\(\int \cos ^7(c+d x) (a+b \tan ^2(c+d x)) \, dx\) [430]
Optimal result
Integrand size = 21, antiderivative size = 76 \[
\int \cos ^7(c+d x) \left (a+b \tan ^2(c+d x)\right ) \, dx=\frac {a \sin (c+d x)}{d}-\frac {(3 a-b) \sin ^3(c+d x)}{3 d}+\frac {(3 a-2 b) \sin ^5(c+d x)}{5 d}-\frac {(a-b) \sin ^7(c+d x)}{7 d}
\]
[Out]
a*sin(d*x+c)/d-1/3*(3*a-b)*sin(d*x+c)^3/d+1/5*(3*a-2*b)*sin(d*x+c)^5/d-1/7*(a-b)*sin(d*x+c)^7/d
Rubi [A] (verified)
Time = 0.07 (sec) , antiderivative size = 76, normalized size of antiderivative = 1.00,
number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {3757, 380}
\[
\int \cos ^7(c+d x) \left (a+b \tan ^2(c+d x)\right ) \, dx=-\frac {(a-b) \sin ^7(c+d x)}{7 d}+\frac {(3 a-2 b) \sin ^5(c+d x)}{5 d}-\frac {(3 a-b) \sin ^3(c+d x)}{3 d}+\frac {a \sin (c+d x)}{d}
\]
[In]
Int[Cos[c + d*x]^7*(a + b*Tan[c + d*x]^2),x]
[Out]
(a*Sin[c + d*x])/d - ((3*a - b)*Sin[c + d*x]^3)/(3*d) + ((3*a - 2*b)*Sin[c + d*x]^5)/(5*d) - ((a - b)*Sin[c +
d*x]^7)/(7*d)
Rule 380
Int[((a_) + (b_.)*(x_)^(n_))^(p_.)*((c_) + (d_.)*(x_)^(n_))^(q_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x^n
)^p*(c + d*x^n)^q, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[p, 0] && IGtQ[q, 0]
Rule 3757
Int[sec[(e_.) + (f_.)*(x_)]^(m_.)*((a_) + (b_.)*tan[(e_.) + (f_.)*(x_)]^(n_))^(p_.), x_Symbol] :> With[{ff = F
reeFactors[Sin[e + f*x], x]}, Dist[ff/f, Subst[Int[ExpandToSum[b*(ff*x)^n + a*(1 - ff^2*x^2)^(n/2), x]^p/(1 -
ff^2*x^2)^((m + n*p + 1)/2), x], x, Sin[e + f*x]/ff], x]] /; FreeQ[{a, b, e, f}, x] && IntegerQ[(m - 1)/2] &&
IntegerQ[n/2] && IntegerQ[p]
Rubi steps \begin{align*}
\text {integral}& = \frac {\text {Subst}\left (\int \left (1-x^2\right )^2 \left (a-(a-b) x^2\right ) \, dx,x,\sin (c+d x)\right )}{d} \\ & = \frac {\text {Subst}\left (\int \left (a-(3 a-b) x^2+(3 a-2 b) x^4-(a-b) x^6\right ) \, dx,x,\sin (c+d x)\right )}{d} \\ & = \frac {a \sin (c+d x)}{d}-\frac {(3 a-b) \sin ^3(c+d x)}{3 d}+\frac {(3 a-2 b) \sin ^5(c+d x)}{5 d}-\frac {(a-b) \sin ^7(c+d x)}{7 d} \\
\end{align*}
Mathematica [A] (verified)
Time = 0.29 (sec) , antiderivative size = 75, normalized size of antiderivative = 0.99
\[
\int \cos ^7(c+d x) \left (a+b \tan ^2(c+d x)\right ) \, dx=\frac {(2286 a+206 b+(897 a-113 b) \cos (2 (c+d x))+6 (27 a-13 b) \cos (4 (c+d x))+15 a \cos (6 (c+d x))-15 b \cos (6 (c+d x))) \sin (c+d x)}{3360 d}
\]
[In]
Integrate[Cos[c + d*x]^7*(a + b*Tan[c + d*x]^2),x]
[Out]
((2286*a + 206*b + (897*a - 113*b)*Cos[2*(c + d*x)] + 6*(27*a - 13*b)*Cos[4*(c + d*x)] + 15*a*Cos[6*(c + d*x)]
- 15*b*Cos[6*(c + d*x)])*Sin[c + d*x])/(3360*d)
Maple [A] (verified)
Time = 20.65 (sec) , antiderivative size = 92, normalized size of antiderivative = 1.21
| | |
| method | result | size |
| | |
| derivativedivides |
\(\frac {b \left (-\frac {\sin \left (d x +c \right ) \cos \left (d x +c \right )^{6}}{7}+\frac {\left (\frac {8}{3}+\cos \left (d x +c \right )^{4}+\frac {4 \cos \left (d x +c \right )^{2}}{3}\right ) \sin \left (d x +c \right )}{35}\right )+\frac {a \left (\frac {16}{5}+\cos \left (d x +c \right )^{6}+\frac {6 \cos \left (d x +c \right )^{4}}{5}+\frac {8 \cos \left (d x +c \right )^{2}}{5}\right ) \sin \left (d x +c \right )}{7}}{d}\) |
\(92\) |
| default |
\(\frac {b \left (-\frac {\sin \left (d x +c \right ) \cos \left (d x +c \right )^{6}}{7}+\frac {\left (\frac {8}{3}+\cos \left (d x +c \right )^{4}+\frac {4 \cos \left (d x +c \right )^{2}}{3}\right ) \sin \left (d x +c \right )}{35}\right )+\frac {a \left (\frac {16}{5}+\cos \left (d x +c \right )^{6}+\frac {6 \cos \left (d x +c \right )^{4}}{5}+\frac {8 \cos \left (d x +c \right )^{2}}{5}\right ) \sin \left (d x +c \right )}{7}}{d}\) |
\(92\) |
| risch |
\(\frac {35 a \sin \left (d x +c \right )}{64 d}+\frac {5 \sin \left (d x +c \right ) b}{64 d}+\frac {\sin \left (7 d x +7 c \right ) a}{448 d}-\frac {\sin \left (7 d x +7 c \right ) b}{448 d}+\frac {7 \sin \left (5 d x +5 c \right ) a}{320 d}-\frac {3 \sin \left (5 d x +5 c \right ) b}{320 d}+\frac {7 \sin \left (3 d x +3 c \right ) a}{64 d}-\frac {\sin \left (3 d x +3 c \right ) b}{192 d}\) |
\(116\) |
| | |
|
|
|
|
[In]
int(cos(d*x+c)^7*(a+b*tan(d*x+c)^2),x,method=_RETURNVERBOSE)
[Out]
1/d*(b*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+1/7*a*(16/5+cos(d*x+
c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))
Fricas [A] (verification not implemented)
none
Time = 0.26 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.83
\[
\int \cos ^7(c+d x) \left (a+b \tan ^2(c+d x)\right ) \, dx=\frac {{\left (15 \, {\left (a - b\right )} \cos \left (d x + c\right )^{6} + 3 \, {\left (6 \, a + b\right )} \cos \left (d x + c\right )^{4} + 4 \, {\left (6 \, a + b\right )} \cos \left (d x + c\right )^{2} + 48 \, a + 8 \, b\right )} \sin \left (d x + c\right )}{105 \, d}
\]
[In]
integrate(cos(d*x+c)^7*(a+b*tan(d*x+c)^2),x, algorithm="fricas")
[Out]
1/105*(15*(a - b)*cos(d*x + c)^6 + 3*(6*a + b)*cos(d*x + c)^4 + 4*(6*a + b)*cos(d*x + c)^2 + 48*a + 8*b)*sin(d
*x + c)/d
Sympy [F]
\[
\int \cos ^7(c+d x) \left (a+b \tan ^2(c+d x)\right ) \, dx=\int \left (a + b \tan ^{2}{\left (c + d x \right )}\right ) \cos ^{7}{\left (c + d x \right )}\, dx
\]
[In]
integrate(cos(d*x+c)**7*(a+b*tan(d*x+c)**2),x)
[Out]
Integral((a + b*tan(c + d*x)**2)*cos(c + d*x)**7, x)
Maxima [A] (verification not implemented)
none
Time = 0.27 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.84
\[
\int \cos ^7(c+d x) \left (a+b \tan ^2(c+d x)\right ) \, dx=-\frac {15 \, {\left (a - b\right )} \sin \left (d x + c\right )^{7} - 21 \, {\left (3 \, a - 2 \, b\right )} \sin \left (d x + c\right )^{5} + 35 \, {\left (3 \, a - b\right )} \sin \left (d x + c\right )^{3} - 105 \, a \sin \left (d x + c\right )}{105 \, d}
\]
[In]
integrate(cos(d*x+c)^7*(a+b*tan(d*x+c)^2),x, algorithm="maxima")
[Out]
-1/105*(15*(a - b)*sin(d*x + c)^7 - 21*(3*a - 2*b)*sin(d*x + c)^5 + 35*(3*a - b)*sin(d*x + c)^3 - 105*a*sin(d*
x + c))/d
Giac [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 29589 vs. \(2 (70) = 140\).
Time = 18.71 (sec) , antiderivative size = 29589, normalized size of antiderivative = 389.33
\[
\int \cos ^7(c+d x) \left (a+b \tan ^2(c+d x)\right ) \, dx=\text {Too large to display}
\]
[In]
integrate(cos(d*x+c)^7*(a+b*tan(d*x+c)^2),x, algorithm="giac")
[Out]
-1/6720*(12705*a*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^13 + 147*a*tan(5/2*d*x)^2*tan(1/2*d*x)
^14*tan(5/2*c)*tan(1/2*c)^14 + 12705*a*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^14 + 147*a*tan(5
/2*d*x)*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^14 + 34230*a*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1
/2*c)^11 + 17920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^11 + 1029*a*tan(5/2*d*x)^2*tan(1/2*d
*x)^14*tan(5/2*c)*tan(1/2*c)^12 - 62475*a*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^12 + 53760*b*
tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^12 + 1029*a*tan(5/2*d*x)*tan(1/2*d*x)^14*tan(5/2*c)^2*t
an(1/2*c)^12 + 12705*a*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(1/2*c)^13 - 62475*a*tan(5/2*d*x)^2*tan(1/2*d*x)^12*t
an(5/2*c)^2*tan(1/2*c)^13 + 53760*b*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^13 + 12705*a*tan(1/
2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^13 + 12705*a*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(1/2*c)^14 - 147*a*tan(5/2*d*
x)*tan(1/2*d*x)^14*tan(1/2*c)^14 + 1029*a*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)*tan(1/2*c)^14 - 147*a*tan(
1/2*d*x)^14*tan(5/2*c)*tan(1/2*c)^14 + 34230*a*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^14 + 179
20*b*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^14 + 1029*a*tan(5/2*d*x)*tan(1/2*d*x)^12*tan(5/2*c
)^2*tan(1/2*c)^14 + 12705*a*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^14 + 113967*a*tan(5/2*d*x)^2*tan(1/2*d*x)^
14*tan(5/2*c)^2*tan(1/2*c)^9 - 14336*b*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^9 + 3087*a*tan(5
/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)*tan(1/2*c)^10 + 193305*a*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(
1/2*c)^10 - 268800*b*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^10 + 3087*a*tan(5/2*d*x)*tan(1/2*d
*x)^14*tan(5/2*c)^2*tan(1/2*c)^10 + 34230*a*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(1/2*c)^11 + 17920*b*tan(5/2*d*x
)^2*tan(1/2*d*x)^14*tan(1/2*c)^11 + 1001070*a*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^11 - 7347
20*b*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^11 + 34230*a*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*
c)^11 + 17920*b*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^11 - 62475*a*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(1/2*c)
^12 + 53760*b*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(1/2*c)^12 - 1029*a*tan(5/2*d*x)*tan(1/2*d*x)^14*tan(1/2*c)^12
+ 7203*a*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)*tan(1/2*c)^12 - 1029*a*tan(1/2*d*x)^14*tan(5/2*c)*tan(1/2*
c)^12 + 1001070*a*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^12 - 734720*b*tan(5/2*d*x)^2*tan(1/2*
d*x)^11*tan(5/2*c)^2*tan(1/2*c)^12 + 7203*a*tan(5/2*d*x)*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^12 - 62475*a*
tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^12 + 53760*b*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^12 - 62475*a*tan(
5/2*d*x)^2*tan(1/2*d*x)^12*tan(1/2*c)^13 + 53760*b*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(1/2*c)^13 + 12705*a*tan(
1/2*d*x)^14*tan(1/2*c)^13 + 193305*a*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^13 - 268800*b*tan(
5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^13 - 62475*a*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^13 + 5
3760*b*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^13 + 34230*a*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(1/2*c)^14 + 179
20*b*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(1/2*c)^14 - 1029*a*tan(5/2*d*x)*tan(1/2*d*x)^12*tan(1/2*c)^14 + 12705*
a*tan(1/2*d*x)^13*tan(1/2*c)^14 + 3087*a*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)*tan(1/2*c)^14 - 1029*a*tan(
1/2*d*x)^12*tan(5/2*c)*tan(1/2*c)^14 + 113967*a*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^14 - 143
36*b*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^14 + 3087*a*tan(5/2*d*x)*tan(1/2*d*x)^10*tan(5/2*c)
^2*tan(1/2*c)^14 + 34230*a*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^14 + 17920*b*tan(1/2*d*x)^11*tan(5/2*c)^2*t
an(1/2*c)^14 + 62004*a*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^7 + 58368*b*tan(5/2*d*x)^2*tan(1
/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^7 + 5145*a*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)*tan(1/2*c)^8 - 591675*
a*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^8 + 537600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(5/2*c
)^2*tan(1/2*c)^8 + 5145*a*tan(5/2*d*x)*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^8 + 113967*a*tan(5/2*d*x)^2*tan
