\(\int \frac {\sin (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx\) [79]
Optimal result
Integrand size = 20, antiderivative size = 79 \[
\int \frac {\sin (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx=\frac {\sin (a+b x)}{5 b \sin ^{\frac {5}{2}}(2 a+2 b x)}-\frac {4 \cos (a+b x)}{15 b \sin ^{\frac {3}{2}}(2 a+2 b x)}+\frac {8 \sin (a+b x)}{15 b \sqrt {\sin (2 a+2 b x)}}
\]
[Out]
1/5*sin(b*x+a)/b/sin(2*b*x+2*a)^(5/2)-4/15*cos(b*x+a)/b/sin(2*b*x+2*a)^(3/2)+8/15*sin(b*x+a)/b/sin(2*b*x+2*a)^
(1/2)
Rubi [A] (verified)
Time = 0.08 (sec) , antiderivative size = 79, normalized size of antiderivative = 1.00, number of
steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {4389, 4388, 4377}
\[
\int \frac {\sin (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx=\frac {\sin (a+b x)}{5 b \sin ^{\frac {5}{2}}(2 a+2 b x)}+\frac {8 \sin (a+b x)}{15 b \sqrt {\sin (2 a+2 b x)}}-\frac {4 \cos (a+b x)}{15 b \sin ^{\frac {3}{2}}(2 a+2 b x)}
\]
[In]
Int[Sin[a + b*x]/Sin[2*a + 2*b*x]^(7/2),x]
[Out]
Sin[a + b*x]/(5*b*Sin[2*a + 2*b*x]^(5/2)) - (4*Cos[a + b*x])/(15*b*Sin[2*a + 2*b*x]^(3/2)) + (8*Sin[a + b*x])/
(15*b*Sqrt[Sin[2*a + 2*b*x]])
Rule 4377
Int[((e_.)*sin[(a_.) + (b_.)*(x_)])^(m_.)*((g_.)*sin[(c_.) + (d_.)*(x_)])^(p_), x_Symbol] :> Simp[(e*Sin[a + b
*x])^m*((g*Sin[c + d*x])^(p + 1)/(b*g*m)), x] /; FreeQ[{a, b, c, d, e, g, m, p}, x] && EqQ[b*c - a*d, 0] && Eq
Q[d/b, 2] && !IntegerQ[p] && EqQ[m + 2*p + 2, 0]
Rule 4388
Int[cos[(a_.) + (b_.)*(x_)]*((g_.)*sin[(c_.) + (d_.)*(x_)])^(p_), x_Symbol] :> Simp[Cos[a + b*x]*((g*Sin[c + d
*x])^(p + 1)/(2*b*g*(p + 1))), x] + Dist[(2*p + 3)/(2*g*(p + 1)), Int[Sin[a + b*x]*(g*Sin[c + d*x])^(p + 1), x
], x] /; FreeQ[{a, b, c, d, g}, x] && EqQ[b*c - a*d, 0] && EqQ[d/b, 2] && !IntegerQ[p] && LtQ[p, -1] && Integ
erQ[2*p]
Rule 4389
Int[sin[(a_.) + (b_.)*(x_)]*((g_.)*sin[(c_.) + (d_.)*(x_)])^(p_), x_Symbol] :> Simp[(-Sin[a + b*x])*((g*Sin[c
+ d*x])^(p + 1)/(2*b*g*(p + 1))), x] + Dist[(2*p + 3)/(2*g*(p + 1)), Int[Cos[a + b*x]*(g*Sin[c + d*x])^(p + 1)
, x], x] /; FreeQ[{a, b, c, d, g}, x] && EqQ[b*c - a*d, 0] && EqQ[d/b, 2] && !IntegerQ[p] && LtQ[p, -1] && In
tegerQ[2*p]
Rubi steps \begin{align*}
\text {integral}& = \frac {\sin (a+b x)}{5 b \sin ^{\frac {5}{2}}(2 a+2 b x)}+\frac {4}{5} \int \frac {\cos (a+b x)}{\sin ^{\frac {5}{2}}(2 a+2 b x)} \, dx \\ & = \frac {\sin (a+b x)}{5 b \sin ^{\frac {5}{2}}(2 a+2 b x)}-\frac {4 \cos (a+b x)}{15 b \sin ^{\frac {3}{2}}(2 a+2 b x)}+\frac {8}{15} \int \frac {\sin (a+b x)}{\sin ^{\frac {3}{2}}(2 a+2 b x)} \, dx \\ & = \frac {\sin (a+b x)}{5 b \sin ^{\frac {5}{2}}(2 a+2 b x)}-\frac {4 \cos (a+b x)}{15 b \sin ^{\frac {3}{2}}(2 a+2 b x)}+\frac {8 \sin (a+b x)}{15 b \sqrt {\sin (2 a+2 b x)}} \\
\end{align*}
Mathematica [A] (verified)
Time = 0.44 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.66
\[
\int \frac {\sin (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx=\frac {\left (-5 \cot (a+b x) \csc (a+b x)+3 \sec (a+b x) \left (9+\sec ^2(a+b x)\right )\right ) \sqrt {\sin (2 (a+b x))}}{120 b}
\]
[In]
Integrate[Sin[a + b*x]/Sin[2*a + 2*b*x]^(7/2),x]
[Out]
((-5*Cot[a + b*x]*Csc[a + b*x] + 3*Sec[a + b*x]*(9 + Sec[a + b*x]^2))*Sqrt[Sin[2*(a + b*x)]])/(120*b)
Maple [C] (verified)
Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 247.66 (sec) , antiderivative size = 308, normalized size of antiderivative =
3.90
| | |
| method | result | size |
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| default |
\(-\frac {\sqrt {-\frac {\tan \left (\frac {a}{2}+\frac {x b}{2}\right )}{\tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{2}-1}}\, \left (\tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{2}-1\right ) \left (5 \sqrt {\tan \left (\frac {a}{2}+\frac {x b}{2}\right )+1}\, \sqrt {-2 \tan \left (\frac {a}{2}+\frac {x b}{2}\right )+2}\, \sqrt {-\tan \left (\frac {a}{2}+\frac {x b}{2}\right )}\, \operatorname {EllipticF}\left (\sqrt {\tan \left (\frac {a}{2}+\frac {x b}{2}\right )+1}, \frac {\sqrt {2}}{2}\right ) \tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{3}-\tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{6}+5 \sqrt {\tan \left (\frac {a}{2}+\frac {x b}{2}\right )+1}\, \sqrt {-2 \tan \left (\frac {a}{2}+\frac {x b}{2}\right )+2}\, \sqrt {-\tan \left (\frac {a}{2}+\frac {x b}{2}\right )}\, \operatorname {EllipticF}\left (\sqrt {\tan \left (\frac {a}{2}+\frac {x b}{2}\right )+1}, \frac {\sqrt {2}}{2}\right ) \tan \left (\frac {a}{2}+\frac {x b}{2}\right )-7 \tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{4}+7 \tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{2}+1\right )}{48 b \tan \left (\frac {a}{2}+\frac {x b}{2}\right ) \sqrt {\tan \left (\frac {a}{2}+\frac {x b}{2}\right ) \left (\tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{2}-1\right )}\, \sqrt {\tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{3}-\tan \left (\frac {a}{2}+\frac {x b}{2}\right )}\, \left (1+\tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{2}\right )}\) |
\(308\) |
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[In]
int(sin(b*x+a)/sin(2*b*x+2*a)^(7/2),x,method=_RETURNVERBOSE)
[Out]
-1/48/b*(-tan(1/2*a+1/2*x*b)/(tan(1/2*a+1/2*x*b)^2-1))^(1/2)*(tan(1/2*a+1/2*x*b)^2-1)/tan(1/2*a+1/2*x*b)*(5*(t
an(1/2*a+1/2*x*b)+1)^(1/2)*(-2*tan(1/2*a+1/2*x*b)+2)^(1/2)*(-tan(1/2*a+1/2*x*b))^(1/2)*EllipticF((tan(1/2*a+1/
2*x*b)+1)^(1/2),1/2*2^(1/2))*tan(1/2*a+1/2*x*b)^3-tan(1/2*a+1/2*x*b)^6+5*(tan(1/2*a+1/2*x*b)+1)^(1/2)*(-2*tan(
1/2*a+1/2*x*b)+2)^(1/2)*(-tan(1/2*a+1/2*x*b))^(1/2)*EllipticF((tan(1/2*a+1/2*x*b)+1)^(1/2),1/2*2^(1/2))*tan(1/
2*a+1/2*x*b)-7*tan(1/2*a+1/2*x*b)^4+7*tan(1/2*a+1/2*x*b)^2+1)/(tan(1/2*a+1/2*x*b)*(tan(1/2*a+1/2*x*b)^2-1))^(1
/2)/(tan(1/2*a+1/2*x*b)^3-tan(1/2*a+1/2*x*b))^(1/2)/(1+tan(1/2*a+1/2*x*b)^2)
Fricas [A] (verification not implemented)
none
Time = 0.26 (sec) , antiderivative size = 88, normalized size of antiderivative = 1.11
\[
\int \frac {\sin (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx=\frac {32 \, \cos \left (b x + a\right )^{5} - 32 \, \cos \left (b x + a\right )^{3} + \sqrt {2} {\left (32 \, \cos \left (b x + a\right )^{4} - 24 \, \cos \left (b x + a\right )^{2} - 3\right )} \sqrt {\cos \left (b x + a\right ) \sin \left (b x + a\right )}}{120 \, {\left (b \cos \left (b x + a\right )^{5} - b \cos \left (b x + a\right )^{3}\right )}}
\]
[In]
integrate(sin(b*x+a)/sin(2*b*x+2*a)^(7/2),x, algorithm="fricas")
[Out]
1/120*(32*cos(b*x + a)^5 - 32*cos(b*x + a)^3 + sqrt(2)*(32*cos(b*x + a)^4 - 24*cos(b*x + a)^2 - 3)*sqrt(cos(b*
x + a)*sin(b*x + a)))/(b*cos(b*x + a)^5 - b*cos(b*x + a)^3)
Sympy [F(-1)]
Timed out. \[
\int \frac {\sin (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx=\text {Timed out}
\]
[In]
integrate(sin(b*x+a)/sin(2*b*x+2*a)**(7/2),x)
[Out]
Timed out
Maxima [F]
\[
\int \frac {\sin (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx=\int { \frac {\sin \left (b x + a\right )}{\sin \left (2 \, b x + 2 \, a\right )^{\frac {7}{2}}} \,d x }
\]
[In]
integrate(sin(b*x+a)/sin(2*b*x+2*a)^(7/2),x, algorithm="maxima")
[Out]
integrate(sin(b*x + a)/sin(2*b*x + 2*a)^(7/2), x)
Giac [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 18022 vs. \(2 (67) = 134\).
