\(\int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx\) [362]

Optimal result

Integrand size = 31, antiderivative size = 224 \[ \int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx=-\frac {2 A \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{a^{5/2} d}+\frac {(A-i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{(a-i b)^{5/2} d}+\frac {(A+i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{(a+i b)^{5/2} d}+\frac {2 b (A b-a B)}{3 a \left (a^2+b^2\right ) d (a+b \tan (c+d x))^{3/2}}+\frac {2 b \left (3 a^2 A b+A b^3-2 a^3 B\right )}{a^2 \left (a^2+b^2\right )^2 d \sqrt {a+b \tan (c+d x)}} \]

[Out]

-2*A*arctanh((a+b*tan(d*x+c))^(1/2)/a^(1/2))/a^(5/2)/d+(A-I*B)*arctanh((a+b*tan(d*x+c))^(1/2)/(a-I*b)^(1/2))/(
a-I*b)^(5/2)/d+(A+I*B)*arctanh((a+b*tan(d*x+c))^(1/2)/(a+I*b)^(1/2))/(a+I*b)^(5/2)/d+2*b*(3*A*a^2*b+A*b^3-2*B*
a^3)/a^2/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^(1/2)+2/3*b*(A*b-B*a)/a/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)

Rubi [A] (verified)

Time = 1.42 (sec) , antiderivative size = 224, normalized size of antiderivative = 1.00, number of steps used = 13, number of rules used = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.258, Rules used = {3690, 3730, 3734, 3620, 3618, 65, 214, 3715} \[ \int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx=-\frac {2 A \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{a^{5/2} d}+\frac {2 b (A b-a B)}{3 a d \left (a^2+b^2\right ) (a+b \tan (c+d x))^{3/2}}+\frac {2 b \left (-2 a^3 B+3 a^2 A b+A b^3\right )}{a^2 d \left (a^2+b^2\right )^2 \sqrt {a+b \tan (c+d x)}}+\frac {(A-i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{d (a-i b)^{5/2}}+\frac {(A+i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{d (a+i b)^{5/2}} \]

[In]

Int[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]

[Out]

(-2*A*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(a^(5/2)*d) + ((A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqr
t[a - I*b]])/((a - I*b)^(5/2)*d) + ((A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(5/2
)*d) + (2*b*(A*b - a*B))/(3*a*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (2*b*(3*a^2*A*b + A*b^3 - 2*a^3*B))/
(a^2*(a^2 + b^2)^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 3730

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*Ta
n[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 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)}{3 a \left (a^2+b^2\right ) d (a+b \tan (c+d x))^{3/2}}+\frac {2 \int \frac {\cot (c+d x) \left (\frac {3}{2} A \left (a^2+b^2\right )-\frac {3}{2} a (A b-a B) \tan (c+d x)+\frac {3}{2} b (A b-a B) \tan ^2(c+d x)\right )}{(a+b \tan (c+d x))^{3/2}} \, dx}{3 a \left (a^2+b^2\right )} \\ & = \frac {2 b (A b-a B)}{3 a \left (a^2+b^2\right ) d (a+b \tan (c+d x))^{3/2}}+\frac {2 b \left (3 a^2 A b+A b^3-2 a^3 B\right )}{a^2 \left (a^2+b^2\right )^2 d \sqrt {a+b \tan (c+d x)}}+\frac {4 \int \frac {\cot (c+d x) \left (\frac {3}{4} A \left (a^2+b^2\right )^2-\frac {3}{4} a^2 \left (2 a A b-a^2 B+b^2 B\right ) \tan (c+d x)+\frac {3}{4} b \left (3 a^2 A b+A b^3-2 a^3 B\right ) \tan ^2(c+d x)\right )}{\sqrt {a+b \tan (c+d x)}} \, dx}{3 a^2 \left (a^2+b^2\right )^2} \\ & = \frac {2 b (A b-a B)}{3 a \left (a^2+b^2\right ) d (a+b \tan (c+d x))^{3/2}}+\frac {2 b \left (3 a^2 A b+A b^3-2 a^3 B\right )}{a^2 \left (a^2+b^2\right )^2 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^2}+\frac {4 \int \frac {-\frac {3}{4} a^2 \left (2 a A b-a^2 B+b^2 B\right )-\frac {3}{4} a^2 \left (a^2 A-A b^2+2 a b B\right ) \tan (c+d x)}{\sqrt {a+b \tan (c+d x)}} \, dx}{3 a^2 \left (a^2+b^2\right )^2} \\ & = \frac {2 b (A b-a B)}{3 a \left (a^2+b^2\right ) d (a+b \tan (c+d x))^{3/2}}+\frac {2 b \left (3 a^2 A b+A b^3-2 a^3 B\right )}{a^2 \left (a^2+b^2\right )^2 d \sqrt {a+b \tan (c+d x)}}-\frac {(i A-B) \int \frac {1-i \tan (c+d x)}{\sqrt {a+b \tan (c+d x)}} \, dx}{2 (a+i b)^2}+\frac {(i A+B) \int \frac {1+i \tan (c+d x)}{\sqrt {a+b \tan (c+d x)}} \, dx}{2 (a-i b)^2}+\frac {A \text {Subst}\left (\int \frac {1}{x \sqrt {a+b x}} \, dx,x,\tan (c+d x)\right )}{a^2 d} \\ & = \frac {2 b (A b-a B)}{3 a \left (a^2+b^2\right ) d (a+b \tan (c+d x))^{3/2}}+\frac {2 b \left (3 a^2 A b+A b^3-2 a^3 B\right )}{a^2 \left (a^2+b^2\right )^2 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^2 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)^2 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)^2 d} \\ & = -\frac {2 A \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{a^{5/2} d}+\frac {2 b (A b-a B)}{3 a \left (a^2+b^2\right ) d (a+b \tan (c+d x))^{3/2}}+\frac {2 b \left (3 a^2 A b+A b^3-2 a^3 B\right )}{a^2 \left (a^2+b^2\right )^2 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)^2 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)^2 b d} \\ & = -\frac {2 A \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{a^{5/2} d}+\frac {(A-i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{(a-i b)^{5/2} d}+\frac {(A+i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{(a+i b)^{5/2} d}+\frac {2 b (A b-a B)}{3 a \left (a^2+b^2\right ) d (a+b \tan (c+d x))^{3/2}}+\frac {2 b \left (3 a^2 A b+A b^3-2 a^3 B\right )}{a^2 \left (a^2+b^2\right )^2 d \sqrt {a+b \tan (c+d x)}} \\ \end{align*}

Mathematica [A] (verified)

Time = 5.47 (sec) , antiderivative size = 242, normalized size of antiderivative = 1.08 \[ \int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx=\frac {2 \left (-\frac {3 A \left (a^2+b^2\right ) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{a^{3/2}}+\frac {3 a (a+i b) (A-i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{2 (a-i b)^{3/2}}+\frac {3 a (a-i b) (A+i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{2 (a+i b)^{3/2}}+\frac {b (A b-a B)}{(a+b \tan (c+d x))^{3/2}}+\frac {3 b \left (3 a^2 A b+A b^3-2 a^3 B\right )}{a \left (a^2+b^2\right ) \sqrt {a+b \tan (c+d x)}}\right )}{3 a \left (a^2+b^2\right ) d} \]

[In]

Integrate[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]

[Out]

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

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(12869\) vs. \(2(194)=388\).

Time = 0.23 (sec) , antiderivative size = 12870, normalized size of antiderivative = 57.46

method	result	size
derivativedivides	\(\text {Expression too large to display}\)	\(12870\)
default	\(\text {Expression too large to display}\)	\(12870\)

[In]

int(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),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. 7342 vs. \(2 (189) = 378\).

Time = 19.73 (sec) , antiderivative size = 14700, normalized size of antiderivative = 65.62 \[ \int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx=\text {Too large to display} \]

[In]

integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm="fricas")

[Out]

Too large to include

Sympy [F]

\[ \int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx=\int \frac {\left (A + B \tan {\left (c + d x \right )}\right ) \cot {\left (c + d x \right )}}{\left (a + b \tan {\left (c + d x \right )}\right )^{\frac {5}{2}}}\, dx \]

[In]

integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)

[Out]

Integral((A + B*tan(c + d*x))*cot(c + d*x)/(a + b*tan(c + d*x))**(5/2), x)

Maxima [F]

\[ \int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx=\int { \frac {{\left (B \tan \left (d x + c\right ) + A\right )} \cot \left (d x + c\right )}{{\left (b \tan \left (d x + c\right ) + a\right )}^{\frac {5}{2}}} \,d x } \]

[In]

integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm="maxima")

[Out]

integrate((B*tan(d*x + c) + A)*cot(d*x + c)/(b*tan(d*x + c) + a)^(5/2), x)

Giac [F(-1)]

Timed out. \[ \int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx=\text {Timed out} \]

[In]

integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm="giac")

[Out]

Timed out

Mupad [B] (verification not implemented)

Time = 18.99 (sec) , antiderivative size = 45681, normalized size of antiderivative = 203.93 \[ \int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx=\text {Too large to display} \]

[In]

int((cot(c + d*x)*(A + B*tan(c + d*x)))/(a + b*tan(c + d*x))^(5/2),x)

[Out]