(1/2*d*x)^14*tan(1/2*c)^9 - 14336*b*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(1/2*c)^9 - 1943781*a*tan(5/2*d*x)^2*tan
(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^9 + 2856448*b*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^9 +
113967*a*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^9 - 14336*b*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^9 + 19330
5*a*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(1/2*c)^10 - 268800*b*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(1/2*c)^10 - 308
7*a*tan(5/2*d*x)*tan(1/2*d*x)^14*tan(1/2*c)^10 + 21609*a*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)*tan(1/2*c)^
10 - 3087*a*tan(1/2*d*x)^14*tan(5/2*c)*tan(1/2*c)^10 - 6072570*a*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(5/2*c)^2*t
an(1/2*c)^10 + 6289920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^10 + 21609*a*tan(5/2*d*x)*tan(
1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^10 + 193305*a*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^10 - 268800*b*tan(1/
2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^10 + 1001070*a*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(1/2*c)^11 - 734720*b*tan(5
/2*d*x)^2*tan(1/2*d*x)^12*tan(1/2*c)^11 + 34230*a*tan(1/2*d*x)^14*tan(1/2*c)^11 + 17920*b*tan(1/2*d*x)^14*tan(
1/2*c)^11 - 6072570*a*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^11 + 6289920*b*tan(5/2*d*x)^2*tan
(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^11 + 1001070*a*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^11 - 734720*b*tan(
1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^11 + 1001070*a*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(1/2*c)^12 - 734720*b*tan
(5/2*d*x)^2*tan(1/2*d*x)^11*tan(1/2*c)^12 - 7203*a*tan(5/2*d*x)*tan(1/2*d*x)^12*tan(1/2*c)^12 - 62475*a*tan(1/
2*d*x)^13*tan(1/2*c)^12 + 53760*b*tan(1/2*d*x)^13*tan(1/2*c)^12 + 21609*a*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5
/2*c)*tan(1/2*c)^12 - 7203*a*tan(1/2*d*x)^12*tan(5/2*c)*tan(1/2*c)^12 - 1943781*a*tan(5/2*d*x)^2*tan(1/2*d*x)^
9*tan(5/2*c)^2*tan(1/2*c)^12 + 2856448*b*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^12 + 21609*a*ta
n(5/2*d*x)*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^12 + 1001070*a*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^12 -
734720*b*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^12 + 193305*a*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(1/2*c)^13 -
268800*b*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(1/2*c)^13 - 62475*a*tan(1/2*d*x)^12*tan(1/2*c)^13 + 53760*b*tan(1
/2*d*x)^12*tan(1/2*c)^13 - 591675*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^13 + 537600*b*tan(5/
2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^13 + 193305*a*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^13 - 268
800*b*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^13 + 113967*a*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(1/2*c)^14 - 1433
6*b*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(1/2*c)^14 - 3087*a*tan(5/2*d*x)*tan(1/2*d*x)^10*tan(1/2*c)^14 + 34230*a*
tan(1/2*d*x)^11*tan(1/2*c)^14 + 17920*b*tan(1/2*d*x)^11*tan(1/2*c)^14 + 5145*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*t
an(5/2*c)*tan(1/2*c)^14 - 3087*a*tan(1/2*d*x)^10*tan(5/2*c)*tan(1/2*c)^14 + 62004*a*tan(5/2*d*x)^2*tan(1/2*d*x
)^7*tan(5/2*c)^2*tan(1/2*c)^14 + 58368*b*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^14 + 5145*a*tan
(5/2*d*x)*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^14 + 113967*a*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^14 - 143
36*b*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^14 + 113967*a*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*
c)^5 - 14336*b*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^5 + 5145*a*tan(5/2*d*x)^2*tan(1/2*d*x)^1
4*tan(5/2*c)*tan(1/2*c)^6 + 591675*a*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^6 - 537600*b*tan(5
/2*d*x)^2*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^6 + 5145*a*tan(5/2*d*x)*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2
*c)^6 + 62004*a*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(1/2*c)^7 + 58368*b*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(1/2*c
)^7 + 5167428*a*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^7 - 3892224*b*tan(5/2*d*x)^2*tan(1/2*d*
x)^12*tan(5/2*c)^2*tan(1/2*c)^7 + 62004*a*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^7 + 58368*b*tan(1/2*d*x)^14*
tan(5/2*c)^2*tan(1/2*c)^7 - 591675*a*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(1/2*c)^8 + 537600*b*tan(5/2*d*x)^2*tan
(1/2*d*x)^13*tan(1/2*c)^8 - 5145*a*tan(5/2*d*x)*tan(1/2*d*x)^14*tan(1/2*c)^8 + 36015*a*tan(5/2*d*x)^2*tan(1/2*
d*x)^12*tan(5/2*c)*tan(1/2*c)^8 - 5145*a*tan(1/2*d*x)^14*tan(5/2*c)*tan(1/2*c)^8 + 15324750*a*tan(5/2*d*x)^2*t
an(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^8 - 15321600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^8
+ 36015*a*tan(5/2*d*x)*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^8 - 591675*a*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(
1/2*c)^8 + 537600*b*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^8 - 1943781*a*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(1
/2*c)^9 + 2856448*b*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(1/2*c)^9 + 113967*a*tan(1/2*d*x)^14*tan(1/2*c)^9 - 1433
6*b*tan(1/2*d*x)^14*tan(1/2*c)^9 + 32337207*a*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^9 - 30137
856*b*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^9 - 1943781*a*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/
2*c)^9 + 2856448*b*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^9 - 6072570*a*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(1/
2*c)^10 + 6289920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(1/2*c)^10 - 21609*a*tan(5/2*d*x)*tan(1/2*d*x)^12*tan(1/
2*c)^10 + 193305*a*tan(1/2*d*x)^13*tan(1/2*c)^10 - 268800*b*tan(1/2*d*x)^13*tan(1/2*c)^10 + 64827*a*tan(5/2*d*
x)^2*tan(1/2*d*x)^10*tan(5/2*c)*tan(1/2*c)^10 - 21609*a*tan(1/2*d*x)^12*tan(5/2*c)*tan(1/2*c)^10 + 32337207*a*
tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^10 - 30137856*b*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(5/2*c)
^2*tan(1/2*c)^10 + 64827*a*tan(5/2*d*x)*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^10 - 6072570*a*tan(1/2*d*x)^11
*tan(5/2*c)^2*tan(1/2*c)^10 + 6289920*b*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^10 - 6072570*a*tan(5/2*d*x)^2*
tan(1/2*d*x)^10*tan(1/2*c)^11 + 6289920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(1/2*c)^11 + 1001070*a*tan(1/2*d*x
)^12*tan(1/2*c)^11 - 734720*b*tan(1/2*d*x)^12*tan(1/2*c)^11 + 15324750*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2
*c)^2*tan(1/2*c)^11 - 15321600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^11 - 6072570*a*tan(1/2*
d*x)^10*tan(5/2*c)^2*tan(1/2*c)^11 + 6289920*b*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^11 - 1943781*a*tan(5/2*
d*x)^2*tan(1/2*d*x)^9*tan(1/2*c)^12 + 2856448*b*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(1/2*c)^12 - 21609*a*tan(5/2*
d*x)*tan(1/2*d*x)^10*tan(1/2*c)^12 + 1001070*a*tan(1/2*d*x)^11*tan(1/2*c)^12 - 734720*b*tan(1/2*d*x)^11*tan(1/
2*c)^12 + 36015*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)*tan(1/2*c)^12 - 21609*a*tan(1/2*d*x)^10*tan(5/2*c)*
tan(1/2*c)^12 + 5167428*a*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^12 - 3892224*b*tan(5/2*d*x)^2*
tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^12 + 36015*a*tan(5/2*d*x)*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^12 - 1
943781*a*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^12 + 2856448*b*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^12 - 591
675*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c)^13 + 537600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c)^13 + 193
305*a*tan(1/2*d*x)^10*tan(1/2*c)^13 - 268800*b*tan(1/2*d*x)^10*tan(1/2*c)^13 + 591675*a*tan(5/2*d*x)^2*tan(1/2
*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^13 - 537600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^13 - 59167
5*a*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^13 + 537600*b*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^13 + 62004*a*t
an(5/2*d*x)^2*tan(1/2*d*x)^7*tan(1/2*c)^14 + 58368*b*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(1/2*c)^14 - 5145*a*tan(
5/2*d*x)*tan(1/2*d*x)^8*tan(1/2*c)^14 + 113967*a*tan(1/2*d*x)^9*tan(1/2*c)^14 - 14336*b*tan(1/2*d*x)^9*tan(1/2
*c)^14 + 5145*a*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)*tan(1/2*c)^14 - 5145*a*tan(1/2*d*x)^8*tan(5/2*c)*tan(
1/2*c)^14 + 113967*a*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^14 - 14336*b*tan(5/2*d*x)^2*tan(1/2
*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^14 + 5145*a*tan(5/2*d*x)*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^14 + 62004*a*t
an(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^14 + 58368*b*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^14 + 34230*a*tan(5/2
*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^3 + 17920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/
2*c)^3 + 3087*a*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)*tan(1/2*c)^4 - 193305*a*tan(5/2*d*x)^2*tan(1/2*d*x)^
13*tan(5/2*c)^2*tan(1/2*c)^4 + 268800*b*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^4 + 3087*a*tan(
5/2*d*x)*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^4 + 113967*a*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(1/2*c)^5 - 14
336*b*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(1/2*c)^5 - 1943781*a*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(
1/2*c)^5 + 2856448*b*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^5 + 113967*a*tan(1/2*d*x)^14*tan(5
/2*c)^2*tan(1/2*c)^5 - 14336*b*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^5 + 591675*a*tan(5/2*d*x)^2*tan(1/2*d*x
)^13*tan(1/2*c)^6 - 537600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(1/2*c)^6 - 5145*a*tan(5/2*d*x)*tan(1/2*d*x)^14
*tan(1/2*c)^6 + 36015*a*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)*tan(1/2*c)^6 - 5145*a*tan(1/2*d*x)^14*tan(5/
2*c)*tan(1/2*c)^6 - 15324750*a*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^6 + 15321600*b*tan(5/2*d
*x)^2*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^6 + 36015*a*tan(5/2*d*x)*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)
^6 + 591675*a*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^6 - 537600*b*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^6 +
5167428*a*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(1/2*c)^7 - 3892224*b*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(1/2*c)^7
+ 62004*a*tan(1/2*d*x)^14*tan(1/2*c)^7 + 58368*b*tan(1/2*d*x)^14*tan(1/2*c)^7 - 45796716*a*tan(5/2*d*x)^2*tan
(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^7 + 49609728*b*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^7 +
