\(\int \cos ^3(c+d x) (a \sin (c+d x)+b \tan (c+d x))^2 \, dx\) [236]

Optimal result

Integrand size = 28, antiderivative size = 106 \[ \int \cos ^3(c+d x) (a \sin (c+d x)+b \tan (c+d x))^2 \, dx=\frac {a b x}{4}-\frac {a b \cos (c+d x) \sin (c+d x)}{4 d}+\frac {\left (4 a^2+b^2\right ) \sin ^3(c+d x)}{30 d}+\frac {b (b+a \cos (c+d x)) \sin ^3(c+d x)}{10 d}+\frac {(b+a \cos (c+d x))^2 \sin ^3(c+d x)}{5 d} \]

[Out]

1/4*a*b*x-1/4*a*b*cos(d*x+c)*sin(d*x+c)/d+1/30*(4*a^2+b^2)*sin(d*x+c)^3/d+1/10*b*(b+a*cos(d*x+c))*sin(d*x+c)^3
/d+1/5*(b+a*cos(d*x+c))^2*sin(d*x+c)^3/d

Rubi [A] (verified)

Time = 0.44 (sec) , antiderivative size = 106, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.179, Rules used = {4482, 2941, 2748, 2715, 8} \[ \int \cos ^3(c+d x) (a \sin (c+d x)+b \tan (c+d x))^2 \, dx=\frac {\left (4 a^2+b^2\right ) \sin ^3(c+d x)}{30 d}+\frac {\sin ^3(c+d x) (a \cos (c+d x)+b)^2}{5 d}+\frac {b \sin ^3(c+d x) (a \cos (c+d x)+b)}{10 d}-\frac {a b \sin (c+d x) \cos (c+d x)}{4 d}+\frac {a b x}{4} \]

[In]

Int[Cos[c + d*x]^3*(a*Sin[c + d*x] + b*Tan[c + d*x])^2,x]

[Out]

(a*b*x)/4 - (a*b*Cos[c + d*x]*Sin[c + d*x])/(4*d) + ((4*a^2 + b^2)*Sin[c + d*x]^3)/(30*d) + (b*(b + a*Cos[c +
d*x])*Sin[c + d*x]^3)/(10*d) + ((b + a*Cos[c + d*x])^2*Sin[c + d*x]^3)/(5*d)

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rule 2715

Int[((b_.)*sin[(c_.) + (d_.)*(x_)])^(n_), x_Symbol] :> Simp[(-b)*Cos[c + d*x]*((b*Sin[c + d*x])^(n - 1)/(d*n))
, x] + Dist[b^2*((n - 1)/n), Int[(b*Sin[c + d*x])^(n - 2), x], x] /; FreeQ[{b, c, d}, x] && GtQ[n, 1] && Integ
erQ[2*n]

Rule 2748

Int[(cos[(e_.) + (f_.)*(x_)]*(g_.))^(p_)*((a_) + (b_.)*sin[(e_.) + (f_.)*(x_)]), x_Symbol] :> Simp[(-b)*((g*Co
s[e + f*x])^(p + 1)/(f*g*(p + 1))), x] + Dist[a, Int[(g*Cos[e + f*x])^p, x], x] /; FreeQ[{a, b, e, f, g, p}, x
] && (IntegerQ[2*p] || NeQ[a^2 - b^2, 0])

Rule 2941

Int[(cos[(e_.) + (f_.)*(x_)]*(g_.))^(p_)*((a_) + (b_.)*sin[(e_.) + (f_.)*(x_)])^(m_.)*((c_.) + (d_.)*sin[(e_.)
+ (f_.)*(x_)]), x_Symbol] :> Simp[(-d)*(g*Cos[e + f*x])^(p + 1)*((a + b*Sin[e + f*x])^m/(f*g*(m + p + 1))), x
] + Dist[1/(m + p + 1), Int[(g*Cos[e + f*x])^p*(a + b*Sin[e + f*x])^(m - 1)*Simp[a*c*(m + p + 1) + b*d*m + (a*
d*m + b*c*(m + p + 1))*Sin[e + f*x], x], x], x] /; FreeQ[{a, b, c, d, e, f, g, p}, x] && NeQ[a^2 - b^2, 0] &&
GtQ[m, 0] &&  !LtQ[p, -1] && IntegerQ[2*m] &&  !(EqQ[m, 1] && NeQ[c^2 - d^2, 0] && SimplerQ[c + d*x, a + b*x])

Rule 4482

Int[u_, x_Symbol] :> Int[TrigSimplify[u], x] /; TrigSimplifyQ[u]

Rubi steps \begin{align*} \text {integral}& = \int \cos (c+d x) (b+a \cos (c+d x))^2 \sin ^2(c+d x) \, dx \\ & = \frac {(b+a \cos (c+d x))^2 \sin ^3(c+d x)}{5 d}+\frac {1}{5} \int (b+a \cos (c+d x)) (2 a+2 b \cos (c+d x)) \sin ^2(c+d x) \, dx \\ & = \frac {b (b+a \cos (c+d x)) \sin ^3(c+d x)}{10 d}+\frac {(b+a \cos (c+d x))^2 \sin ^3(c+d x)}{5 d}+\frac {1}{20} \int \left (10 a b+2 \left (4 a^2+b^2\right ) \cos (c+d x)\right ) \sin ^2(c+d x) \, dx \\ & = \frac {\left (4 a^2+b^2\right ) \sin ^3(c+d x)}{30 d}+\frac {b (b+a \cos (c+d x)) \sin ^3(c+d x)}{10 d}+\frac {(b+a \cos (c+d x))^2 \sin ^3(c+d x)}{5 d}+\frac {1}{2} (a b) \int \sin ^2(c+d x) \, dx \\ & = -\frac {a b \cos (c+d x) \sin (c+d x)}{4 d}+\frac {\left (4 a^2+b^2\right ) \sin ^3(c+d x)}{30 d}+\frac {b (b+a \cos (c+d x)) \sin ^3(c+d x)}{10 d}+\frac {(b+a \cos (c+d x))^2 \sin ^3(c+d x)}{5 d}+\frac {1}{4} (a b) \int 1 \, dx \\ & = \frac {a b x}{4}-\frac {a b \cos (c+d x) \sin (c+d x)}{4 d}+\frac {\left (4 a^2+b^2\right ) \sin ^3(c+d x)}{30 d}+\frac {b (b+a \cos (c+d x)) \sin ^3(c+d x)}{10 d}+\frac {(b+a \cos (c+d x))^2 \sin ^3(c+d x)}{5 d} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.37 (sec) , antiderivative size = 77, normalized size of antiderivative = 0.73 \[ \int \cos ^3(c+d x) (a \sin (c+d x)+b \tan (c+d x))^2 \, dx=\frac {30 \left (a^2+2 b^2\right ) \sin (c+d x)-5 \left (a^2+4 b^2\right ) \sin (3 (c+d x))-3 a (-20 b (c+d x)+5 b \sin (4 (c+d x))+a \sin (5 (c+d x)))}{240 d} \]

[In]

Integrate[Cos[c + d*x]^3*(a*Sin[c + d*x] + b*Tan[c + d*x])^2,x]

[Out]

(30*(a^2 + 2*b^2)*Sin[c + d*x] - 5*(a^2 + 4*b^2)*Sin[3*(c + d*x)] - 3*a*(-20*b*(c + d*x) + 5*b*Sin[4*(c + d*x)
] + a*Sin[5*(c + d*x)]))/(240*d)

Maple [A] (verified)

Time = 9.11 (sec) , antiderivative size = 100, normalized size of antiderivative = 0.94

method	result	size
derivativedivides	\(\frac {a^{2} \left (-\frac {\cos \left (d x +c \right )^{4} \sin \left (d x +c \right )}{5}+\frac {\left (2+\cos \left (d x +c \right )^{2}\right ) \sin \left (d x +c \right )}{15}\right )+2 a b \left (-\frac {\sin \left (d x +c \right ) \cos \left (d x +c \right )^{3}}{4}+\frac {\sin \left (d x +c \right ) \cos \left (d x +c \right )}{8}+\frac {d x}{8}+\frac {c}{8}\right )+\frac {b^{2} \sin \left (d x +c \right )^{3}}{3}}{d}\)	\(100\)
default	\(\frac {a^{2} \left (-\frac {\cos \left (d x +c \right )^{4} \sin \left (d x +c \right )}{5}+\frac {\left (2+\cos \left (d x +c \right )^{2}\right ) \sin \left (d x +c \right )}{15}\right )+2 a b \left (-\frac {\sin \left (d x +c \right ) \cos \left (d x +c \right )^{3}}{4}+\frac {\sin \left (d x +c \right ) \cos \left (d x +c \right )}{8}+\frac {d x}{8}+\frac {c}{8}\right )+\frac {b^{2} \sin \left (d x +c \right )^{3}}{3}}{d}\)	\(100\)
risch	\(\frac {x a b}{4}+\frac {a^{2} \sin \left (d x +c \right )}{8 d}+\frac {b^{2} \sin \left (d x +c \right )}{4 d}-\frac {a^{2} \sin \left (5 d x +5 c \right )}{80 d}-\frac {a b \sin \left (4 d x +4 c \right )}{16 d}-\frac {\sin \left (3 d x +3 c \right ) a^{2}}{48 d}-\frac {\sin \left (3 d x +3 c \right ) b^{2}}{12 d}\)	\(102\)

[In]

int(cos(d*x+c)^3*(sin(d*x+c)*a+b*tan(d*x+c))^2,x,method=_RETURNVERBOSE)

[Out]

1/d*(a^2*(-1/5*cos(d*x+c)^4*sin(d*x+c)+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))+2*a*b*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1
/8*sin(d*x+c)*cos(d*x+c)+1/8*d*x+1/8*c)+1/3*b^2*sin(d*x+c)^3)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 85, normalized size of antiderivative = 0.80 \[ \int \cos ^3(c+d x) (a \sin (c+d x)+b \tan (c+d x))^2 \, dx=\frac {15 \, a b d x - {\left (12 \, a^{2} \cos \left (d x + c\right )^{4} + 30 \, a b \cos \left (d x + c\right )^{3} - 15 \, a b \cos \left (d x + c\right ) - 4 \, {\left (a^{2} - 5 \, b^{2}\right )} \cos \left (d x + c\right )^{2} - 8 \, a^{2} - 20 \, b^{2}\right )} \sin \left (d x + c\right )}{60 \, d} \]

[In]

integrate(cos(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm="fricas")

[Out]

