\(\int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx\) [363]

Optimal result

Integrand size = 33, antiderivative size = 289 \[ \int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx=\frac {(5 A b-2 a B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{a^{7/2} d}+\frac {(i A+B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{(a-i b)^{5/2} d}-\frac {(i A-B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{(a+i b)^{5/2} d}-\frac {b \left (3 a^2 A+5 A b^2-2 a b B\right )}{3 a^2 \left (a^2+b^2\right ) d (a+b \tan (c+d x))^{3/2}}-\frac {A \cot (c+d x)}{a d (a+b \tan (c+d x))^{3/2}}-\frac {b \left (a^4 A+10 a^2 A b^2+5 A b^4-6 a^3 b B-2 a b^3 B\right )}{a^3 \left (a^2+b^2\right )^2 d \sqrt {a+b \tan (c+d x)}} \]

[Out]

(5*A*b-2*B*a)*arctanh((a+b*tan(d*x+c))^(1/2)/a^(1/2))/a^(7/2)/d+(I*A+B)*arctanh((a+b*tan(d*x+c))^(1/2)/(a-I*b)
^(1/2))/(a-I*b)^(5/2)/d-(I*A-B)*arctanh((a+b*tan(d*x+c))^(1/2)/(a+I*b)^(1/2))/(a+I*b)^(5/2)/d-b*(A*a^4+10*A*a^
2*b^2+5*A*b^4-6*B*a^3*b-2*B*a*b^3)/a^3/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^(1/2)-1/3*b*(3*A*a^2+5*A*b^2-2*B*a*b)/a^
2/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)-A*cot(d*x+c)/a/d/(a+b*tan(d*x+c))^(3/2)

Rubi [A] (verified)

Time = 1.51 (sec) , antiderivative size = 289, normalized size of antiderivative = 1.00, number of steps used = 14, 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} \[ \int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx=\frac {(5 A b-2 a B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{a^{7/2} d}-\frac {b \left (3 a^2 A-2 a b B+5 A b^2\right )}{3 a^2 d \left (a^2+b^2\right ) (a+b \tan (c+d x))^{3/2}}-\frac {b \left (a^4 A-6 a^3 b B+10 a^2 A b^2-2 a b^3 B+5 A b^4\right )}{a^3 d \left (a^2+b^2\right )^2 \sqrt {a+b \tan (c+d x)}}+\frac {(B+i A) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{d (a-i b)^{5/2}}-\frac {(-B+i A) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{d (a+i b)^{5/2}}-\frac {A \cot (c+d x)}{a d (a+b \tan (c+d x))^{3/2}} \]

[In]

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

[Out]

((5*A*b - 2*a*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(a^(7/2)*d) + ((I*A + B)*ArcTanh[Sqrt[a + b*Tan[c
+ d*x]]/Sqrt[a - I*b]])/((a - I*b)^(5/2)*d) - ((I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a
+ I*b)^(5/2)*d) - (b*(3*a^2*A + 5*A*b^2 - 2*a*b*B))/(3*a^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) - (A*Cot[
c + d*x])/(a*d*(a + b*Tan[c + d*x])^(3/2)) - (b*(a^4*A + 10*a^2*A*b^2 + 5*A*b^4 - 6*a^3*b*B - 2*a*b^3*B))/(a^3
*(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 {A \cot (c+d x)}{a d (a+b \tan (c+d x))^{3/2}}-\frac {\int \frac {\cot (c+d x) \left (\frac {1}{2} (5 A b-2 a B)+a A \tan (c+d x)+\frac {5}{2} A b \tan ^2(c+d x)\right )}{(a+b \tan (c+d x))^{5/2}} \, dx}{a} \\ & = -\frac {b \left (3 a^2 A+5 A b^2-2 a b B\right )}{3 a^2 \left (a^2+b^2\right ) d (a+b \tan (c+d x))^{3/2}}-\frac {A \cot (c+d x)}{a d (a+b \tan (c+d x))^{3/2}}-\frac {2 \int \frac {\cot (c+d x) \left (\frac {3}{4} \left (a^2+b^2\right ) (5 A b-2 a B)+\frac {3}{2} a^2 (a A+b B) \tan (c+d x)+\frac {3}{4} b \left (3 a^2 A+5 A b^2-2 a b B\right ) \tan ^2(c+d x)\right )}{(a+b \tan (c+d x))^{3/2}} \, dx}{3 a^2 \left (a^2+b^2\right )} \\ & = -\frac {b \left (3 a^2 A+5 A b^2-2 a b B\right )}{3 a^2 \left (a^2+b^2\right ) d (a+b \tan (c+d x))^{3/2}}-\frac {A \cot (c+d x)}{a d (a+b \tan (c+d x))^{3/2}}-\frac {b \left (a^4 A+10 a^2 A b^2+5 A b^4-6 a^3 b B-2 a b^3 B\right )}{a^3 \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}{8} \left (a^2+b^2\right )^2 (5 A b-2 a B)+\frac {3}{4} a^3 \left (a^2 A-A b^2+2 a b B\right ) \tan (c+d x)+\frac {3}{8} b \left (a^4 A+10 a^2 A b^2+5 A b^4-6 a^3 b B-2 a b^3 B\right ) \tan ^2(c+d x)\right )}{\sqrt {a+b \tan (c+d x)}} \, dx}{3 a^3 \left (a^2+b^2\right )^2} \\ & = -\frac {b \left (3 a^2 A+5 A b^2-2 a b B\right )}{3 a^2 \left (a^2+b^2\right ) d (a+b \tan (c+d x))^{3/2}}-\frac {A \cot (c+d x)}{a d (a+b \tan (c+d x))^{3/2}}-\frac {b \left (a^4 A+10 a^2 A b^2+5 A b^4-6 a^3 b B-2 a b^3 B\right )}{a^3 \left (a^2+b^2\right )^2 d \sqrt {a+b \tan (c+d x)}}-\frac {4 \int \frac {\frac {3}{4} a^3 \left (a^2 A-A b^2+2 a b B\right )-\frac {3}{4} a^3 \left (2 a A b-a^2 B+b^2 B\right ) \tan (c+d x)}{\sqrt {a+b \tan (c+d x)}} \, dx}{3 a^3 \left (a^2+b^2\right )^2}-\frac {(5 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^3} \\ & = -\frac {b \left (3 a^2 A+5 A b^2-2 a b B\right )}{3 a^2 \left (a^2+b^2\right ) d (a+b \tan (c+d x))^{3/2}}-\frac {A \cot (c+d x)}{a d (a+b \tan (c+d x))^{3/2}}-\frac {b \left (a^4 A+10 a^2 A b^2+5 A b^4-6 a^3 b B-2 a b^3 B\right )}{a^3 \left (a^2+b^2\right )^2 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)^2}-\frac {(A+i B) \int \frac {1-i \tan (c+d x)}{\sqrt {a+b \tan (c+d x)}} \, dx}{2 (a+i b)^2}-\frac {(5 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^3 d} \\ & = -\frac {b \left (3 a^2 A+5 A b^2-2 a b B\right )}{3 a^2 \left (a^2+b^2\right ) d (a+b \tan (c+d x))^{3/2}}-\frac {A \cot (c+d x)}{a d (a+b \tan (c+d x))^{3/2}}-\frac {b \left (a^4 A+10 a^2 A b^2+5 A b^4-6 a^3 b B-2 a b^3 B\right )}{a^3 \left (a^2+b^2\right )^2 d \sqrt {a+b \tan (c+d x)}}+\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)^2 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)^2 d}-\frac {(5 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^3 b d} \\ & = \frac {(5 A b-2 a B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{a^{7/2} d}-\frac {b \left (3 a^2 A+5 A b^2-2 a b B\right )}{3 a^2 \left (a^2+b^2\right ) d (a+b \tan (c+d x))^{3/2}}-\frac {A \cot (c+d x)}{a d (a+b \tan (c+d x))^{3/2}}-\frac {b \left (a^4 A+10 a^2 A b^2+5 A b^4-6 a^3 b B-2 a b^3 B\right )}{a^3 \left (a^2+b^2\right )^2 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 )}{b (i a+b)^2 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 )}{(i a-b)^2 b d} \\ & = \frac {(5 A b-2 a B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{a^{7/2} d}+\frac {(i A+B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{(a-i b)^{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)^{5/2} d}-\frac {b \left (3 a^2 A+5 A b^2-2 a b B\right )}{3 a^2 \left (a^2+b^2\right ) d (a+b \tan (c+d x))^{3/2}}-\frac {A \cot (c+d x)}{a d (a+b \tan (c+d x))^{3/2}}-\frac {b \left (a^4 A+10 a^2 A b^2+5 A b^4-6 a^3 b B-2 a b^3 B\right )}{a^3 \left (a^2+b^2\right )^2 d \sqrt {a+b \tan (c+d x)}} \\ \end{align*}

Mathematica [A] (verified)

Time = 5.43 (sec) , antiderivative size = 306, normalized size of antiderivative = 1.06 \[ \int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx=\frac {\frac {b \left (-3 a^2 A-5 A b^2+2 a b B\right )}{\left (a^2+b^2\right ) (a+b \tan (c+d x))^{3/2}}-\frac {3 a A \cot (c+d x)}{(a+b \tan (c+d x))^{3/2}}+\frac {3 \left (\frac {\left (a^2+b^2\right )^2 (5 A b-2 a B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{\sqrt {a}}+\frac {a^3 (a+i b)^2 (i A+B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{\sqrt {a-i b}}+\frac {a^3 (a-i b)^2 (-i A+B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{\sqrt {a+i b}}-\frac {b \left (a^4 A+10 a^2 A b^2+5 A b^4-6 a^3 b B-2 a b^3 B\right )}{\sqrt {a+b \tan (c+d x)}}\right )}{a \left (a^2+b^2\right )^2}}{3 a^2 d} \]

[In]

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

[Out]

((b*(-3*a^2*A - 5*A*b^2 + 2*a*b*B))/((a^2 + b^2)*(a + b*Tan[c + d*x])^(3/2)) - (3*a*A*Cot[c + d*x])/(a + b*Tan
[c + d*x])^(3/2) + (3*(((a^2 + b^2)^2*(5*A*b - 2*a*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/Sqrt[a] + (a^
3*(a + I*b)^2*(I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/Sqrt[a - I*b] + (a^3*(a - I*b)^2*((-I
)*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/Sqrt[a + I*b] - (b*(a^4*A + 10*a^2*A*b^2 + 5*A*b^4 -
6*a^3*b*B - 2*a*b^3*B))/Sqrt[a + b*Tan[c + d*x]]))/(a*(a^2 + b^2)^2))/(3*a^2*d)

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(12967\) vs. \(2(257)=514\).

Time = 0.26 (sec) , antiderivative size = 12968, normalized size of antiderivative = 44.87

method	result	size
derivativedivides	\(\text {Expression too large to display}\)	\(12968\)
default	\(\text {Expression too large to display}\)	\(12968\)

[In]

int(cot(d*x+c)^2*(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. 7533 vs. \(2 (252) = 504\).

Time = 57.60 (sec) , antiderivative size = 15082, normalized size of antiderivative = 52.19 \[ \int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx=\text {Too large to display} \]

[In]

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

[Out]

Too large to include

Sympy [F]

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

[In]

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

Maxima [F(-1)]

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

[In]

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

[Out]

Timed out

Giac [F(-1)]

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

[In]

integrate(cot(d*x+c)^2*(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 = 15.51 (sec) , antiderivative size = 67465, normalized size of antiderivative = 233.44 \[ \int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx=\text {Too large to display} \]

[In]

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

[Out]

