\(\int \frac {\cos ^3(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [364]

Optimal result

Integrand size = 25, antiderivative size = 73 \[ \int \frac {\cos ^3(e+f x)}{\left (a+b \sin ^2(e+f x)\right )^{5/2}} \, dx=\frac {\cos ^2(e+f x) \sin (e+f x)}{3 a f \left (a+b \sin ^2(e+f x)\right )^{3/2}}+\frac {2 \sin (e+f x)}{3 a^2 f \sqrt {a+b \sin ^2(e+f x)}} \]

[Out]

1/3*cos(f*x+e)^2*sin(f*x+e)/a/f/(a+b*sin(f*x+e)^2)^(3/2)+2/3*sin(f*x+e)/a^2/f/(a+b*sin(f*x+e)^2)^(1/2)

Rubi [A] (verified)

Time = 0.10 (sec) , antiderivative size = 73, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {3269, 386, 197} \[ \int \frac {\cos ^3(e+f x)}{\left (a+b \sin ^2(e+f x)\right )^{5/2}} \, dx=\frac {2 \sin (e+f x)}{3 a^2 f \sqrt {a+b \sin ^2(e+f x)}}+\frac {\sin (e+f x) \cos ^2(e+f x)}{3 a f \left (a+b \sin ^2(e+f x)\right )^{3/2}} \]

[In]

Int[Cos[e + f*x]^3/(a + b*Sin[e + f*x]^2)^(5/2),x]

[Out]

(Cos[e + f*x]^2*Sin[e + f*x])/(3*a*f*(a + b*Sin[e + f*x]^2)^(3/2)) + (2*Sin[e + f*x])/(3*a^2*f*Sqrt[a + b*Sin[
e + f*x]^2])

Rule 197

Int[((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[x*((a + b*x^n)^(p + 1)/a), x] /; FreeQ[{a, b, n, p}, x] &
& EqQ[1/n + p + 1, 0]

Rule 386

Int[((a_) + (b_.)*(x_)^(n_))^(p_)*((c_) + (d_.)*(x_)^(n_))^(q_.), x_Symbol] :> Simp[(-x)*(a + b*x^n)^(p + 1)*(
(c + d*x^n)^q/(a*n*(p + 1))), x] - Dist[c*(q/(a*(p + 1))), Int[(a + b*x^n)^(p + 1)*(c + d*x^n)^(q - 1), x], x]
/; FreeQ[{a, b, c, d, n, p}, x] && NeQ[b*c - a*d, 0] && EqQ[n*(p + q + 1) + 1, 0] && GtQ[q, 0] && NeQ[p, -1]

Rule 3269

Int[cos[(e_.) + (f_.)*(x_)]^(m_.)*((a_) + (b_.)*sin[(e_.) + (f_.)*(x_)]^2)^(p_.), x_Symbol] :> With[{ff = Free
Factors[Sin[e + f*x], x]}, Dist[ff/f, Subst[Int[(1 - ff^2*x^2)^((m - 1)/2)*(a + b*ff^2*x^2)^p, x], x, Sin[e +
f*x]/ff], x]] /; FreeQ[{a, b, e, f, p}, x] && IntegerQ[(m - 1)/2]

Rubi steps \begin{align*} \text {integral}& = \frac {\text {Subst}\left (\int \frac {1-x^2}{\left (a+b x^2\right )^{5/2}} \, dx,x,\sin (e+f x)\right )}{f} \\ & = \frac {\cos ^2(e+f x) \sin (e+f x)}{3 a f \left (a+b \sin ^2(e+f x)\right )^{3/2}}+\frac {2 \text {Subst}\left (\int \frac {1}{\left (a+b x^2\right )^{3/2}} \, dx,x,\sin (e+f x)\right )}{3 a f} \\ & = \frac {\cos ^2(e+f x) \sin (e+f x)}{3 a f \left (a+b \sin ^2(e+f x)\right )^{3/2}}+\frac {2 \sin (e+f x)}{3 a^2 f \sqrt {a+b \sin ^2(e+f x)}} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.12 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.70 \[ \int \frac {\cos ^3(e+f x)}{\left (a+b \sin ^2(e+f x)\right )^{5/2}} \, dx=\frac {3 a \sin (e+f x)-(a-2 b) \sin ^3(e+f x)}{3 a^2 f \left (a+b \sin ^2(e+f x)\right )^{3/2}} \]

[In]

Integrate[Cos[e + f*x]^3/(a + b*Sin[e + f*x]^2)^(5/2),x]

[Out]

(3*a*Sin[e + f*x] - (a - 2*b)*Sin[e + f*x]^3)/(3*a^2*f*(a + b*Sin[e + f*x]^2)^(3/2))

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(137\) vs. \(2(65)=130\).

Time = 0.35 (sec) , antiderivative size = 138, normalized size of antiderivative = 1.89

method	result	size
derivativedivides	\(\frac {\frac {\sin \left (f x +e \right )}{3 a {\left (a +b \left (\sin ^{2}\left (f x +e \right )\right )\right )}^{\frac {3}{2}}}+\frac {2 \sin \left (f x +e \right )}{3 a^{2} \sqrt {a +b \left (\sin ^{2}\left (f x +e \right )\right )}}+\frac {\sin \left (f x +e \right )}{2 b {\left (a +b \left (\sin ^{2}\left (f x +e \right )\right )\right )}^{\frac {3}{2}}}-\frac {a \left (\frac {\sin \left (f x +e \right )}{3 a {\left (a +b \left (\sin ^{2}\left (f x +e \right )\right )\right )}^{\frac {3}{2}}}+\frac {2 \sin \left (f x +e \right )}{3 a^{2} \sqrt {a +b \left (\sin ^{2}\left (f x +e \right )\right )}}\right )}{2 b}}{f}\)	\(138\)
default	\(\frac {\frac {\sin \left (f x +e \right )}{3 a {\left (a +b \left (\sin ^{2}\left (f x +e \right )\right )\right )}^{\frac {3}{2}}}+\frac {2 \sin \left (f x +e \right )}{3 a^{2} \sqrt {a +b \left (\sin ^{2}\left (f x +e \right )\right )}}+\frac {\sin \left (f x +e \right )}{2 b {\left (a +b \left (\sin ^{2}\left (f x +e \right )\right )\right )}^{\frac {3}{2}}}-\frac {a \left (\frac {\sin \left (f x +e \right )}{3 a {\left (a +b \left (\sin ^{2}\left (f x +e \right )\right )\right )}^{\frac {3}{2}}}+\frac {2 \sin \left (f x +e \right )}{3 a^{2} \sqrt {a +b \left (\sin ^{2}\left (f x +e \right )\right )}}\right )}{2 b}}{f}\)	\(138\)

[In]

int(cos(f*x+e)^3/(a+b*sin(f*x+e)^2)^(5/2),x,method=_RETURNVERBOSE)

[Out]

1/f*(1/3*sin(f*x+e)/a/(a+b*sin(f*x+e)^2)^(3/2)+2/3/a^2*sin(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)+1/2*sin(f*x+e)/b/(a
+b*sin(f*x+e)^2)^(3/2)-1/2*a/b*(1/3*sin(f*x+e)/a/(a+b*sin(f*x+e)^2)^(3/2)+2/3/a^2*sin(f*x+e)/(a+b*sin(f*x+e)^2
)^(1/2)))

Fricas [A] (verification not implemented)

none

Time = 0.46 (sec) , antiderivative size = 107, normalized size of antiderivative = 1.47 \[ \int \frac {\cos ^3(e+f x)}{\left (a+b \sin ^2(e+f x)\right )^{5/2}} \, dx=\frac {{\left ({\left (a - 2 \, b\right )} \cos \left (f x + e\right )^{2} + 2 \, a + 2 \, b\right )} \sqrt {-b \cos \left (f x + e\right )^{2} + a + b} \sin \left (f x + e\right )}{3 \, {\left (a^{2} b^{2} f \cos \left (f x + e\right )^{4} - 2 \, {\left (a^{3} b + a^{2} b^{2}\right )} f \cos \left (f x + e\right )^{2} + {\left (a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right )} f\right )}} \]

[In]

integrate(cos(f*x+e)^3/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm="fricas")

[Out]

1/3*((a - 2*b)*cos(f*x + e)^2 + 2*a + 2*b)*sqrt(-b*cos(f*x + e)^2 + a + b)*sin(f*x + e)/(a^2*b^2*f*cos(f*x + e
)^4 - 2*(a^3*b + a^2*b^2)*f*cos(f*x + e)^2 + (a^4 + 2*a^3*b + a^2*b^2)*f)

Sympy [F(-1)]

Timed out. \[ \int \frac {\cos ^3(e+f x)}{\left (a+b \sin ^2(e+f x)\right )^{5/2}} \, dx=\text {Timed out} \]

[In]

integrate(cos(f*x+e)**3/(a+b*sin(f*x+e)**2)**(5/2),x)

[Out]

Timed out

Maxima [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 107, normalized size of antiderivative = 1.47 \[ \int \frac {\cos ^3(e+f x)}{\left (a+b \sin ^2(e+f x)\right )^{5/2}} \, dx=\frac {\frac {2 \, \sin \left (f x + e\right )}{\sqrt {b \sin \left (f x + e\right )^{2} + a} a^{2}} + \frac {\sin \left (f x + e\right )}{{\left (b \sin \left (f x + e\right )^{2} + a\right )}^{\frac {3}{2}} a} + \frac {\sin \left (f x + e\right )}{{\left (b \sin \left (f x + e\right )^{2} + a\right )}^{\frac {3}{2}} b} - \frac {\sin \left (f x + e\right )}{\sqrt {b \sin \left (f x + e\right )^{2} + a} a b}}{3 \, f} \]

[In]

integrate(cos(f*x+e)^3/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm="maxima")

[Out]

1/3*(2*sin(f*x + e)/(sqrt(b*sin(f*x + e)^2 + a)*a^2) + sin(f*x + e)/((b*sin(f*x + e)^2 + a)^(3/2)*a) + sin(f*x
+ e)/((b*sin(f*x + e)^2 + a)^(3/2)*b) - sin(f*x + e)/(sqrt(b*sin(f*x + e)^2 + a)*a*b))/f

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 35378 vs. \(2 (65) = 130\).

Time = 104.20 (sec) , antiderivative size = 35378, normalized size of antiderivative = 484.63 \[ \int \frac {\cos ^3(e+f x)}{\left (a+b \sin ^2(e+f x)\right )^{5/2}} \, dx=\text {Too large to display} \]

[In]

integrate(cos(f*x+e)^3/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm="giac")

[Out]

