∫ ∘ _______ tan (c + dx) ∘ __________ a + b tan(c + dx) (A + B tan(c + dx)) dx

3.428 \(\int \sqrt {\tan (c+d x)} \sqrt {a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx\)

Optimal. Leaf size=201 \[ \frac {\sqrt {-b+i a} (A+i B) \tan ^{-1}\left (\frac {\sqrt {-b+i a} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{d}+\frac {(a B+2 A b) \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{\sqrt {b} d}-\frac {\sqrt {b+i a} (A-i B) \tanh ^{-1}\left (\frac {\sqrt {b+i a} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{d}+\frac {B \sqrt {\tan (c+d x)} \sqrt {a+b \tan (c+d x)}}{d} \]

[Out]

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

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

(d*x+c))^(1/2))*(I*a+b)^(1/2)/d+B*tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2)/d

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Rubi [A] time = 1.55, antiderivative size = 201, normalized size of antiderivative = 1.00, number of steps used = 13, number of rules used = 9, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.257, Rules used = {3610, 3655, 6725, 63, 217, 206, 93, 205, 208} \[ \frac {\sqrt {-b+i a} (A+i B) \tan ^{-1}\left (\frac {\sqrt {-b+i a} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{d}+\frac {(a B+2 A b) \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{\sqrt {b} d}-\frac {\sqrt {b+i a} (A-i B) \tanh ^{-1}\left (\frac {\sqrt {b+i a} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{d}+\frac {B \sqrt {\tan (c+d x)} \sqrt {a+b \tan (c+d x)}}{d} \]

Antiderivative was successfully veriﬁed.

[In]

Int[Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]

[Out]

(Sqrt[I*a - b]*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + ((2*A*b + a*

B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[b]*d) - (Sqrt[I*a + b]*(A - I*B)*ArcT

anh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (B*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c +

d*x]])/d

Rule 63

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 93

Int[(((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_))/((e_.) + (f_.)*(x_)), x_Symbol] :> With[{q = Denomin

ator[m]}, Dist[q, Subst[Int[x^(q*(m + 1) - 1)/(b*e - a*f - (d*e - c*f)*x^q), x], x, (a + b*x)^(1/q)/(c + d*x)^

(1/q)], x]] /; FreeQ[{a, b, c, d, e, f}, x] && EqQ[m + n + 1, 0] && RationalQ[n] && LtQ[-1, m, 0] && SimplerQ[

a + b*x, c + d*x]

Rule 205

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(Rt[a/b, 2]*ArcTan[x/Rt[a/b, 2]])/a, x] /; FreeQ[{a, b}, x]

&& PosQ[a/b]

Rule 206

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTanh[(Rt[-b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[-b, 2]), x]

/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])

Rule 208

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(Rt[-(a/b), 2]*ArcTanh[x/Rt[-(a/b), 2]])/a, x] /; FreeQ[{a,

b}, x] && NegQ[a/b]

Rule 217

Int[1/Sqrt[(a_) + (b_.)*(x_)^2], x_Symbol] :> Subst[Int[1/(1 - b*x^2), x], x, x/Sqrt[a + b*x^2]] /; FreeQ[{a,

b}, x] && !GtQ[a, 0]

Rule 3610

Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_)*((A_.) + (B_.)*tan[(e_.) + (f_.)*(x_)])*((c_.) + (d_.)*tan[(e

_.) + (f_.)*(x_)])^(n_), x_Symbol] :> Simp[(B*(a + b*Tan[e + f*x])^m*(c + d*Tan[e + f*x])^n)/(f*(m + n)), x] +

Dist[1/(m + n), Int[(a + b*Tan[e + f*x])^(m - 1)*(c + d*Tan[e + f*x])^(n - 1)*Simp[a*A*c*(m + n) - B*(b*c*m +

a*d*n) + (A*b*c + a*B*c + a*A*d - b*B*d)*(m + n)*Tan[e + f*x] + (A*b*d*(m + n) + B*(a*d*m + b*c*n))*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] && LtQ[0, m, 1] && LtQ[0, n, 1]

Rule 3655

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] :> With[{ff = FreeFactors[Tan[e + f*x], x

]}, Dist[ff/f, Subst[Int[((a + b*ff*x)^m*(c + d*ff*x)^n*(A + B*ff*x + C*ff^2*x^2))/(1 + ff^2*x^2), x], x, Tan[

e + f*x]/ff], x]] /; FreeQ[{a, b, c, d, e, f, A, B, C, m, n}, x] && NeQ[b*c - a*d, 0] && NeQ[a^2 + b^2, 0] &&

NeQ[c^2 + d^2, 0]

Rule 6725

Int[(u_)/((a_) + (b_.)*(x_)^(n_)), x_Symbol] :> With[{v = RationalFunctionExpand[u/(a + b*x^n), x]}, Int[v, x]

/; SumQ[v]] /; FreeQ[{a, b}, x] && IGtQ[n, 0]

Rubi steps

\begin {align*} \int \sqrt {\tan (c+d x)} \sqrt {a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx &=\frac {B \sqrt {\tan (c+d x)} \sqrt {a+b \tan (c+d x)}}{d}+\int \frac {-\frac {a B}{2}+(a A-b B) \tan (c+d x)+\frac {1}{2} (2 A b+a B) \tan ^2(c+d x)}{\sqrt {\tan (c+d x)} \sqrt {a+b \tan (c+d x)}} \, dx\\ &=\frac {B \sqrt {\tan (c+d x)} \sqrt {a+b \tan (c+d x)}}{d}+\frac {\operatorname {Subst}\left (\int \frac {-\frac {a B}{2}+(a A-b B) x+\frac {1}{2} (2 A b+a B) x^2}{\sqrt {x} \sqrt {a+b x} \left (1+x^2\right )} \, dx,x,\tan (c+d x)\right )}{d}\\ &=\frac {B \sqrt {\tan (c+d x)} \sqrt {a+b \tan (c+d x)}}{d}+\frac {\operatorname {Subst}\left (\int \left (\frac {2 A b+a B}{2 \sqrt {x} \sqrt {a+b x}}-\frac {A b+a B-(a A-b B) x}{\sqrt {x} \sqrt {a+b x} \left (1+x^2\right )}\right ) \, dx,x,\tan (c+d x)\right )}{d}\\ &=\frac {B \sqrt {\tan (c+d x)} \sqrt {a+b \tan (c+d x)}}{d}-\frac {\operatorname {Subst}\left (\int \frac {A b+a B-(a A-b B) x}{\sqrt {x} \sqrt {a+b x} \left (1+x^2\right )} \, dx,x,\tan (c+d x)\right )}{d}+\frac {(2 A b+a B) \operatorname {Subst}\left (\int \frac {1}{\sqrt {x} \sqrt {a+b x}} \, dx,x,\tan (c+d x)\right )}{2 d}\\ &=\frac {B \sqrt {\tan (c+d x)} \sqrt {a+b \tan (c+d x)}}{d}-\frac {\operatorname {Subst}\left (\int \left (\frac {a A-b B+i (A b+a B)}{2 (i-x) \sqrt {x} \sqrt {a+b x}}+\frac {-a A+b B+i (A b+a B)}{2 \sqrt {x} (i+x) \sqrt {a+b x}}\right ) \, dx,x,\tan (c+d x)\right )}{d}+\frac {(2 A b+a B) \operatorname {Subst}\left (\int \frac {1}{\sqrt {a+b x^2}} \, dx,x,\sqrt {\tan (c+d x)}\right )}{d}\\ &=\frac {B \sqrt {\tan (c+d x)} \sqrt {a+b \tan (c+d x)}}{d}+\frac {((a-i b) (A-i B)) \operatorname {Subst}\left (\int \frac {1}{\sqrt {x} (i+x) \sqrt {a+b x}} \, dx,x,\tan (c+d x)\right )}{2 d}-\frac {((a+i b) (A+i B)) \operatorname {Subst}\left (\int \frac {1}{(i-x) \sqrt {x} \sqrt {a+b x}} \, dx,x,\tan (c+d x)\right )}{2 d}+\frac {(2 A b+a B) \operatorname {Subst}\left (\int \frac {1}{1-b x^2} \, dx,x,\frac {\sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{d}\\ &=\frac {(2 A b+a B) \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{\sqrt {b} d}+\frac {B \sqrt {\tan (c+d x)} \sqrt {a+b \tan (c+d x)}}{d}+\frac {((a-i b) (A-i B)) \operatorname {Subst}\left (\int \frac {1}{i-(-a+i b) x^2} \, dx,x,\frac {\sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{d}-\frac {((a+i b) (A+i B)) \operatorname {Subst}\left (\int \frac {1}{i-(a+i b) x^2} \, dx,x,\frac {\sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{d}\\ &=\frac {\sqrt {i a-b} (A+i B) \tan ^{-1}\left (\frac {\sqrt {i a-b} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{d}+\frac {(2 A b+a B) \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{\sqrt {b} d}-\frac {\sqrt {i a+b} (A-i B) \tanh ^{-1}\left (\frac {\sqrt {i a+b} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{d}+\frac {B \sqrt {\tan (c+d x)} \sqrt {a+b \tan (c+d x)}}{d}\\ \end {align*}

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Mathematica [A] time = 2.89, size = 239, normalized size = 1.19 \[ \frac {\sqrt [4]{-1} \sqrt {-a+i b} (A-i B) \tan ^{-1}\left (\frac {\sqrt [4]{-1} \sqrt {-a+i b} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )+\sqrt [4]{-1} \sqrt {a+i b} (A+i B) \tan ^{-1}\left (\frac {\sqrt [4]{-1} \sqrt {a+i b} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )+\frac {(a B+2 A b) \sqrt {a+b \tan (c+d x)} \sinh ^{-1}\left (\frac {\sqrt {b} \sqrt {\tan (c+d x)}}{\sqrt {a}}\right )}{\sqrt {a} \sqrt {b} \sqrt {\frac {b \tan (c+d x)}{a}+1}}+B \sqrt {\tan (c+d x)} \sqrt {a+b \tan (c+d x)}}{d} \]

Antiderivative was successfully veriﬁed.

[In]

Integrate[Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]

[Out]

((-1)^(1/4)*Sqrt[-a + I*b]*(A - I*B)*ArcTan[((-1)^(1/4)*Sqrt[-a + I*b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c +

d*x]]] + (-1)^(1/4)*Sqrt[a + I*b]*(A + I*B)*ArcTan[((-1)^(1/4)*Sqrt[a + I*b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Ta

n[c + d*x]]] + B*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]] + ((2*A*b + a*B)*ArcSinh[(Sqrt[b]*Sqrt[Tan[c + d*

x]])/Sqrt[a]]*Sqrt[a + b*Tan[c + d*x]])/(Sqrt[a]*Sqrt[b]*Sqrt[1 + (b*Tan[c + d*x])/a]))/d

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fricas [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm="fricas")

[Out]

Timed out

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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm="giac")

[Out]

Timed out

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maple [B] time = 1.04, size = 2179610, normalized size = 10843.83 \[ \text {output too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x)

[Out]

result too large to display

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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (B \tan \left (d x + c\right ) + A\right )} \sqrt {b \tan \left (d x + c\right ) + a} \sqrt {\tan \left (d x + c\right )}\,{d x} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm="maxima")

[Out]

integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*sqrt(tan(d*x + c)), x)

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mupad [B] time = 118.04, size = 61200, normalized size = 304.48 \[ \text {result too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(tan(c + d*x)^(1/2)*(A + B*tan(c + d*x))*(a + b*tan(c + d*x))^(1/2),x)

[Out]

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

c + d*x))^(1/2) - a^(1/2))^3)/(d + (b^2*d*tan(c + d*x)^2)/((a + b*tan(c + d*x))^(1/2) - a^(1/2))^4 - (2*b*d*ta

n(c + d*x))/((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2) - atan(((((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a

+ A*B*b*2i)/(4*d^2))^(1/2)*((((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2)*((((A

^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2)*((((274877906944*(1600*a^12*b^34*d^8 -

16640*a^14*b^32*d^8 + 22784*a^16*b^30*d^8 + 106496*a^18*b^28*d^8 + 65536*a^20*b^26*d^8))/d^8 - (274877906944*

tan(c + d*x)*(1600*a^12*b^35*d^8 - 48000*a^14*b^33*d^8 + 155136*a^16*b^31*d^8 + 466944*a^18*b^29*d^8 + 262144*

a^20*b^27*d^8))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2))*((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*

a + A*B*b*2i)/(4*d^2))^(1/2) - (2199023255552*tan(c + d*x)^(1/2)*(2048*A*a^20*b^27*d^6 - 12536*A*a^16*b^31*d^6

- 3328*A*a^18*b^29*d^6 - 7160*A*a^14*b^33*d^6 + 240*B*a^13*b^34*d^6 - 720*B*a^15*b^32*d^6 + 5696*B*a^17*b^30*

d^6 + 14848*B*a^19*b^28*d^6 + 8192*B*a^21*b^26*d^6))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*b - A

^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2) - (274877906944*(1200*A^2*a^12*b^35*d^6 - 1600

*A^2*a^14*b^33*d^6 + 272464*A^2*a^16*b^31*d^6 + 573952*A^2*a^18*b^29*d^6 + 299008*A^2*a^20*b^27*d^6 - 1440*B^2

*a^12*b^35*d^6 + 8352*B^2*a^14*b^33*d^6 - 320*B^2*a^16*b^31*d^6 + 26880*B^2*a^18*b^29*d^6 + 102400*B^2*a^20*b^

27*d^6 + 65536*B^2*a^22*b^25*d^6 - 11200*A*B*a^13*b^34*d^6 - 25856*A*B*a^15*b^32*d^6 + 303168*A*B*a^17*b^30*d^

6 + 661504*A*B*a^19*b^28*d^6 + 344064*A*B*a^21*b^26*d^6))/d^8 + (274877906944*tan(c + d*x)*(1200*A^2*a^12*b^36

*d^6 - 32160*A^2*a^14*b^34*d^6 + 1125488*A^2*a^16*b^32*d^6 + 2445312*A^2*a^18*b^30*d^6 + 1351680*A^2*a^20*b^28

*d^6 + 65536*A^2*a^22*b^26*d^6 - 1440*B^2*a^12*b^36*d^6 + 32256*B^2*a^14*b^34*d^6 - 41440*B^2*a^16*b^32*d^6 +

68096*B^2*a^18*b^30*d^6 + 405504*B^2*a^20*b^28*d^6 + 262144*B^2*a^22*b^26*d^6 - 16320*A*B*a^13*b^35*d^6 - 3411

2*A*B*a^15*b^33*d^6 + 1294592*A*B*a^17*b^31*d^6 + 2656256*A*B*a^19*b^29*d^6 + 1343488*A*B*a^21*b^27*d^6))/(d^8

*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) + (2199023255552*tan(c + d*x)^(1/2)*(7600*A^3*a^18*b^30*d^4 - 3902

*A^3*a^16*b^32*d^4 - 4590*A^3*a^14*b^34*d^4 + 6912*A^3*a^20*b^28*d^4 - 168*B^3*a^13*b^35*d^4 + 982*B^3*a^15*b^

33*d^4 + 2494*B^3*a^17*b^31*d^4 + 9024*B^3*a^19*b^29*d^4 + 15872*B^3*a^21*b^27*d^4 + 8192*B^3*a^23*b^25*d^4 +

4922*A*B^2*a^14*b^34*d^4 + 21906*A*B^2*a^16*b^32*d^4 + 69720*A*B^2*a^18*b^30*d^4 + 95744*A*B^2*a^20*b^28*d^4 +

43008*A*B^2*a^22*b^26*d^4 - 180*A^2*B*a^13*b^35*d^4 + 4486*A^2*B*a^15*b^33*d^4 + 52154*A^2*B*a^17*b^31*d^4 +

93568*A^2*B*a^19*b^29*d^4 + 46080*A^2*B*a^21*b^27*d^4))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*b

- A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2) + (274877906944*(300*A^4*a^12*b^36*d^4 + 23

60*A^4*a^14*b^34*d^4 + 149228*A^4*a^16*b^32*d^4 + 307152*A^4*a^18*b^30*d^4 + 164352*A^4*a^20*b^28*d^4 + 4096*A

^4*a^22*b^26*d^4 + 484*B^4*a^12*b^36*d^4 + 328*B^4*a^14*b^34*d^4 + 2308*B^4*a^16*b^32*d^4 - 16048*B^4*a^18*b^3

0*d^4 - 43008*B^4*a^20*b^28*d^4 - 24576*B^4*a^22*b^26*d^4 + 7880*A*B^3*a^13*b^35*d^4 + 28592*A*B^3*a^15*b^33*d

^4 - 55832*A*B^3*a^17*b^31*d^4 - 100672*A*B^3*a^19*b^29*d^4 + 57344*A*B^3*a^21*b^27*d^4 + 81920*A*B^3*a^23*b^2

5*d^4 - 5880*A^3*B*a^13*b^35*d^4 + 47408*A^3*B*a^15*b^33*d^4 + 569576*A^3*B*a^17*b^31*d^4 + 1004928*A^3*B*a^19

*b^29*d^4 + 489472*A^3*B*a^21*b^27*d^4 - 320*A^2*B^2*a^12*b^36*d^4 + 1264*A^2*B^2*a^14*b^34*d^4 - 27264*A^2*B^

2*a^16*b^32*d^4 + 294128*A^2*B^2*a^18*b^30*d^4 + 711168*A^2*B^2*a^20*b^28*d^4 + 389120*A^2*B^2*a^22*b^26*d^4))

/d^8 - (274877906944*tan(c + d*x)*(300*A^4*a^12*b^37*d^4 - 6920*A^4*a^14*b^35*d^4 + 738524*A^4*a^16*b^33*d^4 +

1819680*A^4*a^18*b^31*d^4 + 1384960*A^4*a^20*b^29*d^4 + 311296*A^4*a^22*b^27*d^4 + 484*B^4*a^12*b^37*d^4 - 53

68*B^4*a^14*b^35*d^4 + 1236*B^4*a^16*b^33*d^4 - 88064*B^4*a^18*b^31*d^4 - 205824*B^4*a^20*b^29*d^4 - 110592*B^

4*a^22*b^27*d^4 + 11192*A*B^3*a^13*b^36*d^4 + 45712*A*B^3*a^15*b^34*d^4 - 394344*A*B^3*a^17*b^32*d^4 - 599296*

A*B^3*a^19*b^30*d^4 + 124928*A*B^3*a^21*b^28*d^4 + 294912*A*B^3*a^23*b^26*d^4 - 8680*A^3*B*a^13*b^36*d^4 + 163

152*A^3*B*a^15*b^34*d^4 + 2287096*A^3*B*a^17*b^32*d^4 + 4405760*A^3*B*a^19*b^30*d^4 + 2617344*A^3*B*a^21*b^28*

d^4 + 327680*A^3*B*a^23*b^26*d^4 - 320*A^2*B^2*a^12*b^37*d^4 + 23984*A^2*B^2*a^14*b^35*d^4 - 212608*A^2*B^2*a^

16*b^33*d^4 + 865008*A^2*B^2*a^18*b^31*d^4 + 2561024*A^2*B^2*a^20*b^29*d^4 + 1523712*A^2*B^2*a^22*b^27*d^4 + 6

5536*A^2*B^2*a^24*b^25*d^4))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) - (2199023255552*tan(c + d*x)^(1/

2)*(3641*A^5*a^18*b^31*d^2 - 55*A^5*a^16*b^33*d^2 - 960*A^5*a^14*b^35*d^2 + 2864*A^5*a^20*b^29*d^2 + 128*A^5*a

^22*b^27*d^2 + 39*B^5*a^13*b^36*d^2 - 341*B^5*a^15*b^34*d^2 - 2362*B^5*a^17*b^32*d^2 - 6942*B^5*a^19*b^30*d^2

- 8544*B^5*a^21*b^28*d^2 - 3584*B^5*a^23*b^26*d^2 - 1045*A*B^4*a^14*b^35*d^2 - 8795*A*B^4*a^16*b^33*d^2 - 2683

8*A*B^4*a^18*b^31*d^2 - 24592*A*B^4*a^20*b^29*d^2 + 2688*A*B^4*a^22*b^27*d^2 + 8192*A*B^4*a^24*b^25*d^2 - 120*

A^4*B*a^13*b^36*d^2 + 4977*A^4*B*a^15*b^34*d^2 + 33597*A^4*B*a^17*b^32*d^2 + 55284*A^4*B*a^19*b^30*d^2 + 27296

*A^4*B*a^21*b^28*d^2 + 512*A^4*B*a^23*b^26*d^2 + 159*A^2*B^3*a^13*b^36*d^2 - 4656*A^2*B^3*a^15*b^34*d^2 - 1127

7*A^2*B^3*a^17*b^32*d^2 + 28418*A^2*B^3*a^19*b^30*d^2 + 74816*A^2*B^3*a^21*b^28*d^2 + 39936*A^2*B^3*a^23*b^26*

d^2 - 133*A^3*B^2*a^14*b^35*d^2 + 16550*A^3*B^2*a^16*b^33*d^2 + 86411*A^3*B^2*a^18*b^31*d^2 + 127328*A^3*B^2*a

^20*b^29*d^2 + 57600*A^3*B^2*a^22*b^27*d^2))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*b - A^2*a*1i

+ B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2) - (274877906944*(25*A^6*a^12*b^37*d^2 + 430*A^6*a^14*b

^35*d^2 + 25905*A^6*a^16*b^33*d^2 + 68220*A^6*a^18*b^31*d^2 + 59424*A^6*a^20*b^29*d^2 + 16640*A^6*a^22*b^27*d^

2 - 72*B^6*a^12*b^37*d^2 - 679*B^6*a^14*b^35*d^2 - 3030*B^6*a^16*b^33*d^2 - 2263*B^6*a^18*b^31*d^2 + 6544*B^6*

a^20*b^29*d^2 + 10496*B^6*a^22*b^27*d^2 + 4096*B^6*a^24*b^25*d^2 - 1794*A*B^5*a^13*b^36*d^2 - 12040*A*B^5*a^15

*b^34*d^2 - 12202*A*B^5*a^17*b^32*d^2 + 19804*A*B^5*a^19*b^30*d^2 + 35200*A*B^5*a^21*b^28*d^2 + 13312*A*B^5*a^

23*b^26*d^2 - 770*A^5*B*a^13*b^36*d^2 + 21168*A^5*B*a^15*b^34*d^2 + 119398*A^5*B*a^17*b^32*d^2 + 194292*A^5*B*

a^19*b^30*d^2 + 114560*A^5*B*a^21*b^28*d^2 + 17408*A^5*B*a^23*b^26*d^2 - 23*A^2*B^4*a^12*b^37*d^2 - 6472*A^2*B

^4*a^14*b^35*d^2 - 7211*A^2*B^4*a^16*b^33*d^2 + 32614*A^2*B^4*a^18*b^31*d^2 + 79616*A^2*B^4*a^20*b^29*d^2 + 70

400*A^2*B^4*a^22*b^27*d^2 + 24576*A^2*B^4*a^24*b^25*d^2 - 580*A^3*B^3*a^13*b^36*d^2 + 5928*A^3*B^3*a^15*b^34*d

^2 + 92604*A^3*B^3*a^17*b^32*d^2 + 267280*A^3*B^3*a^19*b^30*d^2 + 293120*A^3*B^3*a^21*b^28*d^2 + 112640*A^3*B^

3*a^23*b^26*d^2 + 10*A^4*B^2*a^12*b^37*d^2 + 10653*A^4*B^2*a^14*b^35*d^2 + 123388*A^4*B^2*a^16*b^33*d^2 + 3612

89*A^4*B^2*a^18*b^31*d^2 + 408400*A^4*B^2*a^20*b^29*d^2 + 164608*A^4*B^2*a^22*b^27*d^2 + 4096*A^4*B^2*a^24*b^2

5*d^2))/d^8 + (274877906944*tan(c + d*x)*(25*A^6*a^12*b^38*d^2 - 470*A^6*a^14*b^36*d^2 + 168905*A^6*a^16*b^34*

d^2 + 541176*A^6*a^18*b^32*d^2 + 579072*A^6*a^20*b^30*d^2 + 211456*A^6*a^22*b^28*d^2 + 4096*A^6*a^24*b^26*d^2

- 72*B^6*a^12*b^38*d^2 - 355*B^6*a^14*b^36*d^2 - 3534*B^6*a^16*b^34*d^2 + 9181*B^6*a^18*b^32*d^2 + 43936*B^6*a

^20*b^30*d^2 + 47872*B^6*a^22*b^28*d^2 + 16384*B^6*a^24*b^26*d^2 - 2494*A*B^5*a^13*b^37*d^2 - 20820*A*B^5*a^15

*b^35*d^2 + 15026*A*B^5*a^17*b^33*d^2 + 134984*A*B^5*a^19*b^31*d^2 + 156800*A*B^5*a^21*b^29*d^2 + 55296*A*B^5*

a^23*b^27*d^2 - 1150*A^5*B*a^13*b^37*d^2 + 82036*A^5*B*a^15*b^35*d^2 + 614690*A^5*B*a^17*b^33*d^2 + 1432560*A^

5*B*a^19*b^31*d^2 + 1361536*A^5*B*a^21*b^29*d^2 + 460800*A^5*B*a^23*b^27*d^2 - 23*A^2*B^4*a^12*b^38*d^2 - 1562

0*A^2*B^4*a^14*b^36*d^2 - 11843*A^2*B^4*a^16*b^34*d^2 + 95626*A^2*B^4*a^18*b^32*d^2 + 210240*A^2*B^4*a^20*b^30

*d^2 + 155648*A^2*B^4*a^22*b^28*d^2 + 36864*A^2*B^4*a^24*b^26*d^2 - 764*A^3*B^3*a^13*b^37*d^2 - 21056*A^3*B^3*

a^15*b^35*d^2 + 145044*A^3*B^3*a^17*b^33*d^2 + 566296*A^3*B^3*a^19*b^31*d^2 + 667904*A^3*B^3*a^21*b^29*d^2 + 3

31776*A^3*B^3*a^23*b^27*d^2 + 65536*A^3*B^3*a^25*b^25*d^2 + 10*A^4*B^2*a^12*b^38*d^2 + 19097*A^4*B^2*a^14*b^36

*d^2 + 326196*A^4*B^2*a^16*b^34*d^2 + 1062069*A^4*B^2*a^18*b^32*d^2 + 1527456*A^4*B^2*a^20*b^30*d^2 + 1091328*

A^4*B^2*a^22*b^28*d^2 + 319488*A^4*B^2*a^24*b^26*d^2))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) + (2199

023255552*tan(c + d*x)^(1/2)*(85*A^7*a^16*b^34 - 65*A^7*a^14*b^36 + 729*A^7*a^18*b^32 + 947*A^7*a^20*b^30 + 36

8*A^7*a^22*b^28 - 3*B^7*a^13*b^37 + 36*B^7*a^15*b^35 + 374*B^7*a^17*b^33 + 1363*B^7*a^19*b^31 + 2276*B^7*a^21*

b^29 + 1760*B^7*a^23*b^27 + 512*B^7*a^25*b^25 - 25*A^2*B^5*a^13*b^37 + 818*A^2*B^5*a^15*b^35 + 5373*A^2*B^5*a^

17*b^33 + 12178*A^2*B^5*a^19*b^31 + 12640*A^2*B^5*a^21*b^29 + 6016*A^2*B^5*a^23*b^27 + 1024*A^2*B^5*a^25*b^25

+ 89*A^3*B^4*a^14*b^36 + 2278*A^3*B^4*a^16*b^34 + 10563*A^3*B^4*a^18*b^32 + 18982*A^3*B^4*a^20*b^30 + 14960*A^

3*B^4*a^22*b^28 + 4352*A^3*B^4*a^24*b^26 - 37*A^4*B^3*a^13*b^37 + 1507*A^4*B^3*a^15*b^35 + 9606*A^4*B^3*a^17*b