((2*(a + b*tan(c + d*x))*(5*A*b^5 + 11*A*a^2*b^3 - 8*B*a^3*b^2 - 2*B*a*b^4))/(3*(a*b^2 + a^3)^2) + (2*(A*b^3 -
B*a*b^2))/(3*a*(a^2 + b^2)) - ((a + b*tan(c + d*x))^2*(5*A*b^5 + 10*A*a^2*b^3 - 6*B*a^3*b^2 + A*a^4*b - 2*B*a
*b^4))/(a^3*(a^2 + b^2)^2))/(d*(a + b*tan(c + d*x))^(5/2) - a*d*(a + b*tan(c + d*x))^(3/2)) + 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)*((((((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)*((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^2
7*b^46*d^9 + 9984*a^29*b^44*d^9 + 92160*a^31*b^42*d^9 + 535296*a^33*b^40*d^9 + 2193408*a^35*b^38*d^9 + 6736896
*a^37*b^36*d^9 + 16084992*a^39*b^34*d^9 + 30551040*a^41*b^32*d^9 + 46844928*a^43*b^30*d^9 + 58499584*a^45*b^28
*d^9 + 59744256*a^47*b^26*d^9 + 49900032*a^49*b^24*d^9 + 33945600*a^51*b^22*d^9 + 18643968*a^53*b^20*d^9 + 814
6944*a^55*b^18*d^9 + 2767872*a^57*b^16*d^9 + 705024*a^59*b^14*d^9 + 126720*a^61*b^12*d^9 + 14336*a^63*b^10*d^9
+ 768*a^65*b^8*d^9) + 1280*A*a^24*b^47*d^8 + 24320*A*a^26*b^45*d^8 + 219008*A*a^28*b^43*d^8 + 1241984*A*a^30*
b^41*d^8 + 4970496*A*a^32*b^39*d^8 + 14909440*A*a^34*b^37*d^8 + 34746880*A*a^36*b^35*d^8 + 64356864*A*a^38*b^3
3*d^8 + 96092672*A*a^40*b^31*d^8 + 116633088*A*a^42*b^29*d^8 + 115498240*A*a^44*b^27*d^8 + 93267200*A*a^46*b^2
5*d^8 + 61128704*A*a^48*b^23*d^8 + 32212992*A*a^50*b^21*d^8 + 13439488*A*a^52*b^19*d^8 + 4334080*A*a^54*b^17*d
^8 + 1040640*A*a^56*b^15*d^8 + 174848*A*a^58*b^13*d^8 + 18304*A*a^60*b^11*d^8 + 896*A*a^62*b^9*d^8 - 512*B*a^2
5*b^46*d^8 - 9728*B*a^27*b^44*d^8 - 87936*B*a^29*b^42*d^8 - 502144*B*a^31*b^40*d^8 - 2028544*B*a^33*b^38*d^8 -
6153216*B*a^35*b^36*d^8 - 14518784*B*a^37*b^34*d^8 - 27243008*B*a^39*b^32*d^8 - 41213952*B*a^41*b^30*d^8 - 50
665472*B*a^43*b^28*d^8 - 50775296*B*a^45*b^26*d^8 - 41443584*B*a^47*b^24*d^8 - 27409408*B*a^49*b^22*d^8 - 1454
3872*B*a^51*b^20*d^8 - 6093312*B*a^53*b^18*d^8 - 1966592*B*a^55*b^16*d^8 - 470528*B*a^57*b^14*d^8 - 78336*B*a^
59*b^12*d^8 - 8064*B*a^61*b^10*d^8 - 384*B*a^63*b^8*d^8) - (a + b*tan(c + d*x))^(1/2)*(1600*A^2*a^22*b^46*d^7
+ 28800*A^2*a^24*b^44*d^7 + 244800*A^2*a^26*b^42*d^7 + 1304256*A^2*a^28*b^40*d^7 + 4880128*A^2*a^30*b^38*d^7 +
13627392*A^2*a^32*b^36*d^7 + 29476608*A^2*a^34*b^34*d^7 + 50615552*A^2*a^36*b^32*d^7 + 70152576*A^2*a^38*b^30
*d^7 + 79329536*A^2*a^40*b^28*d^7 + 73600384*A^2*a^42*b^26*d^7 + 56025216*A^2*a^44*b^24*d^7 + 34754304*A^2*a^4
6*b^22*d^7 + 17296384*A^2*a^48*b^20*d^7 + 6713088*A^2*a^50*b^18*d^7 + 1934592*A^2*a^52*b^16*d^7 + 377408*A^2*a
^54*b^14*d^7 + 39552*A^2*a^56*b^12*d^7 + 64*A^2*a^58*b^10*d^7 - 320*A^2*a^60*b^8*d^7 + 256*B^2*a^24*b^44*d^7 +
4608*B^2*a^26*b^42*d^7 + 40512*B^2*a^28*b^40*d^7 + 224768*B^2*a^30*b^38*d^7 + 864768*B^2*a^32*b^36*d^7 + 2419
200*B^2*a^34*b^34*d^7 + 5055232*B^2*a^36*b^32*d^7 + 8007168*B^2*a^38*b^30*d^7 + 9664512*B^2*a^40*b^28*d^7 + 88
59136*B^2*a^42*b^26*d^7 + 6095232*B^2*a^44*b^24*d^7 + 3095040*B^2*a^46*b^22*d^7 + 1164800*B^2*a^48*b^20*d^7 +
376320*B^2*a^50*b^18*d^7 + 154368*B^2*a^52*b^16*d^7 + 76288*B^2*a^54*b^14*d^7 + 28416*B^2*a^56*b^12*d^7 + 6144
*B^2*a^58*b^10*d^7 + 576*B^2*a^60*b^8*d^7 - 1280*A*B*a^23*b^45*d^7 - 23040*A*B*a^25*b^43*d^7 - 196352*A*B*a^27
*b^41*d^7 - 1046016*A*B*a^29*b^39*d^7 - 3887616*A*B*a^31*b^37*d^7 - 10683904*A*B*a^33*b^35*d^7 - 22503936*A*B*
a^35*b^33*d^7 - 37240320*A*B*a^37*b^31*d^7 - 49347584*A*B*a^39*b^29*d^7 - 53228032*A*B*a^41*b^27*d^7 - 4744396
8*A*B*a^43*b^25*d^7 - 35389952*A*B*a^45*b^23*d^7 - 22224384*A*B*a^47*b^21*d^7 - 11665920*A*B*a^49*b^19*d^7 - 4
988416*A*B*a^51*b^17*d^7 - 1657344*A*B*a^53*b^15*d^7 - 397056*A*B*a^55*b^13*d^7 - 60416*A*B*a^57*b^11*d^7 - 43
52*A*B*a^59*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) - 800*A^3*a^21*b^45*d^6 - 10400*A^3*a^23*b^43*d^6 - 54400*A^3
*a^25*b^41*d^6 - 121600*A^3*a^27*b^39*d^6 + 90304*A^3*a^29*b^37*d^6 + 1465856*A^3*a^31*b^35*d^6 + 5014464*A^3*
a^33*b^33*d^6 + 10323456*A^3*a^35*b^31*d^6 + 14661504*A^3*a^37*b^29*d^6 + 14908608*A^3*a^39*b^27*d^6 + 1080851
2*A^3*a^41*b^25*d^6 + 5328128*A^3*a^43*b^23*d^6 + 1531712*A^3*a^45*b^21*d^6 + 87808*A^3*a^47*b^19*d^6 - 85696*
A^3*a^49*b^17*d^6 - 6144*A^3*a^51*b^15*d^6 + 15264*A^3*a^53*b^13*d^6 + 5856*A^3*a^55*b^11*d^6 + 704*A^3*a^57*b
^9*d^6 + 384*B^3*a^24*b^42*d^6 + 7296*B^3*a^26*b^40*d^6 + 59424*B^3*a^28*b^38*d^6 + 280992*B^3*a^30*b^36*d^6 +
866208*B^3*a^32*b^34*d^6 + 1825824*B^3*a^34*b^32*d^6 + 2629536*B^3*a^36*b^30*d^6 + 2374944*B^3*a^38*b^28*d^6
+ 727584*B^3*a^40*b^26*d^6 - 1413984*B^3*a^42*b^24*d^6 - 2649504*B^3*a^44*b^22*d^6 - 2454816*B^3*a^46*b^20*d^6
- 1476384*B^3*a^48*b^18*d^6 - 597408*B^3*a^50*b^16*d^6 - 156192*B^3*a^52*b^14*d^6 - 22944*B^3*a^54*b^12*d^6 -
1056*B^3*a^56*b^10*d^6 + 96*B^3*a^58*b^8*d^6 - 2048*A*B^2*a^23*b^43*d^6 - 35456*A*B^2*a^25*b^41*d^6 - 269824*
A*B^2*a^27*b^39*d^6 - 1203648*A*B^2*a^29*b^37*d^6 - 3500672*A*B^2*a^31*b^35*d^6 - 6889792*A*B^2*a^33*b^33*d^6
- 8968960*A*B^2*a^35*b^31*d^6 - 6452160*A*B^2*a^37*b^29*d^6 + 933504*A*B^2*a^39*b^27*d^6 + 8721856*A*B^2*a^41*
b^25*d^6 + 11714560*A*B^2*a^43*b^23*d^6 + 9184448*A*B^2*a^45*b^21*d^6 + 4647552*A*B^2*a^47*b^19*d^6 + 1433152*
A*B^2*a^49*b^17*d^6 + 182528*A*B^2*a^51*b^15*d^6 - 37696*A*B^2*a^53*b^13*d^6 - 18048*A*B^2*a^55*b^11*d^6 - 211
2*A*B^2*a^57*b^9*d^6 + 3040*A^2*B*a^22*b^44*d^6 + 47200*A^2*B*a^24*b^42*d^6 + 325120*A^2*B*a^26*b^40*d^6 + 130
4352*A^2*B*a^28*b^38*d^6 + 3319840*A^2*B*a^30*b^36*d^6 + 5298720*A^2*B*a^32*b^34*d^6 + 4178720*A^2*B*a^34*b^32
*d^6 - 2452320*A^2*B*a^36*b^30*d^6 - 12167584*A^2*B*a^38*b^28*d^6 - 18281120*A^2*B*a^40*b^26*d^6 - 16496480*A^
2*B*a^42*b^24*d^6 - 9395360*A^2*B*a^44*b^22*d^6 - 2839200*A^2*B*a^46*b^20*d^6 + 167776*A^2*B*a^48*b^18*d^6 + 5
63040*A^2*B*a^50*b^16*d^6 + 239840*A^2*B*a^52*b^14*d^6 + 45120*A^2*B*a^54*b^12*d^6 + 2240*A^2*B*a^56*b^10*d^6
- 288*A^2*B*a^58*b^8*d^6) + (a + b*tan(c + d*x))^(1/2)*(67232*A^4*a^27*b^36*d^5 - 3200*A^4*a^23*b^40*d^5 - 320
0*A^4*a^25*b^38*d^5 - 400*A^4*a^21*b^42*d^5 + 437248*A^4*a^29*b^34*d^5 + 1458912*A^4*a^31*b^32*d^5 + 3214848*A
^4*a^33*b^30*d^5 + 5065632*A^4*a^35*b^28*d^5 + 5898464*A^4*a^37*b^26*d^5 + 5129696*A^4*a^39*b^24*d^5 + 3313024
*A^4*a^41*b^22*d^5 + 1552096*A^4*a^43*b^20*d^5 + 500864*A^4*a^45*b^18*d^5 + 99232*A^4*a^47*b^16*d^5 + 8448*A^4
*a^49*b^14*d^5 - 288*A^4*a^51*b^12*d^5 + 48*A^4*a^53*b^10*d^5 + 32*A^4*a^55*b^8*d^5 + 64*B^4*a^23*b^40*d^5 + 5
12*B^4*a^25*b^38*d^5 + 544*B^4*a^27*b^36*d^5 - 10304*B^4*a^29*b^34*d^5 - 66976*B^4*a^31*b^32*d^5 - 221312*B^4*
a^33*b^30*d^5 - 480480*B^4*a^35*b^28*d^5 - 741312*B^4*a^37*b^26*d^5 - 837408*B^4*a^39*b^24*d^5 - 695552*B^4*a^
41*b^22*d^5 - 416416*B^4*a^43*b^20*d^5 - 168896*B^4*a^45*b^18*d^5 - 37856*B^4*a^47*b^16*d^5 + 896*B^4*a^49*b^1
4*d^5 + 3424*B^4*a^51*b^12*d^5 + 960*B^4*a^53*b^10*d^5 + 96*B^4*a^55*b^8*d^5 - 320*A*B^3*a^22*b^41*d^5 - 2048*
A*B^3*a^24*b^39*d^5 + 4096*A*B^3*a^26*b^37*d^5 + 93184*A*B^3*a^28*b^35*d^5 + 489216*A*B^3*a^30*b^33*d^5 + 1490
944*A*B^3*a^32*b^31*d^5 + 3075072*A*B^3*a^34*b^29*d^5 + 4539392*A*B^3*a^36*b^27*d^5 + 4887168*A*B^3*a^38*b^25*
d^5 + 3807232*A*B^3*a^40*b^23*d^5 + 2050048*A*B^3*a^42*b^21*d^5 + 652288*A*B^3*a^44*b^19*d^5 + 23296*A*B^3*a^4
6*b^17*d^5 - 86016*A*B^3*a^48*b^15*d^5 - 41984*A*B^3*a^50*b^13*d^5 - 9216*A*B^3*a^52*b^11*d^5 - 832*A*B^3*a^54
*b^9*d^5 + 3520*A^3*B*a^22*b^41*d^5 + 44160*A^3*B*a^24*b^39*d^5 + 248960*A^3*B*a^26*b^37*d^5 + 819840*A^3*B*a^
28*b^35*d^5 + 1688960*A^3*B*a^30*b^33*d^5 + 2038400*A^3*B*a^32*b^31*d^5 + 640640*A^3*B*a^34*b^29*d^5 - 2654080
*A^3*B*a^36*b^27*d^5 - 6040320*A^3*B*a^38*b^25*d^5 - 7230080*A^3*B*a^40*b^23*d^5 - 5765760*A^3*B*a^42*b^21*d^5
- 3203200*A^3*B*a^44*b^19*d^5 - 1223040*A^3*B*a^46*b^17*d^5 - 300160*A^3*B*a^48*b^15*d^5 - 39040*A^3*B*a^50*b
^13*d^5 - 640*A^3*B*a^52*b^11*d^5 + 320*A^3*B*a^54*b^9*d^5 + 400*A^2*B^2*a^21*b^42*d^5 + 576*A^2*B^2*a^23*b^40
*d^5 - 30592*A^2*B^2*a^25*b^38*d^5 - 264768*A^2*B^2*a^27*b^36*d^5 - 1124032*A^2*B^2*a^29*b^34*d^5 - 3011008*A^
2*B^2*a^31*b^32*d^5 - 5509504*A^2*B^2*a^33*b^30*d^5 - 7019584*A^2*B^2*a^35*b^28*d^5 - 5999136*A^2*B^2*a^37*b^2
6*d^5 - 2809664*A^2*B^2*a^39*b^24*d^5 + 384384*A^2*B^2*a^41*b^22*d^5 + 1811264*A^2*B^2*a^43*b^20*d^5 + 1555008
*A^2*B^2*a^45*b^18*d^5 + 765632*A^2*B^2*a^47*b^16*d^5 + 234368*A^2*B^2*a^49*b^14*d^5 + 41792*A^2*B^2*a^51*b^12
*d^5 + 3344*A^2*B^2*a^53*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)*(90304*A^3*a^2
9*b^37*d^6 - 800*A^3*a^21*b^45*d^6 - 10400*A^3*a^23*b^43*d^6 - 54400*A^3*a^25*b^41*d^6 - 121600*A^3*a^27*b^39*
d^6 - (((((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 + 1
60*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^27*b^46*d^9 +
9984*a^29*b^44*d^9 + 92160*a^31*b^42*d^9 + 535296*a^33*b^40*d^9 + 2193408*a^35*b^38*d^9 + 6736896*a^37*b^36*d^
9 + 16084992*a^39*b^34*d^9 + 30551040*a^41*b^32*d^9 + 46844928*a^43*b^30*d^9 + 58499584*a^45*b^28*d^9 + 597442
56*a^47*b^26*d^9 + 49900032*a^49*b^24*d^9 + 33945600*a^51*b^22*d^9 + 18643968*a^53*b^20*d^9 + 8146944*a^55*b^1
8*d^9 + 2767872*a^57*b^16*d^9 + 705024*a^59*b^14*d^9 + 126720*a^61*b^12*d^9 + 14336*a^63*b^10*d^9 + 768*a^65*b
^8*d^9) - 1280*A*a^24*b^47*d^8 - 24320*A*a^26*b^45*d^8 - 219008*A*a^28*b^43*d^8 - 1241984*A*a^30*b^41*d^8 - 49
70496*A*a^32*b^39*d^8 - 14909440*A*a^34*b^37*d^8 - 34746880*A*a^36*b^35*d^8 - 64356864*A*a^38*b^33*d^8 - 96092
672*A*a^40*b^31*d^8 - 116633088*A*a^42*b^29*d^8 - 115498240*A*a^44*b^27*d^8 - 93267200*A*a^46*b^25*d^8 - 61128
704*A*a^48*b^23*d^8 - 32212992*A*a^50*b^21*d^8 - 13439488*A*a^52*b^19*d^8 - 4334080*A*a^54*b^17*d^8 - 1040640*
A*a^56*b^15*d^8 - 174848*A*a^58*b^13*d^8 - 18304*A*a^60*b^11*d^8 - 896*A*a^62*b^9*d^8 + 512*B*a^25*b^46*d^8 +
9728*B*a^27*b^44*d^8 + 87936*B*a^29*b^42*d^8 + 502144*B*a^31*b^40*d^8 + 2028544*B*a^33*b^38*d^8 + 6153216*B*a^
35*b^36*d^8 + 14518784*B*a^37*b^34*d^8 + 27243008*B*a^39*b^32*d^8 + 41213952*B*a^41*b^30*d^8 + 50665472*B*a^43
*b^28*d^8 + 50775296*B*a^45*b^26*d^8 + 41443584*B*a^47*b^24*d^8 + 27409408*B*a^49*b^22*d^8 + 14543872*B*a^51*b
^20*d^8 + 6093312*B*a^53*b^18*d^8 + 1966592*B*a^55*b^16*d^8 + 470528*B*a^57*b^14*d^8 + 78336*B*a^59*b^12*d^8 +
8064*B*a^61*b^10*d^8 + 384*B*a^63*b^8*d^8) - (a + b*tan(c + d*x))^(1/2)*(1600*A^2*a^22*b^46*d^7 + 28800*A^2*a
^24*b^44*d^7 + 244800*A^2*a^26*b^42*d^7 + 1304256*A^2*a^28*b^40*d^7 + 4880128*A^2*a^30*b^38*d^7 + 13627392*A^2
*a^32*b^36*d^7 + 29476608*A^2*a^34*b^34*d^7 + 50615552*A^2*a^36*b^32*d^7 + 70152576*A^2*a^38*b^30*d^7 + 793295
36*A^2*a^40*b^28*d^7 + 73600384*A^2*a^42*b^26*d^7 + 56025216*A^2*a^44*b^24*d^7 + 34754304*A^2*a^46*b^22*d^7 +
17296384*A^2*a^48*b^20*d^7 + 6713088*A^2*a^50*b^18*d^7 + 1934592*A^2*a^52*b^16*d^7 + 377408*A^2*a^54*b^14*d^7
+ 39552*A^2*a^56*b^12*d^7 + 64*A^2*a^58*b^10*d^7 - 320*A^2*a^60*b^8*d^7 + 256*B^2*a^24*b^44*d^7 + 4608*B^2*a^2
6*b^42*d^7 + 40512*B^2*a^28*b^40*d^7 + 224768*B^2*a^30*b^38*d^7 + 864768*B^2*a^32*b^36*d^7 + 2419200*B^2*a^34*
b^34*d^7 + 5055232*B^2*a^36*b^32*d^7 + 8007168*B^2*a^38*b^30*d^7 + 9664512*B^2*a^40*b^28*d^7 + 8859136*B^2*a^4
2*b^26*d^7 + 6095232*B^2*a^44*b^24*d^7 + 3095040*B^2*a^46*b^22*d^7 + 1164800*B^2*a^48*b^20*d^7 + 376320*B^2*a^
50*b^18*d^7 + 154368*B^2*a^52*b^16*d^7 + 76288*B^2*a^54*b^14*d^7 + 28416*B^2*a^56*b^12*d^7 + 6144*B^2*a^58*b^1
0*d^7 + 576*B^2*a^60*b^8*d^7 - 1280*A*B*a^23*b^45*d^7 - 23040*A*B*a^25*b^43*d^7 - 196352*A*B*a^27*b^41*d^7 - 1
046016*A*B*a^29*b^39*d^7 - 3887616*A*B*a^31*b^37*d^7 - 10683904*A*B*a^33*b^35*d^7 - 22503936*A*B*a^35*b^33*d^7
- 37240320*A*B*a^37*b^31*d^7 - 49347584*A*B*a^39*b^29*d^7 - 53228032*A*B*a^41*b^27*d^7 - 47443968*A*B*a^43*b^
25*d^7 - 35389952*A*B*a^45*b^23*d^7 - 22224384*A*B*a^47*b^21*d^7 - 11665920*A*B*a^49*b^19*d^7 - 4988416*A*B*a^
51*b^17*d^7 - 1657344*A*B*a^53*b^15*d^7 - 397056*A*B*a^55*b^13*d^7 - 60416*A*B*a^57*b^11*d^7 - 4352*A*B*a^59*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) + 1465856*A^3*a^31*b^35*d^6 + 5014464*A^3*a^33*b^33*d^6 + 10323456*A^3*a^3
5*b^31*d^6 + 14661504*A^3*a^37*b^29*d^6 + 14908608*A^3*a^39*b^27*d^6 + 10808512*A^3*a^41*b^25*d^6 + 5328128*A^
3*a^43*b^23*d^6 + 1531712*A^3*a^45*b^21*d^6 + 87808*A^3*a^47*b^19*d^6 - 85696*A^3*a^49*b^17*d^6 - 6144*A^3*a^5
1*b^15*d^6 + 15264*A^3*a^53*b^13*d^6 + 5856*A^3*a^55*b^11*d^6 + 704*A^3*a^57*b^9*d^6 + 384*B^3*a^24*b^42*d^6 +
7296*B^3*a^26*b^40*d^6 + 59424*B^3*a^28*b^38*d^6 + 280992*B^3*a^30*b^36*d^6 + 866208*B^3*a^32*b^34*d^6 + 1825
824*B^3*a^34*b^32*d^6 + 2629536*B^3*a^36*b^30*d^6 + 2374944*B^3*a^38*b^28*d^6 + 727584*B^3*a^40*b^26*d^6 - 141
3984*B^3*a^42*b^24*d^6 - 2649504*B^3*a^44*b^22*d^6 - 2454816*B^3*a^46*b^20*d^6 - 1476384*B^3*a^48*b^18*d^6 - 5
97408*B^3*a^50*b^16*d^6 - 156192*B^3*a^52*b^14*d^6 - 22944*B^3*a^54*b^12*d^6 - 1056*B^3*a^56*b^10*d^6 + 96*B^3
*a^58*b^8*d^6 - 2048*A*B^2*a^23*b^43*d^6 - 35456*A*B^2*a^25*b^41*d^6 - 269824*A*B^2*a^27*b^39*d^6 - 1203648*A*
B^2*a^29*b^37*d^6 - 3500672*A*B^2*a^31*b^35*d^6 - 6889792*A*B^2*a^33*b^33*d^6 - 8968960*A*B^2*a^35*b^31*d^6 -
6452160*A*B^2*a^37*b^29*d^6 + 933504*A*B^2*a^39*b^27*d^6 + 8721856*A*B^2*a^41*b^25*d^6 + 11714560*A*B^2*a^43*b
^23*d^6 + 9184448*A*B^2*a^45*b^21*d^6 + 4647552*A*B^2*a^47*b^19*d^6 + 1433152*A*B^2*a^49*b^17*d^6 + 182528*A*B
^2*a^51*b^15*d^6 - 37696*A*B^2*a^53*b^13*d^6 - 18048*A*B^2*a^55*b^11*d^6 - 2112*A*B^2*a^57*b^9*d^6 + 3040*A^2*
B*a^22*b^44*d^6 + 47200*A^2*B*a^24*b^42*d^6 + 325120*A^2*B*a^26*b^40*d^6 + 1304352*A^2*B*a^28*b^38*d^6 + 33198
40*A^2*B*a^30*b^36*d^6 + 5298720*A^2*B*a^32*b^34*d^6 + 4178720*A^2*B*a^34*b^32*d^6 - 2452320*A^2*B*a^36*b^30*d
^6 - 12167584*A^2*B*a^38*b^28*d^6 - 18281120*A^2*B*a^40*b^26*d^6 - 16496480*A^2*B*a^42*b^24*d^6 - 9395360*A^2*
B*a^44*b^22*d^6 - 2839200*A^2*B*a^46*b^20*d^6 + 167776*A^2*B*a^48*b^18*d^6 + 563040*A^2*B*a^50*b^16*d^6 + 2398
40*A^2*B*a^52*b^14*d^6 + 45120*A^2*B*a^54*b^12*d^6 + 2240*A^2*B*a^56*b^10*d^6 - 288*A^2*B*a^58*b^8*d^6) - (a +
b*tan(c + d*x))^(1/2)*(67232*A^4*a^27*b^36*d^5 - 3200*A^4*a^23*b^40*d^5 - 3200*A^4*a^25*b^38*d^5 - 400*A^4*a^
21*b^42*d^5 + 437248*A^4*a^29*b^34*d^5 + 1458912*A^4*a^31*b^32*d^5 + 3214848*A^4*a^33*b^30*d^5 + 5065632*A^4*a
^35*b^28*d^5 + 5898464*A^4*a^37*b^26*d^5 + 5129696*A^4*a^39*b^24*d^5 + 3313024*A^4*a^41*b^22*d^5 + 1552096*A^4
*a^43*b^20*d^5 + 500864*A^4*a^45*b^18*d^5 + 99232*A^4*a^47*b^16*d^5 + 8448*A^4*a^49*b^14*d^5 - 288*A^4*a^51*b^
12*d^5 + 48*A^4*a^53*b^10*d^5 + 32*A^4*a^55*b^8*d^5 + 64*B^4*a^23*b^40*d^5 + 512*B^4*a^25*b^38*d^5 + 544*B^4*a
^27*b^36*d^5 - 10304*B^4*a^29*b^34*d^5 - 66976*B^4*a^31*b^32*d^5 - 221312*B^4*a^33*b^30*d^5 - 480480*B^4*a^35*
b^28*d^5 - 741312*B^4*a^37*b^26*d^5 - 837408*B^4*a^39*b^24*d^5 - 695552*B^4*a^41*b^22*d^5 - 416416*B^4*a^43*b^
20*d^5 - 168896*B^4*a^45*b^18*d^5 - 37856*B^4*a^47*b^16*d^5 + 896*B^4*a^49*b^14*d^5 + 3424*B^4*a^51*b^12*d^5 +
960*B^4*a^53*b^10*d^5 + 96*B^4*a^55*b^8*d^5 - 320*A*B^3*a^22*b^41*d^5 - 2048*A*B^3*a^24*b^39*d^5 + 4096*A*B^3
*a^26*b^37*d^5 + 93184*A*B^3*a^28*b^35*d^5 + 489216*A*B^3*a^30*b^33*d^5 + 1490944*A*B^3*a^32*b^31*d^5 + 307507
2*A*B^3*a^34*b^29*d^5 + 4539392*A*B^3*a^36*b^27*d^5 + 4887168*A*B^3*a^38*b^25*d^5 + 3807232*A*B^3*a^40*b^23*d^
