3.71 \(\int \csc ^3(a+b x) \csc ^3(2 a+2 b x) \, dx\)
Optimal. Leaf size=81 \[ -\frac{7 \csc ^5(a+b x)}{80 b}-\frac{7 \csc ^3(a+b x)}{48 b}-\frac{7 \csc (a+b x)}{16 b}+\frac{7 \tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\csc ^5(a+b x) \sec ^2(a+b x)}{16 b} \]
[Out]
(7*ArcTanh[Sin[a + b*x]])/(16*b) - (7*Csc[a + b*x])/(16*b) - (7*Csc[a + b*x]^3)/(48*b) - (7*Csc[a + b*x]^5)/(8
0*b) + (Csc[a + b*x]^5*Sec[a + b*x]^2)/(16*b)
________________________________________________________________________________________
Rubi [A] time = 0.0731432, antiderivative size = 81, normalized size of antiderivative = 1.,
number of steps used = 6, number of rules used = 5, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used =
{4288, 2621, 288, 302, 207} \[ -\frac{7 \csc ^5(a+b x)}{80 b}-\frac{7 \csc ^3(a+b x)}{48 b}-\frac{7 \csc (a+b x)}{16 b}+\frac{7 \tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\csc ^5(a+b x) \sec ^2(a+b x)}{16 b} \]
Antiderivative was successfully verified.
[In]
Int[Csc[a + b*x]^3*Csc[2*a + 2*b*x]^3,x]
[Out]
(7*ArcTanh[Sin[a + b*x]])/(16*b) - (7*Csc[a + b*x])/(16*b) - (7*Csc[a + b*x]^3)/(48*b) - (7*Csc[a + b*x]^5)/(8
0*b) + (Csc[a + b*x]^5*Sec[a + b*x]^2)/(16*b)
Rule 4288
Int[((f_.)*sin[(a_.) + (b_.)*(x_)])^(n_.)*sin[(c_.) + (d_.)*(x_)]^(p_.), x_Symbol] :> Dist[2^p/f^p, Int[Cos[a
+ b*x]^p*(f*Sin[a + b*x])^(n + p), x], x] /; FreeQ[{a, b, c, d, f, n}, x] && EqQ[b*c - a*d, 0] && EqQ[d/b, 2]
&& IntegerQ[p]
Rule 2621
Int[(csc[(e_.) + (f_.)*(x_)]*(a_.))^(m_)*sec[(e_.) + (f_.)*(x_)]^(n_.), x_Symbol] :> -Dist[(f*a^n)^(-1), Subst
[Int[x^(m + n - 1)/(-1 + x^2/a^2)^((n + 1)/2), x], x, a*Csc[e + f*x]], x] /; FreeQ[{a, e, f, m}, x] && Integer
Q[(n + 1)/2] && !(IntegerQ[(m + 1)/2] && LtQ[0, m, n])
Rule 288
Int[((c_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[(c^(n - 1)*(c*x)^(m - n + 1)*(a + b*x^
n)^(p + 1))/(b*n*(p + 1)), x] - Dist[(c^n*(m - n + 1))/(b*n*(p + 1)), Int[(c*x)^(m - n)*(a + b*x^n)^(p + 1), x
], x] /; FreeQ[{a, b, c}, x] && IGtQ[n, 0] && LtQ[p, -1] && GtQ[m + 1, n] && !ILtQ[(m + n*(p + 1) + 1)/n, 0]
&& IntBinomialQ[a, b, c, n, m, p, x]
Rule 302
Int[(x_)^(m_)/((a_) + (b_.)*(x_)^(n_)), x_Symbol] :> Int[PolynomialDivide[x^m, a + b*x^n, x], x] /; FreeQ[{a,
b}, x] && IGtQ[m, 0] && IGtQ[n, 0] && GtQ[m, 2*n - 1]
Rule 207
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> -Simp[ArcTanh[(Rt[b, 2]*x)/Rt[-a, 2]]/(Rt[-a, 2]*Rt[b, 2]), x] /;
FreeQ[{a, b}, x] && NegQ[a/b] && (LtQ[a, 0] || GtQ[b, 0])
Rubi steps
\begin{align*} \int \csc ^3(a+b x) \csc ^3(2 a+2 b x) \, dx &=\frac{1}{8} \int \csc ^6(a+b x) \sec ^3(a+b x) \, dx\\ &=-\frac{\operatorname{Subst}\left (\int \frac{x^8}{\left (-1+x^2\right )^2} \, dx,x,\csc (a+b x)\right )}{8 b}\\ &=\frac{\csc ^5(a+b x) \sec ^2(a+b x)}{16 b}-\frac{7 \operatorname{Subst}\left (\int \frac{x^6}{-1+x^2} \, dx,x,\csc (a+b x)\right )}{16 b}\\ &=\frac{\csc ^5(a+b x) \sec ^2(a+b x)}{16 b}-\frac{7 \operatorname{Subst}\left (\int \left (1+x^2+x^4+\frac{1}{-1+x^2}\right ) \, dx,x,\csc (a+b x)\right )}{16 b}\\ &=-\frac{7 \csc (a+b x)}{16 b}-\frac{7 \csc ^3(a+b x)}{48 b}-\frac{7 \csc ^5(a+b x)}{80 b}+\frac{\csc ^5(a+b x) \sec ^2(a+b x)}{16 b}-\frac{7 \operatorname{Subst}\left (\int \frac{1}{-1+x^2} \, dx,x,\csc (a+b x)\right )}{16 b}\\ &=\frac{7 \tanh ^{-1}(\sin (a+b x))}{16 b}-\frac{7 \csc (a+b x)}{16 b}-\frac{7 \csc ^3(a+b x)}{48 b}-\frac{7 \csc ^5(a+b x)}{80 b}+\frac{\csc ^5(a+b x) \sec ^2(a+b x)}{16 b}\\ \end{align*}
Mathematica [C] time = 0.0347099, size = 31, normalized size = 0.38 \[ -\frac{\csc ^5(a+b x) \text{Hypergeometric2F1}\left (-\frac{5}{2},2,-\frac{3}{2},\sin ^2(a+b x)\right )}{40 b} \]
Antiderivative was successfully verified.