^33 + 20274*A^4*B^3*a^19*b^31 + 18452*A^4*B^3*a^21*b^29 + 6752*A^4*B^3*a^23*b^27 + 512*A^4*B^3*a^25*b^25 - 45*

A^5*B^2*a^14*b^36 + 1265*A^5*B^2*a^16*b^34 + 6366*A^5*B^2*a^18*b^32 + 10912*A^5*B^2*a^20*b^30 + 8032*A^5*B^2*a

^22*b^28 + 2176*A^5*B^2*a^24*b^26 + 69*A*B^6*a^14*b^36 + 1098*A*B^6*a^16*b^34 + 4926*A*B^6*a^18*b^32 + 9017*A*

B^6*a^20*b^30 + 7296*A*B^6*a^22*b^28 + 2176*A*B^6*a^24*b^26 - 15*A^6*B*a^13*b^37 + 725*A^6*B*a^15*b^35 + 4607*

A^6*B*a^17*b^33 + 9459*A^6*B*a^19*b^31 + 8088*A^6*B*a^21*b^29 + 2496*A^6*B*a^23*b^27))/(d^7*((a + b*tan(c + d*

x))^(1/2) - a^(1/2))))*((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2)*1i - (((A^2*

b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2)*((((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b +

2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2)*((((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/

2)*((((274877906944*(1600*a^12*b^34*d^8 - 16640*a^14*b^32*d^8 + 22784*a^16*b^30*d^8 + 106496*a^18*b^28*d^8 + 6

5536*a^20*b^26*d^8))/d^8 - (274877906944*tan(c + d*x)*(1600*a^12*b^35*d^8 - 48000*a^14*b^33*d^8 + 155136*a^16*

b^31*d^8 + 466944*a^18*b^29*d^8 + 262144*a^20*b^27*d^8))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2))*((A^2

*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2) + (2199023255552*tan(c + d*x)^(1/2)*(204

8*A*a^20*b^27*d^6 - 12536*A*a^16*b^31*d^6 - 3328*A*a^18*b^29*d^6 - 7160*A*a^14*b^33*d^6 + 240*B*a^13*b^34*d^6

- 720*B*a^15*b^32*d^6 + 5696*B*a^17*b^30*d^6 + 14848*B*a^19*b^28*d^6 + 8192*B*a^21*b^26*d^6))/(d^7*((a + b*tan

(c + d*x))^(1/2) - a^(1/2))))*((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2) - (27

4877906944*(1200*A^2*a^12*b^35*d^6 - 1600*A^2*a^14*b^33*d^6 + 272464*A^2*a^16*b^31*d^6 + 573952*A^2*a^18*b^29*

d^6 + 299008*A^2*a^20*b^27*d^6 - 1440*B^2*a^12*b^35*d^6 + 8352*B^2*a^14*b^33*d^6 - 320*B^2*a^16*b^31*d^6 + 268

80*B^2*a^18*b^29*d^6 + 102400*B^2*a^20*b^27*d^6 + 65536*B^2*a^22*b^25*d^6 - 11200*A*B*a^13*b^34*d^6 - 25856*A*

B*a^15*b^32*d^6 + 303168*A*B*a^17*b^30*d^6 + 661504*A*B*a^19*b^28*d^6 + 344064*A*B*a^21*b^26*d^6))/d^8 + (2748

77906944*tan(c + d*x)*(1200*A^2*a^12*b^36*d^6 - 32160*A^2*a^14*b^34*d^6 + 1125488*A^2*a^16*b^32*d^6 + 2445312*

A^2*a^18*b^30*d^6 + 1351680*A^2*a^20*b^28*d^6 + 65536*A^2*a^22*b^26*d^6 - 1440*B^2*a^12*b^36*d^6 + 32256*B^2*a

^14*b^34*d^6 - 41440*B^2*a^16*b^32*d^6 + 68096*B^2*a^18*b^30*d^6 + 405504*B^2*a^20*b^28*d^6 + 262144*B^2*a^22*

b^26*d^6 - 16320*A*B*a^13*b^35*d^6 - 34112*A*B*a^15*b^33*d^6 + 1294592*A*B*a^17*b^31*d^6 + 2656256*A*B*a^19*b^

29*d^6 + 1343488*A*B*a^21*b^27*d^6))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) - (2199023255552*tan(c +

d*x)^(1/2)*(7600*A^3*a^18*b^30*d^4 - 3902*A^3*a^16*b^32*d^4 - 4590*A^3*a^14*b^34*d^4 + 6912*A^3*a^20*b^28*d^4

- 168*B^3*a^13*b^35*d^4 + 982*B^3*a^15*b^33*d^4 + 2494*B^3*a^17*b^31*d^4 + 9024*B^3*a^19*b^29*d^4 + 15872*B^3*

a^21*b^27*d^4 + 8192*B^3*a^23*b^25*d^4 + 4922*A*B^2*a^14*b^34*d^4 + 21906*A*B^2*a^16*b^32*d^4 + 69720*A*B^2*a^

18*b^30*d^4 + 95744*A*B^2*a^20*b^28*d^4 + 43008*A*B^2*a^22*b^26*d^4 - 180*A^2*B*a^13*b^35*d^4 + 4486*A^2*B*a^1

5*b^33*d^4 + 52154*A^2*B*a^17*b^31*d^4 + 93568*A^2*B*a^19*b^29*d^4 + 46080*A^2*B*a^21*b^27*d^4))/(d^7*((a + b*

tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2) +

(274877906944*(300*A^4*a^12*b^36*d^4 + 2360*A^4*a^14*b^34*d^4 + 149228*A^4*a^16*b^32*d^4 + 307152*A^4*a^18*b^3

0*d^4 + 164352*A^4*a^20*b^28*d^4 + 4096*A^4*a^22*b^26*d^4 + 484*B^4*a^12*b^36*d^4 + 328*B^4*a^14*b^34*d^4 + 23

08*B^4*a^16*b^32*d^4 - 16048*B^4*a^18*b^30*d^4 - 43008*B^4*a^20*b^28*d^4 - 24576*B^4*a^22*b^26*d^4 + 7880*A*B^

3*a^13*b^35*d^4 + 28592*A*B^3*a^15*b^33*d^4 - 55832*A*B^3*a^17*b^31*d^4 - 100672*A*B^3*a^19*b^29*d^4 + 57344*A

*B^3*a^21*b^27*d^4 + 81920*A*B^3*a^23*b^25*d^4 - 5880*A^3*B*a^13*b^35*d^4 + 47408*A^3*B*a^15*b^33*d^4 + 569576

*A^3*B*a^17*b^31*d^4 + 1004928*A^3*B*a^19*b^29*d^4 + 489472*A^3*B*a^21*b^27*d^4 - 320*A^2*B^2*a^12*b^36*d^4 +

1264*A^2*B^2*a^14*b^34*d^4 - 27264*A^2*B^2*a^16*b^32*d^4 + 294128*A^2*B^2*a^18*b^30*d^4 + 711168*A^2*B^2*a^20*

b^28*d^4 + 389120*A^2*B^2*a^22*b^26*d^4))/d^8 - (274877906944*tan(c + d*x)*(300*A^4*a^12*b^37*d^4 - 6920*A^4*a

^14*b^35*d^4 + 738524*A^4*a^16*b^33*d^4 + 1819680*A^4*a^18*b^31*d^4 + 1384960*A^4*a^20*b^29*d^4 + 311296*A^4*a

^22*b^27*d^4 + 484*B^4*a^12*b^37*d^4 - 5368*B^4*a^14*b^35*d^4 + 1236*B^4*a^16*b^33*d^4 - 88064*B^4*a^18*b^31*d

^4 - 205824*B^4*a^20*b^29*d^4 - 110592*B^4*a^22*b^27*d^4 + 11192*A*B^3*a^13*b^36*d^4 + 45712*A*B^3*a^15*b^34*d

^4 - 394344*A*B^3*a^17*b^32*d^4 - 599296*A*B^3*a^19*b^30*d^4 + 124928*A*B^3*a^21*b^28*d^4 + 294912*A*B^3*a^23*

b^26*d^4 - 8680*A^3*B*a^13*b^36*d^4 + 163152*A^3*B*a^15*b^34*d^4 + 2287096*A^3*B*a^17*b^32*d^4 + 4405760*A^3*B

*a^19*b^30*d^4 + 2617344*A^3*B*a^21*b^28*d^4 + 327680*A^3*B*a^23*b^26*d^4 - 320*A^2*B^2*a^12*b^37*d^4 + 23984*

A^2*B^2*a^14*b^35*d^4 - 212608*A^2*B^2*a^16*b^33*d^4 + 865008*A^2*B^2*a^18*b^31*d^4 + 2561024*A^2*B^2*a^20*b^2

9*d^4 + 1523712*A^2*B^2*a^22*b^27*d^4 + 65536*A^2*B^2*a^24*b^25*d^4))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/

2))^2)) + (2199023255552*tan(c + d*x)^(1/2)*(3641*A^5*a^18*b^31*d^2 - 55*A^5*a^16*b^33*d^2 - 960*A^5*a^14*b^35

*d^2 + 2864*A^5*a^20*b^29*d^2 + 128*A^5*a^22*b^27*d^2 + 39*B^5*a^13*b^36*d^2 - 341*B^5*a^15*b^34*d^2 - 2362*B^

5*a^17*b^32*d^2 - 6942*B^5*a^19*b^30*d^2 - 8544*B^5*a^21*b^28*d^2 - 3584*B^5*a^23*b^26*d^2 - 1045*A*B^4*a^14*b

^35*d^2 - 8795*A*B^4*a^16*b^33*d^2 - 26838*A*B^4*a^18*b^31*d^2 - 24592*A*B^4*a^20*b^29*d^2 + 2688*A*B^4*a^22*b

^27*d^2 + 8192*A*B^4*a^24*b^25*d^2 - 120*A^4*B*a^13*b^36*d^2 + 4977*A^4*B*a^15*b^34*d^2 + 33597*A^4*B*a^17*b^3

2*d^2 + 55284*A^4*B*a^19*b^30*d^2 + 27296*A^4*B*a^21*b^28*d^2 + 512*A^4*B*a^23*b^26*d^2 + 159*A^2*B^3*a^13*b^3

6*d^2 - 4656*A^2*B^3*a^15*b^34*d^2 - 11277*A^2*B^3*a^17*b^32*d^2 + 28418*A^2*B^3*a^19*b^30*d^2 + 74816*A^2*B^3

*a^21*b^28*d^2 + 39936*A^2*B^3*a^23*b^26*d^2 - 133*A^3*B^2*a^14*b^35*d^2 + 16550*A^3*B^2*a^16*b^33*d^2 + 86411

*A^3*B^2*a^18*b^31*d^2 + 127328*A^3*B^2*a^20*b^29*d^2 + 57600*A^3*B^2*a^22*b^27*d^2))/(d^7*((a + b*tan(c + d*x

))^(1/2) - a^(1/2))))*((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2) - (2748779069

44*(25*A^6*a^12*b^37*d^2 + 430*A^6*a^14*b^35*d^2 + 25905*A^6*a^16*b^33*d^2 + 68220*A^6*a^18*b^31*d^2 + 59424*A

^6*a^20*b^29*d^2 + 16640*A^6*a^22*b^27*d^2 - 72*B^6*a^12*b^37*d^2 - 679*B^6*a^14*b^35*d^2 - 3030*B^6*a^16*b^33

*d^2 - 2263*B^6*a^18*b^31*d^2 + 6544*B^6*a^20*b^29*d^2 + 10496*B^6*a^22*b^27*d^2 + 4096*B^6*a^24*b^25*d^2 - 17

94*A*B^5*a^13*b^36*d^2 - 12040*A*B^5*a^15*b^34*d^2 - 12202*A*B^5*a^17*b^32*d^2 + 19804*A*B^5*a^19*b^30*d^2 + 3

5200*A*B^5*a^21*b^28*d^2 + 13312*A*B^5*a^23*b^26*d^2 - 770*A^5*B*a^13*b^36*d^2 + 21168*A^5*B*a^15*b^34*d^2 + 1

19398*A^5*B*a^17*b^32*d^2 + 194292*A^5*B*a^19*b^30*d^2 + 114560*A^5*B*a^21*b^28*d^2 + 17408*A^5*B*a^23*b^26*d^

2 - 23*A^2*B^4*a^12*b^37*d^2 - 6472*A^2*B^4*a^14*b^35*d^2 - 7211*A^2*B^4*a^16*b^33*d^2 + 32614*A^2*B^4*a^18*b^

31*d^2 + 79616*A^2*B^4*a^20*b^29*d^2 + 70400*A^2*B^4*a^22*b^27*d^2 + 24576*A^2*B^4*a^24*b^25*d^2 - 580*A^3*B^3

*a^13*b^36*d^2 + 5928*A^3*B^3*a^15*b^34*d^2 + 92604*A^3*B^3*a^17*b^32*d^2 + 267280*A^3*B^3*a^19*b^30*d^2 + 293

120*A^3*B^3*a^21*b^28*d^2 + 112640*A^3*B^3*a^23*b^26*d^2 + 10*A^4*B^2*a^12*b^37*d^2 + 10653*A^4*B^2*a^14*b^35*

d^2 + 123388*A^4*B^2*a^16*b^33*d^2 + 361289*A^4*B^2*a^18*b^31*d^2 + 408400*A^4*B^2*a^20*b^29*d^2 + 164608*A^4*

B^2*a^22*b^27*d^2 + 4096*A^4*B^2*a^24*b^25*d^2))/d^8 + (274877906944*tan(c + d*x)*(25*A^6*a^12*b^38*d^2 - 470*

A^6*a^14*b^36*d^2 + 168905*A^6*a^16*b^34*d^2 + 541176*A^6*a^18*b^32*d^2 + 579072*A^6*a^20*b^30*d^2 + 211456*A^

6*a^22*b^28*d^2 + 4096*A^6*a^24*b^26*d^2 - 72*B^6*a^12*b^38*d^2 - 355*B^6*a^14*b^36*d^2 - 3534*B^6*a^16*b^34*d

^2 + 9181*B^6*a^18*b^32*d^2 + 43936*B^6*a^20*b^30*d^2 + 47872*B^6*a^22*b^28*d^2 + 16384*B^6*a^24*b^26*d^2 - 24

94*A*B^5*a^13*b^37*d^2 - 20820*A*B^5*a^15*b^35*d^2 + 15026*A*B^5*a^17*b^33*d^2 + 134984*A*B^5*a^19*b^31*d^2 +

156800*A*B^5*a^21*b^29*d^2 + 55296*A*B^5*a^23*b^27*d^2 - 1150*A^5*B*a^13*b^37*d^2 + 82036*A^5*B*a^15*b^35*d^2

+ 614690*A^5*B*a^17*b^33*d^2 + 1432560*A^5*B*a^19*b^31*d^2 + 1361536*A^5*B*a^21*b^29*d^2 + 460800*A^5*B*a^23*b

^27*d^2 - 23*A^2*B^4*a^12*b^38*d^2 - 15620*A^2*B^4*a^14*b^36*d^2 - 11843*A^2*B^4*a^16*b^34*d^2 + 95626*A^2*B^4

*a^18*b^32*d^2 + 210240*A^2*B^4*a^20*b^30*d^2 + 155648*A^2*B^4*a^22*b^28*d^2 + 36864*A^2*B^4*a^24*b^26*d^2 - 7

64*A^3*B^3*a^13*b^37*d^2 - 21056*A^3*B^3*a^15*b^35*d^2 + 145044*A^3*B^3*a^17*b^33*d^2 + 566296*A^3*B^3*a^19*b^

31*d^2 + 667904*A^3*B^3*a^21*b^29*d^2 + 331776*A^3*B^3*a^23*b^27*d^2 + 65536*A^3*B^3*a^25*b^25*d^2 + 10*A^4*B^

2*a^12*b^38*d^2 + 19097*A^4*B^2*a^14*b^36*d^2 + 326196*A^4*B^2*a^16*b^34*d^2 + 1062069*A^4*B^2*a^18*b^32*d^2 +

1527456*A^4*B^2*a^20*b^30*d^2 + 1091328*A^4*B^2*a^22*b^28*d^2 + 319488*A^4*B^2*a^24*b^26*d^2))/(d^8*((a + b*t

an(c + d*x))^(1/2) - a^(1/2))^2)) - (2199023255552*tan(c + d*x)^(1/2)*(85*A^7*a^16*b^34 - 65*A^7*a^14*b^36 + 7

29*A^7*a^18*b^32 + 947*A^7*a^20*b^30 + 368*A^7*a^22*b^28 - 3*B^7*a^13*b^37 + 36*B^7*a^15*b^35 + 374*B^7*a^17*b

^33 + 1363*B^7*a^19*b^31 + 2276*B^7*a^21*b^29 + 1760*B^7*a^23*b^27 + 512*B^7*a^25*b^25 - 25*A^2*B^5*a^13*b^37

+ 818*A^2*B^5*a^15*b^35 + 5373*A^2*B^5*a^17*b^33 + 12178*A^2*B^5*a^19*b^31 + 12640*A^2*B^5*a^21*b^29 + 6016*A^

2*B^5*a^23*b^27 + 1024*A^2*B^5*a^25*b^25 + 89*A^3*B^4*a^14*b^36 + 2278*A^3*B^4*a^16*b^34 + 10563*A^3*B^4*a^18*

b^32 + 18982*A^3*B^4*a^20*b^30 + 14960*A^3*B^4*a^22*b^28 + 4352*A^3*B^4*a^24*b^26 - 37*A^4*B^3*a^13*b^37 + 150

7*A^4*B^3*a^15*b^35 + 9606*A^4*B^3*a^17*b^33 + 20274*A^4*B^3*a^19*b^31 + 18452*A^4*B^3*a^21*b^29 + 6752*A^4*B^

3*a^23*b^27 + 512*A^4*B^3*a^25*b^25 - 45*A^5*B^2*a^14*b^36 + 1265*A^5*B^2*a^16*b^34 + 6366*A^5*B^2*a^18*b^32 +

10912*A^5*B^2*a^20*b^30 + 8032*A^5*B^2*a^22*b^28 + 2176*A^5*B^2*a^24*b^26 + 69*A*B^6*a^14*b^36 + 1098*A*B^6*a

^16*b^34 + 4926*A*B^6*a^18*b^32 + 9017*A*B^6*a^20*b^30 + 7296*A*B^6*a^22*b^28 + 2176*A*B^6*a^24*b^26 - 15*A^6*

B*a^13*b^37 + 725*A^6*B*a^15*b^35 + 4607*A^6*B*a^17*b^33 + 9459*A^6*B*a^19*b^31 + 8088*A^6*B*a^21*b^29 + 2496*

A^6*B*a^23*b^27))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*

a + A*B*b*2i)/(4*d^2))^(1/2)*1i)/((((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2)*

((((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2)*((((A^2*b - A^2*a*1i + B^2*a*1i -

B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2)*((((274877906944*(1600*a^12*b^34*d^8 - 16640*a^14*b^32*d^8 + 22784

*a^16*b^30*d^8 + 106496*a^18*b^28*d^8 + 65536*a^20*b^26*d^8))/d^8 - (274877906944*tan(c + d*x)*(1600*a^12*b^35

*d^8 - 48000*a^14*b^33*d^8 + 155136*a^16*b^31*d^8 + 466944*a^18*b^29*d^8 + 262144*a^20*b^27*d^8))/(d^8*((a + b

*tan(c + d*x))^(1/2) - a^(1/2))^2))*((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2)

- (2199023255552*tan(c + d*x)^(1/2)*(2048*A*a^20*b^27*d^6 - 12536*A*a^16*b^31*d^6 - 3328*A*a^18*b^29*d^6 - 71

60*A*a^14*b^33*d^6 + 240*B*a^13*b^34*d^6 - 720*B*a^15*b^32*d^6 + 5696*B*a^17*b^30*d^6 + 14848*B*a^19*b^28*d^6

+ 8192*B*a^21*b^26*d^6))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b +

2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2) - (274877906944*(1200*A^2*a^12*b^35*d^6 - 1600*A^2*a^14*b^33*d^6 + 272464*

A^2*a^16*b^31*d^6 + 573952*A^2*a^18*b^29*d^6 + 299008*A^2*a^20*b^27*d^6 - 1440*B^2*a^12*b^35*d^6 + 8352*B^2*a^

14*b^33*d^6 - 320*B^2*a^16*b^31*d^6 + 26880*B^2*a^18*b^29*d^6 + 102400*B^2*a^20*b^27*d^6 + 65536*B^2*a^22*b^25

*d^6 - 11200*A*B*a^13*b^34*d^6 - 25856*A*B*a^15*b^32*d^6 + 303168*A*B*a^17*b^30*d^6 + 661504*A*B*a^19*b^28*d^6

+ 344064*A*B*a^21*b^26*d^6))/d^8 + (274877906944*tan(c + d*x)*(1200*A^2*a^12*b^36*d^6 - 32160*A^2*a^14*b^34*d

^6 + 1125488*A^2*a^16*b^32*d^6 + 2445312*A^2*a^18*b^30*d^6 + 1351680*A^2*a^20*b^28*d^6 + 65536*A^2*a^22*b^26*d

^6 - 1440*B^2*a^12*b^36*d^6 + 32256*B^2*a^14*b^34*d^6 - 41440*B^2*a^16*b^32*d^6 + 68096*B^2*a^18*b^30*d^6 + 40

5504*B^2*a^20*b^28*d^6 + 262144*B^2*a^22*b^26*d^6 - 16320*A*B*a^13*b^35*d^6 - 34112*A*B*a^15*b^33*d^6 + 129459

2*A*B*a^17*b^31*d^6 + 2656256*A*B*a^19*b^29*d^6 + 1343488*A*B*a^21*b^27*d^6))/(d^8*((a + b*tan(c + d*x))^(1/2)

- a^(1/2))^2)) + (2199023255552*tan(c + d*x)^(1/2)*(7600*A^3*a^18*b^30*d^4 - 3902*A^3*a^16*b^32*d^4 - 4590*A^

3*a^14*b^34*d^4 + 6912*A^3*a^20*b^28*d^4 - 168*B^3*a^13*b^35*d^4 + 982*B^3*a^15*b^33*d^4 + 2494*B^3*a^17*b^31*

d^4 + 9024*B^3*a^19*b^29*d^4 + 15872*B^3*a^21*b^27*d^4 + 8192*B^3*a^23*b^25*d^4 + 4922*A*B^2*a^14*b^34*d^4 + 2

1906*A*B^2*a^16*b^32*d^4 + 69720*A*B^2*a^18*b^30*d^4 + 95744*A*B^2*a^20*b^28*d^4 + 43008*A*B^2*a^22*b^26*d^4 -

180*A^2*B*a^13*b^35*d^4 + 4486*A^2*B*a^15*b^33*d^4 + 52154*A^2*B*a^17*b^31*d^4 + 93568*A^2*B*a^19*b^29*d^4 +

46080*A^2*B*a^21*b^27*d^4))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*b - A^2*a*1i + B^2*a*1i - B^2*

b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2) + (274877906944*(300*A^4*a^12*b^36*d^4 + 2360*A^4*a^14*b^34*d^4 + 14922

8*A^4*a^16*b^32*d^4 + 307152*A^4*a^18*b^30*d^4 + 164352*A^4*a^20*b^28*d^4 + 4096*A^4*a^22*b^26*d^4 + 484*B^4*a

^12*b^36*d^4 + 328*B^4*a^14*b^34*d^4 + 2308*B^4*a^16*b^32*d^4 - 16048*B^4*a^18*b^30*d^4 - 43008*B^4*a^20*b^28*

d^4 - 24576*B^4*a^22*b^26*d^4 + 7880*A*B^3*a^13*b^35*d^4 + 28592*A*B^3*a^15*b^33*d^4 - 55832*A*B^3*a^17*b^31*d

^4 - 100672*A*B^3*a^19*b^29*d^4 + 57344*A*B^3*a^21*b^27*d^4 + 81920*A*B^3*a^23*b^25*d^4 - 5880*A^3*B*a^13*b^35

*d^4 + 47408*A^3*B*a^15*b^33*d^4 + 569576*A^3*B*a^17*b^31*d^4 + 1004928*A^3*B*a^19*b^29*d^4 + 489472*A^3*B*a^2

1*b^27*d^4 - 320*A^2*B^2*a^12*b^36*d^4 + 1264*A^2*B^2*a^14*b^34*d^4 - 27264*A^2*B^2*a^16*b^32*d^4 + 294128*A^2

*B^2*a^18*b^30*d^4 + 711168*A^2*B^2*a^20*b^28*d^4 + 389120*A^2*B^2*a^22*b^26*d^4))/d^8 - (274877906944*tan(c +

d*x)*(300*A^4*a^12*b^37*d^4 - 6920*A^4*a^14*b^35*d^4 + 738524*A^4*a^16*b^33*d^4 + 1819680*A^4*a^18*b^31*d^4 +

1384960*A^4*a^20*b^29*d^4 + 311296*A^4*a^22*b^27*d^4 + 484*B^4*a^12*b^37*d^4 - 5368*B^4*a^14*b^35*d^4 + 1236*

B^4*a^16*b^33*d^4 - 88064*B^4*a^18*b^31*d^4 - 205824*B^4*a^20*b^29*d^4 - 110592*B^4*a^22*b^27*d^4 + 11192*A*B^

3*a^13*b^36*d^4 + 45712*A*B^3*a^15*b^34*d^4 - 394344*A*B^3*a^17*b^32*d^4 - 599296*A*B^3*a^19*b^30*d^4 + 124928

*A*B^3*a^21*b^28*d^4 + 294912*A*B^3*a^23*b^26*d^4 - 8680*A^3*B*a^13*b^36*d^4 + 163152*A^3*B*a^15*b^34*d^4 + 22

87096*A^3*B*a^17*b^32*d^4 + 4405760*A^3*B*a^19*b^30*d^4 + 2617344*A^3*B*a^21*b^28*d^4 + 327680*A^3*B*a^23*b^26

*d^4 - 320*A^2*B^2*a^12*b^37*d^4 + 23984*A^2*B^2*a^14*b^35*d^4 - 212608*A^2*B^2*a^16*b^33*d^4 + 865008*A^2*B^2

*a^18*b^31*d^4 + 2561024*A^2*B^2*a^20*b^29*d^4 + 1523712*A^2*B^2*a^22*b^27*d^4 + 65536*A^2*B^2*a^24*b^25*d^4))

/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) - (2199023255552*tan(c + d*x)^(1/2)*(3641*A^5*a^18*b^31*d^2 -

55*A^5*a^16*b^33*d^2 - 960*A^5*a^14*b^35*d^2 + 2864*A^5*a^20*b^29*d^2 + 128*A^5*a^22*b^27*d^2 + 39*B^5*a^13*b

^36*d^2 - 341*B^5*a^15*b^34*d^2 - 2362*B^5*a^17*b^32*d^2 - 6942*B^5*a^19*b^30*d^2 - 8544*B^5*a^21*b^28*d^2 - 3

584*B^5*a^23*b^26*d^2 - 1045*A*B^4*a^14*b^35*d^2 - 8795*A*B^4*a^16*b^33*d^2 - 26838*A*B^4*a^18*b^31*d^2 - 2459

2*A*B^4*a^20*b^29*d^2 + 2688*A*B^4*a^22*b^27*d^2 + 8192*A*B^4*a^24*b^25*d^2 - 120*A^4*B*a^13*b^36*d^2 + 4977*A

^4*B*a^15*b^34*d^2 + 33597*A^4*B*a^17*b^32*d^2 + 55284*A^4*B*a^19*b^30*d^2 + 27296*A^4*B*a^21*b^28*d^2 + 512*A

^4*B*a^23*b^26*d^2 + 159*A^2*B^3*a^13*b^36*d^2 - 4656*A^2*B^3*a^15*b^34*d^2 - 11277*A^2*B^3*a^17*b^32*d^2 + 28

