\(\int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx\) [354]
Optimal result
Integrand size = 31, antiderivative size = 171 \[
\int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx=-\frac {2 A \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{a^{3/2} d}+\frac {(A-i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{(a-i b)^{3/2} d}+\frac {(A+i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{(a+i b)^{3/2} d}+\frac {2 b (A b-a B)}{a \left (a^2+b^2\right ) d \sqrt {a+b \tan (c+d x)}}
\]
[Out]
-2*A*arctanh((a+b*tan(d*x+c))^(1/2)/a^(1/2))/a^(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+(A+I*B)*arctanh((a+b*tan(d*x+c))^(1/2)/(a+I*b)^(1/2))/(a+I*b)^(3/2)/d+2*b*(A*b-B*a)/a/(a^2+b^2)
/d/(a+b*tan(d*x+c))^(1/2)
Rubi [A] (verified)
Time = 0.90 (sec) , antiderivative size = 171, normalized size of antiderivative = 1.00, number of
steps used = 12, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.226, Rules used = {3690, 3734, 3620, 3618, 65,
214, 3715} \[
\int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx=-\frac {2 A \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{a^{3/2} d}+\frac {2 b (A b-a B)}{a d \left (a^2+b^2\right ) \sqrt {a+b \tan (c+d x)}}+\frac {(A-i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{d (a-i b)^{3/2}}+\frac {(A+i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{d (a+i b)^{3/2}}
\]
[In]
Int[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]
[Out]
(-2*A*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(a^(3/2)*d) + ((A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqr
t[a - I*b]])/((a - I*b)^(3/2)*d) + ((A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(3/2
)*d) + (2*b*(A*b - a*B))/(a*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])
Rule 65
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 214
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(Rt[-a/b, 2]/a)*ArcTanh[x/Rt[-a/b, 2]], x] /; FreeQ[{a, b},
x] && NegQ[a/b]
Rule 3618
Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_)*((c_) + (d_.)*tan[(e_.) + (f_.)*(x_)]), x_Symbol] :> Dist[c*(
d/f), Subst[Int[(a + (b/d)*x)^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 3620
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 3690
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 3715
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 3734
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*}
\text {integral}& = \frac {2 b (A b-a B)}{a \left (a^2+b^2\right ) d \sqrt {a+b \tan (c+d x)}}+\frac {2 \int \frac {\cot (c+d x) \left (\frac {1}{2} A \left (a^2+b^2\right )-\frac {1}{2} a (A b-a B) \tan (c+d x)+\frac {1}{2} b (A b-a B) \tan ^2(c+d x)\right )}{\sqrt {a+b \tan (c+d x)}} \, dx}{a \left (a^2+b^2\right )} \\ & = \frac {2 b (A b-a B)}{a \left (a^2+b^2\right ) d \sqrt {a+b \tan (c+d x)}}+\frac {A \int \frac {\cot (c+d x) \left (1+\tan ^2(c+d x)\right )}{\sqrt {a+b \tan (c+d x)}} \, dx}{a}+\frac {2 \int \frac {-\frac {1}{2} a (A b-a B)-\frac {1}{2} a (a A+b B) \tan (c+d x)}{\sqrt {a+b \tan (c+d x)}} \, dx}{a \left (a^2+b^2\right )} \\ & = \frac {2 b (A b-a B)}{a \left (a^2+b^2\right ) d \sqrt {a+b \tan (c+d x)}}-\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 {(i A+B) \int \frac {1+i \tan (c+d x)}{\sqrt {a+b \tan (c+d x)}} \, dx}{2 (a-i b)}+\frac {A \text {Subst}\left (\int \frac {1}{x \sqrt {a+b x}} \, dx,x,\tan (c+d x)\right )}{a d} \\ & = \frac {2 b (A b-a B)}{a \left (a^2+b^2\right ) d \sqrt {a+b \tan (c+d x)}}+\frac {(2 A) \text {Subst}\left (\int \frac {1}{-\frac {a}{b}+\frac {x^2}{b}} \, dx,x,\sqrt {a+b \tan (c+d x)}\right )}{a b d}-\frac {(A-i B) \text {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) \text {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 {2 A \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{a^{3/2} d}+\frac {2 b (A b-a B)}{a \left (a^2+b^2\right ) d \sqrt {a+b \tan (c+d x)}}+\frac {(i (A+i B)) \text {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) \text {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 {2 A \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{a^{3/2} d}+\frac {(A-i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{(a-i b)^{3/2} d}+\frac {(A+i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{(a+i b)^{3/2} d}+\frac {2 b (A b-a B)}{a \left (a^2+b^2\right ) d \sqrt {a+b \tan (c+d x)}} \\
\end{align*}
Mathematica [A] (verified)
Time = 1.34 (sec) , antiderivative size = 186, normalized size of antiderivative = 1.09
\[
\int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx=\frac {-\frac {2 A \left (a^2+b^2\right ) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{\sqrt {a}}+\frac {a (a+i b) (A-i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{\sqrt {a-i b}}+\frac {a (a-i b) (A+i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{\sqrt {a+i b}}+\frac {2 b (A b-a B)}{\sqrt {a+b \tan (c+d x)}}}{a \left (a^2+b^2\right ) d}
\]
[In]
Integrate[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]
[Out]
((-2*A*(a^2 + b^2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/Sqrt[a] + (a*(a + I*b)*(A - I*B)*ArcTanh[Sqrt[a
+ b*Tan[c + d*x]]/Sqrt[a - I*b]])/Sqrt[a - I*b] + (a*(a - I*b)*(A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt
[a + I*b]])/Sqrt[a + I*b] + (2*b*(A*b - a*B))/Sqrt[a + b*Tan[c + d*x]])/(a*(a^2 + b^2)*d)
Maple [B] (verified)
Leaf count of result is larger than twice the leaf count of optimal. \(7981\) vs. \(2(145)=290\).
Time = 0.23 (sec) , antiderivative size = 7982, normalized size of antiderivative =
46.68
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| method | result | size |
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| derivativedivides |
\(\text {Expression too large to display}\) |
\(7982\) |
| default |
\(\text {Expression too large to display}\) |
\(7982\) |
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[In]
int(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x,method=_RETURNVERBOSE)
[Out]
result too large to display
Fricas [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 4402 vs. \(2 (139) = 278\).
