\(\int \frac {(a+a \cos (c+d x))^{5/2} (A+C \cos ^2(c+d x))}{\sec ^{\frac {3}{2}}(c+d x)} \, dx\) [1230]

Optimal result

Integrand size = 37, antiderivative size = 332 \[ \int \frac {(a+a \cos (c+d x))^{5/2} \left (A+C \cos ^2(c+d x)\right )}{\sec ^{\frac {3}{2}}(c+d x)} \, dx=\frac {a^{5/2} (1304 A+1015 C) \arcsin \left (\frac {\sqrt {a} \sin (c+d x)}{\sqrt {a+a \cos (c+d x)}}\right ) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}}{512 d}+\frac {a^3 (136 A+109 C) \sin (c+d x)}{192 d \sqrt {a+a \cos (c+d x)} \sec ^{\frac {5}{2}}(c+d x)}+\frac {a^2 (24 A+23 C) \sqrt {a+a \cos (c+d x)} \sin (c+d x)}{96 d \sec ^{\frac {5}{2}}(c+d x)}+\frac {a C (a+a \cos (c+d x))^{3/2} \sin (c+d x)}{12 d \sec ^{\frac {5}{2}}(c+d x)}+\frac {C (a+a \cos (c+d x))^{5/2} \sin (c+d x)}{6 d \sec ^{\frac {5}{2}}(c+d x)}+\frac {a^3 (1304 A+1015 C) \sin (c+d x)}{768 d \sqrt {a+a \cos (c+d x)} \sec ^{\frac {3}{2}}(c+d x)}+\frac {a^3 (1304 A+1015 C) \sin (c+d x)}{512 d \sqrt {a+a \cos (c+d x)} \sqrt {\sec (c+d x)}} \]

[Out]

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

Rubi [A] (verified)

Time = 1.21 (sec) , antiderivative size = 332, normalized size of antiderivative = 1.00, number of steps used = 9, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.189, Rules used = {4306, 3125, 3055, 3060, 2849, 2853, 222} \[ \int \frac {(a+a \cos (c+d x))^{5/2} \left (A+C \cos ^2(c+d x)\right )}{\sec ^{\frac {3}{2}}(c+d x)} \, dx=\frac {a^{5/2} (1304 A+1015 C) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)} \arcsin \left (\frac {\sqrt {a} \sin (c+d x)}{\sqrt {a \cos (c+d x)+a}}\right )}{512 d}+\frac {a^3 (1304 A+1015 C) \sin (c+d x)}{768 d \sec ^{\frac {3}{2}}(c+d x) \sqrt {a \cos (c+d x)+a}}+\frac {a^3 (136 A+109 C) \sin (c+d x)}{192 d \sec ^{\frac {5}{2}}(c+d x) \sqrt {a \cos (c+d x)+a}}+\frac {a^3 (1304 A+1015 C) \sin (c+d x)}{512 d \sqrt {\sec (c+d x)} \sqrt {a \cos (c+d x)+a}}+\frac {a^2 (24 A+23 C) \sin (c+d x) \sqrt {a \cos (c+d x)+a}}{96 d \sec ^{\frac {5}{2}}(c+d x)}+\frac {a C \sin (c+d x) (a \cos (c+d x)+a)^{3/2}}{12 d \sec ^{\frac {5}{2}}(c+d x)}+\frac {C \sin (c+d x) (a \cos (c+d x)+a)^{5/2}}{6 d \sec ^{\frac {5}{2}}(c+d x)} \]

[In]

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

[Out]

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

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]

Rule 4306

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

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

Mathematica [A] (verified)

Time = 3.86 (sec) , antiderivative size = 190, normalized size of antiderivative = 0.57 \[ \int \frac {(a+a \cos (c+d x))^{5/2} \left (A+C \cos ^2(c+d x)\right )}{\sec ^{\frac {3}{2}}(c+d x)} \, dx=\frac {a^2 \sqrt {\cos (c+d x)} \sqrt {a (1+\cos (c+d x))} \sec \left (\frac {1}{2} (c+d x)\right ) \sqrt {\sec (c+d x)} \left (3 \sqrt {2} (1304 A+1015 C) \arcsin \left (\sqrt {2} \sin \left (\frac {1}{2} (c+d x)\right )\right )+2 \sqrt {\cos (c+d x)} (4648 A+4193 C+(2896 A+3234 C) \cos (c+d x)+4 (184 A+315 C) \cos (2 (c+d x))+96 A \cos (3 (c+d x))+428 C \cos (3 (c+d x))+112 C \cos (4 (c+d x))+16 C \cos (5 (c+d x))) \sin \left (\frac {1}{2} (c+d x)\right )\right )}{3072 d} \]

