*A*B*a^25*b^27*d^7 - 11911823360*A*B*a^27*b^25*d^7 - 24930
942976*A*B*a^29*b^23*d^7 - 30182211584*A*B*a^31*b^21*d^7 - 17028874240*A*B*a^33*b^19*d^7 + 5402263552*A*B*a^35
*b^17*d^7 + 16944988160*A*B*a^37*b^15*d^7 + 12775849984*A*B*a^39*b^13*d^7 + 4588568576*A*B*a^41*b^11*d^7 + 671
088640*A*B*a^43*b^9*d^7))/8 + ((64*A^2*a^11 + 225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2 + 192*A*B*a^
10*b - 360*A*B*a^8*b^3)^(1/2)*(480247808*A*a^40*b^14*d^8 - 297795584*A*a^26*b^28*d^8 - 1243611136*A*a^28*b^26*
d^8 - 2990538752*A*a^30*b^24*d^8 - 4508876800*A*a^32*b^22*d^8 - 4286578688*A*a^34*b^20*d^8 - 2319450112*A*a^36
*b^18*d^8 - 310378496*A*a^38*b^16*d^8 - 31457280*A*a^24*b^30*d^8 + 356515840*A*a^42*b^12*d^8 + 106954752*A*a^4
4*b^10*d^8 + 12582912*A*a^46*b^8*d^8 + 25165824*B*a^25*b^29*d^8 + 251658240*B*a^27*b^27*d^8 + 1124073472*B*a^2
9*b^25*d^8 + 2952790016*B*a^31*b^23*d^8 + 5049942016*B*a^33*b^21*d^8 + 5872025600*B*a^35*b^19*d^8 + 4697620480
*B*a^37*b^17*d^8 + 2550136832*B*a^39*b^15*d^8 + 897581056*B*a^41*b^13*d^8 + 184549376*B*a^43*b^11*d^8 + 167772
16*B*a^45*b^9*d^8 - ((a + b*tan(c + d*x))^(1/2)*(64*A^2*a^11 + 225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9
*b^2 + 192*A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2)*(134217728*a^27*b^28*d^9 + 1409286144*a^29*b^26*d^9 + 664377753
6*a^31*b^24*d^9 + 18522046464*a^33*b^22*d^9 + 33822867456*a^35*b^20*d^9 + 42278584320*a^37*b^18*d^9 + 36641439
744*a^39*b^16*d^9 + 21743271936*a^41*b^14*d^9 + 8455716864*a^43*b^12*d^9 + 1946157056*a^45*b^10*d^9 + 20132659
2*a^47*b^8*d^9))/(64*a^7*d)))/(8*a^7*d))*(64*A^2*a^11 + 225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2 +
192*A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2))/(8*a^7*d) - 56623104*A*B^2*a^23*b^28*d^6 - 346030080*A*B^2*a^25*b^26*
d^6 - 918552576*A*B^2*a^27*b^24*d^6 - 1487929344*A*B^2*a^29*b^22*d^6 - 1871708160*A*B^2*a^31*b^20*d^6 - 209190
9120*A*B^2*a^33*b^18*d^6 - 1871708160*A*B^2*a^35*b^16*d^6 - 1091567616*A*B^2*a^37*b^14*d^6 - 324009984*A*B^2*a
^39*b^12*d^6 - 15728640*A*B^2*a^41*b^10*d^6 + 9437184*A*B^2*a^43*b^8*d^6 + 53084160*A^2*B*a^22*b^29*d^6 + 3255
82848*A^2*B*a^24*b^27*d^6 + 894959616*A^2*B*a^26*b^25*d^6 + 1566572544*A^2*B*a^28*b^23*d^6 + 2108424192*A^2*B*
a^30*b^21*d^6 + 2224029696*A^2*B*a^32*b^19*d^6 + 1552416768*A^2*B*a^34*b^17*d^6 + 446693376*A^2*B*a^36*b^15*d^
6 - 189136896*A^2*B*a^38*b^13*d^6 - 184025088*A^2*B*a^40*b^11*d^6 - 40894464*A^2*B*a^42*b^9*d^6))/(8*a^7*d))*(
64*A^2*a^11 + 225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2 + 192*A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2)*1i
)/(a^7*d) + ((((a + b*tan(c + d*x))^(1/2)*(704643072*A^4*a^29*b^20*d^5 - 290979840*A^4*a^23*b^26*d^5 - 4650434
56*A^4*a^25*b^24*d^5 - 37224448*A^4*a^27*b^22*d^5 - 58982400*A^4*a^21*b^28*d^5 + 767033344*A^4*a^31*b^18*d^5 +