Time = 4.11 (sec) , antiderivative size = 8820, normalized size of antiderivative = 51.58
\[
\int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx=\text {Too large to display}
\]
[In]
integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm="fricas")
[Out]
Too large to include
Sympy [F]
\[
\int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx=\int \frac {\left (A + B \tan {\left (c + d x \right )}\right ) \cot {\left (c + d x \right )}}{\left (a + b \tan {\left (c + d x \right )}\right )^{\frac {3}{2}}}\, dx
\]
[In]
integrate(cot(d*x+c)*(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)/(a + b*tan(c + d*x))**(3/2), x)
Maxima [F]
\[
\int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx=\int { \frac {{\left (B \tan \left (d x + c\right ) + A\right )} \cot \left (d x + c\right )}{{\left (b \tan \left (d x + c\right ) + a\right )}^{\frac {3}{2}}} \,d x }
\]
[In]
integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm="maxima")
[Out]
integrate((B*tan(d*x + c) + A)*cot(d*x + c)/(b*tan(d*x + c) + a)^(3/2), x)
Giac [F(-1)]
Timed out. \[
\int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx=\text {Timed out}
\]
[In]
integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm="giac")
[Out]
Timed out
Mupad [B] (verification not implemented)
Time = 15.35 (sec) , antiderivative size = 26139, normalized size of antiderivative = 152.86
\[
\int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx=\text {Too large to display}
\]
[In]
int((cot(c + d*x)*(A + B*tan(c + d*x)))/(a + b*tan(c + d*x))^(3/2),x)
[Out]
atan(-(((-(((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)*(256*A^2*a^8*b^26*d^7 + 14
72*A^2*a^10*b^24*d^7 + 3712*A^2*a^12*b^22*d^7 + 6272*A^2*a^14*b^20*d^7 + 9856*A^2*a^16*b^18*d^7 + 14336*A^2*a^
18*b^16*d^7 + 15232*A^2*a^20*b^14*d^7 + 10112*A^2*a^22*b^12*d^7 + 3712*A^2*a^24*b^10*d^7 + 576*A^2*a^26*b^8*d^
7 + 832*B^2*a^10*b^24*d^7 + 5504*B^2*a^12*b^22*d^7 + 15232*B^2*a^14*b^20*d^7 + 22400*B^2*a^16*b^18*d^7 + 17920
*B^2*a^18*b^16*d^7 + 6272*B^2*a^20*b^14*d^7 - 896*B^2*a^22*b^12*d^7 - 1408*B^2*a^24*b^10*d^7 - 320*B^2*a^26*b^
8*d^7 - 512*A*B*a^9*b^25*d^7 - 1792*A*B*a^11*b^23*d^7 + 1792*A*B*a^13*b^21*d^7 + 19712*A*B*a^15*b^19*d^7 + 448
00*A*B*a^17*b^17*d^7 + 51968*A*B*a^19*b^15*d^7 + 34048*A*B*a^21*b^13*d^7 + 12032*A*B*a^23*b^11*d^7 + 1792*A*B*
a^25*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)*(512*A*a^8*b^28*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)*(512*a^9*b^28*d^9 + 5376*a^11*b^26*d^9 + 25344*a^13*b^24*d^9
+ 70656*a^15*b^22*d^9 + 129024*a^17*b^20*d^9 + 161280*a^19*b^18*d^9 + 139776*a^21*b^16*d^9 + 82944*a^23*b^14*d
^9 + 32256*a^25*b^12*d^9 + 7424*a^27*b^10*d^9 + 768*a^29*b^8*d^9) + 5248*A*a^10*b^26*d^8 + 23936*A*a^12*b^24*d
^8 + 64000*A*a^14*b^22*d^8 + 111104*A*a^16*b^20*d^8 + 130816*A*a^18*b^18*d^8 + 105728*A*a^20*b^16*d^8 + 57856*
A*a^22*b^14*d^8 + 20480*A*a^24*b^12*d^8 + 4224*A*a^26*b^10*d^8 + 384*A*a^28*b^8*d^8 - 256*B*a^11*b^25*d^8 - 20
48*B*a^13*b^23*d^8 - 7168*B*a^15*b^21*d^8 - 14336*B*a^17*b^19*d^8 - 17920*B*a^19*b^17*d^8 - 14336*B*a^21*b^15*
d^8 - 7168*B*a^23*b^13*d^8 - 2048*B*a^25*b^11*d^8 - 256*B*a^27*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) - 128*A^3*a^7*b^26*d^6 - 128*A^3*a^9*b^24*d^6 + 2592*A^3*a^11*b^22*d^6 + 10976*A^3*a^13*b^20*d^6 + 2
0384*A^3*a^15*b^18*d^6 + 20832*A^3*a^17*b^16*d^6 + 11872*A^3*a^19*b^14*d^6 + 3232*A^3*a^21*b^12*d^6 + 96*A^3*a
^23*b^10*d^6 - 96*A^3*a^25*b^8*d^6 + 32*B^3*a^10*b^23*d^6 + 224*B^3*a^12*b^21*d^6 + 672*B^3*a^14*b^19*d^6 + 11
20*B^3*a^16*b^17*d^6 + 1120*B^3*a^18*b^15*d^6 + 672*B^3*a^20*b^13*d^6 + 224*B^3*a^22*b^11*d^6 + 32*B^3*a^24*b^
9*d^6 - 768*A*B^2*a^9*b^24*d^6 - 5088*A*B^2*a^11*b^22*d^6 - 14112*A*B^2*a^13*b^20*d^6 - 20832*A*B^2*a^15*b^18*
d^6 - 16800*A*B^2*a^17*b^16*d^6 - 6048*A*B^2*a^19*b^14*d^6 + 672*A*B^2*a^21*b^12*d^6 + 1248*A*B^2*a^23*b^10*d^
6 + 288*A*B^2*a^25*b^8*d^6 + 768*A^2*B*a^8*b^25*d^6 + 4128*A^2*B*a^10*b^23*d^6 + 7392*A^2*B*a^12*b^21*d^6 + 67
2*A^2*B*a^14*b^19*d^6 - 16800*A^2*B*a^16*b^17*d^6 - 27552*A^2*B*a^18*b^15*d^6 - 20832*A^2*B*a^20*b^13*d^6 - 79
68*A^2*B*a^22*b^11*d^6 - 1248*A^2*B*a^24*b^9*d^6) - (a + b*tan(c + d*x))^(1/2)*(1120*A^4*a^15*b^16*d^5 - 352*A
^4*a^9*b^22*d^5 - 672*A^4*a^11*b^20*d^5 - 224*A^4*a^13*b^18*d^5 - 64*A^4*a^7*b^24*d^5 + 2016*A^4*a^17*b^14*d^5
+ 1568*A^4*a^19*b^12*d^5 + 608*A^4*a^21*b^10*d^5 + 96*A^4*a^23*b^8*d^5 + 32*B^4*a^9*b^22*d^5 + 224*B^4*a^11*b
^20*d^5 + 672*B^4*a^13*b^18*d^5 + 1120*B^4*a^15*b^16*d^5 + 1120*B^4*a^17*b^14*d^5 + 672*B^4*a^19*b^12*d^5 + 22
4*B^4*a^21*b^10*d^5 + 32*B^4*a^23*b^8*d^5 + 256*A^3*B*a^8*b^23*d^5 + 1792*A^3*B*a^10*b^21*d^5 + 5376*A^3*B*a^1
