\(\int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx\) [355]

Optimal result

Integrand size = 33, antiderivative size = 219 \[ \int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx=\frac {(3 A b-2 a B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{a^{5/2} d}+\frac {(i A+B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{(a-i b)^{3/2} d}-\frac {(i A-B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{(a+i b)^{3/2} d}-\frac {b \left (a^2 A+3 A b^2-2 a b B\right )}{a^2 \left (a^2+b^2\right ) d \sqrt {a+b \tan (c+d x)}}-\frac {A \cot (c+d x)}{a d \sqrt {a+b \tan (c+d x)}} \]

[Out]

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

Rubi [A] (verified)

Time = 0.99 (sec) , antiderivative size = 219, normalized size of antiderivative = 1.00, number of steps used = 13, number of rules used = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.242, Rules used = {3690, 3730, 3734, 3620, 3618, 65, 214, 3715} \[ \int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx=\frac {(3 A b-2 a B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{a^{5/2} d}-\frac {b \left (a^2 A-2 a b B+3 A b^2\right )}{a^2 d \left (a^2+b^2\right ) \sqrt {a+b \tan (c+d x)}}+\frac {(B+i A) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{d (a-i b)^{3/2}}-\frac {(-B+i A) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{d (a+i b)^{3/2}}-\frac {A \cot (c+d x)}{a d \sqrt {a+b \tan (c+d x)}} \]

[In]

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

[Out]

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

Mathematica [A] (verified)

Time = 4.17 (sec) , antiderivative size = 208, normalized size of antiderivative = 0.95 \[ \int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx=\frac {\frac {(3 A b-2 a B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{\sqrt {a}}+a^2 \left (\frac {(i A+B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{(a-i b)^{3/2}}+\frac {(-i A+B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{(a+i b)^{3/2}}\right )-\frac {b \left (a^2 A+3 A b^2-2 a b B\right )}{\left (a^2+b^2\right ) \sqrt {a+b \tan (c+d x)}}-\frac {a A \cot (c+d x)}{\sqrt {a+b \tan (c+d x)}}}{a^2 d} \]

[In]

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

[Out]

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

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(8042\) vs. \(2(191)=382\).

Time = 0.24 (sec) , antiderivative size = 8043, normalized size of antiderivative = 36.73

method	result	size
derivativedivides	\(\text {Expression too large to display}\)	\(8043\)
default	\(\text {Expression too large to display}\)	\(8043\)

[In]

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

[Out]

result too large to display

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 4530 vs. \(2 (186) = 372\).

Time = 17.37 (sec) , antiderivative size = 9075, normalized size of antiderivative = 41.44 \[ \int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx=\text {Too large to display} \]

[In]

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

[Out]

Too large to include

Sympy [F]

\[ \int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx=\int \frac {\left (A + B \tan {\left (c + d x \right )}\right ) \cot ^{2}{\left (c + d x \right )}}{\left (a + b \tan {\left (c + d x \right )}\right )^{\frac {3}{2}}}\, dx \]

[In]

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

[Out]

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

Maxima [F]

\[ \int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx=\int { \frac {{\left (B \tan \left (d x + c\right ) + A\right )} \cot \left (d x + c\right )^{2}}{{\left (b \tan \left (d x + c\right ) + a\right )}^{\frac {3}{2}}} \,d x } \]

[In]

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

[Out]

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

Giac [F(-1)]

Timed out. \[ \int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx=\text {Timed out} \]

[In]

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

[Out]

Timed out

Mupad [B] (verification not implemented)

Time = 12.65 (sec) , antiderivative size = 38368, normalized size of antiderivative = 175.20 \[ \int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx=\text {Too large to display} \]

[In]

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

[Out]