238551040*A^4*a^33*b^16*d^5 + 1572864*A^4*a^35*b^14*d^5 + 92536832*A^4*a^37*b^12*d^5 + 96468992*A^4*a^39*b^10
*d^5 + 25165824*A^4*a^41*b^8*d^5 + 37748736*B^4*a^23*b^26*d^5 + 226492416*B^4*a^25*b^24*d^5 + 536870912*B^4*a^
27*b^22*d^5 + 587202560*B^4*a^29*b^20*d^5 + 176160768*B^4*a^31*b^18*d^5 - 234881024*B^4*a^33*b^16*d^5 - 234881
024*B^4*a^35*b^14*d^5 - 50331648*B^4*a^37*b^12*d^5 + 20971520*B^4*a^39*b^10*d^5 + 8388608*B^4*a^41*b^8*d^5 - 9
4371840*A*B^3*a^22*b^27*d^5 - 364904448*A*B^3*a^24*b^25*d^5 + 37748736*A*B^3*a^26*b^23*d^5 + 2554331136*A*B^3*
a^28*b^21*d^5 + 5989466112*A*B^3*a^30*b^19*d^5 + 6606028800*A*B^3*a^32*b^17*d^5 + 3787456512*A*B^3*a^34*b^15*d
^5 + 918552576*A*B^3*a^36*b^13*d^5 - 56623104*A*B^3*a^38*b^11*d^5 - 50331648*A*B^3*a^40*b^9*d^5 + 330301440*A^
3*B*a^22*b^27*d^5 + 1915748352*A^3*B*a^24*b^25*d^5 + 4279238656*A^3*B*a^26*b^23*d^5 + 4059037696*A^3*B*a^28*b^
21*d^5 + 154140672*A^3*B*a^30*b^19*d^5 - 2825912320*A^3*B*a^32*b^17*d^5 - 1901068288*A^3*B*a^34*b^15*d^5 + 220
20096*A^3*B*a^36*b^13*d^5 + 425721856*A^3*B*a^38*b^11*d^5 + 117440512*A^3*B*a^40*b^9*d^5 + 58982400*A^2*B^2*a^
21*b^28*d^5 - 124256256*A^2*B^2*a^23*b^26*d^5 - 2202533888*A^2*B^2*a^25*b^24*d^5 - 6984040448*A^2*B^2*a^27*b^2
2*d^5 - 10041163776*A^2*B^2*a^29*b^20*d^5 - 6404177920*A^2*B^2*a^31*b^18*d^5 + 289931264*A^2*B^2*a^33*b^16*d^5
+ 2993160192*A^2*B^2*a^35*b^14*d^5 + 1694236672*A^2*B^2*a^37*b^12*d^5 + 318767104*A^2*B^2*a^39*b^10*d^5))/8 +
((64*A^2*a^11 + 225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2 + 192*A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2)
*(96731136*A^3*a^35*b^16*d^6 - 87490560*A^3*a^23*b^28*d^6 - 236191744*A^3*a^25*b^26*d^6 - 417071104*A^3*a^27*b
^24*d^6 - 561905664*A^3*a^29*b^22*d^6 - 534904832*A^3*a^31*b^20*d^6 - 240386048*A^3*a^33*b^18*d^6 - 14745600*A
^3*a^21*b^30*d^6 + 177668096*A^3*a^37*b^14*d^6 + 73465856*A^3*a^39*b^12*d^6 + 3145728*A^3*a^41*b^10*d^6 - 3145
728*A^3*a^43*b^8*d^6 + 18874368*B^3*a^24*b^27*d^6 + 113246208*B^3*a^26*b^25*d^6 + 277872640*B^3*a^28*b^23*d^6
+ 359661568*B^3*a^30*b^21*d^6 + 286261248*B^3*a^32*b^19*d^6 + 212860928*B^3*a^34*b^17*d^6 + 212860928*B^3*a^36
*b^15*d^6 + 173015040*B^3*a^38*b^13*d^6 + 76546048*B^3*a^40*b^11*d^6 + 13631488*B^3*a^42*b^9*d^6 - ((((a + b*t
an(c + d*x))^(1/2)*(235929600*A^2*a^22*b^30*d^7 + 1871708160*A^2*a^24*b^28*d^7 + 6295650304*A^2*a^26*b^26*d^7
+ 11144265728*A^2*a^28*b^24*d^7 + 9560915968*A^2*a^30*b^22*d^7 - 337641472*A^2*a^32*b^20*d^7 - 9307160576*A^2*
a^34*b^18*d^7 - 8887730176*A^2*a^36*b^16*d^7 - 2943352832*A^2*a^38*b^14*d^7 + 621805568*A^2*a^40*b^12*d^7 + 72
1420288*A^2*a^42*b^10*d^7 + 150994944*A^2*a^44*b^8*d^7 + 150994944*B^2*a^24*b^28*d^7 + 1358954496*B^2*a^26*b^2
6*d^7 + 5653921792*B^2*a^28*b^24*d^7 + 14126415872*B^2*a^30*b^22*d^7 + 23018340352*B^2*a^32*b^20*d^7 + 2489738
