\(\int \cot ^5(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx\) [339]

Optimal result

Integrand size = 33, antiderivative size = 342 \[ \int \cot ^5(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx=-\frac {\left (128 a^4 A-240 a^2 A b^2-5 A b^4-320 a^3 b B+40 a b^3 B\right ) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{64 a^{3/2} d}+\frac {(a-i b)^{5/2} (A-i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{d}+\frac {(a+i b)^{5/2} (A+i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{d}+\frac {\left (144 a^2 A b-5 A b^3+64 a^3 B-88 a b^2 B\right ) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{64 a d}+\frac {\left (48 a^2 A-59 A b^2-104 a b B\right ) \cot ^2(c+d x) \sqrt {a+b \tan (c+d x)}}{96 d}-\frac {a (11 A b+8 a B) \cot ^3(c+d x) \sqrt {a+b \tan (c+d x)}}{24 d}-\frac {a A \cot ^4(c+d x) (a+b \tan (c+d x))^{3/2}}{4 d} \]

[Out]

-1/64*(128*A*a^4-240*A*a^2*b^2-5*A*b^4-320*B*a^3*b+40*B*a*b^3)*arctanh((a+b*tan(d*x+c))^(1/2)/a^(1/2))/a^(3/2)
/d+(a-I*b)^(5/2)*(A-I*B)*arctanh((a+b*tan(d*x+c))^(1/2)/(a-I*b)^(1/2))/d+(a+I*b)^(5/2)*(A+I*B)*arctanh((a+b*ta
n(d*x+c))^(1/2)/(a+I*b)^(1/2))/d+1/64*(144*A*a^2*b-5*A*b^3+64*B*a^3-88*B*a*b^2)*cot(d*x+c)*(a+b*tan(d*x+c))^(1
/2)/a/d+1/96*(48*A*a^2-59*A*b^2-104*B*a*b)*cot(d*x+c)^2*(a+b*tan(d*x+c))^(1/2)/d-1/24*a*(11*A*b+8*B*a)*cot(d*x
+c)^3*(a+b*tan(d*x+c))^(1/2)/d-1/4*a*A*cot(d*x+c)^4*(a+b*tan(d*x+c))^(3/2)/d

Rubi [A] (verified)

Time = 2.31 (sec) , antiderivative size = 342, normalized size of antiderivative = 1.00, number of steps used = 15, number of rules used = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.273, Rules used = {3686, 3726, 3730, 3734, 3620, 3618, 65, 214, 3715} \[ \int \cot ^5(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx=\frac {\left (48 a^2 A-104 a b B-59 A b^2\right ) \cot ^2(c+d x) \sqrt {a+b \tan (c+d x)}}{96 d}+\frac {\left (64 a^3 B+144 a^2 A b-88 a b^2 B-5 A b^3\right ) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{64 a d}-\frac {\left (128 a^4 A-320 a^3 b B-240 a^2 A b^2+40 a b^3 B-5 A b^4\right ) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{64 a^{3/2} d}+\frac {(a-i b)^{5/2} (A-i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{d}+\frac {(a+i b)^{5/2} (A+i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{d}-\frac {a (8 a B+11 A b) \cot ^3(c+d x) \sqrt {a+b \tan (c+d x)}}{24 d}-\frac {a A \cot ^4(c+d x) (a+b \tan (c+d x))^{3/2}}{4 d} \]

[In]

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

[Out]

-1/64*((128*a^4*A - 240*a^2*A*b^2 - 5*A*b^4 - 320*a^3*b*B + 40*a*b^3*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[
a]])/(a^(3/2)*d) + ((a - I*b)^(5/2)*(A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + ((a + I*b)^
(5/2)*(A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + ((144*a^2*A*b - 5*A*b^3 + 64*a^3*B - 88*a
*b^2*B)*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(64*a*d) + ((48*a^2*A - 59*A*b^2 - 104*a*b*B)*Cot[c + d*x]^2*Sq
rt[a + b*Tan[c + d*x]])/(96*d) - (a*(11*A*b + 8*a*B)*Cot[c + d*x]^3*Sqrt[a + b*Tan[c + d*x]])/(24*d) - (a*A*Co
t[c + d*x]^4*(a + b*Tan[c + d*x])^(3/2))/(4*d)

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 3686

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*c - a*d)*(B*c - A*d)*(a + b*Tan[e + f*x])^(m - 1)*((c + d*Tan[e
+ f*x])^(n + 1)/(d*f*(n + 1)*(c^2 + d^2))), x] - Dist[1/(d*(n + 1)*(c^2 + d^2)), Int[(a + b*Tan[e + f*x])^(m -
2)*(c + d*Tan[e + f*x])^(n + 1)*Simp[a*A*d*(b*d*(m - 1) - a*c*(n + 1)) + (b*B*c - (A*b + a*B)*d)*(b*c*(m - 1)
+ a*d*(n + 1)) - d*((a*A - b*B)*(b*c - a*d) + (A*b + a*B)*(a*c + b*d))*(n + 1)*Tan[e + f*x] - b*(d*(A*b*c + a
*B*c - a*A*d)*(m + n) - b*B*(c^2*(m - 1) - d^2*(n + 1)))*Tan[e + f*x]^2, x], x], x] /; FreeQ[{a, b, c, d, e, f
, A, B}, x] && NeQ[b*c - a*d, 0] && NeQ[a^2 + b^2, 0] && NeQ[c^2 + d^2, 0] && GtQ[m, 1] && LtQ[n, -1] && (Inte
gerQ[m] || IntegersQ[2*m, 2*n])

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 3726

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*d^2 + c*(c*C - B*d))*(a + b*Ta
n[e + f*x])^m*((c + d*Tan[e + f*x])^(n + 1)/(d*f*(n + 1)*(c^2 + d^2))), x] - Dist[1/(d*(n + 1)*(c^2 + d^2)), I
nt[(a + b*Tan[e + f*x])^(m - 1)*(c + d*Tan[e + f*x])^(n + 1)*Simp[A*d*(b*d*m - a*c*(n + 1)) + (c*C - B*d)*(b*c
*m + a*d*(n + 1)) - d*(n + 1)*((A - C)*(b*c - a*d) + B*(a*c + b*d))*Tan[e + f*x] - b*(d*(B*c - A*d)*(m + n + 1
) - C*(c^2*m - d^2*(n + 1)))*Tan[e + f*x]^2, x], x], x] /; FreeQ[{a, b, c, d, e, f, A, B, C}, x] && NeQ[b*c -
a*d, 0] && NeQ[a^2 + b^2, 0] && NeQ[c^2 + d^2, 0] && GtQ[m, 0] && LtQ[n, -1]

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 A \cot ^4(c+d x) (a+b \tan (c+d x))^{3/2}}{4 d}+\frac {1}{4} \int \cot ^4(c+d x) \sqrt {a+b \tan (c+d x)} \left (\frac {1}{2} a (11 A b+8 a B)-4 \left (a^2 A-A b^2-2 a b B\right ) \tan (c+d x)-\frac {1}{2} b (5 a A-8 b B) \tan ^2(c+d x)\right ) \, dx \\ & = -\frac {a (11 A b+8 a B) \cot ^3(c+d x) \sqrt {a+b \tan (c+d x)}}{24 d}-\frac {a A \cot ^4(c+d x) (a+b \tan (c+d x))^{3/2}}{4 d}+\frac {1}{12} \int \frac {\cot ^3(c+d x) \left (-\frac {1}{4} a \left (48 a^2 A-59 A b^2-104 a b B\right )-12 \left (3 a^2 A b-A b^3+a^3 B-3 a b^2 B\right ) \tan (c+d x)-\frac {1}{4} b \left (85 a A b+40 a^2 B-48 b^2 B\right ) \tan ^2(c+d x)\right )}{\sqrt {a+b \tan (c+d x)}} \, dx \\ & = \frac {\left (48 a^2 A-59 A b^2-104 a b B\right ) \cot ^2(c+d x) \sqrt {a+b \tan (c+d x)}}{96 d}-\frac {a (11 A b+8 a B) \cot ^3(c+d x) \sqrt {a+b \tan (c+d x)}}{24 d}-\frac {a A \cot ^4(c+d x) (a+b \tan (c+d x))^{3/2}}{4 d}-\frac {\int \frac {\cot ^2(c+d x) \left (\frac {3}{8} a \left (144 a^2 A b-5 A b^3+64 a^3 B-88 a b^2 B\right )-24 a \left (a^3 A-3 a A b^2-3 a^2 b B+b^3 B\right ) \tan (c+d x)-\frac {3}{8} a b \left (48 a^2 A-59 A b^2-104 a b B\right ) \tan ^2(c+d x)\right )}{\sqrt {a+b \tan (c+d x)}} \, dx}{24 a} \\ & = \frac {\left (144 a^2 A b-5 A b^3+64 a^3 B-88 a b^2 B\right ) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{64 a d}+\frac {\left (48 a^2 A-59 A b^2-104 a b B\right ) \cot ^2(c+d x) \sqrt {a+b \tan (c+d x)}}{96 d}-\frac {a (11 A b+8 a B) \cot ^3(c+d x) \sqrt {a+b \tan (c+d x)}}{24 d}-\frac {a A \cot ^4(c+d x) (a+b \tan (c+d x))^{3/2}}{4 d}+\frac {\int \frac {\cot (c+d x) \left (\frac {3}{16} a \left (128 a^4 A-240 a^2 A b^2-5 A b^4-320 a^3 b B+40 a b^3 B\right )+24 a^2 \left (3 a^2 A b-A b^3+a^3 B-3 a b^2 B\right ) \tan (c+d x)+\frac {3}{16} a b \left (144 a^2 A b-5 A b^3+64 a^3 B-88 a b^2 B\right ) \tan ^2(c+d x)\right )}{\sqrt {a+b \tan (c+d x)}} \, dx}{24 a^2} \\ & = \frac {\left (144 a^2 A b-5 A b^3+64 a^3 B-88 a b^2 B\right ) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{64 a d}+\frac {\left (48 a^2 A-59 A b^2-104 a b B\right ) \cot ^2(c+d x) \sqrt {a+b \tan (c+d x)}}{96 d}-\frac {a (11 A b+8 a B) \cot ^3(c+d x) \sqrt {a+b \tan (c+d x)}}{24 d}-\frac {a A \cot ^4(c+d x) (a+b \tan (c+d x))^{3/2}}{4 d}+\frac {\int \frac {24 a^2 \left (3 a^2 A b-A b^3+a^3 B-3 a b^2 B\right )-24 a^2 \left (a^3 A-3 a A b^2-3 a^2 b B+b^3 B\right ) \tan (c+d x)}{\sqrt {a+b \tan (c+d x)}} \, dx}{24 a^2}+\frac {\left (128 a^4 A-240 a^2 A b^2-5 A b^4-320 a^3 b B+40 a b^3 B\right ) \int \frac {\cot (c+d x) \left (1+\tan ^2(c+d x)\right )}{\sqrt {a+b \tan (c+d x)}} \, dx}{128 a} \\ & = \frac {\left (144 a^2 A b-5 A b^3+64 a^3 B-88 a b^2 B\right ) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{64 a d}+\frac {\left (48 a^2 A-59 A b^2-104 a b B\right ) \cot ^2(c+d x) \sqrt {a+b \tan (c+d x)}}{96 d}-\frac {a (11 A b+8 a B) \cot ^3(c+d x) \sqrt {a+b \tan (c+d x)}}{24 d}-\frac {a A \cot ^4(c+d x) (a+b \tan (c+d x))^{3/2}}{4 d}+\frac {1}{2} \left ((a-i b)^3 (i A+B)\right ) \int \frac {1+i \tan (c+d x)}{\sqrt {a+b \tan (c+d x)}} \, dx+\frac {\left (24 a^2 \left (3 a^2 A b-A b^3+a^3 B-3 a b^2 B\right )-24 i a^2 \left (a^3 A-3 a A b^2-3 a^2 b B+b^3 B\right )\right ) \int \frac {1-i \tan (c+d x)}{\sqrt {a+b \tan (c+d x)}} \, dx}{48 a^2}+\frac {\left (128 a^4 A-240 a^2 A b^2-5 A b^4-320 a^3 b B+40 a b^3 B\right ) \text {Subst}\left (\int \frac {1}{x \sqrt {a+b x}} \, dx,x,\tan (c+d x)\right )}{128 a d} \\ & = \frac {\left (144 a^2 A b-5 A b^3+64 a^3 B-88 a b^2 B\right ) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{64 a d}+\frac {\left (48 a^2 A-59 A b^2-104 a b B\right ) \cot ^2(c+d x) \sqrt {a+b \tan (c+d x)}}{96 d}-\frac {a (11 A b+8 a B) \cot ^3(c+d x) \sqrt {a+b \tan (c+d x)}}{24 d}-\frac {a A \cot ^4(c+d x) (a+b \tan (c+d x))^{3/2}}{4 d}-\frac {\left ((a-i b)^3 (A-i B)\right ) \text {Subst}\left (\int \frac {1}{(-1+x) \sqrt {a-i b x}} \, dx,x,i \tan (c+d x)\right )}{2 d}-\frac {\left ((a+i b)^3 (A+i B)\right ) \text {Subst}\left (\int \frac {1}{(-1+x) \sqrt {a+i b x}} \, dx,x,-i \tan (c+d x)\right )}{2 d}+\frac {\left (128 a^4 A-240 a^2 A b^2-5 A b^4-320 a^3 b B+40 a b^3 B\right ) \text {Subst}\left (\int \frac {1}{-\frac {a}{b}+\frac {x^2}{b}} \, dx,x,\sqrt {a+b \tan (c+d x)}\right )}{64 a b d} \\ & = -\frac {\left (128 a^4 A-240 a^2 A b^2-5 A b^4-320 a^3 b B+40 a b^3 B\right ) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{64 a^{3/2} d}+\frac {\left (144 a^2 A b-5 A b^3+64 a^3 B-88 a b^2 B\right ) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{64 a d}+\frac {\left (48 a^2 A-59 A b^2-104 a b B\right ) \cot ^2(c+d x) \sqrt {a+b \tan (c+d x)}}{96 d}-\frac {a (11 A b+8 a B) \cot ^3(c+d x) \sqrt {a+b \tan (c+d x)}}{24 d}-\frac {a A \cot ^4(c+d x) (a+b \tan (c+d x))^{3/2}}{4 d}+\frac {\left (i (a+i b)^3 (A+i B)\right ) \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 d}-\frac {\left ((a-i b)^3 (i A+B)\right ) \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 d} \\ & = -\frac {\left (128 a^4 A-240 a^2 A b^2-5 A b^4-320 a^3 b B+40 a b^3 B\right ) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{64 a^{3/2} d}+\frac {(a-i b)^{5/2} (A-i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{d}+\frac {(a+i b)^{5/2} (A+i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{d}+\frac {\left (144 a^2 A b-5 A b^3+64 a^3 B-88 a b^2 B\right ) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{64 a d}+\frac {\left (48 a^2 A-59 A b^2-104 a b B\right ) \cot ^2(c+d x) \sqrt {a+b \tan (c+d x)}}{96 d}-\frac {a (11 A b+8 a B) \cot ^3(c+d x) \sqrt {a+b \tan (c+d x)}}{24 d}-\frac {a A \cot ^4(c+d x) (a+b \tan (c+d x))^{3/2}}{4 d} \\ \end{align*}