((2*(A*b^3 - B*a*b^2))/(a*b^2 + a^3) - ((a + b*tan(c + d*x))*(3*A*b^3 + A*a^2*b - 2*B*a*b^2))/(a*(a*b^2 + a^3)
))/(d*(a + b*tan(c + d*x))^(3/2) - a*d*(a + b*tan(c + d*x))^(1/2)) + atan(-((((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2
- 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*
a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2
+ 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*
d^4)))^(1/2)*(((a + b*tan(c + d*x))^(1/2)*(576*A^2*a^15*b^28*d^7 + 5184*A^2*a^17*b^26*d^7 + 21568*A^2*a^19*b^2
4*d^7 + 53888*A^2*a^21*b^22*d^7 + 87808*A^2*a^23*b^20*d^7 + 94976*A^2*a^25*b^18*d^7 + 66304*A^2*a^27*b^16*d^7
+ 27008*A^2*a^29*b^14*d^7 + 4288*A^2*a^31*b^12*d^7 - 832*A^2*a^33*b^10*d^7 - 320*A^2*a^35*b^8*d^7 + 256*B^2*a^
17*b^26*d^7 + 1472*B^2*a^19*b^24*d^7 + 3712*B^2*a^21*b^22*d^7 + 6272*B^2*a^23*b^20*d^7 + 9856*B^2*a^25*b^18*d^
7 + 14336*B^2*a^27*b^16*d^7 + 15232*B^2*a^29*b^14*d^7 + 10112*B^2*a^31*b^12*d^7 + 3712*B^2*a^33*b^10*d^7 + 576
*B^2*a^35*b^8*d^7 - 768*A*B*a^16*b^27*d^7 - 6400*A*B*a^18*b^25*d^7 - 25856*A*B*a^20*b^23*d^7 - 66304*A*B*a^22*
b^21*d^7 - 116480*A*B*a^24*b^19*d^7 - 141568*A*B*a^26*b^17*d^7 - 116480*A*B*a^28*b^15*d^7 - 61696*A*B*a^30*b^1
3*d^7 - 18944*A*B*a^32*b^11*d^7 - 2560*A*B*a^34*b^9*d^7) - ((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2
- 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d
^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^
2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*((a +
b*tan(c + d*x))^(1/2)*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^
2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4
))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*
d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(512*a^18*b^28*d^9 + 5376*a^20*b^26*d^9 +
25344*a^22*b^24*d^9 + 70656*a^24*b^22*d^9 + 129024*a^26*b^20*d^9 + 161280*a^28*b^18*d^9 + 139776*a^30*b^16*d^
9 + 82944*a^32*b^14*d^9 + 32256*a^34*b^12*d^9 + 7424*a^36*b^10*d^9 + 768*a^38*b^8*d^9) - 768*A*a^16*b^29*d^8 -
7680*A*a^18*b^27*d^8 - 34304*A*a^20*b^25*d^8 - 90112*A*a^22*b^23*d^8 - 154112*A*a^24*b^21*d^8 - 179200*A*a^26
*b^19*d^8 - 143360*A*a^28*b^17*d^8 - 77824*A*a^30*b^15*d^8 - 27392*A*a^32*b^13*d^8 - 5632*A*a^34*b^11*d^8 - 51
2*A*a^36*b^9*d^8 + 512*B*a^17*b^28*d^8 + 5248*B*a^19*b^26*d^8 + 23936*B*a^21*b^24*d^8 + 64000*B*a^23*b^22*d^8
+ 111104*B*a^25*b^20*d^8 + 130816*B*a^27*b^18*d^8 + 105728*B*a^29*b^16*d^8 + 57856*B*a^31*b^14*d^8 + 20480*B*a
^33*b^12*d^8 + 4224*B*a^35*b^10*d^8 + 384*B*a^37*b^8*d^8))*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2
- 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d
^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^
2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) + 576
*A^3*a^15*b^27*d^6 + 3456*A^3*a^17*b^25*d^6 + 8480*A^3*a^19*b^23*d^6 + 10976*A^3*a^21*b^21*d^6 + 8736*A^3*a^23
*b^19*d^6 + 6496*A^3*a^25*b^17*d^6 + 6496*A^3*a^27*b^15*d^6 + 5280*A^3*a^29*b^13*d^6 + 2336*A^3*a^31*b^11*d^6
+ 416*A^3*a^33*b^9*d^6 + 128*B^3*a^16*b^26*d^6 + 128*B^3*a^18*b^24*d^6 - 2592*B^3*a^20*b^22*d^6 - 10976*B^3*a^
22*b^20*d^6 - 20384*B^3*a^24*b^18*d^6 - 20832*B^3*a^26*b^16*d^6 - 11872*B^3*a^28*b^14*d^6 - 3232*B^3*a^30*b^12
*d^6 - 96*B^3*a^32*b^10*d^6 + 96*B^3*a^34*b^8*d^6 - 384*A*B^2*a^15*b^27*d^6 - 768*A*B^2*a^17*b^25*d^6 + 4128*A
*B^2*a^19*b^23*d^6 + 18144*A*B^2*a^21*b^21*d^6 + 27552*A*B^2*a^23*b^19*d^6 + 15456*A*B^2*a^25*b^17*d^6 - 6048*
A*B^2*a^27*b^15*d^6 - 13152*A*B^2*a^29*b^13*d^6 - 6816*A*B^2*a^31*b^11*d^6 - 1248*A*B^2*a^33*b^9*d^6 + 288*A^2
*B*a^14*b^28*d^6 + 480*A^2*B*a^16*b^26*d^6 - 2688*A^2*B*a^18*b^24*d^6 - 8352*A^2*B*a^20*b^22*d^6 - 3360*A^2*B*
a^22*b^20*d^6 + 16800*A^2*B*a^24*b^18*d^6 + 30240*A^2*B*a^26*b^16*d^6 + 21792*A^2*B*a^28*b^14*d^6 + 6528*A^2*B
*a^30*b^12*d^6 - 288*A^2*B*a^34*b^8*d^6) - (a + b*tan(c + d*x))^(1/2)*(144*A^4*a^14*b^26*d^5 + 864*A^4*a^16*b^
24*d^5 + 2048*A^4*a^18*b^22*d^5 + 2240*A^4*a^20*b^20*d^5 + 672*A^4*a^22*b^18*d^5 - 896*A^4*a^24*b^16*d^5 - 896
*A^4*a^26*b^14*d^5 - 192*A^4*a^28*b^12*d^5 + 80*A^4*a^30*b^10*d^5 + 32*A^4*a^32*b^8*d^5 - 64*B^4*a^16*b^24*d^5
- 352*B^4*a^18*b^22*d^5 - 672*B^4*a^20*b^20*d^5 - 224*B^4*a^22*b^18*d^5 + 1120*B^4*a^24*b^16*d^5 + 2016*B^4*a
^26*b^14*d^5 + 1568*B^4*a^28*b^12*d^5 + 608*B^4*a^30*b^10*d^5 + 96*B^4*a^32*b^8*d^5 + 192*A*B^3*a^15*b^25*d^5
+ 896*A*B^3*a^17*b^23*d^5 + 896*A*B^3*a^19*b^21*d^5 - 2688*A*B^3*a^21*b^19*d^5 - 8960*A*B^3*a^23*b^17*d^5 - 11
648*A*B^3*a^25*b^15*d^5 - 8064*A*B^3*a^27*b^13*d^5 - 2944*A*B^3*a^29*b^11*d^5 - 448*A*B^3*a^31*b^9*d^5 - 768*A
^3*B*a^15*b^25*d^5 - 5184*A^3*B*a^17*b^23*d^5 - 14784*A^3*B*a^19*b^21*d^5 - 22848*A^3*B*a^21*b^19*d^5 - 20160*
A^3*B*a^23*b^17*d^5 - 9408*A^3*B*a^25*b^15*d^5 - 1344*A^3*B*a^27*b^13*d^5 + 576*A^3*B*a^29*b^11*d^5 + 192*A^3*
B*a^31*b^9*d^5 - 144*A^2*B^2*a^14*b^26*d^5 - 32*A^2*B^2*a^16*b^24*d^5 + 3808*A^2*B^2*a^18*b^22*d^5 + 15456*A^2
*B^2*a^20*b^20*d^5 + 29120*A^2*B^2*a^22*b^18*d^5 + 31136*A^2*B^2*a^24*b^16*d^5 + 19488*A^2*B^2*a^26*b^14*d^5 +
6688*A^2*B^2*a^28*b^12*d^5 + 976*A^2*B^2*a^30*b^10*d^5))*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 -
24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^
4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2
- 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*1i - (
((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2
/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^
2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6
*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(576*A^3*a^15*b^27*d^6 - ((a + b*tan(c + d*x))^(1/2)*(576*A^2*a^
15*b^28*d^7 + 5184*A^2*a^17*b^26*d^7 + 21568*A^2*a^19*b^24*d^7 + 53888*A^2*a^21*b^22*d^7 + 87808*A^2*a^23*b^20
*d^7 + 94976*A^2*a^25*b^18*d^7 + 66304*A^2*a^27*b^16*d^7 + 27008*A^2*a^29*b^14*d^7 + 4288*A^2*a^31*b^12*d^7 -
832*A^2*a^33*b^10*d^7 - 320*A^2*a^35*b^8*d^7 + 256*B^2*a^17*b^26*d^7 + 1472*B^2*a^19*b^24*d^7 + 3712*B^2*a^21*
b^22*d^7 + 6272*B^2*a^23*b^20*d^7 + 9856*B^2*a^25*b^18*d^7 + 14336*B^2*a^27*b^16*d^7 + 15232*B^2*a^29*b^14*d^7
+ 10112*B^2*a^31*b^12*d^7 + 3712*B^2*a^33*b^10*d^7 + 576*B^2*a^35*b^8*d^7 - 768*A*B*a^16*b^27*d^7 - 6400*A*B*
a^18*b^25*d^7 - 25856*A*B*a^20*b^23*d^7 - 66304*A*B*a^22*b^21*d^7 - 116480*A*B*a^24*b^19*d^7 - 141568*A*B*a^26
*b^17*d^7 - 116480*A*B*a^28*b^15*d^7 - 61696*A*B*a^30*b^13*d^7 - 18944*A*B*a^32*b^11*d^7 - 2560*A*B*a^34*b^9*d
^7) - ((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*
d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*
a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4
+ b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*((a + b*tan(c + d*x))^(1/2)*((((8*A^2*a^3*d^2 - 8*B^2*a^3*
d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(
16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*
d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b
^2*d^4)))^(1/2)*(512*a^18*b^28*d^9 + 5376*a^20*b^26*d^9 + 25344*a^22*b^24*d^9 + 70656*a^24*b^22*d^9 + 129024*a
^26*b^20*d^9 + 161280*a^28*b^18*d^9 + 139776*a^30*b^16*d^9 + 82944*a^32*b^14*d^9 + 32256*a^34*b^12*d^9 + 7424*
a^36*b^10*d^9 + 768*a^38*b^8*d^9) + 768*A*a^16*b^29*d^8 + 7680*A*a^18*b^27*d^8 + 34304*A*a^20*b^25*d^8 + 90112
*A*a^22*b^23*d^8 + 154112*A*a^24*b^21*d^8 + 179200*A*a^26*b^19*d^8 + 143360*A*a^28*b^17*d^8 + 77824*A*a^30*b^1
5*d^8 + 27392*A*a^32*b^13*d^8 + 5632*A*a^34*b^11*d^8 + 512*A*a^36*b^9*d^8 - 512*B*a^17*b^28*d^8 - 5248*B*a^19*
b^26*d^8 - 23936*B*a^21*b^24*d^8 - 64000*B*a^23*b^22*d^8 - 111104*B*a^25*b^20*d^8 - 130816*B*a^27*b^18*d^8 - 1
05728*B*a^29*b^16*d^8 - 57856*B*a^31*b^14*d^8 - 20480*B*a^33*b^12*d^8 - 4224*B*a^35*b^10*d^8 - 384*B*a^37*b^8*
d^8))*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*
d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*
a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4
+ b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) + 3456*A^3*a^17*b^25*d^6 + 8480*A^3*a^19*b^23*d^6 + 10976*
A^3*a^21*b^21*d^6 + 8736*A^3*a^23*b^19*d^6 + 6496*A^3*a^25*b^17*d^6 + 6496*A^3*a^27*b^15*d^6 + 5280*A^3*a^29*b
^13*d^6 + 2336*A^3*a^31*b^11*d^6 + 416*A^3*a^33*b^9*d^6 + 128*B^3*a^16*b^26*d^6 + 128*B^3*a^18*b^24*d^6 - 2592
*B^3*a^20*b^22*d^6 - 10976*B^3*a^22*b^20*d^6 - 20384*B^3*a^24*b^18*d^6 - 20832*B^3*a^26*b^16*d^6 - 11872*B^3*a
^28*b^14*d^6 - 3232*B^3*a^30*b^12*d^6 - 96*B^3*a^32*b^10*d^6 + 96*B^3*a^34*b^8*d^6 - 384*A*B^2*a^15*b^27*d^6 -
768*A*B^2*a^17*b^25*d^6 + 4128*A*B^2*a^19*b^23*d^6 + 18144*A*B^2*a^21*b^21*d^6 + 27552*A*B^2*a^23*b^19*d^6 +
15456*A*B^2*a^25*b^17*d^6 - 6048*A*B^2*a^27*b^15*d^6 - 13152*A*B^2*a^29*b^13*d^6 - 6816*A*B^2*a^31*b^11*d^6 -
1248*A*B^2*a^33*b^9*d^6 + 288*A^2*B*a^14*b^28*d^6 + 480*A^2*B*a^16*b^26*d^6 - 2688*A^2*B*a^18*b^24*d^6 - 8352*
A^2*B*a^20*b^22*d^6 - 3360*A^2*B*a^22*b^20*d^6 + 16800*A^2*B*a^24*b^18*d^6 + 30240*A^2*B*a^26*b^16*d^6 + 21792