8544*B^2*a^34*b^18*d^7 + 17381195776*B^2*a^36*b^16*d^7 + 7079985152*B^2*a^38*b^14*d^7 + 1124073472*B^2*a^40*b^
12*d^7 - 218103808*B^2*a^42*b^10*d^7 - 83886080*B^2*a^44*b^8*d^7 - 377487360*A*B*a^23*b^29*d^7 - 3196059648*A*
B*a^25*b^27*d^7 - 11911823360*A*B*a^27*b^25*d^7 - 24930942976*A*B*a^29*b^23*d^7 - 30182211584*A*B*a^31*b^21*d^
7 - 17028874240*A*B*a^33*b^19*d^7 + 5402263552*A*B*a^35*b^17*d^7 + 16944988160*A*B*a^37*b^15*d^7 + 12775849984
*A*B*a^39*b^13*d^7 + 4588568576*A*B*a^41*b^11*d^7 + 671088640*A*B*a^43*b^9*d^7))/8 - ((64*A^2*a^11 + 225*A^2*a
^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2 + 192*A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2)*(480247808*A*a^40*b^14*d^
8 - 297795584*A*a^26*b^28*d^8 - 1243611136*A*a^28*b^26*d^8 - 2990538752*A*a^30*b^24*d^8 - 4508876800*A*a^32*b^
22*d^8 - 4286578688*A*a^34*b^20*d^8 - 2319450112*A*a^36*b^18*d^8 - 310378496*A*a^38*b^16*d^8 - 31457280*A*a^24
*b^30*d^8 + 356515840*A*a^42*b^12*d^8 + 106954752*A*a^44*b^10*d^8 + 12582912*A*a^46*b^8*d^8 + 25165824*B*a^25*
b^29*d^8 + 251658240*B*a^27*b^27*d^8 + 1124073472*B*a^29*b^25*d^8 + 2952790016*B*a^31*b^23*d^8 + 5049942016*B*
a^33*b^21*d^8 + 5872025600*B*a^35*b^19*d^8 + 4697620480*B*a^37*b^17*d^8 + 2550136832*B*a^39*b^15*d^8 + 8975810
56*B*a^41*b^13*d^8 + 184549376*B*a^43*b^11*d^8 + 16777216*B*a^45*b^9*d^8 + ((a + b*tan(c + d*x))^(1/2)*(64*A^2
*a^11 + 225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2 + 192*A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2)*(1342177
28*a^27*b^28*d^9 + 1409286144*a^29*b^26*d^9 + 6643777536*a^31*b^24*d^9 + 18522046464*a^33*b^22*d^9 + 338228674
56*a^35*b^20*d^9 + 42278584320*a^37*b^18*d^9 + 36641439744*a^39*b^16*d^9 + 21743271936*a^41*b^14*d^9 + 8455716
864*a^43*b^12*d^9 + 1946157056*a^45*b^10*d^9 + 201326592*a^47*b^8*d^9))/(64*a^7*d)))/(8*a^7*d))*(64*A^2*a^11 +
225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2 + 192*A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2))/(8*a^7*d) - 56
623104*A*B^2*a^23*b^28*d^6 - 346030080*A*B^2*a^25*b^26*d^6 - 918552576*A*B^2*a^27*b^24*d^6 - 1487929344*A*B^2*
a^29*b^22*d^6 - 1871708160*A*B^2*a^31*b^20*d^6 - 2091909120*A*B^2*a^33*b^18*d^6 - 1871708160*A*B^2*a^35*b^16*d
^6 - 1091567616*A*B^2*a^37*b^14*d^6 - 324009984*A*B^2*a^39*b^12*d^6 - 15728640*A*B^2*a^41*b^10*d^6 + 9437184*A
*B^2*a^43*b^8*d^6 + 53084160*A^2*B*a^22*b^29*d^6 + 325582848*A^2*B*a^24*b^27*d^6 + 894959616*A^2*B*a^26*b^25*d
^6 + 1566572544*A^2*B*a^28*b^23*d^6 + 2108424192*A^2*B*a^30*b^21*d^6 + 2224029696*A^2*B*a^32*b^19*d^6 + 155241
6768*A^2*B*a^34*b^17*d^6 + 446693376*A^2*B*a^36*b^15*d^6 - 189136896*A^2*B*a^38*b^13*d^6 - 184025088*A^2*B*a^4
0*b^11*d^6 - 40894464*A^2*B*a^42*b^9*d^6))/(8*a^7*d))*(64*A^2*a^11 + 225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 144*B
^2*a^9*b^2 + 192*A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2)*1i)/(a^7*d))/(58982400*A^5*a^22*b^26*d^4 + 381419520*A^5*