atan(-(((-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2
*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10
*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 4*A^2*a^5*d
^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^2*a^3*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2 + 20*B^2*a*b^4
*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a
^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(((a + b*tan(c + d*x))^(1/2)*(256*A^2*a^15*b^44*d^7 + 4608*A^2*a^17*b^42*d
^7 + 40512*A^2*a^19*b^40*d^7 + 224768*A^2*a^21*b^38*d^7 + 864768*A^2*a^23*b^36*d^7 + 2419200*A^2*a^25*b^34*d^7
+ 5055232*A^2*a^27*b^32*d^7 + 8007168*A^2*a^29*b^30*d^7 + 9664512*A^2*a^31*b^28*d^7 + 8859136*A^2*a^33*b^26*d
^7 + 6095232*A^2*a^35*b^24*d^7 + 3095040*A^2*a^37*b^22*d^7 + 1164800*A^2*a^39*b^20*d^7 + 376320*A^2*a^41*b^18*
d^7 + 154368*A^2*a^43*b^16*d^7 + 76288*A^2*a^45*b^14*d^7 + 28416*A^2*a^47*b^12*d^7 + 6144*A^2*a^49*b^10*d^7 +
576*A^2*a^51*b^8*d^7 - 1344*B^2*a^19*b^40*d^7 - 15872*B^2*a^21*b^38*d^7 - 81408*B^2*a^23*b^36*d^7 - 225792*B^2
*a^25*b^34*d^7 - 302848*B^2*a^27*b^32*d^7 + 139776*B^2*a^29*b^30*d^7 + 1537536*B^2*a^31*b^28*d^7 + 3587584*B^2
*a^33*b^26*d^7 + 5106816*B^2*a^35*b^24*d^7 + 5051904*B^2*a^37*b^22*d^7 + 3587584*B^2*a^39*b^20*d^7 + 1817088*B
^2*a^41*b^18*d^7 + 628992*B^2*a^43*b^16*d^7 + 132608*B^2*a^45*b^14*d^7 + 10752*B^2*a^47*b^12*d^7 - 1536*B^2*a^
49*b^10*d^7 - 320*B^2*a^51*b^8*d^7 + 512*A*B*a^18*b^41*d^7 + 1536*A*B*a^20*b^39*d^7 - 29184*A*B*a^22*b^37*d^7
- 283136*A*B*a^24*b^35*d^7 - 1257984*A*B*a^26*b^33*d^7 - 3494400*A*B*a^28*b^31*d^7 - 6662656*A*B*a^30*b^29*d^7
- 9005568*A*B*a^32*b^27*d^7 - 8566272*A*B*a^34*b^25*d^7 - 5344768*A*B*a^36*b^23*d^7 - 1537536*A*B*a^38*b^21*d
^7 + 698880*A*B*a^40*b^19*d^7 + 1071616*A*B*a^42*b^17*d^7 + 612864*A*B*a^44*b^15*d^7 + 201216*A*B*a^46*b^13*d^
7 + 37376*A*B*a^48*b^11*d^7 + 3072*A*B*a^50*b^9*d^7) + (-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2
+ 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^
4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6
*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 4*A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^2*a^3*b^2*d^2 -
8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2 + 20*B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b
^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(512*A*a^16*b^46*d^8 - (a +
b*tan(c + d*x))^(1/2)*(-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b
^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2
+ B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2
) - 4*A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^2*a^3*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2
+ 20*B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4
*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(512*a^18*b^46*d^9 + 9984*a^20*b^44*d^9 + 92160*a^22*b^42*d
^9 + 535296*a^24*b^40*d^9 + 2193408*a^26*b^38*d^9 + 6736896*a^28*b^36*d^9 + 16084992*a^30*b^34*d^9 + 30551040*
a^32*b^32*d^9 + 46844928*a^34*b^30*d^9 + 58499584*a^36*b^28*d^9 + 59744256*a^38*b^26*d^9 + 49900032*a^40*b^24*
d^9 + 33945600*a^42*b^22*d^9 + 18643968*a^44*b^20*d^9 + 8146944*a^46*b^18*d^9 + 2767872*a^48*b^16*d^9 + 705024
*a^50*b^14*d^9 + 126720*a^52*b^12*d^9 + 14336*a^54*b^10*d^9 + 768*a^56*b^8*d^9) + 9728*A*a^18*b^44*d^8 + 87936
*A*a^20*b^42*d^8 + 502144*A*a^22*b^40*d^8 + 2028544*A*a^24*b^38*d^8 + 6153216*A*a^26*b^36*d^8 + 14518784*A*a^2
8*b^34*d^8 + 27243008*A*a^30*b^32*d^8 + 41213952*A*a^32*b^30*d^8 + 50665472*A*a^34*b^28*d^8 + 50775296*A*a^36*
b^26*d^8 + 41443584*A*a^38*b^24*d^8 + 27409408*A*a^40*b^22*d^8 + 14543872*A*a^42*b^20*d^8 + 6093312*A*a^44*b^1
8*d^8 + 1966592*A*a^46*b^16*d^8 + 470528*A*a^48*b^14*d^8 + 78336*A*a^50*b^12*d^8 + 8064*A*a^52*b^10*d^8 + 384*
A*a^54*b^8*d^8 + 128*B*a^19*b^43*d^8 + 1664*B*a^21*b^41*d^8 + 9216*B*a^23*b^39*d^8 + 25600*B*a^25*b^37*d^8 + 1
7920*B*a^27*b^35*d^8 - 139776*B*a^29*b^33*d^8 - 652288*B*a^31*b^31*d^8 - 1610752*B*a^33*b^29*d^8 - 2745600*B*a
^35*b^27*d^8 - 3477760*B*a^37*b^25*d^8 - 3367936*B*a^39*b^23*d^8 - 2515968*B*a^41*b^21*d^8 - 1444352*B*a^43*b^
19*d^8 - 627200*B*a^45*b^17*d^8 - 199680*B*a^47*b^15*d^8 - 44032*B*a^49*b^13*d^8 - 6016*B*a^51*b^11*d^8 - 384*
B*a^53*b^9*d^8))*(-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2
+ 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)
*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 4*
A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^2*a^3*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2 + 20*
B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d
^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2) - 384*A^3*a^15*b^42*d^6 - 7296*A^3*a^17*b^40*d^6 - 59424*A^3*a^19
*b^38*d^6 - 280992*A^3*a^21*b^36*d^6 - 866208*A^3*a^23*b^34*d^6 - 1825824*A^3*a^25*b^32*d^6 - 2629536*A^3*a^27
*b^30*d^6 - 2374944*A^3*a^29*b^28*d^6 - 727584*A^3*a^31*b^26*d^6 + 1413984*A^3*a^33*b^24*d^6 + 2649504*A^3*a^3
5*b^22*d^6 + 2454816*A^3*a^37*b^20*d^6 + 1476384*A^3*a^39*b^18*d^6 + 597408*A^3*a^41*b^16*d^6 + 156192*A^3*a^4
3*b^14*d^6 + 22944*A^3*a^45*b^12*d^6 + 1056*A^3*a^47*b^10*d^6 - 96*A^3*a^49*b^8*d^6 + 64*B^3*a^20*b^37*d^6 + 8
96*B^3*a^22*b^35*d^6 + 5824*B^3*a^24*b^33*d^6 + 23296*B^3*a^26*b^31*d^6 + 64064*B^3*a^28*b^29*d^6 + 128128*B^3
*a^30*b^27*d^6 + 192192*B^3*a^32*b^25*d^6 + 219648*B^3*a^34*b^23*d^6 + 192192*B^3*a^36*b^21*d^6 + 128128*B^3*a
^38*b^19*d^6 + 64064*B^3*a^40*b^17*d^6 + 23296*B^3*a^42*b^15*d^6 + 5824*B^3*a^44*b^13*d^6 + 896*B^3*a^46*b^11*
d^6 + 64*B^3*a^48*b^9*d^6 + 1280*A*B^2*a^17*b^40*d^6 + 15328*A*B^2*a^19*b^38*d^6 + 80480*A*B^2*a^21*b^36*d^6 +
234080*A*B^2*a^23*b^34*d^6 + 364000*A*B^2*a^25*b^32*d^6 + 72800*A*B^2*a^27*b^30*d^6 - 1057056*A*B^2*a^29*b^28
*d^6 - 2814240*A*B^2*a^31*b^26*d^6 - 4187040*A*B^2*a^33*b^24*d^6 - 4232800*A*B^2*a^35*b^22*d^6 - 3043040*A*B^2
*a^37*b^20*d^6 - 1552096*A*B^2*a^39*b^18*d^6 - 538720*A*B^2*a^41*b^16*d^6 - 113120*A*B^2*a^43*b^14*d^6 - 8800*
A*B^2*a^45*b^12*d^6 + 1440*A*B^2*a^47*b^10*d^6 + 288*A*B^2*a^49*b^8*d^6 - 128*A^2*B*a^14*b^43*d^6 - 2176*A^2*B
*a^16*b^41*d^6 - 11264*A^2*B*a^18*b^39*d^6 - 3008*A^2*B*a^20*b^37*d^6 + 226688*A^2*B*a^22*b^35*d^6 + 1263808*A
^2*B*a^24*b^33*d^6 + 3843840*A^2*B*a^26*b^31*d^6 + 7824960*A^2*B*a^28*b^29*d^6 + 11366784*A^2*B*a^30*b^27*d^6
+ 12016576*A^2*B*a^32*b^25*d^6 + 9152000*A^2*B*a^34*b^23*d^6 + 4758208*A^2*B*a^36*b^21*d^6 + 1386112*A^2*B*a^3
8*b^19*d^6 - 54208*A^2*B*a^40*b^17*d^6 - 250112*A^2*B*a^42*b^15*d^6 - 111936*A^2*B*a^44*b^13*d^6 - 23808*A^2*B
*a^46*b^11*d^6 - 2112*A^2*B*a^48*b^9*d^6) - (a + b*tan(c + d*x))^(1/2)*(64*A^4*a^14*b^40*d^5 + 512*A^4*a^16*b^
38*d^5 + 544*A^4*a^18*b^36*d^5 - 10304*A^4*a^20*b^34*d^5 - 66976*A^4*a^22*b^32*d^5 - 221312*A^4*a^24*b^30*d^5
- 480480*A^4*a^26*b^28*d^5 - 741312*A^4*a^28*b^26*d^5 - 837408*A^4*a^30*b^24*d^5 - 695552*A^4*a^32*b^22*d^5 -
416416*A^4*a^34*b^20*d^5 - 168896*A^4*a^36*b^18*d^5 - 37856*A^4*a^38*b^16*d^5 + 896*A^4*a^40*b^14*d^5 + 3424*A
^4*a^42*b^12*d^5 + 960*A^4*a^44*b^10*d^5 + 96*A^4*a^46*b^8*d^5 + 32*B^4*a^18*b^36*d^5 + 448*B^4*a^20*b^34*d^5
+ 2912*B^4*a^22*b^32*d^5 + 11648*B^4*a^24*b^30*d^5 + 32032*B^4*a^26*b^28*d^5 + 64064*B^4*a^28*b^26*d^5 + 96096
*B^4*a^30*b^24*d^5 + 109824*B^4*a^32*b^22*d^5 + 96096*B^4*a^34*b^20*d^5 + 64064*B^4*a^36*b^18*d^5 + 32032*B^4*
a^38*b^16*d^5 + 11648*B^4*a^40*b^14*d^5 + 2912*B^4*a^42*b^12*d^5 + 448*B^4*a^44*b^10*d^5 + 32*B^4*a^46*b^8*d^5
- 512*A^3*B*a^15*b^39*d^5 - 6656*A^3*B*a^17*b^37*d^5 - 39424*A^3*B*a^19*b^35*d^5 - 139776*A^3*B*a^21*b^33*d^5
- 326144*A^3*B*a^23*b^31*d^5 - 512512*A^3*B*a^25*b^29*d^5 - 512512*A^3*B*a^27*b^27*d^5 - 219648*A^3*B*a^29*b^
25*d^5 + 219648*A^3*B*a^31*b^23*d^5 + 512512*A^3*B*a^33*b^21*d^5 + 512512*A^3*B*a^35*b^19*d^5 + 326144*A^3*B*a
^37*b^17*d^5 + 139776*A^3*B*a^39*b^15*d^5 + 39424*A^3*B*a^41*b^13*d^5 + 6656*A^3*B*a^43*b^11*d^5 + 512*A^3*B*a
^45*b^9*d^5 - 64*A^2*B^2*a^14*b^40*d^5 - 512*A^2*B^2*a^16*b^38*d^5 - 448*A^2*B^2*a^18*b^36*d^5 + 11648*A^2*B^2
*a^20*b^34*d^5 + 75712*A^2*B^2*a^22*b^32*d^5 + 256256*A^2*B^2*a^24*b^30*d^5 + 576576*A^2*B^2*a^26*b^28*d^5 + 9
33504*A^2*B^2*a^28*b^26*d^5 + 1125696*A^2*B^2*a^30*b^24*d^5 + 1025024*A^2*B^2*a^32*b^22*d^5 + 704704*A^2*B^2*a
^34*b^20*d^5 + 361088*A^2*B^2*a^36*b^18*d^5 + 133952*A^2*B^2*a^38*b^16*d^5 + 34048*A^2*B^2*a^40*b^14*d^5 + 531
2*A^2*B^2*a^42*b^12*d^5 + 384*A^2*B^2*a^44*b^10*d^5))*(-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2
+ 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4
*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*
b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 4*A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^2*a^3*b^2*d^2 - 8
*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2 + 20*B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^
10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*1i - ((-(((8*A^2*a^5*d^2 - 8
*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2
- 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^
8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 4*A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^
3*b^2*d^2 - 40*B^2*a^3*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2 + 20*B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40
*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^
(1/2)*(1413984*A^3*a^33*b^24*d^6 - 384*A^3*a^15*b^42*d^6 - 7296*A^3*a^17*b^40*d^6 - 59424*A^3*a^19*b^38*d^6 -
280992*A^3*a^21*b^36*d^6 - 866208*A^3*a^23*b^34*d^6 - 1825824*A^3*a^25*b^32*d^6 - 2629536*A^3*a^27*b^30*d^6 -
2374944*A^3*a^29*b^28*d^6 - 727584*A^3*a^31*b^26*d^6 - ((a + b*tan(c + d*x))^(1/2)*(256*A^2*a^15*b^44*d^7 + 46
08*A^2*a^17*b^42*d^7 + 40512*A^2*a^19*b^40*d^7 + 224768*A^2*a^21*b^38*d^7 + 864768*A^2*a^23*b^36*d^7 + 2419200
*A^2*a^25*b^34*d^7 + 5055232*A^2*a^27*b^32*d^7 + 8007168*A^2*a^29*b^30*d^7 + 9664512*A^2*a^31*b^28*d^7 + 88591
36*A^2*a^33*b^26*d^7 + 6095232*A^2*a^35*b^24*d^7 + 3095040*A^2*a^37*b^22*d^7 + 1164800*A^2*a^39*b^20*d^7 + 376
320*A^2*a^41*b^18*d^7 + 154368*A^2*a^43*b^16*d^7 + 76288*A^2*a^45*b^14*d^7 + 28416*A^2*a^47*b^12*d^7 + 6144*A^
2*a^49*b^10*d^7 + 576*A^2*a^51*b^8*d^7 - 1344*B^2*a^19*b^40*d^7 - 15872*B^2*a^21*b^38*d^7 - 81408*B^2*a^23*b^3
6*d^7 - 225792*B^2*a^25*b^34*d^7 - 302848*B^2*a^27*b^32*d^7 + 139776*B^2*a^29*b^30*d^7 + 1537536*B^2*a^31*b^28
*d^7 + 3587584*B^2*a^33*b^26*d^7 + 5106816*B^2*a^35*b^24*d^7 + 5051904*B^2*a^37*b^22*d^7 + 3587584*B^2*a^39*b^
20*d^7 + 1817088*B^2*a^41*b^18*d^7 + 628992*B^2*a^43*b^16*d^7 + 132608*B^2*a^45*b^14*d^7 + 10752*B^2*a^47*b^12
*d^7 - 1536*B^2*a^49*b^10*d^7 - 320*B^2*a^51*b^8*d^7 + 512*A*B*a^18*b^41*d^7 + 1536*A*B*a^20*b^39*d^7 - 29184*
A*B*a^22*b^37*d^7 - 283136*A*B*a^24*b^35*d^7 - 1257984*A*B*a^26*b^33*d^7 - 3494400*A*B*a^28*b^31*d^7 - 6662656
*A*B*a^30*b^29*d^7 - 9005568*A*B*a^32*b^27*d^7 - 8566272*A*B*a^34*b^25*d^7 - 5344768*A*B*a^36*b^23*d^7 - 15375
36*A*B*a^38*b^21*d^7 + 698880*A*B*a^40*b^19*d^7 + 1071616*A*B*a^42*b^17*d^7 + 612864*A*B*a^44*b^15*d^7 + 20121
