\(\int \cos ^{\frac {3}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} (A+C \cos ^2(c+d x)) \, dx\) [188]

Optimal result

Integrand size = 37, antiderivative size = 312 \[ \int \cos ^{\frac {3}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \left (A+C \cos ^2(c+d x)\right ) \, dx=\frac {a^{5/2} (1304 A+1015 C) \arcsin \left (\frac {\sqrt {a} \sin (c+d x)}{\sqrt {a+a \cos (c+d x)}}\right )}{512 d}+\frac {a^3 (1304 A+1015 C) \sqrt {\cos (c+d x)} \sin (c+d x)}{512 d \sqrt {a+a \cos (c+d x)}}+\frac {a^3 (1304 A+1015 C) \cos ^{\frac {3}{2}}(c+d x) \sin (c+d x)}{768 d \sqrt {a+a \cos (c+d x)}}+\frac {a^3 (136 A+109 C) \cos ^{\frac {5}{2}}(c+d x) \sin (c+d x)}{192 d \sqrt {a+a \cos (c+d x)}}+\frac {a^2 (24 A+23 C) \cos ^{\frac {5}{2}}(c+d x) \sqrt {a+a \cos (c+d x)} \sin (c+d x)}{96 d}+\frac {a C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{3/2} \sin (c+d x)}{12 d}+\frac {C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \sin (c+d x)}{6 d} \]

[Out]

1/512*a^(5/2)*(1304*A+1015*C)*arcsin(sin(d*x+c)*a^(1/2)/(a+a*cos(d*x+c))^(1/2))/d+1/12*a*C*cos(d*x+c)^(5/2)*(a
+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+1/6*C*cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d+1/768*a^3*(1304*A
+1015*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(1/2)+1/192*a^3*(136*A+109*C)*cos(d*x+c)^(5/2)*sin(d*x
+c)/d/(a+a*cos(d*x+c))^(1/2)+1/512*a^3*(1304*A+1015*C)*sin(d*x+c)*cos(d*x+c)^(1/2)/d/(a+a*cos(d*x+c))^(1/2)+1/
96*a^2*(24*A+23*C)*cos(d*x+c)^(5/2)*sin(d*x+c)*(a+a*cos(d*x+c))^(1/2)/d

Rubi [A] (verified)

Time = 1.07 (sec) , antiderivative size = 312, normalized size of antiderivative = 1.00, number of steps used = 8, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.162, Rules used = {3125, 3055, 3060, 2849, 2853, 222} \[ \int \cos ^{\frac {3}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \left (A+C \cos ^2(c+d x)\right ) \, dx=\frac {a^{5/2} (1304 A+1015 C) \arcsin \left (\frac {\sqrt {a} \sin (c+d x)}{\sqrt {a \cos (c+d x)+a}}\right )}{512 d}+\frac {a^3 (136 A+109 C) \sin (c+d x) \cos ^{\frac {5}{2}}(c+d x)}{192 d \sqrt {a \cos (c+d x)+a}}+\frac {a^3 (1304 A+1015 C) \sin (c+d x) \cos ^{\frac {3}{2}}(c+d x)}{768 d \sqrt {a \cos (c+d x)+a}}+\frac {a^3 (1304 A+1015 C) \sin (c+d x) \sqrt {\cos (c+d x)}}{512 d \sqrt {a \cos (c+d x)+a}}+\frac {a^2 (24 A+23 C) \sin (c+d x) \cos ^{\frac {5}{2}}(c+d x) \sqrt {a \cos (c+d x)+a}}{96 d}+\frac {a C \sin (c+d x) \cos ^{\frac {5}{2}}(c+d x) (a \cos (c+d x)+a)^{3/2}}{12 d}+\frac {C \sin (c+d x) \cos ^{\frac {5}{2}}(c+d x) (a \cos (c+d x)+a)^{5/2}}{6 d} \]

[In]

Int[Cos[c + d*x]^(3/2)*(a + a*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2),x]

[Out]

(a^(5/2)*(1304*A + 1015*C)*ArcSin[(Sqrt[a]*Sin[c + d*x])/Sqrt[a + a*Cos[c + d*x]]])/(512*d) + (a^3*(1304*A + 1
015*C)*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(512*d*Sqrt[a + a*Cos[c + d*x]]) + (a^3*(1304*A + 1015*C)*Cos[c + d*x]
^(3/2)*Sin[c + d*x])/(768*d*Sqrt[a + a*Cos[c + d*x]]) + (a^3*(136*A + 109*C)*Cos[c + d*x]^(5/2)*Sin[c + d*x])/
(192*d*Sqrt[a + a*Cos[c + d*x]]) + (a^2*(24*A + 23*C)*Cos[c + d*x]^(5/2)*Sqrt[a + a*Cos[c + d*x]]*Sin[c + d*x]
)/(96*d) + (a*C*Cos[c + d*x]^(5/2)*(a + a*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(12*d) + (C*Cos[c + d*x]^(5/2)*(a
+ a*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(6*d)

Rule 222

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

Rule 2849

Int[Sqrt[(a_) + (b_.)*sin[(e_.) + (f_.)*(x_)]]*((c_.) + (d_.)*sin[(e_.) + (f_.)*(x_)])^(n_), x_Symbol] :> Simp
[-2*b*Cos[e + f*x]*((c + d*Sin[e + f*x])^n/(f*(2*n + 1)*Sqrt[a + b*Sin[e + f*x]])), x] + Dist[2*n*((b*c + a*d)
/(b*(2*n + 1))), Int[Sqrt[a + b*Sin[e + f*x]]*(c + d*Sin[e + f*x])^(n - 1), x], x] /; FreeQ[{a, b, c, d, e, f}
, x] && NeQ[b*c - a*d, 0] && EqQ[a^2 - b^2, 0] && NeQ[c^2 - d^2, 0] && GtQ[n, 0] && IntegerQ[2*n]

Rule 2853

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

Rule 3055

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

Rule 3060

Int[Sqrt[(a_) + (b_.)*sin[(e_.) + (f_.)*(x_)]]*((A_.) + (B_.)*sin[(e_.) + (f_.)*(x_)])*((c_.) + (d_.)*sin[(e_.
) + (f_.)*(x_)])^(n_), x_Symbol] :> Simp[-2*b*B*Cos[e + f*x]*((c + d*Sin[e + f*x])^(n + 1)/(d*f*(2*n + 3)*Sqrt
[a + b*Sin[e + f*x]])), x] + Dist[(A*b*d*(2*n + 3) - B*(b*c - 2*a*d*(n + 1)))/(b*d*(2*n + 3)), Int[Sqrt[a + b*
Sin[e + f*x]]*(c + d*Sin[e + f*x])^n, x], x] /; FreeQ[{a, b, c, d, e, f, A, B, n}, x] && NeQ[b*c - a*d, 0] &&
EqQ[a^2 - b^2, 0] && NeQ[c^2 - d^2, 0] &&  !LtQ[n, -1]

Rule 3125

Int[((a_) + (b_.)*sin[(e_.) + (f_.)*(x_)])^(m_.)*((c_.) + (d_.)*sin[(e_.) + (f_.)*(x_)])^(n_.)*((A_.) + (C_.)*
sin[(e_.) + (f_.)*(x_)]^2), x_Symbol] :> Simp[(-C)*Cos[e + f*x]*(a + b*Sin[e + f*x])^m*((c + d*Sin[e + f*x])^(
n + 1)/(d*f*(m + n + 2))), x] + Dist[1/(b*d*(m + n + 2)), Int[(a + b*Sin[e + f*x])^m*(c + d*Sin[e + f*x])^n*Si
mp[A*b*d*(m + n + 2) + C*(a*c*m + b*d*(n + 1)) + C*(a*d*m - b*c*(m + 1))*Sin[e + f*x], x], x], x] /; FreeQ[{a,
b, c, d, e, f, A, C, m, n}, x] && NeQ[b*c - a*d, 0] && EqQ[a^2 - b^2, 0] && NeQ[c^2 - d^2, 0] &&  !LtQ[m, -2^
(-1)] && NeQ[m + n + 2, 0]

Rubi steps \begin{align*} \text {integral}& = \frac {C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \sin (c+d x)}{6 d}+\frac {\int \cos ^{\frac {3}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \left (\frac {1}{2} a (12 A+5 C)+\frac {5}{2} a C \cos (c+d x)\right ) \, dx}{6 a} \\ & = \frac {a C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{3/2} \sin (c+d x)}{12 d}+\frac {C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \sin (c+d x)}{6 d}+\frac {\int \cos ^{\frac {3}{2}}(c+d x) (a+a \cos (c+d x))^{3/2} \left (\frac {15}{4} a^2 (8 A+5 C)+\frac {5}{4} a^2 (24 A+23 C) \cos (c+d x)\right ) \, dx}{30 a} \\ & = \frac {a^2 (24 A+23 C) \cos ^{\frac {5}{2}}(c+d x) \sqrt {a+a \cos (c+d x)} \sin (c+d x)}{96 d}+\frac {a C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{3/2} \sin (c+d x)}{12 d}+\frac {C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \sin (c+d x)}{6 d}+\frac {\int \cos ^{\frac {3}{2}}(c+d x) \sqrt {a+a \cos (c+d x)} \left (\frac {5}{8} a^3 (312 A+235 C)+\frac {15}{8} a^3 (136 A+109 C) \cos (c+d x)\right ) \, dx}{120 a} \\ & = \frac {a^3 (136 A+109 C) \cos ^{\frac {5}{2}}(c+d x) \sin (c+d x)}{192 d \sqrt {a+a \cos (c+d x)}}+\frac {a^2 (24 A+23 C) \cos ^{\frac {5}{2}}(c+d x) \sqrt {a+a \cos (c+d x)} \sin (c+d x)}{96 d}+\frac {a C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{3/2} \sin (c+d x)}{12 d}+\frac {C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \sin (c+d x)}{6 d}+\frac {1}{384} \left (a^2 (1304 A+1015 C)\right ) \int \cos ^{\frac {3}{2}}(c+d x) \sqrt {a+a \cos (c+d x)} \, dx \\ & = \frac {a^3 (1304 A+1015 C) \cos ^{\frac {3}{2}}(c+d x) \sin (c+d x)}{768 d \sqrt {a+a \cos (c+d x)}}+\frac {a^3 (136 A+109 C) \cos ^{\frac {5}{2}}(c+d x) \sin (c+d x)}{192 d \sqrt {a+a \cos (c+d x)}}+\frac {a^2 (24 A+23 C) \cos ^{\frac {5}{2}}(c+d x) \sqrt {a+a \cos (c+d x)} \sin (c+d x)}{96 d}+\frac {a C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{3/2} \sin (c+d x)}{12 d}+\frac {C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \sin (c+d x)}{6 d}+\frac {1}{512} \left (a^2 (1304 A+1015 C)\right ) \int \sqrt {\cos (c+d x)} \sqrt {a+a \cos (c+d x)} \, dx \\ & = \frac {a^3 (1304 A+1015 C) \sqrt {\cos (c+d x)} \sin (c+d x)}{512 d \sqrt {a+a \cos (c+d x)}}+\frac {a^3 (1304 A+1015 C) \cos ^{\frac {3}{2}}(c+d x) \sin (c+d x)}{768 d \sqrt {a+a \cos (c+d x)}}+\frac {a^3 (136 A+109 C) \cos ^{\frac {5}{2}}(c+d x) \sin (c+d x)}{192 d \sqrt {a+a \cos (c+d x)}}+\frac {a^2 (24 A+23 C) \cos ^{\frac {5}{2}}(c+d x) \sqrt {a+a \cos (c+d x)} \sin (c+d x)}{96 d}+\frac {a C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{3/2} \sin (c+d x)}{12 d}+\frac {C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \sin (c+d x)}{6 d}+\frac {\left (a^2 (1304 A+1015 C)\right ) \int \frac {\sqrt {a+a \cos (c+d x)}}{\sqrt {\cos (c+d x)}} \, dx}{1024} \\ & = \frac {a^3 (1304 A+1015 C) \sqrt {\cos (c+d x)} \sin (c+d x)}{512 d \sqrt {a+a \cos (c+d x)}}+\frac {a^3 (1304 A+1015 C) \cos ^{\frac {3}{2}}(c+d x) \sin (c+d x)}{768 d \sqrt {a+a \cos (c+d x)}}+\frac {a^3 (136 A+109 C) \cos ^{\frac {5}{2}}(c+d x) \sin (c+d x)}{192 d \sqrt {a+a \cos (c+d x)}}+\frac {a^2 (24 A+23 C) \cos ^{\frac {5}{2}}(c+d x) \sqrt {a+a \cos (c+d x)} \sin (c+d x)}{96 d}+\frac {a C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{3/2} \sin (c+d x)}{12 d}+\frac {C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \sin (c+d x)}{6 d}-\frac {\left (a^2 (1304 A+1015 C)\right ) \text {Subst}\left (\int \frac {1}{\sqrt {1-\frac {x^2}{a}}} \, dx,x,-\frac {a \sin (c+d x)}{\sqrt {a+a \cos (c+d x)}}\right )}{512 d} \\ & = \frac {a^{5/2} (1304 A+1015 C) \arcsin \left (\frac {\sqrt {a} \sin (c+d x)}{\sqrt {a+a \cos (c+d x)}}\right )}{512 d}+\frac {a^3 (1304 A+1015 C) \sqrt {\cos (c+d x)} \sin (c+d x)}{512 d \sqrt {a+a \cos (c+d x)}}+\frac {a^3 (1304 A+1015 C) \cos ^{\frac {3}{2}}(c+d x) \sin (c+d x)}{768 d \sqrt {a+a \cos (c+d x)}}+\frac {a^3 (136 A+109 C) \cos ^{\frac {5}{2}}(c+d x) \sin (c+d x)}{192 d \sqrt {a+a \cos (c+d x)}}+\frac {a^2 (24 A+23 C) \cos ^{\frac {5}{2}}(c+d x) \sqrt {a+a \cos (c+d x)} \sin (c+d x)}{96 d}+\frac {a C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{3/2} \sin (c+d x)}{12 d}+\frac {C \cos ^{\frac {5}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \sin (c+d x)}{6 d} \\ \end{align*}

