\(\int \frac {\cos (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx\) [167]
Optimal result
Integrand size = 20, antiderivative size = 79 \[
\int \frac {\cos (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx=-\frac {\cos (a+b x)}{5 b \sin ^{\frac {5}{2}}(2 a+2 b x)}+\frac {4 \sin (a+b x)}{15 b \sin ^{\frac {3}{2}}(2 a+2 b x)}-\frac {8 \cos (a+b x)}{15 b \sqrt {\sin (2 a+2 b x)}}
\]
[Out]
-1/5*cos(b*x+a)/b/sin(2*b*x+2*a)^(5/2)+4/15*sin(b*x+a)/b/sin(2*b*x+2*a)^(3/2)-8/15*cos(b*x+a)/b/sin(2*b*x+2*a)
^(1/2)
Rubi [A] (verified)
Time = 0.07 (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 = {4388, 4389, 4376}
\[
\int \frac {\cos (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx=\frac {4 \sin (a+b x)}{15 b \sin ^{\frac {3}{2}}(2 a+2 b x)}-\frac {\cos (a+b x)}{5 b \sin ^{\frac {5}{2}}(2 a+2 b x)}-\frac {8 \cos (a+b x)}{15 b \sqrt {\sin (2 a+2 b x)}}
\]
[In]
Int[Cos[a + b*x]/Sin[2*a + 2*b*x]^(7/2),x]
[Out]
-1/5*Cos[a + b*x]/(b*Sin[2*a + 2*b*x]^(5/2)) + (4*Sin[a + b*x])/(15*b*Sin[2*a + 2*b*x]^(3/2)) - (8*Cos[a + b*x
])/(15*b*Sqrt[Sin[2*a + 2*b*x]])
Rule 4376
Int[(cos[(a_.) + (b_.)*(x_)]*(e_.))^(m_.)*((g_.)*sin[(c_.) + (d_.)*(x_)])^(p_), x_Symbol] :> Simp[(-(e*Cos[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] &&
EqQ[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 {\cos (a+b x)}{5 b \sin ^{\frac {5}{2}}(2 a+2 b x)}+\frac {4}{5} \int \frac {\sin (a+b x)}{\sin ^{\frac {5}{2}}(2 a+2 b x)} \, dx \\ & = -\frac {\cos (a+b x)}{5 b \sin ^{\frac {5}{2}}(2 a+2 b x)}+\frac {4 \sin (a+b x)}{15 b \sin ^{\frac {3}{2}}(2 a+2 b x)}+\frac {8}{15} \int \frac {\cos (a+b x)}{\sin ^{\frac {3}{2}}(2 a+2 b x)} \, dx \\ & = -\frac {\cos (a+b x)}{5 b \sin ^{\frac {5}{2}}(2 a+2 b x)}+\frac {4 \sin (a+b x)}{15 b \sin ^{\frac {3}{2}}(2 a+2 b x)}-\frac {8 \cos (a+b x)}{15 b \sqrt {\sin (2 a+2 b x)}} \\
\end{align*}
Mathematica [A] (verified)
Time = 0.39 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.66
\[
\int \frac {\cos (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx=-\frac {\sqrt {\sin (2 (a+b x))} \left (27 \csc (a+b x)+3 \csc ^3(a+b x)-5 \sec (a+b x) \tan (a+b x)\right )}{120 b}
\]
[In]
Integrate[Cos[a + b*x]/Sin[2*a + 2*b*x]^(7/2),x]
[Out]
-1/120*(Sqrt[Sin[2*(a + b*x)]]*(27*Csc[a + b*x] + 3*Csc[a + b*x]^3 - 5*Sec[a + b*x]*Tan[a + b*x]))/b
Maple [C] (verified)
Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 231.20 (sec) , antiderivative size = 481, normalized size of antiderivative =
6.09
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| method | result | size |
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\(-\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 (24 \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 )+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 {EllipticE}\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 )^{2}-12 \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 )+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 )^{2}+\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 )}\, \tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{6}+12 \sqrt {\tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{3}-\tan \left (\frac {a}{2}+\frac {x b}{2}\right )}\, \tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{4}-\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 )}\, \tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{4}-12 \sqrt {\tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{3}-\tan \left (\frac {a}{2}+\frac {x b}{2}\right )}\, \tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{2}-\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 )}\, \tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{2}+\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 )}\right )}{160 b \tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{3} \sqrt {\tan \left (\frac {a}{2}+\frac {x b}{2}\right )^{3}-\tan \left (\frac {a}{2}+\frac {x b}{2}\right )}}\) |
\(481\) |
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[In]
int(cos(b*x+a)/sin(2*b*x+2*a)^(7/2),x,method=_RETURNVERBOSE)