418*A^2*B^3*a^19*b^30*d^2 + 74816*A^2*B^3*a^21*b^28*d^2 + 39936*A^2*B^3*a^23*b^26*d^2 - 133*A^3*B^2*a^14*b^35*

d^2 + 16550*A^3*B^2*a^16*b^33*d^2 + 86411*A^3*B^2*a^18*b^31*d^2 + 127328*A^3*B^2*a^20*b^29*d^2 + 57600*A^3*B^2

*a^22*b^27*d^2))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a

+ A*B*b*2i)/(4*d^2))^(1/2) - (274877906944*(25*A^6*a^12*b^37*d^2 + 430*A^6*a^14*b^35*d^2 + 25905*A^6*a^16*b^3

3*d^2 + 68220*A^6*a^18*b^31*d^2 + 59424*A^6*a^20*b^29*d^2 + 16640*A^6*a^22*b^27*d^2 - 72*B^6*a^12*b^37*d^2 - 6

79*B^6*a^14*b^35*d^2 - 3030*B^6*a^16*b^33*d^2 - 2263*B^6*a^18*b^31*d^2 + 6544*B^6*a^20*b^29*d^2 + 10496*B^6*a^

22*b^27*d^2 + 4096*B^6*a^24*b^25*d^2 - 1794*A*B^5*a^13*b^36*d^2 - 12040*A*B^5*a^15*b^34*d^2 - 12202*A*B^5*a^17

*b^32*d^2 + 19804*A*B^5*a^19*b^30*d^2 + 35200*A*B^5*a^21*b^28*d^2 + 13312*A*B^5*a^23*b^26*d^2 - 770*A^5*B*a^13

*b^36*d^2 + 21168*A^5*B*a^15*b^34*d^2 + 119398*A^5*B*a^17*b^32*d^2 + 194292*A^5*B*a^19*b^30*d^2 + 114560*A^5*B

*a^21*b^28*d^2 + 17408*A^5*B*a^23*b^26*d^2 - 23*A^2*B^4*a^12*b^37*d^2 - 6472*A^2*B^4*a^14*b^35*d^2 - 7211*A^2*

B^4*a^16*b^33*d^2 + 32614*A^2*B^4*a^18*b^31*d^2 + 79616*A^2*B^4*a^20*b^29*d^2 + 70400*A^2*B^4*a^22*b^27*d^2 +

24576*A^2*B^4*a^24*b^25*d^2 - 580*A^3*B^3*a^13*b^36*d^2 + 5928*A^3*B^3*a^15*b^34*d^2 + 92604*A^3*B^3*a^17*b^32

*d^2 + 267280*A^3*B^3*a^19*b^30*d^2 + 293120*A^3*B^3*a^21*b^28*d^2 + 112640*A^3*B^3*a^23*b^26*d^2 + 10*A^4*B^2

*a^12*b^37*d^2 + 10653*A^4*B^2*a^14*b^35*d^2 + 123388*A^4*B^2*a^16*b^33*d^2 + 361289*A^4*B^2*a^18*b^31*d^2 + 4

08400*A^4*B^2*a^20*b^29*d^2 + 164608*A^4*B^2*a^22*b^27*d^2 + 4096*A^4*B^2*a^24*b^25*d^2))/d^8 + (274877906944*

tan(c + d*x)*(25*A^6*a^12*b^38*d^2 - 470*A^6*a^14*b^36*d^2 + 168905*A^6*a^16*b^34*d^2 + 541176*A^6*a^18*b^32*d

^2 + 579072*A^6*a^20*b^30*d^2 + 211456*A^6*a^22*b^28*d^2 + 4096*A^6*a^24*b^26*d^2 - 72*B^6*a^12*b^38*d^2 - 355

*B^6*a^14*b^36*d^2 - 3534*B^6*a^16*b^34*d^2 + 9181*B^6*a^18*b^32*d^2 + 43936*B^6*a^20*b^30*d^2 + 47872*B^6*a^2

2*b^28*d^2 + 16384*B^6*a^24*b^26*d^2 - 2494*A*B^5*a^13*b^37*d^2 - 20820*A*B^5*a^15*b^35*d^2 + 15026*A*B^5*a^17

*b^33*d^2 + 134984*A*B^5*a^19*b^31*d^2 + 156800*A*B^5*a^21*b^29*d^2 + 55296*A*B^5*a^23*b^27*d^2 - 1150*A^5*B*a

^13*b^37*d^2 + 82036*A^5*B*a^15*b^35*d^2 + 614690*A^5*B*a^17*b^33*d^2 + 1432560*A^5*B*a^19*b^31*d^2 + 1361536*

A^5*B*a^21*b^29*d^2 + 460800*A^5*B*a^23*b^27*d^2 - 23*A^2*B^4*a^12*b^38*d^2 - 15620*A^2*B^4*a^14*b^36*d^2 - 11

843*A^2*B^4*a^16*b^34*d^2 + 95626*A^2*B^4*a^18*b^32*d^2 + 210240*A^2*B^4*a^20*b^30*d^2 + 155648*A^2*B^4*a^22*b

^28*d^2 + 36864*A^2*B^4*a^24*b^26*d^2 - 764*A^3*B^3*a^13*b^37*d^2 - 21056*A^3*B^3*a^15*b^35*d^2 + 145044*A^3*B

^3*a^17*b^33*d^2 + 566296*A^3*B^3*a^19*b^31*d^2 + 667904*A^3*B^3*a^21*b^29*d^2 + 331776*A^3*B^3*a^23*b^27*d^2

+ 65536*A^3*B^3*a^25*b^25*d^2 + 10*A^4*B^2*a^12*b^38*d^2 + 19097*A^4*B^2*a^14*b^36*d^2 + 326196*A^4*B^2*a^16*b

^34*d^2 + 1062069*A^4*B^2*a^18*b^32*d^2 + 1527456*A^4*B^2*a^20*b^30*d^2 + 1091328*A^4*B^2*a^22*b^28*d^2 + 3194

88*A^4*B^2*a^24*b^26*d^2))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) + (2199023255552*tan(c + d*x)^(1/2)

*(85*A^7*a^16*b^34 - 65*A^7*a^14*b^36 + 729*A^7*a^18*b^32 + 947*A^7*a^20*b^30 + 368*A^7*a^22*b^28 - 3*B^7*a^13

*b^37 + 36*B^7*a^15*b^35 + 374*B^7*a^17*b^33 + 1363*B^7*a^19*b^31 + 2276*B^7*a^21*b^29 + 1760*B^7*a^23*b^27 +

512*B^7*a^25*b^25 - 25*A^2*B^5*a^13*b^37 + 818*A^2*B^5*a^15*b^35 + 5373*A^2*B^5*a^17*b^33 + 12178*A^2*B^5*a^19

*b^31 + 12640*A^2*B^5*a^21*b^29 + 6016*A^2*B^5*a^23*b^27 + 1024*A^2*B^5*a^25*b^25 + 89*A^3*B^4*a^14*b^36 + 227

8*A^3*B^4*a^16*b^34 + 10563*A^3*B^4*a^18*b^32 + 18982*A^3*B^4*a^20*b^30 + 14960*A^3*B^4*a^22*b^28 + 4352*A^3*B

^4*a^24*b^26 - 37*A^4*B^3*a^13*b^37 + 1507*A^4*B^3*a^15*b^35 + 9606*A^4*B^3*a^17*b^33 + 20274*A^4*B^3*a^19*b^3

1 + 18452*A^4*B^3*a^21*b^29 + 6752*A^4*B^3*a^23*b^27 + 512*A^4*B^3*a^25*b^25 - 45*A^5*B^2*a^14*b^36 + 1265*A^5

*B^2*a^16*b^34 + 6366*A^5*B^2*a^18*b^32 + 10912*A^5*B^2*a^20*b^30 + 8032*A^5*B^2*a^22*b^28 + 2176*A^5*B^2*a^24

*b^26 + 69*A*B^6*a^14*b^36 + 1098*A*B^6*a^16*b^34 + 4926*A*B^6*a^18*b^32 + 9017*A*B^6*a^20*b^30 + 7296*A*B^6*a

^22*b^28 + 2176*A*B^6*a^24*b^26 - 15*A^6*B*a^13*b^37 + 725*A^6*B*a^15*b^35 + 4607*A^6*B*a^17*b^33 + 9459*A^6*B

*a^19*b^31 + 8088*A^6*B*a^21*b^29 + 2496*A^6*B*a^23*b^27))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2

*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2) + (((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b

+ 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2)*((((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(

1/2)*((((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2)*((((274877906944*(1600*a^12*

b^34*d^8 - 16640*a^14*b^32*d^8 + 22784*a^16*b^30*d^8 + 106496*a^18*b^28*d^8 + 65536*a^20*b^26*d^8))/d^8 - (274

877906944*tan(c + d*x)*(1600*a^12*b^35*d^8 - 48000*a^14*b^33*d^8 + 155136*a^16*b^31*d^8 + 466944*a^18*b^29*d^8

+ 262144*a^20*b^27*d^8))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2))*((A^2*b - A^2*a*1i + B^2*a*1i - B^2*

b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2) + (2199023255552*tan(c + d*x)^(1/2)*(2048*A*a^20*b^27*d^6 - 12536*A*a^1

6*b^31*d^6 - 3328*A*a^18*b^29*d^6 - 7160*A*a^14*b^33*d^6 + 240*B*a^13*b^34*d^6 - 720*B*a^15*b^32*d^6 + 5696*B*

a^17*b^30*d^6 + 14848*B*a^19*b^28*d^6 + 8192*B*a^21*b^26*d^6))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*(

(A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2) - (274877906944*(1200*A^2*a^12*b^35*

d^6 - 1600*A^2*a^14*b^33*d^6 + 272464*A^2*a^16*b^31*d^6 + 573952*A^2*a^18*b^29*d^6 + 299008*A^2*a^20*b^27*d^6

- 1440*B^2*a^12*b^35*d^6 + 8352*B^2*a^14*b^33*d^6 - 320*B^2*a^16*b^31*d^6 + 26880*B^2*a^18*b^29*d^6 + 102400*B

^2*a^20*b^27*d^6 + 65536*B^2*a^22*b^25*d^6 - 11200*A*B*a^13*b^34*d^6 - 25856*A*B*a^15*b^32*d^6 + 303168*A*B*a^

17*b^30*d^6 + 661504*A*B*a^19*b^28*d^6 + 344064*A*B*a^21*b^26*d^6))/d^8 + (274877906944*tan(c + d*x)*(1200*A^2

*a^12*b^36*d^6 - 32160*A^2*a^14*b^34*d^6 + 1125488*A^2*a^16*b^32*d^6 + 2445312*A^2*a^18*b^30*d^6 + 1351680*A^2

*a^20*b^28*d^6 + 65536*A^2*a^22*b^26*d^6 - 1440*B^2*a^12*b^36*d^6 + 32256*B^2*a^14*b^34*d^6 - 41440*B^2*a^16*b

^32*d^6 + 68096*B^2*a^18*b^30*d^6 + 405504*B^2*a^20*b^28*d^6 + 262144*B^2*a^22*b^26*d^6 - 16320*A*B*a^13*b^35*

d^6 - 34112*A*B*a^15*b^33*d^6 + 1294592*A*B*a^17*b^31*d^6 + 2656256*A*B*a^19*b^29*d^6 + 1343488*A*B*a^21*b^27*

d^6))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) - (2199023255552*tan(c + d*x)^(1/2)*(7600*A^3*a^18*b^30*

d^4 - 3902*A^3*a^16*b^32*d^4 - 4590*A^3*a^14*b^34*d^4 + 6912*A^3*a^20*b^28*d^4 - 168*B^3*a^13*b^35*d^4 + 982*B

^3*a^15*b^33*d^4 + 2494*B^3*a^17*b^31*d^4 + 9024*B^3*a^19*b^29*d^4 + 15872*B^3*a^21*b^27*d^4 + 8192*B^3*a^23*b

^25*d^4 + 4922*A*B^2*a^14*b^34*d^4 + 21906*A*B^2*a^16*b^32*d^4 + 69720*A*B^2*a^18*b^30*d^4 + 95744*A*B^2*a^20*

b^28*d^4 + 43008*A*B^2*a^22*b^26*d^4 - 180*A^2*B*a^13*b^35*d^4 + 4486*A^2*B*a^15*b^33*d^4 + 52154*A^2*B*a^17*b

^31*d^4 + 93568*A^2*B*a^19*b^29*d^4 + 46080*A^2*B*a^21*b^27*d^4))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2)))

)*((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2) + (274877906944*(300*A^4*a^12*b^3

6*d^4 + 2360*A^4*a^14*b^34*d^4 + 149228*A^4*a^16*b^32*d^4 + 307152*A^4*a^18*b^30*d^4 + 164352*A^4*a^20*b^28*d^

4 + 4096*A^4*a^22*b^26*d^4 + 484*B^4*a^12*b^36*d^4 + 328*B^4*a^14*b^34*d^4 + 2308*B^4*a^16*b^32*d^4 - 16048*B^

4*a^18*b^30*d^4 - 43008*B^4*a^20*b^28*d^4 - 24576*B^4*a^22*b^26*d^4 + 7880*A*B^3*a^13*b^35*d^4 + 28592*A*B^3*a

^15*b^33*d^4 - 55832*A*B^3*a^17*b^31*d^4 - 100672*A*B^3*a^19*b^29*d^4 + 57344*A*B^3*a^21*b^27*d^4 + 81920*A*B^

3*a^23*b^25*d^4 - 5880*A^3*B*a^13*b^35*d^4 + 47408*A^3*B*a^15*b^33*d^4 + 569576*A^3*B*a^17*b^31*d^4 + 1004928*

A^3*B*a^19*b^29*d^4 + 489472*A^3*B*a^21*b^27*d^4 - 320*A^2*B^2*a^12*b^36*d^4 + 1264*A^2*B^2*a^14*b^34*d^4 - 27

264*A^2*B^2*a^16*b^32*d^4 + 294128*A^2*B^2*a^18*b^30*d^4 + 711168*A^2*B^2*a^20*b^28*d^4 + 389120*A^2*B^2*a^22*

b^26*d^4))/d^8 - (274877906944*tan(c + d*x)*(300*A^4*a^12*b^37*d^4 - 6920*A^4*a^14*b^35*d^4 + 738524*A^4*a^16*

b^33*d^4 + 1819680*A^4*a^18*b^31*d^4 + 1384960*A^4*a^20*b^29*d^4 + 311296*A^4*a^22*b^27*d^4 + 484*B^4*a^12*b^3

7*d^4 - 5368*B^4*a^14*b^35*d^4 + 1236*B^4*a^16*b^33*d^4 - 88064*B^4*a^18*b^31*d^4 - 205824*B^4*a^20*b^29*d^4 -

110592*B^4*a^22*b^27*d^4 + 11192*A*B^3*a^13*b^36*d^4 + 45712*A*B^3*a^15*b^34*d^4 - 394344*A*B^3*a^17*b^32*d^4

- 599296*A*B^3*a^19*b^30*d^4 + 124928*A*B^3*a^21*b^28*d^4 + 294912*A*B^3*a^23*b^26*d^4 - 8680*A^3*B*a^13*b^36

*d^4 + 163152*A^3*B*a^15*b^34*d^4 + 2287096*A^3*B*a^17*b^32*d^4 + 4405760*A^3*B*a^19*b^30*d^4 + 2617344*A^3*B*

a^21*b^28*d^4 + 327680*A^3*B*a^23*b^26*d^4 - 320*A^2*B^2*a^12*b^37*d^4 + 23984*A^2*B^2*a^14*b^35*d^4 - 212608*

A^2*B^2*a^16*b^33*d^4 + 865008*A^2*B^2*a^18*b^31*d^4 + 2561024*A^2*B^2*a^20*b^29*d^4 + 1523712*A^2*B^2*a^22*b^

27*d^4 + 65536*A^2*B^2*a^24*b^25*d^4))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) + (2199023255552*tan(c

+ d*x)^(1/2)*(3641*A^5*a^18*b^31*d^2 - 55*A^5*a^16*b^33*d^2 - 960*A^5*a^14*b^35*d^2 + 2864*A^5*a^20*b^29*d^2 +

128*A^5*a^22*b^27*d^2 + 39*B^5*a^13*b^36*d^2 - 341*B^5*a^15*b^34*d^2 - 2362*B^5*a^17*b^32*d^2 - 6942*B^5*a^19

*b^30*d^2 - 8544*B^5*a^21*b^28*d^2 - 3584*B^5*a^23*b^26*d^2 - 1045*A*B^4*a^14*b^35*d^2 - 8795*A*B^4*a^16*b^33*

d^2 - 26838*A*B^4*a^18*b^31*d^2 - 24592*A*B^4*a^20*b^29*d^2 + 2688*A*B^4*a^22*b^27*d^2 + 8192*A*B^4*a^24*b^25*

d^2 - 120*A^4*B*a^13*b^36*d^2 + 4977*A^4*B*a^15*b^34*d^2 + 33597*A^4*B*a^17*b^32*d^2 + 55284*A^4*B*a^19*b^30*d

^2 + 27296*A^4*B*a^21*b^28*d^2 + 512*A^4*B*a^23*b^26*d^2 + 159*A^2*B^3*a^13*b^36*d^2 - 4656*A^2*B^3*a^15*b^34*

d^2 - 11277*A^2*B^3*a^17*b^32*d^2 + 28418*A^2*B^3*a^19*b^30*d^2 + 74816*A^2*B^3*a^21*b^28*d^2 + 39936*A^2*B^3*

a^23*b^26*d^2 - 133*A^3*B^2*a^14*b^35*d^2 + 16550*A^3*B^2*a^16*b^33*d^2 + 86411*A^3*B^2*a^18*b^31*d^2 + 127328

*A^3*B^2*a^20*b^29*d^2 + 57600*A^3*B^2*a^22*b^27*d^2))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*b -

A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2) - (274877906944*(25*A^6*a^12*b^37*d^2 + 430*

A^6*a^14*b^35*d^2 + 25905*A^6*a^16*b^33*d^2 + 68220*A^6*a^18*b^31*d^2 + 59424*A^6*a^20*b^29*d^2 + 16640*A^6*a^

22*b^27*d^2 - 72*B^6*a^12*b^37*d^2 - 679*B^6*a^14*b^35*d^2 - 3030*B^6*a^16*b^33*d^2 - 2263*B^6*a^18*b^31*d^2 +

6544*B^6*a^20*b^29*d^2 + 10496*B^6*a^22*b^27*d^2 + 4096*B^6*a^24*b^25*d^2 - 1794*A*B^5*a^13*b^36*d^2 - 12040*

A*B^5*a^15*b^34*d^2 - 12202*A*B^5*a^17*b^32*d^2 + 19804*A*B^5*a^19*b^30*d^2 + 35200*A*B^5*a^21*b^28*d^2 + 1331

2*A*B^5*a^23*b^26*d^2 - 770*A^5*B*a^13*b^36*d^2 + 21168*A^5*B*a^15*b^34*d^2 + 119398*A^5*B*a^17*b^32*d^2 + 194

292*A^5*B*a^19*b^30*d^2 + 114560*A^5*B*a^21*b^28*d^2 + 17408*A^5*B*a^23*b^26*d^2 - 23*A^2*B^4*a^12*b^37*d^2 -

6472*A^2*B^4*a^14*b^35*d^2 - 7211*A^2*B^4*a^16*b^33*d^2 + 32614*A^2*B^4*a^18*b^31*d^2 + 79616*A^2*B^4*a^20*b^2

9*d^2 + 70400*A^2*B^4*a^22*b^27*d^2 + 24576*A^2*B^4*a^24*b^25*d^2 - 580*A^3*B^3*a^13*b^36*d^2 + 5928*A^3*B^3*a

^15*b^34*d^2 + 92604*A^3*B^3*a^17*b^32*d^2 + 267280*A^3*B^3*a^19*b^30*d^2 + 293120*A^3*B^3*a^21*b^28*d^2 + 112

640*A^3*B^3*a^23*b^26*d^2 + 10*A^4*B^2*a^12*b^37*d^2 + 10653*A^4*B^2*a^14*b^35*d^2 + 123388*A^4*B^2*a^16*b^33*

d^2 + 361289*A^4*B^2*a^18*b^31*d^2 + 408400*A^4*B^2*a^20*b^29*d^2 + 164608*A^4*B^2*a^22*b^27*d^2 + 4096*A^4*B^

2*a^24*b^25*d^2))/d^8 + (274877906944*tan(c + d*x)*(25*A^6*a^12*b^38*d^2 - 470*A^6*a^14*b^36*d^2 + 168905*A^6*

a^16*b^34*d^2 + 541176*A^6*a^18*b^32*d^2 + 579072*A^6*a^20*b^30*d^2 + 211456*A^6*a^22*b^28*d^2 + 4096*A^6*a^24

*b^26*d^2 - 72*B^6*a^12*b^38*d^2 - 355*B^6*a^14*b^36*d^2 - 3534*B^6*a^16*b^34*d^2 + 9181*B^6*a^18*b^32*d^2 + 4

3936*B^6*a^20*b^30*d^2 + 47872*B^6*a^22*b^28*d^2 + 16384*B^6*a^24*b^26*d^2 - 2494*A*B^5*a^13*b^37*d^2 - 20820*

A*B^5*a^15*b^35*d^2 + 15026*A*B^5*a^17*b^33*d^2 + 134984*A*B^5*a^19*b^31*d^2 + 156800*A*B^5*a^21*b^29*d^2 + 55

296*A*B^5*a^23*b^27*d^2 - 1150*A^5*B*a^13*b^37*d^2 + 82036*A^5*B*a^15*b^35*d^2 + 614690*A^5*B*a^17*b^33*d^2 +

1432560*A^5*B*a^19*b^31*d^2 + 1361536*A^5*B*a^21*b^29*d^2 + 460800*A^5*B*a^23*b^27*d^2 - 23*A^2*B^4*a^12*b^38*

d^2 - 15620*A^2*B^4*a^14*b^36*d^2 - 11843*A^2*B^4*a^16*b^34*d^2 + 95626*A^2*B^4*a^18*b^32*d^2 + 210240*A^2*B^4

*a^20*b^30*d^2 + 155648*A^2*B^4*a^22*b^28*d^2 + 36864*A^2*B^4*a^24*b^26*d^2 - 764*A^3*B^3*a^13*b^37*d^2 - 2105

6*A^3*B^3*a^15*b^35*d^2 + 145044*A^3*B^3*a^17*b^33*d^2 + 566296*A^3*B^3*a^19*b^31*d^2 + 667904*A^3*B^3*a^21*b^

29*d^2 + 331776*A^3*B^3*a^23*b^27*d^2 + 65536*A^3*B^3*a^25*b^25*d^2 + 10*A^4*B^2*a^12*b^38*d^2 + 19097*A^4*B^2

*a^14*b^36*d^2 + 326196*A^4*B^2*a^16*b^34*d^2 + 1062069*A^4*B^2*a^18*b^32*d^2 + 1527456*A^4*B^2*a^20*b^30*d^2

+ 1091328*A^4*B^2*a^22*b^28*d^2 + 319488*A^4*B^2*a^24*b^26*d^2))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2

)) - (2199023255552*tan(c + d*x)^(1/2)*(85*A^7*a^16*b^34 - 65*A^7*a^14*b^36 + 729*A^7*a^18*b^32 + 947*A^7*a^20

*b^30 + 368*A^7*a^22*b^28 - 3*B^7*a^13*b^37 + 36*B^7*a^15*b^35 + 374*B^7*a^17*b^33 + 1363*B^7*a^19*b^31 + 2276

*B^7*a^21*b^29 + 1760*B^7*a^23*b^27 + 512*B^7*a^25*b^25 - 25*A^2*B^5*a^13*b^37 + 818*A^2*B^5*a^15*b^35 + 5373*

A^2*B^5*a^17*b^33 + 12178*A^2*B^5*a^19*b^31 + 12640*A^2*B^5*a^21*b^29 + 6016*A^2*B^5*a^23*b^27 + 1024*A^2*B^5*

a^25*b^25 + 89*A^3*B^4*a^14*b^36 + 2278*A^3*B^4*a^16*b^34 + 10563*A^3*B^4*a^18*b^32 + 18982*A^3*B^4*a^20*b^30

+ 14960*A^3*B^4*a^22*b^28 + 4352*A^3*B^4*a^24*b^26 - 37*A^4*B^3*a^13*b^37 + 1507*A^4*B^3*a^15*b^35 + 9606*A^4*

B^3*a^17*b^33 + 20274*A^4*B^3*a^19*b^31 + 18452*A^4*B^3*a^21*b^29 + 6752*A^4*B^3*a^23*b^27 + 512*A^4*B^3*a^25*

b^25 - 45*A^5*B^2*a^14*b^36 + 1265*A^5*B^2*a^16*b^34 + 6366*A^5*B^2*a^18*b^32 + 10912*A^5*B^2*a^20*b^30 + 8032

*A^5*B^2*a^22*b^28 + 2176*A^5*B^2*a^24*b^26 + 69*A*B^6*a^14*b^36 + 1098*A*B^6*a^16*b^34 + 4926*A*B^6*a^18*b^32

+ 9017*A*B^6*a^20*b^30 + 7296*A*B^6*a^22*b^28 + 2176*A*B^6*a^24*b^26 - 15*A^6*B*a^13*b^37 + 725*A^6*B*a^15*b^

35 + 4607*A^6*B*a^17*b^33 + 9459*A^6*B*a^19*b^31 + 8088*A^6*B*a^21*b^29 + 2496*A^6*B*a^23*b^27))/(d^7*((a + b*

tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2) +

(549755813888*(1140*A^8*a^16*b^34 + 3560*A^8*a^18*b^32 + 3700*A^8*a^20*b^30 + 1280*A^8*a^22*b^28 + 4*B^8*a^12*

b^38 + 84*B^8*a^14*b^36 + 545*B^8*a^16*b^34 + 1462*B^8*a^18*b^32 + 1861*B^8*a^20*b^30 + 1120*B^8*a^22*b^28 + 2

56*B^8*a^24*b^26 + 8*A^2*B^6*a^12*b^38 + 1361*A^2*B^6*a^14*b^36 + 8932*A^2*B^6*a^16*b^34 + 23189*A^2*B^6*a^18*

b^32 + 29850*A^2*B^6*a^20*b^30 + 19104*A^2*B^6*a^22*b^28 + 4864*A^2*B^6*a^24*b^26 + 264*A^3*B^5*a^13*b^37 + 60

88*A^3*B^5*a^15*b^35 + 25512*A^3*B^5*a^17*b^33 + 44696*A^3*B^5*a^19*b^31 + 37936*A^3*B^5*a^21*b^29 + 14976*A^3

*B^5*a^23*b^27 + 2048*A^3*B^5*a^25*b^25 + 4*A^4*B^4*a^12*b^38 + 2470*A^4*B^4*a^14*b^36 + 17369*A^4*B^4*a^16*b^

34 + 45552*A^4*B^4*a^18*b^32 + 57817*A^4*B^4*a^20*b^30 + 36128*A^4*B^4*a^22*b^28 + 8960*A^4*B^4*a^24*b^26 + 13

2*A^5*B^3*a^13*b^37 + 7310*A^5*B^3*a^15*b^35 + 32796*A^5*B^3*a^17*b^33 + 57502*A^5*B^3*a^19*b^31 + 46220*A^5*B

^3*a^21*b^29 + 15360*A^5*B^3*a^23*b^27 + 1024*A^5*B^3*a^25*b^25 + 1193*A^6*B^2*a^14*b^36 + 10122*A^6*B^2*a^16*

b^34 + 27385*A^6*B^2*a^18*b^32 + 33528*A^6*B^2*a^20*b^30 + 19424*A^6*B^2*a^22*b^28 + 4352*A^6*B^2*a^24*b^26 +

132*A*B^7*a^13*b^37 + 1622*A*B^7*a^15*b^35 + 6076*A*B^7*a^17*b^33 + 10630*A*B^7*a^19*b^31 + 9884*A*B^7*a^21*b^

