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

Optimal. Leaf size=168 \[ \frac {(-B+i A) \tan ^{-1}\left (\frac {\sqrt {-b+i a} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{d \sqrt {-b+i a}}-\frac {(B+i A) \tanh ^{-1}\left (\frac {\sqrt {b+i a} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{d \sqrt {b+i a}}+\frac {2 B \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{\sqrt {b} d} \]

[Out]

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

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Rubi [A]  time = 0.61, antiderivative size = 168, normalized size of antiderivative = 1.00, number of steps used = 12, number of rules used = 9, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.257, Rules used = {3614, 3616, 3615, 93, 203, 206, 3634, 63, 217} \[ \frac {(-B+i A) \tan ^{-1}\left (\frac {\sqrt {-b+i a} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{d \sqrt {-b+i a}}-\frac {(B+i A) \tanh ^{-1}\left (\frac {\sqrt {b+i a} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{d \sqrt {b+i a}}+\frac {2 B \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{\sqrt {b} d} \]

Antiderivative was successfully verified.

[In]

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

[Out]

((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d) + (2*B*ArcTa
nh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[b]*d) - ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqr
t[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a + b]*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 203

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTan[(Rt[b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[b, 2]), x] /;
 FreeQ[{a, b}, x] && PosQ[a/b] && (GtQ[a, 0] || GtQ[b, 0])

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 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 3614

Int[(Sqrt[(a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)]]*((A_.) + (B_.)*tan[(e_.) + (f_.)*(x_)]))/Sqrt[(c_.) + (d_.)*t
an[(e_.) + (f_.)*(x_)]], x_Symbol] :> Int[Simp[a*A - b*B + (A*b + a*B)*Tan[e + f*x], x]/(Sqrt[a + b*Tan[e + f*
x]]*Sqrt[c + d*Tan[e + f*x]]), x] + Dist[b*B, Int[(1 + Tan[e + f*x]^2)/(Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Ta
n[e + f*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]

Rule 3615

Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_)*((A_.) + (B_.)*tan[(e_.) + (f_.)*(x_)])*((c_.) + (d_.)*tan[(e
_.) + (f_.)*(x_)])^(n_), x_Symbol] :> Dist[A^2/f, Subst[Int[((a + b*x)^m*(c + d*x)^n)/(A - B*x), x], x, Tan[e
+ f*x]], x] /; FreeQ[{a, b, c, d, e, f, A, B, m, n}, x] && NeQ[b*c - a*d, 0] && NeQ[a^2 + b^2, 0] && EqQ[A^2 +
 B^2, 0]

Rule 3616

Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_)*((A_.) + (B_.)*tan[(e_.) + (f_.)*(x_)])*((c_.) + (d_.)*tan[(e
_.) + (f_.)*(x_)])^(n_), x_Symbol] :> Dist[(A + I*B)/2, Int[(a + b*Tan[e + f*x])^m*(c + d*Tan[e + f*x])^n*(1 -
 I*Tan[e + f*x]), x], x] + Dist[(A - I*B)/2, Int[(a + b*Tan[e + f*x])^m*(c + d*Tan[e + f*x])^n*(1 + I*Tan[e +
f*x]), x], x] /; FreeQ[{a, b, c, d, e, f, A, B, m, n}, x] && NeQ[b*c - a*d, 0] && NeQ[a^2 + b^2, 0] && NeQ[A^2
 + B^2, 0]

Rule 3634

Int[((a_.) + (b_.)*tan[(e_.) + (f_.)*(x_)])^(m_.)*((c_.) + (d_.)*tan[(e_.) + (f_.)*(x_)])^(n_.)*((A_) + (C_.)*
tan[(e_.) + (f_.)*(x_)]^2), x_Symbol] :> Dist[A/f, Subst[Int[(a + b*x)^m*(c + d*x)^n, x], x, Tan[e + f*x]], x]
 /; FreeQ[{a, b, c, d, e, f, A, C, m, n}, x] && EqQ[A, C]

Rubi steps

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

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Mathematica [A]  time = 1.28, size = 205, normalized size = 1.22 \[ \frac {\frac {2 \sqrt {a} B \sqrt {\frac {b \tan (c+d x)}{a}+1} \sinh ^{-1}\left (\frac {\sqrt {b} \sqrt {\tan (c+d x)}}{\sqrt {a}}\right )}{\sqrt {b} \sqrt {a+b \tan (c+d x)}}+\sqrt [4]{-1} \left (\frac {(A+i B) \tan ^{-1}\left (\frac {\sqrt [4]{-1} \sqrt {a+i b} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{\sqrt {a+i b}}-\frac {(A-i B) \tan ^{-1}\left (\frac {\sqrt [4]{-1} \sqrt {-a+i b} \sqrt {\tan (c+d x)}}{\sqrt {a+b \tan (c+d x)}}\right )}{\sqrt {-a+i b}}\right )}{d} \]

Antiderivative was successfully verified.

[In]

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

[Out]

((-1)^(1/4)*(-(((A - I*B)*ArcTan[((-1)^(1/4)*Sqrt[-a + I*b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/Sqr
t[-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]]])/Sqrt
[a + I*b]) + (2*Sqrt[a]*B*ArcSinh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]]*Sqrt[1 + (b*Tan[c + d*x])/a])/(Sqrt[b]
*Sqrt[a + b*Tan[c + d*x]]))/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))/(a+b*tan(d*x+c))^(1/2),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))/(a+b*tan(d*x+c))^(1/2),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 1.08, size = 1886894, normalized size = 11231.51 \[ \text {output too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

result too large to display

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [B]  time = 91.16, size = 30600, normalized size = 182.14 \[ \text {result too large to display} \]

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]