[Out]
-1/160/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)^3*(24*(tan(1/2*a+1/2*x*b)*(ta
n(1/2*a+1/2*x*b)^2-1))^(1/2)*(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)*EllipticE((tan(1/2*a+1/2*x*b)+1)^(1/2),1/2*2^(1/2))*tan(1/2*a+1/2*x*b)^2-12*(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)+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)^2+(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)^6+12*(tan(1/2*a+1/2*x*b)^3-tan(1/2*a+1/2*x*b))^(1/2)*tan(1/2*a+1/2*x*b)
^4-(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)^4-12*(tan(1/2*a+1/2*x*b)^3-tan(1/2*a
+1/2*x*b))^(1/2)*tan(1/2*a+1/2*x*b)^2-(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
+(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)
Fricas [A] (verification not implemented)
none
Time = 0.25 (sec) , antiderivative size = 103, normalized size of antiderivative = 1.30
\[
\int \frac {\cos (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx=-\frac {\sqrt {2} {\left (32 \, \cos \left (b x + a\right )^{4} - 40 \, \cos \left (b x + a\right )^{2} + 5\right )} \sqrt {\cos \left (b x + a\right ) \sin \left (b x + a\right )} + 32 \, {\left (\cos \left (b x + a\right )^{4} - \cos \left (b x + a\right )^{2}\right )} \sin \left (b x + a\right )}{120 \, {\left (b \cos \left (b x + a\right )^{4} - b \cos \left (b x + a\right )^{2}\right )} \sin \left (b x + a\right )}
\]
[In]
integrate(cos(b*x+a)/sin(2*b*x+2*a)^(7/2),x, algorithm="fricas")
[Out]
-1/120*(sqrt(2)*(32*cos(b*x + a)^4 - 40*cos(b*x + a)^2 + 5)*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*(cos(b*x + a)
^4 - cos(b*x + a)^2)*sin(b*x + a))/((b*cos(b*x + a)^4 - b*cos(b*x + a)^2)*sin(b*x + a))
Sympy [F(-1)]
Timed out. \[
\int \frac {\cos (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx=\text {Timed out}
\]
[In]
integrate(cos(b*x+a)/sin(2*b*x+2*a)**(7/2),x)
[Out]
Timed out
Maxima [F]
\[
\int \frac {\cos (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx=\int { \frac {\cos \left (b x + a\right )}{\sin \left (2 \, b x + 2 \, a\right )^{\frac {7}{2}}} \,d x }
\]
[In]
integrate(cos(b*x+a)/sin(2*b*x+2*a)^(7/2),x, algorithm="maxima")
[Out]
integrate(cos(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 = 181.76 (sec) , antiderivative size = 18022, normalized size of antiderivative = 228.13
\[
\int \frac {\cos (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx=\text {Too large to display}
\]
[In]
integrate(cos(b*x+a)/sin(2*b*x+2*a)^(7/2),x, algorithm="giac")
[Out]
-1/960*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*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)^8
2 + 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*sqr
t(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)*t
an(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 + 2040819900*sqrt(2)*tan(1/2*a)^44
+ 18717018180*sqrt(2)*tan(1/2*a)^42 + 36190152990*sqrt(2)*tan(1/2*a)^40 + 37658626338*sqrt(2)*tan(1/2*a)^38 +
19969391706*sqrt(2)*tan(1/2*a)^36 - 5629982106*sqrt(2)*tan(1/2*a)^34 - 24685712920*sqrt(2)*tan(1/2*a)^32 - 30
337876456*sqrt(2)*tan(1/2*a)^30 - 25186632744*sqrt(2)*tan(1/2*a)^28 - 16006283224*sqrt(2)*tan(1/2*a)^26 - 8089
589961*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 + 5
916*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 + 304253
964*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 + 96160636*tan(1/2*a)^22 + 4197028
0*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)^1
2 + 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) + 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*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
+ 890085728*sqrt(2)*tan(1/2*a)^65 + 2628022520*sqrt(2)*tan(1/2*a)^63 + 5320760640*sqrt(2)*tan(1/2*a)^61 + 7702
020680*sqrt(2)*tan(1/2*a)^59 + 7118210080*sqrt(2)*tan(1/2*a)^57 + 995931978*sqrt(2)*tan(1/2*a)^55 - 1034040588
0*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)*tan(1/2*a)^41 + 21876041250*sq
rt(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
+ 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*s