Time = 181.63 (sec) , antiderivative size = 18022, normalized size of antiderivative = 228.13
\[
\int \frac {\sin (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx=\text {Too large to display}
\]
[In]
integrate(sin(b*x+a)/sin(2*b*x+2*a)^(7/2),x, algorithm="giac")
[Out]
1/480*sqrt(2)*sqrt(-tan(1/2*b*x)^4*tan(1/2*a)^3 - tan(1/2*b*x)^3*tan(1/2*a)^4 + tan(1/2*b*x)^4*tan(1/2*a) + 6*
tan(1/2*b*x)^3*tan(1/2*a)^2 + 6*tan(1/2*b*x)^2*tan(1/2*a)^3 + tan(1/2*b*x)*tan(1/2*a)^4 - tan(1/2*b*x)^3 - 6*t
an(1/2*b*x)^2*tan(1/2*a) - 6*tan(1/2*b*x)*tan(1/2*a)^2 - tan(1/2*a)^3 + tan(1/2*b*x) + tan(1/2*a))*((((((((((2
*(sqrt(2)*tan(1/2*a)^87 - 92*sqrt(2)*tan(1/2*a)^85 - 3213*sqrt(2)*tan(1/2*a)^83 - 48008*sqrt(2)*tan(1/2*a)^81
- 443462*sqrt(2)*tan(1/2*a)^79 - 2875040*sqrt(2)*tan(1/2*a)^77 - 13907802*sqrt(2)*tan(1/2*a)^75 - 51781432*sqr
t(2)*tan(1/2*a)^73 - 149943911*sqrt(2)*tan(1/2*a)^71 - 333456564*sqrt(2)*tan(1/2*a)^69 - 536442973*sqrt(2)*tan
(1/2*a)^67 - 482080288*sqrt(2)*tan(1/2*a)^65 + 316221080*sqrt(2)*tan(1/2*a)^63 + 2190937152*sqrt(2)*tan(1/2*a)
^61 + 4607763368*sqrt(2)*tan(1/2*a)^59 + 5742984608*sqrt(2)*tan(1/2*a)^57 + 3316624962*sqrt(2)*tan(1/2*a)^55 -
3241815576*sqrt(2)*tan(1/2*a)^53 - 11030972730*sqrt(2)*tan(1/2*a)^51 - 14712027120*sqrt(2)*tan(1/2*a)^49 - 10
524179460*sqrt(2)*tan(1/2*a)^47 + 10524179460*sqrt(2)*tan(1/2*a)^43 + 14712027120*sqrt(2)*tan(1/2*a)^41 + 1103
0972730*sqrt(2)*tan(1/2*a)^39 + 3241815576*sqrt(2)*tan(1/2*a)^37 - 3316624962*sqrt(2)*tan(1/2*a)^35 - 57429846
08*sqrt(2)*tan(1/2*a)^33 - 4607763368*sqrt(2)*tan(1/2*a)^31 - 2190937152*sqrt(2)*tan(1/2*a)^29 - 316221080*sqr
t(2)*tan(1/2*a)^27 + 482080288*sqrt(2)*tan(1/2*a)^25 + 536442973*sqrt(2)*tan(1/2*a)^23 + 333456564*sqrt(2)*tan
(1/2*a)^21 + 149943911*sqrt(2)*tan(1/2*a)^19 + 51781432*sqrt(2)*tan(1/2*a)^17 + 13907802*sqrt(2)*tan(1/2*a)^15
+ 2875040*sqrt(2)*tan(1/2*a)^13 + 443462*sqrt(2)*tan(1/2*a)^11 + 48008*sqrt(2)*tan(1/2*a)^9 + 3213*sqrt(2)*ta
n(1/2*a)^7 + 92*sqrt(2)*tan(1/2*a)^5 - sqrt(2)*tan(1/2*a)^3)*tan(1/2*b*x)/(tan(1/2*a)^78 + 34*tan(1/2*a)^76 +
559*tan(1/2*a)^74 + 5916*tan(1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^66 +
4829088*tan(1/2*a)^64 + 15512772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574864*t
an(1/2*a)^56 + 304253964*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2
*a)^48 - 31635810*tan(1/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a)^40
- 811985790*tan(1/2*a)^38 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 42639
5700*tan(1/2*a)^30 + 408239496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*ta
n(1/2*a)^22 + 41970280*tan(1/2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a)^14
+ 266322*tan(1/2*a)^12 + 45255*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + tan(1/
2*a)^2) + 5*(sqrt(2)*tan(1/2*a)^88 - 97*sqrt(2)*tan(1/2*a)^86 - 2757*sqrt(2)*tan(1/2*a)^84 - 31579*sqrt(2)*tan
(1/2*a)^82 - 190206*sqrt(2)*tan(1/2*a)^80 - 452482*sqrt(2)*tan(1/2*a)^78 + 2446494*sqrt(2)*tan(1/2*a)^76 + 312
36834*sqrt(2)*tan(1/2*a)^74 + 178073713*sqrt(2)*tan(1/2*a)^72 + 692499183*sqrt(2)*tan(1/2*a)^70 + 2006851683*s
qrt(2)*tan(1/2*a)^68 + 4409972669*sqrt(2)*tan(1/2*a)^66 + 7082232504*sqrt(2)*tan(1/2*a)^64 + 6893762888*sqrt(2
)*tan(1/2*a)^62 - 1327875576*sqrt(2)*tan(1/2*a)^60 - 21040534024*sqrt(2)*tan(1/2*a)^58 - 47574053342*sqrt(2)*t
an(1/2*a)^56 - 64972634082*sqrt(2)*tan(1/2*a)^54 - 53236088394*sqrt(2)*tan(1/2*a)^52 - 5004094710*sqrt(2)*tan(
1/2*a)^50 + 61712915820*sqrt(2)*tan(1/2*a)^48 + 110145965460*sqrt(2)*tan(1/2*a)^46 + 110145965460*sqrt(2)*tan(
1/2*a)^44 + 61712915820*sqrt(2)*tan(1/2*a)^42 - 5004094710*sqrt(2)*tan(1/2*a)^40 - 53236088394*sqrt(2)*tan(1/2
*a)^38 - 64972634082*sqrt(2)*tan(1/2*a)^36 - 47574053342*sqrt(2)*tan(1/2*a)^34 - 21040534024*sqrt(2)*tan(1/2*a
)^32 - 1327875576*sqrt(2)*tan(1/2*a)^30 + 6893762888*sqrt(2)*tan(1/2*a)^28 + 7082232504*sqrt(2)*tan(1/2*a)^26
+ 4409972669*sqrt(2)*tan(1/2*a)^24 + 2006851683*sqrt(2)*tan(1/2*a)^22 + 692499183*sqrt(2)*tan(1/2*a)^20 + 1780
73713*sqrt(2)*tan(1/2*a)^18 + 31236834*sqrt(2)*tan(1/2*a)^16 + 2446494*sqrt(2)*tan(1/2*a)^14 - 452482*sqrt(2)*
tan(1/2*a)^12 - 190206*sqrt(2)*tan(1/2*a)^10 - 31579*sqrt(2)*tan(1/2*a)^8 - 2757*sqrt(2)*tan(1/2*a)^6 - 97*sqr
t(2)*tan(1/2*a)^4 + sqrt(2)*tan(1/2*a)^2)/(tan(1/2*a)^78 + 34*tan(1/2*a)^76 + 559*tan(1/2*a)^74 + 5916*tan(1/2
*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^66 + 4829088*tan(1/2*a)^64 + 15512772
*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574864*tan(1/2*a)^56 + 304253964*tan(1/2
*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*a)^48 - 31635810*tan(1/2*a)^46
- 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a)^40 - 811985790*tan(1/2*a)^38 - 4503
45060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426395700*tan(1/2*a)^30 + 408239496*t
an(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*tan(1/2*a)^22 + 41970280*tan(1/2*a
)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a)^14 + 266322*tan(1/2*a)^12 + 45255*t
an(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + tan(1/2*a)^2))*tan(1/2*b*x) - 30*(19*s
qrt(2)*tan(1/2*a)^87 + 300*sqrt(2)*tan(1/2*a)^85 + 393*sqrt(2)*tan(1/2*a)^83 - 31512*sqrt(2)*tan(1/2*a)^81 - 4
18098*sqrt(2)*tan(1/2*a)^79 - 2934240*sqrt(2)*tan(1/2*a)^77 - 13355950*sqrt(2)*tan(1/2*a)^75 - 39534888*sqrt(2
)*tan(1/2*a)^73 - 56342949*sqrt(2)*tan(1/2*a)^71 + 123215524*sqrt(2)*tan(1/2*a)^69 + 1097715993*sqrt(2)*tan(1/
2*a)^67 + 4042423200*sqrt(2)*tan(1/2*a)^65 + 10195869000*sqrt(2)*tan(1/2*a)^63 + 19092105408*sqrt(2)*tan(1/2*a
)^61 + 26200319352*sqrt(2)*tan(1/2*a)^59 + 22729855712*sqrt(2)*tan(1/2*a)^57 + 667102950*sqrt(2)*tan(1/2*a)^55
- 38119807944*sqrt(2)*tan(1/2*a)^53 - 76473192270*sqrt(2)*tan(1/2*a)^51 - 88969283280*sqrt(2)*tan(1/2*a)^49 -
60215972940*sqrt(2)*tan(1/2*a)^47 + 60215972940*sqrt(2)*tan(1/2*a)^43 + 88969283280*sqrt(2)*tan(1/2*a)^41 + 7
6473192270*sqrt(2)*tan(1/2*a)^39 + 38119807944*sqrt(2)*tan(1/2*a)^37 - 667102950*sqrt(2)*tan(1/2*a)^35 - 22729
855712*sqrt(2)*tan(1/2*a)^33 - 26200319352*sqrt(2)*tan(1/2*a)^31 - 19092105408*sqrt(2)*tan(1/2*a)^29 - 1019586
9000*sqrt(2)*tan(1/2*a)^27 - 4042423200*sqrt(2)*tan(1/2*a)^25 - 1097715993*sqrt(2)*tan(1/2*a)^23 - 123215524*s
qrt(2)*tan(1/2*a)^21 + 56342949*sqrt(2)*tan(1/2*a)^19 + 39534888*sqrt(2)*tan(1/2*a)^17 + 13355950*sqrt(2)*tan(
1/2*a)^15 + 2934240*sqrt(2)*tan(1/2*a)^13 + 418098*sqrt(2)*tan(1/2*a)^11 + 31512*sqrt(2)*tan(1/2*a)^9 - 393*sq
rt(2)*tan(1/2*a)^7 - 300*sqrt(2)*tan(1/2*a)^5 - 19*sqrt(2)*tan(1/2*a)^3)/(tan(1/2*a)^78 + 34*tan(1/2*a)^76 + 5
59*tan(1/2*a)^74 + 5916*tan(1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^66 + 4
829088*tan(1/2*a)^64 + 15512772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574864*ta
n(1/2*a)^56 + 304253964*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*
a)^48 - 31635810*tan(1/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a)^40 -
811985790*tan(1/2*a)^38 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426395
700*tan(1/2*a)^30 + 408239496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*tan
(1/2*a)^22 + 41970280*tan(1/2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a)^14 +
266322*tan(1/2*a)^12 + 45255*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + tan(1/2
*a)^2))*tan(1/2*b*x) - 20*(7*sqrt(2)*tan(1/2*a)^88 - 167*sqrt(2)*tan(1/2*a)^86 - 6499*sqrt(2)*tan(1/2*a)^84 -
79741*sqrt(2)*tan(1/2*a)^82 - 493810*sqrt(2)*tan(1/2*a)^80 - 1198222*sqrt(2)*tan(1/2*a)^78 + 6282322*sqrt(2)*t
an(1/2*a)^76 + 80477230*sqrt(2)*tan(1/2*a)^74 + 452737815*sqrt(2)*tan(1/2*a)^72 + 1715629705*sqrt(2)*tan(1/2*a