-2/3*(((((((3*a^8*b^4*tan(1/2*e)^57 + 12*a^7*b^5*tan(1/2*e)^57 + 18*a^6*b^6*tan(1/2*e)^57 + 12*a^5*b^7*tan(1/2
*e)^57 + 3*a^4*b^8*tan(1/2*e)^57 + 80*a^8*b^4*tan(1/2*e)^55 + 340*a^7*b^5*tan(1/2*e)^55 + 560*a^6*b^6*tan(1/2*
e)^55 + 440*a^5*b^7*tan(1/2*e)^55 + 160*a^4*b^8*tan(1/2*e)^55 + 20*a^3*b^9*tan(1/2*e)^55 + 1030*a^8*b^4*tan(1/
2*e)^53 + 4624*a^7*b^5*tan(1/2*e)^53 + 8228*a^6*b^6*tan(1/2*e)^53 + 7272*a^5*b^7*tan(1/2*e)^53 + 3238*a^4*b^8*
tan(1/2*e)^53 + 632*a^3*b^9*tan(1/2*e)^53 + 32*a^2*b^10*tan(1/2*e)^53 + 8528*a^8*b^4*tan(1/2*e)^51 + 40228*a^7
*b^5*tan(1/2*e)^51 + 76400*a^6*b^6*tan(1/2*e)^51 + 73880*a^5*b^7*tan(1/2*e)^51 + 37600*a^4*b^8*tan(1/2*e)^51 +
9188*a^3*b^9*tan(1/2*e)^51 + 768*a^2*b^10*tan(1/2*e)^51 + 51025*a^8*b^4*tan(1/2*e)^49 + 251684*a^7*b^5*tan(1/
2*e)^49 + 505318*a^6*b^6*tan(1/2*e)^49 + 524932*a^5*b^7*tan(1/2*e)^49 + 294353*a^4*b^8*tan(1/2*e)^49 + 82912*a
^3*b^9*tan(1/2*e)^49 + 8832*a^2*b^10*tan(1/2*e)^49 + 235040*a^8*b^4*tan(1/2*e)^47 + 1206776*a^7*b^5*tan(1/2*e)
^47 + 2541472*a^6*b^6*tan(1/2*e)^47 + 2798928*a^5*b^7*tan(1/2*e)^47 + 1690112*a^4*b^8*tan(1/2*e)^47 + 525688*a
^3*b^9*tan(1/2*e)^47 + 64768*a^2*b^10*tan(1/2*e)^47 + 867100*a^8*b^4*tan(1/2*e)^45 + 4613984*a^7*b^5*tan(1/2*e
)^45 + 10124968*a^6*b^6*tan(1/2*e)^45 + 11702032*a^5*b^7*tan(1/2*e)^45 + 7489628*a^4*b^8*tan(1/2*e)^45 + 25057
12*a^3*b^9*tan(1/2*e)^45 + 340032*a^2*b^10*tan(1/2*e)^45 + 2631200*a^8*b^4*tan(1/2*e)^43 + 14449336*a^7*b^5*ta
n(1/2*e)^43 + 32845472*a^6*b^6*tan(1/2*e)^43 + 39512528*a^5*b^7*tan(1/2*e)^43 + 26490112*a^4*b^8*tan(1/2*e)^43
+ 9365048*a^3*b^9*tan(1/2*e)^43 + 1360128*a^2*b^10*tan(1/2*e)^43 + 6693115*a^8*b^4*tan(1/2*e)^41 + 37774924*a
^7*b^5*tan(1/2*e)^41 + 88475618*a^6*b^6*tan(1/2*e)^41 + 110015532*a^5*b^7*tan(1/2*e)^41 + 76545403*a^4*b^8*tan
(1/2*e)^41 + 28230752*a^3*b^9*tan(1/2*e)^41 + 4307072*a^2*b^10*tan(1/2*e)^41 + 14471600*a^8*b^4*tan(1/2*e)^39
+ 83594236*a^7*b^5*tan(1/2*e)^39 + 200736272*a^6*b^6*tan(1/2*e)^39 + 256434728*a^5*b^7*tan(1/2*e)^39 + 1837549
12*a^4*b^8*tan(1/2*e)^39 + 70009148*a^3*b^9*tan(1/2*e)^39 + 11075328*a^2*b^10*tan(1/2*e)^39 + 26871130*a^8*b^4
*tan(1/2*e)^37 + 158207984*a^7*b^5*tan(1/2*e)^37 + 387655708*a^6*b^6*tan(1/2*e)^37 + 505965592*a^5*b^7*tan(1/2
*e)^37 + 370975418*a^4*b^8*tan(1/2*e)^37 + 144863752*a^3*b^9*tan(1/2*e)^37 + 23535072*a^2*b^10*tan(1/2*e)^37 +
43175600*a^8*b^4*tan(1/2*e)^35 + 258017036*a^7*b^5*tan(1/2*e)^35 + 642152272*a^6*b^6*tan(1/2*e)^35 + 85195072
8*a^5*b^7*tan(1/2*e)^35 + 635474912*a^4*b^8*tan(1/2*e)^35 + 252675148*a^3*b^9*tan(1/2*e)^35 + 41840128*a^2*b^1
0*tan(1/2*e)^35 + 60360625*a^8*b^4*tan(1/2*e)^33 + 364585604*a^7*b^5*tan(1/2*e)^33 + 917496358*a^6*b^6*tan(1/2
*e)^33 + 1231341892*a^5*b^7*tan(1/2*e)^33 + 929494193*a^4*b^8*tan(1/2*e)^33 + 374183872*a^3*b^9*tan(1/2*e)^33
+ 62760192*a^2*b^10*tan(1/2*e)^33 + 73695680*a^8*b^4*tan(1/2*e)^31 + 447998416*a^7*b^5*tan(1/2*e)^31 + 1134913
472*a^6*b^6*tan(1/2*e)^31 + 1533583328*a^5*b^7*tan(1/2*e)^31 + 1165818112*a^4*b^8*tan(1/2*e)^31 + 472722128*a^
3*b^9*tan(1/2*e)^31 + 79876608*a^2*b^10*tan(1/2*e)^31 + 78747400*a^8*b^4*tan(1/2*e)^29 + 479735104*a^7*b^5*tan
(1/2*e)^29 + 1217999408*a^6*b^6*tan(1/2*e)^29 + 1649594592*a^5*b^7*tan(1/2*e)^29 + 1256927368*a^4*b^8*tan(1/2*
e)^29 + 510877472*a^3*b^9*tan(1/2*e)^29 + 86532992*a^2*b^10*tan(1/2*e)^29 + 73695680*a^8*b^4*tan(1/2*e)^27 + 4
47998416*a^7*b^5*tan(1/2*e)^27 + 1134913472*a^6*b^6*tan(1/2*e)^27 + 1533583328*a^5*b^7*tan(1/2*e)^27 + 1165818
112*a^4*b^8*tan(1/2*e)^27 + 472722128*a^3*b^9*tan(1/2*e)^27 + 79876608*a^2*b^10*tan(1/2*e)^27 + 60360625*a^8*b
^4*tan(1/2*e)^25 + 364585604*a^7*b^5*tan(1/2*e)^25 + 917496358*a^6*b^6*tan(1/2*e)^25 + 1231341892*a^5*b^7*tan(
1/2*e)^25 + 929494193*a^4*b^8*tan(1/2*e)^25 + 374183872*a^3*b^9*tan(1/2*e)^25 + 62760192*a^2*b^10*tan(1/2*e)^2
5 + 43175600*a^8*b^4*tan(1/2*e)^23 + 258017036*a^7*b^5*tan(1/2*e)^23 + 642152272*a^6*b^6*tan(1/2*e)^23 + 85195
0728*a^5*b^7*tan(1/2*e)^23 + 635474912*a^4*b^8*tan(1/2*e)^23 + 252675148*a^3*b^9*tan(1/2*e)^23 + 41840128*a^2*
b^10*tan(1/2*e)^23 + 26871130*a^8*b^4*tan(1/2*e)^21 + 158207984*a^7*b^5*tan(1/2*e)^21 + 387655708*a^6*b^6*tan(
1/2*e)^21 + 505965592*a^5*b^7*tan(1/2*e)^21 + 370975418*a^4*b^8*tan(1/2*e)^21 + 144863752*a^3*b^9*tan(1/2*e)^2
1 + 23535072*a^2*b^10*tan(1/2*e)^21 + 14471600*a^8*b^4*tan(1/2*e)^19 + 83594236*a^7*b^5*tan(1/2*e)^19 + 200736
272*a^6*b^6*tan(1/2*e)^19 + 256434728*a^5*b^7*tan(1/2*e)^19 + 183754912*a^4*b^8*tan(1/2*e)^19 + 70009148*a^3*b
^9*tan(1/2*e)^19 + 11075328*a^2*b^10*tan(1/2*e)^19 + 6693115*a^8*b^4*tan(1/2*e)^17 + 37774924*a^7*b^5*tan(1/2*
e)^17 + 88475618*a^6*b^6*tan(1/2*e)^17 + 110015532*a^5*b^7*tan(1/2*e)^17 + 76545403*a^4*b^8*tan(1/2*e)^17 + 28
230752*a^3*b^9*tan(1/2*e)^17 + 4307072*a^2*b^10*tan(1/2*e)^17 + 2631200*a^8*b^4*tan(1/2*e)^15 + 14449336*a^7*b
^5*tan(1/2*e)^15 + 32845472*a^6*b^6*tan(1/2*e)^15 + 39512528*a^5*b^7*tan(1/2*e)^15 + 26490112*a^4*b^8*tan(1/2*
e)^15 + 9365048*a^3*b^9*tan(1/2*e)^15 + 1360128*a^2*b^10*tan(1/2*e)^15 + 867100*a^8*b^4*tan(1/2*e)^13 + 461398
4*a^7*b^5*tan(1/2*e)^13 + 10124968*a^6*b^6*tan(1/2*e)^13 + 11702032*a^5*b^7*tan(1/2*e)^13 + 7489628*a^4*b^8*ta
n(1/2*e)^13 + 2505712*a^3*b^9*tan(1/2*e)^13 + 340032*a^2*b^10*tan(1/2*e)^13 + 235040*a^8*b^4*tan(1/2*e)^11 + 1
206776*a^7*b^5*tan(1/2*e)^11 + 2541472*a^6*b^6*tan(1/2*e)^11 + 2798928*a^5*b^7*tan(1/2*e)^11 + 1690112*a^4*b^8
*tan(1/2*e)^11 + 525688*a^3*b^9*tan(1/2*e)^11 + 64768*a^2*b^10*tan(1/2*e)^11 + 51025*a^8*b^4*tan(1/2*e)^9 + 25
1684*a^7*b^5*tan(1/2*e)^9 + 505318*a^6*b^6*tan(1/2*e)^9 + 524932*a^5*b^7*tan(1/2*e)^9 + 294353*a^4*b^8*tan(1/2
*e)^9 + 82912*a^3*b^9*tan(1/2*e)^9 + 8832*a^2*b^10*tan(1/2*e)^9 + 8528*a^8*b^4*tan(1/2*e)^7 + 40228*a^7*b^5*ta
n(1/2*e)^7 + 76400*a^6*b^6*tan(1/2*e)^7 + 73880*a^5*b^7*tan(1/2*e)^7 + 37600*a^4*b^8*tan(1/2*e)^7 + 9188*a^3*b
^9*tan(1/2*e)^7 + 768*a^2*b^10*tan(1/2*e)^7 + 1030*a^8*b^4*tan(1/2*e)^5 + 4624*a^7*b^5*tan(1/2*e)^5 + 8228*a^6
*b^6*tan(1/2*e)^5 + 7272*a^5*b^7*tan(1/2*e)^5 + 3238*a^4*b^8*tan(1/2*e)^5 + 632*a^3*b^9*tan(1/2*e)^5 + 32*a^2*
b^10*tan(1/2*e)^5 + 80*a^8*b^4*tan(1/2*e)^3 + 340*a^7*b^5*tan(1/2*e)^3 + 560*a^6*b^6*tan(1/2*e)^3 + 440*a^5*b^
7*tan(1/2*e)^3 + 160*a^4*b^8*tan(1/2*e)^3 + 20*a^3*b^9*tan(1/2*e)^3 + 3*a^8*b^4*tan(1/2*e) + 12*a^7*b^5*tan(1/
2*e) + 18*a^6*b^6*tan(1/2*e) + 12*a^5*b^7*tan(1/2*e) + 3*a^4*b^8*tan(1/2*e))*tan(1/2*f*x)/(a^9*b^4*tan(1/2*e)^
52 + 4*a^8*b^5*tan(1/2*e)^52 + 6*a^7*b^6*tan(1/2*e)^52 + 4*a^6*b^7*tan(1/2*e)^52 + a^5*b^8*tan(1/2*e)^52 + 26*
a^9*b^4*tan(1/2*e)^50 + 108*a^8*b^5*tan(1/2*e)^50 + 172*a^7*b^6*tan(1/2*e)^50 + 128*a^6*b^7*tan(1/2*e)^50 + 42
*a^5*b^8*tan(1/2*e)^50 + 4*a^4*b^9*tan(1/2*e)^50 + 325*a^9*b^4*tan(1/2*e)^48 + 1396*a^8*b^5*tan(1/2*e)^48 + 23
34*a^7*b^6*tan(1/2*e)^48 + 1876*a^6*b^7*tan(1/2*e)^48 + 709*a^5*b^8*tan(1/2*e)^48 + 96*a^4*b^9*tan(1/2*e)^48 +
2600*a^9*b^4*tan(1/2*e)^46 + 11504*a^8*b^5*tan(1/2*e)^46 + 20016*a^7*b^6*tan(1/2*e)^46 + 17024*a^6*b^7*tan(1/
2*e)^46 + 7016*a^5*b^8*tan(1/2*e)^46 + 1104*a^4*b^9*tan(1/2*e)^46 + 14950*a^9*b^4*tan(1/2*e)^44 + 67896*a^8*b^
5*tan(1/2*e)^44 + 122084*a^7*b^6*tan(1/2*e)^44 + 108376*a^6*b^7*tan(1/2*e)^44 + 47334*a^5*b^8*tan(1/2*e)^44 +
8096*a^4*b^9*tan(1/2*e)^44 + 65780*a^9*b^4*tan(1/2*e)^42 + 305624*a^8*b^5*tan(1/2*e)^42 + 564696*a^7*b^6*tan(1
/2*e)^42 + 518144*a^6*b^7*tan(1/2*e)^42 + 235796*a^5*b^8*tan(1/2*e)^42 + 42504*a^4*b^9*tan(1/2*e)^42 + 230230*
a^9*b^4*tan(1/2*e)^40 + 1090936*a^8*b^5*tan(1/2*e)^40 + 2061444*a^7*b^6*tan(1/2*e)^40 + 1941016*a^6*b^7*tan(1/
2*e)^40 + 910294*a^5*b^8*tan(1/2*e)^40 + 170016*a^4*b^9*tan(1/2*e)^40 + 657800*a^9*b^4*tan(1/2*e)^38 + 3169584
*a^8*b^5*tan(1/2*e)^38 + 6100336*a^7*b^6*tan(1/2*e)^38 + 5861504*a^6*b^7*tan(1/2*e)^38 + 2811336*a^5*b^8*tan(1
/2*e)^38 + 538384*a^4*b^9*tan(1/2*e)^38 + 1562275*a^9*b^4*tan(1/2*e)^36 + 7633516*a^8*b^5*tan(1/2*e)^36 + 1491
1314*a^7*b^6*tan(1/2*e)^36 + 14555596*a^6*b^7*tan(1/2*e)^36 + 7099939*a^5*b^8*tan(1/2*e)^36 + 1384416*a^4*b^9*
tan(1/2*e)^36 + 3124550*a^9*b^4*tan(1/2*e)^34 + 15440084*a^8*b^5*tan(1/2*e)^34 + 30514836*a^7*b^6*tan(1/2*e)^3
4 + 30149504*a^6*b^7*tan(1/2*e)^34 + 14892086*a^5*b^8*tan(1/2*e)^34 + 2941884*a^4*b^9*tan(1/2*e)^34 + 5311735*
a^9*b^4*tan(1/2*e)^32 + 26476956*a^8*b^5*tan(1/2*e)^32 + 52790474*a^7*b^6*tan(1/2*e)^32 + 52627036*a^6*b^7*tan
(1/2*e)^32 + 26231799*a^5*b^8*tan(1/2*e)^32 + 5230016*a^4*b^9*tan(1/2*e)^32 + 7726160*a^9*b^4*tan(1/2*e)^30 +
38749664*a^8*b^5*tan(1/2*e)^30 + 77737056*a^7*b^6*tan(1/2*e)^30 + 77974784*a^6*b^7*tan(1/2*e)^30 + 39106256*a^
5*b^8*tan(1/2*e)^30 + 7845024*a^4*b^9*tan(1/2*e)^30 + 9657700*a^9*b^4*tan(1/2*e)^28 + 48615376*a^8*b^5*tan(1/2
*e)^28 + 97884504*a^7*b^6*tan(1/2*e)^28 + 98538256*a^6*b^7*tan(1/2*e)^28 + 49596004*a^5*b^8*tan(1/2*e)^28 + 99
84576*a^4*b^9*tan(1/2*e)^28 + 10400600*a^9*b^4*tan(1/2*e)^26 + 52419024*a^8*b^5*tan(1/2*e)^26 + 105670096*a^7*
b^6*tan(1/2*e)^26 + 106502144*a^6*b^7*tan(1/2*e)^26 + 53667096*a^5*b^8*tan(1/2*e)^26 + 10816624*a^4*b^9*tan(1/
2*e)^26 + 9657700*a^9*b^4*tan(1/2*e)^24 + 48615376*a^8*b^5*tan(1/2*e)^24 + 97884504*a^7*b^6*tan(1/2*e)^24 + 98
538256*a^6*b^7*tan(1/2*e)^24 + 49596004*a^5*b^8*tan(1/2*e)^24 + 9984576*a^4*b^9*tan(1/2*e)^24 + 7726160*a^9*b^
4*tan(1/2*e)^22 + 38749664*a^8*b^5*tan(1/2*e)^22 + 77737056*a^7*b^6*tan(1/2*e)^22 + 77974784*a^6*b^7*tan(1/2*e
)^22 + 39106256*a^5*b^8*tan(1/2*e)^22 + 7845024*a^4*b^9*tan(1/2*e)^22 + 5311735*a^9*b^4*tan(1/2*e)^20 + 264769
56*a^8*b^5*tan(1/2*e)^20 + 52790474*a^7*b^6*tan(1/2*e)^20 + 52627036*a^6*b^7*tan(1/2*e)^20 + 26231799*a^5*b^8*
tan(1/2*e)^20 + 5230016*a^4*b^9*tan(1/2*e)^20 + 3124550*a^9*b^4*tan(1/2*e)^18 + 15440084*a^8*b^5*tan(1/2*e)^18
+ 30514836*a^7*b^6*tan(1/2*e)^18 + 30149504*a^6*b^7*tan(1/2*e)^18 + 14892086*a^5*b^8*tan(1/2*e)^18 + 2941884*
a^4*b^9*tan(1/2*e)^18 + 1562275*a^9*b^4*tan(1/2*e)^16 + 7633516*a^8*b^5*tan(1/2*e)^16 + 14911314*a^7*b^6*tan(1
/2*e)^16 + 14555596*a^6*b^7*tan(1/2*e)^16 + 7099939*a^5*b^8*tan(1/2*e)^16 + 1384416*a^4*b^9*tan(1/2*e)^16 + 65
7800*a^9*b^4*tan(1/2*e)^14 + 3169584*a^8*b^5*tan(1/2*e)^14 + 6100336*a^7*b^6*tan(1/2*e)^14 + 5861504*a^6*b^7*t
an(1/2*e)^14 + 2811336*a^5*b^8*tan(1/2*e)^14 + 538384*a^4*b^9*tan(1/2*e)^14 + 230230*a^9*b^4*tan(1/2*e)^12 + 1
090936*a^8*b^5*tan(1/2*e)^12 + 2061444*a^7*b^6*tan(1/2*e)^12 + 1941016*a^6*b^7*tan(1/2*e)^12 + 910294*a^5*b^8*
tan(1/2*e)^12 + 170016*a^4*b^9*tan(1/2*e)^12 + 65780*a^9*b^4*tan(1/2*e)^10 + 305624*a^8*b^5*tan(1/2*e)^10 + 56
4696*a^7*b^6*tan(1/2*e)^10 + 518144*a^6*b^7*tan(1/2*e)^10 + 235796*a^5*b^8*tan(1/2*e)^10 + 42504*a^4*b^9*tan(1
/2*e)^10 + 14950*a^9*b^4*tan(1/2*e)^8 + 67896*a^8*b^5*tan(1/2*e)^8 + 122084*a^7*b^6*tan(1/2*e)^8 + 108376*a^6*
b^7*tan(1/2*e)^8 + 47334*a^5*b^8*tan(1/2*e)^8 + 8096*a^4*b^9*tan(1/2*e)^8 + 2600*a^9*b^4*tan(1/2*e)^6 + 11504*
a^8*b^5*tan(1/2*e)^6 + 20016*a^7*b^6*tan(1/2*e)^6 + 17024*a^6*b^7*tan(1/2*e)^6 + 7016*a^5*b^8*tan(1/2*e)^6 + 1
104*a^4*b^9*tan(1/2*e)^6 + 325*a^9*b^4*tan(1/2*e)^4 + 1396*a^8*b^5*tan(1/2*e)^4 + 2334*a^7*b^6*tan(1/2*e)^4 +
1876*a^6*b^7*tan(1/2*e)^4 + 709*a^5*b^8*tan(1/2*e)^4 + 96*a^4*b^9*tan(1/2*e)^4 + 26*a^9*b^4*tan(1/2*e)^2 + 108
*a^8*b^5*tan(1/2*e)^2 + 172*a^7*b^6*tan(1/2*e)^2 + 128*a^6*b^7*tan(1/2*e)^2 + 42*a^5*b^8*tan(1/2*e)^2 + 4*a^4*
b^9*tan(1/2*e)^2 + a^9*b^4 + 4*a^8*b^5 + 6*a^7*b^6 + 4*a^6*b^7 + a^5*b^8) + 3*(a^8*b^4*tan(1/2*e)^58 + 4*a^7*b
^5*tan(1/2*e)^58 + 6*a^6*b^6*tan(1/2*e)^58 + 4*a^5*b^7*tan(1/2*e)^58 + a^4*b^8*tan(1/2*e)^58 + 23*a^8*b^4*tan(
1/2*e)^56 + 104*a^7*b^5*tan(1/2*e)^56 + 186*a^6*b^6*tan(1/2*e)^56 + 164*a^5*b^7*tan(1/2*e)^56 + 71*a^4*b^8*tan
(1/2*e)^56 + 12*a^3*b^9*tan(1/2*e)^56 + 250*a^8*b^4*tan(1/2*e)^54 + 1284*a^7*b^5*tan(1/2*e)^54 + 2668*a^6*b^6*
tan(1/2*e)^54 + 2832*a^5*b^7*tan(1/2*e)^54 + 1578*a^4*b^8*tan(1/2*e)^54 + 412*a^3*b^9*tan(1/2*e)^54 + 32*a^2*b
^10*tan(1/2*e)^54 + 1702*a^8*b^4*tan(1/2*e)^52 + 10028*a^7*b^5*tan(1/2*e)^52 + 23828*a^6*b^6*tan(1/2*e)^52 + 2
9072*a^5*b^7*tan(1/2*e)^52 + 18998*a^4*b^8*tan(1/2*e)^52 + 6164*a^3*b^9*tan(1/2*e)^52 + 736*a^2*b^10*tan(1/2*e
)^52 + 8099*a^8*b^4*tan(1/2*e)^50 + 55664*a^7*b^5*tan(1/2*e)^50 + 149730*a^6*b^6*tan(1/2*e)^50 + 204260*a^5*b^
7*tan(1/2*e)^50 + 149555*a^4*b^8*tan(1/2*e)^50 + 55524*a^3*b^9*tan(1/2*e)^50 + 8064*a^2*b^10*tan(1/2*e)^50 + 2
8405*a^8*b^4*tan(1/2*e)^48 + 233852*a^7*b^5*tan(1/2*e)^48 + 707294*a^6*b^6*tan(1/2*e)^48 + 1058756*a^5*b^7*tan
(1/2*e)^48 + 844949*a^4*b^8*tan(1/2*e)^48 + 343976*a^3*b^9*tan(1/2*e)^48 + 55936*a^2*b^10*tan(1/2*e)^48 + 7514
0*a^8*b^4*tan(1/2*e)^46 + 772888*a^7*b^5*tan(1/2*e)^46 + 2615416*a^6*b^6*tan(1/2*e)^46 + 4235584*a^5*b^7*tan(1
/2*e)^46 + 3616036*a^4*b^8*tan(1/2*e)^46 + 1573384*a^3*b^9*tan(1/2*e)^46 + 275264*a^2*b^10*tan(1/2*e)^46 + 149
500*a^8*b^4*tan(1/2*e)^44 + 2061352*a^7*b^5*tan(1/2*e)^44 + 7770504*a^6*b^6*tan(1/2*e)^44 + 13458496*a^5*b^7*t
an(1/2*e)^44 + 12123484*a^4*b^8*tan(1/2*e)^44 + 5543736*a^3*b^9*tan(1/2*e)^44 + 1020096*a^2*b^10*tan(1/2*e)^44
+ 213785*a^8*b^4*tan(1/2*e)^42 + 4512508*a^7*b^5*tan(1/2*e)^42 + 18859126*a^6*b^6*tan(1/2*e)^42 + 34587124*a^
5*b^7*tan(1/2*e)^42 + 32524921*a^4*b^8*tan(1/2*e)^42 + 15445144*a^3*b^9*tan(1/2*e)^42 + 2946944*a^2*b^10*tan(1
/2*e)^42 + 180895*a^8*b^4*tan(1/2*e)^40 + 8193152*a^7*b^5*tan(1/2*e)^40 + 37731914*a^6*b^6*tan(1/2*e)^40 + 726
14036*a^5*b^7*tan(1/2*e)^40 + 70668719*a^4*b^8*tan(1/2*e)^40 + 34542596*a^3*b^9*tan(1/2*e)^40 + 6768256*a^2*b^