a^24*b^24*d^4 + 1018429440*A^5*a^26*b^22*d^4 + 1403781120*A^5*a^28*b^20*d^4 + 963379200*A^5*a^30*b^18*d^4 + 13
7625600*A^5*a^32*b^16*d^4 - 247726080*A^5*a^34*b^14*d^4 - 161218560*A^5*a^36*b^12*d^4 - 31457280*A^5*a^38*b^10
*d^4 + 37748736*B^5*a^23*b^25*d^4 + 239075328*B^5*a^25*b^23*d^4 + 616562688*B^5*a^27*b^21*d^4 + 792723456*B^5*
a^29*b^19*d^4 + 440401920*B^5*a^31*b^17*d^4 - 88080384*B^5*a^33*b^15*d^4 - 264241152*B^5*a^35*b^13*d^4 - 13841
2032*B^5*a^37*b^11*d^4 - 25165824*B^5*a^39*b^9*d^4 + ((((a + b*tan(c + d*x))^(1/2)*(704643072*A^4*a^29*b^20*d^
5 - 290979840*A^4*a^23*b^26*d^5 - 465043456*A^4*a^25*b^24*d^5 - 37224448*A^4*a^27*b^22*d^5 - 58982400*A^4*a^21
*b^28*d^5 + 767033344*A^4*a^31*b^18*d^5 + 238551040*A^4*a^33*b^16*d^5 + 1572864*A^4*a^35*b^14*d^5 + 92536832*A
^4*a^37*b^12*d^5 + 96468992*A^4*a^39*b^10*d^5 + 25165824*A^4*a^41*b^8*d^5 + 37748736*B^4*a^23*b^26*d^5 + 22649
2416*B^4*a^25*b^24*d^5 + 536870912*B^4*a^27*b^22*d^5 + 587202560*B^4*a^29*b^20*d^5 + 176160768*B^4*a^31*b^18*d
^5 - 234881024*B^4*a^33*b^16*d^5 - 234881024*B^4*a^35*b^14*d^5 - 50331648*B^4*a^37*b^12*d^5 + 20971520*B^4*a^3
9*b^10*d^5 + 8388608*B^4*a^41*b^8*d^5 - 94371840*A*B^3*a^22*b^27*d^5 - 364904448*A*B^3*a^24*b^25*d^5 + 3774873
6*A*B^3*a^26*b^23*d^5 + 2554331136*A*B^3*a^28*b^21*d^5 + 5989466112*A*B^3*a^30*b^19*d^5 + 6606028800*A*B^3*a^3
2*b^17*d^5 + 3787456512*A*B^3*a^34*b^15*d^5 + 918552576*A*B^3*a^36*b^13*d^5 - 56623104*A*B^3*a^38*b^11*d^5 - 5
0331648*A*B^3*a^40*b^9*d^5 + 330301440*A^3*B*a^22*b^27*d^5 + 1915748352*A^3*B*a^24*b^25*d^5 + 4279238656*A^3*B
*a^26*b^23*d^5 + 4059037696*A^3*B*a^28*b^21*d^5 + 154140672*A^3*B*a^30*b^19*d^5 - 2825912320*A^3*B*a^32*b^17*d
^5 - 1901068288*A^3*B*a^34*b^15*d^5 + 22020096*A^3*B*a^36*b^13*d^5 + 425721856*A^3*B*a^38*b^11*d^5 + 117440512
*A^3*B*a^40*b^9*d^5 + 58982400*A^2*B^2*a^21*b^28*d^5 - 124256256*A^2*B^2*a^23*b^26*d^5 - 2202533888*A^2*B^2*a^
25*b^24*d^5 - 6984040448*A^2*B^2*a^27*b^22*d^5 - 10041163776*A^2*B^2*a^29*b^20*d^5 - 6404177920*A^2*B^2*a^31*b
^18*d^5 + 289931264*A^2*B^2*a^33*b^16*d^5 + 2993160192*A^2*B^2*a^35*b^14*d^5 + 1694236672*A^2*B^2*a^37*b^12*d^
5 + 318767104*A^2*B^2*a^39*b^10*d^5))/8 - ((64*A^2*a^11 + 225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2
+ 192*A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2)*(96731136*A^3*a^35*b^16*d^6 - 87490560*A^3*a^23*b^28*d^6 - 236191744
*A^3*a^25*b^26*d^6 - 417071104*A^3*a^27*b^24*d^6 - 561905664*A^3*a^29*b^22*d^6 - 534904832*A^3*a^31*b^20*d^6 -
240386048*A^3*a^33*b^18*d^6 - 14745600*A^3*a^21*b^30*d^6 + 177668096*A^3*a^37*b^14*d^6 + 73465856*A^3*a^39*b^
12*d^6 + 3145728*A^3*a^41*b^10*d^6 - 3145728*A^3*a^43*b^8*d^6 + 18874368*B^3*a^24*b^27*d^6 + 113246208*B^3*a^2
6*b^25*d^6 + 277872640*B^3*a^28*b^23*d^6 + 359661568*B^3*a^30*b^21*d^6 + 286261248*B^3*a^32*b^19*d^6 + 2128609