5 + 2050048*A*B^3*a^42*b^21*d^5 + 652288*A*B^3*a^44*b^19*d^5 + 23296*A*B^3*a^46*b^17*d^5 - 86016*A*B^3*a^48*b^
15*d^5 - 41984*A*B^3*a^50*b^13*d^5 - 9216*A*B^3*a^52*b^11*d^5 - 832*A*B^3*a^54*b^9*d^5 + 3520*A^3*B*a^22*b^41*
d^5 + 44160*A^3*B*a^24*b^39*d^5 + 248960*A^3*B*a^26*b^37*d^5 + 819840*A^3*B*a^28*b^35*d^5 + 1688960*A^3*B*a^30
*b^33*d^5 + 2038400*A^3*B*a^32*b^31*d^5 + 640640*A^3*B*a^34*b^29*d^5 - 2654080*A^3*B*a^36*b^27*d^5 - 6040320*A
^3*B*a^38*b^25*d^5 - 7230080*A^3*B*a^40*b^23*d^5 - 5765760*A^3*B*a^42*b^21*d^5 - 3203200*A^3*B*a^44*b^19*d^5 -
1223040*A^3*B*a^46*b^17*d^5 - 300160*A^3*B*a^48*b^15*d^5 - 39040*A^3*B*a^50*b^13*d^5 - 640*A^3*B*a^52*b^11*d^
5 + 320*A^3*B*a^54*b^9*d^5 + 400*A^2*B^2*a^21*b^42*d^5 + 576*A^2*B^2*a^23*b^40*d^5 - 30592*A^2*B^2*a^25*b^38*d
^5 - 264768*A^2*B^2*a^27*b^36*d^5 - 1124032*A^2*B^2*a^29*b^34*d^5 - 3011008*A^2*B^2*a^31*b^32*d^5 - 5509504*A^
2*B^2*a^33*b^30*d^5 - 7019584*A^2*B^2*a^35*b^28*d^5 - 5999136*A^2*B^2*a^37*b^26*d^5 - 2809664*A^2*B^2*a^39*b^2
4*d^5 + 384384*A^2*B^2*a^41*b^22*d^5 + 1811264*A^2*B^2*a^43*b^20*d^5 + 1555008*A^2*B^2*a^45*b^18*d^5 + 765632*
A^2*B^2*a^47*b^16*d^5 + 234368*A^2*B^2*a^49*b^14*d^5 + 41792*A^2*B^2*a^51*b^12*d^5 + 3344*A^2*B^2*a^53*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)/(800*A^5*a^22*b^39*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 + 16
0*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)*(90304*A^3*a^29*b^37*d
^6 - 800*A^3*a^21*b^45*d^6 - 10400*A^3*a^23*b^43*d^6 - 54400*A^3*a^25*b^41*d^6 - 121600*A^3*a^27*b^39*d^6 - ((
(((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^1
0*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^27*b^46*d^9 + 9984*a^2
9*b^44*d^9 + 92160*a^31*b^42*d^9 + 535296*a^33*b^40*d^9 + 2193408*a^35*b^38*d^9 + 6736896*a^37*b^36*d^9 + 1608
4992*a^39*b^34*d^9 + 30551040*a^41*b^32*d^9 + 46844928*a^43*b^30*d^9 + 58499584*a^45*b^28*d^9 + 59744256*a^47*
b^26*d^9 + 49900032*a^49*b^24*d^9 + 33945600*a^51*b^22*d^9 + 18643968*a^53*b^20*d^9 + 8146944*a^55*b^18*d^9 +
2767872*a^57*b^16*d^9 + 705024*a^59*b^14*d^9 + 126720*a^61*b^12*d^9 + 14336*a^63*b^10*d^9 + 768*a^65*b^8*d^9)
- 1280*A*a^24*b^47*d^8 - 24320*A*a^26*b^45*d^8 - 219008*A*a^28*b^43*d^8 - 1241984*A*a^30*b^41*d^8 - 4970496*A*
a^32*b^39*d^8 - 14909440*A*a^34*b^37*d^8 - 34746880*A*a^36*b^35*d^8 - 64356864*A*a^38*b^33*d^8 - 96092672*A*a^
40*b^31*d^8 - 116633088*A*a^42*b^29*d^8 - 115498240*A*a^44*b^27*d^8 - 93267200*A*a^46*b^25*d^8 - 61128704*A*a^
48*b^23*d^8 - 32212992*A*a^50*b^21*d^8 - 13439488*A*a^52*b^19*d^8 - 4334080*A*a^54*b^17*d^8 - 1040640*A*a^56*b
^15*d^8 - 174848*A*a^58*b^13*d^8 - 18304*A*a^60*b^11*d^8 - 896*A*a^62*b^9*d^8 + 512*B*a^25*b^46*d^8 + 9728*B*a
^27*b^44*d^8 + 87936*B*a^29*b^42*d^8 + 502144*B*a^31*b^40*d^8 + 2028544*B*a^33*b^38*d^8 + 6153216*B*a^35*b^36*
d^8 + 14518784*B*a^37*b^34*d^8 + 27243008*B*a^39*b^32*d^8 + 41213952*B*a^41*b^30*d^8 + 50665472*B*a^43*b^28*d^
8 + 50775296*B*a^45*b^26*d^8 + 41443584*B*a^47*b^24*d^8 + 27409408*B*a^49*b^22*d^8 + 14543872*B*a^51*b^20*d^8
+ 6093312*B*a^53*b^18*d^8 + 1966592*B*a^55*b^16*d^8 + 470528*B*a^57*b^14*d^8 + 78336*B*a^59*b^12*d^8 + 8064*B*
a^61*b^10*d^8 + 384*B*a^63*b^8*d^8) - (a + b*tan(c + d*x))^(1/2)*(1600*A^2*a^22*b^46*d^7 + 28800*A^2*a^24*b^44
*d^7 + 244800*A^2*a^26*b^42*d^7 + 1304256*A^2*a^28*b^40*d^7 + 4880128*A^2*a^30*b^38*d^7 + 13627392*A^2*a^32*b^
36*d^7 + 29476608*A^2*a^34*b^34*d^7 + 50615552*A^2*a^36*b^32*d^7 + 70152576*A^2*a^38*b^30*d^7 + 79329536*A^2*a
^40*b^28*d^7 + 73600384*A^2*a^42*b^26*d^7 + 56025216*A^2*a^44*b^24*d^7 + 34754304*A^2*a^46*b^22*d^7 + 17296384
*A^2*a^48*b^20*d^7 + 6713088*A^2*a^50*b^18*d^7 + 1934592*A^2*a^52*b^16*d^7 + 377408*A^2*a^54*b^14*d^7 + 39552*
A^2*a^56*b^12*d^7 + 64*A^2*a^58*b^10*d^7 - 320*A^2*a^60*b^8*d^7 + 256*B^2*a^24*b^44*d^7 + 4608*B^2*a^26*b^42*d
^7 + 40512*B^2*a^28*b^40*d^7 + 224768*B^2*a^30*b^38*d^7 + 864768*B^2*a^32*b^36*d^7 + 2419200*B^2*a^34*b^34*d^7
+ 5055232*B^2*a^36*b^32*d^7 + 8007168*B^2*a^38*b^30*d^7 + 9664512*B^2*a^40*b^28*d^7 + 8859136*B^2*a^42*b^26*d
^7 + 6095232*B^2*a^44*b^24*d^7 + 3095040*B^2*a^46*b^22*d^7 + 1164800*B^2*a^48*b^20*d^7 + 376320*B^2*a^50*b^18*
d^7 + 154368*B^2*a^52*b^16*d^7 + 76288*B^2*a^54*b^14*d^7 + 28416*B^2*a^56*b^12*d^7 + 6144*B^2*a^58*b^10*d^7 +
576*B^2*a^60*b^8*d^7 - 1280*A*B*a^23*b^45*d^7 - 23040*A*B*a^25*b^43*d^7 - 196352*A*B*a^27*b^41*d^7 - 1046016*A
*B*a^29*b^39*d^7 - 3887616*A*B*a^31*b^37*d^7 - 10683904*A*B*a^33*b^35*d^7 - 22503936*A*B*a^35*b^33*d^7 - 37240
320*A*B*a^37*b^31*d^7 - 49347584*A*B*a^39*b^29*d^7 - 53228032*A*B*a^41*b^27*d^7 - 47443968*A*B*a^43*b^25*d^7 -
35389952*A*B*a^45*b^23*d^7 - 22224384*A*B*a^47*b^21*d^7 - 11665920*A*B*a^49*b^19*d^7 - 4988416*A*B*a^51*b^17*
d^7 - 1657344*A*B*a^53*b^15*d^7 - 397056*A*B*a^55*b^13*d^7 - 60416*A*B*a^57*b^11*d^7 - 4352*A*B*a^59*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 + 1
6*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 + 8
0*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) + 1465856*A^3*a^31*b^35*d^6 + 5014464*A^3*a^33*b^33*d^6 + 10323456*A^3*a^35*b^31*d
^6 + 14661504*A^3*a^37*b^29*d^6 + 14908608*A^3*a^39*b^27*d^6 + 10808512*A^3*a^41*b^25*d^6 + 5328128*A^3*a^43*b
^23*d^6 + 1531712*A^3*a^45*b^21*d^6 + 87808*A^3*a^47*b^19*d^6 - 85696*A^3*a^49*b^17*d^6 - 6144*A^3*a^51*b^15*d
^6 + 15264*A^3*a^53*b^13*d^6 + 5856*A^3*a^55*b^11*d^6 + 704*A^3*a^57*b^9*d^6 + 384*B^3*a^24*b^42*d^6 + 7296*B^
3*a^26*b^40*d^6 + 59424*B^3*a^28*b^38*d^6 + 280992*B^3*a^30*b^36*d^6 + 866208*B^3*a^32*b^34*d^6 + 1825824*B^3*
a^34*b^32*d^6 + 2629536*B^3*a^36*b^30*d^6 + 2374944*B^3*a^38*b^28*d^6 + 727584*B^3*a^40*b^26*d^6 - 1413984*B^3
*a^42*b^24*d^6 - 2649504*B^3*a^44*b^22*d^6 - 2454816*B^3*a^46*b^20*d^6 - 1476384*B^3*a^48*b^18*d^6 - 597408*B^
3*a^50*b^16*d^6 - 156192*B^3*a^52*b^14*d^6 - 22944*B^3*a^54*b^12*d^6 - 1056*B^3*a^56*b^10*d^6 + 96*B^3*a^58*b^
8*d^6 - 2048*A*B^2*a^23*b^43*d^6 - 35456*A*B^2*a^25*b^41*d^6 - 269824*A*B^2*a^27*b^39*d^6 - 1203648*A*B^2*a^29
*b^37*d^6 - 3500672*A*B^2*a^31*b^35*d^6 - 6889792*A*B^2*a^33*b^33*d^6 - 8968960*A*B^2*a^35*b^31*d^6 - 6452160*
A*B^2*a^37*b^29*d^6 + 933504*A*B^2*a^39*b^27*d^6 + 8721856*A*B^2*a^41*b^25*d^6 + 11714560*A*B^2*a^43*b^23*d^6
+ 9184448*A*B^2*a^45*b^21*d^6 + 4647552*A*B^2*a^47*b^19*d^6 + 1433152*A*B^2*a^49*b^17*d^6 + 182528*A*B^2*a^51*
b^15*d^6 - 37696*A*B^2*a^53*b^13*d^6 - 18048*A*B^2*a^55*b^11*d^6 - 2112*A*B^2*a^57*b^9*d^6 + 3040*A^2*B*a^22*b
^44*d^6 + 47200*A^2*B*a^24*b^42*d^6 + 325120*A^2*B*a^26*b^40*d^6 + 1304352*A^2*B*a^28*b^38*d^6 + 3319840*A^2*B
*a^30*b^36*d^6 + 5298720*A^2*B*a^32*b^34*d^6 + 4178720*A^2*B*a^34*b^32*d^6 - 2452320*A^2*B*a^36*b^30*d^6 - 121
67584*A^2*B*a^38*b^28*d^6 - 18281120*A^2*B*a^40*b^26*d^6 - 16496480*A^2*B*a^42*b^24*d^6 - 9395360*A^2*B*a^44*b
^22*d^6 - 2839200*A^2*B*a^46*b^20*d^6 + 167776*A^2*B*a^48*b^18*d^6 + 563040*A^2*B*a^50*b^16*d^6 + 239840*A^2*B
*a^52*b^14*d^6 + 45120*A^2*B*a^54*b^12*d^6 + 2240*A^2*B*a^56*b^10*d^6 - 288*A^2*B*a^58*b^8*d^6) - (a + b*tan(c
+ d*x))^(1/2)*(67232*A^4*a^27*b^36*d^5 - 3200*A^4*a^23*b^40*d^5 - 3200*A^4*a^25*b^38*d^5 - 400*A^4*a^21*b^42*
d^5 + 437248*A^4*a^29*b^34*d^5 + 1458912*A^4*a^31*b^32*d^5 + 3214848*A^4*a^33*b^30*d^5 + 5065632*A^4*a^35*b^28
*d^5 + 5898464*A^4*a^37*b^26*d^5 + 5129696*A^4*a^39*b^24*d^5 + 3313024*A^4*a^41*b^22*d^5 + 1552096*A^4*a^43*b^
20*d^5 + 500864*A^4*a^45*b^18*d^5 + 99232*A^4*a^47*b^16*d^5 + 8448*A^4*a^49*b^14*d^5 - 288*A^4*a^51*b^12*d^5 +
48*A^4*a^53*b^10*d^5 + 32*A^4*a^55*b^8*d^5 + 64*B^4*a^23*b^40*d^5 + 512*B^4*a^25*b^38*d^5 + 544*B^4*a^27*b^36
*d^5 - 10304*B^4*a^29*b^34*d^5 - 66976*B^4*a^31*b^32*d^5 - 221312*B^4*a^33*b^30*d^5 - 480480*B^4*a^35*b^28*d^5
- 741312*B^4*a^37*b^26*d^5 - 837408*B^4*a^39*b^24*d^5 - 695552*B^4*a^41*b^22*d^5 - 416416*B^4*a^43*b^20*d^5 -
168896*B^4*a^45*b^18*d^5 - 37856*B^4*a^47*b^16*d^5 + 896*B^4*a^49*b^14*d^5 + 3424*B^4*a^51*b^12*d^5 + 960*B^4
*a^53*b^10*d^5 + 96*B^4*a^55*b^8*d^5 - 320*A*B^3*a^22*b^41*d^5 - 2048*A*B^3*a^24*b^39*d^5 + 4096*A*B^3*a^26*b^
37*d^5 + 93184*A*B^3*a^28*b^35*d^5 + 489216*A*B^3*a^30*b^33*d^5 + 1490944*A*B^3*a^32*b^31*d^5 + 3075072*A*B^3*
a^34*b^29*d^5 + 4539392*A*B^3*a^36*b^27*d^5 + 4887168*A*B^3*a^38*b^25*d^5 + 3807232*A*B^3*a^40*b^23*d^5 + 2050
048*A*B^3*a^42*b^21*d^5 + 652288*A*B^3*a^44*b^19*d^5 + 23296*A*B^3*a^46*b^17*d^5 - 86016*A*B^3*a^48*b^15*d^5 -
41984*A*B^3*a^50*b^13*d^5 - 9216*A*B^3*a^52*b^11*d^5 - 832*A*B^3*a^54*b^9*d^5 + 3520*A^3*B*a^22*b^41*d^5 + 44
160*A^3*B*a^24*b^39*d^5 + 248960*A^3*B*a^26*b^37*d^5 + 819840*A^3*B*a^28*b^35*d^5 + 1688960*A^3*B*a^30*b^33*d^
5 + 2038400*A^3*B*a^32*b^31*d^5 + 640640*A^3*B*a^34*b^29*d^5 - 2654080*A^3*B*a^36*b^27*d^5 - 6040320*A^3*B*a^3
8*b^25*d^5 - 7230080*A^3*B*a^40*b^23*d^5 - 5765760*A^3*B*a^42*b^21*d^5 - 3203200*A^3*B*a^44*b^19*d^5 - 1223040
*A^3*B*a^46*b^17*d^5 - 300160*A^3*B*a^48*b^15*d^5 - 39040*A^3*B*a^50*b^13*d^5 - 640*A^3*B*a^52*b^11*d^5 + 320*
A^3*B*a^54*b^9*d^5 + 400*A^2*B^2*a^21*b^42*d^5 + 576*A^2*B^2*a^23*b^40*d^5 - 30592*A^2*B^2*a^25*b^38*d^5 - 264
768*A^2*B^2*a^27*b^36*d^5 - 1124032*A^2*B^2*a^29*b^34*d^5 - 3011008*A^2*B^2*a^31*b^32*d^5 - 5509504*A^2*B^2*a^
33*b^30*d^5 - 7019584*A^2*B^2*a^35*b^28*d^5 - 5999136*A^2*B^2*a^37*b^26*d^5 - 2809664*A^2*B^2*a^39*b^24*d^5 +
384384*A^2*B^2*a^41*b^22*d^5 + 1811264*A^2*B^2*a^43*b^20*d^5 + 1555008*A^2*B^2*a^45*b^18*d^5 + 765632*A^2*B^2*
a^47*b^16*d^5 + 234368*A^2*B^2*a^49*b^14*d^5 + 41792*A^2*B^2*a^51*b^12*d^5 + 3344*A^2*B^2*a^53*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^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) - (((((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)*((((((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^27*b^46*d^9 + 9984*a^29*b^44*d^9 + 92160*a^31*b^42*d^9 + 535296*a^33*b^40*d^
9 + 2193408*a^35*b^38*d^9 + 6736896*a^37*b^36*d^9 + 16084992*a^39*b^34*d^9 + 30551040*a^41*b^32*d^9 + 46844928
*a^43*b^30*d^9 + 58499584*a^45*b^28*d^9 + 59744256*a^47*b^26*d^9 + 49900032*a^49*b^24*d^9 + 33945600*a^51*b^22
*d^9 + 18643968*a^53*b^20*d^9 + 8146944*a^55*b^18*d^9 + 2767872*a^57*b^16*d^9 + 705024*a^59*b^14*d^9 + 126720*
a^61*b^12*d^9 + 14336*a^63*b^10*d^9 + 768*a^65*b^8*d^9) + 1280*A*a^24*b^47*d^8 + 24320*A*a^26*b^45*d^8 + 21900
8*A*a^28*b^43*d^8 + 1241984*A*a^30*b^41*d^8 + 4970496*A*a^32*b^39*d^8 + 14909440*A*a^34*b^37*d^8 + 34746880*A*
a^36*b^35*d^8 + 64356864*A*a^38*b^33*d^8 + 96092672*A*a^40*b^31*d^8 + 116633088*A*a^42*b^29*d^8 + 115498240*A*
a^44*b^27*d^8 + 93267200*A*a^46*b^25*d^8 + 61128704*A*a^48*b^23*d^8 + 32212992*A*a^50*b^21*d^8 + 13439488*A*a^
52*b^19*d^8 + 4334080*A*a^54*b^17*d^8 + 1040640*A*a^56*b^15*d^8 + 174848*A*a^58*b^13*d^8 + 18304*A*a^60*b^11*d
^8 + 896*A*a^62*b^9*d^8 - 512*B*a^25*b^46*d^8 - 9728*B*a^27*b^44*d^8 - 87936*B*a^29*b^42*d^8 - 502144*B*a^31*b
^40*d^8 - 2028544*B*a^33*b^38*d^8 - 6153216*B*a^35*b^36*d^8 - 14518784*B*a^37*b^34*d^8 - 27243008*B*a^39*b^32*
d^8 - 41213952*B*a^41*b^30*d^8 - 50665472*B*a^43*b^28*d^8 - 50775296*B*a^45*b^26*d^8 - 41443584*B*a^47*b^24*d^
8 - 27409408*B*a^49*b^22*d^8 - 14543872*B*a^51*b^20*d^8 - 6093312*B*a^53*b^18*d^8 - 1966592*B*a^55*b^16*d^8 -
470528*B*a^57*b^14*d^8 - 78336*B*a^59*b^12*d^8 - 8064*B*a^61*b^10*d^8 - 384*B*a^63*b^8*d^8) - (a + b*tan(c + d
*x))^(1/2)*(1600*A^2*a^22*b^46*d^7 + 28800*A^2*a^24*b^44*d^7 + 244800*A^2*a^26*b^42*d^7 + 1304256*A^2*a^28*b^4
0*d^7 + 4880128*A^2*a^30*b^38*d^7 + 13627392*A^2*a^32*b^36*d^7 + 29476608*A^2*a^34*b^34*d^7 + 50615552*A^2*a^3
6*b^32*d^7 + 70152576*A^2*a^38*b^30*d^7 + 79329536*A^2*a^40*b^28*d^7 + 73600384*A^2*a^42*b^26*d^7 + 56025216*A
^2*a^44*b^24*d^7 + 34754304*A^2*a^46*b^22*d^7 + 17296384*A^2*a^48*b^20*d^7 + 6713088*A^2*a^50*b^18*d^7 + 19345
92*A^2*a^52*b^16*d^7 + 377408*A^2*a^54*b^14*d^7 + 39552*A^2*a^56*b^12*d^7 + 64*A^2*a^58*b^10*d^7 - 320*A^2*a^6
0*b^8*d^7 + 256*B^2*a^24*b^44*d^7 + 4608*B^2*a^26*b^42*d^7 + 40512*B^2*a^28*b^40*d^7 + 224768*B^2*a^30*b^38*d^
7 + 864768*B^2*a^32*b^36*d^7 + 2419200*B^2*a^34*b^34*d^7 + 5055232*B^2*a^36*b^32*d^7 + 8007168*B^2*a^38*b^30*d
^7 + 9664512*B^2*a^40*b^28*d^7 + 8859136*B^2*a^42*b^26*d^7 + 6095232*B^2*a^44*b^24*d^7 + 3095040*B^2*a^46*b^22
*d^7 + 1164800*B^2*a^48*b^20*d^7 + 376320*B^2*a^50*b^18*d^7 + 154368*B^2*a^52*b^16*d^7 + 76288*B^2*a^54*b^14*d
^7 + 28416*B^2*a^56*b^12*d^7 + 6144*B^2*a^58*b^10*d^7 + 576*B^2*a^60*b^8*d^7 - 1280*A*B*a^23*b^45*d^7 - 23040*
A*B*a^25*b^43*d^7 - 196352*A*B*a^27*b^41*d^7 - 1046016*A*B*a^29*b^39*d^7 - 3887616*A*B*a^31*b^37*d^7 - 1068390
4*A*B*a^33*b^35*d^7 - 22503936*A*B*a^35*b^33*d^7 - 37240320*A*B*a^37*b^31*d^7 - 49347584*A*B*a^39*b^29*d^7 - 5
3228032*A*B*a^41*b^27*d^7 - 47443968*A*B*a^43*b^25*d^7 - 35389952*A*B*a^45*b^23*d^7 - 22224384*A*B*a^47*b^21*d
^7 - 11665920*A*B*a^49*b^19*d^7 - 4988416*A*B*a^51*b^17*d^7 - 1657344*A*B*a^53*b^15*d^7 - 397056*A*B*a^55*b^13
*d^7 - 60416*A*B*a^57*b^11*d^7 - 4352*A*B*a^59*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) - 800*A^3*a^21*b^45*d^6 -
10400*A^3*a^23*b^43*d^6 - 54400*A^3*a^25*b^41*d^6 - 121600*A^3*a^27*b^39*d^6 + 90304*A^3*a^29*b^37*d^6 + 14658
56*A^3*a^31*b^35*d^6 + 5014464*A^3*a^33*b^33*d^6 + 10323456*A^3*a^35*b^31*d^6 + 14661504*A^3*a^37*b^29*d^6 + 1
4908608*A^3*a^39*b^27*d^6 + 10808512*A^3*a^41*b^25*d^6 + 5328128*A^3*a^43*b^23*d^6 + 1531712*A^3*a^45*b^21*d^6
+ 87808*A^3*a^47*b^19*d^6 - 85696*A^3*a^49*b^17*d^6 - 6144*A^3*a^51*b^15*d^6 + 15264*A^3*a^53*b^13*d^6 + 5856
*A^3*a^55*b^11*d^6 + 704*A^3*a^57*b^9*d^6 + 384*B^3*a^24*b^42*d^6 + 7296*B^3*a^26*b^40*d^6 + 59424*B^3*a^28*b^
38*d^6 + 280992*B^3*a^30*b^36*d^6 + 866208*B^3*a^32*b^34*d^6 + 1825824*B^3*a^34*b^32*d^6 + 2629536*B^3*a^36*b^
30*d^6 + 2374944*B^3*a^38*b^28*d^6 + 727584*B^3*a^40*b^26*d^6 - 1413984*B^3*a^42*b^24*d^6 - 2649504*B^3*a^44*b
^22*d^6 - 2454816*B^3*a^46*b^20*d^6 - 1476384*B^3*a^48*b^18*d^6 - 597408*B^3*a^50*b^16*d^6 - 156192*B^3*a^52*b
^14*d^6 - 22944*B^3*a^54*b^12*d^6 - 1056*B^3*a^56*b^10*d^6 + 96*B^3*a^58*b^8*d^6 - 2048*A*B^2*a^23*b^43*d^6 -
35456*A*B^2*a^25*b^41*d^6 - 269824*A*B^2*a^27*b^39*d^6 - 1203648*A*B^2*a^29*b^37*d^6 - 3500672*A*B^2*a^31*b^35
*d^6 - 6889792*A*B^2*a^33*b^33*d^6 - 8968960*A*B^2*a^35*b^31*d^6 - 6452160*A*B^2*a^37*b^29*d^6 + 933504*A*B^2*
a^39*b^27*d^6 + 8721856*A*B^2*a^41*b^25*d^6 + 11714560*A*B^2*a^43*b^23*d^6 + 9184448*A*B^2*a^45*b^21*d^6 + 464
7552*A*B^2*a^47*b^19*d^6 + 1433152*A*B^2*a^49*b^17*d^6 + 182528*A*B^2*a^51*b^15*d^6 - 37696*A*B^2*a^53*b^13*d^
6 - 18048*A*B^2*a^55*b^11*d^6 - 2112*A*B^2*a^57*b^9*d^6 + 3040*A^2*B*a^22*b^44*d^6 + 47200*A^2*B*a^24*b^42*d^6
+ 325120*A^2*B*a^26*b^40*d^6 + 1304352*A^2*B*a^28*b^38*d^6 + 3319840*A^2*B*a^30*b^36*d^6 + 5298720*A^2*B*a^32
*b^34*d^6 + 4178720*A^2*B*a^34*b^32*d^6 - 2452320*A^2*B*a^36*b^30*d^6 - 12167584*A^2*B*a^38*b^28*d^6 - 1828112
0*A^2*B*a^40*b^26*d^6 - 16496480*A^2*B*a^42*b^24*d^6 - 9395360*A^2*B*a^44*b^22*d^6 - 2839200*A^2*B*a^46*b^20*d
^6 + 167776*A^2*B*a^48*b^18*d^6 + 563040*A^2*B*a^50*b^16*d^6 + 239840*A^2*B*a^52*b^14*d^6 + 45120*A^2*B*a^54*b
^12*d^6 + 2240*A^2*B*a^56*b^10*d^6 - 288*A^2*B*a^58*b^8*d^6) + (a + b*tan(c + d*x))^(1/2)*(67232*A^4*a^27*b^36
