\(\int \cot ^3(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx\) [337]

Optimal result

Integrand size = 33, antiderivative size = 220 \[ \int \cot ^3(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx=\frac {\sqrt {a} \left (8 a^2 A-15 A b^2-20 a b B\right ) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{4 d}-\frac {(a-i b)^{5/2} (A-i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{d}-\frac {(a+i b)^{5/2} (A+i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{d}-\frac {a (7 A b+4 a B) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{4 d}-\frac {a A \cot ^2(c+d x) (a+b \tan (c+d x))^{3/2}}{2 d} \]

[Out]

-(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*tan(
d*x+c))^(1/2)/(a+I*b)^(1/2))/d+1/4*(8*A*a^2-15*A*b^2-20*B*a*b)*arctanh((a+b*tan(d*x+c))^(1/2)/a^(1/2))*a^(1/2)
/d-1/4*a*(7*A*b+4*B*a)*cot(d*x+c)*(a+b*tan(d*x+c))^(1/2)/d-1/2*a*A*cot(d*x+c)^2*(a+b*tan(d*x+c))^(3/2)/d

Rubi [A] (verified)

Time = 1.08 (sec) , antiderivative size = 220, normalized size of antiderivative = 1.00, number of steps used = 13, number of rules used = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.242, Rules used = {3686, 3726, 3734, 3620, 3618, 65, 214, 3715} \[ \int \cot ^3(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx=\frac {\sqrt {a} \left (8 a^2 A-20 a b B-15 A b^2\right ) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{4 d}-\frac {(a-i b)^{5/2} (A-i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )}{d}-\frac {(a+i b)^{5/2} (A+i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )}{d}-\frac {a (4 a B+7 A b) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{4 d}-\frac {a A \cot ^2(c+d x) (a+b \tan (c+d x))^{3/2}}{2 d} \]

[In]

Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]

[Out]

(Sqrt[a]*(8*a^2*A - 15*A*b^2 - 20*a*b*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(4*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*Ta
n[c + d*x]]/Sqrt[a + I*b]])/d - (a*(7*A*b + 4*a*B)*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(4*d) - (a*A*Cot[c +
d*x]^2*(a + b*Tan[c + d*x])^(3/2))/(2*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 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 ^2(c+d x) (a+b \tan (c+d x))^{3/2}}{2 d}+\frac {1}{2} \int \cot ^2(c+d x) \sqrt {a+b \tan (c+d x)} \left (\frac {1}{2} a (7 A b+4 a B)-2 \left (a^2 A-A b^2-2 a b B\right ) \tan (c+d x)-\frac {1}{2} b (a A-4 b B) \tan ^2(c+d x)\right ) \, dx \\ & = -\frac {a (7 A b+4 a B) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{4 d}-\frac {a A \cot ^2(c+d x) (a+b \tan (c+d x))^{3/2}}{2 d}+\frac {1}{2} \int \frac {\cot (c+d x) \left (-\frac {1}{4} a \left (8 a^2 A-15 A b^2-20 a b B\right )-2 \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 (9 a A b+4 a^2 B-8 b^2 B\right ) \tan ^2(c+d x)\right )}{\sqrt {a+b \tan (c+d x)}} \, dx \\ & = -\frac {a (7 A b+4 a B) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{4 d}-\frac {a A \cot ^2(c+d x) (a+b \tan (c+d x))^{3/2}}{2 d}+\frac {1}{2} \int \frac {-2 \left (3 a^2 A b-A b^3+a^3 B-3 a b^2 B\right )+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-\frac {1}{8} \left (a \left (8 a^2 A-15 A b^2-20 a b B\right )\right ) \int \frac {\cot (c+d x) \left (1+\tan ^2(c+d x)\right )}{\sqrt {a+b \tan (c+d x)}} \, dx \\ & = -\frac {a (7 A b+4 a B) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{4 d}-\frac {a A \cot ^2(c+d x) (a+b \tan (c+d x))^{3/2}}{2 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 {1}{4} \left (-2 \left (3 a^2 A b-A b^3+a^3 B-3 a b^2 B\right )+2 i \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-\frac {\left (a \left (8 a^2 A-15 A b^2-20 a b B\right )\right ) \text {Subst}\left (\int \frac {1}{x \sqrt {a+b x}} \, dx,x,\tan (c+d x)\right )}{8 d} \\ & = -\frac {a (7 A b+4 a B) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{4 d}-\frac {a A \cot ^2(c+d x) (a+b \tan (c+d x))^{3/2}}{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 ((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 \left (8 a^2 A-15 A b^2-20 a b B\right )\right ) \text {Subst}\left (\int \frac {1}{-\frac {a}{b}+\frac {x^2}{b}} \, dx,x,\sqrt {a+b \tan (c+d x)}\right )}{4 b d} \\ & = \frac {\sqrt {a} \left (8 a^2 A-15 A b^2-20 a b B\right ) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{4 d}-\frac {a (7 A b+4 a B) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{4 d}-\frac {a A \cot ^2(c+d x) (a+b \tan (c+d x))^{3/2}}{2 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 {\sqrt {a} \left (8 a^2 A-15 A b^2-20 a b B\right ) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )}{4 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 (7 A b+4 a B) \cot (c+d x) \sqrt {a+b \tan (c+d x)}}{4 d}-\frac {a A \cot ^2(c+d x) (a+b \tan (c+d x))^{3/2}}{2 d} \\ \end{align*}

Mathematica [B] (verified)

Both result and optimal contain complex but leaf count is larger than twice the leaf count of optimal. \(448\) vs. \(2(220)=440\).

Time = 2.55 (sec) , antiderivative size = 448, normalized size of antiderivative = 2.04 \[ \int \cot ^3(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx=-\frac {-\sqrt {a} \left (8 a^2 A-15 A b^2-20 a b B\right ) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a}}\right )+4 (a-i b)^{5/2} (A-i B) \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a-i b}}\right )+4 a^2 A \sqrt {a+i b} \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )+8 i a A \sqrt {a+i b} b \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )-4 A \sqrt {a+i b} b^2 \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )+4 i a^2 \sqrt {a+i b} B \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )-8 a \sqrt {a+i b} b B \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )-4 i \sqrt {a+i b} b^2 B \text {arctanh}\left (\frac {\sqrt {a+b \tan (c+d x)}}{\sqrt {a+i b}}\right )+9 a A b \cot (c+d x) \sqrt {a+b \tan (c+d x)}+4 a^2 B \cot (c+d x) \sqrt {a+b \tan (c+d x)}+2 a^2 A \cot ^2(c+d x) \sqrt {a+b \tan (c+d x)}}{4 d} \]

[In]

Integrate[Cot[c + d*x]^3*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]

[Out]

-1/4*(-(Sqrt[a]*(8*a^2*A - 15*A*b^2 - 20*a*b*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]]) + 4*(a - I*b)^(5/2)
*(A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]] + 4*a^2*A*Sqrt[a + I*b]*ArcTanh[Sqrt[a + b*Tan[c +
d*x]]/Sqrt[a + I*b]] + (8*I)*a*A*Sqrt[a + I*b]*b*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]] - 4*A*Sqrt[a
+ I*b]*b^2*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]] + (4*I)*a^2*Sqrt[a + I*b]*B*ArcTanh[Sqrt[a + b*Tan[
c + d*x]]/Sqrt[a + I*b]] - 8*a*Sqrt[a + I*b]*b*B*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]] - (4*I)*Sqrt[
a + I*b]*b^2*B*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]] + 9*a*A*b*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]]
+ 4*a^2*B*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]] + 2*a^2*A*Cot[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/d

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(2487\) vs. \(2(186)=372\).