2*b^19*d^5 + 8960*A^3*B*a^14*b^17*d^5 + 8960*A^3*B*a^16*b^15*d^5 + 5376*A^3*B*a^18*b^13*d^5 + 1792*A^3*B*a^20*
b^11*d^5 + 256*A^3*B*a^22*b^9*d^5 + 64*A^2*B^2*a^7*b^24*d^5 + 448*A^2*B^2*a^9*b^22*d^5 + 1344*A^2*B^2*a^11*b^2
0*d^5 + 2240*A^2*B^2*a^13*b^18*d^5 + 2240*A^2*B^2*a^15*b^16*d^5 + 1344*A^2*B^2*a^17*b^14*d^5 + 448*A^2*B^2*a^1
9*b^12*d^5 + 64*A^2*B^2*a^21*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)*1i - ((-(((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)*(2592*A^3*a^11*b^22*d^6 - 128*A^3*a^7*b^26*d^6 - 128*A^3*a^9*b^24*d^6 - ((a + b*
tan(c + d*x))^(1/2)*(256*A^2*a^8*b^26*d^7 + 1472*A^2*a^10*b^24*d^7 + 3712*A^2*a^12*b^22*d^7 + 6272*A^2*a^14*b^
20*d^7 + 9856*A^2*a^16*b^18*d^7 + 14336*A^2*a^18*b^16*d^7 + 15232*A^2*a^20*b^14*d^7 + 10112*A^2*a^22*b^12*d^7
+ 3712*A^2*a^24*b^10*d^7 + 576*A^2*a^26*b^8*d^7 + 832*B^2*a^10*b^24*d^7 + 5504*B^2*a^12*b^22*d^7 + 15232*B^2*a
^14*b^20*d^7 + 22400*B^2*a^16*b^18*d^7 + 17920*B^2*a^18*b^16*d^7 + 6272*B^2*a^20*b^14*d^7 - 896*B^2*a^22*b^12*
d^7 - 1408*B^2*a^24*b^10*d^7 - 320*B^2*a^26*b^8*d^7 - 512*A*B*a^9*b^25*d^7 - 1792*A*B*a^11*b^23*d^7 + 1792*A*B
*a^13*b^21*d^7 + 19712*A*B*a^15*b^19*d^7 + 44800*A*B*a^17*b^17*d^7 + 51968*A*B*a^19*b^15*d^7 + 34048*A*B*a^21*
b^13*d^7 + 12032*A*B*a^23*b^11*d^7 + 1792*A*B*a^25*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)*(512*a^9*b^28*d^9 + 5376*a^11*b^26*d
^9 + 25344*a^13*b^24*d^9 + 70656*a^15*b^22*d^9 + 129024*a^17*b^20*d^9 + 161280*a^19*b^18*d^9 + 139776*a^21*b^1
6*d^9 + 82944*a^23*b^14*d^9 + 32256*a^25*b^12*d^9 + 7424*a^27*b^10*d^9 + 768*a^29*b^8*d^9) + 512*A*a^8*b^28*d^
8 + 5248*A*a^10*b^26*d^8 + 23936*A*a^12*b^24*d^8 + 64000*A*a^14*b^22*d^8 + 111104*A*a^16*b^20*d^8 + 130816*A*a
^18*b^18*d^8 + 105728*A*a^20*b^16*d^8 + 57856*A*a^22*b^14*d^8 + 20480*A*a^24*b^12*d^8 + 4224*A*a^26*b^10*d^8 +
384*A*a^28*b^8*d^8 - 256*B*a^11*b^25*d^8 - 2048*B*a^13*b^23*d^8 - 7168*B*a^15*b^21*d^8 - 14336*B*a^17*b^19*d^
8 - 17920*B*a^19*b^17*d^8 - 14336*B*a^21*b^15*d^8 - 7168*B*a^23*b^13*d^8 - 2048*B*a^25*b^11*d^8 - 256*B*a^27*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) + 10976*A^3*a^13*b^20*d^6 + 20384*A^3*a^15*b^18*d^6 +
20832*A^3*a^17*b^16*d^6 + 11872*A^3*a^19*b^14*d^6 + 3232*A^3*a^21*b^12*d^6 + 96*A^3*a^23*b^10*d^6 - 96*A^3*a^2
5*b^8*d^6 + 32*B^3*a^10*b^23*d^6 + 224*B^3*a^12*b^21*d^6 + 672*B^3*a^14*b^19*d^6 + 1120*B^3*a^16*b^17*d^6 + 11
20*B^3*a^18*b^15*d^6 + 672*B^3*a^20*b^13*d^6 + 224*B^3*a^22*b^11*d^6 + 32*B^3*a^24*b^9*d^6 - 768*A*B^2*a^9*b^2
4*d^6 - 5088*A*B^2*a^11*b^22*d^6 - 14112*A*B^2*a^13*b^20*d^6 - 20832*A*B^2*a^15*b^18*d^6 - 16800*A*B^2*a^17*b^
16*d^6 - 6048*A*B^2*a^19*b^14*d^6 + 672*A*B^2*a^21*b^12*d^6 + 1248*A*B^2*a^23*b^10*d^6 + 288*A*B^2*a^25*b^8*d^
6 + 768*A^2*B*a^8*b^25*d^6 + 4128*A^2*B*a^10*b^23*d^6 + 7392*A^2*B*a^12*b^21*d^6 + 672*A^2*B*a^14*b^19*d^6 - 1
6800*A^2*B*a^16*b^17*d^6 - 27552*A^2*B*a^18*b^15*d^6 - 20832*A^2*B*a^20*b^13*d^6 - 7968*A^2*B*a^22*b^11*d^6 -
1248*A^2*B*a^24*b^9*d^6) + (a + b*tan(c + d*x))^(1/2)*(1120*A^4*a^15*b^16*d^5 - 352*A^4*a^9*b^22*d^5 - 672*A^4
*a^11*b^20*d^5 - 224*A^4*a^13*b^18*d^5 - 64*A^4*a^7*b^24*d^5 + 2016*A^4*a^17*b^14*d^5 + 1568*A^4*a^19*b^12*d^5
+ 608*A^4*a^21*b^10*d^5 + 96*A^4*a^23*b^8*d^5 + 32*B^4*a^9*b^22*d^5 + 224*B^4*a^11*b^20*d^5 + 672*B^4*a^13*b^
18*d^5 + 1120*B^4*a^15*b^16*d^5 + 1120*B^4*a^17*b^14*d^5 + 672*B^4*a^19*b^12*d^5 + 224*B^4*a^21*b^10*d^5 + 32*
B^4*a^23*b^8*d^5 + 256*A^3*B*a^8*b^23*d^5 + 1792*A^3*B*a^10*b^21*d^5 + 5376*A^3*B*a^12*b^19*d^5 + 8960*A^3*B*a
^14*b^17*d^5 + 8960*A^3*B*a^16*b^15*d^5 + 5376*A^3*B*a^18*b^13*d^5 + 1792*A^3*B*a^20*b^11*d^5 + 256*A^3*B*a^22
*b^9*d^5 + 64*A^2*B^2*a^7*b^24*d^5 + 448*A^2*B^2*a^9*b^22*d^5 + 1344*A^2*B^2*a^11*b^20*d^5 + 2240*A^2*B^2*a^13
*b^18*d^5 + 2240*A^2*B^2*a^15*b^16*d^5 + 1344*A^2*B^2*a^17*b^14*d^5 + 448*A^2*B^2*a^19*b^12*d^5 + 64*A^2*B^2*a
^21*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)/(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)*1i)/(((-(((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)*(256*A^2*a^8*b^26*d^7 + 1472*A^2*a^10*b^24*d^7 + 3712*A^2*a^12*b^22*d^7 + 62
72*A^2*a^14*b^20*d^7 + 9856*A^2*a^16*b^18*d^7 + 14336*A^2*a^18*b^16*d^7 + 15232*A^2*a^20*b^14*d^7 + 10112*A^2*
a^22*b^12*d^7 + 3712*A^2*a^24*b^10*d^7 + 576*A^2*a^26*b^8*d^7 + 832*B^2*a^10*b^24*d^7 + 5504*B^2*a^12*b^22*d^7
+ 15232*B^2*a^14*b^20*d^7 + 22400*B^2*a^16*b^18*d^7 + 17920*B^2*a^18*b^16*d^7 + 6272*B^2*a^20*b^14*d^7 - 896*
B^2*a^22*b^12*d^7 - 1408*B^2*a^24*b^10*d^7 - 320*B^2*a^26*b^8*d^7 - 512*A*B*a^9*b^25*d^7 - 1792*A*B*a^11*b^23*