Mathematica [A] (verified)

Time = 6.58 (sec) , antiderivative size = 622, normalized size of antiderivative = 1.82 \[ \int \cot ^5(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx=-\frac {2 b B \cot ^4(c+d x) (a+b \tan (c+d x))^{3/2}}{5 d}-\frac {2}{5} \left (\frac {b (5 A b+2 a B) \cot ^4(c+d x) \sqrt {a+b \tan (c+d x)}}{7 d}-\frac {2}{7} \left (-\frac {\left (35 a^2 A-40 A b^2-72 a b B\right ) \cot ^4(c+d x) \sqrt {a+b \tan (c+d x)}}{16 d}-\frac {\frac {7 a \left (85 a A b+40 a^2 B-48 b^2 B\right ) \cot ^3(c+d x) \sqrt {a+b \tan (c+d x)}}{24 d}-\frac {\frac {35 a^2 \left (48 a^2 A-59 A b^2-104 a b B\right ) \cot ^2(c+d x) \sqrt {a+b \tan (c+d x)}}{32 d}-\frac {-\frac {-\frac {105 a^{5/2} \left (128 a^4 A-240 a^2 A b^2-5 A b^4-320 a^3 b B+40 a b^3 B\right ) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{32 d}+\frac {i \sqrt {a-i b} \left (210 a^4 \left (3 a^2 A b-A b^3+a^3 B-3 a b^2 B\right )+210 i a^4 \left (a^3 A-3 a A b^2-3 a^2 b B+b^3 B\right )\right ) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{(-a+i b) d}-\frac {i \sqrt {a+i b} \left (210 a^4 \left (3 a^2 A b-A b^3+a^3 B-3 a b^2 B\right )-210 i a^4 \left (a^3 A-3 a A b^2-3 a^2 b B+b^3 B\right )\right ) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{(-a-i b) d}}{a}-\frac {105 a^2 \left (144 a^2 A b-5 A b^3+64 a^3 B-88 a b^2 B\right ) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{32 d}}{2 a}}{3 a}}{4 a}\right )\right ) \]

[In]

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

[Out]

(-2*b*B*Cot[c + d*x]^4*(a + b*Tan[c + d*x])^(3/2))/(5*d) - (2*((b*(5*A*b + 2*a*B)*Cot[c + d*x]^4*Sqrt[a + b*Ta
n[c + d*x]])/(7*d) - (2*(-1/16*((35*a^2*A - 40*A*b^2 - 72*a*b*B)*Cot[c + d*x]^4*Sqrt[a + b*Tan[c + d*x]])/d -
((7*a*(85*a*A*b + 40*a^2*B - 48*b^2*B)*Cot[c + d*x]^3*Sqrt[a + b*Tan[c + d*x]])/(24*d) - ((35*a^2*(48*a^2*A -
59*A*b^2 - 104*a*b*B)*Cot[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(32*d) - (-(((-105*a^(5/2)*(128*a^4*A - 240*a^2
*A*b^2 - 5*A*b^4 - 320*a^3*b*B + 40*a*b^3*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(32*d) + (I*Sqrt[a - I
*b]*(210*a^4*(3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B) + (210*I)*a^4*(a^3*A - 3*a*A*b^2 - 3*a^2*b*B + b^3*B))*Ar
cTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((-a + I*b)*d) - (I*Sqrt[a + I*b]*(210*a^4*(3*a^2*A*b - A*b^3 +
a^3*B - 3*a*b^2*B) - (210*I)*a^4*(a^3*A - 3*a*A*b^2 - 3*a^2*b*B + b^3*B))*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sq
rt[a + I*b]])/((-a - I*b)*d))/a) - (105*a^2*(144*a^2*A*b - 5*A*b^3 + 64*a^3*B - 88*a*b^2*B)*Cot[c + d*x]*Sqrt[
a + b*Tan[c + d*x]])/(32*d))/(2*a))/(3*a))/(4*a)))/7))/5

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(2913\) vs. \(2(300)=600\).

Time = 0.30 (sec) , antiderivative size = 2914, normalized size of antiderivative = 8.52

method	result	size
derivativedivides	\(\text {Expression too large to display}\)	\(2914\)
default	\(\text {Expression too large to display}\)	\(2914\)

[In]

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

[Out]

-55/24/d/b/tan(d*x+c)^4*B*(a+b*tan(d*x+c))^(3/2)*a^2-2*a^(5/2)*A*arctanh((a+b*tan(d*x+c))^(1/2)/a^(1/2))/d-2/d
*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^
(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)*a+1/4/d/b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*
x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a^2-1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan
(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*
a^2+2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^
2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)*a-3/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+
2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a-3/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*ar
ctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2-1/4/d/b*ln(
(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)
^(1/2)*a^3+1/4/d/b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(
2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+5/64/d*b^4/a^(3/2)*arctanh((a+b*tan(d*x+c))^(1/2)/a^(1/2))*A+55/192/d/tan(d*x
+c)^4*A*(a+b*tan(d*x+c))^(3/2)*a-5/64/d/tan(d*x+c)^4*(a+b*tan(d*x+c))^(1/2)*A*a^2-5/64/d/tan(d*x+c)^4/a*(a+b*t
an(d*x+c))^(7/2)*A-1/4/d*b^2*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^
(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+3/4/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^
(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b
^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^3-3/4/d*ln((a+b*tan(d*x+c))^
(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-1/d/(2
*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)
-2*a)^(1/2))*A*a^3-1/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2
*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B+1/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2
*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B+1/4/d*b^2*ln((a+b*tan(d*x+c))^(1/2)*(2*(a
^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-3/4/d*b*ln(b*tan(d*x+
c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1
/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b
^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)-73/192/d/tan(d*x+c)^4*(a+b*tan(d*x+c))^(5/2)*A+15/4/d*b^2*A*a^(1/2)*ar
ctanh((a+b*tan(d*x+c))^(1/2)/a^(1/2))+5/d*b*a^(3/2)*arctanh((a+b*tan(d*x+c))^(1/2)/a^(1/2))*B-5/8/d*b^3/a^(1/2
)*arctanh((a+b*tan(d*x+c))^(1/2)/a^(1/2))*B-11/8/d/b/tan(d*x+c)^4*(a+b*tan(d*x+c))^(7/2)*B+3/d*b^2/(2*(a^2+b^2
)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/
2))*A*a+3/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2
*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+1/2/d*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-
a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(
((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*tan(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)*a^2-
1/2/d*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(
1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b
^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)*a^2-1/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/
2)*arctan((2*(a+b*tan(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^
(1/2)+1/4/d*b*ln(b*tan(d*x+c)+a+(a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^
2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)-3/d/b^3/tan(d*x+c)^4*(a+b*tan(d*x+c))^(5/2)*B*a^3-1/d/b^3/tan(d*x+c)^4
*(a+b*tan(d*x+c))^(1/2)*B*a^5+5/8/d/b/tan(d*x+c)^4*(a+b*tan(d*x+c))^(1/2)*B*a^3+9/4/d/b^2/tan(d*x+c)^4*a*(a+b*
tan(d*x+c))^(7/2)*A-7/4/d/b^2/tan(d*x+c)^4*(a+b*tan(d*x+c))^(1/2)*A*a^4+73/24/d/b/tan(d*x+c)^4*(a+b*tan(d*x+c)
)^(5/2)*B*a+23/4/d/b^2/tan(d*x+c)^4*A*(a+b*tan(d*x+c))^(3/2)*a^3+3/d/b^3/tan(d*x+c)^4*B*(a+b*tan(d*x+c))^(3/2)
*a^4+1/d/b^3/tan(d*x+c)^4*a^2*(a+b*tan(d*x+c))^(7/2)*B-25/4/d/b^2/tan(d*x+c)^4*(a+b*tan(d*x+c))^(5/2)*A*a^2+3/
4/d*b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(
1/2)+2*a)^(1/2)*a-1/4/d*b*ln((a+b*tan(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*tan(d*x+c)-a-(a^2+b^2)^(1/
2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 5045 vs. \(2 (294) = 588\).

Time = 55.78 (sec) , antiderivative size = 10107, normalized size of antiderivative = 29.55 \[ \int \cot ^5(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx=\text {Too large to display} \]

[In]

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

[Out]

Too large to include

Sympy [F(-1)]

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

[In]

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

[Out]

Timed out

Maxima [F(-1)]

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

[In]

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

[Out]

Timed out

Giac [F(-1)]

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

[In]

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

[Out]

Timed out

Mupad [B] (verification not implemented)

Time = 12.43 (sec) , antiderivative size = 36736, normalized size of antiderivative = 107.42 \[ \int \cot ^5(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx=\text {Too large to display} \]

[In]

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

[Out]