Time = 0.27 (sec) , antiderivative size = 2488, normalized size of antiderivative = 11.31

method	result	size
derivativedivides	\(\text {Expression too large to display}\)	\(2488\)
default	\(\text {Expression too large to display}\)	\(2488\)

[In]

int(cot(d*x+c)^3*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x,method=_RETURNVERBOSE)

[Out]

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)*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+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+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*t
an(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)*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))*A*(a^2+b^2)^(1/2)
-15/4/d*b^2*A*a^(1/2)*arctanh((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+7/4/d*a^2/tan(d*x+c)^2*(a+b*tan(d*x+c))^(1/2)*A-9/4/d*a/tan(d*x+c)^2*A*(a+b*tan(d*x+c))^(3/2)-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)+1/d/b*a^3/tan(d*x+c)^2*(a+b*tan(d*x+c))^(1/2)*B-1/d/b*a^2/t
an(d*x+c)^2*B*(a+b*tan(d*x+c))^(3/2)-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. 4935 vs. \(2 (180) = 360\).

Time = 16.38 (sec) , antiderivative size = 9888, normalized size of antiderivative = 44.95 \[ \int \cot ^3(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx=\text {Too large to display} \]

[In]

integrate(cot(d*x+c)^3*(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. \[ \int \cot ^3(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx=\text {Timed out} \]

[In]

integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)

[Out]

Timed out

Maxima [F(-1)]

Timed out. \[ \int \cot ^3(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx=\text {Timed out} \]

[In]

integrate(cot(d*x+c)^3*(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. \[ \int \cot ^3(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx=\text {Timed out} \]

[In]

integrate(cot(d*x+c)^3*(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 = 12.57 (sec) , antiderivative size = 32561, normalized size of antiderivative = 148.00 \[ \int \cot ^3(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx=\text {Too large to display} \]

[In]

int(cot(c + d*x)^3*(A + B*tan(c + d*x))*(a + b*tan(c + d*x))^(5/2),x)

[Out]