[In]

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

[Out]

(a^2*Sqrt[Cos[c + d*x]]*Sqrt[a*(1 + Cos[c + d*x])]*Sec[(c + d*x)/2]*Sqrt[Sec[c + d*x]]*(3*Sqrt[2]*(1304*A + 10
15*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 = 2.97 (sec) , antiderivative size = 455, normalized size of antiderivative = 1.37

method	result	size
default	\(\frac {a^{2} \sqrt {\left (1+\cos \left (d x +c \right )\right ) a}\, \left (256 C \left (\cos ^{4}\left (d x +c \right )\right ) \sin \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+896 C \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \left (\cos ^{3}\left (d x +c \right )\right ) \sin \left (d x +c \right )+384 A \left (\cos ^{2}\left (d x +c \right )\right ) \sin \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+1392 C \left (\cos ^{2}\left (d x +c \right )\right ) \sin \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+1472 A \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \cos \left (d x +c \right ) \sin \left (d x +c \right )+1624 C \sin \left (d x +c \right ) \cos \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+2608 A \sin \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+2030 C \sin \left (d x +c \right ) \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}+3912 A \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \tan \left (d x +c \right )+3045 C \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \tan \left (d x +c \right )+3912 A \arctan \left (\sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \tan \left (d x +c \right )\right ) \sec \left (d x +c \right )+3045 C \arctan \left (\sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \tan \left (d x +c \right )\right ) \sec \left (d x +c \right )\right )}{1536 d \left (1+\cos \left (d x +c \right )\right ) \sec \left (d x +c \right )^{\frac {3}{2}} \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}}\)	\(455\)
parts	\(\frac {A \,a^{2} \sqrt {\left (1+\cos \left (d x +c \right )\right ) a}\, \left (48 \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \left (\cos ^{2}\left (d x +c \right )\right ) \sin \left (d x +c \right )+184 \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \cos \left (d x +c \right ) \sin \left (d x +c \right )+326 \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \sin \left (d x +c \right )+489 \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \tan \left (d x +c \right )+489 \arctan \left (\sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \tan \left (d x +c \right )\right ) \sec \left (d x +c \right )\right )}{192 d \left (1+\cos \left (d x +c \right )\right ) \sec \left (d x +c \right )^{\frac {3}{2}} \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}}+\frac {C \,a^{2} \sqrt {\left (1+\cos \left (d x +c \right )\right ) a}\, \left (256 \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \left (\cos ^{4}\left (d x +c \right )\right ) \sin \left (d x +c \right )+896 \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \left (\cos ^{3}\left (d x +c \right )\right ) \sin \left (d x +c \right )+1392 \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \left (\cos ^{2}\left (d x +c \right )\right ) \sin \left (d x +c \right )+1624 \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \cos \left (d x +c \right ) \sin \left (d x +c \right )+2030 \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \sin \left (d x +c \right )+3045 \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \tan \left (d x +c \right )+3045 \arctan \left (\sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}\, \tan \left (d x +c \right )\right ) \sec \left (d x +c \right )\right )}{1536 d \left (1+\cos \left (d x +c \right )\right ) \sec \left (d x +c \right )^{\frac {3}{2}} \sqrt {\frac {\cos \left (d x +c \right )}{1+\cos \left (d x +c \right )}}}\)	\(504\)

[In]

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

[Out]

1/1536*a^2/d*((1+cos(d*x+c))*a)^(1/2)/(1+cos(d*x+c))/sec(d*x+c)^(3/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(256*C
*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+896*C*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^
3*sin(d*x+c)+384*A*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+1392*C*cos(d*x+c)^2*sin(d*x+c)*(c
os(d*x+c)/(1+cos(d*x+c)))^(1/2)+1472*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+1624*C*sin(d*x+
c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+2608*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+2030*C*sin
(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3912*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*tan(d*x+c)+3045*C*(cos(d*x+
c)/(1+cos(d*x+c)))^(1/2)*tan(d*x+c)+3912*A*arctan((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*tan(d*x+c))*sec(d*x+c)+304
5*C*arctan((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*tan(d*x+c))*sec(d*x+c))

