\(\int \frac {\cos ^{\frac {3}{2}}(c+d x)}{(a+a \sec (c+d x))^{3/2}} \, dx\) [428]

Optimal result

Integrand size = 25, antiderivative size = 197 \[ \int \frac {\cos ^{\frac {3}{2}}(c+d x)}{(a+a \sec (c+d x))^{3/2}} \, dx=\frac {11 \text {arctanh}\left (\frac {\sqrt {a} \sqrt {\sec (c+d x)} \sin (c+d x)}{\sqrt {2} \sqrt {a+a \sec (c+d x)}}\right ) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}}{2 \sqrt {2} a^{3/2} d}-\frac {\sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}-\frac {19 \sin (c+d x)}{6 a d \sqrt {\cos (c+d x)} \sqrt {a+a \sec (c+d x)}}+\frac {7 \sqrt {\cos (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}} \]

[Out]

-1/2*sin(d*x+c)*cos(d*x+c)^(1/2)/d/(a+a*sec(d*x+c))^(3/2)+11/4*arctanh(1/2*sin(d*x+c)*a^(1/2)*sec(d*x+c)^(1/2)
*2^(1/2)/(a+a*sec(d*x+c))^(1/2))*cos(d*x+c)^(1/2)*sec(d*x+c)^(1/2)/a^(3/2)/d*2^(1/2)-19/6*sin(d*x+c)/a/d/cos(d
*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2)+7/6*sin(d*x+c)*cos(d*x+c)^(1/2)/a/d/(a+a*sec(d*x+c))^(1/2)

Rubi [A] (verified)

Time = 0.57 (sec) , antiderivative size = 197, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.240, Rules used = {4349, 3902, 4107, 4098, 3893, 212} \[ \int \frac {\cos ^{\frac {3}{2}}(c+d x)}{(a+a \sec (c+d x))^{3/2}} \, dx=\frac {11 \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)} \text {arctanh}\left (\frac {\sqrt {a} \sin (c+d x) \sqrt {\sec (c+d x)}}{\sqrt {2} \sqrt {a \sec (c+d x)+a}}\right )}{2 \sqrt {2} a^{3/2} d}+\frac {7 \sin (c+d x) \sqrt {\cos (c+d x)}}{6 a d \sqrt {a \sec (c+d x)+a}}-\frac {19 \sin (c+d x)}{6 a d \sqrt {\cos (c+d x)} \sqrt {a \sec (c+d x)+a}}-\frac {\sin (c+d x) \sqrt {\cos (c+d x)}}{2 d (a \sec (c+d x)+a)^{3/2}} \]

[In]

Int[Cos[c + d*x]^(3/2)/(a + a*Sec[c + d*x])^(3/2),x]

[Out]

(11*ArcTanh[(Sqrt[a]*Sqrt[Sec[c + d*x]]*Sin[c + d*x])/(Sqrt[2]*Sqrt[a + a*Sec[c + d*x]])]*Sqrt[Cos[c + d*x]]*S
qrt[Sec[c + d*x]])/(2*Sqrt[2]*a^(3/2)*d) - (Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(2*d*(a + a*Sec[c + d*x])^(3/2))
- (19*Sin[c + d*x])/(6*a*d*Sqrt[Cos[c + d*x]]*Sqrt[a + a*Sec[c + d*x]]) + (7*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/
(6*a*d*Sqrt[a + a*Sec[c + d*x]])

Rule 212

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1/(Rt[a, 2]*Rt[-b, 2]))*ArcTanh[Rt[-b, 2]*(x/Rt[a, 2])], x]
/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])

Rule 3893

Int[Sqrt[csc[(e_.) + (f_.)*(x_)]*(d_.)]/Sqrt[csc[(e_.) + (f_.)*(x_)]*(b_.) + (a_)], x_Symbol] :> Dist[-2*b*(d/
(a*f)), Subst[Int[1/(2*b - d*x^2), x], x, b*(Cot[e + f*x]/(Sqrt[a + b*Csc[e + f*x]]*Sqrt[d*Csc[e + f*x]]))], x
] /; FreeQ[{a, b, d, e, f}, x] && EqQ[a^2 - b^2, 0]

Rule 3902

Int[(csc[(e_.) + (f_.)*(x_)]*(d_.))^(n_)*(csc[(e_.) + (f_.)*(x_)]*(b_.) + (a_))^(m_), x_Symbol] :> Simp[(-Cot[
e + f*x])*(a + b*Csc[e + f*x])^m*((d*Csc[e + f*x])^n/(f*(2*m + 1))), x] + Dist[1/(a^2*(2*m + 1)), Int[(a + b*C
sc[e + f*x])^(m + 1)*(d*Csc[e + f*x])^n*(a*(2*m + n + 1) - b*(m + n + 1)*Csc[e + f*x]), x], x] /; FreeQ[{a, b,
d, e, f, n}, x] && EqQ[a^2 - b^2, 0] && LtQ[m, -1] && (IntegersQ[2*m, 2*n] || IntegerQ[m])