*d^5 - 3200*A^4*a^23*b^40*d^5 - 3200*A^4*a^25*b^38*d^5 - 400*A^4*a^21*b^42*d^5 + 437248*A^4*a^29*b^34*d^5 + 14
58912*A^4*a^31*b^32*d^5 + 3214848*A^4*a^33*b^30*d^5 + 5065632*A^4*a^35*b^28*d^5 + 5898464*A^4*a^37*b^26*d^5 +
5129696*A^4*a^39*b^24*d^5 + 3313024*A^4*a^41*b^22*d^5 + 1552096*A^4*a^43*b^20*d^5 + 500864*A^4*a^45*b^18*d^5 +
99232*A^4*a^47*b^16*d^5 + 8448*A^4*a^49*b^14*d^5 - 288*A^4*a^51*b^12*d^5 + 48*A^4*a^53*b^10*d^5 + 32*A^4*a^55
*b^8*d^5 + 64*B^4*a^23*b^40*d^5 + 512*B^4*a^25*b^38*d^5 + 544*B^4*a^27*b^36*d^5 - 10304*B^4*a^29*b^34*d^5 - 66
976*B^4*a^31*b^32*d^5 - 221312*B^4*a^33*b^30*d^5 - 480480*B^4*a^35*b^28*d^5 - 741312*B^4*a^37*b^26*d^5 - 83740
8*B^4*a^39*b^24*d^5 - 695552*B^4*a^41*b^22*d^5 - 416416*B^4*a^43*b^20*d^5 - 168896*B^4*a^45*b^18*d^5 - 37856*B
^4*a^47*b^16*d^5 + 896*B^4*a^49*b^14*d^5 + 3424*B^4*a^51*b^12*d^5 + 960*B^4*a^53*b^10*d^5 + 96*B^4*a^55*b^8*d^
5 - 320*A*B^3*a^22*b^41*d^5 - 2048*A*B^3*a^24*b^39*d^5 + 4096*A*B^3*a^26*b^37*d^5 + 93184*A*B^3*a^28*b^35*d^5
+ 489216*A*B^3*a^30*b^33*d^5 + 1490944*A*B^3*a^32*b^31*d^5 + 3075072*A*B^3*a^34*b^29*d^5 + 4539392*A*B^3*a^36*
b^27*d^5 + 4887168*A*B^3*a^38*b^25*d^5 + 3807232*A*B^3*a^40*b^23*d^5 + 2050048*A*B^3*a^42*b^21*d^5 + 652288*A*
B^3*a^44*b^19*d^5 + 23296*A*B^3*a^46*b^17*d^5 - 86016*A*B^3*a^48*b^15*d^5 - 41984*A*B^3*a^50*b^13*d^5 - 9216*A
*B^3*a^52*b^11*d^5 - 832*A*B^3*a^54*b^9*d^5 + 3520*A^3*B*a^22*b^41*d^5 + 44160*A^3*B*a^24*b^39*d^5 + 248960*A^
3*B*a^26*b^37*d^5 + 819840*A^3*B*a^28*b^35*d^5 + 1688960*A^3*B*a^30*b^33*d^5 + 2038400*A^3*B*a^32*b^31*d^5 + 6
40640*A^3*B*a^34*b^29*d^5 - 2654080*A^3*B*a^36*b^27*d^5 - 6040320*A^3*B*a^38*b^25*d^5 - 7230080*A^3*B*a^40*b^2
3*d^5 - 5765760*A^3*B*a^42*b^21*d^5 - 3203200*A^3*B*a^44*b^19*d^5 - 1223040*A^3*B*a^46*b^17*d^5 - 300160*A^3*B
*a^48*b^15*d^5 - 39040*A^3*B*a^50*b^13*d^5 - 640*A^3*B*a^52*b^11*d^5 + 320*A^3*B*a^54*b^9*d^5 + 400*A^2*B^2*a^
21*b^42*d^5 + 576*A^2*B^2*a^23*b^40*d^5 - 30592*A^2*B^2*a^25*b^38*d^5 - 264768*A^2*B^2*a^27*b^36*d^5 - 1124032
*A^2*B^2*a^29*b^34*d^5 - 3011008*A^2*B^2*a^31*b^32*d^5 - 5509504*A^2*B^2*a^33*b^30*d^5 - 7019584*A^2*B^2*a^35*
b^28*d^5 - 5999136*A^2*B^2*a^37*b^26*d^5 - 2809664*A^2*B^2*a^39*b^24*d^5 + 384384*A^2*B^2*a^41*b^22*d^5 + 1811
264*A^2*B^2*a^43*b^20*d^5 + 1555008*A^2*B^2*a^45*b^18*d^5 + 765632*A^2*B^2*a^47*b^16*d^5 + 234368*A^2*B^2*a^49
*b^14*d^5 + 41792*A^2*B^2*a^51*b^12*d^5 + 3344*A^2*B^2*a^53*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)/(1
6*(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) + 11040*A^5*
a^24*b^37*d^4 + 70560*A^5*a^26*b^35*d^4 + 276640*A^5*a^28*b^33*d^4 + 742560*A^5*a^30*b^31*d^4 + 1441440*A^5*a^
32*b^29*d^4 + 2082080*A^5*a^34*b^27*d^4 + 2265120*A^5*a^36*b^25*d^4 + 1853280*A^5*a^38*b^23*d^4 + 1121120*A^5*
a^40*b^21*d^4 + 480480*A^5*a^42*b^19*d^4 + 131040*A^5*a^44*b^17*d^4 + 14560*A^5*a^46*b^15*d^4 - 3360*A^5*a^48*
b^13*d^4 - 1440*A^5*a^50*b^11*d^4 - 160*A^5*a^52*b^9*d^4 + 64*B^5*a^23*b^38*d^4 + 896*B^5*a^25*b^36*d^4 + 5824
*B^5*a^27*b^34*d^4 + 23296*B^5*a^29*b^32*d^4 + 64064*B^5*a^31*b^30*d^4 + 128128*B^5*a^33*b^28*d^4 + 192192*B^5
*a^35*b^26*d^4 + 219648*B^5*a^37*b^24*d^4 + 192192*B^5*a^39*b^22*d^4 + 128128*B^5*a^41*b^20*d^4 + 64064*B^5*a^
43*b^18*d^4 + 23296*B^5*a^45*b^16*d^4 + 5824*B^5*a^47*b^14*d^4 + 896*B^5*a^49*b^12*d^4 + 64*B^5*a^51*b^10*d^4
- 320*A*B^4*a^22*b^39*d^4 - 4192*A*B^4*a^24*b^37*d^4 - 25088*A*B^4*a^26*b^35*d^4 - 90272*A*B^4*a^28*b^33*d^4 -
215488*A*B^4*a^30*b^31*d^4 - 352352*A*B^4*a^32*b^29*d^4 - 384384*A*B^4*a^34*b^27*d^4 - 233376*A*B^4*a^36*b^25
*d^4 + 27456*A*B^4*a^38*b^23*d^4 + 224224*A*B^4*a^40*b^21*d^4 + 256256*A*B^4*a^42*b^19*d^4 + 171808*A*B^4*a^44
*b^17*d^4 + 75712*A*B^4*a^46*b^15*d^4 + 21728*A*B^4*a^48*b^13*d^4 + 3712*A*B^4*a^50*b^11*d^4 + 288*A*B^4*a^52*
b^9*d^4 + 400*A^4*B*a^21*b^40*d^4 + 4560*A^4*B*a^23*b^38*d^4 + 21904*A^4*B*a^25*b^36*d^4 + 51856*A^4*B*a^27*b^
34*d^4 + 27664*A^4*B*a^29*b^32*d^4 - 216944*A^4*B*a^31*b^30*d^4 - 816816*A^4*B*a^33*b^28*d^4 - 1622192*A^4*B*a
^35*b^26*d^4 - 2175888*A^4*B*a^37*b^24*d^4 - 2102672*A^4*B*a^39*b^22*d^4 - 1489488*A^4*B*a^41*b^20*d^4 - 76731
2*A^4*B*a^43*b^18*d^4 - 278096*A^4*B*a^45*b^16*d^4 - 65744*A^4*B*a^47*b^14*d^4 - 8336*A^4*B*a^49*b^12*d^4 - 14
4*A^4*B*a^51*b^10*d^4 + 64*A^4*B*a^53*b^8*d^4 + 400*A^2*B^3*a^21*b^40*d^4 + 4624*A^2*B^3*a^23*b^38*d^4 + 22800
*A^2*B^3*a^25*b^36*d^4 + 57680*A^2*B^3*a^27*b^34*d^4 + 50960*A^2*B^3*a^29*b^32*d^4 - 152880*A^2*B^3*a^31*b^30*
d^4 - 688688*A^2*B^3*a^33*b^28*d^4 - 1430000*A^2*B^3*a^35*b^26*d^4 - 1956240*A^2*B^3*a^37*b^24*d^4 - 1910480*A
^2*B^3*a^39*b^22*d^4 - 1361360*A^2*B^3*a^41*b^20*d^4 - 703248*A^2*B^3*a^43*b^18*d^4 - 254800*A^2*B^3*a^45*b^16
*d^4 - 59920*A^2*B^3*a^47*b^14*d^4 - 7440*A^2*B^3*a^49*b^12*d^4 - 80*A^2*B^3*a^51*b^10*d^4 + 64*A^2*B^3*a^53*b
^8*d^4 + 480*A^3*B^2*a^22*b^39*d^4 + 6848*A^3*B^2*a^24*b^37*d^4 + 45472*A^3*B^2*a^26*b^35*d^4 + 186368*A^3*B^2
*a^28*b^33*d^4 + 527072*A^3*B^2*a^30*b^31*d^4 + 1089088*A^3*B^2*a^32*b^29*d^4 + 1697696*A^3*B^2*a^34*b^27*d^4
+ 2031744*A^3*B^2*a^36*b^25*d^4 + 1880736*A^3*B^2*a^38*b^23*d^4 + 1345344*A^3*B^2*a^40*b^21*d^4 + 736736*A^3*B
^2*a^42*b^19*d^4 + 302848*A^3*B^2*a^44*b^17*d^4 + 90272*A^3*B^2*a^46*b^15*d^4 + 18368*A^3*B^2*a^48*b^13*d^4 +
2272*A^3*B^2*a^50*b^11*d^4 + 128*A^3*B^2*a^52*b^9*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 + 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)*((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^27*b
^46*d^9 + 9984*a^29*b^44*d^9 + 92160*a^31*b^42*d^9 + 535296*a^33*b^40*d^9 + 2193408*a^35*b^38*d^9 + 6736896*a^
37*b^36*d^9 + 16084992*a^39*b^34*d^9 + 30551040*a^41*b^32*d^9 + 46844928*a^43*b^30*d^9 + 58499584*a^45*b^28*d^
9 + 59744256*a^47*b^26*d^9 + 49900032*a^49*b^24*d^9 + 33945600*a^51*b^22*d^9 + 18643968*a^53*b^20*d^9 + 814694
4*a^55*b^18*d^9 + 2767872*a^57*b^16*d^9 + 705024*a^59*b^14*d^9 + 126720*a^61*b^12*d^9 + 14336*a^63*b^10*d^9 +
768*a^65*b^8*d^9) + 1280*A*a^24*b^47*d^8 + 24320*A*a^26*b^45*d^8 + 219008*A*a^28*b^43*d^8 + 1241984*A*a^30*b^4
1*d^8 + 4970496*A*a^32*b^39*d^8 + 14909440*A*a^34*b^37*d^8 + 34746880*A*a^36*b^35*d^8 + 64356864*A*a^38*b^33*d
^8 + 96092672*A*a^40*b^31*d^8 + 116633088*A*a^42*b^29*d^8 + 115498240*A*a^44*b^27*d^8 + 93267200*A*a^46*b^25*d
^8 + 61128704*A*a^48*b^23*d^8 + 32212992*A*a^50*b^21*d^8 + 13439488*A*a^52*b^19*d^8 + 4334080*A*a^54*b^17*d^8
+ 1040640*A*a^56*b^15*d^8 + 174848*A*a^58*b^13*d^8 + 18304*A*a^60*b^11*d^8 + 896*A*a^62*b^9*d^8 - 512*B*a^25*b
^46*d^8 - 9728*B*a^27*b^44*d^8 - 87936*B*a^29*b^42*d^8 - 502144*B*a^31*b^40*d^8 - 2028544*B*a^33*b^38*d^8 - 61
53216*B*a^35*b^36*d^8 - 14518784*B*a^37*b^34*d^8 - 27243008*B*a^39*b^32*d^8 - 41213952*B*a^41*b^30*d^8 - 50665
472*B*a^43*b^28*d^8 - 50775296*B*a^45*b^26*d^8 - 41443584*B*a^47*b^24*d^8 - 27409408*B*a^49*b^22*d^8 - 1454387
2*B*a^51*b^20*d^8 - 6093312*B*a^53*b^18*d^8 - 1966592*B*a^55*b^16*d^8 - 470528*B*a^57*b^14*d^8 - 78336*B*a^59*
b^12*d^8 - 8064*B*a^61*b^10*d^8 - 384*B*a^63*b^8*d^8) - (a + b*tan(c + d*x))^(1/2)*(1600*A^2*a^22*b^46*d^7 + 2
8800*A^2*a^24*b^44*d^7 + 244800*A^2*a^26*b^42*d^7 + 1304256*A^2*a^28*b^40*d^7 + 4880128*A^2*a^30*b^38*d^7 + 13
627392*A^2*a^32*b^36*d^7 + 29476608*A^2*a^34*b^34*d^7 + 50615552*A^2*a^36*b^32*d^7 + 70152576*A^2*a^38*b^30*d^
7 + 79329536*A^2*a^40*b^28*d^7 + 73600384*A^2*a^42*b^26*d^7 + 56025216*A^2*a^44*b^24*d^7 + 34754304*A^2*a^46*b
^22*d^7 + 17296384*A^2*a^48*b^20*d^7 + 6713088*A^2*a^50*b^18*d^7 + 1934592*A^2*a^52*b^16*d^7 + 377408*A^2*a^54
*b^14*d^7 + 39552*A^2*a^56*b^12*d^7 + 64*A^2*a^58*b^10*d^7 - 320*A^2*a^60*b^8*d^7 + 256*B^2*a^24*b^44*d^7 + 46
08*B^2*a^26*b^42*d^7 + 40512*B^2*a^28*b^40*d^7 + 224768*B^2*a^30*b^38*d^7 + 864768*B^2*a^32*b^36*d^7 + 2419200
*B^2*a^34*b^34*d^7 + 5055232*B^2*a^36*b^32*d^7 + 8007168*B^2*a^38*b^30*d^7 + 9664512*B^2*a^40*b^28*d^7 + 88591
36*B^2*a^42*b^26*d^7 + 6095232*B^2*a^44*b^24*d^7 + 3095040*B^2*a^46*b^22*d^7 + 1164800*B^2*a^48*b^20*d^7 + 376
320*B^2*a^50*b^18*d^7 + 154368*B^2*a^52*b^16*d^7 + 76288*B^2*a^54*b^14*d^7 + 28416*B^2*a^56*b^12*d^7 + 6144*B^
2*a^58*b^10*d^7 + 576*B^2*a^60*b^8*d^7 - 1280*A*B*a^23*b^45*d^7 - 23040*A*B*a^25*b^43*d^7 - 196352*A*B*a^27*b^
41*d^7 - 1046016*A*B*a^29*b^39*d^7 - 3887616*A*B*a^31*b^37*d^7 - 10683904*A*B*a^33*b^35*d^7 - 22503936*A*B*a^3
5*b^33*d^7 - 37240320*A*B*a^37*b^31*d^7 - 49347584*A*B*a^39*b^29*d^7 - 53228032*A*B*a^41*b^27*d^7 - 47443968*A
*B*a^43*b^25*d^7 - 35389952*A*B*a^45*b^23*d^7 - 22224384*A*B*a^47*b^21*d^7 - 11665920*A*B*a^49*b^19*d^7 - 4988
416*A*B*a^51*b^17*d^7 - 1657344*A*B*a^53*b^15*d^7 - 397056*A*B*a^55*b^13*d^7 - 60416*A*B*a^57*b^11*d^7 - 4352*
A*B*a^59*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 - 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) - 800*A^3*a^21*b^45*d^6 - 10400*A^3*a^23*b^43*d^6 - 54400*A^3*a
^25*b^41*d^6 - 121600*A^3*a^27*b^39*d^6 + 90304*A^3*a^29*b^37*d^6 + 1465856*A^3*a^31*b^35*d^6 + 5014464*A^3*a^
33*b^33*d^6 + 10323456*A^3*a^35*b^31*d^6 + 14661504*A^3*a^37*b^29*d^6 + 14908608*A^3*a^39*b^27*d^6 + 10808512*
A^3*a^41*b^25*d^6 + 5328128*A^3*a^43*b^23*d^6 + 1531712*A^3*a^45*b^21*d^6 + 87808*A^3*a^47*b^19*d^6 - 85696*A^
3*a^49*b^17*d^6 - 6144*A^3*a^51*b^15*d^6 + 15264*A^3*a^53*b^13*d^6 + 5856*A^3*a^55*b^11*d^6 + 704*A^3*a^57*b^9
*d^6 + 384*B^3*a^24*b^42*d^6 + 7296*B^3*a^26*b^40*d^6 + 59424*B^3*a^28*b^38*d^6 + 280992*B^3*a^30*b^36*d^6 + 8
66208*B^3*a^32*b^34*d^6 + 1825824*B^3*a^34*b^32*d^6 + 2629536*B^3*a^36*b^30*d^6 + 2374944*B^3*a^38*b^28*d^6 +
727584*B^3*a^40*b^26*d^6 - 1413984*B^3*a^42*b^24*d^6 - 2649504*B^3*a^44*b^22*d^6 - 2454816*B^3*a^46*b^20*d^6 -
1476384*B^3*a^48*b^18*d^6 - 597408*B^3*a^50*b^16*d^6 - 156192*B^3*a^52*b^14*d^6 - 22944*B^3*a^54*b^12*d^6 - 1
056*B^3*a^56*b^10*d^6 + 96*B^3*a^58*b^8*d^6 - 2048*A*B^2*a^23*b^43*d^6 - 35456*A*B^2*a^25*b^41*d^6 - 269824*A*
B^2*a^27*b^39*d^6 - 1203648*A*B^2*a^29*b^37*d^6 - 3500672*A*B^2*a^31*b^35*d^6 - 6889792*A*B^2*a^33*b^33*d^6 -
8968960*A*B^2*a^35*b^31*d^6 - 6452160*A*B^2*a^37*b^29*d^6 + 933504*A*B^2*a^39*b^27*d^6 + 8721856*A*B^2*a^41*b^
25*d^6 + 11714560*A*B^2*a^43*b^23*d^6 + 9184448*A*B^2*a^45*b^21*d^6 + 4647552*A*B^2*a^47*b^19*d^6 + 1433152*A*
B^2*a^49*b^17*d^6 + 182528*A*B^2*a^51*b^15*d^6 - 37696*A*B^2*a^53*b^13*d^6 - 18048*A*B^2*a^55*b^11*d^6 - 2112*
A*B^2*a^57*b^9*d^6 + 3040*A^2*B*a^22*b^44*d^6 + 47200*A^2*B*a^24*b^42*d^6 + 325120*A^2*B*a^26*b^40*d^6 + 13043
52*A^2*B*a^28*b^38*d^6 + 3319840*A^2*B*a^30*b^36*d^6 + 5298720*A^2*B*a^32*b^34*d^6 + 4178720*A^2*B*a^34*b^32*d
^6 - 2452320*A^2*B*a^36*b^30*d^6 - 12167584*A^2*B*a^38*b^28*d^6 - 18281120*A^2*B*a^40*b^26*d^6 - 16496480*A^2*
B*a^42*b^24*d^6 - 9395360*A^2*B*a^44*b^22*d^6 - 2839200*A^2*B*a^46*b^20*d^6 + 167776*A^2*B*a^48*b^18*d^6 + 563
040*A^2*B*a^50*b^16*d^6 + 239840*A^2*B*a^52*b^14*d^6 + 45120*A^2*B*a^54*b^12*d^6 + 2240*A^2*B*a^56*b^10*d^6 -
288*A^2*B*a^58*b^8*d^6) + (a + b*tan(c + d*x))^(1/2)*(67232*A^4*a^27*b^36*d^5 - 3200*A^4*a^23*b^40*d^5 - 3200*
A^4*a^25*b^38*d^5 - 400*A^4*a^21*b^42*d^5 + 437248*A^4*a^29*b^34*d^5 + 1458912*A^4*a^31*b^32*d^5 + 3214848*A^4
*a^33*b^30*d^5 + 5065632*A^4*a^35*b^28*d^5 + 5898464*A^4*a^37*b^26*d^5 + 5129696*A^4*a^39*b^24*d^5 + 3313024*A
^4*a^41*b^22*d^5 + 1552096*A^4*a^43*b^20*d^5 + 500864*A^4*a^45*b^18*d^5 + 99232*A^4*a^47*b^16*d^5 + 8448*A^4*a
^49*b^14*d^5 - 288*A^4*a^51*b^12*d^5 + 48*A^4*a^53*b^10*d^5 + 32*A^4*a^55*b^8*d^5 + 64*B^4*a^23*b^40*d^5 + 512
*B^4*a^25*b^38*d^5 + 544*B^4*a^27*b^36*d^5 - 10304*B^4*a^29*b^34*d^5 - 66976*B^4*a^31*b^32*d^5 - 221312*B^4*a^
33*b^30*d^5 - 480480*B^4*a^35*b^28*d^5 - 741312*B^4*a^37*b^26*d^5 - 837408*B^4*a^39*b^24*d^5 - 695552*B^4*a^41
*b^22*d^5 - 416416*B^4*a^43*b^20*d^5 - 168896*B^4*a^45*b^18*d^5 - 37856*B^4*a^47*b^16*d^5 + 896*B^4*a^49*b^14*
d^5 + 3424*B^4*a^51*b^12*d^5 + 960*B^4*a^53*b^10*d^5 + 96*B^4*a^55*b^8*d^5 - 320*A*B^3*a^22*b^41*d^5 - 2048*A*
B^3*a^24*b^39*d^5 + 4096*A*B^3*a^26*b^37*d^5 + 93184*A*B^3*a^28*b^35*d^5 + 489216*A*B^3*a^30*b^33*d^5 + 149094
4*A*B^3*a^32*b^31*d^5 + 3075072*A*B^3*a^34*b^29*d^5 + 4539392*A*B^3*a^36*b^27*d^5 + 4887168*A*B^3*a^38*b^25*d^
5 + 3807232*A*B^3*a^40*b^23*d^5 + 2050048*A*B^3*a^42*b^21*d^5 + 652288*A*B^3*a^44*b^19*d^5 + 23296*A*B^3*a^46*
b^17*d^5 - 86016*A*B^3*a^48*b^15*d^5 - 41984*A*B^3*a^50*b^13*d^5 - 9216*A*B^3*a^52*b^11*d^5 - 832*A*B^3*a^54*b
^9*d^5 + 3520*A^3*B*a^22*b^41*d^5 + 44160*A^3*B*a^24*b^39*d^5 + 248960*A^3*B*a^26*b^37*d^5 + 819840*A^3*B*a^28
*b^35*d^5 + 1688960*A^3*B*a^30*b^33*d^5 + 2038400*A^3*B*a^32*b^31*d^5 + 640640*A^3*B*a^34*b^29*d^5 - 2654080*A
^3*B*a^36*b^27*d^5 - 6040320*A^3*B*a^38*b^25*d^5 - 7230080*A^3*B*a^40*b^23*d^5 - 5765760*A^3*B*a^42*b^21*d^5 -
3203200*A^3*B*a^44*b^19*d^5 - 1223040*A^3*B*a^46*b^17*d^5 - 300160*A^3*B*a^48*b^15*d^5 - 39040*A^3*B*a^50*b^1
3*d^5 - 640*A^3*B*a^52*b^11*d^5 + 320*A^3*B*a^54*b^9*d^5 + 400*A^2*B^2*a^21*b^42*d^5 + 576*A^2*B^2*a^23*b^40*d
^5 - 30592*A^2*B^2*a^25*b^38*d^5 - 264768*A^2*B^2*a^27*b^36*d^5 - 1124032*A^2*B^2*a^29*b^34*d^5 - 3011008*A^2*
B^2*a^31*b^32*d^5 - 5509504*A^2*B^2*a^33*b^30*d^5 - 7019584*A^2*B^2*a^35*b^28*d^5 - 5999136*A^2*B^2*a^37*b^26*
d^5 - 2809664*A^2*B^2*a^39*b^24*d^5 + 384384*A^2*B^2*a^41*b^22*d^5 + 1811264*A^2*B^2*a^43*b^20*d^5 + 1555008*A
^2*B^2*a^45*b^18*d^5 + 765632*A^2*B^2*a^47*b^16*d^5 + 234368*A^2*B^2*a^49*b^14*d^5 + 41792*A^2*B^2*a^51*b^12*d
^5 + 3344*A^2*B^2*a^53*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)*(90304*A^3*a^2
9*b^37*d^6 - 800*A^3*a^21*b^45*d^6 - 10400*A^3*a^23*b^43*d^6 - 54400*A^3*a^25*b^41*d^6 - 121600*A^3*a^27*b^39*
d^6 - ((-(((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 + 8
0*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^27*b^46*d^9
+ 9984*a^29*b^44*d^9 + 92160*a^31*b^42*d^9 + 535296*a^33*b^40*d^9 + 2193408*a^35*b^38*d^9 + 6736896*a^37*b^36*
d^9 + 16084992*a^39*b^34*d^9 + 30551040*a^41*b^32*d^9 + 46844928*a^43*b^30*d^9 + 58499584*a^45*b^28*d^9 + 5974
4256*a^47*b^26*d^9 + 49900032*a^49*b^24*d^9 + 33945600*a^51*b^22*d^9 + 18643968*a^53*b^20*d^9 + 8146944*a^55*b
^18*d^9 + 2767872*a^57*b^16*d^9 + 705024*a^59*b^14*d^9 + 126720*a^61*b^12*d^9 + 14336*a^63*b^10*d^9 + 768*a^65
*b^8*d^9) - 1280*A*a^24*b^47*d^8 - 24320*A*a^26*b^45*d^8 - 219008*A*a^28*b^43*d^8 - 1241984*A*a^30*b^41*d^8 -
4970496*A*a^32*b^39*d^8 - 14909440*A*a^34*b^37*d^8 - 34746880*A*a^36*b^35*d^8 - 64356864*A*a^38*b^33*d^8 - 960
92672*A*a^40*b^31*d^8 - 116633088*A*a^42*b^29*d^8 - 115498240*A*a^44*b^27*d^8 - 93267200*A*a^46*b^25*d^8 - 611
28704*A*a^48*b^23*d^8 - 32212992*A*a^50*b^21*d^8 - 13439488*A*a^52*b^19*d^8 - 4334080*A*a^54*b^17*d^8 - 104064
0*A*a^56*b^15*d^8 - 174848*A*a^58*b^13*d^8 - 18304*A*a^60*b^11*d^8 - 896*A*a^62*b^9*d^8 + 512*B*a^25*b^46*d^8
+ 9728*B*a^27*b^44*d^8 + 87936*B*a^29*b^42*d^8 + 502144*B*a^31*b^40*d^8 + 2028544*B*a^33*b^38*d^8 + 6153216*B*
a^35*b^36*d^8 + 14518784*B*a^37*b^34*d^8 + 27243008*B*a^39*b^32*d^8 + 41213952*B*a^41*b^30*d^8 + 50665472*B*a^
43*b^28*d^8 + 50775296*B*a^45*b^26*d^8 + 41443584*B*a^47*b^24*d^8 + 27409408*B*a^49*b^22*d^8 + 14543872*B*a^51