5167428*a*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^7 - 3892224*b*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^7 + 1
5324750*a*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(1/2*c)^8 - 15321600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(1/2*c)^8
- 36015*a*tan(5/2*d*x)*tan(1/2*d*x)^12*tan(1/2*c)^8 - 591675*a*tan(1/2*d*x)^13*tan(1/2*c)^8 + 537600*b*tan(1/
2*d*x)^13*tan(1/2*c)^8 + 108045*a*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)*tan(1/2*c)^8 - 36015*a*tan(1/2*d*x
)^12*tan(5/2*c)*tan(1/2*c)^8 - 88607925*a*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^8 + 89994240*b
*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^8 + 108045*a*tan(5/2*d*x)*tan(1/2*d*x)^10*tan(5/2*c)^2*
tan(1/2*c)^8 + 15324750*a*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^8 - 15321600*b*tan(1/2*d*x)^11*tan(5/2*c)^2*
tan(1/2*c)^8 + 32337207*a*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(1/2*c)^9 - 30137856*b*tan(5/2*d*x)^2*tan(1/2*d*x)
^10*tan(1/2*c)^9 - 1943781*a*tan(1/2*d*x)^12*tan(1/2*c)^9 + 2856448*b*tan(1/2*d*x)^12*tan(1/2*c)^9 - 88607925*
a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^9 + 89994240*b*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c
)^2*tan(1/2*c)^9 + 32337207*a*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^9 - 30137856*b*tan(1/2*d*x)^10*tan(5/2*c
)^2*tan(1/2*c)^9 + 32337207*a*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(1/2*c)^10 - 30137856*b*tan(5/2*d*x)^2*tan(1/2*
d*x)^9*tan(1/2*c)^10 - 64827*a*tan(5/2*d*x)*tan(1/2*d*x)^10*tan(1/2*c)^10 - 6072570*a*tan(1/2*d*x)^11*tan(1/2*
c)^10 + 6289920*b*tan(1/2*d*x)^11*tan(1/2*c)^10 + 108045*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)*tan(1/2*c)
^10 - 64827*a*tan(1/2*d*x)^10*tan(5/2*c)*tan(1/2*c)^10 - 45796716*a*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(5/2*c)^2
*tan(1/2*c)^10 + 49609728*b*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^10 + 108045*a*tan(5/2*d*x)*t
an(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^10 + 32337207*a*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^10 - 30137856*b*t
an(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^10 + 15324750*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c)^11 - 15321600*b
*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c)^11 - 6072570*a*tan(1/2*d*x)^10*tan(1/2*c)^11 + 6289920*b*tan(1/2*d*x
)^10*tan(1/2*c)^11 - 15324750*a*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^11 + 15321600*b*tan(5/2*
d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^11 + 15324750*a*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^11 - 1532
1600*b*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^11 + 5167428*a*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(1/2*c)^12 - 389
2224*b*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(1/2*c)^12 - 36015*a*tan(5/2*d*x)*tan(1/2*d*x)^8*tan(1/2*c)^12 - 19437
81*a*tan(1/2*d*x)^9*tan(1/2*c)^12 + 2856448*b*tan(1/2*d*x)^9*tan(1/2*c)^12 + 36015*a*tan(5/2*d*x)^2*tan(1/2*d*
x)^6*tan(5/2*c)*tan(1/2*c)^12 - 36015*a*tan(1/2*d*x)^8*tan(5/2*c)*tan(1/2*c)^12 - 1943781*a*tan(5/2*d*x)^2*tan
(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^12 + 2856448*b*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^12 +
36015*a*tan(5/2*d*x)*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^12 + 5167428*a*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2
*c)^12 - 3892224*b*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^12 + 591675*a*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1/2*
c)^13 - 537600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^13 - 591675*a*tan(1/2*d*x)^8*tan(1/2*c)^13 + 537600*
b*tan(1/2*d*x)^8*tan(1/2*c)^13 - 193305*a*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^13 + 268800*b*
tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^13 + 591675*a*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^13
- 537600*b*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^13 + 113967*a*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^14 -
14336*b*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^14 - 5145*a*tan(5/2*d*x)*tan(1/2*d*x)^6*tan(1/2*c)^14 + 62004
*a*tan(1/2*d*x)^7*tan(1/2*c)^14 + 58368*b*tan(1/2*d*x)^7*tan(1/2*c)^14 + 3087*a*tan(5/2*d*x)^2*tan(1/2*d*x)^4*
tan(5/2*c)*tan(1/2*c)^14 - 5145*a*tan(1/2*d*x)^6*tan(5/2*c)*tan(1/2*c)^14 + 34230*a*tan(5/2*d*x)^2*tan(1/2*d*x
)^3*tan(5/2*c)^2*tan(1/2*c)^14 + 17920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^14 + 3087*a*tan
(5/2*d*x)*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^14 + 113967*a*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^14 - 143
36*b*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^14 + 12705*a*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c
) + 1029*a*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)*tan(1/2*c)^2 + 62475*a*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan
(5/2*c)^2*tan(1/2*c)^2 - 53760*b*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^2 + 1029*a*tan(5/2*d*x
)*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^2 + 34230*a*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(1/2*c)^3 + 17920*b*ta
n(5/2*d*x)^2*tan(1/2*d*x)^14*tan(1/2*c)^3 + 1001070*a*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^3
- 734720*b*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^3 + 34230*a*tan(1/2*d*x)^14*tan(5/2*c)^2*ta
n(1/2*c)^3 + 17920*b*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^3 - 193305*a*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(1
/2*c)^4 + 268800*b*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(1/2*c)^4 - 3087*a*tan(5/2*d*x)*tan(1/2*d*x)^14*tan(1/2*c
)^4 + 21609*a*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)*tan(1/2*c)^4 - 3087*a*tan(1/2*d*x)^14*tan(5/2*c)*tan(1
/2*c)^4 + 6072570*a*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^4 - 6289920*b*tan(5/2*d*x)^2*tan(1/
2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^4 + 21609*a*tan(5/2*d*x)*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^4 - 193305*
a*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^4 + 268800*b*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^4 - 1943781*a*t
an(5/2*d*x)^2*tan(1/2*d*x)^12*tan(1/2*c)^5 + 2856448*b*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(1/2*c)^5 + 113967*a*
tan(1/2*d*x)^14*tan(1/2*c)^5 - 14336*b*tan(1/2*d*x)^14*tan(1/2*c)^5 + 32337207*a*tan(5/2*d*x)^2*tan(1/2*d*x)^1
0*tan(5/2*c)^2*tan(1/2*c)^5 - 30137856*b*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^5 - 1943781*a*
tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^5 + 2856448*b*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^5 - 15324750*a*t
an(5/2*d*x)^2*tan(1/2*d*x)^11*tan(1/2*c)^6 + 15321600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(1/2*c)^6 - 36015*a*
tan(5/2*d*x)*tan(1/2*d*x)^12*tan(1/2*c)^6 + 591675*a*tan(1/2*d*x)^13*tan(1/2*c)^6 - 537600*b*tan(1/2*d*x)^13*t
an(1/2*c)^6 + 108045*a*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)*tan(1/2*c)^6 - 36015*a*tan(1/2*d*x)^12*tan(5/
2*c)*tan(1/2*c)^6 + 88607925*a*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^6 - 89994240*b*tan(5/2*d*
x)^2*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^6 + 108045*a*tan(5/2*d*x)*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^
6 - 15324750*a*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^6 + 15321600*b*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^
6 - 45796716*a*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(1/2*c)^7 + 49609728*b*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(1/2
*c)^7 + 5167428*a*tan(1/2*d*x)^12*tan(1/2*c)^7 - 3892224*b*tan(1/2*d*x)^12*tan(1/2*c)^7 + 159959940*a*tan(5/2*
d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^7 - 157301760*b*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1
/2*c)^7 - 45796716*a*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^7 + 49609728*b*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1
/2*c)^7 - 88607925*a*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(1/2*c)^8 + 89994240*b*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan
(1/2*c)^8 - 108045*a*tan(5/2*d*x)*tan(1/2*d*x)^10*tan(1/2*c)^8 + 15324750*a*tan(1/2*d*x)^11*tan(1/2*c)^8 - 153
21600*b*tan(1/2*d*x)^11*tan(1/2*c)^8 + 180075*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)*tan(1/2*c)^8 - 108045
*a*tan(1/2*d*x)^10*tan(5/2*c)*tan(1/2*c)^8 + 159959940*a*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)
^8 - 157301760*b*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^8 + 180075*a*tan(5/2*d*x)*tan(1/2*d*x)^
8*tan(5/2*c)^2*tan(1/2*c)^8 - 88607925*a*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^8 + 89994240*b*tan(1/2*d*x)^9*
tan(5/2*c)^2*tan(1/2*c)^8 - 88607925*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c)^9 + 89994240*b*tan(5/2*d*x)^2*
tan(1/2*d*x)^8*tan(1/2*c)^9 + 32337207*a*tan(1/2*d*x)^10*tan(1/2*c)^9 - 30137856*b*tan(1/2*d*x)^10*tan(1/2*c)^
9 + 88607925*a*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^9 - 89994240*b*tan(5/2*d*x)^2*tan(1/2*d*x
)^6*tan(5/2*c)^2*tan(1/2*c)^9 - 88607925*a*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^9 + 89994240*b*tan(1/2*d*x)^
8*tan(5/2*c)^2*tan(1/2*c)^9 - 45796716*a*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(1/2*c)^10 + 49609728*b*tan(5/2*d*x)
^2*tan(1/2*d*x)^7*tan(1/2*c)^10 - 108045*a*tan(5/2*d*x)*tan(1/2*d*x)^8*tan(1/2*c)^10 + 32337207*a*tan(1/2*d*x)
^9*tan(1/2*c)^10 - 30137856*b*tan(1/2*d*x)^9*tan(1/2*c)^10 + 108045*a*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)
*tan(1/2*c)^10 - 108045*a*tan(1/2*d*x)^8*tan(5/2*c)*tan(1/2*c)^10 + 32337207*a*tan(5/2*d*x)^2*tan(1/2*d*x)^5*t
an(5/2*c)^2*tan(1/2*c)^10 - 30137856*b*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^10 + 108045*a*tan
(5/2*d*x)*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^10 - 45796716*a*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^10 + 4
9609728*b*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^10 - 15324750*a*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^11 +
15321600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^11 + 15324750*a*tan(1/2*d*x)^8*tan(1/2*c)^11 - 15321600*b
*tan(1/2*d*x)^8*tan(1/2*c)^11 + 6072570*a*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^11 - 6289920*b
*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^11 - 15324750*a*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^
11 + 15321600*b*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^11 - 1943781*a*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)
^12 + 2856448*b*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^12 - 36015*a*tan(5/2*d*x)*tan(1/2*d*x)^6*tan(1/2*c)^1
2 + 5167428*a*tan(1/2*d*x)^7*tan(1/2*c)^12 - 3892224*b*tan(1/2*d*x)^7*tan(1/2*c)^12 + 21609*a*tan(5/2*d*x)^2*t
an(1/2*d*x)^4*tan(5/2*c)*tan(1/2*c)^12 - 36015*a*tan(1/2*d*x)^6*tan(5/2*c)*tan(1/2*c)^12 + 1001070*a*tan(5/2*d
*x)^2*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^12 - 734720*b*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*