10*tan(1/2*e)^40 - 32890*a^8*b^4*tan(1/2*e)^38 + 12385868*a^7*b^5*tan(1/2*e)^38 + 62332116*a^6*b^6*tan(1/2*e)^
38 + 124811984*a^5*b^7*tan(1/2*e)^38 + 124795286*a^4*b^8*tan(1/2*e)^38 + 62356404*a^3*b^9*tan(1/2*e)^38 + 1245
9744*a^2*b^10*tan(1/2*e)^38 - 397670*a^8*b^4*tan(1/2*e)^36 + 15503012*a^7*b^5*tan(1/2*e)^36 + 84293804*a^6*b^6
*tan(1/2*e)^36 + 174191696*a^5*b^7*tan(1/2*e)^36 + 177807434*a^4*b^8*tan(1/2*e)^36 + 90313916*a^3*b^9*tan(1/2*
e)^36 + 18305056*a^2*b^10*tan(1/2*e)^36 - 710125*a^8*b^4*tan(1/2*e)^34 + 15672568*a^7*b^5*tan(1/2*e)^34 + 9071
1586*a^6*b^6*tan(1/2*e)^34 + 191918164*a^5*b^7*tan(1/2*e)^34 + 198862531*a^4*b^8*tan(1/2*e)^34 + 102193324*a^3
*b^9*tan(1/2*e)^34 + 20920064*a^2*b^10*tan(1/2*e)^34 - 705755*a^8*b^4*tan(1/2*e)^32 + 11797252*a^7*b^5*tan(1/2
*e)^32 + 71362974*a^6*b^6*tan(1/2*e)^32 + 153364276*a^5*b^7*tan(1/2*e)^32 + 160473829*a^4*b^8*tan(1/2*e)^32 +
83085936*a^3*b^9*tan(1/2*e)^32 + 17116416*a^2*b^10*tan(1/2*e)^32 - 297160*a^8*b^4*tan(1/2*e)^30 + 4397968*a^7*
b^5*tan(1/2*e)^30 + 27219856*a^6*b^6*tan(1/2*e)^30 + 58956544*a^5*b^7*tan(1/2*e)^30 + 61987576*a^4*b^8*tan(1/2
*e)^30 + 32212144*a^3*b^9*tan(1/2*e)^30 + 6656384*a^2*b^10*tan(1/2*e)^30 + 297160*a^8*b^4*tan(1/2*e)^28 - 4397
968*a^7*b^5*tan(1/2*e)^28 - 27219856*a^6*b^6*tan(1/2*e)^28 - 58956544*a^5*b^7*tan(1/2*e)^28 - 61987576*a^4*b^8
*tan(1/2*e)^28 - 32212144*a^3*b^9*tan(1/2*e)^28 - 6656384*a^2*b^10*tan(1/2*e)^28 + 705755*a^8*b^4*tan(1/2*e)^2
6 - 11797252*a^7*b^5*tan(1/2*e)^26 - 71362974*a^6*b^6*tan(1/2*e)^26 - 153364276*a^5*b^7*tan(1/2*e)^26 - 160473
829*a^4*b^8*tan(1/2*e)^26 - 83085936*a^3*b^9*tan(1/2*e)^26 - 17116416*a^2*b^10*tan(1/2*e)^26 + 710125*a^8*b^4*
tan(1/2*e)^24 - 15672568*a^7*b^5*tan(1/2*e)^24 - 90711586*a^6*b^6*tan(1/2*e)^24 - 191918164*a^5*b^7*tan(1/2*e)
^24 - 198862531*a^4*b^8*tan(1/2*e)^24 - 102193324*a^3*b^9*tan(1/2*e)^24 - 20920064*a^2*b^10*tan(1/2*e)^24 + 39
7670*a^8*b^4*tan(1/2*e)^22 - 15503012*a^7*b^5*tan(1/2*e)^22 - 84293804*a^6*b^6*tan(1/2*e)^22 - 174191696*a^5*b
^7*tan(1/2*e)^22 - 177807434*a^4*b^8*tan(1/2*e)^22 - 90313916*a^3*b^9*tan(1/2*e)^22 - 18305056*a^2*b^10*tan(1/
2*e)^22 + 32890*a^8*b^4*tan(1/2*e)^20 - 12385868*a^7*b^5*tan(1/2*e)^20 - 62332116*a^6*b^6*tan(1/2*e)^20 - 1248
11984*a^5*b^7*tan(1/2*e)^20 - 124795286*a^4*b^8*tan(1/2*e)^20 - 62356404*a^3*b^9*tan(1/2*e)^20 - 12459744*a^2*
b^10*tan(1/2*e)^20 - 180895*a^8*b^4*tan(1/2*e)^18 - 8193152*a^7*b^5*tan(1/2*e)^18 - 37731914*a^6*b^6*tan(1/2*e
)^18 - 72614036*a^5*b^7*tan(1/2*e)^18 - 70668719*a^4*b^8*tan(1/2*e)^18 - 34542596*a^3*b^9*tan(1/2*e)^18 - 6768
256*a^2*b^10*tan(1/2*e)^18 - 213785*a^8*b^4*tan(1/2*e)^16 - 4512508*a^7*b^5*tan(1/2*e)^16 - 18859126*a^6*b^6*t
an(1/2*e)^16 - 34587124*a^5*b^7*tan(1/2*e)^16 - 32524921*a^4*b^8*tan(1/2*e)^16 - 15445144*a^3*b^9*tan(1/2*e)^1
6 - 2946944*a^2*b^10*tan(1/2*e)^16 - 149500*a^8*b^4*tan(1/2*e)^14 - 2061352*a^7*b^5*tan(1/2*e)^14 - 7770504*a^
6*b^6*tan(1/2*e)^14 - 13458496*a^5*b^7*tan(1/2*e)^14 - 12123484*a^4*b^8*tan(1/2*e)^14 - 5543736*a^3*b^9*tan(1/
2*e)^14 - 1020096*a^2*b^10*tan(1/2*e)^14 - 75140*a^8*b^4*tan(1/2*e)^12 - 772888*a^7*b^5*tan(1/2*e)^12 - 261541
6*a^6*b^6*tan(1/2*e)^12 - 4235584*a^5*b^7*tan(1/2*e)^12 - 3616036*a^4*b^8*tan(1/2*e)^12 - 1573384*a^3*b^9*tan(
1/2*e)^12 - 275264*a^2*b^10*tan(1/2*e)^12 - 28405*a^8*b^4*tan(1/2*e)^10 - 233852*a^7*b^5*tan(1/2*e)^10 - 70729
4*a^6*b^6*tan(1/2*e)^10 - 1058756*a^5*b^7*tan(1/2*e)^10 - 844949*a^4*b^8*tan(1/2*e)^10 - 343976*a^3*b^9*tan(1/
2*e)^10 - 55936*a^2*b^10*tan(1/2*e)^10 - 8099*a^8*b^4*tan(1/2*e)^8 - 55664*a^7*b^5*tan(1/2*e)^8 - 149730*a^6*b
^6*tan(1/2*e)^8 - 204260*a^5*b^7*tan(1/2*e)^8 - 149555*a^4*b^8*tan(1/2*e)^8 - 55524*a^3*b^9*tan(1/2*e)^8 - 806
4*a^2*b^10*tan(1/2*e)^8 - 1702*a^8*b^4*tan(1/2*e)^6 - 10028*a^7*b^5*tan(1/2*e)^6 - 23828*a^6*b^6*tan(1/2*e)^6
- 29072*a^5*b^7*tan(1/2*e)^6 - 18998*a^4*b^8*tan(1/2*e)^6 - 6164*a^3*b^9*tan(1/2*e)^6 - 736*a^2*b^10*tan(1/2*e
)^6 - 250*a^8*b^4*tan(1/2*e)^4 - 1284*a^7*b^5*tan(1/2*e)^4 - 2668*a^6*b^6*tan(1/2*e)^4 - 2832*a^5*b^7*tan(1/2*
e)^4 - 1578*a^4*b^8*tan(1/2*e)^4 - 412*a^3*b^9*tan(1/2*e)^4 - 32*a^2*b^10*tan(1/2*e)^4 - 23*a^8*b^4*tan(1/2*e)
^2 - 104*a^7*b^5*tan(1/2*e)^2 - 186*a^6*b^6*tan(1/2*e)^2 - 164*a^5*b^7*tan(1/2*e)^2 - 71*a^4*b^8*tan(1/2*e)^2
- 12*a^3*b^9*tan(1/2*e)^2 - a^8*b^4 - 4*a^7*b^5 - 6*a^6*b^6 - 4*a^5*b^7 - a^4*b^8)/(a^9*b^4*tan(1/2*e)^52 + 4*
a^8*b^5*tan(1/2*e)^52 + 6*a^7*b^6*tan(1/2*e)^52 + 4*a^6*b^7*tan(1/2*e)^52 + a^5*b^8*tan(1/2*e)^52 + 26*a^9*b^4
*tan(1/2*e)^50 + 108*a^8*b^5*tan(1/2*e)^50 + 172*a^7*b^6*tan(1/2*e)^50 + 128*a^6*b^7*tan(1/2*e)^50 + 42*a^5*b^
8*tan(1/2*e)^50 + 4*a^4*b^9*tan(1/2*e)^50 + 325*a^9*b^4*tan(1/2*e)^48 + 1396*a^8*b^5*tan(1/2*e)^48 + 2334*a^7*
b^6*tan(1/2*e)^48 + 1876*a^6*b^7*tan(1/2*e)^48 + 709*a^5*b^8*tan(1/2*e)^48 + 96*a^4*b^9*tan(1/2*e)^48 + 2600*a
^9*b^4*tan(1/2*e)^46 + 11504*a^8*b^5*tan(1/2*e)^46 + 20016*a^7*b^6*tan(1/2*e)^46 + 17024*a^6*b^7*tan(1/2*e)^46
+ 7016*a^5*b^8*tan(1/2*e)^46 + 1104*a^4*b^9*tan(1/2*e)^46 + 14950*a^9*b^4*tan(1/2*e)^44 + 67896*a^8*b^5*tan(1
/2*e)^44 + 122084*a^7*b^6*tan(1/2*e)^44 + 108376*a^6*b^7*tan(1/2*e)^44 + 47334*a^5*b^8*tan(1/2*e)^44 + 8096*a^
4*b^9*tan(1/2*e)^44 + 65780*a^9*b^4*tan(1/2*e)^42 + 305624*a^8*b^5*tan(1/2*e)^42 + 564696*a^7*b^6*tan(1/2*e)^4
2 + 518144*a^6*b^7*tan(1/2*e)^42 + 235796*a^5*b^8*tan(1/2*e)^42 + 42504*a^4*b^9*tan(1/2*e)^42 + 230230*a^9*b^4
*tan(1/2*e)^40 + 1090936*a^8*b^5*tan(1/2*e)^40 + 2061444*a^7*b^6*tan(1/2*e)^40 + 1941016*a^6*b^7*tan(1/2*e)^40
+ 910294*a^5*b^8*tan(1/2*e)^40 + 170016*a^4*b^9*tan(1/2*e)^40 + 657800*a^9*b^4*tan(1/2*e)^38 + 3169584*a^8*b^
5*tan(1/2*e)^38 + 6100336*a^7*b^6*tan(1/2*e)^38 + 5861504*a^6*b^7*tan(1/2*e)^38 + 2811336*a^5*b^8*tan(1/2*e)^3
8 + 538384*a^4*b^9*tan(1/2*e)^38 + 1562275*a^9*b^4*tan(1/2*e)^36 + 7633516*a^8*b^5*tan(1/2*e)^36 + 14911314*a^
7*b^6*tan(1/2*e)^36 + 14555596*a^6*b^7*tan(1/2*e)^36 + 7099939*a^5*b^8*tan(1/2*e)^36 + 1384416*a^4*b^9*tan(1/2
*e)^36 + 3124550*a^9*b^4*tan(1/2*e)^34 + 15440084*a^8*b^5*tan(1/2*e)^34 + 30514836*a^7*b^6*tan(1/2*e)^34 + 301
49504*a^6*b^7*tan(1/2*e)^34 + 14892086*a^5*b^8*tan(1/2*e)^34 + 2941884*a^4*b^9*tan(1/2*e)^34 + 5311735*a^9*b^4
*tan(1/2*e)^32 + 26476956*a^8*b^5*tan(1/2*e)^32 + 52790474*a^7*b^6*tan(1/2*e)^32 + 52627036*a^6*b^7*tan(1/2*e)
^32 + 26231799*a^5*b^8*tan(1/2*e)^32 + 5230016*a^4*b^9*tan(1/2*e)^32 + 7726160*a^9*b^4*tan(1/2*e)^30 + 3874966
4*a^8*b^5*tan(1/2*e)^30 + 77737056*a^7*b^6*tan(1/2*e)^30 + 77974784*a^6*b^7*tan(1/2*e)^30 + 39106256*a^5*b^8*t
an(1/2*e)^30 + 7845024*a^4*b^9*tan(1/2*e)^30 + 9657700*a^9*b^4*tan(1/2*e)^28 + 48615376*a^8*b^5*tan(1/2*e)^28
+ 97884504*a^7*b^6*tan(1/2*e)^28 + 98538256*a^6*b^7*tan(1/2*e)^28 + 49596004*a^5*b^8*tan(1/2*e)^28 + 9984576*a
^4*b^9*tan(1/2*e)^28 + 10400600*a^9*b^4*tan(1/2*e)^26 + 52419024*a^8*b^5*tan(1/2*e)^26 + 105670096*a^7*b^6*tan
(1/2*e)^26 + 106502144*a^6*b^7*tan(1/2*e)^26 + 53667096*a^5*b^8*tan(1/2*e)^26 + 10816624*a^4*b^9*tan(1/2*e)^26
+ 9657700*a^9*b^4*tan(1/2*e)^24 + 48615376*a^8*b^5*tan(1/2*e)^24 + 97884504*a^7*b^6*tan(1/2*e)^24 + 98538256*
a^6*b^7*tan(1/2*e)^24 + 49596004*a^5*b^8*tan(1/2*e)^24 + 9984576*a^4*b^9*tan(1/2*e)^24 + 7726160*a^9*b^4*tan(1
/2*e)^22 + 38749664*a^8*b^5*tan(1/2*e)^22 + 77737056*a^7*b^6*tan(1/2*e)^22 + 77974784*a^6*b^7*tan(1/2*e)^22 +
39106256*a^5*b^8*tan(1/2*e)^22 + 7845024*a^4*b^9*tan(1/2*e)^22 + 5311735*a^9*b^4*tan(1/2*e)^20 + 26476956*a^8*
b^5*tan(1/2*e)^20 + 52790474*a^7*b^6*tan(1/2*e)^20 + 52627036*a^6*b^7*tan(1/2*e)^20 + 26231799*a^5*b^8*tan(1/2
*e)^20 + 5230016*a^4*b^9*tan(1/2*e)^20 + 3124550*a^9*b^4*tan(1/2*e)^18 + 15440084*a^8*b^5*tan(1/2*e)^18 + 3051
4836*a^7*b^6*tan(1/2*e)^18 + 30149504*a^6*b^7*tan(1/2*e)^18 + 14892086*a^5*b^8*tan(1/2*e)^18 + 2941884*a^4*b^9
*tan(1/2*e)^18 + 1562275*a^9*b^4*tan(1/2*e)^16 + 7633516*a^8*b^5*tan(1/2*e)^16 + 14911314*a^7*b^6*tan(1/2*e)^1
6 + 14555596*a^6*b^7*tan(1/2*e)^16 + 7099939*a^5*b^8*tan(1/2*e)^16 + 1384416*a^4*b^9*tan(1/2*e)^16 + 657800*a^
9*b^4*tan(1/2*e)^14 + 3169584*a^8*b^5*tan(1/2*e)^14 + 6100336*a^7*b^6*tan(1/2*e)^14 + 5861504*a^6*b^7*tan(1/2*
e)^14 + 2811336*a^5*b^8*tan(1/2*e)^14 + 538384*a^4*b^9*tan(1/2*e)^14 + 230230*a^9*b^4*tan(1/2*e)^12 + 1090936*
a^8*b^5*tan(1/2*e)^12 + 2061444*a^7*b^6*tan(1/2*e)^12 + 1941016*a^6*b^7*tan(1/2*e)^12 + 910294*a^5*b^8*tan(1/2
*e)^12 + 170016*a^4*b^9*tan(1/2*e)^12 + 65780*a^9*b^4*tan(1/2*e)^10 + 305624*a^8*b^5*tan(1/2*e)^10 + 564696*a^
7*b^6*tan(1/2*e)^10 + 518144*a^6*b^7*tan(1/2*e)^10 + 235796*a^5*b^8*tan(1/2*e)^10 + 42504*a^4*b^9*tan(1/2*e)^1
0 + 14950*a^9*b^4*tan(1/2*e)^8 + 67896*a^8*b^5*tan(1/2*e)^8 + 122084*a^7*b^6*tan(1/2*e)^8 + 108376*a^6*b^7*tan
(1/2*e)^8 + 47334*a^5*b^8*tan(1/2*e)^8 + 8096*a^4*b^9*tan(1/2*e)^8 + 2600*a^9*b^4*tan(1/2*e)^6 + 11504*a^8*b^5
*tan(1/2*e)^6 + 20016*a^7*b^6*tan(1/2*e)^6 + 17024*a^6*b^7*tan(1/2*e)^6 + 7016*a^5*b^8*tan(1/2*e)^6 + 1104*a^4
*b^9*tan(1/2*e)^6 + 325*a^9*b^4*tan(1/2*e)^4 + 1396*a^8*b^5*tan(1/2*e)^4 + 2334*a^7*b^6*tan(1/2*e)^4 + 1876*a^
6*b^7*tan(1/2*e)^4 + 709*a^5*b^8*tan(1/2*e)^4 + 96*a^4*b^9*tan(1/2*e)^4 + 26*a^9*b^4*tan(1/2*e)^2 + 108*a^8*b^
5*tan(1/2*e)^2 + 172*a^7*b^6*tan(1/2*e)^2 + 128*a^6*b^7*tan(1/2*e)^2 + 42*a^5*b^8*tan(1/2*e)^2 + 4*a^4*b^9*tan
(1/2*e)^2 + a^9*b^4 + 4*a^8*b^5 + 6*a^7*b^6 + 4*a^6*b^7 + a^5*b^8))*tan(1/2*f*x) - 3*(3*a^8*b^4*tan(1/2*e)^57
+ 4*a^7*b^5*tan(1/2*e)^57 - 14*a^6*b^6*tan(1/2*e)^57 - 36*a^5*b^7*tan(1/2*e)^57 - 29*a^4*b^8*tan(1/2*e)^57 - 8
*a^3*b^9*tan(1/2*e)^57 + 64*a^8*b^4*tan(1/2*e)^55 + 84*a^7*b^5*tan(1/2*e)^55 - 336*a^6*b^6*tan(1/2*e)^55 - 904
*a^5*b^7*tan(1/2*e)^55 - 816*a^4*b^8*tan(1/2*e)^55 - 300*a^3*b^9*tan(1/2*e)^55 - 32*a^2*b^10*tan(1/2*e)^55 + 6
14*a^8*b^4*tan(1/2*e)^53 + 704*a^7*b^5*tan(1/2*e)^53 - 3996*a^6*b^6*tan(1/2*e)^53 - 10744*a^5*b^7*tan(1/2*e)^5
3 - 10426*a^4*b^8*tan(1/2*e)^53 - 4440*a^3*b^9*tan(1/2*e)^53 - 672*a^2*b^10*tan(1/2*e)^53 + 3328*a^8*b^4*tan(1
/2*e)^51 + 2084*a^7*b^5*tan(1/2*e)^51 - 31504*a^6*b^6*tan(1/2*e)^51 - 80296*a^5*b^7*tan(1/2*e)^51 - 80944*a^4*
b^8*tan(1/2*e)^51 - 37468*a^3*b^9*tan(1/2*e)^51 - 6560*a^2*b^10*tan(1/2*e)^51 + 9425*a^8*b^4*tan(1/2*e)^49 - 1
2980*a^7*b^5*tan(1/2*e)^49 - 185210*a^6*b^6*tan(1/2*e)^49 - 422540*a^5*b^7*tan(1/2*e)^49 - 427535*a^4*b^8*tan(
1/2*e)^49 - 206840*a^3*b^9*tan(1/2*e)^49 - 39040*a^2*b^10*tan(1/2*e)^49 - 4160*a^8*b^4*tan(1/2*e)^47 - 187400*
a^7*b^5*tan(1/2*e)^47 - 862560*a^6*b^6*tan(1/2*e)^47 - 1659440*a^5*b^7*tan(1/2*e)^47 - 1614560*a^4*b^8*tan(1/2
*e)^47 - 789000*a^3*b^9*tan(1/2*e)^47 - 154560*a^2*b^10*tan(1/2*e)^47 - 185380*a^8*b^4*tan(1/2*e)^45 - 1184960
*a^7*b^5*tan(1/2*e)^45 - 3290840*a^6*b^6*tan(1/2*e)^45 - 5021360*a^5*b^7*tan(1/2*e)^45 - 4387940*a^4*b^8*tan(1
/2*e)^45 - 2062640*a^3*b^9*tan(1/2*e)^45 - 404800*a^2*b^10*tan(1/2*e)^45 - 1052480*a^8*b^4*tan(1/2*e)^43 - 511
0600*a^7*b^5*tan(1/2*e)^43 - 10484320*a^6*b^6*tan(1/2*e)^43 - 11880880*a^5*b^7*tan(1/2*e)^43 - 8055520*a^4*b^8
*tan(1/2*e)^43 - 3167560*a^3*b^9*tan(1/2*e)^43 - 566720*a^2*b^10*tan(1/2*e)^43 - 3831685*a^8*b^4*tan(1/2*e)^41
- 16753660*a^7*b^5*tan(1/2*e)^41 - 28212030*a^6*b^6*tan(1/2*e)^41 - 21945220*a^5*b^7*tan(1/2*e)^41 - 6624805*
a^4*b^8*tan(1/2*e)^41 + 516120*a^3*b^9*tan(1/2*e)^41 + 485760*a^2*b^10*tan(1/2*e)^41 - 10524800*a^8*b^4*tan(1/
2*e)^39 - 43804420*a^7*b^5*tan(1/2*e)^39 - 64585840*a^6*b^6*tan(1/2*e)^39 - 30795160*a^5*b^7*tan(1/2*e)^39 + 1
4957360*a^4*b^8*tan(1/2*e)^39 + 19830140*a^3*b^9*tan(1/2*e)^39 + 5383840*a^2*b^10*tan(1/2*e)^39 - 23121670*a^8
*b^4*tan(1/2*e)^37 - 93832640*a^7*b^5*tan(1/2*e)^37 - 126424100*a^6*b^6*tan(1/2*e)^37 - 29803400*a^5*b^7*tan(1
/2*e)^37 + 77633050*a^4*b^8*tan(1/2*e)^37 + 69413080*a^3*b^9*tan(1/2*e)^37 + 17689760*a^2*b^10*tan(1/2*e)^37 -
41812160*a^8*b^4*tan(1/2*e)^35 - 167432180*a^7*b^5*tan(1/2*e)^35 - 212382000*a^6*b^6*tan(1/2*e)^35 - 11449400
*a^5*b^7*tan(1/2*e)^35 + 192804400*a^4*b^8*tan(1/2*e)^35 + 156716940*a^3*b^9*tan(1/2*e)^35 + 39225120*a^2*b^10
*tan(1/2*e)^35 - 63257935*a^8*b^4*tan(1/2*e)^33 - 251545940*a^7*b^5*tan(1/2*e)^33 - 307040570*a^6*b^6*tan(1/2*
e)^33 + 22138420*a^5*b^7*tan(1/2*e)^33 + 342068305*a^4*b^8*tan(1/2*e)^33 + 267741160*a^3*b^9*tan(1/2*e)^33 + 6
6563840*a^2*b^10*tan(1/2*e)^33 - 80827520*a^8*b^4*tan(1/2*e)^31 - 320338480*a^7*b^5*tan(1/2*e)^31 - 382742080*
a^6*b^6*tan(1/2*e)^31 + 55866080*a^5*b^7*tan(1/2*e)^31 + 473078720*a^4*b^8*tan(1/2*e)^31 + 364318160*a^3*b^9*t
an(1/2*e)^31 + 90336640*a^2*b^10*tan(1/2*e)^31 - 87662200*a^8*b^4*tan(1/2*e)^29 - 347082880*a^7*b^5*tan(1/2*e)
^29 - 411863760*a^6*b^6*tan(1/2*e)^29 + 70129760*a^5*b^7*tan(1/2*e)^29 + 525676040*a^4*b^8*tan(1/2*e)^29 + 402
948960*a^3*b^9*tan(1/2*e)^29 + 99845760*a^2*b^10*tan(1/2*e)^29 - 80827520*a^8*b^4*tan(1/2*e)^27 - 320338480*a^
7*b^5*tan(1/2*e)^27 - 382742080*a^6*b^6*tan(1/2*e)^27 + 55866080*a^5*b^7*tan(1/2*e)^27 + 473078720*a^4*b^8*tan
(1/2*e)^27 + 364318160*a^3*b^9*tan(1/2*e)^27 + 90336640*a^2*b^10*tan(1/2*e)^27 - 63257935*a^8*b^4*tan(1/2*e)^2
5 - 251545940*a^7*b^5*tan(1/2*e)^25 - 307040570*a^6*b^6*tan(1/2*e)^25 + 22138420*a^5*b^7*tan(1/2*e)^25 + 34206
8305*a^4*b^8*tan(1/2*e)^25 + 267741160*a^3*b^9*tan(1/2*e)^25 + 66563840*a^2*b^10*tan(1/2*e)^25 - 41812160*a^8*
b^4*tan(1/2*e)^23 - 167432180*a^7*b^5*tan(1/2*e)^23 - 212382000*a^6*b^6*tan(1/2*e)^23 - 11449400*a^5*b^7*tan(1