Fricas [A] (verification not implemented)

none

Time = 0.35 (sec) , antiderivative size = 217, normalized size of antiderivative = 0.65 \[ \int \frac {(a+a \cos (c+d x))^{5/2} \left (A+C \cos ^2(c+d x)\right )}{\sec ^{\frac {3}{2}}(c+d x)} \, dx=-\frac {3 \, {\left ({\left (1304 \, A + 1015 \, C\right )} a^{2} \cos \left (d x + c\right ) + {\left (1304 \, A + 1015 \, C\right )} a^{2}\right )} \sqrt {a} \arctan \left (\frac {\sqrt {a \cos \left (d x + c\right ) + a} \sqrt {\cos \left (d x + c\right )}}{\sqrt {a} \sin \left (d x + c\right )}\right ) - \frac {{\left (256 \, C a^{2} \cos \left (d x + c\right )^{6} + 896 \, C a^{2} \cos \left (d x + c\right )^{5} + 48 \, {\left (8 \, A + 29 \, C\right )} a^{2} \cos \left (d x + c\right )^{4} + 8 \, {\left (184 \, A + 203 \, C\right )} a^{2} \cos \left (d x + c\right )^{3} + 2 \, {\left (1304 \, A + 1015 \, C\right )} a^{2} \cos \left (d x + c\right )^{2} + 3 \, {\left (1304 \, A + 1015 \, C\right )} a^{2} \cos \left (d x + c\right )\right )} \sqrt {a \cos \left (d x + c\right ) + a} \sin \left (d x + c\right )}{\sqrt {\cos \left (d x + c\right )}}}{1536 \, {\left (d \cos \left (d x + c\right ) + d\right )}} \]

[In]

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

[Out]

-1/1536*(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))) - (256*C*a^2*cos(d*x + c)^6 + 896*C*a^2*cos(d*x + c)^5 + 48*(8*A
+ 29*C)*a^2*cos(d*x + c)^4 + 8*(184*A + 203*C)*a^2*cos(d*x + c)^3 + 2*(1304*A + 1015*C)*a^2*cos(d*x + c)^2 + 3
*(1304*A + 1015*C)*a^2*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)
+ d)

Sympy [F(-1)]

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

[In]

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

[Out]

Timed out

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 42534 vs. \(2 (284) = 568\).

Time = 3.18 (sec) , antiderivative size = 42534, normalized size of antiderivative = 128.11 \[ \int \frac {(a+a \cos (c+d x))^{5/2} \left (A+C \cos ^2(c+d x)\right )}{\sec ^{\frac {3}{2}}(c+d x)} \, dx=\text {Too large to display} \]

[In]

integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),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)))) + (16*(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)^(
3/4)*((a^2*cos(6*d*x + 6*c)^2*sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c)^3 + 405*(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(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 + 9*(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) + 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(1/2*arctan2(sin(6*d*x + 6*c), cos
(6*d*x + 6*c))) + 45*(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*(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) + 45*(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*(a^2*sin(6*d*x + 6*c)^3 - 180*a^2*cos
(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) - 180*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*cos(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) - 29*a^2)*sin(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(1/2*arctan2(sin
(6*d*x + 6*c), cos(6*d*x + 6*c))) + 90*(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))) + 45*(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(s
in(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 9*(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) + 45*(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*(2*a^2*sin(6*d*x + 6*c)^3 + a^2*cos(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c
) + 6*(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) + 45*
(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*(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))) - 81*a^2*cos(6*d*x + 6*c) + 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))) - 12*(a^2*sin(6*d*x + 6*c)^2 + 45*a^2*si
n(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))) + 90*(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))) + (3*a^2*cos(1/3*arctan
2(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*(a^2*sin(6*d*x + 6*c)^3 + (a^2*cos(6*d*x + 6*c)^2 - a^2*cos(6*d*x + 6*c))*sin(6*d*x + 6*c) + 45*(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*(15*a^2*cos(6*d*x + 6*c)^2 + 13*a^2*sin(6*d*x +
6*c)^2 - 90*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 135*(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 + 135*(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)))^2 + 135*(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*(15*a^2*cos(6*d*x + 6*c)^2 + 13*a
^2*sin(6*d*x + 6*c)^2 - 80*a^2*sin(6*d*x + 6*c)*sin(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 90*a^2*
sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 90*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan
2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 15*a^2*cos(6*d*x + 6*c) + 45*(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))) - (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*(15*a^2*cos(6*d*x + 6*c)^2 + 13*a^2*sin(6*d*x + 6*c)^2 - 90*a^2*sin(6*d*x + 6*c)*sin(1/6*arcta
n2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 15*a^2*cos(6*d*x + 6*c))*cos(1/3*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) + 27*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*(a^2*sin(6*d*x
+ 6*c)^3 - 90*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*cos(6*d*x + 6*
c)^2 + 2*a^2*cos(6*d*x + 6*c) - 14*a^2)*sin(6*d*x + 6*c) + 45*(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))) + (40*a^2*cos(6*d*x + 6*c)
^2 + 40*a^2*sin(6*d*x + 6*c)^2 - 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 - 81*a^2*cos(6*d*x + 6*c) + a^2)*cos(1/3*ar
ctan2(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)))*s
in(6*d*x + 6*c) + 27*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*arcta
n2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 6*(a^2*sin(6*d*x + 6*c)^2 + 45*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*(a^2*sin(6*d*x + 6*c)^2 + 45*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))) + 45*(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*a
rctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) - (a^2*cos(6*d*x + 6*c)^3 - 40*a^2*cos(6*d*x + 6*c)^2 + 405*
(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*(a^2*cos(6*d*x + 6*c)^3 - 12*a^2*cos(6*d*x + 6*c)^2 - 180*a^2*sin(6*d*x + 6*c)*s
in(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 51*a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c) - 10*a^2
)*sin(6*d*x + 6*c)^2 - 40*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(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 90*(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))) - 45*(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*(a^2*cos(6*d*x + 6*c)^3 - 42*a^2*cos(6*d*x
+ 6*c)^2 + 81*a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c) - 40*a^2)*sin(6*d*x + 6*c)^2 - 40*a^2 - 45*(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 + (a^2*cos(6*d*x + 6*c) - 40*a^2)*sin(
6*d*x + 6*c)^2 + 9*(a^2*cos(6*d*x + 6*c)^3 - 38*a^2*cos(6*d*x + 6*c)^2 - 79*a^2*cos(6*d*x + 6*c) + (a^2*cos(6*
d*x + 6*c) - 40*a^2)*sin(6*d*x + 6*c)^2 - 40*a^2 + 45*(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))) + 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(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 4
5*(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*(a^2*cos(6*d*x + 6*c)^3
- 38*a^2*cos(6*d*x + 6*c)^2 - 79*a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c) - 40*a^2)*sin(6*d*x + 6*c)^2 - 4
0*a^2 - 45*(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))))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 3*(2*a^2*cos(6*d*
x + 6*c)^3 - 67*a^2*cos(6*d*x + 6*c)^2 - a^2*sin(6*d*x + 6*c)*sin(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*
c))) + 80*a^2*cos(6*d*x + 6*c) + 135*(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 + (2*a^2*cos(6*d*x + 6*c) - 65*a^2)*sin(6*d*x +
6*c)^2 + 135*(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 + (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))) - 81*a^2*cos(6*d*x + 6*c) + 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*(a^2*cos(6*d*x + 6*c)^3 - 27*a^2*
cos(6*d*x + 6*c)^2 + 66*a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c) - 25*a^2)*sin(6*d*x + 6*c)^2 - 40*a^2 - 4
5*(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))) - 90*(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*(90*a