1/60*(15*a*b*d*x - (12*a^2*cos(d*x + c)^4 + 30*a*b*cos(d*x + c)^3 - 15*a*b*cos(d*x + c) - 4*(a^2 - 5*b^2)*cos(
d*x + c)^2 - 8*a^2 - 20*b^2)*sin(d*x + c))/d

Sympy [F]

\[ \int \cos ^3(c+d x) (a \sin (c+d x)+b \tan (c+d x))^2 \, dx=\int \left (a \sin {\left (c + d x \right )} + b \tan {\left (c + d x \right )}\right )^{2} \cos ^{3}{\left (c + d x \right )}\, dx \]

[In]

integrate(cos(d*x+c)**3*(a*sin(d*x+c)+b*tan(d*x+c))**2,x)

[Out]

Integral((a*sin(c + d*x) + b*tan(c + d*x))**2*cos(c + d*x)**3, x)

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 68, normalized size of antiderivative = 0.64 \[ \int \cos ^3(c+d x) (a \sin (c+d x)+b \tan (c+d x))^2 \, dx=\frac {80 \, b^{2} \sin \left (d x + c\right )^{3} - 16 \, {\left (3 \, \sin \left (d x + c\right )^{5} - 5 \, \sin \left (d x + c\right )^{3}\right )} a^{2} + 15 \, {\left (4 \, d x + 4 \, c - \sin \left (4 \, d x + 4 \, c\right )\right )} a b}{240 \, d} \]

[In]

integrate(cos(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm="maxima")

[Out]

1/240*(80*b^2*sin(d*x + c)^3 - 16*(3*sin(d*x + c)^5 - 5*sin(d*x + c)^3)*a^2 + 15*(4*d*x + 4*c - sin(4*d*x + 4*
c))*a*b)/d

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 43089 vs. \(2 (96) = 192\).

Time = 154.27 (sec) , antiderivative size = 43089, normalized size of antiderivative = 406.50 \[ \int \cos ^3(c+d x) (a \sin (c+d x)+b \tan (c+d x))^2 \, dx=\text {Too large to display} \]

[In]

integrate(cos(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm="giac")

[Out]