atan(-((((3708*A^3*a^2*b^16*d^2 - 6912*A^3*a^4*b^14*d^2 - 5820*A^3*a^6*b^12*d^2 + 4608*A^3*a^8*b^10*d^2 - 192*
A^3*a^10*b^8*d^2 - 6400*B^3*a^3*b^15*d^2 + 2816*B^3*a^5*b^13*d^2 + 7808*B^3*a^7*b^11*d^2 - 1472*B^3*a^9*b^9*d^
2 + 64*B^3*a*b^17*d^2 - 1856*A^2*B*a*b^17*d^2 - 7552*A*B^2*a^2*b^16*d^2 + 23488*A*B^2*a^4*b^14*d^2 + 16256*A*B
^2*a^6*b^12*d^2 - 14208*A*B^2*a^8*b^10*d^2 + 576*A*B^2*a^10*b^8*d^2 + 20504*A^2*B*a^3*b^15*d^2 - 5000*A^2*B*a^
5*b^13*d^2 - 22944*A^2*B*a^7*b^11*d^2 + 4416*A^2*B*a^9*b^9*d^2)/(2*d^5) - (((1664*A*a*b^12*d^4 + 896*A*a^3*b^1
0*d^4 - 768*A*a^5*b^8*d^4 + 2048*B*a^2*b^11*d^4 + 2048*B*a^4*b^9*d^4)/(2*d^5) - ((512*b^10*d^4 + 768*a^2*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 + 1
6*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))/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)*(580*A^2*a^3*b^12*d^2 - 4224*A^2*a^5*
b^10*d^2 + 576*A^2*a^7*b^8*d^2 + 320*B^2*a^3*b^12*d^2 + 4864*B^2*a^5*b^10*d^2 - 320*B^2*a^7*b^8*d^2 - 512*A*B*
b^15*d^2 + 1216*A^2*a*b^14*d^2 - 1216*B^2*a*b^14*d^2 + 3840*A*B*a^2*b^13*d^2 + 7520*A*B*a^4*b^11*d^2 - 4608*A*
B*a^6*b^9*d^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))*((((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*A^4*b^20 + 32*B^4*b^20 + 64*A^2*B^2*b^20 - 33*A^
4*a^2*b^18 + 4095*A^4*a^4*b^16 - 6399*A^4*a^6*b^14 + 5265*A^4*a^8*b^12 - 1008*A^4*a^10*b^10 + 96*A^4*a^12*b^8
+ 192*B^4*a^2*b^18 + 880*B^4*a^4*b^16 - 5360*B^4*a^6*b^14 + 6480*B^4*a^8*b^12 - 208*B^4*a^10*b^10 + 32*B^4*a^1
2*b^8 + 609*A^2*B^2*a^2*b^18 - 10255*A^2*B^2*a^4*b^16 + 42159*A^2*B^2*a^6*b^14 - 29825*A^2*B^2*a^8*b^12 + 5824
*A^2*B^2*a^10*b^10 + 600*A*B^3*a^3*b^17 - 14120*A*B^3*a^5*b^15 + 29800*A*B^3*a^7*b^13 - 10200*A*B^3*a^9*b^11 +
320*A*B^3*a^11*b^9 - 3300*A^3*B*a^3*b^17 + 21200*A^3*B*a^5*b^15 - 26868*A^3*B*a^7*b^13 + 10840*A^3*B*a^9*b^11
- 1088*A^3*B*a^11*b^9))/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 - (((3708*A^3*a^2*b^16*d^2 - 6912*A^3*a^4*b^14*d^2 - 5820*A^3*a^6*b^12*d^2
+ 4608*A^3*a^8*b^10*d^2 - 192*A^3*a^10*b^8*d^2 - 6400*B^3*a^3*b^15*d^2 + 2816*B^3*a^5*b^13*d^2 + 7808*B^3*a^7
*b^11*d^2 - 1472*B^3*a^9*b^9*d^2 + 64*B^3*a*b^17*d^2 - 1856*A^2*B*a*b^17*d^2 - 7552*A*B^2*a^2*b^16*d^2 + 23488
*A*B^2*a^4*b^14*d^2 + 16256*A*B^2*a^6*b^12*d^2 - 14208*A*B^2*a^8*b^10*d^2 + 576*A*B^2*a^10*b^8*d^2 + 20504*A^2
*B*a^3*b^15*d^2 - 5000*A^2*B*a^5*b^13*d^2 - 22944*A^2*B*a^7*b^11*d^2 + 4416*A^2*B*a^9*b^9*d^2)/(2*d^5) - (((16
64*A*a*b^12*d^4 + 896*A*a^3*b^10*d^4 - 768*A*a^5*b^8*d^4 + 2048*B*a^2*b^11*d^4 + 2048*B*a^4*b^9*d^4)/(2*d^5) +
((512*b^10*d^4 + 768*a^2*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))/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^1
0 + 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)*(580*A
^2*a^3*b^12*d^2 - 4224*A^2*a^5*b^10*d^2 + 576*A^2*a^7*b^8*d^2 + 320*B^2*a^3*b^12*d^2 + 4864*B^2*a^5*b^10*d^2 -
320*B^2*a^7*b^8*d^2 - 512*A*B*b^15*d^2 + 1216*A^2*a*b^14*d^2 - 1216*B^2*a*b^14*d^2 + 3840*A*B*a^2*b^13*d^2 +
7520*A*B*a^4*b^11*d^2 - 4608*A*B*a^6*b^9*d^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 - 8
0*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 - 40*A^2*a*b^4*d^2 + 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*
d^2)^2/64 - 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))*((((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*A^4*b^20 + 32*B^4
*b^20 + 64*A^2*B^2*b^20 - 33*A^4*a^2*b^18 + 4095*A^4*a^4*b^16 - 6399*A^4*a^6*b^14 + 5265*A^4*a^8*b^12 - 1008*A
^4*a^10*b^10 + 96*A^4*a^12*b^8 + 192*B^4*a^2*b^18 + 880*B^4*a^4*b^16 - 5360*B^4*a^6*b^14 + 6480*B^4*a^8*b^12 -
208*B^4*a^10*b^10 + 32*B^4*a^12*b^8 + 609*A^2*B^2*a^2*b^18 - 10255*A^2*B^2*a^4*b^16 + 42159*A^2*B^2*a^6*b^14
- 29825*A^2*B^2*a^8*b^12 + 5824*A^2*B^2*a^10*b^10 + 600*A*B^3*a^3*b^17 - 14120*A*B^3*a^5*b^15 + 29800*A*B^3*a^
7*b^13 - 10200*A*B^3*a^9*b^11 + 320*A*B^3*a^11*b^9 - 3300*A^3*B*a^3*b^17 + 21200*A^3*B*a^5*b^15 - 26868*A^3*B*
a^7*b^13 + 10840*A^3*B*a^9*b^11 - 1088*A^3*B*a^11*b^9))/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)/((((3708*A^3*a^2*b^16*d^2 - 6912*A^3*a^4*b
^14*d^2 - 5820*A^3*a^6*b^12*d^2 + 4608*A^3*a^8*b^10*d^2 - 192*A^3*a^10*b^8*d^2 - 6400*B^3*a^3*b^15*d^2 + 2816*
B^3*a^5*b^13*d^2 + 7808*B^3*a^7*b^11*d^2 - 1472*B^3*a^9*b^9*d^2 + 64*B^3*a*b^17*d^2 - 1856*A^2*B*a*b^17*d^2 -
7552*A*B^2*a^2*b^16*d^2 + 23488*A*B^2*a^4*b^14*d^2 + 16256*A*B^2*a^6*b^12*d^2 - 14208*A*B^2*a^8*b^10*d^2 + 576
*A*B^2*a^10*b^8*d^2 + 20504*A^2*B*a^3*b^15*d^2 - 5000*A^2*B*a^5*b^13*d^2 - 22944*A^2*B*a^7*b^11*d^2 + 4416*A^2
*B*a^9*b^9*d^2)/(2*d^5) - (((1664*A*a*b^12*d^4 + 896*A*a^3*b^10*d^4 - 768*A*a^5*b^8*d^4 + 2048*B*a^2*b^11*d^4