atan(((((((10240*A*a*b^14*d^4 + 436224*A*a^3*b^12*d^4 + 229376*A*a^5*b^10*d^4 - 196608*A*a^7*b^8*d^4 - 81920*B
*a^2*b^13*d^4 + 442368*B*a^4*b^11*d^4 + 524288*B*a^6*b^9*d^4)/(512*a^2*d^5) - ((131072*a^2*b^10*d^4 + 196608*a
^4*b^8*d^4)*(a + b*tan(c + d*x))^(1/2)*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d
^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b
^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2
*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*a^5*d^2 - B^2*a^5*d^
2 - 10*A^2*a^3*b^2*d^2 + 10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^4*d^2 + 20*A*B*a^2*b
^3*d^2 - 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2))/(256*a^2*d^4))*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2
*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B
^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*a
^5*d^2 - B^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^4
*d^2 + 20*A*B*a^2*b^3*d^2 - 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2) + ((a + b*tan(c + d*x))^(1/2)*(320896*A^2*a^3*b^1
4*d^2 + 143360*A^2*a^5*b^12*d^2 - 1081344*A^2*a^7*b^10*d^2 + 147456*A^2*a^9*b^8*d^2 - 304896*B^2*a^3*b^14*d^2
- 20480*B^2*a^5*b^12*d^2 + 1245184*B^2*a^7*b^10*d^2 - 81920*B^2*a^9*b^8*d^2 + 100*A^2*a*b^16*d^2 - 132672*A*B*
a^2*b^15*d^2 + 919040*A*B*a^4*b^13*d^2 + 1966080*A*B*a^6*b^11*d^2 - 1179648*A*B*a^8*b^9*d^2))/(256*a^2*d^4))*(
(((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4
*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*
B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A
^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*a^5*d^2 - B^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 10*B^2*a^3*b^2*
d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^4*d^2 + 20*A*B*a^2*b^3*d^2 - 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2
) + (100*A^3*b^20*d^2 - 16000*A^3*a^2*b^18*d^2 - 928868*A^3*a^4*b^16*d^2 + 1805952*A^3*a^6*b^14*d^2 + 1489920*
A^3*a^8*b^12*d^2 - 1179648*A^3*a^10*b^10*d^2 + 49152*A^3*a^12*b^8*d^2 - 208384*B^3*a^3*b^17*d^2 + 1651200*B^3*
a^5*b^15*d^2 - 557056*B^3*a^7*b^13*d^2 - 2039808*B^3*a^9*b^11*d^2 + 376832*B^3*a^11*b^9*d^2 + 8840*A^2*B*a*b^1
9*d^2 - 53120*A*B^2*a^2*b^18*d^2 + 2411392*A*B^2*a^4*b^16*d^2 - 5701888*A*B^2*a^6*b^14*d^2 - 4381696*A*B^2*a^8
*b^12*d^2 + 3637248*A*B^2*a^10*b^10*d^2 - 147456*A*B^2*a^12*b^8*d^2 + 543176*A^2*B*a^3*b^17*d^2 - 5453504*A^2*
B*a^5*b^15*d^2 + 1016320*A^2*B*a^7*b^13*d^2 + 5873664*A^2*B*a^9*b^11*d^2 - 1130496*A^2*B*a^11*b^9*d^2)/(512*a^
2*d^5))*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a
^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8
*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b
^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*a^5*d^2 - B^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 10*B^2
*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^4*d^2 + 20*A*B*a^2*b^3*d^2 - 10*A*B*a^4*b*d^2)/(4*d
^4))^(1/2) - ((a + b*tan(c + d*x))^(1/2)*(25*A^2*B^2*b^22 - 25*A^4*b^22 + 6167*A^4*a^2*b^20 + 28457*A^4*a^4*b^
18 + 993145*A^4*a^6*b^16 - 1616544*A^4*a^8*b^14 + 1346560*A^4*a^10*b^12 - 258048*A^4*a^12*b^10 + 24576*A^4*a^1
4*b^8 + 9792*B^4*a^2*b^20 - 448*B^4*a^4*b^18 + 633280*B^4*a^6*b^16 - 1757760*B^4*a^8*b^14 + 1684480*B^4*a^10*b
^12 - 53248*B^4*a^12*b^10 + 8192*B^4*a^14*b^8 + 21609*A^2*B^2*a^2*b^20 + 344599*A^2*B^2*a^4*b^18 - 3736185*A^2
*B^2*a^6*b^16 + 11758304*A^2*B^2*a^8*b^14 - 7782400*A^2*B^2*a^10*b^12 + 1490944*A^2*B^2*a^12*b^10 - 400*A*B^3*
a*b^21 + 100*A^3*B*a*b^21 - 29200*A*B^3*a^3*b^19 + 769040*A*B^3*a^5*b^17 - 5051120*A*B^3*a^7*b^15 + 8105600*A*
B^3*a^9*b^13 - 2621440*A*B^3*a^11*b^11 + 81920*A*B^3*a^13*b^9 - 17800*A^3*B*a^3*b^19 - 977980*A^3*B*a^5*b^17 +
5740400*A^3*B*a^7*b^15 - 7032448*A^3*B*a^9*b^13 + 2785280*A^3*B*a^11*b^11 - 278528*A^3*B*a^13*b^9))/(256*a^2*
d^4))*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^1
0 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b
^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6
+ 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*a^5*d^2 - B^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 10*B^2*a
^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^4*d^2 + 20*A*B*a^2*b^3*d^2 - 10*A*B*a^4*b*d^2)/(4*d^4
))^(1/2)*1i - (((((10240*A*a*b^14*d^4 + 436224*A*a^3*b^12*d^4 + 229376*A*a^5*b^10*d^4 - 196608*A*a^7*b^8*d^4 -
81920*B*a^2*b^13*d^4 + 442368*B*a^4*b^11*d^4 + 524288*B*a^6*b^9*d^4)/(512*a^2*d^5) + ((131072*a^2*b^10*d^4 +
196608*a^4*b^8*d^4)*(a + b*tan(c + d*x))^(1/2)*((((8*B^2*a^5*d^2 - 8*A^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)^
2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A
^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2
+ 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*a^5*d^2 - B^
2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^4*d^2 + 20*A
*B*a^2*b^3*d^2 - 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2))/(256*a^2*d^4))*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5
*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b
^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2)
+ A^2*a^5*d^2 - B^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B
^2*a*b^4*d^2 + 20*A*B*a^2*b^3*d^2 - 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2) - ((a + b*tan(c + d*x))^(1/2)*(320896*A^2
*a^3*b^14*d^2 + 143360*A^2*a^5*b^12*d^2 - 1081344*A^2*a^7*b^10*d^2 + 147456*A^2*a^9*b^8*d^2 - 304896*B^2*a^3*b
^14*d^2 - 20480*B^2*a^5*b^12*d^2 + 1245184*B^2*a^7*b^10*d^2 - 81920*B^2*a^9*b^8*d^2 + 100*A^2*a*b^16*d^2 - 132
672*A*B*a^2*b^15*d^2 + 919040*A*B*a^4*b^13*d^2 + 1966080*A*B*a^6*b^11*d^2 - 1179648*A*B*a^8*b^9*d^2))/(256*a^2
*d^4))*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^
10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*
b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^
6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*a^5*d^2 - B^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 10*B^2*
a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^4*d^2 + 20*A*B*a^2*b^3*d^2 - 10*A*B*a^4*b*d^2)/(4*d^
4))^(1/2) + (100*A^3*b^20*d^2 - 16000*A^3*a^2*b^18*d^2 - 928868*A^3*a^4*b^16*d^2 + 1805952*A^3*a^6*b^14*d^2 +
1489920*A^3*a^8*b^12*d^2 - 1179648*A^3*a^10*b^10*d^2 + 49152*A^3*a^12*b^8*d^2 - 208384*B^3*a^3*b^17*d^2 + 1651
200*B^3*a^5*b^15*d^2 - 557056*B^3*a^7*b^13*d^2 - 2039808*B^3*a^9*b^11*d^2 + 376832*B^3*a^11*b^9*d^2 + 8840*A^2
*B*a*b^19*d^2 - 53120*A*B^2*a^2*b^18*d^2 + 2411392*A*B^2*a^4*b^16*d^2 - 5701888*A*B^2*a^6*b^14*d^2 - 4381696*A
*B^2*a^8*b^12*d^2 + 3637248*A*B^2*a^10*b^10*d^2 - 147456*A*B^2*a^12*b^8*d^2 + 543176*A^2*B*a^3*b^17*d^2 - 5453
504*A^2*B*a^5*b^15*d^2 + 1016320*A^2*B*a^7*b^13*d^2 + 5873664*A^2*B*a^9*b^11*d^2 - 1130496*A^2*B*a^11*b^9*d^2)
/(512*a^2*d^5))*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10
+ B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5
*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B
^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*a^5*d^2 - B^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2
+ 10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^4*d^2 + 20*A*B*a^2*b^3*d^2 - 10*A*B*a^4*b*d
^2)/(4*d^4))^(1/2) + ((a + b*tan(c + d*x))^(1/2)*(25*A^2*B^2*b^22 - 25*A^4*b^22 + 6167*A^4*a^2*b^20 + 28457*A^
4*a^4*b^18 + 993145*A^4*a^6*b^16 - 1616544*A^4*a^8*b^14 + 1346560*A^4*a^10*b^12 - 258048*A^4*a^12*b^10 + 24576
*A^4*a^14*b^8 + 9792*B^4*a^2*b^20 - 448*B^4*a^4*b^18 + 633280*B^4*a^6*b^16 - 1757760*B^4*a^8*b^14 + 1684480*B^
4*a^10*b^12 - 53248*B^4*a^12*b^10 + 8192*B^4*a^14*b^8 + 21609*A^2*B^2*a^2*b^20 + 344599*A^2*B^2*a^4*b^18 - 373
6185*A^2*B^2*a^6*b^16 + 11758304*A^2*B^2*a^8*b^14 - 7782400*A^2*B^2*a^10*b^12 + 1490944*A^2*B^2*a^12*b^10 - 40
0*A*B^3*a*b^21 + 100*A^3*B*a*b^21 - 29200*A*B^3*a^3*b^19 + 769040*A*B^3*a^5*b^17 - 5051120*A*B^3*a^7*b^15 + 81
05600*A*B^3*a^9*b^13 - 2621440*A*B^3*a^11*b^11 + 81920*A*B^3*a^13*b^9 - 17800*A^3*B*a^3*b^19 - 977980*A^3*B*a^
5*b^17 + 5740400*A^3*B*a^7*b^15 - 7032448*A^3*B*a^9*b^13 + 2785280*A^3*B*a^11*b^11 - 278528*A^3*B*a^13*b^9))/(
256*a^2*d^4))*((((8*B^2*a^5*d^2 - 8*A^2*a^5*d^2 + 80*A^2*a^3*b^2*d^2 - 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 - 4
0*A^2*a*b^4*d^2 + 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/64 - d^4*(A^4*a^10 + A^4*b^10 +
B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A
^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2
*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*a^5*d^2 - B^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 +
10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^4*d^2 + 20*A*B*a^2*b^3*d^2 - 10*A*B*a^4*b*d^2
)/(4*d^4))^(1/2)*1i)/((((((10240*A*a*b^14*d^4 + 436224*A*a^3*b^12*d^4 + 229376*A*a^5*b^10*d^4 - 196608*A*a^7*b
^8*d^4 - 81920*B*a^2*b^13*d^4 + 442368*B*a^4*b^11*d^4 + 524288*B*a^6*b^9*d^4)/(512*a^2*d^5) - ((131072*a^2*b^1
0*d^4 + 196608*a^4*b^8*d^4)*(a + b*tan(c + d*x))^(1/2)*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^