-1/80*a^2*sin(5*d*x + 5*c)/d - 1/48*a^2*sin(3*d*x + 3*c)/d + 1/8*a^2*sin(d*x + c)/d + 1/96*(3*pi*a*b*sgn(2*tan
(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1
/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 + 24*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 + 3*pi*a*b*sgn(-2
*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c
)^4 + 6*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*
tan(c))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d
*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^4 +
9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c)
)*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 + 6*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*
tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 + 6*a*b*
arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 - 6*a*b*arct
an(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 + 48*a*b*d*x*ta
n(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + 6*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*ta
n(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + 72*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^6*tan(
1/2*c)^4*tan(c)^4 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^
4*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^4 + 72*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 + 9*pi*a*b
*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^
6*tan(c)^4 + 48*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 + 6*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) +
2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 + 3*pi*a*b*sgn(2*
tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*ta
n(1/2*d*x)^6*tan(1/2*c)^6 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan
(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 + 18*pi*a*b*sgn(2*tan(d*x)^2*ta
n(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*
tan(1/2*c)^6*tan(c)^2 + 12*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^
2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + 12*a*b*arctan((tan(d*x) + tan(c))
/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 - 12*a*b*arctan(-(tan(d*x) - tan(c))/(
tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + 24*a*b*tan(d*x)^4*tan(1/2*d*x)^6*tan(1
/2*c)^6*tan(c)^3 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*
tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^4 + 27*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2
)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)
^4*tan(c)^4 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(
d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^4 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)
*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^4 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*t
an(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^4 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*t
an(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^
4 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*t
an(c))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) -
1))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1)
)*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 + 3*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*
tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 + 12*a*b*arctan((ta
n(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 - 12*a*b*arctan(-(tan(
d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 + 24*a*b*tan(d*x)^3*tan(
1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 + 24*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^6 + 3*pi*a*b*sgn(-2*tan(d*x
)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^6 + 144*a*b*d*x
*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 +
2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 + 144*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^4
*tan(1/2*c)^6*tan(c)^2 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan
(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^2 + 96*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + 12
*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6*tan(
1/2*c)^6*tan(c)^2 + 72*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^4 + 9*pi*a*b*sgn(-2*tan(d*x)^2*ta
n(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^4 + 216*a*b*
d*x*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^4 + 27*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2
+ 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^4 + 144*a*b*d*x*tan(d*x)^2*tan(1/2*d*x
)^6*tan(1/2*c)^4*tan(c)^4 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*
tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^4 + 72*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^4 +
9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2*ta
n(1/2*c)^6*tan(c)^4 + 144*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 + 18*pi*a*b*sgn(-2*tan(d*x)^
2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 + 24*a
*b*d*x*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 + 3*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(
d*x) - 2*tan(c))*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x
)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^4 + 9*pi*a*b*sg
n(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^
4*tan(1/2*d*x)^4*tan(1/2*c)^6 + 6*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*
tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6 + 6*a*b*arctan((tan(d*x) + tan(c))/(t
an(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^6 - 6*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(
c) + 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^6 - 24*a*b*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c) + 18*pi
*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*ta
n(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 + 54*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan
(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 36*pi*a*b
*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*
x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^
4*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*
tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*t
an(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 + 36*pi*a*b*sgn(2*ta
n(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(
1/2*d*x)^4*tan(1/2*c)^6*tan(c)^2 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2
*d*x)^4*tan(1/2*c)^6*tan(c)^2 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d
*x)^4*tan(1/2*c)^6*tan(c)^2 + 6*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*ta
n(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + 24*a*b*arctan((tan(d*x) + tan(c))/(tan(
d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 - 24*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*
x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 - 144*a*b*tan(d*x)^3*tan(1/2*d*x)^6*tan(1/2*c)
^6*tan(c)^2 + 72*a*b*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^3 + 72*a*b*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/
2*c)^6*tan(c)^3 - 144*a*b*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^3 + 3*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2
- 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^6*tan(c)
^4 + 27*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*
tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(
d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^4 +
18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^4 - 18
*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^4 - 256*
b^2*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^3*tan(c)^4 + 27*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)
^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 + 54*
pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*
tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^4 + 54*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan
(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^4 - 54*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d
*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^4 - 768*b^2*tan(d*x)^4*tan(1/2*d*x)^5*tan(1/2*c)^4*tan(c)^4 + 9*pi*a*
b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1
/2*d*x)^6*tan(1/2*c)^4*tan(c)^4 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*
d*x)^6*tan(1/2*c)^4*tan(c)^4 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*
x)^6*tan(1/2*c)^4*tan(c)^4 + 72*a*b*tan(d*x)^3*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^4 - 768*b^2*tan(d*x)^4*tan(1
/2*d*x)^4*tan(1/2*c)^5*tan(c)^4 + 3*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x
)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*c)^6*tan(c)^4 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2
)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)
^6*tan(c)^4 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^6*
tan(c)^4 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^6*ta
n(c)^4 - 256*b^2*tan(d*x)^4*tan(1/2*d*x)^3*tan(1/2*c)^6*tan(c)^4 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn
(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 + 36
*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 - 36*a*
b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 + 72*a*b*
tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 + 6*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(
1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 - 6*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^6*tan
(1/2*c)^6*tan(c)^4 - 24*a*b*tan(d*x)*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 + 72*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)
^6*tan(1/2*c)^4 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*
tan(1/2*d*x)^6*tan(1/2*c)^4 + 72*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^6 + 9*pi*a*b*sgn(-2*tan(d*x)^2*t
an(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^6 + 48*a*b*d*x*tan(d
*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6 + 6*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*t
an(c))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6 + 144*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 +
18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^6*ta
n(1/2*c)^2*tan(c)^2 + 432*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 54*pi*a*b*sgn(-2*tan(d*x)^
2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 288*
a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 + 36*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(
c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 + 144*a*b*d*x*tan(d*x)^4*tan(1/2
*d*x)^2*tan(1/2*c)^6*tan(c)^2 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(
c))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 + 288*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c
)^2 + 36*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x
)^4*tan(1/2*c)^6*tan(c)^2 + 48*a*b*d*x*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + 6*pi*a*b*sgn(-2*tan(d*x)^2*tan(c
) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + 24*a*b*d*x*tan(d*x)^4*
tan(1/2*d*x)^6*tan(c)^4 + 3*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan
(d*x)^4*tan(1/2*d*x)^6*tan(c)^4 + 216*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 + 27*pi*a*b*sgn(
-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^2*tan
(c)^4 + 144*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^4 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*t
an(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^4 + 216*a*b*d*x*tan(d*
x)^4*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 + 27*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d
*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 + 432*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/
2*c)^4*tan(c)^4 + 54*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2
*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^4 + 72*a*b*d*x*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^4 + 9*pi*a*b*sgn(-2*tan(
d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^4 + 24*a*b*d*x
*tan(d*x)^4*tan(1/2*c)^6*tan(c)^4 + 3*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*t
an(c))*tan(d*x)^4*tan(1/2*c)^6*tan(c)^4 + 144*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^4 + 18*pi*
a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*
c)^6*tan(c)^4 + 72*a*b*d*x*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*
x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2
- 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/
2*c)^2 + 27*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x)
- 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^4 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^
2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4 + 18*a*b*arctan
((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^4 - 18*a*b*arctan(-(tan(d*x)
- tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^4 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 -
2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*
c)^6 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) -
2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*ta
n(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^6 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*ta
n(1/2*d*x)^4*tan(1/2*c)^6 + 3*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(
c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6*tan(1/2*c)^6 + 12*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c)
- 1))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6 - 12*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(
d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6 + 24*a*b*tan(d*x)^3*tan(1/2*d*x)^6*tan(1/2*c)^6 - 72*a*b*tan(d*x)^4*tan(1/2
*d*x)^6*tan(1/2*c)^4*tan(c) - 72*a*b*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c) + 144*a*b*tan(d*x)^2*tan(1/
2*d*x)^6*tan(1/2*c)^6*tan(c) + 6*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*t
an(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^6*tan(c)^2 + 54*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)
*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^
2*tan(c)^2 + 36*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d
*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*
tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*ta
n(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 - 512*b^2*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^3*ta
n(c)^2 + 54*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x)
- 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 108*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2
*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c
)^2 + 108*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^
2 - 108*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2
- 1536*b^2*tan(d*x)^4*tan(1/2*d*x)^5*tan(1/2*c)^4*tan(c)^2 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*
tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 + 72*a*b
*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 - 72*a*b*ar
ctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 - 432*a*b*tan
(d*x)^3*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 - 1536*b^2*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^5*tan(c)^2 + 6*pi
*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*ta
n(d*x)^4*tan(1/2*c)^6*tan(c)^2 + 36*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x
)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 + 36*a*b*arctan((tan(d*x)
+ tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 - 36*a*b*arctan(-(tan(d*x) -
tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 - 512*b^2*tan(d*x)^4*tan(1/2*d*
x)^3*tan(1/2*c)^6*tan(c)^2 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*ta
n(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^2 + 72*a*b*arctan((tan(d*x) + tan(c))/(tan(
d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^2 - 72*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*
x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^2 - 432*a*b*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)
^6*tan(c)^2 + 12*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 -
12*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + 144*a*b*tan(d
*x)*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + 72*a*b*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^3 + 216*a*b*ta
n(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 - 432*a*b*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^3 + 72*a
*b*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^3 - 432*a*b*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^3 +
24*a*b*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^3 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c
) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(c)^4 + 6*pi*a*b*sgn(2*tan(d*x)^
2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x
)^6*tan(c)^4 + 6*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(c)^4 - 6*
a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(c)^4 + 27*pi*a*b*sgn(2*ta