c)^12 + 21609*a*tan(5/2*d*x)*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^12 - 1943781*a*tan(1/2*d*x)^5*tan(5/2*c)^2
*tan(1/2*c)^12 + 2856448*b*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^12 - 193305*a*tan(5/2*d*x)^2*tan(1/2*d*x)^4*
tan(1/2*c)^13 + 268800*b*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^13 + 591675*a*tan(1/2*d*x)^6*tan(1/2*c)^13 -
537600*b*tan(1/2*d*x)^6*tan(1/2*c)^13 + 62475*a*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^13 - 53
760*b*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^13 - 193305*a*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*
c)^13 + 268800*b*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^13 + 34230*a*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^
14 + 17920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^14 - 3087*a*tan(5/2*d*x)*tan(1/2*d*x)^4*tan(1/2*c)^14 +
113967*a*tan(1/2*d*x)^5*tan(1/2*c)^14 - 14336*b*tan(1/2*d*x)^5*tan(1/2*c)^14 + 1029*a*tan(5/2*d*x)^2*tan(1/2*d
*x)^2*tan(5/2*c)*tan(1/2*c)^14 - 3087*a*tan(1/2*d*x)^4*tan(5/2*c)*tan(1/2*c)^14 + 12705*a*tan(5/2*d*x)^2*tan(1
/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^14 + 1029*a*tan(5/2*d*x)*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^14 + 34230*a*t
an(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^14 + 17920*b*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^14 + 147*a*tan(5/2*d
*x)^2*tan(1/2*d*x)^14*tan(5/2*c) - 12705*a*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(5/2*c)^2 + 147*a*tan(5/2*d*x)*ta
n(1/2*d*x)^14*tan(5/2*c)^2 + 12705*a*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(1/2*c) - 62475*a*tan(5/2*d*x)^2*tan(1/
2*d*x)^12*tan(5/2*c)^2*tan(1/2*c) + 53760*b*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c) + 12705*a*t
an(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c) + 62475*a*tan(5/2*d*x)^2*tan(1/2*d*x)^13*tan(1/2*c)^2 - 53760*b*tan(5/2
*d*x)^2*tan(1/2*d*x)^13*tan(1/2*c)^2 - 1029*a*tan(5/2*d*x)*tan(1/2*d*x)^14*tan(1/2*c)^2 + 7203*a*tan(5/2*d*x)^
2*tan(1/2*d*x)^12*tan(5/2*c)*tan(1/2*c)^2 - 1029*a*tan(1/2*d*x)^14*tan(5/2*c)*tan(1/2*c)^2 - 1001070*a*tan(5/2
*d*x)^2*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^2 + 734720*b*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1
/2*c)^2 + 7203*a*tan(5/2*d*x)*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^2 + 62475*a*tan(1/2*d*x)^13*tan(5/2*c)^2
*tan(1/2*c)^2 - 53760*b*tan(1/2*d*x)^13*tan(5/2*c)^2*tan(1/2*c)^2 + 1001070*a*tan(5/2*d*x)^2*tan(1/2*d*x)^12*t
an(1/2*c)^3 - 734720*b*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(1/2*c)^3 + 34230*a*tan(1/2*d*x)^14*tan(1/2*c)^3 + 17
920*b*tan(1/2*d*x)^14*tan(1/2*c)^3 - 6072570*a*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^3 + 6289
920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^3 + 1001070*a*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/
2*c)^3 - 734720*b*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^3 + 6072570*a*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(1/2
*c)^4 - 6289920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(1/2*c)^4 - 21609*a*tan(5/2*d*x)*tan(1/2*d*x)^12*tan(1/2*c
)^4 - 193305*a*tan(1/2*d*x)^13*tan(1/2*c)^4 + 268800*b*tan(1/2*d*x)^13*tan(1/2*c)^4 + 64827*a*tan(5/2*d*x)^2*t
an(1/2*d*x)^10*tan(5/2*c)*tan(1/2*c)^4 - 21609*a*tan(1/2*d*x)^12*tan(5/2*c)*tan(1/2*c)^4 - 32337207*a*tan(5/2*
d*x)^2*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^4 + 30137856*b*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/
2*c)^4 + 64827*a*tan(5/2*d*x)*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^4 + 6072570*a*tan(1/2*d*x)^11*tan(5/2*c)
^2*tan(1/2*c)^4 - 6289920*b*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^4 + 32337207*a*tan(5/2*d*x)^2*tan(1/2*d*x)
^10*tan(1/2*c)^5 - 30137856*b*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(1/2*c)^5 - 1943781*a*tan(1/2*d*x)^12*tan(1/2*
c)^5 + 2856448*b*tan(1/2*d*x)^12*tan(1/2*c)^5 - 88607925*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*
c)^5 + 89994240*b*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^5 + 32337207*a*tan(1/2*d*x)^10*tan(5/2
*c)^2*tan(1/2*c)^5 - 30137856*b*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^5 + 88607925*a*tan(5/2*d*x)^2*tan(1/2*
d*x)^9*tan(1/2*c)^6 - 89994240*b*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(1/2*c)^6 - 108045*a*tan(5/2*d*x)*tan(1/2*d*
x)^10*tan(1/2*c)^6 - 15324750*a*tan(1/2*d*x)^11*tan(1/2*c)^6 + 15321600*b*tan(1/2*d*x)^11*tan(1/2*c)^6 + 18007
5*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)*tan(1/2*c)^6 - 108045*a*tan(1/2*d*x)^10*tan(5/2*c)*tan(1/2*c)^6 -
159959940*a*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^6 + 157301760*b*tan(5/2*d*x)^2*tan(1/2*d*x)
^7*tan(5/2*c)^2*tan(1/2*c)^6 + 180075*a*tan(5/2*d*x)*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^6 + 88607925*a*tan
(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^6 - 89994240*b*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^6 + 159959940*a*tan(
5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c)^7 - 157301760*b*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c)^7 - 45796716*a*t
an(1/2*d*x)^10*tan(1/2*c)^7 + 49609728*b*tan(1/2*d*x)^10*tan(1/2*c)^7 - 159959940*a*tan(5/2*d*x)^2*tan(1/2*d*x
)^6*tan(5/2*c)^2*tan(1/2*c)^7 + 157301760*b*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^7 + 15995994
0*a*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^7 - 157301760*b*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^7 + 15995994
0*a*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(1/2*c)^8 - 157301760*b*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(1/2*c)^8 - 1800
75*a*tan(5/2*d*x)*tan(1/2*d*x)^8*tan(1/2*c)^8 - 88607925*a*tan(1/2*d*x)^9*tan(1/2*c)^8 + 89994240*b*tan(1/2*d*
x)^9*tan(1/2*c)^8 + 180075*a*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)*tan(1/2*c)^8 - 180075*a*tan(1/2*d*x)^8*t
an(5/2*c)*tan(1/2*c)^8 - 88607925*a*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^8 + 89994240*b*tan(5
/2*d*x)^2*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^8 + 180075*a*tan(5/2*d*x)*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2
*c)^8 + 159959940*a*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^8 - 157301760*b*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2
*c)^8 + 88607925*a*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^9 - 89994240*b*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1
/2*c)^9 - 88607925*a*tan(1/2*d*x)^8*tan(1/2*c)^9 + 89994240*b*tan(1/2*d*x)^8*tan(1/2*c)^9 - 32337207*a*tan(5/2
*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^9 + 30137856*b*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1
/2*c)^9 + 88607925*a*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^9 - 89994240*b*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2
*c)^9 + 32337207*a*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^10 - 30137856*b*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(
1/2*c)^10 - 108045*a*tan(5/2*d*x)*tan(1/2*d*x)^6*tan(1/2*c)^10 - 45796716*a*tan(1/2*d*x)^7*tan(1/2*c)^10 + 496
09728*b*tan(1/2*d*x)^7*tan(1/2*c)^10 + 64827*a*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)*tan(1/2*c)^10 - 108045
*a*tan(1/2*d*x)^6*tan(5/2*c)*tan(1/2*c)^10 - 6072570*a*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^1
0 + 6289920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^10 + 64827*a*tan(5/2*d*x)*tan(1/2*d*x)^4*t
an(5/2*c)^2*tan(1/2*c)^10 + 32337207*a*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^10 - 30137856*b*tan(1/2*d*x)^5*t
an(5/2*c)^2*tan(1/2*c)^10 + 6072570*a*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^11 - 6289920*b*tan(5/2*d*x)^2*t
an(1/2*d*x)^4*tan(1/2*c)^11 - 15324750*a*tan(1/2*d*x)^6*tan(1/2*c)^11 + 15321600*b*tan(1/2*d*x)^6*tan(1/2*c)^1
1 - 1001070*a*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^11 + 734720*b*tan(5/2*d*x)^2*tan(1/2*d*x)^
2*tan(5/2*c)^2*tan(1/2*c)^11 + 6072570*a*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^11 - 6289920*b*tan(1/2*d*x)^4*
tan(5/2*c)^2*tan(1/2*c)^11 + 1001070*a*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^12 - 734720*b*tan(5/2*d*x)^2*t
an(1/2*d*x)^3*tan(1/2*c)^12 - 21609*a*tan(5/2*d*x)*tan(1/2*d*x)^4*tan(1/2*c)^12 - 1943781*a*tan(1/2*d*x)^5*tan
(1/2*c)^12 + 2856448*b*tan(1/2*d*x)^5*tan(1/2*c)^12 + 7203*a*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)*tan(1/2*
c)^12 - 21609*a*tan(1/2*d*x)^4*tan(5/2*c)*tan(1/2*c)^12 - 62475*a*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(5/2*c)^2*tan
(1/2*c)^12 + 53760*b*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^12 + 7203*a*tan(5/2*d*x)*tan(1/2*d*x)
^2*tan(5/2*c)^2*tan(1/2*c)^12 + 1001070*a*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^12 - 734720*b*tan(1/2*d*x)^3*
tan(5/2*c)^2*tan(1/2*c)^12 + 62475*a*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^13 - 53760*b*tan(5/2*d*x)^2*tan(
1/2*d*x)^2*tan(1/2*c)^13 - 193305*a*tan(1/2*d*x)^4*tan(1/2*c)^13 + 268800*b*tan(1/2*d*x)^4*tan(1/2*c)^13 - 127
05*a*tan(5/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^13 + 62475*a*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^13 - 53760*b*t
an(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^13 + 12705*a*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(1/2*c)^14 - 1029*a*tan(5/2*
d*x)*tan(1/2*d*x)^2*tan(1/2*c)^14 + 34230*a*tan(1/2*d*x)^3*tan(1/2*c)^14 + 17920*b*tan(1/2*d*x)^3*tan(1/2*c)^1
4 + 147*a*tan(5/2*d*x)^2*tan(5/2*c)*tan(1/2*c)^14 - 1029*a*tan(1/2*d*x)^2*tan(5/2*c)*tan(1/2*c)^14 + 147*a*tan
(5/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^14 + 12705*a*tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^14 - 12705*a*tan(5/2*d*x)^
2*tan(1/2*d*x)^13 - 147*a*tan(5/2*d*x)*tan(1/2*d*x)^14 + 1029*a*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c) - 14
7*a*tan(1/2*d*x)^14*tan(5/2*c) - 34230*a*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(5/2*c)^2 - 17920*b*tan(5/2*d*x)^2*
tan(1/2*d*x)^11*tan(5/2*c)^2 + 1029*a*tan(5/2*d*x)*tan(1/2*d*x)^12*tan(5/2*c)^2 - 12705*a*tan(1/2*d*x)^13*tan(
5/2*c)^2 - 62475*a*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(1/2*c) + 53760*b*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(1/2*
c) + 12705*a*tan(1/2*d*x)^14*tan(1/2*c) + 193305*a*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c) - 26
8800*b*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c) - 62475*a*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c
) + 53760*b*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c) - 1001070*a*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(1/2*c)^2 +
734720*b*tan(5/2*d*x)^2*tan(1/2*d*x)^11*tan(1/2*c)^2 - 7203*a*tan(5/2*d*x)*tan(1/2*d*x)^12*tan(1/2*c)^2 + 6247
5*a*tan(1/2*d*x)^13*tan(1/2*c)^2 - 53760*b*tan(1/2*d*x)^13*tan(1/2*c)^2 + 21609*a*tan(5/2*d*x)^2*tan(1/2*d*x)^
10*tan(5/2*c)*tan(1/2*c)^2 - 7203*a*tan(1/2*d*x)^12*tan(5/2*c)*tan(1/2*c)^2 + 1943781*a*tan(5/2*d*x)^2*tan(1/2
*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^2 - 2856448*b*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^2 + 21609*
