\(\int \frac {\cos (e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [365]

Optimal result

Integrand size = 23, antiderivative size = 65 \[ \int \frac {\cos (e+f x)}{\left (a+b \sin ^2(e+f x)\right )^{5/2}} \, dx=\frac {\sin (e+f x)}{3 a f \left (a+b \sin ^2(e+f x)\right )^{3/2}}+\frac {2 \sin (e+f x)}{3 a^2 f \sqrt {a+b \sin ^2(e+f x)}} \]

[Out]

1/3*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 = 0.06 (sec) , antiderivative size = 65, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, Rules used = {3269, 198, 197} \[ \int \frac {\cos (e+f x)}{\left (a+b \sin ^2(e+f x)\right )^{5/2}} \, dx=\frac {2 \sin (e+f x)}{3 a^2 f \sqrt {a+b \sin ^2(e+f x)}}+\frac {\sin (e+f x)}{3 a f \left (a+b \sin ^2(e+f x)\right )^{3/2}} \]

[In]

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

[Out]

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 198

Int[((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[(-x)*((a + b*x^n)^(p + 1)/(a*n*(p + 1))), x] + Dist[(n*(p
+ 1) + 1)/(a*n*(p + 1)), Int[(a + b*x^n)^(p + 1), x], x] /; FreeQ[{a, b, n, p}, x] && ILtQ[Simplify[1/n + p +
1], 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}{\left (a+b x^2\right )^{5/2}} \, dx,x,\sin (e+f x)\right )}{f} \\ & = \frac {\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 {\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 = 0.05 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.72 \[ \int \frac {\cos (e+f x)}{\left (a+b \sin ^2(e+f x)\right )^{5/2}} \, dx=\frac {\sin (e+f x) \left (3 a+2 b \sin ^2(e+f x)\right )}{3 a^2 f \left (a+b \sin ^2(e+f x)\right )^{3/2}} \]

[In]

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

[Out]

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

Maple [A] (verified)

Time = 0.27 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.86

method	result	size
derivativedivides	\(\frac {\frac {\sin \left (f x +e \right )}{3 a {\left (a +b \left (\sin ^{2}\left (f x +e \right )\right )\right )}^{\frac {3}{2}}}+\frac {2 \sin \left (f x +e \right )}{3 a^{2} \sqrt {a +b \left (\sin ^{2}\left (f x +e \right )\right )}}}{f}\)	\(56\)
default	\(\frac {\frac {\sin \left (f x +e \right )}{3 a {\left (a +b \left (\sin ^{2}\left (f x +e \right )\right )\right )}^{\frac {3}{2}}}+\frac {2 \sin \left (f x +e \right )}{3 a^{2} \sqrt {a +b \left (\sin ^{2}\left (f x +e \right )\right )}}}{f}\)	\(56\)

[In]

int(cos(f*x+e)/(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))

Fricas [A] (verification not implemented)

none

Time = 0.41 (sec) , antiderivative size = 104, normalized size of antiderivative = 1.60 \[ \int \frac {\cos (e+f x)}{\left (a+b \sin ^2(e+f x)\right )^{5/2}} \, dx=-\frac {{\left (2 \, b \cos \left (f x + e\right )^{2} - 3 \, a - 2 \, b\right )} \sqrt {-b \cos \left (f x + e\right )^{2} + a + b} \sin \left (f x + e\right )}{3 \, {\left (a^{2} b^{2} f \cos \left (f x + e\right )^{4} - 2 \, {\left (a^{3} b + a^{2} b^{2}\right )} f \cos \left (f x + e\right )^{2} + {\left (a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right )} f\right )}} \]

[In]

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

[Out]

-1/3*(2*b*cos(f*x + e)^2 - 3*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. \[ \int \frac {\cos (e+f x)}{\left (a+b \sin ^2(e+f x)\right )^{5/2}} \, dx=\text {Timed out} \]

[In]

integrate(cos(f*x+e)/(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 = 55, normalized size of antiderivative = 0.85 \[ \int \frac {\cos (e+f x)}{\left (a+b \sin ^2(e+f x)\right )^{5/2}} \, dx=\frac {\frac {2 \, \sin \left (f x + e\right )}{\sqrt {b \sin \left (f x + e\right )^{2} + a} a^{2}} + \frac {\sin \left (f x + e\right )}{{\left (b \sin \left (f x + e\right )^{2} + a\right )}^{\frac {3}{2}} a}}{3 \, f} \]

[In]

integrate(cos(f*x+e)/(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))/f

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 35375 vs. \(2 (57) = 114\).

Time = 64.00 (sec) , antiderivative size = 35375, normalized size of antiderivative = 544.23 \[ \int \frac {\cos (e+f x)}{\left (a+b \sin ^2(e+f x)\right )^{5/2}} \, dx=\text {Too large to display} \]

[In]