)^70 + 4748442805*sqrt(2)*tan(1/2*a)^68 + 9550300715*sqrt(2)*tan(1/2*a)^66 + 12322646792*sqrt(2)*tan(1/2*a)^64
+ 2388418808*sqrt(2)*tan(1/2*a)^62 - 35649378760*sqrt(2)*tan(1/2*a)^60 - 108847849016*sqrt(2)*tan(1/2*a)^58 -
195926195474*sqrt(2)*tan(1/2*a)^56 - 239921144622*sqrt(2)*tan(1/2*a)^54 - 175285727238*sqrt(2)*tan(1/2*a)^52
+ 16173774150*sqrt(2)*tan(1/2*a)^50 + 265568681460*sqrt(2)*tan(1/2*a)^48 + 442624681740*sqrt(2)*tan(1/2*a)^46
+ 442624681740*sqrt(2)*tan(1/2*a)^44 + 265568681460*sqrt(2)*tan(1/2*a)^42 + 16173774150*sqrt(2)*tan(1/2*a)^40
- 175285727238*sqrt(2)*tan(1/2*a)^38 - 239921144622*sqrt(2)*tan(1/2*a)^36 - 195926195474*sqrt(2)*tan(1/2*a)^34
- 108847849016*sqrt(2)*tan(1/2*a)^32 - 35649378760*sqrt(2)*tan(1/2*a)^30 + 2388418808*sqrt(2)*tan(1/2*a)^28 +
12322646792*sqrt(2)*tan(1/2*a)^26 + 9550300715*sqrt(2)*tan(1/2*a)^24 + 4748442805*sqrt(2)*tan(1/2*a)^22 + 171
5629705*sqrt(2)*tan(1/2*a)^20 + 452737815*sqrt(2)*tan(1/2*a)^18 + 80477230*sqrt(2)*tan(1/2*a)^16 + 6282322*sqr
t(2)*tan(1/2*a)^14 - 1198222*sqrt(2)*tan(1/2*a)^12 - 493810*sqrt(2)*tan(1/2*a)^10 - 79741*sqrt(2)*tan(1/2*a)^8
- 6499*sqrt(2)*tan(1/2*a)^6 - 167*sqrt(2)*tan(1/2*a)^4 + 7*sqrt(2)*tan(1/2*a)^2)/(tan(1/2*a)^78 + 34*tan(1/2*
a)^76 + 559*tan(1/2*a)^74 + 5916*tan(1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*
a)^66 + 4829088*tan(1/2*a)^64 + 15512772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186
574864*tan(1/2*a)^56 + 304253964*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760
*tan(1/2*a)^48 - 31635810*tan(1/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/
2*a)^40 - 811985790*tan(1/2*a)^38 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32
+ 426395700*tan(1/2*a)^30 + 408239496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 961
60636*tan(1/2*a)^22 + 41970280*tan(1/2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/
2*a)^14 + 266322*tan(1/2*a)^12 + 45255*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4
+ tan(1/2*a)^2))*tan(1/2*b*x) + 20*(125*sqrt(2)*tan(1/2*a)^87 + 1812*sqrt(2)*tan(1/2*a)^85 - 2265*sqrt(2)*tan(
1/2*a)^83 - 276840*sqrt(2)*tan(1/2*a)^81 - 3382830*sqrt(2)*tan(1/2*a)^79 - 23385120*sqrt(2)*tan(1/2*a)^77 - 10
7675378*sqrt(2)*tan(1/2*a)^75 - 334648920*sqrt(2)*tan(1/2*a)^73 - 591145035*sqrt(2)*tan(1/2*a)^71 + 300716060*
sqrt(2)*tan(1/2*a)^69 + 6330489495*sqrt(2)*tan(1/2*a)^67 + 25552630368*sqrt(2)*tan(1/2*a)^65 + 66747480120*sqr
t(2)*tan(1/2*a)^63 + 127385090880*sqrt(2)*tan(1/2*a)^61 + 177213720840*sqrt(2)*tan(1/2*a)^59 + 156358539040*sq
rt(2)*tan(1/2*a)^57 + 9311106618*sqrt(2)*tan(1/2*a)^55 - 252641475000*sqrt(2)*tan(1/2*a)^53 - 513622208850*sqr
t(2)*tan(1/2*a)^51 - 600368382000*sqrt(2)*tan(1/2*a)^49 - 407190093300*sqrt(2)*tan(1/2*a)^47 + 407190093300*sq
rt(2)*tan(1/2*a)^43 + 600368382000*sqrt(2)*tan(1/2*a)^41 + 513622208850*sqrt(2)*tan(1/2*a)^39 + 252641475000*s
qrt(2)*tan(1/2*a)^37 - 9311106618*sqrt(2)*tan(1/2*a)^35 - 156358539040*sqrt(2)*tan(1/2*a)^33 - 177213720840*sq
rt(2)*tan(1/2*a)^31 - 127385090880*sqrt(2)*tan(1/2*a)^29 - 66747480120*sqrt(2)*tan(1/2*a)^27 - 25552630368*sqr
t(2)*tan(1/2*a)^25 - 6330489495*sqrt(2)*tan(1/2*a)^23 - 300716060*sqrt(2)*tan(1/2*a)^21 + 591145035*sqrt(2)*ta
n(1/2*a)^19 + 334648920*sqrt(2)*tan(1/2*a)^17 + 107675378*sqrt(2)*tan(1/2*a)^15 + 23385120*sqrt(2)*tan(1/2*a)^
13 + 3382830*sqrt(2)*tan(1/2*a)^11 + 276840*sqrt(2)*tan(1/2*a)^9 + 2265*sqrt(2)*tan(1/2*a)^7 - 1812*sqrt(2)*ta
n(1/2*a)^5 - 125*sqrt(2)*tan(1/2*a)^3)/(tan(1/2*a)^78 + 34*tan(1/2*a)^76 + 559*tan(1/2*a)^74 + 5916*tan(1/2*a)
^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^66 + 4829088*tan(1/2*a)^64 + 15512772*ta
n(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574864*tan(1/2*a)^56 + 304253964*tan(1/2*a)
^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*a)^48 - 31635810*tan(1/2*a)^46 - 4
50345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a)^40 - 811985790*tan(1/2*a)^38 - 4503450
60*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426395700*tan(1/2*a)^30 + 408239496*tan(
1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*tan(1/2*a)^22 + 41970280*tan(1/2*a)^2
0 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a)^14 + 266322*tan(1/2*a)^12 + 45255*tan(
1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + tan(1/2*a)^2))*tan(1/2*b*x) + 6*(37*sqrt(
2)*tan(1/2*a)^88 - 1541*sqrt(2)*tan(1/2*a)^86 - 50809*sqrt(2)*tan(1/2*a)^84 - 603175*sqrt(2)*tan(1/2*a)^82 - 3
687094*sqrt(2)*tan(1/2*a)^80 - 8865226*sqrt(2)*tan(1/2*a)^78 + 47147734*sqrt(2)*tan(1/2*a)^76 + 603040426*sqrt
(2)*tan(1/2*a)^74 + 3413614677*sqrt(2)*tan(1/2*a)^72 + 13095011467*sqrt(2)*tan(1/2*a)^70 + 37055436367*sqrt(2)
*tan(1/2*a)^68 + 77890956881*sqrt(2)*tan(1/2*a)^66 + 113030679704*sqrt(2)*tan(1/2*a)^64 + 71597541224*sqrt(2)*
tan(1/2*a)^62 - 154548395224*sqrt(2)*tan(1/2*a)^60 - 624756202280*sqrt(2)*tan(1/2*a)^58 - 1211871261974*sqrt(2
)*tan(1/2*a)^56 - 1544438285226*sqrt(2)*tan(1/2*a)^54 - 1180267704498*sqrt(2)*tan(1/2*a)^52 + 19658244210*sqrt
(2)*tan(1/2*a)^50 + 1617690968220*sqrt(2)*tan(1/2*a)^48 + 2761812416100*sqrt(2)*tan(1/2*a)^46 + 2761812416100*
sqrt(2)*tan(1/2*a)^44 + 1617690968220*sqrt(2)*tan(1/2*a)^42 + 19658244210*sqrt(2)*tan(1/2*a)^40 - 118026770449
8*sqrt(2)*tan(1/2*a)^38 - 1544438285226*sqrt(2)*tan(1/2*a)^36 - 1211871261974*sqrt(2)*tan(1/2*a)^34 - 62475620
2280*sqrt(2)*tan(1/2*a)^32 - 154548395224*sqrt(2)*tan(1/2*a)^30 + 71597541224*sqrt(2)*tan(1/2*a)^28 + 11303067
9704*sqrt(2)*tan(1/2*a)^26 + 77890956881*sqrt(2)*tan(1/2*a)^24 + 37055436367*sqrt(2)*tan(1/2*a)^22 + 130950114
67*sqrt(2)*tan(1/2*a)^20 + 3413614677*sqrt(2)*tan(1/2*a)^18 + 603040426*sqrt(2)*tan(1/2*a)^16 + 47147734*sqrt(
2)*tan(1/2*a)^14 - 8865226*sqrt(2)*tan(1/2*a)^12 - 3687094*sqrt(2)*tan(1/2*a)^10 - 603175*sqrt(2)*tan(1/2*a)^8
- 50809*sqrt(2)*tan(1/2*a)^6 - 1541*sqrt(2)*tan(1/2*a)^4 + 37*sqrt(2)*tan(1/2*a)^2)/(tan(1/2*a)^78 + 34*tan(1
/2*a)^76 + 559*tan(1/2*a)^74 + 5916*tan(1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1
/2*a)^66 + 4829088*tan(1/2*a)^64 + 15512772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 +
186574864*tan(1/2*a)^56 + 304253964*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097
760*tan(1/2*a)^48 - 31635810*tan(1/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan
(1/2*a)^40 - 811985790*tan(1/2*a)^38 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)
^32 + 426395700*tan(1/2*a)^30 + 408239496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 +
96160636*tan(1/2*a)^22 + 41970280*tan(1/2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan
(1/2*a)^14 + 266322*tan(1/2*a)^12 + 45255*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)
^4 + tan(1/2*a)^2))*tan(1/2*b*x) - 20*(125*sqrt(2)*tan(1/2*a)^87 + 1812*sqrt(2)*tan(1/2*a)^85 - 2265*sqrt(2)*t
an(1/2*a)^83 - 276840*sqrt(2)*tan(1/2*a)^81 - 3382830*sqrt(2)*tan(1/2*a)^79 - 23385120*sqrt(2)*tan(1/2*a)^77 -
107675378*sqrt(2)*tan(1/2*a)^75 - 334648920*sqrt(2)*tan(1/2*a)^73 - 591145035*sqrt(2)*tan(1/2*a)^71 + 3007160
60*sqrt(2)*tan(1/2*a)^69 + 6330489495*sqrt(2)*tan(1/2*a)^67 + 25552630368*sqrt(2)*tan(1/2*a)^65 + 66747480120*
sqrt(2)*tan(1/2*a)^63 + 127385090880*sqrt(2)*tan(1/2*a)^61 + 177213720840*sqrt(2)*tan(1/2*a)^59 + 156358539040
*sqrt(2)*tan(1/2*a)^57 + 9311106618*sqrt(2)*tan(1/2*a)^55 - 252641475000*sqrt(2)*tan(1/2*a)^53 - 513622208850*
sqrt(2)*tan(1/2*a)^51 - 600368382000*sqrt(2)*tan(1/2*a)^49 - 407190093300*sqrt(2)*tan(1/2*a)^47 + 407190093300
*sqrt(2)*tan(1/2*a)^43 + 600368382000*sqrt(2)*tan(1/2*a)^41 + 513622208850*sqrt(2)*tan(1/2*a)^39 + 25264147500