*A^2*B*a^28*b^14*d^6 + 6528*A^2*B*a^30*b^12*d^6 - 288*A^2*B*a^34*b^8*d^6) + (a + b*tan(c + d*x))^(1/2)*(144*A^
4*a^14*b^26*d^5 + 864*A^4*a^16*b^24*d^5 + 2048*A^4*a^18*b^22*d^5 + 2240*A^4*a^20*b^20*d^5 + 672*A^4*a^22*b^18*
d^5 - 896*A^4*a^24*b^16*d^5 - 896*A^4*a^26*b^14*d^5 - 192*A^4*a^28*b^12*d^5 + 80*A^4*a^30*b^10*d^5 + 32*A^4*a^
32*b^8*d^5 - 64*B^4*a^16*b^24*d^5 - 352*B^4*a^18*b^22*d^5 - 672*B^4*a^20*b^20*d^5 - 224*B^4*a^22*b^18*d^5 + 11
20*B^4*a^24*b^16*d^5 + 2016*B^4*a^26*b^14*d^5 + 1568*B^4*a^28*b^12*d^5 + 608*B^4*a^30*b^10*d^5 + 96*B^4*a^32*b
^8*d^5 + 192*A*B^3*a^15*b^25*d^5 + 896*A*B^3*a^17*b^23*d^5 + 896*A*B^3*a^19*b^21*d^5 - 2688*A*B^3*a^21*b^19*d^
5 - 8960*A*B^3*a^23*b^17*d^5 - 11648*A*B^3*a^25*b^15*d^5 - 8064*A*B^3*a^27*b^13*d^5 - 2944*A*B^3*a^29*b^11*d^5
- 448*A*B^3*a^31*b^9*d^5 - 768*A^3*B*a^15*b^25*d^5 - 5184*A^3*B*a^17*b^23*d^5 - 14784*A^3*B*a^19*b^21*d^5 - 2
2848*A^3*B*a^21*b^19*d^5 - 20160*A^3*B*a^23*b^17*d^5 - 9408*A^3*B*a^25*b^15*d^5 - 1344*A^3*B*a^27*b^13*d^5 + 5
76*A^3*B*a^29*b^11*d^5 + 192*A^3*B*a^31*b^9*d^5 - 144*A^2*B^2*a^14*b^26*d^5 - 32*A^2*B^2*a^16*b^24*d^5 + 3808*
A^2*B^2*a^18*b^22*d^5 + 15456*A^2*B^2*a^20*b^20*d^5 + 29120*A^2*B^2*a^22*b^18*d^5 + 31136*A^2*B^2*a^24*b^16*d^
5 + 19488*A^2*B^2*a^26*b^14*d^5 + 6688*A^2*B^2*a^28*b^12*d^5 + 976*A^2*B^2*a^30*b^10*d^5))*((((8*A^2*a^3*d^2 -
8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B
^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 +
8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^
4 + 3*a^4*b^2*d^4)))^(1/2)*1i)/(144*A^5*a^14*b^25*d^4 - (((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 -
24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4
+ 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2
- 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(576*A^
3*a^15*b^27*d^6 - ((a + b*tan(c + d*x))^(1/2)*(576*A^2*a^15*b^28*d^7 + 5184*A^2*a^17*b^26*d^7 + 21568*A^2*a^19
*b^24*d^7 + 53888*A^2*a^21*b^22*d^7 + 87808*A^2*a^23*b^20*d^7 + 94976*A^2*a^25*b^18*d^7 + 66304*A^2*a^27*b^16*
d^7 + 27008*A^2*a^29*b^14*d^7 + 4288*A^2*a^31*b^12*d^7 - 832*A^2*a^33*b^10*d^7 - 320*A^2*a^35*b^8*d^7 + 256*B^
2*a^17*b^26*d^7 + 1472*B^2*a^19*b^24*d^7 + 3712*B^2*a^21*b^22*d^7 + 6272*B^2*a^23*b^20*d^7 + 9856*B^2*a^25*b^1
8*d^7 + 14336*B^2*a^27*b^16*d^7 + 15232*B^2*a^29*b^14*d^7 + 10112*B^2*a^31*b^12*d^7 + 3712*B^2*a^33*b^10*d^7 +
576*B^2*a^35*b^8*d^7 - 768*A*B*a^16*b^27*d^7 - 6400*A*B*a^18*b^25*d^7 - 25856*A*B*a^20*b^23*d^7 - 66304*A*B*a
^22*b^21*d^7 - 116480*A*B*a^24*b^19*d^7 - 141568*A*B*a^26*b^17*d^7 - 116480*A*B*a^28*b^15*d^7 - 61696*A*B*a^30
*b^13*d^7 - 18944*A*B*a^32*b^11*d^7 - 2560*A*B*a^34*b^9*d^7) - ((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*
d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b
^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^
2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(
(a + b*tan(c + d*x))^(1/2)*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^
2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2
*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^
2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(512*a^18*b^28*d^9 + 5376*a^20*b^26*d
^9 + 25344*a^22*b^24*d^9 + 70656*a^24*b^22*d^9 + 129024*a^26*b^20*d^9 + 161280*a^28*b^18*d^9 + 139776*a^30*b^1
6*d^9 + 82944*a^32*b^14*d^9 + 32256*a^34*b^12*d^9 + 7424*a^36*b^10*d^9 + 768*a^38*b^8*d^9) + 768*A*a^16*b^29*d
^8 + 7680*A*a^18*b^27*d^8 + 34304*A*a^20*b^25*d^8 + 90112*A*a^22*b^23*d^8 + 154112*A*a^24*b^21*d^8 + 179200*A*
a^26*b^19*d^8 + 143360*A*a^28*b^17*d^8 + 77824*A*a^30*b^15*d^8 + 27392*A*a^32*b^13*d^8 + 5632*A*a^34*b^11*d^8
+ 512*A*a^36*b^9*d^8 - 512*B*a^17*b^28*d^8 - 5248*B*a^19*b^26*d^8 - 23936*B*a^21*b^24*d^8 - 64000*B*a^23*b^22*
d^8 - 111104*B*a^25*b^20*d^8 - 130816*B*a^27*b^18*d^8 - 105728*B*a^29*b^16*d^8 - 57856*B*a^31*b^14*d^8 - 20480
*B*a^33*b^12*d^8 - 4224*B*a^35*b^10*d^8 - 384*B*a^37*b^8*d^8))*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*
d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b
^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^
2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) +
3456*A^3*a^17*b^25*d^6 + 8480*A^3*a^19*b^23*d^6 + 10976*A^3*a^21*b^21*d^6 + 8736*A^3*a^23*b^19*d^6 + 6496*A^3
*a^25*b^17*d^6 + 6496*A^3*a^27*b^15*d^6 + 5280*A^3*a^29*b^13*d^6 + 2336*A^3*a^31*b^11*d^6 + 416*A^3*a^33*b^9*d
^6 + 128*B^3*a^16*b^26*d^6 + 128*B^3*a^18*b^24*d^6 - 2592*B^3*a^20*b^22*d^6 - 10976*B^3*a^22*b^20*d^6 - 20384*
B^3*a^24*b^18*d^6 - 20832*B^3*a^26*b^16*d^6 - 11872*B^3*a^28*b^14*d^6 - 3232*B^3*a^30*b^12*d^6 - 96*B^3*a^32*b
^10*d^6 + 96*B^3*a^34*b^8*d^6 - 384*A*B^2*a^15*b^27*d^6 - 768*A*B^2*a^17*b^25*d^6 + 4128*A*B^2*a^19*b^23*d^6 +
18144*A*B^2*a^21*b^21*d^6 + 27552*A*B^2*a^23*b^19*d^6 + 15456*A*B^2*a^25*b^17*d^6 - 6048*A*B^2*a^27*b^15*d^6
- 13152*A*B^2*a^29*b^13*d^6 - 6816*A*B^2*a^31*b^11*d^6 - 1248*A*B^2*a^33*b^9*d^6 + 288*A^2*B*a^14*b^28*d^6 + 4
80*A^2*B*a^16*b^26*d^6 - 2688*A^2*B*a^18*b^24*d^6 - 8352*A^2*B*a^20*b^22*d^6 - 3360*A^2*B*a^22*b^20*d^6 + 1680
0*A^2*B*a^24*b^18*d^6 + 30240*A^2*B*a^26*b^16*d^6 + 21792*A^2*B*a^28*b^14*d^6 + 6528*A^2*B*a^30*b^12*d^6 - 288
*A^2*B*a^34*b^8*d^6) + (a + b*tan(c + d*x))^(1/2)*(144*A^4*a^14*b^26*d^5 + 864*A^4*a^16*b^24*d^5 + 2048*A^4*a^
18*b^22*d^5 + 2240*A^4*a^20*b^20*d^5 + 672*A^4*a^22*b^18*d^5 - 896*A^4*a^24*b^16*d^5 - 896*A^4*a^26*b^14*d^5 -
192*A^4*a^28*b^12*d^5 + 80*A^4*a^30*b^10*d^5 + 32*A^4*a^32*b^8*d^5 - 64*B^4*a^16*b^24*d^5 - 352*B^4*a^18*b^22
*d^5 - 672*B^4*a^20*b^20*d^5 - 224*B^4*a^22*b^18*d^5 + 1120*B^4*a^24*b^16*d^5 + 2016*B^4*a^26*b^14*d^5 + 1568*
B^4*a^28*b^12*d^5 + 608*B^4*a^30*b^10*d^5 + 96*B^4*a^32*b^8*d^5 + 192*A*B^3*a^15*b^25*d^5 + 896*A*B^3*a^17*b^2
3*d^5 + 896*A*B^3*a^19*b^21*d^5 - 2688*A*B^3*a^21*b^19*d^5 - 8960*A*B^3*a^23*b^17*d^5 - 11648*A*B^3*a^25*b^15*
d^5 - 8064*A*B^3*a^27*b^13*d^5 - 2944*A*B^3*a^29*b^11*d^5 - 448*A*B^3*a^31*b^9*d^5 - 768*A^3*B*a^15*b^25*d^5 -
5184*A^3*B*a^17*b^23*d^5 - 14784*A^3*B*a^19*b^21*d^5 - 22848*A^3*B*a^21*b^19*d^5 - 20160*A^3*B*a^23*b^17*d^5
- 9408*A^3*B*a^25*b^15*d^5 - 1344*A^3*B*a^27*b^13*d^5 + 576*A^3*B*a^29*b^11*d^5 + 192*A^3*B*a^31*b^9*d^5 - 144
*A^2*B^2*a^14*b^26*d^5 - 32*A^2*B^2*a^16*b^24*d^5 + 3808*A^2*B^2*a^18*b^22*d^5 + 15456*A^2*B^2*a^20*b^20*d^5 +
29120*A^2*B^2*a^22*b^18*d^5 + 31136*A^2*B^2*a^24*b^16*d^5 + 19488*A^2*B^2*a^26*b^14*d^5 + 6688*A^2*B^2*a^28*b
^12*d^5 + 976*A^2*B^2*a^30*b^10*d^5))*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 +
24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 +
48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2
- 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) - (((((8*A^2*a^3*d^2 - 8*B
^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 +
B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A
*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 +
3*a^4*b^2*d^4)))^(1/2)*(((a + b*tan(c + d*x))^(1/2)*(576*A^2*a^15*b^28*d^7 + 5184*A^2*a^17*b^26*d^7 + 21568*A^
2*a^19*b^24*d^7 + 53888*A^2*a^21*b^22*d^7 + 87808*A^2*a^23*b^20*d^7 + 94976*A^2*a^25*b^18*d^7 + 66304*A^2*a^27
*b^16*d^7 + 27008*A^2*a^29*b^14*d^7 + 4288*A^2*a^31*b^12*d^7 - 832*A^2*a^33*b^10*d^7 - 320*A^2*a^35*b^8*d^7 +
256*B^2*a^17*b^26*d^7 + 1472*B^2*a^19*b^24*d^7 + 3712*B^2*a^21*b^22*d^7 + 6272*B^2*a^23*b^20*d^7 + 9856*B^2*a^
25*b^18*d^7 + 14336*B^2*a^27*b^16*d^7 + 15232*B^2*a^29*b^14*d^7 + 10112*B^2*a^31*b^12*d^7 + 3712*B^2*a^33*b^10
*d^7 + 576*B^2*a^35*b^8*d^7 - 768*A*B*a^16*b^27*d^7 - 6400*A*B*a^18*b^25*d^7 - 25856*A*B*a^20*b^23*d^7 - 66304
*A*B*a^22*b^21*d^7 - 116480*A*B*a^24*b^19*d^7 - 141568*A*B*a^26*b^17*d^7 - 116480*A*B*a^28*b^15*d^7 - 61696*A*
B*a^30*b^13*d^7 - 18944*A*B*a^32*b^11*d^7 - 2560*A*B*a^34*b^9*d^7) - ((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*
B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4
+ 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^
2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(
1/2)*((a + b*tan(c + d*x))^(1/2)*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^
2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a
^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*
A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(512*a^18*b^28*d^9 + 5376*a^20*
b^26*d^9 + 25344*a^22*b^24*d^9 + 70656*a^24*b^22*d^9 + 129024*a^26*b^20*d^9 + 161280*a^28*b^18*d^9 + 139776*a^
30*b^16*d^9 + 82944*a^32*b^14*d^9 + 32256*a^34*b^12*d^9 + 7424*a^36*b^10*d^9 + 768*a^38*b^8*d^9) - 768*A*a^16*
b^29*d^8 - 7680*A*a^18*b^27*d^8 - 34304*A*a^20*b^25*d^8 - 90112*A*a^22*b^23*d^8 - 154112*A*a^24*b^21*d^8 - 179
200*A*a^26*b^19*d^8 - 143360*A*a^28*b^17*d^8 - 77824*A*a^30*b^15*d^8 - 27392*A*a^32*b^13*d^8 - 5632*A*a^34*b^1
1*d^8 - 512*A*a^36*b^9*d^8 + 512*B*a^17*b^28*d^8 + 5248*B*a^19*b^26*d^8 + 23936*B*a^21*b^24*d^8 + 64000*B*a^23
*b^22*d^8 + 111104*B*a^25*b^20*d^8 + 130816*B*a^27*b^18*d^8 + 105728*B*a^29*b^16*d^8 + 57856*B*a^31*b^14*d^8 +