integrate(cos(f*x+e)/(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 + 84*a^8*b^4*tan(1/2*e)^55 + 356*a^7*b^5*tan(1/2*e)^55 + 584*a^6*b^6*tan(1/2*
e)^55 + 456*a^5*b^7*tan(1/2*e)^55 + 164*a^4*b^8*tan(1/2*e)^55 + 20*a^3*b^9*tan(1/2*e)^55 + 1134*a^8*b^4*tan(1/
2*e)^53 + 5056*a^7*b^5*tan(1/2*e)^53 + 8916*a^6*b^6*tan(1/2*e)^53 + 7784*a^5*b^7*tan(1/2*e)^53 + 3406*a^4*b^8*
tan(1/2*e)^53 + 648*a^3*b^9*tan(1/2*e)^53 + 32*a^2*b^10*tan(1/2*e)^53 + 9828*a^8*b^4*tan(1/2*e)^51 + 45812*a^7
*b^5*tan(1/2*e)^51 + 85736*a^6*b^6*tan(1/2*e)^51 + 81384*a^5*b^7*tan(1/2*e)^51 + 40436*a^4*b^8*tan(1/2*e)^51 +
9572*a^3*b^9*tan(1/2*e)^51 + 768*a^2*b^10*tan(1/2*e)^51 + 61425*a^8*b^4*tan(1/2*e)^49 + 297700*a^7*b^5*tan(1/
2*e)^49 + 585382*a^6*b^6*tan(1/2*e)^49 + 593028*a^5*b^7*tan(1/2*e)^49 + 322417*a^4*b^8*tan(1/2*e)^49 + 87328*a
^3*b^9*tan(1/2*e)^49 + 8832*a^2*b^10*tan(1/2*e)^49 + 294840*a^8*b^4*tan(1/2*e)^47 + 1478360*a^7*b^5*tan(1/2*e)
^47 + 3029808*a^6*b^6*tan(1/2*e)^47 + 3232432*a^5*b^7*tan(1/2*e)^47 + 1879448*a^4*b^8*tan(1/2*e)^47 + 558072*a
^3*b^9*tan(1/2*e)^47 + 64768*a^2*b^10*tan(1/2*e)^47 + 1130220*a^8*b^4*tan(1/2*e)^45 + 5836480*a^7*b^5*tan(1/2*
e)^45 + 12383752*a^6*b^6*tan(1/2*e)^45 + 13774608*a^5*b^7*tan(1/2*e)^45 + 8432812*a^4*b^8*tan(1/2*e)^45 + 2675
728*a^3*b^9*tan(1/2*e)^45 + 340032*a^2*b^10*tan(1/2*e)^45 + 3552120*a^8*b^4*tan(1/2*e)^43 + 18813080*a^7*b^5*t
an(1/2*e)^43 + 41091248*a^6*b^6*tan(1/2*e)^43 + 47276592*a^5*b^7*tan(1/2*e)^43 + 30131288*a^4*b^8*tan(1/2*e)^4
3 + 10045112*a^3*b^9*tan(1/2*e)^43 + 1360128*a^2*b^10*tan(1/2*e)^43 + 9324315*a^8*b^4*tan(1/2*e)^41 + 50453260
*a^7*b^5*tan(1/2*e)^41 + 112876962*a^6*b^6*tan(1/2*e)^41 + 133461548*a^5*b^7*tan(1/2*e)^41 + 87790747*a^4*b^8*
tan(1/2*e)^41 + 30384288*a^3*b^9*tan(1/2*e)^41 + 4307072*a^2*b^10*tan(1/2*e)^41 + 20720700*a^8*b^4*tan(1/2*e)^
39 + 114128300*a^7*b^5*tan(1/2*e)^39 + 260381528*a^6*b^6*tan(1/2*e)^39 + 314657112*a^5*b^7*tan(1/2*e)^39 + 212
154668*a^4*b^8*tan(1/2*e)^39 + 75546812*a^3*b^9*tan(1/2*e)^39 + 11075328*a^2*b^10*tan(1/2*e)^39 + 39369330*a^8
*b^4*tan(1/2*e)^37 + 219968320*a^7*b^5*tan(1/2*e)^37 + 509715052*a^6*b^6*tan(1/2*e)^37 + 626563608*a^5*b^7*tan
(1/2*e)^37 + 430543762*a^4*b^8*tan(1/2*e)^37 + 156631288*a^3*b^9*tan(1/2*e)^37 + 23535072*a^2*b^10*tan(1/2*e)^
37 + 64422540*a^8*b^4*tan(1/2*e)^35 + 363924860*a^7*b^5*tan(1/2*e)^35 + 853314168*a^6*b^6*tan(1/2*e)^35 + 1062
458872*a^5*b^7*tan(1/2*e)^35 + 740402108*a^4*b^8*tan(1/2*e)^35 + 273595212*a^3*b^9*tan(1/2*e)^35 + 41840128*a^
2*b^10*tan(1/2*e)^35 + 91265265*a^8*b^4*tan(1/2*e)^33 + 519584260*a^7*b^5*tan(1/2*e)^33 + 1228444582*a^6*b^6*t
an(1/2*e)^33 + 1543241028*a^5*b^7*tan(1/2*e)^33 + 1085919217*a^4*b^8*tan(1/2*e)^33 + 405563968*a^3*b^9*tan(1/2
*e)^33 + 62760192*a^2*b^10*tan(1/2*e)^33 + 112326480*a^8*b^4*tan(1/2*e)^31 + 642459920*a^7*b^5*tan(1/2*e)^31 +
1526451488*a^6*b^6*tan(1/2*e)^31 + 1927736352*a^5*b^7*tan(1/2*e)^31 + 1364202128*a^4*b^8*tan(1/2*e)^31 + 5126
60432*a^3*b^9*tan(1/2*e)^31 + 79876608*a^2*b^10*tan(1/2*e)^31 + 120349800*a^8*b^4*tan(1/2*e)^29 + 689411200*a^
7*b^5*tan(1/2*e)^29 + 1640679792*a^6*b^6*tan(1/2*e)^29 + 2075603168*a^5*b^7*tan(1/2*e)^29 + 1471595752*a^4*b^8
*tan(1/2*e)^29 + 554143968*a^3*b^9*tan(1/2*e)^29 + 86532992*a^2*b^10*tan(1/2*e)^29 + 112326480*a^8*b^4*tan(1/2
*e)^27 + 642459920*a^7*b^5*tan(1/2*e)^27 + 1526451488*a^6*b^6*tan(1/2*e)^27 + 1927736352*a^5*b^7*tan(1/2*e)^27
+ 1364202128*a^4*b^8*tan(1/2*e)^27 + 512660432*a^3*b^9*tan(1/2*e)^27 + 79876608*a^2*b^10*tan(1/2*e)^27 + 9126
5265*a^8*b^4*tan(1/2*e)^25 + 519584260*a^7*b^5*tan(1/2*e)^25 + 1228444582*a^6*b^6*tan(1/2*e)^25 + 1543241028*a
^5*b^7*tan(1/2*e)^25 + 1085919217*a^4*b^8*tan(1/2*e)^25 + 405563968*a^3*b^9*tan(1/2*e)^25 + 62760192*a^2*b^10*
tan(1/2*e)^25 + 64422540*a^8*b^4*tan(1/2*e)^23 + 363924860*a^7*b^5*tan(1/2*e)^23 + 853314168*a^6*b^6*tan(1/2*e
)^23 + 1062458872*a^5*b^7*tan(1/2*e)^23 + 740402108*a^4*b^8*tan(1/2*e)^23 + 273595212*a^3*b^9*tan(1/2*e)^23 +
41840128*a^2*b^10*tan(1/2*e)^23 + 39369330*a^8*b^4*tan(1/2*e)^21 + 219968320*a^7*b^5*tan(1/2*e)^21 + 509715052
*a^6*b^6*tan(1/2*e)^21 + 626563608*a^5*b^7*tan(1/2*e)^21 + 430543762*a^4*b^8*tan(1/2*e)^21 + 156631288*a^3*b^9
*tan(1/2*e)^21 + 23535072*a^2*b^10*tan(1/2*e)^21 + 20720700*a^8*b^4*tan(1/2*e)^19 + 114128300*a^7*b^5*tan(1/2*
e)^19 + 260381528*a^6*b^6*tan(1/2*e)^19 + 314657112*a^5*b^7*tan(1/2*e)^19 + 212154668*a^4*b^8*tan(1/2*e)^19 +
75546812*a^3*b^9*tan(1/2*e)^19 + 11075328*a^2*b^10*tan(1/2*e)^19 + 9324315*a^8*b^4*tan(1/2*e)^17 + 50453260*a^
7*b^5*tan(1/2*e)^17 + 112876962*a^6*b^6*tan(1/2*e)^17 + 133461548*a^5*b^7*tan(1/2*e)^17 + 87790747*a^4*b^8*tan
(1/2*e)^17 + 30384288*a^3*b^9*tan(1/2*e)^17 + 4307072*a^2*b^10*tan(1/2*e)^17 + 3552120*a^8*b^4*tan(1/2*e)^15 +
18813080*a^7*b^5*tan(1/2*e)^15 + 41091248*a^6*b^6*tan(1/2*e)^15 + 47276592*a^5*b^7*tan(1/2*e)^15 + 30131288*a
^4*b^8*tan(1/2*e)^15 + 10045112*a^3*b^9*tan(1/2*e)^15 + 1360128*a^2*b^10*tan(1/2*e)^15 + 1130220*a^8*b^4*tan(1
/2*e)^13 + 5836480*a^7*b^5*tan(1/2*e)^13 + 12383752*a^6*b^6*tan(1/2*e)^13 + 13774608*a^5*b^7*tan(1/2*e)^13 + 8
432812*a^4*b^8*tan(1/2*e)^13 + 2675728*a^3*b^9*tan(1/2*e)^13 + 340032*a^2*b^10*tan(1/2*e)^13 + 294840*a^8*b^4*
tan(1/2*e)^11 + 1478360*a^7*b^5*tan(1/2*e)^11 + 3029808*a^6*b^6*tan(1/2*e)^11 + 3232432*a^5*b^7*tan(1/2*e)^11
+ 1879448*a^4*b^8*tan(1/2*e)^11 + 558072*a^3*b^9*tan(1/2*e)^11 + 64768*a^2*b^10*tan(1/2*e)^11 + 61425*a^8*b^4*
tan(1/2*e)^9 + 297700*a^7*b^5*tan(1/2*e)^9 + 585382*a^6*b^6*tan(1/2*e)^9 + 593028*a^5*b^7*tan(1/2*e)^9 + 32241
7*a^4*b^8*tan(1/2*e)^9 + 87328*a^3*b^9*tan(1/2*e)^9 + 8832*a^2*b^10*tan(1/2*e)^9 + 9828*a^8*b^4*tan(1/2*e)^7 +
45812*a^7*b^5*tan(1/2*e)^7 + 85736*a^6*b^6*tan(1/2*e)^7 + 81384*a^5*b^7*tan(1/2*e)^7 + 40436*a^4*b^8*tan(1/2*
e)^7 + 9572*a^3*b^9*tan(1/2*e)^7 + 768*a^2*b^10*tan(1/2*e)^7 + 1134*a^8*b^4*tan(1/2*e)^5 + 5056*a^7*b^5*tan(1/
2*e)^5 + 8916*a^6*b^6*tan(1/2*e)^5 + 7784*a^5*b^7*tan(1/2*e)^5 + 3406*a^4*b^8*tan(1/2*e)^5 + 648*a^3*b^9*tan(1
/2*e)^5 + 32*a^2*b^10*tan(1/2*e)^5 + 84*a^8*b^4*tan(1/2*e)^3 + 356*a^7*b^5*tan(1/2*e)^3 + 584*a^6*b^6*tan(1/2*
e)^3 + 456*a^5*b^7*tan(1/2*e)^3 + 164*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*ta
n(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*t
an(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*t
an(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 + 170
24*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 + 564
696*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 + 19410
16*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 + 2811
336*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*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 + 526
27036*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 + 4861537
6*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*t
an(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 + 108166
24*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*t
an(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 + 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 + 14911
314*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*t
an(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*t
an(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 + 42
504*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*t
an(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