0*sqrt(2)*tan(1/2*a)^37 - 9311106618*sqrt(2)*tan(1/2*a)^35 - 156358539040*sqrt(2)*tan(1/2*a)^33 - 177213720840
*sqrt(2)*tan(1/2*a)^31 - 127385090880*sqrt(2)*tan(1/2*a)^29 - 66747480120*sqrt(2)*tan(1/2*a)^27 - 25552630368*
sqrt(2)*tan(1/2*a)^25 - 6330489495*sqrt(2)*tan(1/2*a)^23 - 300716060*sqrt(2)*tan(1/2*a)^21 + 591145035*sqrt(2)
*tan(1/2*a)^19 + 334648920*sqrt(2)*tan(1/2*a)^17 + 107675378*sqrt(2)*tan(1/2*a)^15 + 23385120*sqrt(2)*tan(1/2*
a)^13 + 3382830*sqrt(2)*tan(1/2*a)^11 + 276840*sqrt(2)*tan(1/2*a)^9 + 2265*sqrt(2)*tan(1/2*a)^7 - 1812*sqrt(2)
*tan(1/2*a)^5 - 125*sqrt(2)*tan(1/2*a)^3)/(tan(1/2*a)^78 + 34*tan(1/2*a)^76 + 559*tan(1/2*a)^74 + 5916*tan(1/2
*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^66 + 4829088*tan(1/2*a)^64 + 15512772
*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574864*tan(1/2*a)^56 + 304253964*tan(1/2
*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*a)^48 - 31635810*tan(1/2*a)^46
- 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a)^40 - 811985790*tan(1/2*a)^38 - 4503
45060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426395700*tan(1/2*a)^30 + 408239496*t
an(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*tan(1/2*a)^22 + 41970280*tan(1/2*a
)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a)^14 + 266322*tan(1/2*a)^12 + 45255*t
an(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + tan(1/2*a)^2))*tan(1/2*b*x) - 20*(7*sq
rt(2)*tan(1/2*a)^88 - 167*sqrt(2)*tan(1/2*a)^86 - 6499*sqrt(2)*tan(1/2*a)^84 - 79741*sqrt(2)*tan(1/2*a)^82 - 4
93810*sqrt(2)*tan(1/2*a)^80 - 1198222*sqrt(2)*tan(1/2*a)^78 + 6282322*sqrt(2)*tan(1/2*a)^76 + 80477230*sqrt(2)
*tan(1/2*a)^74 + 452737815*sqrt(2)*tan(1/2*a)^72 + 1715629705*sqrt(2)*tan(1/2*a)^70 + 4748442805*sqrt(2)*tan(1
/2*a)^68 + 9550300715*sqrt(2)*tan(1/2*a)^66 + 12322646792*sqrt(2)*tan(1/2*a)^64 + 2388418808*sqrt(2)*tan(1/2*a
)^62 - 35649378760*sqrt(2)*tan(1/2*a)^60 - 108847849016*sqrt(2)*tan(1/2*a)^58 - 195926195474*sqrt(2)*tan(1/2*a
)^56 - 239921144622*sqrt(2)*tan(1/2*a)^54 - 175285727238*sqrt(2)*tan(1/2*a)^52 + 16173774150*sqrt(2)*tan(1/2*a
)^50 + 265568681460*sqrt(2)*tan(1/2*a)^48 + 442624681740*sqrt(2)*tan(1/2*a)^46 + 442624681740*sqrt(2)*tan(1/2*
a)^44 + 265568681460*sqrt(2)*tan(1/2*a)^42 + 16173774150*sqrt(2)*tan(1/2*a)^40 - 175285727238*sqrt(2)*tan(1/2*
a)^38 - 239921144622*sqrt(2)*tan(1/2*a)^36 - 195926195474*sqrt(2)*tan(1/2*a)^34 - 108847849016*sqrt(2)*tan(1/2
*a)^32 - 35649378760*sqrt(2)*tan(1/2*a)^30 + 2388418808*sqrt(2)*tan(1/2*a)^28 + 12322646792*sqrt(2)*tan(1/2*a)
^26 + 9550300715*sqrt(2)*tan(1/2*a)^24 + 4748442805*sqrt(2)*tan(1/2*a)^22 + 1715629705*sqrt(2)*tan(1/2*a)^20 +
452737815*sqrt(2)*tan(1/2*a)^18 + 80477230*sqrt(2)*tan(1/2*a)^16 + 6282322*sqrt(2)*tan(1/2*a)^14 - 1198222*sq
rt(2)*tan(1/2*a)^12 - 493810*sqrt(2)*tan(1/2*a)^10 - 79741*sqrt(2)*tan(1/2*a)^8 - 6499*sqrt(2)*tan(1/2*a)^6 -
167*sqrt(2)*tan(1/2*a)^4 + 7*sqrt(2)*tan(1/2*a)^2)/(tan(1/2*a)^78 + 34*tan(1/2*a)^76 + 559*tan(1/2*a)^74 + 591
6*tan(1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^66 + 4829088*tan(1/2*a)^64 +
15512772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574864*tan(1/2*a)^56 + 30425396
4*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*a)^48 - 31635810*tan(1
/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a)^40 - 811985790*tan(1/2*a)^
38 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426395700*tan(1/2*a)^30 + 40
8239496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*tan(1/2*a)^22 + 41970280*
tan(1/2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a)^14 + 266322*tan(1/2*a)^12
+ 45255*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + tan(1/2*a)^2))*tan(1/2*b*x) +
30*(19*sqrt(2)*tan(1/2*a)^87 + 300*sqrt(2)*tan(1/2*a)^85 + 393*sqrt(2)*tan(1/2*a)^83 - 31512*sqrt(2)*tan(1/2*
a)^81 - 418098*sqrt(2)*tan(1/2*a)^79 - 2934240*sqrt(2)*tan(1/2*a)^77 - 13355950*sqrt(2)*tan(1/2*a)^75 - 395348
88*sqrt(2)*tan(1/2*a)^73 - 56342949*sqrt(2)*tan(1/2*a)^71 + 123215524*sqrt(2)*tan(1/2*a)^69 + 1097715993*sqrt(
2)*tan(1/2*a)^67 + 4042423200*sqrt(2)*tan(1/2*a)^65 + 10195869000*sqrt(2)*tan(1/2*a)^63 + 19092105408*sqrt(2)*
tan(1/2*a)^61 + 26200319352*sqrt(2)*tan(1/2*a)^59 + 22729855712*sqrt(2)*tan(1/2*a)^57 + 667102950*sqrt(2)*tan(
1/2*a)^55 - 38119807944*sqrt(2)*tan(1/2*a)^53 - 76473192270*sqrt(2)*tan(1/2*a)^51 - 88969283280*sqrt(2)*tan(1/
2*a)^49 - 60215972940*sqrt(2)*tan(1/2*a)^47 + 60215972940*sqrt(2)*tan(1/2*a)^43 + 88969283280*sqrt(2)*tan(1/2*
a)^41 + 76473192270*sqrt(2)*tan(1/2*a)^39 + 38119807944*sqrt(2)*tan(1/2*a)^37 - 667102950*sqrt(2)*tan(1/2*a)^3
5 - 22729855712*sqrt(2)*tan(1/2*a)^33 - 26200319352*sqrt(2)*tan(1/2*a)^31 - 19092105408*sqrt(2)*tan(1/2*a)^29
- 10195869000*sqrt(2)*tan(1/2*a)^27 - 4042423200*sqrt(2)*tan(1/2*a)^25 - 1097715993*sqrt(2)*tan(1/2*a)^23 - 12
3215524*sqrt(2)*tan(1/2*a)^21 + 56342949*sqrt(2)*tan(1/2*a)^19 + 39534888*sqrt(2)*tan(1/2*a)^17 + 13355950*sqr
t(2)*tan(1/2*a)^15 + 2934240*sqrt(2)*tan(1/2*a)^13 + 418098*sqrt(2)*tan(1/2*a)^11 + 31512*sqrt(2)*tan(1/2*a)^9
- 393*sqrt(2)*tan(1/2*a)^7 - 300*sqrt(2)*tan(1/2*a)^5 - 19*sqrt(2)*tan(1/2*a)^3)/(tan(1/2*a)^78 + 34*tan(1/2*
a)^76 + 559*tan(1/2*a)^74 + 5916*tan(1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*
a)^66 + 4829088*tan(1/2*a)^64 + 15512772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186
574864*tan(1/2*a)^56 + 304253964*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760
*tan(1/2*a)^48 - 31635810*tan(1/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/
2*a)^40 - 811985790*tan(1/2*a)^38 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32
+ 426395700*tan(1/2*a)^30 + 408239496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 961
60636*tan(1/2*a)^22 + 41970280*tan(1/2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/
2*a)^14 + 266322*tan(1/2*a)^12 + 45255*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4
+ tan(1/2*a)^2))*tan(1/2*b*x) + 5*(sqrt(2)*tan(1/2*a)^88 - 97*sqrt(2)*tan(1/2*a)^86 - 2757*sqrt(2)*tan(1/2*a)^
84 - 31579*sqrt(2)*tan(1/2*a)^82 - 190206*sqrt(2)*tan(1/2*a)^80 - 452482*sqrt(2)*tan(1/2*a)^78 + 2446494*sqrt(
2)*tan(1/2*a)^76 + 31236834*sqrt(2)*tan(1/2*a)^74 + 178073713*sqrt(2)*tan(1/2*a)^72 + 692499183*sqrt(2)*tan(1/
2*a)^70 + 2006851683*sqrt(2)*tan(1/2*a)^68 + 4409972669*sqrt(2)*tan(1/2*a)^66 + 7082232504*sqrt(2)*tan(1/2*a)^
64 + 6893762888*sqrt(2)*tan(1/2*a)^62 - 1327875576*sqrt(2)*tan(1/2*a)^60 - 21040534024*sqrt(2)*tan(1/2*a)^58 -
47574053342*sqrt(2)*tan(1/2*a)^56 - 64972634082*sqrt(2)*tan(1/2*a)^54 - 53236088394*sqrt(2)*tan(1/2*a)^52 - 5
004094710*sqrt(2)*tan(1/2*a)^50 + 61712915820*sqrt(2)*tan(1/2*a)^48 + 110145965460*sqrt(2)*tan(1/2*a)^46 + 110
145965460*sqrt(2)*tan(1/2*a)^44 + 61712915820*sqrt(2)*tan(1/2*a)^42 - 5004094710*sqrt(2)*tan(1/2*a)^40 - 53236
088394*sqrt(2)*tan(1/2*a)^38 - 64972634082*sqrt(2)*tan(1/2*a)^36 - 47574053342*sqrt(2)*tan(1/2*a)^34 - 2104053
4024*sqrt(2)*tan(1/2*a)^32 - 1327875576*sqrt(2)*tan(1/2*a)^30 + 6893762888*sqrt(2)*tan(1/2*a)^28 + 7082232504*
sqrt(2)*tan(1/2*a)^26 + 4409972669*sqrt(2)*tan(1/2*a)^24 + 2006851683*sqrt(2)*tan(1/2*a)^22 + 692499183*sqrt(2
)*tan(1/2*a)^20 + 178073713*sqrt(2)*tan(1/2*a)^18 + 31236834*sqrt(2)*tan(1/2*a)^16 + 2446494*sqrt(2)*tan(1/2*a
)^14 - 452482*sqrt(2)*tan(1/2*a)^12 - 190206*sqrt(2)*tan(1/2*a)^10 - 31579*sqrt(2)*tan(1/2*a)^8 - 2757*sqrt(2)
*tan(1/2*a)^6 - 97*sqrt(2)*tan(1/2*a)^4 + sqrt(2)*tan(1/2*a)^2)/(tan(1/2*a)^78 + 34*tan(1/2*a)^76 + 559*tan(1/
2*a)^74 + 5916*tan(1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^66 + 4829088*ta