Rule 4098

Int[(csc[(e_.) + (f_.)*(x_)]*(d_.))^(n_)*(csc[(e_.) + (f_.)*(x_)]*(b_.) + (a_))^(m_)*(csc[(e_.) + (f_.)*(x_)]*
(B_.) + (A_)), x_Symbol] :> Simp[A*Cot[e + f*x]*(a + b*Csc[e + f*x])^m*((d*Csc[e + f*x])^n/(f*n)), x] - Dist[(
a*A*m - b*B*n)/(b*d*n), Int[(a + b*Csc[e + f*x])^m*(d*Csc[e + f*x])^(n + 1), x], x] /; FreeQ[{a, b, d, e, f, A
, B, m, n}, x] && NeQ[A*b - a*B, 0] && EqQ[a^2 - b^2, 0] && EqQ[m + n + 1, 0] &&  !LeQ[m, -1]

Rule 4107

Int[(csc[(e_.) + (f_.)*(x_)]*(d_.))^(n_)*(csc[(e_.) + (f_.)*(x_)]*(b_.) + (a_))^(m_)*(csc[(e_.) + (f_.)*(x_)]*
(B_.) + (A_)), x_Symbol] :> Simp[A*Cot[e + f*x]*(a + b*Csc[e + f*x])^m*((d*Csc[e + f*x])^n/(f*n)), x] - Dist[1
/(b*d*n), Int[(a + b*Csc[e + f*x])^m*(d*Csc[e + f*x])^(n + 1)*Simp[a*A*m - b*B*n - A*b*(m + n + 1)*Csc[e + f*x
], x], x], x] /; FreeQ[{a, b, d, e, f, A, B, m}, x] && NeQ[A*b - a*B, 0] && EqQ[a^2 - b^2, 0] && LtQ[n, 0]

Rule 4349

Int[(u_)*((c_.)*sin[(a_.) + (b_.)*(x_)])^(m_.), x_Symbol] :> Dist[(c*Csc[a + b*x])^m*(c*Sin[a + b*x])^m, Int[A
ctivateTrig[u]/(c*Csc[a + b*x])^m, x], x] /; FreeQ[{a, b, c, m}, x] &&  !IntegerQ[m] && KnownSecantIntegrandQ[
u, x]

Rubi steps \begin{align*} \text {integral}& = \left (\sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \int \frac {1}{\sec ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx \\ & = -\frac {\sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}-\frac {\left (\sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \int \frac {-\frac {7 a}{2}+2 a \sec (c+d x)}{\sec ^{\frac {3}{2}}(c+d x) \sqrt {a+a \sec (c+d x)}} \, dx}{2 a^2} \\ & = -\frac {\sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}+\frac {7 \sqrt {\cos (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}}-\frac {\left (\sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \int \frac {\frac {19 a^2}{4}-\frac {7}{2} a^2 \sec (c+d x)}{\sqrt {\sec (c+d x)} \sqrt {a+a \sec (c+d x)}} \, dx}{3 a^3} \\ & = -\frac {\sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}-\frac {19 \sin (c+d x)}{6 a d \sqrt {\cos (c+d x)} \sqrt {a+a \sec (c+d x)}}+\frac {7 \sqrt {\cos (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}}+\frac {\left (11 \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \int \frac {\sqrt {\sec (c+d x)}}{\sqrt {a+a \sec (c+d x)}} \, dx}{4 a} \\ & = -\frac {\sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}-\frac {19 \sin (c+d x)}{6 a d \sqrt {\cos (c+d x)} \sqrt {a+a \sec (c+d x)}}+\frac {7 \sqrt {\cos (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}}-\frac {\left (11 \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \text {Subst}\left (\int \frac {1}{2 a-x^2} \, dx,x,-\frac {a \sqrt {\sec (c+d x)} \sin (c+d x)}{\sqrt {a+a \sec (c+d x)}}\right )}{2 a d} \\ & = \frac {11 \text {arctanh}\left (\frac {\sqrt {a} \sqrt {\sec (c+d x)} \sin (c+d x)}{\sqrt {2} \sqrt {a+a \sec (c+d x)}}\right ) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}}{2 \sqrt {2} a^{3/2} d}-\frac {\sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}-\frac {19 \sin (c+d x)}{6 a d \sqrt {\cos (c+d x)} \sqrt {a+a \sec (c+d x)}}+\frac {7 \sqrt {\cos (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.49 (sec) , antiderivative size = 133, normalized size of antiderivative = 0.68 \[ \int \frac {\cos ^{\frac {3}{2}}(c+d x)}{(a+a \sec (c+d x))^{3/2}} \, dx=\frac {\left ((-12+4 \cos (c+d x)-19 \sec (c+d x)) \sqrt {1-\sec (c+d x)}-33 \sqrt {2} \arctan \left (\frac {\sqrt {2} \sqrt {\sec (c+d x)}}{\sqrt {1-\sec (c+d x)}}\right ) \cos ^2\left (\frac {1}{2} (c+d x)\right ) \sec ^{\frac {3}{2}}(c+d x)\right ) \sin (c+d x)}{6 d \sqrt {-1+\cos (c+d x)} (a (1+\sec (c+d x)))^{3/2}} \]

[In]

Integrate[Cos[c + d*x]^(3/2)/(a + a*Sec[c + d*x])^(3/2),x]

[Out]