29 + 4864*A*B^7*a^23*b^27 + 1024*A*B^7*a^25*b^25 + 2844*A^7*B*a^15*b^35 + 13360*A^7*B*a^17*b^33 + 23436*A^7*B*

a^19*b^31 + 18168*A^7*B*a^21*b^29 + 5248*A^7*B*a^23*b^27))/d^8 - (549755813888*tan(c + d*x)*(12996*A^8*a^16*b^

35 + 55176*A^8*a^18*b^33 + 87748*A^8*a^20*b^31 + 61952*A^8*a^22*b^29 + 16384*A^8*a^24*b^27 + 4*B^8*a^12*b^39 +

108*B^8*a^14*b^37 + 893*B^8*a^16*b^35 + 2278*B^8*a^18*b^33 + 2545*B^8*a^20*b^31 + 1312*B^8*a^22*b^29 + 256*B^

8*a^24*b^27 + 8*A^2*B^6*a^12*b^39 + 2697*A^2*B^6*a^14*b^37 + 20880*A^2*B^6*a^16*b^35 + 58853*A^2*B^6*a^18*b^33

+ 81686*A^2*B^6*a^20*b^31 + 60992*A^2*B^6*a^22*b^29 + 24064*A^2*B^6*a^24*b^27 + 4096*A^2*B^6*a^26*b^25 + 360*

A^3*B^5*a^13*b^38 + 16184*A^3*B^5*a^15*b^36 + 75064*A^3*B^5*a^17*b^34 + 152168*A^3*B^5*a^19*b^32 + 162560*A^3*

B^5*a^21*b^30 + 90112*A^3*B^5*a^23*b^28 + 20480*A^3*B^5*a^25*b^26 + 4*A^4*B^4*a^12*b^39 + 5070*A^4*B^4*a^14*b^

37 + 52077*A^4*B^4*a^16*b^35 + 166048*A^4*B^4*a^18*b^33 + 243485*A^4*B^4*a^20*b^31 + 180000*A^4*B^4*a^22*b^29

+ 63744*A^4*B^4*a^24*b^27 + 8192*A^4*B^4*a^26*b^25 + 180*A^5*B^3*a^13*b^38 + 23482*A^5*B^3*a^15*b^36 + 115688*

A^5*B^3*a^17*b^34 + 241906*A^5*B^3*a^19*b^32 + 264592*A^5*B^3*a^21*b^30 + 149888*A^5*B^3*a^23*b^28 + 34816*A^5

*B^3*a^25*b^26 + 2481*A^6*B^2*a^14*b^37 + 45086*A^6*B^2*a^16*b^35 + 164649*A^6*B^2*a^18*b^33 + 252092*A^6*B^2*

a^20*b^31 + 182272*A^6*B^2*a^22*b^29 + 56320*A^6*B^2*a^24*b^27 + 4096*A^6*B^2*a^26*b^25 + 180*A*B^7*a^13*b^38

+ 2962*A*B^7*a^15*b^36 + 11480*A*B^7*a^17*b^34 + 20810*A*B^7*a^19*b^32 + 20176*A*B^7*a^21*b^30 + 10112*A*B^7*a

^23*b^28 + 2048*A*B^7*a^25*b^26 + 10260*A^7*B*a^15*b^36 + 52104*A^7*B*a^17*b^34 + 110548*A^7*B*a^19*b^32 + 122

208*A^7*B*a^21*b^30 + 69888*A^7*B*a^23*b^28 + 16384*A^7*B*a^25*b^26))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/

2))^2)))*((A^2*b - A^2*a*1i + B^2*a*1i - B^2*b + 2*A*B*a + A*B*b*2i)/(4*d^2))^(1/2)*2i - atan(((((A^2*a*1i + A

^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2)*((((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a

- A*B*b*2i)/(4*d^2))^(1/2)*((((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2)*((((2

74877906944*(1600*a^12*b^34*d^8 - 16640*a^14*b^32*d^8 + 22784*a^16*b^30*d^8 + 106496*a^18*b^28*d^8 + 65536*a^2

0*b^26*d^8))/d^8 - (274877906944*tan(c + d*x)*(1600*a^12*b^35*d^8 - 48000*a^14*b^33*d^8 + 155136*a^16*b^31*d^8

+ 466944*a^18*b^29*d^8 + 262144*a^20*b^27*d^8))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2))*((A^2*a*1i +

A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2) - (2199023255552*tan(c + d*x)^(1/2)*(2048*A*a^20

*b^27*d^6 - 12536*A*a^16*b^31*d^6 - 3328*A*a^18*b^29*d^6 - 7160*A*a^14*b^33*d^6 + 240*B*a^13*b^34*d^6 - 720*B*

a^15*b^32*d^6 + 5696*B*a^17*b^30*d^6 + 14848*B*a^19*b^28*d^6 + 8192*B*a^21*b^26*d^6))/(d^7*((a + b*tan(c + d*x

))^(1/2) - a^(1/2))))*((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2) - (2748779069

44*(1200*A^2*a^12*b^35*d^6 - 1600*A^2*a^14*b^33*d^6 + 272464*A^2*a^16*b^31*d^6 + 573952*A^2*a^18*b^29*d^6 + 29

9008*A^2*a^20*b^27*d^6 - 1440*B^2*a^12*b^35*d^6 + 8352*B^2*a^14*b^33*d^6 - 320*B^2*a^16*b^31*d^6 + 26880*B^2*a

^18*b^29*d^6 + 102400*B^2*a^20*b^27*d^6 + 65536*B^2*a^22*b^25*d^6 - 11200*A*B*a^13*b^34*d^6 - 25856*A*B*a^15*b

^32*d^6 + 303168*A*B*a^17*b^30*d^6 + 661504*A*B*a^19*b^28*d^6 + 344064*A*B*a^21*b^26*d^6))/d^8 + (274877906944

*tan(c + d*x)*(1200*A^2*a^12*b^36*d^6 - 32160*A^2*a^14*b^34*d^6 + 1125488*A^2*a^16*b^32*d^6 + 2445312*A^2*a^18

*b^30*d^6 + 1351680*A^2*a^20*b^28*d^6 + 65536*A^2*a^22*b^26*d^6 - 1440*B^2*a^12*b^36*d^6 + 32256*B^2*a^14*b^34

*d^6 - 41440*B^2*a^16*b^32*d^6 + 68096*B^2*a^18*b^30*d^6 + 405504*B^2*a^20*b^28*d^6 + 262144*B^2*a^22*b^26*d^6

- 16320*A*B*a^13*b^35*d^6 - 34112*A*B*a^15*b^33*d^6 + 1294592*A*B*a^17*b^31*d^6 + 2656256*A*B*a^19*b^29*d^6 +

1343488*A*B*a^21*b^27*d^6))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) + (2199023255552*tan(c + d*x)^(1/

2)*(7600*A^3*a^18*b^30*d^4 - 3902*A^3*a^16*b^32*d^4 - 4590*A^3*a^14*b^34*d^4 + 6912*A^3*a^20*b^28*d^4 - 168*B^

3*a^13*b^35*d^4 + 982*B^3*a^15*b^33*d^4 + 2494*B^3*a^17*b^31*d^4 + 9024*B^3*a^19*b^29*d^4 + 15872*B^3*a^21*b^2

7*d^4 + 8192*B^3*a^23*b^25*d^4 + 4922*A*B^2*a^14*b^34*d^4 + 21906*A*B^2*a^16*b^32*d^4 + 69720*A*B^2*a^18*b^30*

d^4 + 95744*A*B^2*a^20*b^28*d^4 + 43008*A*B^2*a^22*b^26*d^4 - 180*A^2*B*a^13*b^35*d^4 + 4486*A^2*B*a^15*b^33*d

^4 + 52154*A^2*B*a^17*b^31*d^4 + 93568*A^2*B*a^19*b^29*d^4 + 46080*A^2*B*a^21*b^27*d^4))/(d^7*((a + b*tan(c +

d*x))^(1/2) - a^(1/2))))*((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2) + (2748779

06944*(300*A^4*a^12*b^36*d^4 + 2360*A^4*a^14*b^34*d^4 + 149228*A^4*a^16*b^32*d^4 + 307152*A^4*a^18*b^30*d^4 +

164352*A^4*a^20*b^28*d^4 + 4096*A^4*a^22*b^26*d^4 + 484*B^4*a^12*b^36*d^4 + 328*B^4*a^14*b^34*d^4 + 2308*B^4*a

^16*b^32*d^4 - 16048*B^4*a^18*b^30*d^4 - 43008*B^4*a^20*b^28*d^4 - 24576*B^4*a^22*b^26*d^4 + 7880*A*B^3*a^13*b

^35*d^4 + 28592*A*B^3*a^15*b^33*d^4 - 55832*A*B^3*a^17*b^31*d^4 - 100672*A*B^3*a^19*b^29*d^4 + 57344*A*B^3*a^2

1*b^27*d^4 + 81920*A*B^3*a^23*b^25*d^4 - 5880*A^3*B*a^13*b^35*d^4 + 47408*A^3*B*a^15*b^33*d^4 + 569576*A^3*B*a

^17*b^31*d^4 + 1004928*A^3*B*a^19*b^29*d^4 + 489472*A^3*B*a^21*b^27*d^4 - 320*A^2*B^2*a^12*b^36*d^4 + 1264*A^2

*B^2*a^14*b^34*d^4 - 27264*A^2*B^2*a^16*b^32*d^4 + 294128*A^2*B^2*a^18*b^30*d^4 + 711168*A^2*B^2*a^20*b^28*d^4

+ 389120*A^2*B^2*a^22*b^26*d^4))/d^8 - (274877906944*tan(c + d*x)*(300*A^4*a^12*b^37*d^4 - 6920*A^4*a^14*b^35

*d^4 + 738524*A^4*a^16*b^33*d^4 + 1819680*A^4*a^18*b^31*d^4 + 1384960*A^4*a^20*b^29*d^4 + 311296*A^4*a^22*b^27

*d^4 + 484*B^4*a^12*b^37*d^4 - 5368*B^4*a^14*b^35*d^4 + 1236*B^4*a^16*b^33*d^4 - 88064*B^4*a^18*b^31*d^4 - 205

824*B^4*a^20*b^29*d^4 - 110592*B^4*a^22*b^27*d^4 + 11192*A*B^3*a^13*b^36*d^4 + 45712*A*B^3*a^15*b^34*d^4 - 394

344*A*B^3*a^17*b^32*d^4 - 599296*A*B^3*a^19*b^30*d^4 + 124928*A*B^3*a^21*b^28*d^4 + 294912*A*B^3*a^23*b^26*d^4

- 8680*A^3*B*a^13*b^36*d^4 + 163152*A^3*B*a^15*b^34*d^4 + 2287096*A^3*B*a^17*b^32*d^4 + 4405760*A^3*B*a^19*b^

30*d^4 + 2617344*A^3*B*a^21*b^28*d^4 + 327680*A^3*B*a^23*b^26*d^4 - 320*A^2*B^2*a^12*b^37*d^4 + 23984*A^2*B^2*

a^14*b^35*d^4 - 212608*A^2*B^2*a^16*b^33*d^4 + 865008*A^2*B^2*a^18*b^31*d^4 + 2561024*A^2*B^2*a^20*b^29*d^4 +

1523712*A^2*B^2*a^22*b^27*d^4 + 65536*A^2*B^2*a^24*b^25*d^4))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2))

- (2199023255552*tan(c + d*x)^(1/2)*(3641*A^5*a^18*b^31*d^2 - 55*A^5*a^16*b^33*d^2 - 960*A^5*a^14*b^35*d^2 + 2

864*A^5*a^20*b^29*d^2 + 128*A^5*a^22*b^27*d^2 + 39*B^5*a^13*b^36*d^2 - 341*B^5*a^15*b^34*d^2 - 2362*B^5*a^17*b

^32*d^2 - 6942*B^5*a^19*b^30*d^2 - 8544*B^5*a^21*b^28*d^2 - 3584*B^5*a^23*b^26*d^2 - 1045*A*B^4*a^14*b^35*d^2

- 8795*A*B^4*a^16*b^33*d^2 - 26838*A*B^4*a^18*b^31*d^2 - 24592*A*B^4*a^20*b^29*d^2 + 2688*A*B^4*a^22*b^27*d^2

+ 8192*A*B^4*a^24*b^25*d^2 - 120*A^4*B*a^13*b^36*d^2 + 4977*A^4*B*a^15*b^34*d^2 + 33597*A^4*B*a^17*b^32*d^2 +

55284*A^4*B*a^19*b^30*d^2 + 27296*A^4*B*a^21*b^28*d^2 + 512*A^4*B*a^23*b^26*d^2 + 159*A^2*B^3*a^13*b^36*d^2 -

4656*A^2*B^3*a^15*b^34*d^2 - 11277*A^2*B^3*a^17*b^32*d^2 + 28418*A^2*B^3*a^19*b^30*d^2 + 74816*A^2*B^3*a^21*b^

28*d^2 + 39936*A^2*B^3*a^23*b^26*d^2 - 133*A^3*B^2*a^14*b^35*d^2 + 16550*A^3*B^2*a^16*b^33*d^2 + 86411*A^3*B^2

*a^18*b^31*d^2 + 127328*A^3*B^2*a^20*b^29*d^2 + 57600*A^3*B^2*a^22*b^27*d^2))/(d^7*((a + b*tan(c + d*x))^(1/2)

- a^(1/2))))*((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2) - (274877906944*(25*A

^6*a^12*b^37*d^2 + 430*A^6*a^14*b^35*d^2 + 25905*A^6*a^16*b^33*d^2 + 68220*A^6*a^18*b^31*d^2 + 59424*A^6*a^20*

b^29*d^2 + 16640*A^6*a^22*b^27*d^2 - 72*B^6*a^12*b^37*d^2 - 679*B^6*a^14*b^35*d^2 - 3030*B^6*a^16*b^33*d^2 - 2

263*B^6*a^18*b^31*d^2 + 6544*B^6*a^20*b^29*d^2 + 10496*B^6*a^22*b^27*d^2 + 4096*B^6*a^24*b^25*d^2 - 1794*A*B^5

*a^13*b^36*d^2 - 12040*A*B^5*a^15*b^34*d^2 - 12202*A*B^5*a^17*b^32*d^2 + 19804*A*B^5*a^19*b^30*d^2 + 35200*A*B

^5*a^21*b^28*d^2 + 13312*A*B^5*a^23*b^26*d^2 - 770*A^5*B*a^13*b^36*d^2 + 21168*A^5*B*a^15*b^34*d^2 + 119398*A^

5*B*a^17*b^32*d^2 + 194292*A^5*B*a^19*b^30*d^2 + 114560*A^5*B*a^21*b^28*d^2 + 17408*A^5*B*a^23*b^26*d^2 - 23*A

^2*B^4*a^12*b^37*d^2 - 6472*A^2*B^4*a^14*b^35*d^2 - 7211*A^2*B^4*a^16*b^33*d^2 + 32614*A^2*B^4*a^18*b^31*d^2 +

79616*A^2*B^4*a^20*b^29*d^2 + 70400*A^2*B^4*a^22*b^27*d^2 + 24576*A^2*B^4*a^24*b^25*d^2 - 580*A^3*B^3*a^13*b^

36*d^2 + 5928*A^3*B^3*a^15*b^34*d^2 + 92604*A^3*B^3*a^17*b^32*d^2 + 267280*A^3*B^3*a^19*b^30*d^2 + 293120*A^3*

B^3*a^21*b^28*d^2 + 112640*A^3*B^3*a^23*b^26*d^2 + 10*A^4*B^2*a^12*b^37*d^2 + 10653*A^4*B^2*a^14*b^35*d^2 + 12

3388*A^4*B^2*a^16*b^33*d^2 + 361289*A^4*B^2*a^18*b^31*d^2 + 408400*A^4*B^2*a^20*b^29*d^2 + 164608*A^4*B^2*a^22

*b^27*d^2 + 4096*A^4*B^2*a^24*b^25*d^2))/d^8 + (274877906944*tan(c + d*x)*(25*A^6*a^12*b^38*d^2 - 470*A^6*a^14

*b^36*d^2 + 168905*A^6*a^16*b^34*d^2 + 541176*A^6*a^18*b^32*d^2 + 579072*A^6*a^20*b^30*d^2 + 211456*A^6*a^22*b

^28*d^2 + 4096*A^6*a^24*b^26*d^2 - 72*B^6*a^12*b^38*d^2 - 355*B^6*a^14*b^36*d^2 - 3534*B^6*a^16*b^34*d^2 + 918

1*B^6*a^18*b^32*d^2 + 43936*B^6*a^20*b^30*d^2 + 47872*B^6*a^22*b^28*d^2 + 16384*B^6*a^24*b^26*d^2 - 2494*A*B^5

*a^13*b^37*d^2 - 20820*A*B^5*a^15*b^35*d^2 + 15026*A*B^5*a^17*b^33*d^2 + 134984*A*B^5*a^19*b^31*d^2 + 156800*A

*B^5*a^21*b^29*d^2 + 55296*A*B^5*a^23*b^27*d^2 - 1150*A^5*B*a^13*b^37*d^2 + 82036*A^5*B*a^15*b^35*d^2 + 614690

*A^5*B*a^17*b^33*d^2 + 1432560*A^5*B*a^19*b^31*d^2 + 1361536*A^5*B*a^21*b^29*d^2 + 460800*A^5*B*a^23*b^27*d^2

- 23*A^2*B^4*a^12*b^38*d^2 - 15620*A^2*B^4*a^14*b^36*d^2 - 11843*A^2*B^4*a^16*b^34*d^2 + 95626*A^2*B^4*a^18*b^

32*d^2 + 210240*A^2*B^4*a^20*b^30*d^2 + 155648*A^2*B^4*a^22*b^28*d^2 + 36864*A^2*B^4*a^24*b^26*d^2 - 764*A^3*B

^3*a^13*b^37*d^2 - 21056*A^3*B^3*a^15*b^35*d^2 + 145044*A^3*B^3*a^17*b^33*d^2 + 566296*A^3*B^3*a^19*b^31*d^2 +

667904*A^3*B^3*a^21*b^29*d^2 + 331776*A^3*B^3*a^23*b^27*d^2 + 65536*A^3*B^3*a^25*b^25*d^2 + 10*A^4*B^2*a^12*b

^38*d^2 + 19097*A^4*B^2*a^14*b^36*d^2 + 326196*A^4*B^2*a^16*b^34*d^2 + 1062069*A^4*B^2*a^18*b^32*d^2 + 1527456

*A^4*B^2*a^20*b^30*d^2 + 1091328*A^4*B^2*a^22*b^28*d^2 + 319488*A^4*B^2*a^24*b^26*d^2))/(d^8*((a + b*tan(c + d

*x))^(1/2) - a^(1/2))^2)) + (2199023255552*tan(c + d*x)^(1/2)*(85*A^7*a^16*b^34 - 65*A^7*a^14*b^36 + 729*A^7*a

^18*b^32 + 947*A^7*a^20*b^30 + 368*A^7*a^22*b^28 - 3*B^7*a^13*b^37 + 36*B^7*a^15*b^35 + 374*B^7*a^17*b^33 + 13

63*B^7*a^19*b^31 + 2276*B^7*a^21*b^29 + 1760*B^7*a^23*b^27 + 512*B^7*a^25*b^25 - 25*A^2*B^5*a^13*b^37 + 818*A^

2*B^5*a^15*b^35 + 5373*A^2*B^5*a^17*b^33 + 12178*A^2*B^5*a^19*b^31 + 12640*A^2*B^5*a^21*b^29 + 6016*A^2*B^5*a^

23*b^27 + 1024*A^2*B^5*a^25*b^25 + 89*A^3*B^4*a^14*b^36 + 2278*A^3*B^4*a^16*b^34 + 10563*A^3*B^4*a^18*b^32 + 1

8982*A^3*B^4*a^20*b^30 + 14960*A^3*B^4*a^22*b^28 + 4352*A^3*B^4*a^24*b^26 - 37*A^4*B^3*a^13*b^37 + 1507*A^4*B^

3*a^15*b^35 + 9606*A^4*B^3*a^17*b^33 + 20274*A^4*B^3*a^19*b^31 + 18452*A^4*B^3*a^21*b^29 + 6752*A^4*B^3*a^23*b

^27 + 512*A^4*B^3*a^25*b^25 - 45*A^5*B^2*a^14*b^36 + 1265*A^5*B^2*a^16*b^34 + 6366*A^5*B^2*a^18*b^32 + 10912*A

^5*B^2*a^20*b^30 + 8032*A^5*B^2*a^22*b^28 + 2176*A^5*B^2*a^24*b^26 + 69*A*B^6*a^14*b^36 + 1098*A*B^6*a^16*b^34

+ 4926*A*B^6*a^18*b^32 + 9017*A*B^6*a^20*b^30 + 7296*A*B^6*a^22*b^28 + 2176*A*B^6*a^24*b^26 - 15*A^6*B*a^13*b

^37 + 725*A^6*B*a^15*b^35 + 4607*A^6*B*a^17*b^33 + 9459*A^6*B*a^19*b^31 + 8088*A^6*B*a^21*b^29 + 2496*A^6*B*a^

23*b^27))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*

b*2i)/(4*d^2))^(1/2)*1i - (((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2)*((((A^2*

a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2)*((((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b +

2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2)*((((274877906944*(1600*a^12*b^34*d^8 - 16640*a^14*b^32*d^8 + 22784*a^16*b^

30*d^8 + 106496*a^18*b^28*d^8 + 65536*a^20*b^26*d^8))/d^8 - (274877906944*tan(c + d*x)*(1600*a^12*b^35*d^8 - 4

8000*a^14*b^33*d^8 + 155136*a^16*b^31*d^8 + 466944*a^18*b^29*d^8 + 262144*a^20*b^27*d^8))/(d^8*((a + b*tan(c +

d*x))^(1/2) - a^(1/2))^2))*((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2) + (2199

023255552*tan(c + d*x)^(1/2)*(2048*A*a^20*b^27*d^6 - 12536*A*a^16*b^31*d^6 - 3328*A*a^18*b^29*d^6 - 7160*A*a^1

4*b^33*d^6 + 240*B*a^13*b^34*d^6 - 720*B*a^15*b^32*d^6 + 5696*B*a^17*b^30*d^6 + 14848*B*a^19*b^28*d^6 + 8192*B

*a^21*b^26*d^6))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a

- A*B*b*2i)/(4*d^2))^(1/2) - (274877906944*(1200*A^2*a^12*b^35*d^6 - 1600*A^2*a^14*b^33*d^6 + 272464*A^2*a^16

*b^31*d^6 + 573952*A^2*a^18*b^29*d^6 + 299008*A^2*a^20*b^27*d^6 - 1440*B^2*a^12*b^35*d^6 + 8352*B^2*a^14*b^33*

d^6 - 320*B^2*a^16*b^31*d^6 + 26880*B^2*a^18*b^29*d^6 + 102400*B^2*a^20*b^27*d^6 + 65536*B^2*a^22*b^25*d^6 - 1

1200*A*B*a^13*b^34*d^6 - 25856*A*B*a^15*b^32*d^6 + 303168*A*B*a^17*b^30*d^6 + 661504*A*B*a^19*b^28*d^6 + 34406

4*A*B*a^21*b^26*d^6))/d^8 + (274877906944*tan(c + d*x)*(1200*A^2*a^12*b^36*d^6 - 32160*A^2*a^14*b^34*d^6 + 112

5488*A^2*a^16*b^32*d^6 + 2445312*A^2*a^18*b^30*d^6 + 1351680*A^2*a^20*b^28*d^6 + 65536*A^2*a^22*b^26*d^6 - 144

0*B^2*a^12*b^36*d^6 + 32256*B^2*a^14*b^34*d^6 - 41440*B^2*a^16*b^32*d^6 + 68096*B^2*a^18*b^30*d^6 + 405504*B^2

*a^20*b^28*d^6 + 262144*B^2*a^22*b^26*d^6 - 16320*A*B*a^13*b^35*d^6 - 34112*A*B*a^15*b^33*d^6 + 1294592*A*B*a^

17*b^31*d^6 + 2656256*A*B*a^19*b^29*d^6 + 1343488*A*B*a^21*b^27*d^6))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/

2))^2)) - (2199023255552*tan(c + d*x)^(1/2)*(7600*A^3*a^18*b^30*d^4 - 3902*A^3*a^16*b^32*d^4 - 4590*A^3*a^14*b

^34*d^4 + 6912*A^3*a^20*b^28*d^4 - 168*B^3*a^13*b^35*d^4 + 982*B^3*a^15*b^33*d^4 + 2494*B^3*a^17*b^31*d^4 + 90

24*B^3*a^19*b^29*d^4 + 15872*B^3*a^21*b^27*d^4 + 8192*B^3*a^23*b^25*d^4 + 4922*A*B^2*a^14*b^34*d^4 + 21906*A*B

^2*a^16*b^32*d^4 + 69720*A*B^2*a^18*b^30*d^4 + 95744*A*B^2*a^20*b^28*d^4 + 43008*A*B^2*a^22*b^26*d^4 - 180*A^2

*B*a^13*b^35*d^4 + 4486*A^2*B*a^15*b^33*d^4 + 52154*A^2*B*a^17*b^31*d^4 + 93568*A^2*B*a^19*b^29*d^4 + 46080*A^

2*B*a^21*b^27*d^4))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*

B*a - A*B*b*2i)/(4*d^2))^(1/2) + (274877906944*(300*A^4*a^12*b^36*d^4 + 2360*A^4*a^14*b^34*d^4 + 149228*A^4*a^

16*b^32*d^4 + 307152*A^4*a^18*b^30*d^4 + 164352*A^4*a^20*b^28*d^4 + 4096*A^4*a^22*b^26*d^4 + 484*B^4*a^12*b^36

*d^4 + 328*B^4*a^14*b^34*d^4 + 2308*B^4*a^16*b^32*d^4 - 16048*B^4*a^18*b^30*d^4 - 43008*B^4*a^20*b^28*d^4 - 24

576*B^4*a^22*b^26*d^4 + 7880*A*B^3*a^13*b^35*d^4 + 28592*A*B^3*a^15*b^33*d^4 - 55832*A*B^3*a^17*b^31*d^4 - 100

672*A*B^3*a^19*b^29*d^4 + 57344*A*B^3*a^21*b^27*d^4 + 81920*A*B^3*a^23*b^25*d^4 - 5880*A^3*B*a^13*b^35*d^4 + 4

7408*A^3*B*a^15*b^33*d^4 + 569576*A^3*B*a^17*b^31*d^4 + 1004928*A^3*B*a^19*b^29*d^4 + 489472*A^3*B*a^21*b^27*d

^4 - 320*A^2*B^2*a^12*b^36*d^4 + 1264*A^2*B^2*a^14*b^34*d^4 - 27264*A^2*B^2*a^16*b^32*d^4 + 294128*A^2*B^2*a^1

8*b^30*d^4 + 711168*A^2*B^2*a^20*b^28*d^4 + 389120*A^2*B^2*a^22*b^26*d^4))/d^8 - (274877906944*tan(c + d*x)*(3

00*A^4*a^12*b^37*d^4 - 6920*A^4*a^14*b^35*d^4 + 738524*A^4*a^16*b^33*d^4 + 1819680*A^4*a^18*b^31*d^4 + 1384960

*A^4*a^20*b^29*d^4 + 311296*A^4*a^22*b^27*d^4 + 484*B^4*a^12*b^37*d^4 - 5368*B^4*a^14*b^35*d^4 + 1236*B^4*a^16

*b^33*d^4 - 88064*B^4*a^18*b^31*d^4 - 205824*B^4*a^20*b^29*d^4 - 110592*B^4*a^22*b^27*d^4 + 11192*A*B^3*a^13*b

^36*d^4 + 45712*A*B^3*a^15*b^34*d^4 - 394344*A*B^3*a^17*b^32*d^4 - 599296*A*B^3*a^19*b^30*d^4 + 124928*A*B^3*a

^21*b^28*d^4 + 294912*A*B^3*a^23*b^26*d^4 - 8680*A^3*B*a^13*b^36*d^4 + 163152*A^3*B*a^15*b^34*d^4 + 2287096*A^