n(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(
1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4 + 54*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d
*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 + 54*a*b*arctan((tan(d*x
) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 - 54*a*b*arctan(-(tan(d*x)
- tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 + 768*b^2*tan(d*x)^4*tan(1/2*
d*x)^5*tan(1/2*c)^2*tan(c)^4 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*t
an(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^4 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan
(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^4 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d
*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^4 + 72*a*b*tan(d*x)^3*tan(1/2*d*x)^6*tan(1/2*c)
^2*tan(c)^4 + 2304*b^2*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^3*tan(c)^4 - 512*b^2*tan(d*x)^2*tan(1/2*d*x)^6*tan
(1/2*c)^3*tan(c)^4 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 +
2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*c)^4*tan(c)^4 + 54*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(
d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 +
54*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 - 54
*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 + 2304
*b^2*tan(d*x)^4*tan(1/2*d*x)^3*tan(1/2*c)^4*tan(c)^4 + 27*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x
)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^4 + 108*a*b*arcta
n((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^4 - 108*a*b*arctan(
-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^4 + 216*a*b*tan(d*x)
^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^4 - 1536*b^2*tan(d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^4*tan(c)^4 + 18*a*b*ar
ctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^4 - 18*a*b*arctan(-(tan(d*x
) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^4 - 72*a*b*tan(d*x)*tan(1/2*d*x)^6*tan(1
/2*c)^4*tan(c)^4 + 768*b^2*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^5*tan(c)^4 - 1536*b^2*tan(d*x)^2*tan(1/2*d*x)^
4*tan(1/2*c)^5*tan(c)^4 + 6*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)
^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*c)^6*tan(c)^4 + 6*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(
c) - 1))*tan(d*x)^4*tan(1/2*c)^6*tan(c)^4 - 6*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^
4*tan(1/2*c)^6*tan(c)^4 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)
^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^4 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)
*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^4 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*t
an(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^4 + 72*a*b*tan(d*x)^3*tan(1/2*d*x)^2*tan(1/2*c)^6*ta
n(c)^4 - 512*b^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^6*tan(c)^4 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)
*tan(c) - 1))*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))
*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 - 72*a*b*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 + 72*a*b*d*x*tan(
d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*
tan(c))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2 + 216*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^4 + 27*pi*a*
b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)
^4 + 144*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(
c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4 + 72*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^2*ta
n(1/2*c)^6 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1
/2*d*x)^2*tan(1/2*c)^6 + 144*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(
c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6 + 24*a*b*d*x*tan(1/2*
d*x)^6*tan(1/2*c)^6 + 3*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2
*d*x)^6*tan(1/2*c)^6 + 48*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^6*tan(c)^2 + 6*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*t
an(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^6*tan(c)^2 + 432*a*b*d*x*tan(d*x)^4*tan(1/2*
d*x)^4*tan(1/2*c)^2*tan(c)^2 + 54*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c
))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^2 + 288*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)
^2 + 36*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)
^6*tan(1/2*c)^2*tan(c)^2 + 432*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 54*pi*a*b*sgn(-2*tan(
d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 +
864*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 108*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x
)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 144*a*b*d*x*tan(1/2*d*x)
^6*tan(1/2*c)^4*tan(c)^2 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*t
an(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 + 48*a*b*d*x*tan(d*x)^4*tan(1/2*c)^6*tan(c)^2 + 6*pi*a*b*sgn(-2*tan(d*x)^2
*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*c)^6*tan(c)^2 + 288*a*b*d*x*tan(d*x)
^2*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 + 36*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x
) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 + 144*a*b*d*x*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)
^2 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(1/2*
c)^6*tan(c)^2 + 72*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^4*tan(c)^4 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)
*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(c)^4 + 48*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^6*t
an(c)^4 + 6*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*
d*x)^6*tan(c)^4 + 216*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4 + 27*pi*a*b*sgn(-2*tan(d*x)^2*ta
n(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4 + 432*a*b*
d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 + 54*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2
+ 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 + 72*a*b*d*x*tan(1/2*d*x)^6*tan(1/2*
c)^2*tan(c)^4 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^
6*tan(1/2*c)^2*tan(c)^4 + 72*a*b*d*x*tan(d*x)^4*tan(1/2*c)^4*tan(c)^4 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*
tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*c)^4*tan(c)^4 + 432*a*b*d*x*tan(d*x)^2*tan(1/2*d
*x)^2*tan(1/2*c)^4*tan(c)^4 + 54*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c)
)*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 + 216*a*b*d*x*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^4 + 27*pi*a
*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^
4 + 48*a*b*d*x*tan(d*x)^2*tan(1/2*c)^6*tan(c)^4 + 6*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*
tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*c)^6*tan(c)^4 + 72*a*b*d*x*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^4 + 9*pi
*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c
)^4 + 3*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*
tan(c))*tan(d*x)^4*tan(1/2*d*x)^6 + 27*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(
d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^2 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan
(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6*t
an(1/2*c)^2 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2
- 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2 - 256*b^2*t
an(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^3 + 27*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*
tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^4 + 54*pi*a*b*sgn(2*tan(d*x)^2
*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)
^4*tan(1/2*c)^4 + 54*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c
)^4 - 54*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^4 - 768*b
^2*tan(d*x)^4*tan(1/2*d*x)^5*tan(1/2*c)^4 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) +
2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6*tan(1/2*c)^4 + 36*a*b*arctan((tan(d*x) + tan(c))/
(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*t
an(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4 + 72*a*b*tan(d*x)^3*tan(1/2*d*x)^6*tan(1/2*c)^4 - 768*b^2*t
an(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^5 + 3*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*t
an(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*c)^6 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*s
gn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6
+ 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^6 - 18*a*b*arc
tan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^6 - 256*b^2*tan(d*x)^4*ta
n(1/2*d*x)^3*tan(1/2*c)^6 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(
c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(1/2*c)^6 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c)
- 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(
d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6 + 72*a*b*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^6 + 6*a*b*arctan((tan(d*x) +
tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^6*tan(1/2*c)^6 - 6*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c
) + 1))*tan(1/2*d*x)^6*tan(1/2*c)^6 - 24*a*b*tan(d*x)*tan(1/2*d*x)^6*tan(1/2*c)^6 - 72*a*b*tan(d*x)^4*tan(1/2*
d*x)^6*tan(1/2*c)^2*tan(c) - 216*a*b*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) + 432*a*b*tan(d*x)^2*tan(1/
2*d*x)^6*tan(1/2*c)^4*tan(c) - 72*a*b*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c) + 432*a*b*tan(d*x)^2*tan(1
/2*d*x)^4*tan(1/2*c)^6*tan(c) - 24*a*b*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c) + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^
2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(c
)^2 + 12*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2
*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6*tan(c)^2 + 12*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x
)^4*tan(1/2*d*x)^6*tan(c)^2 - 12*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x
)^6*tan(c)^2 + 54*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan
(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 108*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*
sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2
*tan(c)^2 + 108*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^2*t
an(c)^2 - 108*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^2*ta
n(c)^2 + 1536*b^2*tan(d*x)^4*tan(1/2*d*x)^5*tan(1/2*c)^2*tan(c)^2 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*s
gn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 +
72*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 - 72*
a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 - 432*a
*b*tan(d*x)^3*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 + 4608*b^2*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^3*tan(c)^2
- 1024*b^2*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^3*tan(c)^2 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*t
an(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*c)^4*tan(c)^2 + 108*pi*a*b*
sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x
)^2*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 108*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^
4*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 - 108*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4
*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 4608*b^2*tan(d*x)^4*tan(1/2*d*x)^3*tan(1/2*c)^4*tan(c)^2 + 54*pi*a*b*s
gn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*
d*x)^4*tan(1/2*c)^4*tan(c)^2 + 216*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*
x)^4*tan(1/2*c)^4*tan(c)^2 - 216*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x
)^4*tan(1/2*c)^4*tan(c)^2 - 1296*a*b*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - 3072*b^2*tan(d*x)^2*tan
(1/2*d*x)^5*tan(1/2*c)^4*tan(c)^2 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^6*ta
n(1/2*c)^4*tan(c)^2 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^6*tan(1/2*c)^4*ta
n(c)^2 + 432*a*b*tan(d*x)*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 + 1536*b^2*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)
^5*tan(c)^2 - 3072*b^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^5*tan(c)^2 + 12*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 -
2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*c)^6*tan(c)^2 +
12*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*c)^6*tan(c)^2 - 12*a*b*arctan(-(t
an(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*c)^6*tan(c)^2 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^
2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^2*tan(1/2*c)^6*tan
(c)^2 + 72*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)
^2 - 72*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2
- 432*a*b*tan(d*x)^3*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 - 1024*b^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^6*t
an(c)^2 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^2 - 36*a
*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^2 + 432*a*b*tan(d*x)*
tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^2 + 24*a*b*tan(d*x)^4*tan(1/2*d*x)^6*tan(c)^3 + 216*a*b*tan(d*x)^4*tan(1/2*
d*x)^4*tan(1/2*c)^2*tan(c)^3 - 432*a*b*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^3 + 216*a*b*tan(d*x)^4*ta
n(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^3 - 1296*a*b*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^3 + 72*a*b*tan(1/2
*d*x)^6*tan(1/2*c)^4*tan(c)^3 + 24*a*b*tan(d*x)^4*tan(1/2*c)^6*tan(c)^3 - 432*a*b*tan(d*x)^2*tan(1/2*d*x)^2*ta
n(1/2*c)^6*tan(c)^3 + 72*a*b*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^3 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sg
n(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2*tan(c)^4 + 18*
pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*
tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^4 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1
/2*d*x)^4*tan(c)^4 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^4*tan(c
)^4 + 3*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*
tan(c))*tan(1/2*d*x)^6*tan(c)^4 + 12*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*
d*x)^6*tan(c)^4 - 12*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^6*tan(c)^4
+ 24*a*b*tan(d*x)^3*tan(1/2*d*x)^6*tan(c)^4 - 768*b^2*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)*tan(c)^4 + 9*pi*a*
b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d
*x)^4*tan(1/2*c)^2*tan(c)^4 + 54*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*t
an(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4 + 54*a*b*arctan((tan(d*x) + t
an(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4 - 54*a*b*arctan(-(tan(d*x) - tan
(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4 - 2304*b^2*tan(d*x)^4*tan(1/2*d*x)
^3*tan(1/2*c)^2*tan(c)^4 + 27*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(
c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 + 108*a*b*arctan((tan(d*x) + tan(c))/(tan(d
*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 - 108*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*
x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 + 216*a*b*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)
^2*tan(c)^4 + 1536*b^2*tan(d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^2*tan(c)^4 + 18*a*b*arctan((tan(d*x) + tan(c))/(ta
n(d*x)*tan(c) - 1))*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^4 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c)
+ 1))*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^4 - 72*a*b*tan(d*x)*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^4 - 2304*b^2*
tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^3*tan(c)^4 + 4608*b^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^3*tan(c)^4 - 2
56*b^2*tan(1/2*d*x)^6*tan(1/2*c)^3*tan(c)^4 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c
) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*c)^4*tan(c)^4 + 18*a*b*arctan((tan(d*x) +
tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*c)^4*tan(c)^4 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)
*tan(c) + 1))*tan(d*x)^4*tan(1/2*c)^4*tan(c)^4 - 768*b^2*tan(d*x)^4*tan(1/2*d*x)*tan(1/2*c)^4*tan(c)^4 + 27*pi
*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*ta
n(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 + 108*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(
1/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 - 108*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1
/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 + 216*a*b*tan(d*x)^3*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 + 4608*b^2*tan(d*x)^
2*tan(1/2*d*x)^3*tan(1/2*c)^4*tan(c)^4 + 54*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)
^4*tan(1/2*c)^4*tan(c)^4 - 54*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^4*tan(1/2*c)