28*B^3*a^34*b^17*d^6 + 212860928*B^3*a^36*b^15*d^6 + 173015040*B^3*a^38*b^13*d^6 + 76546048*B^3*a^40*b^11*d^6
+ 13631488*B^3*a^42*b^9*d^6 + ((((a + b*tan(c + d*x))^(1/2)*(235929600*A^2*a^22*b^30*d^7 + 1871708160*A^2*a^24
*b^28*d^7 + 6295650304*A^2*a^26*b^26*d^7 + 11144265728*A^2*a^28*b^24*d^7 + 9560915968*A^2*a^30*b^22*d^7 - 3376
41472*A^2*a^32*b^20*d^7 - 9307160576*A^2*a^34*b^18*d^7 - 8887730176*A^2*a^36*b^16*d^7 - 2943352832*A^2*a^38*b^
14*d^7 + 621805568*A^2*a^40*b^12*d^7 + 721420288*A^2*a^42*b^10*d^7 + 150994944*A^2*a^44*b^8*d^7 + 150994944*B^
2*a^24*b^28*d^7 + 1358954496*B^2*a^26*b^26*d^7 + 5653921792*B^2*a^28*b^24*d^7 + 14126415872*B^2*a^30*b^22*d^7
+ 23018340352*B^2*a^32*b^20*d^7 + 24897388544*B^2*a^34*b^18*d^7 + 17381195776*B^2*a^36*b^16*d^7 + 7079985152*B
^2*a^38*b^14*d^7 + 1124073472*B^2*a^40*b^12*d^7 - 218103808*B^2*a^42*b^10*d^7 - 83886080*B^2*a^44*b^8*d^7 - 37
7487360*A*B*a^23*b^29*d^7 - 3196059648*A*B*a^25*b^27*d^7 - 11911823360*A*B*a^27*b^25*d^7 - 24930942976*A*B*a^2
9*b^23*d^7 - 30182211584*A*B*a^31*b^21*d^7 - 17028874240*A*B*a^33*b^19*d^7 + 5402263552*A*B*a^35*b^17*d^7 + 16
944988160*A*B*a^37*b^15*d^7 + 12775849984*A*B*a^39*b^13*d^7 + 4588568576*A*B*a^41*b^11*d^7 + 671088640*A*B*a^4
3*b^9*d^7))/8 + ((64*A^2*a^11 + 225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2 + 192*A*B*a^10*b - 360*A*B
*a^8*b^3)^(1/2)*(480247808*A*a^40*b^14*d^8 - 297795584*A*a^26*b^28*d^8 - 1243611136*A*a^28*b^26*d^8 - 29905387
52*A*a^30*b^24*d^8 - 4508876800*A*a^32*b^22*d^8 - 4286578688*A*a^34*b^20*d^8 - 2319450112*A*a^36*b^18*d^8 - 31
0378496*A*a^38*b^16*d^8 - 31457280*A*a^24*b^30*d^8 + 356515840*A*a^42*b^12*d^8 + 106954752*A*a^44*b^10*d^8 + 1
2582912*A*a^46*b^8*d^8 + 25165824*B*a^25*b^29*d^8 + 251658240*B*a^27*b^27*d^8 + 1124073472*B*a^29*b^25*d^8 + 2
952790016*B*a^31*b^23*d^8 + 5049942016*B*a^33*b^21*d^8 + 5872025600*B*a^35*b^19*d^8 + 4697620480*B*a^37*b^17*d
^8 + 2550136832*B*a^39*b^15*d^8 + 897581056*B*a^41*b^13*d^8 + 184549376*B*a^43*b^11*d^8 + 16777216*B*a^45*b^9*
d^8 - ((a + b*tan(c + d*x))^(1/2)*(64*A^2*a^11 + 225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2 + 192*A*B
*a^10*b - 360*A*B*a^8*b^3)^(1/2)*(134217728*a^27*b^28*d^9 + 1409286144*a^29*b^26*d^9 + 6643777536*a^31*b^24*d^
9 + 18522046464*a^33*b^22*d^9 + 33822867456*a^35*b^20*d^9 + 42278584320*a^37*b^18*d^9 + 36641439744*a^39*b^16*
d^9 + 21743271936*a^41*b^14*d^9 + 8455716864*a^43*b^12*d^9 + 1946157056*a^45*b^10*d^9 + 201326592*a^47*b^8*d^9
))/(64*a^7*d)))/(8*a^7*d))*(64*A^2*a^11 + 225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2 + 192*A*B*a^10*b
- 360*A*B*a^8*b^3)^(1/2))/(8*a^7*d) - 56623104*A*B^2*a^23*b^28*d^6 - 346030080*A*B^2*a^25*b^26*d^6 - 91855257
6*A*B^2*a^27*b^24*d^6 - 1487929344*A*B^2*a^29*b^22*d^6 - 1871708160*A*B^2*a^31*b^20*d^6 - 2091909120*A*B^2*a^3