(((-12 + 4*Cos[c + d*x] - 19*Sec[c + d*x])*Sqrt[1 - Sec[c + d*x]] - 33*Sqrt[2]*ArcTan[(Sqrt[2]*Sqrt[Sec[c + d*
x]])/Sqrt[1 - Sec[c + d*x]]]*Cos[(c + d*x)/2]^2*Sec[c + d*x]^(3/2))*Sin[c + d*x])/(6*d*Sqrt[-1 + Cos[c + d*x]]
*(a*(1 + Sec[c + d*x]))^(3/2))

Maple [A] (verified)

Time = 1.60 (sec) , antiderivative size = 257, normalized size of antiderivative = 1.30

method	result	size
default	\(\frac {\left (33 \sqrt {2}\, \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (\cos \left (d x +c \right )+1\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}}\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}\, \cos \left (d x +c \right )^{2}+66 \sqrt {2}\, \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (\cos \left (d x +c \right )+1\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}}\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}\, \cos \left (d x +c \right )+33 \sqrt {2}\, \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (\cos \left (d x +c \right )+1\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}}\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}+8 \cos \left (d x +c \right )^{2} \sin \left (d x +c \right )-24 \cos \left (d x +c \right ) \sin \left (d x +c \right )-38 \sin \left (d x +c \right )\right ) \sqrt {\cos \left (d x +c \right )}\, \sqrt {a \left (1+\sec \left (d x +c \right )\right )}}{12 d \,a^{2} \left (\cos \left (d x +c \right )+1\right )^{2}}\)	\(257\)

[In]

int(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x,method=_RETURNVERBOSE)

[Out]

1/12/d/a^2*(33*2^(1/2)*arctan(1/2*sin(d*x+c)*2^(1/2)/(cos(d*x+c)+1)/(-1/(cos(d*x+c)+1))^(1/2))*(-1/(cos(d*x+c)
+1))^(1/2)*cos(d*x+c)^2+66*2^(1/2)*arctan(1/2*sin(d*x+c)*2^(1/2)/(cos(d*x+c)+1)/(-1/(cos(d*x+c)+1))^(1/2))*(-1
/(cos(d*x+c)+1))^(1/2)*cos(d*x+c)+33*2^(1/2)*arctan(1/2*sin(d*x+c)*2^(1/2)/(cos(d*x+c)+1)/(-1/(cos(d*x+c)+1))^
(1/2))*(-1/(cos(d*x+c)+1))^(1/2)+8*cos(d*x+c)^2*sin(d*x+c)-24*cos(d*x+c)*sin(d*x+c)-38*sin(d*x+c))*cos(d*x+c)^
(1/2)*(a*(1+sec(d*x+c)))^(1/2)/(cos(d*x+c)+1)^2

Fricas [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 380, normalized size of antiderivative = 1.93 \[ \int \frac {\cos ^{\frac {3}{2}}(c+d x)}{(a+a \sec (c+d x))^{3/2}} \, dx=\left [\frac {33 \, \sqrt {2} {\left (\cos \left (d x + c\right )^{2} + 2 \, \cos \left (d x + c\right ) + 1\right )} \sqrt {a} \log \left (-\frac {a \cos \left (d x + c\right )^{2} - 2 \, \sqrt {2} \sqrt {a} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sqrt {\cos \left (d x + c\right )} \sin \left (d x + c\right ) - 2 \, a \cos \left (d x + c\right ) - 3 \, a}{\cos \left (d x + c\right )^{2} + 2 \, \cos \left (d x + c\right ) + 1}\right ) + 4 \, {\left (4 \, \cos \left (d x + c\right )^{2} - 12 \, \cos \left (d x + c\right ) - 19\right )} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sqrt {\cos \left (d x + c\right )} \sin \left (d x + c\right )}{24 \, {\left (a^{2} d \cos \left (d x + c\right )^{2} + 2 \, a^{2} d \cos \left (d x + c\right ) + a^{2} d\right )}}, -\frac {33 \, \sqrt {2} {\left (\cos \left (d x + c\right )^{2} + 2 \, \cos \left (d x + c\right ) + 1\right )} \sqrt {-a} \arctan \left (\frac {\sqrt {2} \sqrt {-a} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sqrt {\cos \left (d x + c\right )}}{a \sin \left (d x + c\right )}\right ) - 2 \, {\left (4 \, \cos \left (d x + c\right )^{2} - 12 \, \cos \left (d x + c\right ) - 19\right )} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sqrt {\cos \left (d x + c\right )} \sin \left (d x + c\right )}{12 \, {\left (a^{2} d \cos \left (d x + c\right )^{2} + 2 \, a^{2} d \cos \left (d x + c\right ) + a^{2} d\right )}}\right ] \]

[In]

integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm="fricas")

[Out]

[1/24*(33*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqr
t((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2
+ 2*cos(d*x + c) + 1)) + 4*(4*cos(d*x + c)^2 - 12*cos(d*x + c) - 19)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*
sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), -1/12*(33*sqrt(2)*(cos
(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqr
t(cos(d*x + c))/(a*sin(d*x + c))) - 2*(4*cos(d*x + c)^2 - 12*cos(d*x + c) - 19)*sqrt((a*cos(d*x + c) + a)/cos(
d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]

Sympy [F]

\[ \int \frac {\cos ^{\frac {3}{2}}(c+d x)}{(a+a \sec (c+d x))^{3/2}} \, dx=\int \frac {\cos ^{\frac {3}{2}}{\left (c + d x \right )}}{\left (a \left (\sec {\left (c + d x \right )} + 1\right )\right )^{\frac {3}{2}}}\, dx \]

[In]

integrate(cos(d*x+c)**(3/2)/(a+a*sec(d*x+c))**(3/2),x)

[Out]

Integral(cos(c + d*x)**(3/2)/(a*(sec(c + d*x) + 1))**(3/2), x)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 33960 vs. \(2 (162) = 324\).