6*A*B*a^46*b^13*d^7 + 37376*A*B*a^48*b^11*d^7 + 3072*A*B*a^50*b^9*d^7) - (-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 -
80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b
^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4
*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 4*A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*
B^2*a^3*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2 + 20*B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)
/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*((a + b*t
an(c + d*x))^(1/2)*(-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d
^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^
4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) -
4*A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^2*a^3*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2 + 2
0*B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6
*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(512*a^18*b^46*d^9 + 9984*a^20*b^44*d^9 + 92160*a^22*b^42*d^9 +
535296*a^24*b^40*d^9 + 2193408*a^26*b^38*d^9 + 6736896*a^28*b^36*d^9 + 16084992*a^30*b^34*d^9 + 30551040*a^32
*b^32*d^9 + 46844928*a^34*b^30*d^9 + 58499584*a^36*b^28*d^9 + 59744256*a^38*b^26*d^9 + 49900032*a^40*b^24*d^9
+ 33945600*a^42*b^22*d^9 + 18643968*a^44*b^20*d^9 + 8146944*a^46*b^18*d^9 + 2767872*a^48*b^16*d^9 + 705024*a^5
0*b^14*d^9 + 126720*a^52*b^12*d^9 + 14336*a^54*b^10*d^9 + 768*a^56*b^8*d^9) + 512*A*a^16*b^46*d^8 + 9728*A*a^1
8*b^44*d^8 + 87936*A*a^20*b^42*d^8 + 502144*A*a^22*b^40*d^8 + 2028544*A*a^24*b^38*d^8 + 6153216*A*a^26*b^36*d^
8 + 14518784*A*a^28*b^34*d^8 + 27243008*A*a^30*b^32*d^8 + 41213952*A*a^32*b^30*d^8 + 50665472*A*a^34*b^28*d^8
+ 50775296*A*a^36*b^26*d^8 + 41443584*A*a^38*b^24*d^8 + 27409408*A*a^40*b^22*d^8 + 14543872*A*a^42*b^20*d^8 +
6093312*A*a^44*b^18*d^8 + 1966592*A*a^46*b^16*d^8 + 470528*A*a^48*b^14*d^8 + 78336*A*a^50*b^12*d^8 + 8064*A*a^
52*b^10*d^8 + 384*A*a^54*b^8*d^8 + 128*B*a^19*b^43*d^8 + 1664*B*a^21*b^41*d^8 + 9216*B*a^23*b^39*d^8 + 25600*B
*a^25*b^37*d^8 + 17920*B*a^27*b^35*d^8 - 139776*B*a^29*b^33*d^8 - 652288*B*a^31*b^31*d^8 - 1610752*B*a^33*b^29
*d^8 - 2745600*B*a^35*b^27*d^8 - 3477760*B*a^37*b^25*d^8 - 3367936*B*a^39*b^23*d^8 - 2515968*B*a^41*b^21*d^8 -
1444352*B*a^43*b^19*d^8 - 627200*B*a^45*b^17*d^8 - 199680*B*a^47*b^15*d^8 - 44032*B*a^49*b^13*d^8 - 6016*B*a^
51*b^11*d^8 - 384*B*a^53*b^9*d^8))*(-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^
2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4
+ 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^
2*d^4))^(1/2) - 4*A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^2*a^3*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A
^2*a*b^4*d^2 + 20*B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*
d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2) + 2649504*A^3*a^35*b^22*d^6 + 2454816*A^3*a^37*
b^20*d^6 + 1476384*A^3*a^39*b^18*d^6 + 597408*A^3*a^41*b^16*d^6 + 156192*A^3*a^43*b^14*d^6 + 22944*A^3*a^45*b^
12*d^6 + 1056*A^3*a^47*b^10*d^6 - 96*A^3*a^49*b^8*d^6 + 64*B^3*a^20*b^37*d^6 + 896*B^3*a^22*b^35*d^6 + 5824*B^
3*a^24*b^33*d^6 + 23296*B^3*a^26*b^31*d^6 + 64064*B^3*a^28*b^29*d^6 + 128128*B^3*a^30*b^27*d^6 + 192192*B^3*a^
32*b^25*d^6 + 219648*B^3*a^34*b^23*d^6 + 192192*B^3*a^36*b^21*d^6 + 128128*B^3*a^38*b^19*d^6 + 64064*B^3*a^40*
b^17*d^6 + 23296*B^3*a^42*b^15*d^6 + 5824*B^3*a^44*b^13*d^6 + 896*B^3*a^46*b^11*d^6 + 64*B^3*a^48*b^9*d^6 + 12
80*A*B^2*a^17*b^40*d^6 + 15328*A*B^2*a^19*b^38*d^6 + 80480*A*B^2*a^21*b^36*d^6 + 234080*A*B^2*a^23*b^34*d^6 +
364000*A*B^2*a^25*b^32*d^6 + 72800*A*B^2*a^27*b^30*d^6 - 1057056*A*B^2*a^29*b^28*d^6 - 2814240*A*B^2*a^31*b^26
*d^6 - 4187040*A*B^2*a^33*b^24*d^6 - 4232800*A*B^2*a^35*b^22*d^6 - 3043040*A*B^2*a^37*b^20*d^6 - 1552096*A*B^2
*a^39*b^18*d^6 - 538720*A*B^2*a^41*b^16*d^6 - 113120*A*B^2*a^43*b^14*d^6 - 8800*A*B^2*a^45*b^12*d^6 + 1440*A*B
^2*a^47*b^10*d^6 + 288*A*B^2*a^49*b^8*d^6 - 128*A^2*B*a^14*b^43*d^6 - 2176*A^2*B*a^16*b^41*d^6 - 11264*A^2*B*a
^18*b^39*d^6 - 3008*A^2*B*a^20*b^37*d^6 + 226688*A^2*B*a^22*b^35*d^6 + 1263808*A^2*B*a^24*b^33*d^6 + 3843840*A
^2*B*a^26*b^31*d^6 + 7824960*A^2*B*a^28*b^29*d^6 + 11366784*A^2*B*a^30*b^27*d^6 + 12016576*A^2*B*a^32*b^25*d^6
+ 9152000*A^2*B*a^34*b^23*d^6 + 4758208*A^2*B*a^36*b^21*d^6 + 1386112*A^2*B*a^38*b^19*d^6 - 54208*A^2*B*a^40*
b^17*d^6 - 250112*A^2*B*a^42*b^15*d^6 - 111936*A^2*B*a^44*b^13*d^6 - 23808*A^2*B*a^46*b^11*d^6 - 2112*A^2*B*a^
48*b^9*d^6) + (a + b*tan(c + d*x))^(1/2)*(64*A^4*a^14*b^40*d^5 + 512*A^4*a^16*b^38*d^5 + 544*A^4*a^18*b^36*d^5
- 10304*A^4*a^20*b^34*d^5 - 66976*A^4*a^22*b^32*d^5 - 221312*A^4*a^24*b^30*d^5 - 480480*A^4*a^26*b^28*d^5 - 7
41312*A^4*a^28*b^26*d^5 - 837408*A^4*a^30*b^24*d^5 - 695552*A^4*a^32*b^22*d^5 - 416416*A^4*a^34*b^20*d^5 - 168
896*A^4*a^36*b^18*d^5 - 37856*A^4*a^38*b^16*d^5 + 896*A^4*a^40*b^14*d^5 + 3424*A^4*a^42*b^12*d^5 + 960*A^4*a^4
4*b^10*d^5 + 96*A^4*a^46*b^8*d^5 + 32*B^4*a^18*b^36*d^5 + 448*B^4*a^20*b^34*d^5 + 2912*B^4*a^22*b^32*d^5 + 116
48*B^4*a^24*b^30*d^5 + 32032*B^4*a^26*b^28*d^5 + 64064*B^4*a^28*b^26*d^5 + 96096*B^4*a^30*b^24*d^5 + 109824*B^
4*a^32*b^22*d^5 + 96096*B^4*a^34*b^20*d^5 + 64064*B^4*a^36*b^18*d^5 + 32032*B^4*a^38*b^16*d^5 + 11648*B^4*a^40
*b^14*d^5 + 2912*B^4*a^42*b^12*d^5 + 448*B^4*a^44*b^10*d^5 + 32*B^4*a^46*b^8*d^5 - 512*A^3*B*a^15*b^39*d^5 - 6
656*A^3*B*a^17*b^37*d^5 - 39424*A^3*B*a^19*b^35*d^5 - 139776*A^3*B*a^21*b^33*d^5 - 326144*A^3*B*a^23*b^31*d^5
- 512512*A^3*B*a^25*b^29*d^5 - 512512*A^3*B*a^27*b^27*d^5 - 219648*A^3*B*a^29*b^25*d^5 + 219648*A^3*B*a^31*b^2
3*d^5 + 512512*A^3*B*a^33*b^21*d^5 + 512512*A^3*B*a^35*b^19*d^5 + 326144*A^3*B*a^37*b^17*d^5 + 139776*A^3*B*a^
39*b^15*d^5 + 39424*A^3*B*a^41*b^13*d^5 + 6656*A^3*B*a^43*b^11*d^5 + 512*A^3*B*a^45*b^9*d^5 - 64*A^2*B^2*a^14*
b^40*d^5 - 512*A^2*B^2*a^16*b^38*d^5 - 448*A^2*B^2*a^18*b^36*d^5 + 11648*A^2*B^2*a^20*b^34*d^5 + 75712*A^2*B^2
*a^22*b^32*d^5 + 256256*A^2*B^2*a^24*b^30*d^5 + 576576*A^2*B^2*a^26*b^28*d^5 + 933504*A^2*B^2*a^28*b^26*d^5 +
1125696*A^2*B^2*a^30*b^24*d^5 + 1025024*A^2*B^2*a^32*b^22*d^5 + 704704*A^2*B^2*a^34*b^20*d^5 + 361088*A^2*B^2*
a^36*b^18*d^5 + 133952*A^2*B^2*a^38*b^16*d^5 + 34048*A^2*B^2*a^40*b^14*d^5 + 5312*A^2*B^2*a^42*b^12*d^5 + 384*
A^2*B^2*a^44*b^10*d^5))*(-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*
b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2
+ B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/
2) - 4*A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^2*a^3*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^
2 + 20*B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^
4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*1i)/(((-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*
d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B
*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*
a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 4*A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^2*a^3*b^2*d^2
- 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2 + 20*B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(16*(a^10*d^4
+ b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(((a + b*tan(c + d*x))^(
1/2)*(256*A^2*a^15*b^44*d^7 + 4608*A^2*a^17*b^42*d^7 + 40512*A^2*a^19*b^40*d^7 + 224768*A^2*a^21*b^38*d^7 + 86
4768*A^2*a^23*b^36*d^7 + 2419200*A^2*a^25*b^34*d^7 + 5055232*A^2*a^27*b^32*d^7 + 8007168*A^2*a^29*b^30*d^7 + 9
664512*A^2*a^31*b^28*d^7 + 8859136*A^2*a^33*b^26*d^7 + 6095232*A^2*a^35*b^24*d^7 + 3095040*A^2*a^37*b^22*d^7 +
1164800*A^2*a^39*b^20*d^7 + 376320*A^2*a^41*b^18*d^7 + 154368*A^2*a^43*b^16*d^7 + 76288*A^2*a^45*b^14*d^7 + 2
8416*A^2*a^47*b^12*d^7 + 6144*A^2*a^49*b^10*d^7 + 576*A^2*a^51*b^8*d^7 - 1344*B^2*a^19*b^40*d^7 - 15872*B^2*a^
21*b^38*d^7 - 81408*B^2*a^23*b^36*d^7 - 225792*B^2*a^25*b^34*d^7 - 302848*B^2*a^27*b^32*d^7 + 139776*B^2*a^29*
b^30*d^7 + 1537536*B^2*a^31*b^28*d^7 + 3587584*B^2*a^33*b^26*d^7 + 5106816*B^2*a^35*b^24*d^7 + 5051904*B^2*a^3
7*b^22*d^7 + 3587584*B^2*a^39*b^20*d^7 + 1817088*B^2*a^41*b^18*d^7 + 628992*B^2*a^43*b^16*d^7 + 132608*B^2*a^4
5*b^14*d^7 + 10752*B^2*a^47*b^12*d^7 - 1536*B^2*a^49*b^10*d^7 - 320*B^2*a^51*b^8*d^7 + 512*A*B*a^18*b^41*d^7 +
1536*A*B*a^20*b^39*d^7 - 29184*A*B*a^22*b^37*d^7 - 283136*A*B*a^24*b^35*d^7 - 1257984*A*B*a^26*b^33*d^7 - 349
4400*A*B*a^28*b^31*d^7 - 6662656*A*B*a^30*b^29*d^7 - 9005568*A*B*a^32*b^27*d^7 - 8566272*A*B*a^34*b^25*d^7 - 5
344768*A*B*a^36*b^23*d^7 - 1537536*A*B*a^38*b^21*d^7 + 698880*A*B*a^40*b^19*d^7 + 1071616*A*B*a^42*b^17*d^7 +
612864*A*B*a^44*b^15*d^7 + 201216*A*B*a^46*b^13*d^7 + 37376*A*B*a^48*b^11*d^7 + 3072*A*B*a^50*b^9*d^7) + (-(((
8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 -
40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^1
0*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 4*A^2*a^5*d^2 + 4*B^2*a^
5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^2*a^3*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2 + 20*B^2*a*b^4*d^2 + 80*A*B
*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 +
5*a^8*b^2*d^4)))^(1/2)*(512*A*a^16*b^46*d^8 - (a + b*tan(c + d*x))^(1/2)*(-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 -
80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b
^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4
*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 4*A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*
B^2*a^3*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2 + 20*B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)
/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(512*a^18
*b^46*d^9 + 9984*a^20*b^44*d^9 + 92160*a^22*b^42*d^9 + 535296*a^24*b^40*d^9 + 2193408*a^26*b^38*d^9 + 6736896*
a^28*b^36*d^9 + 16084992*a^30*b^34*d^9 + 30551040*a^32*b^32*d^9 + 46844928*a^34*b^30*d^9 + 58499584*a^36*b^28*
d^9 + 59744256*a^38*b^26*d^9 + 49900032*a^40*b^24*d^9 + 33945600*a^42*b^22*d^9 + 18643968*a^44*b^20*d^9 + 8146
944*a^46*b^18*d^9 + 2767872*a^48*b^16*d^9 + 705024*a^50*b^14*d^9 + 126720*a^52*b^12*d^9 + 14336*a^54*b^10*d^9
+ 768*a^56*b^8*d^9) + 9728*A*a^18*b^44*d^8 + 87936*A*a^20*b^42*d^8 + 502144*A*a^22*b^40*d^8 + 2028544*A*a^24*b
^38*d^8 + 6153216*A*a^26*b^36*d^8 + 14518784*A*a^28*b^34*d^8 + 27243008*A*a^30*b^32*d^8 + 41213952*A*a^32*b^30
*d^8 + 50665472*A*a^34*b^28*d^8 + 50775296*A*a^36*b^26*d^8 + 41443584*A*a^38*b^24*d^8 + 27409408*A*a^40*b^22*d
^8 + 14543872*A*a^42*b^20*d^8 + 6093312*A*a^44*b^18*d^8 + 1966592*A*a^46*b^16*d^8 + 470528*A*a^48*b^14*d^8 + 7
8336*A*a^50*b^12*d^8 + 8064*A*a^52*b^10*d^8 + 384*A*a^54*b^8*d^8 + 128*B*a^19*b^43*d^8 + 1664*B*a^21*b^41*d^8
+ 9216*B*a^23*b^39*d^8 + 25600*B*a^25*b^37*d^8 + 17920*B*a^27*b^35*d^8 - 139776*B*a^29*b^33*d^8 - 652288*B*a^3
1*b^31*d^8 - 1610752*B*a^33*b^29*d^8 - 2745600*B*a^35*b^27*d^8 - 3477760*B*a^37*b^25*d^8 - 3367936*B*a^39*b^23
