\(\int \frac {\cos ^{\frac {3}{2}}(c+d x) (A+C \sec ^2(c+d x))}{(a+a \sec (c+d x))^{3/2}} \, dx\) [1162]

Optimal result

Integrand size = 37, antiderivative size = 221 \[ \int \frac {\cos ^{\frac {3}{2}}(c+d x) \left (A+C \sec ^2(c+d x)\right )}{(a+a \sec (c+d x))^{3/2}} \, dx=\frac {(11 A+3 C) \text {arctanh}\left (\frac {\sqrt {a} \sqrt {\sec (c+d x)} \sin (c+d x)}{\sqrt {2} \sqrt {a+a \sec (c+d x)}}\right ) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}}{2 \sqrt {2} a^{3/2} d}-\frac {(A+C) \sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}-\frac {(19 A+3 C) \sin (c+d x)}{6 a d \sqrt {\cos (c+d x)} \sqrt {a+a \sec (c+d x)}}+\frac {(7 A+3 C) \sqrt {\cos (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}} \]

[Out]

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

Rubi [A] (verified)

Time = 0.80 (sec) , antiderivative size = 221, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.162, Rules used = {4350, 4170, 4107, 4098, 3893, 212} \[ \int \frac {\cos ^{\frac {3}{2}}(c+d x) \left (A+C \sec ^2(c+d x)\right )}{(a+a \sec (c+d x))^{3/2}} \, dx=\frac {(11 A+3 C) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)} \text {arctanh}\left (\frac {\sqrt {a} \sin (c+d x) \sqrt {\sec (c+d x)}}{\sqrt {2} \sqrt {a \sec (c+d x)+a}}\right )}{2 \sqrt {2} a^{3/2} d}+\frac {(7 A+3 C) \sin (c+d x) \sqrt {\cos (c+d x)}}{6 a d \sqrt {a \sec (c+d x)+a}}-\frac {(19 A+3 C) \sin (c+d x)}{6 a d \sqrt {\cos (c+d x)} \sqrt {a \sec (c+d x)+a}}-\frac {(A+C) \sin (c+d x) \sqrt {\cos (c+d x)}}{2 d (a \sec (c+d x)+a)^{3/2}} \]

[In]

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

[Out]

((11*A + 3*C)*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]]*Sqrt[Sec[c + d*x]])/(2*Sqrt[2]*a^(3/2)*d) - ((A + C)*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(2*d*(a + a*Sec
[c + d*x])^(3/2)) - ((19*A + 3*C)*Sin[c + d*x])/(6*a*d*Sqrt[Cos[c + d*x]]*Sqrt[a + a*Sec[c + d*x]]) + ((7*A +
3*C)*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 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 4170