+ 2048*B*a^4*b^9*d^4)/(2*d^5) - ((512*b^10*d^4 + 768*a^2*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))/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)*(580*A^2*a^3*b^12*d^2 - 4224*A^2*a^5*b^10*d^2 + 576*A^2*a^7*b^8*d^2 + 320*B^2*a^3*b^1
2*d^2 + 4864*B^2*a^5*b^10*d^2 - 320*B^2*a^7*b^8*d^2 - 512*A*B*b^15*d^2 + 1216*A^2*a*b^14*d^2 - 1216*B^2*a*b^14
*d^2 + 3840*A*B*a^2*b^13*d^2 + 7520*A*B*a^4*b^11*d^2 - 4608*A*B*a^6*b^9*d^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))*((((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*A^4*b^20 + 32*B^4*b^20 + 64*A^2*B^2*b^20 - 33*A^4*a^2*b^18 + 4095*A^4*a^4*b^16 - 6399*A^4*a^6*b^
14 + 5265*A^4*a^8*b^12 - 1008*A^4*a^10*b^10 + 96*A^4*a^12*b^8 + 192*B^4*a^2*b^18 + 880*B^4*a^4*b^16 - 5360*B^4
*a^6*b^14 + 6480*B^4*a^8*b^12 - 208*B^4*a^10*b^10 + 32*B^4*a^12*b^8 + 609*A^2*B^2*a^2*b^18 - 10255*A^2*B^2*a^4
*b^16 + 42159*A^2*B^2*a^6*b^14 - 29825*A^2*B^2*a^8*b^12 + 5824*A^2*B^2*a^10*b^10 + 600*A*B^3*a^3*b^17 - 14120*
A*B^3*a^5*b^15 + 29800*A*B^3*a^7*b^13 - 10200*A*B^3*a^9*b^11 + 320*A*B^3*a^11*b^9 - 3300*A^3*B*a^3*b^17 + 2120
0*A^3*B*a^5*b^15 - 26868*A^3*B*a^7*b^13 + 10840*A^3*B*a^9*b^11 - 1088*A^3*B*a^11*b^9))/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) - (120*A^5*a*b^
22 - 19*A^5*a^3*b^20 + 336*A^5*a^5*b^18 + 1818*A^5*a^7*b^16 + 1448*A^5*a^9*b^14 - 399*A^5*a^11*b^12 - 504*A^5*
a^13*b^10 + 160*B^5*a^2*b^21 + 1360*B^5*a^4*b^19 + 2400*B^5*a^6*b^17 + 800*B^5*a^8*b^15 - 800*B^5*a^10*b^13 -
240*B^5*a^12*b^11 + 160*B^5*a^14*b^9 + 545*A^2*B^3*a^2*b^21 + 280*A^2*B^3*a^4*b^19 - 326*A^2*B^3*a^6*b^17 + 26
00*A^2*B^3*a^8*b^15 + 4381*A^2*B^3*a^10*b^13 + 1528*A^2*B^3*a^12*b^11 - 192*A^2*B^3*a^14*b^9 + 1237*A^3*B^2*a^
3*b^20 + 232*A^3*B^2*a^5*b^18 - 3542*A^3*B^2*a^7*b^16 - 3312*A^3*B^2*a^9*b^14 + 121*A^3*B^2*a^11*b^12 + 592*A^
3*B^2*a^13*b^10 - 64*A^3*B^2*a^15*b^8 + 120*A*B^4*a*b^22 + 1256*A*B^4*a^3*b^20 - 104*A*B^4*a^5*b^18 - 5360*A*B
^4*a^7*b^16 - 4760*A*B^4*a^9*b^14 + 520*A*B^4*a^11*b^12 + 1096*A*B^4*a^13*b^10 - 64*A*B^4*a^15*b^8 + 240*A^3*B
^2*a*b^22 + 385*A^4*B*a^2*b^21 - 1080*A^4*B*a^4*b^19 - 2726*A^4*B*a^6*b^17 + 1800*A^4*B*a^8*b^15 + 5181*A^4*B*
a^10*b^13 + 1768*A^4*B*a^12*b^11 - 352*A^4*B*a^14*b^9)/d^5 + (((3708*A^3*a^2*b^16*d^2 - 6912*A^3*a^4*b^14*d^2
- 5820*A^3*a^6*b^12*d^2 + 4608*A^3*a^8*b^10*d^2 - 192*A^3*a^10*b^8*d^2 - 6400*B^3*a^3*b^15*d^2 + 2816*B^3*a^5*
b^13*d^2 + 7808*B^3*a^7*b^11*d^2 - 1472*B^3*a^9*b^9*d^2 + 64*B^3*a*b^17*d^2 - 1856*A^2*B*a*b^17*d^2 - 7552*A*B
^2*a^2*b^16*d^2 + 23488*A*B^2*a^4*b^14*d^2 + 16256*A*B^2*a^6*b^12*d^2 - 14208*A*B^2*a^8*b^10*d^2 + 576*A*B^2*a
^10*b^8*d^2 + 20504*A^2*B*a^3*b^15*d^2 - 5000*A^2*B*a^5*b^13*d^2 - 22944*A^2*B*a^7*b^11*d^2 + 4416*A^2*B*a^9*b
^9*d^2)/(2*d^5) - (((1664*A*a*b^12*d^4 + 896*A*a^3*b^10*d^4 - 768*A*a^5*b^8*d^4 + 2048*B*a^2*b^11*d^4 + 2048*B
*a^4*b^9*d^4)/(2*d^5) + ((512*b^10*d^4 + 768*a^2*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 - 16
0*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))/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 + 1
0*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)*(580*A^2*a^3*b^12*d^2 - 4224*A^2*a^5*b^10*d^2 + 576*A^2*a^7*b^8*d^2 + 320*B^2*a^3*b^12*d^2 +
4864*B^2*a^5*b^10*d^2 - 320*B^2*a^7*b^8*d^2 - 512*A*B*b^15*d^2 + 1216*A^2*a*b^14*d^2 - 1216*B^2*a*b^14*d^2 + 3
840*A*B*a^2*b^13*d^2 + 7520*A*B*a^4*b^11*d^2 - 4608*A*B*a^6*b^9*d^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))*((((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*A^4*b^20 + 32*B^4*b^20 + 64*A^2*B^2*b^20 - 33*A^4*a^2*b^18 + 4095*A^4*a^4*b^16 - 6399*A^4*a^6*b^14 + 526
5*A^4*a^8*b^12 - 1008*A^4*a^10*b^10 + 96*A^4*a^12*b^8 + 192*B^4*a^2*b^18 + 880*B^4*a^4*b^16 - 5360*B^4*a^6*b^1
4 + 6480*B^4*a^8*b^12 - 208*B^4*a^10*b^10 + 32*B^4*a^12*b^8 + 609*A^2*B^2*a^2*b^18 - 10255*A^2*B^2*a^4*b^16 +
42159*A^2*B^2*a^6*b^14 - 29825*A^2*B^2*a^8*b^12 + 5824*A^2*B^2*a^10*b^10 + 600*A*B^3*a^3*b^17 - 14120*A*B^3*a^
5*b^15 + 29800*A*B^3*a^7*b^13 - 10200*A*B^3*a^9*b^11 + 320*A*B^3*a^11*b^9 - 3300*A^3*B*a^3*b^17 + 21200*A^3*B*
a^5*b^15 - 26868*A^3*B*a^7*b^13 + 10840*A^3*B*a^9*b^11 - 1088*A^3*B*a^11*b^9))/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)))*((((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(-((((370
8*A^3*a^2*b^16*d^2 - 6912*A^3*a^4*b^14*d^2 - 5820*A^3*a^6*b^12*d^2 + 4608*A^3*a^8*b^10*d^2 - 192*A^3*a^10*b^8*
d^2 - 6400*B^3*a^3*b^15*d^2 + 2816*B^3*a^5*b^13*d^2 + 7808*B^3*a^7*b^11*d^2 - 1472*B^3*a^9*b^9*d^2 + 64*B^3*a*
b^17*d^2 - 1856*A^2*B*a*b^17*d^2 - 7552*A*B^2*a^2*b^16*d^2 + 23488*A*B^2*a^4*b^14*d^2 + 16256*A*B^2*a^6*b^12*d