^4*tan(c)^4 - 216*a*b*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^4 - 768*b^2*tan(1/2*d*x)^5*tan(1/2*c)^4*tan(
c)^4 + 1536*b^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^5*tan(c)^4 - 768*b^2*tan(1/2*d*x)^4*tan(1/2*c)^5*tan(c)^4
+ 3*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan
(c))*tan(1/2*c)^6*tan(c)^4 + 12*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*c)^6*
tan(c)^4 - 12*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*c)^6*tan(c)^4 + 24*a*b
*tan(d*x)^3*tan(1/2*c)^6*tan(c)^4 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^2*ta
n(1/2*c)^6*tan(c)^4 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^2*tan(1/2*c)^6*ta
n(c)^4 - 72*a*b*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^4 - 256*b^2*tan(1/2*d*x)^3*tan(1/2*c)^6*tan(c)^4 +
24*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^6 + 3*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) -
2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^6 + 216*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^2 + 27*pi*a*b*sgn(-2*t
an(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^2 + 144*a
*b*d*x*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*t
an(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2 + 216*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^
4 + 27*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^
2*tan(1/2*c)^4 + 432*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4 + 54*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*t
an(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4 + 72*a*b*d*x*tan(1/2*d*x)^6*t
an(1/2*c)^4 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6*
tan(1/2*c)^4 + 24*a*b*d*x*tan(d*x)^4*tan(1/2*c)^6 + 3*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 +
2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*c)^6 + 144*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6 + 18*pi*a*
b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)
^6 + 72*a*b*d*x*tan(1/2*d*x)^4*tan(1/2*c)^6 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(
d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(1/2*c)^6 + 144*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^4*tan(c)^2 + 18*pi*a*b*sgn(
-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^4*tan(c)^2 + 96*a*
b*d*x*tan(d*x)^2*tan(1/2*d*x)^6*tan(c)^2 + 12*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*
x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6*tan(c)^2 + 432*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^
2 + 54*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^
2*tan(1/2*c)^2*tan(c)^2 + 864*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^2 + 108*pi*a*b*sgn(-2*tan(
d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^2 +
144*a*b*d*x*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 +
2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 + 144*a*b*d*x*tan(d*x)^4*tan(1/2*c)^4*tan(c)^2 +
18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*c)^4*tan(
c)^2 + 864*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 108*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*t
an(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 432*a*b*d*x*tan(1/
2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 54*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan
(c))*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 96*a*b*d*x*tan(d*x)^2*tan(1/2*c)^6*tan(c)^2 + 12*pi*a*b*sgn(-2*tan
(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*c)^6*tan(c)^2 + 144*a*b*d*x*t
an(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) -
2*tan(c))*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 + 72*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^2*tan(c)^4 + 9*pi*a*b*sgn(
-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2*tan(c)^4 + 144*a
*b*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^4 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d
*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^4 + 24*a*b*d*x*tan(1/2*d*x)^6*tan(c)^4 + 3*pi*a*b*sgn(-2*tan(
d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6*tan(c)^4 + 72*a*b*d*x*tan(d*x)^4*t
an(1/2*c)^2*tan(c)^4 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*
x)^4*tan(1/2*c)^2*tan(c)^4 + 432*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4 + 54*pi*a*b*sgn(-2*ta
n(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4
+ 216*a*b*d*x*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 + 27*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2
+ 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 + 144*a*b*d*x*tan(d*x)^2*tan(1/2*c)^4*tan(c)^4
+ 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*c)^4*ta
n(c)^4 + 216*a*b*d*x*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 + 27*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*ta
n(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 + 24*a*b*d*x*tan(1/2*c)^6*tan(c)^4 + 3*pi
*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*c)^6*tan(c)^4 + 9*pi*a*b*
sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x
)^4*tan(1/2*d*x)^4 + 6*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 +
2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6 + 6*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan
(d*x)^4*tan(1/2*d*x)^6 - 6*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^6 +
27*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c
))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^2 + 54*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c)
+ 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2 + 54*a*b*arctan((tan(d*x
) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^2 - 54*a*b*arctan(-(tan(d*x) - tan(c))
/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^2 + 768*b^2*tan(d*x)^4*tan(1/2*d*x)^5*tan(1/2*c)^
2 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*ta
n(c))*tan(1/2*d*x)^6*tan(1/2*c)^2 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/
2*d*x)^6*tan(1/2*c)^2 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^6*ta
n(1/2*c)^2 + 72*a*b*tan(d*x)^3*tan(1/2*d*x)^6*tan(1/2*c)^2 + 2304*b^2*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^3 -
512*b^2*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^3 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*ta
n(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*c)^4 + 54*pi*a*b*sgn(2*tan(d*x)^2*tan(c
)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan
(1/2*c)^4 + 54*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^4 -
54*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^4 + 2304*b^2*ta
n(d*x)^4*tan(1/2*d*x)^3*tan(1/2*c)^4 + 27*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*t
an(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(1/2*c)^4 + 108*a*b*arctan((tan(d*x) + tan(c))/(ta
n(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4 - 108*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan
(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4 + 216*a*b*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^4 - 1536*b^2*t
an(d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^4 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^
6*tan(1/2*c)^4 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^6*tan(1/2*c)^4 - 72*a*
b*tan(d*x)*tan(1/2*d*x)^6*tan(1/2*c)^4 + 768*b^2*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^5 - 1536*b^2*tan(d*x)^2*
tan(1/2*d*x)^4*tan(1/2*c)^5 + 6*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*ta
n(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*c)^6 + 6*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) -
1))*tan(d*x)^4*tan(1/2*c)^6 - 6*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*c)^6
+ 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan
(c))*tan(1/2*d*x)^2*tan(1/2*c)^6 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2
*d*x)^2*tan(1/2*c)^6 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan
(1/2*c)^6 + 72*a*b*tan(d*x)^3*tan(1/2*d*x)^2*tan(1/2*c)^6 - 512*b^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^6 + 1
8*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^4*tan(1/2*c)^6 - 18*a*b*arctan(-(tan(d*x)
- tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^4*tan(1/2*c)^6 - 72*a*b*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^6 -
24*a*b*tan(d*x)^4*tan(1/2*d*x)^6*tan(c) - 216*a*b*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c) + 432*a*b*tan(
d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c) - 216*a*b*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c) + 1296*a*b*t
an(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) - 72*a*b*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c) - 24*a*b*tan(d*x)^4*t
an(1/2*c)^6*tan(c) + 432*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c) - 72*a*b*tan(1/2*d*x)^4*tan(1/2*c)^
6*tan(c) + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x
) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2*tan(c)^2 + 36*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*
tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^2 + 36*a*b*arctan((tan(
d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^4*tan(c)^2 - 36*a*b*arctan(-(tan(d*x) - tan(c))/
(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^4*tan(c)^2 + 6*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan
(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6*tan(c)^2 + 24*a*b*arctan((tan(d*x
) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^6*tan(c)^2 - 24*a*b*arctan(-(tan(d*x) - tan(c))/(ta
n(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^6*tan(c)^2 - 144*a*b*tan(d*x)^3*tan(1/2*d*x)^6*tan(c)^2 - 1536*b^2
*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)*tan(c)^2 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*ta
n(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*c)^2*tan(c)^2 + 108*pi*a*b*sgn(2*tan(d*
x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*
d*x)^2*tan(1/2*c)^2*tan(c)^2 + 108*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*
x)^2*tan(1/2*c)^2*tan(c)^2 - 108*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x
)^2*tan(1/2*c)^2*tan(c)^2 - 4608*b^2*tan(d*x)^4*tan(1/2*d*x)^3*tan(1/2*c)^2*tan(c)^2 + 54*pi*a*b*sgn(2*tan(d*x
)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(1
/2*c)^2*tan(c)^2 + 216*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2
*c)^2*tan(c)^2 - 216*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*
c)^2*tan(c)^2 - 1296*a*b*tan(d*x)^3*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^2 + 3072*b^2*tan(d*x)^2*tan(1/2*d*x)^5*
tan(1/2*c)^2*tan(c)^2 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^6*tan(1/2*c)^2*t
an(c)^2 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 + 432
*a*b*tan(d*x)*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 - 4608*b^2*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^3*tan(c)^2
+ 9216*b^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^3*tan(c)^2 - 512*b^2*tan(1/2*d*x)^6*tan(1/2*c)^3*tan(c)^2 + 36
*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))
*tan(d*x)^2*tan(1/2*c)^4*tan(c)^2 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/
2*c)^4*tan(c)^2 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*c)^4*tan(c)^2 -
1536*b^2*tan(d*x)^4*tan(1/2*d*x)*tan(1/2*c)^4*tan(c)^2 + 54*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(
d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 216*a*b*ar
ctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 - 216*a*b*arct
an(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 - 1296*a*b*tan(
d*x)^3*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 9216*b^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^4*tan(c)^2 + 108*a
*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - 108*a*b*arctan(-(t
an(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 1296*a*b*tan(d*x)*tan(1/2*d*x)
^4*tan(1/2*c)^4*tan(c)^2 - 1536*b^2*tan(1/2*d*x)^5*tan(1/2*c)^4*tan(c)^2 + 3072*b^2*tan(d*x)^2*tan(1/2*d*x)^2*
tan(1/2*c)^5*tan(c)^2 - 1536*b^2*tan(1/2*d*x)^4*tan(1/2*c)^5*tan(c)^2 + 6*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2
)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*c)^6*tan(c)^2 + 24*a*b*arcta
n((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*c)^6*tan(c)^2 - 24*a*b*arctan(-(tan(d*x) - tan
(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*c)^6*tan(c)^2 - 144*a*b*tan(d*x)^3*tan(1/2*c)^6*tan(c)^2 + 36*a
*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 - 36*a*b*arctan(-(ta
n(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 + 432*a*b*tan(d*x)*tan(1/2*d*x)^2
*tan(1/2*c)^6*tan(c)^2 - 512*b^2*tan(1/2*d*x)^3*tan(1/2*c)^6*tan(c)^2 + 72*a*b*tan(d*x)^4*tan(1/2*d*x)^4*tan(c
)^3 - 144*a*b*tan(d*x)^2*tan(1/2*d*x)^6*tan(c)^3 + 216*a*b*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^3 - 1
296*a*b*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^3 + 72*a*b*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^3 + 72*a*b
*tan(d*x)^4*tan(1/2*c)^4*tan(c)^3 - 1296*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^3 + 216*a*b*tan(1/2
*d*x)^4*tan(1/2*c)^4*tan(c)^3 - 144*a*b*tan(d*x)^2*tan(1/2*c)^6*tan(c)^3 + 72*a*b*tan(1/2*d*x)^2*tan(1/2*c)^6*
tan(c)^3 + 3*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x)
- 2*tan(c))*tan(d*x)^4*tan(c)^4 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d
*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^4 + 18*a*b*arctan((tan(d*x) + tan(c))/(
tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^2*tan(c)^4 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c)
+ 1))*tan(d*x)^4*tan(1/2*d*x)^2*tan(c)^4 + 256*b^2*tan(d*x)^4*tan(1/2*d*x)^3*tan(c)^4 + 9*pi*a*b*sgn(2*tan(d*
x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(
c)^4 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^4 - 36*a*b*ar
ctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^4 + 72*a*b*tan(d*x)^3*tan(1/
2*d*x)^4*tan(c)^4 + 6*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^6*tan(c)^4 - 6*a*b*ar
ctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^6*tan(c)^4 - 24*a*b*tan(d*x)*tan(1/2*d*x)^6*tan(
c)^4 + 768*b^2*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)*tan(c)^4 - 1536*b^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)*t
an(c)^4 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x)
- 2*tan(c))*tan(d*x)^2*tan(1/2*c)^2*tan(c)^4 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d
*x)^4*tan(1/2*c)^2*tan(c)^4 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*c)^
2*tan(c)^4 + 768*b^2*tan(d*x)^4*tan(1/2*d*x)*tan(1/2*c)^2*tan(c)^4 + 27*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*
sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4 +
108*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4 - 1
08*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4 + 21
6*a*b*tan(d*x)^3*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4 - 4608*b^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^2*tan(c)
^4 + 54*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 - 54*a*b*ar
ctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 - 216*a*b*tan(d*x)*tan(1
/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 + 768*b^2*tan(1/2*d*x)^5*tan(1/2*c)^2*tan(c)^4 + 256*b^2*tan(d*x)^4*tan(1/2*c)
^3*tan(c)^4 - 4608*b^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^3*tan(c)^4 + 2304*b^2*tan(1/2*d*x)^4*tan(1/2*c)^3*
tan(c)^4 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x)
- 2*tan(c))*tan(1/2*c)^4*tan(c)^4 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1
/2*c)^4*tan(c)^4 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*c)^4*tan(c)^4
+ 72*a*b*tan(d*x)^3*tan(1/2*c)^4*tan(c)^4 - 1536*b^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^4*tan(c)^4 + 54*a*b*ar
ctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 - 54*a*b*arctan(-(tan(d*x
) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 - 216*a*b*tan(d*x)*tan(1/2*d*x)^2*tan(
1/2*c)^4*tan(c)^4 + 2304*b^2*tan(1/2*d*x)^3*tan(1/2*c)^4*tan(c)^4 + 768*b^2*tan(1/2*d*x)^2*tan(1/2*c)^5*tan(c)
^4 + 6*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*c)^6*tan(c)^4 - 6*a*b*arctan(-(tan(d*x) -
tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*c)^6*tan(c)^4 - 24*a*b*tan(d*x)*tan(1/2*c)^6*tan(c)^4 + 72*a*b*d*x*tan
(d*x)^4*tan(1/2*d*x)^4 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(
d*x)^4*tan(1/2*d*x)^4 + 48*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^6 + 6*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*
tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^6 + 216*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)
^2 + 27*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)
^2*tan(1/2*c)^2 + 432*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2 + 54*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*
tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2 + 72*a*b*d*x*tan(1/2*d*x)^6*
tan(1/2*c)^2 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6
*tan(1/2*c)^2 + 72*a*b*d*x*tan(d*x)^4*tan(1/2*c)^4 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 +
2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*c)^4 + 432*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4 + 54*pi*a
*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c