20480*B*a^33*b^12*d^8 + 4224*B*a^35*b^10*d^8 + 384*B*a^37*b^8*d^8))*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*
B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4
+ 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^
2*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(
1/2) + 576*A^3*a^15*b^27*d^6 + 3456*A^3*a^17*b^25*d^6 + 8480*A^3*a^19*b^23*d^6 + 10976*A^3*a^21*b^21*d^6 + 873
6*A^3*a^23*b^19*d^6 + 6496*A^3*a^25*b^17*d^6 + 6496*A^3*a^27*b^15*d^6 + 5280*A^3*a^29*b^13*d^6 + 2336*A^3*a^31
*b^11*d^6 + 416*A^3*a^33*b^9*d^6 + 128*B^3*a^16*b^26*d^6 + 128*B^3*a^18*b^24*d^6 - 2592*B^3*a^20*b^22*d^6 - 10
976*B^3*a^22*b^20*d^6 - 20384*B^3*a^24*b^18*d^6 - 20832*B^3*a^26*b^16*d^6 - 11872*B^3*a^28*b^14*d^6 - 3232*B^3
*a^30*b^12*d^6 - 96*B^3*a^32*b^10*d^6 + 96*B^3*a^34*b^8*d^6 - 384*A*B^2*a^15*b^27*d^6 - 768*A*B^2*a^17*b^25*d^
6 + 4128*A*B^2*a^19*b^23*d^6 + 18144*A*B^2*a^21*b^21*d^6 + 27552*A*B^2*a^23*b^19*d^6 + 15456*A*B^2*a^25*b^17*d
^6 - 6048*A*B^2*a^27*b^15*d^6 - 13152*A*B^2*a^29*b^13*d^6 - 6816*A*B^2*a^31*b^11*d^6 - 1248*A*B^2*a^33*b^9*d^6
+ 288*A^2*B*a^14*b^28*d^6 + 480*A^2*B*a^16*b^26*d^6 - 2688*A^2*B*a^18*b^24*d^6 - 8352*A^2*B*a^20*b^22*d^6 - 3
360*A^2*B*a^22*b^20*d^6 + 16800*A^2*B*a^24*b^18*d^6 + 30240*A^2*B*a^26*b^16*d^6 + 21792*A^2*B*a^28*b^14*d^6 +
6528*A^2*B*a^30*b^12*d^6 - 288*A^2*B*a^34*b^8*d^6) - (a + b*tan(c + d*x))^(1/2)*(144*A^4*a^14*b^26*d^5 + 864*A
^4*a^16*b^24*d^5 + 2048*A^4*a^18*b^22*d^5 + 2240*A^4*a^20*b^20*d^5 + 672*A^4*a^22*b^18*d^5 - 896*A^4*a^24*b^16
*d^5 - 896*A^4*a^26*b^14*d^5 - 192*A^4*a^28*b^12*d^5 + 80*A^4*a^30*b^10*d^5 + 32*A^4*a^32*b^8*d^5 - 64*B^4*a^1
6*b^24*d^5 - 352*B^4*a^18*b^22*d^5 - 672*B^4*a^20*b^20*d^5 - 224*B^4*a^22*b^18*d^5 + 1120*B^4*a^24*b^16*d^5 +
2016*B^4*a^26*b^14*d^5 + 1568*B^4*a^28*b^12*d^5 + 608*B^4*a^30*b^10*d^5 + 96*B^4*a^32*b^8*d^5 + 192*A*B^3*a^15
*b^25*d^5 + 896*A*B^3*a^17*b^23*d^5 + 896*A*B^3*a^19*b^21*d^5 - 2688*A*B^3*a^21*b^19*d^5 - 8960*A*B^3*a^23*b^1
7*d^5 - 11648*A*B^3*a^25*b^15*d^5 - 8064*A*B^3*a^27*b^13*d^5 - 2944*A*B^3*a^29*b^11*d^5 - 448*A*B^3*a^31*b^9*d
^5 - 768*A^3*B*a^15*b^25*d^5 - 5184*A^3*B*a^17*b^23*d^5 - 14784*A^3*B*a^19*b^21*d^5 - 22848*A^3*B*a^21*b^19*d^
5 - 20160*A^3*B*a^23*b^17*d^5 - 9408*A^3*B*a^25*b^15*d^5 - 1344*A^3*B*a^27*b^13*d^5 + 576*A^3*B*a^29*b^11*d^5
+ 192*A^3*B*a^31*b^9*d^5 - 144*A^2*B^2*a^14*b^26*d^5 - 32*A^2*B^2*a^16*b^24*d^5 + 3808*A^2*B^2*a^18*b^22*d^5 +
15456*A^2*B^2*a^20*b^20*d^5 + 29120*A^2*B^2*a^22*b^18*d^5 + 31136*A^2*B^2*a^24*b^16*d^5 + 19488*A^2*B^2*a^26*
b^14*d^5 + 6688*A^2*B^2*a^28*b^12*d^5 + 976*A^2*B^2*a^30*b^10*d^5))*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B
*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 +
16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2
*a*b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1
/2) + 912*A^5*a^16*b^23*d^4 + 2352*A^5*a^18*b^21*d^4 + 3024*A^5*a^20*b^19*d^4 + 1680*A^5*a^22*b^17*d^4 - 336*A
^5*a^24*b^15*d^4 - 1008*A^5*a^26*b^13*d^4 - 528*A^5*a^28*b^11*d^4 - 96*A^5*a^30*b^9*d^4 + 160*A*B^4*a^16*b^23*
d^4 + 1120*A*B^4*a^18*b^21*d^4 + 3360*A*B^4*a^20*b^19*d^4 + 5600*A*B^4*a^22*b^17*d^4 + 5600*A*B^4*a^24*b^15*d^
4 + 3360*A*B^4*a^26*b^13*d^4 + 1120*A*B^4*a^28*b^11*d^4 + 160*A*B^4*a^30*b^9*d^4 - 336*A^4*B*a^15*b^24*d^4 - 2
288*A^4*B*a^17*b^22*d^4 - 6608*A^4*B*a^19*b^20*d^4 - 10416*A^4*B*a^21*b^18*d^4 - 9520*A^4*B*a^23*b^16*d^4 - 48
16*A^4*B*a^25*b^14*d^4 - 1008*A^4*B*a^27*b^12*d^4 + 112*A^4*B*a^29*b^10*d^4 + 64*A^4*B*a^31*b^8*d^4 - 336*A^2*
B^3*a^15*b^24*d^4 - 2288*A^2*B^3*a^17*b^22*d^4 - 6608*A^2*B^3*a^19*b^20*d^4 - 10416*A^2*B^3*a^21*b^18*d^4 - 95
20*A^2*B^3*a^23*b^16*d^4 - 4816*A^2*B^3*a^25*b^14*d^4 - 1008*A^2*B^3*a^27*b^12*d^4 + 112*A^2*B^3*a^29*b^10*d^4
+ 64*A^2*B^3*a^31*b^8*d^4 + 144*A^3*B^2*a^14*b^25*d^4 + 1072*A^3*B^2*a^16*b^23*d^4 + 3472*A^3*B^2*a^18*b^21*d
^4 + 6384*A^3*B^2*a^20*b^19*d^4 + 7280*A^3*B^2*a^22*b^17*d^4 + 5264*A^3*B^2*a^24*b^15*d^4 + 2352*A^3*B^2*a^26*
b^13*d^4 + 592*A^3*B^2*a^28*b^11*d^4 + 64*A^3*B^2*a^30*b^9*d^4))*((((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^
3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16
*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 4*A^2*a^3*d^2 + 4*B^2*a^3*d^2 + 8*A*B*b^3*d^2 + 12*A^2*a*
b^2*d^2 - 12*B^2*a*b^2*d^2 - 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)
*2i + atan(-(((-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A
*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)
+ 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16
*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(((a + b*tan(c + d*x))^(1/2)*(576*A^2*a^15*b^28*d
^7 + 5184*A^2*a^17*b^26*d^7 + 21568*A^2*a^19*b^24*d^7 + 53888*A^2*a^21*b^22*d^7 + 87808*A^2*a^23*b^20*d^7 + 94
976*A^2*a^25*b^18*d^7 + 66304*A^2*a^27*b^16*d^7 + 27008*A^2*a^29*b^14*d^7 + 4288*A^2*a^31*b^12*d^7 - 832*A^2*a
^33*b^10*d^7 - 320*A^2*a^35*b^8*d^7 + 256*B^2*a^17*b^26*d^7 + 1472*B^2*a^19*b^24*d^7 + 3712*B^2*a^21*b^22*d^7
+ 6272*B^2*a^23*b^20*d^7 + 9856*B^2*a^25*b^18*d^7 + 14336*B^2*a^27*b^16*d^7 + 15232*B^2*a^29*b^14*d^7 + 10112*
B^2*a^31*b^12*d^7 + 3712*B^2*a^33*b^10*d^7 + 576*B^2*a^35*b^8*d^7 - 768*A*B*a^16*b^27*d^7 - 6400*A*B*a^18*b^25
*d^7 - 25856*A*B*a^20*b^23*d^7 - 66304*A*B*a^22*b^21*d^7 - 116480*A*B*a^24*b^19*d^7 - 141568*A*B*a^26*b^17*d^7
- 116480*A*B*a^28*b^15*d^7 - 61696*A*B*a^30*b^13*d^7 - 18944*A*B*a^32*b^11*d^7 - 2560*A*B*a^34*b^9*d^7) - (-(
((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4
- (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2
- 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d
^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*((a + b*tan(c + d*x))^(1/2)*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 1
6*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*
d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 1
2*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)
))^(1/2)*(512*a^18*b^28*d^9 + 5376*a^20*b^26*d^9 + 25344*a^22*b^24*d^9 + 70656*a^24*b^22*d^9 + 129024*a^26*b^2
0*d^9 + 161280*a^28*b^18*d^9 + 139776*a^30*b^16*d^9 + 82944*a^32*b^14*d^9 + 32256*a^34*b^12*d^9 + 7424*a^36*b^
10*d^9 + 768*a^38*b^8*d^9) - 768*A*a^16*b^29*d^8 - 7680*A*a^18*b^27*d^8 - 34304*A*a^20*b^25*d^8 - 90112*A*a^22
*b^23*d^8 - 154112*A*a^24*b^21*d^8 - 179200*A*a^26*b^19*d^8 - 143360*A*a^28*b^17*d^8 - 77824*A*a^30*b^15*d^8 -
27392*A*a^32*b^13*d^8 - 5632*A*a^34*b^11*d^8 - 512*A*a^36*b^9*d^8 + 512*B*a^17*b^28*d^8 + 5248*B*a^19*b^26*d^
8 + 23936*B*a^21*b^24*d^8 + 64000*B*a^23*b^22*d^8 + 111104*B*a^25*b^20*d^8 + 130816*B*a^27*b^18*d^8 + 105728*B
*a^29*b^16*d^8 + 57856*B*a^31*b^14*d^8 + 20480*B*a^33*b^12*d^8 + 4224*B*a^35*b^10*d^8 + 384*B*a^37*b^8*d^8))*(
-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2
/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^
2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6
*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) + 576*A^3*a^15*b^27*d^6 + 3456*A^3*a^17*b^25*d^6 + 8480*A^3*a^19
*b^23*d^6 + 10976*A^3*a^21*b^21*d^6 + 8736*A^3*a^23*b^19*d^6 + 6496*A^3*a^25*b^17*d^6 + 6496*A^3*a^27*b^15*d^6
+ 5280*A^3*a^29*b^13*d^6 + 2336*A^3*a^31*b^11*d^6 + 416*A^3*a^33*b^9*d^6 + 128*B^3*a^16*b^26*d^6 + 128*B^3*a^
18*b^24*d^6 - 2592*B^3*a^20*b^22*d^6 - 10976*B^3*a^22*b^20*d^6 - 20384*B^3*a^24*b^18*d^6 - 20832*B^3*a^26*b^16
*d^6 - 11872*B^3*a^28*b^14*d^6 - 3232*B^3*a^30*b^12*d^6 - 96*B^3*a^32*b^10*d^6 + 96*B^3*a^34*b^8*d^6 - 384*A*B
^2*a^15*b^27*d^6 - 768*A*B^2*a^17*b^25*d^6 + 4128*A*B^2*a^19*b^23*d^6 + 18144*A*B^2*a^21*b^21*d^6 + 27552*A*B^
2*a^23*b^19*d^6 + 15456*A*B^2*a^25*b^17*d^6 - 6048*A*B^2*a^27*b^15*d^6 - 13152*A*B^2*a^29*b^13*d^6 - 6816*A*B^
2*a^31*b^11*d^6 - 1248*A*B^2*a^33*b^9*d^6 + 288*A^2*B*a^14*b^28*d^6 + 480*A^2*B*a^16*b^26*d^6 - 2688*A^2*B*a^1
8*b^24*d^6 - 8352*A^2*B*a^20*b^22*d^6 - 3360*A^2*B*a^22*b^20*d^6 + 16800*A^2*B*a^24*b^18*d^6 + 30240*A^2*B*a^2
6*b^16*d^6 + 21792*A^2*B*a^28*b^14*d^6 + 6528*A^2*B*a^30*b^12*d^6 - 288*A^2*B*a^34*b^8*d^6) - (a + b*tan(c + d
*x))^(1/2)*(144*A^4*a^14*b^26*d^5 + 864*A^4*a^16*b^24*d^5 + 2048*A^4*a^18*b^22*d^5 + 2240*A^4*a^20*b^20*d^5 +
672*A^4*a^22*b^18*d^5 - 896*A^4*a^24*b^16*d^5 - 896*A^4*a^26*b^14*d^5 - 192*A^4*a^28*b^12*d^5 + 80*A^4*a^30*b^
10*d^5 + 32*A^4*a^32*b^8*d^5 - 64*B^4*a^16*b^24*d^5 - 352*B^4*a^18*b^22*d^5 - 672*B^4*a^20*b^20*d^5 - 224*B^4*
a^22*b^18*d^5 + 1120*B^4*a^24*b^16*d^5 + 2016*B^4*a^26*b^14*d^5 + 1568*B^4*a^28*b^12*d^5 + 608*B^4*a^30*b^10*d
^5 + 96*B^4*a^32*b^8*d^5 + 192*A*B^3*a^15*b^25*d^5 + 896*A*B^3*a^17*b^23*d^5 + 896*A*B^3*a^19*b^21*d^5 - 2688*
A*B^3*a^21*b^19*d^5 - 8960*A*B^3*a^23*b^17*d^5 - 11648*A*B^3*a^25*b^15*d^5 - 8064*A*B^3*a^27*b^13*d^5 - 2944*A
*B^3*a^29*b^11*d^5 - 448*A*B^3*a^31*b^9*d^5 - 768*A^3*B*a^15*b^25*d^5 - 5184*A^3*B*a^17*b^23*d^5 - 14784*A^3*B