[In]
Integrate[Csc[a + b*x]^3*Csc[2*a + 2*b*x]^3,x]
[Out]
-(Csc[a + b*x]^5*Hypergeometric2F1[-5/2, 2, -3/2, Sin[a + b*x]^2])/(40*b)
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Maple [A] time = 0.039, size = 97, normalized size = 1.2 \begin{align*} -{\frac{1}{40\,b \left ( \sin \left ( bx+a \right ) \right ) ^{5} \left ( \cos \left ( bx+a \right ) \right ) ^{2}}}-{\frac{7}{120\,b \left ( \sin \left ( bx+a \right ) \right ) ^{3} \left ( \cos \left ( bx+a \right ) \right ) ^{2}}}+{\frac{7}{48\,b\sin \left ( bx+a \right ) \left ( \cos \left ( bx+a \right ) \right ) ^{2}}}-{\frac{7}{16\,b\sin \left ( bx+a \right ) }}+{\frac{7\,\ln \left ( \sec \left ( bx+a \right ) +\tan \left ( bx+a \right ) \right ) }{16\,b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(csc(b*x+a)^3*csc(2*b*x+2*a)^3,x)
[Out]
-1/40/b/sin(b*x+a)^5/cos(b*x+a)^2-7/120/b/sin(b*x+a)^3/cos(b*x+a)^2+7/48/b/sin(b*x+a)/cos(b*x+a)^2-7/16/b/sin(
b*x+a)+7/16/b*ln(sec(b*x+a)+tan(b*x+a))
________________________________________________________________________________________
Maxima [B] time = 2.32027, size = 4178, normalized size = 51.58 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(csc(b*x+a)^3*csc(2*b*x+2*a)^3,x, algorithm="maxima")
[Out]
1/480*(4*(105*sin(13*b*x + 13*a) - 350*sin(11*b*x + 11*a) + 231*sin(9*b*x + 9*a) + 412*sin(7*b*x + 7*a) + 231*
sin(5*b*x + 5*a) - 350*sin(3*b*x + 3*a) + 105*sin(b*x + a))*cos(14*b*x + 14*a) + 420*(3*sin(12*b*x + 12*a) - s
in(10*b*x + 10*a) - 5*sin(8*b*x + 8*a) + 5*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*cos(13*b*
x + 13*a) + 12*(350*sin(11*b*x + 11*a) - 231*sin(9*b*x + 9*a) - 412*sin(7*b*x + 7*a) - 231*sin(5*b*x + 5*a) +
350*sin(3*b*x + 3*a) - 105*sin(b*x + a))*cos(12*b*x + 12*a) + 1400*(sin(10*b*x + 10*a) + 5*sin(8*b*x + 8*a) -
5*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*cos(11*b*x + 11*a) + 4*(231*sin(9*b*x + 9*a) + 412
*sin(7*b*x + 7*a) + 231*sin(5*b*x + 5*a) - 350*sin(3*b*x + 3*a) + 105*sin(b*x + a))*cos(10*b*x + 10*a) - 924*(
5*sin(8*b*x + 8*a) - 5*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*cos(9*b*x + 9*a) + 20*(412*si
n(7*b*x + 7*a) + 231*sin(5*b*x + 5*a) - 350*sin(3*b*x + 3*a) + 105*sin(b*x + a))*cos(8*b*x + 8*a) + 1648*(5*si
n(6*b*x + 6*a) + sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*cos(7*b*x + 7*a) - 140*(33*sin(5*b*x + 5*a) - 50*sin(3
*b*x + 3*a) + 15*sin(b*x + a))*cos(6*b*x + 6*a) + 924*(sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*cos(5*b*x + 5*a)
+ 140*(10*sin(3*b*x + 3*a) - 3*sin(b*x + a))*cos(4*b*x + 4*a) + 105*(2*(3*cos(12*b*x + 12*a) - cos(10*b*x + 1
0*a) - 5*cos(8*b*x + 8*a) + 5*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(14*b*x + 14*a)
- cos(14*b*x + 14*a)^2 + 6*(cos(10*b*x + 10*a) + 5*cos(8*b*x + 8*a) - 5*cos(6*b*x + 6*a) - cos(4*b*x + 4*a) +
3*cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - 9*cos(12*b*x + 12*a)^2 - 2*(5*cos(8*b*x + 8*a) - 5*cos(6*b*x + 6
*a) - cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) - cos(10*b*x + 10*a)^2 + 10*(5*cos(6*b*x +
6*a) + cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - 25*cos(8*b*x + 8*a)^2 - 10*(cos(4*b*x +
4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(6*b*x + 6*a) - 25*cos(6*b*x + 6*a)^2 + 2*(3*cos(2*b*x + 2*a) - 1)*cos(4*b*x
+ 4*a) - cos(4*b*x + 4*a)^2 - 9*cos(2*b*x + 2*a)^2 + 2*(3*sin(12*b*x + 12*a) - sin(10*b*x + 10*a) - 5*sin(8*b
*x + 8*a) + 5*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(14*b*x + 14*a) - sin(14*b*x + 14*a
)^2 + 6*(sin(10*b*x + 10*a) + 5*sin(8*b*x + 8*a) - 5*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))
*sin(12*b*x + 12*a) - 9*sin(12*b*x + 12*a)^2 - 2*(5*sin(8*b*x + 8*a) - 5*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) +
3*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - sin(10*b*x + 10*a)^2 + 10*(5*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) - 3
*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 25*sin(8*b*x + 8*a)^2 - 10*(sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(6
*b*x + 6*a) - 25*sin(6*b*x + 6*a)^2 - sin(4*b*x + 4*a)^2 + 6*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 9*sin(2*b*x +