+ 27*a^8*b^4*tan(1/2*e)^56 + 120*a^7*b^5*tan(1/2*e)^56 + 210*a^6*b^6*tan(1/2*e)^56 + 180*a^5*b^7*tan(1/2*e)^56
+ 75*a^4*b^8*tan(1/2*e)^56 + 12*a^3*b^9*tan(1/2*e)^56 + 350*a^8*b^4*tan(1/2*e)^54 + 1700*a^7*b^5*tan(1/2*e)^5
4 + 3332*a^6*b^6*tan(1/2*e)^54 + 3328*a^5*b^7*tan(1/2*e)^54 + 1742*a^4*b^8*tan(1/2*e)^54 + 428*a^3*b^9*tan(1/2
*e)^54 + 32*a^2*b^10*tan(1/2*e)^54 + 2898*a^8*b^4*tan(1/2*e)^52 + 15180*a^7*b^5*tan(1/2*e)^52 + 32476*a^6*b^6*
tan(1/2*e)^52 + 36064*a^5*b^7*tan(1/2*e)^52 + 21666*a^4*b^8*tan(1/2*e)^52 + 6532*a^3*b^9*tan(1/2*e)^52 + 736*a
^2*b^10*tan(1/2*e)^52 + 17199*a^8*b^4*tan(1/2*e)^50 + 96096*a^7*b^5*tan(1/2*e)^50 + 220458*a^6*b^6*tan(1/2*e)^
50 + 264852*a^5*b^7*tan(1/2*e)^50 + 174783*a^4*b^8*tan(1/2*e)^50 + 59556*a^3*b^9*tan(1/2*e)^50 + 8064*a^2*b^10
*tan(1/2*e)^50 + 77805*a^8*b^4*tan(1/2*e)^48 + 459420*a^7*b^5*tan(1/2*e)^48 + 1115566*a^6*b^6*tan(1/2*e)^48 +
1424164*a^5*b^7*tan(1/2*e)^48 + 1006221*a^4*b^8*tan(1/2*e)^48 + 371944*a^3*b^9*tan(1/2*e)^48 + 55936*a^2*b^10*
tan(1/2*e)^48 + 278460*a^8*b^4*tan(1/2*e)^46 + 1723800*a^7*b^5*tan(1/2*e)^46 + 4385864*a^6*b^6*tan(1/2*e)^46 +
5874656*a^5*b^7*tan(1/2*e)^46 + 4369884*a^4*b^8*tan(1/2*e)^46 + 1711016*a^3*b^9*tan(1/2*e)^46 + 275264*a^2*b^
10*tan(1/2*e)^46 + 807300*a^8*b^4*tan(1/2*e)^44 + 5202600*a^7*b^5*tan(1/2*e)^44 + 13757496*a^6*b^6*tan(1/2*e)^
44 + 19149984*a^5*b^7*tan(1/2*e)^44 + 14821476*a^4*b^8*tan(1/2*e)^44 + 6053784*a^3*b^9*tan(1/2*e)^44 + 1020096
*a^2*b^10*tan(1/2*e)^44 + 1924065*a^8*b^4*tan(1/2*e)^42 + 12827100*a^7*b^5*tan(1/2*e)^42 + 35014694*a^6*b^6*ta
n(1/2*e)^42 + 50269076*a^5*b^7*tan(1/2*e)^42 + 40129089*a^4*b^8*tan(1/2*e)^42 + 16918616*a^3*b^9*tan(1/2*e)^42
+ 2946944*a^2*b^10*tan(1/2*e)^42 + 3798795*a^8*b^4*tan(1/2*e)^40 + 26048880*a^7*b^5*tan(1/2*e)^40 + 72975826*
a^6*b^6*tan(1/2*e)^40 + 107390404*a^5*b^7*tan(1/2*e)^40 + 87823131*a^4*b^8*tan(1/2*e)^40 + 37926724*a^3*b^9*ta
n(1/2*e)^40 + 6768256*a^2*b^10*tan(1/2*e)^40 + 6216210*a^8*b^4*tan(1/2*e)^38 + 43612140*a^7*b^5*tan(1/2*e)^38
+ 124746204*a^6*b^6*tan(1/2*e)^38 + 187187616*a^5*b^7*tan(1/2*e)^38 + 155963874*a^4*b^8*tan(1/2*e)^38 + 685862
76*a^3*b^9*tan(1/2*e)^38 + 12459744*a^2*b^10*tan(1/2*e)^38 + 8351070*a^8*b^4*tan(1/2*e)^36 + 59650500*a^7*b^5*
tan(1/2*e)^36 + 173396356*a^6*b^6*tan(1/2*e)^36 + 264101824*a^5*b^7*tan(1/2*e)^36 + 223166286*a^4*b^8*tan(1/2*
e)^36 + 99466444*a^3*b^9*tan(1/2*e)^36 + 18305056*a^2*b^10*tan(1/2*e)^36 + 8947575*a^8*b^4*tan(1/2*e)^34 + 647
63400*a^7*b^5*tan(1/2*e)^34 + 190497914*a^6*b^6*tan(1/2*e)^34 + 293309156*a^5*b^7*tan(1/2*e)^34 + 250360359*a^
4*b^8*tan(1/2*e)^34 + 112653356*a^3*b^9*tan(1/2*e)^34 + 20920064*a^2*b^10*tan(1/2*e)^34 + 7020405*a^8*b^4*tan(
1/2*e)^32 + 51260100*a^7*b^5*tan(1/2*e)^32 + 151952766*a^6*b^6*tan(1/2*e)^32 + 235618164*a^5*b^7*tan(1/2*e)^32
+ 202432821*a^4*b^8*tan(1/2*e)^32 + 91644144*a^3*b^9*tan(1/2*e)^32 + 17116416*a^2*b^10*tan(1/2*e)^32 + 267444
0*a^8*b^4*tan(1/2*e)^30 + 19612560*a^7*b^5*tan(1/2*e)^30 + 58362224*a^6*b^6*tan(1/2*e)^30 + 90812096*a^5*b^7*t
an(1/2*e)^30 + 78271944*a^4*b^8*tan(1/2*e)^30 + 35540336*a^3*b^9*tan(1/2*e)^30 + 6656384*a^2*b^10*tan(1/2*e)^3
0 - 2674440*a^8*b^4*tan(1/2*e)^28 - 19612560*a^7*b^5*tan(1/2*e)^28 - 58362224*a^6*b^6*tan(1/2*e)^28 - 90812096
*a^5*b^7*tan(1/2*e)^28 - 78271944*a^4*b^8*tan(1/2*e)^28 - 35540336*a^3*b^9*tan(1/2*e)^28 - 6656384*a^2*b^10*ta
n(1/2*e)^28 - 7020405*a^8*b^4*tan(1/2*e)^26 - 51260100*a^7*b^5*tan(1/2*e)^26 - 151952766*a^6*b^6*tan(1/2*e)^26
- 235618164*a^5*b^7*tan(1/2*e)^26 - 202432821*a^4*b^8*tan(1/2*e)^26 - 91644144*a^3*b^9*tan(1/2*e)^26 - 171164
16*a^2*b^10*tan(1/2*e)^26 - 8947575*a^8*b^4*tan(1/2*e)^24 - 64763400*a^7*b^5*tan(1/2*e)^24 - 190497914*a^6*b^6
*tan(1/2*e)^24 - 293309156*a^5*b^7*tan(1/2*e)^24 - 250360359*a^4*b^8*tan(1/2*e)^24 - 112653356*a^3*b^9*tan(1/2
*e)^24 - 20920064*a^2*b^10*tan(1/2*e)^24 - 8351070*a^8*b^4*tan(1/2*e)^22 - 59650500*a^7*b^5*tan(1/2*e)^22 - 17
3396356*a^6*b^6*tan(1/2*e)^22 - 264101824*a^5*b^7*tan(1/2*e)^22 - 223166286*a^4*b^8*tan(1/2*e)^22 - 99466444*a
^3*b^9*tan(1/2*e)^22 - 18305056*a^2*b^10*tan(1/2*e)^22 - 6216210*a^8*b^4*tan(1/2*e)^20 - 43612140*a^7*b^5*tan(
1/2*e)^20 - 124746204*a^6*b^6*tan(1/2*e)^20 - 187187616*a^5*b^7*tan(1/2*e)^20 - 155963874*a^4*b^8*tan(1/2*e)^2
0 - 68586276*a^3*b^9*tan(1/2*e)^20 - 12459744*a^2*b^10*tan(1/2*e)^20 - 3798795*a^8*b^4*tan(1/2*e)^18 - 2604888
0*a^7*b^5*tan(1/2*e)^18 - 72975826*a^6*b^6*tan(1/2*e)^18 - 107390404*a^5*b^7*tan(1/2*e)^18 - 87823131*a^4*b^8*
tan(1/2*e)^18 - 37926724*a^3*b^9*tan(1/2*e)^18 - 6768256*a^2*b^10*tan(1/2*e)^18 - 1924065*a^8*b^4*tan(1/2*e)^1
6 - 12827100*a^7*b^5*tan(1/2*e)^16 - 35014694*a^6*b^6*tan(1/2*e)^16 - 50269076*a^5*b^7*tan(1/2*e)^16 - 4012908
9*a^4*b^8*tan(1/2*e)^16 - 16918616*a^3*b^9*tan(1/2*e)^16 - 2946944*a^2*b^10*tan(1/2*e)^16 - 807300*a^8*b^4*tan
(1/2*e)^14 - 5202600*a^7*b^5*tan(1/2*e)^14 - 13757496*a^6*b^6*tan(1/2*e)^14 - 19149984*a^5*b^7*tan(1/2*e)^14 -
14821476*a^4*b^8*tan(1/2*e)^14 - 6053784*a^3*b^9*tan(1/2*e)^14 - 1020096*a^2*b^10*tan(1/2*e)^14 - 278460*a^8*
b^4*tan(1/2*e)^12 - 1723800*a^7*b^5*tan(1/2*e)^12 - 4385864*a^6*b^6*tan(1/2*e)^12 - 5874656*a^5*b^7*tan(1/2*e)
^12 - 4369884*a^4*b^8*tan(1/2*e)^12 - 1711016*a^3*b^9*tan(1/2*e)^12 - 275264*a^2*b^10*tan(1/2*e)^12 - 77805*a^
8*b^4*tan(1/2*e)^10 - 459420*a^7*b^5*tan(1/2*e)^10 - 1115566*a^6*b^6*tan(1/2*e)^10 - 1424164*a^5*b^7*tan(1/2*e
)^10 - 1006221*a^4*b^8*tan(1/2*e)^10 - 371944*a^3*b^9*tan(1/2*e)^10 - 55936*a^2*b^10*tan(1/2*e)^10 - 17199*a^8
*b^4*tan(1/2*e)^8 - 96096*a^7*b^5*tan(1/2*e)^8 - 220458*a^6*b^6*tan(1/2*e)^8 - 264852*a^5*b^7*tan(1/2*e)^8 - 1
74783*a^4*b^8*tan(1/2*e)^8 - 59556*a^3*b^9*tan(1/2*e)^8 - 8064*a^2*b^10*tan(1/2*e)^8 - 2898*a^8*b^4*tan(1/2*e)
^6 - 15180*a^7*b^5*tan(1/2*e)^6 - 32476*a^6*b^6*tan(1/2*e)^6 - 36064*a^5*b^7*tan(1/2*e)^6 - 21666*a^4*b^8*tan(
1/2*e)^6 - 6532*a^3*b^9*tan(1/2*e)^6 - 736*a^2*b^10*tan(1/2*e)^6 - 350*a^8*b^4*tan(1/2*e)^4 - 1700*a^7*b^5*tan
(1/2*e)^4 - 3332*a^6*b^6*tan(1/2*e)^4 - 3328*a^5*b^7*tan(1/2*e)^4 - 1742*a^4*b^8*tan(1/2*e)^4 - 428*a^3*b^9*ta
n(1/2*e)^4 - 32*a^2*b^10*tan(1/2*e)^4 - 27*a^8*b^4*tan(1/2*e)^2 - 120*a^7*b^5*tan(1/2*e)^2 - 210*a^6*b^6*tan(1
/2*e)^2 - 180*a^5*b^7*tan(1/2*e)^2 - 75*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)^4
6 + 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 + 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*ta
n(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 + 96
57700*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 + 53
667096*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 + 77737
056*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)^2
0 + 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)^1
0 + 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*ta
n(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 + 1702
4*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 + 13
96*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 + 9
6*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 + 38*a^6*b^6*tan(1/2*e)^
57 + 52*a^5*b^7*tan(1/2*e)^57 + 33*a^4*b^8*tan(1/2*e)^57 + 8*a^3*b^9*tan(1/2*e)^57 + 28*a^8*b^4*tan(1/2*e)^55
+ 300*a^7*b^5*tan(1/2*e)^55 + 952*a^6*b^6*tan(1/2*e)^55 + 1368*a^5*b^7*tan(1/2*e)^55 + 972*a^4*b^8*tan(1/2*e)^
55 + 316*a^3*b^9*tan(1/2*e)^55 + 32*a^2*b^10*tan(1/2*e)^55 + 378*a^8*b^4*tan(1/2*e)^53 + 3600*a^7*b^5*tan(1/2*