Mathematica [A] (verified)

Time = 3.84 (sec) , antiderivative size = 170, normalized size of antiderivative = 0.54 \[ \int \cos ^{\frac {3}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \left (A+C \cos ^2(c+d x)\right ) \, dx=\frac {a^2 \sqrt {a (1+\cos (c+d x))} \sec \left (\frac {1}{2} (c+d x)\right ) \left (3 \sqrt {2} (1304 A+1015 C) \arcsin \left (\sqrt {2} \sin \left (\frac {1}{2} (c+d x)\right )\right )+2 \sqrt {\cos (c+d x)} (4648 A+4193 C+(2896 A+3234 C) \cos (c+d x)+4 (184 A+315 C) \cos (2 (c+d x))+96 A \cos (3 (c+d x))+428 C \cos (3 (c+d x))+112 C \cos (4 (c+d x))+16 C \cos (5 (c+d x))) \sin \left (\frac {1}{2} (c+d x)\right )\right )}{3072 d} \]

[In]

Integrate[Cos[c + d*x]^(3/2)*(a + a*Cos[c + d*x])^(5/2)*(A + C*Cos[c + d*x]^2),x]

[Out]

(a^2*Sqrt[a*(1 + Cos[c + d*x])]*Sec[(c + d*x)/2]*(3*Sqrt[2]*(1304*A + 1015*C)*ArcSin[Sqrt[2]*Sin[(c + d*x)/2]]
+ 2*Sqrt[Cos[c + d*x]]*(4648*A + 4193*C + (2896*A + 3234*C)*Cos[c + d*x] + 4*(184*A + 315*C)*Cos[2*(c + d*x)]
+ 96*A*Cos[3*(c + d*x)] + 428*C*Cos[3*(c + d*x)] + 112*C*Cos[4*(c + d*x)] + 16*C*Cos[5*(c + d*x)])*Sin[(c + d
*x)/2]))/(3072*d)

Maple [A] (verified)

Time = 24.50 (sec) , antiderivative size = 459, normalized size of antiderivative = 1.47

method	result	size
default	\(\frac {a^{2} \left (256 C \left (\cos ^{5}\left (d x +c \right )\right ) \sin \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+896 C \sin \left (d x +c \right ) \left (\cos ^{4}\left (d x +c \right )\right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+384 A \sin \left (d x +c \right ) \left (\cos ^{3}\left (d x +c \right )\right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+1392 C \left (\cos ^{3}\left (d x +c \right )\right ) \sin \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+1472 A \left (\cos ^{2}\left (d x +c \right )\right ) \sin \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+1624 C \left (\cos ^{2}\left (d x +c \right )\right ) \sin \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+2608 A \cos \left (d x +c \right ) \sin \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+2030 C \cos \left (d x +c \right ) \sin \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+3912 A \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \sin \left (d x +c \right )+3045 C \sin \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+3912 A \arctan \left (\tan \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\right )+3045 C \arctan \left (\tan \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\right )\right ) \left (\sqrt {\cos }\left (d x +c \right )\right ) \sqrt {a \left (1+\cos \left (d x +c \right )\right )}}{1536 d \left (1+\cos \left (d x +c \right )\right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}}\)	\(459\)
parts	\(\frac {A \left (48 \sin \left (d x +c \right ) \left (\cos ^{3}\left (d x +c \right )\right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+184 \sin \left (d x +c \right ) \left (\cos ^{2}\left (d x +c \right )\right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+326 \sin \left (d x +c \right ) \cos \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+489 \sin \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+489 \arctan \left (\tan \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\right )\right ) \sqrt {a \left (1+\cos \left (d x +c \right )\right )}\, \left (\sqrt {\cos }\left (d x +c \right )\right ) a^{2}}{192 d \left (1+\cos \left (d x +c \right )\right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}}+\frac {C \left (256 \sin \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \left (\cos ^{5}\left (d x +c \right )\right )+896 \left (\cos ^{4}\left (d x +c \right )\right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \sin \left (d x +c \right )+1392 \sin \left (d x +c \right ) \left (\cos ^{3}\left (d x +c \right )\right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+1624 \sin \left (d x +c \right ) \left (\cos ^{2}\left (d x +c \right )\right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+2030 \sin \left (d x +c \right ) \cos \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+3045 \sin \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+3045 \arctan \left (\tan \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\right )\right ) \sqrt {a \left (1+\cos \left (d x +c \right )\right )}\, \left (\sqrt {\cos }\left (d x +c \right )\right ) a^{2}}{1536 d \left (1+\cos \left (d x +c \right )\right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}}\)	\(508\)

[In]

int(cos(d*x+c)^(3/2)*(a+cos(d*x+c)*a)^(5/2)*(A+C*cos(d*x+c)^2),x,method=_RETURNVERBOSE)

[Out]

1/1536*a^2/d*(256*C*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+896*C*sin(d*x+c)*cos(d*x+c)^4*(c
os(d*x+c)/(1+cos(d*x+c)))^(1/2)+384*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+1392*C*cos(d*x
+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+1472*A*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^
(1/2)+1624*C*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+2608*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c
)/(1+cos(d*x+c)))^(1/2)+2030*C*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3912*A*(cos(d*x+c)/(1+c
os(d*x+c)))^(1/2)*sin(d*x+c)+3045*C*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3912*A*arctan(tan(d*x+c)*(cos
(d*x+c)/(1+cos(d*x+c)))^(1/2))+3045*C*arctan(tan(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)))*cos(d*x+c)^(1/2)*(
a*(1+cos(d*x+c)))^(1/2)/(1+cos(d*x+c))/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)

Fricas [A] (verification not implemented)

none

Time = 0.37 (sec) , antiderivative size = 208, normalized size of antiderivative = 0.67 \[ \int \cos ^{\frac {3}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \left (A+C \cos ^2(c+d x)\right ) \, dx=\frac {{\left (256 \, C a^{2} \cos \left (d x + c\right )^{5} + 896 \, C a^{2} \cos \left (d x + c\right )^{4} + 48 \, {\left (8 \, A + 29 \, C\right )} a^{2} \cos \left (d x + c\right )^{3} + 8 \, {\left (184 \, A + 203 \, C\right )} a^{2} \cos \left (d x + c\right )^{2} + 2 \, {\left (1304 \, A + 1015 \, C\right )} a^{2} \cos \left (d x + c\right ) + 3 \, {\left (1304 \, A + 1015 \, C\right )} a^{2}\right )} \sqrt {a \cos \left (d x + c\right ) + a} \sqrt {\cos \left (d x + c\right )} \sin \left (d x + c\right ) - 3 \, {\left ({\left (1304 \, A + 1015 \, C\right )} a^{2} \cos \left (d x + c\right ) + {\left (1304 \, A + 1015 \, C\right )} a^{2}\right )} \sqrt {a} \arctan \left (\frac {\sqrt {a \cos \left (d x + c\right ) + a} \sqrt {\cos \left (d x + c\right )}}{\sqrt {a} \sin \left (d x + c\right )}\right )}{1536 \, {\left (d \cos \left (d x + c\right ) + d\right )}} \]

[In]

integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm="fricas")

[Out]

1/1536*((256*C*a^2*cos(d*x + c)^5 + 896*C*a^2*cos(d*x + c)^4 + 48*(8*A + 29*C)*a^2*cos(d*x + c)^3 + 8*(184*A +
203*C)*a^2*cos(d*x + c)^2 + 2*(1304*A + 1015*C)*a^2*cos(d*x + c) + 3*(1304*A + 1015*C)*a^2)*sqrt(a*cos(d*x +
c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((1304*A + 1015*C)*a^2*cos(d*x + c) + (1304*A + 1015*C)*a^2)*sqrt(
a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)

Sympy [F(-1)]

Timed out. \[ \int \cos ^{\frac {3}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \left (A+C \cos ^2(c+d x)\right ) \, dx=\text {Timed out} \]

[In]

integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2),x)

[Out]

Timed out

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 42699 vs. \(2 (268) = 536\).