)^4 + 216*a*b*d*x*tan(1/2*d*x)^4*tan(1/2*c)^4 + 27*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*t
an(d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(1/2*c)^4 + 48*a*b*d*x*tan(d*x)^2*tan(1/2*c)^6 + 6*pi*a*b*sgn(-2*tan(d*x
)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*c)^6 + 72*a*b*d*x*tan(1/2*d*x)^2*
tan(1/2*c)^6 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^2
*tan(1/2*c)^6 + 144*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^2*tan(c)^2 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*
x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2*tan(c)^2 + 288*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^
4*tan(c)^2 + 36*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(
1/2*d*x)^4*tan(c)^2 + 48*a*b*d*x*tan(1/2*d*x)^6*tan(c)^2 + 6*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(
c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6*tan(c)^2 + 144*a*b*d*x*tan(d*x)^4*tan(1/2*c)^2*tan(c)^2 + 18*pi*a
*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*c)^2*tan(c)^2 +
864*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 108*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)
*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 432*a*b*d*x*tan(1/2*d*x)^
4*tan(1/2*c)^2*tan(c)^2 + 54*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*ta
n(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^2 + 288*a*b*d*x*tan(d*x)^2*tan(1/2*c)^4*tan(c)^2 + 36*pi*a*b*sgn(-2*tan(d*x)^
2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*c)^4*tan(c)^2 + 432*a*b*d*x*tan(1/2
*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 54*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(
c))*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 48*a*b*d*x*tan(1/2*c)^6*tan(c)^2 + 6*pi*a*b*sgn(-2*tan(d*x)^2*tan(c
) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*c)^6*tan(c)^2 + 24*a*b*d*x*tan(d*x)^4*tan(c)^4 + 3*pi
*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(c)^4 + 144*a*b*d*x
*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^4 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) -
2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^4 + 72*a*b*d*x*tan(1/2*d*x)^4*tan(c)^4 + 9*pi*a*b*sgn(-2*tan(d*x)^2
*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(c)^4 + 144*a*b*d*x*tan(d*x)^2*tan(1/
2*c)^2*tan(c)^4 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2
*tan(1/2*c)^2*tan(c)^4 + 216*a*b*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4 + 27*pi*a*b*sgn(-2*tan(d*x)^2*tan(c)
+ 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4 + 72*a*b*d*x*tan(1/2*c)^4
*tan(c)^4 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*c)^4*tan(
c)^4 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2
*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan
(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^4 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x
)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^4 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^
4*tan(1/2*d*x)^4 + 3*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*
tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6 + 12*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(
1/2*d*x)^6 - 12*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^6 + 24*a*b*tan(
d*x)^3*tan(1/2*d*x)^6 - 768*b^2*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c) + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)
*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*c)^2 + 54*pi*a*b*s
gn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)
^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 54*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d
*x)^2*tan(1/2*c)^2 - 54*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^2*tan(1
/2*c)^2 - 2304*b^2*tan(d*x)^4*tan(1/2*d*x)^3*tan(1/2*c)^2 + 27*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*ta
n(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(1/2*c)^2 + 108*a*b*arctan((t
an(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2 - 108*a*b*arctan(-(tan(d*x) -
tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2 + 216*a*b*tan(d*x)^3*tan(1/2*d*x)^4*tan(
1/2*c)^2 + 1536*b^2*tan(d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^2 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c
) - 1))*tan(1/2*d*x)^6*tan(1/2*c)^2 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^6
*tan(1/2*c)^2 - 72*a*b*tan(d*x)*tan(1/2*d*x)^6*tan(1/2*c)^2 - 2304*b^2*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^3
+ 4608*b^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^3 - 256*b^2*tan(1/2*d*x)^6*tan(1/2*c)^3 + 18*pi*a*b*sgn(2*tan(
d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/
2*c)^4 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*c)^4 - 18*a*b*arctan(-(ta
n(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*c)^4 - 768*b^2*tan(d*x)^4*tan(1/2*d*x)*tan(1/2*c)^4
+ 27*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*ta
n(c))*tan(1/2*d*x)^2*tan(1/2*c)^4 + 108*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1
/2*d*x)^2*tan(1/2*c)^4 - 108*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^2*
tan(1/2*c)^4 + 216*a*b*tan(d*x)^3*tan(1/2*d*x)^2*tan(1/2*c)^4 + 4608*b^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^
4 + 54*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^4*tan(1/2*c)^4 - 54*a*b*arctan(-(tan
(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^4*tan(1/2*c)^4 - 216*a*b*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c
)^4 - 768*b^2*tan(1/2*d*x)^5*tan(1/2*c)^4 + 1536*b^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^5 - 768*b^2*tan(1/2*
d*x)^4*tan(1/2*c)^5 + 3*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 +
2*tan(d*x) - 2*tan(c))*tan(1/2*c)^6 + 12*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan
(1/2*c)^6 - 12*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*c)^6 + 24*a*b*tan(d*x
)^3*tan(1/2*c)^6 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^2*tan(1/2*c)^6 - 18*a
*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^2*tan(1/2*c)^6 - 72*a*b*tan(d*x)*tan(1/2*d*
x)^2*tan(1/2*c)^6 - 256*b^2*tan(1/2*d*x)^3*tan(1/2*c)^6 - 72*a*b*tan(d*x)^4*tan(1/2*d*x)^4*tan(c) + 144*a*b*ta
n(d*x)^2*tan(1/2*d*x)^6*tan(c) - 216*a*b*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) + 1296*a*b*tan(d*x)^2*t
an(1/2*d*x)^4*tan(1/2*c)^2*tan(c) - 72*a*b*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c) - 72*a*b*tan(d*x)^4*tan(1/2*c)^4
*tan(c) + 1296*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c) - 216*a*b*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)
+ 144*a*b*tan(d*x)^2*tan(1/2*c)^6*tan(c) - 72*a*b*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c) + 6*pi*a*b*sgn(2*tan(d*x)
^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(c)^2 +
36*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(
c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*t
an(1/2*d*x)^2*tan(c)^2 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^2*t
an(c)^2 + 512*b^2*tan(d*x)^4*tan(1/2*d*x)^3*tan(c)^2 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x
)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4*tan(c)^2 + 72*a*b*arctan((tan(d*x) +
tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^2 - 72*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*
x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^2 - 432*a*b*tan(d*x)^3*tan(1/2*d*x)^4*tan(c)^2 + 12*a*b*arcta
n((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^6*tan(c)^2 - 12*a*b*arctan(-(tan(d*x) - tan(c))/(tan
(d*x)*tan(c) + 1))*tan(1/2*d*x)^6*tan(c)^2 + 144*a*b*tan(d*x)*tan(1/2*d*x)^6*tan(c)^2 + 1536*b^2*tan(d*x)^4*ta
n(1/2*d*x)^2*tan(1/2*c)*tan(c)^2 - 3072*b^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)*tan(c)^2 + 36*pi*a*b*sgn(2*ta
n(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(
1/2*c)^2*tan(c)^2 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*c)^2*tan(c)^2
- 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*c)^2*tan(c)^2 + 1536*b^2*tan(d*
x)^4*tan(1/2*d*x)*tan(1/2*c)^2*tan(c)^2 + 54*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) +
2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 216*a*b*arctan((tan(d*x) +
tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 - 216*a*b*arctan(-(tan(d*x) -
tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 - 1296*a*b*tan(d*x)^3*tan(1/2*d
*x)^2*tan(1/2*c)^2*tan(c)^2 - 9216*b^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^2*tan(c)^2 + 108*a*b*arctan((tan(d
*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^2 - 108*a*b*arctan(-(tan(d*x) - tan(c)
)/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^2 + 1296*a*b*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^2*
tan(c)^2 + 1536*b^2*tan(1/2*d*x)^5*tan(1/2*c)^2*tan(c)^2 + 512*b^2*tan(d*x)^4*tan(1/2*c)^3*tan(c)^2 - 9216*b^2
*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^3*tan(c)^2 + 4608*b^2*tan(1/2*d*x)^4*tan(1/2*c)^3*tan(c)^2 + 18*pi*a*b*s
gn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*
c)^4*tan(c)^2 + 72*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*c)^4*tan(c)^2 - 72
*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*c)^4*tan(c)^2 - 432*a*b*tan(d*x)^3*
tan(1/2*c)^4*tan(c)^2 - 3072*b^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^4*tan(c)^2 + 108*a*b*arctan((tan(d*x) + ta
n(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 - 108*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d
*x)*tan(c) + 1))*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 1296*a*b*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2
+ 4608*b^2*tan(1/2*d*x)^3*tan(1/2*c)^4*tan(c)^2 + 1536*b^2*tan(1/2*d*x)^2*tan(1/2*c)^5*tan(c)^2 + 12*a*b*arct
an((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*c)^6*tan(c)^2 - 12*a*b*arctan(-(tan(d*x) - tan(c))/(tan(
d*x)*tan(c) + 1))*tan(1/2*c)^6*tan(c)^2 + 144*a*b*tan(d*x)*tan(1/2*c)^6*tan(c)^2 + 72*a*b*tan(d*x)^4*tan(1/2*d
*x)^2*tan(c)^3 - 432*a*b*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^3 + 24*a*b*tan(1/2*d*x)^6*tan(c)^3 + 72*a*b*tan(d*x)
^4*tan(1/2*c)^2*tan(c)^3 - 1296*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^3 + 216*a*b*tan(1/2*d*x)^4*t
an(1/2*c)^2*tan(c)^3 - 432*a*b*tan(d*x)^2*tan(1/2*c)^4*tan(c)^3 + 216*a*b*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^3
+ 24*a*b*tan(1/2*c)^6*tan(c)^3 + 6*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x
)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(c)^4 + 6*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) -
1))*tan(d*x)^4*tan(c)^4 - 6*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(c)^4 + 9*pi*
a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan
(1/2*d*x)^2*tan(c)^4 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(
c)^4 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^4 + 72*a*b*t
an(d*x)^3*tan(1/2*d*x)^2*tan(c)^4 + 512*b^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(c)^4 + 18*a*b*arctan((tan(d*x) + tan
(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^4*tan(c)^4 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1)
)*tan(1/2*d*x)^4*tan(c)^4 - 72*a*b*tan(d*x)*tan(1/2*d*x)^4*tan(c)^4 + 1536*b^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1
/2*c)*tan(c)^4 - 768*b^2*tan(1/2*d*x)^4*tan(1/2*c)*tan(c)^4 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*t
an(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*c)^2*tan(c)^4 + 36*a*b*arctan((tan(d*x
) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*c)^2*tan(c)^4 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(
d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*c)^2*tan(c)^4 + 72*a*b*tan(d*x)^3*tan(1/2*c)^2*tan(c)^4 + 1536*b^2*tan(d*
x)^2*tan(1/2*d*x)*tan(1/2*c)^2*tan(c)^4 + 54*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x
)^2*tan(1/2*c)^2*tan(c)^4 - 54*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^2*tan(1/2*c
)^2*tan(c)^4 - 216*a*b*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4 - 2304*b^2*tan(1/2*d*x)^3*tan(1/2*c)^2*ta
n(c)^4 + 512*b^2*tan(d*x)^2*tan(1/2*c)^3*tan(c)^4 - 2304*b^2*tan(1/2*d*x)^2*tan(1/2*c)^3*tan(c)^4 + 18*a*b*arc
tan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*c)^4*tan(c)^4 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan
(d*x)*tan(c) + 1))*tan(1/2*c)^4*tan(c)^4 - 72*a*b*tan(d*x)*tan(1/2*c)^4*tan(c)^4 - 768*b^2*tan(1/2*d*x)*tan(1/
2*c)^4*tan(c)^4 + 72*a*b*d*x*tan(d*x)^4*tan(1/2*d*x)^2 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)
^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(1/2*d*x)^2 + 144*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^4 + 18*pi*a*b*sgn(
-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^4 + 24*a*b*d*x*tan
(1/2*d*x)^6 + 3*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^6
+ 72*a*b*d*x*tan(d*x)^4*tan(1/2*c)^2 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) -
2*tan(c))*tan(d*x)^4*tan(1/2*c)^2 + 432*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 54*pi*a*b*sgn(-2*tan(
d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 216*a*b*
d*x*tan(1/2*d*x)^4*tan(1/2*c)^2 + 27*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*ta
n(c))*tan(1/2*d*x)^4*tan(1/2*c)^2 + 144*a*b*d*x*tan(d*x)^2*tan(1/2*c)^4 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) +
2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*c)^4 + 216*a*b*d*x*tan(1/2*d*x)^2*tan(1/2*c)^
4 + 27*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^2*tan(1/2*c
)^4 + 24*a*b*d*x*tan(1/2*c)^6 + 3*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c
))*tan(1/2*c)^6 + 48*a*b*d*x*tan(d*x)^4*tan(c)^2 + 6*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2
*tan(d*x) - 2*tan(c))*tan(d*x)^4*tan(c)^2 + 288*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 + 36*pi*a*b*sgn(-2*
tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 + 144*a*b*
d*x*tan(1/2*d*x)^4*tan(c)^2 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c)
)*tan(1/2*d*x)^4*tan(c)^2 + 288*a*b*d*x*tan(d*x)^2*tan(1/2*c)^2*tan(c)^2 + 36*pi*a*b*sgn(-2*tan(d*x)^2*tan(c)
+ 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*c)^2*tan(c)^2 + 432*a*b*d*x*tan(1/2*d*x)^2*t
an(1/2*c)^2*tan(c)^2 + 54*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1
/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 144*a*b*d*x*tan(1/2*c)^4*tan(c)^2 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*t
an(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*c)^4*tan(c)^2 + 48*a*b*d*x*tan(d*x)^2*tan(c)^4 + 6*pi*a*b*sg
n(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(c)^4 + 72*a*b*d*x*tan(1/2
*d*x)^2*tan(c)^4 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*
x)^2*tan(c)^4 + 72*a*b*d*x*tan(1/2*c)^2*tan(c)^4 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2
*tan(d*x) - 2*tan(c))*tan(1/2*c)^2*tan(c)^4 + 3*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c)
+ 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^4 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*t
an(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2 + 18*a*b*arctan((tan
(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(1/2*d*x)^2 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x
)*tan(c) + 1))*tan(d*x)^4*tan(1/2*d*x)^2 + 256*b^2*tan(d*x)^4*tan(1/2*d*x)^3 + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c
)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4 + 36*a*b*arcta
n((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^4 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(t
an(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^4 + 72*a*b*tan(d*x)^3*tan(1/2*d*x)^4 + 6*a*b*arctan((tan(d*x) + t
an(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^6 - 6*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/
2*d*x)^6 - 24*a*b*tan(d*x)*tan(1/2*d*x)^6 + 768*b^2*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c) - 1536*b^2*tan(d*x)^2
*tan(1/2*d*x)^4*tan(1/2*c) + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*ta
n(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*c)^2 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) -
1))*tan(d*x)^4*tan(1/2*c)^2 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(1/2*c)
^2 + 768*b^2*tan(d*x)^4*tan(1/2*d*x)*tan(1/2*c)^2 + 27*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2
*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 108*a*b*arctan((tan(d*x)
+ tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 108*a*b*arctan(-(tan(d*x) - tan(c))/
(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 216*a*b*tan(d*x)^3*tan(1/2*d*x)^2*tan(1/2*c)^2
- 4608*b^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^2 + 54*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*
tan(1/2*d*x)^4*tan(1/2*c)^2 - 54*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^4*tan(1/2
*c)^2 - 216*a*b*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^2 + 768*b^2*tan(1/2*d*x)^5*tan(1/2*c)^2 + 256*b^2*tan(d*x)^
4*tan(1/2*c)^3 - 4608*b^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^3 + 2304*b^2*tan(1/2*d*x)^4*tan(1/2*c)^3 + 9*pi
*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*ta
n(1/2*c)^4 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*c)^4 - 36*a*b*arctan(