a*tan(5/2*d*x)*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^2 - 1001070*a*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^2
+ 734720*b*tan(1/2*d*x)^11*tan(5/2*c)^2*tan(1/2*c)^2 - 6072570*a*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(1/2*c)^3
+ 6289920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(1/2*c)^3 + 1001070*a*tan(1/2*d*x)^12*tan(1/2*c)^3 - 734720*b*ta
n(1/2*d*x)^12*tan(1/2*c)^3 + 15324750*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^3 - 15321600*b*t
an(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^3 - 6072570*a*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^3 +
6289920*b*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^3 - 32337207*a*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(1/2*c)^4 +
30137856*b*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(1/2*c)^4 - 64827*a*tan(5/2*d*x)*tan(1/2*d*x)^10*tan(1/2*c)^4 + 6
072570*a*tan(1/2*d*x)^11*tan(1/2*c)^4 - 6289920*b*tan(1/2*d*x)^11*tan(1/2*c)^4 + 108045*a*tan(5/2*d*x)^2*tan(1
/2*d*x)^8*tan(5/2*c)*tan(1/2*c)^4 - 64827*a*tan(1/2*d*x)^10*tan(5/2*c)*tan(1/2*c)^4 + 45796716*a*tan(5/2*d*x)^
2*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^4 - 49609728*b*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^
4 + 108045*a*tan(5/2*d*x)*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^4 - 32337207*a*tan(1/2*d*x)^9*tan(5/2*c)^2*ta
n(1/2*c)^4 + 30137856*b*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^4 - 88607925*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*ta
n(1/2*c)^5 + 89994240*b*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c)^5 + 32337207*a*tan(1/2*d*x)^10*tan(1/2*c)^5 -
30137856*b*tan(1/2*d*x)^10*tan(1/2*c)^5 + 88607925*a*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^5
- 89994240*b*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^5 - 88607925*a*tan(1/2*d*x)^8*tan(5/2*c)^2*
tan(1/2*c)^5 + 89994240*b*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^5 - 159959940*a*tan(5/2*d*x)^2*tan(1/2*d*x)^7
*tan(1/2*c)^6 + 157301760*b*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(1/2*c)^6 - 180075*a*tan(5/2*d*x)*tan(1/2*d*x)^8*
tan(1/2*c)^6 + 88607925*a*tan(1/2*d*x)^9*tan(1/2*c)^6 - 89994240*b*tan(1/2*d*x)^9*tan(1/2*c)^6 + 180075*a*tan(
5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)*tan(1/2*c)^6 - 180075*a*tan(1/2*d*x)^8*tan(5/2*c)*tan(1/2*c)^6 + 88607925
*a*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^6 - 89994240*b*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(5/2*
c)^2*tan(1/2*c)^6 + 180075*a*tan(5/2*d*x)*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^6 - 159959940*a*tan(1/2*d*x)^
7*tan(5/2*c)^2*tan(1/2*c)^6 + 157301760*b*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^6 - 159959940*a*tan(5/2*d*x)^
2*tan(1/2*d*x)^6*tan(1/2*c)^7 + 157301760*b*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^7 + 159959940*a*tan(1/2*d
*x)^8*tan(1/2*c)^7 - 157301760*b*tan(1/2*d*x)^8*tan(1/2*c)^7 + 45796716*a*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/
2*c)^2*tan(1/2*c)^7 - 49609728*b*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^7 - 159959940*a*tan(1/2
*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^7 + 157301760*b*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^7 - 88607925*a*tan(5/2*
d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^8 + 89994240*b*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^8 - 180075*a*tan(5/2*
d*x)*tan(1/2*d*x)^6*tan(1/2*c)^8 + 159959940*a*tan(1/2*d*x)^7*tan(1/2*c)^8 - 157301760*b*tan(1/2*d*x)^7*tan(1/
2*c)^8 + 108045*a*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)*tan(1/2*c)^8 - 180075*a*tan(1/2*d*x)^6*tan(5/2*c)*t
an(1/2*c)^8 + 15324750*a*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^8 - 15321600*b*tan(5/2*d*x)^2*t
an(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^8 + 108045*a*tan(5/2*d*x)*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^8 - 886
07925*a*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^8 + 89994240*b*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^8 - 32337
207*a*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^9 + 30137856*b*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^9 + 886
07925*a*tan(1/2*d*x)^6*tan(1/2*c)^9 - 89994240*b*tan(1/2*d*x)^6*tan(1/2*c)^9 + 1943781*a*tan(5/2*d*x)^2*tan(1/
2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^9 - 2856448*b*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^9 - 32337
207*a*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^9 + 30137856*b*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^9 - 6072570
*a*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^10 + 6289920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^10 - 64827
*a*tan(5/2*d*x)*tan(1/2*d*x)^4*tan(1/2*c)^10 + 32337207*a*tan(1/2*d*x)^5*tan(1/2*c)^10 - 30137856*b*tan(1/2*d*
x)^5*tan(1/2*c)^10 + 21609*a*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)*tan(1/2*c)^10 - 64827*a*tan(1/2*d*x)^4*t
an(5/2*c)*tan(1/2*c)^10 + 193305*a*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^10 - 268800*b*tan(5/2*d
*x)^2*tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^10 + 21609*a*tan(5/2*d*x)*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^10
- 6072570*a*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^10 + 6289920*b*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^10 -
1001070*a*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^11 + 734720*b*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^11
+ 6072570*a*tan(1/2*d*x)^4*tan(1/2*c)^11 - 6289920*b*tan(1/2*d*x)^4*tan(1/2*c)^11 - 34230*a*tan(5/2*d*x)^2*tan
(5/2*c)^2*tan(1/2*c)^11 - 17920*b*tan(5/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^11 - 1001070*a*tan(1/2*d*x)^2*tan(5/2
*c)^2*tan(1/2*c)^11 + 734720*b*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^11 - 62475*a*tan(5/2*d*x)^2*tan(1/2*d*x)
*tan(1/2*c)^12 + 53760*b*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(1/2*c)^12 - 7203*a*tan(5/2*d*x)*tan(1/2*d*x)^2*tan(1/
2*c)^12 + 1001070*a*tan(1/2*d*x)^3*tan(1/2*c)^12 - 734720*b*tan(1/2*d*x)^3*tan(1/2*c)^12 + 1029*a*tan(5/2*d*x)
^2*tan(5/2*c)*tan(1/2*c)^12 - 7203*a*tan(1/2*d*x)^2*tan(5/2*c)*tan(1/2*c)^12 + 1029*a*tan(5/2*d*x)*tan(5/2*c)^
2*tan(1/2*c)^12 - 62475*a*tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^12 + 53760*b*tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*
c)^12 - 12705*a*tan(5/2*d*x)^2*tan(1/2*c)^13 + 62475*a*tan(1/2*d*x)^2*tan(1/2*c)^13 - 53760*b*tan(1/2*d*x)^2*t
an(1/2*c)^13 - 12705*a*tan(5/2*c)^2*tan(1/2*c)^13 - 147*a*tan(5/2*d*x)*tan(1/2*c)^14 + 12705*a*tan(1/2*d*x)*ta
n(1/2*c)^14 - 147*a*tan(5/2*c)*tan(1/2*c)^14 - 34230*a*tan(5/2*d*x)^2*tan(1/2*d*x)^11 - 17920*b*tan(5/2*d*x)^2
*tan(1/2*d*x)^11 - 1029*a*tan(5/2*d*x)*tan(1/2*d*x)^12 - 12705*a*tan(1/2*d*x)^13 + 3087*a*tan(5/2*d*x)^2*tan(1
/2*d*x)^10*tan(5/2*c) - 1029*a*tan(1/2*d*x)^12*tan(5/2*c) - 113967*a*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(5/2*c)^
2 + 14336*b*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(5/2*c)^2 + 3087*a*tan(5/2*d*x)*tan(1/2*d*x)^10*tan(5/2*c)^2 - 34
230*a*tan(1/2*d*x)^11*tan(5/2*c)^2 - 17920*b*tan(1/2*d*x)^11*tan(5/2*c)^2 + 193305*a*tan(5/2*d*x)^2*tan(1/2*d*
x)^10*tan(1/2*c) - 268800*b*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(1/2*c) - 62475*a*tan(1/2*d*x)^12*tan(1/2*c) + 5
3760*b*tan(1/2*d*x)^12*tan(1/2*c) - 591675*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c) + 537600*b*
tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c) + 193305*a*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c) - 268
800*b*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c) + 1943781*a*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(1/2*c)^2 - 2856448
*b*tan(5/2*d*x)^2*tan(1/2*d*x)^9*tan(1/2*c)^2 - 21609*a*tan(5/2*d*x)*tan(1/2*d*x)^10*tan(1/2*c)^2 - 1001070*a*
tan(1/2*d*x)^11*tan(1/2*c)^2 + 734720*b*tan(1/2*d*x)^11*tan(1/2*c)^2 + 36015*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*t
an(5/2*c)*tan(1/2*c)^2 - 21609*a*tan(1/2*d*x)^10*tan(5/2*c)*tan(1/2*c)^2 - 5167428*a*tan(5/2*d*x)^2*tan(1/2*d*
x)^7*tan(5/2*c)^2*tan(1/2*c)^2 + 3892224*b*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^2 + 36015*a*t
an(5/2*d*x)*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^2 + 1943781*a*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^2 - 28
56448*b*tan(1/2*d*x)^9*tan(5/2*c)^2*tan(1/2*c)^2 + 15324750*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c)^3 - 153
21600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c)^3 - 6072570*a*tan(1/2*d*x)^10*tan(1/2*c)^3 + 6289920*b*tan(1/
2*d*x)^10*tan(1/2*c)^3 - 15324750*a*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^3 + 15321600*b*tan(5
/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^3 + 15324750*a*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^3 - 153
21600*b*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^3 + 45796716*a*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(1/2*c)^4 - 496
09728*b*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(1/2*c)^4 - 108045*a*tan(5/2*d*x)*tan(1/2*d*x)^8*tan(1/2*c)^4 - 32337
207*a*tan(1/2*d*x)^9*tan(1/2*c)^4 + 30137856*b*tan(1/2*d*x)^9*tan(1/2*c)^4 + 108045*a*tan(5/2*d*x)^2*tan(1/2*d
*x)^6*tan(5/2*c)*tan(1/2*c)^4 - 108045*a*tan(1/2*d*x)^8*tan(5/2*c)*tan(1/2*c)^4 - 32337207*a*tan(5/2*d*x)^2*ta
n(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^4 + 30137856*b*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^4 +
108045*a*tan(5/2*d*x)*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^4 + 45796716*a*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/
2*c)^4 - 49609728*b*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^4 + 88607925*a*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1/
2*c)^5 - 89994240*b*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^5 - 88607925*a*tan(1/2*d*x)^8*tan(1/2*c)^5 + 8999
4240*b*tan(1/2*d*x)^8*tan(1/2*c)^5 - 32337207*a*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^5 + 3013
7856*b*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^5 + 88607925*a*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/
2*c)^5 - 89994240*b*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^5 + 88607925*a*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(1/
2*c)^6 - 89994240*b*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^6 - 180075*a*tan(5/2*d*x)*tan(1/2*d*x)^6*tan(1/2*
c)^6 - 159959940*a*tan(1/2*d*x)^7*tan(1/2*c)^6 + 157301760*b*tan(1/2*d*x)^7*tan(1/2*c)^6 + 108045*a*tan(5/2*d*
x)^2*tan(1/2*d*x)^4*tan(5/2*c)*tan(1/2*c)^6 - 180075*a*tan(1/2*d*x)^6*tan(5/2*c)*tan(1/2*c)^6 - 15324750*a*tan
(5/2*d*x)^2*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^6 + 15321600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(5/2*c)^2*t
an(1/2*c)^6 + 108045*a*tan(5/2*d*x)*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^6 + 88607925*a*tan(1/2*d*x)^5*tan(5