Time = 2.94 (sec) , antiderivative size = 42699, normalized size of antiderivative = 136.86 \[ \int \cos ^{\frac {3}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \left (A+C \cos ^2(c+d x)\right ) \, dx=\text {Too large to display} \]

[In]

integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm="maxima")

[Out]

1/6144*(8*(10*(cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(
4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(3/4)*((3*a^2*cos(4*d*x + 4*c)^
2*sin(4*d*x + 4*c) + 3*a^2*sin(4*d*x + 4*c)^3 + 12*(a^2*sin(4*d*x + 4*c)^3 + (a^2*cos(4*d*x + 4*c)^2 - 2*a^2*c
os(4*d*x + 4*c) + a^2)*sin(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 12*(a^2*sin(
4*d*x + 4*c)^3 + (a^2*cos(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin
(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 3*(2*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x
+ 4*c) + a^2*sin(4*d*x + 4*c) - 2*(a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4
*c))))*cos(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 12*(a^2*sin(4*d*x + 4*c)^3 + (a^2*cos(4*d*x + 4*
c)^2 - a^2*cos(4*d*x + 4*c))*sin(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + (8*a^2*c
os(4*d*x + 4*c)^2 + 8*a^2*sin(4*d*x + 4*c)^2 - 3*a^2*cos(4*d*x + 4*c) + 32*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4
*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 32*(a^2
*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c),
cos(4*d*x + 4*c)))^2 + 2*(16*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*sin(4*d*x + 4*c)^2 - 19*a^2*cos(4*d*x + 4*c) + 3
*a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*(64*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4
*d*x + 4*c)))*sin(4*d*x + 4*c) + 19*a^2*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))
)*sin(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 12*(4*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x
+ 4*c)))*sin(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*c
os(3/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d
*x + 4*c))) + 1)) - (3*a^2*cos(4*d*x + 4*c)^3 - 8*a^2*cos(4*d*x + 4*c)^2 + 4*(3*a^2*cos(4*d*x + 4*c)^3 - 14*a^
2*cos(4*d*x + 4*c)^2 + 19*a^2*cos(4*d*x + 4*c) + (3*a^2*cos(4*d*x + 4*c) - 8*a^2)*sin(4*d*x + 4*c)^2 - 8*a^2)*
cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + (3*a^2*cos(4*d*x + 4*c) - 8*a^2)*sin(4*d*x + 4*c)^2 +
4*(3*a^2*cos(4*d*x + 4*c)^3 - 2*a^2*cos(4*d*x + 4*c)^2 - 13*a^2*cos(4*d*x + 4*c) + (3*a^2*cos(4*d*x + 4*c) -
8*a^2)*sin(4*d*x + 4*c)^2 - 8*a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + (8*a^2*cos(4*d*x +
4*c)^2 + 8*a^2*sin(4*d*x + 4*c)^2 - 3*a^2*cos(4*d*x + 4*c) + 32*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c
)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 32*(a^2*cos(4*d*x
+ 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x
+ 4*c)))^2 + 2*(16*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*sin(4*d*x + 4*c)^2 - 19*a^2*cos(4*d*x + 4*c) + 3*a^2)*cos(
1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*(64*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c
)))*sin(4*d*x + 4*c) + 19*a^2*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*cos(3/4*
arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 4*(3*a^2*cos(4*d*x + 4*c)^3 - 11*a^2*cos(4*d*x + 4*c)^2 + 8*a^2
*cos(4*d*x + 4*c) + (3*a^2*cos(4*d*x + 4*c) - 8*a^2)*sin(4*d*x + 4*c)^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos
(4*d*x + 4*c))) - 3*(2*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a^2*sin(4*d
*x + 4*c) - 2*(a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(3/4*arcta
n2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*(3*a^2*cos(4*d*x + 4*c) - 8*a^2)*cos(1/2*arctan2(sin(4*d*x + 4*
c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + (3*a^2*cos(4*d*x + 4*c) - 8*a^2)*sin(4*d*x + 4*c))*sin(1/2*arctan2(s
in(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(3/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos
(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)))*sqrt(a) - 6*(cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*
d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c),
cos(4*d*x + 4*c))) + 1)^(1/4)*((3*a^2*cos(4*d*x + 4*c)^2*sin(4*d*x + 4*c) + 3*a^2*sin(4*d*x + 4*c)^3 + 3*a^2*c
os(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) - 160*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4
*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^3 + 4*(3*a^
2*sin(4*d*x + 4*c)^3 + 3*(a^2*cos(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(4*d*x + 4*c) - 160*(a^2*c
os(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/4*arctan2(sin(4*d*x + 4*c), c
os(4*d*x + 4*c))))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(3*a^2*sin(4*d*x + 4*c)^3 + 160*
a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + (3*a^2*cos(4*d*x + 4*c)^2 + 6*a^2*
cos(4*d*x + 4*c) + 43*a^2)*sin(4*d*x + 4*c) - 160*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos
(4*d*x + 4*c) + a^2)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(1/2*arctan2(sin(4*d*x + 4*c), c
os(4*d*x + 4*c)))^2 + 2*(6*a^2*sin(4*d*x + 4*c)^3 + 3*a^2*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))
*sin(4*d*x + 4*c) + 6*(a^2*cos(4*d*x + 4*c)^2 - a^2*cos(4*d*x + 4*c))*sin(4*d*x + 4*c) - (320*a^2*cos(4*d*x +
4*c)^2 + 320*a^2*sin(4*d*x + 4*c)^2 - 317*a^2*cos(4*d*x + 4*c) - 3*a^2)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(
4*d*x + 4*c))))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*(20*a^2*cos(4*d*x + 4*c)^2 + 26*a^2*s
in(4*d*x + 4*c)^2 - 317*a^2*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 80*(a^2*co
s(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), co
s(4*d*x + 4*c)))^2 + 8*(10*a^2*cos(4*d*x + 4*c)^2 + 13*a^2*sin(4*d*x + 4*c)^2 - 160*a^2*sin(4*d*x + 4*c)*sin(1
/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 10*a^2*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), c
os(4*d*x + 4*c))) + 3*(a^2*cos(4*d*x + 4*c) + a^2)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(1
/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - (160*a^2*cos(4*d*x + 4*c)^2 + 160*a^2*sin(4*d*x + 4*c)^2 + 3
*a^2*cos(4*d*x + 4*c))*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*cos(1/2*arctan2(sin(1/2*arctan2(s
in(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)) - (3*a^2*cos(4
*d*x + 4*c)^3 + 120*a^2*cos(4*d*x + 4*c)^2 - 160*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(
4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^3 - 3*a^2*sin(4*d*x + 4*c)*sin(1/4*ar
ctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 4*(3*a^2*cos(4*d*x + 4*c)^3 + 74*a^2*cos(4*d*x + 4*c)^2 - 197*a^2
*cos(4*d*x + 4*c) + (3*a^2*cos(4*d*x + 4*c) + 80*a^2)*sin(4*d*x + 4*c)^2 + 120*a^2 - 80*(a^2*cos(4*d*x + 4*c)^
2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))
))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 3*(a^2*cos(4*d*x + 4*c) + 40*a^2)*sin(4*d*x + 4*c)
^2 + 4*(3*a^2*cos(4*d*x + 4*c)^3 + 126*a^2*cos(4*d*x + 4*c)^2 + 243*a^2*cos(4*d*x + 4*c) + 3*(a^2*cos(4*d*x +
4*c) + 40*a^2)*sin(4*d*x + 4*c)^2 + 120*a^2 - 40*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(
4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 80*(a^2*cos(4*d*x + 4*c)^2 + a^2*si
n(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(1/2
*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*(6*a^2*cos(4*d*x + 4*c)^3 + 214*a^2*cos(4*d*x + 4*c)^2 - 3
*a^2*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 240*a^2*cos(4*d*x + 4*c) + 2*(3*a
^2*cos(4*d*x + 4*c) + 110*a^2)*sin(4*d*x + 4*c)^2 - (160*a^2*cos(4*d*x + 4*c)^2 + 160*a^2*sin(4*d*x + 4*c)^2 -
157*a^2*cos(4*d*x + 4*c) - 3*a^2)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*cos(1/2*arctan2(sin(4
*d*x + 4*c), cos(4*d*x + 4*c))) - (80*a^2*cos(4*d*x + 4*c)^2 + 80*a^2*sin(4*d*x + 4*c)^2 + 3*a^2*cos(4*d*x + 4
*c))*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 2*(320*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4
*d*x + 4*c)))^2*sin(4*d*x + 4*c) + 157*a^2*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*
c) + 8*(80*a^2*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) - (3*a^2*cos(4*d*x + 4*c)
+ 110*a^2)*sin(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 6*(a^2*cos(4*d*x + 4*c) +
40*a^2)*sin(4*d*x + 4*c) + 3*(a^2*cos(4*d*x + 4*c) + a^2)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))
))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos
(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)))*sqrt(a) + 489*((a^2*cos(4*d*x + 4
*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) +
a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c
)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x
+ 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - a^2*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))
- 4*(4*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a^2*sin(4*d*x + 4*c))*sin(
1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*arctan2(-(cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)
))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x
+ 4*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin
(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1))*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - cos(1/4*arctan2
(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), co
s(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1))), (cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)
))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x
+ 4*c))) + 1)^(1/4)*(cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*cos(1/2*arctan2(sin(1/2*arctan2(sin(
4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)) + sin(1/4*arctan2
(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), co
s(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1))) + 1) - (a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c
)^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4
*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c
) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x +
4*c)^2 - a^2*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a^2*cos(1/2*arctan2
(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a^2*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c
), cos(4*d*x + 4*c))))*arctan2(-(cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(
4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*(cos(1/
2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x +
4*c))) + 1))*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*
x + 4*c)))*sin(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4
*c), cos(4*d*x + 4*c))) + 1))), (cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(
4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*(cos(1/
4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*cos(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4
*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)) + sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*
x + 4*c)))*sin(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4
*c), cos(4*d*x + 4*c))) + 1))) - 1) - (a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2*cos(4*d*x + 4*
c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*
c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(si
n(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - a^2*cos(4*d*x + 4*
c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*
x + 4*c)))*sin(4*d*x + 4*c) + a^2*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*arct
an2((cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*
c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(1/2*arctan2(sin
(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)), (cos(1/2*arctan
2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*
arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(
4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)) + 1) + (a^2*cos(4*d*x + 4*c)^2 + a^
2*sin(4*d*x + 4*c)^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(
1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^
2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 +
a^2*sin(4*d*x + 4*c)^2 - a^2*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a^
2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a^2*sin(4*d*x + 4*c))*sin(1/2*arctan
2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*arctan2((cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(
1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) +
1)^(1/4)*sin(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c
), cos(4*d*x + 4*c))) + 1)), (cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d