^2 - 14208*A*B^2*a^8*b^10*d^2 + 576*A*B^2*a^10*b^8*d^2 + 20504*A^2*B*a^3*b^15*d^2 - 5000*A^2*B*a^5*b^13*d^2 -
22944*A^2*B*a^7*b^11*d^2 + 4416*A^2*B*a^9*b^9*d^2)/(2*d^5) - (((1664*A*a*b^12*d^4 + 896*A*a^3*b^10*d^4 - 768*A
*a^5*b^8*d^4 + 2048*B*a^2*b^11*d^4 + 2048*B*a^4*b^9*d^4)/(2*d^5) - ((512*b^10*d^4 + 768*a^2*b^8*d^4)*(a + b*ta
n(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))/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 + 1
0*A*B*a^4*b*d^2)/(4*d^4))^(1/2) + ((a + b*tan(c + d*x))^(1/2)*(580*A^2*a^3*b^12*d^2 - 4224*A^2*a^5*b^10*d^2 +
576*A^2*a^7*b^8*d^2 + 320*B^2*a^3*b^12*d^2 + 4864*B^2*a^5*b^10*d^2 - 320*B^2*a^7*b^8*d^2 - 512*A*B*b^15*d^2 +
1216*A^2*a*b^14*d^2 - 1216*B^2*a*b^14*d^2 + 3840*A*B*a^2*b^13*d^2 + 7520*A*B*a^4*b^11*d^2 - 4608*A*B*a^6*b^9*d
^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))*(-(((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*A^4*b^20 + 32*B^4*b^20 + 64*A^2*B^2*b^20 - 33*A^4*a^2*b^1
8 + 4095*A^4*a^4*b^16 - 6399*A^4*a^6*b^14 + 5265*A^4*a^8*b^12 - 1008*A^4*a^10*b^10 + 96*A^4*a^12*b^8 + 192*B^4
*a^2*b^18 + 880*B^4*a^4*b^16 - 5360*B^4*a^6*b^14 + 6480*B^4*a^8*b^12 - 208*B^4*a^10*b^10 + 32*B^4*a^12*b^8 + 6
09*A^2*B^2*a^2*b^18 - 10255*A^2*B^2*a^4*b^16 + 42159*A^2*B^2*a^6*b^14 - 29825*A^2*B^2*a^8*b^12 + 5824*A^2*B^2*
a^10*b^10 + 600*A*B^3*a^3*b^17 - 14120*A*B^3*a^5*b^15 + 29800*A*B^3*a^7*b^13 - 10200*A*B^3*a^9*b^11 + 320*A*B^
3*a^11*b^9 - 3300*A^3*B*a^3*b^17 + 21200*A^3*B*a^5*b^15 - 26868*A^3*B*a^7*b^13 + 10840*A^3*B*a^9*b^11 - 1088*A
^3*B*a^11*b^9))/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 - (((3708*A^3*a^2*b^16*d^2 - 6912*A^3*a^4*b^14*d^2 - 5820*A^3*a^6*b^12*d^2 + 4608*
A^3*a^8*b^10*d^2 - 192*A^3*a^10*b^8*d^2 - 6400*B^3*a^3*b^15*d^2 + 2816*B^3*a^5*b^13*d^2 + 7808*B^3*a^7*b^11*d^
2 - 1472*B^3*a^9*b^9*d^2 + 64*B^3*a*b^17*d^2 - 1856*A^2*B*a*b^17*d^2 - 7552*A*B^2*a^2*b^16*d^2 + 23488*A*B^2*a
^4*b^14*d^2 + 16256*A*B^2*a^6*b^12*d^2 - 14208*A*B^2*a^8*b^10*d^2 + 576*A*B^2*a^10*b^8*d^2 + 20504*A^2*B*a^3*b
^15*d^2 - 5000*A^2*B*a^5*b^13*d^2 - 22944*A^2*B*a^7*b^11*d^2 + 4416*A^2*B*a^9*b^9*d^2)/(2*d^5) - (((1664*A*a*b
^12*d^4 + 896*A*a^3*b^10*d^4 - 768*A*a^5*b^8*d^4 + 2048*B*a^2*b^11*d^4 + 2048*B*a^4*b^9*d^4)/(2*d^5) + ((512*b
^10*d^4 + 768*a^2*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))/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)*(580*A^2*a^3
*b^12*d^2 - 4224*A^2*a^5*b^10*d^2 + 576*A^2*a^7*b^8*d^2 + 320*B^2*a^3*b^12*d^2 + 4864*B^2*a^5*b^10*d^2 - 320*B
^2*a^7*b^8*d^2 - 512*A*B*b^15*d^2 + 1216*A^2*a*b^14*d^2 - 1216*B^2*a*b^14*d^2 + 3840*A*B*a^2*b^13*d^2 + 7520*A
*B*a^4*b^11*d^2 - 4608*A*B*a^6*b^9*d^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))*(-(((8*B^2*a^5*d^2 - 8*A^2*a^5*d^2 + 80*A^2*a^3*b^2*d^2 - 8
0*B^2*a^3*b^2*d^2 + 16*A*B*b^5*d^2 - 40*A^2*a*b^4*d^2 + 40*B^2*a*b^4*d^2 - 160*A*B*a^2*b^3*d^2 + 80*A*B*a^4*b*
d^2)^2/64 - 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*A^4*b^20 + 32*B^4*b^2
0 + 64*A^2*B^2*b^20 - 33*A^4*a^2*b^18 + 4095*A^4*a^4*b^16 - 6399*A^4*a^6*b^14 + 5265*A^4*a^8*b^12 - 1008*A^4*a
^10*b^10 + 96*A^4*a^12*b^8 + 192*B^4*a^2*b^18 + 880*B^4*a^4*b^16 - 5360*B^4*a^6*b^14 + 6480*B^4*a^8*b^12 - 208
*B^4*a^10*b^10 + 32*B^4*a^12*b^8 + 609*A^2*B^2*a^2*b^18 - 10255*A^2*B^2*a^4*b^16 + 42159*A^2*B^2*a^6*b^14 - 29
825*A^2*B^2*a^8*b^12 + 5824*A^2*B^2*a^10*b^10 + 600*A*B^3*a^3*b^17 - 14120*A*B^3*a^5*b^15 + 29800*A*B^3*a^7*b^
13 - 10200*A*B^3*a^9*b^11 + 320*A*B^3*a^11*b^9 - 3300*A^3*B*a^3*b^17 + 21200*A^3*B*a^5*b^15 - 26868*A^3*B*a^7*
b^13 + 10840*A^3*B*a^9*b^11 - 1088*A^3*B*a^11*b^9))/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)/((((3708*A^3*a^2*b^16*d^2 - 6912*A^3*a^4*b^14
*d^2 - 5820*A^3*a^6*b^12*d^2 + 4608*A^3*a^8*b^10*d^2 - 192*A^3*a^10*b^8*d^2 - 6400*B^3*a^3*b^15*d^2 + 2816*B^3
*a^5*b^13*d^2 + 7808*B^3*a^7*b^11*d^2 - 1472*B^3*a^9*b^9*d^2 + 64*B^3*a*b^17*d^2 - 1856*A^2*B*a*b^17*d^2 - 755
2*A*B^2*a^2*b^16*d^2 + 23488*A*B^2*a^4*b^14*d^2 + 16256*A*B^2*a^6*b^12*d^2 - 14208*A*B^2*a^8*b^10*d^2 + 576*A*
B^2*a^10*b^8*d^2 + 20504*A^2*B*a^3*b^15*d^2 - 5000*A^2*B*a^5*b^13*d^2 - 22944*A^2*B*a^7*b^11*d^2 + 4416*A^2*B*
a^9*b^9*d^2)/(2*d^5) - (((1664*A*a*b^12*d^4 + 896*A*a^3*b^10*d^4 - 768*A*a^5*b^8*d^4 + 2048*B*a^2*b^11*d^4 + 2
048*B*a^4*b^9*d^4)/(2*d^5) - ((512*b^10*d^4 + 768*a^2*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 + 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))/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)*(580*A^2*a^3*b^12*d^2 - 4224*A^2*a^5*b^10*d^2 + 576*A^2*a^7*b^8*d^2 + 320*B^2*a^3*b^12
*d^2 + 4864*B^2*a^5*b^10*d^2 - 320*B^2*a^7*b^8*d^2 - 512*A*B*b^15*d^2 + 1216*A^2*a*b^14*d^2 - 1216*B^2*a*b^14*