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

Rule 4350

Int[(cos[(a_.) + (b_.)*(x_)]*(c_.))^(m_.)*(u_), x_Symbol] :> Dist[(c*Cos[a + b*x])^m*(c*Sec[a + b*x])^m, Int[A
ctivateTrig[u]/(c*Sec[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 {A+C \sec ^2(c+d x)}{\sec ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx \\ & = -\frac {(A+C) \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 {1}{2} a (7 A+3 C)+2 a A \sec (c+d x)}{\sec ^{\frac {3}{2}}(c+d x) \sqrt {a+a \sec (c+d x)}} \, dx}{2 a^2} \\ & = -\frac {(A+C) \sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}+\frac {(7 A+3 C) \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 {1}{4} a^2 (19 A+3 C)-\frac {1}{2} a^2 (7 A+3 C) \sec (c+d x)}{\sqrt {\sec (c+d x)} \sqrt {a+a \sec (c+d x)}} \, dx}{3 a^3} \\ & = -\frac {(A+C) \sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}-\frac {(19 A+3 C) \sin (c+d x)}{6 a d \sqrt {\cos (c+d x)} \sqrt {a+a \sec (c+d x)}}+\frac {(7 A+3 C) \sqrt {\cos (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}}+\frac {\left ((11 A+3 C) \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 {(A+C) \sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}-\frac {(19 A+3 C) \sin (c+d x)}{6 a d \sqrt {\cos (c+d x)} \sqrt {a+a \sec (c+d x)}}+\frac {(7 A+3 C) \sqrt {\cos (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}}-\frac {\left ((11 A+3 C) \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 A+3 C) \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 {(A+C) \sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}-\frac {(19 A+3 C) \sin (c+d x)}{6 a d \sqrt {\cos (c+d x)} \sqrt {a+a \sec (c+d x)}}+\frac {(7 A+3 C) \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 = 2.50 (sec) , antiderivative size = 163, normalized size of antiderivative = 0.74 \[ \int \frac {\cos ^{\frac {3}{2}}(c+d x) \left (A+C \sec ^2(c+d x)\right )}{(a+a \sec (c+d x))^{3/2}} \, dx=-\frac {\sqrt {\cos (c+d x)} \left (3 \sqrt {2} (11 A+3 C) \arctan \left (\frac {\sqrt {2} \sqrt {\sec (c+d x)}}{\sqrt {1-\sec (c+d x)}}\right ) \cos ^2\left (\frac {1}{2} (c+d x)\right ) \sec ^{\frac {5}{2}}(c+d x)+\sqrt {1-\sec (c+d x)} \left (-4 A+12 A \sec (c+d x)+(19 A+3 C) \sec ^2(c+d x)\right )\right ) \sin (c+d x)}{6 d \sqrt {1-\sec (c+d x)} (a (1+\sec (c+d x)))^{3/2}} \]

[In]

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

[Out]

-1/6*(Sqrt[Cos[c + d*x]]*(3*Sqrt[2]*(11*A + 3*C)*ArcTan[(Sqrt[2]*Sqrt[Sec[c + d*x]])/Sqrt[1 - Sec[c + d*x]]]*C
os[(c + d*x)/2]^2*Sec[c + d*x]^(5/2) + Sqrt[1 - Sec[c + d*x]]*(-4*A + 12*A*Sec[c + d*x] + (19*A + 3*C)*Sec[c +
d*x]^2))*Sin[c + d*x])/(d*Sqrt[1 - Sec[c + d*x]]*(a*(1 + Sec[c + d*x]))^(3/2))

Maple [A] (verified)

Time = 0.76 (sec) , antiderivative size = 340, normalized size of antiderivative = 1.54

method	result	size
default	\(\frac {\left (8 A \sin \left (d x +c \right ) \cos \left (d x +c \right )^{2} \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}-24 A \cos \left (d x +c \right ) \sin \left (d x +c \right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}-33 A \cos \left (d x +c \right ) \sqrt {2}\, \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (1+\cos \left (d x +c \right )\right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}}\right )-9 C \cos \left (d x +c \right ) \sqrt {2}\, \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (1+\cos \left (d x +c \right )\right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}}\right )-38 A \sin \left (d x +c \right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}-33 A \sqrt {2}\, \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (1+\cos \left (d x +c \right )\right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}}\right )-6 C \sin \left (d x +c \right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}-9 C \sqrt {2}\, \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (1+\cos \left (d x +c \right )\right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}}\right )\right ) \sqrt {\cos \left (d x +c \right )}\, \sqrt {a \left (1+\sec \left (d x +c \right )\right )}}{12 a^{2} d \left (1+\cos \left (d x +c \right )\right )^{2} \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}}\)	\(340\)

[In]

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

[Out]