*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*cos(1/2*ar
ctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)
)) + 1)) - 1))*sqrt(a))*A/(4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - 2*cos(4*d*x + 4*c) + 1)*cos(1/2*arctan
2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 + 2*cos(4*d*x + 4*c) + 1
)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + cos(4*d*x + 4*c)^2 + 4*(cos(4*d*x + 4*c)^2 + sin(4*
d*x + 4*c)^2 - cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + sin(4*d*x + 4*c)^2 - 4
*(4*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + sin(4*d*x + 4*c))*sin(1/2*arctan2(
sin(4*d*x + 4*c), cos(4*d*x + 4*c)))) - (8*(cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*a
rctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(3
/4)*((34*a^2*cos(6*d*x + 6*c)^2*sin(6*d*x + 6*c) + 34*a^2*sin(6*d*x + 6*c)^3 - 1755*(a^2*cos(6*d*x + 6*c)^2 +
a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3
+ 9*(34*a^2*sin(6*d*x + 6*c)^3 + 34*(a^2*cos(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(6*d*x + 6*c) -
80*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/2*arctan2(sin(6*d*x
+ 6*c), cos(6*d*x + 6*c))) - 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) +
a^2)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))
)^2 + 9*(34*a^2*sin(6*d*x + 6*c)^3 + 34*(a^2*cos(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(6*d*x + 6*
c) - 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/6*arctan2(sin(
6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(34*a^2*sin(6*d*x
+ 6*c)^3 + 780*a^2*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 780*a^2*cos(1/3*ar
ctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 2*(17*a^2*cos(6*d*x + 6*c)^2 + 34*a^2*cos(6*d*x
+ 6*c) + 82*a^2)*sin(6*d*x + 6*c) - 80*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*
c) + a^2)*sin(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 390*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x +
6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 195*(a^2*cos(6*
d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*
d*x + 6*c))))*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(34*a^2*sin(6*d*x + 6*c)^3 + 34*(a^2*
cos(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(6*d*x + 6*c) - 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*
d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arc
tan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 6*(34*a^2*sin(6*d*x + 6*c)^3 + 17*a^2*cos(1/2*arctan2(sin(6*d*x
+ 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 3*(34*a^2*sin(6*d*x + 6*c)^3 + 34*(a^2*cos(6*d*x + 6*c)^2 - 2*a^
2*cos(6*d*x + 6*c) + a^2)*sin(6*d*x + 6*c) - 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(
6*d*x + 6*c) + a^2)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(1/3*arctan2(sin(6*d*x + 6*c), co
s(6*d*x + 6*c))) + 34*(a^2*cos(6*d*x + 6*c)^2 - a^2*cos(6*d*x + 6*c))*sin(6*d*x + 6*c) - (80*a^2*cos(6*d*x + 6
*c)^2 + 80*a^2*sin(6*d*x + 6*c)^2 - 480*a^2*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c
))) - 63*a^2*cos(6*d*x + 6*c) - 17*a^2 + 240*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*
x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/2*arctan2(sin(6*d*x + 6*c), cos(6*
d*x + 6*c))) - 6*(34*a^2*sin(6*d*x + 6*c)^2 - 195*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6
*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*
d*x + 6*c)^2 - a^2*cos(6*d*x + 6*c))*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(2/3*arctan2(sin
(6*d*x + 6*c), cos(6*d*x + 6*c))) + 34*(3*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x +
6*c) + a^2*sin(6*d*x + 6*c) - 3*(a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*
c))))*cos(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 6*(34*a^2*sin(6*d*x + 6*c)^3 + 34*(a^2*cos(6*d*x
+ 6*c)^2 - a^2*cos(6*d*x + 6*c))*sin(6*d*x + 6*c) - 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - a^2
*cos(6*d*x + 6*c))*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos
(6*d*x + 6*c))) - 3*(65*a^2*cos(6*d*x + 6*c)^2 + 133*a^2*sin(6*d*x + 6*c)^2 - 390*a^2*sin(6*d*x + 6*c)*sin(1/6
*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 585*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*c
os(6*d*x + 6*c) + a^2)*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 585*(a^2*cos(6*d*x + 6*c)^2 +
a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2
+ 585*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d
*x + 6*c), cos(6*d*x + 6*c)))^2 + 6*(65*a^2*cos(6*d*x + 6*c)^2 + 133*a^2*sin(6*d*x + 6*c)^2 - 160*a^2*sin(6*d*
x + 6*c)*sin(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 390*a^2*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6
*d*x + 6*c), cos(6*d*x + 6*c))) - 390*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))
) - 65*a^2*cos(6*d*x + 6*c) + 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) +
a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))
) + 34*(a^2*cos(6*d*x + 6*c) + a^2)*cos(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 6*(65*a^2*cos(6*d*x
+ 6*c)^2 + 133*a^2*sin(6*d*x + 6*c)^2 - 390*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x
+ 6*c))) - 65*a^2*cos(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 6*(160*a^2*cos(1/3*
arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 21*a^2*sin(6*d*x + 6*c) - 80*(a^2*cos(6*d*x +
6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x +
6*c))))*sin(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 6*(34*a^2*sin(6*d*x + 6*c)^3 + 390*a^2*cos(1/3*
arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + (34*a^2*cos(6*d*x + 6*c)^2 + 68*a^2*cos(6*d*x
+ 6*c) + 99*a^2)*sin(6*d*x + 6*c) - 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6
*c) + a^2)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x +
6*c))))*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 2*(40*a^2*cos(6*d*x + 6*c)^2 + 40*a^2*sin(6*d*
x + 6*c)^2 + 17*a^2*cos(6*d*x + 6*c) + 360*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x
+ 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 360*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6
*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 3*(80*a
^2*cos(6*d*x + 6*c)^2 + 80*a^2*sin(6*d*x + 6*c)^2 - 63*a^2*cos(6*d*x + 6*c) - 17*a^2)*cos(1/3*arctan2(sin(6*d*
x + 6*c), cos(6*d*x + 6*c))) - 9*(160*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c
) + 21*a^2*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/2*arctan2(sin(6*d*x +
6*c), cos(6*d*x + 6*c))) - 6*(34*a^2*sin(6*d*x + 6*c)^2 - 195*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2(sin(6*d*x
+ 6*c), cos(6*d*x + 6*c))) + 6*(34*a^2*sin(6*d*x + 6*c)^2 - 195*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2(sin(6*d*x
+ 6*c), cos(6*d*x + 6*c))))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x +
6*c), cos(6*d*x + 6*c))) - 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2)*sin(1/6*arctan2(sin(6*d*x +
6*c), cos(6*d*x + 6*c))))*cos(3/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan
2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) - (34*a^2*cos(6*d*x + 6*c)^3 + 80*a^2*cos(6*d*x + 6*c)^2 - 1755*(
a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(2/3*arctan2(sin(6*d*x + 6*
c), cos(6*d*x + 6*c)))^3 + 9*(34*a^2*cos(6*d*x + 6*c)^3 - 118*a^2*cos(6*d*x + 6*c)^2 + 780*a^2*sin(6*d*x + 6*c
)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 4*a^2*cos(6*d*x + 6*c) + 2*(17*a^2*cos(6*d*x + 6*c) -
25*a^2)*sin(6*d*x + 6*c)^2 + 80*a^2 - 80*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x +
6*c) + a^2)*cos(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 390*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*
x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 195*(a^2*cos
(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/6*arctan2(sin(6*d*x + 6*c), cos
(6*d*x + 6*c))))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(34*a^2*cos(6*d*x + 6*c)^3 + 12*a^
2*cos(6*d*x + 6*c)^2 - 126*a^2*cos(6*d*x + 6*c) + 2*(17*a^2*cos(6*d*x + 6*c) + 40*a^2)*sin(6*d*x + 6*c)^2 + 80
*a^2 + 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/6*arctan2(si
n(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*(17*a^2*cos(6*d
*x + 6*c) + 40*a^2)*sin(6*d*x + 6*c)^2 + 9*(34*a^2*cos(6*d*x + 6*c)^3 + 148*a^2*cos(6*d*x + 6*c)^2 + 194*a^2*c
os(6*d*x + 6*c) + 2*(17*a^2*cos(6*d*x + 6*c) + 40*a^2)*sin(6*d*x + 6*c)^2 + 80*a^2 - 195*(a^2*cos(6*d*x + 6*c)
^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)
)) - 80*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/2*arctan2(sin(6
*d*x + 6*c), cos(6*d*x + 6*c))) + 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c
) + a^2)*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6
*c)))^2 + 9*(34*a^2*cos(6*d*x + 6*c)^3 + 148*a^2*cos(6*d*x + 6*c)^2 + 194*a^2*cos(6*d*x + 6*c) + 2*(17*a^2*cos
(6*d*x + 6*c) + 40*a^2)*sin(6*d*x + 6*c)^2 + 80*a^2 + 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2
*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x +
6*c), cos(6*d*x + 6*c)))^2 + 3*(68*a^2*cos(6*d*x + 6*c)^3 + 27*a^2*cos(6*d*x + 6*c)^2 - 34*a^2*sin(6*d*x + 6*
c)*sin(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 160*a^2*cos(6*d*x + 6*c) - 585*(a^2*cos(6*d*x + 6*c)
^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)
))^2 + (68*a^2*cos(6*d*x + 6*c) + 95*a^2)*sin(6*d*x + 6*c)^2 - 585*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6
*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 - 2*(80*a^2*cos(6
*d*x + 6*c)^2 + 80*a^2*sin(6*d*x + 6*c)^2 - 480*a^2*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d
*x + 6*c))) - 63*a^2*cos(6*d*x + 6*c) - 17*a^2 + 240*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*
cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(1/2*arctan2(sin(6*d*x + 6*c)
, cos(6*d*x + 6*c))) + 6*(34*a^2*cos(6*d*x + 6*c)^3 - 53*a^2*cos(6*d*x + 6*c)^2 - 61*a^2*cos(6*d*x + 6*c) + (3
4*a^2*cos(6*d*x + 6*c) + 15*a^2)*sin(6*d*x + 6*c)^2 + 80*a^2 + 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6
*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(1/3*arctan2(si
n(6*d*x + 6*c), cos(6*d*x + 6*c))) + 390*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - a^2*cos(6*d*x + 6*
c))*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 6*(390*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*
d*x + 6*c)))*sin(6*d*x + 6*c) - 390*a^2*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c)
- (68*a^2*cos(6*d*x + 6*c) + 95*a^2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*c
os(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 2*(40*a^2*cos(6*d*x + 6*c)^2 + 40*a^2*sin(6*d*x + 6*c)^2
+ 17*a^2*cos(6*d*x + 6*c) + 360*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a
^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 360*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c
)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 3*(80*a^2*cos(6*d
*x + 6*c)^2 + 80*a^2*sin(6*d*x + 6*c)^2 - 63*a^2*cos(6*d*x + 6*c) - 17*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c),
cos(6*d*x + 6*c))) - 9*(160*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 21*a^2
*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(1/2*arctan2(sin(6*d*x + 6*c), cos
(6*d*x + 6*c))) + 6*(34*a^2*cos(6*d*x + 6*c)^3 + 46*a^2*cos(6*d*x + 6*c)^2 - 80*a^2*cos(6*d*x + 6*c) + 2*(17*a
^2*cos(6*d*x + 6*c) + 40*a^2)*sin(6*d*x + 6*c)^2 + 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - a^2*
cos(6*d*x + 6*c))*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(
6*d*x + 6*c))) + 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2)*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6
*d*x + 6*c))) + 6*(1170*a^2*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c) - 195*a^2*
cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 3*(160*a^2*cos(1/2*arctan2(sin(6*d*x +
6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 390*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(
6*d*x + 6*c) - 390*a^2*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) - (68*a^2*cos(6*d
*x + 6*c) + 95*a^2)*sin(6*d*x + 6*c) - 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x
+ 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*
x + 6*c))) + 3*(160*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 21*a^2*sin(6*d
*x + 6*c) - 80*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan
2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 6*(195*a^2*cos(
1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 2*(17*a^2*cos(6*d*x + 6*c) + 40*a^2)*sin(6