8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*
a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*a^5*
d^2 - B^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^4*d^
2 + 20*A*B*a^2*b^3*d^2 - 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2))/(256*a^2*d^4))*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*
b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B
^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2
))^(1/2) + A^2*a^5*d^2 - B^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d
^2 - 5*B^2*a*b^4*d^2 + 20*A*B*a^2*b^3*d^2 - 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2) + ((a + b*tan(c + d*x))^(1/2)*(32
0896*A^2*a^3*b^14*d^2 + 143360*A^2*a^5*b^12*d^2 - 1081344*A^2*a^7*b^10*d^2 + 147456*A^2*a^9*b^8*d^2 - 304896*B
^2*a^3*b^14*d^2 - 20480*B^2*a^5*b^12*d^2 + 1245184*B^2*a^7*b^10*d^2 - 81920*B^2*a^9*b^8*d^2 + 100*A^2*a*b^16*d
^2 - 132672*A*B*a^2*b^15*d^2 + 919040*A*B*a^4*b^13*d^2 + 1966080*A*B*a^6*b^11*d^2 - 1179648*A*B*a^8*b^9*d^2))/
(256*a^2*d^4))*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10
+ B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*
A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^
2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*a^5*d^2 - B^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 +
10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^4*d^2 + 20*A*B*a^2*b^3*d^2 - 10*A*B*a^4*b*d^
2)/(4*d^4))^(1/2) + (100*A^3*b^20*d^2 - 16000*A^3*a^2*b^18*d^2 - 928868*A^3*a^4*b^16*d^2 + 1805952*A^3*a^6*b^1
4*d^2 + 1489920*A^3*a^8*b^12*d^2 - 1179648*A^3*a^10*b^10*d^2 + 49152*A^3*a^12*b^8*d^2 - 208384*B^3*a^3*b^17*d^
2 + 1651200*B^3*a^5*b^15*d^2 - 557056*B^3*a^7*b^13*d^2 - 2039808*B^3*a^9*b^11*d^2 + 376832*B^3*a^11*b^9*d^2 +
8840*A^2*B*a*b^19*d^2 - 53120*A*B^2*a^2*b^18*d^2 + 2411392*A*B^2*a^4*b^16*d^2 - 5701888*A*B^2*a^6*b^14*d^2 - 4
381696*A*B^2*a^8*b^12*d^2 + 3637248*A*B^2*a^10*b^10*d^2 - 147456*A*B^2*a^12*b^8*d^2 + 543176*A^2*B*a^3*b^17*d^
2 - 5453504*A^2*B*a^5*b^15*d^2 + 1016320*A^2*B*a^7*b^13*d^2 + 5873664*A^2*B*a^9*b^11*d^2 - 1130496*A^2*B*a^11*
b^9*d^2)/(512*a^2*d^5))*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 +
A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6
*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 +
20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*a^5*d^2 - B^2*a^5*d^2 - 10*A^2*a^3*
b^2*d^2 + 10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^4*d^2 + 20*A*B*a^2*b^3*d^2 - 10*A*B
*a^4*b*d^2)/(4*d^4))^(1/2) - ((a + b*tan(c + d*x))^(1/2)*(25*A^2*B^2*b^22 - 25*A^4*b^22 + 6167*A^4*a^2*b^20 +
28457*A^4*a^4*b^18 + 993145*A^4*a^6*b^16 - 1616544*A^4*a^8*b^14 + 1346560*A^4*a^10*b^12 - 258048*A^4*a^12*b^10
+ 24576*A^4*a^14*b^8 + 9792*B^4*a^2*b^20 - 448*B^4*a^4*b^18 + 633280*B^4*a^6*b^16 - 1757760*B^4*a^8*b^14 + 16
84480*B^4*a^10*b^12 - 53248*B^4*a^12*b^10 + 8192*B^4*a^14*b^8 + 21609*A^2*B^2*a^2*b^20 + 344599*A^2*B^2*a^4*b^
18 - 3736185*A^2*B^2*a^6*b^16 + 11758304*A^2*B^2*a^8*b^14 - 7782400*A^2*B^2*a^10*b^12 + 1490944*A^2*B^2*a^12*b
^10 - 400*A*B^3*a*b^21 + 100*A^3*B*a*b^21 - 29200*A*B^3*a^3*b^19 + 769040*A*B^3*a^5*b^17 - 5051120*A*B^3*a^7*b
^15 + 8105600*A*B^3*a^9*b^13 - 2621440*A*B^3*a^11*b^11 + 81920*A*B^3*a^13*b^9 - 17800*A^3*B*a^3*b^19 - 977980*
A^3*B*a^5*b^17 + 5740400*A^3*B*a^7*b^15 - 7032448*A^3*B*a^9*b^13 + 2785280*A^3*B*a^11*b^11 - 278528*A^3*B*a^13
*b^9))/(256*a^2*d^4))*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^
4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b
^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20
*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*a^5*d^2 - B^2*a^5*d^2 - 10*A^2*a^3*b^
2*d^2 + 10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^4*d^2 + 20*A*B*a^2*b^3*d^2 - 10*A*B*a
^4*b*d^2)/(4*d^4))^(1/2) + (((((10240*A*a*b^14*d^4 + 436224*A*a^3*b^12*d^4 + 229376*A*a^5*b^10*d^4 - 196608*A*
a^7*b^8*d^4 - 81920*B*a^2*b^13*d^4 + 442368*B*a^4*b^11*d^4 + 524288*B*a^6*b^9*d^4)/(512*a^2*d^5) + ((131072*a^
2*b^10*d^4 + 196608*a^4*b^8*d^4)*(a + b*tan(c + d*x))^(1/2)*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a
^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5
*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2
*a^5*d^2 - B^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b
^4*d^2 + 20*A*B*a^2*b^3*d^2 - 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2))/(256*a^2*d^4))*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2
*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 +
10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^
8*b^2))^(1/2) + A^2*a^5*d^2 - B^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*
b^4*d^2 - 5*B^2*a*b^4*d^2 + 20*A*B*a^2*b^3*d^2 - 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2) - ((a + b*tan(c + d*x))^(1/2
)*(320896*A^2*a^3*b^14*d^2 + 143360*A^2*a^5*b^12*d^2 - 1081344*A^2*a^7*b^10*d^2 + 147456*A^2*a^9*b^8*d^2 - 304
896*B^2*a^3*b^14*d^2 - 20480*B^2*a^5*b^12*d^2 + 1245184*B^2*a^7*b^10*d^2 - 81920*B^2*a^9*b^8*d^2 + 100*A^2*a*b
^16*d^2 - 132672*A*B*a^2*b^15*d^2 + 919040*A*B*a^4*b^13*d^2 + 1966080*A*B*a^6*b^11*d^2 - 1179648*A*B*a^8*b^9*d
^2))/(256*a^2*d^4))*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*
b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4
+ 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A
^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*a^5*d^2 - B^2*a^5*d^2 - 10*A^2*a^3*b^2*
d^2 + 10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^4*d^2 + 20*A*B*a^2*b^3*d^2 - 10*A*B*a^4
*b*d^2)/(4*d^4))^(1/2) + (100*A^3*b^20*d^2 - 16000*A^3*a^2*b^18*d^2 - 928868*A^3*a^4*b^16*d^2 + 1805952*A^3*a^
6*b^14*d^2 + 1489920*A^3*a^8*b^12*d^2 - 1179648*A^3*a^10*b^10*d^2 + 49152*A^3*a^12*b^8*d^2 - 208384*B^3*a^3*b^
17*d^2 + 1651200*B^3*a^5*b^15*d^2 - 557056*B^3*a^7*b^13*d^2 - 2039808*B^3*a^9*b^11*d^2 + 376832*B^3*a^11*b^9*d
^2 + 8840*A^2*B*a*b^19*d^2 - 53120*A*B^2*a^2*b^18*d^2 + 2411392*A*B^2*a^4*b^16*d^2 - 5701888*A*B^2*a^6*b^14*d^
2 - 4381696*A*B^2*a^8*b^12*d^2 + 3637248*A*B^2*a^10*b^10*d^2 - 147456*A*B^2*a^12*b^8*d^2 + 543176*A^2*B*a^3*b^
17*d^2 - 5453504*A^2*B*a^5*b^15*d^2 + 1016320*A^2*B*a^7*b^13*d^2 + 5873664*A^2*B*a^9*b^11*d^2 - 1130496*A^2*B*
a^11*b^9*d^2)/(512*a^2*d^5))*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^
10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^
4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b
^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*a^5*d^2 - B^2*a^5*d^2 - 10*A^2
*a^3*b^2*d^2 + 10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^4*d^2 + 20*A*B*a^2*b^3*d^2 - 1
0*A*B*a^4*b*d^2)/(4*d^4))^(1/2) + ((a + b*tan(c + d*x))^(1/2)*(25*A^2*B^2*b^22 - 25*A^4*b^22 + 6167*A^4*a^2*b^
20 + 28457*A^4*a^4*b^18 + 993145*A^4*a^6*b^16 - 1616544*A^4*a^8*b^14 + 1346560*A^4*a^10*b^12 - 258048*A^4*a^12
*b^10 + 24576*A^4*a^14*b^8 + 9792*B^4*a^2*b^20 - 448*B^4*a^4*b^18 + 633280*B^4*a^6*b^16 - 1757760*B^4*a^8*b^14
+ 1684480*B^4*a^10*b^12 - 53248*B^4*a^12*b^10 + 8192*B^4*a^14*b^8 + 21609*A^2*B^2*a^2*b^20 + 344599*A^2*B^2*a
^4*b^18 - 3736185*A^2*B^2*a^6*b^16 + 11758304*A^2*B^2*a^8*b^14 - 7782400*A^2*B^2*a^10*b^12 + 1490944*A^2*B^2*a
^12*b^10 - 400*A*B^3*a*b^21 + 100*A^3*B*a*b^21 - 29200*A*B^3*a^3*b^19 + 769040*A*B^3*a^5*b^17 - 5051120*A*B^3*
a^7*b^15 + 8105600*A*B^3*a^9*b^13 - 2621440*A*B^3*a^11*b^11 + 81920*A*B^3*a^13*b^9 - 17800*A^3*B*a^3*b^19 - 97
7980*A^3*B*a^5*b^17 + 5740400*A^3*B*a^7*b^15 - 7032448*A^3*B*a^9*b^13 + 2785280*A^3*B*a^11*b^11 - 278528*A^3*B
*a^13*b^9))/(256*a^2*d^4))*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10
+ A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*
a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8
+ 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*a^5*d^2 - B^2*a^5*d^2 - 10*A^2*a
^3*b^2*d^2 + 10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^4*d^2 + 20*A*B*a^2*b^3*d^2 - 10*
A*B*a^4*b*d^2)/(4*d^4))^(1/2) + (25*A^4*B*b^25 + 565*A^5*a*b^24 + 25*A^2*B^3*b^25 + 27160*A^5*a^3*b^22 - 10774
*A^5*a^5*b^20 + 94656*A^5*a^7*b^18 + 482713*A^5*a^9*b^16 + 376928*A^5*a^11*b^14 - 102784*A^5*a^13*b^12 - 12902
4*A^5*a^15*b^10 - 3520*B^5*a^2*b^23 - 15360*B^5*a^4*b^21 + 261760*B^5*a^6*b^19 + 652800*B^5*a^8*b^17 + 328000*
B^5*a^10*b^15 - 158720*B^5*a^12*b^13 - 66560*B^5*a^14*b^11 + 40960*B^5*a^16*b^9 - 5040*A^2*B^3*a^2*b^23 + 1022
50*A^2*B^3*a^4*b^21 - 6440*A^2*B^3*a^6*b^19 - 144971*A^2*B^3*a^8*b^17 + 653200*A^2*B^3*a^10*b^15 + 1124736*A^2
*B^3*a^12*b^13 + 391168*A^2*B^3*a^14*b^11 - 49152*A^2*B^3*a^16*b^9 + 40920*A^3*B^2*a^3*b^22 + 397002*A^3*B^2*a
^5*b^20 + 375232*A^3*B^2*a^7*b^18 - 658487*A^3*B^2*a^9*b^16 - 870112*A^3*B^2*a^11*b^14 - 25344*A^3*B^2*a^13*b^
12 + 151552*A^3*B^2*a^15*b^10 - 16384*A^3*B^2*a^17*b^8 + 240*A*B^4*a*b^24 + 13760*A*B^4*a^3*b^22 + 407776*A*B^
4*a^5*b^20 + 280576*A*B^4*a^7*b^18 - 1141200*A*B^4*a^9*b^16 - 1247040*A*B^4*a^11*b^14 + 77440*A*B^4*a^13*b^12
+ 280576*A*B^4*a^15*b^10 - 16384*A*B^4*a^17*b^8 + 805*A^3*B^2*a*b^24 - 1520*A^4*B*a^2*b^23 + 117610*A^4*B*a^4*