atan(((((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2)*((((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/
2)*((((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2)*((((274877906944*(1600*a^12*b^34*d^8 - 16640*a^14*b^3
2*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)*(1
600*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))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) - (219902
3255552*tan(c + d*x)^(1/2)*(240*A*a^13*b^33*d^6 + 3064*A*a^15*b^31*d^6 + 8960*A*a^17*b^29*d^6 + 6144*A*a^19*b^
27*d^6 + 6920*B*a^14*b^32*d^6 + 9472*B*a^16*b^30*d^6 - 5632*B*a^18*b^28*d^6 - 8192*B*a^20*b^26*d^6))/(d^7*((a
+ b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) - (274877906944*(1921
6*A^2*a^14*b^31*d^6 - 1440*A^2*a^12*b^33*d^6 - 22016*A^2*a^16*b^29*d^6 - 45056*A^2*a^18*b^27*d^6 + 1200*B^2*a^
12*b^33*d^6 - 16640*B^2*a^14*b^31*d^6 + 279040*B^2*a^16*b^29*d^6 + 561152*B^2*a^18*b^27*d^6 + 262144*B^2*a^20*
b^25*d^6 + 16480*A*B*a^13*b^32*d^6 - 25792*A*B*a^15*b^30*d^6 + 34816*A*B*a^17*b^28*d^6 + 81920*A*B*a^19*b^26*d
^6))/d^8 + (274877906944*tan(c + d*x)*(46704*A^2*a^14*b^32*d^6 - 1440*A^2*a^12*b^34*d^6 - 137216*A^2*a^16*b^30
*d^6 - 122880*A^2*a^18*b^28*d^6 + 65536*A^2*a^20*b^26*d^6 + 1200*B^2*a^12*b^34*d^6 - 52320*B^2*a^14*b^32*d^6 +
 1200640*B^2*a^16*b^30*d^6 + 2306048*B^2*a^18*b^28*d^6 + 1048576*B^2*a^20*b^26*d^6 + 21600*A*B*a^13*b^33*d^6 -
 121856*A*B*a^15*b^31*d^6 + 276480*A*B*a^17*b^29*d^6 + 425984*A*B*a^19*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)*(168*A^3*a^13*b^32*d^4 + 1200*A^3*a^15*b^30*d^4 + 2816
*A^3*a^17*b^28*d^4 - 4770*B^3*a^14*b^31*d^4 + 17920*B^3*a^16*b^29*d^4 + 57344*B^3*a^18*b^27*d^4 + 32768*B^3*a^
20*b^25*d^4 + 180*A*B^2*a^13*b^32*d^4 - 26736*A*B^2*a^15*b^30*d^4 - 48896*A*B^2*a^17*b^28*d^4 - 16384*A*B^2*a^
19*b^26*d^4 + 4746*A^2*B*a^14*b^31*d^4 - 2048*A^2*B*a^16*b^29*d^4 - 12288*A^2*B*a^18*b^27*d^4))/(d^7*((a + b*t
an(c + d*x))^(1/2) - a^(1/2))))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) + (274877906944*(484*A^4*a
^12*b^32*d^4 - 6448*A^4*a^14*b^30*d^4 + 8704*A^4*a^16*b^28*d^4 + 4096*A^4*a^18*b^26*d^4 + 300*B^4*a^12*b^32*d^
4 - 5040*B^4*a^14*b^30*d^4 + 217600*B^4*a^16*b^28*d^4 + 217088*B^4*a^18*b^26*d^4 + 7720*A*B^3*a^13*b^31*d^4 -
104960*A*B^3*a^15*b^29*d^4 + 253952*A*B^3*a^17*b^27*d^4 + 327680*A*B^3*a^19*b^25*d^4 - 10392*A^3*B*a^13*b^31*d
^4 + 23808*A^3*B*a^15*b^29*d^4 - 16384*A^3*B*a^17*b^27*d^4 - 320*A^2*B^2*a^12*b^32*d^4 + 46496*A^2*B^2*a^14*b^
30*d^4 - 181248*A^2*B^2*a^16*b^28*d^4 - 155648*A^2*B^2*a^18*b^26*d^4))/d^8 - (274877906944*tan(c + d*x)*(484*A
^4*a^12*b^33*d^4 - 14304*A^4*a^14*b^31*d^4 + 41472*A^4*a^16*b^29*d^4 - 16384*A^4*a^18*b^27*d^4 + 300*B^4*a^12*
b^33*d^4 - 17120*B^4*a^14*b^31*d^4 + 985600*B^4*a^16*b^29*d^4 + 950272*B^4*a^18*b^27*d^4 + 10520*A*B^3*a^13*b^
32*d^4 - 320000*A*B^3*a^15*b^30*d^4 + 1617920*A*B^3*a^17*b^28*d^4 + 1703936*A*B^3*a^19*b^26*d^4 - 13704*A^3*B*
a^13*b^32*d^4 + 73728*A^3*B*a^15*b^30*d^4 - 131072*A^3*B*a^17*b^28*d^4 + 65536*A^3*B*a^19*b^26*d^4 - 320*A^2*B
^2*a^12*b^33*d^4 + 86144*A^2*B^2*a^14*b^31*d^4 - 807936*A^2*B^2*a^16*b^29*d^4 - 229376*A^2*B^2*a^18*b^27*d^4 +
 262144*A^2*B^2*a^20*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)*(10080*B^5*a^16*b^28*d^2 - 48*A^5*a^15*b^29*d^2 - 384*A^5*a^17*b^27*d^2 - 1080*B^5*a^14*b^30*d^2 - 39*A^
5*a^13*b^31*d^2 + 16896*B^5*a^18*b^26*d^2 + 120*A*B^4*a^13*b^31*d^2 - 10800*A*B^4*a^15*b^29*d^2 + 7808*A*B^4*a
^17*b^27*d^2 + 32768*A*B^4*a^19*b^25*d^2 - 1152*A^4*B*a^14*b^30*d^2 + 608*A^4*B*a^16*b^28*d^2 + 512*A^4*B*a^18
*b^26*d^2 + 824*A^2*B^3*a^14*b^30*d^2 - 30272*A^2*B^3*a^16*b^28*d^2 - 39936*A^2*B^3*a^18*b^26*d^2 - 159*A^3*B^
2*a^13*b^31*d^2 + 10400*A^3*B^2*a^15*b^29*d^2 + 9472*A^3*B^2*a^17*b^27*d^2))/(d^7*((a + b*tan(c + d*x))^(1/2)
- a^(1/2))))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) - (274877906944*(672*A^6*a^14*b^29*d^2 - 72*A
^6*a^12*b^31*d^2 - 768*A^6*a^16*b^27*d^2 + 25*B^6*a^12*b^31*d^2 - 480*B^6*a^14*b^29*d^2 + 57600*B^6*a^16*b^27*
d^2 + 16384*B^6*a^18*b^25*d^2 + 900*A*B^5*a^13*b^30*d^2 - 44416*A*B^5*a^15*b^28*d^2 + 115712*A*B^5*a^17*b^26*d
^2 + 2148*A^5*B*a^13*b^30*d^2 - 3456*A^5*B*a^15*b^28*d^2 + 1024*A^5*B*a^17*b^26*d^2 + 10*A^2*B^4*a^12*b^31*d^2
 + 12000*A^2*B^4*a^14*b^29*d^2 - 119040*A^2*B^4*a^16*b^27*d^2 + 98304*A^2*B^4*a^18*b^25*d^2 + 744*A^3*B^3*a^13
*b^30*d^2 + 66816*A^3*B^3*a^15*b^28*d^2 - 79872*A^3*B^3*a^17*b^26*d^2 - 23*A^4*B^2*a^12*b^31*d^2 - 13728*A^4*B
^2*a^14*b^29*d^2 + 43776*A^4*B^2*a^16*b^27*d^2 + 16384*A^4*B^2*a^18*b^25*d^2))/d^8 + (274877906944*tan(c + d*x
)*(1408*A^6*a^14*b^30*d^2 - 72*A^6*a^12*b^32*d^2 - 3584*A^6*a^16*b^28*d^2 + 4096*A^6*a^18*b^26*d^2 + 25*B^6*a^
12*b^32*d^2 - 1760*B^6*a^14*b^30*d^2 + 275200*B^6*a^16*b^28*d^2 + 65536*B^6*a^18*b^26*d^2 + 1280*A*B^5*a^13*b^
31*d^2 - 128640*A*B^5*a^15*b^29*d^2 + 747520*A*B^5*a^17*b^27*d^2 + 2848*A^5*B*a^13*b^31*d^2 - 9856*A^5*B*a^15*
b^29*d^2 + 10240*A^5*B*a^17*b^27*d^2 + 10*A^2*B^4*a^12*b^32*d^2 + 21440*A^2*B^4*a^14*b^30*d^2 - 411648*A^2*B^4
*a^16*b^28*d^2 + 921600*A^2*B^4*a^18*b^26*d^2 + 928*A^3*B^3*a^13*b^31*d^2 + 162560*A^3*B^3*a^15*b^29*d^2 - 503
808*A^3*B^3*a^17*b^27*d^2 + 262144*A^3*B^3*a^19*b^25*d^2 - 23*A^4*B^2*a^12*b^32*d^2 - 25568*A^4*B^2*a^14*b^30*
d^2 + 169728*A^4*B^2*a^16*b^28*d^2 - 57344*A^4*B^2*a^18*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)*(3*A^7*a^13*b^30 - 16*A^7*a^15*b^28 - 80*B^7*a^14*b^29 + 1280*B^7*a^1
6*b^27 + 2048*B^7*a^18*b^25 - 64*A^2*B^5*a^14*b^29 + 2432*A^2*B^5*a^16*b^27 + 4096*A^2*B^5*a^18*b^25 + 37*A^3*
B^4*a^13*b^30 - 2352*A^3*B^4*a^15*b^28 - 3072*A^3*B^4*a^17*b^26 + 112*A^4*B^3*a^14*b^29 + 1024*A^4*B^3*a^16*b^
27 + 2048*A^4*B^3*a^18*b^25 + 25*A^5*B^2*a^13*b^30 - 1200*A^5*B^2*a^15*b^28 - 1536*A^5*B^2*a^17*b^26 + 15*A*B^
6*a^13*b^30 - 1168*A*B^6*a^15*b^28 - 1536*A*B^6*a^17*b^26 + 96*A^6*B*a^14*b^29 - 128*A^6*B*a^16*b^27))/(d^7*((
a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2)*1i - (((B^2 - A^2 +
 A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2)*((((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2)*((((B^2 - A^2 + A
*B*2i)/(4*(a*d^2*1i + b*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))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) + (2199023255552*tan(c + d*x)
^(1/2)*(240*A*a^13*b^33*d^6 + 3064*A*a^15*b^31*d^6 + 8960*A*a^17*b^29*d^6 + 6144*A*a^19*b^27*d^6 + 6920*B*a^14
*b^32*d^6 + 9472*B*a^16*b^30*d^6 - 5632*B*a^18*b^28*d^6 - 8192*B*a^20*b^26*d^6))/(d^7*((a + b*tan(c + d*x))^(1
/2) - a^(1/2))))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) - (274877906944*(19216*A^2*a^14*b^31*d^6
- 1440*A^2*a^12*b^33*d^6 - 22016*A^2*a^16*b^29*d^6 - 45056*A^2*a^18*b^27*d^6 + 1200*B^2*a^12*b^33*d^6 - 16640*
B^2*a^14*b^31*d^6 + 279040*B^2*a^16*b^29*d^6 + 561152*B^2*a^18*b^27*d^6 + 262144*B^2*a^20*b^25*d^6 + 16480*A*B
*a^13*b^32*d^6 - 25792*A*B*a^15*b^30*d^6 + 34816*A*B*a^17*b^28*d^6 + 81920*A*B*a^19*b^26*d^6))/d^8 + (27487790
6944*tan(c + d*x)*(46704*A^2*a^14*b^32*d^6 - 1440*A^2*a^12*b^34*d^6 - 137216*A^2*a^16*b^30*d^6 - 122880*A^2*a^
18*b^28*d^6 + 65536*A^2*a^20*b^26*d^6 + 1200*B^2*a^12*b^34*d^6 - 52320*B^2*a^14*b^32*d^6 + 1200640*B^2*a^16*b^
30*d^6 + 2306048*B^2*a^18*b^28*d^6 + 1048576*B^2*a^20*b^26*d^6 + 21600*A*B*a^13*b^33*d^6 - 121856*A*B*a^15*b^3
1*d^6 + 276480*A*B*a^17*b^29*d^6 + 425984*A*B*a^19*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)*(168*A^3*a^13*b^32*d^4 + 1200*A^3*a^15*b^30*d^4 + 2816*A^3*a^17*b^28*d^4 -
 4770*B^3*a^14*b^31*d^4 + 17920*B^3*a^16*b^29*d^4 + 57344*B^3*a^18*b^27*d^4 + 32768*B^3*a^20*b^25*d^4 + 180*A*
B^2*a^13*b^32*d^4 - 26736*A*B^2*a^15*b^30*d^4 - 48896*A*B^2*a^17*b^28*d^4 - 16384*A*B^2*a^19*b^26*d^4 + 4746*A
^2*B*a^14*b^31*d^4 - 2048*A^2*B*a^16*b^29*d^4 - 12288*A^2*B*a^18*b^27*d^4))/(d^7*((a + b*tan(c + d*x))^(1/2) -
 a^(1/2))))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) + (274877906944*(484*A^4*a^12*b^32*d^4 - 6448*
A^4*a^14*b^30*d^4 + 8704*A^4*a^16*b^28*d^4 + 4096*A^4*a^18*b^26*d^4 + 300*B^4*a^12*b^32*d^4 - 5040*B^4*a^14*b^
30*d^4 + 217600*B^4*a^16*b^28*d^4 + 217088*B^4*a^18*b^26*d^4 + 7720*A*B^3*a^13*b^31*d^4 - 104960*A*B^3*a^15*b^
29*d^4 + 253952*A*B^3*a^17*b^27*d^4 + 327680*A*B^3*a^19*b^25*d^4 - 10392*A^3*B*a^13*b^31*d^4 + 23808*A^3*B*a^1
5*b^29*d^4 - 16384*A^3*B*a^17*b^27*d^4 - 320*A^2*B^2*a^12*b^32*d^4 + 46496*A^2*B^2*a^14*b^30*d^4 - 181248*A^2*