d^2 + 3840*A*B*a^2*b^13*d^2 + 7520*A*B*a^4*b^11*d^2 - 4608*A*B*a^6*b^9*d^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))*(-(((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^1
0 + 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*A^4*b^20 + 32*B^4*b^20 + 64*A^2*B^2*b^20 - 33*A^4*a^2*b^18 + 4095*A^4*a^4*b^16 - 6399*A^4*a^6*b
^14 + 5265*A^4*a^8*b^12 - 1008*A^4*a^10*b^10 + 96*A^4*a^12*b^8 + 192*B^4*a^2*b^18 + 880*B^4*a^4*b^16 - 5360*B^
4*a^6*b^14 + 6480*B^4*a^8*b^12 - 208*B^4*a^10*b^10 + 32*B^4*a^12*b^8 + 609*A^2*B^2*a^2*b^18 - 10255*A^2*B^2*a^
4*b^16 + 42159*A^2*B^2*a^6*b^14 - 29825*A^2*B^2*a^8*b^12 + 5824*A^2*B^2*a^10*b^10 + 600*A*B^3*a^3*b^17 - 14120
*A*B^3*a^5*b^15 + 29800*A*B^3*a^7*b^13 - 10200*A*B^3*a^9*b^11 + 320*A*B^3*a^11*b^9 - 3300*A^3*B*a^3*b^17 + 212
00*A^3*B*a^5*b^15 - 26868*A^3*B*a^7*b^13 + 10840*A^3*B*a^9*b^11 - 1088*A^3*B*a^11*b^9))/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 + 1
0*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) - (120*A^5*a*
b^22 - 19*A^5*a^3*b^20 + 336*A^5*a^5*b^18 + 1818*A^5*a^7*b^16 + 1448*A^5*a^9*b^14 - 399*A^5*a^11*b^12 - 504*A^
5*a^13*b^10 + 160*B^5*a^2*b^21 + 1360*B^5*a^4*b^19 + 2400*B^5*a^6*b^17 + 800*B^5*a^8*b^15 - 800*B^5*a^10*b^13
- 240*B^5*a^12*b^11 + 160*B^5*a^14*b^9 + 545*A^2*B^3*a^2*b^21 + 280*A^2*B^3*a^4*b^19 - 326*A^2*B^3*a^6*b^17 +
2600*A^2*B^3*a^8*b^15 + 4381*A^2*B^3*a^10*b^13 + 1528*A^2*B^3*a^12*b^11 - 192*A^2*B^3*a^14*b^9 + 1237*A^3*B^2*
a^3*b^20 + 232*A^3*B^2*a^5*b^18 - 3542*A^3*B^2*a^7*b^16 - 3312*A^3*B^2*a^9*b^14 + 121*A^3*B^2*a^11*b^12 + 592*
A^3*B^2*a^13*b^10 - 64*A^3*B^2*a^15*b^8 + 120*A*B^4*a*b^22 + 1256*A*B^4*a^3*b^20 - 104*A*B^4*a^5*b^18 - 5360*A
*B^4*a^7*b^16 - 4760*A*B^4*a^9*b^14 + 520*A*B^4*a^11*b^12 + 1096*A*B^4*a^13*b^10 - 64*A*B^4*a^15*b^8 + 240*A^3
*B^2*a*b^22 + 385*A^4*B*a^2*b^21 - 1080*A^4*B*a^4*b^19 - 2726*A^4*B*a^6*b^17 + 1800*A^4*B*a^8*b^15 + 5181*A^4*
B*a^10*b^13 + 1768*A^4*B*a^12*b^11 - 352*A^4*B*a^14*b^9)/d^5 + (((3708*A^3*a^2*b^16*d^2 - 6912*A^3*a^4*b^14*d^
2 - 5820*A^3*a^6*b^12*d^2 + 4608*A^3*a^8*b^10*d^2 - 192*A^3*a^10*b^8*d^2 - 6400*B^3*a^3*b^15*d^2 + 2816*B^3*a^
5*b^13*d^2 + 7808*B^3*a^7*b^11*d^2 - 1472*B^3*a^9*b^9*d^2 + 64*B^3*a*b^17*d^2 - 1856*A^2*B*a*b^17*d^2 - 7552*A
*B^2*a^2*b^16*d^2 + 23488*A*B^2*a^4*b^14*d^2 + 16256*A*B^2*a^6*b^12*d^2 - 14208*A*B^2*a^8*b^10*d^2 + 576*A*B^2
*a^10*b^8*d^2 + 20504*A^2*B*a^3*b^15*d^2 - 5000*A^2*B*a^5*b^13*d^2 - 22944*A^2*B*a^7*b^11*d^2 + 4416*A^2*B*a^9
*b^9*d^2)/(2*d^5) - (((1664*A*a*b^12*d^4 + 896*A*a^3*b^10*d^4 - 768*A*a^5*b^8*d^4 + 2048*B*a^2*b^11*d^4 + 2048
*B*a^4*b^9*d^4)/(2*d^5) + ((512*b^10*d^4 + 768*a^2*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^1
0 + 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))/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)*(580*A^2*a^3*b^12*d^2 - 4224*A^2*a^5*b^10*d^2 + 576*A^2*a^7*b^8*d^2 + 320*B^2*a^3*b^12*d^
2 + 4864*B^2*a^5*b^10*d^2 - 320*B^2*a^7*b^8*d^2 - 512*A*B*b^15*d^2 + 1216*A^2*a*b^14*d^2 - 1216*B^2*a*b^14*d^2
+ 3840*A*B*a^2*b^13*d^2 + 7520*A*B*a^4*b^11*d^2 - 4608*A*B*a^6*b^9*d^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))*(-(((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 - 16
0*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*A^4*b^20 + 32*B^4*b^20 + 64*A^2*B^2*b^20 - 33*A^4*a^2*b^18 + 4095*A^4*a^4*b^16 - 6399*A^4*a^6*b^14
+ 5265*A^4*a^8*b^12 - 1008*A^4*a^10*b^10 + 96*A^4*a^12*b^8 + 192*B^4*a^2*b^18 + 880*B^4*a^4*b^16 - 5360*B^4*a
^6*b^14 + 6480*B^4*a^8*b^12 - 208*B^4*a^10*b^10 + 32*B^4*a^12*b^8 + 609*A^2*B^2*a^2*b^18 - 10255*A^2*B^2*a^4*b
^16 + 42159*A^2*B^2*a^6*b^14 - 29825*A^2*B^2*a^8*b^12 + 5824*A^2*B^2*a^10*b^10 + 600*A*B^3*a^3*b^17 - 14120*A*
B^3*a^5*b^15 + 29800*A*B^3*a^7*b^13 - 10200*A*B^3*a^9*b^11 + 320*A*B^3*a^11*b^9 - 3300*A^3*B*a^3*b^17 + 21200*
A^3*B*a^5*b^15 - 26868*A^3*B*a^7*b^13 + 10840*A^3*B*a^9*b^11 - 1088*A^3*B*a^11*b^9))/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)))*(-(((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 - (((9*
A*a*b^2)/4 + B*a^2*b)*(a + b*tan(c + d*x))^(3/2) - ((7*A*a^2*b^2)/4 + B*a^3*b)*(a + b*tan(c + d*x))^(1/2))/(d*
(a + b*tan(c + d*x))^2 + a^2*d - 2*a*d*(a + b*tan(c + d*x))) + (atan((((((a + b*tan(c + d*x))^(1/2)*(32*A^4*b^
20 + 32*B^4*b^20 + 64*A^2*B^2*b^20 - 33*A^4*a^2*b^18 + 4095*A^4*a^4*b^16 - 6399*A^4*a^6*b^14 + 5265*A^4*a^8*b^
12 - 1008*A^4*a^10*b^10 + 96*A^4*a^12*b^8 + 192*B^4*a^2*b^18 + 880*B^4*a^4*b^16 - 5360*B^4*a^6*b^14 + 6480*B^4
*a^8*b^12 - 208*B^4*a^10*b^10 + 32*B^4*a^12*b^8 + 609*A^2*B^2*a^2*b^18 - 10255*A^2*B^2*a^4*b^16 + 42159*A^2*B^
2*a^6*b^14 - 29825*A^2*B^2*a^8*b^12 + 5824*A^2*B^2*a^10*b^10 + 600*A*B^3*a^3*b^17 - 14120*A*B^3*a^5*b^15 + 298