-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*c)^4 + 72*a*b*tan(d*x)^3*tan(1/2*c)^4 - 1536*b^
2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^4 + 54*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)
^2*tan(1/2*c)^4 - 54*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^2*tan(1/2*c)^4 - 216*
a*b*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^4 + 2304*b^2*tan(1/2*d*x)^3*tan(1/2*c)^4 + 768*b^2*tan(1/2*d*x)^2*tan(1
/2*c)^5 + 6*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*c)^6 - 6*a*b*arctan(-(tan(d*x) - tan
(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*c)^6 - 24*a*b*tan(d*x)*tan(1/2*c)^6 - 72*a*b*tan(d*x)^4*tan(1/2*d*x)^2*tan
(c) + 432*a*b*tan(d*x)^2*tan(1/2*d*x)^4*tan(c) - 24*a*b*tan(1/2*d*x)^6*tan(c) - 72*a*b*tan(d*x)^4*tan(1/2*c)^2
*tan(c) + 1296*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - 216*a*b*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)
+ 432*a*b*tan(d*x)^2*tan(1/2*c)^4*tan(c) - 216*a*b*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c) - 24*a*b*tan(1/2*c)^6*ta
n(c) + 12*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) -
2*tan(c))*tan(d*x)^2*tan(c)^2 + 12*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^4*tan(c)^2 -
12*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4*tan(c)^2 + 18*pi*a*b*sgn(2*tan(d*x)^2*ta
n(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^2*tan(c)^2 +
72*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 - 72*a*b*arctan(-(
tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 - 432*a*b*tan(d*x)^3*tan(1/2*d*x)
^2*tan(c)^2 + 1024*b^2*tan(d*x)^2*tan(1/2*d*x)^3*tan(c)^2 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c)
- 1))*tan(1/2*d*x)^4*tan(c)^2 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^4*tan(
c)^2 + 432*a*b*tan(d*x)*tan(1/2*d*x)^4*tan(c)^2 + 3072*b^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)*tan(c)^2 - 153
6*b^2*tan(1/2*d*x)^4*tan(1/2*c)*tan(c)^2 + 18*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) +
2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*c)^2*tan(c)^2 + 72*a*b*arctan((tan(d*x) + tan(c))/(tan(d
*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*c)^2*tan(c)^2 - 72*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*
tan(d*x)^2*tan(1/2*c)^2*tan(c)^2 - 432*a*b*tan(d*x)^3*tan(1/2*c)^2*tan(c)^2 + 3072*b^2*tan(d*x)^2*tan(1/2*d*x)
*tan(1/2*c)^2*tan(c)^2 + 108*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^2*tan(1/2*c)^2
*tan(c)^2 - 108*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 +
1296*a*b*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 - 4608*b^2*tan(1/2*d*x)^3*tan(1/2*c)^2*tan(c)^2 + 1024*
b^2*tan(d*x)^2*tan(1/2*c)^3*tan(c)^2 - 4608*b^2*tan(1/2*d*x)^2*tan(1/2*c)^3*tan(c)^2 + 36*a*b*arctan((tan(d*x)
+ tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*c)^4*tan(c)^2 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c)
+ 1))*tan(1/2*c)^4*tan(c)^2 + 432*a*b*tan(d*x)*tan(1/2*c)^4*tan(c)^2 - 1536*b^2*tan(1/2*d*x)*tan(1/2*c)^4*tan(
c)^2 + 24*a*b*tan(d*x)^4*tan(c)^3 - 432*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^3 + 72*a*b*tan(1/2*d*x)^4*tan(c)^
3 - 432*a*b*tan(d*x)^2*tan(1/2*c)^2*tan(c)^3 + 216*a*b*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^3 + 72*a*b*tan(1/2*c
)^4*tan(c)^3 + 3*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(
d*x) - 2*tan(c))*tan(c)^4 + 12*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(c)^4 - 12*
a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(c)^4 + 24*a*b*tan(d*x)^3*tan(c)^4 + 18*a
*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^2*tan(c)^4 - 18*a*b*arctan(-(tan(d*x) - tan(
c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^2*tan(c)^4 - 72*a*b*tan(d*x)*tan(1/2*d*x)^2*tan(c)^4 + 256*b^2*tan(1/2
*d*x)^3*tan(c)^4 + 768*b^2*tan(1/2*d*x)^2*tan(1/2*c)*tan(c)^4 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*ta
n(c) - 1))*tan(1/2*c)^2*tan(c)^4 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*c)^2*tan(
c)^4 - 72*a*b*tan(d*x)*tan(1/2*c)^2*tan(c)^4 + 768*b^2*tan(1/2*d*x)*tan(1/2*c)^2*tan(c)^4 + 256*b^2*tan(1/2*c)
^3*tan(c)^4 + 24*a*b*d*x*tan(d*x)^4 + 3*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2
*tan(c))*tan(d*x)^4 + 144*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^2 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*
tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*d*x)^2 + 72*a*b*d*x*tan(1/2*d*x)^4 + 9*pi*a*b*sgn(-2*tan(
d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^4 + 144*a*b*d*x*tan(d*x)^2*tan(1/2*c
)^2 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(1/2*c)^
2 + 216*a*b*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + 27*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan
(d*x) - 2*tan(c))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 72*a*b*d*x*tan(1/2*c)^4 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) +
2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*c)^4 + 96*a*b*d*x*tan(d*x)^2*tan(c)^2 + 12*pi*a*b*sgn(-2*
tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2*tan(c)^2 + 144*a*b*d*x*tan(1/2*d*x
)^2*tan(c)^2 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^
2*tan(c)^2 + 144*a*b*d*x*tan(1/2*c)^2*tan(c)^2 + 18*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*
tan(d*x) - 2*tan(c))*tan(1/2*c)^2*tan(c)^2 + 24*a*b*d*x*tan(c)^4 + 3*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d
*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(c)^4 + 6*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan
(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2 + 6*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan
(c) - 1))*tan(d*x)^4 - 6*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^4 + 9*pi*a*b*sgn(2*ta
n(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^2
+ 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*d*x)^2 - 36*a*b*arctan(-(tan(d*x
) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(1/2*d*x)^2 + 72*a*b*tan(d*x)^3*tan(1/2*d*x)^2 + 512*b^2*tan(
d*x)^2*tan(1/2*d*x)^3 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^4 - 18*a*b*arcta
n(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^4 - 72*a*b*tan(d*x)*tan(1/2*d*x)^4 + 1536*b^2*tan(d
*x)^2*tan(1/2*d*x)^2*tan(1/2*c) - 768*b^2*tan(1/2*d*x)^4*tan(1/2*c) + 9*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*
sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*c)^2 + 36*a*b*arctan((tan(d*x)
+ tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(1/2*c)^2 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c
) + 1))*tan(d*x)^2*tan(1/2*c)^2 + 72*a*b*tan(d*x)^3*tan(1/2*c)^2 + 1536*b^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)
^2 + 54*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 54*a*b*arctan(-(ta
n(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 216*a*b*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*
c)^2 - 2304*b^2*tan(1/2*d*x)^3*tan(1/2*c)^2 + 512*b^2*tan(d*x)^2*tan(1/2*c)^3 - 2304*b^2*tan(1/2*d*x)^2*tan(1/
2*c)^3 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*c)^4 - 18*a*b*arctan(-(tan(d*x) - ta
n(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*c)^4 - 72*a*b*tan(d*x)*tan(1/2*c)^4 - 768*b^2*tan(1/2*d*x)*tan(1/2*c)^4 -
24*a*b*tan(d*x)^4*tan(c) + 432*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(c) - 72*a*b*tan(1/2*d*x)^4*tan(c) + 432*a*b*
tan(d*x)^2*tan(1/2*c)^2*tan(c) - 216*a*b*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - 72*a*b*tan(1/2*c)^4*tan(c) + 6*p
i*a*b*sgn(2*tan(d*x)^2*tan(c)^2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*t
an(c)^2 + 24*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2*tan(c)^2 - 24*a*b*arctan(-(tan(d
*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2*tan(c)^2 - 144*a*b*tan(d*x)^3*tan(c)^2 + 36*a*b*arctan((tan(d*
x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^2*tan(c)^2 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan
(c) + 1))*tan(1/2*d*x)^2*tan(c)^2 + 432*a*b*tan(d*x)*tan(1/2*d*x)^2*tan(c)^2 + 512*b^2*tan(1/2*d*x)^3*tan(c)^2
+ 1536*b^2*tan(1/2*d*x)^2*tan(1/2*c)*tan(c)^2 + 36*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(
1/2*c)^2*tan(c)^2 - 36*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*c)^2*tan(c)^2 + 432*a*b*
tan(d*x)*tan(1/2*c)^2*tan(c)^2 + 1536*b^2*tan(1/2*d*x)*tan(1/2*c)^2*tan(c)^2 + 512*b^2*tan(1/2*c)^3*tan(c)^2 -
144*a*b*tan(d*x)^2*tan(c)^3 + 72*a*b*tan(1/2*d*x)^2*tan(c)^3 + 72*a*b*tan(1/2*c)^2*tan(c)^3 + 6*a*b*arctan((t
an(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(c)^4 - 6*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*t
an(c)^4 - 24*a*b*tan(d*x)*tan(c)^4 + 48*a*b*d*x*tan(d*x)^2 + 6*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*ta
n(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(d*x)^2 + 72*a*b*d*x*tan(1/2*d*x)^2 + 9*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2
*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*d*x)^2 + 72*a*b*d*x*tan(1/2*c)^2 + 9*pi*a*b*sgn(-2*tan(d*x
)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(1/2*c)^2 + 48*a*b*d*x*tan(c)^2 + 6*pi*a*b*sgn(-2
*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c))*tan(c)^2 + 3*pi*a*b*sgn(2*tan(d*x)^2*tan(c)^
2 - 2)*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c)) + 12*a*b*arctan((tan(d*x) + tan
(c))/(tan(d*x)*tan(c) - 1))*tan(d*x)^2 - 12*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(d*x)^2
+ 24*a*b*tan(d*x)^3 + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*d*x)^2 - 18*a*b*arctan(
-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*d*x)^2 - 72*a*b*tan(d*x)*tan(1/2*d*x)^2 + 256*b^2*tan(1/2*
d*x)^3 + 768*b^2*tan(1/2*d*x)^2*tan(1/2*c) + 18*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(1/2*
c)^2 - 18*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(1/2*c)^2 - 72*a*b*tan(d*x)*tan(1/2*c)^2 +
768*b^2*tan(1/2*d*x)*tan(1/2*c)^2 + 256*b^2*tan(1/2*c)^3 + 144*a*b*tan(d*x)^2*tan(c) - 72*a*b*tan(1/2*d*x)^2*
tan(c) - 72*a*b*tan(1/2*c)^2*tan(c) + 12*a*b*arctan((tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1))*tan(c)^2 - 12*a
*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1))*tan(c)^2 + 144*a*b*tan(d*x)*tan(c)^2 + 24*a*b*tan(c)^3 +
24*a*b*d*x + 3*pi*a*b*sgn(-2*tan(d*x)^2*tan(c) + 2*tan(d*x)*tan(c)^2 + 2*tan(d*x) - 2*tan(c)) + 6*a*b*arctan(
(tan(d*x) + tan(c))/(tan(d*x)*tan(c) - 1)) - 6*a*b*arctan(-(tan(d*x) - tan(c))/(tan(d*x)*tan(c) + 1)) - 24*a*b
*tan(d*x) - 24*a*b*tan(c))/(d*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 + 2*d*tan(d*x)^4*tan(1/2*d*x)^6*
tan(1/2*c)^6*tan(c)^2 + 3*d*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^4 + 3*d*tan(d*x)^4*tan(1/2*d*x)^4*ta
n(1/2*c)^6*tan(c)^4 + 2*d*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 + d*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/
2*c)^6 + 6*d*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 + 6*d*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(
c)^2 + 4*d*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + 3*d*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)
^4 + 9*d*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^4 + 6*d*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^4
+ 3*d*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^4 + 6*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 +
d*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^4 + 3*d*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^4 + 3*d*tan(d*x)^4*tan(1/2*
d*x)^4*tan(1/2*c)^6 + 2*d*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6 + 6*d*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2*
tan(c)^2 + 18*d*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 12*d*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4*
tan(c)^2 + 6*d*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 + 12*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6*t
an(c)^2 + 2*d*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + d*tan(d*x)^4*tan(1/2*d*x)^6*tan(c)^4 + 9*d*tan(d*x)^4*tan
(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 + 6*d*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^4 + 9*d*tan(d*x)^4*tan(1
/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 + 18*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^4 + 3*d*tan(1/2*d*x)^6*ta
n(1/2*c)^4*tan(c)^4 + d*tan(d*x)^4*tan(1/2*c)^6*tan(c)^4 + 6*d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^4
+ 3*d*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^4 + 3*d*tan(d*x)^4*tan(1/2*d*x)^6*tan(1/2*c)^2 + 9*d*tan(d*x)^4*tan(
1/2*d*x)^4*tan(1/2*c)^4 + 6*d*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4 + 3*d*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c
)^6 + 6*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6 + d*tan(1/2*d*x)^6*tan(1/2*c)^6 + 2*d*tan(d*x)^4*tan(1/2*d*x)
^6*tan(c)^2 + 18*d*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^2 + 12*d*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)
^2*tan(c)^2 + 18*d*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 36*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)
^4*tan(c)^2 + 6*d*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 + 2*d*tan(d*x)^4*tan(1/2*c)^6*tan(c)^2 + 12*d*tan(d*x)^
2*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 + 6*d*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^2 + 3*d*tan(d*x)^4*tan(1/2*d*x
)^4*tan(c)^4 + 2*d*tan(d*x)^2*tan(1/2*d*x)^6*tan(c)^4 + 9*d*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4 +
18*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 + 3*d*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^4 + 3*d*tan(d*x)
^4*tan(1/2*c)^4*tan(c)^4 + 18*d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^4 + 9*d*tan(1/2*d*x)^4*tan(1/2*c
)^4*tan(c)^4 + 2*d*tan(d*x)^2*tan(1/2*c)^6*tan(c)^4 + 3*d*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^4 + d*tan(d*x)^4*
tan(1/2*d*x)^6 + 9*d*tan(d*x)^4*tan(1/2*d*x)^4*tan(1/2*c)^2 + 6*d*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2 + 9*d
*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^4 + 18*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4 + 3*d*tan(1/2*d*x)^6*tan
(1/2*c)^4 + d*tan(d*x)^4*tan(1/2*c)^6 + 6*d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6 + 3*d*tan(1/2*d*x)^4*tan(1/
2*c)^6 + 6*d*tan(d*x)^4*tan(1/2*d*x)^4*tan(c)^2 + 4*d*tan(d*x)^2*tan(1/2*d*x)^6*tan(c)^2 + 18*d*tan(d*x)^4*tan
(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 36*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^2 + 6*d*tan(1/2*d*x)^6*
tan(1/2*c)^2*tan(c)^2 + 6*d*tan(d*x)^4*tan(1/2*c)^4*tan(c)^2 + 36*d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4*tan
(c)^2 + 18*d*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 4*d*tan(d*x)^2*tan(1/2*c)^6*tan(c)^2 + 6*d*tan(1/2*d*x)^2*
tan(1/2*c)^6*tan(c)^2 + 3*d*tan(d*x)^4*tan(1/2*d*x)^2*tan(c)^4 + 6*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^4 + d*ta
n(1/2*d*x)^6*tan(c)^4 + 3*d*tan(d*x)^4*tan(1/2*c)^2*tan(c)^4 + 18*d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan
(c)^4 + 9*d*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^4 + 6*d*tan(d*x)^2*tan(1/2*c)^4*tan(c)^4 + 9*d*tan(1/2*d*x)^2*t
an(1/2*c)^4*tan(c)^4 + d*tan(1/2*c)^6*tan(c)^4 + 3*d*tan(d*x)^4*tan(1/2*d*x)^4 + 2*d*tan(d*x)^2*tan(1/2*d*x)^6
+ 9*d*tan(d*x)^4*tan(1/2*d*x)^2*tan(1/2*c)^2 + 18*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2 + 3*d*tan(1/2*d*x)
^6*tan(1/2*c)^2 + 3*d*tan(d*x)^4*tan(1/2*c)^4 + 18*d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4 + 9*d*tan(1/2*d*x)
^4*tan(1/2*c)^4 + 2*d*tan(d*x)^2*tan(1/2*c)^6 + 3*d*tan(1/2*d*x)^2*tan(1/2*c)^6 + 6*d*tan(d*x)^4*tan(1/2*d*x)^
2*tan(c)^2 + 12*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^2 + 2*d*tan(1/2*d*x)^6*tan(c)^2 + 6*d*tan(d*x)^4*tan(1/2*c)
^2*tan(c)^2 + 36*d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 18*d*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^2
+ 12*d*tan(d*x)^2*tan(1/2*c)^4*tan(c)^2 + 18*d*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 2*d*tan(1/2*c)^6*tan(c)
^2 + d*tan(d*x)^4*tan(c)^4 + 6*d*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^4 + 3*d*tan(1/2*d*x)^4*tan(c)^4 + 6*d*tan(d*
x)^2*tan(1/2*c)^2*tan(c)^4 + 9*d*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^4 + 3*d*tan(1/2*c)^4*tan(c)^4 + 3*d*tan(d*
x)^4*tan(1/2*d*x)^2 + 6*d*tan(d*x)^2*tan(1/2*d*x)^4 + d*tan(1/2*d*x)^6 + 3*d*tan(d*x)^4*tan(1/2*c)^2 + 18*d*ta
n(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 9*d*tan(1/2*d*x)^4*tan(1/2*c)^2 + 6*d*tan(d*x)^2*tan(1/2*c)^4 + 9*d*tan
(1/2*d*x)^2*tan(1/2*c)^4 + d*tan(1/2*c)^6 + 2*d*tan(d*x)^4*tan(c)^2 + 12*d*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^2
+ 6*d*tan(1/2*d*x)^4*tan(c)^2 + 12*d*tan(d*x)^2*tan(1/2*c)^2*tan(c)^2 + 18*d*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c
)^2 + 6*d*tan(1/2*c)^4*tan(c)^2 + 2*d*tan(d*x)^2*tan(c)^4 + 3*d*tan(1/2*d*x)^2*tan(c)^4 + 3*d*tan(1/2*c)^2*tan
(c)^4 + d*tan(d*x)^4 + 6*d*tan(d*x)^2*tan(1/2*d*x)^2 + 3*d*tan(1/2*d*x)^4 + 6*d*tan(d*x)^2*tan(1/2*c)^2 + 9*d*
tan(1/2*d*x)^2*tan(1/2*c)^2 + 3*d*tan(1/2*c)^4 + 4*d*tan(d*x)^2*tan(c)^2 + 6*d*tan(1/2*d*x)^2*tan(c)^2 + 6*d*t
an(1/2*c)^2*tan(c)^2 + d*tan(c)^4 + 2*d*tan(d*x)^2 + 3*d*tan(1/2*d*x)^2 + 3*d*tan(1/2*c)^2 + 2*d*tan(c)^2 + d)