*b^20*d^8 + 6093312*B*a^53*b^18*d^8 + 1966592*B*a^55*b^16*d^8 + 470528*B*a^57*b^14*d^8 + 78336*B*a^59*b^12*d^8
+ 8064*B*a^61*b^10*d^8 + 384*B*a^63*b^8*d^8) - (a + b*tan(c + d*x))^(1/2)*(1600*A^2*a^22*b^46*d^7 + 28800*A^2
*a^24*b^44*d^7 + 244800*A^2*a^26*b^42*d^7 + 1304256*A^2*a^28*b^40*d^7 + 4880128*A^2*a^30*b^38*d^7 + 13627392*A
^2*a^32*b^36*d^7 + 29476608*A^2*a^34*b^34*d^7 + 50615552*A^2*a^36*b^32*d^7 + 70152576*A^2*a^38*b^30*d^7 + 7932
9536*A^2*a^40*b^28*d^7 + 73600384*A^2*a^42*b^26*d^7 + 56025216*A^2*a^44*b^24*d^7 + 34754304*A^2*a^46*b^22*d^7
+ 17296384*A^2*a^48*b^20*d^7 + 6713088*A^2*a^50*b^18*d^7 + 1934592*A^2*a^52*b^16*d^7 + 377408*A^2*a^54*b^14*d^
7 + 39552*A^2*a^56*b^12*d^7 + 64*A^2*a^58*b^10*d^7 - 320*A^2*a^60*b^8*d^7 + 256*B^2*a^24*b^44*d^7 + 4608*B^2*a
^26*b^42*d^7 + 40512*B^2*a^28*b^40*d^7 + 224768*B^2*a^30*b^38*d^7 + 864768*B^2*a^32*b^36*d^7 + 2419200*B^2*a^3
4*b^34*d^7 + 5055232*B^2*a^36*b^32*d^7 + 8007168*B^2*a^38*b^30*d^7 + 9664512*B^2*a^40*b^28*d^7 + 8859136*B^2*a
^42*b^26*d^7 + 6095232*B^2*a^44*b^24*d^7 + 3095040*B^2*a^46*b^22*d^7 + 1164800*B^2*a^48*b^20*d^7 + 376320*B^2*
a^50*b^18*d^7 + 154368*B^2*a^52*b^16*d^7 + 76288*B^2*a^54*b^14*d^7 + 28416*B^2*a^56*b^12*d^7 + 6144*B^2*a^58*b
^10*d^7 + 576*B^2*a^60*b^8*d^7 - 1280*A*B*a^23*b^45*d^7 - 23040*A*B*a^25*b^43*d^7 - 196352*A*B*a^27*b^41*d^7 -
1046016*A*B*a^29*b^39*d^7 - 3887616*A*B*a^31*b^37*d^7 - 10683904*A*B*a^33*b^35*d^7 - 22503936*A*B*a^35*b^33*d
^7 - 37240320*A*B*a^37*b^31*d^7 - 49347584*A*B*a^39*b^29*d^7 - 53228032*A*B*a^41*b^27*d^7 - 47443968*A*B*a^43*
b^25*d^7 - 35389952*A*B*a^45*b^23*d^7 - 22224384*A*B*a^47*b^21*d^7 - 11665920*A*B*a^49*b^19*d^7 - 4988416*A*B*
a^51*b^17*d^7 - 1657344*A*B*a^53*b^15*d^7 - 397056*A*B*a^55*b^13*d^7 - 60416*A*B*a^57*b^11*d^7 - 4352*A*B*a^59
*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 + 1
0*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2) + 1465856*A^3*a^31*b^35*d^6 + 5014464*A^3*a^33*b^33*d^6 + 10323456*A^3*
a^35*b^31*d^6 + 14661504*A^3*a^37*b^29*d^6 + 14908608*A^3*a^39*b^27*d^6 + 10808512*A^3*a^41*b^25*d^6 + 5328128
*A^3*a^43*b^23*d^6 + 1531712*A^3*a^45*b^21*d^6 + 87808*A^3*a^47*b^19*d^6 - 85696*A^3*a^49*b^17*d^6 - 6144*A^3*
a^51*b^15*d^6 + 15264*A^3*a^53*b^13*d^6 + 5856*A^3*a^55*b^11*d^6 + 704*A^3*a^57*b^9*d^6 + 384*B^3*a^24*b^42*d^
6 + 7296*B^3*a^26*b^40*d^6 + 59424*B^3*a^28*b^38*d^6 + 280992*B^3*a^30*b^36*d^6 + 866208*B^3*a^32*b^34*d^6 + 1
825824*B^3*a^34*b^32*d^6 + 2629536*B^3*a^36*b^30*d^6 + 2374944*B^3*a^38*b^28*d^6 + 727584*B^3*a^40*b^26*d^6 -
1413984*B^3*a^42*b^24*d^6 - 2649504*B^3*a^44*b^22*d^6 - 2454816*B^3*a^46*b^20*d^6 - 1476384*B^3*a^48*b^18*d^6
- 597408*B^3*a^50*b^16*d^6 - 156192*B^3*a^52*b^14*d^6 - 22944*B^3*a^54*b^12*d^6 - 1056*B^3*a^56*b^10*d^6 + 96*
B^3*a^58*b^8*d^6 - 2048*A*B^2*a^23*b^43*d^6 - 35456*A*B^2*a^25*b^41*d^6 - 269824*A*B^2*a^27*b^39*d^6 - 1203648
*A*B^2*a^29*b^37*d^6 - 3500672*A*B^2*a^31*b^35*d^6 - 6889792*A*B^2*a^33*b^33*d^6 - 8968960*A*B^2*a^35*b^31*d^6
- 6452160*A*B^2*a^37*b^29*d^6 + 933504*A*B^2*a^39*b^27*d^6 + 8721856*A*B^2*a^41*b^25*d^6 + 11714560*A*B^2*a^4
3*b^23*d^6 + 9184448*A*B^2*a^45*b^21*d^6 + 4647552*A*B^2*a^47*b^19*d^6 + 1433152*A*B^2*a^49*b^17*d^6 + 182528*
A*B^2*a^51*b^15*d^6 - 37696*A*B^2*a^53*b^13*d^6 - 18048*A*B^2*a^55*b^11*d^6 - 2112*A*B^2*a^57*b^9*d^6 + 3040*A
^2*B*a^22*b^44*d^6 + 47200*A^2*B*a^24*b^42*d^6 + 325120*A^2*B*a^26*b^40*d^6 + 1304352*A^2*B*a^28*b^38*d^6 + 33
19840*A^2*B*a^30*b^36*d^6 + 5298720*A^2*B*a^32*b^34*d^6 + 4178720*A^2*B*a^34*b^32*d^6 - 2452320*A^2*B*a^36*b^3
0*d^6 - 12167584*A^2*B*a^38*b^28*d^6 - 18281120*A^2*B*a^40*b^26*d^6 - 16496480*A^2*B*a^42*b^24*d^6 - 9395360*A
^2*B*a^44*b^22*d^6 - 2839200*A^2*B*a^46*b^20*d^6 + 167776*A^2*B*a^48*b^18*d^6 + 563040*A^2*B*a^50*b^16*d^6 + 2
39840*A^2*B*a^52*b^14*d^6 + 45120*A^2*B*a^54*b^12*d^6 + 2240*A^2*B*a^56*b^10*d^6 - 288*A^2*B*a^58*b^8*d^6) - (
a + b*tan(c + d*x))^(1/2)*(67232*A^4*a^27*b^36*d^5 - 3200*A^4*a^23*b^40*d^5 - 3200*A^4*a^25*b^38*d^5 - 400*A^4
*a^21*b^42*d^5 + 437248*A^4*a^29*b^34*d^5 + 1458912*A^4*a^31*b^32*d^5 + 3214848*A^4*a^33*b^30*d^5 + 5065632*A^
4*a^35*b^28*d^5 + 5898464*A^4*a^37*b^26*d^5 + 5129696*A^4*a^39*b^24*d^5 + 3313024*A^4*a^41*b^22*d^5 + 1552096*
A^4*a^43*b^20*d^5 + 500864*A^4*a^45*b^18*d^5 + 99232*A^4*a^47*b^16*d^5 + 8448*A^4*a^49*b^14*d^5 - 288*A^4*a^51
*b^12*d^5 + 48*A^4*a^53*b^10*d^5 + 32*A^4*a^55*b^8*d^5 + 64*B^4*a^23*b^40*d^5 + 512*B^4*a^25*b^38*d^5 + 544*B^
4*a^27*b^36*d^5 - 10304*B^4*a^29*b^34*d^5 - 66976*B^4*a^31*b^32*d^5 - 221312*B^4*a^33*b^30*d^5 - 480480*B^4*a^
35*b^28*d^5 - 741312*B^4*a^37*b^26*d^5 - 837408*B^4*a^39*b^24*d^5 - 695552*B^4*a^41*b^22*d^5 - 416416*B^4*a^43
*b^20*d^5 - 168896*B^4*a^45*b^18*d^5 - 37856*B^4*a^47*b^16*d^5 + 896*B^4*a^49*b^14*d^5 + 3424*B^4*a^51*b^12*d^
5 + 960*B^4*a^53*b^10*d^5 + 96*B^4*a^55*b^8*d^5 - 320*A*B^3*a^22*b^41*d^5 - 2048*A*B^3*a^24*b^39*d^5 + 4096*A*
B^3*a^26*b^37*d^5 + 93184*A*B^3*a^28*b^35*d^5 + 489216*A*B^3*a^30*b^33*d^5 + 1490944*A*B^3*a^32*b^31*d^5 + 307
5072*A*B^3*a^34*b^29*d^5 + 4539392*A*B^3*a^36*b^27*d^5 + 4887168*A*B^3*a^38*b^25*d^5 + 3807232*A*B^3*a^40*b^23
*d^5 + 2050048*A*B^3*a^42*b^21*d^5 + 652288*A*B^3*a^44*b^19*d^5 + 23296*A*B^3*a^46*b^17*d^5 - 86016*A*B^3*a^48
*b^15*d^5 - 41984*A*B^3*a^50*b^13*d^5 - 9216*A*B^3*a^52*b^11*d^5 - 832*A*B^3*a^54*b^9*d^5 + 3520*A^3*B*a^22*b^
41*d^5 + 44160*A^3*B*a^24*b^39*d^5 + 248960*A^3*B*a^26*b^37*d^5 + 819840*A^3*B*a^28*b^35*d^5 + 1688960*A^3*B*a
^30*b^33*d^5 + 2038400*A^3*B*a^32*b^31*d^5 + 640640*A^3*B*a^34*b^29*d^5 - 2654080*A^3*B*a^36*b^27*d^5 - 604032
0*A^3*B*a^38*b^25*d^5 - 7230080*A^3*B*a^40*b^23*d^5 - 5765760*A^3*B*a^42*b^21*d^5 - 3203200*A^3*B*a^44*b^19*d^
5 - 1223040*A^3*B*a^46*b^17*d^5 - 300160*A^3*B*a^48*b^15*d^5 - 39040*A^3*B*a^50*b^13*d^5 - 640*A^3*B*a^52*b^11
*d^5 + 320*A^3*B*a^54*b^9*d^5 + 400*A^2*B^2*a^21*b^42*d^5 + 576*A^2*B^2*a^23*b^40*d^5 - 30592*A^2*B^2*a^25*b^3
8*d^5 - 264768*A^2*B^2*a^27*b^36*d^5 - 1124032*A^2*B^2*a^29*b^34*d^5 - 3011008*A^2*B^2*a^31*b^32*d^5 - 5509504
*A^2*B^2*a^33*b^30*d^5 - 7019584*A^2*B^2*a^35*b^28*d^5 - 5999136*A^2*B^2*a^37*b^26*d^5 - 2809664*A^2*B^2*a^39*
b^24*d^5 + 384384*A^2*B^2*a^41*b^22*d^5 + 1811264*A^2*B^2*a^43*b^20*d^5 + 1555008*A^2*B^2*a^45*b^18*d^5 + 7656
32*A^2*B^2*a^47*b^16*d^5 + 234368*A^2*B^2*a^49*b^14*d^5 + 41792*A^2*B^2*a^51*b^12*d^5 + 3344*A^2*B^2*a^53*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)/(800*A^5*a^22*b^39*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)*(90304*A^3*a^29*b
^37*d^6 - 800*A^3*a^21*b^45*d^6 - 10400*A^3*a^23*b^43*d^6 - 54400*A^3*a^25*b^41*d^6 - 121600*A^3*a^27*b^39*d^6
- ((-(((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 + 16
0*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^27*b^46*d^9 + 9
984*a^29*b^44*d^9 + 92160*a^31*b^42*d^9 + 535296*a^33*b^40*d^9 + 2193408*a^35*b^38*d^9 + 6736896*a^37*b^36*d^9
+ 16084992*a^39*b^34*d^9 + 30551040*a^41*b^32*d^9 + 46844928*a^43*b^30*d^9 + 58499584*a^45*b^28*d^9 + 5974425
6*a^47*b^26*d^9 + 49900032*a^49*b^24*d^9 + 33945600*a^51*b^22*d^9 + 18643968*a^53*b^20*d^9 + 8146944*a^55*b^18
*d^9 + 2767872*a^57*b^16*d^9 + 705024*a^59*b^14*d^9 + 126720*a^61*b^12*d^9 + 14336*a^63*b^10*d^9 + 768*a^65*b^
8*d^9) - 1280*A*a^24*b^47*d^8 - 24320*A*a^26*b^45*d^8 - 219008*A*a^28*b^43*d^8 - 1241984*A*a^30*b^41*d^8 - 497
0496*A*a^32*b^39*d^8 - 14909440*A*a^34*b^37*d^8 - 34746880*A*a^36*b^35*d^8 - 64356864*A*a^38*b^33*d^8 - 960926
72*A*a^40*b^31*d^8 - 116633088*A*a^42*b^29*d^8 - 115498240*A*a^44*b^27*d^8 - 93267200*A*a^46*b^25*d^8 - 611287
04*A*a^48*b^23*d^8 - 32212992*A*a^50*b^21*d^8 - 13439488*A*a^52*b^19*d^8 - 4334080*A*a^54*b^17*d^8 - 1040640*A
*a^56*b^15*d^8 - 174848*A*a^58*b^13*d^8 - 18304*A*a^60*b^11*d^8 - 896*A*a^62*b^9*d^8 + 512*B*a^25*b^46*d^8 + 9
728*B*a^27*b^44*d^8 + 87936*B*a^29*b^42*d^8 + 502144*B*a^31*b^40*d^8 + 2028544*B*a^33*b^38*d^8 + 6153216*B*a^3
5*b^36*d^8 + 14518784*B*a^37*b^34*d^8 + 27243008*B*a^39*b^32*d^8 + 41213952*B*a^41*b^30*d^8 + 50665472*B*a^43*
b^28*d^8 + 50775296*B*a^45*b^26*d^8 + 41443584*B*a^47*b^24*d^8 + 27409408*B*a^49*b^22*d^8 + 14543872*B*a^51*b^
20*d^8 + 6093312*B*a^53*b^18*d^8 + 1966592*B*a^55*b^16*d^8 + 470528*B*a^57*b^14*d^8 + 78336*B*a^59*b^12*d^8 +
8064*B*a^61*b^10*d^8 + 384*B*a^63*b^8*d^8) - (a + b*tan(c + d*x))^(1/2)*(1600*A^2*a^22*b^46*d^7 + 28800*A^2*a^
24*b^44*d^7 + 244800*A^2*a^26*b^42*d^7 + 1304256*A^2*a^28*b^40*d^7 + 4880128*A^2*a^30*b^38*d^7 + 13627392*A^2*
a^32*b^36*d^7 + 29476608*A^2*a^34*b^34*d^7 + 50615552*A^2*a^36*b^32*d^7 + 70152576*A^2*a^38*b^30*d^7 + 7932953
6*A^2*a^40*b^28*d^7 + 73600384*A^2*a^42*b^26*d^7 + 56025216*A^2*a^44*b^24*d^7 + 34754304*A^2*a^46*b^22*d^7 + 1
7296384*A^2*a^48*b^20*d^7 + 6713088*A^2*a^50*b^18*d^7 + 1934592*A^2*a^52*b^16*d^7 + 377408*A^2*a^54*b^14*d^7 +
39552*A^2*a^56*b^12*d^7 + 64*A^2*a^58*b^10*d^7 - 320*A^2*a^60*b^8*d^7 + 256*B^2*a^24*b^44*d^7 + 4608*B^2*a^26
*b^42*d^7 + 40512*B^2*a^28*b^40*d^7 + 224768*B^2*a^30*b^38*d^7 + 864768*B^2*a^32*b^36*d^7 + 2419200*B^2*a^34*b
^34*d^7 + 5055232*B^2*a^36*b^32*d^7 + 8007168*B^2*a^38*b^30*d^7 + 9664512*B^2*a^40*b^28*d^7 + 8859136*B^2*a^42
*b^26*d^7 + 6095232*B^2*a^44*b^24*d^7 + 3095040*B^2*a^46*b^22*d^7 + 1164800*B^2*a^48*b^20*d^7 + 376320*B^2*a^5
0*b^18*d^7 + 154368*B^2*a^52*b^16*d^7 + 76288*B^2*a^54*b^14*d^7 + 28416*B^2*a^56*b^12*d^7 + 6144*B^2*a^58*b^10
*d^7 + 576*B^2*a^60*b^8*d^7 - 1280*A*B*a^23*b^45*d^7 - 23040*A*B*a^25*b^43*d^7 - 196352*A*B*a^27*b^41*d^7 - 10
46016*A*B*a^29*b^39*d^7 - 3887616*A*B*a^31*b^37*d^7 - 10683904*A*B*a^33*b^35*d^7 - 22503936*A*B*a^35*b^33*d^7
- 37240320*A*B*a^37*b^31*d^7 - 49347584*A*B*a^39*b^29*d^7 - 53228032*A*B*a^41*b^27*d^7 - 47443968*A*B*a^43*b^2
5*d^7 - 35389952*A*B*a^45*b^23*d^7 - 22224384*A*B*a^47*b^21*d^7 - 11665920*A*B*a^49*b^19*d^7 - 4988416*A*B*a^5
1*b^17*d^7 - 1657344*A*B*a^53*b^15*d^7 - 397056*A*B*a^55*b^13*d^7 - 60416*A*B*a^57*b^11*d^7 - 4352*A*B*a^59*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) + 1465856*A^3*a^31*b^35*d^6 + 5014464*A^3*a^33*b^33*d^6 + 10323456*A^3*a^3
5*b^31*d^6 + 14661504*A^3*a^37*b^29*d^6 + 14908608*A^3*a^39*b^27*d^6 + 10808512*A^3*a^41*b^25*d^6 + 5328128*A^
3*a^43*b^23*d^6 + 1531712*A^3*a^45*b^21*d^6 + 87808*A^3*a^47*b^19*d^6 - 85696*A^3*a^49*b^17*d^6 - 6144*A^3*a^5
1*b^15*d^6 + 15264*A^3*a^53*b^13*d^6 + 5856*A^3*a^55*b^11*d^6 + 704*A^3*a^57*b^9*d^6 + 384*B^3*a^24*b^42*d^6 +
7296*B^3*a^26*b^40*d^6 + 59424*B^3*a^28*b^38*d^6 + 280992*B^3*a^30*b^36*d^6 + 866208*B^3*a^32*b^34*d^6 + 1825
824*B^3*a^34*b^32*d^6 + 2629536*B^3*a^36*b^30*d^6 + 2374944*B^3*a^38*b^28*d^6 + 727584*B^3*a^40*b^26*d^6 - 141
3984*B^3*a^42*b^24*d^6 - 2649504*B^3*a^44*b^22*d^6 - 2454816*B^3*a^46*b^20*d^6 - 1476384*B^3*a^48*b^18*d^6 - 5
97408*B^3*a^50*b^16*d^6 - 156192*B^3*a^52*b^14*d^6 - 22944*B^3*a^54*b^12*d^6 - 1056*B^3*a^56*b^10*d^6 + 96*B^3
*a^58*b^8*d^6 - 2048*A*B^2*a^23*b^43*d^6 - 35456*A*B^2*a^25*b^41*d^6 - 269824*A*B^2*a^27*b^39*d^6 - 1203648*A*
B^2*a^29*b^37*d^6 - 3500672*A*B^2*a^31*b^35*d^6 - 6889792*A*B^2*a^33*b^33*d^6 - 8968960*A*B^2*a^35*b^31*d^6 -
6452160*A*B^2*a^37*b^29*d^6 + 933504*A*B^2*a^39*b^27*d^6 + 8721856*A*B^2*a^41*b^25*d^6 + 11714560*A*B^2*a^43*b
^23*d^6 + 9184448*A*B^2*a^45*b^21*d^6 + 4647552*A*B^2*a^47*b^19*d^6 + 1433152*A*B^2*a^49*b^17*d^6 + 182528*A*B
^2*a^51*b^15*d^6 - 37696*A*B^2*a^53*b^13*d^6 - 18048*A*B^2*a^55*b^11*d^6 - 2112*A*B^2*a^57*b^9*d^6 + 3040*A^2*
B*a^22*b^44*d^6 + 47200*A^2*B*a^24*b^42*d^6 + 325120*A^2*B*a^26*b^40*d^6 + 1304352*A^2*B*a^28*b^38*d^6 + 33198
40*A^2*B*a^30*b^36*d^6 + 5298720*A^2*B*a^32*b^34*d^6 + 4178720*A^2*B*a^34*b^32*d^6 - 2452320*A^2*B*a^36*b^30*d
^6 - 12167584*A^2*B*a^38*b^28*d^6 - 18281120*A^2*B*a^40*b^26*d^6 - 16496480*A^2*B*a^42*b^24*d^6 - 9395360*A^2*
B*a^44*b^22*d^6 - 2839200*A^2*B*a^46*b^20*d^6 + 167776*A^2*B*a^48*b^18*d^6 + 563040*A^2*B*a^50*b^16*d^6 + 2398
40*A^2*B*a^52*b^14*d^6 + 45120*A^2*B*a^54*b^12*d^6 + 2240*A^2*B*a^56*b^10*d^6 - 288*A^2*B*a^58*b^8*d^6) - (a +
b*tan(c + d*x))^(1/2)*(67232*A^4*a^27*b^36*d^5 - 3200*A^4*a^23*b^40*d^5 - 3200*A^4*a^25*b^38*d^5 - 400*A^4*a^
21*b^42*d^5 + 437248*A^4*a^29*b^34*d^5 + 1458912*A^4*a^31*b^32*d^5 + 3214848*A^4*a^33*b^30*d^5 + 5065632*A^4*a
^35*b^28*d^5 + 5898464*A^4*a^37*b^26*d^5 + 5129696*A^4*a^39*b^24*d^5 + 3313024*A^4*a^41*b^22*d^5 + 1552096*A^4
*a^43*b^20*d^5 + 500864*A^4*a^45*b^18*d^5 + 99232*A^4*a^47*b^16*d^5 + 8448*A^4*a^49*b^14*d^5 - 288*A^4*a^51*b^
12*d^5 + 48*A^4*a^53*b^10*d^5 + 32*A^4*a^55*b^8*d^5 + 64*B^4*a^23*b^40*d^5 + 512*B^4*a^25*b^38*d^5 + 544*B^4*a
^27*b^36*d^5 - 10304*B^4*a^29*b^34*d^5 - 66976*B^4*a^31*b^32*d^5 - 221312*B^4*a^33*b^30*d^5 - 480480*B^4*a^35*
b^28*d^5 - 741312*B^4*a^37*b^26*d^5 - 837408*B^4*a^39*b^24*d^5 - 695552*B^4*a^41*b^22*d^5 - 416416*B^4*a^43*b^
20*d^5 - 168896*B^4*a^45*b^18*d^5 - 37856*B^4*a^47*b^16*d^5 + 896*B^4*a^49*b^14*d^5 + 3424*B^4*a^51*b^12*d^5 +
960*B^4*a^53*b^10*d^5 + 96*B^4*a^55*b^8*d^5 - 320*A*B^3*a^22*b^41*d^5 - 2048*A*B^3*a^24*b^39*d^5 + 4096*A*B^3
*a^26*b^37*d^5 + 93184*A*B^3*a^28*b^35*d^5 + 489216*A*B^3*a^30*b^33*d^5 + 1490944*A*B^3*a^32*b^31*d^5 + 307507
2*A*B^3*a^34*b^29*d^5 + 4539392*A*B^3*a^36*b^27*d^5 + 4887168*A*B^3*a^38*b^25*d^5 + 3807232*A*B^3*a^40*b^23*d^
5 + 2050048*A*B^3*a^42*b^21*d^5 + 652288*A*B^3*a^44*b^19*d^5 + 23296*A*B^3*a^46*b^17*d^5 - 86016*A*B^3*a^48*b^
15*d^5 - 41984*A*B^3*a^50*b^13*d^5 - 9216*A*B^3*a^52*b^11*d^5 - 832*A*B^3*a^54*b^9*d^5 + 3520*A^3*B*a^22*b^41*
d^5 + 44160*A^3*B*a^24*b^39*d^5 + 248960*A^3*B*a^26*b^37*d^5 + 819840*A^3*B*a^28*b^35*d^5 + 1688960*A^3*B*a^30
*b^33*d^5 + 2038400*A^3*B*a^32*b^31*d^5 + 640640*A^3*B*a^34*b^29*d^5 - 2654080*A^3*B*a^36*b^27*d^5 - 6040320*A
^3*B*a^38*b^25*d^5 - 7230080*A^3*B*a^40*b^23*d^5 - 5765760*A^3*B*a^42*b^21*d^5 - 3203200*A^3*B*a^44*b^19*d^5 -
1223040*A^3*B*a^46*b^17*d^5 - 300160*A^3*B*a^48*b^15*d^5 - 39040*A^3*B*a^50*b^13*d^5 - 640*A^3*B*a^52*b^11*d^
5 + 320*A^3*B*a^54*b^9*d^5 + 400*A^2*B^2*a^21*b^42*d^5 + 576*A^2*B^2*a^23*b^40*d^5 - 30592*A^2*B^2*a^25*b^38*d
^5 - 264768*A^2*B^2*a^27*b^36*d^5 - 1124032*A^2*B^2*a^29*b^34*d^5 - 3011008*A^2*B^2*a^31*b^32*d^5 - 5509504*A^
2*B^2*a^33*b^30*d^5 - 7019584*A^2*B^2*a^35*b^28*d^5 - 5999136*A^2*B^2*a^37*b^26*d^5 - 2809664*A^2*B^2*a^39*b^2
4*d^5 + 384384*A^2*B^2*a^41*b^22*d^5 + 1811264*A^2*B^2*a^43*b^20*d^5 + 1555008*A^2*B^2*a^45*b^18*d^5 + 765632*
A^2*B^2*a^47*b^16*d^5 + 234368*A^2*B^2*a^49*b^14*d^5 + 41792*A^2*B^2*a^51*b^12*d^5 + 3344*A^2*B^2*a^53*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) - ((-(((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)*(((-(((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 + 1
0*a^6*b^4*d^4 + 5*a^8*b^2*d^4)))^(1/2)*(512*a^27*b^46*d^9 + 9984*a^29*b^44*d^9 + 92160*a^31*b^42*d^9 + 535296*
a^33*b^40*d^9 + 2193408*a^35*b^38*d^9 + 6736896*a^37*b^36*d^9 + 16084992*a^39*b^34*d^9 + 30551040*a^41*b^32*d^
9 + 46844928*a^43*b^30*d^9 + 58499584*a^45*b^28*d^9 + 59744256*a^47*b^26*d^9 + 49900032*a^49*b^24*d^9 + 339456
00*a^51*b^22*d^9 + 18643968*a^53*b^20*d^9 + 8146944*a^55*b^18*d^9 + 2767872*a^57*b^16*d^9 + 705024*a^59*b^14*d