d^7 + 1792*A*B*a^13*b^21*d^7 + 19712*A*B*a^15*b^19*d^7 + 44800*A*B*a^17*b^17*d^7 + 51968*A*B*a^19*b^15*d^7 + 3
4048*A*B*a^21*b^13*d^7 + 12032*A*B*a^23*b^11*d^7 + 1792*A*B*a^25*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)*(512*A*a^8*b^28*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)*(
512*a^9*b^28*d^9 + 5376*a^11*b^26*d^9 + 25344*a^13*b^24*d^9 + 70656*a^15*b^22*d^9 + 129024*a^17*b^20*d^9 + 161
280*a^19*b^18*d^9 + 139776*a^21*b^16*d^9 + 82944*a^23*b^14*d^9 + 32256*a^25*b^12*d^9 + 7424*a^27*b^10*d^9 + 76
8*a^29*b^8*d^9) + 5248*A*a^10*b^26*d^8 + 23936*A*a^12*b^24*d^8 + 64000*A*a^14*b^22*d^8 + 111104*A*a^16*b^20*d^
8 + 130816*A*a^18*b^18*d^8 + 105728*A*a^20*b^16*d^8 + 57856*A*a^22*b^14*d^8 + 20480*A*a^24*b^12*d^8 + 4224*A*a
^26*b^10*d^8 + 384*A*a^28*b^8*d^8 - 256*B*a^11*b^25*d^8 - 2048*B*a^13*b^23*d^8 - 7168*B*a^15*b^21*d^8 - 14336*
B*a^17*b^19*d^8 - 17920*B*a^19*b^17*d^8 - 14336*B*a^21*b^15*d^8 - 7168*B*a^23*b^13*d^8 - 2048*B*a^25*b^11*d^8
- 256*B*a^27*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) - 128*A^3*a^7*b^26*d^6 - 128*A^3*a^9*b^2
4*d^6 + 2592*A^3*a^11*b^22*d^6 + 10976*A^3*a^13*b^20*d^6 + 20384*A^3*a^15*b^18*d^6 + 20832*A^3*a^17*b^16*d^6 +
11872*A^3*a^19*b^14*d^6 + 3232*A^3*a^21*b^12*d^6 + 96*A^3*a^23*b^10*d^6 - 96*A^3*a^25*b^8*d^6 + 32*B^3*a^10*b
^23*d^6 + 224*B^3*a^12*b^21*d^6 + 672*B^3*a^14*b^19*d^6 + 1120*B^3*a^16*b^17*d^6 + 1120*B^3*a^18*b^15*d^6 + 67
2*B^3*a^20*b^13*d^6 + 224*B^3*a^22*b^11*d^6 + 32*B^3*a^24*b^9*d^6 - 768*A*B^2*a^9*b^24*d^6 - 5088*A*B^2*a^11*b
^22*d^6 - 14112*A*B^2*a^13*b^20*d^6 - 20832*A*B^2*a^15*b^18*d^6 - 16800*A*B^2*a^17*b^16*d^6 - 6048*A*B^2*a^19*
b^14*d^6 + 672*A*B^2*a^21*b^12*d^6 + 1248*A*B^2*a^23*b^10*d^6 + 288*A*B^2*a^25*b^8*d^6 + 768*A^2*B*a^8*b^25*d^
6 + 4128*A^2*B*a^10*b^23*d^6 + 7392*A^2*B*a^12*b^21*d^6 + 672*A^2*B*a^14*b^19*d^6 - 16800*A^2*B*a^16*b^17*d^6
- 27552*A^2*B*a^18*b^15*d^6 - 20832*A^2*B*a^20*b^13*d^6 - 7968*A^2*B*a^22*b^11*d^6 - 1248*A^2*B*a^24*b^9*d^6)
- (a + b*tan(c + d*x))^(1/2)*(1120*A^4*a^15*b^16*d^5 - 352*A^4*a^9*b^22*d^5 - 672*A^4*a^11*b^20*d^5 - 224*A^4*
a^13*b^18*d^5 - 64*A^4*a^7*b^24*d^5 + 2016*A^4*a^17*b^14*d^5 + 1568*A^4*a^19*b^12*d^5 + 608*A^4*a^21*b^10*d^5
+ 96*A^4*a^23*b^8*d^5 + 32*B^4*a^9*b^22*d^5 + 224*B^4*a^11*b^20*d^5 + 672*B^4*a^13*b^18*d^5 + 1120*B^4*a^15*b^
16*d^5 + 1120*B^4*a^17*b^14*d^5 + 672*B^4*a^19*b^12*d^5 + 224*B^4*a^21*b^10*d^5 + 32*B^4*a^23*b^8*d^5 + 256*A^
3*B*a^8*b^23*d^5 + 1792*A^3*B*a^10*b^21*d^5 + 5376*A^3*B*a^12*b^19*d^5 + 8960*A^3*B*a^14*b^17*d^5 + 8960*A^3*B
*a^16*b^15*d^5 + 5376*A^3*B*a^18*b^13*d^5 + 1792*A^3*B*a^20*b^11*d^5 + 256*A^3*B*a^22*b^9*d^5 + 64*A^2*B^2*a^7
*b^24*d^5 + 448*A^2*B^2*a^9*b^22*d^5 + 1344*A^2*B^2*a^11*b^20*d^5 + 2240*A^2*B^2*a^13*b^18*d^5 + 2240*A^2*B^2*
a^15*b^16*d^5 + 1344*A^2*B^2*a^17*b^14*d^5 + 448*A^2*B^2*a^19*b^12*d^5 + 64*A^2*B^2*a^21*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) + ((-(((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)*(2592*A^3*a^11*b^22*d^6
- 128*A^3*a^7*b^26*d^6 - 128*A^3*a^9*b^24*d^6 - ((a + b*tan(c + d*x))^(1/2)*(256*A^2*a^8*b^26*d^7 + 1472*A^2*
a^10*b^24*d^7 + 3712*A^2*a^12*b^22*d^7 + 6272*A^2*a^14*b^20*d^7 + 9856*A^2*a^16*b^18*d^7 + 14336*A^2*a^18*b^16
*d^7 + 15232*A^2*a^20*b^14*d^7 + 10112*A^2*a^22*b^12*d^7 + 3712*A^2*a^24*b^10*d^7 + 576*A^2*a^26*b^8*d^7 + 832
*B^2*a^10*b^24*d^7 + 5504*B^2*a^12*b^22*d^7 + 15232*B^2*a^14*b^20*d^7 + 22400*B^2*a^16*b^18*d^7 + 17920*B^2*a^
18*b^16*d^7 + 6272*B^2*a^20*b^14*d^7 - 896*B^2*a^22*b^12*d^7 - 1408*B^2*a^24*b^10*d^7 - 320*B^2*a^26*b^8*d^7 -
512*A*B*a^9*b^25*d^7 - 1792*A*B*a^11*b^23*d^7 + 1792*A*B*a^13*b^21*d^7 + 19712*A*B*a^15*b^19*d^7 + 44800*A*B*
a^17*b^17*d^7 + 51968*A*B*a^19*b^15*d^7 + 34048*A*B*a^21*b^13*d^7 + 12032*A*B*a^23*b^11*d^7 + 1792*A*B*a^25*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)*(512*a^9*b^28*d^9 + 5376*a^11*b^26*d^9 + 25344*a^13*b^24*d^9 + 70656*a^15*b^22*d^9 + 1290
24*a^17*b^20*d^9 + 161280*a^19*b^18*d^9 + 139776*a^21*b^16*d^9 + 82944*a^23*b^14*d^9 + 32256*a^25*b^12*d^9 + 7
424*a^27*b^10*d^9 + 768*a^29*b^8*d^9) + 512*A*a^8*b^28*d^8 + 5248*A*a^10*b^26*d^8 + 23936*A*a^12*b^24*d^8 + 64
000*A*a^14*b^22*d^8 + 111104*A*a^16*b^20*d^8 + 130816*A*a^18*b^18*d^8 + 105728*A*a^20*b^16*d^8 + 57856*A*a^22*
b^14*d^8 + 20480*A*a^24*b^12*d^8 + 4224*A*a^26*b^10*d^8 + 384*A*a^28*b^8*d^8 - 256*B*a^11*b^25*d^8 - 2048*B*a^
13*b^23*d^8 - 7168*B*a^15*b^21*d^8 - 14336*B*a^17*b^19*d^8 - 17920*B*a^19*b^17*d^8 - 14336*B*a^21*b^15*d^8 - 7
168*B*a^23*b^13*d^8 - 2048*B*a^25*b^11*d^8 - 256*B*a^27*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) + 10976*A^3*a^13*b^20*d^6 + 20384*A^3*a^15*b^18*d^6 + 20832*A^3*a^17*b^16*d^6 + 11872*A^3*a^19*b^14*d^6 + 3