2*a)^2 + 6*cos(2*b*x + 2*a) - 1)*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^
2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a
)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) - 4*(105*cos(13*b*x + 13*a) - 350*cos(11*b*x + 11*a) + 231*cos(9*b*
x + 9*a) + 412*cos(7*b*x + 7*a) + 231*cos(5*b*x + 5*a) - 350*cos(3*b*x + 3*a) + 105*cos(b*x + a))*sin(14*b*x +
14*a) - 420*(3*cos(12*b*x + 12*a) - cos(10*b*x + 10*a) - 5*cos(8*b*x + 8*a) + 5*cos(6*b*x + 6*a) + cos(4*b*x
+ 4*a) - 3*cos(2*b*x + 2*a) + 1)*sin(13*b*x + 13*a) - 12*(350*cos(11*b*x + 11*a) - 231*cos(9*b*x + 9*a) - 412*
cos(7*b*x + 7*a) - 231*cos(5*b*x + 5*a) + 350*cos(3*b*x + 3*a) - 105*cos(b*x + a))*sin(12*b*x + 12*a) - 1400*(
cos(10*b*x + 10*a) + 5*cos(8*b*x + 8*a) - 5*cos(6*b*x + 6*a) - cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) - 1)*sin(
11*b*x + 11*a) - 4*(231*cos(9*b*x + 9*a) + 412*cos(7*b*x + 7*a) + 231*cos(5*b*x + 5*a) - 350*cos(3*b*x + 3*a)
+ 105*cos(b*x + a))*sin(10*b*x + 10*a) + 924*(5*cos(8*b*x + 8*a) - 5*cos(6*b*x + 6*a) - cos(4*b*x + 4*a) + 3*c
os(2*b*x + 2*a) - 1)*sin(9*b*x + 9*a) - 20*(412*cos(7*b*x + 7*a) + 231*cos(5*b*x + 5*a) - 350*cos(3*b*x + 3*a)
+ 105*cos(b*x + a))*sin(8*b*x + 8*a) - 1648*(5*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*
sin(7*b*x + 7*a) + 140*(33*cos(5*b*x + 5*a) - 50*cos(3*b*x + 3*a) + 15*cos(b*x + a))*sin(6*b*x + 6*a) - 924*(c
os(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*sin(5*b*x + 5*a) - 140*(10*cos(3*b*x + 3*a) - 3*cos(b*x + a))*sin(4*
b*x + 4*a) - 1400*(3*cos(2*b*x + 2*a) - 1)*sin(3*b*x + 3*a) + 4200*cos(3*b*x + 3*a)*sin(2*b*x + 2*a) - 1260*co
s(b*x + a)*sin(2*b*x + 2*a) + 1260*cos(2*b*x + 2*a)*sin(b*x + a) - 420*sin(b*x + a))/(b*cos(14*b*x + 14*a)^2 +
9*b*cos(12*b*x + 12*a)^2 + b*cos(10*b*x + 10*a)^2 + 25*b*cos(8*b*x + 8*a)^2 + 25*b*cos(6*b*x + 6*a)^2 + b*cos
(4*b*x + 4*a)^2 + 9*b*cos(2*b*x + 2*a)^2 + b*sin(14*b*x + 14*a)^2 + 9*b*sin(12*b*x + 12*a)^2 + b*sin(10*b*x +
10*a)^2 + 25*b*sin(8*b*x + 8*a)^2 + 25*b*sin(6*b*x + 6*a)^2 + b*sin(4*b*x + 4*a)^2 - 6*b*sin(4*b*x + 4*a)*sin(
2*b*x + 2*a) + 9*b*sin(2*b*x + 2*a)^2 - 2*(3*b*cos(12*b*x + 12*a) - b*cos(10*b*x + 10*a) - 5*b*cos(8*b*x + 8*a
) + 5*b*cos(6*b*x + 6*a) + b*cos(4*b*x + 4*a) - 3*b*cos(2*b*x + 2*a) + b)*cos(14*b*x + 14*a) - 6*(b*cos(10*b*x
+ 10*a) + 5*b*cos(8*b*x + 8*a) - 5*b*cos(6*b*x + 6*a) - b*cos(4*b*x + 4*a) + 3*b*cos(2*b*x + 2*a) - b)*cos(12
*b*x + 12*a) + 2*(5*b*cos(8*b*x + 8*a) - 5*b*cos(6*b*x + 6*a) - b*cos(4*b*x + 4*a) + 3*b*cos(2*b*x + 2*a) - b)
*cos(10*b*x + 10*a) - 10*(5*b*cos(6*b*x + 6*a) + b*cos(4*b*x + 4*a) - 3*b*cos(2*b*x + 2*a) + b)*cos(8*b*x + 8*
a) + 10*(b*cos(4*b*x + 4*a) - 3*b*cos(2*b*x + 2*a) + b)*cos(6*b*x + 6*a) - 2*(3*b*cos(2*b*x + 2*a) - b)*cos(4*
b*x + 4*a) - 6*b*cos(2*b*x + 2*a) - 2*(3*b*sin(12*b*x + 12*a) - b*sin(10*b*x + 10*a) - 5*b*sin(8*b*x + 8*a) +
5*b*sin(6*b*x + 6*a) + b*sin(4*b*x + 4*a) - 3*b*sin(2*b*x + 2*a))*sin(14*b*x + 14*a) - 6*(b*sin(10*b*x + 10*a)
+ 5*b*sin(8*b*x + 8*a) - 5*b*sin(6*b*x + 6*a) - b*sin(4*b*x + 4*a) + 3*b*sin(2*b*x + 2*a))*sin(12*b*x + 12*a)
+ 2*(5*b*sin(8*b*x + 8*a) - 5*b*sin(6*b*x + 6*a) - b*sin(4*b*x + 4*a) + 3*b*sin(2*b*x + 2*a))*sin(10*b*x + 10
*a) - 10*(5*b*sin(6*b*x + 6*a) + b*sin(4*b*x + 4*a) - 3*b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + 10*(b*sin(4*b*x
+ 4*a) - 3*b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)
________________________________________________________________________________________
Fricas [B] time = 0.516404, size = 458, normalized size = 5.65 \begin{align*} -\frac{210 \, \cos \left (b x + a\right )^{6} - 490 \, \cos \left (b x + a\right )^{4} - 105 \,{\left (\cos \left (b x + a\right )^{6} - 2 \, \cos \left (b x + a\right )^{4} + \cos \left (b x + a\right )^{2}\right )} \log \left (\sin \left (b x + a\right ) + 1\right ) \sin \left (b x + a\right ) + 105 \,{\left (\cos \left (b x + a\right )^{6} - 2 \, \cos \left (b x + a\right )^{4} + \cos \left (b x + a\right )^{2}\right )} \log \left (-\sin \left (b x + a\right ) + 1\right ) \sin \left (b x + a\right ) + 322 \, \cos \left (b x + a\right )^{2} - 30}{480 \,{\left (b \cos \left (b x + a\right )^{6} - 2 \, b \cos \left (b x + a\right )^{4} + b \cos \left (b x + a\right )^{2}\right )} \sin \left (b x + a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(csc(b*x+a)^3*csc(2*b*x+2*a)^3,x, algorithm="fricas")