b^21 - 268200*A^4*B*a^6*b^19 - 797771*A^4*B*a^8*b^17 + 325200*A^4*B*a^10*b^15 + 1283456*A^4*B*a^12*b^13 + 4577
28*A^4*B*a^14*b^11 - 90112*A^4*B*a^16*b^9)/(256*a^2*d^5)))*((((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^
2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*
B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) + A^2*
a^5*d^2 - B^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 10*B^2*a^3*b^2*d^2 - 2*A*B*b^5*d^2 + 5*A^2*a*b^4*d^2 - 5*B^2*a*b^
4*d^2 + 20*A*B*a^2*b^3*d^2 - 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2)*2i + atan(((((((10240*A*a*b^14*d^4 + 436224*A*a^
3*b^12*d^4 + 229376*A*a^5*b^10*d^4 - 196608*A*a^7*b^8*d^4 - 81920*B*a^2*b^13*d^4 + 442368*B*a^4*b^11*d^4 + 524
288*B*a^6*b^9*d^4)/(512*a^2*d^5) - ((131072*a^2*b^10*d^4 + 196608*a^4*b^8*d^4)*(a + b*tan(c + d*x))^(1/2)*(-((
(8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b
^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^
4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2
*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 10*B^2*a^3*b^2*d^
2 + 2*A*B*b^5*d^2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 + 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2))
/(256*a^2*d^4))*(-(((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^1
0 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 +
5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*
B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2
- 10*B^2*a^3*b^2*d^2 + 2*A*B*b^5*d^2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 + 10*A*B*a^4*b*
d^2)/(4*d^4))^(1/2) + ((a + b*tan(c + d*x))^(1/2)*(320896*A^2*a^3*b^14*d^2 + 143360*A^2*a^5*b^12*d^2 - 1081344
*A^2*a^7*b^10*d^2 + 147456*A^2*a^9*b^8*d^2 - 304896*B^2*a^3*b^14*d^2 - 20480*B^2*a^5*b^12*d^2 + 1245184*B^2*a^
7*b^10*d^2 - 81920*B^2*a^9*b^8*d^2 + 100*A^2*a*b^16*d^2 - 132672*A*B*a^2*b^15*d^2 + 919040*A*B*a^4*b^13*d^2 +
1966080*A*B*a^6*b^11*d^2 - 1179648*A*B*a^8*b^9*d^2))/(256*a^2*d^4))*(-(((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10
+ 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^
6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1
/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 10*B^2*a^3*b^2*d^2 + 2*A*B*b^5*d^2 - 5*A^2*a*b^4*d^2 +
5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 + 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2) + (100*A^3*b^20*d^2 - 16000*A^3*a^2*b^
18*d^2 - 928868*A^3*a^4*b^16*d^2 + 1805952*A^3*a^6*b^14*d^2 + 1489920*A^3*a^8*b^12*d^2 - 1179648*A^3*a^10*b^10
*d^2 + 49152*A^3*a^12*b^8*d^2 - 208384*B^3*a^3*b^17*d^2 + 1651200*B^3*a^5*b^15*d^2 - 557056*B^3*a^7*b^13*d^2 -
2039808*B^3*a^9*b^11*d^2 + 376832*B^3*a^11*b^9*d^2 + 8840*A^2*B*a*b^19*d^2 - 53120*A*B^2*a^2*b^18*d^2 + 24113
92*A*B^2*a^4*b^16*d^2 - 5701888*A*B^2*a^6*b^14*d^2 - 4381696*A*B^2*a^8*b^12*d^2 + 3637248*A*B^2*a^10*b^10*d^2
- 147456*A*B^2*a^12*b^8*d^2 + 543176*A^2*B*a^3*b^17*d^2 - 5453504*A^2*B*a^5*b^15*d^2 + 1016320*A^2*B*a^7*b^13*
d^2 + 5873664*A^2*B*a^9*b^11*d^2 - 1130496*A^2*B*a^11*b^9*d^2)/(512*a^2*d^5))*(-(((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2
*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 +
10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^
8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 10*B^2*a^3*b^2*d^2 + 2*A*B*b^5*d^2 - 5*A^2*a*
b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 + 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2) - ((a + b*tan(c + d*x))^(1/2
)*(25*A^2*B^2*b^22 - 25*A^4*b^22 + 6167*A^4*a^2*b^20 + 28457*A^4*a^4*b^18 + 993145*A^4*a^6*b^16 - 1616544*A^4*
a^8*b^14 + 1346560*A^4*a^10*b^12 - 258048*A^4*a^12*b^10 + 24576*A^4*a^14*b^8 + 9792*B^4*a^2*b^20 - 448*B^4*a^4
*b^18 + 633280*B^4*a^6*b^16 - 1757760*B^4*a^8*b^14 + 1684480*B^4*a^10*b^12 - 53248*B^4*a^12*b^10 + 8192*B^4*a^
14*b^8 + 21609*A^2*B^2*a^2*b^20 + 344599*A^2*B^2*a^4*b^18 - 3736185*A^2*B^2*a^6*b^16 + 11758304*A^2*B^2*a^8*b^
14 - 7782400*A^2*B^2*a^10*b^12 + 1490944*A^2*B^2*a^12*b^10 - 400*A*B^3*a*b^21 + 100*A^3*B*a*b^21 - 29200*A*B^3
*a^3*b^19 + 769040*A*B^3*a^5*b^17 - 5051120*A*B^3*a^7*b^15 + 8105600*A*B^3*a^9*b^13 - 2621440*A*B^3*a^11*b^11
+ 81920*A*B^3*a^13*b^9 - 17800*A^3*B*a^3*b^19 - 977980*A^3*B*a^5*b^17 + 5740400*A^3*B*a^7*b^15 - 7032448*A^3*B
*a^9*b^13 + 2785280*A^3*B*a^11*b^11 - 278528*A^3*B*a^13*b^9))/(256*a^2*d^4))*(-(((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*
B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 +
10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8
*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 10*B^2*a^3*b^2*d^2 + 2*A*B*b^5*d^2 - 5*A^2*a*b
^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 + 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2)*1i - (((((10240*A*a*b^14*d^4
+ 436224*A*a^3*b^12*d^4 + 229376*A*a^5*b^10*d^4 - 196608*A*a^7*b^8*d^4 - 81920*B*a^2*b^13*d^4 + 442368*B*a^4*b
^11*d^4 + 524288*B*a^6*b^9*d^4)/(512*a^2*d^5) + ((131072*a^2*b^10*d^4 + 196608*a^4*b^8*d^4)*(a + b*tan(c + d*x
))^(1/2)*(-(((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4
*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a
^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4
*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 10*B
^2*a^3*b^2*d^2 + 2*A*B*b^5*d^2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 + 10*A*B*a^4*b*d^2)/(4
*d^4))^(1/2))/(256*a^2*d^4))*(-(((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a
^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A
^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*
b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^
2*a^3*b^2*d^2 - 10*B^2*a^3*b^2*d^2 + 2*A*B*b^5*d^2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 +
10*A*B*a^4*b*d^2)/(4*d^4))^(1/2) - ((a + b*tan(c + d*x))^(1/2)*(320896*A^2*a^3*b^14*d^2 + 143360*A^2*a^5*b^12*
d^2 - 1081344*A^2*a^7*b^10*d^2 + 147456*A^2*a^9*b^8*d^2 - 304896*B^2*a^3*b^14*d^2 - 20480*B^2*a^5*b^12*d^2 + 1
245184*B^2*a^7*b^10*d^2 - 81920*B^2*a^9*b^8*d^2 + 100*A^2*a*b^16*d^2 - 132672*A*B*a^2*b^15*d^2 + 919040*A*B*a^
4*b^13*d^2 + 1966080*A*B*a^6*b^11*d^2 - 1179648*A*B*a^8*b^9*d^2))/(256*a^2*d^4))*(-(((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*
A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^
6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2
*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 10*B^2*a^3*b^2*d^2 + 2*A*B*b^5*d^2 - 5*A^2
*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 + 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2) + (100*A^3*b^20*d^2 - 160
00*A^3*a^2*b^18*d^2 - 928868*A^3*a^4*b^16*d^2 + 1805952*A^3*a^6*b^14*d^2 + 1489920*A^3*a^8*b^12*d^2 - 1179648*
A^3*a^10*b^10*d^2 + 49152*A^3*a^12*b^8*d^2 - 208384*B^3*a^3*b^17*d^2 + 1651200*B^3*a^5*b^15*d^2 - 557056*B^3*a
^7*b^13*d^2 - 2039808*B^3*a^9*b^11*d^2 + 376832*B^3*a^11*b^9*d^2 + 8840*A^2*B*a*b^19*d^2 - 53120*A*B^2*a^2*b^1
8*d^2 + 2411392*A*B^2*a^4*b^16*d^2 - 5701888*A*B^2*a^6*b^14*d^2 - 4381696*A*B^2*a^8*b^12*d^2 + 3637248*A*B^2*a
^10*b^10*d^2 - 147456*A*B^2*a^12*b^8*d^2 + 543176*A^2*B*a^3*b^17*d^2 - 5453504*A^2*B*a^5*b^15*d^2 + 1016320*A^
2*B*a^7*b^13*d^2 + 5873664*A^2*B*a^9*b^11*d^2 - 1130496*A^2*B*a^11*b^9*d^2)/(512*a^2*d^5))*(-(((8*B^2*a^5*d^2
- 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2
*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*
B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 +
10*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 10*B^2*a^3*b^2*d^2 + 2*A*B*b^5*d
^2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 + 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2) + ((a + b*tan(c
+ d*x))^(1/2)*(25*A^2*B^2*b^22 - 25*A^4*b^22 + 6167*A^4*a^2*b^20 + 28457*A^4*a^4*b^18 + 993145*A^4*a^6*b^16 -
1616544*A^4*a^8*b^14 + 1346560*A^4*a^10*b^12 - 258048*A^4*a^12*b^10 + 24576*A^4*a^14*b^8 + 9792*B^4*a^2*b^20
- 448*B^4*a^4*b^18 + 633280*B^4*a^6*b^16 - 1757760*B^4*a^8*b^14 + 1684480*B^4*a^10*b^12 - 53248*B^4*a^12*b^10
+ 8192*B^4*a^14*b^8 + 21609*A^2*B^2*a^2*b^20 + 344599*A^2*B^2*a^4*b^18 - 3736185*A^2*B^2*a^6*b^16 + 11758304*A
^2*B^2*a^8*b^14 - 7782400*A^2*B^2*a^10*b^12 + 1490944*A^2*B^2*a^12*b^10 - 400*A*B^3*a*b^21 + 100*A^3*B*a*b^21
- 29200*A*B^3*a^3*b^19 + 769040*A*B^3*a^5*b^17 - 5051120*A*B^3*a^7*b^15 + 8105600*A*B^3*a^9*b^13 - 2621440*A*B
^3*a^11*b^11 + 81920*A*B^3*a^13*b^9 - 17800*A^3*B*a^3*b^19 - 977980*A^3*B*a^5*b^17 + 5740400*A^3*B*a^7*b^15 -
7032448*A^3*B*a^9*b^13 + 2785280*A^3*B*a^11*b^11 - 278528*A^3*B*a^13*b^9))/(256*a^2*d^4))*(-(((8*B^2*a^5*d^2 -
8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*
a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B
^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 1
0*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 10*B^2*a^3*b^2*d^2 + 2*A*B*b^5*d^
2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 + 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2)*1i)/((((((10240*