*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 2*(17*a^2*cos(6*d*x + 6*c) + 40*a^2)*sin(6
*d*x + 6*c) + 17*(a^2*cos(6*d*x + 6*c) + a^2)*sin(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 3*(34*a^2
*cos(6*d*x + 6*c)^3 + 148*a^2*cos(6*d*x + 6*c)^2 + 194*a^2*cos(6*d*x + 6*c) + 2*(17*a^2*cos(6*d*x + 6*c) + 40*
a^2)*sin(6*d*x + 6*c)^2 + 80*a^2 + 195*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*
c) + a^2)*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x +
6*c))))*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 34*(3*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos
(6*d*x + 6*c)))*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c) - 3*(a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6
*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 6*(195*a^2*cos(1/6*arc
tan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 6*(195*a^2*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(
6*d*x + 6*c)))*sin(6*d*x + 6*c) + 2*(17*a^2*cos(6*d*x + 6*c) + 40*a^2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6
*d*x + 6*c), cos(6*d*x + 6*c))) + 2*(17*a^2*cos(6*d*x + 6*c) + 40*a^2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6
*d*x + 6*c), cos(6*d*x + 6*c))))*sin(3/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3
*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)))*sqrt(a) - 6*(cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x
+ 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(
6*d*x + 6*c))) + 1)^(1/4)*((261*(a^2*sin(6*d*x + 6*c)^3 + (a^2*cos(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a
^2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^4 + 29*a^2*cos(6*d*x + 6*c)^2*sin(6
*d*x + 6*c) + 29*a^2*sin(6*d*x + 6*c)^3 + 261*(a^2*sin(6*d*x + 6*c)^3 + (a^2*cos(6*d*x + 6*c)^2 + 2*a^2*cos(6*
d*x + 6*c) + a^2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^4 + 174*(4*a^2*sin(6*
d*x + 6*c)^3 + (4*a^2*cos(6*d*x + 6*c)^2 - 7*a^2*cos(6*d*x + 6*c) + 3*a^2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(s
in(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 - 174*(6*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*
d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 + 261*(a^2*sin(6
*d*x + 6*c)^3 + (a^2*sin(6*d*x + 6*c)^3 + (a^2*cos(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(6*d*x +
6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (a^2*sin(6*d*x + 6*c)^3 + (a^2*cos(6*d*x + 6*c)
^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 +
2*(a^2*sin(6*d*x + 6*c)^3 + (a^2*cos(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(6*d*x + 6*c))*cos(1/3*
arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + (a^2*cos(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(6*d
*x + 6*c))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 29*(22*a^2*sin(6*d*x + 6*c)^3 + (22*a^2*co
s(6*d*x + 6*c)^2 - 30*a^2*cos(6*d*x + 6*c) + 9*a^2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*
d*x + 6*c)))^2 + 261*(a^2*sin(6*d*x + 6*c)^3 + (a^2*sin(6*d*x + 6*c)^3 + (a^2*cos(6*d*x + 6*c)^2 + 2*a^2*cos(6
*d*x + 6*c) + a^2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (a^2*sin(6*d*x +
6*c)^3 + (a^2*cos(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x
+ 6*c), cos(6*d*x + 6*c)))^2 + 2*(a^2*sin(6*d*x + 6*c)^3 + (a^2*cos(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) +
a^2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + (a^2*cos(6*d*x + 6*c)^2 + 2*a^2*
cos(6*d*x + 6*c) + a^2)*sin(6*d*x + 6*c))*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 29*(10*a^2*
sin(6*d*x + 6*c)^3 + 18*(a^2*sin(6*d*x + 6*c)^3 + (a^2*cos(6*d*x + 6*c)^2 + a^2)*sin(6*d*x + 6*c))*cos(1/3*arc
tan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 6*(4*a^2*sin(6*d*x + 6*c)^3 + (4*a^2*cos(6*d*x + 6*c)^2 + 5*a^2*
cos(6*d*x + 6*c) + 3*a^2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + (10*a^2*cos
(6*d*x + 6*c)^2 + 18*a^2*cos(6*d*x + 6*c) + 9*a^2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d
*x + 6*c)))^2 + 29*(3*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3*sin(6*d*x + 6*c) + 7*a^2*cos(
1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c) + 5*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c),
cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) - 3*(a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d
*x + 6*c)))^3 + a^2*sin(6*d*x + 6*c) + (3*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x +
6*c) + a^2*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 3*(a^2*cos(1/3*arctan2(
sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x + 6*c
), cos(6*d*x + 6*c)))^2 + 2*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + a^2*si
n(6*d*x + 6*c))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 3*(a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*
x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*
arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + a^2 + 2*(a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*
x + 6*c), cos(6*d*x + 6*c))))*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 3*(a^2*cos(6*d*x + 6*c) +
(a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + a^2 + 2*(a^2*cos(6*d*x
+ 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*
x + 6*c))))*cos(5/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 174*(6*a^2*sin(6*d*x + 6*c)^2*sin(1/3*arcta
n2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 - a^2*sin(6*d*x + 6*c)^3 - 3*(a^2*sin(6*d*x + 6*c)^3 + (a^2*cos(6*d*
x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c
)))^3 - (7*a^2*sin(6*d*x + 6*c)^3 + (7*a^2*cos(6*d*x + 6*c)^2 - 13*a^2*cos(6*d*x + 6*c) + 6*a^2)*sin(6*d*x + 6
*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 - (a^2*sin(6*d*x + 6*c)^3 + 3*(a^2*sin(6*d*x + 6*c
)^3 + (a^2*cos(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*
c), cos(6*d*x + 6*c))) + (a^2*cos(6*d*x + 6*c)^2 - a^2*cos(6*d*x + 6*c))*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin
(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 - (5*a^2*sin(6*d*x + 6*c)^3 + (5*a^2*cos(6*d*x + 6*c)^2 - 8*a^2*cos(6*d*x
+ 6*c) + 3*a^2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - (a^2*cos(6*d*x + 6*c)
^2 - a^2*cos(6*d*x + 6*c))*sin(6*d*x + 6*c) + 6*(a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*si
n(6*d*x + 6*c)^2 + 2*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c)^2 + a^2*sin(6*d
*x + 6*c)^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x
+ 6*c))) + 58*(4*a^2*sin(6*d*x + 6*c)^3 + (4*a^2*cos(6*d*x + 6*c)^2 - 3*a^2*cos(6*d*x + 6*c))*sin(6*d*x + 6*c
))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + (144*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^
2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^4 + 144*(a^2*cos(6*d*x
+ 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x
+ 6*c)))^4 + 16*a^2*cos(6*d*x + 6*c)^2 + 3*(128*a^2*cos(6*d*x + 6*c)^2 + 128*a^2*sin(6*d*x + 6*c)^2 - 253*a^2*
cos(6*d*x + 6*c) + 125*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 + 16*a^2*sin(6*d*x + 6*c)^2
- 3*(192*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 61*a^2*sin(6*d*x + 6*c))
*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 - 29*a^2*cos(6*d*x + 6*c) + 144*(a^2*cos(6*d*x + 6*c)^
2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2
*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (a^2*cos(6*d*x + 6*c)^2 + a^
2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 +
a^2 + 2*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6
*d*x + 6*c), cos(6*d*x + 6*c))))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (352*a^2*cos(6*d*x +
6*c)^2 + 352*a^2*sin(6*d*x + 6*c)^2 - 683*a^2*cos(6*d*x + 6*c) + 318*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), c
os(6*d*x + 6*c)))^2 + 144*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + (a^2*cos
(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos
(6*d*x + 6*c)))^2 + (a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*a
rctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + a^2 + 2*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a
^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(2/3*arctan2(sin(6*d*x + 6
*c), cos(6*d*x + 6*c)))^2 + (160*a^2*cos(6*d*x + 6*c)^2 + 160*a^2*sin(6*d*x + 6*c)^2 + 259*a^2*cos(6*d*x + 6*c
) + 288*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x +
6*c)))^2 + 144*a^2 + 3*(128*a^2*cos(6*d*x + 6*c)^2 + 128*a^2*sin(6*d*x + 6*c)^2 + 131*a^2*cos(6*d*x + 6*c) + 1
25*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*
c)))^2 - 3*(192*a^2*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 - 32*a^2*cos(6*d*x
+ 6*c)^2 - 96*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan
2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 - 32*a^2*sin(6*d*x + 6*c)^2 + 61*a^2*cos(6*d*x + 6*c) - (224*a^2*cos(
6*d*x + 6*c)^2 + 224*a^2*sin(6*d*x + 6*c)^2 - 445*a^2*cos(6*d*x + 6*c) + 221*a^2)*cos(1/3*arctan2(sin(6*d*x +
6*c), cos(6*d*x + 6*c)))^2 - (32*a^2*cos(6*d*x + 6*c)^2 + 32*a^2*sin(6*d*x + 6*c)^2 - 61*a^2*cos(6*d*x + 6*c)
+ 29*a^2 + 96*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2
(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 - 29*a^2 - 2*(80
*a^2*cos(6*d*x + 6*c)^2 + 80*a^2*sin(6*d*x + 6*c)^2 - 157*a^2*cos(6*d*x + 6*c) + 77*a^2)*cos(1/3*arctan2(sin(6
*d*x + 6*c), cos(6*d*x + 6*c))) + 192*(a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*d*x +
6*c) + 2*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c))*sin
(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + (128
*a^2*cos(6*d*x + 6*c)^2 + 128*a^2*sin(6*d*x + 6*c)^2 - 241*a^2*cos(6*d*x + 6*c) + 87*a^2)*cos(1/3*arctan2(sin(
6*d*x + 6*c), cos(6*d*x + 6*c))) - 3*(192*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3*sin(6*d*x
+ 6*c) + 445*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c) + 314*a^2*cos(1/3*ar
ctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) - 96*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c
)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 + 61*a^2*sin(6*d*x
+ 6*c) + (192*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 61*a^2*sin(6*d*x + 6
*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 192*(a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6
*d*x + 6*c)))^2*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2
+ 2*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c))*cos(2/3
*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 96*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*co
s(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arct
an2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + a^2 + 2*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*
cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x + 6*c)
, cos(6*d*x + 6*c))))*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 3*(192*a^2*cos(1/3*arctan2(sin(6*
d*x + 6*c), cos(6*d*x + 6*c)))^3*sin(6*d*x + 6*c) + 445*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)
))^2*sin(6*d*x + 6*c) + 314*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 61*a^2
*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(5/6*arctan2(sin(6*d*x + 6*c), cos
(6*d*x + 6*c))) - 174*(6*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3*sin(6*d*x + 6*c)^2 + 13*a^
2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c)^2 + 8*a^2*cos(1/3*arctan2(sin(6*d*x
+ 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 3*(a^2*sin(6*d*x + 6*c)^3 + (a^2*cos(
6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x +
6*c)))^3 + (6*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6
*c)^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 6*(a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6
*d*x + 6*c)))^2*sin(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)
))^2 + 2*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2)
*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 3*(a^2*sin(6*d*x + 6*c)^3 + (a^2*sin(6*d*x + 6*c)^3 +
(a^2*cos(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), co
s(6*d*x + 6*c)))^2 + 2*(a^2*sin(6*d*x + 6*c)^3 + (a^2*cos(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(6
*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + (a^2*cos(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x
+ 6*c) + a^2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(2/3*arctan2(sin(6*d*
x + 6*c), cos(6*d*x + 6*c))) - 174*(6*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3*sin(6*d*x + 6
*c)^2 + 13*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c)^2 + 8*a^2*cos(1/3*arcta
n2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2)*sin(1/3*arctan2(sin(6*d*x