00*A*B^3*a^7*b^13 - 10200*A*B^3*a^9*b^11 + 320*A*B^3*a^11*b^9 - 3300*A^3*B*a^3*b^17 + 21200*A^3*B*a^5*b^15 - 2
6868*A^3*B*a^7*b^13 + 10840*A^3*B*a^9*b^11 - 1088*A^3*B*a^11*b^9))/(8*d^4) + (((1854*A^3*a^2*b^16*d^2 - 3456*A
^3*a^4*b^14*d^2 - 2910*A^3*a^6*b^12*d^2 + 2304*A^3*a^8*b^10*d^2 - 96*A^3*a^10*b^8*d^2 - 3200*B^3*a^3*b^15*d^2
+ 1408*B^3*a^5*b^13*d^2 + 3904*B^3*a^7*b^11*d^2 - 736*B^3*a^9*b^9*d^2 + 32*B^3*a*b^17*d^2 - 928*A^2*B*a*b^17*d
^2 - 3776*A*B^2*a^2*b^16*d^2 + 11744*A*B^2*a^4*b^14*d^2 + 8128*A*B^2*a^6*b^12*d^2 - 7104*A*B^2*a^8*b^10*d^2 +
288*A*B^2*a^10*b^8*d^2 + 10252*A^2*B*a^3*b^15*d^2 - 2500*A^2*B*a^5*b^13*d^2 - 11472*A^2*B*a^7*b^11*d^2 + 2208*
A^2*B*a^9*b^9*d^2)/(8*d^5) - ((((a + b*tan(c + d*x))^(1/2)*(580*A^2*a^3*b^12*d^2 - 4224*A^2*a^5*b^10*d^2 + 576
*A^2*a^7*b^8*d^2 + 320*B^2*a^3*b^12*d^2 + 4864*B^2*a^5*b^10*d^2 - 320*B^2*a^7*b^8*d^2 - 512*A*B*b^15*d^2 + 121
6*A^2*a*b^14*d^2 - 1216*B^2*a*b^14*d^2 + 3840*A*B*a^2*b^13*d^2 + 7520*A*B*a^4*b^11*d^2 - 4608*A*B*a^6*b^9*d^2)
)/(8*d^4) + (((832*A*a*b^12*d^4 + 448*A*a^3*b^10*d^4 - 384*A*a^5*b^8*d^4 + 1024*B*a^2*b^11*d^4 + 1024*B*a^4*b^
9*d^4)/(8*d^5) - ((512*b^10*d^4 + 768*a^2*b^8*d^4)*(a + b*tan(c + d*x))^(1/2)*(64*A^2*a^5 + 225*A^2*a*b^4 - 24
0*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3)^(1/2))/(64*d^5))*(64*A^2*a^5 + 225*A^2*a*b^
4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3)^(1/2))/(8*d))*(64*A^2*a^5 + 225*A^2*a
*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3)^(1/2))/(8*d))*(64*A^2*a^5 + 225*A^
2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3)^(1/2))/(8*d))*(64*A^2*a^5 + 225
*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3)^(1/2)*1i)/d + ((((a + b*tan(
c + d*x))^(1/2)*(32*A^4*b^20 + 32*B^4*b^20 + 64*A^2*B^2*b^20 - 33*A^4*a^2*b^18 + 4095*A^4*a^4*b^16 - 6399*A^4*
a^6*b^14 + 5265*A^4*a^8*b^12 - 1008*A^4*a^10*b^10 + 96*A^4*a^12*b^8 + 192*B^4*a^2*b^18 + 880*B^4*a^4*b^16 - 53
60*B^4*a^6*b^14 + 6480*B^4*a^8*b^12 - 208*B^4*a^10*b^10 + 32*B^4*a^12*b^8 + 609*A^2*B^2*a^2*b^18 - 10255*A^2*B
^2*a^4*b^16 + 42159*A^2*B^2*a^6*b^14 - 29825*A^2*B^2*a^8*b^12 + 5824*A^2*B^2*a^10*b^10 + 600*A*B^3*a^3*b^17 -
14120*A*B^3*a^5*b^15 + 29800*A*B^3*a^7*b^13 - 10200*A*B^3*a^9*b^11 + 320*A*B^3*a^11*b^9 - 3300*A^3*B*a^3*b^17
+ 21200*A^3*B*a^5*b^15 - 26868*A^3*B*a^7*b^13 + 10840*A^3*B*a^9*b^11 - 1088*A^3*B*a^11*b^9))/(8*d^4) - (((1854
*A^3*a^2*b^16*d^2 - 3456*A^3*a^4*b^14*d^2 - 2910*A^3*a^6*b^12*d^2 + 2304*A^3*a^8*b^10*d^2 - 96*A^3*a^10*b^8*d^
2 - 3200*B^3*a^3*b^15*d^2 + 1408*B^3*a^5*b^13*d^2 + 3904*B^3*a^7*b^11*d^2 - 736*B^3*a^9*b^9*d^2 + 32*B^3*a*b^1
7*d^2 - 928*A^2*B*a*b^17*d^2 - 3776*A*B^2*a^2*b^16*d^2 + 11744*A*B^2*a^4*b^14*d^2 + 8128*A*B^2*a^6*b^12*d^2 -
7104*A*B^2*a^8*b^10*d^2 + 288*A*B^2*a^10*b^8*d^2 + 10252*A^2*B*a^3*b^15*d^2 - 2500*A^2*B*a^5*b^13*d^2 - 11472*
A^2*B*a^7*b^11*d^2 + 2208*A^2*B*a^9*b^9*d^2)/(8*d^5) + ((((a + b*tan(c + d*x))^(1/2)*(580*A^2*a^3*b^12*d^2 - 4
224*A^2*a^5*b^10*d^2 + 576*A^2*a^7*b^8*d^2 + 320*B^2*a^3*b^12*d^2 + 4864*B^2*a^5*b^10*d^2 - 320*B^2*a^7*b^8*d^
2 - 512*A*B*b^15*d^2 + 1216*A^2*a*b^14*d^2 - 1216*B^2*a*b^14*d^2 + 3840*A*B*a^2*b^13*d^2 + 7520*A*B*a^4*b^11*d
^2 - 4608*A*B*a^6*b^9*d^2))/(8*d^4) - (((832*A*a*b^12*d^4 + 448*A*a^3*b^10*d^4 - 384*A*a^5*b^8*d^4 + 1024*B*a^
2*b^11*d^4 + 1024*B*a^4*b^9*d^4)/(8*d^5) + ((512*b^10*d^4 + 768*a^2*b^8*d^4)*(a + b*tan(c + d*x))^(1/2)*(64*A^
2*a^5 + 225*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3)^(1/2))/(64*d^5))*
(64*A^2*a^5 + 225*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3)^(1/2))/(8*d
))*(64*A^2*a^5 + 225*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3)^(1/2))/(
8*d))*(64*A^2*a^5 + 225*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3)^(1/2)
)/(8*d))*(64*A^2*a^5 + 225*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3)^(1
/2)*1i)/d)/((120*A^5*a*b^22 - 19*A^5*a^3*b^20 + 336*A^5*a^5*b^18 + 1818*A^5*a^7*b^16 + 1448*A^5*a^9*b^14 - 399
*A^5*a^11*b^12 - 504*A^5*a^13*b^10 + 160*B^5*a^2*b^21 + 1360*B^5*a^4*b^19 + 2400*B^5*a^6*b^17 + 800*B^5*a^8*b^
15 - 800*B^5*a^10*b^13 - 240*B^5*a^12*b^11 + 160*B^5*a^14*b^9 + 545*A^2*B^3*a^2*b^21 + 280*A^2*B^3*a^4*b^19 -
326*A^2*B^3*a^6*b^17 + 2600*A^2*B^3*a^8*b^15 + 4381*A^2*B^3*a^10*b^13 + 1528*A^2*B^3*a^12*b^11 - 192*A^2*B^3*a
^14*b^9 + 1237*A^3*B^2*a^3*b^20 + 232*A^3*B^2*a^5*b^18 - 3542*A^3*B^2*a^7*b^16 - 3312*A^3*B^2*a^9*b^14 + 121*A
^3*B^2*a^11*b^12 + 592*A^3*B^2*a^13*b^10 - 64*A^3*B^2*a^15*b^8 + 120*A*B^4*a*b^22 + 1256*A*B^4*a^3*b^20 - 104*
A*B^4*a^5*b^18 - 5360*A*B^4*a^7*b^16 - 4760*A*B^4*a^9*b^14 + 520*A*B^4*a^11*b^12 + 1096*A*B^4*a^13*b^10 - 64*A