B^2*a^16*b^28*d^4 - 155648*A^2*B^2*a^18*b^26*d^4))/d^8 - (274877906944*tan(c + d*x)*(484*A^4*a^12*b^33*d^4 - 1
4304*A^4*a^14*b^31*d^4 + 41472*A^4*a^16*b^29*d^4 - 16384*A^4*a^18*b^27*d^4 + 300*B^4*a^12*b^33*d^4 - 17120*B^4
*a^14*b^31*d^4 + 985600*B^4*a^16*b^29*d^4 + 950272*B^4*a^18*b^27*d^4 + 10520*A*B^3*a^13*b^32*d^4 - 320000*A*B^
3*a^15*b^30*d^4 + 1617920*A*B^3*a^17*b^28*d^4 + 1703936*A*B^3*a^19*b^26*d^4 - 13704*A^3*B*a^13*b^32*d^4 + 7372
8*A^3*B*a^15*b^30*d^4 - 131072*A^3*B*a^17*b^28*d^4 + 65536*A^3*B*a^19*b^26*d^4 - 320*A^2*B^2*a^12*b^33*d^4 + 8
6144*A^2*B^2*a^14*b^31*d^4 - 807936*A^2*B^2*a^16*b^29*d^4 - 229376*A^2*B^2*a^18*b^27*d^4 + 262144*A^2*B^2*a^20
*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)*(10080*B^5*a^1
6*b^28*d^2 - 48*A^5*a^15*b^29*d^2 - 384*A^5*a^17*b^27*d^2 - 1080*B^5*a^14*b^30*d^2 - 39*A^5*a^13*b^31*d^2 + 16
896*B^5*a^18*b^26*d^2 + 120*A*B^4*a^13*b^31*d^2 - 10800*A*B^4*a^15*b^29*d^2 + 7808*A*B^4*a^17*b^27*d^2 + 32768
*A*B^4*a^19*b^25*d^2 - 1152*A^4*B*a^14*b^30*d^2 + 608*A^4*B*a^16*b^28*d^2 + 512*A^4*B*a^18*b^26*d^2 + 824*A^2*
B^3*a^14*b^30*d^2 - 30272*A^2*B^3*a^16*b^28*d^2 - 39936*A^2*B^3*a^18*b^26*d^2 - 159*A^3*B^2*a^13*b^31*d^2 + 10
400*A^3*B^2*a^15*b^29*d^2 + 9472*A^3*B^2*a^17*b^27*d^2))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2 -
 A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) - (274877906944*(672*A^6*a^14*b^29*d^2 - 72*A^6*a^12*b^31*d^2 - 7
68*A^6*a^16*b^27*d^2 + 25*B^6*a^12*b^31*d^2 - 480*B^6*a^14*b^29*d^2 + 57600*B^6*a^16*b^27*d^2 + 16384*B^6*a^18
*b^25*d^2 + 900*A*B^5*a^13*b^30*d^2 - 44416*A*B^5*a^15*b^28*d^2 + 115712*A*B^5*a^17*b^26*d^2 + 2148*A^5*B*a^13
*b^30*d^2 - 3456*A^5*B*a^15*b^28*d^2 + 1024*A^5*B*a^17*b^26*d^2 + 10*A^2*B^4*a^12*b^31*d^2 + 12000*A^2*B^4*a^1
4*b^29*d^2 - 119040*A^2*B^4*a^16*b^27*d^2 + 98304*A^2*B^4*a^18*b^25*d^2 + 744*A^3*B^3*a^13*b^30*d^2 + 66816*A^
3*B^3*a^15*b^28*d^2 - 79872*A^3*B^3*a^17*b^26*d^2 - 23*A^4*B^2*a^12*b^31*d^2 - 13728*A^4*B^2*a^14*b^29*d^2 + 4
3776*A^4*B^2*a^16*b^27*d^2 + 16384*A^4*B^2*a^18*b^25*d^2))/d^8 + (274877906944*tan(c + d*x)*(1408*A^6*a^14*b^3
0*d^2 - 72*A^6*a^12*b^32*d^2 - 3584*A^6*a^16*b^28*d^2 + 4096*A^6*a^18*b^26*d^2 + 25*B^6*a^12*b^32*d^2 - 1760*B
^6*a^14*b^30*d^2 + 275200*B^6*a^16*b^28*d^2 + 65536*B^6*a^18*b^26*d^2 + 1280*A*B^5*a^13*b^31*d^2 - 128640*A*B^
5*a^15*b^29*d^2 + 747520*A*B^5*a^17*b^27*d^2 + 2848*A^5*B*a^13*b^31*d^2 - 9856*A^5*B*a^15*b^29*d^2 + 10240*A^5
*B*a^17*b^27*d^2 + 10*A^2*B^4*a^12*b^32*d^2 + 21440*A^2*B^4*a^14*b^30*d^2 - 411648*A^2*B^4*a^16*b^28*d^2 + 921
600*A^2*B^4*a^18*b^26*d^2 + 928*A^3*B^3*a^13*b^31*d^2 + 162560*A^3*B^3*a^15*b^29*d^2 - 503808*A^3*B^3*a^17*b^2
7*d^2 + 262144*A^3*B^3*a^19*b^25*d^2 - 23*A^4*B^2*a^12*b^32*d^2 - 25568*A^4*B^2*a^14*b^30*d^2 + 169728*A^4*B^2
*a^16*b^28*d^2 - 57344*A^4*B^2*a^18*b^26*d^2))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) + (219902325555
2*tan(c + d*x)^(1/2)*(3*A^7*a^13*b^30 - 16*A^7*a^15*b^28 - 80*B^7*a^14*b^29 + 1280*B^7*a^16*b^27 + 2048*B^7*a^
18*b^25 - 64*A^2*B^5*a^14*b^29 + 2432*A^2*B^5*a^16*b^27 + 4096*A^2*B^5*a^18*b^25 + 37*A^3*B^4*a^13*b^30 - 2352
*A^3*B^4*a^15*b^28 - 3072*A^3*B^4*a^17*b^26 + 112*A^4*B^3*a^14*b^29 + 1024*A^4*B^3*a^16*b^27 + 2048*A^4*B^3*a^
18*b^25 + 25*A^5*B^2*a^13*b^30 - 1200*A^5*B^2*a^15*b^28 - 1536*A^5*B^2*a^17*b^26 + 15*A*B^6*a^13*b^30 - 1168*A
*B^6*a^15*b^28 - 1536*A*B^6*a^17*b^26 + 96*A^6*B*a^14*b^29 - 128*A^6*B*a^16*b^27))/(d^7*((a + b*tan(c + d*x))^
(1/2) - a^(1/2))))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2)*1i)/((549755813888*(4*A^8*a^12*b^30 + 5
120*B^8*a^16*b^26 + 1536*A^2*B^6*a^14*b^28 + 7168*A^2*B^6*a^16*b^26 - 144*A^3*B^5*a^13*b^29 - 10496*A^3*B^5*a^
15*b^27 + 8192*A^3*B^5*a^17*b^25 + 4*A^4*B^4*a^12*b^30 + 3072*A^4*B^4*a^14*b^28 - 1024*A^4*B^4*a^16*b^26 - 288
*A^5*B^3*a^13*b^29 - 4864*A^5*B^3*a^15*b^27 + 4096*A^5*B^3*a^17*b^25 + 8*A^6*B^2*a^12*b^30 + 1536*A^6*B^2*a^14
*b^28 - 3072*A^6*B^2*a^16*b^26 - 5376*A*B^7*a^15*b^27 + 4096*A*B^7*a^17*b^25 - 144*A^7*B*a^13*b^29 + 256*A^7*B
*a^15*b^27))/d^8 + (((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2)*((((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i +
 b*d^2)))^(1/2)*((((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2)*((((274877906944*(1600*a^12*b^34*d^8 - 1
6640*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*ta
n(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))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1
/2) - (2199023255552*tan(c + d*x)^(1/2)*(240*A*a^13*b^33*d^6 + 3064*A*a^15*b^31*d^6 + 8960*A*a^17*b^29*d^6 + 6
144*A*a^19*b^27*d^6 + 6920*B*a^14*b^32*d^6 + 9472*B*a^16*b^30*d^6 - 5632*B*a^18*b^28*d^6 - 8192*B*a^20*b^26*d^
6))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) - (27487
7906944*(19216*A^2*a^14*b^31*d^6 - 1440*A^2*a^12*b^33*d^6 - 22016*A^2*a^16*b^29*d^6 - 45056*A^2*a^18*b^27*d^6
+ 1200*B^2*a^12*b^33*d^6 - 16640*B^2*a^14*b^31*d^6 + 279040*B^2*a^16*b^29*d^6 + 561152*B^2*a^18*b^27*d^6 + 262
144*B^2*a^20*b^25*d^6 + 16480*A*B*a^13*b^32*d^6 - 25792*A*B*a^15*b^30*d^6 + 34816*A*B*a^17*b^28*d^6 + 81920*A*
B*a^19*b^26*d^6))/d^8 + (274877906944*tan(c + d*x)*(46704*A^2*a^14*b^32*d^6 - 1440*A^2*a^12*b^34*d^6 - 137216*
A^2*a^16*b^30*d^6 - 122880*A^2*a^18*b^28*d^6 + 65536*A^2*a^20*b^26*d^6 + 1200*B^2*a^12*b^34*d^6 - 52320*B^2*a^
14*b^32*d^6 + 1200640*B^2*a^16*b^30*d^6 + 2306048*B^2*a^18*b^28*d^6 + 1048576*B^2*a^20*b^26*d^6 + 21600*A*B*a^
13*b^33*d^6 - 121856*A*B*a^15*b^31*d^6 + 276480*A*B*a^17*b^29*d^6 + 425984*A*B*a^19*b^27*d^6))/(d^8*((a + b*ta
n(c + d*x))^(1/2) - a^(1/2))^2)) - (2199023255552*tan(c + d*x)^(1/2)*(168*A^3*a^13*b^32*d^4 + 1200*A^3*a^15*b^
30*d^4 + 2816*A^3*a^17*b^28*d^4 - 4770*B^3*a^14*b^31*d^4 + 17920*B^3*a^16*b^29*d^4 + 57344*B^3*a^18*b^27*d^4 +
 32768*B^3*a^20*b^25*d^4 + 180*A*B^2*a^13*b^32*d^4 - 26736*A*B^2*a^15*b^30*d^4 - 48896*A*B^2*a^17*b^28*d^4 - 1
6384*A*B^2*a^19*b^26*d^4 + 4746*A^2*B*a^14*b^31*d^4 - 2048*A^2*B*a^16*b^29*d^4 - 12288*A^2*B*a^18*b^27*d^4))/(
d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) + (2748779069
44*(484*A^4*a^12*b^32*d^4 - 6448*A^4*a^14*b^30*d^4 + 8704*A^4*a^16*b^28*d^4 + 4096*A^4*a^18*b^26*d^4 + 300*B^4
*a^12*b^32*d^4 - 5040*B^4*a^14*b^30*d^4 + 217600*B^4*a^16*b^28*d^4 + 217088*B^4*a^18*b^26*d^4 + 7720*A*B^3*a^1
3*b^31*d^4 - 104960*A*B^3*a^15*b^29*d^4 + 253952*A*B^3*a^17*b^27*d^4 + 327680*A*B^3*a^19*b^25*d^4 - 10392*A^3*
B*a^13*b^31*d^4 + 23808*A^3*B*a^15*b^29*d^4 - 16384*A^3*B*a^17*b^27*d^4 - 320*A^2*B^2*a^12*b^32*d^4 + 46496*A^
2*B^2*a^14*b^30*d^4 - 181248*A^2*B^2*a^16*b^28*d^4 - 155648*A^2*B^2*a^18*b^26*d^4))/d^8 - (274877906944*tan(c
+ d*x)*(484*A^4*a^12*b^33*d^4 - 14304*A^4*a^14*b^31*d^4 + 41472*A^4*a^16*b^29*d^4 - 16384*A^4*a^18*b^27*d^4 +
300*B^4*a^12*b^33*d^4 - 17120*B^4*a^14*b^31*d^4 + 985600*B^4*a^16*b^29*d^4 + 950272*B^4*a^18*b^27*d^4 + 10520*
A*B^3*a^13*b^32*d^4 - 320000*A*B^3*a^15*b^30*d^4 + 1617920*A*B^3*a^17*b^28*d^4 + 1703936*A*B^3*a^19*b^26*d^4 -
 13704*A^3*B*a^13*b^32*d^4 + 73728*A^3*B*a^15*b^30*d^4 - 131072*A^3*B*a^17*b^28*d^4 + 65536*A^3*B*a^19*b^26*d^
4 - 320*A^2*B^2*a^12*b^33*d^4 + 86144*A^2*B^2*a^14*b^31*d^4 - 807936*A^2*B^2*a^16*b^29*d^4 - 229376*A^2*B^2*a^
18*b^27*d^4 + 262144*A^2*B^2*a^20*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)*(10080*B^5*a^16*b^28*d^2 - 48*A^5*a^15*b^29*d^2 - 384*A^5*a^17*b^27*d^2 - 1080*B^5*a^14*b^3
0*d^2 - 39*A^5*a^13*b^31*d^2 + 16896*B^5*a^18*b^26*d^2 + 120*A*B^4*a^13*b^31*d^2 - 10800*A*B^4*a^15*b^29*d^2 +
 7808*A*B^4*a^17*b^27*d^2 + 32768*A*B^4*a^19*b^25*d^2 - 1152*A^4*B*a^14*b^30*d^2 + 608*A^4*B*a^16*b^28*d^2 + 5
12*A^4*B*a^18*b^26*d^2 + 824*A^2*B^3*a^14*b^30*d^2 - 30272*A^2*B^3*a^16*b^28*d^2 - 39936*A^2*B^3*a^18*b^26*d^2
 - 159*A^3*B^2*a^13*b^31*d^2 + 10400*A^3*B^2*a^15*b^29*d^2 + 9472*A^3*B^2*a^17*b^27*d^2))/(d^7*((a + b*tan(c +
 d*x))^(1/2) - a^(1/2))))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) - (274877906944*(672*A^6*a^14*b^
29*d^2 - 72*A^6*a^12*b^31*d^2 - 768*A^6*a^16*b^27*d^2 + 25*B^6*a^12*b^31*d^2 - 480*B^6*a^14*b^29*d^2 + 57600*B
^6*a^16*b^27*d^2 + 16384*B^6*a^18*b^25*d^2 + 900*A*B^5*a^13*b^30*d^2 - 44416*A*B^5*a^15*b^28*d^2 + 115712*A*B^
5*a^17*b^26*d^2 + 2148*A^5*B*a^13*b^30*d^2 - 3456*A^5*B*a^15*b^28*d^2 + 1024*A^5*B*a^17*b^26*d^2 + 10*A^2*B^4*