232*A^3*a^21*b^12*d^6 + 96*A^3*a^23*b^10*d^6 - 96*A^3*a^25*b^8*d^6 + 32*B^3*a^10*b^23*d^6 + 224*B^3*a^12*b^21*
d^6 + 672*B^3*a^14*b^19*d^6 + 1120*B^3*a^16*b^17*d^6 + 1120*B^3*a^18*b^15*d^6 + 672*B^3*a^20*b^13*d^6 + 224*B^
3*a^22*b^11*d^6 + 32*B^3*a^24*b^9*d^6 - 768*A*B^2*a^9*b^24*d^6 - 5088*A*B^2*a^11*b^22*d^6 - 14112*A*B^2*a^13*b
^20*d^6 - 20832*A*B^2*a^15*b^18*d^6 - 16800*A*B^2*a^17*b^16*d^6 - 6048*A*B^2*a^19*b^14*d^6 + 672*A*B^2*a^21*b^
12*d^6 + 1248*A*B^2*a^23*b^10*d^6 + 288*A*B^2*a^25*b^8*d^6 + 768*A^2*B*a^8*b^25*d^6 + 4128*A^2*B*a^10*b^23*d^6
+ 7392*A^2*B*a^12*b^21*d^6 + 672*A^2*B*a^14*b^19*d^6 - 16800*A^2*B*a^16*b^17*d^6 - 27552*A^2*B*a^18*b^15*d^6
- 20832*A^2*B*a^20*b^13*d^6 - 7968*A^2*B*a^22*b^11*d^6 - 1248*A^2*B*a^24*b^9*d^6) + (a + b*tan(c + d*x))^(1/2)
*(1120*A^4*a^15*b^16*d^5 - 352*A^4*a^9*b^22*d^5 - 672*A^4*a^11*b^20*d^5 - 224*A^4*a^13*b^18*d^5 - 64*A^4*a^7*b
^24*d^5 + 2016*A^4*a^17*b^14*d^5 + 1568*A^4*a^19*b^12*d^5 + 608*A^4*a^21*b^10*d^5 + 96*A^4*a^23*b^8*d^5 + 32*B
^4*a^9*b^22*d^5 + 224*B^4*a^11*b^20*d^5 + 672*B^4*a^13*b^18*d^5 + 1120*B^4*a^15*b^16*d^5 + 1120*B^4*a^17*b^14*
d^5 + 672*B^4*a^19*b^12*d^5 + 224*B^4*a^21*b^10*d^5 + 32*B^4*a^23*b^8*d^5 + 256*A^3*B*a^8*b^23*d^5 + 1792*A^3*
B*a^10*b^21*d^5 + 5376*A^3*B*a^12*b^19*d^5 + 8960*A^3*B*a^14*b^17*d^5 + 8960*A^3*B*a^16*b^15*d^5 + 5376*A^3*B*
a^18*b^13*d^5 + 1792*A^3*B*a^20*b^11*d^5 + 256*A^3*B*a^22*b^9*d^5 + 64*A^2*B^2*a^7*b^24*d^5 + 448*A^2*B^2*a^9*
b^22*d^5 + 1344*A^2*B^2*a^11*b^20*d^5 + 2240*A^2*B^2*a^13*b^18*d^5 + 2240*A^2*B^2*a^15*b^16*d^5 + 1344*A^2*B^2
*a^17*b^14*d^5 + 448*A^2*B^2*a^19*b^12*d^5 + 64*A^2*B^2*a^21*b^10*d^5))*(-(((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) + 64*A*B^4*a^8*b^22*d^4 + 448*A*B^4*a^10*b^20*d^4 + 1344*A*B^4*a^12*b^18*d^4 + 2240*A*B^4*a^14*b^16*d
^4 + 2240*A*B^4*a^16*b^14*d^4 + 1344*A*B^4*a^18*b^12*d^4 + 448*A*B^4*a^20*b^10*d^4 + 64*A*B^4*a^22*b^8*d^4 - 6
4*A^4*B*a^7*b^23*d^4 - 448*A^4*B*a^9*b^21*d^4 - 1344*A^4*B*a^11*b^19*d^4 - 2240*A^4*B*a^13*b^17*d^4 - 2240*A^4
*B*a^15*b^15*d^4 - 1344*A^4*B*a^17*b^13*d^4 - 448*A^4*B*a^19*b^11*d^4 - 64*A^4*B*a^21*b^9*d^4 - 64*A^2*B^3*a^7
*b^23*d^4 - 448*A^2*B^3*a^9*b^21*d^4 - 1344*A^2*B^3*a^11*b^19*d^4 - 2240*A^2*B^3*a^13*b^17*d^4 - 2240*A^2*B^3*
a^15*b^15*d^4 - 1344*A^2*B^3*a^17*b^13*d^4 - 448*A^2*B^3*a^19*b^11*d^4 - 64*A^2*B^3*a^21*b^9*d^4 + 64*A^3*B^2*
a^8*b^22*d^4 + 448*A^3*B^2*a^10*b^20*d^4 + 1344*A^3*B^2*a^12*b^18*d^4 + 2240*A^3*B^2*a^14*b^16*d^4 + 2240*A^3*
B^2*a^16*b^14*d^4 + 1344*A^3*B^2*a^18*b^12*d^4 + 448*A^3*B^2*a^20*b^10*d^4 + 64*A^3*B^2*a^22*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(-((((((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 + 4
8*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*ta
n(c + d*x))^(1/2)*(256*A^2*a^8*b^26*d^7 + 1472*A^2*a^10*b^24*d^7 + 3712*A^2*a^12*b^22*d^7 + 6272*A^2*a^14*b^20
*d^7 + 9856*A^2*a^16*b^18*d^7 + 14336*A^2*a^18*b^16*d^7 + 15232*A^2*a^20*b^14*d^7 + 10112*A^2*a^22*b^12*d^7 +
3712*A^2*a^24*b^10*d^7 + 576*A^2*a^26*b^8*d^7 + 832*B^2*a^10*b^24*d^7 + 5504*B^2*a^12*b^22*d^7 + 15232*B^2*a^1
4*b^20*d^7 + 22400*B^2*a^16*b^18*d^7 + 17920*B^2*a^18*b^16*d^7 + 6272*B^2*a^20*b^14*d^7 - 896*B^2*a^22*b^12*d^
7 - 1408*B^2*a^24*b^10*d^7 - 320*B^2*a^26*b^8*d^7 - 512*A*B*a^9*b^25*d^7 - 1792*A*B*a^11*b^23*d^7 + 1792*A*B*a
^13*b^21*d^7 + 19712*A*B*a^15*b^19*d^7 + 44800*A*B*a^17*b^17*d^7 + 51968*A*B*a^19*b^15*d^7 + 34048*A*B*a^21*b^
13*d^7 + 12032*A*B*a^23*b^11*d^7 + 1792*A*B*a^25*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)*(512
*A*a^8*b^28*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)*(512*a^9*b^28*d^9 +
5376*a^11*b^26*d^9 + 25344*a^13*b^24*d^9 + 70656*a^15*b^22*d^9 + 129024*a^17*b^20*d^9 + 161280*a^19*b^18*d^9
+ 139776*a^21*b^16*d^9 + 82944*a^23*b^14*d^9 + 32256*a^25*b^12*d^9 + 7424*a^27*b^10*d^9 + 768*a^29*b^8*d^9) +
5248*A*a^10*b^26*d^8 + 23936*A*a^12*b^24*d^8 + 64000*A*a^14*b^22*d^8 + 111104*A*a^16*b^20*d^8 + 130816*A*a^18*
b^18*d^8 + 105728*A*a^20*b^16*d^8 + 57856*A*a^22*b^14*d^8 + 20480*A*a^24*b^12*d^8 + 4224*A*a^26*b^10*d^8 + 384
*A*a^28*b^8*d^8 - 256*B*a^11*b^25*d^8 - 2048*B*a^13*b^23*d^8 - 7168*B*a^15*b^21*d^8 - 14336*B*a^17*b^19*d^8 -
17920*B*a^19*b^17*d^8 - 14336*B*a^21*b^15*d^8 - 7168*B*a^23*b^13*d^8 - 2048*B*a^25*b^11*d^8 - 256*B*a^27*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) - 128*A^3*a^7*b^26*d^6 - 128*A^3*a^9*b^24*d^6 + 2592*A^3*a^
11*b^22*d^6 + 10976*A^3*a^13*b^20*d^6 + 20384*A^3*a^15*b^18*d^6 + 20832*A^3*a^17*b^16*d^6 + 11872*A^3*a^19*b^1