3*b^18*d^6 - 1871708160*A*B^2*a^35*b^16*d^6 - 1091567616*A*B^2*a^37*b^14*d^6 - 324009984*A*B^2*a^39*b^12*d^6 -
15728640*A*B^2*a^41*b^10*d^6 + 9437184*A*B^2*a^43*b^8*d^6 + 53084160*A^2*B*a^22*b^29*d^6 + 325582848*A^2*B*a^
24*b^27*d^6 + 894959616*A^2*B*a^26*b^25*d^6 + 1566572544*A^2*B*a^28*b^23*d^6 + 2108424192*A^2*B*a^30*b^21*d^6
+ 2224029696*A^2*B*a^32*b^19*d^6 + 1552416768*A^2*B*a^34*b^17*d^6 + 446693376*A^2*B*a^36*b^15*d^6 - 189136896*
A^2*B*a^38*b^13*d^6 - 184025088*A^2*B*a^40*b^11*d^6 - 40894464*A^2*B*a^42*b^9*d^6))/(8*a^7*d))*(64*A^2*a^11 +
225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2 + 192*A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2))/(a^7*d) - ((((a
+ b*tan(c + d*x))^(1/2)*(704643072*A^4*a^29*b^20*d^5 - 290979840*A^4*a^23*b^26*d^5 - 465043456*A^4*a^25*b^24*
d^5 - 37224448*A^4*a^27*b^22*d^5 - 58982400*A^4*a^21*b^28*d^5 + 767033344*A^4*a^31*b^18*d^5 + 238551040*A^4*a^
33*b^16*d^5 + 1572864*A^4*a^35*b^14*d^5 + 92536832*A^4*a^37*b^12*d^5 + 96468992*A^4*a^39*b^10*d^5 + 25165824*A
^4*a^41*b^8*d^5 + 37748736*B^4*a^23*b^26*d^5 + 226492416*B^4*a^25*b^24*d^5 + 536870912*B^4*a^27*b^22*d^5 + 587
202560*B^4*a^29*b^20*d^5 + 176160768*B^4*a^31*b^18*d^5 - 234881024*B^4*a^33*b^16*d^5 - 234881024*B^4*a^35*b^14
*d^5 - 50331648*B^4*a^37*b^12*d^5 + 20971520*B^4*a^39*b^10*d^5 + 8388608*B^4*a^41*b^8*d^5 - 94371840*A*B^3*a^2
2*b^27*d^5 - 364904448*A*B^3*a^24*b^25*d^5 + 37748736*A*B^3*a^26*b^23*d^5 + 2554331136*A*B^3*a^28*b^21*d^5 + 5
989466112*A*B^3*a^30*b^19*d^5 + 6606028800*A*B^3*a^32*b^17*d^5 + 3787456512*A*B^3*a^34*b^15*d^5 + 918552576*A*
B^3*a^36*b^13*d^5 - 56623104*A*B^3*a^38*b^11*d^5 - 50331648*A*B^3*a^40*b^9*d^5 + 330301440*A^3*B*a^22*b^27*d^5
+ 1915748352*A^3*B*a^24*b^25*d^5 + 4279238656*A^3*B*a^26*b^23*d^5 + 4059037696*A^3*B*a^28*b^21*d^5 + 15414067
2*A^3*B*a^30*b^19*d^5 - 2825912320*A^3*B*a^32*b^17*d^5 - 1901068288*A^3*B*a^34*b^15*d^5 + 22020096*A^3*B*a^36*
b^13*d^5 + 425721856*A^3*B*a^38*b^11*d^5 + 117440512*A^3*B*a^40*b^9*d^5 + 58982400*A^2*B^2*a^21*b^28*d^5 - 124
256256*A^2*B^2*a^23*b^26*d^5 - 2202533888*A^2*B^2*a^25*b^24*d^5 - 6984040448*A^2*B^2*a^27*b^22*d^5 - 100411637
76*A^2*B^2*a^29*b^20*d^5 - 6404177920*A^2*B^2*a^31*b^18*d^5 + 289931264*A^2*B^2*a^33*b^16*d^5 + 2993160192*A^2
*B^2*a^35*b^14*d^5 + 1694236672*A^2*B^2*a^37*b^12*d^5 + 318767104*A^2*B^2*a^39*b^10*d^5))/8 + ((64*A^2*a^11 +
225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2 + 192*A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2)*(96731136*A^3*a^
35*b^16*d^6 - 87490560*A^3*a^23*b^28*d^6 - 236191744*A^3*a^25*b^26*d^6 - 417071104*A^3*a^27*b^24*d^6 - 5619056
64*A^3*a^29*b^22*d^6 - 534904832*A^3*a^31*b^20*d^6 - 240386048*A^3*a^33*b^18*d^6 - 14745600*A^3*a^21*b^30*d^6
+ 177668096*A^3*a^37*b^14*d^6 + 73465856*A^3*a^39*b^12*d^6 + 3145728*A^3*a^41*b^10*d^6 - 3145728*A^3*a^43*b^8*