a^12*b^31*d^2 + 12000*A^2*B^4*a^14*b^29*d^2 - 119040*A^2*B^4*a^16*b^27*d^2 + 98304*A^2*B^4*a^18*b^25*d^2 + 744
*A^3*B^3*a^13*b^30*d^2 + 66816*A^3*B^3*a^15*b^28*d^2 - 79872*A^3*B^3*a^17*b^26*d^2 - 23*A^4*B^2*a^12*b^31*d^2
- 13728*A^4*B^2*a^14*b^29*d^2 + 43776*A^4*B^2*a^16*b^27*d^2 + 16384*A^4*B^2*a^18*b^25*d^2))/d^8 + (27487790694
4*tan(c + d*x)*(1408*A^6*a^14*b^30*d^2 - 72*A^6*a^12*b^32*d^2 - 3584*A^6*a^16*b^28*d^2 + 4096*A^6*a^18*b^26*d^
2 + 25*B^6*a^12*b^32*d^2 - 1760*B^6*a^14*b^30*d^2 + 275200*B^6*a^16*b^28*d^2 + 65536*B^6*a^18*b^26*d^2 + 1280*
A*B^5*a^13*b^31*d^2 - 128640*A*B^5*a^15*b^29*d^2 + 747520*A*B^5*a^17*b^27*d^2 + 2848*A^5*B*a^13*b^31*d^2 - 985
6*A^5*B*a^15*b^29*d^2 + 10240*A^5*B*a^17*b^27*d^2 + 10*A^2*B^4*a^12*b^32*d^2 + 21440*A^2*B^4*a^14*b^30*d^2 - 4
11648*A^2*B^4*a^16*b^28*d^2 + 921600*A^2*B^4*a^18*b^26*d^2 + 928*A^3*B^3*a^13*b^31*d^2 + 162560*A^3*B^3*a^15*b
^29*d^2 - 503808*A^3*B^3*a^17*b^27*d^2 + 262144*A^3*B^3*a^19*b^25*d^2 - 23*A^4*B^2*a^12*b^32*d^2 - 25568*A^4*B
^2*a^14*b^30*d^2 + 169728*A^4*B^2*a^16*b^28*d^2 - 57344*A^4*B^2*a^18*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)*(3*A^7*a^13*b^30 - 16*A^7*a^15*b^28 - 80*B^7*a^14*b^29 +
 1280*B^7*a^16*b^27 + 2048*B^7*a^18*b^25 - 64*A^2*B^5*a^14*b^29 + 2432*A^2*B^5*a^16*b^27 + 4096*A^2*B^5*a^18*b
^25 + 37*A^3*B^4*a^13*b^30 - 2352*A^3*B^4*a^15*b^28 - 3072*A^3*B^4*a^17*b^26 + 112*A^4*B^3*a^14*b^29 + 1024*A^
4*B^3*a^16*b^27 + 2048*A^4*B^3*a^18*b^25 + 25*A^5*B^2*a^13*b^30 - 1200*A^5*B^2*a^15*b^28 - 1536*A^5*B^2*a^17*b
^26 + 15*A*B^6*a^13*b^30 - 1168*A*B^6*a^15*b^28 - 1536*A*B^6*a^17*b^26 + 96*A^6*B*a^14*b^29 - 128*A^6*B*a^16*b
^27))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) + (((B
^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2)*((((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2)*((((B^2
 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2)*((((274877906944*(1600*a^12*b^34*d^8 - 16640*a^14*b^32*d^8 + 22
784*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))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) + (2199023255552*ta
n(c + d*x)^(1/2)*(240*A*a^13*b^33*d^6 + 3064*A*a^15*b^31*d^6 + 8960*A*a^17*b^29*d^6 + 6144*A*a^19*b^27*d^6 + 6
920*B*a^14*b^32*d^6 + 9472*B*a^16*b^30*d^6 - 5632*B*a^18*b^28*d^6 - 8192*B*a^20*b^26*d^6))/(d^7*((a + b*tan(c
+ d*x))^(1/2) - a^(1/2))))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) - (274877906944*(19216*A^2*a^14
*b^31*d^6 - 1440*A^2*a^12*b^33*d^6 - 22016*A^2*a^16*b^29*d^6 - 45056*A^2*a^18*b^27*d^6 + 1200*B^2*a^12*b^33*d^
6 - 16640*B^2*a^14*b^31*d^6 + 279040*B^2*a^16*b^29*d^6 + 561152*B^2*a^18*b^27*d^6 + 262144*B^2*a^20*b^25*d^6 +
 16480*A*B*a^13*b^32*d^6 - 25792*A*B*a^15*b^30*d^6 + 34816*A*B*a^17*b^28*d^6 + 81920*A*B*a^19*b^26*d^6))/d^8 +
 (274877906944*tan(c + d*x)*(46704*A^2*a^14*b^32*d^6 - 1440*A^2*a^12*b^34*d^6 - 137216*A^2*a^16*b^30*d^6 - 122
880*A^2*a^18*b^28*d^6 + 65536*A^2*a^20*b^26*d^6 + 1200*B^2*a^12*b^34*d^6 - 52320*B^2*a^14*b^32*d^6 + 1200640*B
^2*a^16*b^30*d^6 + 2306048*B^2*a^18*b^28*d^6 + 1048576*B^2*a^20*b^26*d^6 + 21600*A*B*a^13*b^33*d^6 - 121856*A*
B*a^15*b^31*d^6 + 276480*A*B*a^17*b^29*d^6 + 425984*A*B*a^19*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)*(168*A^3*a^13*b^32*d^4 + 1200*A^3*a^15*b^30*d^4 + 2816*A^3*a^17*
b^28*d^4 - 4770*B^3*a^14*b^31*d^4 + 17920*B^3*a^16*b^29*d^4 + 57344*B^3*a^18*b^27*d^4 + 32768*B^3*a^20*b^25*d^
4 + 180*A*B^2*a^13*b^32*d^4 - 26736*A*B^2*a^15*b^30*d^4 - 48896*A*B^2*a^17*b^28*d^4 - 16384*A*B^2*a^19*b^26*d^
4 + 4746*A^2*B*a^14*b^31*d^4 - 2048*A^2*B*a^16*b^29*d^4 - 12288*A^2*B*a^18*b^27*d^4))/(d^7*((a + b*tan(c + d*x
))^(1/2) - a^(1/2))))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) + (274877906944*(484*A^4*a^12*b^32*d
^4 - 6448*A^4*a^14*b^30*d^4 + 8704*A^4*a^16*b^28*d^4 + 4096*A^4*a^18*b^26*d^4 + 300*B^4*a^12*b^32*d^4 - 5040*B
^4*a^14*b^30*d^4 + 217600*B^4*a^16*b^28*d^4 + 217088*B^4*a^18*b^26*d^4 + 7720*A*B^3*a^13*b^31*d^4 - 104960*A*B
^3*a^15*b^29*d^4 + 253952*A*B^3*a^17*b^27*d^4 + 327680*A*B^3*a^19*b^25*d^4 - 10392*A^3*B*a^13*b^31*d^4 + 23808
*A^3*B*a^15*b^29*d^4 - 16384*A^3*B*a^17*b^27*d^4 - 320*A^2*B^2*a^12*b^32*d^4 + 46496*A^2*B^2*a^14*b^30*d^4 - 1
81248*A^2*B^2*a^16*b^28*d^4 - 155648*A^2*B^2*a^18*b^26*d^4))/d^8 - (274877906944*tan(c + d*x)*(484*A^4*a^12*b^
33*d^4 - 14304*A^4*a^14*b^31*d^4 + 41472*A^4*a^16*b^29*d^4 - 16384*A^4*a^18*b^27*d^4 + 300*B^4*a^12*b^33*d^4 -
 17120*B^4*a^14*b^31*d^4 + 985600*B^4*a^16*b^29*d^4 + 950272*B^4*a^18*b^27*d^4 + 10520*A*B^3*a^13*b^32*d^4 - 3
20000*A*B^3*a^15*b^30*d^4 + 1617920*A*B^3*a^17*b^28*d^4 + 1703936*A*B^3*a^19*b^26*d^4 - 13704*A^3*B*a^13*b^32*
d^4 + 73728*A^3*B*a^15*b^30*d^4 - 131072*A^3*B*a^17*b^28*d^4 + 65536*A^3*B*a^19*b^26*d^4 - 320*A^2*B^2*a^12*b^
33*d^4 + 86144*A^2*B^2*a^14*b^31*d^4 - 807936*A^2*B^2*a^16*b^29*d^4 - 229376*A^2*B^2*a^18*b^27*d^4 + 262144*A^
2*B^2*a^20*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)*(100
80*B^5*a^16*b^28*d^2 - 48*A^5*a^15*b^29*d^2 - 384*A^5*a^17*b^27*d^2 - 1080*B^5*a^14*b^30*d^2 - 39*A^5*a^13*b^3
1*d^2 + 16896*B^5*a^18*b^26*d^2 + 120*A*B^4*a^13*b^31*d^2 - 10800*A*B^4*a^15*b^29*d^2 + 7808*A*B^4*a^17*b^27*d
^2 + 32768*A*B^4*a^19*b^25*d^2 - 1152*A^4*B*a^14*b^30*d^2 + 608*A^4*B*a^16*b^28*d^2 + 512*A^4*B*a^18*b^26*d^2
+ 824*A^2*B^3*a^14*b^30*d^2 - 30272*A^2*B^3*a^16*b^28*d^2 - 39936*A^2*B^3*a^18*b^26*d^2 - 159*A^3*B^2*a^13*b^3
1*d^2 + 10400*A^3*B^2*a^15*b^29*d^2 + 9472*A^3*B^2*a^17*b^27*d^2))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))
))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) - (274877906944*(672*A^6*a^14*b^29*d^2 - 72*A^6*a^12*b^
31*d^2 - 768*A^6*a^16*b^27*d^2 + 25*B^6*a^12*b^31*d^2 - 480*B^6*a^14*b^29*d^2 + 57600*B^6*a^16*b^27*d^2 + 1638
4*B^6*a^18*b^25*d^2 + 900*A*B^5*a^13*b^30*d^2 - 44416*A*B^5*a^15*b^28*d^2 + 115712*A*B^5*a^17*b^26*d^2 + 2148*
A^5*B*a^13*b^30*d^2 - 3456*A^5*B*a^15*b^28*d^2 + 1024*A^5*B*a^17*b^26*d^2 + 10*A^2*B^4*a^12*b^31*d^2 + 12000*A
^2*B^4*a^14*b^29*d^2 - 119040*A^2*B^4*a^16*b^27*d^2 + 98304*A^2*B^4*a^18*b^25*d^2 + 744*A^3*B^3*a^13*b^30*d^2
+ 66816*A^3*B^3*a^15*b^28*d^2 - 79872*A^3*B^3*a^17*b^26*d^2 - 23*A^4*B^2*a^12*b^31*d^2 - 13728*A^4*B^2*a^14*b^
29*d^2 + 43776*A^4*B^2*a^16*b^27*d^2 + 16384*A^4*B^2*a^18*b^25*d^2))/d^8 + (274877906944*tan(c + d*x)*(1408*A^
6*a^14*b^30*d^2 - 72*A^6*a^12*b^32*d^2 - 3584*A^6*a^16*b^28*d^2 + 4096*A^6*a^18*b^26*d^2 + 25*B^6*a^12*b^32*d^
2 - 1760*B^6*a^14*b^30*d^2 + 275200*B^6*a^16*b^28*d^2 + 65536*B^6*a^18*b^26*d^2 + 1280*A*B^5*a^13*b^31*d^2 - 1
28640*A*B^5*a^15*b^29*d^2 + 747520*A*B^5*a^17*b^27*d^2 + 2848*A^5*B*a^13*b^31*d^2 - 9856*A^5*B*a^15*b^29*d^2 +
 10240*A^5*B*a^17*b^27*d^2 + 10*A^2*B^4*a^12*b^32*d^2 + 21440*A^2*B^4*a^14*b^30*d^2 - 411648*A^2*B^4*a^16*b^28
*d^2 + 921600*A^2*B^4*a^18*b^26*d^2 + 928*A^3*B^3*a^13*b^31*d^2 + 162560*A^3*B^3*a^15*b^29*d^2 - 503808*A^3*B^
3*a^17*b^27*d^2 + 262144*A^3*B^3*a^19*b^25*d^2 - 23*A^4*B^2*a^12*b^32*d^2 - 25568*A^4*B^2*a^14*b^30*d^2 + 1697
28*A^4*B^2*a^16*b^28*d^2 - 57344*A^4*B^2*a^18*b^26*d^2))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) + (21
99023255552*tan(c + d*x)^(1/2)*(3*A^7*a^13*b^30 - 16*A^7*a^15*b^28 - 80*B^7*a^14*b^29 + 1280*B^7*a^16*b^27 + 2
048*B^7*a^18*b^25 - 64*A^2*B^5*a^14*b^29 + 2432*A^2*B^5*a^16*b^27 + 4096*A^2*B^5*a^18*b^25 + 37*A^3*B^4*a^13*b
^30 - 2352*A^3*B^4*a^15*b^28 - 3072*A^3*B^4*a^17*b^26 + 112*A^4*B^3*a^14*b^29 + 1024*A^4*B^3*a^16*b^27 + 2048*
A^4*B^3*a^18*b^25 + 25*A^5*B^2*a^13*b^30 - 1200*A^5*B^2*a^15*b^28 - 1536*A^5*B^2*a^17*b^26 + 15*A*B^6*a^13*b^3
0 - 1168*A*B^6*a^15*b^28 - 1536*A*B^6*a^17*b^26 + 96*A^6*B*a^14*b^29 - 128*A^6*B*a^16*b^27))/(d^7*((a + b*tan(
c + d*x))^(1/2) - a^(1/2))))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2) - (549755813888*tan(c + d*x)*
(4*A^8*a^12*b^31 + 25600*B^8*a^16*b^27 + 2944*A^2*B^6*a^14*b^29 + 38912*A^2*B^6*a^16*b^27 + 16384*A^2*B^6*a^18
*b^25 - 192*A^3*B^5*a^13*b^30 - 30208*A^3*B^5*a^15*b^28 + 81920*A^3*B^5*a^17*b^26 + 4*A^4*B^4*a^12*b^31 + 5888
*A^4*B^4*a^14*b^29 + 1024*A^4*B^4*a^16*b^27 + 32768*A^4*B^4*a^18*b^25 - 384*A^5*B^3*a^13*b^30 - 14336*A^5*B^3*
a^15*b^28 + 40960*A^5*B^3*a^17*b^26 + 8*A^6*B^2*a^12*b^31 + 2944*A^6*B^2*a^14*b^29 - 12288*A^6*B^2*a^16*b^27 +
 16384*A^6*B^2*a^18*b^25 - 15360*A*B^7*a^15*b^28 + 40960*A*B^7*a^17*b^26 - 192*A^7*B*a^13*b^30 + 512*A^7*B*a^1