1/12/a^2/d*(8*A*sin(d*x+c)*cos(d*x+c)^2*(-1/(1+cos(d*x+c)))^(1/2)-24*A*cos(d*x+c)*sin(d*x+c)*(-1/(1+cos(d*x+c)
))^(1/2)-33*A*cos(d*x+c)*2^(1/2)*arctan(1/2*sin(d*x+c)*2^(1/2)/(1+cos(d*x+c))/(-1/(1+cos(d*x+c)))^(1/2))-9*C*c
os(d*x+c)*2^(1/2)*arctan(1/2*sin(d*x+c)*2^(1/2)/(1+cos(d*x+c))/(-1/(1+cos(d*x+c)))^(1/2))-38*A*sin(d*x+c)*(-1/
(1+cos(d*x+c)))^(1/2)-33*A*2^(1/2)*arctan(1/2*sin(d*x+c)*2^(1/2)/(1+cos(d*x+c))/(-1/(1+cos(d*x+c)))^(1/2))-6*C
*sin(d*x+c)*(-1/(1+cos(d*x+c)))^(1/2)-9*C*2^(1/2)*arctan(1/2*sin(d*x+c)*2^(1/2)/(1+cos(d*x+c))/(-1/(1+cos(d*x+
c)))^(1/2)))*cos(d*x+c)^(1/2)*(a*(1+sec(d*x+c)))^(1/2)/(1+cos(d*x+c))^2/(-1/(1+cos(d*x+c)))^(1/2)

Fricas [A] (verification not implemented)

none

Time = 0.30 (sec) , antiderivative size = 434, normalized size of antiderivative = 1.96 \[ \int \frac {\cos ^{\frac {3}{2}}(c+d x) \left (A+C \sec ^2(c+d x)\right )}{(a+a \sec (c+d x))^{3/2}} \, dx=\left [\frac {3 \, \sqrt {2} {\left ({\left (11 \, A + 3 \, C\right )} \cos \left (d x + c\right )^{2} + 2 \, {\left (11 \, A + 3 \, C\right )} \cos \left (d x + c\right ) + 11 \, A + 3 \, C\right )} \sqrt {a} \log \left (-\frac {a \cos \left (d x + c\right )^{2} - 2 \, \sqrt {2} \sqrt {a} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sqrt {\cos \left (d x + c\right )} \sin \left (d x + c\right ) - 2 \, a \cos \left (d x + c\right ) - 3 \, a}{\cos \left (d x + c\right )^{2} + 2 \, \cos \left (d x + c\right ) + 1}\right ) + 4 \, {\left (4 \, A \cos \left (d x + c\right )^{2} - 12 \, A \cos \left (d x + c\right ) - 19 \, A - 3 \, C\right )} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sqrt {\cos \left (d x + c\right )} \sin \left (d x + c\right )}{24 \, {\left (a^{2} d \cos \left (d x + c\right )^{2} + 2 \, a^{2} d \cos \left (d x + c\right ) + a^{2} d\right )}}, -\frac {3 \, \sqrt {2} {\left ({\left (11 \, A + 3 \, C\right )} \cos \left (d x + c\right )^{2} + 2 \, {\left (11 \, A + 3 \, C\right )} \cos \left (d x + c\right ) + 11 \, A + 3 \, C\right )} \sqrt {-a} \arctan \left (\frac {\sqrt {2} \sqrt {-a} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sqrt {\cos \left (d x + c\right )}}{a \sin \left (d x + c\right )}\right ) - 2 \, {\left (4 \, A \cos \left (d x + c\right )^{2} - 12 \, A \cos \left (d x + c\right ) - 19 \, A - 3 \, C\right )} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sqrt {\cos \left (d x + c\right )} \sin \left (d x + c\right )}{12 \, {\left (a^{2} d \cos \left (d x + c\right )^{2} + 2 \, a^{2} d \cos \left (d x + c\right ) + a^{2} d\right )}}\right ] \]

[In]

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

[Out]

[1/24*(3*sqrt(2)*((11*A + 3*C)*cos(d*x + c)^2 + 2*(11*A + 3*C)*cos(d*x + c) + 11*A + 3*C)*sqrt(a)*log(-(a*cos(
d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*c
os(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*(4*A*cos(d*x + c)^2 - 12*A*cos(d*x + c) - 19*A -
3*C)*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*(3*sqrt(2)*((11*A + 3*C)*cos(d*x + c)^2 + 2*(11*A + 3*C)*cos(d*x + c) + 11*A + 3
*C)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c
))) - 2*(4*A*cos(d*x + c)^2 - 12*A*cos(d*x + c) - 19*A - 3*C)*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(-1)]

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

[In]

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

[Out]

Timed out

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 34992 vs. \(2 (186) = 372\).