/2*e)^23 + 192804400*a^4*b^8*tan(1/2*e)^23 + 156716940*a^3*b^9*tan(1/2*e)^23 + 39225120*a^2*b^10*tan(1/2*e)^23
- 23121670*a^8*b^4*tan(1/2*e)^21 - 93832640*a^7*b^5*tan(1/2*e)^21 - 126424100*a^6*b^6*tan(1/2*e)^21 - 2980340
0*a^5*b^7*tan(1/2*e)^21 + 77633050*a^4*b^8*tan(1/2*e)^21 + 69413080*a^3*b^9*tan(1/2*e)^21 + 17689760*a^2*b^10*
tan(1/2*e)^21 - 10524800*a^8*b^4*tan(1/2*e)^19 - 43804420*a^7*b^5*tan(1/2*e)^19 - 64585840*a^6*b^6*tan(1/2*e)^
19 - 30795160*a^5*b^7*tan(1/2*e)^19 + 14957360*a^4*b^8*tan(1/2*e)^19 + 19830140*a^3*b^9*tan(1/2*e)^19 + 538384
0*a^2*b^10*tan(1/2*e)^19 - 3831685*a^8*b^4*tan(1/2*e)^17 - 16753660*a^7*b^5*tan(1/2*e)^17 - 28212030*a^6*b^6*t
an(1/2*e)^17 - 21945220*a^5*b^7*tan(1/2*e)^17 - 6624805*a^4*b^8*tan(1/2*e)^17 + 516120*a^3*b^9*tan(1/2*e)^17 +
485760*a^2*b^10*tan(1/2*e)^17 - 1052480*a^8*b^4*tan(1/2*e)^15 - 5110600*a^7*b^5*tan(1/2*e)^15 - 10484320*a^6*
b^6*tan(1/2*e)^15 - 11880880*a^5*b^7*tan(1/2*e)^15 - 8055520*a^4*b^8*tan(1/2*e)^15 - 3167560*a^3*b^9*tan(1/2*e
)^15 - 566720*a^2*b^10*tan(1/2*e)^15 - 185380*a^8*b^4*tan(1/2*e)^13 - 1184960*a^7*b^5*tan(1/2*e)^13 - 3290840*
a^6*b^6*tan(1/2*e)^13 - 5021360*a^5*b^7*tan(1/2*e)^13 - 4387940*a^4*b^8*tan(1/2*e)^13 - 2062640*a^3*b^9*tan(1/
2*e)^13 - 404800*a^2*b^10*tan(1/2*e)^13 - 4160*a^8*b^4*tan(1/2*e)^11 - 187400*a^7*b^5*tan(1/2*e)^11 - 862560*a
^6*b^6*tan(1/2*e)^11 - 1659440*a^5*b^7*tan(1/2*e)^11 - 1614560*a^4*b^8*tan(1/2*e)^11 - 789000*a^3*b^9*tan(1/2*
e)^11 - 154560*a^2*b^10*tan(1/2*e)^11 + 9425*a^8*b^4*tan(1/2*e)^9 - 12980*a^7*b^5*tan(1/2*e)^9 - 185210*a^6*b^
6*tan(1/2*e)^9 - 422540*a^5*b^7*tan(1/2*e)^9 - 427535*a^4*b^8*tan(1/2*e)^9 - 206840*a^3*b^9*tan(1/2*e)^9 - 390
40*a^2*b^10*tan(1/2*e)^9 + 3328*a^8*b^4*tan(1/2*e)^7 + 2084*a^7*b^5*tan(1/2*e)^7 - 31504*a^6*b^6*tan(1/2*e)^7
- 80296*a^5*b^7*tan(1/2*e)^7 - 80944*a^4*b^8*tan(1/2*e)^7 - 37468*a^3*b^9*tan(1/2*e)^7 - 6560*a^2*b^10*tan(1/2
*e)^7 + 614*a^8*b^4*tan(1/2*e)^5 + 704*a^7*b^5*tan(1/2*e)^5 - 3996*a^6*b^6*tan(1/2*e)^5 - 10744*a^5*b^7*tan(1/
2*e)^5 - 10426*a^4*b^8*tan(1/2*e)^5 - 4440*a^3*b^9*tan(1/2*e)^5 - 672*a^2*b^10*tan(1/2*e)^5 + 64*a^8*b^4*tan(1
/2*e)^3 + 84*a^7*b^5*tan(1/2*e)^3 - 336*a^6*b^6*tan(1/2*e)^3 - 904*a^5*b^7*tan(1/2*e)^3 - 816*a^4*b^8*tan(1/2*
e)^3 - 300*a^3*b^9*tan(1/2*e)^3 - 32*a^2*b^10*tan(1/2*e)^3 + 3*a^8*b^4*tan(1/2*e) + 4*a^7*b^5*tan(1/2*e) - 14*
a^6*b^6*tan(1/2*e) - 36*a^5*b^7*tan(1/2*e) - 29*a^4*b^8*tan(1/2*e) - 8*a^3*b^9*tan(1/2*e))/(a^9*b^4*tan(1/2*e)
^52 + 4*a^8*b^5*tan(1/2*e)^52 + 6*a^7*b^6*tan(1/2*e)^52 + 4*a^6*b^7*tan(1/2*e)^52 + a^5*b^8*tan(1/2*e)^52 + 26
*a^9*b^4*tan(1/2*e)^50 + 108*a^8*b^5*tan(1/2*e)^50 + 172*a^7*b^6*tan(1/2*e)^50 + 128*a^6*b^7*tan(1/2*e)^50 + 4
2*a^5*b^8*tan(1/2*e)^50 + 4*a^4*b^9*tan(1/2*e)^50 + 325*a^9*b^4*tan(1/2*e)^48 + 1396*a^8*b^5*tan(1/2*e)^48 + 2
334*a^7*b^6*tan(1/2*e)^48 + 1876*a^6*b^7*tan(1/2*e)^48 + 709*a^5*b^8*tan(1/2*e)^48 + 96*a^4*b^9*tan(1/2*e)^48
+ 2600*a^9*b^4*tan(1/2*e)^46 + 11504*a^8*b^5*tan(1/2*e)^46 + 20016*a^7*b^6*tan(1/2*e)^46 + 17024*a^6*b^7*tan(1
/2*e)^46 + 7016*a^5*b^8*tan(1/2*e)^46 + 1104*a^4*b^9*tan(1/2*e)^46 + 14950*a^9*b^4*tan(1/2*e)^44 + 67896*a^8*b
^5*tan(1/2*e)^44 + 122084*a^7*b^6*tan(1/2*e)^44 + 108376*a^6*b^7*tan(1/2*e)^44 + 47334*a^5*b^8*tan(1/2*e)^44 +
8096*a^4*b^9*tan(1/2*e)^44 + 65780*a^9*b^4*tan(1/2*e)^42 + 305624*a^8*b^5*tan(1/2*e)^42 + 564696*a^7*b^6*tan(
1/2*e)^42 + 518144*a^6*b^7*tan(1/2*e)^42 + 235796*a^5*b^8*tan(1/2*e)^42 + 42504*a^4*b^9*tan(1/2*e)^42 + 230230
*a^9*b^4*tan(1/2*e)^40 + 1090936*a^8*b^5*tan(1/2*e)^40 + 2061444*a^7*b^6*tan(1/2*e)^40 + 1941016*a^6*b^7*tan(1
/2*e)^40 + 910294*a^5*b^8*tan(1/2*e)^40 + 170016*a^4*b^9*tan(1/2*e)^40 + 657800*a^9*b^4*tan(1/2*e)^38 + 316958
4*a^8*b^5*tan(1/2*e)^38 + 6100336*a^7*b^6*tan(1/2*e)^38 + 5861504*a^6*b^7*tan(1/2*e)^38 + 2811336*a^5*b^8*tan(
1/2*e)^38 + 538384*a^4*b^9*tan(1/2*e)^38 + 1562275*a^9*b^4*tan(1/2*e)^36 + 7633516*a^8*b^5*tan(1/2*e)^36 + 149
11314*a^7*b^6*tan(1/2*e)^36 + 14555596*a^6*b^7*tan(1/2*e)^36 + 7099939*a^5*b^8*tan(1/2*e)^36 + 1384416*a^4*b^9
*tan(1/2*e)^36 + 3124550*a^9*b^4*tan(1/2*e)^34 + 15440084*a^8*b^5*tan(1/2*e)^34 + 30514836*a^7*b^6*tan(1/2*e)^
34 + 30149504*a^6*b^7*tan(1/2*e)^34 + 14892086*a^5*b^8*tan(1/2*e)^34 + 2941884*a^4*b^9*tan(1/2*e)^34 + 5311735
*a^9*b^4*tan(1/2*e)^32 + 26476956*a^8*b^5*tan(1/2*e)^32 + 52790474*a^7*b^6*tan(1/2*e)^32 + 52627036*a^6*b^7*ta
n(1/2*e)^32 + 26231799*a^5*b^8*tan(1/2*e)^32 + 5230016*a^4*b^9*tan(1/2*e)^32 + 7726160*a^9*b^4*tan(1/2*e)^30 +
38749664*a^8*b^5*tan(1/2*e)^30 + 77737056*a^7*b^6*tan(1/2*e)^30 + 77974784*a^6*b^7*tan(1/2*e)^30 + 39106256*a
^5*b^8*tan(1/2*e)^30 + 7845024*a^4*b^9*tan(1/2*e)^30 + 9657700*a^9*b^4*tan(1/2*e)^28 + 48615376*a^8*b^5*tan(1/
2*e)^28 + 97884504*a^7*b^6*tan(1/2*e)^28 + 98538256*a^6*b^7*tan(1/2*e)^28 + 49596004*a^5*b^8*tan(1/2*e)^28 + 9
984576*a^4*b^9*tan(1/2*e)^28 + 10400600*a^9*b^4*tan(1/2*e)^26 + 52419024*a^8*b^5*tan(1/2*e)^26 + 105670096*a^7
*b^6*tan(1/2*e)^26 + 106502144*a^6*b^7*tan(1/2*e)^26 + 53667096*a^5*b^8*tan(1/2*e)^26 + 10816624*a^4*b^9*tan(1
/2*e)^26 + 9657700*a^9*b^4*tan(1/2*e)^24 + 48615376*a^8*b^5*tan(1/2*e)^24 + 97884504*a^7*b^6*tan(1/2*e)^24 + 9
8538256*a^6*b^7*tan(1/2*e)^24 + 49596004*a^5*b^8*tan(1/2*e)^24 + 9984576*a^4*b^9*tan(1/2*e)^24 + 7726160*a^9*b
^4*tan(1/2*e)^22 + 38749664*a^8*b^5*tan(1/2*e)^22 + 77737056*a^7*b^6*tan(1/2*e)^22 + 77974784*a^6*b^7*tan(1/2*
e)^22 + 39106256*a^5*b^8*tan(1/2*e)^22 + 7845024*a^4*b^9*tan(1/2*e)^22 + 5311735*a^9*b^4*tan(1/2*e)^20 + 26476
956*a^8*b^5*tan(1/2*e)^20 + 52790474*a^7*b^6*tan(1/2*e)^20 + 52627036*a^6*b^7*tan(1/2*e)^20 + 26231799*a^5*b^8
*tan(1/2*e)^20 + 5230016*a^4*b^9*tan(1/2*e)^20 + 3124550*a^9*b^4*tan(1/2*e)^18 + 15440084*a^8*b^5*tan(1/2*e)^1
8 + 30514836*a^7*b^6*tan(1/2*e)^18 + 30149504*a^6*b^7*tan(1/2*e)^18 + 14892086*a^5*b^8*tan(1/2*e)^18 + 2941884
*a^4*b^9*tan(1/2*e)^18 + 1562275*a^9*b^4*tan(1/2*e)^16 + 7633516*a^8*b^5*tan(1/2*e)^16 + 14911314*a^7*b^6*tan(
1/2*e)^16 + 14555596*a^6*b^7*tan(1/2*e)^16 + 7099939*a^5*b^8*tan(1/2*e)^16 + 1384416*a^4*b^9*tan(1/2*e)^16 + 6
57800*a^9*b^4*tan(1/2*e)^14 + 3169584*a^8*b^5*tan(1/2*e)^14 + 6100336*a^7*b^6*tan(1/2*e)^14 + 5861504*a^6*b^7*
tan(1/2*e)^14 + 2811336*a^5*b^8*tan(1/2*e)^14 + 538384*a^4*b^9*tan(1/2*e)^14 + 230230*a^9*b^4*tan(1/2*e)^12 +
1090936*a^8*b^5*tan(1/2*e)^12 + 2061444*a^7*b^6*tan(1/2*e)^12 + 1941016*a^6*b^7*tan(1/2*e)^12 + 910294*a^5*b^8
*tan(1/2*e)^12 + 170016*a^4*b^9*tan(1/2*e)^12 + 65780*a^9*b^4*tan(1/2*e)^10 + 305624*a^8*b^5*tan(1/2*e)^10 + 5
64696*a^7*b^6*tan(1/2*e)^10 + 518144*a^6*b^7*tan(1/2*e)^10 + 235796*a^5*b^8*tan(1/2*e)^10 + 42504*a^4*b^9*tan(
1/2*e)^10 + 14950*a^9*b^4*tan(1/2*e)^8 + 67896*a^8*b^5*tan(1/2*e)^8 + 122084*a^7*b^6*tan(1/2*e)^8 + 108376*a^6
*b^7*tan(1/2*e)^8 + 47334*a^5*b^8*tan(1/2*e)^8 + 8096*a^4*b^9*tan(1/2*e)^8 + 2600*a^9*b^4*tan(1/2*e)^6 + 11504
*a^8*b^5*tan(1/2*e)^6 + 20016*a^7*b^6*tan(1/2*e)^6 + 17024*a^6*b^7*tan(1/2*e)^6 + 7016*a^5*b^8*tan(1/2*e)^6 +
1104*a^4*b^9*tan(1/2*e)^6 + 325*a^9*b^4*tan(1/2*e)^4 + 1396*a^8*b^5*tan(1/2*e)^4 + 2334*a^7*b^6*tan(1/2*e)^4 +
1876*a^6*b^7*tan(1/2*e)^4 + 709*a^5*b^8*tan(1/2*e)^4 + 96*a^4*b^9*tan(1/2*e)^4 + 26*a^9*b^4*tan(1/2*e)^2 + 10
8*a^8*b^5*tan(1/2*e)^2 + 172*a^7*b^6*tan(1/2*e)^2 + 128*a^6*b^7*tan(1/2*e)^2 + 42*a^5*b^8*tan(1/2*e)^2 + 4*a^4
*b^9*tan(1/2*e)^2 + a^9*b^4 + 4*a^8*b^5 + 6*a^7*b^6 + 4*a^6*b^7 + a^5*b^8))*tan(1/2*f*x) + 2*(a^8*b^4*tan(1/2*
e)^58 + 8*a^7*b^5*tan(1/2*e)^58 + 22*a^6*b^6*tan(1/2*e)^58 + 28*a^5*b^7*tan(1/2*e)^58 + 17*a^4*b^8*tan(1/2*e)^
58 + 4*a^3*b^9*tan(1/2*e)^58 + 47*a^8*b^4*tan(1/2*e)^56 + 260*a^7*b^5*tan(1/2*e)^56 + 586*a^6*b^6*tan(1/2*e)^5
6 + 684*a^5*b^7*tan(1/2*e)^56 + 431*a^4*b^8*tan(1/2*e)^56 + 136*a^3*b^9*tan(1/2*e)^56 + 16*a^2*b^10*tan(1/2*e)
^56 + 850*a^8*b^4*tan(1/2*e)^54 + 3980*a^7*b^5*tan(1/2*e)^54 + 7660*a^6*b^6*tan(1/2*e)^54 + 7840*a^5*b^7*tan(1
/2*e)^54 + 4610*a^4*b^8*tan(1/2*e)^54 + 1540*a^3*b^9*tan(1/2*e)^54 + 240*a^2*b^10*tan(1/2*e)^54 + 8878*a^8*b^4
*tan(1/2*e)^52 + 38180*a^7*b^5*tan(1/2*e)^52 + 65044*a^6*b^6*tan(1/2*e)^52 + 55936*a^5*b^7*tan(1/2*e)^52 + 261
74*a^4*b^8*tan(1/2*e)^52 + 7084*a^3*b^9*tan(1/2*e)^52 + 1104*a^2*b^10*tan(1/2*e)^52 + 62699*a^8*b^4*tan(1/2*e)
^50 + 257852*a^7*b^5*tan(1/2*e)^50 + 400498*a^6*b^6*tan(1/2*e)^50 + 277452*a^5*b^7*tan(1/2*e)^50 + 67403*a^4*b
^8*tan(1/2*e)^50 - 8624*a^3*b^9*tan(1/2*e)^50 - 3920*a^2*b^10*tan(1/2*e)^50 + 324805*a^8*b^4*tan(1/2*e)^48 + 1
305680*a^7*b^5*tan(1/2*e)^48 + 1892590*a^6*b^6*tan(1/2*e)^48 + 1009660*a^5*b^7*tan(1/2*e)^48 - 141835*a^4*b^8*
tan(1/2*e)^48 - 321860*a^3*b^9*tan(1/2*e)^48 - 82080*a^2*b^10*tan(1/2*e)^48 + 1295060*a^8*b^4*tan(1/2*e)^46 +
5152360*a^7*b^5*tan(1/2*e)^46 + 7095800*a^6*b^6*tan(1/2*e)^46 + 2760800*a^5*b^7*tan(1/2*e)^46 - 2194700*a^4*b^
8*tan(1/2*e)^46 - 2280040*a^3*b^9*tan(1/2*e)^46 - 563040*a^2*b^10*tan(1/2*e)^46 + 4096300*a^8*b^4*tan(1/2*e)^4
4 + 16244440*a^7*b^5*tan(1/2*e)^44 + 21545480*a^6*b^6*tan(1/2*e)^44 + 5663520*a^5*b^7*tan(1/2*e)^44 - 11282420
*a^4*b^8*tan(1/2*e)^44 - 10017880*a^3*b^9*tan(1/2*e)^44 - 2469280*a^2*b^10*tan(1/2*e)^44 + 10475465*a^8*b^4*ta
n(1/2*e)^42 + 41572960*a^7*b^5*tan(1/2*e)^42 + 53643590*a^6*b^6*tan(1/2*e)^42 + 8354060*a^5*b^7*tan(1/2*e)^42
- 38201735*a^4*b^8*tan(1/2*e)^42 - 31903300*a^3*b^9*tan(1/2*e)^42 - 7893600*a^2*b^10*tan(1/2*e)^42 + 21888295*
a^8*b^4*tan(1/2*e)^40 + 87107900*a^7*b^5*tan(1/2*e)^40 + 110178970*a^6*b^6*tan(1/2*e)^40 + 7402780*a^5*b^7*tan
(1/2*e)^40 - 96110905*a^4*b^8*tan(1/2*e)^40 - 77924000*a^3*b^9*tan(1/2*e)^40 - 19369680*a^2*b^10*tan(1/2*e)^40
+ 37461710*a^8*b^4*tan(1/2*e)^38 + 149619140*a^7*b^5*tan(1/2*e)^38 + 186557140*a^6*b^6*tan(1/2*e)^38 - 728640
*a^5*b^7*tan(1/2*e)^38 - 187263010*a^4*b^8*tan(1/2*e)^38 - 149436980*a^3*b^9*tan(1/2*e)^38 - 37302320*a^2*b^10
*tan(1/2*e)^38 + 52094770*a^8*b^4*tan(1/2*e)^36 + 208807340*a^7*b^5*tan(1/2*e)^36 + 257751340*a^6*b^6*tan(1/2*
e)^36 - 15172640*a^5*b^7*tan(1/2*e)^36 - 285374110*a^4*b^8*tan(1/2*e)^36 - 225693020*a^3*b^9*tan(1/2*e)^36 - 5
6530320*a^2*b^10*tan(1/2*e)^36 + 57236075*a^8*b^4*tan(1/2*e)^34 + 230115460*a^7*b^5*tan(1/2*e)^34 + 282131570*
a^6*b^6*tan(1/2*e)^34 - 27906820*a^5*b^7*tan(1/2*e)^34 - 333896405*a^4*b^8*tan(1/2*e)^34 - 262706920*a^3*b^9*t
an(1/2*e)^34 - 65969520*a^2*b^10*tan(1/2*e)^34 + 45651205*a^8*b^4*tan(1/2*e)^32 + 183942040*a^7*b^5*tan(1/2*e)
^32 + 224578670*a^6*b^6*tan(1/2*e)^32 - 28081620*a^5*b^7*tan(1/2*e)^32 - 277064555*a^4*b^8*tan(1/2*e)^32 - 217
372540*a^3*b^9*tan(1/2*e)^32 - 54677440*a^2*b^10*tan(1/2*e)^32 + 17532440*a^8*b^4*tan(1/2*e)^30 + 70724080*a^7
*b^5*tan(1/2*e)^30 + 86176400*a^6*b^6*tan(1/2*e)^30 - 11886400*a^5*b^7*tan(1/2*e)^30 - 108463400*a^4*b^8*tan(1
/2*e)^30 - 84987760*a^3*b^9*tan(1/2*e)^30 - 21395520*a^2*b^10*tan(1/2*e)^30 - 17532440*a^8*b^4*tan(1/2*e)^28 -
70724080*a^7*b^5*tan(1/2*e)^28 - 86176400*a^6*b^6*tan(1/2*e)^28 + 11886400*a^5*b^7*tan(1/2*e)^28 + 108463400*
a^4*b^8*tan(1/2*e)^28 + 84987760*a^3*b^9*tan(1/2*e)^28 + 21395520*a^2*b^10*tan(1/2*e)^28 - 45651205*a^8*b^4*ta
n(1/2*e)^26 - 183942040*a^7*b^5*tan(1/2*e)^26 - 224578670*a^6*b^6*tan(1/2*e)^26 + 28081620*a^5*b^7*tan(1/2*e)^
26 + 277064555*a^4*b^8*tan(1/2*e)^26 + 217372540*a^3*b^9*tan(1/2*e)^26 + 54677440*a^2*b^10*tan(1/2*e)^26 - 572
36075*a^8*b^4*tan(1/2*e)^24 - 230115460*a^7*b^5*tan(1/2*e)^24 - 282131570*a^6*b^6*tan(1/2*e)^24 + 27906820*a^5
*b^7*tan(1/2*e)^24 + 333896405*a^4*b^8*tan(1/2*e)^24 + 262706920*a^3*b^9*tan(1/2*e)^24 + 65969520*a^2*b^10*tan
(1/2*e)^24 - 52094770*a^8*b^4*tan(1/2*e)^22 - 208807340*a^7*b^5*tan(1/2*e)^22 - 257751340*a^6*b^6*tan(1/2*e)^2
2 + 15172640*a^5*b^7*tan(1/2*e)^22 + 285374110*a^4*b^8*tan(1/2*e)^22 + 225693020*a^3*b^9*tan(1/2*e)^22 + 56530
320*a^2*b^10*tan(1/2*e)^22 - 37461710*a^8*b^4*tan(1/2*e)^20 - 149619140*a^7*b^5*tan(1/2*e)^20 - 186557140*a^6*
b^6*tan(1/2*e)^20 + 728640*a^5*b^7*tan(1/2*e)^20 + 187263010*a^4*b^8*tan(1/2*e)^20 + 149436980*a^3*b^9*tan(1/2
*e)^20 + 37302320*a^2*b^10*tan(1/2*e)^20 - 21888295*a^8*b^4*tan(1/2*e)^18 - 87107900*a^7*b^5*tan(1/2*e)^18 - 1
10178970*a^6*b^6*tan(1/2*e)^18 - 7402780*a^5*b^7*tan(1/2*e)^18 + 96110905*a^4*b^8*tan(1/2*e)^18 + 77924000*a^3
*b^9*tan(1/2*e)^18 + 19369680*a^2*b^10*tan(1/2*e)^18 - 10475465*a^8*b^4*tan(1/2*e)^16 - 41572960*a^7*b^5*tan(1
/2*e)^16 - 53643590*a^6*b^6*tan(1/2*e)^16 - 8354060*a^5*b^7*tan(1/2*e)^16 + 38201735*a^4*b^8*tan(1/2*e)^16 + 3
1903300*a^3*b^9*tan(1/2*e)^16 + 7893600*a^2*b^10*tan(1/2*e)^16 - 4096300*a^8*b^4*tan(1/2*e)^14 - 16244440*a^7*
b^5*tan(1/2*e)^14 - 21545480*a^6*b^6*tan(1/2*e)^14 - 5663520*a^5*b^7*tan(1/2*e)^14 + 11282420*a^4*b^8*tan(1/2*
e)^14 + 10017880*a^3*b^9*tan(1/2*e)^14 + 2469280*a^2*b^10*tan(1/2*e)^14 - 1295060*a^8*b^4*tan(1/2*e)^12 - 5152
360*a^7*b^5*tan(1/2*e)^12 - 7095800*a^6*b^6*tan(1/2*e)^12 - 2760800*a^5*b^7*tan(1/2*e)^12 + 2194700*a^4*b^8*ta
n(1/2*e)^12 + 2280040*a^3*b^9*tan(1/2*e)^12 + 563040*a^2*b^10*tan(1/2*e)^12 - 324805*a^8*b^4*tan(1/2*e)^10 - 1
305680*a^7*b^5*tan(1/2*e)^10 - 1892590*a^6*b^6*tan(1/2*e)^10 - 1009660*a^5*b^7*tan(1/2*e)^10 + 141835*a^4*b^8*
tan(1/2*e)^10 + 321860*a^3*b^9*tan(1/2*e)^10 + 82080*a^2*b^10*tan(1/2*e)^10 - 62699*a^8*b^4*tan(1/2*e)^8 - 257
852*a^7*b^5*tan(1/2*e)^8 - 400498*a^6*b^6*tan(1/2*e)^8 - 277452*a^5*b^7*tan(1/2*e)^8 - 67403*a^4*b^8*tan(1/2*e
)^8 + 8624*a^3*b^9*tan(1/2*e)^8 + 3920*a^2*b^10*tan(1/2*e)^8 - 8878*a^8*b^4*tan(1/2*e)^6 - 38180*a^7*b^5*tan(1