e)^53 + 11292*a^6*b^6*tan(1/2*e)^53 + 16728*a^5*b^7*tan(1/2*e)^53 + 12762*a^4*b^8*tan(1/2*e)^53 + 4776*a^3*b^9
*tan(1/2*e)^53 + 672*a^2*b^10*tan(1/2*e)^53 + 3276*a^8*b^4*tan(1/2*e)^51 + 27612*a^7*b^5*tan(1/2*e)^51 + 84248
*a^6*b^6*tan(1/2*e)^51 + 126392*a^5*b^7*tan(1/2*e)^51 + 100668*a^4*b^8*tan(1/2*e)^51 + 40748*a^3*b^9*tan(1/2*e
)^51 + 6560*a^2*b^10*tan(1/2*e)^51 + 20475*a^8*b^4*tan(1/2*e)^49 + 152100*a^7*b^5*tan(1/2*e)^49 + 442690*a^6*b
^6*tan(1/2*e)^49 + 659260*a^5*b^7*tan(1/2*e)^49 + 535515*a^4*b^8*tan(1/2*e)^49 + 226360*a^3*b^9*tan(1/2*e)^49
+ 39040*a^2*b^10*tan(1/2*e)^49 + 98280*a^8*b^4*tan(1/2*e)^47 + 641160*a^7*b^5*tan(1/2*e)^47 + 1736400*a^6*b^6*
tan(1/2*e)^47 + 2499600*a^5*b^7*tan(1/2*e)^47 + 2017800*a^4*b^8*tan(1/2*e)^47 + 866280*a^3*b^9*tan(1/2*e)^47 +
154560*a^2*b^10*tan(1/2*e)^47 + 376740*a^8*b^4*tan(1/2*e)^45 + 2152800*a^7*b^5*tan(1/2*e)^45 + 5248600*a^6*b^
6*tan(1/2*e)^45 + 7001200*a^5*b^7*tan(1/2*e)^45 + 5388900*a^4*b^8*tan(1/2*e)^45 + 2265040*a^3*b^9*tan(1/2*e)^4
5 + 404800*a^2*b^10*tan(1/2*e)^45 + 1184040*a^8*b^4*tan(1/2*e)^43 + 5920200*a^7*b^5*tan(1/2*e)^43 + 12407120*a
^6*b^6*tan(1/2*e)^43 + 14107280*a^5*b^7*tan(1/2*e)^43 + 9320520*a^4*b^8*tan(1/2*e)^43 + 3450920*a^3*b^9*tan(1/
2*e)^43 + 566720*a^2*b^10*tan(1/2*e)^43 + 3108105*a^8*b^4*tan(1/2*e)^41 + 13616460*a^7*b^5*tan(1/2*e)^41 + 228
99030*a^6*b^6*tan(1/2*e)^41 + 17593620*a^5*b^7*tan(1/2*e)^41 + 4929705*a^4*b^8*tan(1/2*e)^41 - 759000*a^3*b^9*
tan(1/2*e)^41 - 485760*a^2*b^10*tan(1/2*e)^41 + 6906900*a^8*b^4*tan(1/2*e)^39 + 26640900*a^7*b^5*tan(1/2*e)^39
+ 32110760*a^6*b^6*tan(1/2*e)^39 + 172040*a^5*b^7*tan(1/2*e)^39 - 29342940*a^4*b^8*tan(1/2*e)^39 - 22522060*a
^3*b^9*tan(1/2*e)^39 - 5383840*a^2*b^10*tan(1/2*e)^39 + 13123110*a^8*b^4*tan(1/2*e)^37 + 44993520*a^7*b^5*tan(
1/2*e)^37 + 31053220*a^6*b^6*tan(1/2*e)^37 - 63260120*a^5*b^7*tan(1/2*e)^37 - 123011130*a^4*b^8*tan(1/2*e)^37
- 78257960*a^3*b^9*tan(1/2*e)^37 - 17689760*a^2*b^10*tan(1/2*e)^37 + 21474180*a^8*b^4*tan(1/2*e)^35 + 66467700
*a^7*b^5*tan(1/2*e)^35 + 11903880*a^6*b^6*tan(1/2*e)^35 - 187577880*a^5*b^7*tan(1/2*e)^35 - 291592620*a^4*b^8*
tan(1/2*e)^35 - 176329500*a^3*b^9*tan(1/2*e)^35 - 39225120*a^2*b^10*tan(1/2*e)^35 + 30421755*a^8*b^4*tan(1/2*e
)^33 + 86919300*a^7*b^5*tan(1/2*e)^33 - 23104190*a^6*b^6*tan(1/2*e)^33 - 353174660*a^5*b^7*tan(1/2*e)^33 - 508
032165*a^4*b^8*tan(1/2*e)^33 - 301023080*a^3*b^9*tan(1/2*e)^33 - 66563840*a^2*b^10*tan(1/2*e)^33 + 37442160*a^
8*b^4*tan(1/2*e)^31 + 101628720*a^7*b^5*tan(1/2*e)^31 - 58243360*a^6*b^6*tan(1/2*e)^31 - 500417440*a^5*b^7*tan
(1/2*e)^31 - 697137360*a^4*b^8*tan(1/2*e)^31 - 409486480*a^3*b^9*tan(1/2*e)^31 - 90336640*a^2*b^10*tan(1/2*e)^
31 + 40116600*a^8*b^4*tan(1/2*e)^29 + 106977600*a^7*b^5*tan(1/2*e)^29 - 73101360*a^6*b^6*tan(1/2*e)^29 - 55984
9440*a^5*b^7*tan(1/2*e)^29 - 772913160*a^4*b^8*tan(1/2*e)^29 - 452871840*a^3*b^9*tan(1/2*e)^29 - 99845760*a^2*
b^10*tan(1/2*e)^29 + 37442160*a^8*b^4*tan(1/2*e)^27 + 101628720*a^7*b^5*tan(1/2*e)^27 - 58243360*a^6*b^6*tan(1
/2*e)^27 - 500417440*a^5*b^7*tan(1/2*e)^27 - 697137360*a^4*b^8*tan(1/2*e)^27 - 409486480*a^3*b^9*tan(1/2*e)^27
- 90336640*a^2*b^10*tan(1/2*e)^27 + 30421755*a^8*b^4*tan(1/2*e)^25 + 86919300*a^7*b^5*tan(1/2*e)^25 - 2310419
0*a^6*b^6*tan(1/2*e)^25 - 353174660*a^5*b^7*tan(1/2*e)^25 - 508032165*a^4*b^8*tan(1/2*e)^25 - 301023080*a^3*b^
9*tan(1/2*e)^25 - 66563840*a^2*b^10*tan(1/2*e)^25 + 21474180*a^8*b^4*tan(1/2*e)^23 + 66467700*a^7*b^5*tan(1/2*
e)^23 + 11903880*a^6*b^6*tan(1/2*e)^23 - 187577880*a^5*b^7*tan(1/2*e)^23 - 291592620*a^4*b^8*tan(1/2*e)^23 - 1
76329500*a^3*b^9*tan(1/2*e)^23 - 39225120*a^2*b^10*tan(1/2*e)^23 + 13123110*a^8*b^4*tan(1/2*e)^21 + 44993520*a
^7*b^5*tan(1/2*e)^21 + 31053220*a^6*b^6*tan(1/2*e)^21 - 63260120*a^5*b^7*tan(1/2*e)^21 - 123011130*a^4*b^8*tan
(1/2*e)^21 - 78257960*a^3*b^9*tan(1/2*e)^21 - 17689760*a^2*b^10*tan(1/2*e)^21 + 6906900*a^8*b^4*tan(1/2*e)^19
+ 26640900*a^7*b^5*tan(1/2*e)^19 + 32110760*a^6*b^6*tan(1/2*e)^19 + 172040*a^5*b^7*tan(1/2*e)^19 - 29342940*a^
4*b^8*tan(1/2*e)^19 - 22522060*a^3*b^9*tan(1/2*e)^19 - 5383840*a^2*b^10*tan(1/2*e)^19 + 3108105*a^8*b^4*tan(1/
2*e)^17 + 13616460*a^7*b^5*tan(1/2*e)^17 + 22899030*a^6*b^6*tan(1/2*e)^17 + 17593620*a^5*b^7*tan(1/2*e)^17 + 4
929705*a^4*b^8*tan(1/2*e)^17 - 759000*a^3*b^9*tan(1/2*e)^17 - 485760*a^2*b^10*tan(1/2*e)^17 + 1184040*a^8*b^4*
tan(1/2*e)^15 + 5920200*a^7*b^5*tan(1/2*e)^15 + 12407120*a^6*b^6*tan(1/2*e)^15 + 14107280*a^5*b^7*tan(1/2*e)^1
5 + 9320520*a^4*b^8*tan(1/2*e)^15 + 3450920*a^3*b^9*tan(1/2*e)^15 + 566720*a^2*b^10*tan(1/2*e)^15 + 376740*a^8
*b^4*tan(1/2*e)^13 + 2152800*a^7*b^5*tan(1/2*e)^13 + 5248600*a^6*b^6*tan(1/2*e)^13 + 7001200*a^5*b^7*tan(1/2*e
)^13 + 5388900*a^4*b^8*tan(1/2*e)^13 + 2265040*a^3*b^9*tan(1/2*e)^13 + 404800*a^2*b^10*tan(1/2*e)^13 + 98280*a
^8*b^4*tan(1/2*e)^11 + 641160*a^7*b^5*tan(1/2*e)^11 + 1736400*a^6*b^6*tan(1/2*e)^11 + 2499600*a^5*b^7*tan(1/2*
e)^11 + 2017800*a^4*b^8*tan(1/2*e)^11 + 866280*a^3*b^9*tan(1/2*e)^11 + 154560*a^2*b^10*tan(1/2*e)^11 + 20475*a
^8*b^4*tan(1/2*e)^9 + 152100*a^7*b^5*tan(1/2*e)^9 + 442690*a^6*b^6*tan(1/2*e)^9 + 659260*a^5*b^7*tan(1/2*e)^9
+ 535515*a^4*b^8*tan(1/2*e)^9 + 226360*a^3*b^9*tan(1/2*e)^9 + 39040*a^2*b^10*tan(1/2*e)^9 + 3276*a^8*b^4*tan(1
/2*e)^7 + 27612*a^7*b^5*tan(1/2*e)^7 + 84248*a^6*b^6*tan(1/2*e)^7 + 126392*a^5*b^7*tan(1/2*e)^7 + 100668*a^4*b
^8*tan(1/2*e)^7 + 40748*a^3*b^9*tan(1/2*e)^7 + 6560*a^2*b^10*tan(1/2*e)^7 + 378*a^8*b^4*tan(1/2*e)^5 + 3600*a^
7*b^5*tan(1/2*e)^5 + 11292*a^6*b^6*tan(1/2*e)^5 + 16728*a^5*b^7*tan(1/2*e)^5 + 12762*a^4*b^8*tan(1/2*e)^5 + 47
76*a^3*b^9*tan(1/2*e)^5 + 672*a^2*b^10*tan(1/2*e)^5 + 28*a^8*b^4*tan(1/2*e)^3 + 300*a^7*b^5*tan(1/2*e)^3 + 952
*a^6*b^6*tan(1/2*e)^3 + 1368*a^5*b^7*tan(1/2*e)^3 + 972*a^4*b^8*tan(1/2*e)^3 + 316*a^3*b^9*tan(1/2*e)^3 + 32*a
^2*b^10*tan(1/2*e)^3 + a^8*b^4*tan(1/2*e) + 12*a^7*b^5*tan(1/2*e) + 38*a^6*b^6*tan(1/2*e) + 52*a^5*b^7*tan(1/2
*e) + 33*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*ta
n(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)^42 + 518144*a^6*b^7*tan(1/2*e)^4
2 + 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)^3
8 + 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 + 1
4892086*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 + 77737
056*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)^2
8 + 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)^2
4 + 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 + 4959600
4*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 + 30
149504*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 + 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*t
an(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*ta
n(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*(3*a^8*b^4*tan(1/2*e)^58 + 16*a^7*b^5*tan(1/2*e)^58 + 34
*a^6*b^6*tan(1/2*e)^58 + 36*a^5*b^7*tan(1/2*e)^58 + 19*a^4*b^8*tan(1/2*e)^58 + 4*a^3*b^9*tan(1/2*e)^58 + 81*a^
8*b^4*tan(1/2*e)^56 + 404*a^7*b^5*tan(1/2*e)^56 + 822*a^6*b^6*tan(1/2*e)^56 + 868*a^5*b^7*tan(1/2*e)^56 + 497*
a^4*b^8*tan(1/2*e)^56 + 144*a^3*b^9*tan(1/2*e)^56 + 16*a^2*b^10*tan(1/2*e)^56 + 1050*a^8*b^4*tan(1/2*e)^54 + 4
900*a^7*b^5*tan(1/2*e)^54 + 9340*a^6*b^6*tan(1/2*e)^54 + 9360*a^5*b^7*tan(1/2*e)^54 + 5290*a^4*b^8*tan(1/2*e)^
54 + 1660*a^3*b^9*tan(1/2*e)^54 + 240*a^2*b^10*tan(1/2*e)^54 + 8694*a^8*b^4*tan(1/2*e)^52 + 37996*a^7*b^5*tan(