/2*c)^2*tan(1/2*c)^6 - 89994240*b*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^6 + 45796716*a*tan(5/2*d*x)^2*tan(1/2
*d*x)^4*tan(1/2*c)^7 - 49609728*b*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^7 - 159959940*a*tan(1/2*d*x)^6*tan(
1/2*c)^7 + 157301760*b*tan(1/2*d*x)^6*tan(1/2*c)^7 - 5167428*a*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(
1/2*c)^7 + 3892224*b*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^7 + 45796716*a*tan(1/2*d*x)^4*tan(5
/2*c)^2*tan(1/2*c)^7 - 49609728*b*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^7 + 15324750*a*tan(5/2*d*x)^2*tan(1/2
*d*x)^3*tan(1/2*c)^8 - 15321600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^8 - 108045*a*tan(5/2*d*x)*tan(1/2*d
*x)^4*tan(1/2*c)^8 - 88607925*a*tan(1/2*d*x)^5*tan(1/2*c)^8 + 89994240*b*tan(1/2*d*x)^5*tan(1/2*c)^8 + 36015*a
*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)*tan(1/2*c)^8 - 108045*a*tan(1/2*d*x)^4*tan(5/2*c)*tan(1/2*c)^8 - 591
675*a*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^8 + 537600*b*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(5/2*c)^
2*tan(1/2*c)^8 + 36015*a*tan(5/2*d*x)*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^8 + 15324750*a*tan(1/2*d*x)^3*tan
(5/2*c)^2*tan(1/2*c)^8 - 15321600*b*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^8 + 1943781*a*tan(5/2*d*x)^2*tan(1/
2*d*x)^2*tan(1/2*c)^9 - 2856448*b*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^9 - 32337207*a*tan(1/2*d*x)^4*tan(1
/2*c)^9 + 30137856*b*tan(1/2*d*x)^4*tan(1/2*c)^9 - 113967*a*tan(5/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^9 + 14336*b
*tan(5/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^9 + 1943781*a*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^9 - 2856448*b*tan
(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^9 + 193305*a*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(1/2*c)^10 - 268800*b*tan(5/2*
d*x)^2*tan(1/2*d*x)*tan(1/2*c)^10 - 21609*a*tan(5/2*d*x)*tan(1/2*d*x)^2*tan(1/2*c)^10 - 6072570*a*tan(1/2*d*x)
^3*tan(1/2*c)^10 + 6289920*b*tan(1/2*d*x)^3*tan(1/2*c)^10 + 3087*a*tan(5/2*d*x)^2*tan(5/2*c)*tan(1/2*c)^10 - 2
1609*a*tan(1/2*d*x)^2*tan(5/2*c)*tan(1/2*c)^10 + 3087*a*tan(5/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^10 + 193305*a*tan
(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^10 - 268800*b*tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^10 - 34230*a*tan(5/2*d*x)
^2*tan(1/2*c)^11 - 17920*b*tan(5/2*d*x)^2*tan(1/2*c)^11 - 1001070*a*tan(1/2*d*x)^2*tan(1/2*c)^11 + 734720*b*ta
n(1/2*d*x)^2*tan(1/2*c)^11 - 34230*a*tan(5/2*c)^2*tan(1/2*c)^11 - 17920*b*tan(5/2*c)^2*tan(1/2*c)^11 - 1029*a*
tan(5/2*d*x)*tan(1/2*c)^12 - 62475*a*tan(1/2*d*x)*tan(1/2*c)^12 + 53760*b*tan(1/2*d*x)*tan(1/2*c)^12 - 1029*a*
tan(5/2*c)*tan(1/2*c)^12 - 12705*a*tan(1/2*c)^13 - 113967*a*tan(5/2*d*x)^2*tan(1/2*d*x)^9 + 14336*b*tan(5/2*d*
x)^2*tan(1/2*d*x)^9 - 3087*a*tan(5/2*d*x)*tan(1/2*d*x)^10 - 34230*a*tan(1/2*d*x)^11 - 17920*b*tan(1/2*d*x)^11
+ 5145*a*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c) - 3087*a*tan(1/2*d*x)^10*tan(5/2*c) - 62004*a*tan(5/2*d*x)^2
*tan(1/2*d*x)^7*tan(5/2*c)^2 - 58368*b*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(5/2*c)^2 + 5145*a*tan(5/2*d*x)*tan(1/
2*d*x)^8*tan(5/2*c)^2 - 113967*a*tan(1/2*d*x)^9*tan(5/2*c)^2 + 14336*b*tan(1/2*d*x)^9*tan(5/2*c)^2 - 591675*a*
tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c) + 537600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c) + 193305*a*tan(1/
2*d*x)^10*tan(1/2*c) - 268800*b*tan(1/2*d*x)^10*tan(1/2*c) + 591675*a*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)
^2*tan(1/2*c) - 537600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c) - 591675*a*tan(1/2*d*x)^8*tan(5
/2*c)^2*tan(1/2*c) + 537600*b*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c) - 5167428*a*tan(5/2*d*x)^2*tan(1/2*d*x)^7
*tan(1/2*c)^2 + 3892224*b*tan(5/2*d*x)^2*tan(1/2*d*x)^7*tan(1/2*c)^2 - 36015*a*tan(5/2*d*x)*tan(1/2*d*x)^8*tan
(1/2*c)^2 + 1943781*a*tan(1/2*d*x)^9*tan(1/2*c)^2 - 2856448*b*tan(1/2*d*x)^9*tan(1/2*c)^2 + 36015*a*tan(5/2*d*
x)^2*tan(1/2*d*x)^6*tan(5/2*c)*tan(1/2*c)^2 - 36015*a*tan(1/2*d*x)^8*tan(5/2*c)*tan(1/2*c)^2 + 1943781*a*tan(5
/2*d*x)^2*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^2 - 2856448*b*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(
1/2*c)^2 + 36015*a*tan(5/2*d*x)*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^2 - 5167428*a*tan(1/2*d*x)^7*tan(5/2*c)
^2*tan(1/2*c)^2 + 3892224*b*tan(1/2*d*x)^7*tan(5/2*c)^2*tan(1/2*c)^2 - 15324750*a*tan(5/2*d*x)^2*tan(1/2*d*x)^
6*tan(1/2*c)^3 + 15321600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^3 + 15324750*a*tan(1/2*d*x)^8*tan(1/2*c)^
3 - 15321600*b*tan(1/2*d*x)^8*tan(1/2*c)^3 + 6072570*a*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^3
- 6289920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^3 - 15324750*a*tan(1/2*d*x)^6*tan(5/2*c)^2*
tan(1/2*c)^3 + 15321600*b*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^3 - 32337207*a*tan(5/2*d*x)^2*tan(1/2*d*x)^5*
tan(1/2*c)^4 + 30137856*b*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^4 - 108045*a*tan(5/2*d*x)*tan(1/2*d*x)^6*ta
n(1/2*c)^4 + 45796716*a*tan(1/2*d*x)^7*tan(1/2*c)^4 - 49609728*b*tan(1/2*d*x)^7*tan(1/2*c)^4 + 64827*a*tan(5/2
*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)*tan(1/2*c)^4 - 108045*a*tan(1/2*d*x)^6*tan(5/2*c)*tan(1/2*c)^4 + 6072570*a*t
an(5/2*d*x)^2*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^4 - 6289920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(5/2*c)^2*
tan(1/2*c)^4 + 64827*a*tan(5/2*d*x)*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^4 - 32337207*a*tan(1/2*d*x)^5*tan(5
/2*c)^2*tan(1/2*c)^4 + 30137856*b*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^4 - 32337207*a*tan(5/2*d*x)^2*tan(1/2
*d*x)^4*tan(1/2*c)^5 + 30137856*b*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^5 + 88607925*a*tan(1/2*d*x)^6*tan(1
/2*c)^5 - 89994240*b*tan(1/2*d*x)^6*tan(1/2*c)^5 + 1943781*a*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/
2*c)^5 - 2856448*b*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^5 - 32337207*a*tan(1/2*d*x)^4*tan(5/2
*c)^2*tan(1/2*c)^5 + 30137856*b*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^5 - 15324750*a*tan(5/2*d*x)^2*tan(1/2*d
*x)^3*tan(1/2*c)^6 + 15321600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^6 - 108045*a*tan(5/2*d*x)*tan(1/2*d*x
)^4*tan(1/2*c)^6 + 88607925*a*tan(1/2*d*x)^5*tan(1/2*c)^6 - 89994240*b*tan(1/2*d*x)^5*tan(1/2*c)^6 + 36015*a*t
an(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)*tan(1/2*c)^6 - 108045*a*tan(1/2*d*x)^4*tan(5/2*c)*tan(1/2*c)^6 + 59167
5*a*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^6 - 537600*b*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(5/2*c)^2*
tan(1/2*c)^6 + 36015*a*tan(5/2*d*x)*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^6 - 15324750*a*tan(1/2*d*x)^3*tan(5
/2*c)^2*tan(1/2*c)^6 + 15321600*b*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^6 - 5167428*a*tan(5/2*d*x)^2*tan(1/2*
d*x)^2*tan(1/2*c)^7 + 3892224*b*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^7 + 45796716*a*tan(1/2*d*x)^4*tan(1/2
*c)^7 - 49609728*b*tan(1/2*d*x)^4*tan(1/2*c)^7 - 62004*a*tan(5/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^7 - 58368*b*ta
n(5/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^7 - 5167428*a*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^7 + 3892224*b*tan(1/
2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^7 - 591675*a*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(1/2*c)^8 + 537600*b*tan(5/2*d*x)
^2*tan(1/2*d*x)*tan(1/2*c)^8 - 36015*a*tan(5/2*d*x)*tan(1/2*d*x)^2*tan(1/2*c)^8 + 15324750*a*tan(1/2*d*x)^3*ta
n(1/2*c)^8 - 15321600*b*tan(1/2*d*x)^3*tan(1/2*c)^8 + 5145*a*tan(5/2*d*x)^2*tan(5/2*c)*tan(1/2*c)^8 - 36015*a*
tan(1/2*d*x)^2*tan(5/2*c)*tan(1/2*c)^8 + 5145*a*tan(5/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^8 - 591675*a*tan(1/2*d*x)
*tan(5/2*c)^2*tan(1/2*c)^8 + 537600*b*tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^8 - 113967*a*tan(5/2*d*x)^2*tan(1/2
*c)^9 + 14336*b*tan(5/2*d*x)^2*tan(1/2*c)^9 + 1943781*a*tan(1/2*d*x)^2*tan(1/2*c)^9 - 2856448*b*tan(1/2*d*x)^2
*tan(1/2*c)^9 - 113967*a*tan(5/2*c)^2*tan(1/2*c)^9 + 14336*b*tan(5/2*c)^2*tan(1/2*c)^9 - 3087*a*tan(5/2*d*x)*t
an(1/2*c)^10 + 193305*a*tan(1/2*d*x)*tan(1/2*c)^10 - 268800*b*tan(1/2*d*x)*tan(1/2*c)^10 - 3087*a*tan(5/2*c)*t
an(1/2*c)^10 - 34230*a*tan(1/2*c)^11 - 17920*b*tan(1/2*c)^11 - 62004*a*tan(5/2*d*x)^2*tan(1/2*d*x)^7 - 58368*b
*tan(5/2*d*x)^2*tan(1/2*d*x)^7 - 5145*a*tan(5/2*d*x)*tan(1/2*d*x)^8 - 113967*a*tan(1/2*d*x)^9 + 14336*b*tan(1/
2*d*x)^9 + 5145*a*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c) - 5145*a*tan(1/2*d*x)^8*tan(5/2*c) - 113967*a*tan(5
/2*d*x)^2*tan(1/2*d*x)^5*tan(5/2*c)^2 + 14336*b*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(5/2*c)^2 + 5145*a*tan(5/2*d*
x)*tan(1/2*d*x)^6*tan(5/2*c)^2 - 62004*a*tan(1/2*d*x)^7*tan(5/2*c)^2 - 58368*b*tan(1/2*d*x)^7*tan(5/2*c)^2 + 5
91675*a*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1/2*c) - 537600*b*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1/2*c) - 591675*
a*tan(1/2*d*x)^8*tan(1/2*c) + 537600*b*tan(1/2*d*x)^8*tan(1/2*c) - 193305*a*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(
5/2*c)^2*tan(1/2*c) + 268800*b*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c) + 591675*a*tan(1/2*d*x)^6
*tan(5/2*c)^2*tan(1/2*c) - 537600*b*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c) + 1943781*a*tan(5/2*d*x)^2*tan(1/2*
d*x)^5*tan(1/2*c)^2 - 2856448*b*tan(5/2*d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^2 - 36015*a*tan(5/2*d*x)*tan(1/2*d*x)
^6*tan(1/2*c)^2 - 5167428*a*tan(1/2*d*x)^7*tan(1/2*c)^2 + 3892224*b*tan(1/2*d*x)^7*tan(1/2*c)^2 + 21609*a*tan(
5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)*tan(1/2*c)^2 - 36015*a*tan(1/2*d*x)^6*tan(5/2*c)*tan(1/2*c)^2 - 1001070*a
*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^2 + 734720*b*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(5/2*c)^2
*tan(1/2*c)^2 + 21609*a*tan(5/2*d*x)*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^2 + 1943781*a*tan(1/2*d*x)^5*tan(5
/2*c)^2*tan(1/2*c)^2 - 2856448*b*tan(1/2*d*x)^5*tan(5/2*c)^2*tan(1/2*c)^2 + 6072570*a*tan(5/2*d*x)^2*tan(1/2*d
*x)^4*tan(1/2*c)^3 - 6289920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^3 - 15324750*a*tan(1/2*d*x)^6*tan(1/2*
c)^3 + 15321600*b*tan(1/2*d*x)^6*tan(1/2*c)^3 - 1001070*a*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c
)^3 + 734720*b*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^3 + 6072570*a*tan(1/2*d*x)^4*tan(5/2*c)^2
*tan(1/2*c)^3 - 6289920*b*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^3 + 6072570*a*tan(5/2*d*x)^2*tan(1/2*d*x)^3*t
an(1/2*c)^4 - 6289920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^4 - 64827*a*tan(5/2*d*x)*tan(1/2*d*x)^4*tan(1
/2*c)^4 - 32337207*a*tan(1/2*d*x)^5*tan(1/2*c)^4 + 30137856*b*tan(1/2*d*x)^5*tan(1/2*c)^4 + 21609*a*tan(5/2*d*
x)^2*tan(1/2*d*x)^2*tan(5/2*c)*tan(1/2*c)^4 - 64827*a*tan(1/2*d*x)^4*tan(5/2*c)*tan(1/2*c)^4 - 193305*a*tan(5/