5*b^28))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)))*((B^2 - A^2 + A*B*2i)/(4*(a*d^2*1i + b*d^2)))^(1/2)*
2i + atan(((((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2)*((((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 +
b*d^2*1i)))^(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))*((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2) - (2199023255552*tan(c + d*x)^(1/2)*(240*
A*a^13*b^33*d^6 + 3064*A*a^15*b^31*d^6 + 8960*A*a^17*b^29*d^6 + 6144*A*a^19*b^27*d^6 + 6920*B*a^14*b^32*d^6 +
9472*B*a^16*b^30*d^6 - 5632*B*a^18*b^28*d^6 - 8192*B*a^20*b^26*d^6))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2
))))*((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2) - (274877906944*(19216*A^2*a^14*b^31*d^6 - 1440*
A^2*a^12*b^33*d^6 - 22016*A^2*a^16*b^29*d^6 - 45056*A^2*a^18*b^27*d^6 + 1200*B^2*a^12*b^33*d^6 - 16640*B^2*a^1
4*b^31*d^6 + 279040*B^2*a^16*b^29*d^6 + 561152*B^2*a^18*b^27*d^6 + 262144*B^2*a^20*b^25*d^6 + 16480*A*B*a^13*b
^32*d^6 - 25792*A*B*a^15*b^30*d^6 + 34816*A*B*a^17*b^28*d^6 + 81920*A*B*a^19*b^26*d^6))/d^8 + (274877906944*ta
n(c + d*x)*(46704*A^2*a^14*b^32*d^6 - 1440*A^2*a^12*b^34*d^6 - 137216*A^2*a^16*b^30*d^6 - 122880*A^2*a^18*b^28
*d^6 + 65536*A^2*a^20*b^26*d^6 + 1200*B^2*a^12*b^34*d^6 - 52320*B^2*a^14*b^32*d^6 + 1200640*B^2*a^16*b^30*d^6
+ 2306048*B^2*a^18*b^28*d^6 + 1048576*B^2*a^20*b^26*d^6 + 21600*A*B*a^13*b^33*d^6 - 121856*A*B*a^15*b^31*d^6 +
 276480*A*B*a^17*b^29*d^6 + 425984*A*B*a^19*b^27*d^6))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2))*((B^2*1
i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2) - (2199023255552*tan(c + d*x)^(1/2)*(168*A^3*a^13*b^32*d^4 +
 1200*A^3*a^15*b^30*d^4 + 2816*A^3*a^17*b^28*d^4 - 4770*B^3*a^14*b^31*d^4 + 17920*B^3*a^16*b^29*d^4 + 57344*B^
3*a^18*b^27*d^4 + 32768*B^3*a^20*b^25*d^4 + 180*A*B^2*a^13*b^32*d^4 - 26736*A*B^2*a^15*b^30*d^4 - 48896*A*B^2*
a^17*b^28*d^4 - 16384*A*B^2*a^19*b^26*d^4 + 4746*A^2*B*a^14*b^31*d^4 - 2048*A^2*B*a^16*b^29*d^4 - 12288*A^2*B*
a^18*b^27*d^4))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)
))^(1/2) + (274877906944*(484*A^4*a^12*b^32*d^4 - 6448*A^4*a^14*b^30*d^4 + 8704*A^4*a^16*b^28*d^4 + 4096*A^4*a
^18*b^26*d^4 + 300*B^4*a^12*b^32*d^4 - 5040*B^4*a^14*b^30*d^4 + 217600*B^4*a^16*b^28*d^4 + 217088*B^4*a^18*b^2
6*d^4 + 7720*A*B^3*a^13*b^31*d^4 - 104960*A*B^3*a^15*b^29*d^4 + 253952*A*B^3*a^17*b^27*d^4 + 327680*A*B^3*a^19
*b^25*d^4 - 10392*A^3*B*a^13*b^31*d^4 + 23808*A^3*B*a^15*b^29*d^4 - 16384*A^3*B*a^17*b^27*d^4 - 320*A^2*B^2*a^
12*b^32*d^4 + 46496*A^2*B^2*a^14*b^30*d^4 - 181248*A^2*B^2*a^16*b^28*d^4 - 155648*A^2*B^2*a^18*b^26*d^4))/d^8
- (274877906944*tan(c + d*x)*(484*A^4*a^12*b^33*d^4 - 14304*A^4*a^14*b^31*d^4 + 41472*A^4*a^16*b^29*d^4 - 1638
4*A^4*a^18*b^27*d^4 + 300*B^4*a^12*b^33*d^4 - 17120*B^4*a^14*b^31*d^4 + 985600*B^4*a^16*b^29*d^4 + 950272*B^4*
a^18*b^27*d^4 + 10520*A*B^3*a^13*b^32*d^4 - 320000*A*B^3*a^15*b^30*d^4 + 1617920*A*B^3*a^17*b^28*d^4 + 1703936
*A*B^3*a^19*b^26*d^4 - 13704*A^3*B*a^13*b^32*d^4 + 73728*A^3*B*a^15*b^30*d^4 - 131072*A^3*B*a^17*b^28*d^4 + 65
536*A^3*B*a^19*b^26*d^4 - 320*A^2*B^2*a^12*b^33*d^4 + 86144*A^2*B^2*a^14*b^31*d^4 - 807936*A^2*B^2*a^16*b^29*d
^4 - 229376*A^2*B^2*a^18*b^27*d^4 + 262144*A^2*B^2*a^20*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)*(10080*B^5*a^16*b^28*d^2 - 48*A^5*a^15*b^29*d^2 - 384*A^5*a^17*b^27*d
^2 - 1080*B^5*a^14*b^30*d^2 - 39*A^5*a^13*b^31*d^2 + 16896*B^5*a^18*b^26*d^2 + 120*A*B^4*a^13*b^31*d^2 - 10800
*A*B^4*a^15*b^29*d^2 + 7808*A*B^4*a^17*b^27*d^2 + 32768*A*B^4*a^19*b^25*d^2 - 1152*A^4*B*a^14*b^30*d^2 + 608*A
^4*B*a^16*b^28*d^2 + 512*A^4*B*a^18*b^26*d^2 + 824*A^2*B^3*a^14*b^30*d^2 - 30272*A^2*B^3*a^16*b^28*d^2 - 39936
*A^2*B^3*a^18*b^26*d^2 - 159*A^3*B^2*a^13*b^31*d^2 + 10400*A^3*B^2*a^15*b^29*d^2 + 9472*A^3*B^2*a^17*b^27*d^2)
)/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2) - (27
4877906944*(672*A^6*a^14*b^29*d^2 - 72*A^6*a^12*b^31*d^2 - 768*A^6*a^16*b^27*d^2 + 25*B^6*a^12*b^31*d^2 - 480*
B^6*a^14*b^29*d^2 + 57600*B^6*a^16*b^27*d^2 + 16384*B^6*a^18*b^25*d^2 + 900*A*B^5*a^13*b^30*d^2 - 44416*A*B^5*
a^15*b^28*d^2 + 115712*A*B^5*a^17*b^26*d^2 + 2148*A^5*B*a^13*b^30*d^2 - 3456*A^5*B*a^15*b^28*d^2 + 1024*A^5*B*
a^17*b^26*d^2 + 10*A^2*B^4*a^12*b^31*d^2 + 12000*A^2*B^4*a^14*b^29*d^2 - 119040*A^2*B^4*a^16*b^27*d^2 + 98304*
A^2*B^4*a^18*b^25*d^2 + 744*A^3*B^3*a^13*b^30*d^2 + 66816*A^3*B^3*a^15*b^28*d^2 - 79872*A^3*B^3*a^17*b^26*d^2
- 23*A^4*B^2*a^12*b^31*d^2 - 13728*A^4*B^2*a^14*b^29*d^2 + 43776*A^4*B^2*a^16*b^27*d^2 + 16384*A^4*B^2*a^18*b^
25*d^2))/d^8 + (274877906944*tan(c + d*x)*(1408*A^6*a^14*b^30*d^2 - 72*A^6*a^12*b^32*d^2 - 3584*A^6*a^16*b^28*
d^2 + 4096*A^6*a^18*b^26*d^2 + 25*B^6*a^12*b^32*d^2 - 1760*B^6*a^14*b^30*d^2 + 275200*B^6*a^16*b^28*d^2 + 6553
6*B^6*a^18*b^26*d^2 + 1280*A*B^5*a^13*b^31*d^2 - 128640*A*B^5*a^15*b^29*d^2 + 747520*A*B^5*a^17*b^27*d^2 + 284
8*A^5*B*a^13*b^31*d^2 - 9856*A^5*B*a^15*b^29*d^2 + 10240*A^5*B*a^17*b^27*d^2 + 10*A^2*B^4*a^12*b^32*d^2 + 2144
0*A^2*B^4*a^14*b^30*d^2 - 411648*A^2*B^4*a^16*b^28*d^2 + 921600*A^2*B^4*a^18*b^26*d^2 + 928*A^3*B^3*a^13*b^31*
d^2 + 162560*A^3*B^3*a^15*b^29*d^2 - 503808*A^3*B^3*a^17*b^27*d^2 + 262144*A^3*B^3*a^19*b^25*d^2 - 23*A^4*B^2*
a^12*b^32*d^2 - 25568*A^4*B^2*a^14*b^30*d^2 + 169728*A^4*B^2*a^16*b^28*d^2 - 57344*A^4*B^2*a^18*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)*(3*A^7*a^13*b^30 - 16*A^7*a^1
5*b^28 - 80*B^7*a^14*b^29 + 1280*B^7*a^16*b^27 + 2048*B^7*a^18*b^25 - 64*A^2*B^5*a^14*b^29 + 2432*A^2*B^5*a^16
*b^27 + 4096*A^2*B^5*a^18*b^25 + 37*A^3*B^4*a^13*b^30 - 2352*A^3*B^4*a^15*b^28 - 3072*A^3*B^4*a^17*b^26 + 112*
A^4*B^3*a^14*b^29 + 1024*A^4*B^3*a^16*b^27 + 2048*A^4*B^3*a^18*b^25 + 25*A^5*B^2*a^13*b^30 - 1200*A^5*B^2*a^15
*b^28 - 1536*A^5*B^2*a^17*b^26 + 15*A*B^6*a^13*b^30 - 1168*A*B^6*a^15*b^28 - 1536*A*B^6*a^17*b^26 + 96*A^6*B*a
^14*b^29 - 128*A^6*B*a^16*b^27))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2*1i - A^2*1i + 2*A*B)/(4*(
a*d^2 + b*d^2*1i)))^(1/2)*1i - (((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2)*((((B^2*1i - A^2*1i +
 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2)*((((((274877906944*(1600*a^12*b^34*d^8 - 16640*a^14*b^32*d^8 + 22784*a^1
6*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))*((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2) + (2199023255552*tan(
c + d*x)^(1/2)*(240*A*a^13*b^33*d^6 + 3064*A*a^15*b^31*d^6 + 8960*A*a^17*b^29*d^6 + 6144*A*a^19*b^27*d^6 + 692
0*B*a^14*b^32*d^6 + 9472*B*a^16*b^30*d^6 - 5632*B*a^18*b^28*d^6 - 8192*B*a^20*b^26*d^6))/(d^7*((a + b*tan(c +
d*x))^(1/2) - a^(1/2))))*((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2) - (274877906944*(19216*A^2*a
^14*b^31*d^6 - 1440*A^2*a^12*b^33*d^6 - 22016*A^2*a^16*b^29*d^6 - 45056*A^2*a^18*b^27*d^6 + 1200*B^2*a^12*b^33
*d^6 - 16640*B^2*a^14*b^31*d^6 + 279040*B^2*a^16*b^29*d^6 + 561152*B^2*a^18*b^27*d^6 + 262144*B^2*a^20*b^25*d^
6 + 16480*A*B*a^13*b^32*d^6 - 25792*A*B*a^15*b^30*d^6 + 34816*A*B*a^17*b^28*d^6 + 81920*A*B*a^19*b^26*d^6))/d^
8 + (274877906944*tan(c + d*x)*(46704*A^2*a^14*b^32*d^6 - 1440*A^2*a^12*b^34*d^6 - 137216*A^2*a^16*b^30*d^6 -
122880*A^2*a^18*b^28*d^6 + 65536*A^2*a^20*b^26*d^6 + 1200*B^2*a^12*b^34*d^6 - 52320*B^2*a^14*b^32*d^6 + 120064
0*B^2*a^16*b^30*d^6 + 2306048*B^2*a^18*b^28*d^6 + 1048576*B^2*a^20*b^26*d^6 + 21600*A*B*a^13*b^33*d^6 - 121856
*A*B*a^15*b^31*d^6 + 276480*A*B*a^17*b^29*d^6 + 425984*A*B*a^19*b^27*d^6))/(d^8*((a + b*tan(c + d*x))^(1/2) -
a^(1/2))^2))*((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2) + (2199023255552*tan(c + d*x)^(1/2)*(168
*A^3*a^13*b^32*d^4 + 1200*A^3*a^15*b^30*d^4 + 2816*A^3*a^17*b^28*d^4 - 4770*B^3*a^14*b^31*d^4 + 17920*B^3*a^16
*b^29*d^4 + 57344*B^3*a^18*b^27*d^4 + 32768*B^3*a^20*b^25*d^4 + 180*A*B^2*a^13*b^32*d^4 - 26736*A*B^2*a^15*b^3
0*d^4 - 48896*A*B^2*a^17*b^28*d^4 - 16384*A*B^2*a^19*b^26*d^4 + 4746*A^2*B*a^14*b^31*d^4 - 2048*A^2*B*a^16*b^2
9*d^4 - 12288*A^2*B*a^18*b^27*d^4))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2*1i - A^2*1i + 2*A*B)/(
4*(a*d^2 + b*d^2*1i)))^(1/2) + (274877906944*(484*A^4*a^12*b^32*d^4 - 6448*A^4*a^14*b^30*d^4 + 8704*A^4*a^16*b
^28*d^4 + 4096*A^4*a^18*b^26*d^4 + 300*B^4*a^12*b^32*d^4 - 5040*B^4*a^14*b^30*d^4 + 217600*B^4*a^16*b^28*d^4 +
 217088*B^4*a^18*b^26*d^4 + 7720*A*B^3*a^13*b^31*d^4 - 104960*A*B^3*a^15*b^29*d^4 + 253952*A*B^3*a^17*b^27*d^4