1/2*e)^52 + 66148*a^6*b^6*tan(1/2*e)^52 + 58512*a^5*b^7*tan(1/2*e)^52 + 28198*a^4*b^8*tan(1/2*e)^52 + 7636*a^3
*b^9*tan(1/2*e)^52 + 1104*a^2*b^10*tan(1/2*e)^52 + 51597*a^8*b^4*tan(1/2*e)^50 + 211484*a^7*b^5*tan(1/2*e)^50
+ 326046*a^6*b^6*tan(1/2*e)^50 + 221284*a^5*b^7*tan(1/2*e)^50 + 48461*a^4*b^8*tan(1/2*e)^50 - 10584*a^3*b^9*ta
n(1/2*e)^50 - 3920*a^2*b^10*tan(1/2*e)^50 + 233415*a^8*b^4*tan(1/2*e)^48 + 899080*a^7*b^5*tan(1/2*e)^48 + 1180
090*a^6*b^6*tan(1/2*e)^48 + 397860*a^5*b^7*tan(1/2*e)^48 - 397385*a^4*b^8*tan(1/2*e)^48 - 362900*a^3*b^9*tan(1
/2*e)^48 - 82080*a^2*b^10*tan(1/2*e)^48 + 835380*a^8*b^4*tan(1/2*e)^46 + 3032120*a^7*b^5*tan(1/2*e)^46 + 32116
40*a^6*b^6*tan(1/2*e)^46 - 767040*a^5*b^7*tan(1/2*e)^46 - 3780460*a^4*b^8*tan(1/2*e)^46 - 2561560*a^3*b^9*tan(
1/2*e)^46 - 563040*a^2*b^10*tan(1/2*e)^46 + 2421900*a^8*b^4*tan(1/2*e)^44 + 8312200*a^7*b^5*tan(1/2*e)^44 + 65
60520*a^6*b^6*tan(1/2*e)^44 - 8441920*a^5*b^7*tan(1/2*e)^44 - 17895380*a^4*b^8*tan(1/2*e)^44 - 11252520*a^3*b^
9*tan(1/2*e)^44 - 2469280*a^2*b^10*tan(1/2*e)^44 + 5772195*a^8*b^4*tan(1/2*e)^42 + 18813080*a^7*b^5*tan(1/2*e)
^42 + 9636770*a^6*b^6*tan(1/2*e)^42 - 34139820*a^5*b^7*tan(1/2*e)^42 - 58692205*a^4*b^8*tan(1/2*e)^42 - 358501
00*a^3*b^9*tan(1/2*e)^42 - 7893600*a^2*b^10*tan(1/2*e)^42 + 11396385*a^8*b^4*tan(1/2*e)^40 + 35455420*a^7*b^5*
tan(1/2*e)^40 + 8488150*a^6*b^6*tan(1/2*e)^40 - 92673900*a^5*b^7*tan(1/2*e)^40 - 145342175*a^4*b^8*tan(1/2*e)^
40 - 87608840*a^3*b^9*tan(1/2*e)^40 - 19369680*a^2*b^10*tan(1/2*e)^40 + 18648630*a^8*b^4*tan(1/2*e)^38 + 55715
660*a^7*b^5*tan(1/2*e)^38 - 925980*a^6*b^6*tan(1/2*e)^38 - 187887920*a^5*b^7*tan(1/2*e)^38 - 280680730*a^4*b^8
*tan(1/2*e)^38 - 168088140*a^3*b^9*tan(1/2*e)^38 - 37302320*a^2*b^10*tan(1/2*e)^38 + 25053210*a^8*b^4*tan(1/2*
e)^36 + 72375940*a^7*b^5*tan(1/2*e)^36 - 17558660*a^6*b^6*tan(1/2*e)^36 - 292929840*a^5*b^7*tan(1/2*e)^36 - 42
5476310*a^4*b^8*tan(1/2*e)^36 - 253958180*a^3*b^9*tan(1/2*e)^36 - 56530320*a^2*b^10*tan(1/2*e)^36 + 26842725*a
^8*b^4*tan(1/2*e)^34 + 75557300*a^7*b^5*tan(1/2*e)^34 - 32167570*a^6*b^6*tan(1/2*e)^34 - 347388780*a^5*b^7*tan
(1/2*e)^34 - 496228795*a^4*b^8*tan(1/2*e)^34 - 295691680*a^3*b^9*tan(1/2*e)^34 - 65969520*a^2*b^10*tan(1/2*e)^
34 + 21061215*a^8*b^4*tan(1/2*e)^32 + 58243360*a^7*b^5*tan(1/2*e)^32 - 32316150*a^6*b^6*tan(1/2*e)^32 - 290473
900*a^5*b^7*tan(1/2*e)^32 - 411009425*a^4*b^8*tan(1/2*e)^32 - 244711260*a^3*b^9*tan(1/2*e)^32 - 54677440*a^2*b
^10*tan(1/2*e)^32 + 8023320*a^8*b^4*tan(1/2*e)^30 + 21989840*a^7*b^5*tan(1/2*e)^30 - 13669360*a^6*b^6*tan(1/2*
e)^30 - 114109440*a^5*b^7*tan(1/2*e)^30 - 160763560*a^4*b^8*tan(1/2*e)^30 - 95685520*a^3*b^9*tan(1/2*e)^30 - 2
1395520*a^2*b^10*tan(1/2*e)^30 - 8023320*a^8*b^4*tan(1/2*e)^28 - 21989840*a^7*b^5*tan(1/2*e)^28 + 13669360*a^6
*b^6*tan(1/2*e)^28 + 114109440*a^5*b^7*tan(1/2*e)^28 + 160763560*a^4*b^8*tan(1/2*e)^28 + 95685520*a^3*b^9*tan(
1/2*e)^28 + 21395520*a^2*b^10*tan(1/2*e)^28 - 21061215*a^8*b^4*tan(1/2*e)^26 - 58243360*a^7*b^5*tan(1/2*e)^26
+ 32316150*a^6*b^6*tan(1/2*e)^26 + 290473900*a^5*b^7*tan(1/2*e)^26 + 411009425*a^4*b^8*tan(1/2*e)^26 + 2447112
60*a^3*b^9*tan(1/2*e)^26 + 54677440*a^2*b^10*tan(1/2*e)^26 - 26842725*a^8*b^4*tan(1/2*e)^24 - 75557300*a^7*b^5
*tan(1/2*e)^24 + 32167570*a^6*b^6*tan(1/2*e)^24 + 347388780*a^5*b^7*tan(1/2*e)^24 + 496228795*a^4*b^8*tan(1/2*
e)^24 + 295691680*a^3*b^9*tan(1/2*e)^24 + 65969520*a^2*b^10*tan(1/2*e)^24 - 25053210*a^8*b^4*tan(1/2*e)^22 - 7
2375940*a^7*b^5*tan(1/2*e)^22 + 17558660*a^6*b^6*tan(1/2*e)^22 + 292929840*a^5*b^7*tan(1/2*e)^22 + 425476310*a
^4*b^8*tan(1/2*e)^22 + 253958180*a^3*b^9*tan(1/2*e)^22 + 56530320*a^2*b^10*tan(1/2*e)^22 - 18648630*a^8*b^4*ta
n(1/2*e)^20 - 55715660*a^7*b^5*tan(1/2*e)^20 + 925980*a^6*b^6*tan(1/2*e)^20 + 187887920*a^5*b^7*tan(1/2*e)^20
+ 280680730*a^4*b^8*tan(1/2*e)^20 + 168088140*a^3*b^9*tan(1/2*e)^20 + 37302320*a^2*b^10*tan(1/2*e)^20 - 113963
85*a^8*b^4*tan(1/2*e)^18 - 35455420*a^7*b^5*tan(1/2*e)^18 - 8488150*a^6*b^6*tan(1/2*e)^18 + 92673900*a^5*b^7*t
an(1/2*e)^18 + 145342175*a^4*b^8*tan(1/2*e)^18 + 87608840*a^3*b^9*tan(1/2*e)^18 + 19369680*a^2*b^10*tan(1/2*e)
^18 - 5772195*a^8*b^4*tan(1/2*e)^16 - 18813080*a^7*b^5*tan(1/2*e)^16 - 9636770*a^6*b^6*tan(1/2*e)^16 + 3413982
0*a^5*b^7*tan(1/2*e)^16 + 58692205*a^4*b^8*tan(1/2*e)^16 + 35850100*a^3*b^9*tan(1/2*e)^16 + 7893600*a^2*b^10*t
an(1/2*e)^16 - 2421900*a^8*b^4*tan(1/2*e)^14 - 8312200*a^7*b^5*tan(1/2*e)^14 - 6560520*a^6*b^6*tan(1/2*e)^14 +
8441920*a^5*b^7*tan(1/2*e)^14 + 17895380*a^4*b^8*tan(1/2*e)^14 + 11252520*a^3*b^9*tan(1/2*e)^14 + 2469280*a^2
*b^10*tan(1/2*e)^14 - 835380*a^8*b^4*tan(1/2*e)^12 - 3032120*a^7*b^5*tan(1/2*e)^12 - 3211640*a^6*b^6*tan(1/2*e
)^12 + 767040*a^5*b^7*tan(1/2*e)^12 + 3780460*a^4*b^8*tan(1/2*e)^12 + 2561560*a^3*b^9*tan(1/2*e)^12 + 563040*a
^2*b^10*tan(1/2*e)^12 - 233415*a^8*b^4*tan(1/2*e)^10 - 899080*a^7*b^5*tan(1/2*e)^10 - 1180090*a^6*b^6*tan(1/2*
e)^10 - 397860*a^5*b^7*tan(1/2*e)^10 + 397385*a^4*b^8*tan(1/2*e)^10 + 362900*a^3*b^9*tan(1/2*e)^10 + 82080*a^2
*b^10*tan(1/2*e)^10 - 51597*a^8*b^4*tan(1/2*e)^8 - 211484*a^7*b^5*tan(1/2*e)^8 - 326046*a^6*b^6*tan(1/2*e)^8 -
221284*a^5*b^7*tan(1/2*e)^8 - 48461*a^4*b^8*tan(1/2*e)^8 + 10584*a^3*b^9*tan(1/2*e)^8 + 3920*a^2*b^10*tan(1/2
*e)^8 - 8694*a^8*b^4*tan(1/2*e)^6 - 37996*a^7*b^5*tan(1/2*e)^6 - 66148*a^6*b^6*tan(1/2*e)^6 - 58512*a^5*b^7*ta
n(1/2*e)^6 - 28198*a^4*b^8*tan(1/2*e)^6 - 7636*a^3*b^9*tan(1/2*e)^6 - 1104*a^2*b^10*tan(1/2*e)^6 - 1050*a^8*b^
4*tan(1/2*e)^4 - 4900*a^7*b^5*tan(1/2*e)^4 - 9340*a^6*b^6*tan(1/2*e)^4 - 9360*a^5*b^7*tan(1/2*e)^4 - 5290*a^4*
b^8*tan(1/2*e)^4 - 1660*a^3*b^9*tan(1/2*e)^4 - 240*a^2*b^10*tan(1/2*e)^4 - 81*a^8*b^4*tan(1/2*e)^2 - 404*a^7*b
^5*tan(1/2*e)^2 - 822*a^6*b^6*tan(1/2*e)^2 - 868*a^5*b^7*tan(1/2*e)^2 - 497*a^4*b^8*tan(1/2*e)^2 - 144*a^3*b^9
*tan(1/2*e)^2 - 16*a^2*b^10*tan(1/2*e)^2 - 3*a^8*b^4 - 16*a^7*b^5 - 34*a^6*b^6 - 36*a^5*b^7 - 19*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 + 12
8*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 + 139
6*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 + 47
334*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 + 3
0514836*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 + 26231799*a^5*b^8*tan(1/2*e)^32 + 5230016*a^4*b^9*tan(1/2*e)^32 + 7726
160*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)^2
8 + 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 + 4959600
4*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*ta
n(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 + 9788450
4*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*ta
n(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 + 15
440084*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 + 138441
6*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 + 2302
30*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 + 30562
4*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 + 7
016*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 + 2
6*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 + 38*a^6*b^6*tan(1/2*e)^57 + 52*a^5*b^7*tan(1/2*e)
^57 + 33*a^4*b^8*tan(1/2*e)^57 + 8*a^3*b^9*tan(1/2*e)^57 + 28*a^8*b^4*tan(1/2*e)^55 + 300*a^7*b^5*tan(1/2*e)^5
5 + 952*a^6*b^6*tan(1/2*e)^55 + 1368*a^5*b^7*tan(1/2*e)^55 + 972*a^4*b^8*tan(1/2*e)^55 + 316*a^3*b^9*tan(1/2*e