d^6 + 18874368*B^3*a^24*b^27*d^6 + 113246208*B^3*a^26*b^25*d^6 + 277872640*B^3*a^28*b^23*d^6 + 359661568*B^3*a
^30*b^21*d^6 + 286261248*B^3*a^32*b^19*d^6 + 212860928*B^3*a^34*b^17*d^6 + 212860928*B^3*a^36*b^15*d^6 + 17301
5040*B^3*a^38*b^13*d^6 + 76546048*B^3*a^40*b^11*d^6 + 13631488*B^3*a^42*b^9*d^6 - ((((a + b*tan(c + d*x))^(1/2
)*(235929600*A^2*a^22*b^30*d^7 + 1871708160*A^2*a^24*b^28*d^7 + 6295650304*A^2*a^26*b^26*d^7 + 11144265728*A^2
*a^28*b^24*d^7 + 9560915968*A^2*a^30*b^22*d^7 - 337641472*A^2*a^32*b^20*d^7 - 9307160576*A^2*a^34*b^18*d^7 - 8
887730176*A^2*a^36*b^16*d^7 - 2943352832*A^2*a^38*b^14*d^7 + 621805568*A^2*a^40*b^12*d^7 + 721420288*A^2*a^42*
b^10*d^7 + 150994944*A^2*a^44*b^8*d^7 + 150994944*B^2*a^24*b^28*d^7 + 1358954496*B^2*a^26*b^26*d^7 + 565392179
2*B^2*a^28*b^24*d^7 + 14126415872*B^2*a^30*b^22*d^7 + 23018340352*B^2*a^32*b^20*d^7 + 24897388544*B^2*a^34*b^1
8*d^7 + 17381195776*B^2*a^36*b^16*d^7 + 7079985152*B^2*a^38*b^14*d^7 + 1124073472*B^2*a^40*b^12*d^7 - 21810380
8*B^2*a^42*b^10*d^7 - 83886080*B^2*a^44*b^8*d^7 - 377487360*A*B*a^23*b^29*d^7 - 3196059648*A*B*a^25*b^27*d^7 -
11911823360*A*B*a^27*b^25*d^7 - 24930942976*A*B*a^29*b^23*d^7 - 30182211584*A*B*a^31*b^21*d^7 - 17028874240*A
*B*a^33*b^19*d^7 + 5402263552*A*B*a^35*b^17*d^7 + 16944988160*A*B*a^37*b^15*d^7 + 12775849984*A*B*a^39*b^13*d^
7 + 4588568576*A*B*a^41*b^11*d^7 + 671088640*A*B*a^43*b^9*d^7))/8 - ((64*A^2*a^11 + 225*A^2*a^7*b^4 - 240*A^2*
a^9*b^2 + 144*B^2*a^9*b^2 + 192*A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2)*(480247808*A*a^40*b^14*d^8 - 297795584*A*a
^26*b^28*d^8 - 1243611136*A*a^28*b^26*d^8 - 2990538752*A*a^30*b^24*d^8 - 4508876800*A*a^32*b^22*d^8 - 42865786
88*A*a^34*b^20*d^8 - 2319450112*A*a^36*b^18*d^8 - 310378496*A*a^38*b^16*d^8 - 31457280*A*a^24*b^30*d^8 + 35651
5840*A*a^42*b^12*d^8 + 106954752*A*a^44*b^10*d^8 + 12582912*A*a^46*b^8*d^8 + 25165824*B*a^25*b^29*d^8 + 251658
240*B*a^27*b^27*d^8 + 1124073472*B*a^29*b^25*d^8 + 2952790016*B*a^31*b^23*d^8 + 5049942016*B*a^33*b^21*d^8 + 5
872025600*B*a^35*b^19*d^8 + 4697620480*B*a^37*b^17*d^8 + 2550136832*B*a^39*b^15*d^8 + 897581056*B*a^41*b^13*d^
8 + 184549376*B*a^43*b^11*d^8 + 16777216*B*a^45*b^9*d^8 + ((a + b*tan(c + d*x))^(1/2)*(64*A^2*a^11 + 225*A^2*a
^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2 + 192*A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2)*(134217728*a^27*b^28*d^9
+ 1409286144*a^29*b^26*d^9 + 6643777536*a^31*b^24*d^9 + 18522046464*a^33*b^22*d^9 + 33822867456*a^35*b^20*d^9
+ 42278584320*a^37*b^18*d^9 + 36641439744*a^39*b^16*d^9 + 21743271936*a^41*b^14*d^9 + 8455716864*a^43*b^12*d^9
+ 1946157056*a^45*b^10*d^9 + 201326592*a^47*b^8*d^9))/(64*a^7*d)))/(8*a^7*d))*(64*A^2*a^11 + 225*A^2*a^7*b^4
- 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2 + 192*A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2))/(8*a^7*d) - 56623104*A*B^2*a^23