4*d^6 + 3232*A^3*a^21*b^12*d^6 + 96*A^3*a^23*b^10*d^6 - 96*A^3*a^25*b^8*d^6 + 32*B^3*a^10*b^23*d^6 + 224*B^3*a
^12*b^21*d^6 + 672*B^3*a^14*b^19*d^6 + 1120*B^3*a^16*b^17*d^6 + 1120*B^3*a^18*b^15*d^6 + 672*B^3*a^20*b^13*d^6
+ 224*B^3*a^22*b^11*d^6 + 32*B^3*a^24*b^9*d^6 - 768*A*B^2*a^9*b^24*d^6 - 5088*A*B^2*a^11*b^22*d^6 - 14112*A*B
^2*a^13*b^20*d^6 - 20832*A*B^2*a^15*b^18*d^6 - 16800*A*B^2*a^17*b^16*d^6 - 6048*A*B^2*a^19*b^14*d^6 + 672*A*B^
2*a^21*b^12*d^6 + 1248*A*B^2*a^23*b^10*d^6 + 288*A*B^2*a^25*b^8*d^6 + 768*A^2*B*a^8*b^25*d^6 + 4128*A^2*B*a^10
*b^23*d^6 + 7392*A^2*B*a^12*b^21*d^6 + 672*A^2*B*a^14*b^19*d^6 - 16800*A^2*B*a^16*b^17*d^6 - 27552*A^2*B*a^18*
b^15*d^6 - 20832*A^2*B*a^20*b^13*d^6 - 7968*A^2*B*a^22*b^11*d^6 - 1248*A^2*B*a^24*b^9*d^6) - (a + b*tan(c + d*
x))^(1/2)*(1120*A^4*a^15*b^16*d^5 - 352*A^4*a^9*b^22*d^5 - 672*A^4*a^11*b^20*d^5 - 224*A^4*a^13*b^18*d^5 - 64*
A^4*a^7*b^24*d^5 + 2016*A^4*a^17*b^14*d^5 + 1568*A^4*a^19*b^12*d^5 + 608*A^4*a^21*b^10*d^5 + 96*A^4*a^23*b^8*d
^5 + 32*B^4*a^9*b^22*d^5 + 224*B^4*a^11*b^20*d^5 + 672*B^4*a^13*b^18*d^5 + 1120*B^4*a^15*b^16*d^5 + 1120*B^4*a
^17*b^14*d^5 + 672*B^4*a^19*b^12*d^5 + 224*B^4*a^21*b^10*d^5 + 32*B^4*a^23*b^8*d^5 + 256*A^3*B*a^8*b^23*d^5 +
1792*A^3*B*a^10*b^21*d^5 + 5376*A^3*B*a^12*b^19*d^5 + 8960*A^3*B*a^14*b^17*d^5 + 8960*A^3*B*a^16*b^15*d^5 + 53
76*A^3*B*a^18*b^13*d^5 + 1792*A^3*B*a^20*b^11*d^5 + 256*A^3*B*a^22*b^9*d^5 + 64*A^2*B^2*a^7*b^24*d^5 + 448*A^2
*B^2*a^9*b^22*d^5 + 1344*A^2*B^2*a^11*b^20*d^5 + 2240*A^2*B^2*a^13*b^18*d^5 + 2240*A^2*B^2*a^15*b^16*d^5 + 134
4*A^2*B^2*a^17*b^14*d^5 + 448*A^2*B^2*a^19*b^12*d^5 + 64*A^2*B^2*a^21*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)*1i - (((((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)*(2592*A^3*a^11*b^22*d^6 - 128*A^3*a^7*b^2
6*d^6 - 128*A^3*a^9*b^24*d^6 - ((a + b*tan(c + d*x))^(1/2)*(256*A^2*a^8*b^26*d^7 + 1472*A^2*a^10*b^24*d^7 + 37
12*A^2*a^12*b^22*d^7 + 6272*A^2*a^14*b^20*d^7 + 9856*A^2*a^16*b^18*d^7 + 14336*A^2*a^18*b^16*d^7 + 15232*A^2*a
^20*b^14*d^7 + 10112*A^2*a^22*b^12*d^7 + 3712*A^2*a^24*b^10*d^7 + 576*A^2*a^26*b^8*d^7 + 832*B^2*a^10*b^24*d^7
+ 5504*B^2*a^12*b^22*d^7 + 15232*B^2*a^14*b^20*d^7 + 22400*B^2*a^16*b^18*d^7 + 17920*B^2*a^18*b^16*d^7 + 6272
*B^2*a^20*b^14*d^7 - 896*B^2*a^22*b^12*d^7 - 1408*B^2*a^24*b^10*d^7 - 320*B^2*a^26*b^8*d^7 - 512*A*B*a^9*b^25*
d^7 - 1792*A*B*a^11*b^23*d^7 + 1792*A*B*a^13*b^21*d^7 + 19712*A*B*a^15*b^19*d^7 + 44800*A*B*a^17*b^17*d^7 + 51
968*A*B*a^19*b^15*d^7 + 34048*A*B*a^21*b^13*d^7 + 12032*A*B*a^23*b^11*d^7 + 1792*A*B*a^25*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)
*(512*a^9*b^28*d^9 + 5376*a^11*b^26*d^9 + 25344*a^13*b^24*d^9 + 70656*a^15*b^22*d^9 + 129024*a^17*b^20*d^9 + 1
61280*a^19*b^18*d^9 + 139776*a^21*b^16*d^9 + 82944*a^23*b^14*d^9 + 32256*a^25*b^12*d^9 + 7424*a^27*b^10*d^9 +
768*a^29*b^8*d^9) + 512*A*a^8*b^28*d^8 + 5248*A*a^10*b^26*d^8 + 23936*A*a^12*b^24*d^8 + 64000*A*a^14*b^22*d^8
+ 111104*A*a^16*b^20*d^8 + 130816*A*a^18*b^18*d^8 + 105728*A*a^20*b^16*d^8 + 57856*A*a^22*b^14*d^8 + 20480*A*a
^24*b^12*d^8 + 4224*A*a^26*b^10*d^8 + 384*A*a^28*b^8*d^8 - 256*B*a^11*b^25*d^8 - 2048*B*a^13*b^23*d^8 - 7168*B
*a^15*b^21*d^8 - 14336*B*a^17*b^19*d^8 - 17920*B*a^19*b^17*d^8 - 14336*B*a^21*b^15*d^8 - 7168*B*a^23*b^13*d^8
- 2048*B*a^25*b^11*d^8 - 256*B*a^27*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) + 10976*A^3*a^13*b
^20*d^6 + 20384*A^3*a^15*b^18*d^6 + 20832*A^3*a^17*b^16*d^6 + 11872*A^3*a^19*b^14*d^6 + 3232*A^3*a^21*b^12*d^6
+ 96*A^3*a^23*b^10*d^6 - 96*A^3*a^25*b^8*d^6 + 32*B^3*a^10*b^23*d^6 + 224*B^3*a^12*b^21*d^6 + 672*B^3*a^14*b^
19*d^6 + 1120*B^3*a^16*b^17*d^6 + 1120*B^3*a^18*b^15*d^6 + 672*B^3*a^20*b^13*d^6 + 224*B^3*a^22*b^11*d^6 + 32*
B^3*a^24*b^9*d^6 - 768*A*B^2*a^9*b^24*d^6 - 5088*A*B^2*a^11*b^22*d^6 - 14112*A*B^2*a^13*b^20*d^6 - 20832*A*B^2
*a^15*b^18*d^6 - 16800*A*B^2*a^17*b^16*d^6 - 6048*A*B^2*a^19*b^14*d^6 + 672*A*B^2*a^21*b^12*d^6 + 1248*A*B^2*a
^23*b^10*d^6 + 288*A*B^2*a^25*b^8*d^6 + 768*A^2*B*a^8*b^25*d^6 + 4128*A^2*B*a^10*b^23*d^6 + 7392*A^2*B*a^12*b^
21*d^6 + 672*A^2*B*a^14*b^19*d^6 - 16800*A^2*B*a^16*b^17*d^6 - 27552*A^2*B*a^18*b^15*d^6 - 20832*A^2*B*a^20*b^
13*d^6 - 7968*A^2*B*a^22*b^11*d^6 - 1248*A^2*B*a^24*b^9*d^6) + (a + b*tan(c + d*x))^(1/2)*(1120*A^4*a^15*b^16*
d^5 - 352*A^4*a^9*b^22*d^5 - 672*A^4*a^11*b^20*d^5 - 224*A^4*a^13*b^18*d^5 - 64*A^4*a^7*b^24*d^5 + 2016*A^4*a^
17*b^14*d^5 + 1568*A^4*a^19*b^12*d^5 + 608*A^4*a^21*b^10*d^5 + 96*A^4*a^23*b^8*d^5 + 32*B^4*a^9*b^22*d^5 + 224
*B^4*a^11*b^20*d^5 + 672*B^4*a^13*b^18*d^5 + 1120*B^4*a^15*b^16*d^5 + 1120*B^4*a^17*b^14*d^5 + 672*B^4*a^19*b^