3*B*a^17*b^32*d^4 + 4405760*A^3*B*a^19*b^30*d^4 + 2617344*A^3*B*a^21*b^28*d^4 + 327680*A^3*B*a^23*b^26*d^4 - 3

20*A^2*B^2*a^12*b^37*d^4 + 23984*A^2*B^2*a^14*b^35*d^4 - 212608*A^2*B^2*a^16*b^33*d^4 + 865008*A^2*B^2*a^18*b^

31*d^4 + 2561024*A^2*B^2*a^20*b^29*d^4 + 1523712*A^2*B^2*a^22*b^27*d^4 + 65536*A^2*B^2*a^24*b^25*d^4))/(d^8*((

a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) + (2199023255552*tan(c + d*x)^(1/2)*(3641*A^5*a^18*b^31*d^2 - 55*A^5*

a^16*b^33*d^2 - 960*A^5*a^14*b^35*d^2 + 2864*A^5*a^20*b^29*d^2 + 128*A^5*a^22*b^27*d^2 + 39*B^5*a^13*b^36*d^2

- 341*B^5*a^15*b^34*d^2 - 2362*B^5*a^17*b^32*d^2 - 6942*B^5*a^19*b^30*d^2 - 8544*B^5*a^21*b^28*d^2 - 3584*B^5*

a^23*b^26*d^2 - 1045*A*B^4*a^14*b^35*d^2 - 8795*A*B^4*a^16*b^33*d^2 - 26838*A*B^4*a^18*b^31*d^2 - 24592*A*B^4*

a^20*b^29*d^2 + 2688*A*B^4*a^22*b^27*d^2 + 8192*A*B^4*a^24*b^25*d^2 - 120*A^4*B*a^13*b^36*d^2 + 4977*A^4*B*a^1

5*b^34*d^2 + 33597*A^4*B*a^17*b^32*d^2 + 55284*A^4*B*a^19*b^30*d^2 + 27296*A^4*B*a^21*b^28*d^2 + 512*A^4*B*a^2

3*b^26*d^2 + 159*A^2*B^3*a^13*b^36*d^2 - 4656*A^2*B^3*a^15*b^34*d^2 - 11277*A^2*B^3*a^17*b^32*d^2 + 28418*A^2*

B^3*a^19*b^30*d^2 + 74816*A^2*B^3*a^21*b^28*d^2 + 39936*A^2*B^3*a^23*b^26*d^2 - 133*A^3*B^2*a^14*b^35*d^2 + 16

550*A^3*B^2*a^16*b^33*d^2 + 86411*A^3*B^2*a^18*b^31*d^2 + 127328*A^3*B^2*a^20*b^29*d^2 + 57600*A^3*B^2*a^22*b^

27*d^2))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b

*2i)/(4*d^2))^(1/2) - (274877906944*(25*A^6*a^12*b^37*d^2 + 430*A^6*a^14*b^35*d^2 + 25905*A^6*a^16*b^33*d^2 +

68220*A^6*a^18*b^31*d^2 + 59424*A^6*a^20*b^29*d^2 + 16640*A^6*a^22*b^27*d^2 - 72*B^6*a^12*b^37*d^2 - 679*B^6*a

^14*b^35*d^2 - 3030*B^6*a^16*b^33*d^2 - 2263*B^6*a^18*b^31*d^2 + 6544*B^6*a^20*b^29*d^2 + 10496*B^6*a^22*b^27*

d^2 + 4096*B^6*a^24*b^25*d^2 - 1794*A*B^5*a^13*b^36*d^2 - 12040*A*B^5*a^15*b^34*d^2 - 12202*A*B^5*a^17*b^32*d^

2 + 19804*A*B^5*a^19*b^30*d^2 + 35200*A*B^5*a^21*b^28*d^2 + 13312*A*B^5*a^23*b^26*d^2 - 770*A^5*B*a^13*b^36*d^

2 + 21168*A^5*B*a^15*b^34*d^2 + 119398*A^5*B*a^17*b^32*d^2 + 194292*A^5*B*a^19*b^30*d^2 + 114560*A^5*B*a^21*b^

28*d^2 + 17408*A^5*B*a^23*b^26*d^2 - 23*A^2*B^4*a^12*b^37*d^2 - 6472*A^2*B^4*a^14*b^35*d^2 - 7211*A^2*B^4*a^16

*b^33*d^2 + 32614*A^2*B^4*a^18*b^31*d^2 + 79616*A^2*B^4*a^20*b^29*d^2 + 70400*A^2*B^4*a^22*b^27*d^2 + 24576*A^

2*B^4*a^24*b^25*d^2 - 580*A^3*B^3*a^13*b^36*d^2 + 5928*A^3*B^3*a^15*b^34*d^2 + 92604*A^3*B^3*a^17*b^32*d^2 + 2

67280*A^3*B^3*a^19*b^30*d^2 + 293120*A^3*B^3*a^21*b^28*d^2 + 112640*A^3*B^3*a^23*b^26*d^2 + 10*A^4*B^2*a^12*b^

37*d^2 + 10653*A^4*B^2*a^14*b^35*d^2 + 123388*A^4*B^2*a^16*b^33*d^2 + 361289*A^4*B^2*a^18*b^31*d^2 + 408400*A^

4*B^2*a^20*b^29*d^2 + 164608*A^4*B^2*a^22*b^27*d^2 + 4096*A^4*B^2*a^24*b^25*d^2))/d^8 + (274877906944*tan(c +

d*x)*(25*A^6*a^12*b^38*d^2 - 470*A^6*a^14*b^36*d^2 + 168905*A^6*a^16*b^34*d^2 + 541176*A^6*a^18*b^32*d^2 + 579

072*A^6*a^20*b^30*d^2 + 211456*A^6*a^22*b^28*d^2 + 4096*A^6*a^24*b^26*d^2 - 72*B^6*a^12*b^38*d^2 - 355*B^6*a^1

4*b^36*d^2 - 3534*B^6*a^16*b^34*d^2 + 9181*B^6*a^18*b^32*d^2 + 43936*B^6*a^20*b^30*d^2 + 47872*B^6*a^22*b^28*d

^2 + 16384*B^6*a^24*b^26*d^2 - 2494*A*B^5*a^13*b^37*d^2 - 20820*A*B^5*a^15*b^35*d^2 + 15026*A*B^5*a^17*b^33*d^

2 + 134984*A*B^5*a^19*b^31*d^2 + 156800*A*B^5*a^21*b^29*d^2 + 55296*A*B^5*a^23*b^27*d^2 - 1150*A^5*B*a^13*b^37

*d^2 + 82036*A^5*B*a^15*b^35*d^2 + 614690*A^5*B*a^17*b^33*d^2 + 1432560*A^5*B*a^19*b^31*d^2 + 1361536*A^5*B*a^

21*b^29*d^2 + 460800*A^5*B*a^23*b^27*d^2 - 23*A^2*B^4*a^12*b^38*d^2 - 15620*A^2*B^4*a^14*b^36*d^2 - 11843*A^2*

B^4*a^16*b^34*d^2 + 95626*A^2*B^4*a^18*b^32*d^2 + 210240*A^2*B^4*a^20*b^30*d^2 + 155648*A^2*B^4*a^22*b^28*d^2

+ 36864*A^2*B^4*a^24*b^26*d^2 - 764*A^3*B^3*a^13*b^37*d^2 - 21056*A^3*B^3*a^15*b^35*d^2 + 145044*A^3*B^3*a^17*

b^33*d^2 + 566296*A^3*B^3*a^19*b^31*d^2 + 667904*A^3*B^3*a^21*b^29*d^2 + 331776*A^3*B^3*a^23*b^27*d^2 + 65536*

A^3*B^3*a^25*b^25*d^2 + 10*A^4*B^2*a^12*b^38*d^2 + 19097*A^4*B^2*a^14*b^36*d^2 + 326196*A^4*B^2*a^16*b^34*d^2

+ 1062069*A^4*B^2*a^18*b^32*d^2 + 1527456*A^4*B^2*a^20*b^30*d^2 + 1091328*A^4*B^2*a^22*b^28*d^2 + 319488*A^4*B

^2*a^24*b^26*d^2))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) - (2199023255552*tan(c + d*x)^(1/2)*(85*A^7

*a^16*b^34 - 65*A^7*a^14*b^36 + 729*A^7*a^18*b^32 + 947*A^7*a^20*b^30 + 368*A^7*a^22*b^28 - 3*B^7*a^13*b^37 +

36*B^7*a^15*b^35 + 374*B^7*a^17*b^33 + 1363*B^7*a^19*b^31 + 2276*B^7*a^21*b^29 + 1760*B^7*a^23*b^27 + 512*B^7*

a^25*b^25 - 25*A^2*B^5*a^13*b^37 + 818*A^2*B^5*a^15*b^35 + 5373*A^2*B^5*a^17*b^33 + 12178*A^2*B^5*a^19*b^31 +

12640*A^2*B^5*a^21*b^29 + 6016*A^2*B^5*a^23*b^27 + 1024*A^2*B^5*a^25*b^25 + 89*A^3*B^4*a^14*b^36 + 2278*A^3*B^

4*a^16*b^34 + 10563*A^3*B^4*a^18*b^32 + 18982*A^3*B^4*a^20*b^30 + 14960*A^3*B^4*a^22*b^28 + 4352*A^3*B^4*a^24*

b^26 - 37*A^4*B^3*a^13*b^37 + 1507*A^4*B^3*a^15*b^35 + 9606*A^4*B^3*a^17*b^33 + 20274*A^4*B^3*a^19*b^31 + 1845

2*A^4*B^3*a^21*b^29 + 6752*A^4*B^3*a^23*b^27 + 512*A^4*B^3*a^25*b^25 - 45*A^5*B^2*a^14*b^36 + 1265*A^5*B^2*a^1

6*b^34 + 6366*A^5*B^2*a^18*b^32 + 10912*A^5*B^2*a^20*b^30 + 8032*A^5*B^2*a^22*b^28 + 2176*A^5*B^2*a^24*b^26 +

69*A*B^6*a^14*b^36 + 1098*A*B^6*a^16*b^34 + 4926*A*B^6*a^18*b^32 + 9017*A*B^6*a^20*b^30 + 7296*A*B^6*a^22*b^28

+ 2176*A*B^6*a^24*b^26 - 15*A^6*B*a^13*b^37 + 725*A^6*B*a^15*b^35 + 4607*A^6*B*a^17*b^33 + 9459*A^6*B*a^19*b^

31 + 8088*A^6*B*a^21*b^29 + 2496*A^6*B*a^23*b^27))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*a*1i +

A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2)*1i)/((((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*

A*B*a - A*B*b*2i)/(4*d^2))^(1/2)*((((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2)*

((((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2)*((((274877906944*(1600*a^12*b^34*

d^8 - 16640*a^14*b^32*d^8 + 22784*a^16*b^30*d^8 + 106496*a^18*b^28*d^8 + 65536*a^20*b^26*d^8))/d^8 - (27487790

6944*tan(c + d*x)*(1600*a^12*b^35*d^8 - 48000*a^14*b^33*d^8 + 155136*a^16*b^31*d^8 + 466944*a^18*b^29*d^8 + 26

2144*a^20*b^27*d^8))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2))*((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2

*A*B*a - A*B*b*2i)/(4*d^2))^(1/2) - (2199023255552*tan(c + d*x)^(1/2)*(2048*A*a^20*b^27*d^6 - 12536*A*a^16*b^3

1*d^6 - 3328*A*a^18*b^29*d^6 - 7160*A*a^14*b^33*d^6 + 240*B*a^13*b^34*d^6 - 720*B*a^15*b^32*d^6 + 5696*B*a^17*

b^30*d^6 + 14848*B*a^19*b^28*d^6 + 8192*B*a^21*b^26*d^6))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*

a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2) - (274877906944*(1200*A^2*a^12*b^35*d^6 -

1600*A^2*a^14*b^33*d^6 + 272464*A^2*a^16*b^31*d^6 + 573952*A^2*a^18*b^29*d^6 + 299008*A^2*a^20*b^27*d^6 - 144

0*B^2*a^12*b^35*d^6 + 8352*B^2*a^14*b^33*d^6 - 320*B^2*a^16*b^31*d^6 + 26880*B^2*a^18*b^29*d^6 + 102400*B^2*a^

20*b^27*d^6 + 65536*B^2*a^22*b^25*d^6 - 11200*A*B*a^13*b^34*d^6 - 25856*A*B*a^15*b^32*d^6 + 303168*A*B*a^17*b^

30*d^6 + 661504*A*B*a^19*b^28*d^6 + 344064*A*B*a^21*b^26*d^6))/d^8 + (274877906944*tan(c + d*x)*(1200*A^2*a^12

*b^36*d^6 - 32160*A^2*a^14*b^34*d^6 + 1125488*A^2*a^16*b^32*d^6 + 2445312*A^2*a^18*b^30*d^6 + 1351680*A^2*a^20

*b^28*d^6 + 65536*A^2*a^22*b^26*d^6 - 1440*B^2*a^12*b^36*d^6 + 32256*B^2*a^14*b^34*d^6 - 41440*B^2*a^16*b^32*d

^6 + 68096*B^2*a^18*b^30*d^6 + 405504*B^2*a^20*b^28*d^6 + 262144*B^2*a^22*b^26*d^6 - 16320*A*B*a^13*b^35*d^6 -

34112*A*B*a^15*b^33*d^6 + 1294592*A*B*a^17*b^31*d^6 + 2656256*A*B*a^19*b^29*d^6 + 1343488*A*B*a^21*b^27*d^6))

/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) + (2199023255552*tan(c + d*x)^(1/2)*(7600*A^3*a^18*b^30*d^4 -

3902*A^3*a^16*b^32*d^4 - 4590*A^3*a^14*b^34*d^4 + 6912*A^3*a^20*b^28*d^4 - 168*B^3*a^13*b^35*d^4 + 982*B^3*a^

15*b^33*d^4 + 2494*B^3*a^17*b^31*d^4 + 9024*B^3*a^19*b^29*d^4 + 15872*B^3*a^21*b^27*d^4 + 8192*B^3*a^23*b^25*d

^4 + 4922*A*B^2*a^14*b^34*d^4 + 21906*A*B^2*a^16*b^32*d^4 + 69720*A*B^2*a^18*b^30*d^4 + 95744*A*B^2*a^20*b^28*

d^4 + 43008*A*B^2*a^22*b^26*d^4 - 180*A^2*B*a^13*b^35*d^4 + 4486*A^2*B*a^15*b^33*d^4 + 52154*A^2*B*a^17*b^31*d

^4 + 93568*A^2*B*a^19*b^29*d^4 + 46080*A^2*B*a^21*b^27*d^4))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A

^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2) + (274877906944*(300*A^4*a^12*b^36*d^4

+ 2360*A^4*a^14*b^34*d^4 + 149228*A^4*a^16*b^32*d^4 + 307152*A^4*a^18*b^30*d^4 + 164352*A^4*a^20*b^28*d^4 + 4

096*A^4*a^22*b^26*d^4 + 484*B^4*a^12*b^36*d^4 + 328*B^4*a^14*b^34*d^4 + 2308*B^4*a^16*b^32*d^4 - 16048*B^4*a^1

8*b^30*d^4 - 43008*B^4*a^20*b^28*d^4 - 24576*B^4*a^22*b^26*d^4 + 7880*A*B^3*a^13*b^35*d^4 + 28592*A*B^3*a^15*b

^33*d^4 - 55832*A*B^3*a^17*b^31*d^4 - 100672*A*B^3*a^19*b^29*d^4 + 57344*A*B^3*a^21*b^27*d^4 + 81920*A*B^3*a^2

3*b^25*d^4 - 5880*A^3*B*a^13*b^35*d^4 + 47408*A^3*B*a^15*b^33*d^4 + 569576*A^3*B*a^17*b^31*d^4 + 1004928*A^3*B

*a^19*b^29*d^4 + 489472*A^3*B*a^21*b^27*d^4 - 320*A^2*B^2*a^12*b^36*d^4 + 1264*A^2*B^2*a^14*b^34*d^4 - 27264*A

^2*B^2*a^16*b^32*d^4 + 294128*A^2*B^2*a^18*b^30*d^4 + 711168*A^2*B^2*a^20*b^28*d^4 + 389120*A^2*B^2*a^22*b^26*

d^4))/d^8 - (274877906944*tan(c + d*x)*(300*A^4*a^12*b^37*d^4 - 6920*A^4*a^14*b^35*d^4 + 738524*A^4*a^16*b^33*

d^4 + 1819680*A^4*a^18*b^31*d^4 + 1384960*A^4*a^20*b^29*d^4 + 311296*A^4*a^22*b^27*d^4 + 484*B^4*a^12*b^37*d^4

- 5368*B^4*a^14*b^35*d^4 + 1236*B^4*a^16*b^33*d^4 - 88064*B^4*a^18*b^31*d^4 - 205824*B^4*a^20*b^29*d^4 - 1105

92*B^4*a^22*b^27*d^4 + 11192*A*B^3*a^13*b^36*d^4 + 45712*A*B^3*a^15*b^34*d^4 - 394344*A*B^3*a^17*b^32*d^4 - 59

9296*A*B^3*a^19*b^30*d^4 + 124928*A*B^3*a^21*b^28*d^4 + 294912*A*B^3*a^23*b^26*d^4 - 8680*A^3*B*a^13*b^36*d^4

+ 163152*A^3*B*a^15*b^34*d^4 + 2287096*A^3*B*a^17*b^32*d^4 + 4405760*A^3*B*a^19*b^30*d^4 + 2617344*A^3*B*a^21*

b^28*d^4 + 327680*A^3*B*a^23*b^26*d^4 - 320*A^2*B^2*a^12*b^37*d^4 + 23984*A^2*B^2*a^14*b^35*d^4 - 212608*A^2*B

^2*a^16*b^33*d^4 + 865008*A^2*B^2*a^18*b^31*d^4 + 2561024*A^2*B^2*a^20*b^29*d^4 + 1523712*A^2*B^2*a^22*b^27*d^

4 + 65536*A^2*B^2*a^24*b^25*d^4))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) - (2199023255552*tan(c + d*x

)^(1/2)*(3641*A^5*a^18*b^31*d^2 - 55*A^5*a^16*b^33*d^2 - 960*A^5*a^14*b^35*d^2 + 2864*A^5*a^20*b^29*d^2 + 128*

A^5*a^22*b^27*d^2 + 39*B^5*a^13*b^36*d^2 - 341*B^5*a^15*b^34*d^2 - 2362*B^5*a^17*b^32*d^2 - 6942*B^5*a^19*b^30

*d^2 - 8544*B^5*a^21*b^28*d^2 - 3584*B^5*a^23*b^26*d^2 - 1045*A*B^4*a^14*b^35*d^2 - 8795*A*B^4*a^16*b^33*d^2 -

26838*A*B^4*a^18*b^31*d^2 - 24592*A*B^4*a^20*b^29*d^2 + 2688*A*B^4*a^22*b^27*d^2 + 8192*A*B^4*a^24*b^25*d^2 -

120*A^4*B*a^13*b^36*d^2 + 4977*A^4*B*a^15*b^34*d^2 + 33597*A^4*B*a^17*b^32*d^2 + 55284*A^4*B*a^19*b^30*d^2 +

27296*A^4*B*a^21*b^28*d^2 + 512*A^4*B*a^23*b^26*d^2 + 159*A^2*B^3*a^13*b^36*d^2 - 4656*A^2*B^3*a^15*b^34*d^2 -

11277*A^2*B^3*a^17*b^32*d^2 + 28418*A^2*B^3*a^19*b^30*d^2 + 74816*A^2*B^3*a^21*b^28*d^2 + 39936*A^2*B^3*a^23*

b^26*d^2 - 133*A^3*B^2*a^14*b^35*d^2 + 16550*A^3*B^2*a^16*b^33*d^2 + 86411*A^3*B^2*a^18*b^31*d^2 + 127328*A^3*

B^2*a^20*b^29*d^2 + 57600*A^3*B^2*a^22*b^27*d^2))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*a*1i + A

^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2) - (274877906944*(25*A^6*a^12*b^37*d^2 + 430*A^6*a

^14*b^35*d^2 + 25905*A^6*a^16*b^33*d^2 + 68220*A^6*a^18*b^31*d^2 + 59424*A^6*a^20*b^29*d^2 + 16640*A^6*a^22*b^

27*d^2 - 72*B^6*a^12*b^37*d^2 - 679*B^6*a^14*b^35*d^2 - 3030*B^6*a^16*b^33*d^2 - 2263*B^6*a^18*b^31*d^2 + 6544

*B^6*a^20*b^29*d^2 + 10496*B^6*a^22*b^27*d^2 + 4096*B^6*a^24*b^25*d^2 - 1794*A*B^5*a^13*b^36*d^2 - 12040*A*B^5

*a^15*b^34*d^2 - 12202*A*B^5*a^17*b^32*d^2 + 19804*A*B^5*a^19*b^30*d^2 + 35200*A*B^5*a^21*b^28*d^2 + 13312*A*B

^5*a^23*b^26*d^2 - 770*A^5*B*a^13*b^36*d^2 + 21168*A^5*B*a^15*b^34*d^2 + 119398*A^5*B*a^17*b^32*d^2 + 194292*A

^5*B*a^19*b^30*d^2 + 114560*A^5*B*a^21*b^28*d^2 + 17408*A^5*B*a^23*b^26*d^2 - 23*A^2*B^4*a^12*b^37*d^2 - 6472*

A^2*B^4*a^14*b^35*d^2 - 7211*A^2*B^4*a^16*b^33*d^2 + 32614*A^2*B^4*a^18*b^31*d^2 + 79616*A^2*B^4*a^20*b^29*d^2

+ 70400*A^2*B^4*a^22*b^27*d^2 + 24576*A^2*B^4*a^24*b^25*d^2 - 580*A^3*B^3*a^13*b^36*d^2 + 5928*A^3*B^3*a^15*b

^34*d^2 + 92604*A^3*B^3*a^17*b^32*d^2 + 267280*A^3*B^3*a^19*b^30*d^2 + 293120*A^3*B^3*a^21*b^28*d^2 + 112640*A

^3*B^3*a^23*b^26*d^2 + 10*A^4*B^2*a^12*b^37*d^2 + 10653*A^4*B^2*a^14*b^35*d^2 + 123388*A^4*B^2*a^16*b^33*d^2 +

361289*A^4*B^2*a^18*b^31*d^2 + 408400*A^4*B^2*a^20*b^29*d^2 + 164608*A^4*B^2*a^22*b^27*d^2 + 4096*A^4*B^2*a^2

4*b^25*d^2))/d^8 + (274877906944*tan(c + d*x)*(25*A^6*a^12*b^38*d^2 - 470*A^6*a^14*b^36*d^2 + 168905*A^6*a^16*

b^34*d^2 + 541176*A^6*a^18*b^32*d^2 + 579072*A^6*a^20*b^30*d^2 + 211456*A^6*a^22*b^28*d^2 + 4096*A^6*a^24*b^26

*d^2 - 72*B^6*a^12*b^38*d^2 - 355*B^6*a^14*b^36*d^2 - 3534*B^6*a^16*b^34*d^2 + 9181*B^6*a^18*b^32*d^2 + 43936*

B^6*a^20*b^30*d^2 + 47872*B^6*a^22*b^28*d^2 + 16384*B^6*a^24*b^26*d^2 - 2494*A*B^5*a^13*b^37*d^2 - 20820*A*B^5

*a^15*b^35*d^2 + 15026*A*B^5*a^17*b^33*d^2 + 134984*A*B^5*a^19*b^31*d^2 + 156800*A*B^5*a^21*b^29*d^2 + 55296*A

*B^5*a^23*b^27*d^2 - 1150*A^5*B*a^13*b^37*d^2 + 82036*A^5*B*a^15*b^35*d^2 + 614690*A^5*B*a^17*b^33*d^2 + 14325

60*A^5*B*a^19*b^31*d^2 + 1361536*A^5*B*a^21*b^29*d^2 + 460800*A^5*B*a^23*b^27*d^2 - 23*A^2*B^4*a^12*b^38*d^2 -

15620*A^2*B^4*a^14*b^36*d^2 - 11843*A^2*B^4*a^16*b^34*d^2 + 95626*A^2*B^4*a^18*b^32*d^2 + 210240*A^2*B^4*a^20

*b^30*d^2 + 155648*A^2*B^4*a^22*b^28*d^2 + 36864*A^2*B^4*a^24*b^26*d^2 - 764*A^3*B^3*a^13*b^37*d^2 - 21056*A^3

*B^3*a^15*b^35*d^2 + 145044*A^3*B^3*a^17*b^33*d^2 + 566296*A^3*B^3*a^19*b^31*d^2 + 667904*A^3*B^3*a^21*b^29*d^

2 + 331776*A^3*B^3*a^23*b^27*d^2 + 65536*A^3*B^3*a^25*b^25*d^2 + 10*A^4*B^2*a^12*b^38*d^2 + 19097*A^4*B^2*a^14

*b^36*d^2 + 326196*A^4*B^2*a^16*b^34*d^2 + 1062069*A^4*B^2*a^18*b^32*d^2 + 1527456*A^4*B^2*a^20*b^30*d^2 + 109

1328*A^4*B^2*a^22*b^28*d^2 + 319488*A^4*B^2*a^24*b^26*d^2))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) +

(2199023255552*tan(c + d*x)^(1/2)*(85*A^7*a^16*b^34 - 65*A^7*a^14*b^36 + 729*A^7*a^18*b^32 + 947*A^7*a^20*b^30

+ 368*A^7*a^22*b^28 - 3*B^7*a^13*b^37 + 36*B^7*a^15*b^35 + 374*B^7*a^17*b^33 + 1363*B^7*a^19*b^31 + 2276*B^7*

a^21*b^29 + 1760*B^7*a^23*b^27 + 512*B^7*a^25*b^25 - 25*A^2*B^5*a^13*b^37 + 818*A^2*B^5*a^15*b^35 + 5373*A^2*B

^5*a^17*b^33 + 12178*A^2*B^5*a^19*b^31 + 12640*A^2*B^5*a^21*b^29 + 6016*A^2*B^5*a^23*b^27 + 1024*A^2*B^5*a^25*

b^25 + 89*A^3*B^4*a^14*b^36 + 2278*A^3*B^4*a^16*b^34 + 10563*A^3*B^4*a^18*b^32 + 18982*A^3*B^4*a^20*b^30 + 149

60*A^3*B^4*a^22*b^28 + 4352*A^3*B^4*a^24*b^26 - 37*A^4*B^3*a^13*b^37 + 1507*A^4*B^3*a^15*b^35 + 9606*A^4*B^3*a

^17*b^33 + 20274*A^4*B^3*a^19*b^31 + 18452*A^4*B^3*a^21*b^29 + 6752*A^4*B^3*a^23*b^27 + 512*A^4*B^3*a^25*b^25

- 45*A^5*B^2*a^14*b^36 + 1265*A^5*B^2*a^16*b^34 + 6366*A^5*B^2*a^18*b^32 + 10912*A^5*B^2*a^20*b^30 + 8032*A^5*

B^2*a^22*b^28 + 2176*A^5*B^2*a^24*b^26 + 69*A*B^6*a^14*b^36 + 1098*A*B^6*a^16*b^34 + 4926*A*B^6*a^18*b^32 + 90

17*A*B^6*a^20*b^30 + 7296*A*B^6*a^22*b^28 + 2176*A*B^6*a^24*b^26 - 15*A^6*B*a^13*b^37 + 725*A^6*B*a^15*b^35 +

4607*A^6*B*a^17*b^33 + 9459*A^6*B*a^19*b^31 + 8088*A^6*B*a^21*b^29 + 2496*A^6*B*a^23*b^27))/(d^7*((a + b*tan(c

+ d*x))^(1/2) - a^(1/2))))*((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2) + (((A^

2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2)*((((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b

+ 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2)*((((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(

1/2)*((((274877906944*(1600*a^12*b^34*d^8 - 16640*a^14*b^32*d^8 + 22784*a^16*b^30*d^8 + 106496*a^18*b^28*d^8 +