[Out]
-1/480*(210*cos(b*x + a)^6 - 490*cos(b*x + a)^4 - 105*(cos(b*x + a)^6 - 2*cos(b*x + a)^4 + cos(b*x + a)^2)*log
(sin(b*x + a) + 1)*sin(b*x + a) + 105*(cos(b*x + a)^6 - 2*cos(b*x + a)^4 + cos(b*x + a)^2)*log(-sin(b*x + a) +
1)*sin(b*x + a) + 322*cos(b*x + a)^2 - 30)/((b*cos(b*x + a)^6 - 2*b*cos(b*x + a)^4 + b*cos(b*x + a)^2)*sin(b*
x + a))
________________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(csc(b*x+a)**3*csc(2*b*x+2*a)**3,x)
[Out]
Timed out
________________________________________________________________________________________
Giac [B] time = 11.8856, size = 8529, normalized size = 105.3 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(csc(b*x+a)^3*csc(2*b*x+2*a)^3,x, algorithm="giac")
[Out]
-1/3840*(480*(tan(1/2*b*x + 2*a)^3*tan(1/2*a)^24 + 30*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^22 - 6*tan(1/2*b*x + 2*a
)^2*tan(1/2*a)^23 + tan(1/2*b*x + 2*a)*tan(1/2*a)^24 - 756*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^20 + 614*tan(1/2*b*
x + 2*a)^2*tan(1/2*a)^21 - 114*tan(1/2*b*x + 2*a)*tan(1/2*a)^22 + 6*tan(1/2*a)^23 + 2058*tan(1/2*b*x + 2*a)^3*
tan(1/2*a)^18 - 4578*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^19 + 1932*tan(1/2*b*x + 2*a)*tan(1/2*a)^20 - 182*tan(1/2*
a)^21 - 27*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^16 + 6210*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^17 - 7462*tan(1/2*b*x + 2
*a)*tan(1/2*a)^18 + 1554*tan(1/2*a)^19 - 9396*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^14 + 15588*tan(1/2*b*x + 2*a)^2*
tan(1/2*a)^15 - 2331*tan(1/2*b*x + 2*a)*tan(1/2*a)^16 - 2178*tan(1/2*a)^17 - 21924*tan(1/2*b*x + 2*a)^2*tan(1/
2*a)^13 + 26028*tan(1/2*b*x + 2*a)*tan(1/2*a)^14 - 5668*tan(1/2*a)^15 + 9396*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^1
0 - 21924*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^11 + 6468*tan(1/2*a)^13 + 27*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^8 + 155
88*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^9 - 26028*tan(1/2*b*x + 2*a)*tan(1/2*a)^10 + 6468*tan(1/2*a)^11 - 2058*tan(
1/2*b*x + 2*a)^3*tan(1/2*a)^6 + 6210*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^7 + 2331*tan(1/2*b*x + 2*a)*tan(1/2*a)^8
- 5668*tan(1/2*a)^9 + 756*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^4 - 4578*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 + 7462*ta
n(1/2*b*x + 2*a)*tan(1/2*a)^6 - 2178*tan(1/2*a)^7 - 30*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^2 + 614*tan(1/2*b*x + 2
*a)^2*tan(1/2*a)^3 - 1932*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 1554*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)^3 - 6*tan(1
/2*b*x + 2*a)^2*tan(1/2*a) + 114*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 182*tan(1/2*a)^3 - tan(1/2*b*x + 2*a) + 6*t
an(1/2*a))/((tan(1/2*a)^12 - 30*tan(1/2*a)^10 + 255*tan(1/2*a)^8 - 452*tan(1/2*a)^6 + 255*tan(1/2*a)^4 - 30*ta
n(1/2*a)^2 + 1)*(tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 12*tan(1/2*b*x + 2
*a)*tan(1/2*a)^5 - tan(1/2*a)^6 + 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 +
15*tan(1/2*a)^4 - tan(1/2*b*x + 2*a)^2 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^2) + (1215*ta
n(1/2*b*x + 2*a)^9*tan(1/2*a)^56 - 810*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^57 + 270*tan(1/2*b*x + 2*a)^7*tan(1/2*a
)^58 - 45*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^59 + 3*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^60 + 71280*tan(1/2*b*x + 2*a)
^9*tan(1/2*a)^54 - 59940*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^55 + 17640*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^56 - 795*t
an(1/2*b*x + 2*a)^6*tan(1/2*a)^57 - 360*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^58 + 45*tan(1/2*b*x + 2*a)^4*tan(1/2*a
)^59 + 2407725*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^52 - 2568780*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^53 + 1013880*tan(1
/2*b*x + 2*a)^7*tan(1/2*a)^54 - 144900*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^55 - 1635*tan(1/2*b*x + 2*a)^5*tan(1/2*