^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) - 90*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*a^2*cos(6*d*x + 6*c) - 65*a^2)*sin(6*d*x + 6*c))*sin(1/3*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))) + (40*a^2*cos(6*d
*x + 6*c)^2 + 40*a^2*sin(6*d*x + 6*c)^2 - 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 - 81*a^2*cos(6*d*x + 6*c) + a^2)*c
os(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) + 27*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*(a^2*cos(6*d*x + 6*c)^3 - 41*a^2*cos(6*d*x + 6*c)^2 + 40*
a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c) - 40*a^2)*sin(6*d*x + 6*c)^2 - 45*(a^2*cos(6*d*x + 6*c)^2 + a^2*s
in(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*arctan
2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 45*(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))) - 3*(540*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) - 90*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*(80*a^2*cos(1/2
*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 90*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(
6*d*x + 6*c)))*sin(6*d*x + 6*c) - 90*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*a^2*cos(6*d*x + 6*c) - 65*a^2)*sin(6*d*x + 6*c) - 45*(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)
+ 27*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))))*cos(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) -
12*(45*a^2*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) - (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*(a^2*cos(6*d*x + 6*c) - 40*a^
2)*sin(6*d*x + 6*c) - (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))) - 6*(a
^2*cos(6*d*x + 6*c)^3 - 38*a^2*cos(6*d*x + 6*c)^2 - 79*a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c) - 40*a^2)*
sin(6*d*x + 6*c)^2 - 40*a^2 - 45*(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))) - (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*(45*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*(45*a^2*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c
)))*sin(6*d*x + 6*c) - (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))) - (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)*((9*(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))*c
os(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*sin(6*d*x + 6*c) + a^2*sin(6*d*
x + 6*c)^3 + 9*(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 + 6*(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(sin(6*d*x + 6*c), cos(6*d*x + 6*c)
))^3 - 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)^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 + 9*(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)*si
n(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 + (22*a^2*sin(6*d*x + 6*c)^3 + (22*a^2*cos(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 + 9*(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 + (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*arctan2(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))*c
os(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 + (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*co
s(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(si
n(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(si
n(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(si
n(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), co
s(6*d*x + 6*c))) - 6*(6*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 - a^2*si
n(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*sin(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))) + 2*(4*a^2*sin(6*d*x + 6*c)^3 + (4*a^2*c
os(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(s
in(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 - 225*a^2*cos(6*d*x + 6*c) + 97*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 - 9*(64*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6
*d*x + 6*c)))*sin(6*d*x + 6*c) + 11*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 - 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 - 487*a^2*cos(6*d*x
+ 6*c) + 150*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 + 287*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 + 159*a^2*cos(6*d*x + 6*c) + 97*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*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 - 32*a^2*sin(6*d
*x + 6*c)^2 + 33*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 - 417*a^2*cos
(6*d*x + 6*c) + 193*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 - 33*a^2*cos(6*d*x + 6*c) + 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 - a^2 - 2*(80*a^2*cos(6*d*x + 6*c)^2 + 80*a^2*sin(6*d*x + 6*c)^2 - 129*a^2*c
os(6*d*x + 6*c) + 49*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*arct
an2(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 - 101*a^2*
cos(6*d*x + 6*c) + 3*a^2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 9*(64*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) + 139*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) + 86*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) - 32*(
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 + 11*a^2*sin(6*d*x + 6*c) + (64*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c
)))*sin(6*d*x + 6*c) + 11*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 + 64*(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*arct
an2(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))) - 32*(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))) - 9*(64*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) + 139*a^2*cos(1/3*a
rctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2*sin(6*d*x + 6*c) + 86*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(
6*d*x + 6*c)))*sin(6*d*x + 6*c) + 11*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))) - 6*(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*c
os(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*arct
an2(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), 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(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)))^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)*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*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) - (a^2*cos(6*d*x + 6*c)^2*