65536*a^20*b^26*d^8))/d^8 - (274877906944*tan(c + d*x)*(1600*a^12*b^35*d^8 - 48000*a^14*b^33*d^8 + 155136*a^1

6*b^31*d^8 + 466944*a^18*b^29*d^8 + 262144*a^20*b^27*d^8))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2))*((A

^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2) + (2199023255552*tan(c + d*x)^(1/2)*(2

048*A*a^20*b^27*d^6 - 12536*A*a^16*b^31*d^6 - 3328*A*a^18*b^29*d^6 - 7160*A*a^14*b^33*d^6 + 240*B*a^13*b^34*d^

6 - 720*B*a^15*b^32*d^6 + 5696*B*a^17*b^30*d^6 + 14848*B*a^19*b^28*d^6 + 8192*B*a^21*b^26*d^6))/(d^7*((a + b*t

an(c + d*x))^(1/2) - a^(1/2))))*((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2) - (

274877906944*(1200*A^2*a^12*b^35*d^6 - 1600*A^2*a^14*b^33*d^6 + 272464*A^2*a^16*b^31*d^6 + 573952*A^2*a^18*b^2

9*d^6 + 299008*A^2*a^20*b^27*d^6 - 1440*B^2*a^12*b^35*d^6 + 8352*B^2*a^14*b^33*d^6 - 320*B^2*a^16*b^31*d^6 + 2

6880*B^2*a^18*b^29*d^6 + 102400*B^2*a^20*b^27*d^6 + 65536*B^2*a^22*b^25*d^6 - 11200*A*B*a^13*b^34*d^6 - 25856*

A*B*a^15*b^32*d^6 + 303168*A*B*a^17*b^30*d^6 + 661504*A*B*a^19*b^28*d^6 + 344064*A*B*a^21*b^26*d^6))/d^8 + (27

4877906944*tan(c + d*x)*(1200*A^2*a^12*b^36*d^6 - 32160*A^2*a^14*b^34*d^6 + 1125488*A^2*a^16*b^32*d^6 + 244531

2*A^2*a^18*b^30*d^6 + 1351680*A^2*a^20*b^28*d^6 + 65536*A^2*a^22*b^26*d^6 - 1440*B^2*a^12*b^36*d^6 + 32256*B^2

*a^14*b^34*d^6 - 41440*B^2*a^16*b^32*d^6 + 68096*B^2*a^18*b^30*d^6 + 405504*B^2*a^20*b^28*d^6 + 262144*B^2*a^2

2*b^26*d^6 - 16320*A*B*a^13*b^35*d^6 - 34112*A*B*a^15*b^33*d^6 + 1294592*A*B*a^17*b^31*d^6 + 2656256*A*B*a^19*

b^29*d^6 + 1343488*A*B*a^21*b^27*d^6))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) - (2199023255552*tan(c

+ d*x)^(1/2)*(7600*A^3*a^18*b^30*d^4 - 3902*A^3*a^16*b^32*d^4 - 4590*A^3*a^14*b^34*d^4 + 6912*A^3*a^20*b^28*d^

4 - 168*B^3*a^13*b^35*d^4 + 982*B^3*a^15*b^33*d^4 + 2494*B^3*a^17*b^31*d^4 + 9024*B^3*a^19*b^29*d^4 + 15872*B^

3*a^21*b^27*d^4 + 8192*B^3*a^23*b^25*d^4 + 4922*A*B^2*a^14*b^34*d^4 + 21906*A*B^2*a^16*b^32*d^4 + 69720*A*B^2*

a^18*b^30*d^4 + 95744*A*B^2*a^20*b^28*d^4 + 43008*A*B^2*a^22*b^26*d^4 - 180*A^2*B*a^13*b^35*d^4 + 4486*A^2*B*a

^15*b^33*d^4 + 52154*A^2*B*a^17*b^31*d^4 + 93568*A^2*B*a^19*b^29*d^4 + 46080*A^2*B*a^21*b^27*d^4))/(d^7*((a +

b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2)

+ (274877906944*(300*A^4*a^12*b^36*d^4 + 2360*A^4*a^14*b^34*d^4 + 149228*A^4*a^16*b^32*d^4 + 307152*A^4*a^18*b

^30*d^4 + 164352*A^4*a^20*b^28*d^4 + 4096*A^4*a^22*b^26*d^4 + 484*B^4*a^12*b^36*d^4 + 328*B^4*a^14*b^34*d^4 +

2308*B^4*a^16*b^32*d^4 - 16048*B^4*a^18*b^30*d^4 - 43008*B^4*a^20*b^28*d^4 - 24576*B^4*a^22*b^26*d^4 + 7880*A*

B^3*a^13*b^35*d^4 + 28592*A*B^3*a^15*b^33*d^4 - 55832*A*B^3*a^17*b^31*d^4 - 100672*A*B^3*a^19*b^29*d^4 + 57344

*A*B^3*a^21*b^27*d^4 + 81920*A*B^3*a^23*b^25*d^4 - 5880*A^3*B*a^13*b^35*d^4 + 47408*A^3*B*a^15*b^33*d^4 + 5695

76*A^3*B*a^17*b^31*d^4 + 1004928*A^3*B*a^19*b^29*d^4 + 489472*A^3*B*a^21*b^27*d^4 - 320*A^2*B^2*a^12*b^36*d^4

+ 1264*A^2*B^2*a^14*b^34*d^4 - 27264*A^2*B^2*a^16*b^32*d^4 + 294128*A^2*B^2*a^18*b^30*d^4 + 711168*A^2*B^2*a^2

0*b^28*d^4 + 389120*A^2*B^2*a^22*b^26*d^4))/d^8 - (274877906944*tan(c + d*x)*(300*A^4*a^12*b^37*d^4 - 6920*A^4

*a^14*b^35*d^4 + 738524*A^4*a^16*b^33*d^4 + 1819680*A^4*a^18*b^31*d^4 + 1384960*A^4*a^20*b^29*d^4 + 311296*A^4

*a^22*b^27*d^4 + 484*B^4*a^12*b^37*d^4 - 5368*B^4*a^14*b^35*d^4 + 1236*B^4*a^16*b^33*d^4 - 88064*B^4*a^18*b^31

*d^4 - 205824*B^4*a^20*b^29*d^4 - 110592*B^4*a^22*b^27*d^4 + 11192*A*B^3*a^13*b^36*d^4 + 45712*A*B^3*a^15*b^34

*d^4 - 394344*A*B^3*a^17*b^32*d^4 - 599296*A*B^3*a^19*b^30*d^4 + 124928*A*B^3*a^21*b^28*d^4 + 294912*A*B^3*a^2

3*b^26*d^4 - 8680*A^3*B*a^13*b^36*d^4 + 163152*A^3*B*a^15*b^34*d^4 + 2287096*A^3*B*a^17*b^32*d^4 + 4405760*A^3

*B*a^19*b^30*d^4 + 2617344*A^3*B*a^21*b^28*d^4 + 327680*A^3*B*a^23*b^26*d^4 - 320*A^2*B^2*a^12*b^37*d^4 + 2398

4*A^2*B^2*a^14*b^35*d^4 - 212608*A^2*B^2*a^16*b^33*d^4 + 865008*A^2*B^2*a^18*b^31*d^4 + 2561024*A^2*B^2*a^20*b

^29*d^4 + 1523712*A^2*B^2*a^22*b^27*d^4 + 65536*A^2*B^2*a^24*b^25*d^4))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(

1/2))^2)) + (2199023255552*tan(c + d*x)^(1/2)*(3641*A^5*a^18*b^31*d^2 - 55*A^5*a^16*b^33*d^2 - 960*A^5*a^14*b^

35*d^2 + 2864*A^5*a^20*b^29*d^2 + 128*A^5*a^22*b^27*d^2 + 39*B^5*a^13*b^36*d^2 - 341*B^5*a^15*b^34*d^2 - 2362*

B^5*a^17*b^32*d^2 - 6942*B^5*a^19*b^30*d^2 - 8544*B^5*a^21*b^28*d^2 - 3584*B^5*a^23*b^26*d^2 - 1045*A*B^4*a^14

*b^35*d^2 - 8795*A*B^4*a^16*b^33*d^2 - 26838*A*B^4*a^18*b^31*d^2 - 24592*A*B^4*a^20*b^29*d^2 + 2688*A*B^4*a^22

*b^27*d^2 + 8192*A*B^4*a^24*b^25*d^2 - 120*A^4*B*a^13*b^36*d^2 + 4977*A^4*B*a^15*b^34*d^2 + 33597*A^4*B*a^17*b

^32*d^2 + 55284*A^4*B*a^19*b^30*d^2 + 27296*A^4*B*a^21*b^28*d^2 + 512*A^4*B*a^23*b^26*d^2 + 159*A^2*B^3*a^13*b

^36*d^2 - 4656*A^2*B^3*a^15*b^34*d^2 - 11277*A^2*B^3*a^17*b^32*d^2 + 28418*A^2*B^3*a^19*b^30*d^2 + 74816*A^2*B

^3*a^21*b^28*d^2 + 39936*A^2*B^3*a^23*b^26*d^2 - 133*A^3*B^2*a^14*b^35*d^2 + 16550*A^3*B^2*a^16*b^33*d^2 + 864

11*A^3*B^2*a^18*b^31*d^2 + 127328*A^3*B^2*a^20*b^29*d^2 + 57600*A^3*B^2*a^22*b^27*d^2))/(d^7*((a + b*tan(c + d

*x))^(1/2) - a^(1/2))))*((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))^(1/2) - (27487790

6944*(25*A^6*a^12*b^37*d^2 + 430*A^6*a^14*b^35*d^2 + 25905*A^6*a^16*b^33*d^2 + 68220*A^6*a^18*b^31*d^2 + 59424

*A^6*a^20*b^29*d^2 + 16640*A^6*a^22*b^27*d^2 - 72*B^6*a^12*b^37*d^2 - 679*B^6*a^14*b^35*d^2 - 3030*B^6*a^16*b^

33*d^2 - 2263*B^6*a^18*b^31*d^2 + 6544*B^6*a^20*b^29*d^2 + 10496*B^6*a^22*b^27*d^2 + 4096*B^6*a^24*b^25*d^2 -

1794*A*B^5*a^13*b^36*d^2 - 12040*A*B^5*a^15*b^34*d^2 - 12202*A*B^5*a^17*b^32*d^2 + 19804*A*B^5*a^19*b^30*d^2 +

35200*A*B^5*a^21*b^28*d^2 + 13312*A*B^5*a^23*b^26*d^2 - 770*A^5*B*a^13*b^36*d^2 + 21168*A^5*B*a^15*b^34*d^2 +

119398*A^5*B*a^17*b^32*d^2 + 194292*A^5*B*a^19*b^30*d^2 + 114560*A^5*B*a^21*b^28*d^2 + 17408*A^5*B*a^23*b^26*

d^2 - 23*A^2*B^4*a^12*b^37*d^2 - 6472*A^2*B^4*a^14*b^35*d^2 - 7211*A^2*B^4*a^16*b^33*d^2 + 32614*A^2*B^4*a^18*

b^31*d^2 + 79616*A^2*B^4*a^20*b^29*d^2 + 70400*A^2*B^4*a^22*b^27*d^2 + 24576*A^2*B^4*a^24*b^25*d^2 - 580*A^3*B

^3*a^13*b^36*d^2 + 5928*A^3*B^3*a^15*b^34*d^2 + 92604*A^3*B^3*a^17*b^32*d^2 + 267280*A^3*B^3*a^19*b^30*d^2 + 2

93120*A^3*B^3*a^21*b^28*d^2 + 112640*A^3*B^3*a^23*b^26*d^2 + 10*A^4*B^2*a^12*b^37*d^2 + 10653*A^4*B^2*a^14*b^3

5*d^2 + 123388*A^4*B^2*a^16*b^33*d^2 + 361289*A^4*B^2*a^18*b^31*d^2 + 408400*A^4*B^2*a^20*b^29*d^2 + 164608*A^

4*B^2*a^22*b^27*d^2 + 4096*A^4*B^2*a^24*b^25*d^2))/d^8 + (274877906944*tan(c + d*x)*(25*A^6*a^12*b^38*d^2 - 47

0*A^6*a^14*b^36*d^2 + 168905*A^6*a^16*b^34*d^2 + 541176*A^6*a^18*b^32*d^2 + 579072*A^6*a^20*b^30*d^2 + 211456*

A^6*a^22*b^28*d^2 + 4096*A^6*a^24*b^26*d^2 - 72*B^6*a^12*b^38*d^2 - 355*B^6*a^14*b^36*d^2 - 3534*B^6*a^16*b^34

*d^2 + 9181*B^6*a^18*b^32*d^2 + 43936*B^6*a^20*b^30*d^2 + 47872*B^6*a^22*b^28*d^2 + 16384*B^6*a^24*b^26*d^2 -

2494*A*B^5*a^13*b^37*d^2 - 20820*A*B^5*a^15*b^35*d^2 + 15026*A*B^5*a^17*b^33*d^2 + 134984*A*B^5*a^19*b^31*d^2

+ 156800*A*B^5*a^21*b^29*d^2 + 55296*A*B^5*a^23*b^27*d^2 - 1150*A^5*B*a^13*b^37*d^2 + 82036*A^5*B*a^15*b^35*d^

2 + 614690*A^5*B*a^17*b^33*d^2 + 1432560*A^5*B*a^19*b^31*d^2 + 1361536*A^5*B*a^21*b^29*d^2 + 460800*A^5*B*a^23

*b^27*d^2 - 23*A^2*B^4*a^12*b^38*d^2 - 15620*A^2*B^4*a^14*b^36*d^2 - 11843*A^2*B^4*a^16*b^34*d^2 + 95626*A^2*B

^4*a^18*b^32*d^2 + 210240*A^2*B^4*a^20*b^30*d^2 + 155648*A^2*B^4*a^22*b^28*d^2 + 36864*A^2*B^4*a^24*b^26*d^2 -

764*A^3*B^3*a^13*b^37*d^2 - 21056*A^3*B^3*a^15*b^35*d^2 + 145044*A^3*B^3*a^17*b^33*d^2 + 566296*A^3*B^3*a^19*

b^31*d^2 + 667904*A^3*B^3*a^21*b^29*d^2 + 331776*A^3*B^3*a^23*b^27*d^2 + 65536*A^3*B^3*a^25*b^25*d^2 + 10*A^4*

B^2*a^12*b^38*d^2 + 19097*A^4*B^2*a^14*b^36*d^2 + 326196*A^4*B^2*a^16*b^34*d^2 + 1062069*A^4*B^2*a^18*b^32*d^2

+ 1527456*A^4*B^2*a^20*b^30*d^2 + 1091328*A^4*B^2*a^22*b^28*d^2 + 319488*A^4*B^2*a^24*b^26*d^2))/(d^8*((a + b

*tan(c + d*x))^(1/2) - a^(1/2))^2)) - (2199023255552*tan(c + d*x)^(1/2)*(85*A^7*a^16*b^34 - 65*A^7*a^14*b^36 +

729*A^7*a^18*b^32 + 947*A^7*a^20*b^30 + 368*A^7*a^22*b^28 - 3*B^7*a^13*b^37 + 36*B^7*a^15*b^35 + 374*B^7*a^17

*b^33 + 1363*B^7*a^19*b^31 + 2276*B^7*a^21*b^29 + 1760*B^7*a^23*b^27 + 512*B^7*a^25*b^25 - 25*A^2*B^5*a^13*b^3

7 + 818*A^2*B^5*a^15*b^35 + 5373*A^2*B^5*a^17*b^33 + 12178*A^2*B^5*a^19*b^31 + 12640*A^2*B^5*a^21*b^29 + 6016*

A^2*B^5*a^23*b^27 + 1024*A^2*B^5*a^25*b^25 + 89*A^3*B^4*a^14*b^36 + 2278*A^3*B^4*a^16*b^34 + 10563*A^3*B^4*a^1

8*b^32 + 18982*A^3*B^4*a^20*b^30 + 14960*A^3*B^4*a^22*b^28 + 4352*A^3*B^4*a^24*b^26 - 37*A^4*B^3*a^13*b^37 + 1

507*A^4*B^3*a^15*b^35 + 9606*A^4*B^3*a^17*b^33 + 20274*A^4*B^3*a^19*b^31 + 18452*A^4*B^3*a^21*b^29 + 6752*A^4*

B^3*a^23*b^27 + 512*A^4*B^3*a^25*b^25 - 45*A^5*B^2*a^14*b^36 + 1265*A^5*B^2*a^16*b^34 + 6366*A^5*B^2*a^18*b^32

+ 10912*A^5*B^2*a^20*b^30 + 8032*A^5*B^2*a^22*b^28 + 2176*A^5*B^2*a^24*b^26 + 69*A*B^6*a^14*b^36 + 1098*A*B^6

*a^16*b^34 + 4926*A*B^6*a^18*b^32 + 9017*A*B^6*a^20*b^30 + 7296*A*B^6*a^22*b^28 + 2176*A*B^6*a^24*b^26 - 15*A^

6*B*a^13*b^37 + 725*A^6*B*a^15*b^35 + 4607*A^6*B*a^17*b^33 + 9459*A^6*B*a^19*b^31 + 8088*A^6*B*a^21*b^29 + 249

6*A^6*B*a^23*b^27))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*

B*a - A*B*b*2i)/(4*d^2))^(1/2) + (549755813888*(1140*A^8*a^16*b^34 + 3560*A^8*a^18*b^32 + 3700*A^8*a^20*b^30 +

1280*A^8*a^22*b^28 + 4*B^8*a^12*b^38 + 84*B^8*a^14*b^36 + 545*B^8*a^16*b^34 + 1462*B^8*a^18*b^32 + 1861*B^8*a

^20*b^30 + 1120*B^8*a^22*b^28 + 256*B^8*a^24*b^26 + 8*A^2*B^6*a^12*b^38 + 1361*A^2*B^6*a^14*b^36 + 8932*A^2*B^

6*a^16*b^34 + 23189*A^2*B^6*a^18*b^32 + 29850*A^2*B^6*a^20*b^30 + 19104*A^2*B^6*a^22*b^28 + 4864*A^2*B^6*a^24*

b^26 + 264*A^3*B^5*a^13*b^37 + 6088*A^3*B^5*a^15*b^35 + 25512*A^3*B^5*a^17*b^33 + 44696*A^3*B^5*a^19*b^31 + 37

936*A^3*B^5*a^21*b^29 + 14976*A^3*B^5*a^23*b^27 + 2048*A^3*B^5*a^25*b^25 + 4*A^4*B^4*a^12*b^38 + 2470*A^4*B^4*

a^14*b^36 + 17369*A^4*B^4*a^16*b^34 + 45552*A^4*B^4*a^18*b^32 + 57817*A^4*B^4*a^20*b^30 + 36128*A^4*B^4*a^22*b

^28 + 8960*A^4*B^4*a^24*b^26 + 132*A^5*B^3*a^13*b^37 + 7310*A^5*B^3*a^15*b^35 + 32796*A^5*B^3*a^17*b^33 + 5750

2*A^5*B^3*a^19*b^31 + 46220*A^5*B^3*a^21*b^29 + 15360*A^5*B^3*a^23*b^27 + 1024*A^5*B^3*a^25*b^25 + 1193*A^6*B^

2*a^14*b^36 + 10122*A^6*B^2*a^16*b^34 + 27385*A^6*B^2*a^18*b^32 + 33528*A^6*B^2*a^20*b^30 + 19424*A^6*B^2*a^22

*b^28 + 4352*A^6*B^2*a^24*b^26 + 132*A*B^7*a^13*b^37 + 1622*A*B^7*a^15*b^35 + 6076*A*B^7*a^17*b^33 + 10630*A*B

^7*a^19*b^31 + 9884*A*B^7*a^21*b^29 + 4864*A*B^7*a^23*b^27 + 1024*A*B^7*a^25*b^25 + 2844*A^7*B*a^15*b^35 + 133

60*A^7*B*a^17*b^33 + 23436*A^7*B*a^19*b^31 + 18168*A^7*B*a^21*b^29 + 5248*A^7*B*a^23*b^27))/d^8 - (54975581388

8*tan(c + d*x)*(12996*A^8*a^16*b^35 + 55176*A^8*a^18*b^33 + 87748*A^8*a^20*b^31 + 61952*A^8*a^22*b^29 + 16384*

A^8*a^24*b^27 + 4*B^8*a^12*b^39 + 108*B^8*a^14*b^37 + 893*B^8*a^16*b^35 + 2278*B^8*a^18*b^33 + 2545*B^8*a^20*b

^31 + 1312*B^8*a^22*b^29 + 256*B^8*a^24*b^27 + 8*A^2*B^6*a^12*b^39 + 2697*A^2*B^6*a^14*b^37 + 20880*A^2*B^6*a^

16*b^35 + 58853*A^2*B^6*a^18*b^33 + 81686*A^2*B^6*a^20*b^31 + 60992*A^2*B^6*a^22*b^29 + 24064*A^2*B^6*a^24*b^2

7 + 4096*A^2*B^6*a^26*b^25 + 360*A^3*B^5*a^13*b^38 + 16184*A^3*B^5*a^15*b^36 + 75064*A^3*B^5*a^17*b^34 + 15216

8*A^3*B^5*a^19*b^32 + 162560*A^3*B^5*a^21*b^30 + 90112*A^3*B^5*a^23*b^28 + 20480*A^3*B^5*a^25*b^26 + 4*A^4*B^4

*a^12*b^39 + 5070*A^4*B^4*a^14*b^37 + 52077*A^4*B^4*a^16*b^35 + 166048*A^4*B^4*a^18*b^33 + 243485*A^4*B^4*a^20

*b^31 + 180000*A^4*B^4*a^22*b^29 + 63744*A^4*B^4*a^24*b^27 + 8192*A^4*B^4*a^26*b^25 + 180*A^5*B^3*a^13*b^38 +

23482*A^5*B^3*a^15*b^36 + 115688*A^5*B^3*a^17*b^34 + 241906*A^5*B^3*a^19*b^32 + 264592*A^5*B^3*a^21*b^30 + 149

888*A^5*B^3*a^23*b^28 + 34816*A^5*B^3*a^25*b^26 + 2481*A^6*B^2*a^14*b^37 + 45086*A^6*B^2*a^16*b^35 + 164649*A^

6*B^2*a^18*b^33 + 252092*A^6*B^2*a^20*b^31 + 182272*A^6*B^2*a^22*b^29 + 56320*A^6*B^2*a^24*b^27 + 4096*A^6*B^2

*a^26*b^25 + 180*A*B^7*a^13*b^38 + 2962*A*B^7*a^15*b^36 + 11480*A*B^7*a^17*b^34 + 20810*A*B^7*a^19*b^32 + 2017

6*A*B^7*a^21*b^30 + 10112*A*B^7*a^23*b^28 + 2048*A*B^7*a^25*b^26 + 10260*A^7*B*a^15*b^36 + 52104*A^7*B*a^17*b^

34 + 110548*A^7*B*a^19*b^32 + 122208*A^7*B*a^21*b^30 + 69888*A^7*B*a^23*b^28 + 16384*A^7*B*a^25*b^26))/(d^8*((

a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)))*((A^2*a*1i + A^2*b - B^2*a*1i - B^2*b + 2*A*B*a - A*B*b*2i)/(4*d^2))

^(1/2)*2i - (atan(-(((2*A*b + B*a)*((((281474976710656*(15*A^7*a^16*b^36*d^2 + 3205*A^7*a^18*b^34*d^2 + 9813*A

^7*a^20*b^32*d^2 + 10135*A^7*a^22*b^30*d^2 + 3576*A^7*a^24*b^28*d^2 + 64*A^7*a^26*b^26*d^2 - 9*B^7*a^17*b^35*d

^2 - 291*B^7*a^19*b^33*d^2 - 507*B^7*a^21*b^31*d^2 + 79*B^7*a^23*b^29*d^2 + 560*B^7*a^25*b^27*d^2 + 256*B^7*a^

27*b^25*d^2 - 65*A*B^6*a^16*b^36*d^2 - 1191*A*B^6*a^18*b^34*d^2 - 1639*A*B^6*a^20*b^32*d^2 + 1187*A*B^6*a^22*b

^30*d^2 + 2852*A*B^6*a^24*b^28*d^2 + 1152*A*B^6*a^26*b^26*d^2 + 423*A^6*B*a^17*b^35*d^2 + 8837*A^6*B*a^19*b^33

*d^2 + 24869*A^6*B*a^21*b^31*d^2 + 24919*A^6*B*a^23*b^29*d^2 + 8464*A^6*B*a^25*b^27*d^2 - 939*A^2*B^5*a^17*b^3

5*d^2 - 801*A^2*B^5*a^19*b^33*d^2 + 3759*A^2*B^5*a^21*b^31*d^2 + 7701*A^2*B^5*a^23*b^29*d^2 + 5616*A^2*B^5*a^2

5*b^27*d^2 + 1536*A^2*B^5*a^27*b^25*d^2 - 51*A^3*B^4*a^16*b^36*d^2 + 231*A^3*B^4*a^18*b^34*d^2 + 7223*A^3*B^4*

a^20*b^32*d^2 + 20781*A^3*B^4*a^22*b^30*d^2 + 21072*A^3*B^4*a^24*b^28*d^2 + 7232*A^3*B^4*a^26*b^26*d^2 - 507*A

^4*B^3*a^17*b^35*d^2 + 8327*A^4*B^3*a^19*b^33*d^2 + 29135*A^4*B^3*a^21*b^31*d^2 + 32541*A^4*B^3*a^23*b^29*d^2

+ 13520*A^4*B^3*a^25*b^27*d^2 + 1280*A^4*B^3*a^27*b^25*d^2 + 29*A^5*B^2*a^16*b^36*d^2 + 4627*A^5*B^2*a^18*b^34

*d^2 + 18675*A^5*B^2*a^20*b^32*d^2 + 29729*A^5*B^2*a^22*b^30*d^2 + 21796*A^5*B^2*a^24*b^28*d^2 + 6144*A^5*B^2*

a^26*b^26*d^2))/d^9 - ((2*A*b + B*a)*(((2*A*b + B*a)*((281474976710656*(180*A^5*a^16*b^35*d^4 + 15076*A^5*a^18

*b^33*d^4 + 34540*A^5*a^20*b^31*d^4 + 24572*A^5*a^22*b^29*d^4 + 4928*A^5*a^24*b^27*d^4 - 88*B^5*a^17*b^34*d^4

+ 1056*B^5*a^19*b^32*d^4 + 840*B^5*a^21*b^30*d^4 - 1840*B^5*a^23*b^28*d^4 - 1536*B^5*a^25*b^26*d^4 + 388*A*B^4

*a^16*b^35*d^4 + 5188*A*B^4*a^18*b^33*d^4 - 1092*A*B^4*a^20*b^31*d^4 - 11076*A*B^4*a^22*b^29*d^4 - 64*A*B^4*a^

24*b^27*d^4 + 5120*A*B^4*a^26*b^25*d^4 - 760*A^4*B*a^17*b^34*d^4 + 43248*A^4*B*a^19*b^32*d^4 + 94152*A^4*B*a^2

1*b^30*d^4 + 55520*A^4*B*a^23*b^28*d^4 + 5376*A^4*B*a^25*b^26*d^4 + 3248*A^2*B^3*a^17*b^34*d^4 - 12080*A^2*B^3

*a^19*b^32*d^4 - 4464*A^2*B^3*a^21*b^30*d^4 + 40304*A^2*B^3*a^23*b^28*d^4 + 29440*A^2*B^3*a^25*b^26*d^4 - 200*

A^3*B^2*a^16*b^35*d^4 - 12312*A^3*B^2*a^18*b^33*d^4 + 30504*A^3*B^2*a^20*b^31*d^4 + 98168*A^3*B^2*a^22*b^29*d^

4 + 56576*A^3*B^2*a^24*b^27*d^4 + 1024*A^3*B^2*a^26*b^25*d^4))/d^9 + (((562949953421312*tan(c + d*x)^(1/2)*(23