/2*e)^6 - 65044*a^6*b^6*tan(1/2*e)^6 - 55936*a^5*b^7*tan(1/2*e)^6 - 26174*a^4*b^8*tan(1/2*e)^6 - 7084*a^3*b^9*
tan(1/2*e)^6 - 1104*a^2*b^10*tan(1/2*e)^6 - 850*a^8*b^4*tan(1/2*e)^4 - 3980*a^7*b^5*tan(1/2*e)^4 - 7660*a^6*b^
6*tan(1/2*e)^4 - 7840*a^5*b^7*tan(1/2*e)^4 - 4610*a^4*b^8*tan(1/2*e)^4 - 1540*a^3*b^9*tan(1/2*e)^4 - 240*a^2*b
^10*tan(1/2*e)^4 - 47*a^8*b^4*tan(1/2*e)^2 - 260*a^7*b^5*tan(1/2*e)^2 - 586*a^6*b^6*tan(1/2*e)^2 - 684*a^5*b^7
*tan(1/2*e)^2 - 431*a^4*b^8*tan(1/2*e)^2 - 136*a^3*b^9*tan(1/2*e)^2 - 16*a^2*b^10*tan(1/2*e)^2 - a^8*b^4 - 8*a
^7*b^5 - 22*a^6*b^6 - 28*a^5*b^7 - 17*a^4*b^8 - 4*a^3*b^9)/(a^9*b^4*tan(1/2*e)^52 + 4*a^8*b^5*tan(1/2*e)^52 +
6*a^7*b^6*tan(1/2*e)^52 + 4*a^6*b^7*tan(1/2*e)^52 + a^5*b^8*tan(1/2*e)^52 + 26*a^9*b^4*tan(1/2*e)^50 + 108*a^8
*b^5*tan(1/2*e)^50 + 172*a^7*b^6*tan(1/2*e)^50 + 128*a^6*b^7*tan(1/2*e)^50 + 42*a^5*b^8*tan(1/2*e)^50 + 4*a^4*
b^9*tan(1/2*e)^50 + 325*a^9*b^4*tan(1/2*e)^48 + 1396*a^8*b^5*tan(1/2*e)^48 + 2334*a^7*b^6*tan(1/2*e)^48 + 1876
*a^6*b^7*tan(1/2*e)^48 + 709*a^5*b^8*tan(1/2*e)^48 + 96*a^4*b^9*tan(1/2*e)^48 + 2600*a^9*b^4*tan(1/2*e)^46 + 1
1504*a^8*b^5*tan(1/2*e)^46 + 20016*a^7*b^6*tan(1/2*e)^46 + 17024*a^6*b^7*tan(1/2*e)^46 + 7016*a^5*b^8*tan(1/2*
e)^46 + 1104*a^4*b^9*tan(1/2*e)^46 + 14950*a^9*b^4*tan(1/2*e)^44 + 67896*a^8*b^5*tan(1/2*e)^44 + 122084*a^7*b^
6*tan(1/2*e)^44 + 108376*a^6*b^7*tan(1/2*e)^44 + 47334*a^5*b^8*tan(1/2*e)^44 + 8096*a^4*b^9*tan(1/2*e)^44 + 65
780*a^9*b^4*tan(1/2*e)^42 + 305624*a^8*b^5*tan(1/2*e)^42 + 564696*a^7*b^6*tan(1/2*e)^42 + 518144*a^6*b^7*tan(1
/2*e)^42 + 235796*a^5*b^8*tan(1/2*e)^42 + 42504*a^4*b^9*tan(1/2*e)^42 + 230230*a^9*b^4*tan(1/2*e)^40 + 1090936
*a^8*b^5*tan(1/2*e)^40 + 2061444*a^7*b^6*tan(1/2*e)^40 + 1941016*a^6*b^7*tan(1/2*e)^40 + 910294*a^5*b^8*tan(1/
2*e)^40 + 170016*a^4*b^9*tan(1/2*e)^40 + 657800*a^9*b^4*tan(1/2*e)^38 + 3169584*a^8*b^5*tan(1/2*e)^38 + 610033
6*a^7*b^6*tan(1/2*e)^38 + 5861504*a^6*b^7*tan(1/2*e)^38 + 2811336*a^5*b^8*tan(1/2*e)^38 + 538384*a^4*b^9*tan(1
/2*e)^38 + 1562275*a^9*b^4*tan(1/2*e)^36 + 7633516*a^8*b^5*tan(1/2*e)^36 + 14911314*a^7*b^6*tan(1/2*e)^36 + 14
555596*a^6*b^7*tan(1/2*e)^36 + 7099939*a^5*b^8*tan(1/2*e)^36 + 1384416*a^4*b^9*tan(1/2*e)^36 + 3124550*a^9*b^4
*tan(1/2*e)^34 + 15440084*a^8*b^5*tan(1/2*e)^34 + 30514836*a^7*b^6*tan(1/2*e)^34 + 30149504*a^6*b^7*tan(1/2*e)
^34 + 14892086*a^5*b^8*tan(1/2*e)^34 + 2941884*a^4*b^9*tan(1/2*e)^34 + 5311735*a^9*b^4*tan(1/2*e)^32 + 2647695
6*a^8*b^5*tan(1/2*e)^32 + 52790474*a^7*b^6*tan(1/2*e)^32 + 52627036*a^6*b^7*tan(1/2*e)^32 + 26231799*a^5*b^8*t
an(1/2*e)^32 + 5230016*a^4*b^9*tan(1/2*e)^32 + 7726160*a^9*b^4*tan(1/2*e)^30 + 38749664*a^8*b^5*tan(1/2*e)^30
+ 77737056*a^7*b^6*tan(1/2*e)^30 + 77974784*a^6*b^7*tan(1/2*e)^30 + 39106256*a^5*b^8*tan(1/2*e)^30 + 7845024*a
^4*b^9*tan(1/2*e)^30 + 9657700*a^9*b^4*tan(1/2*e)^28 + 48615376*a^8*b^5*tan(1/2*e)^28 + 97884504*a^7*b^6*tan(1
/2*e)^28 + 98538256*a^6*b^7*tan(1/2*e)^28 + 49596004*a^5*b^8*tan(1/2*e)^28 + 9984576*a^4*b^9*tan(1/2*e)^28 + 1
0400600*a^9*b^4*tan(1/2*e)^26 + 52419024*a^8*b^5*tan(1/2*e)^26 + 105670096*a^7*b^6*tan(1/2*e)^26 + 106502144*a
^6*b^7*tan(1/2*e)^26 + 53667096*a^5*b^8*tan(1/2*e)^26 + 10816624*a^4*b^9*tan(1/2*e)^26 + 9657700*a^9*b^4*tan(1
/2*e)^24 + 48615376*a^8*b^5*tan(1/2*e)^24 + 97884504*a^7*b^6*tan(1/2*e)^24 + 98538256*a^6*b^7*tan(1/2*e)^24 +
49596004*a^5*b^8*tan(1/2*e)^24 + 9984576*a^4*b^9*tan(1/2*e)^24 + 7726160*a^9*b^4*tan(1/2*e)^22 + 38749664*a^8*
b^5*tan(1/2*e)^22 + 77737056*a^7*b^6*tan(1/2*e)^22 + 77974784*a^6*b^7*tan(1/2*e)^22 + 39106256*a^5*b^8*tan(1/2
*e)^22 + 7845024*a^4*b^9*tan(1/2*e)^22 + 5311735*a^9*b^4*tan(1/2*e)^20 + 26476956*a^8*b^5*tan(1/2*e)^20 + 5279
0474*a^7*b^6*tan(1/2*e)^20 + 52627036*a^6*b^7*tan(1/2*e)^20 + 26231799*a^5*b^8*tan(1/2*e)^20 + 5230016*a^4*b^9
*tan(1/2*e)^20 + 3124550*a^9*b^4*tan(1/2*e)^18 + 15440084*a^8*b^5*tan(1/2*e)^18 + 30514836*a^7*b^6*tan(1/2*e)^
18 + 30149504*a^6*b^7*tan(1/2*e)^18 + 14892086*a^5*b^8*tan(1/2*e)^18 + 2941884*a^4*b^9*tan(1/2*e)^18 + 1562275
*a^9*b^4*tan(1/2*e)^16 + 7633516*a^8*b^5*tan(1/2*e)^16 + 14911314*a^7*b^6*tan(1/2*e)^16 + 14555596*a^6*b^7*tan
(1/2*e)^16 + 7099939*a^5*b^8*tan(1/2*e)^16 + 1384416*a^4*b^9*tan(1/2*e)^16 + 657800*a^9*b^4*tan(1/2*e)^14 + 31
69584*a^8*b^5*tan(1/2*e)^14 + 6100336*a^7*b^6*tan(1/2*e)^14 + 5861504*a^6*b^7*tan(1/2*e)^14 + 2811336*a^5*b^8*
tan(1/2*e)^14 + 538384*a^4*b^9*tan(1/2*e)^14 + 230230*a^9*b^4*tan(1/2*e)^12 + 1090936*a^8*b^5*tan(1/2*e)^12 +
2061444*a^7*b^6*tan(1/2*e)^12 + 1941016*a^6*b^7*tan(1/2*e)^12 + 910294*a^5*b^8*tan(1/2*e)^12 + 170016*a^4*b^9*
tan(1/2*e)^12 + 65780*a^9*b^4*tan(1/2*e)^10 + 305624*a^8*b^5*tan(1/2*e)^10 + 564696*a^7*b^6*tan(1/2*e)^10 + 51
8144*a^6*b^7*tan(1/2*e)^10 + 235796*a^5*b^8*tan(1/2*e)^10 + 42504*a^4*b^9*tan(1/2*e)^10 + 14950*a^9*b^4*tan(1/
2*e)^8 + 67896*a^8*b^5*tan(1/2*e)^8 + 122084*a^7*b^6*tan(1/2*e)^8 + 108376*a^6*b^7*tan(1/2*e)^8 + 47334*a^5*b^
8*tan(1/2*e)^8 + 8096*a^4*b^9*tan(1/2*e)^8 + 2600*a^9*b^4*tan(1/2*e)^6 + 11504*a^8*b^5*tan(1/2*e)^6 + 20016*a^
7*b^6*tan(1/2*e)^6 + 17024*a^6*b^7*tan(1/2*e)^6 + 7016*a^5*b^8*tan(1/2*e)^6 + 1104*a^4*b^9*tan(1/2*e)^6 + 325*
a^9*b^4*tan(1/2*e)^4 + 1396*a^8*b^5*tan(1/2*e)^4 + 2334*a^7*b^6*tan(1/2*e)^4 + 1876*a^6*b^7*tan(1/2*e)^4 + 709
*a^5*b^8*tan(1/2*e)^4 + 96*a^4*b^9*tan(1/2*e)^4 + 26*a^9*b^4*tan(1/2*e)^2 + 108*a^8*b^5*tan(1/2*e)^2 + 172*a^7
*b^6*tan(1/2*e)^2 + 128*a^6*b^7*tan(1/2*e)^2 + 42*a^5*b^8*tan(1/2*e)^2 + 4*a^4*b^9*tan(1/2*e)^2 + a^9*b^4 + 4*
a^8*b^5 + 6*a^7*b^6 + 4*a^6*b^7 + a^5*b^8))*tan(1/2*f*x) + 3*(3*a^8*b^4*tan(1/2*e)^57 + 4*a^7*b^5*tan(1/2*e)^5
7 - 14*a^6*b^6*tan(1/2*e)^57 - 36*a^5*b^7*tan(1/2*e)^57 - 29*a^4*b^8*tan(1/2*e)^57 - 8*a^3*b^9*tan(1/2*e)^57 +
64*a^8*b^4*tan(1/2*e)^55 + 84*a^7*b^5*tan(1/2*e)^55 - 336*a^6*b^6*tan(1/2*e)^55 - 904*a^5*b^7*tan(1/2*e)^55 -
816*a^4*b^8*tan(1/2*e)^55 - 300*a^3*b^9*tan(1/2*e)^55 - 32*a^2*b^10*tan(1/2*e)^55 + 614*a^8*b^4*tan(1/2*e)^53
+ 704*a^7*b^5*tan(1/2*e)^53 - 3996*a^6*b^6*tan(1/2*e)^53 - 10744*a^5*b^7*tan(1/2*e)^53 - 10426*a^4*b^8*tan(1/
2*e)^53 - 4440*a^3*b^9*tan(1/2*e)^53 - 672*a^2*b^10*tan(1/2*e)^53 + 3328*a^8*b^4*tan(1/2*e)^51 + 2084*a^7*b^5*
tan(1/2*e)^51 - 31504*a^6*b^6*tan(1/2*e)^51 - 80296*a^5*b^7*tan(1/2*e)^51 - 80944*a^4*b^8*tan(1/2*e)^51 - 3746
8*a^3*b^9*tan(1/2*e)^51 - 6560*a^2*b^10*tan(1/2*e)^51 + 9425*a^8*b^4*tan(1/2*e)^49 - 12980*a^7*b^5*tan(1/2*e)^
49 - 185210*a^6*b^6*tan(1/2*e)^49 - 422540*a^5*b^7*tan(1/2*e)^49 - 427535*a^4*b^8*tan(1/2*e)^49 - 206840*a^3*b
^9*tan(1/2*e)^49 - 39040*a^2*b^10*tan(1/2*e)^49 - 4160*a^8*b^4*tan(1/2*e)^47 - 187400*a^7*b^5*tan(1/2*e)^47 -
862560*a^6*b^6*tan(1/2*e)^47 - 1659440*a^5*b^7*tan(1/2*e)^47 - 1614560*a^4*b^8*tan(1/2*e)^47 - 789000*a^3*b^9*
tan(1/2*e)^47 - 154560*a^2*b^10*tan(1/2*e)^47 - 185380*a^8*b^4*tan(1/2*e)^45 - 1184960*a^7*b^5*tan(1/2*e)^45 -
3290840*a^6*b^6*tan(1/2*e)^45 - 5021360*a^5*b^7*tan(1/2*e)^45 - 4387940*a^4*b^8*tan(1/2*e)^45 - 2062640*a^3*b
^9*tan(1/2*e)^45 - 404800*a^2*b^10*tan(1/2*e)^45 - 1052480*a^8*b^4*tan(1/2*e)^43 - 5110600*a^7*b^5*tan(1/2*e)^
43 - 10484320*a^6*b^6*tan(1/2*e)^43 - 11880880*a^5*b^7*tan(1/2*e)^43 - 8055520*a^4*b^8*tan(1/2*e)^43 - 3167560
*a^3*b^9*tan(1/2*e)^43 - 566720*a^2*b^10*tan(1/2*e)^43 - 3831685*a^8*b^4*tan(1/2*e)^41 - 16753660*a^7*b^5*tan(
1/2*e)^41 - 28212030*a^6*b^6*tan(1/2*e)^41 - 21945220*a^5*b^7*tan(1/2*e)^41 - 6624805*a^4*b^8*tan(1/2*e)^41 +
516120*a^3*b^9*tan(1/2*e)^41 + 485760*a^2*b^10*tan(1/2*e)^41 - 10524800*a^8*b^4*tan(1/2*e)^39 - 43804420*a^7*b
^5*tan(1/2*e)^39 - 64585840*a^6*b^6*tan(1/2*e)^39 - 30795160*a^5*b^7*tan(1/2*e)^39 + 14957360*a^4*b^8*tan(1/2*
e)^39 + 19830140*a^3*b^9*tan(1/2*e)^39 + 5383840*a^2*b^10*tan(1/2*e)^39 - 23121670*a^8*b^4*tan(1/2*e)^37 - 938
32640*a^7*b^5*tan(1/2*e)^37 - 126424100*a^6*b^6*tan(1/2*e)^37 - 29803400*a^5*b^7*tan(1/2*e)^37 + 77633050*a^4*
b^8*tan(1/2*e)^37 + 69413080*a^3*b^9*tan(1/2*e)^37 + 17689760*a^2*b^10*tan(1/2*e)^37 - 41812160*a^8*b^4*tan(1/
2*e)^35 - 167432180*a^7*b^5*tan(1/2*e)^35 - 212382000*a^6*b^6*tan(1/2*e)^35 - 11449400*a^5*b^7*tan(1/2*e)^35 +
192804400*a^4*b^8*tan(1/2*e)^35 + 156716940*a^3*b^9*tan(1/2*e)^35 + 39225120*a^2*b^10*tan(1/2*e)^35 - 6325793
5*a^8*b^4*tan(1/2*e)^33 - 251545940*a^7*b^5*tan(1/2*e)^33 - 307040570*a^6*b^6*tan(1/2*e)^33 + 22138420*a^5*b^7
*tan(1/2*e)^33 + 342068305*a^4*b^8*tan(1/2*e)^33 + 267741160*a^3*b^9*tan(1/2*e)^33 + 66563840*a^2*b^10*tan(1/2
*e)^33 - 80827520*a^8*b^4*tan(1/2*e)^31 - 320338480*a^7*b^5*tan(1/2*e)^31 - 382742080*a^6*b^6*tan(1/2*e)^31 +
55866080*a^5*b^7*tan(1/2*e)^31 + 473078720*a^4*b^8*tan(1/2*e)^31 + 364318160*a^3*b^9*tan(1/2*e)^31 + 90336640*
a^2*b^10*tan(1/2*e)^31 - 87662200*a^8*b^4*tan(1/2*e)^29 - 347082880*a^7*b^5*tan(1/2*e)^29 - 411863760*a^6*b^6*
tan(1/2*e)^29 + 70129760*a^5*b^7*tan(1/2*e)^29 + 525676040*a^4*b^8*tan(1/2*e)^29 + 402948960*a^3*b^9*tan(1/2*e
)^29 + 99845760*a^2*b^10*tan(1/2*e)^29 - 80827520*a^8*b^4*tan(1/2*e)^27 - 320338480*a^7*b^5*tan(1/2*e)^27 - 38
2742080*a^6*b^6*tan(1/2*e)^27 + 55866080*a^5*b^7*tan(1/2*e)^27 + 473078720*a^4*b^8*tan(1/2*e)^27 + 364318160*a
^3*b^9*tan(1/2*e)^27 + 90336640*a^2*b^10*tan(1/2*e)^27 - 63257935*a^8*b^4*tan(1/2*e)^25 - 251545940*a^7*b^5*ta
n(1/2*e)^25 - 307040570*a^6*b^6*tan(1/2*e)^25 + 22138420*a^5*b^7*tan(1/2*e)^25 + 342068305*a^4*b^8*tan(1/2*e)^
25 + 267741160*a^3*b^9*tan(1/2*e)^25 + 66563840*a^2*b^10*tan(1/2*e)^25 - 41812160*a^8*b^4*tan(1/2*e)^23 - 1674
32180*a^7*b^5*tan(1/2*e)^23 - 212382000*a^6*b^6*tan(1/2*e)^23 - 11449400*a^5*b^7*tan(1/2*e)^23 + 192804400*a^4
*b^8*tan(1/2*e)^23 + 156716940*a^3*b^9*tan(1/2*e)^23 + 39225120*a^2*b^10*tan(1/2*e)^23 - 23121670*a^8*b^4*tan(
1/2*e)^21 - 93832640*a^7*b^5*tan(1/2*e)^21 - 126424100*a^6*b^6*tan(1/2*e)^21 - 29803400*a^5*b^7*tan(1/2*e)^21
+ 77633050*a^4*b^8*tan(1/2*e)^21 + 69413080*a^3*b^9*tan(1/2*e)^21 + 17689760*a^2*b^10*tan(1/2*e)^21 - 10524800
*a^8*b^4*tan(1/2*e)^19 - 43804420*a^7*b^5*tan(1/2*e)^19 - 64585840*a^6*b^6*tan(1/2*e)^19 - 30795160*a^5*b^7*ta
n(1/2*e)^19 + 14957360*a^4*b^8*tan(1/2*e)^19 + 19830140*a^3*b^9*tan(1/2*e)^19 + 5383840*a^2*b^10*tan(1/2*e)^19
- 3831685*a^8*b^4*tan(1/2*e)^17 - 16753660*a^7*b^5*tan(1/2*e)^17 - 28212030*a^6*b^6*tan(1/2*e)^17 - 21945220*
a^5*b^7*tan(1/2*e)^17 - 6624805*a^4*b^8*tan(1/2*e)^17 + 516120*a^3*b^9*tan(1/2*e)^17 + 485760*a^2*b^10*tan(1/2
*e)^17 - 1052480*a^8*b^4*tan(1/2*e)^15 - 5110600*a^7*b^5*tan(1/2*e)^15 - 10484320*a^6*b^6*tan(1/2*e)^15 - 1188
0880*a^5*b^7*tan(1/2*e)^15 - 8055520*a^4*b^8*tan(1/2*e)^15 - 3167560*a^3*b^9*tan(1/2*e)^15 - 566720*a^2*b^10*t
an(1/2*e)^15 - 185380*a^8*b^4*tan(1/2*e)^13 - 1184960*a^7*b^5*tan(1/2*e)^13 - 3290840*a^6*b^6*tan(1/2*e)^13 -
5021360*a^5*b^7*tan(1/2*e)^13 - 4387940*a^4*b^8*tan(1/2*e)^13 - 2062640*a^3*b^9*tan(1/2*e)^13 - 404800*a^2*b^1
0*tan(1/2*e)^13 - 4160*a^8*b^4*tan(1/2*e)^11 - 187400*a^7*b^5*tan(1/2*e)^11 - 862560*a^6*b^6*tan(1/2*e)^11 - 1
659440*a^5*b^7*tan(1/2*e)^11 - 1614560*a^4*b^8*tan(1/2*e)^11 - 789000*a^3*b^9*tan(1/2*e)^11 - 154560*a^2*b^10*
tan(1/2*e)^11 + 9425*a^8*b^4*tan(1/2*e)^9 - 12980*a^7*b^5*tan(1/2*e)^9 - 185210*a^6*b^6*tan(1/2*e)^9 - 422540*
a^5*b^7*tan(1/2*e)^9 - 427535*a^4*b^8*tan(1/2*e)^9 - 206840*a^3*b^9*tan(1/2*e)^9 - 39040*a^2*b^10*tan(1/2*e)^9
+ 3328*a^8*b^4*tan(1/2*e)^7 + 2084*a^7*b^5*tan(1/2*e)^7 - 31504*a^6*b^6*tan(1/2*e)^7 - 80296*a^5*b^7*tan(1/2*
e)^7 - 80944*a^4*b^8*tan(1/2*e)^7 - 37468*a^3*b^9*tan(1/2*e)^7 - 6560*a^2*b^10*tan(1/2*e)^7 + 614*a^8*b^4*tan(
1/2*e)^5 + 704*a^7*b^5*tan(1/2*e)^5 - 3996*a^6*b^6*tan(1/2*e)^5 - 10744*a^5*b^7*tan(1/2*e)^5 - 10426*a^4*b^8*t
an(1/2*e)^5 - 4440*a^3*b^9*tan(1/2*e)^5 - 672*a^2*b^10*tan(1/2*e)^5 + 64*a^8*b^4*tan(1/2*e)^3 + 84*a^7*b^5*tan
(1/2*e)^3 - 336*a^6*b^6*tan(1/2*e)^3 - 904*a^5*b^7*tan(1/2*e)^3 - 816*a^4*b^8*tan(1/2*e)^3 - 300*a^3*b^9*tan(1
/2*e)^3 - 32*a^2*b^10*tan(1/2*e)^3 + 3*a^8*b^4*tan(1/2*e) + 4*a^7*b^5*tan(1/2*e) - 14*a^6*b^6*tan(1/2*e) - 36*
a^5*b^7*tan(1/2*e) - 29*a^4*b^8*tan(1/2*e) - 8*a^3*b^9*tan(1/2*e))/(a^9*b^4*tan(1/2*e)^52 + 4*a^8*b^5*tan(1/2*
e)^52 + 6*a^7*b^6*tan(1/2*e)^52 + 4*a^6*b^7*tan(1/2*e)^52 + a^5*b^8*tan(1/2*e)^52 + 26*a^9*b^4*tan(1/2*e)^50 +
108*a^8*b^5*tan(1/2*e)^50 + 172*a^7*b^6*tan(1/2*e)^50 + 128*a^6*b^7*tan(1/2*e)^50 + 42*a^5*b^8*tan(1/2*e)^50
+ 4*a^4*b^9*tan(1/2*e)^50 + 325*a^9*b^4*tan(1/2*e)^48 + 1396*a^8*b^5*tan(1/2*e)^48 + 2334*a^7*b^6*tan(1/2*e)^4
8 + 1876*a^6*b^7*tan(1/2*e)^48 + 709*a^5*b^8*tan(1/2*e)^48 + 96*a^4*b^9*tan(1/2*e)^48 + 2600*a^9*b^4*tan(1/2*e
)^46 + 11504*a^8*b^5*tan(1/2*e)^46 + 20016*a^7*b^6*tan(1/2*e)^46 + 17024*a^6*b^7*tan(1/2*e)^46 + 7016*a^5*b^8*
tan(1/2*e)^46 + 1104*a^4*b^9*tan(1/2*e)^46 + 14950*a^9*b^4*tan(1/2*e)^44 + 67896*a^8*b^5*tan(1/2*e)^44 + 12208
4*a^7*b^6*tan(1/2*e)^44 + 108376*a^6*b^7*tan(1/2*e)^44 + 47334*a^5*b^8*tan(1/2*e)^44 + 8096*a^4*b^9*tan(1/2*e)
^44 + 65780*a^9*b^4*tan(1/2*e)^42 + 305624*a^8*b^5*tan(1/2*e)^42 + 564696*a^7*b^6*tan(1/2*e)^42 + 518144*a^6*b
^7*tan(1/2*e)^42 + 235796*a^5*b^8*tan(1/2*e)^42 + 42504*a^4*b^9*tan(1/2*e)^42 + 230230*a^9*b^4*tan(1/2*e)^40 +
1090936*a^8*b^5*tan(1/2*e)^40 + 2061444*a^7*b^6*tan(1/2*e)^40 + 1941016*a^6*b^7*tan(1/2*e)^40 + 910294*a^5*b^
8*tan(1/2*e)^40 + 170016*a^4*b^9*tan(1/2*e)^40 + 657800*a^9*b^4*tan(1/2*e)^38 + 3169584*a^8*b^5*tan(1/2*e)^38
+ 6100336*a^7*b^6*tan(1/2*e)^38 + 5861504*a^6*b^7*tan(1/2*e)^38 + 2811336*a^5*b^8*tan(1/2*e)^38 + 538384*a^4*b