2*d*x)^2*tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^4 + 268800*b*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)
^4 + 21609*a*tan(5/2*d*x)*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^4 + 6072570*a*tan(1/2*d*x)^3*tan(5/2*c)^2*tan
(1/2*c)^4 - 6289920*b*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^4 + 1943781*a*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(1
/2*c)^5 - 2856448*b*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^5 - 32337207*a*tan(1/2*d*x)^4*tan(1/2*c)^5 + 3013
7856*b*tan(1/2*d*x)^4*tan(1/2*c)^5 - 113967*a*tan(5/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^5 + 14336*b*tan(5/2*d*x)^
2*tan(5/2*c)^2*tan(1/2*c)^5 + 1943781*a*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^5 - 2856448*b*tan(1/2*d*x)^2*ta
n(5/2*c)^2*tan(1/2*c)^5 + 591675*a*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(1/2*c)^6 - 537600*b*tan(5/2*d*x)^2*tan(1/2*
d*x)*tan(1/2*c)^6 - 36015*a*tan(5/2*d*x)*tan(1/2*d*x)^2*tan(1/2*c)^6 - 15324750*a*tan(1/2*d*x)^3*tan(1/2*c)^6
+ 15321600*b*tan(1/2*d*x)^3*tan(1/2*c)^6 + 5145*a*tan(5/2*d*x)^2*tan(5/2*c)*tan(1/2*c)^6 - 36015*a*tan(1/2*d*x
)^2*tan(5/2*c)*tan(1/2*c)^6 + 5145*a*tan(5/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^6 + 591675*a*tan(1/2*d*x)*tan(5/2*c)
^2*tan(1/2*c)^6 - 537600*b*tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^6 - 62004*a*tan(5/2*d*x)^2*tan(1/2*c)^7 - 5836
8*b*tan(5/2*d*x)^2*tan(1/2*c)^7 - 5167428*a*tan(1/2*d*x)^2*tan(1/2*c)^7 + 3892224*b*tan(1/2*d*x)^2*tan(1/2*c)^
7 - 62004*a*tan(5/2*c)^2*tan(1/2*c)^7 - 58368*b*tan(5/2*c)^2*tan(1/2*c)^7 - 5145*a*tan(5/2*d*x)*tan(1/2*c)^8 -
591675*a*tan(1/2*d*x)*tan(1/2*c)^8 + 537600*b*tan(1/2*d*x)*tan(1/2*c)^8 - 5145*a*tan(5/2*c)*tan(1/2*c)^8 - 11
3967*a*tan(1/2*c)^9 + 14336*b*tan(1/2*c)^9 - 113967*a*tan(5/2*d*x)^2*tan(1/2*d*x)^5 + 14336*b*tan(5/2*d*x)^2*t
an(1/2*d*x)^5 - 5145*a*tan(5/2*d*x)*tan(1/2*d*x)^6 - 62004*a*tan(1/2*d*x)^7 - 58368*b*tan(1/2*d*x)^7 + 3087*a*
tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c) - 5145*a*tan(1/2*d*x)^6*tan(5/2*c) - 34230*a*tan(5/2*d*x)^2*tan(1/2*d
*x)^3*tan(5/2*c)^2 - 17920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(5/2*c)^2 + 3087*a*tan(5/2*d*x)*tan(1/2*d*x)^4*t
an(5/2*c)^2 - 113967*a*tan(1/2*d*x)^5*tan(5/2*c)^2 + 14336*b*tan(1/2*d*x)^5*tan(5/2*c)^2 - 193305*a*tan(5/2*d*
x)^2*tan(1/2*d*x)^4*tan(1/2*c) + 268800*b*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(1/2*c) + 591675*a*tan(1/2*d*x)^6*t
an(1/2*c) - 537600*b*tan(1/2*d*x)^6*tan(1/2*c) + 62475*a*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)
- 53760*b*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c) - 193305*a*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/
2*c) + 268800*b*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c) - 1001070*a*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^2
+ 734720*b*tan(5/2*d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^2 - 21609*a*tan(5/2*d*x)*tan(1/2*d*x)^4*tan(1/2*c)^2 + 194
3781*a*tan(1/2*d*x)^5*tan(1/2*c)^2 - 2856448*b*tan(1/2*d*x)^5*tan(1/2*c)^2 + 7203*a*tan(5/2*d*x)^2*tan(1/2*d*x
)^2*tan(5/2*c)*tan(1/2*c)^2 - 21609*a*tan(1/2*d*x)^4*tan(5/2*c)*tan(1/2*c)^2 + 62475*a*tan(5/2*d*x)^2*tan(1/2*
d*x)*tan(5/2*c)^2*tan(1/2*c)^2 - 53760*b*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^2 + 7203*a*tan(5/
2*d*x)*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^2 - 1001070*a*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^2 + 734720*
b*tan(1/2*d*x)^3*tan(5/2*c)^2*tan(1/2*c)^2 - 1001070*a*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^3 + 734720*b*t
an(5/2*d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^3 + 6072570*a*tan(1/2*d*x)^4*tan(1/2*c)^3 - 6289920*b*tan(1/2*d*x)^4*t
an(1/2*c)^3 - 34230*a*tan(5/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^3 - 17920*b*tan(5/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c
)^3 - 1001070*a*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^3 + 734720*b*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^3 -
193305*a*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(1/2*c)^4 + 268800*b*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(1/2*c)^4 - 21609
*a*tan(5/2*d*x)*tan(1/2*d*x)^2*tan(1/2*c)^4 + 6072570*a*tan(1/2*d*x)^3*tan(1/2*c)^4 - 6289920*b*tan(1/2*d*x)^3
*tan(1/2*c)^4 + 3087*a*tan(5/2*d*x)^2*tan(5/2*c)*tan(1/2*c)^4 - 21609*a*tan(1/2*d*x)^2*tan(5/2*c)*tan(1/2*c)^4
+ 3087*a*tan(5/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^4 - 193305*a*tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^4 + 268800*b*
tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^4 - 113967*a*tan(5/2*d*x)^2*tan(1/2*c)^5 + 14336*b*tan(5/2*d*x)^2*tan(1/2
*c)^5 + 1943781*a*tan(1/2*d*x)^2*tan(1/2*c)^5 - 2856448*b*tan(1/2*d*x)^2*tan(1/2*c)^5 - 113967*a*tan(5/2*c)^2*
tan(1/2*c)^5 + 14336*b*tan(5/2*c)^2*tan(1/2*c)^5 - 5145*a*tan(5/2*d*x)*tan(1/2*c)^6 + 591675*a*tan(1/2*d*x)*ta
n(1/2*c)^6 - 537600*b*tan(1/2*d*x)*tan(1/2*c)^6 - 5145*a*tan(5/2*c)*tan(1/2*c)^6 - 62004*a*tan(1/2*c)^7 - 5836
8*b*tan(1/2*c)^7 - 34230*a*tan(5/2*d*x)^2*tan(1/2*d*x)^3 - 17920*b*tan(5/2*d*x)^2*tan(1/2*d*x)^3 - 3087*a*tan(
5/2*d*x)*tan(1/2*d*x)^4 - 113967*a*tan(1/2*d*x)^5 + 14336*b*tan(1/2*d*x)^5 + 1029*a*tan(5/2*d*x)^2*tan(1/2*d*x
)^2*tan(5/2*c) - 3087*a*tan(1/2*d*x)^4*tan(5/2*c) - 12705*a*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(5/2*c)^2 + 1029*a*
tan(5/2*d*x)*tan(1/2*d*x)^2*tan(5/2*c)^2 - 34230*a*tan(1/2*d*x)^3*tan(5/2*c)^2 - 17920*b*tan(1/2*d*x)^3*tan(5/
2*c)^2 + 62475*a*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(1/2*c) - 53760*b*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(1/2*c) -
193305*a*tan(1/2*d*x)^4*tan(1/2*c) + 268800*b*tan(1/2*d*x)^4*tan(1/2*c) - 12705*a*tan(5/2*d*x)^2*tan(5/2*c)^2
*tan(1/2*c) + 62475*a*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c) - 53760*b*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)
+ 62475*a*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(1/2*c)^2 - 53760*b*tan(5/2*d*x)^2*tan(1/2*d*x)*tan(1/2*c)^2 - 7203*a
*tan(5/2*d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 1001070*a*tan(1/2*d*x)^3*tan(1/2*c)^2 + 734720*b*tan(1/2*d*x)^3*ta
n(1/2*c)^2 + 1029*a*tan(5/2*d*x)^2*tan(5/2*c)*tan(1/2*c)^2 - 7203*a*tan(1/2*d*x)^2*tan(5/2*c)*tan(1/2*c)^2 + 1
029*a*tan(5/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^2 + 62475*a*tan(1/2*d*x)*tan(5/2*c)^2*tan(1/2*c)^2 - 53760*b*tan(1/
2*d*x)*tan(5/2*c)^2*tan(1/2*c)^2 - 34230*a*tan(5/2*d*x)^2*tan(1/2*c)^3 - 17920*b*tan(5/2*d*x)^2*tan(1/2*c)^3 -
1001070*a*tan(1/2*d*x)^2*tan(1/2*c)^3 + 734720*b*tan(1/2*d*x)^2*tan(1/2*c)^3 - 34230*a*tan(5/2*c)^2*tan(1/2*c
)^3 - 17920*b*tan(5/2*c)^2*tan(1/2*c)^3 - 3087*a*tan(5/2*d*x)*tan(1/2*c)^4 - 193305*a*tan(1/2*d*x)*tan(1/2*c)^
4 + 268800*b*tan(1/2*d*x)*tan(1/2*c)^4 - 3087*a*tan(5/2*c)*tan(1/2*c)^4 - 113967*a*tan(1/2*c)^5 + 14336*b*tan(
1/2*c)^5 - 12705*a*tan(5/2*d*x)^2*tan(1/2*d*x) - 1029*a*tan(5/2*d*x)*tan(1/2*d*x)^2 - 34230*a*tan(1/2*d*x)^3 -
17920*b*tan(1/2*d*x)^3 + 147*a*tan(5/2*d*x)^2*tan(5/2*c) - 1029*a*tan(1/2*d*x)^2*tan(5/2*c) + 147*a*tan(5/2*d
*x)*tan(5/2*c)^2 - 12705*a*tan(1/2*d*x)*tan(5/2*c)^2 - 12705*a*tan(5/2*d*x)^2*tan(1/2*c) + 62475*a*tan(1/2*d*x
)^2*tan(1/2*c) - 53760*b*tan(1/2*d*x)^2*tan(1/2*c) - 12705*a*tan(5/2*c)^2*tan(1/2*c) - 1029*a*tan(5/2*d*x)*tan
(1/2*c)^2 + 62475*a*tan(1/2*d*x)*tan(1/2*c)^2 - 53760*b*tan(1/2*d*x)*tan(1/2*c)^2 - 1029*a*tan(5/2*c)*tan(1/2*
c)^2 - 34230*a*tan(1/2*c)^3 - 17920*b*tan(1/2*c)^3 - 147*a*tan(5/2*d*x) - 12705*a*tan(1/2*d*x) - 147*a*tan(5/2
*c) - 12705*a*tan(1/2*c))/(d*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^14 + 7*d*tan(5/2*d*x)^2*ta
n(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^12 + d*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(1/2*c)^14 + 7*d*tan(5/2*d*x)^2
*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^14 + d*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^14 + 21*d*tan(5/2*d*x)
^2*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^10 + 7*d*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(1/2*c)^12 + 49*d*tan(5/
2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^12 + 7*d*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^12 + 7*d*tan
(5/2*d*x)^2*tan(1/2*d*x)^12*tan(1/2*c)^14 + d*tan(1/2*d*x)^14*tan(1/2*c)^14 + 21*d*tan(5/2*d*x)^2*tan(1/2*d*x)
^10*tan(5/2*c)^2*tan(1/2*c)^14 + 7*d*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^14 + 35*d*tan(5/2*d*x)^2*tan(1/2*
d*x)^14*tan(5/2*c)^2*tan(1/2*c)^8 + 21*d*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(1/2*c)^10 + 147*d*tan(5/2*d*x)^2*t
an(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^10 + 21*d*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^10 + 49*d*tan(5/2*d*x
)^2*tan(1/2*d*x)^12*tan(1/2*c)^12 + 7*d*tan(1/2*d*x)^14*tan(1/2*c)^12 + 147*d*tan(5/2*d*x)^2*tan(1/2*d*x)^10*t
an(5/2*c)^2*tan(1/2*c)^12 + 49*d*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^12 + 21*d*tan(5/2*d*x)^2*tan(1/2*d*x)
^10*tan(1/2*c)^14 + 7*d*tan(1/2*d*x)^12*tan(1/2*c)^14 + 35*d*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/
2*c)^14 + 21*d*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^14 + 35*d*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)^2*t
an(1/2*c)^6 + 35*d*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(1/2*c)^8 + 245*d*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*
c)^2*tan(1/2*c)^8 + 35*d*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^8 + 147*d*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(
1/2*c)^10 + 21*d*tan(1/2*d*x)^14*tan(1/2*c)^10 + 441*d*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^
10 + 147*d*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^10 + 147*d*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(1/2*c)^12 + 4
9*d*tan(1/2*d*x)^12*tan(1/2*c)^12 + 245*d*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^12 + 147*d*tan
(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^12 + 35*d*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c)^14 + 21*d*tan(1/2*d*x)
^10*tan(1/2*c)^14 + 35*d*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^14 + 35*d*tan(1/2*d*x)^8*tan(5/
2*c)^2*tan(1/2*c)^14 + 21*d*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^4 + 35*d*tan(5/2*d*x)^2*tan
(1/2*d*x)^14*tan(1/2*c)^6 + 245*d*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^6 + 35*d*tan(1/2*d*x)
^14*tan(5/2*c)^2*tan(1/2*c)^6 + 245*d*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(1/2*c)^8 + 35*d*tan(1/2*d*x)^14*tan(1
/2*c)^8 + 735*d*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^8 + 245*d*tan(1/2*d*x)^12*tan(5/2*c)^2*
tan(1/2*c)^8 + 441*d*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(1/2*c)^10 + 147*d*tan(1/2*d*x)^12*tan(1/2*c)^10 + 735*
d*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^10 + 441*d*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^10
+ 245*d*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c)^12 + 147*d*tan(1/2*d*x)^10*tan(1/2*c)^12 + 245*d*tan(5/2*d*x)