*a^19*b^21*d^5 - 22848*A^3*B*a^21*b^19*d^5 - 20160*A^3*B*a^23*b^17*d^5 - 9408*A^3*B*a^25*b^15*d^5 - 1344*A^3*B
*a^27*b^13*d^5 + 576*A^3*B*a^29*b^11*d^5 + 192*A^3*B*a^31*b^9*d^5 - 144*A^2*B^2*a^14*b^26*d^5 - 32*A^2*B^2*a^1
6*b^24*d^5 + 3808*A^2*B^2*a^18*b^22*d^5 + 15456*A^2*B^2*a^20*b^20*d^5 + 29120*A^2*B^2*a^22*b^18*d^5 + 31136*A^
2*B^2*a^24*b^16*d^5 + 19488*A^2*B^2*a^26*b^14*d^5 + 6688*A^2*B^2*a^28*b^12*d^5 + 976*A^2*B^2*a^30*b^10*d^5))*(
-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2
/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^
2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6
*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*1i - ((-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A
^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 4
8*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12
*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(576*A^3*a^
15*b^27*d^6 - ((a + b*tan(c + d*x))^(1/2)*(576*A^2*a^15*b^28*d^7 + 5184*A^2*a^17*b^26*d^7 + 21568*A^2*a^19*b^2
4*d^7 + 53888*A^2*a^21*b^22*d^7 + 87808*A^2*a^23*b^20*d^7 + 94976*A^2*a^25*b^18*d^7 + 66304*A^2*a^27*b^16*d^7
+ 27008*A^2*a^29*b^14*d^7 + 4288*A^2*a^31*b^12*d^7 - 832*A^2*a^33*b^10*d^7 - 320*A^2*a^35*b^8*d^7 + 256*B^2*a^
17*b^26*d^7 + 1472*B^2*a^19*b^24*d^7 + 3712*B^2*a^21*b^22*d^7 + 6272*B^2*a^23*b^20*d^7 + 9856*B^2*a^25*b^18*d^
7 + 14336*B^2*a^27*b^16*d^7 + 15232*B^2*a^29*b^14*d^7 + 10112*B^2*a^31*b^12*d^7 + 3712*B^2*a^33*b^10*d^7 + 576
*B^2*a^35*b^8*d^7 - 768*A*B*a^16*b^27*d^7 - 6400*A*B*a^18*b^25*d^7 - 25856*A*B*a^20*b^23*d^7 - 66304*A*B*a^22*
b^21*d^7 - 116480*A*B*a^24*b^19*d^7 - 141568*A*B*a^26*b^17*d^7 - 116480*A*B*a^28*b^15*d^7 - 61696*A*B*a^30*b^1
3*d^7 - 18944*A*B*a^32*b^11*d^7 - 2560*A*B*a^34*b^9*d^7) - (-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2
- 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*
d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d
^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*((a
+ b*tan(c + d*x))^(1/2)*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*
d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d
^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*
b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(512*a^18*b^28*d^9 + 5376*a^20*b^26*d^9
+ 25344*a^22*b^24*d^9 + 70656*a^24*b^22*d^9 + 129024*a^26*b^20*d^9 + 161280*a^28*b^18*d^9 + 139776*a^30*b^16*
d^9 + 82944*a^32*b^14*d^9 + 32256*a^34*b^12*d^9 + 7424*a^36*b^10*d^9 + 768*a^38*b^8*d^9) + 768*A*a^16*b^29*d^8
+ 7680*A*a^18*b^27*d^8 + 34304*A*a^20*b^25*d^8 + 90112*A*a^22*b^23*d^8 + 154112*A*a^24*b^21*d^8 + 179200*A*a^
26*b^19*d^8 + 143360*A*a^28*b^17*d^8 + 77824*A*a^30*b^15*d^8 + 27392*A*a^32*b^13*d^8 + 5632*A*a^34*b^11*d^8 +
512*A*a^36*b^9*d^8 - 512*B*a^17*b^28*d^8 - 5248*B*a^19*b^26*d^8 - 23936*B*a^21*b^24*d^8 - 64000*B*a^23*b^22*d^
8 - 111104*B*a^25*b^20*d^8 - 130816*B*a^27*b^18*d^8 - 105728*B*a^29*b^16*d^8 - 57856*B*a^31*b^14*d^8 - 20480*B
*a^33*b^12*d^8 - 4224*B*a^35*b^10*d^8 - 384*B*a^37*b^8*d^8))*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d
^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^
6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2
*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) +
3456*A^3*a^17*b^25*d^6 + 8480*A^3*a^19*b^23*d^6 + 10976*A^3*a^21*b^21*d^6 + 8736*A^3*a^23*b^19*d^6 + 6496*A^3*
a^25*b^17*d^6 + 6496*A^3*a^27*b^15*d^6 + 5280*A^3*a^29*b^13*d^6 + 2336*A^3*a^31*b^11*d^6 + 416*A^3*a^33*b^9*d^
6 + 128*B^3*a^16*b^26*d^6 + 128*B^3*a^18*b^24*d^6 - 2592*B^3*a^20*b^22*d^6 - 10976*B^3*a^22*b^20*d^6 - 20384*B
^3*a^24*b^18*d^6 - 20832*B^3*a^26*b^16*d^6 - 11872*B^3*a^28*b^14*d^6 - 3232*B^3*a^30*b^12*d^6 - 96*B^3*a^32*b^
10*d^6 + 96*B^3*a^34*b^8*d^6 - 384*A*B^2*a^15*b^27*d^6 - 768*A*B^2*a^17*b^25*d^6 + 4128*A*B^2*a^19*b^23*d^6 +
18144*A*B^2*a^21*b^21*d^6 + 27552*A*B^2*a^23*b^19*d^6 + 15456*A*B^2*a^25*b^17*d^6 - 6048*A*B^2*a^27*b^15*d^6 -
13152*A*B^2*a^29*b^13*d^6 - 6816*A*B^2*a^31*b^11*d^6 - 1248*A*B^2*a^33*b^9*d^6 + 288*A^2*B*a^14*b^28*d^6 + 48
0*A^2*B*a^16*b^26*d^6 - 2688*A^2*B*a^18*b^24*d^6 - 8352*A^2*B*a^20*b^22*d^6 - 3360*A^2*B*a^22*b^20*d^6 + 16800
*A^2*B*a^24*b^18*d^6 + 30240*A^2*B*a^26*b^16*d^6 + 21792*A^2*B*a^28*b^14*d^6 + 6528*A^2*B*a^30*b^12*d^6 - 288*
A^2*B*a^34*b^8*d^6) + (a + b*tan(c + d*x))^(1/2)*(144*A^4*a^14*b^26*d^5 + 864*A^4*a^16*b^24*d^5 + 2048*A^4*a^1
8*b^22*d^5 + 2240*A^4*a^20*b^20*d^5 + 672*A^4*a^22*b^18*d^5 - 896*A^4*a^24*b^16*d^5 - 896*A^4*a^26*b^14*d^5 -
192*A^4*a^28*b^12*d^5 + 80*A^4*a^30*b^10*d^5 + 32*A^4*a^32*b^8*d^5 - 64*B^4*a^16*b^24*d^5 - 352*B^4*a^18*b^22*
d^5 - 672*B^4*a^20*b^20*d^5 - 224*B^4*a^22*b^18*d^5 + 1120*B^4*a^24*b^16*d^5 + 2016*B^4*a^26*b^14*d^5 + 1568*B
^4*a^28*b^12*d^5 + 608*B^4*a^30*b^10*d^5 + 96*B^4*a^32*b^8*d^5 + 192*A*B^3*a^15*b^25*d^5 + 896*A*B^3*a^17*b^23
*d^5 + 896*A*B^3*a^19*b^21*d^5 - 2688*A*B^3*a^21*b^19*d^5 - 8960*A*B^3*a^23*b^17*d^5 - 11648*A*B^3*a^25*b^15*d
^5 - 8064*A*B^3*a^27*b^13*d^5 - 2944*A*B^3*a^29*b^11*d^5 - 448*A*B^3*a^31*b^9*d^5 - 768*A^3*B*a^15*b^25*d^5 -
5184*A^3*B*a^17*b^23*d^5 - 14784*A^3*B*a^19*b^21*d^5 - 22848*A^3*B*a^21*b^19*d^5 - 20160*A^3*B*a^23*b^17*d^5 -
9408*A^3*B*a^25*b^15*d^5 - 1344*A^3*B*a^27*b^13*d^5 + 576*A^3*B*a^29*b^11*d^5 + 192*A^3*B*a^31*b^9*d^5 - 144*
A^2*B^2*a^14*b^26*d^5 - 32*A^2*B^2*a^16*b^24*d^5 + 3808*A^2*B^2*a^18*b^22*d^5 + 15456*A^2*B^2*a^20*b^20*d^5 +
29120*A^2*B^2*a^22*b^18*d^5 + 31136*A^2*B^2*a^24*b^16*d^5 + 19488*A^2*B^2*a^26*b^14*d^5 + 6688*A^2*B^2*a^28*b^
12*d^5 + 976*A^2*B^2*a^30*b^10*d^5))*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 +
24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 +
48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2
+ 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*1i)/(144*A^5*a^14*b^25*d^4
- ((-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d
^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a
^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4
+ b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(576*A^3*a^15*b^27*d^6 - ((a + b*tan(c + d*x))^(1/2)*(576*A
^2*a^15*b^28*d^7 + 5184*A^2*a^17*b^26*d^7 + 21568*A^2*a^19*b^24*d^7 + 53888*A^2*a^21*b^22*d^7 + 87808*A^2*a^23
*b^20*d^7 + 94976*A^2*a^25*b^18*d^7 + 66304*A^2*a^27*b^16*d^7 + 27008*A^2*a^29*b^14*d^7 + 4288*A^2*a^31*b^12*d
^7 - 832*A^2*a^33*b^10*d^7 - 320*A^2*a^35*b^8*d^7 + 256*B^2*a^17*b^26*d^7 + 1472*B^2*a^19*b^24*d^7 + 3712*B^2*
a^21*b^22*d^7 + 6272*B^2*a^23*b^20*d^7 + 9856*B^2*a^25*b^18*d^7 + 14336*B^2*a^27*b^16*d^7 + 15232*B^2*a^29*b^1
4*d^7 + 10112*B^2*a^31*b^12*d^7 + 3712*B^2*a^33*b^10*d^7 + 576*B^2*a^35*b^8*d^7 - 768*A*B*a^16*b^27*d^7 - 6400
*A*B*a^18*b^25*d^7 - 25856*A*B*a^20*b^23*d^7 - 66304*A*B*a^22*b^21*d^7 - 116480*A*B*a^24*b^19*d^7 - 141568*A*B
*a^26*b^17*d^7 - 116480*A*B*a^28*b^15*d^7 - 61696*A*B*a^30*b^13*d^7 - 18944*A*B*a^32*b^11*d^7 - 2560*A*B*a^34*
b^9*d^7) - (-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*
a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) +
4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a
^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*((a + b*tan(c + d*x))^(1/2)*(-(((8*A^2*a^3*d^2 - 8*B
^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 +
B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A
*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 +
3*a^4*b^2*d^4)))^(1/2)*(512*a^18*b^28*d^9 + 5376*a^20*b^26*d^9 + 25344*a^22*b^24*d^9 + 70656*a^24*b^22*d^9 + 1
29024*a^26*b^20*d^9 + 161280*a^28*b^18*d^9 + 139776*a^30*b^16*d^9 + 82944*a^32*b^14*d^9 + 32256*a^34*b^12*d^9
+ 7424*a^36*b^10*d^9 + 768*a^38*b^8*d^9) + 768*A*a^16*b^29*d^8 + 7680*A*a^18*b^27*d^8 + 34304*A*a^20*b^25*d^8
+ 90112*A*a^22*b^23*d^8 + 154112*A*a^24*b^21*d^8 + 179200*A*a^26*b^19*d^8 + 143360*A*a^28*b^17*d^8 + 77824*A*a
^30*b^15*d^8 + 27392*A*a^32*b^13*d^8 + 5632*A*a^34*b^11*d^8 + 512*A*a^36*b^9*d^8 - 512*B*a^17*b^28*d^8 - 5248*
B*a^19*b^26*d^8 - 23936*B*a^21*b^24*d^8 - 64000*B*a^23*b^22*d^8 - 111104*B*a^25*b^20*d^8 - 130816*B*a^27*b^18*
d^8 - 105728*B*a^29*b^16*d^8 - 57856*B*a^31*b^14*d^8 - 20480*B*a^33*b^12*d^8 - 4224*B*a^35*b^10*d^8 - 384*B*a^
37*b^8*d^8))*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*
B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)
+ 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*
(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) + 3456*A^3*a^17*b^25*d^6 + 8480*A^3*a^19*b^23*d^6
+ 10976*A^3*a^21*b^21*d^6 + 8736*A^3*a^23*b^19*d^6 + 6496*A^3*a^25*b^17*d^6 + 6496*A^3*a^27*b^15*d^6 + 5280*A^
3*a^29*b^13*d^6 + 2336*A^3*a^31*b^11*d^6 + 416*A^3*a^33*b^9*d^6 + 128*B^3*a^16*b^26*d^6 + 128*B^3*a^18*b^24*d^
6 - 2592*B^3*a^20*b^22*d^6 - 10976*B^3*a^22*b^20*d^6 - 20384*B^3*a^24*b^18*d^6 - 20832*B^3*a^26*b^16*d^6 - 118
72*B^3*a^28*b^14*d^6 - 3232*B^3*a^30*b^12*d^6 - 96*B^3*a^32*b^10*d^6 + 96*B^3*a^34*b^8*d^6 - 384*A*B^2*a^15*b^