)^55 + 32*a^2*b^10*tan(1/2*e)^55 + 378*a^8*b^4*tan(1/2*e)^53 + 3600*a^7*b^5*tan(1/2*e)^53 + 11292*a^6*b^6*tan(
1/2*e)^53 + 16728*a^5*b^7*tan(1/2*e)^53 + 12762*a^4*b^8*tan(1/2*e)^53 + 4776*a^3*b^9*tan(1/2*e)^53 + 672*a^2*b
^10*tan(1/2*e)^53 + 3276*a^8*b^4*tan(1/2*e)^51 + 27612*a^7*b^5*tan(1/2*e)^51 + 84248*a^6*b^6*tan(1/2*e)^51 + 1
26392*a^5*b^7*tan(1/2*e)^51 + 100668*a^4*b^8*tan(1/2*e)^51 + 40748*a^3*b^9*tan(1/2*e)^51 + 6560*a^2*b^10*tan(1
/2*e)^51 + 20475*a^8*b^4*tan(1/2*e)^49 + 152100*a^7*b^5*tan(1/2*e)^49 + 442690*a^6*b^6*tan(1/2*e)^49 + 659260*
a^5*b^7*tan(1/2*e)^49 + 535515*a^4*b^8*tan(1/2*e)^49 + 226360*a^3*b^9*tan(1/2*e)^49 + 39040*a^2*b^10*tan(1/2*e
)^49 + 98280*a^8*b^4*tan(1/2*e)^47 + 641160*a^7*b^5*tan(1/2*e)^47 + 1736400*a^6*b^6*tan(1/2*e)^47 + 2499600*a^
5*b^7*tan(1/2*e)^47 + 2017800*a^4*b^8*tan(1/2*e)^47 + 866280*a^3*b^9*tan(1/2*e)^47 + 154560*a^2*b^10*tan(1/2*e
)^47 + 376740*a^8*b^4*tan(1/2*e)^45 + 2152800*a^7*b^5*tan(1/2*e)^45 + 5248600*a^6*b^6*tan(1/2*e)^45 + 7001200*
a^5*b^7*tan(1/2*e)^45 + 5388900*a^4*b^8*tan(1/2*e)^45 + 2265040*a^3*b^9*tan(1/2*e)^45 + 404800*a^2*b^10*tan(1/
2*e)^45 + 1184040*a^8*b^4*tan(1/2*e)^43 + 5920200*a^7*b^5*tan(1/2*e)^43 + 12407120*a^6*b^6*tan(1/2*e)^43 + 141
07280*a^5*b^7*tan(1/2*e)^43 + 9320520*a^4*b^8*tan(1/2*e)^43 + 3450920*a^3*b^9*tan(1/2*e)^43 + 566720*a^2*b^10*
tan(1/2*e)^43 + 3108105*a^8*b^4*tan(1/2*e)^41 + 13616460*a^7*b^5*tan(1/2*e)^41 + 22899030*a^6*b^6*tan(1/2*e)^4
1 + 17593620*a^5*b^7*tan(1/2*e)^41 + 4929705*a^4*b^8*tan(1/2*e)^41 - 759000*a^3*b^9*tan(1/2*e)^41 - 485760*a^2
*b^10*tan(1/2*e)^41 + 6906900*a^8*b^4*tan(1/2*e)^39 + 26640900*a^7*b^5*tan(1/2*e)^39 + 32110760*a^6*b^6*tan(1/
2*e)^39 + 172040*a^5*b^7*tan(1/2*e)^39 - 29342940*a^4*b^8*tan(1/2*e)^39 - 22522060*a^3*b^9*tan(1/2*e)^39 - 538
3840*a^2*b^10*tan(1/2*e)^39 + 13123110*a^8*b^4*tan(1/2*e)^37 + 44993520*a^7*b^5*tan(1/2*e)^37 + 31053220*a^6*b
^6*tan(1/2*e)^37 - 63260120*a^5*b^7*tan(1/2*e)^37 - 123011130*a^4*b^8*tan(1/2*e)^37 - 78257960*a^3*b^9*tan(1/2
*e)^37 - 17689760*a^2*b^10*tan(1/2*e)^37 + 21474180*a^8*b^4*tan(1/2*e)^35 + 66467700*a^7*b^5*tan(1/2*e)^35 + 1
1903880*a^6*b^6*tan(1/2*e)^35 - 187577880*a^5*b^7*tan(1/2*e)^35 - 291592620*a^4*b^8*tan(1/2*e)^35 - 176329500*
a^3*b^9*tan(1/2*e)^35 - 39225120*a^2*b^10*tan(1/2*e)^35 + 30421755*a^8*b^4*tan(1/2*e)^33 + 86919300*a^7*b^5*ta
n(1/2*e)^33 - 23104190*a^6*b^6*tan(1/2*e)^33 - 353174660*a^5*b^7*tan(1/2*e)^33 - 508032165*a^4*b^8*tan(1/2*e)^
33 - 301023080*a^3*b^9*tan(1/2*e)^33 - 66563840*a^2*b^10*tan(1/2*e)^33 + 37442160*a^8*b^4*tan(1/2*e)^31 + 1016
28720*a^7*b^5*tan(1/2*e)^31 - 58243360*a^6*b^6*tan(1/2*e)^31 - 500417440*a^5*b^7*tan(1/2*e)^31 - 697137360*a^4
*b^8*tan(1/2*e)^31 - 409486480*a^3*b^9*tan(1/2*e)^31 - 90336640*a^2*b^10*tan(1/2*e)^31 + 40116600*a^8*b^4*tan(
1/2*e)^29 + 106977600*a^7*b^5*tan(1/2*e)^29 - 73101360*a^6*b^6*tan(1/2*e)^29 - 559849440*a^5*b^7*tan(1/2*e)^29
- 772913160*a^4*b^8*tan(1/2*e)^29 - 452871840*a^3*b^9*tan(1/2*e)^29 - 99845760*a^2*b^10*tan(1/2*e)^29 + 37442
160*a^8*b^4*tan(1/2*e)^27 + 101628720*a^7*b^5*tan(1/2*e)^27 - 58243360*a^6*b^6*tan(1/2*e)^27 - 500417440*a^5*b
^7*tan(1/2*e)^27 - 697137360*a^4*b^8*tan(1/2*e)^27 - 409486480*a^3*b^9*tan(1/2*e)^27 - 90336640*a^2*b^10*tan(1
/2*e)^27 + 30421755*a^8*b^4*tan(1/2*e)^25 + 86919300*a^7*b^5*tan(1/2*e)^25 - 23104190*a^6*b^6*tan(1/2*e)^25 -
353174660*a^5*b^7*tan(1/2*e)^25 - 508032165*a^4*b^8*tan(1/2*e)^25 - 301023080*a^3*b^9*tan(1/2*e)^25 - 66563840
*a^2*b^10*tan(1/2*e)^25 + 21474180*a^8*b^4*tan(1/2*e)^23 + 66467700*a^7*b^5*tan(1/2*e)^23 + 11903880*a^6*b^6*t
an(1/2*e)^23 - 187577880*a^5*b^7*tan(1/2*e)^23 - 291592620*a^4*b^8*tan(1/2*e)^23 - 176329500*a^3*b^9*tan(1/2*e
)^23 - 39225120*a^2*b^10*tan(1/2*e)^23 + 13123110*a^8*b^4*tan(1/2*e)^21 + 44993520*a^7*b^5*tan(1/2*e)^21 + 310
53220*a^6*b^6*tan(1/2*e)^21 - 63260120*a^5*b^7*tan(1/2*e)^21 - 123011130*a^4*b^8*tan(1/2*e)^21 - 78257960*a^3*
b^9*tan(1/2*e)^21 - 17689760*a^2*b^10*tan(1/2*e)^21 + 6906900*a^8*b^4*tan(1/2*e)^19 + 26640900*a^7*b^5*tan(1/2
*e)^19 + 32110760*a^6*b^6*tan(1/2*e)^19 + 172040*a^5*b^7*tan(1/2*e)^19 - 29342940*a^4*b^8*tan(1/2*e)^19 - 2252
2060*a^3*b^9*tan(1/2*e)^19 - 5383840*a^2*b^10*tan(1/2*e)^19 + 3108105*a^8*b^4*tan(1/2*e)^17 + 13616460*a^7*b^5
*tan(1/2*e)^17 + 22899030*a^6*b^6*tan(1/2*e)^17 + 17593620*a^5*b^7*tan(1/2*e)^17 + 4929705*a^4*b^8*tan(1/2*e)^
17 - 759000*a^3*b^9*tan(1/2*e)^17 - 485760*a^2*b^10*tan(1/2*e)^17 + 1184040*a^8*b^4*tan(1/2*e)^15 + 5920200*a^
7*b^5*tan(1/2*e)^15 + 12407120*a^6*b^6*tan(1/2*e)^15 + 14107280*a^5*b^7*tan(1/2*e)^15 + 9320520*a^4*b^8*tan(1/
2*e)^15 + 3450920*a^3*b^9*tan(1/2*e)^15 + 566720*a^2*b^10*tan(1/2*e)^15 + 376740*a^8*b^4*tan(1/2*e)^13 + 21528
00*a^7*b^5*tan(1/2*e)^13 + 5248600*a^6*b^6*tan(1/2*e)^13 + 7001200*a^5*b^7*tan(1/2*e)^13 + 5388900*a^4*b^8*tan
(1/2*e)^13 + 2265040*a^3*b^9*tan(1/2*e)^13 + 404800*a^2*b^10*tan(1/2*e)^13 + 98280*a^8*b^4*tan(1/2*e)^11 + 641
160*a^7*b^5*tan(1/2*e)^11 + 1736400*a^6*b^6*tan(1/2*e)^11 + 2499600*a^5*b^7*tan(1/2*e)^11 + 2017800*a^4*b^8*ta
n(1/2*e)^11 + 866280*a^3*b^9*tan(1/2*e)^11 + 154560*a^2*b^10*tan(1/2*e)^11 + 20475*a^8*b^4*tan(1/2*e)^9 + 1521
00*a^7*b^5*tan(1/2*e)^9 + 442690*a^6*b^6*tan(1/2*e)^9 + 659260*a^5*b^7*tan(1/2*e)^9 + 535515*a^4*b^8*tan(1/2*e
)^9 + 226360*a^3*b^9*tan(1/2*e)^9 + 39040*a^2*b^10*tan(1/2*e)^9 + 3276*a^8*b^4*tan(1/2*e)^7 + 27612*a^7*b^5*ta
n(1/2*e)^7 + 84248*a^6*b^6*tan(1/2*e)^7 + 126392*a^5*b^7*tan(1/2*e)^7 + 100668*a^4*b^8*tan(1/2*e)^7 + 40748*a^
3*b^9*tan(1/2*e)^7 + 6560*a^2*b^10*tan(1/2*e)^7 + 378*a^8*b^4*tan(1/2*e)^5 + 3600*a^7*b^5*tan(1/2*e)^5 + 11292
*a^6*b^6*tan(1/2*e)^5 + 16728*a^5*b^7*tan(1/2*e)^5 + 12762*a^4*b^8*tan(1/2*e)^5 + 4776*a^3*b^9*tan(1/2*e)^5 +
672*a^2*b^10*tan(1/2*e)^5 + 28*a^8*b^4*tan(1/2*e)^3 + 300*a^7*b^5*tan(1/2*e)^3 + 952*a^6*b^6*tan(1/2*e)^3 + 13
68*a^5*b^7*tan(1/2*e)^3 + 972*a^4*b^8*tan(1/2*e)^3 + 316*a^3*b^9*tan(1/2*e)^3 + 32*a^2*b^10*tan(1/2*e)^3 + a^8
*b^4*tan(1/2*e) + 12*a^7*b^5*tan(1/2*e) + 38*a^6*b^6*tan(1/2*e) + 52*a^5*b^7*tan(1/2*e) + 33*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*t
an(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 + 2001
6*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)^4
6 + 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 + 30562
4*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 + 70
99939*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 + 5279047
4*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*ta
n(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 + 10400600*a^9*b^4*tan(1/2*e)^26 + 5
2419024*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 + 5262
7036*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 + 610
0336*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*ta
n(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 + 1
941016*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 + 2357
96*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*t
an(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 + 27*a^8*b^4*tan(1/2*e)^56 + 120*a^7*b^5*tan(1/2*e)^56 + 210*a^6*b^
6*tan(1/2*e)^56 + 180*a^5*b^7*tan(1/2*e)^56 + 75*a^4*b^8*tan(1/2*e)^56 + 12*a^3*b^9*tan(1/2*e)^56 + 350*a^8*b^
4*tan(1/2*e)^54 + 1700*a^7*b^5*tan(1/2*e)^54 + 3332*a^6*b^6*tan(1/2*e)^54 + 3328*a^5*b^7*tan(1/2*e)^54 + 1742*
a^4*b^8*tan(1/2*e)^54 + 428*a^3*b^9*tan(1/2*e)^54 + 32*a^2*b^10*tan(1/2*e)^54 + 2898*a^8*b^4*tan(1/2*e)^52 + 1