*d^8 - 2515968*B*a^41*b^21*d^8 - 1444352*B*a^43*b^19*d^8 - 627200*B*a^45*b^17*d^8 - 199680*B*a^47*b^15*d^8 - 4
4032*B*a^49*b^13*d^8 - 6016*B*a^51*b^11*d^8 - 384*B*a^53*b^9*d^8))*(-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2
*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2
+ 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d
^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 4*A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^2*a^
3*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2 + 20*B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(16*(
a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2) - 384*A^3*a^15*
b^42*d^6 - 7296*A^3*a^17*b^40*d^6 - 59424*A^3*a^19*b^38*d^6 - 280992*A^3*a^21*b^36*d^6 - 866208*A^3*a^23*b^34*
d^6 - 1825824*A^3*a^25*b^32*d^6 - 2629536*A^3*a^27*b^30*d^6 - 2374944*A^3*a^29*b^28*d^6 - 727584*A^3*a^31*b^26
*d^6 + 1413984*A^3*a^33*b^24*d^6 + 2649504*A^3*a^35*b^22*d^6 + 2454816*A^3*a^37*b^20*d^6 + 1476384*A^3*a^39*b^
18*d^6 + 597408*A^3*a^41*b^16*d^6 + 156192*A^3*a^43*b^14*d^6 + 22944*A^3*a^45*b^12*d^6 + 1056*A^3*a^47*b^10*d^
6 - 96*A^3*a^49*b^8*d^6 + 64*B^3*a^20*b^37*d^6 + 896*B^3*a^22*b^35*d^6 + 5824*B^3*a^24*b^33*d^6 + 23296*B^3*a^
26*b^31*d^6 + 64064*B^3*a^28*b^29*d^6 + 128128*B^3*a^30*b^27*d^6 + 192192*B^3*a^32*b^25*d^6 + 219648*B^3*a^34*
b^23*d^6 + 192192*B^3*a^36*b^21*d^6 + 128128*B^3*a^38*b^19*d^6 + 64064*B^3*a^40*b^17*d^6 + 23296*B^3*a^42*b^15
*d^6 + 5824*B^3*a^44*b^13*d^6 + 896*B^3*a^46*b^11*d^6 + 64*B^3*a^48*b^9*d^6 + 1280*A*B^2*a^17*b^40*d^6 + 15328
*A*B^2*a^19*b^38*d^6 + 80480*A*B^2*a^21*b^36*d^6 + 234080*A*B^2*a^23*b^34*d^6 + 364000*A*B^2*a^25*b^32*d^6 + 7
2800*A*B^2*a^27*b^30*d^6 - 1057056*A*B^2*a^29*b^28*d^6 - 2814240*A*B^2*a^31*b^26*d^6 - 4187040*A*B^2*a^33*b^24
*d^6 - 4232800*A*B^2*a^35*b^22*d^6 - 3043040*A*B^2*a^37*b^20*d^6 - 1552096*A*B^2*a^39*b^18*d^6 - 538720*A*B^2*
a^41*b^16*d^6 - 113120*A*B^2*a^43*b^14*d^6 - 8800*A*B^2*a^45*b^12*d^6 + 1440*A*B^2*a^47*b^10*d^6 + 288*A*B^2*a
^49*b^8*d^6 - 128*A^2*B*a^14*b^43*d^6 - 2176*A^2*B*a^16*b^41*d^6 - 11264*A^2*B*a^18*b^39*d^6 - 3008*A^2*B*a^20
*b^37*d^6 + 226688*A^2*B*a^22*b^35*d^6 + 1263808*A^2*B*a^24*b^33*d^6 + 3843840*A^2*B*a^26*b^31*d^6 + 7824960*A
^2*B*a^28*b^29*d^6 + 11366784*A^2*B*a^30*b^27*d^6 + 12016576*A^2*B*a^32*b^25*d^6 + 9152000*A^2*B*a^34*b^23*d^6
+ 4758208*A^2*B*a^36*b^21*d^6 + 1386112*A^2*B*a^38*b^19*d^6 - 54208*A^2*B*a^40*b^17*d^6 - 250112*A^2*B*a^42*b
^15*d^6 - 111936*A^2*B*a^44*b^13*d^6 - 23808*A^2*B*a^46*b^11*d^6 - 2112*A^2*B*a^48*b^9*d^6) - (a + b*tan(c + d
*x))^(1/2)*(64*A^4*a^14*b^40*d^5 + 512*A^4*a^16*b^38*d^5 + 544*A^4*a^18*b^36*d^5 - 10304*A^4*a^20*b^34*d^5 - 6
6976*A^4*a^22*b^32*d^5 - 221312*A^4*a^24*b^30*d^5 - 480480*A^4*a^26*b^28*d^5 - 741312*A^4*a^28*b^26*d^5 - 8374
08*A^4*a^30*b^24*d^5 - 695552*A^4*a^32*b^22*d^5 - 416416*A^4*a^34*b^20*d^5 - 168896*A^4*a^36*b^18*d^5 - 37856*
A^4*a^38*b^16*d^5 + 896*A^4*a^40*b^14*d^5 + 3424*A^4*a^42*b^12*d^5 + 960*A^4*a^44*b^10*d^5 + 96*A^4*a^46*b^8*d
^5 + 32*B^4*a^18*b^36*d^5 + 448*B^4*a^20*b^34*d^5 + 2912*B^4*a^22*b^32*d^5 + 11648*B^4*a^24*b^30*d^5 + 32032*B
^4*a^26*b^28*d^5 + 64064*B^4*a^28*b^26*d^5 + 96096*B^4*a^30*b^24*d^5 + 109824*B^4*a^32*b^22*d^5 + 96096*B^4*a^
34*b^20*d^5 + 64064*B^4*a^36*b^18*d^5 + 32032*B^4*a^38*b^16*d^5 + 11648*B^4*a^40*b^14*d^5 + 2912*B^4*a^42*b^12
*d^5 + 448*B^4*a^44*b^10*d^5 + 32*B^4*a^46*b^8*d^5 - 512*A^3*B*a^15*b^39*d^5 - 6656*A^3*B*a^17*b^37*d^5 - 3942
4*A^3*B*a^19*b^35*d^5 - 139776*A^3*B*a^21*b^33*d^5 - 326144*A^3*B*a^23*b^31*d^5 - 512512*A^3*B*a^25*b^29*d^5 -
512512*A^3*B*a^27*b^27*d^5 - 219648*A^3*B*a^29*b^25*d^5 + 219648*A^3*B*a^31*b^23*d^5 + 512512*A^3*B*a^33*b^21
*d^5 + 512512*A^3*B*a^35*b^19*d^5 + 326144*A^3*B*a^37*b^17*d^5 + 139776*A^3*B*a^39*b^15*d^5 + 39424*A^3*B*a^41
*b^13*d^5 + 6656*A^3*B*a^43*b^11*d^5 + 512*A^3*B*a^45*b^9*d^5 - 64*A^2*B^2*a^14*b^40*d^5 - 512*A^2*B^2*a^16*b^
38*d^5 - 448*A^2*B^2*a^18*b^36*d^5 + 11648*A^2*B^2*a^20*b^34*d^5 + 75712*A^2*B^2*a^22*b^32*d^5 + 256256*A^2*B^
2*a^24*b^30*d^5 + 576576*A^2*B^2*a^26*b^28*d^5 + 933504*A^2*B^2*a^28*b^26*d^5 + 1125696*A^2*B^2*a^30*b^24*d^5
+ 1025024*A^2*B^2*a^32*b^22*d^5 + 704704*A^2*B^2*a^34*b^20*d^5 + 361088*A^2*B^2*a^36*b^18*d^5 + 133952*A^2*B^2
*a^38*b^16*d^5 + 34048*A^2*B^2*a^40*b^14*d^5 + 5312*A^2*B^2*a^42*b^12*d^5 + 384*A^2*B^2*a^44*b^10*d^5))*(-(((8
*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 4
0*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10
*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 4*A^2*a^5*d^2 + 4*B^2*a^5
*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^2*a^3*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2 + 20*B^2*a*b^4*d^2 + 80*A*B*
a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5
*a^8*b^2*d^4)))^(1/2) + ((-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B
*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^
2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1
/2) - 4*A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^2*a^3*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d
^2 + 20*B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a
^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(1413984*A^3*a^33*b^24*d^6 - 384*A^3*a^15*b^42*d^6 - 7296
*A^3*a^17*b^40*d^6 - 59424*A^3*a^19*b^38*d^6 - 280992*A^3*a^21*b^36*d^6 - 866208*A^3*a^23*b^34*d^6 - 1825824*A
^3*a^25*b^32*d^6 - 2629536*A^3*a^27*b^30*d^6 - 2374944*A^3*a^29*b^28*d^6 - 727584*A^3*a^31*b^26*d^6 - ((a + b*
tan(c + d*x))^(1/2)*(256*A^2*a^15*b^44*d^7 + 4608*A^2*a^17*b^42*d^7 + 40512*A^2*a^19*b^40*d^7 + 224768*A^2*a^2
1*b^38*d^7 + 864768*A^2*a^23*b^36*d^7 + 2419200*A^2*a^25*b^34*d^7 + 5055232*A^2*a^27*b^32*d^7 + 8007168*A^2*a^
29*b^30*d^7 + 9664512*A^2*a^31*b^28*d^7 + 8859136*A^2*a^33*b^26*d^7 + 6095232*A^2*a^35*b^24*d^7 + 3095040*A^2*
a^37*b^22*d^7 + 1164800*A^2*a^39*b^20*d^7 + 376320*A^2*a^41*b^18*d^7 + 154368*A^2*a^43*b^16*d^7 + 76288*A^2*a^
45*b^14*d^7 + 28416*A^2*a^47*b^12*d^7 + 6144*A^2*a^49*b^10*d^7 + 576*A^2*a^51*b^8*d^7 - 1344*B^2*a^19*b^40*d^7
- 15872*B^2*a^21*b^38*d^7 - 81408*B^2*a^23*b^36*d^7 - 225792*B^2*a^25*b^34*d^7 - 302848*B^2*a^27*b^32*d^7 + 1
39776*B^2*a^29*b^30*d^7 + 1537536*B^2*a^31*b^28*d^7 + 3587584*B^2*a^33*b^26*d^7 + 5106816*B^2*a^35*b^24*d^7 +
5051904*B^2*a^37*b^22*d^7 + 3587584*B^2*a^39*b^20*d^7 + 1817088*B^2*a^41*b^18*d^7 + 628992*B^2*a^43*b^16*d^7 +
132608*B^2*a^45*b^14*d^7 + 10752*B^2*a^47*b^12*d^7 - 1536*B^2*a^49*b^10*d^7 - 320*B^2*a^51*b^8*d^7 + 512*A*B*
a^18*b^41*d^7 + 1536*A*B*a^20*b^39*d^7 - 29184*A*B*a^22*b^37*d^7 - 283136*A*B*a^24*b^35*d^7 - 1257984*A*B*a^26
*b^33*d^7 - 3494400*A*B*a^28*b^31*d^7 - 6662656*A*B*a^30*b^29*d^7 - 9005568*A*B*a^32*b^27*d^7 - 8566272*A*B*a^
34*b^25*d^7 - 5344768*A*B*a^36*b^23*d^7 - 1537536*A*B*a^38*b^21*d^7 + 698880*A*B*a^40*b^19*d^7 + 1071616*A*B*a
^42*b^17*d^7 + 612864*A*B*a^44*b^15*d^7 + 201216*A*B*a^46*b^13*d^7 + 37376*A*B*a^48*b^11*d^7 + 3072*A*B*a^50*b
^9*d^7) - (-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A
^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^
10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 4*A^2*a^5
*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^2*a^3*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2 + 20*B^2*a*b
^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10
*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*((a + b*tan(c + d*x))^(1/2)*(-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*
a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2
+ 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^
4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 4*A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^2*a^3
*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2 + 20*B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(16*(a
^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(512*a^18*b^46*d
^9 + 9984*a^20*b^44*d^9 + 92160*a^22*b^42*d^9 + 535296*a^24*b^40*d^9 + 2193408*a^26*b^38*d^9 + 6736896*a^28*b^
36*d^9 + 16084992*a^30*b^34*d^9 + 30551040*a^32*b^32*d^9 + 46844928*a^34*b^30*d^9 + 58499584*a^36*b^28*d^9 + 5
9744256*a^38*b^26*d^9 + 49900032*a^40*b^24*d^9 + 33945600*a^42*b^22*d^9 + 18643968*a^44*b^20*d^9 + 8146944*a^4
6*b^18*d^9 + 2767872*a^48*b^16*d^9 + 705024*a^50*b^14*d^9 + 126720*a^52*b^12*d^9 + 14336*a^54*b^10*d^9 + 768*a
^56*b^8*d^9) + 512*A*a^16*b^46*d^8 + 9728*A*a^18*b^44*d^8 + 87936*A*a^20*b^42*d^8 + 502144*A*a^22*b^40*d^8 + 2
028544*A*a^24*b^38*d^8 + 6153216*A*a^26*b^36*d^8 + 14518784*A*a^28*b^34*d^8 + 27243008*A*a^30*b^32*d^8 + 41213
952*A*a^32*b^30*d^8 + 50665472*A*a^34*b^28*d^8 + 50775296*A*a^36*b^26*d^8 + 41443584*A*a^38*b^24*d^8 + 2740940
8*A*a^40*b^22*d^8 + 14543872*A*a^42*b^20*d^8 + 6093312*A*a^44*b^18*d^8 + 1966592*A*a^46*b^16*d^8 + 470528*A*a^
48*b^14*d^8 + 78336*A*a^50*b^12*d^8 + 8064*A*a^52*b^10*d^8 + 384*A*a^54*b^8*d^8 + 128*B*a^19*b^43*d^8 + 1664*B
*a^21*b^41*d^8 + 9216*B*a^23*b^39*d^8 + 25600*B*a^25*b^37*d^8 + 17920*B*a^27*b^35*d^8 - 139776*B*a^29*b^33*d^8
- 652288*B*a^31*b^31*d^8 - 1610752*B*a^33*b^29*d^8 - 2745600*B*a^35*b^27*d^8 - 3477760*B*a^37*b^25*d^8 - 3367
936*B*a^39*b^23*d^8 - 2515968*B*a^41*b^21*d^8 - 1444352*B*a^43*b^19*d^8 - 627200*B*a^45*b^17*d^8 - 199680*B*a^
47*b^15*d^8 - 44032*B*a^49*b^13*d^8 - 6016*B*a^51*b^11*d^8 - 384*B*a^53*b^9*d^8))*(-(((8*A^2*a^5*d^2 - 8*B^2*a
^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*
A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4
+ 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 4*A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*
d^2 - 40*B^2*a^3*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2 + 20*B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a
^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)
+ 2649504*A^3*a^35*b^22*d^6 + 2454816*A^3*a^37*b^20*d^6 + 1476384*A^3*a^39*b^18*d^6 + 597408*A^3*a^41*b^16*d^6
+ 156192*A^3*a^43*b^14*d^6 + 22944*A^3*a^45*b^12*d^6 + 1056*A^3*a^47*b^10*d^6 - 96*A^3*a^49*b^8*d^6 + 64*B^3*
a^20*b^37*d^6 + 896*B^3*a^22*b^35*d^6 + 5824*B^3*a^24*b^33*d^6 + 23296*B^3*a^26*b^31*d^6 + 64064*B^3*a^28*b^29
*d^6 + 128128*B^3*a^30*b^27*d^6 + 192192*B^3*a^32*b^25*d^6 + 219648*B^3*a^34*b^23*d^6 + 192192*B^3*a^36*b^21*d
^6 + 128128*B^3*a^38*b^19*d^6 + 64064*B^3*a^40*b^17*d^6 + 23296*B^3*a^42*b^15*d^6 + 5824*B^3*a^44*b^13*d^6 + 8
96*B^3*a^46*b^11*d^6 + 64*B^3*a^48*b^9*d^6 + 1280*A*B^2*a^17*b^40*d^6 + 15328*A*B^2*a^19*b^38*d^6 + 80480*A*B^
2*a^21*b^36*d^6 + 234080*A*B^2*a^23*b^34*d^6 + 364000*A*B^2*a^25*b^32*d^6 + 72800*A*B^2*a^27*b^30*d^6 - 105705
6*A*B^2*a^29*b^28*d^6 - 2814240*A*B^2*a^31*b^26*d^6 - 4187040*A*B^2*a^33*b^24*d^6 - 4232800*A*B^2*a^35*b^22*d^
6 - 3043040*A*B^2*a^37*b^20*d^6 - 1552096*A*B^2*a^39*b^18*d^6 - 538720*A*B^2*a^41*b^16*d^6 - 113120*A*B^2*a^43
*b^14*d^6 - 8800*A*B^2*a^45*b^12*d^6 + 1440*A*B^2*a^47*b^10*d^6 + 288*A*B^2*a^49*b^8*d^6 - 128*A^2*B*a^14*b^43
*d^6 - 2176*A^2*B*a^16*b^41*d^6 - 11264*A^2*B*a^18*b^39*d^6 - 3008*A^2*B*a^20*b^37*d^6 + 226688*A^2*B*a^22*b^3