a)^56 + 795*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^57 + 270*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^58 - 164020320*tan(1/2*b*
x + 2*a)^9*tan(1/2*a)^50 + 294234150*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^51 - 204257160*tan(1/2*b*x + 2*a)^7*tan(1
/2*a)^52 + 68740740*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^53 - 10958240*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^54 + 567720*
tan(1/2*b*x + 2*a)^4*tan(1/2*a)^55 + 17640*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^56 + 810*tan(1/2*b*x + 2*a)^2*tan(1
/2*a)^57 + 2847265170*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^48 - 7061366340*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^49 + 684
8508750*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^50 - 3360350485*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^51 + 882126585*tan(1/2
*b*x + 2*a)^5*tan(1/2*a)^52 - 115984800*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^53 + 5446200*tan(1/2*b*x + 2*a)^3*tan(
1/2*a)^54 + 86670*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^55 + 1215*tan(1/2*b*x + 2*a)*tan(1/2*a)^56 - 25466109120*tan
(1/2*b*x + 2*a)^9*tan(1/2*a)^46 + 82199042640*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^47 - 104745094160*tan(1/2*b*x +
2*a)^7*tan(1/2*a)^48 + 68829859005*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^49 - 25315144296*tan(1/2*b*x + 2*a)^5*tan(1
/2*a)^50 + 5205627685*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^51 - 546245640*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^52 + 2089
5030*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^53 + 187920*tan(1/2*b*x + 2*a)*tan(1/2*a)^54 + 1458*tan(1/2*a)^55 + 13790
5936830*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^44 - 562989334800*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^45 + 911808828960*ta
n(1/2*b*x + 2*a)^7*tan(1/2*a)^46 - 768698936880*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^47 + 370049962295*tan(1/2*b*x
+ 2*a)^5*tan(1/2*a)^48 - 104054449965*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^49 + 16540981710*tan(1/2*b*x + 2*a)^3*ta
n(1/2*a)^50 - 1323596190*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^51 + 37166445*tan(1/2*b*x + 2*a)*tan(1/2*a)^52 + 1725
30*tan(1/2*a)^53 - 472782926880*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^42 + 2429658984060*tan(1/2*b*x + 2*a)^8*tan(1/
2*a)^43 - 4936681833840*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^44 + 5227899617200*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^45
- 3184356059520*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^46 + 1153540125240*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^47 - 245839
387280*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^48 + 28942646220*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^49 - 1600947360*tan(1/
2*b*x + 2*a)*tan(1/2*a)^50 + 25793640*tan(1/2*a)^51 + 985566407445*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^40 - 659470
1846310*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^41 + 17020352439990*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^42 - 2262838924354
5*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^43 + 17235607351635*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^44 - 7834375816360*tan(1
/2*b*x + 2*a)^4*tan(1/2*a)^45 + 2124636283680*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^46 - 329145687420*tan(1/2*b*x +
2*a)^2*tan(1/2*a)^47 + 25919270610*tan(1/2*b*x + 2*a)*tan(1/2*a)^48 - 753655320*tan(1/2*a)^49 - 941937351120*t
an(1/2*b*x + 2*a)^9*tan(1/2*a)^38 + 10024213003740*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^39 - 35619165658440*tan(1/2
*b*x + 2*a)^7*tan(1/2*a)^40 + 61660501611345*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^41 - 59571399047240*tan(1/2*b*x +
2*a)^5*tan(1/2*a)^42 + 33928676906985*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^43 - 11501138427120*tan(1/2*b*x + 2*a)^
3*tan(1/2*a)^44 + 2245614722020*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^45 - 228535536960*tan(1/2*b*x + 2*a)*tan(1/2*a