^9*tan(1/2*e)^38 + 1562275*a^9*b^4*tan(1/2*e)^36 + 7633516*a^8*b^5*tan(1/2*e)^36 + 14911314*a^7*b^6*tan(1/2*e)
^36 + 14555596*a^6*b^7*tan(1/2*e)^36 + 7099939*a^5*b^8*tan(1/2*e)^36 + 1384416*a^4*b^9*tan(1/2*e)^36 + 3124550
*a^9*b^4*tan(1/2*e)^34 + 15440084*a^8*b^5*tan(1/2*e)^34 + 30514836*a^7*b^6*tan(1/2*e)^34 + 30149504*a^6*b^7*ta
n(1/2*e)^34 + 14892086*a^5*b^8*tan(1/2*e)^34 + 2941884*a^4*b^9*tan(1/2*e)^34 + 5311735*a^9*b^4*tan(1/2*e)^32 +
26476956*a^8*b^5*tan(1/2*e)^32 + 52790474*a^7*b^6*tan(1/2*e)^32 + 52627036*a^6*b^7*tan(1/2*e)^32 + 26231799*a
^5*b^8*tan(1/2*e)^32 + 5230016*a^4*b^9*tan(1/2*e)^32 + 7726160*a^9*b^4*tan(1/2*e)^30 + 38749664*a^8*b^5*tan(1/
2*e)^30 + 77737056*a^7*b^6*tan(1/2*e)^30 + 77974784*a^6*b^7*tan(1/2*e)^30 + 39106256*a^5*b^8*tan(1/2*e)^30 + 7
845024*a^4*b^9*tan(1/2*e)^30 + 9657700*a^9*b^4*tan(1/2*e)^28 + 48615376*a^8*b^5*tan(1/2*e)^28 + 97884504*a^7*b
^6*tan(1/2*e)^28 + 98538256*a^6*b^7*tan(1/2*e)^28 + 49596004*a^5*b^8*tan(1/2*e)^28 + 9984576*a^4*b^9*tan(1/2*e
)^28 + 10400600*a^9*b^4*tan(1/2*e)^26 + 52419024*a^8*b^5*tan(1/2*e)^26 + 105670096*a^7*b^6*tan(1/2*e)^26 + 106
502144*a^6*b^7*tan(1/2*e)^26 + 53667096*a^5*b^8*tan(1/2*e)^26 + 10816624*a^4*b^9*tan(1/2*e)^26 + 9657700*a^9*b
^4*tan(1/2*e)^24 + 48615376*a^8*b^5*tan(1/2*e)^24 + 97884504*a^7*b^6*tan(1/2*e)^24 + 98538256*a^6*b^7*tan(1/2*
e)^24 + 49596004*a^5*b^8*tan(1/2*e)^24 + 9984576*a^4*b^9*tan(1/2*e)^24 + 7726160*a^9*b^4*tan(1/2*e)^22 + 38749
664*a^8*b^5*tan(1/2*e)^22 + 77737056*a^7*b^6*tan(1/2*e)^22 + 77974784*a^6*b^7*tan(1/2*e)^22 + 39106256*a^5*b^8
*tan(1/2*e)^22 + 7845024*a^4*b^9*tan(1/2*e)^22 + 5311735*a^9*b^4*tan(1/2*e)^20 + 26476956*a^8*b^5*tan(1/2*e)^2
0 + 52790474*a^7*b^6*tan(1/2*e)^20 + 52627036*a^6*b^7*tan(1/2*e)^20 + 26231799*a^5*b^8*tan(1/2*e)^20 + 5230016
*a^4*b^9*tan(1/2*e)^20 + 3124550*a^9*b^4*tan(1/2*e)^18 + 15440084*a^8*b^5*tan(1/2*e)^18 + 30514836*a^7*b^6*tan
(1/2*e)^18 + 30149504*a^6*b^7*tan(1/2*e)^18 + 14892086*a^5*b^8*tan(1/2*e)^18 + 2941884*a^4*b^9*tan(1/2*e)^18 +
1562275*a^9*b^4*tan(1/2*e)^16 + 7633516*a^8*b^5*tan(1/2*e)^16 + 14911314*a^7*b^6*tan(1/2*e)^16 + 14555596*a^6
*b^7*tan(1/2*e)^16 + 7099939*a^5*b^8*tan(1/2*e)^16 + 1384416*a^4*b^9*tan(1/2*e)^16 + 657800*a^9*b^4*tan(1/2*e)
^14 + 3169584*a^8*b^5*tan(1/2*e)^14 + 6100336*a^7*b^6*tan(1/2*e)^14 + 5861504*a^6*b^7*tan(1/2*e)^14 + 2811336*
a^5*b^8*tan(1/2*e)^14 + 538384*a^4*b^9*tan(1/2*e)^14 + 230230*a^9*b^4*tan(1/2*e)^12 + 1090936*a^8*b^5*tan(1/2*
e)^12 + 2061444*a^7*b^6*tan(1/2*e)^12 + 1941016*a^6*b^7*tan(1/2*e)^12 + 910294*a^5*b^8*tan(1/2*e)^12 + 170016*
a^4*b^9*tan(1/2*e)^12 + 65780*a^9*b^4*tan(1/2*e)^10 + 305624*a^8*b^5*tan(1/2*e)^10 + 564696*a^7*b^6*tan(1/2*e)
^10 + 518144*a^6*b^7*tan(1/2*e)^10 + 235796*a^5*b^8*tan(1/2*e)^10 + 42504*a^4*b^9*tan(1/2*e)^10 + 14950*a^9*b^
4*tan(1/2*e)^8 + 67896*a^8*b^5*tan(1/2*e)^8 + 122084*a^7*b^6*tan(1/2*e)^8 + 108376*a^6*b^7*tan(1/2*e)^8 + 4733
4*a^5*b^8*tan(1/2*e)^8 + 8096*a^4*b^9*tan(1/2*e)^8 + 2600*a^9*b^4*tan(1/2*e)^6 + 11504*a^8*b^5*tan(1/2*e)^6 +
20016*a^7*b^6*tan(1/2*e)^6 + 17024*a^6*b^7*tan(1/2*e)^6 + 7016*a^5*b^8*tan(1/2*e)^6 + 1104*a^4*b^9*tan(1/2*e)^
6 + 325*a^9*b^4*tan(1/2*e)^4 + 1396*a^8*b^5*tan(1/2*e)^4 + 2334*a^7*b^6*tan(1/2*e)^4 + 1876*a^6*b^7*tan(1/2*e)
^4 + 709*a^5*b^8*tan(1/2*e)^4 + 96*a^4*b^9*tan(1/2*e)^4 + 26*a^9*b^4*tan(1/2*e)^2 + 108*a^8*b^5*tan(1/2*e)^2 +
172*a^7*b^6*tan(1/2*e)^2 + 128*a^6*b^7*tan(1/2*e)^2 + 42*a^5*b^8*tan(1/2*e)^2 + 4*a^4*b^9*tan(1/2*e)^2 + a^9*
b^4 + 4*a^8*b^5 + 6*a^7*b^6 + 4*a^6*b^7 + a^5*b^8))*tan(1/2*f*x) + 3*(a^8*b^4*tan(1/2*e)^58 + 4*a^7*b^5*tan(1/
2*e)^58 + 6*a^6*b^6*tan(1/2*e)^58 + 4*a^5*b^7*tan(1/2*e)^58 + a^4*b^8*tan(1/2*e)^58 + 23*a^8*b^4*tan(1/2*e)^56
+ 104*a^7*b^5*tan(1/2*e)^56 + 186*a^6*b^6*tan(1/2*e)^56 + 164*a^5*b^7*tan(1/2*e)^56 + 71*a^4*b^8*tan(1/2*e)^5
6 + 12*a^3*b^9*tan(1/2*e)^56 + 250*a^8*b^4*tan(1/2*e)^54 + 1284*a^7*b^5*tan(1/2*e)^54 + 2668*a^6*b^6*tan(1/2*e
)^54 + 2832*a^5*b^7*tan(1/2*e)^54 + 1578*a^4*b^8*tan(1/2*e)^54 + 412*a^3*b^9*tan(1/2*e)^54 + 32*a^2*b^10*tan(1
/2*e)^54 + 1702*a^8*b^4*tan(1/2*e)^52 + 10028*a^7*b^5*tan(1/2*e)^52 + 23828*a^6*b^6*tan(1/2*e)^52 + 29072*a^5*
b^7*tan(1/2*e)^52 + 18998*a^4*b^8*tan(1/2*e)^52 + 6164*a^3*b^9*tan(1/2*e)^52 + 736*a^2*b^10*tan(1/2*e)^52 + 80
99*a^8*b^4*tan(1/2*e)^50 + 55664*a^7*b^5*tan(1/2*e)^50 + 149730*a^6*b^6*tan(1/2*e)^50 + 204260*a^5*b^7*tan(1/2
*e)^50 + 149555*a^4*b^8*tan(1/2*e)^50 + 55524*a^3*b^9*tan(1/2*e)^50 + 8064*a^2*b^10*tan(1/2*e)^50 + 28405*a^8*
b^4*tan(1/2*e)^48 + 233852*a^7*b^5*tan(1/2*e)^48 + 707294*a^6*b^6*tan(1/2*e)^48 + 1058756*a^5*b^7*tan(1/2*e)^4
8 + 844949*a^4*b^8*tan(1/2*e)^48 + 343976*a^3*b^9*tan(1/2*e)^48 + 55936*a^2*b^10*tan(1/2*e)^48 + 75140*a^8*b^4
*tan(1/2*e)^46 + 772888*a^7*b^5*tan(1/2*e)^46 + 2615416*a^6*b^6*tan(1/2*e)^46 + 4235584*a^5*b^7*tan(1/2*e)^46
+ 3616036*a^4*b^8*tan(1/2*e)^46 + 1573384*a^3*b^9*tan(1/2*e)^46 + 275264*a^2*b^10*tan(1/2*e)^46 + 149500*a^8*b
^4*tan(1/2*e)^44 + 2061352*a^7*b^5*tan(1/2*e)^44 + 7770504*a^6*b^6*tan(1/2*e)^44 + 13458496*a^5*b^7*tan(1/2*e)
^44 + 12123484*a^4*b^8*tan(1/2*e)^44 + 5543736*a^3*b^9*tan(1/2*e)^44 + 1020096*a^2*b^10*tan(1/2*e)^44 + 213785
*a^8*b^4*tan(1/2*e)^42 + 4512508*a^7*b^5*tan(1/2*e)^42 + 18859126*a^6*b^6*tan(1/2*e)^42 + 34587124*a^5*b^7*tan
(1/2*e)^42 + 32524921*a^4*b^8*tan(1/2*e)^42 + 15445144*a^3*b^9*tan(1/2*e)^42 + 2946944*a^2*b^10*tan(1/2*e)^42
+ 180895*a^8*b^4*tan(1/2*e)^40 + 8193152*a^7*b^5*tan(1/2*e)^40 + 37731914*a^6*b^6*tan(1/2*e)^40 + 72614036*a^5
*b^7*tan(1/2*e)^40 + 70668719*a^4*b^8*tan(1/2*e)^40 + 34542596*a^3*b^9*tan(1/2*e)^40 + 6768256*a^2*b^10*tan(1/
2*e)^40 - 32890*a^8*b^4*tan(1/2*e)^38 + 12385868*a^7*b^5*tan(1/2*e)^38 + 62332116*a^6*b^6*tan(1/2*e)^38 + 1248
11984*a^5*b^7*tan(1/2*e)^38 + 124795286*a^4*b^8*tan(1/2*e)^38 + 62356404*a^3*b^9*tan(1/2*e)^38 + 12459744*a^2*
b^10*tan(1/2*e)^38 - 397670*a^8*b^4*tan(1/2*e)^36 + 15503012*a^7*b^5*tan(1/2*e)^36 + 84293804*a^6*b^6*tan(1/2*
e)^36 + 174191696*a^5*b^7*tan(1/2*e)^36 + 177807434*a^4*b^8*tan(1/2*e)^36 + 90313916*a^3*b^9*tan(1/2*e)^36 + 1
8305056*a^2*b^10*tan(1/2*e)^36 - 710125*a^8*b^4*tan(1/2*e)^34 + 15672568*a^7*b^5*tan(1/2*e)^34 + 90711586*a^6*
b^6*tan(1/2*e)^34 + 191918164*a^5*b^7*tan(1/2*e)^34 + 198862531*a^4*b^8*tan(1/2*e)^34 + 102193324*a^3*b^9*tan(
1/2*e)^34 + 20920064*a^2*b^10*tan(1/2*e)^34 - 705755*a^8*b^4*tan(1/2*e)^32 + 11797252*a^7*b^5*tan(1/2*e)^32 +
71362974*a^6*b^6*tan(1/2*e)^32 + 153364276*a^5*b^7*tan(1/2*e)^32 + 160473829*a^4*b^8*tan(1/2*e)^32 + 83085936*
a^3*b^9*tan(1/2*e)^32 + 17116416*a^2*b^10*tan(1/2*e)^32 - 297160*a^8*b^4*tan(1/2*e)^30 + 4397968*a^7*b^5*tan(1
/2*e)^30 + 27219856*a^6*b^6*tan(1/2*e)^30 + 58956544*a^5*b^7*tan(1/2*e)^30 + 61987576*a^4*b^8*tan(1/2*e)^30 +
32212144*a^3*b^9*tan(1/2*e)^30 + 6656384*a^2*b^10*tan(1/2*e)^30 + 297160*a^8*b^4*tan(1/2*e)^28 - 4397968*a^7*b
^5*tan(1/2*e)^28 - 27219856*a^6*b^6*tan(1/2*e)^28 - 58956544*a^5*b^7*tan(1/2*e)^28 - 61987576*a^4*b^8*tan(1/2*
e)^28 - 32212144*a^3*b^9*tan(1/2*e)^28 - 6656384*a^2*b^10*tan(1/2*e)^28 + 705755*a^8*b^4*tan(1/2*e)^26 - 11797
252*a^7*b^5*tan(1/2*e)^26 - 71362974*a^6*b^6*tan(1/2*e)^26 - 153364276*a^5*b^7*tan(1/2*e)^26 - 160473829*a^4*b
^8*tan(1/2*e)^26 - 83085936*a^3*b^9*tan(1/2*e)^26 - 17116416*a^2*b^10*tan(1/2*e)^26 + 710125*a^8*b^4*tan(1/2*e
)^24 - 15672568*a^7*b^5*tan(1/2*e)^24 - 90711586*a^6*b^6*tan(1/2*e)^24 - 191918164*a^5*b^7*tan(1/2*e)^24 - 198
862531*a^4*b^8*tan(1/2*e)^24 - 102193324*a^3*b^9*tan(1/2*e)^24 - 20920064*a^2*b^10*tan(1/2*e)^24 + 397670*a^8*
b^4*tan(1/2*e)^22 - 15503012*a^7*b^5*tan(1/2*e)^22 - 84293804*a^6*b^6*tan(1/2*e)^22 - 174191696*a^5*b^7*tan(1/
2*e)^22 - 177807434*a^4*b^8*tan(1/2*e)^22 - 90313916*a^3*b^9*tan(1/2*e)^22 - 18305056*a^2*b^10*tan(1/2*e)^22 +
32890*a^8*b^4*tan(1/2*e)^20 - 12385868*a^7*b^5*tan(1/2*e)^20 - 62332116*a^6*b^6*tan(1/2*e)^20 - 124811984*a^5
*b^7*tan(1/2*e)^20 - 124795286*a^4*b^8*tan(1/2*e)^20 - 62356404*a^3*b^9*tan(1/2*e)^20 - 12459744*a^2*b^10*tan(
1/2*e)^20 - 180895*a^8*b^4*tan(1/2*e)^18 - 8193152*a^7*b^5*tan(1/2*e)^18 - 37731914*a^6*b^6*tan(1/2*e)^18 - 72
614036*a^5*b^7*tan(1/2*e)^18 - 70668719*a^4*b^8*tan(1/2*e)^18 - 34542596*a^3*b^9*tan(1/2*e)^18 - 6768256*a^2*b
^10*tan(1/2*e)^18 - 213785*a^8*b^4*tan(1/2*e)^16 - 4512508*a^7*b^5*tan(1/2*e)^16 - 18859126*a^6*b^6*tan(1/2*e)
^16 - 34587124*a^5*b^7*tan(1/2*e)^16 - 32524921*a^4*b^8*tan(1/2*e)^16 - 15445144*a^3*b^9*tan(1/2*e)^16 - 29469
44*a^2*b^10*tan(1/2*e)^16 - 149500*a^8*b^4*tan(1/2*e)^14 - 2061352*a^7*b^5*tan(1/2*e)^14 - 7770504*a^6*b^6*tan
(1/2*e)^14 - 13458496*a^5*b^7*tan(1/2*e)^14 - 12123484*a^4*b^8*tan(1/2*e)^14 - 5543736*a^3*b^9*tan(1/2*e)^14 -
1020096*a^2*b^10*tan(1/2*e)^14 - 75140*a^8*b^4*tan(1/2*e)^12 - 772888*a^7*b^5*tan(1/2*e)^12 - 2615416*a^6*b^6
*tan(1/2*e)^12 - 4235584*a^5*b^7*tan(1/2*e)^12 - 3616036*a^4*b^8*tan(1/2*e)^12 - 1573384*a^3*b^9*tan(1/2*e)^12
- 275264*a^2*b^10*tan(1/2*e)^12 - 28405*a^8*b^4*tan(1/2*e)^10 - 233852*a^7*b^5*tan(1/2*e)^10 - 707294*a^6*b^6
*tan(1/2*e)^10 - 1058756*a^5*b^7*tan(1/2*e)^10 - 844949*a^4*b^8*tan(1/2*e)^10 - 343976*a^3*b^9*tan(1/2*e)^10 -
55936*a^2*b^10*tan(1/2*e)^10 - 8099*a^8*b^4*tan(1/2*e)^8 - 55664*a^7*b^5*tan(1/2*e)^8 - 149730*a^6*b^6*tan(1/
2*e)^8 - 204260*a^5*b^7*tan(1/2*e)^8 - 149555*a^4*b^8*tan(1/2*e)^8 - 55524*a^3*b^9*tan(1/2*e)^8 - 8064*a^2*b^1
0*tan(1/2*e)^8 - 1702*a^8*b^4*tan(1/2*e)^6 - 10028*a^7*b^5*tan(1/2*e)^6 - 23828*a^6*b^6*tan(1/2*e)^6 - 29072*a
^5*b^7*tan(1/2*e)^6 - 18998*a^4*b^8*tan(1/2*e)^6 - 6164*a^3*b^9*tan(1/2*e)^6 - 736*a^2*b^10*tan(1/2*e)^6 - 250
*a^8*b^4*tan(1/2*e)^4 - 1284*a^7*b^5*tan(1/2*e)^4 - 2668*a^6*b^6*tan(1/2*e)^4 - 2832*a^5*b^7*tan(1/2*e)^4 - 15
78*a^4*b^8*tan(1/2*e)^4 - 412*a^3*b^9*tan(1/2*e)^4 - 32*a^2*b^10*tan(1/2*e)^4 - 23*a^8*b^4*tan(1/2*e)^2 - 104*
a^7*b^5*tan(1/2*e)^2 - 186*a^6*b^6*tan(1/2*e)^2 - 164*a^5*b^7*tan(1/2*e)^2 - 71*a^4*b^8*tan(1/2*e)^2 - 12*a^3*
b^9*tan(1/2*e)^2 - a^8*b^4 - 4*a^7*b^5 - 6*a^6*b^6 - 4*a^5*b^7 - a^4*b^8)/(a^9*b^4*tan(1/2*e)^52 + 4*a^8*b^5*t
an(1/2*e)^52 + 6*a^7*b^6*tan(1/2*e)^52 + 4*a^6*b^7*tan(1/2*e)^52 + a^5*b^8*tan(1/2*e)^52 + 26*a^9*b^4*tan(1/2*
e)^50 + 108*a^8*b^5*tan(1/2*e)^50 + 172*a^7*b^6*tan(1/2*e)^50 + 128*a^6*b^7*tan(1/2*e)^50 + 42*a^5*b^8*tan(1/2
*e)^50 + 4*a^4*b^9*tan(1/2*e)^50 + 325*a^9*b^4*tan(1/2*e)^48 + 1396*a^8*b^5*tan(1/2*e)^48 + 2334*a^7*b^6*tan(1
/2*e)^48 + 1876*a^6*b^7*tan(1/2*e)^48 + 709*a^5*b^8*tan(1/2*e)^48 + 96*a^4*b^9*tan(1/2*e)^48 + 2600*a^9*b^4*ta
n(1/2*e)^46 + 11504*a^8*b^5*tan(1/2*e)^46 + 20016*a^7*b^6*tan(1/2*e)^46 + 17024*a^6*b^7*tan(1/2*e)^46 + 7016*a
^5*b^8*tan(1/2*e)^46 + 1104*a^4*b^9*tan(1/2*e)^46 + 14950*a^9*b^4*tan(1/2*e)^44 + 67896*a^8*b^5*tan(1/2*e)^44
+ 122084*a^7*b^6*tan(1/2*e)^44 + 108376*a^6*b^7*tan(1/2*e)^44 + 47334*a^5*b^8*tan(1/2*e)^44 + 8096*a^4*b^9*tan
(1/2*e)^44 + 65780*a^9*b^4*tan(1/2*e)^42 + 305624*a^8*b^5*tan(1/2*e)^42 + 564696*a^7*b^6*tan(1/2*e)^42 + 51814
4*a^6*b^7*tan(1/2*e)^42 + 235796*a^5*b^8*tan(1/2*e)^42 + 42504*a^4*b^9*tan(1/2*e)^42 + 230230*a^9*b^4*tan(1/2*
e)^40 + 1090936*a^8*b^5*tan(1/2*e)^40 + 2061444*a^7*b^6*tan(1/2*e)^40 + 1941016*a^6*b^7*tan(1/2*e)^40 + 910294
*a^5*b^8*tan(1/2*e)^40 + 170016*a^4*b^9*tan(1/2*e)^40 + 657800*a^9*b^4*tan(1/2*e)^38 + 3169584*a^8*b^5*tan(1/2
*e)^38 + 6100336*a^7*b^6*tan(1/2*e)^38 + 5861504*a^6*b^7*tan(1/2*e)^38 + 2811336*a^5*b^8*tan(1/2*e)^38 + 53838
4*a^4*b^9*tan(1/2*e)^38 + 1562275*a^9*b^4*tan(1/2*e)^36 + 7633516*a^8*b^5*tan(1/2*e)^36 + 14911314*a^7*b^6*tan
(1/2*e)^36 + 14555596*a^6*b^7*tan(1/2*e)^36 + 7099939*a^5*b^8*tan(1/2*e)^36 + 1384416*a^4*b^9*tan(1/2*e)^36 +
3124550*a^9*b^4*tan(1/2*e)^34 + 15440084*a^8*b^5*tan(1/2*e)^34 + 30514836*a^7*b^6*tan(1/2*e)^34 + 30149504*a^6
*b^7*tan(1/2*e)^34 + 14892086*a^5*b^8*tan(1/2*e)^34 + 2941884*a^4*b^9*tan(1/2*e)^34 + 5311735*a^9*b^4*tan(1/2*
e)^32 + 26476956*a^8*b^5*tan(1/2*e)^32 + 52790474*a^7*b^6*tan(1/2*e)^32 + 52627036*a^6*b^7*tan(1/2*e)^32 + 262
31799*a^5*b^8*tan(1/2*e)^32 + 5230016*a^4*b^9*tan(1/2*e)^32 + 7726160*a^9*b^4*tan(1/2*e)^30 + 38749664*a^8*b^5
*tan(1/2*e)^30 + 77737056*a^7*b^6*tan(1/2*e)^30 + 77974784*a^6*b^7*tan(1/2*e)^30 + 39106256*a^5*b^8*tan(1/2*e)
^30 + 7845024*a^4*b^9*tan(1/2*e)^30 + 9657700*a^9*b^4*tan(1/2*e)^28 + 48615376*a^8*b^5*tan(1/2*e)^28 + 9788450
4*a^7*b^6*tan(1/2*e)^28 + 98538256*a^6*b^7*tan(1/2*e)^28 + 49596004*a^5*b^8*tan(1/2*e)^28 + 9984576*a^4*b^9*ta
n(1/2*e)^28 + 10400600*a^9*b^4*tan(1/2*e)^26 + 52419024*a^8*b^5*tan(1/2*e)^26 + 105670096*a^7*b^6*tan(1/2*e)^2
6 + 106502144*a^6*b^7*tan(1/2*e)^26 + 53667096*a^5*b^8*tan(1/2*e)^26 + 10816624*a^4*b^9*tan(1/2*e)^26 + 965770
0*a^9*b^4*tan(1/2*e)^24 + 48615376*a^8*b^5*tan(1/2*e)^24 + 97884504*a^7*b^6*tan(1/2*e)^24 + 98538256*a^6*b^7*t
an(1/2*e)^24 + 49596004*a^5*b^8*tan(1/2*e)^24 + 9984576*a^4*b^9*tan(1/2*e)^24 + 7726160*a^9*b^4*tan(1/2*e)^22
+ 38749664*a^8*b^5*tan(1/2*e)^22 + 77737056*a^7*b^6*tan(1/2*e)^22 + 77974784*a^6*b^7*tan(1/2*e)^22 + 39106256*
a^5*b^8*tan(1/2*e)^22 + 7845024*a^4*b^9*tan(1/2*e)^22 + 5311735*a^9*b^4*tan(1/2*e)^20 + 26476956*a^8*b^5*tan(1
/2*e)^20 + 52790474*a^7*b^6*tan(1/2*e)^20 + 52627036*a^6*b^7*tan(1/2*e)^20 + 26231799*a^5*b^8*tan(1/2*e)^20 +
5230016*a^4*b^9*tan(1/2*e)^20 + 3124550*a^9*b^4*tan(1/2*e)^18 + 15440084*a^8*b^5*tan(1/2*e)^18 + 30514836*a^7*
b^6*tan(1/2*e)^18 + 30149504*a^6*b^7*tan(1/2*e)^18 + 14892086*a^5*b^8*tan(1/2*e)^18 + 2941884*a^4*b^9*tan(1/2*