5*d^6 + 1263808*A^2*B*a^24*b^33*d^6 + 3843840*A^2*B*a^26*b^31*d^6 + 7824960*A^2*B*a^28*b^29*d^6 + 11366784*A^2
*B*a^30*b^27*d^6 + 12016576*A^2*B*a^32*b^25*d^6 + 9152000*A^2*B*a^34*b^23*d^6 + 4758208*A^2*B*a^36*b^21*d^6 +
1386112*A^2*B*a^38*b^19*d^6 - 54208*A^2*B*a^40*b^17*d^6 - 250112*A^2*B*a^42*b^15*d^6 - 111936*A^2*B*a^44*b^13*
d^6 - 23808*A^2*B*a^46*b^11*d^6 - 2112*A^2*B*a^48*b^9*d^6) + (a + b*tan(c + d*x))^(1/2)*(64*A^4*a^14*b^40*d^5
+ 512*A^4*a^16*b^38*d^5 + 544*A^4*a^18*b^36*d^5 - 10304*A^4*a^20*b^34*d^5 - 66976*A^4*a^22*b^32*d^5 - 221312*A
^4*a^24*b^30*d^5 - 480480*A^4*a^26*b^28*d^5 - 741312*A^4*a^28*b^26*d^5 - 837408*A^4*a^30*b^24*d^5 - 695552*A^4
*a^32*b^22*d^5 - 416416*A^4*a^34*b^20*d^5 - 168896*A^4*a^36*b^18*d^5 - 37856*A^4*a^38*b^16*d^5 + 896*A^4*a^40*
b^14*d^5 + 3424*A^4*a^42*b^12*d^5 + 960*A^4*a^44*b^10*d^5 + 96*A^4*a^46*b^8*d^5 + 32*B^4*a^18*b^36*d^5 + 448*B
^4*a^20*b^34*d^5 + 2912*B^4*a^22*b^32*d^5 + 11648*B^4*a^24*b^30*d^5 + 32032*B^4*a^26*b^28*d^5 + 64064*B^4*a^28
*b^26*d^5 + 96096*B^4*a^30*b^24*d^5 + 109824*B^4*a^32*b^22*d^5 + 96096*B^4*a^34*b^20*d^5 + 64064*B^4*a^36*b^18
*d^5 + 32032*B^4*a^38*b^16*d^5 + 11648*B^4*a^40*b^14*d^5 + 2912*B^4*a^42*b^12*d^5 + 448*B^4*a^44*b^10*d^5 + 32
*B^4*a^46*b^8*d^5 - 512*A^3*B*a^15*b^39*d^5 - 6656*A^3*B*a^17*b^37*d^5 - 39424*A^3*B*a^19*b^35*d^5 - 139776*A^
3*B*a^21*b^33*d^5 - 326144*A^3*B*a^23*b^31*d^5 - 512512*A^3*B*a^25*b^29*d^5 - 512512*A^3*B*a^27*b^27*d^5 - 219
648*A^3*B*a^29*b^25*d^5 + 219648*A^3*B*a^31*b^23*d^5 + 512512*A^3*B*a^33*b^21*d^5 + 512512*A^3*B*a^35*b^19*d^5
+ 326144*A^3*B*a^37*b^17*d^5 + 139776*A^3*B*a^39*b^15*d^5 + 39424*A^3*B*a^41*b^13*d^5 + 6656*A^3*B*a^43*b^11*
d^5 + 512*A^3*B*a^45*b^9*d^5 - 64*A^2*B^2*a^14*b^40*d^5 - 512*A^2*B^2*a^16*b^38*d^5 - 448*A^2*B^2*a^18*b^36*d^
5 + 11648*A^2*B^2*a^20*b^34*d^5 + 75712*A^2*B^2*a^22*b^32*d^5 + 256256*A^2*B^2*a^24*b^30*d^5 + 576576*A^2*B^2*
a^26*b^28*d^5 + 933504*A^2*B^2*a^28*b^26*d^5 + 1125696*A^2*B^2*a^30*b^24*d^5 + 1025024*A^2*B^2*a^32*b^22*d^5 +
704704*A^2*B^2*a^34*b^20*d^5 + 361088*A^2*B^2*a^36*b^18*d^5 + 133952*A^2*B^2*a^38*b^16*d^5 + 34048*A^2*B^2*a^
40*b^14*d^5 + 5312*A^2*B^2*a^42*b^12*d^5 + 384*A^2*B^2*a^44*b^10*d^5))*(-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80
*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3
*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b
^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 4*A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^
2*a^3*b^2*d^2 - 8*A*B*b^5*d^2 - 20*A^2*a*b^4*d^2 + 20*B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(
16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2) + 64*A^5*a^
14*b^38*d^4 + 896*A^5*a^16*b^36*d^4 + 5824*A^5*a^18*b^34*d^4 + 23296*A^5*a^20*b^32*d^4 + 64064*A^5*a^22*b^30*d
^4 + 128128*A^5*a^24*b^28*d^4 + 192192*A^5*a^26*b^26*d^4 + 219648*A^5*a^28*b^24*d^4 + 192192*A^5*a^30*b^22*d^4
+ 128128*A^5*a^32*b^20*d^4 + 64064*A^5*a^34*b^18*d^4 + 23296*A^5*a^36*b^16*d^4 + 5824*A^5*a^38*b^14*d^4 + 896
*A^5*a^40*b^12*d^4 + 64*A^5*a^42*b^10*d^4 + 64*A*B^4*a^16*b^36*d^4 + 896*A*B^4*a^18*b^34*d^4 + 5824*A*B^4*a^20
*b^32*d^4 + 23296*A*B^4*a^22*b^30*d^4 + 64064*A*B^4*a^24*b^28*d^4 + 128128*A*B^4*a^26*b^26*d^4 + 192192*A*B^4*
a^28*b^24*d^4 + 219648*A*B^4*a^30*b^22*d^4 + 192192*A*B^4*a^32*b^20*d^4 + 128128*A*B^4*a^34*b^18*d^4 + 64064*A
*B^4*a^36*b^16*d^4 + 23296*A*B^4*a^38*b^14*d^4 + 5824*A*B^4*a^40*b^12*d^4 + 896*A*B^4*a^42*b^10*d^4 + 64*A*B^4
*a^44*b^8*d^4 - 128*A^4*B*a^15*b^37*d^4 - 1792*A^4*B*a^17*b^35*d^4 - 11648*A^4*B*a^19*b^33*d^4 - 46592*A^4*B*a
^21*b^31*d^4 - 128128*A^4*B*a^23*b^29*d^4 - 256256*A^4*B*a^25*b^27*d^4 - 384384*A^4*B*a^27*b^25*d^4 - 439296*A
^4*B*a^29*b^23*d^4 - 384384*A^4*B*a^31*b^21*d^4 - 256256*A^4*B*a^33*b^19*d^4 - 128128*A^4*B*a^35*b^17*d^4 - 46
592*A^4*B*a^37*b^15*d^4 - 11648*A^4*B*a^39*b^13*d^4 - 1792*A^4*B*a^41*b^11*d^4 - 128*A^4*B*a^43*b^9*d^4 - 128*
A^2*B^3*a^15*b^37*d^4 - 1792*A^2*B^3*a^17*b^35*d^4 - 11648*A^2*B^3*a^19*b^33*d^4 - 46592*A^2*B^3*a^21*b^31*d^4
- 128128*A^2*B^3*a^23*b^29*d^4 - 256256*A^2*B^3*a^25*b^27*d^4 - 384384*A^2*B^3*a^27*b^25*d^4 - 439296*A^2*B^3
*a^29*b^23*d^4 - 384384*A^2*B^3*a^31*b^21*d^4 - 256256*A^2*B^3*a^33*b^19*d^4 - 128128*A^2*B^3*a^35*b^17*d^4 -
46592*A^2*B^3*a^37*b^15*d^4 - 11648*A^2*B^3*a^39*b^13*d^4 - 1792*A^2*B^3*a^41*b^11*d^4 - 128*A^2*B^3*a^43*b^9*
d^4 + 64*A^3*B^2*a^14*b^38*d^4 + 960*A^3*B^2*a^16*b^36*d^4 + 6720*A^3*B^2*a^18*b^34*d^4 + 29120*A^3*B^2*a^20*b
^32*d^4 + 87360*A^3*B^2*a^22*b^30*d^4 + 192192*A^3*B^2*a^24*b^28*d^4 + 320320*A^3*B^2*a^26*b^26*d^4 + 411840*A
^3*B^2*a^28*b^24*d^4 + 411840*A^3*B^2*a^30*b^22*d^4 + 320320*A^3*B^2*a^32*b^20*d^4 + 192192*A^3*B^2*a^34*b^18*
d^4 + 87360*A^3*B^2*a^36*b^16*d^4 + 29120*A^3*B^2*a^38*b^14*d^4 + 6720*A^3*B^2*a^40*b^12*d^4 + 960*A^3*B^2*a^4
2*b^10*d^4 + 64*A^3*B^2*a^44*b^8*d^4))*(-(((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^
2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (
A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^
8*b^2*d^4))^(1/2) - 4*A^2*a^5*d^2 + 4*B^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 40*B^2*a^3*b^2*d^2 - 8*A*B*b^5*d^2 -
20*A^2*a*b^4*d^2 + 20*B^2*a*b^4*d^2 + 80*A*B*a^2*b^3*d^2 - 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*
b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*2i + atan(-((((((8*A^2*a^5*d^2 - 8*B^2*a^5*
d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B
*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 1
60*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^2*a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2
+ 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^2*a*b^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*B*a^4*
b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(((
a + b*tan(c + d*x))^(1/2)*(256*A^2*a^15*b^44*d^7 + 4608*A^2*a^17*b^42*d^7 + 40512*A^2*a^19*b^40*d^7 + 224768*A
^2*a^21*b^38*d^7 + 864768*A^2*a^23*b^36*d^7 + 2419200*A^2*a^25*b^34*d^7 + 5055232*A^2*a^27*b^32*d^7 + 8007168*
A^2*a^29*b^30*d^7 + 9664512*A^2*a^31*b^28*d^7 + 8859136*A^2*a^33*b^26*d^7 + 6095232*A^2*a^35*b^24*d^7 + 309504
0*A^2*a^37*b^22*d^7 + 1164800*A^2*a^39*b^20*d^7 + 376320*A^2*a^41*b^18*d^7 + 154368*A^2*a^43*b^16*d^7 + 76288*
A^2*a^45*b^14*d^7 + 28416*A^2*a^47*b^12*d^7 + 6144*A^2*a^49*b^10*d^7 + 576*A^2*a^51*b^8*d^7 - 1344*B^2*a^19*b^
40*d^7 - 15872*B^2*a^21*b^38*d^7 - 81408*B^2*a^23*b^36*d^7 - 225792*B^2*a^25*b^34*d^7 - 302848*B^2*a^27*b^32*d
^7 + 139776*B^2*a^29*b^30*d^7 + 1537536*B^2*a^31*b^28*d^7 + 3587584*B^2*a^33*b^26*d^7 + 5106816*B^2*a^35*b^24*
d^7 + 5051904*B^2*a^37*b^22*d^7 + 3587584*B^2*a^39*b^20*d^7 + 1817088*B^2*a^41*b^18*d^7 + 628992*B^2*a^43*b^16
*d^7 + 132608*B^2*a^45*b^14*d^7 + 10752*B^2*a^47*b^12*d^7 - 1536*B^2*a^49*b^10*d^7 - 320*B^2*a^51*b^8*d^7 + 51
2*A*B*a^18*b^41*d^7 + 1536*A*B*a^20*b^39*d^7 - 29184*A*B*a^22*b^37*d^7 - 283136*A*B*a^24*b^35*d^7 - 1257984*A*
B*a^26*b^33*d^7 - 3494400*A*B*a^28*b^31*d^7 - 6662656*A*B*a^30*b^29*d^7 - 9005568*A*B*a^32*b^27*d^7 - 8566272*
A*B*a^34*b^25*d^7 - 5344768*A*B*a^36*b^23*d^7 - 1537536*A*B*a^38*b^21*d^7 + 698880*A*B*a^40*b^19*d^7 + 1071616
*A*B*a^42*b^17*d^7 + 612864*A*B*a^44*b^15*d^7 + 201216*A*B*a^46*b^13*d^7 + 37376*A*B*a^48*b^11*d^7 + 3072*A*B*
a^50*b^9*d^7) + ((((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 +
40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(
16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^
2*a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^
2*a*b^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4
+ 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(512*A*a^16*b^46*d^8 - (a + b*tan(c + d*x))^(1/2)*((((8*A^2*a^5*d^2
- 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*
d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^
2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^2*a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^
2*a^3*b^2*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^2*a*b^4*d^2 - 80*A*B*a^2*b^3*d^2
+ 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4
)))^(1/2)*(512*a^18*b^46*d^9 + 9984*a^20*b^44*d^9 + 92160*a^22*b^42*d^9 + 535296*a^24*b^40*d^9 + 2193408*a^26*
b^38*d^9 + 6736896*a^28*b^36*d^9 + 16084992*a^30*b^34*d^9 + 30551040*a^32*b^32*d^9 + 46844928*a^34*b^30*d^9 +
58499584*a^36*b^28*d^9 + 59744256*a^38*b^26*d^9 + 49900032*a^40*b^24*d^9 + 33945600*a^42*b^22*d^9 + 18643968*a
^44*b^20*d^9 + 8146944*a^46*b^18*d^9 + 2767872*a^48*b^16*d^9 + 705024*a^50*b^14*d^9 + 126720*a^52*b^12*d^9 + 1
4336*a^54*b^10*d^9 + 768*a^56*b^8*d^9) + 9728*A*a^18*b^44*d^8 + 87936*A*a^20*b^42*d^8 + 502144*A*a^22*b^40*d^8
+ 2028544*A*a^24*b^38*d^8 + 6153216*A*a^26*b^36*d^8 + 14518784*A*a^28*b^34*d^8 + 27243008*A*a^30*b^32*d^8 + 4
1213952*A*a^32*b^30*d^8 + 50665472*A*a^34*b^28*d^8 + 50775296*A*a^36*b^26*d^8 + 41443584*A*a^38*b^24*d^8 + 274
09408*A*a^40*b^22*d^8 + 14543872*A*a^42*b^20*d^8 + 6093312*A*a^44*b^18*d^8 + 1966592*A*a^46*b^16*d^8 + 470528*
A*a^48*b^14*d^8 + 78336*A*a^50*b^12*d^8 + 8064*A*a^52*b^10*d^8 + 384*A*a^54*b^8*d^8 + 128*B*a^19*b^43*d^8 + 16
64*B*a^21*b^41*d^8 + 9216*B*a^23*b^39*d^8 + 25600*B*a^25*b^37*d^8 + 17920*B*a^27*b^35*d^8 - 139776*B*a^29*b^33
*d^8 - 652288*B*a^31*b^31*d^8 - 1610752*B*a^33*b^29*d^8 - 2745600*B*a^35*b^27*d^8 - 3477760*B*a^37*b^25*d^8 -
3367936*B*a^39*b^23*d^8 - 2515968*B*a^41*b^21*d^8 - 1444352*B*a^43*b^19*d^8 - 627200*B*a^45*b^17*d^8 - 199680*
B*a^47*b^15*d^8 - 44032*B*a^49*b^13*d^8 - 6016*B*a^51*b^11*d^8 - 384*B*a^53*b^9*d^8))*((((8*A^2*a^5*d^2 - 8*B^
2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 1
60*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d
^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^2*a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b
^2*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^2*a*b^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*
B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/
2) - 384*A^3*a^15*b^42*d^6 - 7296*A^3*a^17*b^40*d^6 - 59424*A^3*a^19*b^38*d^6 - 280992*A^3*a^21*b^36*d^6 - 866
208*A^3*a^23*b^34*d^6 - 1825824*A^3*a^25*b^32*d^6 - 2629536*A^3*a^27*b^30*d^6 - 2374944*A^3*a^29*b^28*d^6 - 72
7584*A^3*a^31*b^26*d^6 + 1413984*A^3*a^33*b^24*d^6 + 2649504*A^3*a^35*b^22*d^6 + 2454816*A^3*a^37*b^20*d^6 + 1
476384*A^3*a^39*b^18*d^6 + 597408*A^3*a^41*b^16*d^6 + 156192*A^3*a^43*b^14*d^6 + 22944*A^3*a^45*b^12*d^6 + 105
6*A^3*a^47*b^10*d^6 - 96*A^3*a^49*b^8*d^6 + 64*B^3*a^20*b^37*d^6 + 896*B^3*a^22*b^35*d^6 + 5824*B^3*a^24*b^33*
d^6 + 23296*B^3*a^26*b^31*d^6 + 64064*B^3*a^28*b^29*d^6 + 128128*B^3*a^30*b^27*d^6 + 192192*B^3*a^32*b^25*d^6
+ 219648*B^3*a^34*b^23*d^6 + 192192*B^3*a^36*b^21*d^6 + 128128*B^3*a^38*b^19*d^6 + 64064*B^3*a^40*b^17*d^6 + 2
3296*B^3*a^42*b^15*d^6 + 5824*B^3*a^44*b^13*d^6 + 896*B^3*a^46*b^11*d^6 + 64*B^3*a^48*b^9*d^6 + 1280*A*B^2*a^1
7*b^40*d^6 + 15328*A*B^2*a^19*b^38*d^6 + 80480*A*B^2*a^21*b^36*d^6 + 234080*A*B^2*a^23*b^34*d^6 + 364000*A*B^2