Time = 0.93 (sec) , antiderivative size = 34992, normalized size of antiderivative = 158.33 \[ \int \frac {\cos ^{\frac {3}{2}}(c+d x) \left (A+C \sec ^2(c+d x)\right )}{(a+a \sec (c+d x))^{3/2}} \, dx=\text {Too large to display} \]

[In]

integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^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*
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)))^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),
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)))^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) +
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(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), c
os(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*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)))^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 + 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(si
n(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))*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) + 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*((co
s(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),
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 + 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*
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*arc
tan2(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 +
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))) - 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*s
in(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)*
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)))^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(si
n(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) + 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) + 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*c
os(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)))^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*arcta
n2(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*arcta
n2(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)))^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))*si
n(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) + (si
n(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)*co
s(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*c
os(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)*s
in(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)*s
in(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) + si
n(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*arct
an2(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 + c
os(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(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)*si
n(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*arct
an2(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*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + c
os(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(s
in(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) + 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))*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(s
in(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 + co
s(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*(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*arctan
2(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)*si
n(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*s
in(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*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))*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(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) - 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*ar
ctan2(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*
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))))*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(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),
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))*c
os(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*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))*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)*si
n(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(si
n(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*(
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)))^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*(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 + 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)*si
n(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 + si
n(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*arct
an2(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(s
in(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*ar
ctan2(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*ar
ctan2(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) +
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) + 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(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)*
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)))^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(s
in(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*(co
s(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(s
in(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) +
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*a
rctan2(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(si
n(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*(
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(si
n(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*arc
tan2(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), c
os(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*arcta
n2(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(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*co
s(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))))*A/((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*
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)*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 + s
qrt(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*co
s(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 +
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))))*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)
*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)))^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
)*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*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 +
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*ar
ctan2(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) + sq
rt(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*a
rctan2(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 +
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 + (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*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 + 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) + sqr
t(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))) + 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))) + 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
)*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*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(si
n(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*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*arct
an2(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) + sq
rt(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) + s
qrt(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))*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*c
os(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)*si
n(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*c
os(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)*c
os(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
+ 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) + 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 + 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 + 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))))*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
)*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), co
s(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*arcta
n2(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)) + 3*(3*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c
) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c)^2
+ 12*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1
/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 3*(log(cos(1/2*d*x + 1/2*c)^2
+ sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2
- 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 12*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 +
2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1
))*sin(d*x + c)^2 + 2*(6*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) -
log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*log(cos(1/
2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1
/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 2*sin(3/2*d*x + 3/2*c) + 2*sin(1/2*d*x + 1/2*c))*cos(2*d*x +
2*c) + 4*(3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*log(cos(1/2
*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 2*sin(1/2*d*x + 1/2*c))*cos(d*x + c)
+ 4*(3*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x +
1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + cos(3/2*d*x + 3/2*c) - cos(1/2
*d*x + 1/2*c))*sin(2*d*x + 2*c) - 4*(2*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) + 8*cos(3/2*d*x + 3/2*c)*sin(d*x
+ c) - 8*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/
2*d*x + 1/2*c) + 1) - 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 4*
sin(1/2*d*x + 1/2*c))*C/((sqrt(2)*a*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*a*cos(d*x + c)^2 + sqrt(2)*a*sin(2*d*x + 2*
c)^2 + 4*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 4*sqrt(2)*a*sin(d*x + c)^2 + 4*sqrt(2)*a*cos(d*x + c) + 2*(
2*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + sqrt(2)*a)*sqrt(a)))/d

Giac [F]

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

[In]

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

[Out]

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

Mupad [F(-1)]

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

[In]

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

[Out]

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