^9 + 126720*a^61*b^12*d^9 + 14336*a^63*b^10*d^9 + 768*a^65*b^8*d^9) + 1280*A*a^24*b^47*d^8 + 24320*A*a^26*b^45
*d^8 + 219008*A*a^28*b^43*d^8 + 1241984*A*a^30*b^41*d^8 + 4970496*A*a^32*b^39*d^8 + 14909440*A*a^34*b^37*d^8 +
34746880*A*a^36*b^35*d^8 + 64356864*A*a^38*b^33*d^8 + 96092672*A*a^40*b^31*d^8 + 116633088*A*a^42*b^29*d^8 +
115498240*A*a^44*b^27*d^8 + 93267200*A*a^46*b^25*d^8 + 61128704*A*a^48*b^23*d^8 + 32212992*A*a^50*b^21*d^8 + 1
3439488*A*a^52*b^19*d^8 + 4334080*A*a^54*b^17*d^8 + 1040640*A*a^56*b^15*d^8 + 174848*A*a^58*b^13*d^8 + 18304*A
*a^60*b^11*d^8 + 896*A*a^62*b^9*d^8 - 512*B*a^25*b^46*d^8 - 9728*B*a^27*b^44*d^8 - 87936*B*a^29*b^42*d^8 - 502
144*B*a^31*b^40*d^8 - 2028544*B*a^33*b^38*d^8 - 6153216*B*a^35*b^36*d^8 - 14518784*B*a^37*b^34*d^8 - 27243008*
B*a^39*b^32*d^8 - 41213952*B*a^41*b^30*d^8 - 50665472*B*a^43*b^28*d^8 - 50775296*B*a^45*b^26*d^8 - 41443584*B*
a^47*b^24*d^8 - 27409408*B*a^49*b^22*d^8 - 14543872*B*a^51*b^20*d^8 - 6093312*B*a^53*b^18*d^8 - 1966592*B*a^55
*b^16*d^8 - 470528*B*a^57*b^14*d^8 - 78336*B*a^59*b^12*d^8 - 8064*B*a^61*b^10*d^8 - 384*B*a^63*b^8*d^8) - (a +
b*tan(c + d*x))^(1/2)*(1600*A^2*a^22*b^46*d^7 + 28800*A^2*a^24*b^44*d^7 + 244800*A^2*a^26*b^42*d^7 + 1304256*
A^2*a^28*b^40*d^7 + 4880128*A^2*a^30*b^38*d^7 + 13627392*A^2*a^32*b^36*d^7 + 29476608*A^2*a^34*b^34*d^7 + 5061
5552*A^2*a^36*b^32*d^7 + 70152576*A^2*a^38*b^30*d^7 + 79329536*A^2*a^40*b^28*d^7 + 73600384*A^2*a^42*b^26*d^7
+ 56025216*A^2*a^44*b^24*d^7 + 34754304*A^2*a^46*b^22*d^7 + 17296384*A^2*a^48*b^20*d^7 + 6713088*A^2*a^50*b^18
*d^7 + 1934592*A^2*a^52*b^16*d^7 + 377408*A^2*a^54*b^14*d^7 + 39552*A^2*a^56*b^12*d^7 + 64*A^2*a^58*b^10*d^7 -
320*A^2*a^60*b^8*d^7 + 256*B^2*a^24*b^44*d^7 + 4608*B^2*a^26*b^42*d^7 + 40512*B^2*a^28*b^40*d^7 + 224768*B^2*
a^30*b^38*d^7 + 864768*B^2*a^32*b^36*d^7 + 2419200*B^2*a^34*b^34*d^7 + 5055232*B^2*a^36*b^32*d^7 + 8007168*B^2
*a^38*b^30*d^7 + 9664512*B^2*a^40*b^28*d^7 + 8859136*B^2*a^42*b^26*d^7 + 6095232*B^2*a^44*b^24*d^7 + 3095040*B
^2*a^46*b^22*d^7 + 1164800*B^2*a^48*b^20*d^7 + 376320*B^2*a^50*b^18*d^7 + 154368*B^2*a^52*b^16*d^7 + 76288*B^2
*a^54*b^14*d^7 + 28416*B^2*a^56*b^12*d^7 + 6144*B^2*a^58*b^10*d^7 + 576*B^2*a^60*b^8*d^7 - 1280*A*B*a^23*b^45*
d^7 - 23040*A*B*a^25*b^43*d^7 - 196352*A*B*a^27*b^41*d^7 - 1046016*A*B*a^29*b^39*d^7 - 3887616*A*B*a^31*b^37*d
^7 - 10683904*A*B*a^33*b^35*d^7 - 22503936*A*B*a^35*b^33*d^7 - 37240320*A*B*a^37*b^31*d^7 - 49347584*A*B*a^39*
b^29*d^7 - 53228032*A*B*a^41*b^27*d^7 - 47443968*A*B*a^43*b^25*d^7 - 35389952*A*B*a^45*b^23*d^7 - 22224384*A*B
*a^47*b^21*d^7 - 11665920*A*B*a^49*b^19*d^7 - 4988416*A*B*a^51*b^17*d^7 - 1657344*A*B*a^53*b^15*d^7 - 397056*A
*B*a^55*b^13*d^7 - 60416*A*B*a^57*b^11*d^7 - 4352*A*B*a^59*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) - 800*A^3*a^2
1*b^45*d^6 - 10400*A^3*a^23*b^43*d^6 - 54400*A^3*a^25*b^41*d^6 - 121600*A^3*a^27*b^39*d^6 + 90304*A^3*a^29*b^3
7*d^6 + 1465856*A^3*a^31*b^35*d^6 + 5014464*A^3*a^33*b^33*d^6 + 10323456*A^3*a^35*b^31*d^6 + 14661504*A^3*a^37
*b^29*d^6 + 14908608*A^3*a^39*b^27*d^6 + 10808512*A^3*a^41*b^25*d^6 + 5328128*A^3*a^43*b^23*d^6 + 1531712*A^3*
a^45*b^21*d^6 + 87808*A^3*a^47*b^19*d^6 - 85696*A^3*a^49*b^17*d^6 - 6144*A^3*a^51*b^15*d^6 + 15264*A^3*a^53*b^
13*d^6 + 5856*A^3*a^55*b^11*d^6 + 704*A^3*a^57*b^9*d^6 + 384*B^3*a^24*b^42*d^6 + 7296*B^3*a^26*b^40*d^6 + 5942
4*B^3*a^28*b^38*d^6 + 280992*B^3*a^30*b^36*d^6 + 866208*B^3*a^32*b^34*d^6 + 1825824*B^3*a^34*b^32*d^6 + 262953
6*B^3*a^36*b^30*d^6 + 2374944*B^3*a^38*b^28*d^6 + 727584*B^3*a^40*b^26*d^6 - 1413984*B^3*a^42*b^24*d^6 - 26495
04*B^3*a^44*b^22*d^6 - 2454816*B^3*a^46*b^20*d^6 - 1476384*B^3*a^48*b^18*d^6 - 597408*B^3*a^50*b^16*d^6 - 1561
92*B^3*a^52*b^14*d^6 - 22944*B^3*a^54*b^12*d^6 - 1056*B^3*a^56*b^10*d^6 + 96*B^3*a^58*b^8*d^6 - 2048*A*B^2*a^2
3*b^43*d^6 - 35456*A*B^2*a^25*b^41*d^6 - 269824*A*B^2*a^27*b^39*d^6 - 1203648*A*B^2*a^29*b^37*d^6 - 3500672*A*
B^2*a^31*b^35*d^6 - 6889792*A*B^2*a^33*b^33*d^6 - 8968960*A*B^2*a^35*b^31*d^6 - 6452160*A*B^2*a^37*b^29*d^6 +
933504*A*B^2*a^39*b^27*d^6 + 8721856*A*B^2*a^41*b^25*d^6 + 11714560*A*B^2*a^43*b^23*d^6 + 9184448*A*B^2*a^45*b
^21*d^6 + 4647552*A*B^2*a^47*b^19*d^6 + 1433152*A*B^2*a^49*b^17*d^6 + 182528*A*B^2*a^51*b^15*d^6 - 37696*A*B^2
*a^53*b^13*d^6 - 18048*A*B^2*a^55*b^11*d^6 - 2112*A*B^2*a^57*b^9*d^6 + 3040*A^2*B*a^22*b^44*d^6 + 47200*A^2*B*
a^24*b^42*d^6 + 325120*A^2*B*a^26*b^40*d^6 + 1304352*A^2*B*a^28*b^38*d^6 + 3319840*A^2*B*a^30*b^36*d^6 + 52987
20*A^2*B*a^32*b^34*d^6 + 4178720*A^2*B*a^34*b^32*d^6 - 2452320*A^2*B*a^36*b^30*d^6 - 12167584*A^2*B*a^38*b^28*
d^6 - 18281120*A^2*B*a^40*b^26*d^6 - 16496480*A^2*B*a^42*b^24*d^6 - 9395360*A^2*B*a^44*b^22*d^6 - 2839200*A^2*
B*a^46*b^20*d^6 + 167776*A^2*B*a^48*b^18*d^6 + 563040*A^2*B*a^50*b^16*d^6 + 239840*A^2*B*a^52*b^14*d^6 + 45120
*A^2*B*a^54*b^12*d^6 + 2240*A^2*B*a^56*b^10*d^6 - 288*A^2*B*a^58*b^8*d^6) + (a + b*tan(c + d*x))^(1/2)*(67232*
A^4*a^27*b^36*d^5 - 3200*A^4*a^23*b^40*d^5 - 3200*A^4*a^25*b^38*d^5 - 400*A^4*a^21*b^42*d^5 + 437248*A^4*a^29*
b^34*d^5 + 1458912*A^4*a^31*b^32*d^5 + 3214848*A^4*a^33*b^30*d^5 + 5065632*A^4*a^35*b^28*d^5 + 5898464*A^4*a^3
7*b^26*d^5 + 5129696*A^4*a^39*b^24*d^5 + 3313024*A^4*a^41*b^22*d^5 + 1552096*A^4*a^43*b^20*d^5 + 500864*A^4*a^
45*b^18*d^5 + 99232*A^4*a^47*b^16*d^5 + 8448*A^4*a^49*b^14*d^5 - 288*A^4*a^51*b^12*d^5 + 48*A^4*a^53*b^10*d^5
+ 32*A^4*a^55*b^8*d^5 + 64*B^4*a^23*b^40*d^5 + 512*B^4*a^25*b^38*d^5 + 544*B^4*a^27*b^36*d^5 - 10304*B^4*a^29*
b^34*d^5 - 66976*B^4*a^31*b^32*d^5 - 221312*B^4*a^33*b^30*d^5 - 480480*B^4*a^35*b^28*d^5 - 741312*B^4*a^37*b^2
6*d^5 - 837408*B^4*a^39*b^24*d^5 - 695552*B^4*a^41*b^22*d^5 - 416416*B^4*a^43*b^20*d^5 - 168896*B^4*a^45*b^18*
d^5 - 37856*B^4*a^47*b^16*d^5 + 896*B^4*a^49*b^14*d^5 + 3424*B^4*a^51*b^12*d^5 + 960*B^4*a^53*b^10*d^5 + 96*B^
4*a^55*b^8*d^5 - 320*A*B^3*a^22*b^41*d^5 - 2048*A*B^3*a^24*b^39*d^5 + 4096*A*B^3*a^26*b^37*d^5 + 93184*A*B^3*a
^28*b^35*d^5 + 489216*A*B^3*a^30*b^33*d^5 + 1490944*A*B^3*a^32*b^31*d^5 + 3075072*A*B^3*a^34*b^29*d^5 + 453939
2*A*B^3*a^36*b^27*d^5 + 4887168*A*B^3*a^38*b^25*d^5 + 3807232*A*B^3*a^40*b^23*d^5 + 2050048*A*B^3*a^42*b^21*d^
5 + 652288*A*B^3*a^44*b^19*d^5 + 23296*A*B^3*a^46*b^17*d^5 - 86016*A*B^3*a^48*b^15*d^5 - 41984*A*B^3*a^50*b^13
*d^5 - 9216*A*B^3*a^52*b^11*d^5 - 832*A*B^3*a^54*b^9*d^5 + 3520*A^3*B*a^22*b^41*d^5 + 44160*A^3*B*a^24*b^39*d^
5 + 248960*A^3*B*a^26*b^37*d^5 + 819840*A^3*B*a^28*b^35*d^5 + 1688960*A^3*B*a^30*b^33*d^5 + 2038400*A^3*B*a^32
*b^31*d^5 + 640640*A^3*B*a^34*b^29*d^5 - 2654080*A^3*B*a^36*b^27*d^5 - 6040320*A^3*B*a^38*b^25*d^5 - 7230080*A
^3*B*a^40*b^23*d^5 - 5765760*A^3*B*a^42*b^21*d^5 - 3203200*A^3*B*a^44*b^19*d^5 - 1223040*A^3*B*a^46*b^17*d^5 -
300160*A^3*B*a^48*b^15*d^5 - 39040*A^3*B*a^50*b^13*d^5 - 640*A^3*B*a^52*b^11*d^5 + 320*A^3*B*a^54*b^9*d^5 + 4
00*A^2*B^2*a^21*b^42*d^5 + 576*A^2*B^2*a^23*b^40*d^5 - 30592*A^2*B^2*a^25*b^38*d^5 - 264768*A^2*B^2*a^27*b^36*
d^5 - 1124032*A^2*B^2*a^29*b^34*d^5 - 3011008*A^2*B^2*a^31*b^32*d^5 - 5509504*A^2*B^2*a^33*b^30*d^5 - 7019584*
A^2*B^2*a^35*b^28*d^5 - 5999136*A^2*B^2*a^37*b^26*d^5 - 2809664*A^2*B^2*a^39*b^24*d^5 + 384384*A^2*B^2*a^41*b^
22*d^5 + 1811264*A^2*B^2*a^43*b^20*d^5 + 1555008*A^2*B^2*a^45*b^18*d^5 + 765632*A^2*B^2*a^47*b^16*d^5 + 234368
*A^2*B^2*a^49*b^14*d^5 + 41792*A^2*B^2*a^51*b^12*d^5 + 3344*A^2*B^2*a^53*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 - 16
0*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
) + 11040*A^5*a^24*b^37*d^4 + 70560*A^5*a^26*b^35*d^4 + 276640*A^5*a^28*b^33*d^4 + 742560*A^5*a^30*b^31*d^4 +
1441440*A^5*a^32*b^29*d^4 + 2082080*A^5*a^34*b^27*d^4 + 2265120*A^5*a^36*b^25*d^4 + 1853280*A^5*a^38*b^23*d^4
+ 1121120*A^5*a^40*b^21*d^4 + 480480*A^5*a^42*b^19*d^4 + 131040*A^5*a^44*b^17*d^4 + 14560*A^5*a^46*b^15*d^4 -
3360*A^5*a^48*b^13*d^4 - 1440*A^5*a^50*b^11*d^4 - 160*A^5*a^52*b^9*d^4 + 64*B^5*a^23*b^38*d^4 + 896*B^5*a^25*b
^36*d^4 + 5824*B^5*a^27*b^34*d^4 + 23296*B^5*a^29*b^32*d^4 + 64064*B^5*a^31*b^30*d^4 + 128128*B^5*a^33*b^28*d^
4 + 192192*B^5*a^35*b^26*d^4 + 219648*B^5*a^37*b^24*d^4 + 192192*B^5*a^39*b^22*d^4 + 128128*B^5*a^41*b^20*d^4
+ 64064*B^5*a^43*b^18*d^4 + 23296*B^5*a^45*b^16*d^4 + 5824*B^5*a^47*b^14*d^4 + 896*B^5*a^49*b^12*d^4 + 64*B^5*
a^51*b^10*d^4 - 320*A*B^4*a^22*b^39*d^4 - 4192*A*B^4*a^24*b^37*d^4 - 25088*A*B^4*a^26*b^35*d^4 - 90272*A*B^4*a
^28*b^33*d^4 - 215488*A*B^4*a^30*b^31*d^4 - 352352*A*B^4*a^32*b^29*d^4 - 384384*A*B^4*a^34*b^27*d^4 - 233376*A
*B^4*a^36*b^25*d^4 + 27456*A*B^4*a^38*b^23*d^4 + 224224*A*B^4*a^40*b^21*d^4 + 256256*A*B^4*a^42*b^19*d^4 + 171
808*A*B^4*a^44*b^17*d^4 + 75712*A*B^4*a^46*b^15*d^4 + 21728*A*B^4*a^48*b^13*d^4 + 3712*A*B^4*a^50*b^11*d^4 + 2
88*A*B^4*a^52*b^9*d^4 + 400*A^4*B*a^21*b^40*d^4 + 4560*A^4*B*a^23*b^38*d^4 + 21904*A^4*B*a^25*b^36*d^4 + 51856
*A^4*B*a^27*b^34*d^4 + 27664*A^4*B*a^29*b^32*d^4 - 216944*A^4*B*a^31*b^30*d^4 - 816816*A^4*B*a^33*b^28*d^4 - 1
622192*A^4*B*a^35*b^26*d^4 - 2175888*A^4*B*a^37*b^24*d^4 - 2102672*A^4*B*a^39*b^22*d^4 - 1489488*A^4*B*a^41*b^
20*d^4 - 767312*A^4*B*a^43*b^18*d^4 - 278096*A^4*B*a^45*b^16*d^4 - 65744*A^4*B*a^47*b^14*d^4 - 8336*A^4*B*a^49
*b^12*d^4 - 144*A^4*B*a^51*b^10*d^4 + 64*A^4*B*a^53*b^8*d^4 + 400*A^2*B^3*a^21*b^40*d^4 + 4624*A^2*B^3*a^23*b^
38*d^4 + 22800*A^2*B^3*a^25*b^36*d^4 + 57680*A^2*B^3*a^27*b^34*d^4 + 50960*A^2*B^3*a^29*b^32*d^4 - 152880*A^2*
B^3*a^31*b^30*d^4 - 688688*A^2*B^3*a^33*b^28*d^4 - 1430000*A^2*B^3*a^35*b^26*d^4 - 1956240*A^2*B^3*a^37*b^24*d
^4 - 1910480*A^2*B^3*a^39*b^22*d^4 - 1361360*A^2*B^3*a^41*b^20*d^4 - 703248*A^2*B^3*a^43*b^18*d^4 - 254800*A^2
*B^3*a^45*b^16*d^4 - 59920*A^2*B^3*a^47*b^14*d^4 - 7440*A^2*B^3*a^49*b^12*d^4 - 80*A^2*B^3*a^51*b^10*d^4 + 64*
A^2*B^3*a^53*b^8*d^4 + 480*A^3*B^2*a^22*b^39*d^4 + 6848*A^3*B^2*a^24*b^37*d^4 + 45472*A^3*B^2*a^26*b^35*d^4 +
186368*A^3*B^2*a^28*b^33*d^4 + 527072*A^3*B^2*a^30*b^31*d^4 + 1089088*A^3*B^2*a^32*b^29*d^4 + 1697696*A^3*B^2*
a^34*b^27*d^4 + 2031744*A^3*B^2*a^36*b^25*d^4 + 1880736*A^3*B^2*a^38*b^23*d^4 + 1345344*A^3*B^2*a^40*b^21*d^4
+ 736736*A^3*B^2*a^42*b^19*d^4 + 302848*A^3*B^2*a^44*b^17*d^4 + 90272*A^3*B^2*a^46*b^15*d^4 + 18368*A^3*B^2*a^
48*b^13*d^4 + 2272*A^3*B^2*a^50*b^11*d^4 + 128*A^3*B^2*a^52*b^9*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)/(1
6*(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((
(((a + b*tan(c + d*x))^(1/2)*(67232*A^4*a^27*b^36*d^5 - 3200*A^4*a^23*b^40*d^5 - 3200*A^4*a^25*b^38*d^5 - 400*
A^4*a^21*b^42*d^5 + 437248*A^4*a^29*b^34*d^5 + 1458912*A^4*a^31*b^32*d^5 + 3214848*A^4*a^33*b^30*d^5 + 5065632
*A^4*a^35*b^28*d^5 + 5898464*A^4*a^37*b^26*d^5 + 5129696*A^4*a^39*b^24*d^5 + 3313024*A^4*a^41*b^22*d^5 + 15520
96*A^4*a^43*b^20*d^5 + 500864*A^4*a^45*b^18*d^5 + 99232*A^4*a^47*b^16*d^5 + 8448*A^4*a^49*b^14*d^5 - 288*A^4*a
^51*b^12*d^5 + 48*A^4*a^53*b^10*d^5 + 32*A^4*a^55*b^8*d^5 + 64*B^4*a^23*b^40*d^5 + 512*B^4*a^25*b^38*d^5 + 544
*B^4*a^27*b^36*d^5 - 10304*B^4*a^29*b^34*d^5 - 66976*B^4*a^31*b^32*d^5 - 221312*B^4*a^33*b^30*d^5 - 480480*B^4
*a^35*b^28*d^5 - 741312*B^4*a^37*b^26*d^5 - 837408*B^4*a^39*b^24*d^5 - 695552*B^4*a^41*b^22*d^5 - 416416*B^4*a
^43*b^20*d^5 - 168896*B^4*a^45*b^18*d^5 - 37856*B^4*a^47*b^16*d^5 + 896*B^4*a^49*b^14*d^5 + 3424*B^4*a^51*b^12
*d^5 + 960*B^4*a^53*b^10*d^5 + 96*B^4*a^55*b^8*d^5 - 320*A*B^3*a^22*b^41*d^5 - 2048*A*B^3*a^24*b^39*d^5 + 4096
*A*B^3*a^26*b^37*d^5 + 93184*A*B^3*a^28*b^35*d^5 + 489216*A*B^3*a^30*b^33*d^5 + 1490944*A*B^3*a^32*b^31*d^5 +
3075072*A*B^3*a^34*b^29*d^5 + 4539392*A*B^3*a^36*b^27*d^5 + 4887168*A*B^3*a^38*b^25*d^5 + 3807232*A*B^3*a^40*b
^23*d^5 + 2050048*A*B^3*a^42*b^21*d^5 + 652288*A*B^3*a^44*b^19*d^5 + 23296*A*B^3*a^46*b^17*d^5 - 86016*A*B^3*a
^48*b^15*d^5 - 41984*A*B^3*a^50*b^13*d^5 - 9216*A*B^3*a^52*b^11*d^5 - 832*A*B^3*a^54*b^9*d^5 + 3520*A^3*B*a^22
*b^41*d^5 + 44160*A^3*B*a^24*b^39*d^5 + 248960*A^3*B*a^26*b^37*d^5 + 819840*A^3*B*a^28*b^35*d^5 + 1688960*A^3*
B*a^30*b^33*d^5 + 2038400*A^3*B*a^32*b^31*d^5 + 640640*A^3*B*a^34*b^29*d^5 - 2654080*A^3*B*a^36*b^27*d^5 - 604
0320*A^3*B*a^38*b^25*d^5 - 7230080*A^3*B*a^40*b^23*d^5 - 5765760*A^3*B*a^42*b^21*d^5 - 3203200*A^3*B*a^44*b^19
*d^5 - 1223040*A^3*B*a^46*b^17*d^5 - 300160*A^3*B*a^48*b^15*d^5 - 39040*A^3*B*a^50*b^13*d^5 - 640*A^3*B*a^52*b
^11*d^5 + 320*A^3*B*a^54*b^9*d^5 + 400*A^2*B^2*a^21*b^42*d^5 + 576*A^2*B^2*a^23*b^40*d^5 - 30592*A^2*B^2*a^25*
b^38*d^5 - 264768*A^2*B^2*a^27*b^36*d^5 - 1124032*A^2*B^2*a^29*b^34*d^5 - 3011008*A^2*B^2*a^31*b^32*d^5 - 5509
504*A^2*B^2*a^33*b^30*d^5 - 7019584*A^2*B^2*a^35*b^28*d^5 - 5999136*A^2*B^2*a^37*b^26*d^5 - 2809664*A^2*B^2*a^
39*b^24*d^5 + 384384*A^2*B^2*a^41*b^22*d^5 + 1811264*A^2*B^2*a^43*b^20*d^5 + 1555008*A^2*B^2*a^45*b^18*d^5 + 7
65632*A^2*B^2*a^47*b^16*d^5 + 234368*A^2*B^2*a^49*b^14*d^5 + 41792*A^2*B^2*a^51*b^12*d^5 + 3344*A^2*B^2*a^53*b
^10*d^5) - ((5*A*b - 2*B*a)*(90304*A^3*a^29*b^37*d^6 - 10400*A^3*a^23*b^43*d^6 - 54400*A^3*a^25*b^41*d^6 - 121
600*A^3*a^27*b^39*d^6 - 800*A^3*a^21*b^45*d^6 + 1465856*A^3*a^31*b^35*d^6 + 5014464*A^3*a^33*b^33*d^6 + 103234
56*A^3*a^35*b^31*d^6 + 14661504*A^3*a^37*b^29*d^6 + 14908608*A^3*a^39*b^27*d^6 + 10808512*A^3*a^41*b^25*d^6 +
5328128*A^3*a^43*b^23*d^6 + 1531712*A^3*a^45*b^21*d^6 + 87808*A^3*a^47*b^19*d^6 - 85696*A^3*a^49*b^17*d^6 - 61
44*A^3*a^51*b^15*d^6 + 15264*A^3*a^53*b^13*d^6 + 5856*A^3*a^55*b^11*d^6 + 704*A^3*a^57*b^9*d^6 + 384*B^3*a^24*
b^42*d^6 + 7296*B^3*a^26*b^40*d^6 + 59424*B^3*a^28*b^38*d^6 + 280992*B^3*a^30*b^36*d^6 + 866208*B^3*a^32*b^34*
d^6 + 1825824*B^3*a^34*b^32*d^6 + 2629536*B^3*a^36*b^30*d^6 + 2374944*B^3*a^38*b^28*d^6 + 727584*B^3*a^40*b^26
*d^6 - 1413984*B^3*a^42*b^24*d^6 - 2649504*B^3*a^44*b^22*d^6 - 2454816*B^3*a^46*b^20*d^6 - 1476384*B^3*a^48*b^
18*d^6 - 597408*B^3*a^50*b^16*d^6 - 156192*B^3*a^52*b^14*d^6 - 22944*B^3*a^54*b^12*d^6 - 1056*B^3*a^56*b^10*d^
6 + 96*B^3*a^58*b^8*d^6 + ((5*A*b - 2*B*a)*((a + b*tan(c + d*x))^(1/2)*(1600*A^2*a^22*b^46*d^7 + 28800*A^2*a^2
4*b^44*d^7 + 244800*A^2*a^26*b^42*d^7 + 1304256*A^2*a^28*b^40*d^7 + 4880128*A^2*a^30*b^38*d^7 + 13627392*A^2*a
^32*b^36*d^7 + 29476608*A^2*a^34*b^34*d^7 + 50615552*A^2*a^36*b^32*d^7 + 70152576*A^2*a^38*b^30*d^7 + 79329536
*A^2*a^40*b^28*d^7 + 73600384*A^2*a^42*b^26*d^7 + 56025216*A^2*a^44*b^24*d^7 + 34754304*A^2*a^46*b^22*d^7 + 17
296384*A^2*a^48*b^20*d^7 + 6713088*A^2*a^50*b^18*d^7 + 1934592*A^2*a^52*b^16*d^7 + 377408*A^2*a^54*b^14*d^7 +
39552*A^2*a^56*b^12*d^7 + 64*A^2*a^58*b^10*d^7 - 320*A^2*a^60*b^8*d^7 + 256*B^2*a^24*b^44*d^7 + 4608*B^2*a^26*
b^42*d^7 + 40512*B^2*a^28*b^40*d^7 + 224768*B^2*a^30*b^38*d^7 + 864768*B^2*a^32*b^36*d^7 + 2419200*B^2*a^34*b^
34*d^7 + 5055232*B^2*a^36*b^32*d^7 + 8007168*B^2*a^38*b^30*d^7 + 9664512*B^2*a^40*b^28*d^7 + 8859136*B^2*a^42*
b^26*d^7 + 6095232*B^2*a^44*b^24*d^7 + 3095040*B^2*a^46*b^22*d^7 + 1164800*B^2*a^48*b^20*d^7 + 376320*B^2*a^50
*b^18*d^7 + 154368*B^2*a^52*b^16*d^7 + 76288*B^2*a^54*b^14*d^7 + 28416*B^2*a^56*b^12*d^7 + 6144*B^2*a^58*b^10*
d^7 + 576*B^2*a^60*b^8*d^7 - 1280*A*B*a^23*b^45*d^7 - 23040*A*B*a^25*b^43*d^7 - 196352*A*B*a^27*b^41*d^7 - 104