sin(6*d*x + 6*c) + a^2*sin(6*d*x + 6*c)^3 + a^2*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x
+ 6*c) + 648*(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 - 1872*(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 + 9*(a^2*sin(6*d*x + 6*c)^3 + (a^2*co
s(6*d*x + 6*c)^2 - 2*a^2*cos(6*d*x + 6*c) + a^2)*sin(6*d*x + 6*c) + 72*(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))) - 208*(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))) - 944*(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*(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) - 944*(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*(a^2*sin(6*d*x + 6*c)^3 - 288*a^2*co
s(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) - 288*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*cos(6*d*x + 6*c)^2 + 2*a^2*cos(6*d*x + 6*c) - 47*a^2)*sin(6*d*x +
6*c) + 72*(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(si
n(6*d*x + 6*c), cos(6*d*x + 6*c))) - 64*(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))) - 944*(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*(3*a^2*sin(6*d*x + 6*c)^3 + 2496*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)^2 + 6*a^2*cos(6*d*x + 6*c) + 419*a^2)*sin(6
*d*x + 6*c) - 2832*(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*ar
ctan2(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*(2*a^2*
sin(6*d*x + 6*c)^3 + 2496*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 + a^2*co
s(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 6*(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) - 944*(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(si
n(6*d*x + 6*c), cos(6*d*x + 6*c))) + 2*(a^2*cos(6*d*x + 6*c)^2 - a^2*cos(6*d*x + 6*c))*sin(6*d*x + 6*c) + 144*
(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))))*sin(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d
*x + 6*c))) - 4*(104*a^2*cos(6*d*x + 6*c)^2 + 107*a^2*sin(6*d*x + 6*c)^2 - 2832*a^2*sin(6*d*x + 6*c)*sin(1/6*a
rctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 104*a^2*cos(6*d*x + 6*c) + 312*(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))) - (1888*a^2*cos(6*d*x + 6*c)^2 + 1888*a^2*sin(6*d*x + 6*c)^2 - 18
87*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))) + 3*(2*a^2*sin(6*d*x + 6*c)^3 + 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*(a^2*cos(6*d*x + 6*c)^2 - a^2*cos(6*d*x + 6*c))*sin(6*d*x + 6*c) - (1888*a^2*cos(6
*d*x + 6*c)^2 + 1888*a^2*sin(6*d*x + 6*c)^2 - 1887*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))) + 3*(24*a^2*cos(6*d*x + 6*c)^2 + 2
2*a^2*sin(6*d*x + 6*c)^2 + 1887*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 21
6*(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 + 216*(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 - 1032*(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*(12*a^2*cos(
6*d*x + 6*c)^2 + 11*a^2*sin(6*d*x + 6*c)^2 - 72*a^2*sin(6*d*x + 6*c)*sin(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d
*x + 6*c))) + 136*a^2*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 944*a^2*sin(6*d*
x + 6*c)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 12*a^2*cos(6*d*x + 6*c) + 36*(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*(12*a^2*cos(6*d*x + 6*c)^2 + 11*a^2*sin(6*d*
x + 6*c)^2 + 944*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 12*a^2*cos(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) + a^2)*cos(1/6*arctan2(si
n(6*d*x + 6*c), cos(6*d*x + 6*c))) - 144*(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)
)) + 2*(3*a^2*sin(6*d*x + 6*c)^3 + 816*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)^2 + 6*a^2*cos(6*d*x + 6*c) + 139*a^2)*sin(6*d*x + 6*c) - 2832*(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)
)) + 72*(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))))*sin(1/2*arctan2(sin(6*d*x + 6*c),
cos(6*d*x + 6*c))) - (208*a^2*cos(6*d*x + 6*c)^2 + 214*a^2*sin(6*d*x + 6*c)^2 - 5661*a^2*sin(6*d*x + 6*c)*sin(
1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1872*(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*(104*a^2*cos(6*d*x + 6*
c)^2 + 107*a^2*sin(6*d*x + 6*c)^2 - 2832*a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*
c))) - 104*a^2*cos(6*d*x + 6*c))*cos(1/3*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(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))) - (944*a^2*cos(6*d*x + 6*c)^2 + 944*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(1/2*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)) - (a^2*cos(6*d*x + 6*c)^3 + 9*(a^2*cos(6*d*x + 6*c)^3 - 18
*a^2*cos(6*d*x + 6*c)^2 + 33*a^2*cos(6*d*x + 6*c) + (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*(a^2*cos(6*d*x + 6*c)^3 - 14*a^2*cos(6*d*x + 6*c
)^2 - 31*a^2*cos(6*d*x + 6*c) + (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(s
in(6*d*x + 6*c), cos(6*d*x + 6*c)))^4 - 16*a^2*cos(6*d*x + 6*c)^2 + 6*(4*a^2*cos(6*d*x + 6*c)^3 - 71*a^2*cos(6
*d*x + 6*c)^2 + 115*a^2*cos(6*d*x + 6*c) + 4*(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*(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) + (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*(a^2*cos(6*d*x + 6*c)^3 - 18*a^2*cos(6*d*x + 6*c)^2 + 33*a^
2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c)^3 - 18*a^2*cos(6*d*x + 6*c)^2 + 33*a^2*cos(6*d*x + 6*c) + (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 + (
a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 + (a^2*cos(6*d*x + 6*c)^3 - 18*a^2*cos(6*d*x + 6*c)^2 + 33*a
^2*cos(6*d*x + 6*c) + (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*(a^2*cos(6*d*x + 6*c)^3 - 18*a^2*cos(6*d*x + 6*c)^2 + 33*a^2*cos(6*d*
x + 6*c) + (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 + (22*a^2*cos(6*d*x + 6*c)^3 - 382*a^2*
cos(6*d*x + 6*c)^2 + 489*a^2*cos(6*d*x + 6*c) + 22*(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 + (a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c)^2
+ 9*(a^2*cos(6*d*x + 6*c)^3 - 14*a^2*cos(6*d*x + 6*c)^2 - 31*a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c)^3 -
14*a^2*cos(6*d*x + 6*c)^2 - 31*a^2*cos(6*d*x + 6*c) + (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 + (a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x + 6*c