qrt(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 + 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)^3
8 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426395700*tan(1/2*a)^30 + 408
239496*tan(1/2*a)^28 + 304253964*tan(1/2*a)^26 + 186574864*tan(1/2*a)^24 + 96160636*tan(1/2*a)^22 + 41970280*t
an(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 + 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)*t
an(1/2*a)^62 - 35649378760*sqrt(2)*tan(1/2*a)^60 - 108847849016*sqrt(2)*tan(1/2*a)^58 - 195926195474*sqrt(2)*t
an(1/2*a)^56 - 239921144622*sqrt(2)*tan(1/2*a)^54 - 175285727238*sqrt(2)*tan(1/2*a)^52 + 16173774150*sqrt(2)*t
an(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)*ta
n(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 - 11
98222*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 + 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) - 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)^73 - 56342949*sqrt(2)*tan(1/2*a)^71 + 123215524*sqrt(2)*tan(1/2*a)^69 + 1097715
993*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*sqr
t(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)^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 + 133
55950*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 +
286097760*tan(1/2*a)^48 - 31635810*tan(1/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 9552774
00*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 + 12527
13*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*sqr
t(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 + 12
733143623*sqrt(2)*tan(1/2*a)^70 + 35783324123*sqrt(2)*tan(1/2*a)^68 + 74211339589*sqrt(2)*tan(1/2*a)^66 + 1041
06628984*sqrt(2)*tan(1/2*a)^64 + 53304671368*sqrt(2)*tan(1/2*a)^62 - 186214147256*sqrt(2)*tan(1/2*a)^60 - 6704
82449224*sqrt(2)*tan(1/2*a)^58 - 1265075297422*sqrt(2)*tan(1/2*a)^56 - 1589441527602*sqrt(2)*tan(1/2*a)^54 - 1
195845166554*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)^
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)^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)^
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 - 361028
6*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 + 40823
9496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*a)^48 - 31635810*tan(1/2*a)^46 - 450345060*ta
n(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 + 1551277
2*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*sqr
t(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)^6
7 + 24180464352*sqrt(2)*tan(1/2*a)^65 + 64435678680*sqrt(2)*tan(1/2*a)^63 + 124255267392*sqrt(2)*tan(1/2*a)^61
+ 174119463528*sqrt(2)*tan(1/2*a)^59 + 154983313568*sqrt(2)*tan(1/2*a)^57 + 11631799602*sqrt(2)*tan(1/2*a)^55
- 245542884696*sqrt(2)*tan(1/2*a)^53 - 502777140330*sqrt(2)*tan(1/2*a)^51 - 589160081520*sqrt(2)*tan(1/2*a)^4
9 - 400029234660*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
- 19819756*sqrt(2)*tan(1/2*a)^21 + 689517231*sqrt(2)*tan(1/2*a)^19 + 363601272*sqrt(2)*tan(1/2*a)^17 + 114767
242*sqrt(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)*ta
n(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 + 125
2713*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)^5
0 + 286097760*tan(1/2*a)^48 - 31635810*tan(1/2*a)^46 - 450345060*tan(1/2*a)^44 - 811985790*tan(1/2*a)^42 - 955
277400*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 + 1
252713*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
+ 12733143623*sqrt(2)*tan(1/2*a)^70 + 35783324123*sqrt(2)*tan(1/2*a)^68 + 74211339589*sqrt(2)*tan(1/2*a)^66 +
104106628984*sqrt(2)*tan(1/2*a)^64 + 53304671368*sqrt(2)*tan(1/2*a)^62 - 186214147256*sqrt(2)*tan(1/2*a)^60 -
670482449224*sqrt(2)*tan(1/2*a)^58 - 1265075297422*sqrt(2)*tan(1/2*a)^56 - 1589441527602*sqrt(2)*tan(1/2*a)^54
- 1195845166554*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)^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)^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)^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 - 36