+ 6*c), cos(6*d*x + 6*c))))*cos(5/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arc
tan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) + (19*a^2*cos(6*d*x + 6*c)^2*sin(6*d*x + 6*c) + 19*a^2*sin(6*d
*x + 6*c)^3 + 19*a^2*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) - 1980*(a^2*cos(6*d
*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d
*x + 6*c)))^3 + 360*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*a
rctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 + 9*(19*a^2*sin(6*d*x + 6*c)^3 + 19*(a^2*cos(6*d*x + 6*c)^2 - 2*
a^2*cos(6*d*x + 6*c) + a^2)*sin(6*d*x + 6*c) - 220*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*co
s(6*d*x + 6*c) + a^2)*sin(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 40*(a^2*cos(6*d*x + 6*c)^2 + a^2*
sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 776*
(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/6*arctan2(sin(6*d*x + 6
*c), cos(6*d*x + 6*c))))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(19*a^2*sin(6*d*x + 6*c)^3
+ 19*(a^2*cos(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(6*d*x + 6*c) + 776*(a^2*cos(6*d*x + 6*c)^2 +
a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*
cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 3*(57*a^2*sin(6*d*x + 6*c)^3 + 2640*a^2*cos(2/3*arcta
n2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 2640*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*
x + 6*c)))*sin(6*d*x + 6*c) + (57*a^2*cos(6*d*x + 6*c)^2 + 114*a^2*cos(6*d*x + 6*c) + 497*a^2)*sin(6*d*x + 6*c
) - 660*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/2*arctan2(sin(6
*d*x + 6*c), cos(6*d*x + 6*c))) - 1200*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*
c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 2328*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x
+ 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(2/3*arctan2
(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 3*(57*a^2*sin(6*d*x + 6*c)^3 - 480*a^2*cos(1/3*arctan2(sin(6*d*x + 6
*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + (57*a^2*cos(6*d*x + 6*c)^2 + 114*a^2*cos(6*d*x + 6*c) - 23*a^2)*sin
(6*d*x + 6*c) + 2328*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/6*
arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 3*(38*a
^2*sin(6*d*x + 6*c)^3 - 480*a^2*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 19*a
^2*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 6*(19*a^2*sin(6*d*x + 6*c)^3 + 19*(
a^2*cos(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(6*d*x + 6*c) + 776*(a^2*cos(6*d*x + 6*c)^2 + a^2*si
n(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(1/3
*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 38*(a^2*cos(6*d*x + 6*c)^2 - a^2*cos(6*d*x + 6*c))*sin(6*d*x +
6*c) - 440*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 6*a^2*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*
x + 6*c), cos(6*d*x + 6*c))) - a^2*cos(6*d*x + 6*c) + 3*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a
^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/2*arctan2(sin(6*d*x + 6
*c), cos(6*d*x + 6*c))) + 4*(20*a^2*cos(6*d*x + 6*c)^2 - 37*a^2*sin(6*d*x + 6*c)^2 - 2328*a^2*sin(6*d*x + 6*c)
*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 20*a^2*cos(6*d*x + 6*c) + 60*(a^2*cos(6*d*x + 6*c)^2 +
a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*
sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + (1552*a^2*cos(6*d*x + 6*c)^2 + 1552*a^2*sin(6*d*x + 6*c
)^2 - 1571*a^2*cos(6*d*x + 6*c) + 19*a^2)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(2/3*arctan
2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 3*(38*a^2*sin(6*d*x + 6*c)^3 + 19*a^2*cos(1/6*arctan2(sin(6*d*x + 6*c
), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 38*(a^2*cos(6*d*x + 6*c)^2 - a^2*cos(6*d*x + 6*c))*sin(6*d*x + 6*c) +
(1552*a^2*cos(6*d*x + 6*c)^2 + 1552*a^2*sin(6*d*x + 6*c)^2 - 1571*a^2*cos(6*d*x + 6*c) + 19*a^2)*sin(1/6*arct
an2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - (220*a^2*cos(
6*d*x + 6*c)^2 + 334*a^2*sin(6*d*x + 6*c)^2 + 4713*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(
6*d*x + 6*c))) + 1980*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(2/3
*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 1980*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^
2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 1260*(a^2*cos(6*d*x + 6*c)^
2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))
)^2 + 12*(110*a^2*cos(6*d*x + 6*c)^2 + 167*a^2*sin(6*d*x + 6*c)^2 - 660*a^2*sin(6*d*x + 6*c)*sin(1/2*arctan2(s
in(6*d*x + 6*c), cos(6*d*x + 6*c))) - 540*a^2*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6
*c))) + 2328*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 110*a^2*cos(6*d*x + 6
*c) + 330*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin
(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 12*(110*a^2*cos(6*d*
x + 6*c)^2 + 167*a^2*sin(6*d*x + 6*c)^2 + 2328*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*
x + 6*c))) - 110*a^2*cos(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 57*(a^2*cos(6*d*
x + 6*c) + a^2)*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 1320*(6*a^2*cos(1/3*arctan2(sin(6*d*x +
6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c) - 3*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x
+ 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/2*arctan2
(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 18*(19*a^2*sin(6*d*x + 6*c)^3 + 360*a^2*cos(1/3*arctan2(sin(6*d*x + 6*
c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + (19*a^2*cos(6*d*x + 6*c)^2 + 38*a^2*cos(6*d*x + 6*c) + 79*a^2)*sin(6
*d*x + 6*c) + 776*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/6*arc
tan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(2/3*arcta
n2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 220*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 9*(a^2*cos(6*
d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*
d*x + 6*c)))^2 + 9*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*ar
ctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 6*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - a^2*cos(6*
d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 6*(6*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c),
cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)
)))*sin(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + (40*a^2*cos(6*d*x + 6*c)^2 - 74*a^2*sin(6*d*x + 6*c
)^2 - 4713*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 360*(a^2*cos(6*d*x + 6*
c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*
c)))^2 + 12*(20*a^2*cos(6*d*x + 6*c)^2 - 37*a^2*sin(6*d*x + 6*c)^2 - 2328*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2
(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 20*a^2*cos(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x +
6*c))) - 57*(a^2*cos(6*d*x + 6*c) + a^2)*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan
2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + (776*a^2*cos(6*d*x + 6*c)^2 + 776*a^2*sin(6*d*x + 6*c)^2 - 19*a^2*cos
(6*d*x + 6*c))*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x
+ 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) - (29*a^2*cos(6*d*x +
6*c)^3 + 9*(29*a^2*cos(6*d*x + 6*c)^3 - 74*a^2*cos(6*d*x + 6*c)^2 + 61*a^2*cos(6*d*x + 6*c) + (29*a^2*cos(6*d*
x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^4 + 9*(29
*a^2*cos(6*d*x + 6*c)^3 + 42*a^2*cos(6*d*x + 6*c)^2 - 3*a^2*cos(6*d*x + 6*c) + (29*a^2*cos(6*d*x + 6*c) - 16*a
^2)*sin(6*d*x + 6*c)^2 - 16*a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^4 - 16*a^2*cos(6*d*x + 6
*c)^2 + 6*(116*a^2*cos(6*d*x + 6*c)^3 - 267*a^2*cos(6*d*x + 6*c)^2 + 199*a^2*cos(6*d*x + 6*c) + 4*(29*a^2*cos(
6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 - 48*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 - 6
*(6*(29*a^2*cos(6*d*x + 6*c) - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) +
(29*a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 +
9*(29*a^2*cos(6*d*x + 6*c)^3 - 74*a^2*cos(6*d*x + 6*c)^2 + 61*a^2*cos(6*d*x + 6*c) + (29*a^2*cos(6*d*x + 6*c)
^3 - 74*a^2*cos(6*d*x + 6*c)^2 + 61*a^2*cos(6*d*x + 6*c) + (29*a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)
^2 - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (29*a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6
*d*x + 6*c)^2 + (29*a^2*cos(6*d*x + 6*c)^3 - 74*a^2*cos(6*d*x + 6*c)^2 + 61*a^2*cos(6*d*x + 6*c) + (29*a^2*cos
(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 - 16*a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 -
16*a^2 + 2*(29*a^2*cos(6*d*x + 6*c)^3 - 74*a^2*cos(6*d*x + 6*c)^2 + 61*a^2*cos(6*d*x + 6*c) + (29*a^2*cos(6*d*
x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(2/3*
arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (638*a^2*cos(6*d*x + 6*c)^3 - 1222*a^2*cos(6*d*x + 6*c)^2 + 7
41*a^2*cos(6*d*x + 6*c) + 22*(29*a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 - 144*a^2)*cos(1/3*arctan2(
sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (29*a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 + 9*(29*a^2*cos
(6*d*x + 6*c)^3 + 42*a^2*cos(6*d*x + 6*c)^2 - 3*a^2*cos(6*d*x + 6*c) + (29*a^2*cos(6*d*x + 6*c)^3 + 42*a^2*cos
(6*d*x + 6*c)^2 - 3*a^2*cos(6*d*x + 6*c) + (29*a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 - 16*a^2)*cos
(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (29*a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 +
(29*a^2*cos(6*d*x + 6*c)^3 + 42*a^2*cos(6*d*x + 6*c)^2 - 3*a^2*cos(6*d*x + 6*c) + (29*a^2*cos(6*d*x + 6*c) - 1
6*a^2)*sin(6*d*x + 6*c)^2 - 16*a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 - 16*a^2 + 2*(29*a^
2*cos(6*d*x + 6*c)^3 + 42*a^2*cos(6*d*x + 6*c)^2 - 3*a^2*cos(6*d*x + 6*c) + (29*a^2*cos(6*d*x + 6*c) - 16*a^2)
*sin(6*d*x + 6*c)^2 - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(2/3*arctan2(sin(6*d*x
+ 6*c), cos(6*d*x + 6*c)))^2 + (290*a^2*cos(6*d*x + 6*c)^3 + 362*a^2*cos(6*d*x + 6*c)^2 - 27*a^2*cos(6*d*x + 6
*c) + 18*(29*a^2*cos(6*d*x + 6*c)^3 - 16*a^2*cos(6*d*x + 6*c)^2 + 29*a^2*cos(6*d*x + 6*c) + (29*a^2*cos(6*d*x
+ 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 10*(29*
a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 - 144*a^2 + 6*(116*a^2*cos(6*d*x + 6*c)^3 + 81*a^2*cos(6*d*x
+ 6*c)^2 + 7*a^2*cos(6*d*x + 6*c) + 4*(29*a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 - 48*a^2)*cos(1/3
*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (144*(
a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*
c), cos(6*d*x + 6*c)))^4 + 144*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2
)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^4 + 16*a^2*cos(6*d*x + 6*c)^2 + 3*(128*a^2*cos(6*d*x +
6*c)^2 + 128*a^2*sin(6*d*x + 6*c)^2 - 253*a^2*cos(6*d*x + 6*c) + 125*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), co
s(6*d*x + 6*c)))^3 + 16*a^2*sin(6*d*x + 6*c)^2 - 3*(192*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)
))*sin(6*d*x + 6*c) + 61*a^2*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 - 29*a^2
*cos(6*d*x + 6*c) + 144*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + (a^2*cos(6
*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6
*d*x + 6*c)))^2 + (a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arc
tan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + a^2 + 2*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2
*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(2/3*arctan2(sin(6*d*x + 6*c
), cos(6*d*x + 6*c)))^2 + (352*a^2*cos(6*d*x + 6*c)^2 + 352*a^2*sin(6*d*x + 6*c)^2 - 683*a^2*cos(6*d*x + 6*c)
+ 318*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 144*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*
x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c
) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*
c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + a^2 + 2*(a^2*cos
(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos
(6*d*x + 6*c))))*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (160*a^2*cos(6*d*x + 6*c)^2 + 160*a^
2*sin(6*d*x + 6*c)^2 + 259*a^2*cos(6*d*x + 6*c) + 288*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + a^2)*
cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 144*a^2 + 3*(128*a^2*cos(6*d*x + 6*c)^2 + 128*a^2*sin
(6*d*x + 6*c)^2 + 131*a^2*cos(6*d*x + 6*c) + 125*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*si
n(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 - 3*(192*a^2*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x +