Time = 0.79 (sec) , antiderivative size = 33960, normalized size of antiderivative = 172.39 \[ \int \frac {\cos ^{\frac {3}{2}}(c+d x)}{(a+a \sec (c+d x))^{3/2}} \, dx=\text {Too large to display} \]

[In]

integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm="maxima")

[Out]

1/12*(4*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*
c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3
/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 64*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*s
in(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/
2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 4*sin(3/2*d*x + 3/2*c)^5 +
4*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 +
sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 64*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2
*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 4*(2*cos(3*d*x + 3*c)^2*cos(3/2*d
*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*
x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x +
3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c)
, cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(sin(3/2*d*x + 3/2*
c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c)
, cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), c
os(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2
+ cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x +
3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 32*(2*cos(3*
d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x
+ 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(
3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3
/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x +
3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3
/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 4*(2*cos(3/2*d*x + 3/2*c)^
2 + 7)*sin(3/2*d*x + 3/2*c)^3 + 4*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)
^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3
/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2
*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c)
, cos(3/2*d*x + 3/2*c))) + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c
) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*
sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + s
in(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x
+ 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c),
cos(3/2*d*x + 3/2*c)))^3 + 32*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 +
1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c
)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c),
cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), co
s(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) +
cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x +
3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 4*(4*cos(3*d*
x + 3*c)*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + (sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*
sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c)^2 + 24*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*si
n(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2
*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sin(3/2*d*x + 3/2*c)^3 + (c
os(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c)^2 + sin(3/2*d*x + 3/2*c)^3 + 8*(cos(3*d*x +
3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*
c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(
3/2*d*x + 3/2*c)))^2 + 6*(2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2
*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2
*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(
sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin
(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)
*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*a
rctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c
))) - 20*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(s
in(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*
sin(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(cos(3/2*d*x + 3/2*c)*s
in(3/2*d*x + 3/2*c)^2 + 3*cos(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2 + 6)*sin(3/2*d*x +
3/2*c) + 2*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c
)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x
+ 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*
c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))
) - 18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*
c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 20*(cos(3*d*x + 3*c)^2*cos(3/2*d*x
+ 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 2*sin(3*d*x +
3*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^
2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 2
*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 9*((cos
(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 +
(cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c
)*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c)
, cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 16*(4*cos(3*d*x + 3
*c)*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + (sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3
/2*d*x + 3/2*c))*cos(3*d*x + 3*c)^2 + (sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2
*c))*sin(3*d*x + 3*c)^2 + sin(3/2*d*x + 3/2*c)^3 - 20*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3
*c)^2*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)
^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3
/2*d*x + 3/2*c))) + 4*(cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + 3*cos(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c)
+ (cos(3/2*d*x + 3/2*c)^2 + 6)*sin(3/2*d*x + 3/2*c) + 20*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*
x + 3/2*c)*sin(3*d*x + 3*c)^2 + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 2*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2
*c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)
+ cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 2*sin(3*d*x + 3*c)*sin(
3/2*d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 9*((cos(3/2*d*x + 3/2*c)^2 +
sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)
^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)
+ cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)
)))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*((sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x
+ 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c)^2 + 2*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3
*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x +
3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*(cos(3*d*x
+ 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x +
3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), c
os(3/2*d*x + 3/2*c)))^2 + (sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*sin(3*d
*x + 3*c)^2 + sin(3/2*d*x + 3/2*c)^3 + 24*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/
2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*(2*sin(3/2*d*x + 3/2*c)^3 + 7*
sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c) + (2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*c
os(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*
d*x + 3/2*c) + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3
*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arct
an2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3
*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*
x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x
+ 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c
) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7
/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2
*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*
x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + s
in(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(
3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*
d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3
*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/
2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 20*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(
3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - 2*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(4/3*
arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x
+ 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - 2*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2
*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/
2*c)^2 + cos(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2 + 6)*sin(3/2*d*x + 3/2*c) + 6*((2*si
n(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d
*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(
3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d
*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x
+ 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*
c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(
5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 20*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3
/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*
x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c
), cos(3/2*d*x + 3/2*c))) - 9*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + (cos(3/2
*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2
*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*s
in(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c)))^2 + 16*((sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3
*c)^2 + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x +
3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin
(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d
*x + 3/2*c))*sin(3*d*x + 3*c)^2 + sin(3/2*d*x + 3/2*c)^3 - 2*(2*sin(3/2*d*x + 3/2*c)^3 + 7*sin(3/2*d*x + 3/2*c
))*cos(3*d*x + 3*c) + 2*(2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*
c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*
(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(s
in(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(