)^46 + 9122039460*tan(1/2*a)^47 - 756859069305*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^36 - 2938166946540*tan(1/2*b*x
+ 2*a)^8*tan(1/2*a)^37 + 33963536732760*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^38 - 93824947269780*tan(1/2*b*x + 2*a)
^6*tan(1/2*a)^39 + 124880209066749*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^40 - 92522313305985*tan(1/2*b*x + 2*a)^4*ta
n(1/2*a)^41 + 39714192559670*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^42 - 9707168584980*tan(1/2*b*x + 2*a)^2*tan(1/2*a
)^43 + 1237500036990*tan(1/2*b*x + 2*a)*tan(1/2*a)^44 - 62831824476*tan(1/2*a)^45 + 3403775131200*tan(1/2*b*x
+ 2*a)^9*tan(1/2*a)^34 - 19290846651030*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^35 + 27663473408040*tan(1/2*b*x + 2*a)
^7*tan(1/2*a)^36 + 27109136872980*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^37 - 118939479927840*tan(1/2*b*x + 2*a)^5*ta
n(1/2*a)^38 + 140811947469040*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^39 - 83200102704840*tan(1/2*b*x + 2*a)^3*tan(1/2
*a)^40 + 26404824927630*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^41 - 4255065187040*tan(1/2*b*x + 2*a)*tan(1/2*a)^42 +
270445183560*tan(1/2*a)^43 - 3650513198580*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^32 + 36323787336840*tan(1/2*b*x + 2
*a)^8*tan(1/2*a)^33 - 122659045084170*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^34 + 180766125659295*tan(1/2*b*x + 2*a)^
6*tan(1/2*a)^35 - 97447951446495*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^36 - 40571312613240*tan(1/2*b*x + 2*a)^4*tan(
1/2*a)^37 + 79276457792280*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^38 - 40160124218470*tan(1/2*b*x + 2*a)^2*tan(1/2*a)
^39 + 8888251621845*tan(1/2*b*x + 2*a)*tan(1/2*a)^40 - 731644643640*tan(1/2*a)^41 - 19469403725760*tan(1/2*b*x
+ 2*a)^8*tan(1/2*a)^31 + 130628272644000*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^32 - 338314460497335*tan(1/2*b*x + 2
*a)^6*tan(1/2*a)^33 + 429435328442040*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^34 - 271342502839935*tan(1/2*b*x + 2*a)^
4*tan(1/2*a)^35 + 64809044724520*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^36 + 11678391455970*tan(1/2*b*x + 2*a)^2*tan(
1/2*a)^37 - 8484705136560*tan(1/2*b*x + 2*a)*tan(1/2*a)^38 + 1111051397230*tan(1/2*a)^39 + 3650513198580*tan(1
/2*b*x + 2*a)^9*tan(1/2*a)^28 - 19469403725760*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^29 + 180715347146880*tan(1/2*b*
x + 2*a)^6*tan(1/2*a)^31 - 456090384021345*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^32 + 507272799301335*tan(1/2*b*x +
2*a)^4*tan(1/2*a)^33 - 286258153276170*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^34 + 77334987640230*tan(1/2*b*x + 2*a)^
2*tan(1/2*a)^35 - 6866537353465*tan(1/2*b*x + 2*a)*tan(1/2*a)^36 - 329444622930*tan(1/2*a)^37 - 3403775131200*
tan(1/2*b*x + 2*a)^9*tan(1/2*a)^26 + 36323787336840*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^27 - 130628272644000*tan(1
/2*b*x + 2*a)^7*tan(1/2*a)^28 + 180715347146880*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^29 - 270808903495440*tan(1/2*b
*x + 2*a)^4*tan(1/2*a)^31 + 304337156718240*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^32 - 145126844230520*tan(1/2*b*x +
2*a)^2*tan(1/2*a)^33 + 30650585964480*tan(1/2*b*x + 2*a)*tan(1/2*a)^34 - 2135547006768*tan(1/2*a)^35 + 756859
069305*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^24 - 19290846651030*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^25 + 12265904508417
0*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^26 - 338314460497335*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^27 + 456090384021345*ta
n(1/2*b*x + 2*a)^5*tan(1/2*a)^28 - 270808903495440*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^29 + 77638534829400*tan(1/2
*b*x + 2*a)^2*tan(1/2*a)^31 - 32750159843700*tan(1/2*b*x + 2*a)*tan(1/2*a)^32 + 4042939650000*tan(1/2*a)^33 +
941937351120*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^22 - 2938166946540*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^23 - 276634734
08040*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^24 + 180766125659295*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^25 - 42943532844204