5180*a^7*b^5*tan(1/2*e)^52 + 32476*a^6*b^6*tan(1/2*e)^52 + 36064*a^5*b^7*tan(1/2*e)^52 + 21666*a^4*b^8*tan(1/2
*e)^52 + 6532*a^3*b^9*tan(1/2*e)^52 + 736*a^2*b^10*tan(1/2*e)^52 + 17199*a^8*b^4*tan(1/2*e)^50 + 96096*a^7*b^5
*tan(1/2*e)^50 + 220458*a^6*b^6*tan(1/2*e)^50 + 264852*a^5*b^7*tan(1/2*e)^50 + 174783*a^4*b^8*tan(1/2*e)^50 +
59556*a^3*b^9*tan(1/2*e)^50 + 8064*a^2*b^10*tan(1/2*e)^50 + 77805*a^8*b^4*tan(1/2*e)^48 + 459420*a^7*b^5*tan(1
/2*e)^48 + 1115566*a^6*b^6*tan(1/2*e)^48 + 1424164*a^5*b^7*tan(1/2*e)^48 + 1006221*a^4*b^8*tan(1/2*e)^48 + 371
944*a^3*b^9*tan(1/2*e)^48 + 55936*a^2*b^10*tan(1/2*e)^48 + 278460*a^8*b^4*tan(1/2*e)^46 + 1723800*a^7*b^5*tan(
1/2*e)^46 + 4385864*a^6*b^6*tan(1/2*e)^46 + 5874656*a^5*b^7*tan(1/2*e)^46 + 4369884*a^4*b^8*tan(1/2*e)^46 + 17
11016*a^3*b^9*tan(1/2*e)^46 + 275264*a^2*b^10*tan(1/2*e)^46 + 807300*a^8*b^4*tan(1/2*e)^44 + 5202600*a^7*b^5*t
an(1/2*e)^44 + 13757496*a^6*b^6*tan(1/2*e)^44 + 19149984*a^5*b^7*tan(1/2*e)^44 + 14821476*a^4*b^8*tan(1/2*e)^4
4 + 6053784*a^3*b^9*tan(1/2*e)^44 + 1020096*a^2*b^10*tan(1/2*e)^44 + 1924065*a^8*b^4*tan(1/2*e)^42 + 12827100*
a^7*b^5*tan(1/2*e)^42 + 35014694*a^6*b^6*tan(1/2*e)^42 + 50269076*a^5*b^7*tan(1/2*e)^42 + 40129089*a^4*b^8*tan
(1/2*e)^42 + 16918616*a^3*b^9*tan(1/2*e)^42 + 2946944*a^2*b^10*tan(1/2*e)^42 + 3798795*a^8*b^4*tan(1/2*e)^40 +
26048880*a^7*b^5*tan(1/2*e)^40 + 72975826*a^6*b^6*tan(1/2*e)^40 + 107390404*a^5*b^7*tan(1/2*e)^40 + 87823131*
a^4*b^8*tan(1/2*e)^40 + 37926724*a^3*b^9*tan(1/2*e)^40 + 6768256*a^2*b^10*tan(1/2*e)^40 + 6216210*a^8*b^4*tan(
1/2*e)^38 + 43612140*a^7*b^5*tan(1/2*e)^38 + 124746204*a^6*b^6*tan(1/2*e)^38 + 187187616*a^5*b^7*tan(1/2*e)^38
+ 155963874*a^4*b^8*tan(1/2*e)^38 + 68586276*a^3*b^9*tan(1/2*e)^38 + 12459744*a^2*b^10*tan(1/2*e)^38 + 835107
0*a^8*b^4*tan(1/2*e)^36 + 59650500*a^7*b^5*tan(1/2*e)^36 + 173396356*a^6*b^6*tan(1/2*e)^36 + 264101824*a^5*b^7
*tan(1/2*e)^36 + 223166286*a^4*b^8*tan(1/2*e)^36 + 99466444*a^3*b^9*tan(1/2*e)^36 + 18305056*a^2*b^10*tan(1/2*
e)^36 + 8947575*a^8*b^4*tan(1/2*e)^34 + 64763400*a^7*b^5*tan(1/2*e)^34 + 190497914*a^6*b^6*tan(1/2*e)^34 + 293
309156*a^5*b^7*tan(1/2*e)^34 + 250360359*a^4*b^8*tan(1/2*e)^34 + 112653356*a^3*b^9*tan(1/2*e)^34 + 20920064*a^
2*b^10*tan(1/2*e)^34 + 7020405*a^8*b^4*tan(1/2*e)^32 + 51260100*a^7*b^5*tan(1/2*e)^32 + 151952766*a^6*b^6*tan(
1/2*e)^32 + 235618164*a^5*b^7*tan(1/2*e)^32 + 202432821*a^4*b^8*tan(1/2*e)^32 + 91644144*a^3*b^9*tan(1/2*e)^32
+ 17116416*a^2*b^10*tan(1/2*e)^32 + 2674440*a^8*b^4*tan(1/2*e)^30 + 19612560*a^7*b^5*tan(1/2*e)^30 + 58362224
*a^6*b^6*tan(1/2*e)^30 + 90812096*a^5*b^7*tan(1/2*e)^30 + 78271944*a^4*b^8*tan(1/2*e)^30 + 35540336*a^3*b^9*ta
n(1/2*e)^30 + 6656384*a^2*b^10*tan(1/2*e)^30 - 2674440*a^8*b^4*tan(1/2*e)^28 - 19612560*a^7*b^5*tan(1/2*e)^28
- 58362224*a^6*b^6*tan(1/2*e)^28 - 90812096*a^5*b^7*tan(1/2*e)^28 - 78271944*a^4*b^8*tan(1/2*e)^28 - 35540336*
a^3*b^9*tan(1/2*e)^28 - 6656384*a^2*b^10*tan(1/2*e)^28 - 7020405*a^8*b^4*tan(1/2*e)^26 - 51260100*a^7*b^5*tan(
1/2*e)^26 - 151952766*a^6*b^6*tan(1/2*e)^26 - 235618164*a^5*b^7*tan(1/2*e)^26 - 202432821*a^4*b^8*tan(1/2*e)^2
6 - 91644144*a^3*b^9*tan(1/2*e)^26 - 17116416*a^2*b^10*tan(1/2*e)^26 - 8947575*a^8*b^4*tan(1/2*e)^24 - 6476340
0*a^7*b^5*tan(1/2*e)^24 - 190497914*a^6*b^6*tan(1/2*e)^24 - 293309156*a^5*b^7*tan(1/2*e)^24 - 250360359*a^4*b^
8*tan(1/2*e)^24 - 112653356*a^3*b^9*tan(1/2*e)^24 - 20920064*a^2*b^10*tan(1/2*e)^24 - 8351070*a^8*b^4*tan(1/2*
e)^22 - 59650500*a^7*b^5*tan(1/2*e)^22 - 173396356*a^6*b^6*tan(1/2*e)^22 - 264101824*a^5*b^7*tan(1/2*e)^22 - 2
23166286*a^4*b^8*tan(1/2*e)^22 - 99466444*a^3*b^9*tan(1/2*e)^22 - 18305056*a^2*b^10*tan(1/2*e)^22 - 6216210*a^
8*b^4*tan(1/2*e)^20 - 43612140*a^7*b^5*tan(1/2*e)^20 - 124746204*a^6*b^6*tan(1/2*e)^20 - 187187616*a^5*b^7*tan
(1/2*e)^20 - 155963874*a^4*b^8*tan(1/2*e)^20 - 68586276*a^3*b^9*tan(1/2*e)^20 - 12459744*a^2*b^10*tan(1/2*e)^2
0 - 3798795*a^8*b^4*tan(1/2*e)^18 - 26048880*a^7*b^5*tan(1/2*e)^18 - 72975826*a^6*b^6*tan(1/2*e)^18 - 10739040
4*a^5*b^7*tan(1/2*e)^18 - 87823131*a^4*b^8*tan(1/2*e)^18 - 37926724*a^3*b^9*tan(1/2*e)^18 - 6768256*a^2*b^10*t
an(1/2*e)^18 - 1924065*a^8*b^4*tan(1/2*e)^16 - 12827100*a^7*b^5*tan(1/2*e)^16 - 35014694*a^6*b^6*tan(1/2*e)^16
- 50269076*a^5*b^7*tan(1/2*e)^16 - 40129089*a^4*b^8*tan(1/2*e)^16 - 16918616*a^3*b^9*tan(1/2*e)^16 - 2946944*
a^2*b^10*tan(1/2*e)^16 - 807300*a^8*b^4*tan(1/2*e)^14 - 5202600*a^7*b^5*tan(1/2*e)^14 - 13757496*a^6*b^6*tan(1
/2*e)^14 - 19149984*a^5*b^7*tan(1/2*e)^14 - 14821476*a^4*b^8*tan(1/2*e)^14 - 6053784*a^3*b^9*tan(1/2*e)^14 - 1
020096*a^2*b^10*tan(1/2*e)^14 - 278460*a^8*b^4*tan(1/2*e)^12 - 1723800*a^7*b^5*tan(1/2*e)^12 - 4385864*a^6*b^6
*tan(1/2*e)^12 - 5874656*a^5*b^7*tan(1/2*e)^12 - 4369884*a^4*b^8*tan(1/2*e)^12 - 1711016*a^3*b^9*tan(1/2*e)^12
- 275264*a^2*b^10*tan(1/2*e)^12 - 77805*a^8*b^4*tan(1/2*e)^10 - 459420*a^7*b^5*tan(1/2*e)^10 - 1115566*a^6*b^
6*tan(1/2*e)^10 - 1424164*a^5*b^7*tan(1/2*e)^10 - 1006221*a^4*b^8*tan(1/2*e)^10 - 371944*a^3*b^9*tan(1/2*e)^10
- 55936*a^2*b^10*tan(1/2*e)^10 - 17199*a^8*b^4*tan(1/2*e)^8 - 96096*a^7*b^5*tan(1/2*e)^8 - 220458*a^6*b^6*tan
(1/2*e)^8 - 264852*a^5*b^7*tan(1/2*e)^8 - 174783*a^4*b^8*tan(1/2*e)^8 - 59556*a^3*b^9*tan(1/2*e)^8 - 8064*a^2*
b^10*tan(1/2*e)^8 - 2898*a^8*b^4*tan(1/2*e)^6 - 15180*a^7*b^5*tan(1/2*e)^6 - 32476*a^6*b^6*tan(1/2*e)^6 - 3606
4*a^5*b^7*tan(1/2*e)^6 - 21666*a^4*b^8*tan(1/2*e)^6 - 6532*a^3*b^9*tan(1/2*e)^6 - 736*a^2*b^10*tan(1/2*e)^6 -
350*a^8*b^4*tan(1/2*e)^4 - 1700*a^7*b^5*tan(1/2*e)^4 - 3332*a^6*b^6*tan(1/2*e)^4 - 3328*a^5*b^7*tan(1/2*e)^4 -
1742*a^4*b^8*tan(1/2*e)^4 - 428*a^3*b^9*tan(1/2*e)^4 - 32*a^2*b^10*tan(1/2*e)^4 - 27*a^8*b^4*tan(1/2*e)^2 - 1
20*a^7*b^5*tan(1/2*e)^2 - 210*a^6*b^6*tan(1/2*e)^2 - 180*a^5*b^7*tan(1/2*e)^2 - 75*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*ta
n(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 + 701
6*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 + 51
8144*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 + 910
294*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 + 53
8384*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 +
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 + 9788
4504*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 + 965
7700*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 + 391062
56*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*ta
n(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 + 14
555596*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 + 14
950*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*t
an(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 + 84*a^8*b^
4*tan(1/2*e)^55 + 356*a^7*b^5*tan(1/2*e)^55 + 584*a^6*b^6*tan(1/2*e)^55 + 456*a^5*b^7*tan(1/2*e)^55 + 164*a^4*
b^8*tan(1/2*e)^55 + 20*a^3*b^9*tan(1/2*e)^55 + 1134*a^8*b^4*tan(1/2*e)^53 + 5056*a^7*b^5*tan(1/2*e)^53 + 8916*
a^6*b^6*tan(1/2*e)^53 + 7784*a^5*b^7*tan(1/2*e)^53 + 3406*a^4*b^8*tan(1/2*e)^53 + 648*a^3*b^9*tan(1/2*e)^53 +
32*a^2*b^10*tan(1/2*e)^53 + 9828*a^8*b^4*tan(1/2*e)^51 + 45812*a^7*b^5*tan(1/2*e)^51 + 85736*a^6*b^6*tan(1/2*e
)^51 + 81384*a^5*b^7*tan(1/2*e)^51 + 40436*a^4*b^8*tan(1/2*e)^51 + 9572*a^3*b^9*tan(1/2*e)^51 + 768*a^2*b^10*t
an(1/2*e)^51 + 61425*a^8*b^4*tan(1/2*e)^49 + 297700*a^7*b^5*tan(1/2*e)^49 + 585382*a^6*b^6*tan(1/2*e)^49 + 593