12*d^5 + 224*B^4*a^21*b^10*d^5 + 32*B^4*a^23*b^8*d^5 + 256*A^3*B*a^8*b^23*d^5 + 1792*A^3*B*a^10*b^21*d^5 + 537
6*A^3*B*a^12*b^19*d^5 + 8960*A^3*B*a^14*b^17*d^5 + 8960*A^3*B*a^16*b^15*d^5 + 5376*A^3*B*a^18*b^13*d^5 + 1792*
A^3*B*a^20*b^11*d^5 + 256*A^3*B*a^22*b^9*d^5 + 64*A^2*B^2*a^7*b^24*d^5 + 448*A^2*B^2*a^9*b^22*d^5 + 1344*A^2*B
^2*a^11*b^20*d^5 + 2240*A^2*B^2*a^13*b^18*d^5 + 2240*A^2*B^2*a^15*b^16*d^5 + 1344*A^2*B^2*a^17*b^14*d^5 + 448*
A^2*B^2*a^19*b^12*d^5 + 64*A^2*B^2*a^21*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)*1i)/((((((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)*(256*A^2*a^8*b^26*d^7 + 1472*A^2*a^10*b^24
*d^7 + 3712*A^2*a^12*b^22*d^7 + 6272*A^2*a^14*b^20*d^7 + 9856*A^2*a^16*b^18*d^7 + 14336*A^2*a^18*b^16*d^7 + 15
232*A^2*a^20*b^14*d^7 + 10112*A^2*a^22*b^12*d^7 + 3712*A^2*a^24*b^10*d^7 + 576*A^2*a^26*b^8*d^7 + 832*B^2*a^10
*b^24*d^7 + 5504*B^2*a^12*b^22*d^7 + 15232*B^2*a^14*b^20*d^7 + 22400*B^2*a^16*b^18*d^7 + 17920*B^2*a^18*b^16*d
^7 + 6272*B^2*a^20*b^14*d^7 - 896*B^2*a^22*b^12*d^7 - 1408*B^2*a^24*b^10*d^7 - 320*B^2*a^26*b^8*d^7 - 512*A*B*
a^9*b^25*d^7 - 1792*A*B*a^11*b^23*d^7 + 1792*A*B*a^13*b^21*d^7 + 19712*A*B*a^15*b^19*d^7 + 44800*A*B*a^17*b^17
*d^7 + 51968*A*B*a^19*b^15*d^7 + 34048*A*B*a^21*b^13*d^7 + 12032*A*B*a^23*b^11*d^7 + 1792*A*B*a^25*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)*(512*A*a^8*b^28*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)*(512*a^9*b^28*d^9 + 5376*a^11*b^26*d^9 + 25344*a^13*b^24*d^9 + 70656*a^15*b^22*
d^9 + 129024*a^17*b^20*d^9 + 161280*a^19*b^18*d^9 + 139776*a^21*b^16*d^9 + 82944*a^23*b^14*d^9 + 32256*a^25*b^
12*d^9 + 7424*a^27*b^10*d^9 + 768*a^29*b^8*d^9) + 5248*A*a^10*b^26*d^8 + 23936*A*a^12*b^24*d^8 + 64000*A*a^14*
b^22*d^8 + 111104*A*a^16*b^20*d^8 + 130816*A*a^18*b^18*d^8 + 105728*A*a^20*b^16*d^8 + 57856*A*a^22*b^14*d^8 +
20480*A*a^24*b^12*d^8 + 4224*A*a^26*b^10*d^8 + 384*A*a^28*b^8*d^8 - 256*B*a^11*b^25*d^8 - 2048*B*a^13*b^23*d^8
- 7168*B*a^15*b^21*d^8 - 14336*B*a^17*b^19*d^8 - 17920*B*a^19*b^17*d^8 - 14336*B*a^21*b^15*d^8 - 7168*B*a^23*
b^13*d^8 - 2048*B*a^25*b^11*d^8 - 256*B*a^27*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) - 128*A^3
*a^7*b^26*d^6 - 128*A^3*a^9*b^24*d^6 + 2592*A^3*a^11*b^22*d^6 + 10976*A^3*a^13*b^20*d^6 + 20384*A^3*a^15*b^18*
d^6 + 20832*A^3*a^17*b^16*d^6 + 11872*A^3*a^19*b^14*d^6 + 3232*A^3*a^21*b^12*d^6 + 96*A^3*a^23*b^10*d^6 - 96*A
^3*a^25*b^8*d^6 + 32*B^3*a^10*b^23*d^6 + 224*B^3*a^12*b^21*d^6 + 672*B^3*a^14*b^19*d^6 + 1120*B^3*a^16*b^17*d^
6 + 1120*B^3*a^18*b^15*d^6 + 672*B^3*a^20*b^13*d^6 + 224*B^3*a^22*b^11*d^6 + 32*B^3*a^24*b^9*d^6 - 768*A*B^2*a
^9*b^24*d^6 - 5088*A*B^2*a^11*b^22*d^6 - 14112*A*B^2*a^13*b^20*d^6 - 20832*A*B^2*a^15*b^18*d^6 - 16800*A*B^2*a
^17*b^16*d^6 - 6048*A*B^2*a^19*b^14*d^6 + 672*A*B^2*a^21*b^12*d^6 + 1248*A*B^2*a^23*b^10*d^6 + 288*A*B^2*a^25*
b^8*d^6 + 768*A^2*B*a^8*b^25*d^6 + 4128*A^2*B*a^10*b^23*d^6 + 7392*A^2*B*a^12*b^21*d^6 + 672*A^2*B*a^14*b^19*d
^6 - 16800*A^2*B*a^16*b^17*d^6 - 27552*A^2*B*a^18*b^15*d^6 - 20832*A^2*B*a^20*b^13*d^6 - 7968*A^2*B*a^22*b^11*
d^6 - 1248*A^2*B*a^24*b^9*d^6) - (a + b*tan(c + d*x))^(1/2)*(1120*A^4*a^15*b^16*d^5 - 352*A^4*a^9*b^22*d^5 - 6
72*A^4*a^11*b^20*d^5 - 224*A^4*a^13*b^18*d^5 - 64*A^4*a^7*b^24*d^5 + 2016*A^4*a^17*b^14*d^5 + 1568*A^4*a^19*b^
12*d^5 + 608*A^4*a^21*b^10*d^5 + 96*A^4*a^23*b^8*d^5 + 32*B^4*a^9*b^22*d^5 + 224*B^4*a^11*b^20*d^5 + 672*B^4*a
^13*b^18*d^5 + 1120*B^4*a^15*b^16*d^5 + 1120*B^4*a^17*b^14*d^5 + 672*B^4*a^19*b^12*d^5 + 224*B^4*a^21*b^10*d^5
+ 32*B^4*a^23*b^8*d^5 + 256*A^3*B*a^8*b^23*d^5 + 1792*A^3*B*a^10*b^21*d^5 + 5376*A^3*B*a^12*b^19*d^5 + 8960*A
^3*B*a^14*b^17*d^5 + 8960*A^3*B*a^16*b^15*d^5 + 5376*A^3*B*a^18*b^13*d^5 + 1792*A^3*B*a^20*b^11*d^5 + 256*A^3*
B*a^22*b^9*d^5 + 64*A^2*B^2*a^7*b^24*d^5 + 448*A^2*B^2*a^9*b^22*d^5 + 1344*A^2*B^2*a^11*b^20*d^5 + 2240*A^2*B^
2*a^13*b^18*d^5 + 2240*A^2*B^2*a^15*b^16*d^5 + 1344*A^2*B^2*a^17*b^14*d^5 + 448*A^2*B^2*a^19*b^12*d^5 + 64*A^2
*B^2*a^21*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) + (((((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)*(2592*A^3*a^11*b^22*d^6 - 128*A^3*a^7*b^26*d^6 - 128*A^3*a^9*b^24*d^6 - ((a + b*tan(c + d*x))^(1/2)*(256
*A^2*a^8*b^26*d^7 + 1472*A^2*a^10*b^24*d^7 + 3712*A^2*a^12*b^22*d^7 + 6272*A^2*a^14*b^20*d^7 + 9856*A^2*a^16*b
^18*d^7 + 14336*A^2*a^18*b^16*d^7 + 15232*A^2*a^20*b^14*d^7 + 10112*A^2*a^22*b^12*d^7 + 3712*A^2*a^24*b^10*d^7
+ 576*A^2*a^26*b^8*d^7 + 832*B^2*a^10*b^24*d^7 + 5504*B^2*a^12*b^22*d^7 + 15232*B^2*a^14*b^20*d^7 + 22400*B^2