 + 327680*A*B^3*a^19*b^25*d^4 - 10392*A^3*B*a^13*b^31*d^4 + 23808*A^3*B*a^15*b^29*d^4 - 16384*A^3*B*a^17*b^27*
d^4 - 320*A^2*B^2*a^12*b^32*d^4 + 46496*A^2*B^2*a^14*b^30*d^4 - 181248*A^2*B^2*a^16*b^28*d^4 - 155648*A^2*B^2*
a^18*b^26*d^4))/d^8 - (274877906944*tan(c + d*x)*(484*A^4*a^12*b^33*d^4 - 14304*A^4*a^14*b^31*d^4 + 41472*A^4*
a^16*b^29*d^4 - 16384*A^4*a^18*b^27*d^4 + 300*B^4*a^12*b^33*d^4 - 17120*B^4*a^14*b^31*d^4 + 985600*B^4*a^16*b^
29*d^4 + 950272*B^4*a^18*b^27*d^4 + 10520*A*B^3*a^13*b^32*d^4 - 320000*A*B^3*a^15*b^30*d^4 + 1617920*A*B^3*a^1
7*b^28*d^4 + 1703936*A*B^3*a^19*b^26*d^4 - 13704*A^3*B*a^13*b^32*d^4 + 73728*A^3*B*a^15*b^30*d^4 - 131072*A^3*
B*a^17*b^28*d^4 + 65536*A^3*B*a^19*b^26*d^4 - 320*A^2*B^2*a^12*b^33*d^4 + 86144*A^2*B^2*a^14*b^31*d^4 - 807936
*A^2*B^2*a^16*b^29*d^4 - 229376*A^2*B^2*a^18*b^27*d^4 + 262144*A^2*B^2*a^20*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)*(10080*B^5*a^16*b^28*d^2 - 48*A^5*a^15*b^29*d^2 -
 384*A^5*a^17*b^27*d^2 - 1080*B^5*a^14*b^30*d^2 - 39*A^5*a^13*b^31*d^2 + 16896*B^5*a^18*b^26*d^2 + 120*A*B^4*a
^13*b^31*d^2 - 10800*A*B^4*a^15*b^29*d^2 + 7808*A*B^4*a^17*b^27*d^2 + 32768*A*B^4*a^19*b^25*d^2 - 1152*A^4*B*a
^14*b^30*d^2 + 608*A^4*B*a^16*b^28*d^2 + 512*A^4*B*a^18*b^26*d^2 + 824*A^2*B^3*a^14*b^30*d^2 - 30272*A^2*B^3*a
^16*b^28*d^2 - 39936*A^2*B^3*a^18*b^26*d^2 - 159*A^3*B^2*a^13*b^31*d^2 + 10400*A^3*B^2*a^15*b^29*d^2 + 9472*A^
3*B^2*a^17*b^27*d^2))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d
^2*1i)))^(1/2) - (274877906944*(672*A^6*a^14*b^29*d^2 - 72*A^6*a^12*b^31*d^2 - 768*A^6*a^16*b^27*d^2 + 25*B^6*
a^12*b^31*d^2 - 480*B^6*a^14*b^29*d^2 + 57600*B^6*a^16*b^27*d^2 + 16384*B^6*a^18*b^25*d^2 + 900*A*B^5*a^13*b^3
0*d^2 - 44416*A*B^5*a^15*b^28*d^2 + 115712*A*B^5*a^17*b^26*d^2 + 2148*A^5*B*a^13*b^30*d^2 - 3456*A^5*B*a^15*b^
28*d^2 + 1024*A^5*B*a^17*b^26*d^2 + 10*A^2*B^4*a^12*b^31*d^2 + 12000*A^2*B^4*a^14*b^29*d^2 - 119040*A^2*B^4*a^
16*b^27*d^2 + 98304*A^2*B^4*a^18*b^25*d^2 + 744*A^3*B^3*a^13*b^30*d^2 + 66816*A^3*B^3*a^15*b^28*d^2 - 79872*A^
3*B^3*a^17*b^26*d^2 - 23*A^4*B^2*a^12*b^31*d^2 - 13728*A^4*B^2*a^14*b^29*d^2 + 43776*A^4*B^2*a^16*b^27*d^2 + 1
6384*A^4*B^2*a^18*b^25*d^2))/d^8 + (274877906944*tan(c + d*x)*(1408*A^6*a^14*b^30*d^2 - 72*A^6*a^12*b^32*d^2 -
 3584*A^6*a^16*b^28*d^2 + 4096*A^6*a^18*b^26*d^2 + 25*B^6*a^12*b^32*d^2 - 1760*B^6*a^14*b^30*d^2 + 275200*B^6*
a^16*b^28*d^2 + 65536*B^6*a^18*b^26*d^2 + 1280*A*B^5*a^13*b^31*d^2 - 128640*A*B^5*a^15*b^29*d^2 + 747520*A*B^5
*a^17*b^27*d^2 + 2848*A^5*B*a^13*b^31*d^2 - 9856*A^5*B*a^15*b^29*d^2 + 10240*A^5*B*a^17*b^27*d^2 + 10*A^2*B^4*
a^12*b^32*d^2 + 21440*A^2*B^4*a^14*b^30*d^2 - 411648*A^2*B^4*a^16*b^28*d^2 + 921600*A^2*B^4*a^18*b^26*d^2 + 92
8*A^3*B^3*a^13*b^31*d^2 + 162560*A^3*B^3*a^15*b^29*d^2 - 503808*A^3*B^3*a^17*b^27*d^2 + 262144*A^3*B^3*a^19*b^
25*d^2 - 23*A^4*B^2*a^12*b^32*d^2 - 25568*A^4*B^2*a^14*b^30*d^2 + 169728*A^4*B^2*a^16*b^28*d^2 - 57344*A^4*B^2
*a^18*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)*(3*A^7*a^
13*b^30 - 16*A^7*a^15*b^28 - 80*B^7*a^14*b^29 + 1280*B^7*a^16*b^27 + 2048*B^7*a^18*b^25 - 64*A^2*B^5*a^14*b^29
 + 2432*A^2*B^5*a^16*b^27 + 4096*A^2*B^5*a^18*b^25 + 37*A^3*B^4*a^13*b^30 - 2352*A^3*B^4*a^15*b^28 - 3072*A^3*
B^4*a^17*b^26 + 112*A^4*B^3*a^14*b^29 + 1024*A^4*B^3*a^16*b^27 + 2048*A^4*B^3*a^18*b^25 + 25*A^5*B^2*a^13*b^30
 - 1200*A^5*B^2*a^15*b^28 - 1536*A^5*B^2*a^17*b^26 + 15*A*B^6*a^13*b^30 - 1168*A*B^6*a^15*b^28 - 1536*A*B^6*a^
17*b^26 + 96*A^6*B*a^14*b^29 - 128*A^6*B*a^16*b^27))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2*1i -
A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2)*1i)/((549755813888*(4*A^8*a^12*b^30 + 5120*B^8*a^16*b^26 + 1536*
A^2*B^6*a^14*b^28 + 7168*A^2*B^6*a^16*b^26 - 144*A^3*B^5*a^13*b^29 - 10496*A^3*B^5*a^15*b^27 + 8192*A^3*B^5*a^
17*b^25 + 4*A^4*B^4*a^12*b^30 + 3072*A^4*B^4*a^14*b^28 - 1024*A^4*B^4*a^16*b^26 - 288*A^5*B^3*a^13*b^29 - 4864
*A^5*B^3*a^15*b^27 + 4096*A^5*B^3*a^17*b^25 + 8*A^6*B^2*a^12*b^30 + 1536*A^6*B^2*a^14*b^28 - 3072*A^6*B^2*a^16
*b^26 - 5376*A*B^7*a^15*b^27 + 4096*A*B^7*a^17*b^25 - 144*A^7*B*a^13*b^29 + 256*A^7*B*a^15*b^27))/d^8 + (((B^2
*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2)*((((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(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))*((B^2
*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2) - (2199023255552*tan(c + d*x)^(1/2)*(240*A*a^13*b^33*d^6 +
 3064*A*a^15*b^31*d^6 + 8960*A*a^17*b^29*d^6 + 6144*A*a^19*b^27*d^6 + 6920*B*a^14*b^32*d^6 + 9472*B*a^16*b^30*
d^6 - 5632*B*a^18*b^28*d^6 - 8192*B*a^20*b^26*d^6))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2*1i - A
^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2) - (274877906944*(19216*A^2*a^14*b^31*d^6 - 1440*A^2*a^12*b^33*d^6
 - 22016*A^2*a^16*b^29*d^6 - 45056*A^2*a^18*b^27*d^6 + 1200*B^2*a^12*b^33*d^6 - 16640*B^2*a^14*b^31*d^6 + 2790
40*B^2*a^16*b^29*d^6 + 561152*B^2*a^18*b^27*d^6 + 262144*B^2*a^20*b^25*d^6 + 16480*A*B*a^13*b^32*d^6 - 25792*A
*B*a^15*b^30*d^6 + 34816*A*B*a^17*b^28*d^6 + 81920*A*B*a^19*b^26*d^6))/d^8 + (274877906944*tan(c + d*x)*(46704
*A^2*a^14*b^32*d^6 - 1440*A^2*a^12*b^34*d^6 - 137216*A^2*a^16*b^30*d^6 - 122880*A^2*a^18*b^28*d^6 + 65536*A^2*
a^20*b^26*d^6 + 1200*B^2*a^12*b^34*d^6 - 52320*B^2*a^14*b^32*d^6 + 1200640*B^2*a^16*b^30*d^6 + 2306048*B^2*a^1
8*b^28*d^6 + 1048576*B^2*a^20*b^26*d^6 + 21600*A*B*a^13*b^33*d^6 - 121856*A*B*a^15*b^31*d^6 + 276480*A*B*a^17*
b^29*d^6 + 425984*A*B*a^19*b^27*d^6))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2))*((B^2*1i - A^2*1i + 2*A*
B)/(4*(a*d^2 + b*d^2*1i)))^(1/2) - (2199023255552*tan(c + d*x)^(1/2)*(168*A^3*a^13*b^32*d^4 + 1200*A^3*a^15*b^
30*d^4 + 2816*A^3*a^17*b^28*d^4 - 4770*B^3*a^14*b^31*d^4 + 17920*B^3*a^16*b^29*d^4 + 57344*B^3*a^18*b^27*d^4 +
 32768*B^3*a^20*b^25*d^4 + 180*A*B^2*a^13*b^32*d^4 - 26736*A*B^2*a^15*b^30*d^4 - 48896*A*B^2*a^17*b^28*d^4 - 1
6384*A*B^2*a^19*b^26*d^4 + 4746*A^2*B*a^14*b^31*d^4 - 2048*A^2*B*a^16*b^29*d^4 - 12288*A^2*B*a^18*b^27*d^4))/(
d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2) + (27487
7906944*(484*A^4*a^12*b^32*d^4 - 6448*A^4*a^14*b^30*d^4 + 8704*A^4*a^16*b^28*d^4 + 4096*A^4*a^18*b^26*d^4 + 30
0*B^4*a^12*b^32*d^4 - 5040*B^4*a^14*b^30*d^4 + 217600*B^4*a^16*b^28*d^4 + 217088*B^4*a^18*b^26*d^4 + 7720*A*B^
3*a^13*b^31*d^4 - 104960*A*B^3*a^15*b^29*d^4 + 253952*A*B^3*a^17*b^27*d^4 + 327680*A*B^3*a^19*b^25*d^4 - 10392
*A^3*B*a^13*b^31*d^4 + 23808*A^3*B*a^15*b^29*d^4 - 16384*A^3*B*a^17*b^27*d^4 - 320*A^2*B^2*a^12*b^32*d^4 + 464
96*A^2*B^2*a^14*b^30*d^4 - 181248*A^2*B^2*a^16*b^28*d^4 - 155648*A^2*B^2*a^18*b^26*d^4))/d^8 - (274877906944*t
an(c + d*x)*(484*A^4*a^12*b^33*d^4 - 14304*A^4*a^14*b^31*d^4 + 41472*A^4*a^16*b^29*d^4 - 16384*A^4*a^18*b^27*d
^4 + 300*B^4*a^12*b^33*d^4 - 17120*B^4*a^14*b^31*d^4 + 985600*B^4*a^16*b^29*d^4 + 950272*B^4*a^18*b^27*d^4 + 1
0520*A*B^3*a^13*b^32*d^4 - 320000*A*B^3*a^15*b^30*d^4 + 1617920*A*B^3*a^17*b^28*d^4 + 1703936*A*B^3*a^19*b^26*
d^4 - 13704*A^3*B*a^13*b^32*d^4 + 73728*A^3*B*a^15*b^30*d^4 - 131072*A^3*B*a^17*b^28*d^4 + 65536*A^3*B*a^19*b^
26*d^4 - 320*A^2*B^2*a^12*b^33*d^4 + 86144*A^2*B^2*a^14*b^31*d^4 - 807936*A^2*B^2*a^16*b^29*d^4 - 229376*A^2*B
^2*a^18*b^27*d^4 + 262144*A^2*B^2*a^20*b^25*d^4))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)) + (219902325
5552*tan(c + d*x)^(1/2)*(10080*B^5*a^16*b^28*d^2 - 48*A^5*a^15*b^29*d^2 - 384*A^5*a^17*b^27*d^2 - 1080*B^5*a^1
4*b^30*d^2 - 39*A^5*a^13*b^31*d^2 + 16896*B^5*a^18*b^26*d^2 + 120*A*B^4*a^13*b^31*d^2 - 10800*A*B^4*a^15*b^29*
d^2 + 7808*A*B^4*a^17*b^27*d^2 + 32768*A*B^4*a^19*b^25*d^2 - 1152*A^4*B*a^14*b^30*d^2 + 608*A^4*B*a^16*b^28*d^
2 + 512*A^4*B*a^18*b^26*d^2 + 824*A^2*B^3*a^14*b^30*d^2 - 30272*A^2*B^3*a^16*b^28*d^2 - 39936*A^2*B^3*a^18*b^2
6*d^2 - 159*A^3*B^2*a^13*b^31*d^2 + 10400*A^3*B^2*a^15*b^29*d^2 + 9472*A^3*B^2*a^17*b^27*d^2))/(d^7*((a + b*ta
n(c + d*x))^(1/2) - a^(1/2))))*((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2) - (274877906944*(672*A
^6*a^14*b^29*d^2 - 72*A^6*a^12*b^31*d^2 - 768*A^6*a^16*b^27*d^2 + 25*B^6*a^12*b^31*d^2 - 480*B^6*a^14*b^29*d^2
 + 57600*B^6*a^16*b^27*d^2 + 16384*B^6*a^18*b^25*d^2 + 900*A*B^5*a^13*b^30*d^2 - 44416*A*B^5*a^15*b^28*d^2 + 1