0*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^26 + 507272799301335*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^27 - 304337156718240*ta
n(1/2*b*x + 2*a)^3*tan(1/2*a)^28 + 77638534829400*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^29 - 2175308641800*tan(1/2*a
)^31 - 985566407445*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^20 + 10024213003740*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^21 - 3
3963536732760*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^22 + 27109136872980*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^23 + 9744795
1446495*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^24 - 271342502839935*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^25 + 286258153276
170*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^26 - 145126844230520*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^27 + 32750159843700*t
an(1/2*b*x + 2*a)*tan(1/2*a)^28 - 2175308641800*tan(1/2*a)^29 + 472782926880*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^1
8 - 6594701846310*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^19 + 35619165658440*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^20 - 938
24947269780*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^21 + 118939479927840*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^22 - 40571312
613240*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^23 - 64809044724520*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^24 + 77334987640230
*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^25 - 30650585964480*tan(1/2*b*x + 2*a)*tan(1/2*a)^26 + 4042939650000*tan(1/2*
a)^27 - 137905936830*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^16 + 2429658984060*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^17 - 1
7020352439990*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^18 + 61660501611345*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^19 - 1248802
09066749*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^20 + 140811947469040*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^21 - 79276457792
280*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^22 + 11678391455970*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^23 + 6866537353465*tan
(1/2*b*x + 2*a)*tan(1/2*a)^24 - 2135547006768*tan(1/2*a)^25 + 25466109120*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^14 -
562989334800*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^15 + 4936681833840*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^16 - 22628389
243545*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^17 + 59571399047240*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^18 - 92522313305985
*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^19 + 83200102704840*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^20 - 40160124218470*tan(1
/2*b*x + 2*a)^2*tan(1/2*a)^21 + 8484705136560*tan(1/2*b*x + 2*a)*tan(1/2*a)^22 - 329444622930*tan(1/2*a)^23 -
2847265170*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^12 + 82199042640*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^13 - 911808828960*
tan(1/2*b*x + 2*a)^7*tan(1/2*a)^14 + 5227899617200*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^15 - 17235607351635*tan(1/2
*b*x + 2*a)^5*tan(1/2*a)^16 + 33928676906985*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^17 - 39714192559670*tan(1/2*b*x +
2*a)^3*tan(1/2*a)^18 + 26404824927630*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^19 - 8888251621845*tan(1/2*b*x + 2*a)*t
an(1/2*a)^20 + 1111051397230*tan(1/2*a)^21 + 164020320*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^10 - 7061366340*tan(1/2
*b*x + 2*a)^8*tan(1/2*a)^11 + 104745094160*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^12 - 768698936880*tan(1/2*b*x + 2*a
)^6*tan(1/2*a)^13 + 3184356059520*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^14 - 7834375816360*tan(1/2*b*x + 2*a)^4*tan(
1/2*a)^15 + 11501138427120*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^16 - 9707168584980*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^
17 + 4255065187040*tan(1/2*b*x + 2*a)*tan(1/2*a)^18 - 731644643640*tan(1/2*a)^19 - 2407725*tan(1/2*b*x + 2*a)^