*B^4*a^15*b^8 + 240*A^3*B^2*a*b^22 + 385*A^4*B*a^2*b^21 - 1080*A^4*B*a^4*b^19 - 2726*A^4*B*a^6*b^17 + 1800*A^4
*B*a^8*b^15 + 5181*A^4*B*a^10*b^13 + 1768*A^4*B*a^12*b^11 - 352*A^4*B*a^14*b^9)/d^5 - ((((a + b*tan(c + d*x))^
(1/2)*(32*A^4*b^20 + 32*B^4*b^20 + 64*A^2*B^2*b^20 - 33*A^4*a^2*b^18 + 4095*A^4*a^4*b^16 - 6399*A^4*a^6*b^14 +
5265*A^4*a^8*b^12 - 1008*A^4*a^10*b^10 + 96*A^4*a^12*b^8 + 192*B^4*a^2*b^18 + 880*B^4*a^4*b^16 - 5360*B^4*a^6
*b^14 + 6480*B^4*a^8*b^12 - 208*B^4*a^10*b^10 + 32*B^4*a^12*b^8 + 609*A^2*B^2*a^2*b^18 - 10255*A^2*B^2*a^4*b^1
6 + 42159*A^2*B^2*a^6*b^14 - 29825*A^2*B^2*a^8*b^12 + 5824*A^2*B^2*a^10*b^10 + 600*A*B^3*a^3*b^17 - 14120*A*B^
3*a^5*b^15 + 29800*A*B^3*a^7*b^13 - 10200*A*B^3*a^9*b^11 + 320*A*B^3*a^11*b^9 - 3300*A^3*B*a^3*b^17 + 21200*A^
3*B*a^5*b^15 - 26868*A^3*B*a^7*b^13 + 10840*A^3*B*a^9*b^11 - 1088*A^3*B*a^11*b^9))/(8*d^4) + (((1854*A^3*a^2*b
^16*d^2 - 3456*A^3*a^4*b^14*d^2 - 2910*A^3*a^6*b^12*d^2 + 2304*A^3*a^8*b^10*d^2 - 96*A^3*a^10*b^8*d^2 - 3200*B
^3*a^3*b^15*d^2 + 1408*B^3*a^5*b^13*d^2 + 3904*B^3*a^7*b^11*d^2 - 736*B^3*a^9*b^9*d^2 + 32*B^3*a*b^17*d^2 - 92
8*A^2*B*a*b^17*d^2 - 3776*A*B^2*a^2*b^16*d^2 + 11744*A*B^2*a^4*b^14*d^2 + 8128*A*B^2*a^6*b^12*d^2 - 7104*A*B^2
*a^8*b^10*d^2 + 288*A*B^2*a^10*b^8*d^2 + 10252*A^2*B*a^3*b^15*d^2 - 2500*A^2*B*a^5*b^13*d^2 - 11472*A^2*B*a^7*
b^11*d^2 + 2208*A^2*B*a^9*b^9*d^2)/(8*d^5) - ((((a + b*tan(c + d*x))^(1/2)*(580*A^2*a^3*b^12*d^2 - 4224*A^2*a^
5*b^10*d^2 + 576*A^2*a^7*b^8*d^2 + 320*B^2*a^3*b^12*d^2 + 4864*B^2*a^5*b^10*d^2 - 320*B^2*a^7*b^8*d^2 - 512*A*
B*b^15*d^2 + 1216*A^2*a*b^14*d^2 - 1216*B^2*a*b^14*d^2 + 3840*A*B*a^2*b^13*d^2 + 7520*A*B*a^4*b^11*d^2 - 4608*
A*B*a^6*b^9*d^2))/(8*d^4) + (((832*A*a*b^12*d^4 + 448*A*a^3*b^10*d^4 - 384*A*a^5*b^8*d^4 + 1024*B*a^2*b^11*d^4
+ 1024*B*a^4*b^9*d^4)/(8*d^5) - ((512*b^10*d^4 + 768*a^2*b^8*d^4)*(a + b*tan(c + d*x))^(1/2)*(64*A^2*a^5 + 22
5*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3)^(1/2))/(64*d^5))*(64*A^2*a^
5 + 225*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3)^(1/2))/(8*d))*(64*A^2
*a^5 + 225*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3)^(1/2))/(8*d))*(64*
A^2*a^5 + 225*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3)^(1/2))/(8*d))*(
64*A^2*a^5 + 225*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3)^(1/2))/d + (
(((a + b*tan(c + d*x))^(1/2)*(32*A^4*b^20 + 32*B^4*b^20 + 64*A^2*B^2*b^20 - 33*A^4*a^2*b^18 + 4095*A^4*a^4*b^1
6 - 6399*A^4*a^6*b^14 + 5265*A^4*a^8*b^12 - 1008*A^4*a^10*b^10 + 96*A^4*a^12*b^8 + 192*B^4*a^2*b^18 + 880*B^4*
a^4*b^16 - 5360*B^4*a^6*b^14 + 6480*B^4*a^8*b^12 - 208*B^4*a^10*b^10 + 32*B^4*a^12*b^8 + 609*A^2*B^2*a^2*b^18
- 10255*A^2*B^2*a^4*b^16 + 42159*A^2*B^2*a^6*b^14 - 29825*A^2*B^2*a^8*b^12 + 5824*A^2*B^2*a^10*b^10 + 600*A*B^
3*a^3*b^17 - 14120*A*B^3*a^5*b^15 + 29800*A*B^3*a^7*b^13 - 10200*A*B^3*a^9*b^11 + 320*A*B^3*a^11*b^9 - 3300*A^
3*B*a^3*b^17 + 21200*A^3*B*a^5*b^15 - 26868*A^3*B*a^7*b^13 + 10840*A^3*B*a^9*b^11 - 1088*A^3*B*a^11*b^9))/(8*d
^4) - (((1854*A^3*a^2*b^16*d^2 - 3456*A^3*a^4*b^14*d^2 - 2910*A^3*a^6*b^12*d^2 + 2304*A^3*a^8*b^10*d^2 - 96*A^
3*a^10*b^8*d^2 - 3200*B^3*a^3*b^15*d^2 + 1408*B^3*a^5*b^13*d^2 + 3904*B^3*a^7*b^11*d^2 - 736*B^3*a^9*b^9*d^2 +
32*B^3*a*b^17*d^2 - 928*A^2*B*a*b^17*d^2 - 3776*A*B^2*a^2*b^16*d^2 + 11744*A*B^2*a^4*b^14*d^2 + 8128*A*B^2*a^
6*b^12*d^2 - 7104*A*B^2*a^8*b^10*d^2 + 288*A*B^2*a^10*b^8*d^2 + 10252*A^2*B*a^3*b^15*d^2 - 2500*A^2*B*a^5*b^13
*d^2 - 11472*A^2*B*a^7*b^11*d^2 + 2208*A^2*B*a^9*b^9*d^2)/(8*d^5) + ((((a + b*tan(c + d*x))^(1/2)*(580*A^2*a^3
*b^12*d^2 - 4224*A^2*a^5*b^10*d^2 + 576*A^2*a^7*b^8*d^2 + 320*B^2*a^3*b^12*d^2 + 4864*B^2*a^5*b^10*d^2 - 320*B
^2*a^7*b^8*d^2 - 512*A*B*b^15*d^2 + 1216*A^2*a*b^14*d^2 - 1216*B^2*a*b^14*d^2 + 3840*A*B*a^2*b^13*d^2 + 7520*A
*B*a^4*b^11*d^2 - 4608*A*B*a^6*b^9*d^2))/(8*d^4) - (((832*A*a*b^12*d^4 + 448*A*a^3*b^10*d^4 - 384*A*a^5*b^8*d^
4 + 1024*B*a^2*b^11*d^4 + 1024*B*a^4*b^9*d^4)/(8*d^5) + ((512*b^10*d^4 + 768*a^2*b^8*d^4)*(a + b*tan(c + d*x))
^(1/2)*(64*A^2*a^5 + 225*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3)^(1/2
))/(64*d^5))*(64*A^2*a^5 + 225*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*b^3
)^(1/2))/(8*d))*(64*A^2*a^5 + 225*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a^2*
b^3)^(1/2))/(8*d))*(64*A^2*a^5 + 225*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*B*a
^2*b^3)^(1/2))/(8*d))*(64*A^2*a^5 + 225*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*
B*a^2*b^3)^(1/2))/d))*(64*A^2*a^5 + 225*A^2*a*b^4 - 240*A^2*a^3*b^2 + 400*B^2*a^3*b^2 - 320*A*B*a^4*b + 600*A*
B*a^2*b^3)^(1/2)*1i)/(4*d)