3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*
sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*ar
ctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)
)) - 20*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3
/2*c)*sin(3*d*x + 3*c) - 2*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/
2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*co
s(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - 2*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3
/2*c), cos(3/2*d*x + 3/2*c))) + 2*(2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c))*sin(3
*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2 + 6)*sin(3/2*d*x + 3/2*c) + 20*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)
+ cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(c
os(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))) - 9*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + (
cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*
sin(3/2*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*
c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(
3/2*d*x + 3/2*c)))^2 + 4*(32*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c
) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*
cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^3
+ 12*(2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c
)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*(sin(3/2*d*x + 3/2
*c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c
), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c),
cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2
+ cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(2*cos(3*
d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x
+ 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x +
3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan
2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) +
2*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan
2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(s
in(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*
c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3
*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2
*c)))^2 + 2*(cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c))*sin
(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c) + 4*(4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + (sin
(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c)^2 + (sin(3/2*d*x + 3
/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c)^2 + sin(3/2*d*x + 3/2*c)^3 - 20*
(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(3/2*d*
x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d
*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(cos(3/2*d*x + 3/2*c)*sin(3/2*d*
x + 3/2*c)^2 + 3*cos(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2 + 6)*sin(3/2*d*x + 3/2*c) +
20*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + 2*cos(3*d*x + 3*c)*cos
(3/2*d*x + 3/2*c) + 2*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c))) + 7*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + 2*cos(3*d
*x + 3*c)*cos(3/2*d*x + 3/2*c) + 2*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c)
, cos(3/2*d*x + 3/2*c))) - 9*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*d
*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*co
s(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*si
n(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c))) - 40*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3
/2*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 14*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2
*c)*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(
3/2*d*x + 3/2*c))) + 2*(sin(3/2*d*x + 3/2*c)^4 + (cos(3/2*d*x + 3/2*c)^2 + 4)*sin(3/2*d*x + 3/2*c)^2 + 3*cos(3
/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c) + 2*(cos(3/2*d*x + 3/2*c)^3 + 6*cos(3/2*d*x + 3/2*c))*sin(3/2*d*x + 3/2*c)
- 4*(18*(cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*
c), cos(3/2*d*x + 3/2*c))) + 5*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) - 2*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3
*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*si
n(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*
c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^
2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c)
+ sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d
*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c
), cos(3/2*d*x + 3/2*c))) + 20*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))
*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin
(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - (2*sin(3/2*
d*x + 3/2*c)^3 + (2*cos(3/2*d*x + 3/2*c)^2 + 7)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) - 20*(cos(3/2*d*x + 3/2
*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*
x + 3/2*c))) - 7*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(2/3*arcta
n2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
+ 20*(2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)
+ cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)
)) + 7*(2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*
c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*
c))) - 18*(cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^3 + co
s(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + s
in(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3
*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^3 + 2*(
cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c))*sin(3/2*d*x + 3/
2*c))*cos(3*d*x + 3*c) - 40*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin
(3/2*d*x + 3/2*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 14*(cos(3*d*x + 3*c)*cos(3
/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2)*cos(2/3*arctan2(sin(3/2*d*x +
3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(sin(3/2*d*x + 3/2*c)^4 + (cos(3/2*d*x + 3/2*c)^2 + 4)*sin(3/2*d*x + 3/2*c)
^2 + 3*cos(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c) + 2*(cos(3/2*d*x + 3/2*c)^3 + 6*cos(3/2*d*x + 3/2*c))*sin(3/2*
d*x + 3/2*c) + 20*(2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2
*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2
*d*x + 3/2*c))) + 7*(2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3
/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3
/2*d*x + 3/2*c))) - 18*(cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x +
3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x
+ 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*
c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 80*(cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x +
3/2*c) + sin(3/2*d*x + 3/2*c)^3)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 28*(cos(3/2*d*
x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c))) + 33*((cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c)))^4 + 16*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c)))^4 + (cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/
2*c)))^4 + 16*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/
2*c)))^4 + cos(3/2*d*x + 3/2*c)^4 + 2*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*
x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arcta
n2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(7/3*arctan2(sin(3
/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 16*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)
*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*a
rctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 2*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c)^2 + sin(
3/2*d*x + 3/2*c)^4 + 2*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + co
s(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*
x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c)
, cos(3/2*d*x + 3/2*c)))^3 + 16*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/
2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*
d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + ((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2
+ 4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 24*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(si
n(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3
*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 8*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c
)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + cos(3/2*d*x + 3/2*c)^2 + 12*(cos(3*d*x +
3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)
+ sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3
/2*d*x + 3/2*c)^2 + 4*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos
(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*
c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*((cos(3/2*d*x +
3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + (cos(3/2*
d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*
d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*
d*x + 3/2*c)))^2 + ((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 2*(cos(3*d*x + 3*c)
^2 + sin(3*d*x + 3*c)^2)*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*(cos(3*d*x + 3*c)^
2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)
^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)
- 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + 24*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(si
n(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + cos(3/2*d*x + 3/2*c)^2 + 2*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/
2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2
+ sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3*d*x + 3*c)*sin(3/2
*d*x + 3/2*c))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(cos(3*d*x + 3*c)^2*cos(3/2*d*
x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c
)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3/2*d*x + 3/2*c)^2
+ 12*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)
*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*((cos(3/2*d*x + 3/2*c)^2 + sin(3