n(1/2*a)^64 + 15512772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574864*tan(1/2*a)^
56 + 304253964*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*a)^48 - 3
1635810*tan(1/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a)^40 - 81198579
0*tan(1/2*a)^38 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426395700*tan(1
/2*a)^30 + 408239496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*tan(1/2*a)^2
2 + 41970280*tan(1/2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a)^14 + 266322*t
an(1/2*a)^12 + 45255*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + tan(1/2*a)^2))*t
an(1/2*b*x) - 2*(sqrt(2)*tan(1/2*a)^87 - 92*sqrt(2)*tan(1/2*a)^85 - 3213*sqrt(2)*tan(1/2*a)^83 - 48008*sqrt(2)
*tan(1/2*a)^81 - 443462*sqrt(2)*tan(1/2*a)^79 - 2875040*sqrt(2)*tan(1/2*a)^77 - 13907802*sqrt(2)*tan(1/2*a)^75
- 51781432*sqrt(2)*tan(1/2*a)^73 - 149943911*sqrt(2)*tan(1/2*a)^71 - 333456564*sqrt(2)*tan(1/2*a)^69 - 536442
973*sqrt(2)*tan(1/2*a)^67 - 482080288*sqrt(2)*tan(1/2*a)^65 + 316221080*sqrt(2)*tan(1/2*a)^63 + 2190937152*sqr
t(2)*tan(1/2*a)^61 + 4607763368*sqrt(2)*tan(1/2*a)^59 + 5742984608*sqrt(2)*tan(1/2*a)^57 + 3316624962*sqrt(2)*
tan(1/2*a)^55 - 3241815576*sqrt(2)*tan(1/2*a)^53 - 11030972730*sqrt(2)*tan(1/2*a)^51 - 14712027120*sqrt(2)*tan
(1/2*a)^49 - 10524179460*sqrt(2)*tan(1/2*a)^47 + 10524179460*sqrt(2)*tan(1/2*a)^43 + 14712027120*sqrt(2)*tan(1
/2*a)^41 + 11030972730*sqrt(2)*tan(1/2*a)^39 + 3241815576*sqrt(2)*tan(1/2*a)^37 - 3316624962*sqrt(2)*tan(1/2*a
)^35 - 5742984608*sqrt(2)*tan(1/2*a)^33 - 4607763368*sqrt(2)*tan(1/2*a)^31 - 2190937152*sqrt(2)*tan(1/2*a)^29
- 316221080*sqrt(2)*tan(1/2*a)^27 + 482080288*sqrt(2)*tan(1/2*a)^25 + 536442973*sqrt(2)*tan(1/2*a)^23 + 333456
564*sqrt(2)*tan(1/2*a)^21 + 149943911*sqrt(2)*tan(1/2*a)^19 + 51781432*sqrt(2)*tan(1/2*a)^17 + 13907802*sqrt(2
)*tan(1/2*a)^15 + 2875040*sqrt(2)*tan(1/2*a)^13 + 443462*sqrt(2)*tan(1/2*a)^11 + 48008*sqrt(2)*tan(1/2*a)^9 +
3213*sqrt(2)*tan(1/2*a)^7 + 92*sqrt(2)*tan(1/2*a)^5 - sqrt(2)*tan(1/2*a)^3)/(tan(1/2*a)^78 + 34*tan(1/2*a)^76
+ 559*tan(1/2*a)^74 + 5916*tan(1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^66
+ 4829088*tan(1/2*a)^64 + 15512772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574864
*tan(1/2*a)^56 + 304253964*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1
/2*a)^48 - 31635810*tan(1/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a)^4
0 - 811985790*tan(1/2*a)^38 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426
395700*tan(1/2*a)^30 + 408239496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*
tan(1/2*a)^22 + 41970280*tan(1/2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a)^1
4 + 266322*tan(1/2*a)^12 + 45255*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + tan(
1/2*a)^2))*cos(a)/((tan(1/2*b*x)^4*tan(1/2*a)^3 + tan(1/2*b*x)^3*tan(1/2*a)^4 - tan(1/2*b*x)^4*tan(1/2*a) - 6*
tan(1/2*b*x)^3*tan(1/2*a)^2 - 6*tan(1/2*b*x)^2*tan(1/2*a)^3 - tan(1/2*b*x)*tan(1/2*a)^4 + tan(1/2*b*x)^3 + 6*t
an(1/2*b*x)^2*tan(1/2*a) + 6*tan(1/2*b*x)*tan(1/2*a)^2 + tan(1/2*a)^3 - tan(1/2*b*x) - tan(1/2*a))^3*b) - 1/96
0*sqrt(2)*sqrt(-tan(1/2*b*x)^4*tan(1/2*a)^3 - tan(1/2*b*x)^3*tan(1/2*a)^4 + tan(1/2*b*x)^4*tan(1/2*a) + 6*tan(
1/2*b*x)^3*tan(1/2*a)^2 + 6*tan(1/2*b*x)^2*tan(1/2*a)^3 + tan(1/2*b*x)*tan(1/2*a)^4 - tan(1/2*b*x)^3 - 6*tan(1
/2*b*x)^2*tan(1/2*a) - 6*tan(1/2*b*x)*tan(1/2*a)^2 - tan(1/2*a)^3 + tan(1/2*b*x) + tan(1/2*a))*(((((((((((3*sq
rt(2)*tan(1/2*a)^88 + 221*sqrt(2)*tan(1/2*a)^86 + 4529*sqrt(2)*tan(1/2*a)^84 + 46575*sqrt(2)*tan(1/2*a)^82 + 2
67014*sqrt(2)*tan(1/2*a)^80 + 611706*sqrt(2)*tan(1/2*a)^78 - 3503654*sqrt(2)*tan(1/2*a)^76 - 44470106*sqrt(2)*
tan(1/2*a)^74 - 259557037*sqrt(2)*tan(1/2*a)^72 - 1054367027*sqrt(2)*tan(1/2*a)^70 - 3278963927*sqrt(2)*tan(1/
2*a)^68 - 8089589961*sqrt(2)*tan(1/2*a)^66 - 16006283224*sqrt(2)*tan(1/2*a)^64 - 25186632744*sqrt(2)*tan(1/2*a
)^62 - 30337876456*sqrt(2)*tan(1/2*a)^60 - 24685712920*sqrt(2)*tan(1/2*a)^58 - 5629982106*sqrt(2)*tan(1/2*a)^5
6 + 19969391706*sqrt(2)*tan(1/2*a)^54 + 37658626338*sqrt(2)*tan(1/2*a)^52 + 36190152990*sqrt(2)*tan(1/2*a)^50
+ 18717018180*sqrt(2)*tan(1/2*a)^48 + 2040819900*sqrt(2)*tan(1/2*a)^46 + 2040819900*sqrt(2)*tan(1/2*a)^44 + 18
717018180*sqrt(2)*tan(1/2*a)^42 + 36190152990*sqrt(2)*tan(1/2*a)^40 + 37658626338*sqrt(2)*tan(1/2*a)^38 + 1996
9391706*sqrt(2)*tan(1/2*a)^36 - 5629982106*sqrt(2)*tan(1/2*a)^34 - 24685712920*sqrt(2)*tan(1/2*a)^32 - 3033787
6456*sqrt(2)*tan(1/2*a)^30 - 25186632744*sqrt(2)*tan(1/2*a)^28 - 16006283224*sqrt(2)*tan(1/2*a)^26 - 808958996
1*sqrt(2)*tan(1/2*a)^24 - 3278963927*sqrt(2)*tan(1/2*a)^22 - 1054367027*sqrt(2)*tan(1/2*a)^20 - 259557037*sqrt
(2)*tan(1/2*a)^18 - 44470106*sqrt(2)*tan(1/2*a)^16 - 3503654*sqrt(2)*tan(1/2*a)^14 + 611706*sqrt(2)*tan(1/2*a)
^12 + 267014*sqrt(2)*tan(1/2*a)^10 + 46575*sqrt(2)*tan(1/2*a)^8 + 4529*sqrt(2)*tan(1/2*a)^6 + 221*sqrt(2)*tan(
1/2*a)^4 + 3*sqrt(2)*tan(1/2*a)^2)*tan(1/2*b*x)/(tan(1/2*a)^78 + 34*tan(1/2*a)^76 + 559*tan(1/2*a)^74 + 5916*t
an(1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^66 + 4829088*tan(1/2*a)^64 + 15
512772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574864*tan(1/2*a)^56 + 304253964*t
an(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*a)^48 - 31635810*tan(1/2*
a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a)^40 - 811985790*tan(1/2*a)^38
- 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426395700*tan(1/2*a)^30 + 40823
9496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*tan(1/2*a)^22 + 41970280*tan
(1/2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a)^14 + 266322*tan(1/2*a)^12 + 4
5255*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + tan(1/2*a)^2) + 40*(5*sqrt(2)*ta
n(1/2*a)^87 + 52*sqrt(2)*tan(1/2*a)^85 - 705*sqrt(2)*tan(1/2*a)^83 - 19880*sqrt(2)*tan(1/2*a)^81 - 215390*sqrt
(2)*tan(1/2*a)^79 - 1452320*sqrt(2)*tan(1/2*a)^77 - 6815938*sqrt(2)*tan(1/2*a)^75 - 22829080*sqrt(2)*tan(1/2*a
)^73 - 51571715*sqrt(2)*tan(1/2*a)^71 - 52560260*sqrt(2)*tan(1/2*a)^69 + 140318255*sqrt(2)*tan(1/2*a)^67 + 890
085728*sqrt(2)*tan(1/2*a)^65 + 2628022520*sqrt(2)*tan(1/2*a)^63 + 5320760640*sqrt(2)*tan(1/2*a)^61 + 770202068
0*sqrt(2)*tan(1/2*a)^59 + 7118210080*sqrt(2)*tan(1/2*a)^57 + 995931978*sqrt(2)*tan(1/2*a)^55 - 10340405880*sqr
t(2)*tan(1/2*a)^53 - 21876041250*sqrt(2)*tan(1/2*a)^51 - 25920327600*sqrt(2)*tan(1/2*a)^49 - 17685038100*sqrt(
2)*tan(1/2*a)^47 + 17685038100*sqrt(2)*tan(1/2*a)^43 + 25920327600*sqrt(2)*tan(1/2*a)^41 + 21876041250*sqrt(2)
*tan(1/2*a)^39 + 10340405880*sqrt(2)*tan(1/2*a)^37 - 995931978*sqrt(2)*tan(1/2*a)^35 - 7118210080*sqrt(2)*tan(
1/2*a)^33 - 7702020680*sqrt(2)*tan(1/2*a)^31 - 5320760640*sqrt(2)*tan(1/2*a)^29 - 2628022520*sqrt(2)*tan(1/2*a
)^27 - 890085728*sqrt(2)*tan(1/2*a)^25 - 140318255*sqrt(2)*tan(1/2*a)^23 + 52560260*sqrt(2)*tan(1/2*a)^21 + 51
571715*sqrt(2)*tan(1/2*a)^19 + 22829080*sqrt(2)*tan(1/2*a)^17 + 6815938*sqrt(2)*tan(1/2*a)^15 + 1452320*sqrt(2
)*tan(1/2*a)^13 + 215390*sqrt(2)*tan(1/2*a)^11 + 19880*sqrt(2)*tan(1/2*a)^9 + 705*sqrt(2)*tan(1/2*a)^7 - 52*sq
rt(2)*tan(1/2*a)^5 - 5*sqrt(2)*tan(1/2*a)^3)/(tan(1/2*a)^78 + 34*tan(1/2*a)^76 + 559*tan(1/2*a)^74 + 5916*tan(
1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^66 + 4829088*tan(1/2*a)^64 + 15512
772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574864*tan(1/2*a)^56 + 304253964*tan(
1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*a)^48 - 31635810*tan(1/2*a)^
46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a)^40 - 811985790*tan(1/2*a)^38 - 4