6*c), cos(6*d*x + 6*c)))^3 - 32*a^2*cos(6*d*x + 6*c)^2 - 96*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2
- 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 - 32*a^2*sin(6*d*x + 6*
c)^2 + 61*a^2*cos(6*d*x + 6*c) - (224*a^2*cos(6*d*x + 6*c)^2 + 224*a^2*sin(6*d*x + 6*c)^2 - 445*a^2*cos(6*d*x
+ 6*c) + 221*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 - (32*a^2*cos(6*d*x + 6*c)^2 + 32*a^2
*sin(6*d*x + 6*c)^2 - 61*a^2*cos(6*d*x + 6*c) + 29*a^2 + 96*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 -
2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x
+ 6*c), cos(6*d*x + 6*c)))^2 - 29*a^2 - 2*(80*a^2*cos(6*d*x + 6*c)^2 + 80*a^2*sin(6*d*x + 6*c)^2 - 157*a^2*co
s(6*d*x + 6*c) + 77*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 192*(a^2*cos(1/3*arctan2(sin(6
*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c) + 2*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))
)*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(2/3*arcta
n2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + (128*a^2*cos(6*d*x + 6*c)^2 + 128*a^2*sin(6*d*x + 6*c)^2 - 241*a^2*c
os(6*d*x + 6*c) + 87*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 3*(192*a^2*cos(1/3*arctan2(si
n(6*d*x + 6*c), cos(6*d*x + 6*c)))^3*sin(6*d*x + 6*c) + 445*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x +
6*c)))^2*sin(6*d*x + 6*c) + 314*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) - 96
*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x +
6*c), cos(6*d*x + 6*c)))^3 + 61*a^2*sin(6*d*x + 6*c) + (192*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x +
6*c)))*sin(6*d*x + 6*c) + 61*a^2*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 19
2*(a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c)*sin(1/3*
arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*si
n(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 96*(a^2*cos(6*d*
x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^
2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + a^2 + 2*(a^2*cos(6*
d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*
d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*
x + 6*c))) - 3*(192*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3*sin(6*d*x + 6*c) + 445*a^2*cos(
1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c) + 314*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c)
, cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 61*a^2*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x +
6*c))))*cos(5/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 6*(29*a^2*cos(6*d*x + 6*c)^3 - 6*(29*a^2*cos(6
*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 - 45*a^2*cos(6*d
*x + 6*c)^2 + 3*(29*a^2*cos(6*d*x + 6*c)^3 - 74*a^2*cos(6*d*x + 6*c)^2 + 61*a^2*cos(6*d*x + 6*c) + (29*a^2*cos
(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 +
16*a^2*cos(6*d*x + 6*c) + (203*a^2*cos(6*d*x + 6*c)^3 - 489*a^2*cos(6*d*x + 6*c)^2 + 382*a^2*cos(6*d*x + 6*c)
+ 7*(29*a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 - 96*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*
x + 6*c)))^2 + (29*a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 + (29*a^2*cos(6*d*x + 6*c)^3 - 45*a^2*cos
(6*d*x + 6*c)^2 + 16*a^2*cos(6*d*x + 6*c) + (29*a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 + 3*(29*a^2*
cos(6*d*x + 6*c)^3 - 74*a^2*cos(6*d*x + 6*c)^2 + 61*a^2*cos(6*d*x + 6*c) + (29*a^2*cos(6*d*x + 6*c) - 16*a^2)*
sin(6*d*x + 6*c)^2 - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x +
6*c), cos(6*d*x + 6*c)))^2 + (145*a^2*cos(6*d*x + 6*c)^3 - 312*a^2*cos(6*d*x + 6*c)^2 + 215*a^2*cos(6*d*x + 6
*c) + 5*(29*a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 - 48*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(
6*d*x + 6*c))) - 6*((29*a^2*cos(6*d*x + 6*c) - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*
sin(6*d*x + 6*c) + 2*(29*a^2*cos(6*d*x + 6*c) - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*s
in(6*d*x + 6*c) + (29*a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6
*d*x + 6*c))))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 2*(116*a^2*cos(6*d*x + 6*c)^3 - 151*a^2*
cos(6*d*x + 6*c)^2 + 48*a^2*cos(6*d*x + 6*c) + 4*(29*a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2)*cos(1/
3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 29*(3*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))
)^3*sin(6*d*x + 6*c) + 7*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c) + 5*a^2*c
os(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) - 3*(a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*
arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 + a^2*sin(6*d*x + 6*c) + (3*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c
), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6
*c)))^2 + 3*(a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c
)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x +
6*c)))*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 3*(a^2
*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (a^2
*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + a^2 + 2*(a^2*cos(6*d*x + 6*c
) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6
*c))) - 3*(a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6
*c)))^2 + a^2 + 2*(a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*a
rctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(5/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 6*(6*(29*a
^2*cos(6*d*x + 6*c) - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3*sin(6*d*x + 6*c) + 13*(29
*a^2*cos(6*d*x + 6*c) - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c) - 3*(2
9*a^2*cos(6*d*x + 6*c)^3 + 42*a^2*cos(6*d*x + 6*c)^2 - 3*a^2*cos(6*d*x + 6*c) + (29*a^2*cos(6*d*x + 6*c) - 16*
a^2)*sin(6*d*x + 6*c)^2 - 16*a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 + 8*(29*a^2*cos(6*d*x
+ 6*c) - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + (6*(29*a^2*cos(6*d*x
+ 6*c) - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + (29*a^2*cos(6*d*x +
6*c) - 16*a^2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 6*((29*a^2*cos(6*d*x
+ 6*c) - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c) + (29*a^2*cos(6*d*x
+ 6*c) - 16*a^2)*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*(29*a^2*cos(6*d*x
+ 6*c) - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + (29*a^2*cos(6*d*x +
6*c) - 16*a^2)*sin(6*d*x + 6*c))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + (29*a^2*cos(6*d*x + 6*
c) - 16*a^2)*sin(6*d*x + 6*c) - 3*(29*a^2*cos(6*d*x + 6*c)^3 + 42*a^2*cos(6*d*x + 6*c)^2 - 3*a^2*cos(6*d*x + 6
*c) + (29*a^2*cos(6*d*x + 6*c)^3 + 42*a^2*cos(6*d*x + 6*c)^2 - 3*a^2*cos(6*d*x + 6*c) + (29*a^2*cos(6*d*x + 6*
c) - 16*a^2)*sin(6*d*x + 6*c)^2 - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (29*a^2*cos
(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 - 16*a^2 + 2*(29*a^2*cos(6*d*x + 6*c)^3 + 42*a^2*cos(6*d*x + 6*c)^2
- 3*a^2*cos(6*d*x + 6*c) + (29*a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 - 16*a^2)*cos(1/3*arctan2(si
n(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(2/3*arctan2(sin(
6*d*x + 6*c), cos(6*d*x + 6*c))) - 6*(6*(29*a^2*cos(6*d*x + 6*c) - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), c
os(6*d*x + 6*c)))^3*sin(6*d*x + 6*c) + 13*(29*a^2*cos(6*d*x + 6*c) - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c),
cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c) + 8*(29*a^2*cos(6*d*x + 6*c) - 16*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c)
, cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + (29*a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(s
in(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(5/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos
(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) - (19*a^2*cos(6*d*x + 6*c)^3 - 736*a^2*cos(6*d*x + 6*c
)^2 - 1980*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(2/3*arctan2(si
n(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 + 360*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x
+ 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 - 19*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2
(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 3*(57*a^2*cos(6*d*x + 6*c)^3 - 2762*a^2*cos(6*d*x + 6*c)^2 + 2640*a^2*
sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 4913*a^2*cos(6*d*x + 6*c) + (57*a^2*co
s(6*d*x + 6*c) - 2648*a^2)*sin(6*d*x + 6*c)^2 - 2208*a^2 + 660*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^
2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 1200*(a^2*cos(6*d*x +
6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x +
6*c))) + 2088*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/6*arctan
2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 3*(57*a^2*cos
(6*d*x + 6*c)^3 - 2242*a^2*cos(6*d*x + 6*c)^2 + 4393*a^2*cos(6*d*x + 6*c) + 19*(3*a^2*cos(6*d*x + 6*c) - 112*a
^2)*sin(6*d*x + 6*c)^2 - 2208*a^2 + 2088*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x +
6*c) + a^2)*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x
+ 6*c)))^2 + (19*a^2*cos(6*d*x + 6*c) - 736*a^2)*sin(6*d*x + 6*c)^2 + 9*(19*a^2*cos(6*d*x + 6*c)^3 - 698*a^2*c
os(6*d*x + 6*c)^2 - 1453*a^2*cos(6*d*x + 6*c) + (19*a^2*cos(6*d*x + 6*c) - 736*a^2)*sin(6*d*x + 6*c)^2 - 736*a
^2 - 220*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(2/3*arctan2(sin(
6*d*x + 6*c), cos(6*d*x + 6*c))) + 220*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*
c) + a^2)*cos(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 40*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x +
6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 696*(a^2*cos(6*d
*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d
*x + 6*c))))*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(19*a^2*cos(6*d*x + 6*c)^3 - 698*a^2*c
os(6*d*x + 6*c)^2 - 1453*a^2*cos(6*d*x + 6*c) + (19*a^2*cos(6*d*x + 6*c) - 736*a^2)*sin(6*d*x + 6*c)^2 - 736*a
^2 + 40*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6
*d*x + 6*c), cos(6*d*x + 6*c))) + 696*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c
) + a^2)*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6
*c)))^2 + (114*a^2*cos(6*d*x + 6*c)^3 - 4750*a^2*cos(6*d*x + 6*c)^2 - 57*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2(
sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 4416*a^2*cos(6*d*x + 6*c) - 1260*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*
x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 38*(3*a^2*
cos(6*d*x + 6*c) - 122*a^2)*sin(6*d*x + 6*c)^2 - 1980*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2
*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 1320*(a^2*cos(6*d*x + 6*c)^2
+ a^2*sin(6*d*x + 6*c)^2 - 6*a^2*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - a^2*
cos(6*d*x + 6*c) + 3*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*
arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 18*(19*a^
2*cos(6*d*x + 6*c)^3 - 834*a^2*cos(6*d*x + 6*c)^2 + 1551*a^2*cos(6*d*x + 6*c) + (19*a^2*cos(6*d*x + 6*c) - 796
*a^2)*sin(6*d*x + 6*c)^2 - 736*a^2 + 696*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x +
6*c) + a^2)*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x
+ 6*c))) + 3*(1392*a^2*cos(6*d*x + 6*c)^2 + 1392*a^2*sin(6*d*x + 6*c)^2 - 1411*a^2*cos(6*d*x + 6*c) + 19*a^2)*
cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 12*(540*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x
+ 6*c)))*sin(6*d*x + 6*c) - 2088*a^2*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) -
19*(3*a^2*cos(6*d*x + 6*c) - 122*a^2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*
cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 220*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 +
9*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x +
6*c), cos(6*d*x + 6*c)))^2 + 9*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^
2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 6*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2
- a^2*cos(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 6*(6*a^2*cos(1/3*arctan2(sin(6
*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos
(6*d*x + 6*c))))*cos(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + (114*a^2*cos(6*d*x + 6*c)^3 - 4490*a^2
*cos(6*d*x + 6*c)^2 - 57*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 4416*a^2*
cos(6*d*x + 6*c) + 2*(57*a^2*cos(6*d*x + 6*c) - 2188*a^2)*sin(6*d*x + 6*c)^2 + 3*(1392*a^2*cos(6*d*x + 6*c)^2
+ 1392*a^2*sin(6*d*x + 6*c)^2 - 1411*a^2*cos(6*d*x + 6*c) + 19*a^2)*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*