*a^25*b^32*d^6 + 72800*A*B^2*a^27*b^30*d^6 - 1057056*A*B^2*a^29*b^28*d^6 - 2814240*A*B^2*a^31*b^26*d^6 - 41870
40*A*B^2*a^33*b^24*d^6 - 4232800*A*B^2*a^35*b^22*d^6 - 3043040*A*B^2*a^37*b^20*d^6 - 1552096*A*B^2*a^39*b^18*d
^6 - 538720*A*B^2*a^41*b^16*d^6 - 113120*A*B^2*a^43*b^14*d^6 - 8800*A*B^2*a^45*b^12*d^6 + 1440*A*B^2*a^47*b^10
*d^6 + 288*A*B^2*a^49*b^8*d^6 - 128*A^2*B*a^14*b^43*d^6 - 2176*A^2*B*a^16*b^41*d^6 - 11264*A^2*B*a^18*b^39*d^6
- 3008*A^2*B*a^20*b^37*d^6 + 226688*A^2*B*a^22*b^35*d^6 + 1263808*A^2*B*a^24*b^33*d^6 + 3843840*A^2*B*a^26*b^
31*d^6 + 7824960*A^2*B*a^28*b^29*d^6 + 11366784*A^2*B*a^30*b^27*d^6 + 12016576*A^2*B*a^32*b^25*d^6 + 9152000*A
^2*B*a^34*b^23*d^6 + 4758208*A^2*B*a^36*b^21*d^6 + 1386112*A^2*B*a^38*b^19*d^6 - 54208*A^2*B*a^40*b^17*d^6 - 2
50112*A^2*B*a^42*b^15*d^6 - 111936*A^2*B*a^44*b^13*d^6 - 23808*A^2*B*a^46*b^11*d^6 - 2112*A^2*B*a^48*b^9*d^6)
- (a + b*tan(c + d*x))^(1/2)*(64*A^4*a^14*b^40*d^5 + 512*A^4*a^16*b^38*d^5 + 544*A^4*a^18*b^36*d^5 - 10304*A^4
*a^20*b^34*d^5 - 66976*A^4*a^22*b^32*d^5 - 221312*A^4*a^24*b^30*d^5 - 480480*A^4*a^26*b^28*d^5 - 741312*A^4*a^
28*b^26*d^5 - 837408*A^4*a^30*b^24*d^5 - 695552*A^4*a^32*b^22*d^5 - 416416*A^4*a^34*b^20*d^5 - 168896*A^4*a^36
*b^18*d^5 - 37856*A^4*a^38*b^16*d^5 + 896*A^4*a^40*b^14*d^5 + 3424*A^4*a^42*b^12*d^5 + 960*A^4*a^44*b^10*d^5 +
96*A^4*a^46*b^8*d^5 + 32*B^4*a^18*b^36*d^5 + 448*B^4*a^20*b^34*d^5 + 2912*B^4*a^22*b^32*d^5 + 11648*B^4*a^24*
b^30*d^5 + 32032*B^4*a^26*b^28*d^5 + 64064*B^4*a^28*b^26*d^5 + 96096*B^4*a^30*b^24*d^5 + 109824*B^4*a^32*b^22*
d^5 + 96096*B^4*a^34*b^20*d^5 + 64064*B^4*a^36*b^18*d^5 + 32032*B^4*a^38*b^16*d^5 + 11648*B^4*a^40*b^14*d^5 +
2912*B^4*a^42*b^12*d^5 + 448*B^4*a^44*b^10*d^5 + 32*B^4*a^46*b^8*d^5 - 512*A^3*B*a^15*b^39*d^5 - 6656*A^3*B*a^
17*b^37*d^5 - 39424*A^3*B*a^19*b^35*d^5 - 139776*A^3*B*a^21*b^33*d^5 - 326144*A^3*B*a^23*b^31*d^5 - 512512*A^3
*B*a^25*b^29*d^5 - 512512*A^3*B*a^27*b^27*d^5 - 219648*A^3*B*a^29*b^25*d^5 + 219648*A^3*B*a^31*b^23*d^5 + 5125
12*A^3*B*a^33*b^21*d^5 + 512512*A^3*B*a^35*b^19*d^5 + 326144*A^3*B*a^37*b^17*d^5 + 139776*A^3*B*a^39*b^15*d^5
+ 39424*A^3*B*a^41*b^13*d^5 + 6656*A^3*B*a^43*b^11*d^5 + 512*A^3*B*a^45*b^9*d^5 - 64*A^2*B^2*a^14*b^40*d^5 - 5
12*A^2*B^2*a^16*b^38*d^5 - 448*A^2*B^2*a^18*b^36*d^5 + 11648*A^2*B^2*a^20*b^34*d^5 + 75712*A^2*B^2*a^22*b^32*d
^5 + 256256*A^2*B^2*a^24*b^30*d^5 + 576576*A^2*B^2*a^26*b^28*d^5 + 933504*A^2*B^2*a^28*b^26*d^5 + 1125696*A^2*
B^2*a^30*b^24*d^5 + 1025024*A^2*B^2*a^32*b^22*d^5 + 704704*A^2*B^2*a^34*b^20*d^5 + 361088*A^2*B^2*a^36*b^18*d^
5 + 133952*A^2*B^2*a^38*b^16*d^5 + 34048*A^2*B^2*a^40*b^14*d^5 + 5312*A^2*B^2*a^42*b^12*d^5 + 384*A^2*B^2*a^44
*b^10*d^5))*((((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*
A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a
^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^2*a^
5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^2*a*
b^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 1
0*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*1i - (((((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a
^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/
4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 +
80*a^8*b^2*d^4))^(1/2) + 4*A^2*a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d
^2 + 20*A^2*a*b^4*d^2 - 20*B^2*a*b^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5
*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(1413984*A^3*a^33*b^24*d^6 - 384*A^3*a
^15*b^42*d^6 - 7296*A^3*a^17*b^40*d^6 - 59424*A^3*a^19*b^38*d^6 - 280992*A^3*a^21*b^36*d^6 - 866208*A^3*a^23*b
^34*d^6 - 1825824*A^3*a^25*b^32*d^6 - 2629536*A^3*a^27*b^30*d^6 - 2374944*A^3*a^29*b^28*d^6 - 727584*A^3*a^31*
b^26*d^6 - ((a + b*tan(c + d*x))^(1/2)*(256*A^2*a^15*b^44*d^7 + 4608*A^2*a^17*b^42*d^7 + 40512*A^2*a^19*b^40*d
^7 + 224768*A^2*a^21*b^38*d^7 + 864768*A^2*a^23*b^36*d^7 + 2419200*A^2*a^25*b^34*d^7 + 5055232*A^2*a^27*b^32*d
^7 + 8007168*A^2*a^29*b^30*d^7 + 9664512*A^2*a^31*b^28*d^7 + 8859136*A^2*a^33*b^26*d^7 + 6095232*A^2*a^35*b^24
*d^7 + 3095040*A^2*a^37*b^22*d^7 + 1164800*A^2*a^39*b^20*d^7 + 376320*A^2*a^41*b^18*d^7 + 154368*A^2*a^43*b^16
*d^7 + 76288*A^2*a^45*b^14*d^7 + 28416*A^2*a^47*b^12*d^7 + 6144*A^2*a^49*b^10*d^7 + 576*A^2*a^51*b^8*d^7 - 134
4*B^2*a^19*b^40*d^7 - 15872*B^2*a^21*b^38*d^7 - 81408*B^2*a^23*b^36*d^7 - 225792*B^2*a^25*b^34*d^7 - 302848*B^
2*a^27*b^32*d^7 + 139776*B^2*a^29*b^30*d^7 + 1537536*B^2*a^31*b^28*d^7 + 3587584*B^2*a^33*b^26*d^7 + 5106816*B
^2*a^35*b^24*d^7 + 5051904*B^2*a^37*b^22*d^7 + 3587584*B^2*a^39*b^20*d^7 + 1817088*B^2*a^41*b^18*d^7 + 628992*
B^2*a^43*b^16*d^7 + 132608*B^2*a^45*b^14*d^7 + 10752*B^2*a^47*b^12*d^7 - 1536*B^2*a^49*b^10*d^7 - 320*B^2*a^51
*b^8*d^7 + 512*A*B*a^18*b^41*d^7 + 1536*A*B*a^20*b^39*d^7 - 29184*A*B*a^22*b^37*d^7 - 283136*A*B*a^24*b^35*d^7
- 1257984*A*B*a^26*b^33*d^7 - 3494400*A*B*a^28*b^31*d^7 - 6662656*A*B*a^30*b^29*d^7 - 9005568*A*B*a^32*b^27*d
^7 - 8566272*A*B*a^34*b^25*d^7 - 5344768*A*B*a^36*b^23*d^7 - 1537536*A*B*a^38*b^21*d^7 + 698880*A*B*a^40*b^19*
d^7 + 1071616*A*B*a^42*b^17*d^7 + 612864*A*B*a^44*b^15*d^7 + 201216*A*B*a^46*b^13*d^7 + 37376*A*B*a^48*b^11*d^
7 + 3072*A*B*a^50*b^9*d^7) - ((((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*
A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2
*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))
^(1/2) + 4*A^2*a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^
4*d^2 - 20*B^2*a*b^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 1
0*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*((a + b*tan(c + d*x))^(1/2)*((((8*A^2*a^5*d^2 - 8*B^2*
a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160
*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4
+ 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^2*a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b^2
*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^2*a*b^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*B*
a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)
*(512*a^18*b^46*d^9 + 9984*a^20*b^44*d^9 + 92160*a^22*b^42*d^9 + 535296*a^24*b^40*d^9 + 2193408*a^26*b^38*d^9
+ 6736896*a^28*b^36*d^9 + 16084992*a^30*b^34*d^9 + 30551040*a^32*b^32*d^9 + 46844928*a^34*b^30*d^9 + 58499584*
a^36*b^28*d^9 + 59744256*a^38*b^26*d^9 + 49900032*a^40*b^24*d^9 + 33945600*a^42*b^22*d^9 + 18643968*a^44*b^20*
d^9 + 8146944*a^46*b^18*d^9 + 2767872*a^48*b^16*d^9 + 705024*a^50*b^14*d^9 + 126720*a^52*b^12*d^9 + 14336*a^54
*b^10*d^9 + 768*a^56*b^8*d^9) + 512*A*a^16*b^46*d^8 + 9728*A*a^18*b^44*d^8 + 87936*A*a^20*b^42*d^8 + 502144*A*
a^22*b^40*d^8 + 2028544*A*a^24*b^38*d^8 + 6153216*A*a^26*b^36*d^8 + 14518784*A*a^28*b^34*d^8 + 27243008*A*a^30
*b^32*d^8 + 41213952*A*a^32*b^30*d^8 + 50665472*A*a^34*b^28*d^8 + 50775296*A*a^36*b^26*d^8 + 41443584*A*a^38*b
^24*d^8 + 27409408*A*a^40*b^22*d^8 + 14543872*A*a^42*b^20*d^8 + 6093312*A*a^44*b^18*d^8 + 1966592*A*a^46*b^16*
d^8 + 470528*A*a^48*b^14*d^8 + 78336*A*a^50*b^12*d^8 + 8064*A*a^52*b^10*d^8 + 384*A*a^54*b^8*d^8 + 128*B*a^19*
b^43*d^8 + 1664*B*a^21*b^41*d^8 + 9216*B*a^23*b^39*d^8 + 25600*B*a^25*b^37*d^8 + 17920*B*a^27*b^35*d^8 - 13977
6*B*a^29*b^33*d^8 - 652288*B*a^31*b^31*d^8 - 1610752*B*a^33*b^29*d^8 - 2745600*B*a^35*b^27*d^8 - 3477760*B*a^3
7*b^25*d^8 - 3367936*B*a^39*b^23*d^8 - 2515968*B*a^41*b^21*d^8 - 1444352*B*a^43*b^19*d^8 - 627200*B*a^45*b^17*
d^8 - 199680*B*a^47*b^15*d^8 - 44032*B*a^49*b^13*d^8 - 6016*B*a^51*b^11*d^8 - 384*B*a^53*b^9*d^8))*((((8*A^2*a
^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*
a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 +
80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^2*a^5*d^2 - 4*B^2*a^5*d^2 -
40*A^2*a^3*b^2*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^2*a*b^4*d^2 - 80*A*B*a^2*b^
3*d^2 + 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b
^2*d^4)))^(1/2) + 2649504*A^3*a^35*b^22*d^6 + 2454816*A^3*a^37*b^20*d^6 + 1476384*A^3*a^39*b^18*d^6 + 597408*A
^3*a^41*b^16*d^6 + 156192*A^3*a^43*b^14*d^6 + 22944*A^3*a^45*b^12*d^6 + 1056*A^3*a^47*b^10*d^6 - 96*A^3*a^49*b
^8*d^6 + 64*B^3*a^20*b^37*d^6 + 896*B^3*a^22*b^35*d^6 + 5824*B^3*a^24*b^33*d^6 + 23296*B^3*a^26*b^31*d^6 + 640
64*B^3*a^28*b^29*d^6 + 128128*B^3*a^30*b^27*d^6 + 192192*B^3*a^32*b^25*d^6 + 219648*B^3*a^34*b^23*d^6 + 192192
*B^3*a^36*b^21*d^6 + 128128*B^3*a^38*b^19*d^6 + 64064*B^3*a^40*b^17*d^6 + 23296*B^3*a^42*b^15*d^6 + 5824*B^3*a
^44*b^13*d^6 + 896*B^3*a^46*b^11*d^6 + 64*B^3*a^48*b^9*d^6 + 1280*A*B^2*a^17*b^40*d^6 + 15328*A*B^2*a^19*b^38*
d^6 + 80480*A*B^2*a^21*b^36*d^6 + 234080*A*B^2*a^23*b^34*d^6 + 364000*A*B^2*a^25*b^32*d^6 + 72800*A*B^2*a^27*b
^30*d^6 - 1057056*A*B^2*a^29*b^28*d^6 - 2814240*A*B^2*a^31*b^26*d^6 - 4187040*A*B^2*a^33*b^24*d^6 - 4232800*A*
B^2*a^35*b^22*d^6 - 3043040*A*B^2*a^37*b^20*d^6 - 1552096*A*B^2*a^39*b^18*d^6 - 538720*A*B^2*a^41*b^16*d^6 - 1
13120*A*B^2*a^43*b^14*d^6 - 8800*A*B^2*a^45*b^12*d^6 + 1440*A*B^2*a^47*b^10*d^6 + 288*A*B^2*a^49*b^8*d^6 - 128
*A^2*B*a^14*b^43*d^6 - 2176*A^2*B*a^16*b^41*d^6 - 11264*A^2*B*a^18*b^39*d^6 - 3008*A^2*B*a^20*b^37*d^6 + 22668
8*A^2*B*a^22*b^35*d^6 + 1263808*A^2*B*a^24*b^33*d^6 + 3843840*A^2*B*a^26*b^31*d^6 + 7824960*A^2*B*a^28*b^29*d^
6 + 11366784*A^2*B*a^30*b^27*d^6 + 12016576*A^2*B*a^32*b^25*d^6 + 9152000*A^2*B*a^34*b^23*d^6 + 4758208*A^2*B*
a^36*b^21*d^6 + 1386112*A^2*B*a^38*b^19*d^6 - 54208*A^2*B*a^40*b^17*d^6 - 250112*A^2*B*a^42*b^15*d^6 - 111936*
A^2*B*a^44*b^13*d^6 - 23808*A^2*B*a^46*b^11*d^6 - 2112*A^2*B*a^48*b^9*d^6) + (a + b*tan(c + d*x))^(1/2)*(64*A^
4*a^14*b^40*d^5 + 512*A^4*a^16*b^38*d^5 + 544*A^4*a^18*b^36*d^5 - 10304*A^4*a^20*b^34*d^5 - 66976*A^4*a^22*b^3
2*d^5 - 221312*A^4*a^24*b^30*d^5 - 480480*A^4*a^26*b^28*d^5 - 741312*A^4*a^28*b^26*d^5 - 837408*A^4*a^30*b^24*
d^5 - 695552*A^4*a^32*b^22*d^5 - 416416*A^4*a^34*b^20*d^5 - 168896*A^4*a^36*b^18*d^5 - 37856*A^4*a^38*b^16*d^5
+ 896*A^4*a^40*b^14*d^5 + 3424*A^4*a^42*b^12*d^5 + 960*A^4*a^44*b^10*d^5 + 96*A^4*a^46*b^8*d^5 + 32*B^4*a^18*
b^36*d^5 + 448*B^4*a^20*b^34*d^5 + 2912*B^4*a^22*b^32*d^5 + 11648*B^4*a^24*b^30*d^5 + 32032*B^4*a^26*b^28*d^5
+ 64064*B^4*a^28*b^26*d^5 + 96096*B^4*a^30*b^24*d^5 + 109824*B^4*a^32*b^22*d^5 + 96096*B^4*a^34*b^20*d^5 + 640
64*B^4*a^36*b^18*d^5 + 32032*B^4*a^38*b^16*d^5 + 11648*B^4*a^40*b^14*d^5 + 2912*B^4*a^42*b^12*d^5 + 448*B^4*a^
44*b^10*d^5 + 32*B^4*a^46*b^8*d^5 - 512*A^3*B*a^15*b^39*d^5 - 6656*A^3*B*a^17*b^37*d^5 - 39424*A^3*B*a^19*b^35
*d^5 - 139776*A^3*B*a^21*b^33*d^5 - 326144*A^3*B*a^23*b^31*d^5 - 512512*A^3*B*a^25*b^29*d^5 - 512512*A^3*B*a^2
7*b^27*d^5 - 219648*A^3*B*a^29*b^25*d^5 + 219648*A^3*B*a^31*b^23*d^5 + 512512*A^3*B*a^33*b^21*d^5 + 512512*A^3
*B*a^35*b^19*d^5 + 326144*A^3*B*a^37*b^17*d^5 + 139776*A^3*B*a^39*b^15*d^5 + 39424*A^3*B*a^41*b^13*d^5 + 6656*
A^3*B*a^43*b^11*d^5 + 512*A^3*B*a^45*b^9*d^5 - 64*A^2*B^2*a^14*b^40*d^5 - 512*A^2*B^2*a^16*b^38*d^5 - 448*A^2*
B^2*a^18*b^36*d^5 + 11648*A^2*B^2*a^20*b^34*d^5 + 75712*A^2*B^2*a^22*b^32*d^5 + 256256*A^2*B^2*a^24*b^30*d^5 +