A*a*b^14*d^4 + 436224*A*a^3*b^12*d^4 + 229376*A*a^5*b^10*d^4 - 196608*A*a^7*b^8*d^4 - 81920*B*a^2*b^13*d^4 + 4
42368*B*a^4*b^11*d^4 + 524288*B*a^6*b^9*d^4)/(512*a^2*d^5) - ((131072*a^2*b^10*d^4 + 196608*a^4*b^8*d^4)*(a +
b*tan(c + d*x))^(1/2)*(-(((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A
^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*
b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 2
0*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^2*a^3*b
^2*d^2 - 10*B^2*a^3*b^2*d^2 + 2*A*B*b^5*d^2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 + 10*A*B*
a^4*b*d^2)/(4*d^4))^(1/2))/(256*a^2*d^4))*(-(((8*B^2*a^5*d^2 - 8*A^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)^2/64
- d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a
^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10
*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^
5*d^2 + 10*A^2*a^3*b^2*d^2 - 10*B^2*a^3*b^2*d^2 + 2*A*B*b^5*d^2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a
^2*b^3*d^2 + 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2) + ((a + b*tan(c + d*x))^(1/2)*(320896*A^2*a^3*b^14*d^2 + 143360*
A^2*a^5*b^12*d^2 - 1081344*A^2*a^7*b^10*d^2 + 147456*A^2*a^9*b^8*d^2 - 304896*B^2*a^3*b^14*d^2 - 20480*B^2*a^5
*b^12*d^2 + 1245184*B^2*a^7*b^10*d^2 - 81920*B^2*a^9*b^8*d^2 + 100*A^2*a*b^16*d^2 - 132672*A*B*a^2*b^15*d^2 +
919040*A*B*a^4*b^13*d^2 + 1966080*A*B*a^6*b^11*d^2 - 1179648*A*B*a^8*b^9*d^2))/(256*a^2*d^4))*(-(((8*B^2*a^5*d
^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*
B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 +
10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4
+ 10*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 10*B^2*a^3*b^2*d^2 + 2*A*B*b^
5*d^2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 + 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2) + (100*A^3*b
^20*d^2 - 16000*A^3*a^2*b^18*d^2 - 928868*A^3*a^4*b^16*d^2 + 1805952*A^3*a^6*b^14*d^2 + 1489920*A^3*a^8*b^12*d
^2 - 1179648*A^3*a^10*b^10*d^2 + 49152*A^3*a^12*b^8*d^2 - 208384*B^3*a^3*b^17*d^2 + 1651200*B^3*a^5*b^15*d^2 -
557056*B^3*a^7*b^13*d^2 - 2039808*B^3*a^9*b^11*d^2 + 376832*B^3*a^11*b^9*d^2 + 8840*A^2*B*a*b^19*d^2 - 53120*
A*B^2*a^2*b^18*d^2 + 2411392*A*B^2*a^4*b^16*d^2 - 5701888*A*B^2*a^6*b^14*d^2 - 4381696*A*B^2*a^8*b^12*d^2 + 36
37248*A*B^2*a^10*b^10*d^2 - 147456*A*B^2*a^12*b^8*d^2 + 543176*A^2*B*a^3*b^17*d^2 - 5453504*A^2*B*a^5*b^15*d^2
+ 1016320*A^2*B*a^7*b^13*d^2 + 5873664*A^2*B*a^9*b^11*d^2 - 1130496*A^2*B*a^11*b^9*d^2)/(512*a^2*d^5))*(-(((8
*B^2*a^5*d^2 - 8*A^2*a^5*d^2 + 80*A^2*a^3*b^2*d^2 - 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 - 40*A^2*a*b^4*d^2 + 4
0*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^1
0 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*
a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B
^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 10*B^2*a^3*b^2*d^2
+ 2*A*B*b^5*d^2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 + 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2) -
((a + b*tan(c + d*x))^(1/2)*(25*A^2*B^2*b^22 - 25*A^4*b^22 + 6167*A^4*a^2*b^20 + 28457*A^4*a^4*b^18 + 993145*A
^4*a^6*b^16 - 1616544*A^4*a^8*b^14 + 1346560*A^4*a^10*b^12 - 258048*A^4*a^12*b^10 + 24576*A^4*a^14*b^8 + 9792*
B^4*a^2*b^20 - 448*B^4*a^4*b^18 + 633280*B^4*a^6*b^16 - 1757760*B^4*a^8*b^14 + 1684480*B^4*a^10*b^12 - 53248*B
^4*a^12*b^10 + 8192*B^4*a^14*b^8 + 21609*A^2*B^2*a^2*b^20 + 344599*A^2*B^2*a^4*b^18 - 3736185*A^2*B^2*a^6*b^16
+ 11758304*A^2*B^2*a^8*b^14 - 7782400*A^2*B^2*a^10*b^12 + 1490944*A^2*B^2*a^12*b^10 - 400*A*B^3*a*b^21 + 100*
A^3*B*a*b^21 - 29200*A*B^3*a^3*b^19 + 769040*A*B^3*a^5*b^17 - 5051120*A*B^3*a^7*b^15 + 8105600*A*B^3*a^9*b^13
- 2621440*A*B^3*a^11*b^11 + 81920*A*B^3*a^13*b^9 - 17800*A^3*B*a^3*b^19 - 977980*A^3*B*a^5*b^17 + 5740400*A^3*
B*a^7*b^15 - 7032448*A^3*B*a^9*b^13 + 2785280*A^3*B*a^11*b^11 - 278528*A^3*B*a^13*b^9))/(256*a^2*d^4))*(-(((8*
B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10
+ 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a
^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^
2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 10*B^2*a^3*b^2*d^2 +
2*A*B*b^5*d^2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 + 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2) + (
((((10240*A*a*b^14*d^4 + 436224*A*a^3*b^12*d^4 + 229376*A*a^5*b^10*d^4 - 196608*A*a^7*b^8*d^4 - 81920*B*a^2*b^
13*d^4 + 442368*B*a^4*b^11*d^4 + 524288*B*a^6*b^9*d^4)/(512*a^2*d^5) + ((131072*a^2*b^10*d^4 + 196608*a^4*b^8*
d^4)*(a + b*tan(c + d*x))^(1/2)*(-(((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^
4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 1
0*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a
^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10
*A^2*a^3*b^2*d^2 - 10*B^2*a^3*b^2*d^2 + 2*A*B*b^5*d^2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2
+ 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2))/(256*a^2*d^4))*(-(((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8
+ 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^
8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^
2 + B^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 10*B^2*a^3*b^2*d^2 + 2*A*B*b^5*d^2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2
- 20*A*B*a^2*b^3*d^2 + 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2) - ((a + b*tan(c + d*x))^(1/2)*(320896*A^2*a^3*b^14*d^2
+ 143360*A^2*a^5*b^12*d^2 - 1081344*A^2*a^7*b^10*d^2 + 147456*A^2*a^9*b^8*d^2 - 304896*B^2*a^3*b^14*d^2 - 204
80*B^2*a^5*b^12*d^2 + 1245184*B^2*a^7*b^10*d^2 - 81920*B^2*a^9*b^8*d^2 + 100*A^2*a*b^16*d^2 - 132672*A*B*a^2*b
^15*d^2 + 919040*A*B*a^4*b^13*d^2 + 1966080*A*B*a^6*b^11*d^2 - 1179648*A*B*a^8*b^9*d^2))/(256*a^2*d^4))*(-(((8
*B^2*a^5*d^2 - 8*A^2*a^5*d^2 + 80*A^2*a^3*b^2*d^2 - 80*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 - 40*A^2*a*b^4*d^2 + 4
0*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*d^2)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^1
0 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*
a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B
^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 10*B^2*a^3*b^2*d^2
+ 2*A*B*b^5*d^2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 + 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2) +
(100*A^3*b^20*d^2 - 16000*A^3*a^2*b^18*d^2 - 928868*A^3*a^4*b^16*d^2 + 1805952*A^3*a^6*b^14*d^2 + 1489920*A^3*
a^8*b^12*d^2 - 1179648*A^3*a^10*b^10*d^2 + 49152*A^3*a^12*b^8*d^2 - 208384*B^3*a^3*b^17*d^2 + 1651200*B^3*a^5*
b^15*d^2 - 557056*B^3*a^7*b^13*d^2 - 2039808*B^3*a^9*b^11*d^2 + 376832*B^3*a^11*b^9*d^2 + 8840*A^2*B*a*b^19*d^
2 - 53120*A*B^2*a^2*b^18*d^2 + 2411392*A*B^2*a^4*b^16*d^2 - 5701888*A*B^2*a^6*b^14*d^2 - 4381696*A*B^2*a^8*b^1
2*d^2 + 3637248*A*B^2*a^10*b^10*d^2 - 147456*A*B^2*a^12*b^8*d^2 + 543176*A^2*B*a^3*b^17*d^2 - 5453504*A^2*B*a^
5*b^15*d^2 + 1016320*A^2*B*a^7*b^13*d^2 + 5873664*A^2*B*a^9*b^11*d^2 - 1130496*A^2*B*a^11*b^9*d^2)/(512*a^2*d^
5))*(-(((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10
+ B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^
2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6
+ 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 10*B^2*a^
3*b^2*d^2 + 2*A*B*b^5*d^2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 + 10*A*B*a^4*b*d^2)/(4*d^4)
)^(1/2) + ((a + b*tan(c + d*x))^(1/2)*(25*A^2*B^2*b^22 - 25*A^4*b^22 + 6167*A^4*a^2*b^20 + 28457*A^4*a^4*b^18
+ 993145*A^4*a^6*b^16 - 1616544*A^4*a^8*b^14 + 1346560*A^4*a^10*b^12 - 258048*A^4*a^12*b^10 + 24576*A^4*a^14*b
^8 + 9792*B^4*a^2*b^20 - 448*B^4*a^4*b^18 + 633280*B^4*a^6*b^16 - 1757760*B^4*a^8*b^14 + 1684480*B^4*a^10*b^12
- 53248*B^4*a^12*b^10 + 8192*B^4*a^14*b^8 + 21609*A^2*B^2*a^2*b^20 + 344599*A^2*B^2*a^4*b^18 - 3736185*A^2*B^
2*a^6*b^16 + 11758304*A^2*B^2*a^8*b^14 - 7782400*A^2*B^2*a^10*b^12 + 1490944*A^2*B^2*a^12*b^10 - 400*A*B^3*a*b
^21 + 100*A^3*B*a*b^21 - 29200*A*B^3*a^3*b^19 + 769040*A*B^3*a^5*b^17 - 5051120*A*B^3*a^7*b^15 + 8105600*A*B^3
*a^9*b^13 - 2621440*A*B^3*a^11*b^11 + 81920*A*B^3*a^13*b^9 - 17800*A^3*B*a^3*b^19 - 977980*A^3*B*a^5*b^17 + 57
40400*A^3*B*a^7*b^15 - 7032448*A^3*B*a^9*b^13 + 2785280*A^3*B*a^11*b^11 - 278528*A^3*B*a^13*b^9))/(256*a^2*d^4
))*(-(((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4*(A^4*a^10 + A^4*b^10 + B^4*a^10
+ B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6 + 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2
+ 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 +
20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 10*B^2*a^3
*b^2*d^2 + 2*A*B*b^5*d^2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3*d^2 + 10*A*B*a^4*b*d^2)/(4*d^4))
^(1/2) + (25*A^4*B*b^25 + 565*A^5*a*b^24 + 25*A^2*B^3*b^25 + 27160*A^5*a^3*b^22 - 10774*A^5*a^5*b^20 + 94656*A
^5*a^7*b^18 + 482713*A^5*a^9*b^16 + 376928*A^5*a^11*b^14 - 102784*A^5*a^13*b^12 - 129024*A^5*a^15*b^10 - 3520*