/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 8*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*
x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 +
4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos
(3/2*d*x + 3/2*c)^2 + 4*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + c
os(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/
2*c), cos(3/2*d*x + 3/2*c))) + sin(3/2*d*x + 3/2*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2
*c)))^2 + 2*(16*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c)))^3 + cos(3/2*d*x + 3/2*c)^3 + 12*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3
*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2
(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + 4*(cos(3*d*x +
3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)
+ 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) +
sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3
/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + 2*((cos(3/2*d*x + 3/2*c)^2
+ sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2
*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2
*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2
*c))) + (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c) + 4*(2*(cos(3*
d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x +
3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) +
(cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(
3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(cos(3/2*d*x + 3/2*c)^3 +
cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/
2*c)^2)*cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x +
3*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(16*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3
*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + (cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*
c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/
2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(cos(3*d*x + 3*c)^2*sin(3/2*d*
x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c
)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(cos(3/2*d*x + 3/2*
c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3*d*x + 3*c) +
cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3 + 12*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3
/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin
(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - (cos(3/2*d*x + 3/2*c)^2*si
n(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*cos(3*d*x + 3*c) + 2*(2*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c)
+ sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d
*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*
d*x + 3/2*c)^2)*sin(3*d*x + 3*c) + 2*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x
+ 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan
2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/
2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (cos(3/
2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c) + 2*((cos(3/2*d*x + 3/2*c)^2
+ sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 8*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin
(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*
c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^
2 + cos(3/2*d*x + 3/2*c)^2 + 4*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c
)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d
*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3/2*d*x + 3/2*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*
x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(4*(cos(3*d*x + 3*c)^2*sin(3/2*
d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3
*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(cos(3/2*d*x + 3/
2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3*d*x + 3*c)
+ cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3 - (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x
+ 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d
*x + 3/2*c)^2)*sin(3*d*x + 3*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*log(cos(1/3*arc
tan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*
c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 33*((cos(3*d*x + 3*c)^2 + sin(3
*d*x + 3*c)^2)*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 16*(cos(3*d*x + 3*c)^2 + sin(3
*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + (cos(3*d*x + 3*c)^2 + sin(3*d*
x + 3*c)^2)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 16*(cos(3*d*x + 3*c)^2 + sin(3*d*
x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + cos(3/2*d*x + 3/2*c)^4 + 2*(cos(3
*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x +
3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c
))) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 +
16*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3
/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3
/2*c)))^3 + 2*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^4 + 2*(cos(3*d*x + 3*c)^2*s
in(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*
d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/
2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 16*(cos(3*d*x +
3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)
- cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + ((c
os(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2
+ 24*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2
+ (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3
*c)*sin(3/2*d*x + 3/2*c) + 8*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), c
os(3/2*d*x + 3/2*c)))^2 + cos(3/2*d*x + 3/2*c)^2 + 12*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x +
3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*co
s(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3/2*d*x + 3/2*c)^2 + 4*(cos(3*d*x + 3*c)^2*si
n(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d
*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(
sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*
x + 3*c)^2 + 4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin
(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(
3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + ((cos(3/2*d*x + 3/2*c)^2
+ sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 2*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(7/3*arctan2(sin
(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(
3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c
)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2
+ 24*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2
+ cos(3/2*d*x + 3/2*c)^2 + 2*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)
^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3
/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(7/3*arctan2(sin(3/2*d*x +
3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x
+ 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(
3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3/2*d*x + 3/2*c)^2 + 12*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c
) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2
*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2
*c), cos(3/2*d*x + 3/2*c)))^2 + 4*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 8*(c
os(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(
3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(
3/2*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + 4*(cos(3*d*x + 3*c)^2*
cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3
*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3/2*d*x +
3/2*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(16*(cos(3*d*x + 3*c)^2 + sin(3*
d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + cos(3/2*d*x + 3/2*c)^3 + 12*(co
s(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x
+ 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))
)^2 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + 4*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x +
3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^
2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5
/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin
(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + 2*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^
2 + 4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x +
3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x +
3/2*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x
+ 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c) + 4*(2*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*
x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c
))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*
c)^2)*sin(3*d*x + 3*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*
d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2
+ (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/
2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c),
cos(3/2*d*x + 3/2*c))) + 2*(16*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c),
cos(3/2*d*x + 3/2*c)))^3 + (cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c)
+ cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin
(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3
/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x
+ 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(
3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arcta
n2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3*d*x + 3*c) + cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c)
+ sin(3/2*d*x + 3/2*c)^3 + 12*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2
*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d
*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)
*cos(3*d*x + 3*c) + 2*(2*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) +
cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3
/2*c), cos(3/2*d*x + 3/2*c))) + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c) + 2*(cos(3*
d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3