10286*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 + 4
5255*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 + 4
08239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*a)^48 - 31635810*tan(1/2*a)^46 - 45034506
0*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 + 155
12772*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)*ta
n(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*sqr
t(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 + 26
200319352*sqrt(2)*tan(1/2*a)^59 + 22729855712*sqrt(2)*tan(1/2*a)^57 + 667102950*sqrt(2)*tan(1/2*a)^55 - 381198
07944*sqrt(2)*tan(1/2*a)^53 - 76473192270*sqrt(2)*tan(1/2*a)^51 - 88969283280*sqrt(2)*tan(1/2*a)^49 - 60215972
940*sqrt(2)*tan(1/2*a)^47 + 60215972940*sqrt(2)*tan(1/2*a)^43 + 88969283280*sqrt(2)*tan(1/2*a)^41 + 7647319227
0*sqrt(2)*tan(1/2*a)^39 + 38119807944*sqrt(2)*tan(1/2*a)^37 - 667102950*sqrt(2)*tan(1/2*a)^35 - 22729855712*sq
rt(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)*ta
n(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*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) - 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*sqr
t(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 + 47
48442805*sqrt(2)*tan(1/2*a)^68 + 9550300715*sqrt(2)*tan(1/2*a)^66 + 12322646792*sqrt(2)*tan(1/2*a)^64 + 238841
8808*sqrt(2)*tan(1/2*a)^62 - 35649378760*sqrt(2)*tan(1/2*a)^60 - 108847849016*sqrt(2)*tan(1/2*a)^58 - 19592619
5474*sqrt(2)*tan(1/2*a)^56 - 239921144622*sqrt(2)*tan(1/2*a)^54 - 175285727238*sqrt(2)*tan(1/2*a)^52 + 1617377
4150*sqrt(2)*tan(1/2*a)^50 + 265568681460*sqrt(2)*tan(1/2*a)^48 + 442624681740*sqrt(2)*tan(1/2*a)^46 + 4426246
81740*sqrt(2)*tan(1/2*a)^44 + 265568681460*sqrt(2)*tan(1/2*a)^42 + 16173774150*sqrt(2)*tan(1/2*a)^40 - 1752857
27238*sqrt(2)*tan(1/2*a)^38 - 239921144622*sqrt(2)*tan(1/2*a)^36 - 195926195474*sqrt(2)*tan(1/2*a)^34 - 108847
849016*sqrt(2)*tan(1/2*a)^32 - 35649378760*sqrt(2)*tan(1/2*a)^30 + 2388418808*sqrt(2)*tan(1/2*a)^28 + 12322646
792*sqrt(2)*tan(1/2*a)^26 + 9550300715*sqrt(2)*tan(1/2*a)^24 + 4748442805*sqrt(2)*tan(1/2*a)^22 + 1715629705*s
qrt(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*s
qrt(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 + 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) + 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 - 19
880*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 + 890085728*sqrt(2)*tan(1/2*a)^65 + 2628022520*sqrt(2)*tan(1/2*a)^63 + 53207
60640*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*sq
rt(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)^2
3 + 52560260*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 + 1
86574864*tan(1/2*a)^56 + 304253964*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 2860977
60*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 + 9
6160636*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) - (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*sq
rt(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)*ta
n(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
+ 2040819900*sqrt(2)*tan(1/2*a)^44 + 18717018180*sqrt(2)*tan(1/2*a)^42 + 36190152990*sqrt(2)*tan(1/2*a)^40 + 3
7658626338*sqrt(2)*tan(1/2*a)^38 + 19969391706*sqrt(2)*tan(1/2*a)^36 - 5629982106*sqrt(2)*tan(1/2*a)^34 - 2468
5712920*sqrt(2)*tan(1/2*a)^32 - 30337876456*sqrt(2)*tan(1/2*a)^30 - 25186632744*sqrt(2)*tan(1/2*a)^28 - 160062
83224*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)*ta
n(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*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))*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*ta
n(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) - 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*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))*((((((((((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 - 4434
62*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)*t
an(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 - 32418
15576*sqrt(2)*tan(1/2*a)^53 - 11030972730*sqrt(2)*tan(1/2*a)^51 - 14712027120*sqrt(2)*tan(1/2*a)^49 - 10524179