6016*A*B*a^29*b^39*d^7 - 3887616*A*B*a^31*b^37*d^7 - 10683904*A*B*a^33*b^35*d^7 - 22503936*A*B*a^35*b^33*d^7 -
37240320*A*B*a^37*b^31*d^7 - 49347584*A*B*a^39*b^29*d^7 - 53228032*A*B*a^41*b^27*d^7 - 47443968*A*B*a^43*b^25
*d^7 - 35389952*A*B*a^45*b^23*d^7 - 22224384*A*B*a^47*b^21*d^7 - 11665920*A*B*a^49*b^19*d^7 - 4988416*A*B*a^51
*b^17*d^7 - 1657344*A*B*a^53*b^15*d^7 - 397056*A*B*a^55*b^13*d^7 - 60416*A*B*a^57*b^11*d^7 - 4352*A*B*a^59*b^9
*d^7) - ((5*A*b - 2*B*a)*(512*B*a^25*b^46*d^8 - 24320*A*a^26*b^45*d^8 - 219008*A*a^28*b^43*d^8 - 1241984*A*a^3
0*b^41*d^8 - 4970496*A*a^32*b^39*d^8 - 14909440*A*a^34*b^37*d^8 - 34746880*A*a^36*b^35*d^8 - 64356864*A*a^38*b
^33*d^8 - 96092672*A*a^40*b^31*d^8 - 116633088*A*a^42*b^29*d^8 - 115498240*A*a^44*b^27*d^8 - 93267200*A*a^46*b
^25*d^8 - 61128704*A*a^48*b^23*d^8 - 32212992*A*a^50*b^21*d^8 - 13439488*A*a^52*b^19*d^8 - 4334080*A*a^54*b^17
*d^8 - 1040640*A*a^56*b^15*d^8 - 174848*A*a^58*b^13*d^8 - 18304*A*a^60*b^11*d^8 - 896*A*a^62*b^9*d^8 - 1280*A*
a^24*b^47*d^8 + 9728*B*a^27*b^44*d^8 + 87936*B*a^29*b^42*d^8 + 502144*B*a^31*b^40*d^8 + 2028544*B*a^33*b^38*d^
8 + 6153216*B*a^35*b^36*d^8 + 14518784*B*a^37*b^34*d^8 + 27243008*B*a^39*b^32*d^8 + 41213952*B*a^41*b^30*d^8 +
50665472*B*a^43*b^28*d^8 + 50775296*B*a^45*b^26*d^8 + 41443584*B*a^47*b^24*d^8 + 27409408*B*a^49*b^22*d^8 + 1
4543872*B*a^51*b^20*d^8 + 6093312*B*a^53*b^18*d^8 + 1966592*B*a^55*b^16*d^8 + 470528*B*a^57*b^14*d^8 + 78336*B
*a^59*b^12*d^8 + 8064*B*a^61*b^10*d^8 + 384*B*a^63*b^8*d^8 + ((5*A*b - 2*B*a)*(a + b*tan(c + d*x))^(1/2)*(512*
a^27*b^46*d^9 + 9984*a^29*b^44*d^9 + 92160*a^31*b^42*d^9 + 535296*a^33*b^40*d^9 + 2193408*a^35*b^38*d^9 + 6736
896*a^37*b^36*d^9 + 16084992*a^39*b^34*d^9 + 30551040*a^41*b^32*d^9 + 46844928*a^43*b^30*d^9 + 58499584*a^45*b
^28*d^9 + 59744256*a^47*b^26*d^9 + 49900032*a^49*b^24*d^9 + 33945600*a^51*b^22*d^9 + 18643968*a^53*b^20*d^9 +
8146944*a^55*b^18*d^9 + 2767872*a^57*b^16*d^9 + 705024*a^59*b^14*d^9 + 126720*a^61*b^12*d^9 + 14336*a^63*b^10*
d^9 + 768*a^65*b^8*d^9))/(2*d*(a^7)^(1/2))))/(2*d*(a^7)^(1/2))))/(2*d*(a^7)^(1/2)) - 2048*A*B^2*a^23*b^43*d^6
- 35456*A*B^2*a^25*b^41*d^6 - 269824*A*B^2*a^27*b^39*d^6 - 1203648*A*B^2*a^29*b^37*d^6 - 3500672*A*B^2*a^31*b^
35*d^6 - 6889792*A*B^2*a^33*b^33*d^6 - 8968960*A*B^2*a^35*b^31*d^6 - 6452160*A*B^2*a^37*b^29*d^6 + 933504*A*B^
2*a^39*b^27*d^6 + 8721856*A*B^2*a^41*b^25*d^6 + 11714560*A*B^2*a^43*b^23*d^6 + 9184448*A*B^2*a^45*b^21*d^6 + 4
647552*A*B^2*a^47*b^19*d^6 + 1433152*A*B^2*a^49*b^17*d^6 + 182528*A*B^2*a^51*b^15*d^6 - 37696*A*B^2*a^53*b^13*
d^6 - 18048*A*B^2*a^55*b^11*d^6 - 2112*A*B^2*a^57*b^9*d^6 + 3040*A^2*B*a^22*b^44*d^6 + 47200*A^2*B*a^24*b^42*d
^6 + 325120*A^2*B*a^26*b^40*d^6 + 1304352*A^2*B*a^28*b^38*d^6 + 3319840*A^2*B*a^30*b^36*d^6 + 5298720*A^2*B*a^
32*b^34*d^6 + 4178720*A^2*B*a^34*b^32*d^6 - 2452320*A^2*B*a^36*b^30*d^6 - 12167584*A^2*B*a^38*b^28*d^6 - 18281
120*A^2*B*a^40*b^26*d^6 - 16496480*A^2*B*a^42*b^24*d^6 - 9395360*A^2*B*a^44*b^22*d^6 - 2839200*A^2*B*a^46*b^20
*d^6 + 167776*A^2*B*a^48*b^18*d^6 + 563040*A^2*B*a^50*b^16*d^6 + 239840*A^2*B*a^52*b^14*d^6 + 45120*A^2*B*a^54
*b^12*d^6 + 2240*A^2*B*a^56*b^10*d^6 - 288*A^2*B*a^58*b^8*d^6))/(2*d*(a^7)^(1/2)))*(5*A*b - 2*B*a)*1i)/(2*d*(a
^7)^(1/2)) + (((a + b*tan(c + d*x))^(1/2)*(67232*A^4*a^27*b^36*d^5 - 3200*A^4*a^23*b^40*d^5 - 3200*A^4*a^25*b^
38*d^5 - 400*A^4*a^21*b^42*d^5 + 437248*A^4*a^29*b^34*d^5 + 1458912*A^4*a^31*b^32*d^5 + 3214848*A^4*a^33*b^30*
d^5 + 5065632*A^4*a^35*b^28*d^5 + 5898464*A^4*a^37*b^26*d^5 + 5129696*A^4*a^39*b^24*d^5 + 3313024*A^4*a^41*b^2
2*d^5 + 1552096*A^4*a^43*b^20*d^5 + 500864*A^4*a^45*b^18*d^5 + 99232*A^4*a^47*b^16*d^5 + 8448*A^4*a^49*b^14*d^
5 - 288*A^4*a^51*b^12*d^5 + 48*A^4*a^53*b^10*d^5 + 32*A^4*a^55*b^8*d^5 + 64*B^4*a^23*b^40*d^5 + 512*B^4*a^25*b
^38*d^5 + 544*B^4*a^27*b^36*d^5 - 10304*B^4*a^29*b^34*d^5 - 66976*B^4*a^31*b^32*d^5 - 221312*B^4*a^33*b^30*d^5
- 480480*B^4*a^35*b^28*d^5 - 741312*B^4*a^37*b^26*d^5 - 837408*B^4*a^39*b^24*d^5 - 695552*B^4*a^41*b^22*d^5 -
416416*B^4*a^43*b^20*d^5 - 168896*B^4*a^45*b^18*d^5 - 37856*B^4*a^47*b^16*d^5 + 896*B^4*a^49*b^14*d^5 + 3424*
B^4*a^51*b^12*d^5 + 960*B^4*a^53*b^10*d^5 + 96*B^4*a^55*b^8*d^5 - 320*A*B^3*a^22*b^41*d^5 - 2048*A*B^3*a^24*b^
39*d^5 + 4096*A*B^3*a^26*b^37*d^5 + 93184*A*B^3*a^28*b^35*d^5 + 489216*A*B^3*a^30*b^33*d^5 + 1490944*A*B^3*a^3
2*b^31*d^5 + 3075072*A*B^3*a^34*b^29*d^5 + 4539392*A*B^3*a^36*b^27*d^5 + 4887168*A*B^3*a^38*b^25*d^5 + 3807232
*A*B^3*a^40*b^23*d^5 + 2050048*A*B^3*a^42*b^21*d^5 + 652288*A*B^3*a^44*b^19*d^5 + 23296*A*B^3*a^46*b^17*d^5 -
86016*A*B^3*a^48*b^15*d^5 - 41984*A*B^3*a^50*b^13*d^5 - 9216*A*B^3*a^52*b^11*d^5 - 832*A*B^3*a^54*b^9*d^5 + 35
20*A^3*B*a^22*b^41*d^5 + 44160*A^3*B*a^24*b^39*d^5 + 248960*A^3*B*a^26*b^37*d^5 + 819840*A^3*B*a^28*b^35*d^5 +
1688960*A^3*B*a^30*b^33*d^5 + 2038400*A^3*B*a^32*b^31*d^5 + 640640*A^3*B*a^34*b^29*d^5 - 2654080*A^3*B*a^36*b
^27*d^5 - 6040320*A^3*B*a^38*b^25*d^5 - 7230080*A^3*B*a^40*b^23*d^5 - 5765760*A^3*B*a^42*b^21*d^5 - 3203200*A^
3*B*a^44*b^19*d^5 - 1223040*A^3*B*a^46*b^17*d^5 - 300160*A^3*B*a^48*b^15*d^5 - 39040*A^3*B*a^50*b^13*d^5 - 640
*A^3*B*a^52*b^11*d^5 + 320*A^3*B*a^54*b^9*d^5 + 400*A^2*B^2*a^21*b^42*d^5 + 576*A^2*B^2*a^23*b^40*d^5 - 30592*
A^2*B^2*a^25*b^38*d^5 - 264768*A^2*B^2*a^27*b^36*d^5 - 1124032*A^2*B^2*a^29*b^34*d^5 - 3011008*A^2*B^2*a^31*b^
32*d^5 - 5509504*A^2*B^2*a^33*b^30*d^5 - 7019584*A^2*B^2*a^35*b^28*d^5 - 5999136*A^2*B^2*a^37*b^26*d^5 - 28096
64*A^2*B^2*a^39*b^24*d^5 + 384384*A^2*B^2*a^41*b^22*d^5 + 1811264*A^2*B^2*a^43*b^20*d^5 + 1555008*A^2*B^2*a^45
*b^18*d^5 + 765632*A^2*B^2*a^47*b^16*d^5 + 234368*A^2*B^2*a^49*b^14*d^5 + 41792*A^2*B^2*a^51*b^12*d^5 + 3344*A
^2*B^2*a^53*b^10*d^5) + ((5*A*b - 2*B*a)*(90304*A^3*a^29*b^37*d^6 - 10400*A^3*a^23*b^43*d^6 - 54400*A^3*a^25*b
^41*d^6 - 121600*A^3*a^27*b^39*d^6 - 800*A^3*a^21*b^45*d^6 + 1465856*A^3*a^31*b^35*d^6 + 5014464*A^3*a^33*b^33
*d^6 + 10323456*A^3*a^35*b^31*d^6 + 14661504*A^3*a^37*b^29*d^6 + 14908608*A^3*a^39*b^27*d^6 + 10808512*A^3*a^4
1*b^25*d^6 + 5328128*A^3*a^43*b^23*d^6 + 1531712*A^3*a^45*b^21*d^6 + 87808*A^3*a^47*b^19*d^6 - 85696*A^3*a^49*
b^17*d^6 - 6144*A^3*a^51*b^15*d^6 + 15264*A^3*a^53*b^13*d^6 + 5856*A^3*a^55*b^11*d^6 + 704*A^3*a^57*b^9*d^6 +
384*B^3*a^24*b^42*d^6 + 7296*B^3*a^26*b^40*d^6 + 59424*B^3*a^28*b^38*d^6 + 280992*B^3*a^30*b^36*d^6 + 866208*B
^3*a^32*b^34*d^6 + 1825824*B^3*a^34*b^32*d^6 + 2629536*B^3*a^36*b^30*d^6 + 2374944*B^3*a^38*b^28*d^6 + 727584*
B^3*a^40*b^26*d^6 - 1413984*B^3*a^42*b^24*d^6 - 2649504*B^3*a^44*b^22*d^6 - 2454816*B^3*a^46*b^20*d^6 - 147638
4*B^3*a^48*b^18*d^6 - 597408*B^3*a^50*b^16*d^6 - 156192*B^3*a^52*b^14*d^6 - 22944*B^3*a^54*b^12*d^6 - 1056*B^3
*a^56*b^10*d^6 + 96*B^3*a^58*b^8*d^6 - ((5*A*b - 2*B*a)*((a + b*tan(c + d*x))^(1/2)*(1600*A^2*a^22*b^46*d^7 +
28800*A^2*a^24*b^44*d^7 + 244800*A^2*a^26*b^42*d^7 + 1304256*A^2*a^28*b^40*d^7 + 4880128*A^2*a^30*b^38*d^7 + 1
3627392*A^2*a^32*b^36*d^7 + 29476608*A^2*a^34*b^34*d^7 + 50615552*A^2*a^36*b^32*d^7 + 70152576*A^2*a^38*b^30*d
^7 + 79329536*A^2*a^40*b^28*d^7 + 73600384*A^2*a^42*b^26*d^7 + 56025216*A^2*a^44*b^24*d^7 + 34754304*A^2*a^46*
b^22*d^7 + 17296384*A^2*a^48*b^20*d^7 + 6713088*A^2*a^50*b^18*d^7 + 1934592*A^2*a^52*b^16*d^7 + 377408*A^2*a^5
4*b^14*d^7 + 39552*A^2*a^56*b^12*d^7 + 64*A^2*a^58*b^10*d^7 - 320*A^2*a^60*b^8*d^7 + 256*B^2*a^24*b^44*d^7 + 4
608*B^2*a^26*b^42*d^7 + 40512*B^2*a^28*b^40*d^7 + 224768*B^2*a^30*b^38*d^7 + 864768*B^2*a^32*b^36*d^7 + 241920
0*B^2*a^34*b^34*d^7 + 5055232*B^2*a^36*b^32*d^7 + 8007168*B^2*a^38*b^30*d^7 + 9664512*B^2*a^40*b^28*d^7 + 8859
136*B^2*a^42*b^26*d^7 + 6095232*B^2*a^44*b^24*d^7 + 3095040*B^2*a^46*b^22*d^7 + 1164800*B^2*a^48*b^20*d^7 + 37
6320*B^2*a^50*b^18*d^7 + 154368*B^2*a^52*b^16*d^7 + 76288*B^2*a^54*b^14*d^7 + 28416*B^2*a^56*b^12*d^7 + 6144*B
^2*a^58*b^10*d^7 + 576*B^2*a^60*b^8*d^7 - 1280*A*B*a^23*b^45*d^7 - 23040*A*B*a^25*b^43*d^7 - 196352*A*B*a^27*b
^41*d^7 - 1046016*A*B*a^29*b^39*d^7 - 3887616*A*B*a^31*b^37*d^7 - 10683904*A*B*a^33*b^35*d^7 - 22503936*A*B*a^
35*b^33*d^7 - 37240320*A*B*a^37*b^31*d^7 - 49347584*A*B*a^39*b^29*d^7 - 53228032*A*B*a^41*b^27*d^7 - 47443968*
A*B*a^43*b^25*d^7 - 35389952*A*B*a^45*b^23*d^7 - 22224384*A*B*a^47*b^21*d^7 - 11665920*A*B*a^49*b^19*d^7 - 498
8416*A*B*a^51*b^17*d^7 - 1657344*A*B*a^53*b^15*d^7 - 397056*A*B*a^55*b^13*d^7 - 60416*A*B*a^57*b^11*d^7 - 4352
*A*B*a^59*b^9*d^7) - ((5*A*b - 2*B*a)*(1280*A*a^24*b^47*d^8 + 24320*A*a^26*b^45*d^8 + 219008*A*a^28*b^43*d^8 +
1241984*A*a^30*b^41*d^8 + 4970496*A*a^32*b^39*d^8 + 14909440*A*a^34*b^37*d^8 + 34746880*A*a^36*b^35*d^8 + 643
56864*A*a^38*b^33*d^8 + 96092672*A*a^40*b^31*d^8 + 116633088*A*a^42*b^29*d^8 + 115498240*A*a^44*b^27*d^8 + 932
67200*A*a^46*b^25*d^8 + 61128704*A*a^48*b^23*d^8 + 32212992*A*a^50*b^21*d^8 + 13439488*A*a^52*b^19*d^8 + 43340
80*A*a^54*b^17*d^8 + 1040640*A*a^56*b^15*d^8 + 174848*A*a^58*b^13*d^8 + 18304*A*a^60*b^11*d^8 + 896*A*a^62*b^9
*d^8 - 512*B*a^25*b^46*d^8 - 9728*B*a^27*b^44*d^8 - 87936*B*a^29*b^42*d^8 - 502144*B*a^31*b^40*d^8 - 2028544*B
*a^33*b^38*d^8 - 6153216*B*a^35*b^36*d^8 - 14518784*B*a^37*b^34*d^8 - 27243008*B*a^39*b^32*d^8 - 41213952*B*a^
41*b^30*d^8 - 50665472*B*a^43*b^28*d^8 - 50775296*B*a^45*b^26*d^8 - 41443584*B*a^47*b^24*d^8 - 27409408*B*a^49
*b^22*d^8 - 14543872*B*a^51*b^20*d^8 - 6093312*B*a^53*b^18*d^8 - 1966592*B*a^55*b^16*d^8 - 470528*B*a^57*b^14*
d^8 - 78336*B*a^59*b^12*d^8 - 8064*B*a^61*b^10*d^8 - 384*B*a^63*b^8*d^8 + ((5*A*b - 2*B*a)*(a + b*tan(c + d*x)
)^(1/2)*(512*a^27*b^46*d^9 + 9984*a^29*b^44*d^9 + 92160*a^31*b^42*d^9 + 535296*a^33*b^40*d^9 + 2193408*a^35*b^
38*d^9 + 6736896*a^37*b^36*d^9 + 16084992*a^39*b^34*d^9 + 30551040*a^41*b^32*d^9 + 46844928*a^43*b^30*d^9 + 58
499584*a^45*b^28*d^9 + 59744256*a^47*b^26*d^9 + 49900032*a^49*b^24*d^9 + 33945600*a^51*b^22*d^9 + 18643968*a^5
3*b^20*d^9 + 8146944*a^55*b^18*d^9 + 2767872*a^57*b^16*d^9 + 705024*a^59*b^14*d^9 + 126720*a^61*b^12*d^9 + 143
36*a^63*b^10*d^9 + 768*a^65*b^8*d^9))/(2*d*(a^7)^(1/2))))/(2*d*(a^7)^(1/2))))/(2*d*(a^7)^(1/2)) - 2048*A*B^2*a
^23*b^43*d^6 - 35456*A*B^2*a^25*b^41*d^6 - 269824*A*B^2*a^27*b^39*d^6 - 1203648*A*B^2*a^29*b^37*d^6 - 3500672*
A*B^2*a^31*b^35*d^6 - 6889792*A*B^2*a^33*b^33*d^6 - 8968960*A*B^2*a^35*b^31*d^6 - 6452160*A*B^2*a^37*b^29*d^6
+ 933504*A*B^2*a^39*b^27*d^6 + 8721856*A*B^2*a^41*b^25*d^6 + 11714560*A*B^2*a^43*b^23*d^6 + 9184448*A*B^2*a^45
*b^21*d^6 + 4647552*A*B^2*a^47*b^19*d^6 + 1433152*A*B^2*a^49*b^17*d^6 + 182528*A*B^2*a^51*b^15*d^6 - 37696*A*B
^2*a^53*b^13*d^6 - 18048*A*B^2*a^55*b^11*d^6 - 2112*A*B^2*a^57*b^9*d^6 + 3040*A^2*B*a^22*b^44*d^6 + 47200*A^2*
B*a^24*b^42*d^6 + 325120*A^2*B*a^26*b^40*d^6 + 1304352*A^2*B*a^28*b^38*d^6 + 3319840*A^2*B*a^30*b^36*d^6 + 529
8720*A^2*B*a^32*b^34*d^6 + 4178720*A^2*B*a^34*b^32*d^6 - 2452320*A^2*B*a^36*b^30*d^6 - 12167584*A^2*B*a^38*b^2
8*d^6 - 18281120*A^2*B*a^40*b^26*d^6 - 16496480*A^2*B*a^42*b^24*d^6 - 9395360*A^2*B*a^44*b^22*d^6 - 2839200*A^
2*B*a^46*b^20*d^6 + 167776*A^2*B*a^48*b^18*d^6 + 563040*A^2*B*a^50*b^16*d^6 + 239840*A^2*B*a^52*b^14*d^6 + 451
20*A^2*B*a^54*b^12*d^6 + 2240*A^2*B*a^56*b^10*d^6 - 288*A^2*B*a^58*b^8*d^6))/(2*d*(a^7)^(1/2)))*(5*A*b - 2*B*a
)*1i)/(2*d*(a^7)^(1/2)))/(800*A^5*a^22*b^39*d^4 + 11040*A^5*a^24*b^37*d^4 + 70560*A^5*a^26*b^35*d^4 + 276640*A
^5*a^28*b^33*d^4 + 742560*A^5*a^30*b^31*d^4 + 1441440*A^5*a^32*b^29*d^4 + 2082080*A^5*a^34*b^27*d^4 + 2265120*
A^5*a^36*b^25*d^4 + 1853280*A^5*a^38*b^23*d^4 + 1121120*A^5*a^40*b^21*d^4 + 480480*A^5*a^42*b^19*d^4 + 131040*
A^5*a^44*b^17*d^4 + 14560*A^5*a^46*b^15*d^4 - 3360*A^5*a^48*b^13*d^4 - 1440*A^5*a^50*b^11*d^4 - 160*A^5*a^52*b
^9*d^4 + 64*B^5*a^23*b^38*d^4 + 896*B^5*a^25*b^36*d^4 + 5824*B^5*a^27*b^34*d^4 + 23296*B^5*a^29*b^32*d^4 + 640
64*B^5*a^31*b^30*d^4 + 128128*B^5*a^33*b^28*d^4 + 192192*B^5*a^35*b^26*d^4 + 219648*B^5*a^37*b^24*d^4 + 192192
*B^5*a^39*b^22*d^4 + 128128*B^5*a^41*b^20*d^4 + 64064*B^5*a^43*b^18*d^4 + 23296*B^5*a^45*b^16*d^4 + 5824*B^5*a
^47*b^14*d^4 + 896*B^5*a^49*b^12*d^4 + 64*B^5*a^51*b^10*d^4 + (((a + b*tan(c + d*x))^(1/2)*(67232*A^4*a^27*b^3
6*d^5 - 3200*A^4*a^23*b^40*d^5 - 3200*A^4*a^25*b^38*d^5 - 400*A^4*a^21*b^42*d^5 + 437248*A^4*a^29*b^34*d^5 + 1
458912*A^4*a^31*b^32*d^5 + 3214848*A^4*a^33*b^30*d^5 + 5065632*A^4*a^35*b^28*d^5 + 5898464*A^4*a^37*b^26*d^5 +
5129696*A^4*a^39*b^24*d^5 + 3313024*A^4*a^41*b^22*d^5 + 1552096*A^4*a^43*b^20*d^5 + 500864*A^4*a^45*b^18*d^5
+ 99232*A^4*a^47*b^16*d^5 + 8448*A^4*a^49*b^14*d^5 - 288*A^4*a^51*b^12*d^5 + 48*A^4*a^53*b^10*d^5 + 32*A^4*a^5
5*b^8*d^5 + 64*B^4*a^23*b^40*d^5 + 512*B^4*a^25*b^38*d^5 + 544*B^4*a^27*b^36*d^5 - 10304*B^4*a^29*b^34*d^5 - 6
6976*B^4*a^31*b^32*d^5 - 221312*B^4*a^33*b^30*d^5 - 480480*B^4*a^35*b^28*d^5 - 741312*B^4*a^37*b^26*d^5 - 8374
08*B^4*a^39*b^24*d^5 - 695552*B^4*a^41*b^22*d^5 - 416416*B^4*a^43*b^20*d^5 - 168896*B^4*a^45*b^18*d^5 - 37856*
B^4*a^47*b^16*d^5 + 896*B^4*a^49*b^14*d^5 + 3424*B^4*a^51*b^12*d^5 + 960*B^4*a^53*b^10*d^5 + 96*B^4*a^55*b^8*d
^5 - 320*A*B^3*a^22*b^41*d^5 - 2048*A*B^3*a^24*b^39*d^5 + 4096*A*B^3*a^26*b^37*d^5 + 93184*A*B^3*a^28*b^35*d^5
+ 489216*A*B^3*a^30*b^33*d^5 + 1490944*A*B^3*a^32*b^31*d^5 + 3075072*A*B^3*a^34*b^29*d^5 + 4539392*A*B^3*a^36
*b^27*d^5 + 4887168*A*B^3*a^38*b^25*d^5 + 3807232*A*B^3*a^40*b^23*d^5 + 2050048*A*B^3*a^42*b^21*d^5 + 652288*A
*B^3*a^44*b^19*d^5 + 23296*A*B^3*a^46*b^17*d^5 - 86016*A*B^3*a^48*b^15*d^5 - 41984*A*B^3*a^50*b^13*d^5 - 9216*
A*B^3*a^52*b^11*d^5 - 832*A*B^3*a^54*b^9*d^5 + 3520*A^3*B*a^22*b^41*d^5 + 44160*A^3*B*a^24*b^39*d^5 + 248960*A
^3*B*a^26*b^37*d^5 + 819840*A^3*B*a^28*b^35*d^5 + 1688960*A^3*B*a^30*b^33*d^5 + 2038400*A^3*B*a^32*b^31*d^5 +
640640*A^3*B*a^34*b^29*d^5 - 2654080*A^3*B*a^36*b^27*d^5 - 6040320*A^3*B*a^38*b^25*d^5 - 7230080*A^3*B*a^40*b^
23*d^5 - 5765760*A^3*B*a^42*b^21*d^5 - 3203200*A^3*B*a^44*b^19*d^5 - 1223040*A^3*B*a^46*b^17*d^5 - 300160*A^3*
B*a^48*b^15*d^5 - 39040*A^3*B*a^50*b^13*d^5 - 640*A^3*B*a^52*b^11*d^5 + 320*A^3*B*a^54*b^9*d^5 + 400*A^2*B^2*a
^21*b^42*d^5 + 576*A^2*B^2*a^23*b^40*d^5 - 30592*A^2*B^2*a^25*b^38*d^5 - 264768*A^2*B^2*a^27*b^36*d^5 - 112403
2*A^2*B^2*a^29*b^34*d^5 - 3011008*A^2*B^2*a^31*b^32*d^5 - 5509504*A^2*B^2*a^33*b^30*d^5 - 7019584*A^2*B^2*a^35
*b^28*d^5 - 5999136*A^2*B^2*a^37*b^26*d^5 - 2809664*A^2*B^2*a^39*b^24*d^5 + 384384*A^2*B^2*a^41*b^22*d^5 + 181
1264*A^2*B^2*a^43*b^20*d^5 + 1555008*A^2*B^2*a^45*b^18*d^5 + 765632*A^2*B^2*a^47*b^16*d^5 + 234368*A^2*B^2*a^4
9*b^14*d^5 + 41792*A^2*B^2*a^51*b^12*d^5 + 3344*A^2*B^2*a^53*b^10*d^5) - ((5*A*b - 2*B*a)*(90304*A^3*a^29*b^37
*d^6 - 10400*A^3*a^23*b^43*d^6 - 54400*A^3*a^25*b^41*d^6 - 121600*A^3*a^27*b^39*d^6 - 800*A^3*a^21*b^45*d^6 +
1465856*A^3*a^31*b^35*d^6 + 5014464*A^3*a^33*b^33*d^6 + 10323456*A^3*a^35*b^31*d^6 + 14661504*A^3*a^37*b^29*d^
6 + 14908608*A^3*a^39*b^27*d^6 + 10808512*A^3*a^41*b^25*d^6 + 5328128*A^3*a^43*b^23*d^6 + 1531712*A^3*a^45*b^2
1*d^6 + 87808*A^3*a^47*b^19*d^6 - 85696*A^3*a^49*b^17*d^6 - 6144*A^3*a^51*b^15*d^6 + 15264*A^3*a^53*b^13*d^6 +