028*a^5*b^7*tan(1/2*e)^49 + 322417*a^4*b^8*tan(1/2*e)^49 + 87328*a^3*b^9*tan(1/2*e)^49 + 8832*a^2*b^10*tan(1/2
*e)^49 + 294840*a^8*b^4*tan(1/2*e)^47 + 1478360*a^7*b^5*tan(1/2*e)^47 + 3029808*a^6*b^6*tan(1/2*e)^47 + 323243
2*a^5*b^7*tan(1/2*e)^47 + 1879448*a^4*b^8*tan(1/2*e)^47 + 558072*a^3*b^9*tan(1/2*e)^47 + 64768*a^2*b^10*tan(1/
2*e)^47 + 1130220*a^8*b^4*tan(1/2*e)^45 + 5836480*a^7*b^5*tan(1/2*e)^45 + 12383752*a^6*b^6*tan(1/2*e)^45 + 137
74608*a^5*b^7*tan(1/2*e)^45 + 8432812*a^4*b^8*tan(1/2*e)^45 + 2675728*a^3*b^9*tan(1/2*e)^45 + 340032*a^2*b^10*
tan(1/2*e)^45 + 3552120*a^8*b^4*tan(1/2*e)^43 + 18813080*a^7*b^5*tan(1/2*e)^43 + 41091248*a^6*b^6*tan(1/2*e)^4
3 + 47276592*a^5*b^7*tan(1/2*e)^43 + 30131288*a^4*b^8*tan(1/2*e)^43 + 10045112*a^3*b^9*tan(1/2*e)^43 + 1360128
*a^2*b^10*tan(1/2*e)^43 + 9324315*a^8*b^4*tan(1/2*e)^41 + 50453260*a^7*b^5*tan(1/2*e)^41 + 112876962*a^6*b^6*t
an(1/2*e)^41 + 133461548*a^5*b^7*tan(1/2*e)^41 + 87790747*a^4*b^8*tan(1/2*e)^41 + 30384288*a^3*b^9*tan(1/2*e)^
41 + 4307072*a^2*b^10*tan(1/2*e)^41 + 20720700*a^8*b^4*tan(1/2*e)^39 + 114128300*a^7*b^5*tan(1/2*e)^39 + 26038
1528*a^6*b^6*tan(1/2*e)^39 + 314657112*a^5*b^7*tan(1/2*e)^39 + 212154668*a^4*b^8*tan(1/2*e)^39 + 75546812*a^3*
b^9*tan(1/2*e)^39 + 11075328*a^2*b^10*tan(1/2*e)^39 + 39369330*a^8*b^4*tan(1/2*e)^37 + 219968320*a^7*b^5*tan(1
/2*e)^37 + 509715052*a^6*b^6*tan(1/2*e)^37 + 626563608*a^5*b^7*tan(1/2*e)^37 + 430543762*a^4*b^8*tan(1/2*e)^37
+ 156631288*a^3*b^9*tan(1/2*e)^37 + 23535072*a^2*b^10*tan(1/2*e)^37 + 64422540*a^8*b^4*tan(1/2*e)^35 + 363924
860*a^7*b^5*tan(1/2*e)^35 + 853314168*a^6*b^6*tan(1/2*e)^35 + 1062458872*a^5*b^7*tan(1/2*e)^35 + 740402108*a^4
*b^8*tan(1/2*e)^35 + 273595212*a^3*b^9*tan(1/2*e)^35 + 41840128*a^2*b^10*tan(1/2*e)^35 + 91265265*a^8*b^4*tan(
1/2*e)^33 + 519584260*a^7*b^5*tan(1/2*e)^33 + 1228444582*a^6*b^6*tan(1/2*e)^33 + 1543241028*a^5*b^7*tan(1/2*e)
^33 + 1085919217*a^4*b^8*tan(1/2*e)^33 + 405563968*a^3*b^9*tan(1/2*e)^33 + 62760192*a^2*b^10*tan(1/2*e)^33 + 1
12326480*a^8*b^4*tan(1/2*e)^31 + 642459920*a^7*b^5*tan(1/2*e)^31 + 1526451488*a^6*b^6*tan(1/2*e)^31 + 19277363
52*a^5*b^7*tan(1/2*e)^31 + 1364202128*a^4*b^8*tan(1/2*e)^31 + 512660432*a^3*b^9*tan(1/2*e)^31 + 79876608*a^2*b
^10*tan(1/2*e)^31 + 120349800*a^8*b^4*tan(1/2*e)^29 + 689411200*a^7*b^5*tan(1/2*e)^29 + 1640679792*a^6*b^6*tan
(1/2*e)^29 + 2075603168*a^5*b^7*tan(1/2*e)^29 + 1471595752*a^4*b^8*tan(1/2*e)^29 + 554143968*a^3*b^9*tan(1/2*e
)^29 + 86532992*a^2*b^10*tan(1/2*e)^29 + 112326480*a^8*b^4*tan(1/2*e)^27 + 642459920*a^7*b^5*tan(1/2*e)^27 + 1
526451488*a^6*b^6*tan(1/2*e)^27 + 1927736352*a^5*b^7*tan(1/2*e)^27 + 1364202128*a^4*b^8*tan(1/2*e)^27 + 512660
432*a^3*b^9*tan(1/2*e)^27 + 79876608*a^2*b^10*tan(1/2*e)^27 + 91265265*a^8*b^4*tan(1/2*e)^25 + 519584260*a^7*b
^5*tan(1/2*e)^25 + 1228444582*a^6*b^6*tan(1/2*e)^25 + 1543241028*a^5*b^7*tan(1/2*e)^25 + 1085919217*a^4*b^8*ta
n(1/2*e)^25 + 405563968*a^3*b^9*tan(1/2*e)^25 + 62760192*a^2*b^10*tan(1/2*e)^25 + 64422540*a^8*b^4*tan(1/2*e)^
23 + 363924860*a^7*b^5*tan(1/2*e)^23 + 853314168*a^6*b^6*tan(1/2*e)^23 + 1062458872*a^5*b^7*tan(1/2*e)^23 + 74
0402108*a^4*b^8*tan(1/2*e)^23 + 273595212*a^3*b^9*tan(1/2*e)^23 + 41840128*a^2*b^10*tan(1/2*e)^23 + 39369330*a
^8*b^4*tan(1/2*e)^21 + 219968320*a^7*b^5*tan(1/2*e)^21 + 509715052*a^6*b^6*tan(1/2*e)^21 + 626563608*a^5*b^7*t
an(1/2*e)^21 + 430543762*a^4*b^8*tan(1/2*e)^21 + 156631288*a^3*b^9*tan(1/2*e)^21 + 23535072*a^2*b^10*tan(1/2*e
)^21 + 20720700*a^8*b^4*tan(1/2*e)^19 + 114128300*a^7*b^5*tan(1/2*e)^19 + 260381528*a^6*b^6*tan(1/2*e)^19 + 31
4657112*a^5*b^7*tan(1/2*e)^19 + 212154668*a^4*b^8*tan(1/2*e)^19 + 75546812*a^3*b^9*tan(1/2*e)^19 + 11075328*a^
2*b^10*tan(1/2*e)^19 + 9324315*a^8*b^4*tan(1/2*e)^17 + 50453260*a^7*b^5*tan(1/2*e)^17 + 112876962*a^6*b^6*tan(
1/2*e)^17 + 133461548*a^5*b^7*tan(1/2*e)^17 + 87790747*a^4*b^8*tan(1/2*e)^17 + 30384288*a^3*b^9*tan(1/2*e)^17
+ 4307072*a^2*b^10*tan(1/2*e)^17 + 3552120*a^8*b^4*tan(1/2*e)^15 + 18813080*a^7*b^5*tan(1/2*e)^15 + 41091248*a
^6*b^6*tan(1/2*e)^15 + 47276592*a^5*b^7*tan(1/2*e)^15 + 30131288*a^4*b^8*tan(1/2*e)^15 + 10045112*a^3*b^9*tan(
1/2*e)^15 + 1360128*a^2*b^10*tan(1/2*e)^15 + 1130220*a^8*b^4*tan(1/2*e)^13 + 5836480*a^7*b^5*tan(1/2*e)^13 + 1
2383752*a^6*b^6*tan(1/2*e)^13 + 13774608*a^5*b^7*tan(1/2*e)^13 + 8432812*a^4*b^8*tan(1/2*e)^13 + 2675728*a^3*b
^9*tan(1/2*e)^13 + 340032*a^2*b^10*tan(1/2*e)^13 + 294840*a^8*b^4*tan(1/2*e)^11 + 1478360*a^7*b^5*tan(1/2*e)^1
1 + 3029808*a^6*b^6*tan(1/2*e)^11 + 3232432*a^5*b^7*tan(1/2*e)^11 + 1879448*a^4*b^8*tan(1/2*e)^11 + 558072*a^3
*b^9*tan(1/2*e)^11 + 64768*a^2*b^10*tan(1/2*e)^11 + 61425*a^8*b^4*tan(1/2*e)^9 + 297700*a^7*b^5*tan(1/2*e)^9 +
585382*a^6*b^6*tan(1/2*e)^9 + 593028*a^5*b^7*tan(1/2*e)^9 + 322417*a^4*b^8*tan(1/2*e)^9 + 87328*a^3*b^9*tan(1
/2*e)^9 + 8832*a^2*b^10*tan(1/2*e)^9 + 9828*a^8*b^4*tan(1/2*e)^7 + 45812*a^7*b^5*tan(1/2*e)^7 + 85736*a^6*b^6*
tan(1/2*e)^7 + 81384*a^5*b^7*tan(1/2*e)^7 + 40436*a^4*b^8*tan(1/2*e)^7 + 9572*a^3*b^9*tan(1/2*e)^7 + 768*a^2*b
^10*tan(1/2*e)^7 + 1134*a^8*b^4*tan(1/2*e)^5 + 5056*a^7*b^5*tan(1/2*e)^5 + 8916*a^6*b^6*tan(1/2*e)^5 + 7784*a^
5*b^7*tan(1/2*e)^5 + 3406*a^4*b^8*tan(1/2*e)^5 + 648*a^3*b^9*tan(1/2*e)^5 + 32*a^2*b^10*tan(1/2*e)^5 + 84*a^8*
b^4*tan(1/2*e)^3 + 356*a^7*b^5*tan(1/2*e)^3 + 584*a^6*b^6*tan(1/2*e)^3 + 456*a^5*b^7*tan(1/2*e)^3 + 164*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 + 1
104*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 + 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 + 148
92086*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 + 7773705
6*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*ta
n(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*ta
n(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 + 30514836*a^7*b^6*tan(1/2*e)^18 + 3014
9504*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)^1
6 + 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*t
an(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*t
an(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 = 19.36 (sec) , antiderivative size = 164, normalized size of antiderivative = 2.52 \[ \int \frac {\cos (e+f x)}{\left (a+b \sin ^2(e+f x)\right )^{5/2}} \, dx=\frac {4\,{\mathrm {e}}^{e\,1{}\mathrm {i}+f\,x\,1{}\mathrm {i}}\,\left ({\mathrm {e}}^{e\,2{}\mathrm {i}+f\,x\,2{}\mathrm {i}}-1\right )\,\sqrt {a+b\,{\left (\frac {{\mathrm {e}}^{-e\,1{}\mathrm {i}-f\,x\,1{}\mathrm {i}}\,1{}\mathrm {i}}{2}-\frac {{\mathrm {e}}^{e\,1{}\mathrm {i}+f\,x\,1{}\mathrm {i}}\,1{}\mathrm {i}}{2}\right )}^2}\,\left (b\,1{}\mathrm {i}-a\,{\mathrm {e}}^{e\,2{}\mathrm {i}+f\,x\,2{}\mathrm {i}}\,6{}\mathrm {i}-b\,{\mathrm {e}}^{e\,2{}\mathrm {i}+f\,x\,2{}\mathrm {i}}\,2{}\mathrm {i}+b\,{\mathrm {e}}^{e\,4{}\mathrm {i}+f\,x\,4{}\mathrm {i}}\,1{}\mathrm {i}\right )}{3\,a^2\,f\,{\left (b-4\,a\,{\mathrm {e}}^{e\,2{}\mathrm {i}+f\,x\,2{}\mathrm {i}}-2\,b\,{\mathrm {e}}^{e\,2{}\mathrm {i}+f\,x\,2{}\mathrm {i}}+b\,{\mathrm {e}}^{e\,4{}\mathrm {i}+f\,x\,4{}\mathrm {i}}\right )}^2} \]

[In]

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

[Out]

(4*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)*(b*1i - a*exp(e*2i + f*x*2i)*6i - b*exp(e*2i + f*x*2i)*2i + b*exp(e*4i + f*x*4i)*1i))/(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)