B^5*a^2*b^23 - 15360*B^5*a^4*b^21 + 261760*B^5*a^6*b^19 + 652800*B^5*a^8*b^17 + 328000*B^5*a^10*b^15 - 158720*
B^5*a^12*b^13 - 66560*B^5*a^14*b^11 + 40960*B^5*a^16*b^9 - 5040*A^2*B^3*a^2*b^23 + 102250*A^2*B^3*a^4*b^21 - 6
440*A^2*B^3*a^6*b^19 - 144971*A^2*B^3*a^8*b^17 + 653200*A^2*B^3*a^10*b^15 + 1124736*A^2*B^3*a^12*b^13 + 391168
*A^2*B^3*a^14*b^11 - 49152*A^2*B^3*a^16*b^9 + 40920*A^3*B^2*a^3*b^22 + 397002*A^3*B^2*a^5*b^20 + 375232*A^3*B^
2*a^7*b^18 - 658487*A^3*B^2*a^9*b^16 - 870112*A^3*B^2*a^11*b^14 - 25344*A^3*B^2*a^13*b^12 + 151552*A^3*B^2*a^1
5*b^10 - 16384*A^3*B^2*a^17*b^8 + 240*A*B^4*a*b^24 + 13760*A*B^4*a^3*b^22 + 407776*A*B^4*a^5*b^20 + 280576*A*B
^4*a^7*b^18 - 1141200*A*B^4*a^9*b^16 - 1247040*A*B^4*a^11*b^14 + 77440*A*B^4*a^13*b^12 + 280576*A*B^4*a^15*b^1
0 - 16384*A*B^4*a^17*b^8 + 805*A^3*B^2*a*b^24 - 1520*A^4*B*a^2*b^23 + 117610*A^4*B*a^4*b^21 - 268200*A^4*B*a^6
*b^19 - 797771*A^4*B*a^8*b^17 + 325200*A^4*B*a^10*b^15 + 1283456*A^4*B*a^12*b^13 + 457728*A^4*B*a^14*b^11 - 90
112*A^4*B*a^16*b^9)/(256*a^2*d^5)))*(-(((8*B^2*a^5*d^2 - 8*A^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)^2/64 - d^4
*(A^4*a^10 + A^4*b^10 + B^4*a^10 + B^4*b^10 + 2*A^2*B^2*a^10 + 2*A^2*B^2*b^10 + 5*A^4*a^2*b^8 + 10*A^4*a^4*b^6
+ 10*A^4*a^6*b^4 + 5*A^4*a^8*b^2 + 5*B^4*a^2*b^8 + 10*B^4*a^4*b^6 + 10*B^4*a^6*b^4 + 5*B^4*a^8*b^2 + 10*A^2*B
^2*a^2*b^8 + 20*A^2*B^2*a^4*b^6 + 20*A^2*B^2*a^6*b^4 + 10*A^2*B^2*a^8*b^2))^(1/2) - A^2*a^5*d^2 + B^2*a^5*d^2
+ 10*A^2*a^3*b^2*d^2 - 10*B^2*a^3*b^2*d^2 + 2*A*B*b^5*d^2 - 5*A^2*a*b^4*d^2 + 5*B^2*a*b^4*d^2 - 20*A*B*a^2*b^3
*d^2 + 10*A*B*a^4*b*d^2)/(4*d^4))^(1/2)*2i - ((a + b*tan(c + d*x))^(5/2)*((73*A*b^4)/192 + (25*A*a^2*b^2)/4 -
(73*B*a*b^3)/24 + 3*B*a^3*b) + (a + b*tan(c + d*x))^(1/2)*((5*A*a^2*b^4)/64 + (7*A*a^4*b^2)/4 - (5*B*a^3*b^3)/
8 + B*a^5*b) - (a + b*tan(c + d*x))^(3/2)*((23*A*a^3*b^2)/4 - (55*B*a^2*b^3)/24 + (55*A*a*b^4)/192 + 3*B*a^4*b
) + ((a + b*tan(c + d*x))^(7/2)*(5*A*b^4 - 144*A*a^2*b^2 + 88*B*a*b^3 - 64*B*a^3*b))/(64*a))/(d*(a + b*tan(c +
d*x))^4 + a^4*d - 4*a*d*(a + b*tan(c + d*x))^3 - 4*a^3*d*(a + b*tan(c + d*x)) + 6*a^2*d*(a + b*tan(c + d*x))^
2) - (atan((((((a + b*tan(c + d*x))^(1/2)*(25*A^2*B^2*b^22 - 25*A^4*b^22 + 6167*A^4*a^2*b^20 + 28457*A^4*a^4*b
^18 + 993145*A^4*a^6*b^16 - 1616544*A^4*a^8*b^14 + 1346560*A^4*a^10*b^12 - 258048*A^4*a^12*b^10 + 24576*A^4*a^
14*b^8 + 9792*B^4*a^2*b^20 - 448*B^4*a^4*b^18 + 633280*B^4*a^6*b^16 - 1757760*B^4*a^8*b^14 + 1684480*B^4*a^10*
b^12 - 53248*B^4*a^12*b^10 + 8192*B^4*a^14*b^8 + 21609*A^2*B^2*a^2*b^20 + 344599*A^2*B^2*a^4*b^18 - 3736185*A^
2*B^2*a^6*b^16 + 11758304*A^2*B^2*a^8*b^14 - 7782400*A^2*B^2*a^10*b^12 + 1490944*A^2*B^2*a^12*b^10 - 400*A*B^3
*a*b^21 + 100*A^3*B*a*b^21 - 29200*A*B^3*a^3*b^19 + 769040*A*B^3*a^5*b^17 - 5051120*A*B^3*a^7*b^15 + 8105600*A
*B^3*a^9*b^13 - 2621440*A*B^3*a^11*b^11 + 81920*A*B^3*a^13*b^9 - 17800*A^3*B*a^3*b^19 - 977980*A^3*B*a^5*b^17
+ 5740400*A^3*B*a^7*b^15 - 7032448*A^3*B*a^9*b^13 + 2785280*A^3*B*a^11*b^11 - 278528*A^3*B*a^13*b^9))/(32768*a
^2*d^4) - ((((25*A^3*b^20*d^2)/128 - (125*A^3*a^2*b^18*d^2)/4 - (232217*A^3*a^4*b^16*d^2)/128 + (14109*A^3*a^6
*b^14*d^2)/4 + 2910*A^3*a^8*b^12*d^2 - 2304*A^3*a^10*b^10*d^2 + 96*A^3*a^12*b^8*d^2 - 407*B^3*a^3*b^17*d^2 + 3
225*B^3*a^5*b^15*d^2 - 1088*B^3*a^7*b^13*d^2 - 3984*B^3*a^9*b^11*d^2 + 736*B^3*a^11*b^9*d^2 + (1105*A^2*B*a*b^
19*d^2)/64 - (415*A*B^2*a^2*b^18*d^2)/4 + (18839*A*B^2*a^4*b^16*d^2)/4 - (22273*A*B^2*a^6*b^14*d^2)/2 - 8558*A
*B^2*a^8*b^12*d^2 + 7104*A*B^2*a^10*b^10*d^2 - 288*A*B^2*a^12*b^8*d^2 + (67897*A^2*B*a^3*b^17*d^2)/64 - (85211
*A^2*B*a^5*b^15*d^2)/8 + 1985*A^2*B*a^7*b^13*d^2 + 11472*A^2*B*a^9*b^11*d^2 - 2208*A^2*B*a^11*b^9*d^2)/(128*a^
2*d^5) + ((((a + b*tan(c + d*x))^(1/2)*(320896*A^2*a^3*b^14*d^2 + 143360*A^2*a^5*b^12*d^2 - 1081344*A^2*a^7*b^
10*d^2 + 147456*A^2*a^9*b^8*d^2 - 304896*B^2*a^3*b^14*d^2 - 20480*B^2*a^5*b^12*d^2 + 1245184*B^2*a^7*b^10*d^2
- 81920*B^2*a^9*b^8*d^2 + 100*A^2*a*b^16*d^2 - 132672*A*B*a^2*b^15*d^2 + 919040*A*B*a^4*b^13*d^2 + 1966080*A*B
*a^6*b^11*d^2 - 1179648*A*B*a^8*b^9*d^2))/(32768*a^2*d^4) + (((20*A*a*b^14*d^4 + 852*A*a^3*b^12*d^4 + 448*A*a^
5*b^10*d^4 - 384*A*a^7*b^8*d^4 - 160*B*a^2*b^13*d^4 + 864*B*a^4*b^11*d^4 + 1024*B*a^6*b^9*d^4)/(128*a^2*d^5) -
((131072*a^2*b^10*d^4 + 196608*a^4*b^8*d^4)*(a + b*tan(c + d*x))^(1/2)*(16384*A^2*a^11 + 25*A^2*a^3*b^8 + 240
0*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b^2 + 1600*B^2*a^5*b^6 - 25600*B^2*a^7*b^4 + 102400*B^2*a^9*
b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*B*a^6*b^5 + 163840*A*B*a^8*b^3)^(1/2))/(4194304*a^5*d^5))*(
16384*A^2*a^11 + 25*A^2*a^3*b^8 + 2400*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b^2 + 1600*B^2*a^5*b^6
- 25600*B^2*a^7*b^4 + 102400*B^2*a^9*b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*B*a^6*b^5 + 163840*A*B
*a^8*b^3)^(1/2))/(128*a^3*d))*(16384*A^2*a^11 + 25*A^2*a^3*b^8 + 2400*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440*
A^2*a^9*b^2 + 1600*B^2*a^5*b^6 - 25600*B^2*a^7*b^4 + 102400*B^2*a^9*b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7 -
16000*A*B*a^6*b^5 + 163840*A*B*a^8*b^3)^(1/2))/(128*a^3*d))*(16384*A^2*a^11 + 25*A^2*a^3*b^8 + 2400*A^2*a^5*b
^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b^2 + 1600*B^2*a^5*b^6 - 25600*B^2*a^7*b^4 + 102400*B^2*a^9*b^2 - 81920
*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*B*a^6*b^5 + 163840*A*B*a^8*b^3)^(1/2))/(128*a^3*d))*(16384*A^2*a^11 +
25*A^2*a^3*b^8 + 2400*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b^2 + 1600*B^2*a^5*b^6 - 25600*B^2*a^7*b
^4 + 102400*B^2*a^9*b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*B*a^6*b^5 + 163840*A*B*a^8*b^3)^(1/2)*1
i)/(a^3*d) + ((((a + b*tan(c + d*x))^(1/2)*(25*A^2*B^2*b^22 - 25*A^4*b^22 + 6167*A^4*a^2*b^20 + 28457*A^4*a^4*
b^18 + 993145*A^4*a^6*b^16 - 1616544*A^4*a^8*b^14 + 1346560*A^4*a^10*b^12 - 258048*A^4*a^12*b^10 + 24576*A^4*a
^14*b^8 + 9792*B^4*a^2*b^20 - 448*B^4*a^4*b^18 + 633280*B^4*a^6*b^16 - 1757760*B^4*a^8*b^14 + 1684480*B^4*a^10
*b^12 - 53248*B^4*a^12*b^10 + 8192*B^4*a^14*b^8 + 21609*A^2*B^2*a^2*b^20 + 344599*A^2*B^2*a^4*b^18 - 3736185*A
^2*B^2*a^6*b^16 + 11758304*A^2*B^2*a^8*b^14 - 7782400*A^2*B^2*a^10*b^12 + 1490944*A^2*B^2*a^12*b^10 - 400*A*B^
3*a*b^21 + 100*A^3*B*a*b^21 - 29200*A*B^3*a^3*b^19 + 769040*A*B^3*a^5*b^17 - 5051120*A*B^3*a^7*b^15 + 8105600*
A*B^3*a^9*b^13 - 2621440*A*B^3*a^11*b^11 + 81920*A*B^3*a^13*b^9 - 17800*A^3*B*a^3*b^19 - 977980*A^3*B*a^5*b^17
+ 5740400*A^3*B*a^7*b^15 - 7032448*A^3*B*a^9*b^13 + 2785280*A^3*B*a^11*b^11 - 278528*A^3*B*a^13*b^9))/(32768*
a^2*d^4) + ((((25*A^3*b^20*d^2)/128 - (125*A^3*a^2*b^18*d^2)/4 - (232217*A^3*a^4*b^16*d^2)/128 + (14109*A^3*a^
6*b^14*d^2)/4 + 2910*A^3*a^8*b^12*d^2 - 2304*A^3*a^10*b^10*d^2 + 96*A^3*a^12*b^8*d^2 - 407*B^3*a^3*b^17*d^2 +
3225*B^3*a^5*b^15*d^2 - 1088*B^3*a^7*b^13*d^2 - 3984*B^3*a^9*b^11*d^2 + 736*B^3*a^11*b^9*d^2 + (1105*A^2*B*a*b
^19*d^2)/64 - (415*A*B^2*a^2*b^18*d^2)/4 + (18839*A*B^2*a^4*b^16*d^2)/4 - (22273*A*B^2*a^6*b^14*d^2)/2 - 8558*
A*B^2*a^8*b^12*d^2 + 7104*A*B^2*a^10*b^10*d^2 - 288*A*B^2*a^12*b^8*d^2 + (67897*A^2*B*a^3*b^17*d^2)/64 - (8521
1*A^2*B*a^5*b^15*d^2)/8 + 1985*A^2*B*a^7*b^13*d^2 + 11472*A^2*B*a^9*b^11*d^2 - 2208*A^2*B*a^11*b^9*d^2)/(128*a
^2*d^5) - ((((a + b*tan(c + d*x))^(1/2)*(320896*A^2*a^3*b^14*d^2 + 143360*A^2*a^5*b^12*d^2 - 1081344*A^2*a^7*b
^10*d^2 + 147456*A^2*a^9*b^8*d^2 - 304896*B^2*a^3*b^14*d^2 - 20480*B^2*a^5*b^12*d^2 + 1245184*B^2*a^7*b^10*d^2
- 81920*B^2*a^9*b^8*d^2 + 100*A^2*a*b^16*d^2 - 132672*A*B*a^2*b^15*d^2 + 919040*A*B*a^4*b^13*d^2 + 1966080*A*
B*a^6*b^11*d^2 - 1179648*A*B*a^8*b^9*d^2))/(32768*a^2*d^4) - (((20*A*a*b^14*d^4 + 852*A*a^3*b^12*d^4 + 448*A*a
^5*b^10*d^4 - 384*A*a^7*b^8*d^4 - 160*B*a^2*b^13*d^4 + 864*B*a^4*b^11*d^4 + 1024*B*a^6*b^9*d^4)/(128*a^2*d^5)
+ ((131072*a^2*b^10*d^4 + 196608*a^4*b^8*d^4)*(a + b*tan(c + d*x))^(1/2)*(16384*A^2*a^11 + 25*A^2*a^3*b^8 + 24
00*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b^2 + 1600*B^2*a^5*b^6 - 25600*B^2*a^7*b^4 + 102400*B^2*a^9
*b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*B*a^6*b^5 + 163840*A*B*a^8*b^3)^(1/2))/(4194304*a^5*d^5))*
(16384*A^2*a^11 + 25*A^2*a^3*b^8 + 2400*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b^2 + 1600*B^2*a^5*b^6
- 25600*B^2*a^7*b^4 + 102400*B^2*a^9*b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*B*a^6*b^5 + 163840*A*
B*a^8*b^3)^(1/2))/(128*a^3*d))*(16384*A^2*a^11 + 25*A^2*a^3*b^8 + 2400*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440
*A^2*a^9*b^2 + 1600*B^2*a^5*b^6 - 25600*B^2*a^7*b^4 + 102400*B^2*a^9*b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7
- 16000*A*B*a^6*b^5 + 163840*A*B*a^8*b^3)^(1/2))/(128*a^3*d))*(16384*A^2*a^11 + 25*A^2*a^3*b^8 + 2400*A^2*a^5*
b^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b^2 + 1600*B^2*a^5*b^6 - 25600*B^2*a^7*b^4 + 102400*B^2*a^9*b^2 - 8192