)^2 + (a^2*cos(6*d*x + 6*c)^3 - 14*a^2*cos(6*d*x + 6*c)^2 - 31*a^2*cos(6*d*x + 6*c) + (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*(a^2*
cos(6*d*x + 6*c)^3 - 14*a^2*cos(6*d*x + 6*c)^2 - 31*a^2*cos(6*d*x + 6*c) + (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 + (10*a^2*cos(6*d*x + 6*c)^3 - 142*a^2*cos(6*d*x + 6*c)^2 - 279*a^2*cos(6*d*x + 6*c)
+ 18*(a^2*cos(6*d*x + 6*c)^3 - 16*a^2*cos(6*d*x + 6*c)^2 + a^2*cos(6*d*x + 6*c) + (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*(a^2*cos(6*d*x +
6*c) - 16*a^2)*sin(6*d*x + 6*c)^2 - 144*a^2 + 6*(4*a^2*cos(6*d*x + 6*c)^3 - 59*a^2*cos(6*d*x + 6*c)^2 - 77*a^2
*cos(6*d*x + 6*c) + 4*(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(si
n(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 - 225*a^2*cos(6*d*x + 6*c) + 97*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 - 9*(64*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) +
11*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 - 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*co
s(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), co
s(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 - 487*a^2*cos(6*d*x + 6*c) + 150*a^2)*cos(1/3*arctan
2(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 + 28
7*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 + 159*a^2
*cos(6*d*x + 6*c) + 97*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*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3 - 32*a^2*sin(6*d*x + 6*c)^2 + 33*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 - 417*a^2*cos(6*d*x + 6*c) + 193*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 - 33*a
^2*cos(6*d*x + 6*c) + 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
- a^2 - 2*(80*a^2*cos(6*d*x + 6*c)^2 + 80*a^2*sin(6*d*x + 6*c)^2 - 129*a^2*cos(6*d*x + 6*c) + 49*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 - 101*a^2*cos(6*d*x + 6*c) + 3*a^2)*cos(1/3
*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 9*(64*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) + 139*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) + 86*a^2
*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) - 32*(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 + 11*a^2
*sin(6*d*x + 6*c) + (64*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 11*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 + 64*(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))) - 32*(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))) - 9*(64*a^2*cos(1/3*arctan
2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^3*sin(6*d*x + 6*c) + 139*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) + 86*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) +
11*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*(a^2*cos(6*d*x + 6*c)^3 - 6*(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 - 17*a^2*cos(6*d*x + 6*c)^2 + 3*(a^2*cos(6*d*x + 6*c)^3 - 18*
a^2*cos(6*d*x + 6*c)^2 + 33*a^2*cos(6*d*x + 6*c) + (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) + (7*a^2*cos(6*d*x + 6*c)^3
- 125*a^2*cos(6*d*x + 6*c)^2 + 214*a^2*cos(6*d*x + 6*c) + 7*(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 + (a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d*x
+ 6*c)^2 + (a^2*cos(6*d*x + 6*c)^3 - 17*a^2*cos(6*d*x + 6*c)^2 + 16*a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6
*c) - 16*a^2)*sin(6*d*x + 6*c)^2 + 3*(a^2*cos(6*d*x + 6*c)^3 - 18*a^2*cos(6*d*x + 6*c)^2 + 33*a^2*cos(6*d*x +
6*c) + (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 + (5*a^2*cos(6*d*x + 6*c)^3 - 88*a^2*cos(6*
d*x + 6*c)^2 + 131*a^2*cos(6*d*x + 6*c) + 5*(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*((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*(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) + (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*(4*a^2*cos(6*d
*x + 6*c)^3 - 67*a^2*cos(6*d*x + 6*c)^2 + 48*a^2*cos(6*d*x + 6*c) + 4*(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))) - (3*a^2*cos(1/3*arctan2(sin(6*d*x + 6*c), co
s(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*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*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)
)) - 6*(6*(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*(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*(a^2*cos(6*d*x + 6*c)^3 - 14*a^2*cos(6*d*x + 6*c)^2 - 31*a^2*cos(6*d*x + 6*c) + (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*(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*(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) + (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*((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) + (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*(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) + (a^2*cos(6*d*x + 6*c) - 16*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))) + (a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*d
*x + 6*c) - 3*(a^2*cos(6*d*x + 6*c)^3 - 14*a^2*cos(6*d*x + 6*c)^2 - 31*a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x +
6*c)^3 - 14*a^2*cos(6*d*x + 6*c)^2 - 31*a^2*cos(6*d*x + 6*c) + (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 + (a^2*cos(6*d*x + 6*c) - 16*a^2)*sin(6*
d*x + 6*c)^2 - 16*a^2 + 2*(a^2*cos(6*d*x + 6*c)^3 - 14*a^2*cos(6*d*x + 6*c)^2 - 31*a^2*cos(6*d*x + 6*c) + (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))))*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) -
6*(6*(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*(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*(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) + (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))))*sin(5/2*ar
ctan2(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)) + (a^2*cos(6*d*x + 6*c)^3 + 736*a^2*cos(6*d*x + 6*c)^2 + 648*(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 - 1872*(a^2*co
s(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), co
s(6*d*x + 6*c)))^3 - a^2*sin(6*d*x + 6*c)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 9*(a^2*cos(6*
d*x + 6*c)^3 + 782*a^2*cos(6*d*x + 6*c)^2 - 288*a^2*sin(6*d*x + 6*c)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d
*x + 6*c))) - 1519*a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c) + 784*a^2)*sin(6*d*x + 6*c)^2 + 736*a^2 - 72*(