*b^28*d^6 - 346030080*A*B^2*a^25*b^26*d^6 - 918552576*A*B^2*a^27*b^24*d^6 - 1487929344*A*B^2*a^29*b^22*d^6 - 1
871708160*A*B^2*a^31*b^20*d^6 - 2091909120*A*B^2*a^33*b^18*d^6 - 1871708160*A*B^2*a^35*b^16*d^6 - 1091567616*A
*B^2*a^37*b^14*d^6 - 324009984*A*B^2*a^39*b^12*d^6 - 15728640*A*B^2*a^41*b^10*d^6 + 9437184*A*B^2*a^43*b^8*d^6
+ 53084160*A^2*B*a^22*b^29*d^6 + 325582848*A^2*B*a^24*b^27*d^6 + 894959616*A^2*B*a^26*b^25*d^6 + 1566572544*A
^2*B*a^28*b^23*d^6 + 2108424192*A^2*B*a^30*b^21*d^6 + 2224029696*A^2*B*a^32*b^19*d^6 + 1552416768*A^2*B*a^34*b
^17*d^6 + 446693376*A^2*B*a^36*b^15*d^6 - 189136896*A^2*B*a^38*b^13*d^6 - 184025088*A^2*B*a^40*b^11*d^6 - 4089
4464*A^2*B*a^42*b^9*d^6))/(8*a^7*d))*(64*A^2*a^11 + 225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2 + 192*
A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2))/(a^7*d) - 94371840*A*B^4*a^22*b^26*d^4 - 541065216*A*B^4*a^24*b^24*d^4 -
1161822208*A*B^4*a^26*b^22*d^4 - 910163968*A*B^4*a^28*b^20*d^4 + 528482304*A*B^4*a^30*b^18*d^4 + 1614807040*A*
B^4*a^32*b^16*d^4 + 1262485504*A*B^4*a^34*b^14*d^4 + 390070272*A*B^4*a^36*b^12*d^4 + 2097152*A*B^4*a^38*b^10*d
^4 - 16777216*A*B^4*a^40*b^8*d^4 + 58982400*A^4*B*a^21*b^27*d^4 + 255590400*A^4*B*a^23*b^25*d^4 + 179568640*A^
4*B*a^25*b^23*d^4 - 945029120*A^4*B*a^27*b^21*d^4 - 2559836160*A^4*B*a^29*b^19*d^4 - 2798387200*A^4*B*a^31*b^1
7*d^4 - 1422131200*A^4*B*a^33*b^15*d^4 - 161218560*A^4*B*a^35*b^13*d^4 + 136314880*A^4*B*a^37*b^11*d^4 + 41943
040*A^4*B*a^39*b^9*d^4 + 58982400*A^2*B^3*a^21*b^27*d^4 + 293339136*A^2*B^3*a^23*b^25*d^4 + 418643968*A^2*B^3*
a^25*b^23*d^4 - 328466432*A^2*B^3*a^27*b^21*d^4 - 1767112704*A^2*B^3*a^29*b^19*d^4 - 2357985280*A^2*B^3*a^31*b
^17*d^4 - 1510211584*A^2*B^3*a^33*b^15*d^4 - 425459712*A^2*B^3*a^35*b^13*d^4 - 2097152*A^2*B^3*a^37*b^11*d^4 +
16777216*A^2*B^3*a^39*b^9*d^4 - 35389440*A^3*B^2*a^22*b^26*d^4 - 159645696*A^3*B^2*a^24*b^24*d^4 - 143392768*
A^3*B^2*a^26*b^22*d^4 + 493617152*A^3*B^2*a^28*b^20*d^4 + 1491861504*A^3*B^2*a^30*b^18*d^4 + 1752432640*A^3*B^
2*a^32*b^16*d^4 + 1014759424*A^3*B^2*a^34*b^14*d^4 + 228851712*A^3*B^2*a^36*b^12*d^4 - 29360128*A^3*B^2*a^38*b
^10*d^4 - 16777216*A^3*B^2*a^40*b^8*d^4))*(64*A^2*a^11 + 225*A^2*a^7*b^4 - 240*A^2*a^9*b^2 + 144*B^2*a^9*b^2 +
192*A*B*a^10*b - 360*A*B*a^8*b^3)^(1/2)*1i)/(4*a^7*d)

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sympy [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (A + B \tan {\left (c + d x \right )}\right ) \cot ^{3}{\left (c + d x \right )}}{\left (a + b \tan {\left (c + d x \right )}\right )^{\frac {3}{2}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)

[Out]

Integral((A + B*tan(c + d*x))*cot(c + d*x)**3/(a + b*tan(c + d*x))**(3/2), x)

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