0*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*B*a^6*b^5 + 163840*A*B*a^8*b^3)^(1/2))/(128*a^3*d))*(16384*A^2*a^11 +
25*A^2*a^3*b^8 + 2400*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b^2 + 1600*B^2*a^5*b^6 - 25600*B^2*a^7*
b^4 + 102400*B^2*a^9*b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*B*a^6*b^5 + 163840*A*B*a^8*b^3)^(1/2)*
1i)/(a^3*d))/(((25*A^4*B*b^25)/256 + (565*A^5*a*b^24)/256 + (25*A^2*B^3*b^25)/256 + (3395*A^5*a^3*b^22)/32 - (
5387*A^5*a^5*b^20)/128 + (1479*A^5*a^7*b^18)/4 + (482713*A^5*a^9*b^16)/256 + (11779*A^5*a^11*b^14)/8 - (803*A^
5*a^13*b^12)/2 - 504*A^5*a^15*b^10 - (55*B^5*a^2*b^23)/4 - 60*B^5*a^4*b^21 + (2045*B^5*a^6*b^19)/2 + 2550*B^5*
a^8*b^17 + (5125*B^5*a^10*b^15)/4 - 620*B^5*a^12*b^13 - 260*B^5*a^14*b^11 + 160*B^5*a^16*b^9 - (315*A^2*B^3*a^
2*b^23)/16 + (51125*A^2*B^3*a^4*b^21)/128 - (805*A^2*B^3*a^6*b^19)/32 - (144971*A^2*B^3*a^8*b^17)/256 + (40825
*A^2*B^3*a^10*b^15)/16 + (8787*A^2*B^3*a^12*b^13)/2 + 1528*A^2*B^3*a^14*b^11 - 192*A^2*B^3*a^16*b^9 + (5115*A^
3*B^2*a^3*b^22)/32 + (198501*A^3*B^2*a^5*b^20)/128 + (5863*A^3*B^2*a^7*b^18)/4 - (658487*A^3*B^2*a^9*b^16)/256
- (27191*A^3*B^2*a^11*b^14)/8 - 99*A^3*B^2*a^13*b^12 + 592*A^3*B^2*a^15*b^10 - 64*A^3*B^2*a^17*b^8 + (15*A*B^
4*a*b^24)/16 + (215*A*B^4*a^3*b^22)/4 + (12743*A*B^4*a^5*b^20)/8 + 1096*A*B^4*a^7*b^18 - (71325*A*B^4*a^9*b^16
)/16 - (19485*A*B^4*a^11*b^14)/4 + (605*A*B^4*a^13*b^12)/2 + 1096*A*B^4*a^15*b^10 - 64*A*B^4*a^17*b^8 + (805*A
^3*B^2*a*b^24)/256 - (95*A^4*B*a^2*b^23)/16 + (58805*A^4*B*a^4*b^21)/128 - (33525*A^4*B*a^6*b^19)/32 - (797771
*A^4*B*a^8*b^17)/256 + (20325*A^4*B*a^10*b^15)/16 + (10027*A^4*B*a^12*b^13)/2 + 1788*A^4*B*a^14*b^11 - 352*A^4
*B*a^16*b^9)/(a^2*d^5) - ((((a + b*tan(c + d*x))^(1/2)*(25*A^2*B^2*b^22 - 25*A^4*b^22 + 6167*A^4*a^2*b^20 + 28
457*A^4*a^4*b^18 + 993145*A^4*a^6*b^16 - 1616544*A^4*a^8*b^14 + 1346560*A^4*a^10*b^12 - 258048*A^4*a^12*b^10 +
24576*A^4*a^14*b^8 + 9792*B^4*a^2*b^20 - 448*B^4*a^4*b^18 + 633280*B^4*a^6*b^16 - 1757760*B^4*a^8*b^14 + 1684
480*B^4*a^10*b^12 - 53248*B^4*a^12*b^10 + 8192*B^4*a^14*b^8 + 21609*A^2*B^2*a^2*b^20 + 344599*A^2*B^2*a^4*b^18
- 3736185*A^2*B^2*a^6*b^16 + 11758304*A^2*B^2*a^8*b^14 - 7782400*A^2*B^2*a^10*b^12 + 1490944*A^2*B^2*a^12*b^1
0 - 400*A*B^3*a*b^21 + 100*A^3*B*a*b^21 - 29200*A*B^3*a^3*b^19 + 769040*A*B^3*a^5*b^17 - 5051120*A*B^3*a^7*b^1
5 + 8105600*A*B^3*a^9*b^13 - 2621440*A*B^3*a^11*b^11 + 81920*A*B^3*a^13*b^9 - 17800*A^3*B*a^3*b^19 - 977980*A^
3*B*a^5*b^17 + 5740400*A^3*B*a^7*b^15 - 7032448*A^3*B*a^9*b^13 + 2785280*A^3*B*a^11*b^11 - 278528*A^3*B*a^13*b
^9))/(32768*a^2*d^4) - ((((25*A^3*b^20*d^2)/128 - (125*A^3*a^2*b^18*d^2)/4 - (232217*A^3*a^4*b^16*d^2)/128 + (
14109*A^3*a^6*b^14*d^2)/4 + 2910*A^3*a^8*b^12*d^2 - 2304*A^3*a^10*b^10*d^2 + 96*A^3*a^12*b^8*d^2 - 407*B^3*a^3
*b^17*d^2 + 3225*B^3*a^5*b^15*d^2 - 1088*B^3*a^7*b^13*d^2 - 3984*B^3*a^9*b^11*d^2 + 736*B^3*a^11*b^9*d^2 + (11
05*A^2*B*a*b^19*d^2)/64 - (415*A*B^2*a^2*b^18*d^2)/4 + (18839*A*B^2*a^4*b^16*d^2)/4 - (22273*A*B^2*a^6*b^14*d^
2)/2 - 8558*A*B^2*a^8*b^12*d^2 + 7104*A*B^2*a^10*b^10*d^2 - 288*A*B^2*a^12*b^8*d^2 + (67897*A^2*B*a^3*b^17*d^2
)/64 - (85211*A^2*B*a^5*b^15*d^2)/8 + 1985*A^2*B*a^7*b^13*d^2 + 11472*A^2*B*a^9*b^11*d^2 - 2208*A^2*B*a^11*b^9
*d^2)/(128*a^2*d^5) + ((((a + b*tan(c + d*x))^(1/2)*(320896*A^2*a^3*b^14*d^2 + 143360*A^2*a^5*b^12*d^2 - 10813
44*A^2*a^7*b^10*d^2 + 147456*A^2*a^9*b^8*d^2 - 304896*B^2*a^3*b^14*d^2 - 20480*B^2*a^5*b^12*d^2 + 1245184*B^2*
a^7*b^10*d^2 - 81920*B^2*a^9*b^8*d^2 + 100*A^2*a*b^16*d^2 - 132672*A*B*a^2*b^15*d^2 + 919040*A*B*a^4*b^13*d^2
+ 1966080*A*B*a^6*b^11*d^2 - 1179648*A*B*a^8*b^9*d^2))/(32768*a^2*d^4) + (((20*A*a*b^14*d^4 + 852*A*a^3*b^12*d
^4 + 448*A*a^5*b^10*d^4 - 384*A*a^7*b^8*d^4 - 160*B*a^2*b^13*d^4 + 864*B*a^4*b^11*d^4 + 1024*B*a^6*b^9*d^4)/(1
28*a^2*d^5) - ((131072*a^2*b^10*d^4 + 196608*a^4*b^8*d^4)*(a + b*tan(c + d*x))^(1/2)*(16384*A^2*a^11 + 25*A^2*
a^3*b^8 + 2400*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b^2 + 1600*B^2*a^5*b^6 - 25600*B^2*a^7*b^4 + 10
2400*B^2*a^9*b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*B*a^6*b^5 + 163840*A*B*a^8*b^3)^(1/2))/(419430
4*a^5*d^5))*(16384*A^2*a^11 + 25*A^2*a^3*b^8 + 2400*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b^2 + 1600
*B^2*a^5*b^6 - 25600*B^2*a^7*b^4 + 102400*B^2*a^9*b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*B*a^6*b^5
+ 163840*A*B*a^8*b^3)^(1/2))/(128*a^3*d))*(16384*A^2*a^11 + 25*A^2*a^3*b^8 + 2400*A^2*a^5*b^6 + 56320*A^2*a^7
*b^4 - 61440*A^2*a^9*b^2 + 1600*B^2*a^5*b^6 - 25600*B^2*a^7*b^4 + 102400*B^2*a^9*b^2 - 81920*A*B*a^10*b - 400*
A*B*a^4*b^7 - 16000*A*B*a^6*b^5 + 163840*A*B*a^8*b^3)^(1/2))/(128*a^3*d))*(16384*A^2*a^11 + 25*A^2*a^3*b^8 + 2
400*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b^2 + 1600*B^2*a^5*b^6 - 25600*B^2*a^7*b^4 + 102400*B^2*a^
9*b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*B*a^6*b^5 + 163840*A*B*a^8*b^3)^(1/2))/(128*a^3*d))*(1638
4*A^2*a^11 + 25*A^2*a^3*b^8 + 2400*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b^2 + 1600*B^2*a^5*b^6 - 25
600*B^2*a^7*b^4 + 102400*B^2*a^9*b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*B*a^6*b^5 + 163840*A*B*a^8
*b^3)^(1/2))/(a^3*d) + ((((a + b*tan(c + d*x))^(1/2)*(25*A^2*B^2*b^22 - 25*A^4*b^22 + 6167*A^4*a^2*b^20 + 2845
7*A^4*a^4*b^18 + 993145*A^4*a^6*b^16 - 1616544*A^4*a^8*b^14 + 1346560*A^4*a^10*b^12 - 258048*A^4*a^12*b^10 + 2
4576*A^4*a^14*b^8 + 9792*B^4*a^2*b^20 - 448*B^4*a^4*b^18 + 633280*B^4*a^6*b^16 - 1757760*B^4*a^8*b^14 + 168448
0*B^4*a^10*b^12 - 53248*B^4*a^12*b^10 + 8192*B^4*a^14*b^8 + 21609*A^2*B^2*a^2*b^20 + 344599*A^2*B^2*a^4*b^18 -
3736185*A^2*B^2*a^6*b^16 + 11758304*A^2*B^2*a^8*b^14 - 7782400*A^2*B^2*a^10*b^12 + 1490944*A^2*B^2*a^12*b^10
- 400*A*B^3*a*b^21 + 100*A^3*B*a*b^21 - 29200*A*B^3*a^3*b^19 + 769040*A*B^3*a^5*b^17 - 5051120*A*B^3*a^7*b^15
+ 8105600*A*B^3*a^9*b^13 - 2621440*A*B^3*a^11*b^11 + 81920*A*B^3*a^13*b^9 - 17800*A^3*B*a^3*b^19 - 977980*A^3*
B*a^5*b^17 + 5740400*A^3*B*a^7*b^15 - 7032448*A^3*B*a^9*b^13 + 2785280*A^3*B*a^11*b^11 - 278528*A^3*B*a^13*b^9
))/(32768*a^2*d^4) + ((((25*A^3*b^20*d^2)/128 - (125*A^3*a^2*b^18*d^2)/4 - (232217*A^3*a^4*b^16*d^2)/128 + (14
109*A^3*a^6*b^14*d^2)/4 + 2910*A^3*a^8*b^12*d^2 - 2304*A^3*a^10*b^10*d^2 + 96*A^3*a^12*b^8*d^2 - 407*B^3*a^3*b
^17*d^2 + 3225*B^3*a^5*b^15*d^2 - 1088*B^3*a^7*b^13*d^2 - 3984*B^3*a^9*b^11*d^2 + 736*B^3*a^11*b^9*d^2 + (1105
*A^2*B*a*b^19*d^2)/64 - (415*A*B^2*a^2*b^18*d^2)/4 + (18839*A*B^2*a^4*b^16*d^2)/4 - (22273*A*B^2*a^6*b^14*d^2)
/2 - 8558*A*B^2*a^8*b^12*d^2 + 7104*A*B^2*a^10*b^10*d^2 - 288*A*B^2*a^12*b^8*d^2 + (67897*A^2*B*a^3*b^17*d^2)/
64 - (85211*A^2*B*a^5*b^15*d^2)/8 + 1985*A^2*B*a^7*b^13*d^2 + 11472*A^2*B*a^9*b^11*d^2 - 2208*A^2*B*a^11*b^9*d
^2)/(128*a^2*d^5) - ((((a + b*tan(c + d*x))^(1/2)*(320896*A^2*a^3*b^14*d^2 + 143360*A^2*a^5*b^12*d^2 - 1081344
*A^2*a^7*b^10*d^2 + 147456*A^2*a^9*b^8*d^2 - 304896*B^2*a^3*b^14*d^2 - 20480*B^2*a^5*b^12*d^2 + 1245184*B^2*a^
7*b^10*d^2 - 81920*B^2*a^9*b^8*d^2 + 100*A^2*a*b^16*d^2 - 132672*A*B*a^2*b^15*d^2 + 919040*A*B*a^4*b^13*d^2 +
1966080*A*B*a^6*b^11*d^2 - 1179648*A*B*a^8*b^9*d^2))/(32768*a^2*d^4) - (((20*A*a*b^14*d^4 + 852*A*a^3*b^12*d^4
+ 448*A*a^5*b^10*d^4 - 384*A*a^7*b^8*d^4 - 160*B*a^2*b^13*d^4 + 864*B*a^4*b^11*d^4 + 1024*B*a^6*b^9*d^4)/(128
*a^2*d^5) + ((131072*a^2*b^10*d^4 + 196608*a^4*b^8*d^4)*(a + b*tan(c + d*x))^(1/2)*(16384*A^2*a^11 + 25*A^2*a^
3*b^8 + 2400*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b^2 + 1600*B^2*a^5*b^6 - 25600*B^2*a^7*b^4 + 1024
00*B^2*a^9*b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*B*a^6*b^5 + 163840*A*B*a^8*b^3)^(1/2))/(4194304*
a^5*d^5))*(16384*A^2*a^11 + 25*A^2*a^3*b^8 + 2400*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b^2 + 1600*B
^2*a^5*b^6 - 25600*B^2*a^7*b^4 + 102400*B^2*a^9*b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*B*a^6*b^5 +
163840*A*B*a^8*b^3)^(1/2))/(128*a^3*d))*(16384*A^2*a^11 + 25*A^2*a^3*b^8 + 2400*A^2*a^5*b^6 + 56320*A^2*a^7*b
^4 - 61440*A^2*a^9*b^2 + 1600*B^2*a^5*b^6 - 25600*B^2*a^7*b^4 + 102400*B^2*a^9*b^2 - 81920*A*B*a^10*b - 400*A*
B*a^4*b^7 - 16000*A*B*a^6*b^5 + 163840*A*B*a^8*b^3)^(1/2))/(128*a^3*d))*(16384*A^2*a^11 + 25*A^2*a^3*b^8 + 240
0*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b^2 + 1600*B^2*a^5*b^6 - 25600*B^2*a^7*b^4 + 102400*B^2*a^9*
b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*B*a^6*b^5 + 163840*A*B*a^8*b^3)^(1/2))/(128*a^3*d))*(16384*
A^2*a^11 + 25*A^2*a^3*b^8 + 2400*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b^2 + 1600*B^2*a^5*b^6 - 2560
0*B^2*a^7*b^4 + 102400*B^2*a^9*b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*B*a^6*b^5 + 163840*A*B*a^8*b
^3)^(1/2))/(a^3*d)))*(16384*A^2*a^11 + 25*A^2*a^3*b^8 + 2400*A^2*a^5*b^6 + 56320*A^2*a^7*b^4 - 61440*A^2*a^9*b
^2 + 1600*B^2*a^5*b^6 - 25600*B^2*a^7*b^4 + 102400*B^2*a^9*b^2 - 81920*A*B*a^10*b - 400*A*B*a^4*b^7 - 16000*A*
B*a^6*b^5 + 163840*A*B*a^8*b^3)^(1/2)*1i)/(64*a^3*d)