^2*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^12 + 245*d*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^12 + 35*d*tan(5/2*
d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^14 + 35*d*tan(1/2*d*x)^8*tan(1/2*c)^14 + 21*d*tan(5/2*d*x)^2*tan(1/2*d*x)^4*t
an(5/2*c)^2*tan(1/2*c)^14 + 35*d*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^14 + 7*d*tan(5/2*d*x)^2*tan(1/2*d*x)^1
4*tan(5/2*c)^2*tan(1/2*c)^2 + 21*d*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(1/2*c)^4 + 147*d*tan(5/2*d*x)^2*tan(1/2*
d*x)^12*tan(5/2*c)^2*tan(1/2*c)^4 + 21*d*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^4 + 245*d*tan(5/2*d*x)^2*tan(
1/2*d*x)^12*tan(1/2*c)^6 + 35*d*tan(1/2*d*x)^14*tan(1/2*c)^6 + 735*d*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)
^2*tan(1/2*c)^6 + 245*d*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^6 + 735*d*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(1
/2*c)^8 + 245*d*tan(1/2*d*x)^12*tan(1/2*c)^8 + 1225*d*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^8
+ 735*d*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^8 + 735*d*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c)^10 + 441*d*
tan(1/2*d*x)^10*tan(1/2*c)^10 + 735*d*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^10 + 735*d*tan(1/2
*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^10 + 245*d*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^12 + 245*d*tan(1/2*d*x)^8*
tan(1/2*c)^12 + 147*d*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^12 + 245*d*tan(1/2*d*x)^6*tan(5/2*
c)^2*tan(1/2*c)^12 + 21*d*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^14 + 35*d*tan(1/2*d*x)^6*tan(1/2*c)^14 + 7*
d*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^14 + 21*d*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^14 +
d*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(5/2*c)^2 + 7*d*tan(5/2*d*x)^2*tan(1/2*d*x)^14*tan(1/2*c)^2 + 49*d*tan(5/2
*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^2 + 7*d*tan(1/2*d*x)^14*tan(5/2*c)^2*tan(1/2*c)^2 + 147*d*tan(
5/2*d*x)^2*tan(1/2*d*x)^12*tan(1/2*c)^4 + 21*d*tan(1/2*d*x)^14*tan(1/2*c)^4 + 441*d*tan(5/2*d*x)^2*tan(1/2*d*x
)^10*tan(5/2*c)^2*tan(1/2*c)^4 + 147*d*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^4 + 735*d*tan(5/2*d*x)^2*tan(1/
2*d*x)^10*tan(1/2*c)^6 + 245*d*tan(1/2*d*x)^12*tan(1/2*c)^6 + 1225*d*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^
2*tan(1/2*c)^6 + 735*d*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^6 + 1225*d*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/
2*c)^8 + 735*d*tan(1/2*d*x)^10*tan(1/2*c)^8 + 1225*d*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^8 +
1225*d*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^8 + 735*d*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^10 + 735*d*t
an(1/2*d*x)^8*tan(1/2*c)^10 + 441*d*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^10 + 735*d*tan(1/2*d
*x)^6*tan(5/2*c)^2*tan(1/2*c)^10 + 147*d*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^12 + 245*d*tan(1/2*d*x)^6*ta
n(1/2*c)^12 + 49*d*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^12 + 147*d*tan(1/2*d*x)^4*tan(5/2*c)^
2*tan(1/2*c)^12 + 7*d*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^14 + 21*d*tan(1/2*d*x)^4*tan(1/2*c)^14 + d*tan(
5/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^14 + 7*d*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^14 + d*tan(5/2*d*x)^2*tan(1
/2*d*x)^14 + 7*d*tan(5/2*d*x)^2*tan(1/2*d*x)^12*tan(5/2*c)^2 + d*tan(1/2*d*x)^14*tan(5/2*c)^2 + 49*d*tan(5/2*d
*x)^2*tan(1/2*d*x)^12*tan(1/2*c)^2 + 7*d*tan(1/2*d*x)^14*tan(1/2*c)^2 + 147*d*tan(5/2*d*x)^2*tan(1/2*d*x)^10*t
an(5/2*c)^2*tan(1/2*c)^2 + 49*d*tan(1/2*d*x)^12*tan(5/2*c)^2*tan(1/2*c)^2 + 441*d*tan(5/2*d*x)^2*tan(1/2*d*x)^
10*tan(1/2*c)^4 + 147*d*tan(1/2*d*x)^12*tan(1/2*c)^4 + 735*d*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/
2*c)^4 + 441*d*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^4 + 1225*d*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c)^6 +
735*d*tan(1/2*d*x)^10*tan(1/2*c)^6 + 1225*d*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^6 + 1225*d*
tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^6 + 1225*d*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^8 + 1225*d*tan(1/2*
d*x)^8*tan(1/2*c)^8 + 735*d*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^8 + 1225*d*tan(1/2*d*x)^6*ta
n(5/2*c)^2*tan(1/2*c)^8 + 441*d*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^10 + 735*d*tan(1/2*d*x)^6*tan(1/2*c)^
10 + 147*d*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^10 + 441*d*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/
2*c)^10 + 49*d*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^12 + 147*d*tan(1/2*d*x)^4*tan(1/2*c)^12 + 7*d*tan(5/2*
d*x)^2*tan(5/2*c)^2*tan(1/2*c)^12 + 49*d*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^12 + d*tan(5/2*d*x)^2*tan(1/2*
c)^14 + 7*d*tan(1/2*d*x)^2*tan(1/2*c)^14 + d*tan(5/2*c)^2*tan(1/2*c)^14 + 7*d*tan(5/2*d*x)^2*tan(1/2*d*x)^12 +
d*tan(1/2*d*x)^14 + 21*d*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(5/2*c)^2 + 7*d*tan(1/2*d*x)^12*tan(5/2*c)^2 + 147
*d*tan(5/2*d*x)^2*tan(1/2*d*x)^10*tan(1/2*c)^2 + 49*d*tan(1/2*d*x)^12*tan(1/2*c)^2 + 245*d*tan(5/2*d*x)^2*tan(
1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^2 + 147*d*tan(1/2*d*x)^10*tan(5/2*c)^2*tan(1/2*c)^2 + 735*d*tan(5/2*d*x)^2*
tan(1/2*d*x)^8*tan(1/2*c)^4 + 441*d*tan(1/2*d*x)^10*tan(1/2*c)^4 + 735*d*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2
*c)^2*tan(1/2*c)^4 + 735*d*tan(1/2*d*x)^8*tan(5/2*c)^2*tan(1/2*c)^4 + 1225*d*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan
(1/2*c)^6 + 1225*d*tan(1/2*d*x)^8*tan(1/2*c)^6 + 735*d*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^6
+ 1225*d*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^6 + 735*d*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^8 + 1225*d
*tan(1/2*d*x)^6*tan(1/2*c)^8 + 245*d*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^8 + 735*d*tan(1/2*d
*x)^4*tan(5/2*c)^2*tan(1/2*c)^8 + 147*d*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^10 + 441*d*tan(1/2*d*x)^4*tan
(1/2*c)^10 + 21*d*tan(5/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^10 + 147*d*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^10
+ 7*d*tan(5/2*d*x)^2*tan(1/2*c)^12 + 49*d*tan(1/2*d*x)^2*tan(1/2*c)^12 + 7*d*tan(5/2*c)^2*tan(1/2*c)^12 + d*ta
n(1/2*c)^14 + 21*d*tan(5/2*d*x)^2*tan(1/2*d*x)^10 + 7*d*tan(1/2*d*x)^12 + 35*d*tan(5/2*d*x)^2*tan(1/2*d*x)^8*t
an(5/2*c)^2 + 21*d*tan(1/2*d*x)^10*tan(5/2*c)^2 + 245*d*tan(5/2*d*x)^2*tan(1/2*d*x)^8*tan(1/2*c)^2 + 147*d*tan
(1/2*d*x)^10*tan(1/2*c)^2 + 245*d*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^2 + 245*d*tan(1/2*d*x)
^8*tan(5/2*c)^2*tan(1/2*c)^2 + 735*d*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4 + 735*d*tan(1/2*d*x)^8*tan(1/2
*c)^4 + 441*d*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^4 + 735*d*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(
1/2*c)^4 + 735*d*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6 + 1225*d*tan(1/2*d*x)^6*tan(1/2*c)^6 + 245*d*tan(5
/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^6 + 735*d*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^6 + 245*d*ta
n(5/2*d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^8 + 735*d*tan(1/2*d*x)^4*tan(1/2*c)^8 + 35*d*tan(5/2*d*x)^2*tan(5/2*c)^
2*tan(1/2*c)^8 + 245*d*tan(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^8 + 21*d*tan(5/2*d*x)^2*tan(1/2*c)^10 + 147*d*ta
n(1/2*d*x)^2*tan(1/2*c)^10 + 21*d*tan(5/2*c)^2*tan(1/2*c)^10 + 7*d*tan(1/2*c)^12 + 35*d*tan(5/2*d*x)^2*tan(1/2
*d*x)^8 + 21*d*tan(1/2*d*x)^10 + 35*d*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(5/2*c)^2 + 35*d*tan(1/2*d*x)^8*tan(5/2
*c)^2 + 245*d*tan(5/2*d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2 + 245*d*tan(1/2*d*x)^8*tan(1/2*c)^2 + 147*d*tan(5/2*d
*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^2 + 245*d*tan(1/2*d*x)^6*tan(5/2*c)^2*tan(1/2*c)^2 + 441*d*tan(5/
2*d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4 + 735*d*tan(1/2*d*x)^6*tan(1/2*c)^4 + 147*d*tan(5/2*d*x)^2*tan(1/2*d*x)^2
*tan(5/2*c)^2*tan(1/2*c)^4 + 441*d*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^4 + 245*d*tan(5/2*d*x)^2*tan(1/2*d*x
)^2*tan(1/2*c)^6 + 735*d*tan(1/2*d*x)^4*tan(1/2*c)^6 + 35*d*tan(5/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^6 + 245*d*t
an(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^6 + 35*d*tan(5/2*d*x)^2*tan(1/2*c)^8 + 245*d*tan(1/2*d*x)^2*tan(1/2*c)^8
+ 35*d*tan(5/2*c)^2*tan(1/2*c)^8 + 21*d*tan(1/2*c)^10 + 35*d*tan(5/2*d*x)^2*tan(1/2*d*x)^6 + 35*d*tan(1/2*d*x
)^8 + 21*d*tan(5/2*d*x)^2*tan(1/2*d*x)^4*tan(5/2*c)^2 + 35*d*tan(1/2*d*x)^6*tan(5/2*c)^2 + 147*d*tan(5/2*d*x)^
2*tan(1/2*d*x)^4*tan(1/2*c)^2 + 245*d*tan(1/2*d*x)^6*tan(1/2*c)^2 + 49*d*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2
*c)^2*tan(1/2*c)^2 + 147*d*tan(1/2*d*x)^4*tan(5/2*c)^2*tan(1/2*c)^2 + 147*d*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(
1/2*c)^4 + 441*d*tan(1/2*d*x)^4*tan(1/2*c)^4 + 21*d*tan(5/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^4 + 147*d*tan(1/2*d
*x)^2*tan(5/2*c)^2*tan(1/2*c)^4 + 35*d*tan(5/2*d*x)^2*tan(1/2*c)^6 + 245*d*tan(1/2*d*x)^2*tan(1/2*c)^6 + 35*d*
tan(5/2*c)^2*tan(1/2*c)^6 + 35*d*tan(1/2*c)^8 + 21*d*tan(5/2*d*x)^2*tan(1/2*d*x)^4 + 35*d*tan(1/2*d*x)^6 + 7*d
*tan(5/2*d*x)^2*tan(1/2*d*x)^2*tan(5/2*c)^2 + 21*d*tan(1/2*d*x)^4*tan(5/2*c)^2 + 49*d*tan(5/2*d*x)^2*tan(1/2*d
*x)^2*tan(1/2*c)^2 + 147*d*tan(1/2*d*x)^4*tan(1/2*c)^2 + 7*d*tan(5/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^2 + 49*d*t
an(1/2*d*x)^2*tan(5/2*c)^2*tan(1/2*c)^2 + 21*d*tan(5/2*d*x)^2*tan(1/2*c)^4 + 147*d*tan(1/2*d*x)^2*tan(1/2*c)^4
+ 21*d*tan(5/2*c)^2*tan(1/2*c)^4 + 35*d*tan(1/2*c)^6 + 7*d*tan(5/2*d*x)^2*tan(1/2*d*x)^2 + 21*d*tan(1/2*d*x)^
4 + d*tan(5/2*d*x)^2*tan(5/2*c)^2 + 7*d*tan(1/2*d*x)^2*tan(5/2*c)^2 + 7*d*tan(5/2*d*x)^2*tan(1/2*c)^2 + 49*d*t
an(1/2*d*x)^2*tan(1/2*c)^2 + 7*d*tan(5/2*c)^2*tan(1/2*c)^2 + 21*d*tan(1/2*c)^4 + d*tan(5/2*d*x)^2 + 7*d*tan(1/
2*d*x)^2 + d*tan(5/2*c)^2 + 7*d*tan(1/2*c)^2 + d)
Mupad [B] (verification not implemented)
Time = 12.18 (sec) , antiderivative size = 95, normalized size of antiderivative = 1.25
\[
\int \cos ^7(c+d x) \left (a+b \tan ^2(c+d x)\right ) \, dx=\frac {\frac {35\,a\,\sin \left (c+d\,x\right )}{64}+\frac {5\,b\,\sin \left (c+d\,x\right )}{64}+\frac {7\,a\,\sin \left (3\,c+3\,d\,x\right )}{64}+\frac {7\,a\,\sin \left (5\,c+5\,d\,x\right )}{320}+\frac {a\,\sin \left (7\,c+7\,d\,x\right )}{448}-\frac {b\,\sin \left (3\,c+3\,d\,x\right )}{192}-\frac {3\,b\,\sin \left (5\,c+5\,d\,x\right )}{320}-\frac {b\,\sin \left (7\,c+7\,d\,x\right )}{448}}{d}
\]
[In]
int(cos(c + d*x)^7*(a + b*tan(c + d*x)^2),x)
[Out]
((35*a*sin(c + d*x))/64 + (5*b*sin(c + d*x))/64 + (7*a*sin(3*c + 3*d*x))/64 + (7*a*sin(5*c + 5*d*x))/320 + (a*
sin(7*c + 7*d*x))/448 - (b*sin(3*c + 3*d*x))/192 - (3*b*sin(5*c + 5*d*x))/320 - (b*sin(7*c + 7*d*x))/448)/d