576576*A^2*B^2*a^26*b^28*d^5 + 933504*A^2*B^2*a^28*b^26*d^5 + 1125696*A^2*B^2*a^30*b^24*d^5 + 1025024*A^2*B^2
*a^32*b^22*d^5 + 704704*A^2*B^2*a^34*b^20*d^5 + 361088*A^2*B^2*a^36*b^18*d^5 + 133952*A^2*B^2*a^38*b^16*d^5 +
34048*A^2*B^2*a^40*b^14*d^5 + 5312*A^2*B^2*a^42*b^12*d^5 + 384*A^2*B^2*a^44*b^10*d^5))*((((8*A^2*a^5*d^2 - 8*B
^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 -
160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*
d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^2*a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*
b^2*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^2*a*b^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A
*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1
/2)*1i)/((((((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^
2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^1
0*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^2*a^5*
d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^2*a*b^
4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*
a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(((a + b*tan(c + d*x))^(1/2)*(256*A^2*a^15*b^44*d^7 + 4608*A^2*a^17*b^42*
d^7 + 40512*A^2*a^19*b^40*d^7 + 224768*A^2*a^21*b^38*d^7 + 864768*A^2*a^23*b^36*d^7 + 2419200*A^2*a^25*b^34*d^
7 + 5055232*A^2*a^27*b^32*d^7 + 8007168*A^2*a^29*b^30*d^7 + 9664512*A^2*a^31*b^28*d^7 + 8859136*A^2*a^33*b^26*
d^7 + 6095232*A^2*a^35*b^24*d^7 + 3095040*A^2*a^37*b^22*d^7 + 1164800*A^2*a^39*b^20*d^7 + 376320*A^2*a^41*b^18
*d^7 + 154368*A^2*a^43*b^16*d^7 + 76288*A^2*a^45*b^14*d^7 + 28416*A^2*a^47*b^12*d^7 + 6144*A^2*a^49*b^10*d^7 +
576*A^2*a^51*b^8*d^7 - 1344*B^2*a^19*b^40*d^7 - 15872*B^2*a^21*b^38*d^7 - 81408*B^2*a^23*b^36*d^7 - 225792*B^
2*a^25*b^34*d^7 - 302848*B^2*a^27*b^32*d^7 + 139776*B^2*a^29*b^30*d^7 + 1537536*B^2*a^31*b^28*d^7 + 3587584*B^
2*a^33*b^26*d^7 + 5106816*B^2*a^35*b^24*d^7 + 5051904*B^2*a^37*b^22*d^7 + 3587584*B^2*a^39*b^20*d^7 + 1817088*
B^2*a^41*b^18*d^7 + 628992*B^2*a^43*b^16*d^7 + 132608*B^2*a^45*b^14*d^7 + 10752*B^2*a^47*b^12*d^7 - 1536*B^2*a
^49*b^10*d^7 - 320*B^2*a^51*b^8*d^7 + 512*A*B*a^18*b^41*d^7 + 1536*A*B*a^20*b^39*d^7 - 29184*A*B*a^22*b^37*d^7
- 283136*A*B*a^24*b^35*d^7 - 1257984*A*B*a^26*b^33*d^7 - 3494400*A*B*a^28*b^31*d^7 - 6662656*A*B*a^30*b^29*d^
7 - 9005568*A*B*a^32*b^27*d^7 - 8566272*A*B*a^34*b^25*d^7 - 5344768*A*B*a^36*b^23*d^7 - 1537536*A*B*a^38*b^21*
d^7 + 698880*A*B*a^40*b^19*d^7 + 1071616*A*B*a^42*b^17*d^7 + 612864*A*B*a^44*b^15*d^7 + 201216*A*B*a^46*b^13*d
^7 + 37376*A*B*a^48*b^11*d^7 + 3072*A*B*a^50*b^9*d^7) + ((((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2
+ 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^
4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6
*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^2*a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 40*B^2*a^3*b^2*d^2 +
8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^2*a*b^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b
^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(512*A*a^16*b^46*d^8 - (a +
b*tan(c + d*x))^(1/2)*((((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^
5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 +
B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)
+ 4*A^2*a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2
- 20*B^2*a*b^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*
b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(512*a^18*b^46*d^9 + 9984*a^20*b^44*d^9 + 92160*a^22*b^42*d^
9 + 535296*a^24*b^40*d^9 + 2193408*a^26*b^38*d^9 + 6736896*a^28*b^36*d^9 + 16084992*a^30*b^34*d^9 + 30551040*a
^32*b^32*d^9 + 46844928*a^34*b^30*d^9 + 58499584*a^36*b^28*d^9 + 59744256*a^38*b^26*d^9 + 49900032*a^40*b^24*d
^9 + 33945600*a^42*b^22*d^9 + 18643968*a^44*b^20*d^9 + 8146944*a^46*b^18*d^9 + 2767872*a^48*b^16*d^9 + 705024*
a^50*b^14*d^9 + 126720*a^52*b^12*d^9 + 14336*a^54*b^10*d^9 + 768*a^56*b^8*d^9) + 9728*A*a^18*b^44*d^8 + 87936*
A*a^20*b^42*d^8 + 502144*A*a^22*b^40*d^8 + 2028544*A*a^24*b^38*d^8 + 6153216*A*a^26*b^36*d^8 + 14518784*A*a^28
*b^34*d^8 + 27243008*A*a^30*b^32*d^8 + 41213952*A*a^32*b^30*d^8 + 50665472*A*a^34*b^28*d^8 + 50775296*A*a^36*b
^26*d^8 + 41443584*A*a^38*b^24*d^8 + 27409408*A*a^40*b^22*d^8 + 14543872*A*a^42*b^20*d^8 + 6093312*A*a^44*b^18
*d^8 + 1966592*A*a^46*b^16*d^8 + 470528*A*a^48*b^14*d^8 + 78336*A*a^50*b^12*d^8 + 8064*A*a^52*b^10*d^8 + 384*A
*a^54*b^8*d^8 + 128*B*a^19*b^43*d^8 + 1664*B*a^21*b^41*d^8 + 9216*B*a^23*b^39*d^8 + 25600*B*a^25*b^37*d^8 + 17
920*B*a^27*b^35*d^8 - 139776*B*a^29*b^33*d^8 - 652288*B*a^31*b^31*d^8 - 1610752*B*a^33*b^29*d^8 - 2745600*B*a^
35*b^27*d^8 - 3477760*B*a^37*b^25*d^8 - 3367936*B*a^39*b^23*d^8 - 2515968*B*a^41*b^21*d^8 - 1444352*B*a^43*b^1
9*d^8 - 627200*B*a^45*b^17*d^8 - 199680*B*a^47*b^15*d^8 - 44032*B*a^49*b^13*d^8 - 6016*B*a^51*b^11*d^8 - 384*B
*a^53*b^9*d^8))*((((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 +
40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(
16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^
2*a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^
2*a*b^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4
+ 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2) - 384*A^3*a^15*b^42*d^6 - 7296*A^3*a^17*b^40*d^6 - 59424*A^3*a^19*b
^38*d^6 - 280992*A^3*a^21*b^36*d^6 - 866208*A^3*a^23*b^34*d^6 - 1825824*A^3*a^25*b^32*d^6 - 2629536*A^3*a^27*b
^30*d^6 - 2374944*A^3*a^29*b^28*d^6 - 727584*A^3*a^31*b^26*d^6 + 1413984*A^3*a^33*b^24*d^6 + 2649504*A^3*a^35*
b^22*d^6 + 2454816*A^3*a^37*b^20*d^6 + 1476384*A^3*a^39*b^18*d^6 + 597408*A^3*a^41*b^16*d^6 + 156192*A^3*a^43*
b^14*d^6 + 22944*A^3*a^45*b^12*d^6 + 1056*A^3*a^47*b^10*d^6 - 96*A^3*a^49*b^8*d^6 + 64*B^3*a^20*b^37*d^6 + 896
*B^3*a^22*b^35*d^6 + 5824*B^3*a^24*b^33*d^6 + 23296*B^3*a^26*b^31*d^6 + 64064*B^3*a^28*b^29*d^6 + 128128*B^3*a
^30*b^27*d^6 + 192192*B^3*a^32*b^25*d^6 + 219648*B^3*a^34*b^23*d^6 + 192192*B^3*a^36*b^21*d^6 + 128128*B^3*a^3
8*b^19*d^6 + 64064*B^3*a^40*b^17*d^6 + 23296*B^3*a^42*b^15*d^6 + 5824*B^3*a^44*b^13*d^6 + 896*B^3*a^46*b^11*d^
6 + 64*B^3*a^48*b^9*d^6 + 1280*A*B^2*a^17*b^40*d^6 + 15328*A*B^2*a^19*b^38*d^6 + 80480*A*B^2*a^21*b^36*d^6 + 2
34080*A*B^2*a^23*b^34*d^6 + 364000*A*B^2*a^25*b^32*d^6 + 72800*A*B^2*a^27*b^30*d^6 - 1057056*A*B^2*a^29*b^28*d
^6 - 2814240*A*B^2*a^31*b^26*d^6 - 4187040*A*B^2*a^33*b^24*d^6 - 4232800*A*B^2*a^35*b^22*d^6 - 3043040*A*B^2*a
^37*b^20*d^6 - 1552096*A*B^2*a^39*b^18*d^6 - 538720*A*B^2*a^41*b^16*d^6 - 113120*A*B^2*a^43*b^14*d^6 - 8800*A*
B^2*a^45*b^12*d^6 + 1440*A*B^2*a^47*b^10*d^6 + 288*A*B^2*a^49*b^8*d^6 - 128*A^2*B*a^14*b^43*d^6 - 2176*A^2*B*a
^16*b^41*d^6 - 11264*A^2*B*a^18*b^39*d^6 - 3008*A^2*B*a^20*b^37*d^6 + 226688*A^2*B*a^22*b^35*d^6 + 1263808*A^2
*B*a^24*b^33*d^6 + 3843840*A^2*B*a^26*b^31*d^6 + 7824960*A^2*B*a^28*b^29*d^6 + 11366784*A^2*B*a^30*b^27*d^6 +
12016576*A^2*B*a^32*b^25*d^6 + 9152000*A^2*B*a^34*b^23*d^6 + 4758208*A^2*B*a^36*b^21*d^6 + 1386112*A^2*B*a^38*
b^19*d^6 - 54208*A^2*B*a^40*b^17*d^6 - 250112*A^2*B*a^42*b^15*d^6 - 111936*A^2*B*a^44*b^13*d^6 - 23808*A^2*B*a
^46*b^11*d^6 - 2112*A^2*B*a^48*b^9*d^6) - (a + b*tan(c + d*x))^(1/2)*(64*A^4*a^14*b^40*d^5 + 512*A^4*a^16*b^38
*d^5 + 544*A^4*a^18*b^36*d^5 - 10304*A^4*a^20*b^34*d^5 - 66976*A^4*a^22*b^32*d^5 - 221312*A^4*a^24*b^30*d^5 -
480480*A^4*a^26*b^28*d^5 - 741312*A^4*a^28*b^26*d^5 - 837408*A^4*a^30*b^24*d^5 - 695552*A^4*a^32*b^22*d^5 - 41
6416*A^4*a^34*b^20*d^5 - 168896*A^4*a^36*b^18*d^5 - 37856*A^4*a^38*b^16*d^5 + 896*A^4*a^40*b^14*d^5 + 3424*A^4
*a^42*b^12*d^5 + 960*A^4*a^44*b^10*d^5 + 96*A^4*a^46*b^8*d^5 + 32*B^4*a^18*b^36*d^5 + 448*B^4*a^20*b^34*d^5 +
2912*B^4*a^22*b^32*d^5 + 11648*B^4*a^24*b^30*d^5 + 32032*B^4*a^26*b^28*d^5 + 64064*B^4*a^28*b^26*d^5 + 96096*B
^4*a^30*b^24*d^5 + 109824*B^4*a^32*b^22*d^5 + 96096*B^4*a^34*b^20*d^5 + 64064*B^4*a^36*b^18*d^5 + 32032*B^4*a^
38*b^16*d^5 + 11648*B^4*a^40*b^14*d^5 + 2912*B^4*a^42*b^12*d^5 + 448*B^4*a^44*b^10*d^5 + 32*B^4*a^46*b^8*d^5 -
512*A^3*B*a^15*b^39*d^5 - 6656*A^3*B*a^17*b^37*d^5 - 39424*A^3*B*a^19*b^35*d^5 - 139776*A^3*B*a^21*b^33*d^5 -
326144*A^3*B*a^23*b^31*d^5 - 512512*A^3*B*a^25*b^29*d^5 - 512512*A^3*B*a^27*b^27*d^5 - 219648*A^3*B*a^29*b^25
*d^5 + 219648*A^3*B*a^31*b^23*d^5 + 512512*A^3*B*a^33*b^21*d^5 + 512512*A^3*B*a^35*b^19*d^5 + 326144*A^3*B*a^3
7*b^17*d^5 + 139776*A^3*B*a^39*b^15*d^5 + 39424*A^3*B*a^41*b^13*d^5 + 6656*A^3*B*a^43*b^11*d^5 + 512*A^3*B*a^4
5*b^9*d^5 - 64*A^2*B^2*a^14*b^40*d^5 - 512*A^2*B^2*a^16*b^38*d^5 - 448*A^2*B^2*a^18*b^36*d^5 + 11648*A^2*B^2*a
^20*b^34*d^5 + 75712*A^2*B^2*a^22*b^32*d^5 + 256256*A^2*B^2*a^24*b^30*d^5 + 576576*A^2*B^2*a^26*b^28*d^5 + 933
504*A^2*B^2*a^28*b^26*d^5 + 1125696*A^2*B^2*a^30*b^24*d^5 + 1025024*A^2*B^2*a^32*b^22*d^5 + 704704*A^2*B^2*a^3
4*b^20*d^5 + 361088*A^2*B^2*a^36*b^18*d^5 + 133952*A^2*B^2*a^38*b^16*d^5 + 34048*A^2*B^2*a^40*b^14*d^5 + 5312*
A^2*B^2*a^42*b^12*d^5 + 384*A^2*B^2*a^44*b^10*d^5))*((((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 8
0*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*
d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4
*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^2*a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*
B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^2*a*b^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*
d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2) + (((((8*A^2*a^5*d^2 - 8*B^2*a^
5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A
*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 +
160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^2*a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b^2*d
^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^2*a*b^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*B*a^
4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(
1413984*A^3*a^33*b^24*d^6 - 384*A^3*a^15*b^42*d^6 - 7296*A^3*a^17*b^40*d^6 - 59424*A^3*a^19*b^38*d^6 - 280992*
A^3*a^21*b^36*d^6 - 866208*A^3*a^23*b^34*d^6 - 1825824*A^3*a^25*b^32*d^6 - 2629536*A^3*a^27*b^30*d^6 - 2374944
*A^3*a^29*b^28*d^6 - 727584*A^3*a^31*b^26*d^6 - ((a + b*tan(c + d*x))^(1/2)*(256*A^2*a^15*b^44*d^7 + 4608*A^2*
a^17*b^42*d^7 + 40512*A^2*a^19*b^40*d^7 + 224768*A^2*a^21*b^38*d^7 + 864768*A^2*a^23*b^36*d^7 + 2419200*A^2*a^
25*b^34*d^7 + 5055232*A^2*a^27*b^32*d^7 + 8007168*A^2*a^29*b^30*d^7 + 9664512*A^2*a^31*b^28*d^7 + 8859136*A^2*
a^33*b^26*d^7 + 6095232*A^2*a^35*b^24*d^7 + 3095040*A^2*a^37*b^22*d^7 + 1164800*A^2*a^39*b^20*d^7 + 376320*A^2
*a^41*b^18*d^7 + 154368*A^2*a^43*b^16*d^7 + 76288*A^2*a^45*b^14*d^7 + 28416*A^2*a^47*b^12*d^7 + 6144*A^2*a^49*
b^10*d^7 + 576*A^2*a^51*b^8*d^7 - 1344*B^2*a^19*b^40*d^7 - 15872*B^2*a^21*b^38*d^7 - 81408*B^2*a^23*b^36*d^7 -
225792*B^2*a^25*b^34*d^7 - 302848*B^2*a^27*b^32*d^7 + 139776*B^2*a^29*b^30*d^7 + 1537536*B^2*a^31*b^28*d^7 +