50345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426395700*tan(1/2*a)^30 + 40823949
6*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*tan(1/2*a)^22 + 41970280*tan(1/
2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a)^14 + 266322*tan(1/2*a)^12 + 4525
5*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + tan(1/2*a)^2))*tan(1/2*b*x) + 15*(7
*sqrt(2)*tan(1/2*a)^88 - 167*sqrt(2)*tan(1/2*a)^86 - 6499*sqrt(2)*tan(1/2*a)^84 - 79741*sqrt(2)*tan(1/2*a)^82
- 493810*sqrt(2)*tan(1/2*a)^80 - 1198222*sqrt(2)*tan(1/2*a)^78 + 6282322*sqrt(2)*tan(1/2*a)^76 + 80477230*sqrt
(2)*tan(1/2*a)^74 + 452737815*sqrt(2)*tan(1/2*a)^72 + 1715629705*sqrt(2)*tan(1/2*a)^70 + 4748442805*sqrt(2)*ta
n(1/2*a)^68 + 9550300715*sqrt(2)*tan(1/2*a)^66 + 12322646792*sqrt(2)*tan(1/2*a)^64 + 2388418808*sqrt(2)*tan(1/
2*a)^62 - 35649378760*sqrt(2)*tan(1/2*a)^60 - 108847849016*sqrt(2)*tan(1/2*a)^58 - 195926195474*sqrt(2)*tan(1/
2*a)^56 - 239921144622*sqrt(2)*tan(1/2*a)^54 - 175285727238*sqrt(2)*tan(1/2*a)^52 + 16173774150*sqrt(2)*tan(1/
2*a)^50 + 265568681460*sqrt(2)*tan(1/2*a)^48 + 442624681740*sqrt(2)*tan(1/2*a)^46 + 442624681740*sqrt(2)*tan(1
/2*a)^44 + 265568681460*sqrt(2)*tan(1/2*a)^42 + 16173774150*sqrt(2)*tan(1/2*a)^40 - 175285727238*sqrt(2)*tan(1
/2*a)^38 - 239921144622*sqrt(2)*tan(1/2*a)^36 - 195926195474*sqrt(2)*tan(1/2*a)^34 - 108847849016*sqrt(2)*tan(
1/2*a)^32 - 35649378760*sqrt(2)*tan(1/2*a)^30 + 2388418808*sqrt(2)*tan(1/2*a)^28 + 12322646792*sqrt(2)*tan(1/2
*a)^26 + 9550300715*sqrt(2)*tan(1/2*a)^24 + 4748442805*sqrt(2)*tan(1/2*a)^22 + 1715629705*sqrt(2)*tan(1/2*a)^2
0 + 452737815*sqrt(2)*tan(1/2*a)^18 + 80477230*sqrt(2)*tan(1/2*a)^16 + 6282322*sqrt(2)*tan(1/2*a)^14 - 1198222
*sqrt(2)*tan(1/2*a)^12 - 493810*sqrt(2)*tan(1/2*a)^10 - 79741*sqrt(2)*tan(1/2*a)^8 - 6499*sqrt(2)*tan(1/2*a)^6
- 167*sqrt(2)*tan(1/2*a)^4 + 7*sqrt(2)*tan(1/2*a)^2)/(tan(1/2*a)^78 + 34*tan(1/2*a)^76 + 559*tan(1/2*a)^74 +
5916*tan(1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^66 + 4829088*tan(1/2*a)^6
4 + 15512772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574864*tan(1/2*a)^56 + 30425
3964*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*a)^48 - 31635810*ta
n(1/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a)^40 - 811985790*tan(1/2*
a)^38 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426395700*tan(1/2*a)^30 +
408239496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*tan(1/2*a)^22 + 419702
80*tan(1/2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a)^14 + 266322*tan(1/2*a)^
12 + 45255*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + tan(1/2*a)^2))*tan(1/2*b*x
) - 160*(19*sqrt(2)*tan(1/2*a)^87 + 300*sqrt(2)*tan(1/2*a)^85 + 393*sqrt(2)*tan(1/2*a)^83 - 31512*sqrt(2)*tan(
1/2*a)^81 - 418098*sqrt(2)*tan(1/2*a)^79 - 2934240*sqrt(2)*tan(1/2*a)^77 - 13355950*sqrt(2)*tan(1/2*a)^75 - 39
534888*sqrt(2)*tan(1/2*a)^73 - 56342949*sqrt(2)*tan(1/2*a)^71 + 123215524*sqrt(2)*tan(1/2*a)^69 + 1097715993*s
qrt(2)*tan(1/2*a)^67 + 4042423200*sqrt(2)*tan(1/2*a)^65 + 10195869000*sqrt(2)*tan(1/2*a)^63 + 19092105408*sqrt
(2)*tan(1/2*a)^61 + 26200319352*sqrt(2)*tan(1/2*a)^59 + 22729855712*sqrt(2)*tan(1/2*a)^57 + 667102950*sqrt(2)*
tan(1/2*a)^55 - 38119807944*sqrt(2)*tan(1/2*a)^53 - 76473192270*sqrt(2)*tan(1/2*a)^51 - 88969283280*sqrt(2)*ta
n(1/2*a)^49 - 60215972940*sqrt(2)*tan(1/2*a)^47 + 60215972940*sqrt(2)*tan(1/2*a)^43 + 88969283280*sqrt(2)*tan(
1/2*a)^41 + 76473192270*sqrt(2)*tan(1/2*a)^39 + 38119807944*sqrt(2)*tan(1/2*a)^37 - 667102950*sqrt(2)*tan(1/2*
a)^35 - 22729855712*sqrt(2)*tan(1/2*a)^33 - 26200319352*sqrt(2)*tan(1/2*a)^31 - 19092105408*sqrt(2)*tan(1/2*a)
^29 - 10195869000*sqrt(2)*tan(1/2*a)^27 - 4042423200*sqrt(2)*tan(1/2*a)^25 - 1097715993*sqrt(2)*tan(1/2*a)^23
- 123215524*sqrt(2)*tan(1/2*a)^21 + 56342949*sqrt(2)*tan(1/2*a)^19 + 39534888*sqrt(2)*tan(1/2*a)^17 + 13355950
*sqrt(2)*tan(1/2*a)^15 + 2934240*sqrt(2)*tan(1/2*a)^13 + 418098*sqrt(2)*tan(1/2*a)^11 + 31512*sqrt(2)*tan(1/2*
a)^9 - 393*sqrt(2)*tan(1/2*a)^7 - 300*sqrt(2)*tan(1/2*a)^5 - 19*sqrt(2)*tan(1/2*a)^3)/(tan(1/2*a)^78 + 34*tan(
1/2*a)^76 + 559*tan(1/2*a)^74 + 5916*tan(1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(
1/2*a)^66 + 4829088*tan(1/2*a)^64 + 15512772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 +
186574864*tan(1/2*a)^56 + 304253964*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 28609
7760*tan(1/2*a)^48 - 31635810*tan(1/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*ta
n(1/2*a)^40 - 811985790*tan(1/2*a)^38 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a
)^32 + 426395700*tan(1/2*a)^30 + 408239496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 +
96160636*tan(1/2*a)^22 + 41970280*tan(1/2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*ta
n(1/2*a)^14 + 266322*tan(1/2*a)^12 + 45255*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a
)^4 + tan(1/2*a)^2))*tan(1/2*b*x) - 10*(41*sqrt(2)*tan(1/2*a)^88 - 1417*sqrt(2)*tan(1/2*a)^86 - 49037*sqrt(2)*
tan(1/2*a)^84 - 588179*sqrt(2)*tan(1/2*a)^82 - 3610286*sqrt(2)*tan(1/2*a)^80 - 8706002*sqrt(2)*tan(1/2*a)^78 +
46090574*sqrt(2)*tan(1/2*a)^76 + 589807154*sqrt(2)*tan(1/2*a)^74 + 3332131353*sqrt(2)*tan(1/2*a)^72 + 1273314
3623*sqrt(2)*tan(1/2*a)^70 + 35783324123*sqrt(2)*tan(1/2*a)^68 + 74211339589*sqrt(2)*tan(1/2*a)^66 + 104106628
984*sqrt(2)*tan(1/2*a)^64 + 53304671368*sqrt(2)*tan(1/2*a)^62 - 186214147256*sqrt(2)*tan(1/2*a)^60 - 670482449
224*sqrt(2)*tan(1/2*a)^58 - 1265075297422*sqrt(2)*tan(1/2*a)^56 - 1589441527602*sqrt(2)*tan(1/2*a)^54 - 119584
5166554*sqrt(2)*tan(1/2*a)^52 + 50844302490*sqrt(2)*tan(1/2*a)^50 + 1698120902220*sqrt(2)*tan(1/2*a)^48 + 2873
999201460*sqrt(2)*tan(1/2*a)^46 + 2873999201460*sqrt(2)*tan(1/2*a)^44 + 1698120902220*sqrt(2)*tan(1/2*a)^42 +
50844302490*sqrt(2)*tan(1/2*a)^40 - 1195845166554*sqrt(2)*tan(1/2*a)^38 - 1589441527602*sqrt(2)*tan(1/2*a)^36
- 1265075297422*sqrt(2)*tan(1/2*a)^34 - 670482449224*sqrt(2)*tan(1/2*a)^32 - 186214147256*sqrt(2)*tan(1/2*a)^3
0 + 53304671368*sqrt(2)*tan(1/2*a)^28 + 104106628984*sqrt(2)*tan(1/2*a)^26 + 74211339589*sqrt(2)*tan(1/2*a)^24
+ 35783324123*sqrt(2)*tan(1/2*a)^22 + 12733143623*sqrt(2)*tan(1/2*a)^20 + 3332131353*sqrt(2)*tan(1/2*a)^18 +
589807154*sqrt(2)*tan(1/2*a)^16 + 46090574*sqrt(2)*tan(1/2*a)^14 - 8706002*sqrt(2)*tan(1/2*a)^12 - 3610286*sqr
t(2)*tan(1/2*a)^10 - 588179*sqrt(2)*tan(1/2*a)^8 - 49037*sqrt(2)*tan(1/2*a)^6 - 1417*sqrt(2)*tan(1/2*a)^4 + 41
*sqrt(2)*tan(1/2*a)^2)/(tan(1/2*a)^78 + 34*tan(1/2*a)^76 + 559*tan(1/2*a)^74 + 5916*tan(1/2*a)^72 + 45255*tan(
1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^66 + 4829088*tan(1/2*a)^64 + 15512772*tan(1/2*a)^62 + 41
970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574864*tan(1/2*a)^56 + 304253964*tan(1/2*a)^54 + 408239496*
tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*a)^48 - 31635810*tan(1/2*a)^46 - 450345060*tan(1/2
*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a)^40 - 811985790*tan(1/2*a)^38 - 450345060*tan(1/2*a)^36
- 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426395700*tan(1/2*a)^30 + 408239496*tan(1/2*a)^28 + 3042
53964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*tan(1/2*a)^22 + 41970280*tan(1/2*a)^20 + 15512772*tan
(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a)^14 + 266322*tan(1/2*a)^12 + 45255*tan(1/2*a)^10 + 5916
*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + tan(1/2*a)^2))*tan(1/2*b*x) + 48*(121*sqrt(2)*tan(1/2*a)^
87 + 1668*sqrt(2)*tan(1/2*a)^85 - 4773*sqrt(2)*tan(1/2*a)^83 - 304968*sqrt(2)*tan(1/2*a)^81 - 3610902*sqrt(2)*