5856*A^3*a^55*b^11*d^6 + 704*A^3*a^57*b^9*d^6 + 384*B^3*a^24*b^42*d^6 + 7296*B^3*a^26*b^40*d^6 + 59424*B^3*a^
28*b^38*d^6 + 280992*B^3*a^30*b^36*d^6 + 866208*B^3*a^32*b^34*d^6 + 1825824*B^3*a^34*b^32*d^6 + 2629536*B^3*a^
36*b^30*d^6 + 2374944*B^3*a^38*b^28*d^6 + 727584*B^3*a^40*b^26*d^6 - 1413984*B^3*a^42*b^24*d^6 - 2649504*B^3*a
^44*b^22*d^6 - 2454816*B^3*a^46*b^20*d^6 - 1476384*B^3*a^48*b^18*d^6 - 597408*B^3*a^50*b^16*d^6 - 156192*B^3*a
^52*b^14*d^6 - 22944*B^3*a^54*b^12*d^6 - 1056*B^3*a^56*b^10*d^6 + 96*B^3*a^58*b^8*d^6 + ((5*A*b - 2*B*a)*((a +
b*tan(c + d*x))^(1/2)*(1600*A^2*a^22*b^46*d^7 + 28800*A^2*a^24*b^44*d^7 + 244800*A^2*a^26*b^42*d^7 + 1304256*
A^2*a^28*b^40*d^7 + 4880128*A^2*a^30*b^38*d^7 + 13627392*A^2*a^32*b^36*d^7 + 29476608*A^2*a^34*b^34*d^7 + 5061
5552*A^2*a^36*b^32*d^7 + 70152576*A^2*a^38*b^30*d^7 + 79329536*A^2*a^40*b^28*d^7 + 73600384*A^2*a^42*b^26*d^7
+ 56025216*A^2*a^44*b^24*d^7 + 34754304*A^2*a^46*b^22*d^7 + 17296384*A^2*a^48*b^20*d^7 + 6713088*A^2*a^50*b^18
*d^7 + 1934592*A^2*a^52*b^16*d^7 + 377408*A^2*a^54*b^14*d^7 + 39552*A^2*a^56*b^12*d^7 + 64*A^2*a^58*b^10*d^7 -
320*A^2*a^60*b^8*d^7 + 256*B^2*a^24*b^44*d^7 + 4608*B^2*a^26*b^42*d^7 + 40512*B^2*a^28*b^40*d^7 + 224768*B^2*
a^30*b^38*d^7 + 864768*B^2*a^32*b^36*d^7 + 2419200*B^2*a^34*b^34*d^7 + 5055232*B^2*a^36*b^32*d^7 + 8007168*B^2
*a^38*b^30*d^7 + 9664512*B^2*a^40*b^28*d^7 + 8859136*B^2*a^42*b^26*d^7 + 6095232*B^2*a^44*b^24*d^7 + 3095040*B
^2*a^46*b^22*d^7 + 1164800*B^2*a^48*b^20*d^7 + 376320*B^2*a^50*b^18*d^7 + 154368*B^2*a^52*b^16*d^7 + 76288*B^2
*a^54*b^14*d^7 + 28416*B^2*a^56*b^12*d^7 + 6144*B^2*a^58*b^10*d^7 + 576*B^2*a^60*b^8*d^7 - 1280*A*B*a^23*b^45*
d^7 - 23040*A*B*a^25*b^43*d^7 - 196352*A*B*a^27*b^41*d^7 - 1046016*A*B*a^29*b^39*d^7 - 3887616*A*B*a^31*b^37*d
^7 - 10683904*A*B*a^33*b^35*d^7 - 22503936*A*B*a^35*b^33*d^7 - 37240320*A*B*a^37*b^31*d^7 - 49347584*A*B*a^39*
b^29*d^7 - 53228032*A*B*a^41*b^27*d^7 - 47443968*A*B*a^43*b^25*d^7 - 35389952*A*B*a^45*b^23*d^7 - 22224384*A*B
*a^47*b^21*d^7 - 11665920*A*B*a^49*b^19*d^7 - 4988416*A*B*a^51*b^17*d^7 - 1657344*A*B*a^53*b^15*d^7 - 397056*A
*B*a^55*b^13*d^7 - 60416*A*B*a^57*b^11*d^7 - 4352*A*B*a^59*b^9*d^7) - ((5*A*b - 2*B*a)*(512*B*a^25*b^46*d^8 -
24320*A*a^26*b^45*d^8 - 219008*A*a^28*b^43*d^8 - 1241984*A*a^30*b^41*d^8 - 4970496*A*a^32*b^39*d^8 - 14909440*
A*a^34*b^37*d^8 - 34746880*A*a^36*b^35*d^8 - 64356864*A*a^38*b^33*d^8 - 96092672*A*a^40*b^31*d^8 - 116633088*A
*a^42*b^29*d^8 - 115498240*A*a^44*b^27*d^8 - 93267200*A*a^46*b^25*d^8 - 61128704*A*a^48*b^23*d^8 - 32212992*A*
a^50*b^21*d^8 - 13439488*A*a^52*b^19*d^8 - 4334080*A*a^54*b^17*d^8 - 1040640*A*a^56*b^15*d^8 - 174848*A*a^58*b
^13*d^8 - 18304*A*a^60*b^11*d^8 - 896*A*a^62*b^9*d^8 - 1280*A*a^24*b^47*d^8 + 9728*B*a^27*b^44*d^8 + 87936*B*a
^29*b^42*d^8 + 502144*B*a^31*b^40*d^8 + 2028544*B*a^33*b^38*d^8 + 6153216*B*a^35*b^36*d^8 + 14518784*B*a^37*b^
34*d^8 + 27243008*B*a^39*b^32*d^8 + 41213952*B*a^41*b^30*d^8 + 50665472*B*a^43*b^28*d^8 + 50775296*B*a^45*b^26
*d^8 + 41443584*B*a^47*b^24*d^8 + 27409408*B*a^49*b^22*d^8 + 14543872*B*a^51*b^20*d^8 + 6093312*B*a^53*b^18*d^
8 + 1966592*B*a^55*b^16*d^8 + 470528*B*a^57*b^14*d^8 + 78336*B*a^59*b^12*d^8 + 8064*B*a^61*b^10*d^8 + 384*B*a^
63*b^8*d^8 + ((5*A*b - 2*B*a)*(a + b*tan(c + d*x))^(1/2)*(512*a^27*b^46*d^9 + 9984*a^29*b^44*d^9 + 92160*a^31*
b^42*d^9 + 535296*a^33*b^40*d^9 + 2193408*a^35*b^38*d^9 + 6736896*a^37*b^36*d^9 + 16084992*a^39*b^34*d^9 + 305
51040*a^41*b^32*d^9 + 46844928*a^43*b^30*d^9 + 58499584*a^45*b^28*d^9 + 59744256*a^47*b^26*d^9 + 49900032*a^49
*b^24*d^9 + 33945600*a^51*b^22*d^9 + 18643968*a^53*b^20*d^9 + 8146944*a^55*b^18*d^9 + 2767872*a^57*b^16*d^9 +
705024*a^59*b^14*d^9 + 126720*a^61*b^12*d^9 + 14336*a^63*b^10*d^9 + 768*a^65*b^8*d^9))/(2*d*(a^7)^(1/2))))/(2*
d*(a^7)^(1/2))))/(2*d*(a^7)^(1/2)) - 2048*A*B^2*a^23*b^43*d^6 - 35456*A*B^2*a^25*b^41*d^6 - 269824*A*B^2*a^27*
b^39*d^6 - 1203648*A*B^2*a^29*b^37*d^6 - 3500672*A*B^2*a^31*b^35*d^6 - 6889792*A*B^2*a^33*b^33*d^6 - 8968960*A
*B^2*a^35*b^31*d^6 - 6452160*A*B^2*a^37*b^29*d^6 + 933504*A*B^2*a^39*b^27*d^6 + 8721856*A*B^2*a^41*b^25*d^6 +
11714560*A*B^2*a^43*b^23*d^6 + 9184448*A*B^2*a^45*b^21*d^6 + 4647552*A*B^2*a^47*b^19*d^6 + 1433152*A*B^2*a^49*
b^17*d^6 + 182528*A*B^2*a^51*b^15*d^6 - 37696*A*B^2*a^53*b^13*d^6 - 18048*A*B^2*a^55*b^11*d^6 - 2112*A*B^2*a^5
7*b^9*d^6 + 3040*A^2*B*a^22*b^44*d^6 + 47200*A^2*B*a^24*b^42*d^6 + 325120*A^2*B*a^26*b^40*d^6 + 1304352*A^2*B*
a^28*b^38*d^6 + 3319840*A^2*B*a^30*b^36*d^6 + 5298720*A^2*B*a^32*b^34*d^6 + 4178720*A^2*B*a^34*b^32*d^6 - 2452
320*A^2*B*a^36*b^30*d^6 - 12167584*A^2*B*a^38*b^28*d^6 - 18281120*A^2*B*a^40*b^26*d^6 - 16496480*A^2*B*a^42*b^
24*d^6 - 9395360*A^2*B*a^44*b^22*d^6 - 2839200*A^2*B*a^46*b^20*d^6 + 167776*A^2*B*a^48*b^18*d^6 + 563040*A^2*B
*a^50*b^16*d^6 + 239840*A^2*B*a^52*b^14*d^6 + 45120*A^2*B*a^54*b^12*d^6 + 2240*A^2*B*a^56*b^10*d^6 - 288*A^2*B
*a^58*b^8*d^6))/(2*d*(a^7)^(1/2)))*(5*A*b - 2*B*a))/(2*d*(a^7)^(1/2)) - (((a + b*tan(c + d*x))^(1/2)*(67232*A^
4*a^27*b^36*d^5 - 3200*A^4*a^23*b^40*d^5 - 3200*A^4*a^25*b^38*d^5 - 400*A^4*a^21*b^42*d^5 + 437248*A^4*a^29*b^
34*d^5 + 1458912*A^4*a^31*b^32*d^5 + 3214848*A^4*a^33*b^30*d^5 + 5065632*A^4*a^35*b^28*d^5 + 5898464*A^4*a^37*
b^26*d^5 + 5129696*A^4*a^39*b^24*d^5 + 3313024*A^4*a^41*b^22*d^5 + 1552096*A^4*a^43*b^20*d^5 + 500864*A^4*a^45
*b^18*d^5 + 99232*A^4*a^47*b^16*d^5 + 8448*A^4*a^49*b^14*d^5 - 288*A^4*a^51*b^12*d^5 + 48*A^4*a^53*b^10*d^5 +
32*A^4*a^55*b^8*d^5 + 64*B^4*a^23*b^40*d^5 + 512*B^4*a^25*b^38*d^5 + 544*B^4*a^27*b^36*d^5 - 10304*B^4*a^29*b^
34*d^5 - 66976*B^4*a^31*b^32*d^5 - 221312*B^4*a^33*b^30*d^5 - 480480*B^4*a^35*b^28*d^5 - 741312*B^4*a^37*b^26*
d^5 - 837408*B^4*a^39*b^24*d^5 - 695552*B^4*a^41*b^22*d^5 - 416416*B^4*a^43*b^20*d^5 - 168896*B^4*a^45*b^18*d^
5 - 37856*B^4*a^47*b^16*d^5 + 896*B^4*a^49*b^14*d^5 + 3424*B^4*a^51*b^12*d^5 + 960*B^4*a^53*b^10*d^5 + 96*B^4*
a^55*b^8*d^5 - 320*A*B^3*a^22*b^41*d^5 - 2048*A*B^3*a^24*b^39*d^5 + 4096*A*B^3*a^26*b^37*d^5 + 93184*A*B^3*a^2
8*b^35*d^5 + 489216*A*B^3*a^30*b^33*d^5 + 1490944*A*B^3*a^32*b^31*d^5 + 3075072*A*B^3*a^34*b^29*d^5 + 4539392*
A*B^3*a^36*b^27*d^5 + 4887168*A*B^3*a^38*b^25*d^5 + 3807232*A*B^3*a^40*b^23*d^5 + 2050048*A*B^3*a^42*b^21*d^5
+ 652288*A*B^3*a^44*b^19*d^5 + 23296*A*B^3*a^46*b^17*d^5 - 86016*A*B^3*a^48*b^15*d^5 - 41984*A*B^3*a^50*b^13*d
^5 - 9216*A*B^3*a^52*b^11*d^5 - 832*A*B^3*a^54*b^9*d^5 + 3520*A^3*B*a^22*b^41*d^5 + 44160*A^3*B*a^24*b^39*d^5
+ 248960*A^3*B*a^26*b^37*d^5 + 819840*A^3*B*a^28*b^35*d^5 + 1688960*A^3*B*a^30*b^33*d^5 + 2038400*A^3*B*a^32*b
^31*d^5 + 640640*A^3*B*a^34*b^29*d^5 - 2654080*A^3*B*a^36*b^27*d^5 - 6040320*A^3*B*a^38*b^25*d^5 - 7230080*A^3
*B*a^40*b^23*d^5 - 5765760*A^3*B*a^42*b^21*d^5 - 3203200*A^3*B*a^44*b^19*d^5 - 1223040*A^3*B*a^46*b^17*d^5 - 3
00160*A^3*B*a^48*b^15*d^5 - 39040*A^3*B*a^50*b^13*d^5 - 640*A^3*B*a^52*b^11*d^5 + 320*A^3*B*a^54*b^9*d^5 + 400
*A^2*B^2*a^21*b^42*d^5 + 576*A^2*B^2*a^23*b^40*d^5 - 30592*A^2*B^2*a^25*b^38*d^5 - 264768*A^2*B^2*a^27*b^36*d^
5 - 1124032*A^2*B^2*a^29*b^34*d^5 - 3011008*A^2*B^2*a^31*b^32*d^5 - 5509504*A^2*B^2*a^33*b^30*d^5 - 7019584*A^
2*B^2*a^35*b^28*d^5 - 5999136*A^2*B^2*a^37*b^26*d^5 - 2809664*A^2*B^2*a^39*b^24*d^5 + 384384*A^2*B^2*a^41*b^22
*d^5 + 1811264*A^2*B^2*a^43*b^20*d^5 + 1555008*A^2*B^2*a^45*b^18*d^5 + 765632*A^2*B^2*a^47*b^16*d^5 + 234368*A
^2*B^2*a^49*b^14*d^5 + 41792*A^2*B^2*a^51*b^12*d^5 + 3344*A^2*B^2*a^53*b^10*d^5) + ((5*A*b - 2*B*a)*(90304*A^3
*a^29*b^37*d^6 - 10400*A^3*a^23*b^43*d^6 - 54400*A^3*a^25*b^41*d^6 - 121600*A^3*a^27*b^39*d^6 - 800*A^3*a^21*b
^45*d^6 + 1465856*A^3*a^31*b^35*d^6 + 5014464*A^3*a^33*b^33*d^6 + 10323456*A^3*a^35*b^31*d^6 + 14661504*A^3*a^
37*b^29*d^6 + 14908608*A^3*a^39*b^27*d^6 + 10808512*A^3*a^41*b^25*d^6 + 5328128*A^3*a^43*b^23*d^6 + 1531712*A^
3*a^45*b^21*d^6 + 87808*A^3*a^47*b^19*d^6 - 85696*A^3*a^49*b^17*d^6 - 6144*A^3*a^51*b^15*d^6 + 15264*A^3*a^53*
b^13*d^6 + 5856*A^3*a^55*b^11*d^6 + 704*A^3*a^57*b^9*d^6 + 384*B^3*a^24*b^42*d^6 + 7296*B^3*a^26*b^40*d^6 + 59
424*B^3*a^28*b^38*d^6 + 280992*B^3*a^30*b^36*d^6 + 866208*B^3*a^32*b^34*d^6 + 1825824*B^3*a^34*b^32*d^6 + 2629
536*B^3*a^36*b^30*d^6 + 2374944*B^3*a^38*b^28*d^6 + 727584*B^3*a^40*b^26*d^6 - 1413984*B^3*a^42*b^24*d^6 - 264
9504*B^3*a^44*b^22*d^6 - 2454816*B^3*a^46*b^20*d^6 - 1476384*B^3*a^48*b^18*d^6 - 597408*B^3*a^50*b^16*d^6 - 15
6192*B^3*a^52*b^14*d^6 - 22944*B^3*a^54*b^12*d^6 - 1056*B^3*a^56*b^10*d^6 + 96*B^3*a^58*b^8*d^6 - ((5*A*b - 2*
B*a)*((a + b*tan(c + d*x))^(1/2)*(1600*A^2*a^22*b^46*d^7 + 28800*A^2*a^24*b^44*d^7 + 244800*A^2*a^26*b^42*d^7
+ 1304256*A^2*a^28*b^40*d^7 + 4880128*A^2*a^30*b^38*d^7 + 13627392*A^2*a^32*b^36*d^7 + 29476608*A^2*a^34*b^34*
d^7 + 50615552*A^2*a^36*b^32*d^7 + 70152576*A^2*a^38*b^30*d^7 + 79329536*A^2*a^40*b^28*d^7 + 73600384*A^2*a^42
*b^26*d^7 + 56025216*A^2*a^44*b^24*d^7 + 34754304*A^2*a^46*b^22*d^7 + 17296384*A^2*a^48*b^20*d^7 + 6713088*A^2
*a^50*b^18*d^7 + 1934592*A^2*a^52*b^16*d^7 + 377408*A^2*a^54*b^14*d^7 + 39552*A^2*a^56*b^12*d^7 + 64*A^2*a^58*
b^10*d^7 - 320*A^2*a^60*b^8*d^7 + 256*B^2*a^24*b^44*d^7 + 4608*B^2*a^26*b^42*d^7 + 40512*B^2*a^28*b^40*d^7 + 2
24768*B^2*a^30*b^38*d^7 + 864768*B^2*a^32*b^36*d^7 + 2419200*B^2*a^34*b^34*d^7 + 5055232*B^2*a^36*b^32*d^7 + 8
007168*B^2*a^38*b^30*d^7 + 9664512*B^2*a^40*b^28*d^7 + 8859136*B^2*a^42*b^26*d^7 + 6095232*B^2*a^44*b^24*d^7 +
3095040*B^2*a^46*b^22*d^7 + 1164800*B^2*a^48*b^20*d^7 + 376320*B^2*a^50*b^18*d^7 + 154368*B^2*a^52*b^16*d^7 +
76288*B^2*a^54*b^14*d^7 + 28416*B^2*a^56*b^12*d^7 + 6144*B^2*a^58*b^10*d^7 + 576*B^2*a^60*b^8*d^7 - 1280*A*B*
a^23*b^45*d^7 - 23040*A*B*a^25*b^43*d^7 - 196352*A*B*a^27*b^41*d^7 - 1046016*A*B*a^29*b^39*d^7 - 3887616*A*B*a
^31*b^37*d^7 - 10683904*A*B*a^33*b^35*d^7 - 22503936*A*B*a^35*b^33*d^7 - 37240320*A*B*a^37*b^31*d^7 - 49347584
*A*B*a^39*b^29*d^7 - 53228032*A*B*a^41*b^27*d^7 - 47443968*A*B*a^43*b^25*d^7 - 35389952*A*B*a^45*b^23*d^7 - 22
224384*A*B*a^47*b^21*d^7 - 11665920*A*B*a^49*b^19*d^7 - 4988416*A*B*a^51*b^17*d^7 - 1657344*A*B*a^53*b^15*d^7
- 397056*A*B*a^55*b^13*d^7 - 60416*A*B*a^57*b^11*d^7 - 4352*A*B*a^59*b^9*d^7) - ((5*A*b - 2*B*a)*(1280*A*a^24*
b^47*d^8 + 24320*A*a^26*b^45*d^8 + 219008*A*a^28*b^43*d^8 + 1241984*A*a^30*b^41*d^8 + 4970496*A*a^32*b^39*d^8
+ 14909440*A*a^34*b^37*d^8 + 34746880*A*a^36*b^35*d^8 + 64356864*A*a^38*b^33*d^8 + 96092672*A*a^40*b^31*d^8 +
116633088*A*a^42*b^29*d^8 + 115498240*A*a^44*b^27*d^8 + 93267200*A*a^46*b^25*d^8 + 61128704*A*a^48*b^23*d^8 +
32212992*A*a^50*b^21*d^8 + 13439488*A*a^52*b^19*d^8 + 4334080*A*a^54*b^17*d^8 + 1040640*A*a^56*b^15*d^8 + 1748
48*A*a^58*b^13*d^8 + 18304*A*a^60*b^11*d^8 + 896*A*a^62*b^9*d^8 - 512*B*a^25*b^46*d^8 - 9728*B*a^27*b^44*d^8 -
87936*B*a^29*b^42*d^8 - 502144*B*a^31*b^40*d^8 - 2028544*B*a^33*b^38*d^8 - 6153216*B*a^35*b^36*d^8 - 14518784
*B*a^37*b^34*d^8 - 27243008*B*a^39*b^32*d^8 - 41213952*B*a^41*b^30*d^8 - 50665472*B*a^43*b^28*d^8 - 50775296*B
*a^45*b^26*d^8 - 41443584*B*a^47*b^24*d^8 - 27409408*B*a^49*b^22*d^8 - 14543872*B*a^51*b^20*d^8 - 6093312*B*a^
53*b^18*d^8 - 1966592*B*a^55*b^16*d^8 - 470528*B*a^57*b^14*d^8 - 78336*B*a^59*b^12*d^8 - 8064*B*a^61*b^10*d^8
- 384*B*a^63*b^8*d^8 + ((5*A*b - 2*B*a)*(a + b*tan(c + d*x))^(1/2)*(512*a^27*b^46*d^9 + 9984*a^29*b^44*d^9 + 9
2160*a^31*b^42*d^9 + 535296*a^33*b^40*d^9 + 2193408*a^35*b^38*d^9 + 6736896*a^37*b^36*d^9 + 16084992*a^39*b^34
*d^9 + 30551040*a^41*b^32*d^9 + 46844928*a^43*b^30*d^9 + 58499584*a^45*b^28*d^9 + 59744256*a^47*b^26*d^9 + 499
00032*a^49*b^24*d^9 + 33945600*a^51*b^22*d^9 + 18643968*a^53*b^20*d^9 + 8146944*a^55*b^18*d^9 + 2767872*a^57*b
^16*d^9 + 705024*a^59*b^14*d^9 + 126720*a^61*b^12*d^9 + 14336*a^63*b^10*d^9 + 768*a^65*b^8*d^9))/(2*d*(a^7)^(1
/2))))/(2*d*(a^7)^(1/2))))/(2*d*(a^7)^(1/2)) - 2048*A*B^2*a^23*b^43*d^6 - 35456*A*B^2*a^25*b^41*d^6 - 269824*A
*B^2*a^27*b^39*d^6 - 1203648*A*B^2*a^29*b^37*d^6 - 3500672*A*B^2*a^31*b^35*d^6 - 6889792*A*B^2*a^33*b^33*d^6 -
8968960*A*B^2*a^35*b^31*d^6 - 6452160*A*B^2*a^37*b^29*d^6 + 933504*A*B^2*a^39*b^27*d^6 + 8721856*A*B^2*a^41*b
^25*d^6 + 11714560*A*B^2*a^43*b^23*d^6 + 9184448*A*B^2*a^45*b^21*d^6 + 4647552*A*B^2*a^47*b^19*d^6 + 1433152*A
*B^2*a^49*b^17*d^6 + 182528*A*B^2*a^51*b^15*d^6 - 37696*A*B^2*a^53*b^13*d^6 - 18048*A*B^2*a^55*b^11*d^6 - 2112
*A*B^2*a^57*b^9*d^6 + 3040*A^2*B*a^22*b^44*d^6 + 47200*A^2*B*a^24*b^42*d^6 + 325120*A^2*B*a^26*b^40*d^6 + 1304
352*A^2*B*a^28*b^38*d^6 + 3319840*A^2*B*a^30*b^36*d^6 + 5298720*A^2*B*a^32*b^34*d^6 + 4178720*A^2*B*a^34*b^32*
d^6 - 2452320*A^2*B*a^36*b^30*d^6 - 12167584*A^2*B*a^38*b^28*d^6 - 18281120*A^2*B*a^40*b^26*d^6 - 16496480*A^2
*B*a^42*b^24*d^6 - 9395360*A^2*B*a^44*b^22*d^6 - 2839200*A^2*B*a^46*b^20*d^6 + 167776*A^2*B*a^48*b^18*d^6 + 56
3040*A^2*B*a^50*b^16*d^6 + 239840*A^2*B*a^52*b^14*d^6 + 45120*A^2*B*a^54*b^12*d^6 + 2240*A^2*B*a^56*b^10*d^6 -
288*A^2*B*a^58*b^8*d^6))/(2*d*(a^7)^(1/2)))*(5*A*b - 2*B*a))/(2*d*(a^7)^(1/2)) - 320*A*B^4*a^22*b^39*d^4 - 41
92*A*B^4*a^24*b^37*d^4 - 25088*A*B^4*a^26*b^35*d^4 - 90272*A*B^4*a^28*b^33*d^4 - 215488*A*B^4*a^30*b^31*d^4 -
352352*A*B^4*a^32*b^29*d^4 - 384384*A*B^4*a^34*b^27*d^4 - 233376*A*B^4*a^36*b^25*d^4 + 27456*A*B^4*a^38*b^23*d
^4 + 224224*A*B^4*a^40*b^21*d^4 + 256256*A*B^4*a^42*b^19*d^4 + 171808*A*B^4*a^44*b^17*d^4 + 75712*A*B^4*a^46*b
^15*d^4 + 21728*A*B^4*a^48*b^13*d^4 + 3712*A*B^4*a^50*b^11*d^4 + 288*A*B^4*a^52*b^9*d^4 + 400*A^4*B*a^21*b^40*
d^4 + 4560*A^4*B*a^23*b^38*d^4 + 21904*A^4*B*a^25*b^36*d^4 + 51856*A^4*B*a^27*b^34*d^4 + 27664*A^4*B*a^29*b^32
*d^4 - 216944*A^4*B*a^31*b^30*d^4 - 816816*A^4*B*a^33*b^28*d^4 - 1622192*A^4*B*a^35*b^26*d^4 - 2175888*A^4*B*a
^37*b^24*d^4 - 2102672*A^4*B*a^39*b^22*d^4 - 1489488*A^4*B*a^41*b^20*d^4 - 767312*A^4*B*a^43*b^18*d^4 - 278096
*A^4*B*a^45*b^16*d^4 - 65744*A^4*B*a^47*b^14*d^4 - 8336*A^4*B*a^49*b^12*d^4 - 144*A^4*B*a^51*b^10*d^4 + 64*A^4
*B*a^53*b^8*d^4 + 400*A^2*B^3*a^21*b^40*d^4 + 4624*A^2*B^3*a^23*b^38*d^4 + 22800*A^2*B^3*a^25*b^36*d^4 + 57680
*A^2*B^3*a^27*b^34*d^4 + 50960*A^2*B^3*a^29*b^32*d^4 - 152880*A^2*B^3*a^31*b^30*d^4 - 688688*A^2*B^3*a^33*b^28
*d^4 - 1430000*A^2*B^3*a^35*b^26*d^4 - 1956240*A^2*B^3*a^37*b^24*d^4 - 1910480*A^2*B^3*a^39*b^22*d^4 - 1361360
*A^2*B^3*a^41*b^20*d^4 - 703248*A^2*B^3*a^43*b^18*d^4 - 254800*A^2*B^3*a^45*b^16*d^4 - 59920*A^2*B^3*a^47*b^14
*d^4 - 7440*A^2*B^3*a^49*b^12*d^4 - 80*A^2*B^3*a^51*b^10*d^4 + 64*A^2*B^3*a^53*b^8*d^4 + 480*A^3*B^2*a^22*b^39
*d^4 + 6848*A^3*B^2*a^24*b^37*d^4 + 45472*A^3*B^2*a^26*b^35*d^4 + 186368*A^3*B^2*a^28*b^33*d^4 + 527072*A^3*B^
2*a^30*b^31*d^4 + 1089088*A^3*B^2*a^32*b^29*d^4 + 1697696*A^3*B^2*a^34*b^27*d^4 + 2031744*A^3*B^2*a^36*b^25*d^
4 + 1880736*A^3*B^2*a^38*b^23*d^4 + 1345344*A^3*B^2*a^40*b^21*d^4 + 736736*A^3*B^2*a^42*b^19*d^4 + 302848*A^3*
B^2*a^44*b^17*d^4 + 90272*A^3*B^2*a^46*b^15*d^4 + 18368*A^3*B^2*a^48*b^13*d^4 + 2272*A^3*B^2*a^50*b^11*d^4 + 1
28*A^3*B^2*a^52*b^9*d^4))*(5*A*b - 2*B*a)*1i)/(d*(a^7)^(1/2))