27*d^6 - 768*A*B^2*a^17*b^25*d^6 + 4128*A*B^2*a^19*b^23*d^6 + 18144*A*B^2*a^21*b^21*d^6 + 27552*A*B^2*a^23*b^1
9*d^6 + 15456*A*B^2*a^25*b^17*d^6 - 6048*A*B^2*a^27*b^15*d^6 - 13152*A*B^2*a^29*b^13*d^6 - 6816*A*B^2*a^31*b^1
1*d^6 - 1248*A*B^2*a^33*b^9*d^6 + 288*A^2*B*a^14*b^28*d^6 + 480*A^2*B*a^16*b^26*d^6 - 2688*A^2*B*a^18*b^24*d^6
- 8352*A^2*B*a^20*b^22*d^6 - 3360*A^2*B*a^22*b^20*d^6 + 16800*A^2*B*a^24*b^18*d^6 + 30240*A^2*B*a^26*b^16*d^6
+ 21792*A^2*B*a^28*b^14*d^6 + 6528*A^2*B*a^30*b^12*d^6 - 288*A^2*B*a^34*b^8*d^6) + (a + b*tan(c + d*x))^(1/2)
*(144*A^4*a^14*b^26*d^5 + 864*A^4*a^16*b^24*d^5 + 2048*A^4*a^18*b^22*d^5 + 2240*A^4*a^20*b^20*d^5 + 672*A^4*a^
22*b^18*d^5 - 896*A^4*a^24*b^16*d^5 - 896*A^4*a^26*b^14*d^5 - 192*A^4*a^28*b^12*d^5 + 80*A^4*a^30*b^10*d^5 + 3
2*A^4*a^32*b^8*d^5 - 64*B^4*a^16*b^24*d^5 - 352*B^4*a^18*b^22*d^5 - 672*B^4*a^20*b^20*d^5 - 224*B^4*a^22*b^18*
d^5 + 1120*B^4*a^24*b^16*d^5 + 2016*B^4*a^26*b^14*d^5 + 1568*B^4*a^28*b^12*d^5 + 608*B^4*a^30*b^10*d^5 + 96*B^
4*a^32*b^8*d^5 + 192*A*B^3*a^15*b^25*d^5 + 896*A*B^3*a^17*b^23*d^5 + 896*A*B^3*a^19*b^21*d^5 - 2688*A*B^3*a^21
*b^19*d^5 - 8960*A*B^3*a^23*b^17*d^5 - 11648*A*B^3*a^25*b^15*d^5 - 8064*A*B^3*a^27*b^13*d^5 - 2944*A*B^3*a^29*
b^11*d^5 - 448*A*B^3*a^31*b^9*d^5 - 768*A^3*B*a^15*b^25*d^5 - 5184*A^3*B*a^17*b^23*d^5 - 14784*A^3*B*a^19*b^21
*d^5 - 22848*A^3*B*a^21*b^19*d^5 - 20160*A^3*B*a^23*b^17*d^5 - 9408*A^3*B*a^25*b^15*d^5 - 1344*A^3*B*a^27*b^13
*d^5 + 576*A^3*B*a^29*b^11*d^5 + 192*A^3*B*a^31*b^9*d^5 - 144*A^2*B^2*a^14*b^26*d^5 - 32*A^2*B^2*a^16*b^24*d^5
+ 3808*A^2*B^2*a^18*b^22*d^5 + 15456*A^2*B^2*a^20*b^20*d^5 + 29120*A^2*B^2*a^22*b^18*d^5 + 31136*A^2*B^2*a^24
*b^16*d^5 + 19488*A^2*B^2*a^26*b^14*d^5 + 6688*A^2*B^2*a^28*b^12*d^5 + 976*A^2*B^2*a^30*b^10*d^5))*(-(((8*A^2*
a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4
+ 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*
a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a
^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) - ((-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2
+ 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4
+ 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^
2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(((a + b*tan(c + d*x))^(
1/2)*(576*A^2*a^15*b^28*d^7 + 5184*A^2*a^17*b^26*d^7 + 21568*A^2*a^19*b^24*d^7 + 53888*A^2*a^21*b^22*d^7 + 878
08*A^2*a^23*b^20*d^7 + 94976*A^2*a^25*b^18*d^7 + 66304*A^2*a^27*b^16*d^7 + 27008*A^2*a^29*b^14*d^7 + 4288*A^2*
a^31*b^12*d^7 - 832*A^2*a^33*b^10*d^7 - 320*A^2*a^35*b^8*d^7 + 256*B^2*a^17*b^26*d^7 + 1472*B^2*a^19*b^24*d^7
+ 3712*B^2*a^21*b^22*d^7 + 6272*B^2*a^23*b^20*d^7 + 9856*B^2*a^25*b^18*d^7 + 14336*B^2*a^27*b^16*d^7 + 15232*B
^2*a^29*b^14*d^7 + 10112*B^2*a^31*b^12*d^7 + 3712*B^2*a^33*b^10*d^7 + 576*B^2*a^35*b^8*d^7 - 768*A*B*a^16*b^27
*d^7 - 6400*A*B*a^18*b^25*d^7 - 25856*A*B*a^20*b^23*d^7 - 66304*A*B*a^22*b^21*d^7 - 116480*A*B*a^24*b^19*d^7 -
141568*A*B*a^26*b^17*d^7 - 116480*A*B*a^28*b^15*d^7 - 61696*A*B*a^30*b^13*d^7 - 18944*A*B*a^32*b^11*d^7 - 256
0*A*B*a^34*b^9*d^7) - (-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^
2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4
))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*
d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*((a + b*tan(c + d*x))^(1/2)*(-(((8*A^2*a^
3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 +
2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^
3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2
*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(512*a^18*b^28*d^9 + 5376*a^20*b^26*d^9 + 25344*a^22*b^24*d^9 + 70656*a^24*b
^22*d^9 + 129024*a^26*b^20*d^9 + 161280*a^28*b^18*d^9 + 139776*a^30*b^16*d^9 + 82944*a^32*b^14*d^9 + 32256*a^3
4*b^12*d^9 + 7424*a^36*b^10*d^9 + 768*a^38*b^8*d^9) - 768*A*a^16*b^29*d^8 - 7680*A*a^18*b^27*d^8 - 34304*A*a^2
0*b^25*d^8 - 90112*A*a^22*b^23*d^8 - 154112*A*a^24*b^21*d^8 - 179200*A*a^26*b^19*d^8 - 143360*A*a^28*b^17*d^8
- 77824*A*a^30*b^15*d^8 - 27392*A*a^32*b^13*d^8 - 5632*A*a^34*b^11*d^8 - 512*A*a^36*b^9*d^8 + 512*B*a^17*b^28*
d^8 + 5248*B*a^19*b^26*d^8 + 23936*B*a^21*b^24*d^8 + 64000*B*a^23*b^22*d^8 + 111104*B*a^25*b^20*d^8 + 130816*B
*a^27*b^18*d^8 + 105728*B*a^29*b^16*d^8 + 57856*B*a^31*b^14*d^8 + 20480*B*a^33*b^12*d^8 + 4224*B*a^35*b^10*d^8
+ 384*B*a^37*b^8*d^8))*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*
d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d
^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*
b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) + 576*A^3*a^15*b^27*d^6 + 3456*A^3*a^17
*b^25*d^6 + 8480*A^3*a^19*b^23*d^6 + 10976*A^3*a^21*b^21*d^6 + 8736*A^3*a^23*b^19*d^6 + 6496*A^3*a^25*b^17*d^6
+ 6496*A^3*a^27*b^15*d^6 + 5280*A^3*a^29*b^13*d^6 + 2336*A^3*a^31*b^11*d^6 + 416*A^3*a^33*b^9*d^6 + 128*B^3*a
^16*b^26*d^6 + 128*B^3*a^18*b^24*d^6 - 2592*B^3*a^20*b^22*d^6 - 10976*B^3*a^22*b^20*d^6 - 20384*B^3*a^24*b^18*
d^6 - 20832*B^3*a^26*b^16*d^6 - 11872*B^3*a^28*b^14*d^6 - 3232*B^3*a^30*b^12*d^6 - 96*B^3*a^32*b^10*d^6 + 96*B
^3*a^34*b^8*d^6 - 384*A*B^2*a^15*b^27*d^6 - 768*A*B^2*a^17*b^25*d^6 + 4128*A*B^2*a^19*b^23*d^6 + 18144*A*B^2*a
^21*b^21*d^6 + 27552*A*B^2*a^23*b^19*d^6 + 15456*A*B^2*a^25*b^17*d^6 - 6048*A*B^2*a^27*b^15*d^6 - 13152*A*B^2*
a^29*b^13*d^6 - 6816*A*B^2*a^31*b^11*d^6 - 1248*A*B^2*a^33*b^9*d^6 + 288*A^2*B*a^14*b^28*d^6 + 480*A^2*B*a^16*
b^26*d^6 - 2688*A^2*B*a^18*b^24*d^6 - 8352*A^2*B*a^20*b^22*d^6 - 3360*A^2*B*a^22*b^20*d^6 + 16800*A^2*B*a^24*b
^18*d^6 + 30240*A^2*B*a^26*b^16*d^6 + 21792*A^2*B*a^28*b^14*d^6 + 6528*A^2*B*a^30*b^12*d^6 - 288*A^2*B*a^34*b^
8*d^6) - (a + b*tan(c + d*x))^(1/2)*(144*A^4*a^14*b^26*d^5 + 864*A^4*a^16*b^24*d^5 + 2048*A^4*a^18*b^22*d^5 +
2240*A^4*a^20*b^20*d^5 + 672*A^4*a^22*b^18*d^5 - 896*A^4*a^24*b^16*d^5 - 896*A^4*a^26*b^14*d^5 - 192*A^4*a^28*
b^12*d^5 + 80*A^4*a^30*b^10*d^5 + 32*A^4*a^32*b^8*d^5 - 64*B^4*a^16*b^24*d^5 - 352*B^4*a^18*b^22*d^5 - 672*B^4
*a^20*b^20*d^5 - 224*B^4*a^22*b^18*d^5 + 1120*B^4*a^24*b^16*d^5 + 2016*B^4*a^26*b^14*d^5 + 1568*B^4*a^28*b^12*
d^5 + 608*B^4*a^30*b^10*d^5 + 96*B^4*a^32*b^8*d^5 + 192*A*B^3*a^15*b^25*d^5 + 896*A*B^3*a^17*b^23*d^5 + 896*A*
B^3*a^19*b^21*d^5 - 2688*A*B^3*a^21*b^19*d^5 - 8960*A*B^3*a^23*b^17*d^5 - 11648*A*B^3*a^25*b^15*d^5 - 8064*A*B
^3*a^27*b^13*d^5 - 2944*A*B^3*a^29*b^11*d^5 - 448*A*B^3*a^31*b^9*d^5 - 768*A^3*B*a^15*b^25*d^5 - 5184*A^3*B*a^
17*b^23*d^5 - 14784*A^3*B*a^19*b^21*d^5 - 22848*A^3*B*a^21*b^19*d^5 - 20160*A^3*B*a^23*b^17*d^5 - 9408*A^3*B*a
^25*b^15*d^5 - 1344*A^3*B*a^27*b^13*d^5 + 576*A^3*B*a^29*b^11*d^5 + 192*A^3*B*a^31*b^9*d^5 - 144*A^2*B^2*a^14*
b^26*d^5 - 32*A^2*B^2*a^16*b^24*d^5 + 3808*A^2*B^2*a^18*b^22*d^5 + 15456*A^2*B^2*a^20*b^20*d^5 + 29120*A^2*B^2
*a^22*b^18*d^5 + 31136*A^2*B^2*a^24*b^16*d^5 + 19488*A^2*B^2*a^26*b^14*d^5 + 6688*A^2*B^2*a^28*b^12*d^5 + 976*
A^2*B^2*a^30*b^10*d^5))*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*
d^2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d
^4))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*
b*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) + 912*A^5*a^16*b^23*d^4 + 2352*A^5*a^18
*b^21*d^4 + 3024*A^5*a^20*b^19*d^4 + 1680*A^5*a^22*b^17*d^4 - 336*A^5*a^24*b^15*d^4 - 1008*A^5*a^26*b^13*d^4 -
528*A^5*a^28*b^11*d^4 - 96*A^5*a^30*b^9*d^4 + 160*A*B^4*a^16*b^23*d^4 + 1120*A*B^4*a^18*b^21*d^4 + 3360*A*B^4
*a^20*b^19*d^4 + 5600*A*B^4*a^22*b^17*d^4 + 5600*A*B^4*a^24*b^15*d^4 + 3360*A*B^4*a^26*b^13*d^4 + 1120*A*B^4*a
^28*b^11*d^4 + 160*A*B^4*a^30*b^9*d^4 - 336*A^4*B*a^15*b^24*d^4 - 2288*A^4*B*a^17*b^22*d^4 - 6608*A^4*B*a^19*b
^20*d^4 - 10416*A^4*B*a^21*b^18*d^4 - 9520*A^4*B*a^23*b^16*d^4 - 4816*A^4*B*a^25*b^14*d^4 - 1008*A^4*B*a^27*b^
12*d^4 + 112*A^4*B*a^29*b^10*d^4 + 64*A^4*B*a^31*b^8*d^4 - 336*A^2*B^3*a^15*b^24*d^4 - 2288*A^2*B^3*a^17*b^22*
d^4 - 6608*A^2*B^3*a^19*b^20*d^4 - 10416*A^2*B^3*a^21*b^18*d^4 - 9520*A^2*B^3*a^23*b^16*d^4 - 4816*A^2*B^3*a^2
5*b^14*d^4 - 1008*A^2*B^3*a^27*b^12*d^4 + 112*A^2*B^3*a^29*b^10*d^4 + 64*A^2*B^3*a^31*b^8*d^4 + 144*A^3*B^2*a^
14*b^25*d^4 + 1072*A^3*B^2*a^16*b^23*d^4 + 3472*A^3*B^2*a^18*b^21*d^4 + 6384*A^3*B^2*a^20*b^19*d^4 + 7280*A^3*
B^2*a^22*b^17*d^4 + 5264*A^3*B^2*a^24*b^15*d^4 + 2352*A^3*B^2*a^26*b^13*d^4 + 592*A^3*B^2*a^28*b^11*d^4 + 64*A
^3*B^2*a^30*b^9*d^4))*(-(((8*A^2*a^3*d^2 - 8*B^2*a^3*d^2 - 16*A*B*b^3*d^2 - 24*A^2*a*b^2*d^2 + 24*B^2*a*b^2*d^
2 + 48*A*B*a^2*b*d^2)^2/4 - (A^4 + 2*A^2*B^2 + B^4)*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4
))^(1/2) + 4*A^2*a^3*d^2 - 4*B^2*a^3*d^2 - 8*A*B*b^3*d^2 - 12*A^2*a*b^2*d^2 + 12*B^2*a*b^2*d^2 + 24*A*B*a^2*b*
d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*2i + (atan((((3*A*b - 2*B*a)*((a + b*tan(
c + d*x))^(1/2)*(144*A^4*a^14*b^26*d^5 + 864*A^4*a^16*b^24*d^5 + 2048*A^4*a^18*b^22*d^5 + 2240*A^4*a^20*b^20*d