e)^18 + 1562275*a^9*b^4*tan(1/2*e)^16 + 7633516*a^8*b^5*tan(1/2*e)^16 + 14911314*a^7*b^6*tan(1/2*e)^16 + 14555
596*a^6*b^7*tan(1/2*e)^16 + 7099939*a^5*b^8*tan(1/2*e)^16 + 1384416*a^4*b^9*tan(1/2*e)^16 + 657800*a^9*b^4*tan
(1/2*e)^14 + 3169584*a^8*b^5*tan(1/2*e)^14 + 6100336*a^7*b^6*tan(1/2*e)^14 + 5861504*a^6*b^7*tan(1/2*e)^14 + 2
811336*a^5*b^8*tan(1/2*e)^14 + 538384*a^4*b^9*tan(1/2*e)^14 + 230230*a^9*b^4*tan(1/2*e)^12 + 1090936*a^8*b^5*t
an(1/2*e)^12 + 2061444*a^7*b^6*tan(1/2*e)^12 + 1941016*a^6*b^7*tan(1/2*e)^12 + 910294*a^5*b^8*tan(1/2*e)^12 +
170016*a^4*b^9*tan(1/2*e)^12 + 65780*a^9*b^4*tan(1/2*e)^10 + 305624*a^8*b^5*tan(1/2*e)^10 + 564696*a^7*b^6*tan
(1/2*e)^10 + 518144*a^6*b^7*tan(1/2*e)^10 + 235796*a^5*b^8*tan(1/2*e)^10 + 42504*a^4*b^9*tan(1/2*e)^10 + 14950
*a^9*b^4*tan(1/2*e)^8 + 67896*a^8*b^5*tan(1/2*e)^8 + 122084*a^7*b^6*tan(1/2*e)^8 + 108376*a^6*b^7*tan(1/2*e)^8
+ 47334*a^5*b^8*tan(1/2*e)^8 + 8096*a^4*b^9*tan(1/2*e)^8 + 2600*a^9*b^4*tan(1/2*e)^6 + 11504*a^8*b^5*tan(1/2*
e)^6 + 20016*a^7*b^6*tan(1/2*e)^6 + 17024*a^6*b^7*tan(1/2*e)^6 + 7016*a^5*b^8*tan(1/2*e)^6 + 1104*a^4*b^9*tan(
1/2*e)^6 + 325*a^9*b^4*tan(1/2*e)^4 + 1396*a^8*b^5*tan(1/2*e)^4 + 2334*a^7*b^6*tan(1/2*e)^4 + 1876*a^6*b^7*tan
(1/2*e)^4 + 709*a^5*b^8*tan(1/2*e)^4 + 96*a^4*b^9*tan(1/2*e)^4 + 26*a^9*b^4*tan(1/2*e)^2 + 108*a^8*b^5*tan(1/2
*e)^2 + 172*a^7*b^6*tan(1/2*e)^2 + 128*a^6*b^7*tan(1/2*e)^2 + 42*a^5*b^8*tan(1/2*e)^2 + 4*a^4*b^9*tan(1/2*e)^2
+ a^9*b^4 + 4*a^8*b^5 + 6*a^7*b^6 + 4*a^6*b^7 + a^5*b^8))*tan(1/2*f*x) - (3*a^8*b^4*tan(1/2*e)^57 + 12*a^7*b^
5*tan(1/2*e)^57 + 18*a^6*b^6*tan(1/2*e)^57 + 12*a^5*b^7*tan(1/2*e)^57 + 3*a^4*b^8*tan(1/2*e)^57 + 80*a^8*b^4*t
an(1/2*e)^55 + 340*a^7*b^5*tan(1/2*e)^55 + 560*a^6*b^6*tan(1/2*e)^55 + 440*a^5*b^7*tan(1/2*e)^55 + 160*a^4*b^8
*tan(1/2*e)^55 + 20*a^3*b^9*tan(1/2*e)^55 + 1030*a^8*b^4*tan(1/2*e)^53 + 4624*a^7*b^5*tan(1/2*e)^53 + 8228*a^6
*b^6*tan(1/2*e)^53 + 7272*a^5*b^7*tan(1/2*e)^53 + 3238*a^4*b^8*tan(1/2*e)^53 + 632*a^3*b^9*tan(1/2*e)^53 + 32*
a^2*b^10*tan(1/2*e)^53 + 8528*a^8*b^4*tan(1/2*e)^51 + 40228*a^7*b^5*tan(1/2*e)^51 + 76400*a^6*b^6*tan(1/2*e)^5
1 + 73880*a^5*b^7*tan(1/2*e)^51 + 37600*a^4*b^8*tan(1/2*e)^51 + 9188*a^3*b^9*tan(1/2*e)^51 + 768*a^2*b^10*tan(
1/2*e)^51 + 51025*a^8*b^4*tan(1/2*e)^49 + 251684*a^7*b^5*tan(1/2*e)^49 + 505318*a^6*b^6*tan(1/2*e)^49 + 524932
*a^5*b^7*tan(1/2*e)^49 + 294353*a^4*b^8*tan(1/2*e)^49 + 82912*a^3*b^9*tan(1/2*e)^49 + 8832*a^2*b^10*tan(1/2*e)
^49 + 235040*a^8*b^4*tan(1/2*e)^47 + 1206776*a^7*b^5*tan(1/2*e)^47 + 2541472*a^6*b^6*tan(1/2*e)^47 + 2798928*a
^5*b^7*tan(1/2*e)^47 + 1690112*a^4*b^8*tan(1/2*e)^47 + 525688*a^3*b^9*tan(1/2*e)^47 + 64768*a^2*b^10*tan(1/2*e
)^47 + 867100*a^8*b^4*tan(1/2*e)^45 + 4613984*a^7*b^5*tan(1/2*e)^45 + 10124968*a^6*b^6*tan(1/2*e)^45 + 1170203
2*a^5*b^7*tan(1/2*e)^45 + 7489628*a^4*b^8*tan(1/2*e)^45 + 2505712*a^3*b^9*tan(1/2*e)^45 + 340032*a^2*b^10*tan(
1/2*e)^45 + 2631200*a^8*b^4*tan(1/2*e)^43 + 14449336*a^7*b^5*tan(1/2*e)^43 + 32845472*a^6*b^6*tan(1/2*e)^43 +
39512528*a^5*b^7*tan(1/2*e)^43 + 26490112*a^4*b^8*tan(1/2*e)^43 + 9365048*a^3*b^9*tan(1/2*e)^43 + 1360128*a^2*
b^10*tan(1/2*e)^43 + 6693115*a^8*b^4*tan(1/2*e)^41 + 37774924*a^7*b^5*tan(1/2*e)^41 + 88475618*a^6*b^6*tan(1/2
*e)^41 + 110015532*a^5*b^7*tan(1/2*e)^41 + 76545403*a^4*b^8*tan(1/2*e)^41 + 28230752*a^3*b^9*tan(1/2*e)^41 + 4
307072*a^2*b^10*tan(1/2*e)^41 + 14471600*a^8*b^4*tan(1/2*e)^39 + 83594236*a^7*b^5*tan(1/2*e)^39 + 200736272*a^
6*b^6*tan(1/2*e)^39 + 256434728*a^5*b^7*tan(1/2*e)^39 + 183754912*a^4*b^8*tan(1/2*e)^39 + 70009148*a^3*b^9*tan
(1/2*e)^39 + 11075328*a^2*b^10*tan(1/2*e)^39 + 26871130*a^8*b^4*tan(1/2*e)^37 + 158207984*a^7*b^5*tan(1/2*e)^3
7 + 387655708*a^6*b^6*tan(1/2*e)^37 + 505965592*a^5*b^7*tan(1/2*e)^37 + 370975418*a^4*b^8*tan(1/2*e)^37 + 1448
63752*a^3*b^9*tan(1/2*e)^37 + 23535072*a^2*b^10*tan(1/2*e)^37 + 43175600*a^8*b^4*tan(1/2*e)^35 + 258017036*a^7
*b^5*tan(1/2*e)^35 + 642152272*a^6*b^6*tan(1/2*e)^35 + 851950728*a^5*b^7*tan(1/2*e)^35 + 635474912*a^4*b^8*tan
(1/2*e)^35 + 252675148*a^3*b^9*tan(1/2*e)^35 + 41840128*a^2*b^10*tan(1/2*e)^35 + 60360625*a^8*b^4*tan(1/2*e)^3
3 + 364585604*a^7*b^5*tan(1/2*e)^33 + 917496358*a^6*b^6*tan(1/2*e)^33 + 1231341892*a^5*b^7*tan(1/2*e)^33 + 929
494193*a^4*b^8*tan(1/2*e)^33 + 374183872*a^3*b^9*tan(1/2*e)^33 + 62760192*a^2*b^10*tan(1/2*e)^33 + 73695680*a^
8*b^4*tan(1/2*e)^31 + 447998416*a^7*b^5*tan(1/2*e)^31 + 1134913472*a^6*b^6*tan(1/2*e)^31 + 1533583328*a^5*b^7*
tan(1/2*e)^31 + 1165818112*a^4*b^8*tan(1/2*e)^31 + 472722128*a^3*b^9*tan(1/2*e)^31 + 79876608*a^2*b^10*tan(1/2
*e)^31 + 78747400*a^8*b^4*tan(1/2*e)^29 + 479735104*a^7*b^5*tan(1/2*e)^29 + 1217999408*a^6*b^6*tan(1/2*e)^29 +
1649594592*a^5*b^7*tan(1/2*e)^29 + 1256927368*a^4*b^8*tan(1/2*e)^29 + 510877472*a^3*b^9*tan(1/2*e)^29 + 86532
992*a^2*b^10*tan(1/2*e)^29 + 73695680*a^8*b^4*tan(1/2*e)^27 + 447998416*a^7*b^5*tan(1/2*e)^27 + 1134913472*a^6
*b^6*tan(1/2*e)^27 + 1533583328*a^5*b^7*tan(1/2*e)^27 + 1165818112*a^4*b^8*tan(1/2*e)^27 + 472722128*a^3*b^9*t
an(1/2*e)^27 + 79876608*a^2*b^10*tan(1/2*e)^27 + 60360625*a^8*b^4*tan(1/2*e)^25 + 364585604*a^7*b^5*tan(1/2*e)
^25 + 917496358*a^6*b^6*tan(1/2*e)^25 + 1231341892*a^5*b^7*tan(1/2*e)^25 + 929494193*a^4*b^8*tan(1/2*e)^25 + 3
74183872*a^3*b^9*tan(1/2*e)^25 + 62760192*a^2*b^10*tan(1/2*e)^25 + 43175600*a^8*b^4*tan(1/2*e)^23 + 258017036*
a^7*b^5*tan(1/2*e)^23 + 642152272*a^6*b^6*tan(1/2*e)^23 + 851950728*a^5*b^7*tan(1/2*e)^23 + 635474912*a^4*b^8*
tan(1/2*e)^23 + 252675148*a^3*b^9*tan(1/2*e)^23 + 41840128*a^2*b^10*tan(1/2*e)^23 + 26871130*a^8*b^4*tan(1/2*e
)^21 + 158207984*a^7*b^5*tan(1/2*e)^21 + 387655708*a^6*b^6*tan(1/2*e)^21 + 505965592*a^5*b^7*tan(1/2*e)^21 + 3
70975418*a^4*b^8*tan(1/2*e)^21 + 144863752*a^3*b^9*tan(1/2*e)^21 + 23535072*a^2*b^10*tan(1/2*e)^21 + 14471600*
a^8*b^4*tan(1/2*e)^19 + 83594236*a^7*b^5*tan(1/2*e)^19 + 200736272*a^6*b^6*tan(1/2*e)^19 + 256434728*a^5*b^7*t
an(1/2*e)^19 + 183754912*a^4*b^8*tan(1/2*e)^19 + 70009148*a^3*b^9*tan(1/2*e)^19 + 11075328*a^2*b^10*tan(1/2*e)
^19 + 6693115*a^8*b^4*tan(1/2*e)^17 + 37774924*a^7*b^5*tan(1/2*e)^17 + 88475618*a^6*b^6*tan(1/2*e)^17 + 110015
532*a^5*b^7*tan(1/2*e)^17 + 76545403*a^4*b^8*tan(1/2*e)^17 + 28230752*a^3*b^9*tan(1/2*e)^17 + 4307072*a^2*b^10
*tan(1/2*e)^17 + 2631200*a^8*b^4*tan(1/2*e)^15 + 14449336*a^7*b^5*tan(1/2*e)^15 + 32845472*a^6*b^6*tan(1/2*e)^
15 + 39512528*a^5*b^7*tan(1/2*e)^15 + 26490112*a^4*b^8*tan(1/2*e)^15 + 9365048*a^3*b^9*tan(1/2*e)^15 + 1360128
*a^2*b^10*tan(1/2*e)^15 + 867100*a^8*b^4*tan(1/2*e)^13 + 4613984*a^7*b^5*tan(1/2*e)^13 + 10124968*a^6*b^6*tan(
1/2*e)^13 + 11702032*a^5*b^7*tan(1/2*e)^13 + 7489628*a^4*b^8*tan(1/2*e)^13 + 2505712*a^3*b^9*tan(1/2*e)^13 + 3
40032*a^2*b^10*tan(1/2*e)^13 + 235040*a^8*b^4*tan(1/2*e)^11 + 1206776*a^7*b^5*tan(1/2*e)^11 + 2541472*a^6*b^6*
tan(1/2*e)^11 + 2798928*a^5*b^7*tan(1/2*e)^11 + 1690112*a^4*b^8*tan(1/2*e)^11 + 525688*a^3*b^9*tan(1/2*e)^11 +
64768*a^2*b^10*tan(1/2*e)^11 + 51025*a^8*b^4*tan(1/2*e)^9 + 251684*a^7*b^5*tan(1/2*e)^9 + 505318*a^6*b^6*tan(
1/2*e)^9 + 524932*a^5*b^7*tan(1/2*e)^9 + 294353*a^4*b^8*tan(1/2*e)^9 + 82912*a^3*b^9*tan(1/2*e)^9 + 8832*a^2*b
^10*tan(1/2*e)^9 + 8528*a^8*b^4*tan(1/2*e)^7 + 40228*a^7*b^5*tan(1/2*e)^7 + 76400*a^6*b^6*tan(1/2*e)^7 + 73880
*a^5*b^7*tan(1/2*e)^7 + 37600*a^4*b^8*tan(1/2*e)^7 + 9188*a^3*b^9*tan(1/2*e)^7 + 768*a^2*b^10*tan(1/2*e)^7 + 1
030*a^8*b^4*tan(1/2*e)^5 + 4624*a^7*b^5*tan(1/2*e)^5 + 8228*a^6*b^6*tan(1/2*e)^5 + 7272*a^5*b^7*tan(1/2*e)^5 +
3238*a^4*b^8*tan(1/2*e)^5 + 632*a^3*b^9*tan(1/2*e)^5 + 32*a^2*b^10*tan(1/2*e)^5 + 80*a^8*b^4*tan(1/2*e)^3 + 3
40*a^7*b^5*tan(1/2*e)^3 + 560*a^6*b^6*tan(1/2*e)^3 + 440*a^5*b^7*tan(1/2*e)^3 + 160*a^4*b^8*tan(1/2*e)^3 + 20*
a^3*b^9*tan(1/2*e)^3 + 3*a^8*b^4*tan(1/2*e) + 12*a^7*b^5*tan(1/2*e) + 18*a^6*b^6*tan(1/2*e) + 12*a^5*b^7*tan(1
/2*e) + 3*a^4*b^8*tan(1/2*e))/(a^9*b^4*tan(1/2*e)^52 + 4*a^8*b^5*tan(1/2*e)^52 + 6*a^7*b^6*tan(1/2*e)^52 + 4*a
^6*b^7*tan(1/2*e)^52 + a^5*b^8*tan(1/2*e)^52 + 26*a^9*b^4*tan(1/2*e)^50 + 108*a^8*b^5*tan(1/2*e)^50 + 172*a^7*
b^6*tan(1/2*e)^50 + 128*a^6*b^7*tan(1/2*e)^50 + 42*a^5*b^8*tan(1/2*e)^50 + 4*a^4*b^9*tan(1/2*e)^50 + 325*a^9*b
^4*tan(1/2*e)^48 + 1396*a^8*b^5*tan(1/2*e)^48 + 2334*a^7*b^6*tan(1/2*e)^48 + 1876*a^6*b^7*tan(1/2*e)^48 + 709*
a^5*b^8*tan(1/2*e)^48 + 96*a^4*b^9*tan(1/2*e)^48 + 2600*a^9*b^4*tan(1/2*e)^46 + 11504*a^8*b^5*tan(1/2*e)^46 +
20016*a^7*b^6*tan(1/2*e)^46 + 17024*a^6*b^7*tan(1/2*e)^46 + 7016*a^5*b^8*tan(1/2*e)^46 + 1104*a^4*b^9*tan(1/2*
e)^46 + 14950*a^9*b^4*tan(1/2*e)^44 + 67896*a^8*b^5*tan(1/2*e)^44 + 122084*a^7*b^6*tan(1/2*e)^44 + 108376*a^6*
b^7*tan(1/2*e)^44 + 47334*a^5*b^8*tan(1/2*e)^44 + 8096*a^4*b^9*tan(1/2*e)^44 + 65780*a^9*b^4*tan(1/2*e)^42 + 3
05624*a^8*b^5*tan(1/2*e)^42 + 564696*a^7*b^6*tan(1/2*e)^42 + 518144*a^6*b^7*tan(1/2*e)^42 + 235796*a^5*b^8*tan
(1/2*e)^42 + 42504*a^4*b^9*tan(1/2*e)^42 + 230230*a^9*b^4*tan(1/2*e)^40 + 1090936*a^8*b^5*tan(1/2*e)^40 + 2061
444*a^7*b^6*tan(1/2*e)^40 + 1941016*a^6*b^7*tan(1/2*e)^40 + 910294*a^5*b^8*tan(1/2*e)^40 + 170016*a^4*b^9*tan(
1/2*e)^40 + 657800*a^9*b^4*tan(1/2*e)^38 + 3169584*a^8*b^5*tan(1/2*e)^38 + 6100336*a^7*b^6*tan(1/2*e)^38 + 586
1504*a^6*b^7*tan(1/2*e)^38 + 2811336*a^5*b^8*tan(1/2*e)^38 + 538384*a^4*b^9*tan(1/2*e)^38 + 1562275*a^9*b^4*ta
n(1/2*e)^36 + 7633516*a^8*b^5*tan(1/2*e)^36 + 14911314*a^7*b^6*tan(1/2*e)^36 + 14555596*a^6*b^7*tan(1/2*e)^36
+ 7099939*a^5*b^8*tan(1/2*e)^36 + 1384416*a^4*b^9*tan(1/2*e)^36 + 3124550*a^9*b^4*tan(1/2*e)^34 + 15440084*a^8
*b^5*tan(1/2*e)^34 + 30514836*a^7*b^6*tan(1/2*e)^34 + 30149504*a^6*b^7*tan(1/2*e)^34 + 14892086*a^5*b^8*tan(1/
2*e)^34 + 2941884*a^4*b^9*tan(1/2*e)^34 + 5311735*a^9*b^4*tan(1/2*e)^32 + 26476956*a^8*b^5*tan(1/2*e)^32 + 527
90474*a^7*b^6*tan(1/2*e)^32 + 52627036*a^6*b^7*tan(1/2*e)^32 + 26231799*a^5*b^8*tan(1/2*e)^32 + 5230016*a^4*b^
9*tan(1/2*e)^32 + 7726160*a^9*b^4*tan(1/2*e)^30 + 38749664*a^8*b^5*tan(1/2*e)^30 + 77737056*a^7*b^6*tan(1/2*e)
^30 + 77974784*a^6*b^7*tan(1/2*e)^30 + 39106256*a^5*b^8*tan(1/2*e)^30 + 7845024*a^4*b^9*tan(1/2*e)^30 + 965770
0*a^9*b^4*tan(1/2*e)^28 + 48615376*a^8*b^5*tan(1/2*e)^28 + 97884504*a^7*b^6*tan(1/2*e)^28 + 98538256*a^6*b^7*t
an(1/2*e)^28 + 49596004*a^5*b^8*tan(1/2*e)^28 + 9984576*a^4*b^9*tan(1/2*e)^28 + 10400600*a^9*b^4*tan(1/2*e)^26
+ 52419024*a^8*b^5*tan(1/2*e)^26 + 105670096*a^7*b^6*tan(1/2*e)^26 + 106502144*a^6*b^7*tan(1/2*e)^26 + 536670
96*a^5*b^8*tan(1/2*e)^26 + 10816624*a^4*b^9*tan(1/2*e)^26 + 9657700*a^9*b^4*tan(1/2*e)^24 + 48615376*a^8*b^5*t
an(1/2*e)^24 + 97884504*a^7*b^6*tan(1/2*e)^24 + 98538256*a^6*b^7*tan(1/2*e)^24 + 49596004*a^5*b^8*tan(1/2*e)^2
4 + 9984576*a^4*b^9*tan(1/2*e)^24 + 7726160*a^9*b^4*tan(1/2*e)^22 + 38749664*a^8*b^5*tan(1/2*e)^22 + 77737056*
a^7*b^6*tan(1/2*e)^22 + 77974784*a^6*b^7*tan(1/2*e)^22 + 39106256*a^5*b^8*tan(1/2*e)^22 + 7845024*a^4*b^9*tan(
1/2*e)^22 + 5311735*a^9*b^4*tan(1/2*e)^20 + 26476956*a^8*b^5*tan(1/2*e)^20 + 52790474*a^7*b^6*tan(1/2*e)^20 +
52627036*a^6*b^7*tan(1/2*e)^20 + 26231799*a^5*b^8*tan(1/2*e)^20 + 5230016*a^4*b^9*tan(1/2*e)^20 + 3124550*a^9*
b^4*tan(1/2*e)^18 + 15440084*a^8*b^5*tan(1/2*e)^18 + 30514836*a^7*b^6*tan(1/2*e)^18 + 30149504*a^6*b^7*tan(1/2
*e)^18 + 14892086*a^5*b^8*tan(1/2*e)^18 + 2941884*a^4*b^9*tan(1/2*e)^18 + 1562275*a^9*b^4*tan(1/2*e)^16 + 7633
516*a^8*b^5*tan(1/2*e)^16 + 14911314*a^7*b^6*tan(1/2*e)^16 + 14555596*a^6*b^7*tan(1/2*e)^16 + 7099939*a^5*b^8*
tan(1/2*e)^16 + 1384416*a^4*b^9*tan(1/2*e)^16 + 657800*a^9*b^4*tan(1/2*e)^14 + 3169584*a^8*b^5*tan(1/2*e)^14 +
6100336*a^7*b^6*tan(1/2*e)^14 + 5861504*a^6*b^7*tan(1/2*e)^14 + 2811336*a^5*b^8*tan(1/2*e)^14 + 538384*a^4*b^
9*tan(1/2*e)^14 + 230230*a^9*b^4*tan(1/2*e)^12 + 1090936*a^8*b^5*tan(1/2*e)^12 + 2061444*a^7*b^6*tan(1/2*e)^12
+ 1941016*a^6*b^7*tan(1/2*e)^12 + 910294*a^5*b^8*tan(1/2*e)^12 + 170016*a^4*b^9*tan(1/2*e)^12 + 65780*a^9*b^4
*tan(1/2*e)^10 + 305624*a^8*b^5*tan(1/2*e)^10 + 564696*a^7*b^6*tan(1/2*e)^10 + 518144*a^6*b^7*tan(1/2*e)^10 +
235796*a^5*b^8*tan(1/2*e)^10 + 42504*a^4*b^9*tan(1/2*e)^10 + 14950*a^9*b^4*tan(1/2*e)^8 + 67896*a^8*b^5*tan(1/
2*e)^8 + 122084*a^7*b^6*tan(1/2*e)^8 + 108376*a^6*b^7*tan(1/2*e)^8 + 47334*a^5*b^8*tan(1/2*e)^8 + 8096*a^4*b^9
*tan(1/2*e)^8 + 2600*a^9*b^4*tan(1/2*e)^6 + 11504*a^8*b^5*tan(1/2*e)^6 + 20016*a^7*b^6*tan(1/2*e)^6 + 17024*a^
6*b^7*tan(1/2*e)^6 + 7016*a^5*b^8*tan(1/2*e)^6 + 1104*a^4*b^9*tan(1/2*e)^6 + 325*a^9*b^4*tan(1/2*e)^4 + 1396*a
^8*b^5*tan(1/2*e)^4 + 2334*a^7*b^6*tan(1/2*e)^4 + 1876*a^6*b^7*tan(1/2*e)^4 + 709*a^5*b^8*tan(1/2*e)^4 + 96*a^
4*b^9*tan(1/2*e)^4 + 26*a^9*b^4*tan(1/2*e)^2 + 108*a^8*b^5*tan(1/2*e)^2 + 172*a^7*b^6*tan(1/2*e)^2 + 128*a^6*b
^7*tan(1/2*e)^2 + 42*a^5*b^8*tan(1/2*e)^2 + 4*a^4*b^9*tan(1/2*e)^2 + a^9*b^4 + 4*a^8*b^5 + 6*a^7*b^6 + 4*a^6*b
^7 + a^5*b^8))/((a*tan(1/2*f*x)^4*tan(1/2*e)^4 + 2*a*tan(1/2*f*x)^4*tan(1/2*e)^2 + 4*b*tan(1/2*f*x)^4*tan(1/2*
e)^2 + 8*b*tan(1/2*f*x)^3*tan(1/2*e)^3 + 2*a*tan(1/2*f*x)^2*tan(1/2*e)^4 + 4*b*tan(1/2*f*x)^2*tan(1/2*e)^4 + a
*tan(1/2*f*x)^4 - 8*b*tan(1/2*f*x)^3*tan(1/2*e) + 4*a*tan(1/2*f*x)^2*tan(1/2*e)^2 - 16*b*tan(1/2*f*x)^2*tan(1/
2*e)^2 - 8*b*tan(1/2*f*x)*tan(1/2*e)^3 + a*tan(1/2*e)^4 + 2*a*tan(1/2*f*x)^2 + 4*b*tan(1/2*f*x)^2 + 8*b*tan(1/
2*f*x)*tan(1/2*e) + 2*a*tan(1/2*e)^2 + 4*b*tan(1/2*e)^2 + a)^(3/2)*f)