448*A^4*a^18*b^33*d^4 - 300*A^4*a^16*b^35*d^4 + 57252*A^4*a^20*b^31*d^4 + 43232*A^4*a^22*b^29*d^4 + 9728*A^4*a

^24*b^27*d^4 - 108*B^4*a^16*b^35*d^4 + 1096*B^4*a^18*b^33*d^4 - 1660*B^4*a^20*b^31*d^4 - 9008*B^4*a^22*b^29*d^

4 - 8192*B^4*a^24*b^27*d^4 - 2048*B^4*a^26*b^25*d^4 - 16*A*B^3*a^17*b^34*d^4 - 23520*A*B^3*a^19*b^32*d^4 - 485

92*A*B^3*a^21*b^30*d^4 - 27136*A*B^3*a^23*b^28*d^4 - 2048*A*B^3*a^25*b^26*d^4 + 3600*A^3*B*a^17*b^34*d^4 + 648

64*A^3*B*a^19*b^32*d^4 + 128336*A^3*B*a^21*b^30*d^4 + 77312*A^3*B*a^23*b^28*d^4 + 10240*A^3*B*a^25*b^26*d^4 +

264*A^2*B^2*a^16*b^35*d^4 - 18624*A^2*B^2*a^18*b^33*d^4 - 7928*A^2*B^2*a^20*b^31*d^4 + 42192*A^2*B^2*a^22*b^29

*d^4 + 33280*A^2*B^2*a^24*b^27*d^4 + 2048*A^2*B^2*a^26*b^25*d^4))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2)))

- ((2*A*b + B*a)*((281474976710656*(720*A^3*a^16*b^34*d^6 + 25376*A^3*a^18*b^32*d^6 + 49616*A^3*a^20*b^30*d^6

+ 25984*A^3*a^22*b^28*d^6 + 1024*A^3*a^24*b^26*d^6 + 624*B^3*a^17*b^33*d^6 - 2080*B^3*a^19*b^31*d^6 - 1936*B^

3*a^21*b^29*d^6 + 4864*B^3*a^23*b^27*d^6 + 4096*B^3*a^25*b^25*d^6 - 1008*A*B^2*a^16*b^34*d^6 - 10400*A*B^2*a^1

8*b^32*d^6 + 8848*A*B^2*a^20*b^30*d^6 + 44864*A*B^2*a^22*b^28*d^6 + 26624*A*B^2*a^24*b^26*d^6 - 4304*A^2*B*a^1

7*b^33*d^6 + 35680*A^2*B*a^19*b^31*d^6 + 84272*A^2*B*a^21*b^29*d^6 + 44288*A^2*B*a^23*b^27*d^6))/d^9 - ((2*A*b

+ B*a)*((((281474976710656*(960*A*a^16*b^33*d^8 + 7040*A*a^18*b^31*d^8 + 11200*A*a^20*b^29*d^8 + 5120*A*a^22*

b^27*d^8 - 1024*B*a^17*b^32*d^8 + 2048*B*a^19*b^30*d^8 + 7168*B*a^21*b^28*d^8 + 4096*B*a^23*b^26*d^8))/d^9 + (

562949953421312*tan(c + d*x)^(1/2)*(2*A*b + B*a)*(7616*a^18*b^31*d^8 - 320*a^16*b^33*d^8 + 16128*a^20*b^29*d^8

+ 8192*a^22*b^27*d^8))/(b^(1/2)*d^9*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*(2*A*b + B*a))/(b^(1/2)*d) - (56

2949953421312*tan(c + d*x)^(1/2)*(37600*A^2*a^18*b^32*d^6 - 560*A^2*a^16*b^34*d^6 + 78608*A^2*a^20*b^30*d^6 +

42496*A^2*a^22*b^28*d^6 + 2048*A^2*a^24*b^26*d^6 + 304*B^2*a^16*b^34*d^6 - 5152*B^2*a^18*b^32*d^6 - 4944*B^2*a

^20*b^30*d^6 + 6656*B^2*a^22*b^28*d^6 + 6144*B^2*a^24*b^26*d^6 + 128*A*B*a^17*b^33*d^6 + 41600*A*B*a^19*b^31*d

^6 + 82432*A*B*a^21*b^29*d^6 + 40960*A*B*a^23*b^27*d^6))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2)))))/(b^(1/

2)*d)))/(b^(1/2)*d))*(2*A*b + B*a))/(b^(1/2)*d)))/(b^(1/2)*d) - (562949953421312*tan(c + d*x)^(1/2)*(5135*A^6*

a^18*b^34*d^2 - 65*A^6*a^16*b^36*d^2 + 16769*A^6*a^20*b^32*d^2 + 18065*A^6*a^22*b^30*d^2 + 6624*A^6*a^24*b^28*

d^2 + 128*A^6*a^26*b^26*d^2 + 17*B^6*a^16*b^36*d^2 - 59*B^6*a^18*b^34*d^2 + 903*B^6*a^20*b^32*d^2 + 3443*B^6*a

^22*b^30*d^2 + 3872*B^6*a^24*b^28*d^2 + 1408*B^6*a^26*b^26*d^2 - 20*A*B^5*a^17*b^35*d^2 + 4712*A*B^5*a^19*b^33

*d^2 + 13964*A*B^5*a^21*b^31*d^2 + 11792*A*B^5*a^23*b^29*d^2 + 512*A*B^5*a^25*b^27*d^2 - 2048*A*B^5*a^27*b^25*

d^2 + 1836*A^5*B*a^17*b^35*d^2 + 15288*A^5*B*a^19*b^33*d^2 + 39084*A^5*B*a^21*b^31*d^2 + 39968*A^5*B*a^23*b^29

*d^2 + 14336*A^5*B*a^25*b^27*d^2 - 31*A^2*B^4*a^16*b^36*d^2 + 3193*A^2*B^4*a^18*b^34*d^2 + 6351*A^2*B^4*a^20*b

^32*d^2 - 5929*A^2*B^4*a^22*b^30*d^2 - 18400*A^2*B^4*a^24*b^28*d^2 - 9344*A^2*B^4*a^26*b^26*d^2 - 1768*A^3*B^3

*a^17*b^35*d^2 - 7744*A^3*B^3*a^19*b^33*d^2 - 20232*A^3*B^3*a^21*b^31*d^2 - 22960*A^3*B^3*a^23*b^29*d^2 - 6656

*A^3*B^3*a^25*b^27*d^2 + 2048*A^3*B^3*a^27*b^25*d^2 + 15*A^4*B^2*a^16*b^36*d^2 + 3619*A^4*B^2*a^18*b^34*d^2 +

11401*A^4*B^2*a^20*b^32*d^2 + 21205*A^4*B^2*a^22*b^30*d^2 + 23264*A^4*B^2*a^24*b^28*d^2 + 9856*A^4*B^2*a^26*b^

26*d^2))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2)))))/(b^(1/2)*d))*(2*A*b + B*a))/(b^(1/2)*d) + (56294995342

1312*tan(c + d*x)^(1/2)*(5*A^8*a^16*b^37 - 376*A^8*a^18*b^35 - 1662*A^8*a^20*b^33 - 2688*A^8*a^22*b^31 - 1919*

A^8*a^24*b^29 - 512*A^8*a^26*b^27 + B^8*a^16*b^37 + 3*B^8*a^18*b^35 + 101*B^8*a^20*b^33 + 421*B^8*a^22*b^31 +

674*B^8*a^24*b^29 + 480*B^8*a^26*b^27 + 128*B^8*a^28*b^25 + 155*A^2*B^6*a^18*b^35 + 1051*A^2*B^6*a^20*b^33 + 2

373*A^2*B^6*a^22*b^31 + 2341*A^2*B^6*a^24*b^29 + 992*A^2*B^6*a^26*b^27 + 128*A^2*B^6*a^28*b^25 - 244*A^3*B^5*a

^17*b^36 - 476*A^3*B^5*a^19*b^34 + 548*A^3*B^5*a^21*b^32 + 2060*A^3*B^5*a^23*b^30 + 1792*A^3*B^5*a^25*b^28 + 5

12*A^3*B^5*a^27*b^26 + 2*A^4*B^4*a^16*b^37 - 75*A^4*B^4*a^18*b^35 + 137*A^4*B^4*a^20*b^33 + 795*A^4*B^4*a^22*b

^31 + 741*A^4*B^4*a^24*b^29 + 32*A^4*B^4*a^26*b^27 - 128*A^4*B^4*a^28*b^25 - 476*A^5*B^3*a^17*b^36 - 1912*A^5*

B^3*a^19*b^34 - 3356*A^5*B^3*a^21*b^32 - 3392*A^5*B^3*a^23*b^30 - 1984*A^5*B^3*a^25*b^28 - 512*A^5*B^3*a^27*b^

26 + 8*A^6*B^2*a^16*b^37 - 603*A^6*B^2*a^18*b^35 - 2475*A^6*B^2*a^20*b^33 - 3845*A^6*B^2*a^22*b^31 - 2845*A^6*

B^2*a^24*b^29 - 992*A^6*B^2*a^26*b^27 - 128*A^6*B^2*a^28*b^25 - 4*A*B^7*a^17*b^36 + 320*A*B^7*a^19*b^34 + 1484

*A*B^7*a^21*b^32 + 2504*A*B^7*a^23*b^30 + 1856*A*B^7*a^25*b^28 + 512*A*B^7*a^27*b^26 - 236*A^7*B*a^17*b^36 - 1

116*A^7*B*a^19*b^34 - 2420*A^7*B*a^21*b^32 - 2948*A^7*B*a^23*b^30 - 1920*A^7*B*a^25*b^28 - 512*A^7*B*a^27*b^26

))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*1i)/(b^(1/2)*d) - ((2*A*b + B*a)*((((281474976710656*(15*A^7*

a^16*b^36*d^2 + 3205*A^7*a^18*b^34*d^2 + 9813*A^7*a^20*b^32*d^2 + 10135*A^7*a^22*b^30*d^2 + 3576*A^7*a^24*b^28

*d^2 + 64*A^7*a^26*b^26*d^2 - 9*B^7*a^17*b^35*d^2 - 291*B^7*a^19*b^33*d^2 - 507*B^7*a^21*b^31*d^2 + 79*B^7*a^2

3*b^29*d^2 + 560*B^7*a^25*b^27*d^2 + 256*B^7*a^27*b^25*d^2 - 65*A*B^6*a^16*b^36*d^2 - 1191*A*B^6*a^18*b^34*d^2

- 1639*A*B^6*a^20*b^32*d^2 + 1187*A*B^6*a^22*b^30*d^2 + 2852*A*B^6*a^24*b^28*d^2 + 1152*A*B^6*a^26*b^26*d^2 +

423*A^6*B*a^17*b^35*d^2 + 8837*A^6*B*a^19*b^33*d^2 + 24869*A^6*B*a^21*b^31*d^2 + 24919*A^6*B*a^23*b^29*d^2 +

8464*A^6*B*a^25*b^27*d^2 - 939*A^2*B^5*a^17*b^35*d^2 - 801*A^2*B^5*a^19*b^33*d^2 + 3759*A^2*B^5*a^21*b^31*d^2

+ 7701*A^2*B^5*a^23*b^29*d^2 + 5616*A^2*B^5*a^25*b^27*d^2 + 1536*A^2*B^5*a^27*b^25*d^2 - 51*A^3*B^4*a^16*b^36*

d^2 + 231*A^3*B^4*a^18*b^34*d^2 + 7223*A^3*B^4*a^20*b^32*d^2 + 20781*A^3*B^4*a^22*b^30*d^2 + 21072*A^3*B^4*a^2

4*b^28*d^2 + 7232*A^3*B^4*a^26*b^26*d^2 - 507*A^4*B^3*a^17*b^35*d^2 + 8327*A^4*B^3*a^19*b^33*d^2 + 29135*A^4*B

^3*a^21*b^31*d^2 + 32541*A^4*B^3*a^23*b^29*d^2 + 13520*A^4*B^3*a^25*b^27*d^2 + 1280*A^4*B^3*a^27*b^25*d^2 + 29

*A^5*B^2*a^16*b^36*d^2 + 4627*A^5*B^2*a^18*b^34*d^2 + 18675*A^5*B^2*a^20*b^32*d^2 + 29729*A^5*B^2*a^22*b^30*d^

2 + 21796*A^5*B^2*a^24*b^28*d^2 + 6144*A^5*B^2*a^26*b^26*d^2))/d^9 - ((2*A*b + B*a)*(((2*A*b + B*a)*((28147497

6710656*(180*A^5*a^16*b^35*d^4 + 15076*A^5*a^18*b^33*d^4 + 34540*A^5*a^20*b^31*d^4 + 24572*A^5*a^22*b^29*d^4 +

4928*A^5*a^24*b^27*d^4 - 88*B^5*a^17*b^34*d^4 + 1056*B^5*a^19*b^32*d^4 + 840*B^5*a^21*b^30*d^4 - 1840*B^5*a^2

3*b^28*d^4 - 1536*B^5*a^25*b^26*d^4 + 388*A*B^4*a^16*b^35*d^4 + 5188*A*B^4*a^18*b^33*d^4 - 1092*A*B^4*a^20*b^3

1*d^4 - 11076*A*B^4*a^22*b^29*d^4 - 64*A*B^4*a^24*b^27*d^4 + 5120*A*B^4*a^26*b^25*d^4 - 760*A^4*B*a^17*b^34*d^

4 + 43248*A^4*B*a^19*b^32*d^4 + 94152*A^4*B*a^21*b^30*d^4 + 55520*A^4*B*a^23*b^28*d^4 + 5376*A^4*B*a^25*b^26*d

^4 + 3248*A^2*B^3*a^17*b^34*d^4 - 12080*A^2*B^3*a^19*b^32*d^4 - 4464*A^2*B^3*a^21*b^30*d^4 + 40304*A^2*B^3*a^2

3*b^28*d^4 + 29440*A^2*B^3*a^25*b^26*d^4 - 200*A^3*B^2*a^16*b^35*d^4 - 12312*A^3*B^2*a^18*b^33*d^4 + 30504*A^3

*B^2*a^20*b^31*d^4 + 98168*A^3*B^2*a^22*b^29*d^4 + 56576*A^3*B^2*a^24*b^27*d^4 + 1024*A^3*B^2*a^26*b^25*d^4))/

d^9 - (((562949953421312*tan(c + d*x)^(1/2)*(23448*A^4*a^18*b^33*d^4 - 300*A^4*a^16*b^35*d^4 + 57252*A^4*a^20*

b^31*d^4 + 43232*A^4*a^22*b^29*d^4 + 9728*A^4*a^24*b^27*d^4 - 108*B^4*a^16*b^35*d^4 + 1096*B^4*a^18*b^33*d^4 -

1660*B^4*a^20*b^31*d^4 - 9008*B^4*a^22*b^29*d^4 - 8192*B^4*a^24*b^27*d^4 - 2048*B^4*a^26*b^25*d^4 - 16*A*B^3*

a^17*b^34*d^4 - 23520*A*B^3*a^19*b^32*d^4 - 48592*A*B^3*a^21*b^30*d^4 - 27136*A*B^3*a^23*b^28*d^4 - 2048*A*B^3

*a^25*b^26*d^4 + 3600*A^3*B*a^17*b^34*d^4 + 64864*A^3*B*a^19*b^32*d^4 + 128336*A^3*B*a^21*b^30*d^4 + 77312*A^3

*B*a^23*b^28*d^4 + 10240*A^3*B*a^25*b^26*d^4 + 264*A^2*B^2*a^16*b^35*d^4 - 18624*A^2*B^2*a^18*b^33*d^4 - 7928*

A^2*B^2*a^20*b^31*d^4 + 42192*A^2*B^2*a^22*b^29*d^4 + 33280*A^2*B^2*a^24*b^27*d^4 + 2048*A^2*B^2*a^26*b^25*d^4

))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))) + ((2*A*b + B*a)*((281474976710656*(720*A^3*a^16*b^34*d^6 + 25

376*A^3*a^18*b^32*d^6 + 49616*A^3*a^20*b^30*d^6 + 25984*A^3*a^22*b^28*d^6 + 1024*A^3*a^24*b^26*d^6 + 624*B^3*a

^17*b^33*d^6 - 2080*B^3*a^19*b^31*d^6 - 1936*B^3*a^21*b^29*d^6 + 4864*B^3*a^23*b^27*d^6 + 4096*B^3*a^25*b^25*d

^6 - 1008*A*B^2*a^16*b^34*d^6 - 10400*A*B^2*a^18*b^32*d^6 + 8848*A*B^2*a^20*b^30*d^6 + 44864*A*B^2*a^22*b^28*d

^6 + 26624*A*B^2*a^24*b^26*d^6 - 4304*A^2*B*a^17*b^33*d^6 + 35680*A^2*B*a^19*b^31*d^6 + 84272*A^2*B*a^21*b^29*

d^6 + 44288*A^2*B*a^23*b^27*d^6))/d^9 - ((2*A*b + B*a)*((((281474976710656*(960*A*a^16*b^33*d^8 + 7040*A*a^18*

b^31*d^8 + 11200*A*a^20*b^29*d^8 + 5120*A*a^22*b^27*d^8 - 1024*B*a^17*b^32*d^8 + 2048*B*a^19*b^30*d^8 + 7168*B

*a^21*b^28*d^8 + 4096*B*a^23*b^26*d^8))/d^9 - (562949953421312*tan(c + d*x)^(1/2)*(2*A*b + B*a)*(7616*a^18*b^3

1*d^8 - 320*a^16*b^33*d^8 + 16128*a^20*b^29*d^8 + 8192*a^22*b^27*d^8))/(b^(1/2)*d^9*((a + b*tan(c + d*x))^(1/2

) - a^(1/2))))*(2*A*b + B*a))/(b^(1/2)*d) + (562949953421312*tan(c + d*x)^(1/2)*(37600*A^2*a^18*b^32*d^6 - 560

*A^2*a^16*b^34*d^6 + 78608*A^2*a^20*b^30*d^6 + 42496*A^2*a^22*b^28*d^6 + 2048*A^2*a^24*b^26*d^6 + 304*B^2*a^16

*b^34*d^6 - 5152*B^2*a^18*b^32*d^6 - 4944*B^2*a^20*b^30*d^6 + 6656*B^2*a^22*b^28*d^6 + 6144*B^2*a^24*b^26*d^6

+ 128*A*B*a^17*b^33*d^6 + 41600*A*B*a^19*b^31*d^6 + 82432*A*B*a^21*b^29*d^6 + 40960*A*B*a^23*b^27*d^6))/(d^8*(

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

(562949953421312*tan(c + d*x)^(1/2)*(5135*A^6*a^18*b^34*d^2 - 65*A^6*a^16*b^36*d^2 + 16769*A^6*a^20*b^32*d^2

+ 18065*A^6*a^22*b^30*d^2 + 6624*A^6*a^24*b^28*d^2 + 128*A^6*a^26*b^26*d^2 + 17*B^6*a^16*b^36*d^2 - 59*B^6*a^1

8*b^34*d^2 + 903*B^6*a^20*b^32*d^2 + 3443*B^6*a^22*b^30*d^2 + 3872*B^6*a^24*b^28*d^2 + 1408*B^6*a^26*b^26*d^2

- 20*A*B^5*a^17*b^35*d^2 + 4712*A*B^5*a^19*b^33*d^2 + 13964*A*B^5*a^21*b^31*d^2 + 11792*A*B^5*a^23*b^29*d^2 +

512*A*B^5*a^25*b^27*d^2 - 2048*A*B^5*a^27*b^25*d^2 + 1836*A^5*B*a^17*b^35*d^2 + 15288*A^5*B*a^19*b^33*d^2 + 39

084*A^5*B*a^21*b^31*d^2 + 39968*A^5*B*a^23*b^29*d^2 + 14336*A^5*B*a^25*b^27*d^2 - 31*A^2*B^4*a^16*b^36*d^2 + 3

193*A^2*B^4*a^18*b^34*d^2 + 6351*A^2*B^4*a^20*b^32*d^2 - 5929*A^2*B^4*a^22*b^30*d^2 - 18400*A^2*B^4*a^24*b^28*

d^2 - 9344*A^2*B^4*a^26*b^26*d^2 - 1768*A^3*B^3*a^17*b^35*d^2 - 7744*A^3*B^3*a^19*b^33*d^2 - 20232*A^3*B^3*a^2

1*b^31*d^2 - 22960*A^3*B^3*a^23*b^29*d^2 - 6656*A^3*B^3*a^25*b^27*d^2 + 2048*A^3*B^3*a^27*b^25*d^2 + 15*A^4*B^

2*a^16*b^36*d^2 + 3619*A^4*B^2*a^18*b^34*d^2 + 11401*A^4*B^2*a^20*b^32*d^2 + 21205*A^4*B^2*a^22*b^30*d^2 + 232

64*A^4*B^2*a^24*b^28*d^2 + 9856*A^4*B^2*a^26*b^26*d^2))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2)))))/(b^(1/2

)*d))*(2*A*b + B*a))/(b^(1/2)*d) - (562949953421312*tan(c + d*x)^(1/2)*(5*A^8*a^16*b^37 - 376*A^8*a^18*b^35 -

1662*A^8*a^20*b^33 - 2688*A^8*a^22*b^31 - 1919*A^8*a^24*b^29 - 512*A^8*a^26*b^27 + B^8*a^16*b^37 + 3*B^8*a^18*

b^35 + 101*B^8*a^20*b^33 + 421*B^8*a^22*b^31 + 674*B^8*a^24*b^29 + 480*B^8*a^26*b^27 + 128*B^8*a^28*b^25 + 155

*A^2*B^6*a^18*b^35 + 1051*A^2*B^6*a^20*b^33 + 2373*A^2*B^6*a^22*b^31 + 2341*A^2*B^6*a^24*b^29 + 992*A^2*B^6*a^

26*b^27 + 128*A^2*B^6*a^28*b^25 - 244*A^3*B^5*a^17*b^36 - 476*A^3*B^5*a^19*b^34 + 548*A^3*B^5*a^21*b^32 + 2060

*A^3*B^5*a^23*b^30 + 1792*A^3*B^5*a^25*b^28 + 512*A^3*B^5*a^27*b^26 + 2*A^4*B^4*a^16*b^37 - 75*A^4*B^4*a^18*b^

35 + 137*A^4*B^4*a^20*b^33 + 795*A^4*B^4*a^22*b^31 + 741*A^4*B^4*a^24*b^29 + 32*A^4*B^4*a^26*b^27 - 128*A^4*B^

4*a^28*b^25 - 476*A^5*B^3*a^17*b^36 - 1912*A^5*B^3*a^19*b^34 - 3356*A^5*B^3*a^21*b^32 - 3392*A^5*B^3*a^23*b^30

- 1984*A^5*B^3*a^25*b^28 - 512*A^5*B^3*a^27*b^26 + 8*A^6*B^2*a^16*b^37 - 603*A^6*B^2*a^18*b^35 - 2475*A^6*B^2

*a^20*b^33 - 3845*A^6*B^2*a^22*b^31 - 2845*A^6*B^2*a^24*b^29 - 992*A^6*B^2*a^26*b^27 - 128*A^6*B^2*a^28*b^25 -

4*A*B^7*a^17*b^36 + 320*A*B^7*a^19*b^34 + 1484*A*B^7*a^21*b^32 + 2504*A*B^7*a^23*b^30 + 1856*A*B^7*a^25*b^28

+ 512*A*B^7*a^27*b^26 - 236*A^7*B*a^17*b^36 - 1116*A^7*B*a^19*b^34 - 2420*A^7*B*a^21*b^32 - 2948*A^7*B*a^23*b^

30 - 1920*A^7*B*a^25*b^28 - 512*A^7*B*a^27*b^26))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*1i)/(b^(1/2)*d

))/(((2*A*b + B*a)*((((281474976710656*(15*A^7*a^16*b^36*d^2 + 3205*A^7*a^18*b^34*d^2 + 9813*A^7*a^20*b^32*d^2

+ 10135*A^7*a^22*b^30*d^2 + 3576*A^7*a^24*b^28*d^2 + 64*A^7*a^26*b^26*d^2 - 9*B^7*a^17*b^35*d^2 - 291*B^7*a^1

9*b^33*d^2 - 507*B^7*a^21*b^31*d^2 + 79*B^7*a^23*b^29*d^2 + 560*B^7*a^25*b^27*d^2 + 256*B^7*a^27*b^25*d^2 - 65

*A*B^6*a^16*b^36*d^2 - 1191*A*B^6*a^18*b^34*d^2 - 1639*A*B^6*a^20*b^32*d^2 + 1187*A*B^6*a^22*b^30*d^2 + 2852*A

*B^6*a^24*b^28*d^2 + 1152*A*B^6*a^26*b^26*d^2 + 423*A^6*B*a^17*b^35*d^2 + 8837*A^6*B*a^19*b^33*d^2 + 24869*A^6

*B*a^21*b^31*d^2 + 24919*A^6*B*a^23*b^29*d^2 + 8464*A^6*B*a^25*b^27*d^2 - 939*A^2*B^5*a^17*b^35*d^2 - 801*A^2*

B^5*a^19*b^33*d^2 + 3759*A^2*B^5*a^21*b^31*d^2 + 7701*A^2*B^5*a^23*b^29*d^2 + 5616*A^2*B^5*a^25*b^27*d^2 + 153

6*A^2*B^5*a^27*b^25*d^2 - 51*A^3*B^4*a^16*b^36*d^2 + 231*A^3*B^4*a^18*b^34*d^2 + 7223*A^3*B^4*a^20*b^32*d^2 +

20781*A^3*B^4*a^22*b^30*d^2 + 21072*A^3*B^4*a^24*b^28*d^2 + 7232*A^3*B^4*a^26*b^26*d^2 - 507*A^4*B^3*a^17*b^35

*d^2 + 8327*A^4*B^3*a^19*b^33*d^2 + 29135*A^4*B^3*a^21*b^31*d^2 + 32541*A^4*B^3*a^23*b^29*d^2 + 13520*A^4*B^3*

a^25*b^27*d^2 + 1280*A^4*B^3*a^27*b^25*d^2 + 29*A^5*B^2*a^16*b^36*d^2 + 4627*A^5*B^2*a^18*b^34*d^2 + 18675*A^5

*B^2*a^20*b^32*d^2 + 29729*A^5*B^2*a^22*b^30*d^2 + 21796*A^5*B^2*a^24*b^28*d^2 + 6144*A^5*B^2*a^26*b^26*d^2))/

d^9 - ((2*A*b + B*a)*(((2*A*b + B*a)*((281474976710656*(180*A^5*a^16*b^35*d^4 + 15076*A^5*a^18*b^33*d^4 + 3454

0*A^5*a^20*b^31*d^4 + 24572*A^5*a^22*b^29*d^4 + 4928*A^5*a^24*b^27*d^4 - 88*B^5*a^17*b^34*d^4 + 1056*B^5*a^19*

b^32*d^4 + 840*B^5*a^21*b^30*d^4 - 1840*B^5*a^23*b^28*d^4 - 1536*B^5*a^25*b^26*d^4 + 388*A*B^4*a^16*b^35*d^4 +

5188*A*B^4*a^18*b^33*d^4 - 1092*A*B^4*a^20*b^31*d^4 - 11076*A*B^4*a^22*b^29*d^4 - 64*A*B^4*a^24*b^27*d^4 + 51

20*A*B^4*a^26*b^25*d^4 - 760*A^4*B*a^17*b^34*d^4 + 43248*A^4*B*a^19*b^32*d^4 + 94152*A^4*B*a^21*b^30*d^4 + 555

20*A^4*B*a^23*b^28*d^4 + 5376*A^4*B*a^25*b^26*d^4 + 3248*A^2*B^3*a^17*b^34*d^4 - 12080*A^2*B^3*a^19*b^32*d^4 -

4464*A^2*B^3*a^21*b^30*d^4 + 40304*A^2*B^3*a^23*b^28*d^4 + 29440*A^2*B^3*a^25*b^26*d^4 - 200*A^3*B^2*a^16*b^3