460*sqrt(2)*tan(1/2*a)^47 + 10524179460*sqrt(2)*tan(1/2*a)^43 + 14712027120*sqrt(2)*tan(1/2*a)^41 + 1103097273
0*sqrt(2)*tan(1/2*a)^39 + 3241815576*sqrt(2)*tan(1/2*a)^37 - 3316624962*sqrt(2)*tan(1/2*a)^35 - 5742984608*sqr
t(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)*t
an(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 + 287
5040*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*b*x)/(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
) + 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 - 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 + 4409
972669*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)*t
an(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 - 4503
45060*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) - 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 - 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)^6
7 + 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 - 381
19807944*sqrt(2)*tan(1/2*a)^53 - 76473192270*sqrt(2)*tan(1/2*a)^51 - 88969283280*sqrt(2)*tan(1/2*a)^49 - 60215
972940*sqrt(2)*tan(1/2*a)^47 + 60215972940*sqrt(2)*tan(1/2*a)^43 + 88969283280*sqrt(2)*tan(1/2*a)^41 + 7647319
2270*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*s
qrt(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 + 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 - 81198
5790*tan(1/2*a)^38 - 450345060*tan(1/2*a)^36 - 31635810*tan(1/2*a)^34 + 286097760*tan(1/2*a)^32 + 426395700*ta
n(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 + 26632
2*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)*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 + 238
8418808*sqrt(2)*tan(1/2*a)^62 - 35649378760*sqrt(2)*tan(1/2*a)^60 - 108847849016*sqrt(2)*tan(1/2*a)^58 - 19592
6195474*sqrt(2)*tan(1/2*a)^56 - 239921144622*sqrt(2)*tan(1/2*a)^54 - 175285727238*sqrt(2)*tan(1/2*a)^52 + 1617
3774150*sqrt(2)*tan(1/2*a)^50 + 265568681460*sqrt(2)*tan(1/2*a)^48 + 442624681740*sqrt(2)*tan(1/2*a)^46 + 4426
24681740*sqrt(2)*tan(1/2*a)^44 + 265568681460*sqrt(2)*tan(1/2*a)^42 + 16173774150*sqrt(2)*tan(1/2*a)^40 - 1752
85727238*sqrt(2)*tan(1/2*a)^38 - 239921144622*sqrt(2)*tan(1/2*a)^36 - 195926195474*sqrt(2)*tan(1/2*a)^34 - 108
847849016*sqrt(2)*tan(1/2*a)^32 - 35649378760*sqrt(2)*tan(1/2*a)^30 + 2388418808*sqrt(2)*tan(1/2*a)^28 + 12322
646792*sqrt(2)*tan(1/2*a)^26 + 9550300715*sqrt(2)*tan(1/2*a)^24 + 4748442805*sqrt(2)*tan(1/2*a)^22 + 171562970
5*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)*t
an(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 - 649
9*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 + 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))*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 - 10767537
8*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*sqrt(2)*t
an(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)*t
an(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 + 252641475000*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)*t
an(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 + 3
382830*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 - 4503450
60*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 + 15
512772*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 - 3687094
*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)*ta
n(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)*ta
n(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 - 1180267704498*sqrt
(2)*tan(1/2*a)^38 - 1544438285226*sqrt(2)*tan(1/2*a)^36 - 1211871261974*sqrt(2)*tan(1/2*a)^34 - 624756202280*s
qrt(2)*tan(1/2*a)^32 - 154548395224*sqrt(2)*tan(1/2*a)^30 + 71597541224*sqrt(2)*tan(1/2*a)^28 + 113030679704*s
qrt(2)*tan(1/2*a)^26 + 77890956881*sqrt(2)*tan(1/2*a)^24 + 37055436367*sqrt(2)*tan(1/2*a)^22 + 13095011467*sqr
t(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 - 508
09*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 + 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) - 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 - 10767