Mupad [B] (verification not implemented)

Time = 24.06 (sec) , antiderivative size = 101, normalized size of antiderivative = 0.95 \[ \int \cos ^3(c+d x) (a \sin (c+d x)+b \tan (c+d x))^2 \, dx=\frac {a^2\,\sin \left (c+d\,x\right )}{8\,d}+\frac {b^2\,\sin \left (c+d\,x\right )}{4\,d}+\frac {a\,b\,x}{4}-\frac {a^2\,\sin \left (3\,c+3\,d\,x\right )}{48\,d}-\frac {a^2\,\sin \left (5\,c+5\,d\,x\right )}{80\,d}-\frac {b^2\,\sin \left (3\,c+3\,d\,x\right )}{12\,d}-\frac {a\,b\,\sin \left (4\,c+4\,d\,x\right )}{16\,d} \]

[In]

int(cos(c + d*x)^3*(a*sin(c + d*x) + b*tan(c + d*x))^2,x)

[Out]

(a^2*sin(c + d*x))/(8*d) + (b^2*sin(c + d*x))/(4*d) + (a*b*x)/4 - (a^2*sin(3*c + 3*d*x))/(48*d) - (a^2*sin(5*c
+ 5*d*x))/(80*d) - (b^2*sin(3*c + 3*d*x))/(12*d) - (a*b*sin(4*c + 4*d*x))/(16*d)