/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)
)) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(
7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(
3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c) + 2*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2
+ 8*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2
+ (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*
c)*sin(3/2*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + 4*(cos(3*d*x +
3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)
+ sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3/
2*d*x + 3/2*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x +
3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(4*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*
x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(si
n(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arc
tan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3*d*x + 3*c) + cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*
c) + sin(3/2*d*x + 3/2*c)^3 - (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*cos(3*d*x
+ 3*c) + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c))*sin(5/3*arc
tan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2
*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2
*c), cos(3/2*d*x + 3/2*c))) + 1) + 4*(cos(3/2*d*x + 3/2*c)^4 + 7*cos(3/2*d*x + 3/2*c)^2)*sin(3/2*d*x + 3/2*c)
+ 4*(2*sin(3/2*d*x + 3/2*c)^4 + 32*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x +
3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*
c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + ((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d
*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(
3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)
^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)
*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + s
in(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d
*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*
d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x +
3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*c
os(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x +
3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d
*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*c
os(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(
2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3
*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/
2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(
3/2*d*x + 3/2*c)))^2 + (2*cos(3/2*d*x + 3/2*c)^2 + 13)*sin(3/2*d*x + 3/2*c)^2 + 12*((2*sin(3/2*d*x + 3/2*c)^2
+ 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x
+ 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(
3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d
*x + 3*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x
+ 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)
*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d
*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*(sin(3/2*d*x + 3/2*c)^4 + (cos(3/2*d*x + 3/2*c)^2 + 4)*sin(3/2*d*x +
3/2*c)^2 + 3*cos(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + cos(3/2*d*x + 3/2*c)^2 - 2*(18*(cos(3/2*d*x + 3/2*c)^
2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 5*
cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) - 2*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d*x
+ 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2
*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3/2*d
*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(2/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*
x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(si
n(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 20*
(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(3/2*d*x +
3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2
*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - (2*sin(3/2*d*x + 3/2*c)^3 + (2*cos(3/2*d*x
+ 3/2*c)^2 + 7)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) - 2*(2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2
*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*
x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x
+ 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2
*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x
+ 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2
*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)
)) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*
cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*
x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 20*(cos(3/2*d*x + 3/2*c)*sin(3*d*
x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
- 7*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d
*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 4*(18*(cos
(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d
*x + 3/2*c))) + 5*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 20*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*
x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3
*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/
2*d*x + 3/2*c))) - (2*sin(3/2*d*x + 3/2*c)^3 + (2*cos(3/2*d*x + 3/2*c)^2 + 7)*sin(3/2*d*x + 3/2*c))*sin(3*d*x
+ 3*c) - 20*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(si
n(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3
/2*d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3
/2*c), cos(3/2*d*x + 3/2*c))) - 20*(2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*cos(3*d*x
+ 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(4/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*cos(3*d
*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(2/3*arctan2(sin(3/2*d*
x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^3
+ cos(3/2*d*x + 3/2*c))*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + 4*((sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3
/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c)^2 + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x
+ 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2
*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sin(3/2*d*x + 3
/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c)^2 + sin(3/2*d*x + 3/2*c)^3 - 2*(
2*sin(3/2*d*x + 3/2*c)^3 + 7*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c) + 2*(2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/
2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c
)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x
+ 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3
*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c
)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + s
in(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*ar
ctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 20*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x +
3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - 2*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*
c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c)
+ sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - 2*cos(3*d*x + 3*c)*sin(3
/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(2*cos(3/2*d*x + 3/2*c)*sin(
3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2 + 6)*sin(3/2*d*x + 3/2*c
) + 20*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin
(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*
sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 9*((cos(3/2*d*x + 3/2*c)^2
+ sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3
*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)
^2 + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*
c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 40*(cos(3/2*d*x + 3/2*c)^2*sin(3*d*x + 3*
c) - cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2
*d*x + 3/2*c))) + 14*(cos(3/2*d*x + 3/2*c)^2*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*
d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3/2*d*x + 3/2*c)^2*sin(3/
2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3 - (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^
3)*cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c))
*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d
*x + 3/2*c))) + 8*(2*sin(3/2*d*x + 3/2*c)^4 + 4*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/
2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(s
in(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(sin
(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(2/3*arctan2(sin(3/
2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(
3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arct
an2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
^2 + (2*cos(3/2*d*x + 3/2*c)^2 + 13)*sin(3/2*d*x + 3/2*c)^2 - 2*(sin(3/2*d*x + 3/2*c)^4 + (cos(3/2*d*x + 3/2*c
)^2 + 4)*sin(3/2*d*x + 3/2*c)^2 + 3*cos(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + cos(3/2*d*x + 3/2*c)^2 - 4*(18*
(cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3
/2*d*x + 3/2*c))) + 5*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 20*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(
3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x
+ 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), co
s(3/2*d*x + 3/2*c))) - (2*sin(3/2*d*x + 3/2*c)^3 + (2*cos(3/2*d*x + 3/2*c)^2 + 7)*sin(3/2*d*x + 3/2*c))*sin(3*
d*x + 3*c) - 20*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan
2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*s
in(3/2*d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))) - 20*(2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*cos(3
*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(4/3*arctan2(sin(3/2*
d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*cos
(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(2/3*arctan2(sin(3/
2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c
)^3 + cos(3/2*d*x + 3/2*c))*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + 40*(cos(3/2*d*x + 3/2*c)^2*sin(3*d*x + 3*
c) - cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2
*d*x + 3/2*c))) + 14*(cos(3/2*d*x + 3/2*c)^2*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*
d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3/2*d*x + 3/2*c)^2*sin(3/
2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3 - (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^
3)*cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c))
*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d
*x + 3/2*c))) + 80*(cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(4/3*arctan2(sin(
3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 28*(cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2
*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 36*(cos(3/2*d*x + 3/2*c)^4 + 2*cos(3/2*d
*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^4)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d
*x + 3/2*c))))/((sqrt(2)*a*cos(3/2*d*x + 3/2*c)^4 + 2*sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c)^2
+ sqrt(2)*a*sin(3/2*d*x + 3/2*c)^4 + (sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(7/3*arc
tan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 16*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x +
3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + (sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt
(2)*a*sin(3*d*x + 3*c)^2)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 16*(sqrt(2)*a*cos(3
*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 +
2*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + sq
rt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(sqrt(2)*a
*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)
)))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 16*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*
d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/
2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/
2*c)))^3 + 2*(sqrt(2)*a*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3
/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*
(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*
x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 16*(sqrt(2)*a*cos(3*d*x + 3*c)^
2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*si
n(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/
2*d*x + 3/2*c)))^3 + (4*sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 4*sqrt(2)*a*cos(3/2*d*x + 3/2*c)*s
in(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2 + (
sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 24*(sqrt(2)*a*cos(3*
d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 +
(sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 8*(sqrt(2)*a*cos(3*
d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 +
12*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + sq
rt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arcta
n2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(
2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*cos
(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arct
an2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(4*sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 +
4*sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sq
rt(2)*a*sin(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*cos(3*d
*x + 3*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2)*cos(5/
3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (4*sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*
sin(3/2*d*x + 3/2*c) - 4*sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2
+ sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*cos
(3*d*x + 3*c)^2 + 2*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(7/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*a
rctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*
d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 24*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*sin(5/3*
arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)
+ sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2
)*a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*co
s(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c))) + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x +
3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*c
os(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(sqrt(2)*a*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3
/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) -
sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))
*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(4*sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*
x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*cos(3/2*d*x +
3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*
c)^2)*cos(3*d*x + 3*c)^2 + 8*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin
(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*
c)^2)*sin(3*d*x + 3*c)^2 + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*
c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d
*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c
), cos(3/2*d*x + 3/2*c)))^2 + 2*(sqrt(2)*a*cos(3/2*d*x + 3/2*c)^3 + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x
+ 3/2*c)^2 + 16*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3
/2*c), cos(3/2*d*x + 3/2*c)))^3 + 12*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*
x + 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*s
in(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(sqrt(2)*a*cos(3*d*x +
3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*
cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqr
t(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3
/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^3 + sqrt(2)*a*cos(3/2*d*x + 3/2*c)
*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + 2*(4*sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 4*sqrt(2)
*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*s
in(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)
^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2
(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(
2)*a*sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c) + 4*(2*(sqrt(2)*a*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt
(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*co
s(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (sqrt(2)*a
*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/
2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(sqrt(2)*a*cos(
3/2*d*x + 3/2*c)^3 + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^3
+ sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2
*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*
c), cos(3/2*d*x + 3/2*c))) + 2*(sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3/2*d*x
+ 3/2*c)^3 + 16*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/
2*c), cos(3/2*d*x + 3/2*c)))^3 + (sqrt(2)*a*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*
c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3
/2*d*x + 3/2*c) + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(sqrt(2)*
a*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(
3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d
*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2
)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3*d*x + 3*c) + 12*(sqrt(2)*a*cos(3*d*x + 3*
c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)
*sin(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos
(3/2*d*x + 3/2*c)))^2 - (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3/2*d*x + 3/2*c
)^3)*cos(3*d*x + 3*c) + 2*(2*(sqrt(2)*a*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2
*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d
*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2
+ sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c) + 2*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) +
sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*
a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(
5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^3 + s
qrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c) + 2*(4*sqrt(2)*a*cos(3/2*d*x + 3/2*c)*s
in(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*cos(3/2
*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x
+ 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 8*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arct
an2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x
+ 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x
+ 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*si
n(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(sqrt(2)*a*
cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^3 + 4*(sqrt(2)*a*cos(3*d*x + 3*c)
^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*s
in(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3
/2*d*x + 3/2*c)))^2 + 4*(sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(
sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3*d*x + 3*c) - (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x
+ 3/2*c) + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^3)*cos(3*d*x + 3*c) + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^3 + sqrt(2)*a*
cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d
*x + 3/2*c))))*sqrt(a)*d)

Giac [F]

\[ \int \frac {\cos ^{\frac {3}{2}}(c+d x)}{(a+a \sec (c+d x))^{3/2}} \, dx=\int { \frac {\cos \left (d x + c\right )^{\frac {3}{2}}}{{\left (a \sec \left (d x + c\right ) + a\right )}^{\frac {3}{2}}} \,d x } \]

[In]

integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm="giac")

[Out]

integrate(cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(3/2), x)

Mupad [F(-1)]

Timed out. \[ \int \frac {\cos ^{\frac {3}{2}}(c+d x)}{(a+a \sec (c+d x))^{3/2}} \, dx=\int \frac {{\cos \left (c+d\,x\right )}^{3/2}}{{\left (a+\frac {a}{\cos \left (c+d\,x\right )}\right )}^{3/2}} \,d x \]

[In]

int(cos(c + d*x)^(3/2)/(a + a/cos(c + d*x))^(3/2),x)

[Out]

int(cos(c + d*x)^(3/2)/(a + a/cos(c + d*x))^(3/2), x)