^5 + 672*A^4*a^22*b^18*d^5 - 896*A^4*a^24*b^16*d^5 - 896*A^4*a^26*b^14*d^5 - 192*A^4*a^28*b^12*d^5 + 80*A^4*a^
30*b^10*d^5 + 32*A^4*a^32*b^8*d^5 - 64*B^4*a^16*b^24*d^5 - 352*B^4*a^18*b^22*d^5 - 672*B^4*a^20*b^20*d^5 - 224
*B^4*a^22*b^18*d^5 + 1120*B^4*a^24*b^16*d^5 + 2016*B^4*a^26*b^14*d^5 + 1568*B^4*a^28*b^12*d^5 + 608*B^4*a^30*b
^10*d^5 + 96*B^4*a^32*b^8*d^5 + 192*A*B^3*a^15*b^25*d^5 + 896*A*B^3*a^17*b^23*d^5 + 896*A*B^3*a^19*b^21*d^5 -
2688*A*B^3*a^21*b^19*d^5 - 8960*A*B^3*a^23*b^17*d^5 - 11648*A*B^3*a^25*b^15*d^5 - 8064*A*B^3*a^27*b^13*d^5 - 2
944*A*B^3*a^29*b^11*d^5 - 448*A*B^3*a^31*b^9*d^5 - 768*A^3*B*a^15*b^25*d^5 - 5184*A^3*B*a^17*b^23*d^5 - 14784*
A^3*B*a^19*b^21*d^5 - 22848*A^3*B*a^21*b^19*d^5 - 20160*A^3*B*a^23*b^17*d^5 - 9408*A^3*B*a^25*b^15*d^5 - 1344*
A^3*B*a^27*b^13*d^5 + 576*A^3*B*a^29*b^11*d^5 + 192*A^3*B*a^31*b^9*d^5 - 144*A^2*B^2*a^14*b^26*d^5 - 32*A^2*B^
2*a^16*b^24*d^5 + 3808*A^2*B^2*a^18*b^22*d^5 + 15456*A^2*B^2*a^20*b^20*d^5 + 29120*A^2*B^2*a^22*b^18*d^5 + 311
36*A^2*B^2*a^24*b^16*d^5 + 19488*A^2*B^2*a^26*b^14*d^5 + 6688*A^2*B^2*a^28*b^12*d^5 + 976*A^2*B^2*a^30*b^10*d^
5) - ((3*A*b - 2*B*a)*(576*A^3*a^15*b^27*d^6 + 3456*A^3*a^17*b^25*d^6 + 8480*A^3*a^19*b^23*d^6 + 10976*A^3*a^2
1*b^21*d^6 + 8736*A^3*a^23*b^19*d^6 + 6496*A^3*a^25*b^17*d^6 + 6496*A^3*a^27*b^15*d^6 + 5280*A^3*a^29*b^13*d^6
+ 2336*A^3*a^31*b^11*d^6 + 416*A^3*a^33*b^9*d^6 + 128*B^3*a^16*b^26*d^6 + 128*B^3*a^18*b^24*d^6 - 2592*B^3*a^
20*b^22*d^6 - 10976*B^3*a^22*b^20*d^6 - 20384*B^3*a^24*b^18*d^6 - 20832*B^3*a^26*b^16*d^6 - 11872*B^3*a^28*b^1
4*d^6 - 3232*B^3*a^30*b^12*d^6 - 96*B^3*a^32*b^10*d^6 + 96*B^3*a^34*b^8*d^6 + ((3*A*b - 2*B*a)*((a + b*tan(c +
d*x))^(1/2)*(576*A^2*a^15*b^28*d^7 + 5184*A^2*a^17*b^26*d^7 + 21568*A^2*a^19*b^24*d^7 + 53888*A^2*a^21*b^22*d
^7 + 87808*A^2*a^23*b^20*d^7 + 94976*A^2*a^25*b^18*d^7 + 66304*A^2*a^27*b^16*d^7 + 27008*A^2*a^29*b^14*d^7 + 4
288*A^2*a^31*b^12*d^7 - 832*A^2*a^33*b^10*d^7 - 320*A^2*a^35*b^8*d^7 + 256*B^2*a^17*b^26*d^7 + 1472*B^2*a^19*b
^24*d^7 + 3712*B^2*a^21*b^22*d^7 + 6272*B^2*a^23*b^20*d^7 + 9856*B^2*a^25*b^18*d^7 + 14336*B^2*a^27*b^16*d^7 +
15232*B^2*a^29*b^14*d^7 + 10112*B^2*a^31*b^12*d^7 + 3712*B^2*a^33*b^10*d^7 + 576*B^2*a^35*b^8*d^7 - 768*A*B*a
^16*b^27*d^7 - 6400*A*B*a^18*b^25*d^7 - 25856*A*B*a^20*b^23*d^7 - 66304*A*B*a^22*b^21*d^7 - 116480*A*B*a^24*b^
19*d^7 - 141568*A*B*a^26*b^17*d^7 - 116480*A*B*a^28*b^15*d^7 - 61696*A*B*a^30*b^13*d^7 - 18944*A*B*a^32*b^11*d
^7 - 2560*A*B*a^34*b^9*d^7) - ((3*A*b - 2*B*a)*(512*B*a^17*b^28*d^8 - 7680*A*a^18*b^27*d^8 - 34304*A*a^20*b^25
*d^8 - 90112*A*a^22*b^23*d^8 - 154112*A*a^24*b^21*d^8 - 179200*A*a^26*b^19*d^8 - 143360*A*a^28*b^17*d^8 - 7782
4*A*a^30*b^15*d^8 - 27392*A*a^32*b^13*d^8 - 5632*A*a^34*b^11*d^8 - 512*A*a^36*b^9*d^8 - 768*A*a^16*b^29*d^8 +
5248*B*a^19*b^26*d^8 + 23936*B*a^21*b^24*d^8 + 64000*B*a^23*b^22*d^8 + 111104*B*a^25*b^20*d^8 + 130816*B*a^27*
b^18*d^8 + 105728*B*a^29*b^16*d^8 + 57856*B*a^31*b^14*d^8 + 20480*B*a^33*b^12*d^8 + 4224*B*a^35*b^10*d^8 + 384
*B*a^37*b^8*d^8 + ((3*A*b - 2*B*a)*(a + b*tan(c + d*x))^(1/2)*(512*a^18*b^28*d^9 + 5376*a^20*b^26*d^9 + 25344*
a^22*b^24*d^9 + 70656*a^24*b^22*d^9 + 129024*a^26*b^20*d^9 + 161280*a^28*b^18*d^9 + 139776*a^30*b^16*d^9 + 829
44*a^32*b^14*d^9 + 32256*a^34*b^12*d^9 + 7424*a^36*b^10*d^9 + 768*a^38*b^8*d^9))/(2*d*(a^5)^(1/2))))/(2*d*(a^5
)^(1/2))))/(2*d*(a^5)^(1/2)) - 384*A*B^2*a^15*b^27*d^6 - 768*A*B^2*a^17*b^25*d^6 + 4128*A*B^2*a^19*b^23*d^6 +
18144*A*B^2*a^21*b^21*d^6 + 27552*A*B^2*a^23*b^19*d^6 + 15456*A*B^2*a^25*b^17*d^6 - 6048*A*B^2*a^27*b^15*d^6 -
13152*A*B^2*a^29*b^13*d^6 - 6816*A*B^2*a^31*b^11*d^6 - 1248*A*B^2*a^33*b^9*d^6 + 288*A^2*B*a^14*b^28*d^6 + 48
0*A^2*B*a^16*b^26*d^6 - 2688*A^2*B*a^18*b^24*d^6 - 8352*A^2*B*a^20*b^22*d^6 - 3360*A^2*B*a^22*b^20*d^6 + 16800
*A^2*B*a^24*b^18*d^6 + 30240*A^2*B*a^26*b^16*d^6 + 21792*A^2*B*a^28*b^14*d^6 + 6528*A^2*B*a^30*b^12*d^6 - 288*
A^2*B*a^34*b^8*d^6))/(2*d*(a^5)^(1/2)))*1i)/(2*d*(a^5)^(1/2)) + ((3*A*b - 2*B*a)*((a + b*tan(c + d*x))^(1/2)*(
144*A^4*a^14*b^26*d^5 + 864*A^4*a^16*b^24*d^5 + 2048*A^4*a^18*b^22*d^5 + 2240*A^4*a^20*b^20*d^5 + 672*A^4*a^22
*b^18*d^5 - 896*A^4*a^24*b^16*d^5 - 896*A^4*a^26*b^14*d^5 - 192*A^4*a^28*b^12*d^5 + 80*A^4*a^30*b^10*d^5 + 32*
A^4*a^32*b^8*d^5 - 64*B^4*a^16*b^24*d^5 - 352*B^4*a^18*b^22*d^5 - 672*B^4*a^20*b^20*d^5 - 224*B^4*a^22*b^18*d^
5 + 1120*B^4*a^24*b^16*d^5 + 2016*B^4*a^26*b^14*d^5 + 1568*B^4*a^28*b^12*d^5 + 608*B^4*a^30*b^10*d^5 + 96*B^4*
a^32*b^8*d^5 + 192*A*B^3*a^15*b^25*d^5 + 896*A*B^3*a^17*b^23*d^5 + 896*A*B^3*a^19*b^21*d^5 - 2688*A*B^3*a^21*b
^19*d^5 - 8960*A*B^3*a^23*b^17*d^5 - 11648*A*B^3*a^25*b^15*d^5 - 8064*A*B^3*a^27*b^13*d^5 - 2944*A*B^3*a^29*b^
11*d^5 - 448*A*B^3*a^31*b^9*d^5 - 768*A^3*B*a^15*b^25*d^5 - 5184*A^3*B*a^17*b^23*d^5 - 14784*A^3*B*a^19*b^21*d
^5 - 22848*A^3*B*a^21*b^19*d^5 - 20160*A^3*B*a^23*b^17*d^5 - 9408*A^3*B*a^25*b^15*d^5 - 1344*A^3*B*a^27*b^13*d
^5 + 576*A^3*B*a^29*b^11*d^5 + 192*A^3*B*a^31*b^9*d^5 - 144*A^2*B^2*a^14*b^26*d^5 - 32*A^2*B^2*a^16*b^24*d^5 +
3808*A^2*B^2*a^18*b^22*d^5 + 15456*A^2*B^2*a^20*b^20*d^5 + 29120*A^2*B^2*a^22*b^18*d^5 + 31136*A^2*B^2*a^24*b
^16*d^5 + 19488*A^2*B^2*a^26*b^14*d^5 + 6688*A^2*B^2*a^28*b^12*d^5 + 976*A^2*B^2*a^30*b^10*d^5) + ((3*A*b - 2*
B*a)*(576*A^3*a^15*b^27*d^6 + 3456*A^3*a^17*b^25*d^6 + 8480*A^3*a^19*b^23*d^6 + 10976*A^3*a^21*b^21*d^6 + 8736
*A^3*a^23*b^19*d^6 + 6496*A^3*a^25*b^17*d^6 + 6496*A^3*a^27*b^15*d^6 + 5280*A^3*a^29*b^13*d^6 + 2336*A^3*a^31*
b^11*d^6 + 416*A^3*a^33*b^9*d^6 + 128*B^3*a^16*b^26*d^6 + 128*B^3*a^18*b^24*d^6 - 2592*B^3*a^20*b^22*d^6 - 109
76*B^3*a^22*b^20*d^6 - 20384*B^3*a^24*b^18*d^6 - 20832*B^3*a^26*b^16*d^6 - 11872*B^3*a^28*b^14*d^6 - 3232*B^3*
a^30*b^12*d^6 - 96*B^3*a^32*b^10*d^6 + 96*B^3*a^34*b^8*d^6 - ((3*A*b - 2*B*a)*((a + b*tan(c + d*x))^(1/2)*(576
*A^2*a^15*b^28*d^7 + 5184*A^2*a^17*b^26*d^7 + 21568*A^2*a^19*b^24*d^7 + 53888*A^2*a^21*b^22*d^7 + 87808*A^2*a^
23*b^20*d^7 + 94976*A^2*a^25*b^18*d^7 + 66304*A^2*a^27*b^16*d^7 + 27008*A^2*a^29*b^14*d^7 + 4288*A^2*a^31*b^12
*d^7 - 832*A^2*a^33*b^10*d^7 - 320*A^2*a^35*b^8*d^7 + 256*B^2*a^17*b^26*d^7 + 1472*B^2*a^19*b^24*d^7 + 3712*B^
2*a^21*b^22*d^7 + 6272*B^2*a^23*b^20*d^7 + 9856*B^2*a^25*b^18*d^7 + 14336*B^2*a^27*b^16*d^7 + 15232*B^2*a^29*b
^14*d^7 + 10112*B^2*a^31*b^12*d^7 + 3712*B^2*a^33*b^10*d^7 + 576*B^2*a^35*b^8*d^7 - 768*A*B*a^16*b^27*d^7 - 64
00*A*B*a^18*b^25*d^7 - 25856*A*B*a^20*b^23*d^7 - 66304*A*B*a^22*b^21*d^7 - 116480*A*B*a^24*b^19*d^7 - 141568*A
*B*a^26*b^17*d^7 - 116480*A*B*a^28*b^15*d^7 - 61696*A*B*a^30*b^13*d^7 - 18944*A*B*a^32*b^11*d^7 - 2560*A*B*a^3
4*b^9*d^7) - ((3*A*b - 2*B*a)*(768*A*a^16*b^29*d^8 + 7680*A*a^18*b^27*d^8 + 34304*A*a^20*b^25*d^8 + 90112*A*a^
22*b^23*d^8 + 154112*A*a^24*b^21*d^8 + 179200*A*a^26*b^19*d^8 + 143360*A*a^28*b^17*d^8 + 77824*A*a^30*b^15*d^8
+ 27392*A*a^32*b^13*d^8 + 5632*A*a^34*b^11*d^8 + 512*A*a^36*b^9*d^8 - 512*B*a^17*b^28*d^8 - 5248*B*a^19*b^26*
d^8 - 23936*B*a^21*b^24*d^8 - 64000*B*a^23*b^22*d^8 - 111104*B*a^25*b^20*d^8 - 130816*B*a^27*b^18*d^8 - 105728
*B*a^29*b^16*d^8 - 57856*B*a^31*b^14*d^8 - 20480*B*a^33*b^12*d^8 - 4224*B*a^35*b^10*d^8 - 384*B*a^37*b^8*d^8 +
((3*A*b - 2*B*a)*(a + b*tan(c + d*x))^(1/2)*(512*a^18*b^28*d^9 + 5376*a^20*b^26*d^9 + 25344*a^22*b^24*d^9 + 7
0656*a^24*b^22*d^9 + 129024*a^26*b^20*d^9 + 161280*a^28*b^18*d^9 + 139776*a^30*b^16*d^9 + 82944*a^32*b^14*d^9
+ 32256*a^34*b^12*d^9 + 7424*a^36*b^10*d^9 + 768*a^38*b^8*d^9))/(2*d*(a^5)^(1/2))))/(2*d*(a^5)^(1/2))))/(2*d*(
a^5)^(1/2)) - 384*A*B^2*a^15*b^27*d^6 - 768*A*B^2*a^17*b^25*d^6 + 4128*A*B^2*a^19*b^23*d^6 + 18144*A*B^2*a^21*
b^21*d^6 + 27552*A*B^2*a^23*b^19*d^6 + 15456*A*B^2*a^25*b^17*d^6 - 6048*A*B^2*a^27*b^15*d^6 - 13152*A*B^2*a^29
*b^13*d^6 - 6816*A*B^2*a^31*b^11*d^6 - 1248*A*B^2*a^33*b^9*d^6 + 288*A^2*B*a^14*b^28*d^6 + 480*A^2*B*a^16*b^26
*d^6 - 2688*A^2*B*a^18*b^24*d^6 - 8352*A^2*B*a^20*b^22*d^6 - 3360*A^2*B*a^22*b^20*d^6 + 16800*A^2*B*a^24*b^18*
d^6 + 30240*A^2*B*a^26*b^16*d^6 + 21792*A^2*B*a^28*b^14*d^6 + 6528*A^2*B*a^30*b^12*d^6 - 288*A^2*B*a^34*b^8*d^
6))/(2*d*(a^5)^(1/2)))*1i)/(2*d*(a^5)^(1/2)))/(144*A^5*a^14*b^25*d^4 + 912*A^5*a^16*b^23*d^4 + 2352*A^5*a^18*b
^21*d^4 + 3024*A^5*a^20*b^19*d^4 + 1680*A^5*a^22*b^17*d^4 - 336*A^5*a^24*b^15*d^4 - 1008*A^5*a^26*b^13*d^4 - 5
28*A^5*a^28*b^11*d^4 - 96*A^5*a^30*b^9*d^4 + ((3*A*b - 2*B*a)*((a + b*tan(c + d*x))^(1/2)*(144*A^4*a^14*b^26*d
^5 + 864*A^4*a^16*b^24*d^5 + 2048*A^4*a^18*b^22*d^5 + 2240*A^4*a^20*b^20*d^5 + 672*A^4*a^22*b^18*d^5 - 896*A^4
*a^24*b^16*d^5 - 896*A^4*a^26*b^14*d^5 - 192*A^4*a^28*b^12*d^5 + 80*A^4*a^30*b^10*d^5 + 32*A^4*a^32*b^8*d^5 -
64*B^4*a^16*b^24*d^5 - 352*B^4*a^18*b^22*d^5 - 672*B^4*a^20*b^20*d^5 - 224*B^4*a^22*b^18*d^5 + 1120*B^4*a^24*b