9*tan(1/2*a)^8 + 294234150*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^9 - 6848508750*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^10 +
68829859005*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^11 - 370049962295*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^12 + 1153540125
240*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^13 - 2124636283680*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^14 + 2245614722020*tan(
1/2*b*x + 2*a)^2*tan(1/2*a)^15 - 1237500036990*tan(1/2*b*x + 2*a)*tan(1/2*a)^16 + 270445183560*tan(1/2*a)^17 -
71280*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^6 - 2568780*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^7 + 204257160*tan(1/2*b*x +
2*a)^7*tan(1/2*a)^8 - 3360350485*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^9 + 25315144296*tan(1/2*b*x + 2*a)^5*tan(1/2
*a)^10 - 104054449965*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^11 + 245839387280*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^12 - 3
29145687420*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^13 + 228535536960*tan(1/2*b*x + 2*a)*tan(1/2*a)^14 - 62831824476*t
an(1/2*a)^15 - 1215*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^4 - 59940*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^5 - 1013880*tan(
1/2*b*x + 2*a)^7*tan(1/2*a)^6 + 68740740*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^7 - 882126585*tan(1/2*b*x + 2*a)^5*ta
n(1/2*a)^8 + 5205627685*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^9 - 16540981710*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^10 + 2
8942646220*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^11 - 25919270610*tan(1/2*b*x + 2*a)*tan(1/2*a)^12 + 9122039460*tan(
1/2*a)^13 - 810*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^3 - 17640*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^4 - 144900*tan(1/2*b
*x + 2*a)^6*tan(1/2*a)^5 + 10958240*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^6 - 115984800*tan(1/2*b*x + 2*a)^4*tan(1/2
*a)^7 + 546245640*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^8 - 1323596190*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^9 + 160094736
0*tan(1/2*b*x + 2*a)*tan(1/2*a)^10 - 753655320*tan(1/2*a)^11 - 270*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^2 - 795*tan
(1/2*b*x + 2*a)^6*tan(1/2*a)^3 + 1635*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^4 + 567720*tan(1/2*b*x + 2*a)^4*tan(1/2*
a)^5 - 5446200*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^6 + 20895030*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^7 - 37166445*tan(1
/2*b*x + 2*a)*tan(1/2*a)^8 + 25793640*tan(1/2*a)^9 - 45*tan(1/2*b*x + 2*a)^6*tan(1/2*a) + 360*tan(1/2*b*x + 2*
a)^5*tan(1/2*a)^2 + 795*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^3 - 17640*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^4 + 86670*ta
n(1/2*b*x + 2*a)^2*tan(1/2*a)^5 - 187920*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 + 172530*tan(1/2*a)^7 - 3*tan(1/2*b*x
+ 2*a)^5 + 45*tan(1/2*b*x + 2*a)^4*tan(1/2*a) - 270*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^2 + 810*tan(1/2*b*x + 2*a
)^2*tan(1/2*a)^3 - 1215*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 1458*tan(1/2*a)^5)/((243*tan(1/2*a)^25 - 4050*tan(1/
2*a)^23 + 28215*tan(1/2*a)^21 - 106200*tan(1/2*a)^19 + 233430*tan(1/2*a)^17 - 304300*tan(1/2*a)^15 + 233430*ta
n(1/2*a)^13 - 106200*tan(1/2*a)^11 + 28215*tan(1/2*a)^9 - 4050*tan(1/2*a)^7 + 243*tan(1/2*a)^5)*(3*tan(1/2*b*x
+ 2*a)^2*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 10*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 + 15*tan(1/2*b
*x + 2*a)*tan(1/2*a)^4 - 3*tan(1/2*a)^5 + 3*tan(1/2*b*x + 2*a)^2*tan(1/2*a) - 15*tan(1/2*b*x + 2*a)*tan(1/2*a)
^2 + 10*tan(1/2*a)^3 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a))^5) - 1680*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 +
3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - tan(1/2*
b*x + 2*a) + 3*tan(1/2*a) - 1)) + 1680*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*
a)^2 + tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a) - 1
)))/b