tan(1/2*a)^79 - 24807840*sqrt(2)*tan(1/2*a)^77 - 114767242*sqrt(2)*tan(1/2*a)^75 - 363601272*sqrt(2)*tan(1/2*a
)^73 - 689517231*sqrt(2)*tan(1/2*a)^71 + 19819756*sqrt(2)*tan(1/2*a)^69 + 5653728267*sqrt(2)*tan(1/2*a)^67 + 2
4180464352*sqrt(2)*tan(1/2*a)^65 + 64435678680*sqrt(2)*tan(1/2*a)^63 + 124255267392*sqrt(2)*tan(1/2*a)^61 + 17
4119463528*sqrt(2)*tan(1/2*a)^59 + 154983313568*sqrt(2)*tan(1/2*a)^57 + 11631799602*sqrt(2)*tan(1/2*a)^55 - 24
5542884696*sqrt(2)*tan(1/2*a)^53 - 502777140330*sqrt(2)*tan(1/2*a)^51 - 589160081520*sqrt(2)*tan(1/2*a)^49 - 4
00029234660*sqrt(2)*tan(1/2*a)^47 + 400029234660*sqrt(2)*tan(1/2*a)^43 + 589160081520*sqrt(2)*tan(1/2*a)^41 +
502777140330*sqrt(2)*tan(1/2*a)^39 + 245542884696*sqrt(2)*tan(1/2*a)^37 - 11631799602*sqrt(2)*tan(1/2*a)^35 -
154983313568*sqrt(2)*tan(1/2*a)^33 - 174119463528*sqrt(2)*tan(1/2*a)^31 - 124255267392*sqrt(2)*tan(1/2*a)^29 -
64435678680*sqrt(2)*tan(1/2*a)^27 - 24180464352*sqrt(2)*tan(1/2*a)^25 - 5653728267*sqrt(2)*tan(1/2*a)^23 - 19
819756*sqrt(2)*tan(1/2*a)^21 + 689517231*sqrt(2)*tan(1/2*a)^19 + 363601272*sqrt(2)*tan(1/2*a)^17 + 114767242*s
qrt(2)*tan(1/2*a)^15 + 24807840*sqrt(2)*tan(1/2*a)^13 + 3610902*sqrt(2)*tan(1/2*a)^11 + 304968*sqrt(2)*tan(1/2
*a)^9 + 4773*sqrt(2)*tan(1/2*a)^7 - 1668*sqrt(2)*tan(1/2*a)^5 - 121*sqrt(2)*tan(1/2*a)^3)/(tan(1/2*a)^78 + 34*
tan(1/2*a)^76 + 559*tan(1/2*a)^74 + 5916*tan(1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*
tan(1/2*a)^66 + 4829088*tan(1/2*a)^64 + 15512772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^
58 + 186574864*tan(1/2*a)^56 + 304253964*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 2
86097760*tan(1/2*a)^48 - 31635810*tan(1/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 95527740
0*tan(1/2*a)^40 - 811985790*tan(1/2*a)^38 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1
/2*a)^32 + 426395700*tan(1/2*a)^30 + 408239496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^
24 + 96160636*tan(1/2*a)^22 + 41970280*tan(1/2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 125271
3*tan(1/2*a)^14 + 266322*tan(1/2*a)^12 + 45255*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1
/2*a)^4 + tan(1/2*a)^2))*tan(1/2*b*x) + 10*(41*sqrt(2)*tan(1/2*a)^88 - 1417*sqrt(2)*tan(1/2*a)^86 - 49037*sqrt
(2)*tan(1/2*a)^84 - 588179*sqrt(2)*tan(1/2*a)^82 - 3610286*sqrt(2)*tan(1/2*a)^80 - 8706002*sqrt(2)*tan(1/2*a)^
78 + 46090574*sqrt(2)*tan(1/2*a)^76 + 589807154*sqrt(2)*tan(1/2*a)^74 + 3332131353*sqrt(2)*tan(1/2*a)^72 + 127
33143623*sqrt(2)*tan(1/2*a)^70 + 35783324123*sqrt(2)*tan(1/2*a)^68 + 74211339589*sqrt(2)*tan(1/2*a)^66 + 10410
6628984*sqrt(2)*tan(1/2*a)^64 + 53304671368*sqrt(2)*tan(1/2*a)^62 - 186214147256*sqrt(2)*tan(1/2*a)^60 - 67048
2449224*sqrt(2)*tan(1/2*a)^58 - 1265075297422*sqrt(2)*tan(1/2*a)^56 - 1589441527602*sqrt(2)*tan(1/2*a)^54 - 11
95845166554*sqrt(2)*tan(1/2*a)^52 + 50844302490*sqrt(2)*tan(1/2*a)^50 + 1698120902220*sqrt(2)*tan(1/2*a)^48 +
2873999201460*sqrt(2)*tan(1/2*a)^46 + 2873999201460*sqrt(2)*tan(1/2*a)^44 + 1698120902220*sqrt(2)*tan(1/2*a)^4
2 + 50844302490*sqrt(2)*tan(1/2*a)^40 - 1195845166554*sqrt(2)*tan(1/2*a)^38 - 1589441527602*sqrt(2)*tan(1/2*a)
^36 - 1265075297422*sqrt(2)*tan(1/2*a)^34 - 670482449224*sqrt(2)*tan(1/2*a)^32 - 186214147256*sqrt(2)*tan(1/2*
a)^30 + 53304671368*sqrt(2)*tan(1/2*a)^28 + 104106628984*sqrt(2)*tan(1/2*a)^26 + 74211339589*sqrt(2)*tan(1/2*a
)^24 + 35783324123*sqrt(2)*tan(1/2*a)^22 + 12733143623*sqrt(2)*tan(1/2*a)^20 + 3332131353*sqrt(2)*tan(1/2*a)^1
8 + 589807154*sqrt(2)*tan(1/2*a)^16 + 46090574*sqrt(2)*tan(1/2*a)^14 - 8706002*sqrt(2)*tan(1/2*a)^12 - 3610286
*sqrt(2)*tan(1/2*a)^10 - 588179*sqrt(2)*tan(1/2*a)^8 - 49037*sqrt(2)*tan(1/2*a)^6 - 1417*sqrt(2)*tan(1/2*a)^4
+ 41*sqrt(2)*tan(1/2*a)^2)/(tan(1/2*a)^78 + 34*tan(1/2*a)^76 + 559*tan(1/2*a)^74 + 5916*tan(1/2*a)^72 + 45255*
tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^66 + 4829088*tan(1/2*a)^64 + 15512772*tan(1/2*a)^62
+ 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574864*tan(1/2*a)^56 + 304253964*tan(1/2*a)^54 + 408239
496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*a)^48 - 31635810*tan(1/2*a)^46 - 450345060*tan
(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a)^40 - 811985790*tan(1/2*a)^38 - 450345060*tan(1/2*a
)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426395700*tan(1/2*a)^30 + 408239496*tan(1/2*a)^28 +
304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*tan(1/2*a)^22 + 41970280*tan(1/2*a)^20 + 15512772
*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a)^14 + 266322*tan(1/2*a)^12 + 45255*tan(1/2*a)^10 +
5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + tan(1/2*a)^2))*tan(1/2*b*x) - 160*(19*sqrt(2)*tan(1/2
*a)^87 + 300*sqrt(2)*tan(1/2*a)^85 + 393*sqrt(2)*tan(1/2*a)^83 - 31512*sqrt(2)*tan(1/2*a)^81 - 418098*sqrt(2)*
tan(1/2*a)^79 - 2934240*sqrt(2)*tan(1/2*a)^77 - 13355950*sqrt(2)*tan(1/2*a)^75 - 39534888*sqrt(2)*tan(1/2*a)^7
3 - 56342949*sqrt(2)*tan(1/2*a)^71 + 123215524*sqrt(2)*tan(1/2*a)^69 + 1097715993*sqrt(2)*tan(1/2*a)^67 + 4042
423200*sqrt(2)*tan(1/2*a)^65 + 10195869000*sqrt(2)*tan(1/2*a)^63 + 19092105408*sqrt(2)*tan(1/2*a)^61 + 2620031
9352*sqrt(2)*tan(1/2*a)^59 + 22729855712*sqrt(2)*tan(1/2*a)^57 + 667102950*sqrt(2)*tan(1/2*a)^55 - 38119807944
*sqrt(2)*tan(1/2*a)^53 - 76473192270*sqrt(2)*tan(1/2*a)^51 - 88969283280*sqrt(2)*tan(1/2*a)^49 - 60215972940*s
qrt(2)*tan(1/2*a)^47 + 60215972940*sqrt(2)*tan(1/2*a)^43 + 88969283280*sqrt(2)*tan(1/2*a)^41 + 76473192270*sqr
t(2)*tan(1/2*a)^39 + 38119807944*sqrt(2)*tan(1/2*a)^37 - 667102950*sqrt(2)*tan(1/2*a)^35 - 22729855712*sqrt(2)
*tan(1/2*a)^33 - 26200319352*sqrt(2)*tan(1/2*a)^31 - 19092105408*sqrt(2)*tan(1/2*a)^29 - 10195869000*sqrt(2)*t
an(1/2*a)^27 - 4042423200*sqrt(2)*tan(1/2*a)^25 - 1097715993*sqrt(2)*tan(1/2*a)^23 - 123215524*sqrt(2)*tan(1/2
*a)^21 + 56342949*sqrt(2)*tan(1/2*a)^19 + 39534888*sqrt(2)*tan(1/2*a)^17 + 13355950*sqrt(2)*tan(1/2*a)^15 + 29
34240*sqrt(2)*tan(1/2*a)^13 + 418098*sqrt(2)*tan(1/2*a)^11 + 31512*sqrt(2)*tan(1/2*a)^9 - 393*sqrt(2)*tan(1/2*
a)^7 - 300*sqrt(2)*tan(1/2*a)^5 - 19*sqrt(2)*tan(1/2*a)^3)/(tan(1/2*a)^78 + 34*tan(1/2*a)^76 + 559*tan(1/2*a)^
74 + 5916*tan(1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^66 + 4829088*tan(1/2
*a)^64 + 15512772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574864*tan(1/2*a)^56 +
304253964*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*a)^48 - 316358
10*tan(1/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a)^40 - 811985790*tan
(1/2*a)^38 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426395700*tan(1/2*a)
^30 + 408239496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*tan(1/2*a)^22 + 4
1970280*tan(1/2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a)^14 + 266322*tan(1/
2*a)^12 + 45255*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + tan(1/2*a)^2))*tan(1/
2*b*x) - 15*(7*sqrt(2)*tan(1/2*a)^88 - 167*sqrt(2)*tan(1/2*a)^86 - 6499*sqrt(2)*tan(1/2*a)^84 - 79741*sqrt(2)*
tan(1/2*a)^82 - 493810*sqrt(2)*tan(1/2*a)^80 - 1198222*sqrt(2)*tan(1/2*a)^78 + 6282322*sqrt(2)*tan(1/2*a)^76 +
80477230*sqrt(2)*tan(1/2*a)^74 + 452737815*sqrt(2)*tan(1/2*a)^72 + 1715629705*sqrt(2)*tan(1/2*a)^70 + 4748442
805*sqrt(2)*tan(1/2*a)^68 + 9550300715*sqrt(2)*tan(1/2*a)^66 + 12322646792*sqrt(2)*tan(1/2*a)^64 + 2388418808*
sqrt(2)*tan(1/2*a)^62 - 35649378760*sqrt(2)*tan(1/2*a)^60 - 108847849016*sqrt(2)*tan(1/2*a)^58 - 195926195474*
sqrt(2)*tan(1/2*a)^56 - 239921144622*sqrt(2)*tan(1/2*a)^54 - 175285727238*sqrt(2)*tan(1/2*a)^52 + 16173774150*
sqrt(2)*tan(1/2*a)^50 + 265568681460*sqrt(2)*tan(1/2*a)^48 + 442624681740*sqrt(2)*tan(1/2*a)^46 + 442624681740