3587584*B^2*a^33*b^26*d^7 + 5106816*B^2*a^35*b^24*d^7 + 5051904*B^2*a^37*b^22*d^7 + 3587584*B^2*a^39*b^20*d^7
+ 1817088*B^2*a^41*b^18*d^7 + 628992*B^2*a^43*b^16*d^7 + 132608*B^2*a^45*b^14*d^7 + 10752*B^2*a^47*b^12*d^7 -
1536*B^2*a^49*b^10*d^7 - 320*B^2*a^51*b^8*d^7 + 512*A*B*a^18*b^41*d^7 + 1536*A*B*a^20*b^39*d^7 - 29184*A*B*a^2
2*b^37*d^7 - 283136*A*B*a^24*b^35*d^7 - 1257984*A*B*a^26*b^33*d^7 - 3494400*A*B*a^28*b^31*d^7 - 6662656*A*B*a^
30*b^29*d^7 - 9005568*A*B*a^32*b^27*d^7 - 8566272*A*B*a^34*b^25*d^7 - 5344768*A*B*a^36*b^23*d^7 - 1537536*A*B*
a^38*b^21*d^7 + 698880*A*B*a^40*b^19*d^7 + 1071616*A*B*a^42*b^17*d^7 + 612864*A*B*a^44*b^15*d^7 + 201216*A*B*a
^46*b^13*d^7 + 37376*A*B*a^48*b^11*d^7 + 3072*A*B*a^50*b^9*d^7) - ((((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a
^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 +
80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4
+ 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^2*a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 40*B^2*a^3*
b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^2*a*b^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*B*a^4*b*d^2)/(16*(a^
10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*((a + b*tan(c + d
*x))^(1/2)*((((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A
^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^
10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^2*a^5
*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^2*a*b
^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10
*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(512*a^18*b^46*d^9 + 9984*a^20*b^44*d^9 + 92160*a^22*b^42*d^9 + 535296*a
^24*b^40*d^9 + 2193408*a^26*b^38*d^9 + 6736896*a^28*b^36*d^9 + 16084992*a^30*b^34*d^9 + 30551040*a^32*b^32*d^9
+ 46844928*a^34*b^30*d^9 + 58499584*a^36*b^28*d^9 + 59744256*a^38*b^26*d^9 + 49900032*a^40*b^24*d^9 + 3394560
0*a^42*b^22*d^9 + 18643968*a^44*b^20*d^9 + 8146944*a^46*b^18*d^9 + 2767872*a^48*b^16*d^9 + 705024*a^50*b^14*d^
9 + 126720*a^52*b^12*d^9 + 14336*a^54*b^10*d^9 + 768*a^56*b^8*d^9) + 512*A*a^16*b^46*d^8 + 9728*A*a^18*b^44*d^
8 + 87936*A*a^20*b^42*d^8 + 502144*A*a^22*b^40*d^8 + 2028544*A*a^24*b^38*d^8 + 6153216*A*a^26*b^36*d^8 + 14518
784*A*a^28*b^34*d^8 + 27243008*A*a^30*b^32*d^8 + 41213952*A*a^32*b^30*d^8 + 50665472*A*a^34*b^28*d^8 + 5077529
6*A*a^36*b^26*d^8 + 41443584*A*a^38*b^24*d^8 + 27409408*A*a^40*b^22*d^8 + 14543872*A*a^42*b^20*d^8 + 6093312*A
*a^44*b^18*d^8 + 1966592*A*a^46*b^16*d^8 + 470528*A*a^48*b^14*d^8 + 78336*A*a^50*b^12*d^8 + 8064*A*a^52*b^10*d
^8 + 384*A*a^54*b^8*d^8 + 128*B*a^19*b^43*d^8 + 1664*B*a^21*b^41*d^8 + 9216*B*a^23*b^39*d^8 + 25600*B*a^25*b^3
7*d^8 + 17920*B*a^27*b^35*d^8 - 139776*B*a^29*b^33*d^8 - 652288*B*a^31*b^31*d^8 - 1610752*B*a^33*b^29*d^8 - 27
45600*B*a^35*b^27*d^8 - 3477760*B*a^37*b^25*d^8 - 3367936*B*a^39*b^23*d^8 - 2515968*B*a^41*b^21*d^8 - 1444352*
B*a^43*b^19*d^8 - 627200*B*a^45*b^17*d^8 - 199680*B*a^47*b^15*d^8 - 44032*B*a^49*b^13*d^8 - 6016*B*a^51*b^11*d
^8 - 384*B*a^53*b^9*d^8))*((((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B
*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^
2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1
/2) + 4*A^2*a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d
^2 - 20*B^2*a*b^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a
^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2) + 2649504*A^3*a^35*b^22*d^6 + 2454816*A^3*a^37*b^20*d^6 +
1476384*A^3*a^39*b^18*d^6 + 597408*A^3*a^41*b^16*d^6 + 156192*A^3*a^43*b^14*d^6 + 22944*A^3*a^45*b^12*d^6 + 1
056*A^3*a^47*b^10*d^6 - 96*A^3*a^49*b^8*d^6 + 64*B^3*a^20*b^37*d^6 + 896*B^3*a^22*b^35*d^6 + 5824*B^3*a^24*b^3
3*d^6 + 23296*B^3*a^26*b^31*d^6 + 64064*B^3*a^28*b^29*d^6 + 128128*B^3*a^30*b^27*d^6 + 192192*B^3*a^32*b^25*d^
6 + 219648*B^3*a^34*b^23*d^6 + 192192*B^3*a^36*b^21*d^6 + 128128*B^3*a^38*b^19*d^6 + 64064*B^3*a^40*b^17*d^6 +
23296*B^3*a^42*b^15*d^6 + 5824*B^3*a^44*b^13*d^6 + 896*B^3*a^46*b^11*d^6 + 64*B^3*a^48*b^9*d^6 + 1280*A*B^2*a
^17*b^40*d^6 + 15328*A*B^2*a^19*b^38*d^6 + 80480*A*B^2*a^21*b^36*d^6 + 234080*A*B^2*a^23*b^34*d^6 + 364000*A*B
^2*a^25*b^32*d^6 + 72800*A*B^2*a^27*b^30*d^6 - 1057056*A*B^2*a^29*b^28*d^6 - 2814240*A*B^2*a^31*b^26*d^6 - 418
7040*A*B^2*a^33*b^24*d^6 - 4232800*A*B^2*a^35*b^22*d^6 - 3043040*A*B^2*a^37*b^20*d^6 - 1552096*A*B^2*a^39*b^18
*d^6 - 538720*A*B^2*a^41*b^16*d^6 - 113120*A*B^2*a^43*b^14*d^6 - 8800*A*B^2*a^45*b^12*d^6 + 1440*A*B^2*a^47*b^
10*d^6 + 288*A*B^2*a^49*b^8*d^6 - 128*A^2*B*a^14*b^43*d^6 - 2176*A^2*B*a^16*b^41*d^6 - 11264*A^2*B*a^18*b^39*d
^6 - 3008*A^2*B*a^20*b^37*d^6 + 226688*A^2*B*a^22*b^35*d^6 + 1263808*A^2*B*a^24*b^33*d^6 + 3843840*A^2*B*a^26*
b^31*d^6 + 7824960*A^2*B*a^28*b^29*d^6 + 11366784*A^2*B*a^30*b^27*d^6 + 12016576*A^2*B*a^32*b^25*d^6 + 9152000
*A^2*B*a^34*b^23*d^6 + 4758208*A^2*B*a^36*b^21*d^6 + 1386112*A^2*B*a^38*b^19*d^6 - 54208*A^2*B*a^40*b^17*d^6 -
250112*A^2*B*a^42*b^15*d^6 - 111936*A^2*B*a^44*b^13*d^6 - 23808*A^2*B*a^46*b^11*d^6 - 2112*A^2*B*a^48*b^9*d^6
) + (a + b*tan(c + d*x))^(1/2)*(64*A^4*a^14*b^40*d^5 + 512*A^4*a^16*b^38*d^5 + 544*A^4*a^18*b^36*d^5 - 10304*A
^4*a^20*b^34*d^5 - 66976*A^4*a^22*b^32*d^5 - 221312*A^4*a^24*b^30*d^5 - 480480*A^4*a^26*b^28*d^5 - 741312*A^4*
a^28*b^26*d^5 - 837408*A^4*a^30*b^24*d^5 - 695552*A^4*a^32*b^22*d^5 - 416416*A^4*a^34*b^20*d^5 - 168896*A^4*a^
36*b^18*d^5 - 37856*A^4*a^38*b^16*d^5 + 896*A^4*a^40*b^14*d^5 + 3424*A^4*a^42*b^12*d^5 + 960*A^4*a^44*b^10*d^5
+ 96*A^4*a^46*b^8*d^5 + 32*B^4*a^18*b^36*d^5 + 448*B^4*a^20*b^34*d^5 + 2912*B^4*a^22*b^32*d^5 + 11648*B^4*a^2
4*b^30*d^5 + 32032*B^4*a^26*b^28*d^5 + 64064*B^4*a^28*b^26*d^5 + 96096*B^4*a^30*b^24*d^5 + 109824*B^4*a^32*b^2
2*d^5 + 96096*B^4*a^34*b^20*d^5 + 64064*B^4*a^36*b^18*d^5 + 32032*B^4*a^38*b^16*d^5 + 11648*B^4*a^40*b^14*d^5
+ 2912*B^4*a^42*b^12*d^5 + 448*B^4*a^44*b^10*d^5 + 32*B^4*a^46*b^8*d^5 - 512*A^3*B*a^15*b^39*d^5 - 6656*A^3*B*
a^17*b^37*d^5 - 39424*A^3*B*a^19*b^35*d^5 - 139776*A^3*B*a^21*b^33*d^5 - 326144*A^3*B*a^23*b^31*d^5 - 512512*A
^3*B*a^25*b^29*d^5 - 512512*A^3*B*a^27*b^27*d^5 - 219648*A^3*B*a^29*b^25*d^5 + 219648*A^3*B*a^31*b^23*d^5 + 51
2512*A^3*B*a^33*b^21*d^5 + 512512*A^3*B*a^35*b^19*d^5 + 326144*A^3*B*a^37*b^17*d^5 + 139776*A^3*B*a^39*b^15*d^
5 + 39424*A^3*B*a^41*b^13*d^5 + 6656*A^3*B*a^43*b^11*d^5 + 512*A^3*B*a^45*b^9*d^5 - 64*A^2*B^2*a^14*b^40*d^5 -
512*A^2*B^2*a^16*b^38*d^5 - 448*A^2*B^2*a^18*b^36*d^5 + 11648*A^2*B^2*a^20*b^34*d^5 + 75712*A^2*B^2*a^22*b^32
*d^5 + 256256*A^2*B^2*a^24*b^30*d^5 + 576576*A^2*B^2*a^26*b^28*d^5 + 933504*A^2*B^2*a^28*b^26*d^5 + 1125696*A^
2*B^2*a^30*b^24*d^5 + 1025024*A^2*B^2*a^32*b^22*d^5 + 704704*A^2*B^2*a^34*b^20*d^5 + 361088*A^2*B^2*a^36*b^18*
d^5 + 133952*A^2*B^2*a^38*b^16*d^5 + 34048*A^2*B^2*a^40*b^14*d^5 + 5312*A^2*B^2*a^42*b^12*d^5 + 384*A^2*B^2*a^
44*b^10*d^5))*((((8*A^2*a^5*d^2 - 8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 4
0*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16
*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^2*
a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^2*
a*b^4*d^2 - 80*A*B*a^2*b^3*d^2 + 40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 +
10*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2) + 64*A^5*a^14*b^38*d^4 + 896*A^5*a^16*b^36*d^4 + 5824*A^5*a^18*b^34*d
^4 + 23296*A^5*a^20*b^32*d^4 + 64064*A^5*a^22*b^30*d^4 + 128128*A^5*a^24*b^28*d^4 + 192192*A^5*a^26*b^26*d^4 +
219648*A^5*a^28*b^24*d^4 + 192192*A^5*a^30*b^22*d^4 + 128128*A^5*a^32*b^20*d^4 + 64064*A^5*a^34*b^18*d^4 + 23
296*A^5*a^36*b^16*d^4 + 5824*A^5*a^38*b^14*d^4 + 896*A^5*a^40*b^12*d^4 + 64*A^5*a^42*b^10*d^4 + 64*A*B^4*a^16*
b^36*d^4 + 896*A*B^4*a^18*b^34*d^4 + 5824*A*B^4*a^20*b^32*d^4 + 23296*A*B^4*a^22*b^30*d^4 + 64064*A*B^4*a^24*b
^28*d^4 + 128128*A*B^4*a^26*b^26*d^4 + 192192*A*B^4*a^28*b^24*d^4 + 219648*A*B^4*a^30*b^22*d^4 + 192192*A*B^4*
a^32*b^20*d^4 + 128128*A*B^4*a^34*b^18*d^4 + 64064*A*B^4*a^36*b^16*d^4 + 23296*A*B^4*a^38*b^14*d^4 + 5824*A*B^
4*a^40*b^12*d^4 + 896*A*B^4*a^42*b^10*d^4 + 64*A*B^4*a^44*b^8*d^4 - 128*A^4*B*a^15*b^37*d^4 - 1792*A^4*B*a^17*
b^35*d^4 - 11648*A^4*B*a^19*b^33*d^4 - 46592*A^4*B*a^21*b^31*d^4 - 128128*A^4*B*a^23*b^29*d^4 - 256256*A^4*B*a
^25*b^27*d^4 - 384384*A^4*B*a^27*b^25*d^4 - 439296*A^4*B*a^29*b^23*d^4 - 384384*A^4*B*a^31*b^21*d^4 - 256256*A
^4*B*a^33*b^19*d^4 - 128128*A^4*B*a^35*b^17*d^4 - 46592*A^4*B*a^37*b^15*d^4 - 11648*A^4*B*a^39*b^13*d^4 - 1792
*A^4*B*a^41*b^11*d^4 - 128*A^4*B*a^43*b^9*d^4 - 128*A^2*B^3*a^15*b^37*d^4 - 1792*A^2*B^3*a^17*b^35*d^4 - 11648
*A^2*B^3*a^19*b^33*d^4 - 46592*A^2*B^3*a^21*b^31*d^4 - 128128*A^2*B^3*a^23*b^29*d^4 - 256256*A^2*B^3*a^25*b^27
*d^4 - 384384*A^2*B^3*a^27*b^25*d^4 - 439296*A^2*B^3*a^29*b^23*d^4 - 384384*A^2*B^3*a^31*b^21*d^4 - 256256*A^2
*B^3*a^33*b^19*d^4 - 128128*A^2*B^3*a^35*b^17*d^4 - 46592*A^2*B^3*a^37*b^15*d^4 - 11648*A^2*B^3*a^39*b^13*d^4
- 1792*A^2*B^3*a^41*b^11*d^4 - 128*A^2*B^3*a^43*b^9*d^4 + 64*A^3*B^2*a^14*b^38*d^4 + 960*A^3*B^2*a^16*b^36*d^4
+ 6720*A^3*B^2*a^18*b^34*d^4 + 29120*A^3*B^2*a^20*b^32*d^4 + 87360*A^3*B^2*a^22*b^30*d^4 + 192192*A^3*B^2*a^2
4*b^28*d^4 + 320320*A^3*B^2*a^26*b^26*d^4 + 411840*A^3*B^2*a^28*b^24*d^4 + 411840*A^3*B^2*a^30*b^22*d^4 + 3203
20*A^3*B^2*a^32*b^20*d^4 + 192192*A^3*B^2*a^34*b^18*d^4 + 87360*A^3*B^2*a^36*b^16*d^4 + 29120*A^3*B^2*a^38*b^1
4*d^4 + 6720*A^3*B^2*a^40*b^12*d^4 + 960*A^3*B^2*a^42*b^10*d^4 + 64*A^3*B^2*a^44*b^8*d^4))*((((8*A^2*a^5*d^2 -
8*B^2*a^5*d^2 - 80*A^2*a^3*b^2*d^2 + 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 + 40*A^2*a*b^4*d^2 - 40*B^2*a*b^4*d^
2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*
b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 4*A^2*a^5*d^2 - 4*B^2*a^5*d^2 - 40*A^2*
a^3*b^2*d^2 + 40*B^2*a^3*b^2*d^2 + 8*A*B*b^5*d^2 + 20*A^2*a*b^4*d^2 - 20*B^2*a*b^4*d^2 - 80*A*B*a^2*b^3*d^2 +
40*A*B*a^4*b*d^2)/(16*(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))
)^(1/2)*2i + ((2*(A*b^2 - B*a*b))/(3*a*(a^2 + b^2)) + (2*(a + b*tan(c + d*x))*(A*b^4 + 3*A*a^2*b^2 - 2*B*a^3*b
))/(a*b^2 + a^3)^2)/(d*(a + b*tan(c + d*x))^(3/2)) + (A*atan((A^4*a^22*(a + b*tan(c + d*x))^(1/2)*9i + B^4*a^2
2*(a + b*tan(c + d*x))^(1/2)*1i + A^2*B^2*a^22*(a + b*tan(c + d*x))^(1/2)*10i + A^4*a^12*b^10*(a + b*tan(c + d
*x))^(1/2)*16i + A^4*a^14*b^8*(a + b*tan(c + d*x))^(1/2)*80i + A^4*a^16*b^6*(a + b*tan(c + d*x))^(1/2)*160i +
A^4*a^18*b^4*(a + b*tan(c + d*x))^(1/2)*120i + A^4*a^20*b^2*(a + b*tan(c + d*x))^(1/2)*160i - A^3*B*a^17*b^5*(
a + b*tan(c + d*x))^(1/2)*16i + A^3*B*a^19*b^3*(a + b*tan(c + d*x))^(1/2)*160i + A^2*B^2*a^18*b^4*(a + b*tan(c
+ d*x))^(1/2)*40i - A^2*B^2*a^20*b^2*(a + b*tan(c + d*x))^(1/2)*80i - A^3*B*a^21*b*(a + b*tan(c + d*x))^(1/2)
*80i)/(a^10*(a^5)^(1/2)*(16*A^4*b^10 + a^5*(a^5*(9*A^4 + 10*A^2*B^2 + B^4) - 16*A^3*B*b^5 + 120*A^4*a*b^4 + 16
0*A^4*a^3*b^2 - 80*A^2*B^2*a^3*b^2 - 80*A^3*B*a^4*b + 40*A^2*B^2*a*b^4 + 160*A^3*B*a^2*b^3) + 80*A^4*a^2*b^8 +
160*A^4*a^4*b^6)))*2i)/(d*(a^5)^(1/2))