15712*A*B^5*a^17*b^26*d^2 + 2148*A^5*B*a^13*b^30*d^2 - 3456*A^5*B*a^15*b^28*d^2 + 1024*A^5*B*a^17*b^26*d^2 + 1
0*A^2*B^4*a^12*b^31*d^2 + 12000*A^2*B^4*a^14*b^29*d^2 - 119040*A^2*B^4*a^16*b^27*d^2 + 98304*A^2*B^4*a^18*b^25
*d^2 + 744*A^3*B^3*a^13*b^30*d^2 + 66816*A^3*B^3*a^15*b^28*d^2 - 79872*A^3*B^3*a^17*b^26*d^2 - 23*A^4*B^2*a^12
*b^31*d^2 - 13728*A^4*B^2*a^14*b^29*d^2 + 43776*A^4*B^2*a^16*b^27*d^2 + 16384*A^4*B^2*a^18*b^25*d^2))/d^8 + (2
74877906944*tan(c + d*x)*(1408*A^6*a^14*b^30*d^2 - 72*A^6*a^12*b^32*d^2 - 3584*A^6*a^16*b^28*d^2 + 4096*A^6*a^
18*b^26*d^2 + 25*B^6*a^12*b^32*d^2 - 1760*B^6*a^14*b^30*d^2 + 275200*B^6*a^16*b^28*d^2 + 65536*B^6*a^18*b^26*d
^2 + 1280*A*B^5*a^13*b^31*d^2 - 128640*A*B^5*a^15*b^29*d^2 + 747520*A*B^5*a^17*b^27*d^2 + 2848*A^5*B*a^13*b^31
*d^2 - 9856*A^5*B*a^15*b^29*d^2 + 10240*A^5*B*a^17*b^27*d^2 + 10*A^2*B^4*a^12*b^32*d^2 + 21440*A^2*B^4*a^14*b^
30*d^2 - 411648*A^2*B^4*a^16*b^28*d^2 + 921600*A^2*B^4*a^18*b^26*d^2 + 928*A^3*B^3*a^13*b^31*d^2 + 162560*A^3*
B^3*a^15*b^29*d^2 - 503808*A^3*B^3*a^17*b^27*d^2 + 262144*A^3*B^3*a^19*b^25*d^2 - 23*A^4*B^2*a^12*b^32*d^2 - 2
5568*A^4*B^2*a^14*b^30*d^2 + 169728*A^4*B^2*a^16*b^28*d^2 - 57344*A^4*B^2*a^18*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)*(3*A^7*a^13*b^30 - 16*A^7*a^15*b^28 - 80*B^7*a
^14*b^29 + 1280*B^7*a^16*b^27 + 2048*B^7*a^18*b^25 - 64*A^2*B^5*a^14*b^29 + 2432*A^2*B^5*a^16*b^27 + 4096*A^2*
B^5*a^18*b^25 + 37*A^3*B^4*a^13*b^30 - 2352*A^3*B^4*a^15*b^28 - 3072*A^3*B^4*a^17*b^26 + 112*A^4*B^3*a^14*b^29
 + 1024*A^4*B^3*a^16*b^27 + 2048*A^4*B^3*a^18*b^25 + 25*A^5*B^2*a^13*b^30 - 1200*A^5*B^2*a^15*b^28 - 1536*A^5*
B^2*a^17*b^26 + 15*A*B^6*a^13*b^30 - 1168*A*B^6*a^15*b^28 - 1536*A*B^6*a^17*b^26 + 96*A^6*B*a^14*b^29 - 128*A^
6*B*a^16*b^27))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)
))^(1/2) + (((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2)*((((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 +
b*d^2*1i)))^(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))*((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2) + (2199023255552*tan(c + d*x)^(1/2)*(240*
A*a^13*b^33*d^6 + 3064*A*a^15*b^31*d^6 + 8960*A*a^17*b^29*d^6 + 6144*A*a^19*b^27*d^6 + 6920*B*a^14*b^32*d^6 +
9472*B*a^16*b^30*d^6 - 5632*B*a^18*b^28*d^6 - 8192*B*a^20*b^26*d^6))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2
))))*((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2) - (274877906944*(19216*A^2*a^14*b^31*d^6 - 1440*
A^2*a^12*b^33*d^6 - 22016*A^2*a^16*b^29*d^6 - 45056*A^2*a^18*b^27*d^6 + 1200*B^2*a^12*b^33*d^6 - 16640*B^2*a^1
4*b^31*d^6 + 279040*B^2*a^16*b^29*d^6 + 561152*B^2*a^18*b^27*d^6 + 262144*B^2*a^20*b^25*d^6 + 16480*A*B*a^13*b
^32*d^6 - 25792*A*B*a^15*b^30*d^6 + 34816*A*B*a^17*b^28*d^6 + 81920*A*B*a^19*b^26*d^6))/d^8 + (274877906944*ta
n(c + d*x)*(46704*A^2*a^14*b^32*d^6 - 1440*A^2*a^12*b^34*d^6 - 137216*A^2*a^16*b^30*d^6 - 122880*A^2*a^18*b^28
*d^6 + 65536*A^2*a^20*b^26*d^6 + 1200*B^2*a^12*b^34*d^6 - 52320*B^2*a^14*b^32*d^6 + 1200640*B^2*a^16*b^30*d^6
+ 2306048*B^2*a^18*b^28*d^6 + 1048576*B^2*a^20*b^26*d^6 + 21600*A*B*a^13*b^33*d^6 - 121856*A*B*a^15*b^31*d^6 +
 276480*A*B*a^17*b^29*d^6 + 425984*A*B*a^19*b^27*d^6))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2))*((B^2*1
i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2) + (2199023255552*tan(c + d*x)^(1/2)*(168*A^3*a^13*b^32*d^4 +
 1200*A^3*a^15*b^30*d^4 + 2816*A^3*a^17*b^28*d^4 - 4770*B^3*a^14*b^31*d^4 + 17920*B^3*a^16*b^29*d^4 + 57344*B^
3*a^18*b^27*d^4 + 32768*B^3*a^20*b^25*d^4 + 180*A*B^2*a^13*b^32*d^4 - 26736*A*B^2*a^15*b^30*d^4 - 48896*A*B^2*
a^17*b^28*d^4 - 16384*A*B^2*a^19*b^26*d^4 + 4746*A^2*B*a^14*b^31*d^4 - 2048*A^2*B*a^16*b^29*d^4 - 12288*A^2*B*
a^18*b^27*d^4))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)
))^(1/2) + (274877906944*(484*A^4*a^12*b^32*d^4 - 6448*A^4*a^14*b^30*d^4 + 8704*A^4*a^16*b^28*d^4 + 4096*A^4*a
^18*b^26*d^4 + 300*B^4*a^12*b^32*d^4 - 5040*B^4*a^14*b^30*d^4 + 217600*B^4*a^16*b^28*d^4 + 217088*B^4*a^18*b^2
6*d^4 + 7720*A*B^3*a^13*b^31*d^4 - 104960*A*B^3*a^15*b^29*d^4 + 253952*A*B^3*a^17*b^27*d^4 + 327680*A*B^3*a^19
*b^25*d^4 - 10392*A^3*B*a^13*b^31*d^4 + 23808*A^3*B*a^15*b^29*d^4 - 16384*A^3*B*a^17*b^27*d^4 - 320*A^2*B^2*a^
12*b^32*d^4 + 46496*A^2*B^2*a^14*b^30*d^4 - 181248*A^2*B^2*a^16*b^28*d^4 - 155648*A^2*B^2*a^18*b^26*d^4))/d^8
- (274877906944*tan(c + d*x)*(484*A^4*a^12*b^33*d^4 - 14304*A^4*a^14*b^31*d^4 + 41472*A^4*a^16*b^29*d^4 - 1638
4*A^4*a^18*b^27*d^4 + 300*B^4*a^12*b^33*d^4 - 17120*B^4*a^14*b^31*d^4 + 985600*B^4*a^16*b^29*d^4 + 950272*B^4*
a^18*b^27*d^4 + 10520*A*B^3*a^13*b^32*d^4 - 320000*A*B^3*a^15*b^30*d^4 + 1617920*A*B^3*a^17*b^28*d^4 + 1703936
*A*B^3*a^19*b^26*d^4 - 13704*A^3*B*a^13*b^32*d^4 + 73728*A^3*B*a^15*b^30*d^4 - 131072*A^3*B*a^17*b^28*d^4 + 65
536*A^3*B*a^19*b^26*d^4 - 320*A^2*B^2*a^12*b^33*d^4 + 86144*A^2*B^2*a^14*b^31*d^4 - 807936*A^2*B^2*a^16*b^29*d
^4 - 229376*A^2*B^2*a^18*b^27*d^4 + 262144*A^2*B^2*a^20*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)*(10080*B^5*a^16*b^28*d^2 - 48*A^5*a^15*b^29*d^2 - 384*A^5*a^17*b^27*d
^2 - 1080*B^5*a^14*b^30*d^2 - 39*A^5*a^13*b^31*d^2 + 16896*B^5*a^18*b^26*d^2 + 120*A*B^4*a^13*b^31*d^2 - 10800
*A*B^4*a^15*b^29*d^2 + 7808*A*B^4*a^17*b^27*d^2 + 32768*A*B^4*a^19*b^25*d^2 - 1152*A^4*B*a^14*b^30*d^2 + 608*A
^4*B*a^16*b^28*d^2 + 512*A^4*B*a^18*b^26*d^2 + 824*A^2*B^3*a^14*b^30*d^2 - 30272*A^2*B^3*a^16*b^28*d^2 - 39936
*A^2*B^3*a^18*b^26*d^2 - 159*A^3*B^2*a^13*b^31*d^2 + 10400*A^3*B^2*a^15*b^29*d^2 + 9472*A^3*B^2*a^17*b^27*d^2)
)/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2) - (27
4877906944*(672*A^6*a^14*b^29*d^2 - 72*A^6*a^12*b^31*d^2 - 768*A^6*a^16*b^27*d^2 + 25*B^6*a^12*b^31*d^2 - 480*
B^6*a^14*b^29*d^2 + 57600*B^6*a^16*b^27*d^2 + 16384*B^6*a^18*b^25*d^2 + 900*A*B^5*a^13*b^30*d^2 - 44416*A*B^5*
a^15*b^28*d^2 + 115712*A*B^5*a^17*b^26*d^2 + 2148*A^5*B*a^13*b^30*d^2 - 3456*A^5*B*a^15*b^28*d^2 + 1024*A^5*B*
a^17*b^26*d^2 + 10*A^2*B^4*a^12*b^31*d^2 + 12000*A^2*B^4*a^14*b^29*d^2 - 119040*A^2*B^4*a^16*b^27*d^2 + 98304*
A^2*B^4*a^18*b^25*d^2 + 744*A^3*B^3*a^13*b^30*d^2 + 66816*A^3*B^3*a^15*b^28*d^2 - 79872*A^3*B^3*a^17*b^26*d^2
- 23*A^4*B^2*a^12*b^31*d^2 - 13728*A^4*B^2*a^14*b^29*d^2 + 43776*A^4*B^2*a^16*b^27*d^2 + 16384*A^4*B^2*a^18*b^
25*d^2))/d^8 + (274877906944*tan(c + d*x)*(1408*A^6*a^14*b^30*d^2 - 72*A^6*a^12*b^32*d^2 - 3584*A^6*a^16*b^28*
d^2 + 4096*A^6*a^18*b^26*d^2 + 25*B^6*a^12*b^32*d^2 - 1760*B^6*a^14*b^30*d^2 + 275200*B^6*a^16*b^28*d^2 + 6553
6*B^6*a^18*b^26*d^2 + 1280*A*B^5*a^13*b^31*d^2 - 128640*A*B^5*a^15*b^29*d^2 + 747520*A*B^5*a^17*b^27*d^2 + 284
8*A^5*B*a^13*b^31*d^2 - 9856*A^5*B*a^15*b^29*d^2 + 10240*A^5*B*a^17*b^27*d^2 + 10*A^2*B^4*a^12*b^32*d^2 + 2144
0*A^2*B^4*a^14*b^30*d^2 - 411648*A^2*B^4*a^16*b^28*d^2 + 921600*A^2*B^4*a^18*b^26*d^2 + 928*A^3*B^3*a^13*b^31*
d^2 + 162560*A^3*B^3*a^15*b^29*d^2 - 503808*A^3*B^3*a^17*b^27*d^2 + 262144*A^3*B^3*a^19*b^25*d^2 - 23*A^4*B^2*
a^12*b^32*d^2 - 25568*A^4*B^2*a^14*b^30*d^2 + 169728*A^4*B^2*a^16*b^28*d^2 - 57344*A^4*B^2*a^18*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)*(3*A^7*a^13*b^30 - 16*A^7*a^1
5*b^28 - 80*B^7*a^14*b^29 + 1280*B^7*a^16*b^27 + 2048*B^7*a^18*b^25 - 64*A^2*B^5*a^14*b^29 + 2432*A^2*B^5*a^16
*b^27 + 4096*A^2*B^5*a^18*b^25 + 37*A^3*B^4*a^13*b^30 - 2352*A^3*B^4*a^15*b^28 - 3072*A^3*B^4*a^17*b^26 + 112*
A^4*B^3*a^14*b^29 + 1024*A^4*B^3*a^16*b^27 + 2048*A^4*B^3*a^18*b^25 + 25*A^5*B^2*a^13*b^30 - 1200*A^5*B^2*a^15
*b^28 - 1536*A^5*B^2*a^17*b^26 + 15*A*B^6*a^13*b^30 - 1168*A*B^6*a^15*b^28 - 1536*A*B^6*a^17*b^26 + 96*A^6*B*a
^14*b^29 - 128*A^6*B*a^16*b^27))/(d^7*((a + b*tan(c + d*x))^(1/2) - a^(1/2))))*((B^2*1i - A^2*1i + 2*A*B)/(4*(
a*d^2 + b*d^2*1i)))^(1/2) - (549755813888*tan(c + d*x)*(4*A^8*a^12*b^31 + 25600*B^8*a^16*b^27 + 2944*A^2*B^6*a
^14*b^29 + 38912*A^2*B^6*a^16*b^27 + 16384*A^2*B^6*a^18*b^25 - 192*A^3*B^5*a^13*b^30 - 30208*A^3*B^5*a^15*b^28
 + 81920*A^3*B^5*a^17*b^26 + 4*A^4*B^4*a^12*b^31 + 5888*A^4*B^4*a^14*b^29 + 1024*A^4*B^4*a^16*b^27 + 32768*A^4
*B^4*a^18*b^25 - 384*A^5*B^3*a^13*b^30 - 14336*A^5*B^3*a^15*b^28 + 40960*A^5*B^3*a^17*b^26 + 8*A^6*B^2*a^12*b^
31 + 2944*A^6*B^2*a^14*b^29 - 12288*A^6*B^2*a^16*b^27 + 16384*A^6*B^2*a^18*b^25 - 15360*A*B^7*a^15*b^28 + 4096
0*A*B^7*a^17*b^26 - 192*A^7*B*a^13*b^30 + 512*A^7*B*a^15*b^28))/(d^8*((a + b*tan(c + d*x))^(1/2) - a^(1/2))^2)