5378*sqrt(2)*tan(1/2*a)^75 - 334648920*sqrt(2)*tan(1/2*a)^73 - 591145035*sqrt(2)*tan(1/2*a)^71 + 300716060*sqr
t(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 + 252641475000*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 - 4503
45060*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*(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)*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 + 45273
7815*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*sq
rt(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 + 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) + 30*(1
9*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*sqr
t(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)^4
9 - 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 - 22
729855712*sqrt(2)*tan(1/2*a)^33 - 26200319352*sqrt(2)*tan(1/2*a)^31 - 19092105408*sqrt(2)*tan(1/2*a)^29 - 1019
5869000*sqrt(2)*tan(1/2*a)^27 - 4042423200*sqrt(2)*tan(1/2*a)^25 - 1097715993*sqrt(2)*tan(1/2*a)^23 - 12321552
4*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)*t
an(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 + 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))*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 - 3
1579*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)^7
0 + 2006851683*sqrt(2)*tan(1/2*a)^68 + 4409972669*sqrt(2)*tan(1/2*a)^66 + 7082232504*sqrt(2)*tan(1/2*a)^64 + 6
893762888*sqrt(2)*tan(1/2*a)^62 - 1327875576*sqrt(2)*tan(1/2*a)^60 - 21040534024*sqrt(2)*tan(1/2*a)^58 - 47574
053342*sqrt(2)*tan(1/2*a)^56 - 64972634082*sqrt(2)*tan(1/2*a)^54 - 53236088394*sqrt(2)*tan(1/2*a)^52 - 5004094
710*sqrt(2)*tan(1/2*a)^50 + 61712915820*sqrt(2)*tan(1/2*a)^48 + 110145965460*sqrt(2)*tan(1/2*a)^46 + 110145965
460*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*s
qrt(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)^7
4 + 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 + 3
04253964*tan(1/2*a)^54 + 408239496*tan(1/2*a)^52 + 426395700*tan(1/2*a)^50 + 286097760*tan(1/2*a)^48 - 3163581
0*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 + 41
970280*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) - 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 - 517
81432*sqrt(2)*tan(1/2*a)^73 - 149943911*sqrt(2)*tan(1/2*a)^71 - 333456564*sqrt(2)*tan(1/2*a)^69 - 536442973*sq
rt(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)*t
an(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 - 3162
21080*sqrt(2)*tan(1/2*a)^27 + 482080288*sqrt(2)*tan(1/2*a)^25 + 536442973*sqrt(2)*tan(1/2*a)^23 + 333456564*sq
rt(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*s
qrt(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 + 4829
088*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 - 81
1985790*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 + 26
6322*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 = 23.30 (sec) , antiderivative size = 136, normalized size of antiderivative = 1.72
\[
\int \frac {\cos (a+b x)}{\sin ^{\frac {7}{2}}(2 a+2 b x)} \, dx=\frac {4\,{\mathrm {e}}^{a\,1{}\mathrm {i}+b\,x\,1{}\mathrm {i}}\,\sqrt {\frac {{\mathrm {e}}^{-a\,2{}\mathrm {i}-b\,x\,2{}\mathrm {i}}\,1{}\mathrm {i}}{2}-\frac {{\mathrm {e}}^{a\,2{}\mathrm {i}+b\,x\,2{}\mathrm {i}}\,1{}\mathrm {i}}{2}}\,\left ({\mathrm {e}}^{a\,2{}\mathrm {i}+b\,x\,2{}\mathrm {i}}\,2{}\mathrm {i}+{\mathrm {e}}^{a\,4{}\mathrm {i}+b\,x\,4{}\mathrm {i}}\,3{}\mathrm {i}+{\mathrm {e}}^{a\,6{}\mathrm {i}+b\,x\,6{}\mathrm {i}}\,2{}\mathrm {i}-{\mathrm {e}}^{a\,8{}\mathrm {i}+b\,x\,8{}\mathrm {i}}\,2{}\mathrm {i}-2{}\mathrm {i}\right )}{15\,b\,{\left ({\mathrm {e}}^{a\,2{}\mathrm {i}+b\,x\,2{}\mathrm {i}}-1\right )}^3\,{\left ({\mathrm {e}}^{a\,2{}\mathrm {i}+b\,x\,2{}\mathrm {i}}+1\right )}^2}
\]
[In]
int(cos(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)*(exp(a*2i + b*x*2i)*2i +
exp(a*4i + b*x*4i)*3i + exp(a*6i + b*x*6i)*2i - exp(a*8i + b*x*8i)*2i - 2i))/(15*b*(exp(a*2i + b*x*2i) - 1)^3
*(exp(a*2i + b*x*2i) + 1)^2)