Mupad [B] (verification not implemented)

Time = 21.07 (sec) , antiderivative size = 183, normalized size of antiderivative = 2.51 \[ \int \frac {\cos ^3(e+f x)}{\left (a+b \sin ^2(e+f x)\right )^{5/2}} \, dx=-\frac {2\,{\mathrm {e}}^{e\,1{}\mathrm {i}+f\,x\,1{}\mathrm {i}}\,\left ({\mathrm {e}}^{e\,2{}\mathrm {i}+f\,x\,2{}\mathrm {i}}-1\right )\,\sqrt {a+b\,{\left (\frac {{\mathrm {e}}^{-e\,1{}\mathrm {i}-f\,x\,1{}\mathrm {i}}\,1{}\mathrm {i}}{2}-\frac {{\mathrm {e}}^{e\,1{}\mathrm {i}+f\,x\,1{}\mathrm {i}}\,1{}\mathrm {i}}{2}\right )}^2}\,\left (a\,1{}\mathrm {i}-b\,2{}\mathrm {i}+a\,{\mathrm {e}}^{e\,2{}\mathrm {i}+f\,x\,2{}\mathrm {i}}\,10{}\mathrm {i}+a\,{\mathrm {e}}^{e\,4{}\mathrm {i}+f\,x\,4{}\mathrm {i}}\,1{}\mathrm {i}+b\,{\mathrm {e}}^{e\,2{}\mathrm {i}+f\,x\,2{}\mathrm {i}}\,4{}\mathrm {i}-b\,{\mathrm {e}}^{e\,4{}\mathrm {i}+f\,x\,4{}\mathrm {i}}\,2{}\mathrm {i}\right )}{3\,a^2\,f\,{\left (b-4\,a\,{\mathrm {e}}^{e\,2{}\mathrm {i}+f\,x\,2{}\mathrm {i}}-2\,b\,{\mathrm {e}}^{e\,2{}\mathrm {i}+f\,x\,2{}\mathrm {i}}+b\,{\mathrm {e}}^{e\,4{}\mathrm {i}+f\,x\,4{}\mathrm {i}}\right )}^2} \]

[In]

int(cos(e + f*x)^3/(a + b*sin(e + f*x)^2)^(5/2),x)

[Out]

-(2*exp(e*1i + f*x*1i)*(exp(e*2i + f*x*2i) - 1)*(a + b*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/
2)^2)^(1/2)*(a*1i - b*2i + a*exp(e*2i + f*x*2i)*10i + a*exp(e*4i + f*x*4i)*1i + b*exp(e*2i + f*x*2i)*4i - b*ex
p(e*4i + f*x*4i)*2i))/(3*a^2*f*(b - 4*a*exp(e*2i + f*x*2i) - 2*b*exp(e*2i + f*x*2i) + b*exp(e*4i + f*x*4i))^2)