))*((B^2*1i - A^2*1i + 2*A*B)/(4*(a*d^2 + b*d^2*1i)))^(1/2)*2i + (4*B*atanh((147573952589676412928*B^9*a^20*b^
(49/2)*tan(c + d*x)^(1/2))/(((a + b*tan(c + d*x))^(1/2) - a^(1/2))*(113997365567815680000*B^9*a^16*b^28 + 2594
07338536540569600*B^9*a^18*b^26 + 147573952589676412928*B^9*a^20*b^24 + 34452537149384294400*A^2*B^7*a^16*b^28
 + 48422703193487572992*A^2*B^7*a^18*b^26 - 9799832789158199296*A^3*B^6*a^17*b^27 + 3616390500778508288*A^4*B^
5*a^16*b^28 + 1152921504606846976*A^4*B^5*a^18*b^26 - 288230376151711744*A^5*B^4*a^17*b^27 + 15312238733059686
4*A^6*B^3*a^16*b^28 - 64851834634135142400*A*B^8*a^17*b^27 - 73786976294838206464*A*B^8*a^19*b^25 + 2251799813
685248*A^8*B*a^16*b^28)) + (259407338536540569600*B^9*a^18*b^(53/2)*tan(c + d*x)^(1/2))/(((a + b*tan(c + d*x))
^(1/2) - a^(1/2))*(113997365567815680000*B^9*a^16*b^28 + 259407338536540569600*B^9*a^18*b^26 + 147573952589676
412928*B^9*a^20*b^24 + 34452537149384294400*A^2*B^7*a^16*b^28 + 48422703193487572992*A^2*B^7*a^18*b^26 - 97998
32789158199296*A^3*B^6*a^17*b^27 + 3616390500778508288*A^4*B^5*a^16*b^28 + 1152921504606846976*A^4*B^5*a^18*b^
26 - 288230376151711744*A^5*B^4*a^17*b^27 + 153122387330596864*A^6*B^3*a^16*b^28 - 64851834634135142400*A*B^8*
a^17*b^27 - 73786976294838206464*A*B^8*a^19*b^25 + 2251799813685248*A^8*B*a^16*b^28)) + (113997365567815680000
*B^9*a^16*b^(57/2)*tan(c + d*x)^(1/2))/(((a + b*tan(c + d*x))^(1/2) - a^(1/2))*(113997365567815680000*B^9*a^16
*b^28 + 259407338536540569600*B^9*a^18*b^26 + 147573952589676412928*B^9*a^20*b^24 + 34452537149384294400*A^2*B
^7*a^16*b^28 + 48422703193487572992*A^2*B^7*a^18*b^26 - 9799832789158199296*A^3*B^6*a^17*b^27 + 36163905007785
08288*A^4*B^5*a^16*b^28 + 1152921504606846976*A^4*B^5*a^18*b^26 - 288230376151711744*A^5*B^4*a^17*b^27 + 15312
2387330596864*A^6*B^3*a^16*b^28 - 64851834634135142400*A*B^8*a^17*b^27 - 73786976294838206464*A*B^8*a^19*b^25
+ 2251799813685248*A^8*B*a^16*b^28)) - (73786976294838206464*A*B^8*a^19*b^(51/2)*tan(c + d*x)^(1/2))/(((a + b*
tan(c + d*x))^(1/2) - a^(1/2))*(113997365567815680000*B^9*a^16*b^28 + 259407338536540569600*B^9*a^18*b^26 + 14
7573952589676412928*B^9*a^20*b^24 + 34452537149384294400*A^2*B^7*a^16*b^28 + 48422703193487572992*A^2*B^7*a^18
*b^26 - 9799832789158199296*A^3*B^6*a^17*b^27 + 3616390500778508288*A^4*B^5*a^16*b^28 + 1152921504606846976*A^
4*B^5*a^18*b^26 - 288230376151711744*A^5*B^4*a^17*b^27 + 153122387330596864*A^6*B^3*a^16*b^28 - 64851834634135
142400*A*B^8*a^17*b^27 - 73786976294838206464*A*B^8*a^19*b^25 + 2251799813685248*A^8*B*a^16*b^28)) - (64851834
634135142400*A*B^8*a^17*b^(55/2)*tan(c + d*x)^(1/2))/(((a + b*tan(c + d*x))^(1/2) - a^(1/2))*(1139973655678156
80000*B^9*a^16*b^28 + 259407338536540569600*B^9*a^18*b^26 + 147573952589676412928*B^9*a^20*b^24 + 344525371493
84294400*A^2*B^7*a^16*b^28 + 48422703193487572992*A^2*B^7*a^18*b^26 - 9799832789158199296*A^3*B^6*a^17*b^27 +
3616390500778508288*A^4*B^5*a^16*b^28 + 1152921504606846976*A^4*B^5*a^18*b^26 - 288230376151711744*A^5*B^4*a^1
7*b^27 + 153122387330596864*A^6*B^3*a^16*b^28 - 64851834634135142400*A*B^8*a^17*b^27 - 73786976294838206464*A*
B^8*a^19*b^25 + 2251799813685248*A^8*B*a^16*b^28)) + (2251799813685248*A^8*B*a^16*b^(57/2)*tan(c + d*x)^(1/2))
/(((a + b*tan(c + d*x))^(1/2) - a^(1/2))*(113997365567815680000*B^9*a^16*b^28 + 259407338536540569600*B^9*a^18
*b^26 + 147573952589676412928*B^9*a^20*b^24 + 34452537149384294400*A^2*B^7*a^16*b^28 + 48422703193487572992*A^
2*B^7*a^18*b^26 - 9799832789158199296*A^3*B^6*a^17*b^27 + 3616390500778508288*A^4*B^5*a^16*b^28 + 115292150460
6846976*A^4*B^5*a^18*b^26 - 288230376151711744*A^5*B^4*a^17*b^27 + 153122387330596864*A^6*B^3*a^16*b^28 - 6485
1834634135142400*A*B^8*a^17*b^27 - 73786976294838206464*A*B^8*a^19*b^25 + 2251799813685248*A^8*B*a^16*b^28)) +
 (48422703193487572992*A^2*B^7*a^18*b^(53/2)*tan(c + d*x)^(1/2))/(((a + b*tan(c + d*x))^(1/2) - a^(1/2))*(1139
97365567815680000*B^9*a^16*b^28 + 259407338536540569600*B^9*a^18*b^26 + 147573952589676412928*B^9*a^20*b^24 +
34452537149384294400*A^2*B^7*a^16*b^28 + 48422703193487572992*A^2*B^7*a^18*b^26 - 9799832789158199296*A^3*B^6*
a^17*b^27 + 3616390500778508288*A^4*B^5*a^16*b^28 + 1152921504606846976*A^4*B^5*a^18*b^26 - 288230376151711744
*A^5*B^4*a^17*b^27 + 153122387330596864*A^6*B^3*a^16*b^28 - 64851834634135142400*A*B^8*a^17*b^27 - 73786976294
838206464*A*B^8*a^19*b^25 + 2251799813685248*A^8*B*a^16*b^28)) + (1152921504606846976*A^4*B^5*a^18*b^(53/2)*ta
n(c + d*x)^(1/2))/(((a + b*tan(c + d*x))^(1/2) - a^(1/2))*(113997365567815680000*B^9*a^16*b^28 + 2594073385365
40569600*B^9*a^18*b^26 + 147573952589676412928*B^9*a^20*b^24 + 34452537149384294400*A^2*B^7*a^16*b^28 + 484227
03193487572992*A^2*B^7*a^18*b^26 - 9799832789158199296*A^3*B^6*a^17*b^27 + 3616390500778508288*A^4*B^5*a^16*b^
28 + 1152921504606846976*A^4*B^5*a^18*b^26 - 288230376151711744*A^5*B^4*a^17*b^27 + 153122387330596864*A^6*B^3
*a^16*b^28 - 64851834634135142400*A*B^8*a^17*b^27 - 73786976294838206464*A*B^8*a^19*b^25 + 2251799813685248*A^
8*B*a^16*b^28)) - (9799832789158199296*A^3*B^6*a^17*b^(55/2)*tan(c + d*x)^(1/2))/(((a + b*tan(c + d*x))^(1/2)
- a^(1/2))*(113997365567815680000*B^9*a^16*b^28 + 259407338536540569600*B^9*a^18*b^26 + 147573952589676412928*
B^9*a^20*b^24 + 34452537149384294400*A^2*B^7*a^16*b^28 + 48422703193487572992*A^2*B^7*a^18*b^26 - 979983278915
8199296*A^3*B^6*a^17*b^27 + 3616390500778508288*A^4*B^5*a^16*b^28 + 1152921504606846976*A^4*B^5*a^18*b^26 - 28
8230376151711744*A^5*B^4*a^17*b^27 + 153122387330596864*A^6*B^3*a^16*b^28 - 64851834634135142400*A*B^8*a^17*b^
27 - 73786976294838206464*A*B^8*a^19*b^25 + 2251799813685248*A^8*B*a^16*b^28)) - (288230376151711744*A^5*B^4*a
^17*b^(55/2)*tan(c + d*x)^(1/2))/(((a + b*tan(c + d*x))^(1/2) - a^(1/2))*(113997365567815680000*B^9*a^16*b^28
+ 259407338536540569600*B^9*a^18*b^26 + 147573952589676412928*B^9*a^20*b^24 + 34452537149384294400*A^2*B^7*a^1
6*b^28 + 48422703193487572992*A^2*B^7*a^18*b^26 - 9799832789158199296*A^3*B^6*a^17*b^27 + 3616390500778508288*
A^4*B^5*a^16*b^28 + 1152921504606846976*A^4*B^5*a^18*b^26 - 288230376151711744*A^5*B^4*a^17*b^27 + 15312238733
0596864*A^6*B^3*a^16*b^28 - 64851834634135142400*A*B^8*a^17*b^27 - 73786976294838206464*A*B^8*a^19*b^25 + 2251
799813685248*A^8*B*a^16*b^28)) + (34452537149384294400*A^2*B^7*a^16*b^(57/2)*tan(c + d*x)^(1/2))/(((a + b*tan(
c + d*x))^(1/2) - a^(1/2))*(113997365567815680000*B^9*a^16*b^28 + 259407338536540569600*B^9*a^18*b^26 + 147573
952589676412928*B^9*a^20*b^24 + 34452537149384294400*A^2*B^7*a^16*b^28 + 48422703193487572992*A^2*B^7*a^18*b^2
6 - 9799832789158199296*A^3*B^6*a^17*b^27 + 3616390500778508288*A^4*B^5*a^16*b^28 + 1152921504606846976*A^4*B^
5*a^18*b^26 - 288230376151711744*A^5*B^4*a^17*b^27 + 153122387330596864*A^6*B^3*a^16*b^28 - 648518346341351424
00*A*B^8*a^17*b^27 - 73786976294838206464*A*B^8*a^19*b^25 + 2251799813685248*A^8*B*a^16*b^28)) + (361639050077
8508288*A^4*B^5*a^16*b^(57/2)*tan(c + d*x)^(1/2))/(((a + b*tan(c + d*x))^(1/2) - a^(1/2))*(1139973655678156800
00*B^9*a^16*b^28 + 259407338536540569600*B^9*a^18*b^26 + 147573952589676412928*B^9*a^20*b^24 + 344525371493842
94400*A^2*B^7*a^16*b^28 + 48422703193487572992*A^2*B^7*a^18*b^26 - 9799832789158199296*A^3*B^6*a^17*b^27 + 361
6390500778508288*A^4*B^5*a^16*b^28 + 1152921504606846976*A^4*B^5*a^18*b^26 - 288230376151711744*A^5*B^4*a^17*b
^27 + 153122387330596864*A^6*B^3*a^16*b^28 - 64851834634135142400*A*B^8*a^17*b^27 - 73786976294838206464*A*B^8
*a^19*b^25 + 2251799813685248*A^8*B*a^16*b^28)) + (153122387330596864*A^6*B^3*a^16*b^(57/2)*tan(c + d*x)^(1/2)
)/(((a + b*tan(c + d*x))^(1/2) - a^(1/2))*(113997365567815680000*B^9*a^16*b^28 + 259407338536540569600*B^9*a^1
8*b^26 + 147573952589676412928*B^9*a^20*b^24 + 34452537149384294400*A^2*B^7*a^16*b^28 + 48422703193487572992*A
^2*B^7*a^18*b^26 - 9799832789158199296*A^3*B^6*a^17*b^27 + 3616390500778508288*A^4*B^5*a^16*b^28 + 11529215046
06846976*A^4*B^5*a^18*b^26 - 288230376151711744*A^5*B^4*a^17*b^27 + 153122387330596864*A^6*B^3*a^16*b^28 - 648
51834634135142400*A*B^8*a^17*b^27 - 73786976294838206464*A*B^8*a^19*b^25 + 2251799813685248*A^8*B*a^16*b^28)))
)/(b^(1/2)*d)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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