*a^16*b^18*d^7 + 17920*B^2*a^18*b^16*d^7 + 6272*B^2*a^20*b^14*d^7 - 896*B^2*a^22*b^12*d^7 - 1408*B^2*a^24*b^10
*d^7 - 320*B^2*a^26*b^8*d^7 - 512*A*B*a^9*b^25*d^7 - 1792*A*B*a^11*b^23*d^7 + 1792*A*B*a^13*b^21*d^7 + 19712*A
*B*a^15*b^19*d^7 + 44800*A*B*a^17*b^17*d^7 + 51968*A*B*a^19*b^15*d^7 + 34048*A*B*a^21*b^13*d^7 + 12032*A*B*a^2
3*b^11*d^7 + 1792*A*B*a^25*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)*(512*a^9*b^28*d^9 + 5376*a^11*b^26*d^9 + 25344*a^13*b^24*d^9 +
70656*a^15*b^22*d^9 + 129024*a^17*b^20*d^9 + 161280*a^19*b^18*d^9 + 139776*a^21*b^16*d^9 + 82944*a^23*b^14*d^
9 + 32256*a^25*b^12*d^9 + 7424*a^27*b^10*d^9 + 768*a^29*b^8*d^9) + 512*A*a^8*b^28*d^8 + 5248*A*a^10*b^26*d^8 +
23936*A*a^12*b^24*d^8 + 64000*A*a^14*b^22*d^8 + 111104*A*a^16*b^20*d^8 + 130816*A*a^18*b^18*d^8 + 105728*A*a^
20*b^16*d^8 + 57856*A*a^22*b^14*d^8 + 20480*A*a^24*b^12*d^8 + 4224*A*a^26*b^10*d^8 + 384*A*a^28*b^8*d^8 - 256*
B*a^11*b^25*d^8 - 2048*B*a^13*b^23*d^8 - 7168*B*a^15*b^21*d^8 - 14336*B*a^17*b^19*d^8 - 17920*B*a^19*b^17*d^8
- 14336*B*a^21*b^15*d^8 - 7168*B*a^23*b^13*d^8 - 2048*B*a^25*b^11*d^8 - 256*B*a^27*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) + 10976*A^3*a^13*b^20*d^6 + 20384*A^3*a^15*b^18*d^6 + 20832*A^3*a^17*b^16*d^6 + 1
1872*A^3*a^19*b^14*d^6 + 3232*A^3*a^21*b^12*d^6 + 96*A^3*a^23*b^10*d^6 - 96*A^3*a^25*b^8*d^6 + 32*B^3*a^10*b^2
3*d^6 + 224*B^3*a^12*b^21*d^6 + 672*B^3*a^14*b^19*d^6 + 1120*B^3*a^16*b^17*d^6 + 1120*B^3*a^18*b^15*d^6 + 672*
B^3*a^20*b^13*d^6 + 224*B^3*a^22*b^11*d^6 + 32*B^3*a^24*b^9*d^6 - 768*A*B^2*a^9*b^24*d^6 - 5088*A*B^2*a^11*b^2
2*d^6 - 14112*A*B^2*a^13*b^20*d^6 - 20832*A*B^2*a^15*b^18*d^6 - 16800*A*B^2*a^17*b^16*d^6 - 6048*A*B^2*a^19*b^
14*d^6 + 672*A*B^2*a^21*b^12*d^6 + 1248*A*B^2*a^23*b^10*d^6 + 288*A*B^2*a^25*b^8*d^6 + 768*A^2*B*a^8*b^25*d^6
+ 4128*A^2*B*a^10*b^23*d^6 + 7392*A^2*B*a^12*b^21*d^6 + 672*A^2*B*a^14*b^19*d^6 - 16800*A^2*B*a^16*b^17*d^6 -
27552*A^2*B*a^18*b^15*d^6 - 20832*A^2*B*a^20*b^13*d^6 - 7968*A^2*B*a^22*b^11*d^6 - 1248*A^2*B*a^24*b^9*d^6) +
(a + b*tan(c + d*x))^(1/2)*(1120*A^4*a^15*b^16*d^5 - 352*A^4*a^9*b^22*d^5 - 672*A^4*a^11*b^20*d^5 - 224*A^4*a^
13*b^18*d^5 - 64*A^4*a^7*b^24*d^5 + 2016*A^4*a^17*b^14*d^5 + 1568*A^4*a^19*b^12*d^5 + 608*A^4*a^21*b^10*d^5 +
96*A^4*a^23*b^8*d^5 + 32*B^4*a^9*b^22*d^5 + 224*B^4*a^11*b^20*d^5 + 672*B^4*a^13*b^18*d^5 + 1120*B^4*a^15*b^16
*d^5 + 1120*B^4*a^17*b^14*d^5 + 672*B^4*a^19*b^12*d^5 + 224*B^4*a^21*b^10*d^5 + 32*B^4*a^23*b^8*d^5 + 256*A^3*
B*a^8*b^23*d^5 + 1792*A^3*B*a^10*b^21*d^5 + 5376*A^3*B*a^12*b^19*d^5 + 8960*A^3*B*a^14*b^17*d^5 + 8960*A^3*B*a
^16*b^15*d^5 + 5376*A^3*B*a^18*b^13*d^5 + 1792*A^3*B*a^20*b^11*d^5 + 256*A^3*B*a^22*b^9*d^5 + 64*A^2*B^2*a^7*b
^24*d^5 + 448*A^2*B^2*a^9*b^22*d^5 + 1344*A^2*B^2*a^11*b^20*d^5 + 2240*A^2*B^2*a^13*b^18*d^5 + 2240*A^2*B^2*a^
15*b^16*d^5 + 1344*A^2*B^2*a^17*b^14*d^5 + 448*A^2*B^2*a^19*b^12*d^5 + 64*A^2*B^2*a^21*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) + 64*A*B^4*a^8*b^22*d^4 + 448*A*B^4*a^10*b^20*d^4 + 1344*A*B^4*a^12*b^18*d^4
+ 2240*A*B^4*a^14*b^16*d^4 + 2240*A*B^4*a^16*b^14*d^4 + 1344*A*B^4*a^18*b^12*d^4 + 448*A*B^4*a^20*b^10*d^4 +
64*A*B^4*a^22*b^8*d^4 - 64*A^4*B*a^7*b^23*d^4 - 448*A^4*B*a^9*b^21*d^4 - 1344*A^4*B*a^11*b^19*d^4 - 2240*A^4*B
*a^13*b^17*d^4 - 2240*A^4*B*a^15*b^15*d^4 - 1344*A^4*B*a^17*b^13*d^4 - 448*A^4*B*a^19*b^11*d^4 - 64*A^4*B*a^21
*b^9*d^4 - 64*A^2*B^3*a^7*b^23*d^4 - 448*A^2*B^3*a^9*b^21*d^4 - 1344*A^2*B^3*a^11*b^19*d^4 - 2240*A^2*B^3*a^13
*b^17*d^4 - 2240*A^2*B^3*a^15*b^15*d^4 - 1344*A^2*B^3*a^17*b^13*d^4 - 448*A^2*B^3*a^19*b^11*d^4 - 64*A^2*B^3*a
^21*b^9*d^4 + 64*A^3*B^2*a^8*b^22*d^4 + 448*A^3*B^2*a^10*b^20*d^4 + 1344*A^3*B^2*a^12*b^18*d^4 + 2240*A^3*B^2*
a^14*b^16*d^4 + 2240*A^3*B^2*a^16*b^14*d^4 + 1344*A^3*B^2*a^18*b^12*d^4 + 448*A^3*B^2*a^20*b^10*d^4 + 64*A^3*B
^2*a^22*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 + 4
8*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 + (2*(A*b^2 - B*a*b))/(d*(a*b^2 + a^3)*(a +
b*tan(c + d*x))^(1/2)) + (A*atan((A^4*a^13*(a + b*tan(c + d*x))^(1/2)*9i + B^4*a^13*(a + b*tan(c + d*x))^(1/2
)*1i + A^2*B^2*a^13*(a + b*tan(c + d*x))^(1/2)*10i + A^4*a^7*b^6*(a + b*tan(c + d*x))^(1/2)*16i + A^4*a^9*b^4*
(a + b*tan(c + d*x))^(1/2)*48i + A^4*a^11*b^2*(a + b*tan(c + d*x))^(1/2)*72i + A^3*B*a^10*b^3*(a + b*tan(c + d
*x))^(1/2)*16i - A^2*B^2*a^11*b^2*(a + b*tan(c + d*x))^(1/2)*24i - A^3*B*a^12*b*(a + b*tan(c + d*x))^(1/2)*48i
)/(a^6*(a^3)^(1/2)*(a^3*(a^3*(9*A^4 + 10*A^2*B^2 + B^4) + 16*A^3*B*b^3 + 72*A^4*a*b^2 - 48*A^3*B*a^2*b - 24*A^
2*B^2*a*b^2) + 16*A^4*b^6 + 48*A^4*a^2*b^4)))*2i)/(d*(a^3)^(1/2))