5*d^4 - 12312*A^3*B^2*a^18*b^33*d^4 + 30504*A^3*B^2*a^20*b^31*d^4 + 98168*A^3*B^2*a^22*b^29*d^4 + 56576*A^3*B^

2*a^24*b^27*d^4 + 1024*A^3*B^2*a^26*b^25*d^4))/d^9 + (((562949953421312*tan(c + d*x)^(1/2)*(23448*A^4*a^18*b^3

3*d^4 - 300*A^4*a^16*b^35*d^4 + 57252*A^4*a^20*b^31*d^4 + 43232*A^4*a^22*b^29*d^4 + 9728*A^4*a^24*b^27*d^4 - 1

08*B^4*a^16*b^35*d^4 + 1096*B^4*a^18*b^33*d^4 - 1660*B^4*a^20*b^31*d^4 - 9008*B^4*a^22*b^29*d^4 - 8192*B^4*a^2

4*b^27*d^4 - 2048*B^4*a^26*b^25*d^4 - 16*A*B^3*a^17*b^34*d^4 - 23520*A*B^3*a^19*b^32*d^4 - 48592*A*B^3*a^21*b^

30*d^4 - 27136*A*B^3*a^23*b^28*d^4 - 2048*A*B^3*a^25*b^26*d^4 + 3600*A^3*B*a^17*b^34*d^4 + 64864*A^3*B*a^19*b^

32*d^4 + 128336*A^3*B*a^21*b^30*d^4 + 77312*A^3*B*a^23*b^28*d^4 + 10240*A^3*B*a^25*b^26*d^4 + 264*A^2*B^2*a^16

*b^35*d^4 - 18624*A^2*B^2*a^18*b^33*d^4 - 7928*A^2*B^2*a^20*b^31*d^4 + 42192*A^2*B^2*a^22*b^29*d^4 + 33280*A^2

*B^2*a^24*b^27*d^4 + 2048*A^2*B^2*a^26*b^25*d^4))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))) - ((2*A*b + B*a

)*((281474976710656*(720*A^3*a^16*b^34*d^6 + 25376*A^3*a^18*b^32*d^6 + 49616*A^3*a^20*b^30*d^6 + 25984*A^3*a^2

2*b^28*d^6 + 1024*A^3*a^24*b^26*d^6 + 624*B^3*a^17*b^33*d^6 - 2080*B^3*a^19*b^31*d^6 - 1936*B^3*a^21*b^29*d^6

+ 4864*B^3*a^23*b^27*d^6 + 4096*B^3*a^25*b^25*d^6 - 1008*A*B^2*a^16*b^34*d^6 - 10400*A*B^2*a^18*b^32*d^6 + 884

8*A*B^2*a^20*b^30*d^6 + 44864*A*B^2*a^22*b^28*d^6 + 26624*A*B^2*a^24*b^26*d^6 - 4304*A^2*B*a^17*b^33*d^6 + 356

80*A^2*B*a^19*b^31*d^6 + 84272*A^2*B*a^21*b^29*d^6 + 44288*A^2*B*a^23*b^27*d^6))/d^9 - ((2*A*b + B*a)*((((2814

74976710656*(960*A*a^16*b^33*d^8 + 7040*A*a^18*b^31*d^8 + 11200*A*a^20*b^29*d^8 + 5120*A*a^22*b^27*d^8 - 1024*

B*a^17*b^32*d^8 + 2048*B*a^19*b^30*d^8 + 7168*B*a^21*b^28*d^8 + 4096*B*a^23*b^26*d^8))/d^9 + (562949953421312*

tan(c + d*x)^(1/2)*(2*A*b + B*a)*(7616*a^18*b^31*d^8 - 320*a^16*b^33*d^8 + 16128*a^20*b^29*d^8 + 8192*a^22*b^2

7*d^8))/(b^(1/2)*d^9*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*(2*A*b + B*a))/(b^(1/2)*d) - (562949953421312*ta

n(c + d*x)^(1/2)*(37600*A^2*a^18*b^32*d^6 - 560*A^2*a^16*b^34*d^6 + 78608*A^2*a^20*b^30*d^6 + 42496*A^2*a^22*b

^28*d^6 + 2048*A^2*a^24*b^26*d^6 + 304*B^2*a^16*b^34*d^6 - 5152*B^2*a^18*b^32*d^6 - 4944*B^2*a^20*b^30*d^6 + 6

656*B^2*a^22*b^28*d^6 + 6144*B^2*a^24*b^26*d^6 + 128*A*B*a^17*b^33*d^6 + 41600*A*B*a^19*b^31*d^6 + 82432*A*B*a

^21*b^29*d^6 + 40960*A*B*a^23*b^27*d^6))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2)))))/(b^(1/2)*d)))/(b^(1/2)

*d))*(2*A*b + B*a))/(b^(1/2)*d)))/(b^(1/2)*d) - (562949953421312*tan(c + d*x)^(1/2)*(5135*A^6*a^18*b^34*d^2 -

65*A^6*a^16*b^36*d^2 + 16769*A^6*a^20*b^32*d^2 + 18065*A^6*a^22*b^30*d^2 + 6624*A^6*a^24*b^28*d^2 + 128*A^6*a^

26*b^26*d^2 + 17*B^6*a^16*b^36*d^2 - 59*B^6*a^18*b^34*d^2 + 903*B^6*a^20*b^32*d^2 + 3443*B^6*a^22*b^30*d^2 + 3

872*B^6*a^24*b^28*d^2 + 1408*B^6*a^26*b^26*d^2 - 20*A*B^5*a^17*b^35*d^2 + 4712*A*B^5*a^19*b^33*d^2 + 13964*A*B

^5*a^21*b^31*d^2 + 11792*A*B^5*a^23*b^29*d^2 + 512*A*B^5*a^25*b^27*d^2 - 2048*A*B^5*a^27*b^25*d^2 + 1836*A^5*B

*a^17*b^35*d^2 + 15288*A^5*B*a^19*b^33*d^2 + 39084*A^5*B*a^21*b^31*d^2 + 39968*A^5*B*a^23*b^29*d^2 + 14336*A^5

*B*a^25*b^27*d^2 - 31*A^2*B^4*a^16*b^36*d^2 + 3193*A^2*B^4*a^18*b^34*d^2 + 6351*A^2*B^4*a^20*b^32*d^2 - 5929*A

^2*B^4*a^22*b^30*d^2 - 18400*A^2*B^4*a^24*b^28*d^2 - 9344*A^2*B^4*a^26*b^26*d^2 - 1768*A^3*B^3*a^17*b^35*d^2 -

7744*A^3*B^3*a^19*b^33*d^2 - 20232*A^3*B^3*a^21*b^31*d^2 - 22960*A^3*B^3*a^23*b^29*d^2 - 6656*A^3*B^3*a^25*b^

27*d^2 + 2048*A^3*B^3*a^27*b^25*d^2 + 15*A^4*B^2*a^16*b^36*d^2 + 3619*A^4*B^2*a^18*b^34*d^2 + 11401*A^4*B^2*a^

20*b^32*d^2 + 21205*A^4*B^2*a^22*b^30*d^2 + 23264*A^4*B^2*a^24*b^28*d^2 + 9856*A^4*B^2*a^26*b^26*d^2))/(d^8*((

a + b*tan(c + d*x))^(1/2) - a^(1/2)))))/(b^(1/2)*d))*(2*A*b + B*a))/(b^(1/2)*d) + (562949953421312*tan(c + d*x

)^(1/2)*(5*A^8*a^16*b^37 - 376*A^8*a^18*b^35 - 1662*A^8*a^20*b^33 - 2688*A^8*a^22*b^31 - 1919*A^8*a^24*b^29 -

512*A^8*a^26*b^27 + B^8*a^16*b^37 + 3*B^8*a^18*b^35 + 101*B^8*a^20*b^33 + 421*B^8*a^22*b^31 + 674*B^8*a^24*b^2

9 + 480*B^8*a^26*b^27 + 128*B^8*a^28*b^25 + 155*A^2*B^6*a^18*b^35 + 1051*A^2*B^6*a^20*b^33 + 2373*A^2*B^6*a^22

*b^31 + 2341*A^2*B^6*a^24*b^29 + 992*A^2*B^6*a^26*b^27 + 128*A^2*B^6*a^28*b^25 - 244*A^3*B^5*a^17*b^36 - 476*A

^3*B^5*a^19*b^34 + 548*A^3*B^5*a^21*b^32 + 2060*A^3*B^5*a^23*b^30 + 1792*A^3*B^5*a^25*b^28 + 512*A^3*B^5*a^27*

b^26 + 2*A^4*B^4*a^16*b^37 - 75*A^4*B^4*a^18*b^35 + 137*A^4*B^4*a^20*b^33 + 795*A^4*B^4*a^22*b^31 + 741*A^4*B^

4*a^24*b^29 + 32*A^4*B^4*a^26*b^27 - 128*A^4*B^4*a^28*b^25 - 476*A^5*B^3*a^17*b^36 - 1912*A^5*B^3*a^19*b^34 -

3356*A^5*B^3*a^21*b^32 - 3392*A^5*B^3*a^23*b^30 - 1984*A^5*B^3*a^25*b^28 - 512*A^5*B^3*a^27*b^26 + 8*A^6*B^2*a

^16*b^37 - 603*A^6*B^2*a^18*b^35 - 2475*A^6*B^2*a^20*b^33 - 3845*A^6*B^2*a^22*b^31 - 2845*A^6*B^2*a^24*b^29 -

992*A^6*B^2*a^26*b^27 - 128*A^6*B^2*a^28*b^25 - 4*A*B^7*a^17*b^36 + 320*A*B^7*a^19*b^34 + 1484*A*B^7*a^21*b^32

+ 2504*A*B^7*a^23*b^30 + 1856*A*B^7*a^25*b^28 + 512*A*B^7*a^27*b^26 - 236*A^7*B*a^17*b^36 - 1116*A^7*B*a^19*b

^34 - 2420*A^7*B*a^21*b^32 - 2948*A^7*B*a^23*b^30 - 1920*A^7*B*a^25*b^28 - 512*A^7*B*a^27*b^26))/(d^8*((a + b*

tan(c + d*x))^(1/2) - a^(1/2)))))/(b^(1/2)*d) - (562949953421312*(228*A^9*a^18*b^35 + 940*A^9*a^20*b^33 + 1452

*A^9*a^22*b^31 + 996*A^9*a^24*b^29 + 256*A^9*a^26*b^27 + 2*B^9*a^17*b^36 + 31*B^9*a^19*b^34 + 97*B^9*a^21*b^32

+ 125*B^9*a^23*b^30 + 73*B^9*a^25*b^28 + 16*B^9*a^27*b^26 + 96*A^2*B^7*a^17*b^36 + 653*A^2*B^7*a^19*b^34 + 16

87*A^2*B^7*a^21*b^32 + 2103*A^2*B^7*a^23*b^30 + 1277*A^2*B^7*a^25*b^28 + 304*A^2*B^7*a^27*b^26 + 12*A^3*B^6*a^

16*b^37 + 549*A^3*B^6*a^18*b^35 + 2191*A^3*B^6*a^20*b^33 + 3591*A^3*B^6*a^22*b^31 + 2937*A^3*B^6*a^24*b^29 + 1

192*A^3*B^6*a^26*b^27 + 192*A^3*B^6*a^28*b^25 + 276*A^4*B^5*a^17*b^36 + 1773*A^4*B^5*a^19*b^34 + 4479*A^4*B^5*

a^21*b^32 + 5559*A^4*B^5*a^23*b^30 + 3393*A^4*B^5*a^25*b^28 + 816*A^4*B^5*a^27*b^26 + 12*A^5*B^4*a^16*b^37 + 1

005*A^5*B^4*a^18*b^35 + 4071*A^5*B^4*a^20*b^33 + 6495*A^5*B^4*a^22*b^31 + 4929*A^5*B^4*a^24*b^29 + 1704*A^5*B^

4*a^26*b^27 + 192*A^5*B^4*a^28*b^25 + 272*A^6*B^3*a^17*b^36 + 1711*A^6*B^3*a^19*b^34 + 4285*A^6*B^3*a^21*b^32

+ 5309*A^6*B^3*a^23*b^30 + 3247*A^6*B^3*a^25*b^28 + 784*A^6*B^3*a^27*b^26 + 4*A^7*B^2*a^16*b^37 + 791*A^7*B^2*

a^18*b^35 + 3237*A^7*B^2*a^20*b^33 + 5069*A^7*B^2*a^22*b^31 + 3635*A^7*B^2*a^24*b^29 + 1080*A^7*B^2*a^26*b^27

+ 64*A^7*B^2*a^28*b^25 + 4*A*B^8*a^16*b^37 + 107*A*B^8*a^18*b^35 + 417*A*B^8*a^20*b^33 + 713*A*B^8*a^22*b^31 +

647*A*B^8*a^24*b^29 + 312*A*B^8*a^26*b^27 + 64*A*B^8*a^28*b^25 + 90*A^8*B*a^17*b^36 + 560*A^8*B*a^19*b^34 + 1

396*A^8*B*a^21*b^32 + 1728*A^8*B*a^23*b^30 + 1058*A^8*B*a^25*b^28 + 256*A^8*B*a^27*b^26))/d^9 + ((2*A*b + B*a)

*((((281474976710656*(15*A^7*a^16*b^36*d^2 + 3205*A^7*a^18*b^34*d^2 + 9813*A^7*a^20*b^32*d^2 + 10135*A^7*a^22*

b^30*d^2 + 3576*A^7*a^24*b^28*d^2 + 64*A^7*a^26*b^26*d^2 - 9*B^7*a^17*b^35*d^2 - 291*B^7*a^19*b^33*d^2 - 507*B

^7*a^21*b^31*d^2 + 79*B^7*a^23*b^29*d^2 + 560*B^7*a^25*b^27*d^2 + 256*B^7*a^27*b^25*d^2 - 65*A*B^6*a^16*b^36*d

^2 - 1191*A*B^6*a^18*b^34*d^2 - 1639*A*B^6*a^20*b^32*d^2 + 1187*A*B^6*a^22*b^30*d^2 + 2852*A*B^6*a^24*b^28*d^2

+ 1152*A*B^6*a^26*b^26*d^2 + 423*A^6*B*a^17*b^35*d^2 + 8837*A^6*B*a^19*b^33*d^2 + 24869*A^6*B*a^21*b^31*d^2 +

24919*A^6*B*a^23*b^29*d^2 + 8464*A^6*B*a^25*b^27*d^2 - 939*A^2*B^5*a^17*b^35*d^2 - 801*A^2*B^5*a^19*b^33*d^2

+ 3759*A^2*B^5*a^21*b^31*d^2 + 7701*A^2*B^5*a^23*b^29*d^2 + 5616*A^2*B^5*a^25*b^27*d^2 + 1536*A^2*B^5*a^27*b^2

5*d^2 - 51*A^3*B^4*a^16*b^36*d^2 + 231*A^3*B^4*a^18*b^34*d^2 + 7223*A^3*B^4*a^20*b^32*d^2 + 20781*A^3*B^4*a^22

*b^30*d^2 + 21072*A^3*B^4*a^24*b^28*d^2 + 7232*A^3*B^4*a^26*b^26*d^2 - 507*A^4*B^3*a^17*b^35*d^2 + 8327*A^4*B^

3*a^19*b^33*d^2 + 29135*A^4*B^3*a^21*b^31*d^2 + 32541*A^4*B^3*a^23*b^29*d^2 + 13520*A^4*B^3*a^25*b^27*d^2 + 12

80*A^4*B^3*a^27*b^25*d^2 + 29*A^5*B^2*a^16*b^36*d^2 + 4627*A^5*B^2*a^18*b^34*d^2 + 18675*A^5*B^2*a^20*b^32*d^2

+ 29729*A^5*B^2*a^22*b^30*d^2 + 21796*A^5*B^2*a^24*b^28*d^2 + 6144*A^5*B^2*a^26*b^26*d^2))/d^9 - ((2*A*b + B*

a)*(((2*A*b + B*a)*((281474976710656*(180*A^5*a^16*b^35*d^4 + 15076*A^5*a^18*b^33*d^4 + 34540*A^5*a^20*b^31*d^

4 + 24572*A^5*a^22*b^29*d^4 + 4928*A^5*a^24*b^27*d^4 - 88*B^5*a^17*b^34*d^4 + 1056*B^5*a^19*b^32*d^4 + 840*B^5

*a^21*b^30*d^4 - 1840*B^5*a^23*b^28*d^4 - 1536*B^5*a^25*b^26*d^4 + 388*A*B^4*a^16*b^35*d^4 + 5188*A*B^4*a^18*b

^33*d^4 - 1092*A*B^4*a^20*b^31*d^4 - 11076*A*B^4*a^22*b^29*d^4 - 64*A*B^4*a^24*b^27*d^4 + 5120*A*B^4*a^26*b^25

*d^4 - 760*A^4*B*a^17*b^34*d^4 + 43248*A^4*B*a^19*b^32*d^4 + 94152*A^4*B*a^21*b^30*d^4 + 55520*A^4*B*a^23*b^28

*d^4 + 5376*A^4*B*a^25*b^26*d^4 + 3248*A^2*B^3*a^17*b^34*d^4 - 12080*A^2*B^3*a^19*b^32*d^4 - 4464*A^2*B^3*a^21

*b^30*d^4 + 40304*A^2*B^3*a^23*b^28*d^4 + 29440*A^2*B^3*a^25*b^26*d^4 - 200*A^3*B^2*a^16*b^35*d^4 - 12312*A^3*

B^2*a^18*b^33*d^4 + 30504*A^3*B^2*a^20*b^31*d^4 + 98168*A^3*B^2*a^22*b^29*d^4 + 56576*A^3*B^2*a^24*b^27*d^4 +

1024*A^3*B^2*a^26*b^25*d^4))/d^9 - (((562949953421312*tan(c + d*x)^(1/2)*(23448*A^4*a^18*b^33*d^4 - 300*A^4*a^

16*b^35*d^4 + 57252*A^4*a^20*b^31*d^4 + 43232*A^4*a^22*b^29*d^4 + 9728*A^4*a^24*b^27*d^4 - 108*B^4*a^16*b^35*d

^4 + 1096*B^4*a^18*b^33*d^4 - 1660*B^4*a^20*b^31*d^4 - 9008*B^4*a^22*b^29*d^4 - 8192*B^4*a^24*b^27*d^4 - 2048*

B^4*a^26*b^25*d^4 - 16*A*B^3*a^17*b^34*d^4 - 23520*A*B^3*a^19*b^32*d^4 - 48592*A*B^3*a^21*b^30*d^4 - 27136*A*B

^3*a^23*b^28*d^4 - 2048*A*B^3*a^25*b^26*d^4 + 3600*A^3*B*a^17*b^34*d^4 + 64864*A^3*B*a^19*b^32*d^4 + 128336*A^

3*B*a^21*b^30*d^4 + 77312*A^3*B*a^23*b^28*d^4 + 10240*A^3*B*a^25*b^26*d^4 + 264*A^2*B^2*a^16*b^35*d^4 - 18624*

A^2*B^2*a^18*b^33*d^4 - 7928*A^2*B^2*a^20*b^31*d^4 + 42192*A^2*B^2*a^22*b^29*d^4 + 33280*A^2*B^2*a^24*b^27*d^4

+ 2048*A^2*B^2*a^26*b^25*d^4))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))) + ((2*A*b + B*a)*((28147497671065

6*(720*A^3*a^16*b^34*d^6 + 25376*A^3*a^18*b^32*d^6 + 49616*A^3*a^20*b^30*d^6 + 25984*A^3*a^22*b^28*d^6 + 1024*

A^3*a^24*b^26*d^6 + 624*B^3*a^17*b^33*d^6 - 2080*B^3*a^19*b^31*d^6 - 1936*B^3*a^21*b^29*d^6 + 4864*B^3*a^23*b^

27*d^6 + 4096*B^3*a^25*b^25*d^6 - 1008*A*B^2*a^16*b^34*d^6 - 10400*A*B^2*a^18*b^32*d^6 + 8848*A*B^2*a^20*b^30*

d^6 + 44864*A*B^2*a^22*b^28*d^6 + 26624*A*B^2*a^24*b^26*d^6 - 4304*A^2*B*a^17*b^33*d^6 + 35680*A^2*B*a^19*b^31

*d^6 + 84272*A^2*B*a^21*b^29*d^6 + 44288*A^2*B*a^23*b^27*d^6))/d^9 - ((2*A*b + B*a)*((((281474976710656*(960*A

*a^16*b^33*d^8 + 7040*A*a^18*b^31*d^8 + 11200*A*a^20*b^29*d^8 + 5120*A*a^22*b^27*d^8 - 1024*B*a^17*b^32*d^8 +

2048*B*a^19*b^30*d^8 + 7168*B*a^21*b^28*d^8 + 4096*B*a^23*b^26*d^8))/d^9 - (562949953421312*tan(c + d*x)^(1/2)

*(2*A*b + B*a)*(7616*a^18*b^31*d^8 - 320*a^16*b^33*d^8 + 16128*a^20*b^29*d^8 + 8192*a^22*b^27*d^8))/(b^(1/2)*d

^9*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*(2*A*b + B*a))/(b^(1/2)*d) + (562949953421312*tan(c + d*x)^(1/2)*(

37600*A^2*a^18*b^32*d^6 - 560*A^2*a^16*b^34*d^6 + 78608*A^2*a^20*b^30*d^6 + 42496*A^2*a^22*b^28*d^6 + 2048*A^2

*a^24*b^26*d^6 + 304*B^2*a^16*b^34*d^6 - 5152*B^2*a^18*b^32*d^6 - 4944*B^2*a^20*b^30*d^6 + 6656*B^2*a^22*b^28*

d^6 + 6144*B^2*a^24*b^26*d^6 + 128*A*B*a^17*b^33*d^6 + 41600*A*B*a^19*b^31*d^6 + 82432*A*B*a^21*b^29*d^6 + 409

60*A*B*a^23*b^27*d^6))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2)))))/(b^(1/2)*d)))/(b^(1/2)*d))*(2*A*b + B*a)

)/(b^(1/2)*d)))/(b^(1/2)*d) + (562949953421312*tan(c + d*x)^(1/2)*(5135*A^6*a^18*b^34*d^2 - 65*A^6*a^16*b^36*d

^2 + 16769*A^6*a^20*b^32*d^2 + 18065*A^6*a^22*b^30*d^2 + 6624*A^6*a^24*b^28*d^2 + 128*A^6*a^26*b^26*d^2 + 17*B

^6*a^16*b^36*d^2 - 59*B^6*a^18*b^34*d^2 + 903*B^6*a^20*b^32*d^2 + 3443*B^6*a^22*b^30*d^2 + 3872*B^6*a^24*b^28*

d^2 + 1408*B^6*a^26*b^26*d^2 - 20*A*B^5*a^17*b^35*d^2 + 4712*A*B^5*a^19*b^33*d^2 + 13964*A*B^5*a^21*b^31*d^2 +

11792*A*B^5*a^23*b^29*d^2 + 512*A*B^5*a^25*b^27*d^2 - 2048*A*B^5*a^27*b^25*d^2 + 1836*A^5*B*a^17*b^35*d^2 + 1

5288*A^5*B*a^19*b^33*d^2 + 39084*A^5*B*a^21*b^31*d^2 + 39968*A^5*B*a^23*b^29*d^2 + 14336*A^5*B*a^25*b^27*d^2 -

31*A^2*B^4*a^16*b^36*d^2 + 3193*A^2*B^4*a^18*b^34*d^2 + 6351*A^2*B^4*a^20*b^32*d^2 - 5929*A^2*B^4*a^22*b^30*d

^2 - 18400*A^2*B^4*a^24*b^28*d^2 - 9344*A^2*B^4*a^26*b^26*d^2 - 1768*A^3*B^3*a^17*b^35*d^2 - 7744*A^3*B^3*a^19

*b^33*d^2 - 20232*A^3*B^3*a^21*b^31*d^2 - 22960*A^3*B^3*a^23*b^29*d^2 - 6656*A^3*B^3*a^25*b^27*d^2 + 2048*A^3*

B^3*a^27*b^25*d^2 + 15*A^4*B^2*a^16*b^36*d^2 + 3619*A^4*B^2*a^18*b^34*d^2 + 11401*A^4*B^2*a^20*b^32*d^2 + 2120

5*A^4*B^2*a^22*b^30*d^2 + 23264*A^4*B^2*a^24*b^28*d^2 + 9856*A^4*B^2*a^26*b^26*d^2))/(d^8*((a + b*tan(c + d*x)

)^(1/2) - a^(1/2)))))/(b^(1/2)*d))*(2*A*b + B*a))/(b^(1/2)*d) - (562949953421312*tan(c + d*x)^(1/2)*(5*A^8*a^1

6*b^37 - 376*A^8*a^18*b^35 - 1662*A^8*a^20*b^33 - 2688*A^8*a^22*b^31 - 1919*A^8*a^24*b^29 - 512*A^8*a^26*b^27

+ B^8*a^16*b^37 + 3*B^8*a^18*b^35 + 101*B^8*a^20*b^33 + 421*B^8*a^22*b^31 + 674*B^8*a^24*b^29 + 480*B^8*a^26*b

^27 + 128*B^8*a^28*b^25 + 155*A^2*B^6*a^18*b^35 + 1051*A^2*B^6*a^20*b^33 + 2373*A^2*B^6*a^22*b^31 + 2341*A^2*B

^6*a^24*b^29 + 992*A^2*B^6*a^26*b^27 + 128*A^2*B^6*a^28*b^25 - 244*A^3*B^5*a^17*b^36 - 476*A^3*B^5*a^19*b^34 +

548*A^3*B^5*a^21*b^32 + 2060*A^3*B^5*a^23*b^30 + 1792*A^3*B^5*a^25*b^28 + 512*A^3*B^5*a^27*b^26 + 2*A^4*B^4*a

^16*b^37 - 75*A^4*B^4*a^18*b^35 + 137*A^4*B^4*a^20*b^33 + 795*A^4*B^4*a^22*b^31 + 741*A^4*B^4*a^24*b^29 + 32*A

^4*B^4*a^26*b^27 - 128*A^4*B^4*a^28*b^25 - 476*A^5*B^3*a^17*b^36 - 1912*A^5*B^3*a^19*b^34 - 3356*A^5*B^3*a^21*

b^32 - 3392*A^5*B^3*a^23*b^30 - 1984*A^5*B^3*a^25*b^28 - 512*A^5*B^3*a^27*b^26 + 8*A^6*B^2*a^16*b^37 - 603*A^6

*B^2*a^18*b^35 - 2475*A^6*B^2*a^20*b^33 - 3845*A^6*B^2*a^22*b^31 - 2845*A^6*B^2*a^24*b^29 - 992*A^6*B^2*a^26*b

^27 - 128*A^6*B^2*a^28*b^25 - 4*A*B^7*a^17*b^36 + 320*A*B^7*a^19*b^34 + 1484*A*B^7*a^21*b^32 + 2504*A*B^7*a^23

*b^30 + 1856*A*B^7*a^25*b^28 + 512*A*B^7*a^27*b^26 - 236*A^7*B*a^17*b^36 - 1116*A^7*B*a^19*b^34 - 2420*A^7*B*a

^21*b^32 - 2948*A^7*B*a^23*b^30 - 1920*A^7*B*a^25*b^28 - 512*A^7*B*a^27*b^26))/(d^8*((a + b*tan(c + d*x))^(1/2

) - a^(1/2)))))/(b^(1/2)*d)))*(2*A*b + B*a)*2i)/(b^(1/2)*d)

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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (A + B \tan {\left (c + d x \right )}\right ) \sqrt {a + b \tan {\left (c + d x \right )}} \sqrt {\tan {\left (c + d x \right )}}\, dx \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(tan(d*x+c)**(1/2)*(a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)

[Out]

Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))*sqrt(tan(c + d*x)), x)

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