x + 6*c))))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + (696*a^2*cos(6*d*x + 6*c)^2 + 696*a^2*sin(6
*d*x + 6*c)^2 - 19*a^2*cos(6*d*x + 6*c))*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 3*(2640*a^2*co
s(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c) - 480*a^2*cos(1/3*arctan2(sin(6*d*x + 6*
c), cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c) - 1411*a^2*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(
6*d*x + 6*c) - 4*(660*a^2*cos(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) - 540*a^2*cos(
1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 2088*a^2*cos(1/6*arctan2(sin(6*d*x + 6*c),
cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 19*(3*a^2*cos(6*d*x + 6*c) - 122*a^2)*sin(6*d*x + 6*c) + 330*(a^2*cos(6
*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6
*d*x + 6*c))))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 440*(6*a^2*cos(1/3*arctan2(sin(6*d*x + 6
*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c) - 3*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x +
6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(1/2*arctan2(s
in(6*d*x + 6*c), cos(6*d*x + 6*c))) - 4*(2088*a^2*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d
*x + 6*c) + (57*a^2*cos(6*d*x + 6*c) - 2188*a^2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x
+ 6*c))) - 2*(19*a^2*cos(6*d*x + 6*c) - 736*a^2)*sin(6*d*x + 6*c) + 6*(19*a^2*cos(6*d*x + 6*c)^3 - 698*a^2*co
s(6*d*x + 6*c)^2 - 1453*a^2*cos(6*d*x + 6*c) + (19*a^2*cos(6*d*x + 6*c) - 736*a^2)*sin(6*d*x + 6*c)^2 - 736*a^
2 + 40*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*
d*x + 6*c), cos(6*d*x + 6*c))) + 696*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c)
+ a^2)*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*
c))) + 19*(a^2*cos(6*d*x + 6*c) + a^2)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(2/3*arctan2(s
in(6*d*x + 6*c), cos(6*d*x + 6*c))) - 3*(480*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*
d*x + 6*c) + 1411*a^2*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 4*(2088*a^2*cos(
1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + (57*a^2*cos(6*d*x + 6*c) - 2188*a^2)*sin(6
*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 2*(19*a^2*cos(6*d*x + 6*c) - 736*a^2)*sin(
6*d*x + 6*c) - 19*(a^2*cos(6*d*x + 6*c) + a^2)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/3*a
rctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c
))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)))*sqrt(a) - 3045*((a^2*cos(6*d*x + 6*c)^2 + a^2
*sin(6*d*x + 6*c)^2 + 9*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(2
/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2
*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(a^2*cos(6*d*x + 6*c)^2 +
a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2
+ 9*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x
+ 6*c), cos(6*d*x + 6*c)))^2 + 6*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 6*a^2*sin(6*d*x + 6*c)*si
n(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - a^2*cos(6*d*x + 6*c) + 3*(a^2*cos(6*d*x + 6*c)^2 + a^2*si
n(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(2/3
*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 6*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - a^2*cos(6
*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 6*(6*a^2*cos(2/3*arctan2(sin(6*d*x + 6*c),
cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 6*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x +
6*c) + a^2*sin(6*d*x + 6*c) - 3*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^
2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))
- 6*(6*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c))*sin(1
/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*arctan2(-(cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))
)^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x +
6*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(
6*d*x + 6*c), cos(6*d*x + 6*c))) + 1))*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - cos(1/6*arctan2(
sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos
(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1))), (cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))
)^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x +
6*c))) + 1)^(1/4)*(cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*cos(1/2*arctan2(sin(1/3*arctan2(sin(6
*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) + sin(1/6*arctan2(
sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos
(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1))) + 1) - (a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)
^2 + 9*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(2/3*arctan2(sin(6*
d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c)
+ a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6
*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(a^2*cos(6*d*
x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*
x + 6*c)))^2 + 6*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 6*a^2*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin
(6*d*x + 6*c), cos(6*d*x + 6*c))) - a^2*cos(6*d*x + 6*c) + 3*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2
- 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(2/3*arctan2(sin(6*d*
x + 6*c), cos(6*d*x + 6*c))) + 6*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - a^2*cos(6*d*x + 6*c))*cos(
1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 6*(6*a^2*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)
))*sin(6*d*x + 6*c) + 6*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + a^2*sin(6*
d*x + 6*c) - 3*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan
2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 6*(6*a^2*cos(1/
3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*
d*x + 6*c), cos(6*d*x + 6*c))))*arctan2(-(cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arc
tan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4
)*(cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos
(6*d*x + 6*c))) + 1))*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - cos(1/6*arctan2(sin(6*d*x + 6*c),
cos(6*d*x + 6*c)))*sin(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(
6*d*x + 6*c), cos(6*d*x + 6*c))) + 1))), (cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arc
tan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4
)*(cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(
6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) + sin(1/6*arctan2(sin(6*d*x + 6*c),
cos(6*d*x + 6*c)))*sin(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(
6*d*x + 6*c), cos(6*d*x + 6*c))) + 1))) - 1) - (a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 9*(a^2*cos(6
*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6
*d*x + 6*c)))^2 + 9*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*a
rctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos
(6*d*x + 6*c) + a^2)*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(a^2*cos(6*d*x + 6*c)^2 + a^2*
sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 6*
(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 6*a^2*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x + 6*c), co
s(6*d*x + 6*c))) - a^2*cos(6*d*x + 6*c) + 3*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x
+ 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d
*x + 6*c))) + 6*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - a^2*cos(6*d*x + 6*c))*cos(1/3*arctan2(sin(6
*d*x + 6*c), cos(6*d*x + 6*c))) - 6*(6*a^2*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*
c) + 6*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c) - 3*(a
^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c
), cos(6*d*x + 6*c))))*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 6*(6*a^2*cos(1/3*arctan2(sin(6*d
*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6
*d*x + 6*c))))*arctan2((cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6
*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*sin(1/2*arctan2(
sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1
)), (cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*
c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/3*arctan2(sin
(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) + 1) + (a^2*cos(
6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 9*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x
+ 6*c) + a^2)*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*
d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(a^2*c
os(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(2/3*arctan2(sin(6*d*x + 6*c), c
os(6*d*x + 6*c)))^2 + 9*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(1
/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 6*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 6*a^2
*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - a^2*cos(6*d*x + 6*c) + 3*(a^2*cos(6*d
*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d
*x + 6*c))))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 6*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x
+ 6*c)^2 - a^2*cos(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 6*(6*a^2*cos(2/3*arcta
n2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 6*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x +
6*c)))*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c) - 3*(a^2*cos(6*d*x + 6*c)^2 + a^2*sin(6*d*x + 6*c)^2 + 2*a^2*c
os(6*d*x + 6*c) + a^2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*sin(2/3*arctan2(sin(6*d*x + 6*c),
cos(6*d*x + 6*c))) - 6*(6*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + a^2*sin
(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))))*arctan2((cos(1/3*arctan2(sin(6*d*x + 6*c)
, cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x
+ 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), co
s(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)), (cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))
)^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x +
6*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6
*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) - 1))*sqrt(a))*C/(9*(cos(6*d*x + 6*c)^2 + sin(6*d*x + 6*c)^2 - 2*cos(6*d
*x + 6*c) + 1)*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(cos(6*d*x + 6*c)^2 + sin(6*d*x + 6*
c)^2 - 2*cos(6*d*x + 6*c) + 1)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(cos(6*d*x + 6*c)^2
+ sin(6*d*x + 6*c)^2 + 2*cos(6*d*x + 6*c) + 1)*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(cos
(6*d*x + 6*c)^2 + sin(6*d*x + 6*c)^2 + 2*cos(6*d*x + 6*c) + 1)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6
*c)))^2 + cos(6*d*x + 6*c)^2 + 6*(cos(6*d*x + 6*c)^2 + 3*(cos(6*d*x + 6*c)^2 + sin(6*d*x + 6*c)^2 - 2*cos(6*d*
x + 6*c) + 1)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + sin(6*d*x + 6*c)^2 - 6*sin(6*d*x + 6*c)*s
in(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - cos(6*d*x + 6*c))*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(
6*d*x + 6*c))) + 6*(cos(6*d*x + 6*c)^2 + sin(6*d*x + 6*c)^2 - cos(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*
c), cos(6*d*x + 6*c))) + sin(6*d*x + 6*c)^2 - 6*(6*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*
d*x + 6*c) + 6*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) - 3*(cos(6*d*x + 6*c)^2 +
sin(6*d*x + 6*c)^2 + 2*cos(6*d*x + 6*c) + 1)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + sin(6*d*x
+ 6*c))*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 6*(6*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d
*x + 6*c)))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))))/d

Giac [F]

\[ \int \cos ^{\frac {3}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \left (A+C \cos ^2(c+d x)\right ) \, dx=\int { {\left (C \cos \left (d x + c\right )^{2} + A\right )} {\left (a \cos \left (d x + c\right ) + a\right )}^{\frac {5}{2}} \cos \left (d x + c\right )^{\frac {3}{2}} \,d x } \]

[In]

integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm="giac")

[Out]

integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2), x)

Mupad [F(-1)]

Timed out. \[ \int \cos ^{\frac {3}{2}}(c+d x) (a+a \cos (c+d x))^{5/2} \left (A+C \cos ^2(c+d x)\right ) \, dx=\int {\cos \left (c+d\,x\right )}^{3/2}\,\left (C\,{\cos \left (c+d\,x\right )}^2+A\right )\,{\left (a+a\,\cos \left (c+d\,x\right )\right )}^{5/2} \,d x \]

[In]

int(cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2),x)

[Out]

int(cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2), x)