^16*d^5 + 2016*B^4*a^26*b^14*d^5 + 1568*B^4*a^28*b^12*d^5 + 608*B^4*a^30*b^10*d^5 + 96*B^4*a^32*b^8*d^5 + 192*
A*B^3*a^15*b^25*d^5 + 896*A*B^3*a^17*b^23*d^5 + 896*A*B^3*a^19*b^21*d^5 - 2688*A*B^3*a^21*b^19*d^5 - 8960*A*B^
3*a^23*b^17*d^5 - 11648*A*B^3*a^25*b^15*d^5 - 8064*A*B^3*a^27*b^13*d^5 - 2944*A*B^3*a^29*b^11*d^5 - 448*A*B^3*
a^31*b^9*d^5 - 768*A^3*B*a^15*b^25*d^5 - 5184*A^3*B*a^17*b^23*d^5 - 14784*A^3*B*a^19*b^21*d^5 - 22848*A^3*B*a^
21*b^19*d^5 - 20160*A^3*B*a^23*b^17*d^5 - 9408*A^3*B*a^25*b^15*d^5 - 1344*A^3*B*a^27*b^13*d^5 + 576*A^3*B*a^29
*b^11*d^5 + 192*A^3*B*a^31*b^9*d^5 - 144*A^2*B^2*a^14*b^26*d^5 - 32*A^2*B^2*a^16*b^24*d^5 + 3808*A^2*B^2*a^18*
b^22*d^5 + 15456*A^2*B^2*a^20*b^20*d^5 + 29120*A^2*B^2*a^22*b^18*d^5 + 31136*A^2*B^2*a^24*b^16*d^5 + 19488*A^2
*B^2*a^26*b^14*d^5 + 6688*A^2*B^2*a^28*b^12*d^5 + 976*A^2*B^2*a^30*b^10*d^5) - ((3*A*b - 2*B*a)*(576*A^3*a^15*
b^27*d^6 + 3456*A^3*a^17*b^25*d^6 + 8480*A^3*a^19*b^23*d^6 + 10976*A^3*a^21*b^21*d^6 + 8736*A^3*a^23*b^19*d^6
+ 6496*A^3*a^25*b^17*d^6 + 6496*A^3*a^27*b^15*d^6 + 5280*A^3*a^29*b^13*d^6 + 2336*A^3*a^31*b^11*d^6 + 416*A^3*
a^33*b^9*d^6 + 128*B^3*a^16*b^26*d^6 + 128*B^3*a^18*b^24*d^6 - 2592*B^3*a^20*b^22*d^6 - 10976*B^3*a^22*b^20*d^
6 - 20384*B^3*a^24*b^18*d^6 - 20832*B^3*a^26*b^16*d^6 - 11872*B^3*a^28*b^14*d^6 - 3232*B^3*a^30*b^12*d^6 - 96*
B^3*a^32*b^10*d^6 + 96*B^3*a^34*b^8*d^6 + ((3*A*b - 2*B*a)*((a + b*tan(c + d*x))^(1/2)*(576*A^2*a^15*b^28*d^7
+ 5184*A^2*a^17*b^26*d^7 + 21568*A^2*a^19*b^24*d^7 + 53888*A^2*a^21*b^22*d^7 + 87808*A^2*a^23*b^20*d^7 + 94976
*A^2*a^25*b^18*d^7 + 66304*A^2*a^27*b^16*d^7 + 27008*A^2*a^29*b^14*d^7 + 4288*A^2*a^31*b^12*d^7 - 832*A^2*a^33
*b^10*d^7 - 320*A^2*a^35*b^8*d^7 + 256*B^2*a^17*b^26*d^7 + 1472*B^2*a^19*b^24*d^7 + 3712*B^2*a^21*b^22*d^7 + 6
272*B^2*a^23*b^20*d^7 + 9856*B^2*a^25*b^18*d^7 + 14336*B^2*a^27*b^16*d^7 + 15232*B^2*a^29*b^14*d^7 + 10112*B^2
*a^31*b^12*d^7 + 3712*B^2*a^33*b^10*d^7 + 576*B^2*a^35*b^8*d^7 - 768*A*B*a^16*b^27*d^7 - 6400*A*B*a^18*b^25*d^
7 - 25856*A*B*a^20*b^23*d^7 - 66304*A*B*a^22*b^21*d^7 - 116480*A*B*a^24*b^19*d^7 - 141568*A*B*a^26*b^17*d^7 -
116480*A*B*a^28*b^15*d^7 - 61696*A*B*a^30*b^13*d^7 - 18944*A*B*a^32*b^11*d^7 - 2560*A*B*a^34*b^9*d^7) - ((3*A*
b - 2*B*a)*(512*B*a^17*b^28*d^8 - 7680*A*a^18*b^27*d^8 - 34304*A*a^20*b^25*d^8 - 90112*A*a^22*b^23*d^8 - 15411
2*A*a^24*b^21*d^8 - 179200*A*a^26*b^19*d^8 - 143360*A*a^28*b^17*d^8 - 77824*A*a^30*b^15*d^8 - 27392*A*a^32*b^1
3*d^8 - 5632*A*a^34*b^11*d^8 - 512*A*a^36*b^9*d^8 - 768*A*a^16*b^29*d^8 + 5248*B*a^19*b^26*d^8 + 23936*B*a^21*
b^24*d^8 + 64000*B*a^23*b^22*d^8 + 111104*B*a^25*b^20*d^8 + 130816*B*a^27*b^18*d^8 + 105728*B*a^29*b^16*d^8 +
57856*B*a^31*b^14*d^8 + 20480*B*a^33*b^12*d^8 + 4224*B*a^35*b^10*d^8 + 384*B*a^37*b^8*d^8 + ((3*A*b - 2*B*a)*(
a + b*tan(c + d*x))^(1/2)*(512*a^18*b^28*d^9 + 5376*a^20*b^26*d^9 + 25344*a^22*b^24*d^9 + 70656*a^24*b^22*d^9
+ 129024*a^26*b^20*d^9 + 161280*a^28*b^18*d^9 + 139776*a^30*b^16*d^9 + 82944*a^32*b^14*d^9 + 32256*a^34*b^12*d
^9 + 7424*a^36*b^10*d^9 + 768*a^38*b^8*d^9))/(2*d*(a^5)^(1/2))))/(2*d*(a^5)^(1/2))))/(2*d*(a^5)^(1/2)) - 384*A
*B^2*a^15*b^27*d^6 - 768*A*B^2*a^17*b^25*d^6 + 4128*A*B^2*a^19*b^23*d^6 + 18144*A*B^2*a^21*b^21*d^6 + 27552*A*
B^2*a^23*b^19*d^6 + 15456*A*B^2*a^25*b^17*d^6 - 6048*A*B^2*a^27*b^15*d^6 - 13152*A*B^2*a^29*b^13*d^6 - 6816*A*
B^2*a^31*b^11*d^6 - 1248*A*B^2*a^33*b^9*d^6 + 288*A^2*B*a^14*b^28*d^6 + 480*A^2*B*a^16*b^26*d^6 - 2688*A^2*B*a
^18*b^24*d^6 - 8352*A^2*B*a^20*b^22*d^6 - 3360*A^2*B*a^22*b^20*d^6 + 16800*A^2*B*a^24*b^18*d^6 + 30240*A^2*B*a
^26*b^16*d^6 + 21792*A^2*B*a^28*b^14*d^6 + 6528*A^2*B*a^30*b^12*d^6 - 288*A^2*B*a^34*b^8*d^6))/(2*d*(a^5)^(1/2
))))/(2*d*(a^5)^(1/2)) - ((3*A*b - 2*B*a)*((a + b*tan(c + d*x))^(1/2)*(144*A^4*a^14*b^26*d^5 + 864*A^4*a^16*b^
24*d^5 + 2048*A^4*a^18*b^22*d^5 + 2240*A^4*a^20*b^20*d^5 + 672*A^4*a^22*b^18*d^5 - 896*A^4*a^24*b^16*d^5 - 896
*A^4*a^26*b^14*d^5 - 192*A^4*a^28*b^12*d^5 + 80*A^4*a^30*b^10*d^5 + 32*A^4*a^32*b^8*d^5 - 64*B^4*a^16*b^24*d^5
- 352*B^4*a^18*b^22*d^5 - 672*B^4*a^20*b^20*d^5 - 224*B^4*a^22*b^18*d^5 + 1120*B^4*a^24*b^16*d^5 + 2016*B^4*a
^26*b^14*d^5 + 1568*B^4*a^28*b^12*d^5 + 608*B^4*a^30*b^10*d^5 + 96*B^4*a^32*b^8*d^5 + 192*A*B^3*a^15*b^25*d^5
+ 896*A*B^3*a^17*b^23*d^5 + 896*A*B^3*a^19*b^21*d^5 - 2688*A*B^3*a^21*b^19*d^5 - 8960*A*B^3*a^23*b^17*d^5 - 11
648*A*B^3*a^25*b^15*d^5 - 8064*A*B^3*a^27*b^13*d^5 - 2944*A*B^3*a^29*b^11*d^5 - 448*A*B^3*a^31*b^9*d^5 - 768*A
^3*B*a^15*b^25*d^5 - 5184*A^3*B*a^17*b^23*d^5 - 14784*A^3*B*a^19*b^21*d^5 - 22848*A^3*B*a^21*b^19*d^5 - 20160*
A^3*B*a^23*b^17*d^5 - 9408*A^3*B*a^25*b^15*d^5 - 1344*A^3*B*a^27*b^13*d^5 + 576*A^3*B*a^29*b^11*d^5 + 192*A^3*
B*a^31*b^9*d^5 - 144*A^2*B^2*a^14*b^26*d^5 - 32*A^2*B^2*a^16*b^24*d^5 + 3808*A^2*B^2*a^18*b^22*d^5 + 15456*A^2
*B^2*a^20*b^20*d^5 + 29120*A^2*B^2*a^22*b^18*d^5 + 31136*A^2*B^2*a^24*b^16*d^5 + 19488*A^2*B^2*a^26*b^14*d^5 +
6688*A^2*B^2*a^28*b^12*d^5 + 976*A^2*B^2*a^30*b^10*d^5) + ((3*A*b - 2*B*a)*(576*A^3*a^15*b^27*d^6 + 3456*A^3*
a^17*b^25*d^6 + 8480*A^3*a^19*b^23*d^6 + 10976*A^3*a^21*b^21*d^6 + 8736*A^3*a^23*b^19*d^6 + 6496*A^3*a^25*b^17
*d^6 + 6496*A^3*a^27*b^15*d^6 + 5280*A^3*a^29*b^13*d^6 + 2336*A^3*a^31*b^11*d^6 + 416*A^3*a^33*b^9*d^6 + 128*B
^3*a^16*b^26*d^6 + 128*B^3*a^18*b^24*d^6 - 2592*B^3*a^20*b^22*d^6 - 10976*B^3*a^22*b^20*d^6 - 20384*B^3*a^24*b
^18*d^6 - 20832*B^3*a^26*b^16*d^6 - 11872*B^3*a^28*b^14*d^6 - 3232*B^3*a^30*b^12*d^6 - 96*B^3*a^32*b^10*d^6 +
96*B^3*a^34*b^8*d^6 - ((3*A*b - 2*B*a)*((a + b*tan(c + d*x))^(1/2)*(576*A^2*a^15*b^28*d^7 + 5184*A^2*a^17*b^26
*d^7 + 21568*A^2*a^19*b^24*d^7 + 53888*A^2*a^21*b^22*d^7 + 87808*A^2*a^23*b^20*d^7 + 94976*A^2*a^25*b^18*d^7 +
66304*A^2*a^27*b^16*d^7 + 27008*A^2*a^29*b^14*d^7 + 4288*A^2*a^31*b^12*d^7 - 832*A^2*a^33*b^10*d^7 - 320*A^2*
a^35*b^8*d^7 + 256*B^2*a^17*b^26*d^7 + 1472*B^2*a^19*b^24*d^7 + 3712*B^2*a^21*b^22*d^7 + 6272*B^2*a^23*b^20*d^
7 + 9856*B^2*a^25*b^18*d^7 + 14336*B^2*a^27*b^16*d^7 + 15232*B^2*a^29*b^14*d^7 + 10112*B^2*a^31*b^12*d^7 + 371
2*B^2*a^33*b^10*d^7 + 576*B^2*a^35*b^8*d^7 - 768*A*B*a^16*b^27*d^7 - 6400*A*B*a^18*b^25*d^7 - 25856*A*B*a^20*b
^23*d^7 - 66304*A*B*a^22*b^21*d^7 - 116480*A*B*a^24*b^19*d^7 - 141568*A*B*a^26*b^17*d^7 - 116480*A*B*a^28*b^15
*d^7 - 61696*A*B*a^30*b^13*d^7 - 18944*A*B*a^32*b^11*d^7 - 2560*A*B*a^34*b^9*d^7) - ((3*A*b - 2*B*a)*(768*A*a^
16*b^29*d^8 + 7680*A*a^18*b^27*d^8 + 34304*A*a^20*b^25*d^8 + 90112*A*a^22*b^23*d^8 + 154112*A*a^24*b^21*d^8 +
179200*A*a^26*b^19*d^8 + 143360*A*a^28*b^17*d^8 + 77824*A*a^30*b^15*d^8 + 27392*A*a^32*b^13*d^8 + 5632*A*a^34*
b^11*d^8 + 512*A*a^36*b^9*d^8 - 512*B*a^17*b^28*d^8 - 5248*B*a^19*b^26*d^8 - 23936*B*a^21*b^24*d^8 - 64000*B*a
^23*b^22*d^8 - 111104*B*a^25*b^20*d^8 - 130816*B*a^27*b^18*d^8 - 105728*B*a^29*b^16*d^8 - 57856*B*a^31*b^14*d^
8 - 20480*B*a^33*b^12*d^8 - 4224*B*a^35*b^10*d^8 - 384*B*a^37*b^8*d^8 + ((3*A*b - 2*B*a)*(a + b*tan(c + d*x))^
(1/2)*(512*a^18*b^28*d^9 + 5376*a^20*b^26*d^9 + 25344*a^22*b^24*d^9 + 70656*a^24*b^22*d^9 + 129024*a^26*b^20*d
^9 + 161280*a^28*b^18*d^9 + 139776*a^30*b^16*d^9 + 82944*a^32*b^14*d^9 + 32256*a^34*b^12*d^9 + 7424*a^36*b^10*
d^9 + 768*a^38*b^8*d^9))/(2*d*(a^5)^(1/2))))/(2*d*(a^5)^(1/2))))/(2*d*(a^5)^(1/2)) - 384*A*B^2*a^15*b^27*d^6 -
768*A*B^2*a^17*b^25*d^6 + 4128*A*B^2*a^19*b^23*d^6 + 18144*A*B^2*a^21*b^21*d^6 + 27552*A*B^2*a^23*b^19*d^6 +
15456*A*B^2*a^25*b^17*d^6 - 6048*A*B^2*a^27*b^15*d^6 - 13152*A*B^2*a^29*b^13*d^6 - 6816*A*B^2*a^31*b^11*d^6 -
1248*A*B^2*a^33*b^9*d^6 + 288*A^2*B*a^14*b^28*d^6 + 480*A^2*B*a^16*b^26*d^6 - 2688*A^2*B*a^18*b^24*d^6 - 8352*
A^2*B*a^20*b^22*d^6 - 3360*A^2*B*a^22*b^20*d^6 + 16800*A^2*B*a^24*b^18*d^6 + 30240*A^2*B*a^26*b^16*d^6 + 21792
*A^2*B*a^28*b^14*d^6 + 6528*A^2*B*a^30*b^12*d^6 - 288*A^2*B*a^34*b^8*d^6))/(2*d*(a^5)^(1/2))))/(2*d*(a^5)^(1/2
)) + 160*A*B^4*a^16*b^23*d^4 + 1120*A*B^4*a^18*b^21*d^4 + 3360*A*B^4*a^20*b^19*d^4 + 5600*A*B^4*a^22*b^17*d^4
+ 5600*A*B^4*a^24*b^15*d^4 + 3360*A*B^4*a^26*b^13*d^4 + 1120*A*B^4*a^28*b^11*d^4 + 160*A*B^4*a^30*b^9*d^4 - 33
6*A^4*B*a^15*b^24*d^4 - 2288*A^4*B*a^17*b^22*d^4 - 6608*A^4*B*a^19*b^20*d^4 - 10416*A^4*B*a^21*b^18*d^4 - 9520
*A^4*B*a^23*b^16*d^4 - 4816*A^4*B*a^25*b^14*d^4 - 1008*A^4*B*a^27*b^12*d^4 + 112*A^4*B*a^29*b^10*d^4 + 64*A^4*
B*a^31*b^8*d^4 - 336*A^2*B^3*a^15*b^24*d^4 - 2288*A^2*B^3*a^17*b^22*d^4 - 6608*A^2*B^3*a^19*b^20*d^4 - 10416*A
^2*B^3*a^21*b^18*d^4 - 9520*A^2*B^3*a^23*b^16*d^4 - 4816*A^2*B^3*a^25*b^14*d^4 - 1008*A^2*B^3*a^27*b^12*d^4 +
112*A^2*B^3*a^29*b^10*d^4 + 64*A^2*B^3*a^31*b^8*d^4 + 144*A^3*B^2*a^14*b^25*d^4 + 1072*A^3*B^2*a^16*b^23*d^4 +
3472*A^3*B^2*a^18*b^21*d^4 + 6384*A^3*B^2*a^20*b^19*d^4 + 7280*A^3*B^2*a^22*b^17*d^4 + 5264*A^3*B^2*a^24*b^15
*d^4 + 2352*A^3*B^2*a^26*b^13*d^4 + 592*A^3*B^2*a^28*b^11*d^4 + 64*A^3*B^2*a^30*b^9*d^4))*(3*A*b - 2*B*a)*1i)/
(d*(a^5)^(1/2))