*sqrt(2)*tan(1/2*a)^44 + 265568681460*sqrt(2)*tan(1/2*a)^42 + 16173774150*sqrt(2)*tan(1/2*a)^40 - 175285727238
*sqrt(2)*tan(1/2*a)^38 - 239921144622*sqrt(2)*tan(1/2*a)^36 - 195926195474*sqrt(2)*tan(1/2*a)^34 - 10884784901
6*sqrt(2)*tan(1/2*a)^32 - 35649378760*sqrt(2)*tan(1/2*a)^30 + 2388418808*sqrt(2)*tan(1/2*a)^28 + 12322646792*s
qrt(2)*tan(1/2*a)^26 + 9550300715*sqrt(2)*tan(1/2*a)^24 + 4748442805*sqrt(2)*tan(1/2*a)^22 + 1715629705*sqrt(2
)*tan(1/2*a)^20 + 452737815*sqrt(2)*tan(1/2*a)^18 + 80477230*sqrt(2)*tan(1/2*a)^16 + 6282322*sqrt(2)*tan(1/2*a
)^14 - 1198222*sqrt(2)*tan(1/2*a)^12 - 493810*sqrt(2)*tan(1/2*a)^10 - 79741*sqrt(2)*tan(1/2*a)^8 - 6499*sqrt(2
)*tan(1/2*a)^6 - 167*sqrt(2)*tan(1/2*a)^4 + 7*sqrt(2)*tan(1/2*a)^2)/(tan(1/2*a)^78 + 34*tan(1/2*a)^76 + 559*ta
n(1/2*a)^74 + 5916*tan(1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^66 + 482908
8*tan(1/2*a)^64 + 15512772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574864*tan(1/2
*a)^56 + 304253964*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*a)^48
- 31635810*tan(1/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a)^40 - 8119
85790*tan(1/2*a)^38 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426395700*t
an(1/2*a)^30 + 408239496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*tan(1/2*
a)^22 + 41970280*tan(1/2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a)^14 + 2663
22*tan(1/2*a)^12 + 45255*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + tan(1/2*a)^2
))*tan(1/2*b*x) + 40*(5*sqrt(2)*tan(1/2*a)^87 + 52*sqrt(2)*tan(1/2*a)^85 - 705*sqrt(2)*tan(1/2*a)^83 - 19880*s
qrt(2)*tan(1/2*a)^81 - 215390*sqrt(2)*tan(1/2*a)^79 - 1452320*sqrt(2)*tan(1/2*a)^77 - 6815938*sqrt(2)*tan(1/2*
a)^75 - 22829080*sqrt(2)*tan(1/2*a)^73 - 51571715*sqrt(2)*tan(1/2*a)^71 - 52560260*sqrt(2)*tan(1/2*a)^69 + 140
318255*sqrt(2)*tan(1/2*a)^67 + 890085728*sqrt(2)*tan(1/2*a)^65 + 2628022520*sqrt(2)*tan(1/2*a)^63 + 5320760640
*sqrt(2)*tan(1/2*a)^61 + 7702020680*sqrt(2)*tan(1/2*a)^59 + 7118210080*sqrt(2)*tan(1/2*a)^57 + 995931978*sqrt(
2)*tan(1/2*a)^55 - 10340405880*sqrt(2)*tan(1/2*a)^53 - 21876041250*sqrt(2)*tan(1/2*a)^51 - 25920327600*sqrt(2)
*tan(1/2*a)^49 - 17685038100*sqrt(2)*tan(1/2*a)^47 + 17685038100*sqrt(2)*tan(1/2*a)^43 + 25920327600*sqrt(2)*t
an(1/2*a)^41 + 21876041250*sqrt(2)*tan(1/2*a)^39 + 10340405880*sqrt(2)*tan(1/2*a)^37 - 995931978*sqrt(2)*tan(1
/2*a)^35 - 7118210080*sqrt(2)*tan(1/2*a)^33 - 7702020680*sqrt(2)*tan(1/2*a)^31 - 5320760640*sqrt(2)*tan(1/2*a)
^29 - 2628022520*sqrt(2)*tan(1/2*a)^27 - 890085728*sqrt(2)*tan(1/2*a)^25 - 140318255*sqrt(2)*tan(1/2*a)^23 + 5
2560260*sqrt(2)*tan(1/2*a)^21 + 51571715*sqrt(2)*tan(1/2*a)^19 + 22829080*sqrt(2)*tan(1/2*a)^17 + 6815938*sqrt
(2)*tan(1/2*a)^15 + 1452320*sqrt(2)*tan(1/2*a)^13 + 215390*sqrt(2)*tan(1/2*a)^11 + 19880*sqrt(2)*tan(1/2*a)^9
+ 705*sqrt(2)*tan(1/2*a)^7 - 52*sqrt(2)*tan(1/2*a)^5 - 5*sqrt(2)*tan(1/2*a)^3)/(tan(1/2*a)^78 + 34*tan(1/2*a)^
76 + 559*tan(1/2*a)^74 + 5916*tan(1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^
66 + 4829088*tan(1/2*a)^64 + 15512772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574
864*tan(1/2*a)^56 + 304253964*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*ta
n(1/2*a)^48 - 31635810*tan(1/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a
)^40 - 811985790*tan(1/2*a)^38 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 +
426395700*tan(1/2*a)^30 + 408239496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 961606
36*tan(1/2*a)^22 + 41970280*tan(1/2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a
)^14 + 266322*tan(1/2*a)^12 + 45255*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + t
an(1/2*a)^2))*tan(1/2*b*x) - (3*sqrt(2)*tan(1/2*a)^88 + 221*sqrt(2)*tan(1/2*a)^86 + 4529*sqrt(2)*tan(1/2*a)^84
+ 46575*sqrt(2)*tan(1/2*a)^82 + 267014*sqrt(2)*tan(1/2*a)^80 + 611706*sqrt(2)*tan(1/2*a)^78 - 3503654*sqrt(2)
*tan(1/2*a)^76 - 44470106*sqrt(2)*tan(1/2*a)^74 - 259557037*sqrt(2)*tan(1/2*a)^72 - 1054367027*sqrt(2)*tan(1/2
*a)^70 - 3278963927*sqrt(2)*tan(1/2*a)^68 - 8089589961*sqrt(2)*tan(1/2*a)^66 - 16006283224*sqrt(2)*tan(1/2*a)^
64 - 25186632744*sqrt(2)*tan(1/2*a)^62 - 30337876456*sqrt(2)*tan(1/2*a)^60 - 24685712920*sqrt(2)*tan(1/2*a)^58
- 5629982106*sqrt(2)*tan(1/2*a)^56 + 19969391706*sqrt(2)*tan(1/2*a)^54 + 37658626338*sqrt(2)*tan(1/2*a)^52 +
36190152990*sqrt(2)*tan(1/2*a)^50 + 18717018180*sqrt(2)*tan(1/2*a)^48 + 2040819900*sqrt(2)*tan(1/2*a)^46 + 204
0819900*sqrt(2)*tan(1/2*a)^44 + 18717018180*sqrt(2)*tan(1/2*a)^42 + 36190152990*sqrt(2)*tan(1/2*a)^40 + 376586
26338*sqrt(2)*tan(1/2*a)^38 + 19969391706*sqrt(2)*tan(1/2*a)^36 - 5629982106*sqrt(2)*tan(1/2*a)^34 - 246857129
20*sqrt(2)*tan(1/2*a)^32 - 30337876456*sqrt(2)*tan(1/2*a)^30 - 25186632744*sqrt(2)*tan(1/2*a)^28 - 16006283224
*sqrt(2)*tan(1/2*a)^26 - 8089589961*sqrt(2)*tan(1/2*a)^24 - 3278963927*sqrt(2)*tan(1/2*a)^22 - 1054367027*sqrt
(2)*tan(1/2*a)^20 - 259557037*sqrt(2)*tan(1/2*a)^18 - 44470106*sqrt(2)*tan(1/2*a)^16 - 3503654*sqrt(2)*tan(1/2
*a)^14 + 611706*sqrt(2)*tan(1/2*a)^12 + 267014*sqrt(2)*tan(1/2*a)^10 + 46575*sqrt(2)*tan(1/2*a)^8 + 4529*sqrt(
2)*tan(1/2*a)^6 + 221*sqrt(2)*tan(1/2*a)^4 + 3*sqrt(2)*tan(1/2*a)^2)/(tan(1/2*a)^78 + 34*tan(1/2*a)^76 + 559*t
an(1/2*a)^74 + 5916*tan(1/2*a)^72 + 45255*tan(1/2*a)^70 + 266322*tan(1/2*a)^68 + 1252713*tan(1/2*a)^66 + 48290
88*tan(1/2*a)^64 + 15512772*tan(1/2*a)^62 + 41970280*tan(1/2*a)^60 + 96160636*tan(1/2*a)^58 + 186574864*tan(1/
2*a)^56 + 304253964*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*a)^4
8 - 31635810*tan(1/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955277400*tan(1/2*a)^40 - 811
985790*tan(1/2*a)^38 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426395700*
tan(1/2*a)^30 + 408239496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*tan(1/2
*a)^22 + 41970280*tan(1/2*a)^20 + 15512772*tan(1/2*a)^18 + 4829088*tan(1/2*a)^16 + 1252713*tan(1/2*a)^14 + 266
322*tan(1/2*a)^12 + 45255*tan(1/2*a)^10 + 5916*tan(1/2*a)^8 + 559*tan(1/2*a)^6 + 34*tan(1/2*a)^4 + tan(1/2*a)^
2))*sin(a)/((tan(1/2*b*x)^4*tan(1/2*a)^3 + tan(1/2*b*x)^3*tan(1/2*a)^4 - tan(1/2*b*x)^4*tan(1/2*a) - 6*tan(1/2
*b*x)^3*tan(1/2*a)^2 - 6*tan(1/2*b*x)^2*tan(1/2*a)^3 - tan(1/2*b*x)*tan(1/2*a)^4 + tan(1/2*b*x)^3 + 6*tan(1/2*
b*x)^2*tan(1/2*a) + 6*tan(1/2*b*x)*tan(1/2*a)^2 + tan(1/2*a)^3 - tan(1/2*b*x) - tan(1/2*a))^3*b)
Mupad [B] (verification not implemented)
Time = 24.05 (sec) , antiderivative size = 131, normalized size of antiderivative = 1.66
\[
\int \frac {\sin (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx=\frac {4\,{\mathrm {e}}^{a\,1{}\mathrm {i}+b\,x\,1{}\mathrm {i}}\,\sqrt {\frac {{\mathrm {e}}^{-a\,2{}\mathrm {i}-b\,x\,2{}\mathrm {i}}\,1{}\mathrm {i}}{2}-\frac {{\mathrm {e}}^{a\,2{}\mathrm {i}+b\,x\,2{}\mathrm {i}}\,1{}\mathrm {i}}{2}}\,\left (2\,{\mathrm {e}}^{a\,2{}\mathrm {i}+b\,x\,2{}\mathrm {i}}-3\,{\mathrm {e}}^{a\,4{}\mathrm {i}+b\,x\,4{}\mathrm {i}}+2\,{\mathrm {e}}^{a\,6{}\mathrm {i}+b\,x\,6{}\mathrm {i}}+2\,{\mathrm {e}}^{a\,8{}\mathrm {i}+b\,x\,8{}\mathrm {i}}+2\right )}{15\,b\,{\left ({\mathrm {e}}^{a\,2{}\mathrm {i}+b\,x\,2{}\mathrm {i}}-1\right )}^2\,{\left ({\mathrm {e}}^{a\,2{}\mathrm {i}+b\,x\,2{}\mathrm {i}}+1\right )}^3}
\]
[In]
int(sin(a + b*x)/sin(2*a + 2*b*x)^(7/2),x)
[Out]
(4*exp(a*1i + b*x*1i)*((exp(- a*2i - b*x*2i)*1i)/2 - (exp(a*2i + b*x*2i)*1i)/2)^(1/2)*(2*exp(a*2i + b*x*2i) -
3*exp(a*4i + b*x*4i) + 2*exp(a*6i + b*x*6i) + 2*exp(a*8i + b*x*8i) + 2))/(15*b*(exp(a*2i + b*x*2i) - 1)^2*(exp
(a*2i + b*x*2i) + 1)^3)