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))) - 64*(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)*c
os(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 528*(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 + 3*(3*a^2*cos(6*d*x + 6*c)^3 + 1786*a^2*cos(6*d*x + 6*c)^2 - 3997*a^2*cos(6*d*x +
6*c) + (3*a^2*cos(6*d*x + 6*c) + 1792*a^2)*sin(6*d*x + 6*c)^2 + 2208*a^2 - 1584*(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 + (a^2*cos(6*d*x + 6*c) + 736*a^2)*sin(6*d*x + 6*c)^2 + 9*(
a^2*cos(6*d*x + 6*c)^3 + 738*a^2*cos(6*d*x + 6*c)^2 + 1473*a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c) + 736*
a^2)*sin(6*d*x + 6*c)^2 + 736*a^2 + 72*(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))) - 72*(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))) - 208*(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))) - 528*(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*arc
tan2(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*(a^2*cos
(6*d*x + 6*c)^3 + 738*a^2*cos(6*d*x + 6*c)^2 + 1473*a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c) + 736*a^2)*si
n(6*d*x + 6*c)^2 + 736*a^2 - 208*(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))) - 528*(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*(2*a^2*cos(6*d*x + 6*c)^3 + 1494*a^2*cos(6*d*x + 6*c)^2 - a^2*sin(6*d*x +
6*c)*sin(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 1472*a^2*cos(6*d*x + 6*c) - 1032*(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 + 2*(a^2*cos(6*d*x + 6*c) + 748*a^2)*sin(6*d*x + 6*c)^2 + 216*(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 - 144*(a^2*c
os(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))) + 2*(3*a^2*cos(6*d*x + 6*c)^3 + 2066*a^2*cos(6*d*x + 6*c)^2 - 4277*a^2*cos(6*d*x + 6*c) + (3*a^2*cos(6*d
*x + 6*c) + 2072*a^2)*sin(6*d*x + 6*c)^2 + 2208*a^2 - 1584*(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))) - (1056*a^2*cos(6*d*x + 6*c)^2 + 1056*a^2*sin(6*d*x + 6*c)^2 - 1055*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))) + 12*(136*a^2*cos(1/3*arctan2(sin(6*d*x + 6*
c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 528*a^2*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d
*x + 6*c) - (a^2*cos(6*d*x + 6*c) + 748*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))) - 72*(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))) + (6*a^2*cos(6*d*x + 6*c)^3 + 4202
*a^2*cos(6*d*x + 6*c)^2 - 3*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*(3*a^2*cos(6*d*x + 6*c) + 2104*a^2)*sin(6*d*x + 6*c)^2 - 3*(1056*a^2*cos(6*d*x + 6*c)^
2 + 1056*a^2*sin(6*d*x + 6*c)^2 - 1055*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))) - (528*a^2*cos(6*d*x + 6*c)^2 + 528*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))) - 3*(864*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) - 2496*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) - 1055*a^2*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*
x + 6*c) - 12*(72*a^2*cos(1/2*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 136*a^2*cos(1/3*
arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))*sin(6*d*x + 6*c) + 528*a^2*cos(1/6*arctan2(sin(6*d*x + 6*c), cos(
6*d*x + 6*c)))*sin(6*d*x + 6*c) - (a^2*cos(6*d*x + 6*c) + 748*a^2)*sin(6*d*x + 6*c) + 36*(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))) - 144*(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(sin(6*d*x +
6*c), cos(6*d*x + 6*c))) - 4*(1584*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*a^2*cos(6*d*x + 6*c) + 2104*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*cos(6*d*x + 6*c) + 736*a^2)*sin(6*d*x + 6*c) - 6*(a^2*cos(6*d*x + 6*c)^3 + 738*a^2*cos(6*d*x + 6*c)^2 +
1473*a^2*cos(6*d*x + 6*c) + (a^2*cos(6*d*x + 6*c) + 736*a^2)*sin(6*d*x + 6*c)^2 + 736*a^2 - 208*(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))) - 528*(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*arct
an2(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))) - (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))) + 3*(2496*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) + 1055*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*(1584*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*a^2*cos(6*d*x + 6*c) + 2104*a^2)*sin(6*d*x + 6*c))*cos(1/3*ar
ctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 2*(a^2*cos(6*d*x + 6*c) + 736*a^2)*sin(6*d*x + 6*c) + (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(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)*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), co
s(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(si
n(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*a
rctan2(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*a
rctan2(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*c
os(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), c
os(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*ar
ctan2(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*a
rctan2(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*arcta
n2(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*a
rctan2(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*co
s(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*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))) + 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(si
n(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*s
in(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(si
n(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*arctan
2(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*arc
tan2(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*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*arctan
2(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*ar
ctan2(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*arctan
2(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)*sin(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*arctan
2(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]

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

[In]

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

[Out]

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

Mupad [F(-1)]

Timed out. \[ \int \frac {(a+a \cos (c+d x))^{5/2} \left (A+C \cos ^2(c+d x)\right )}{\sec ^{\frac {3}{2}}(c+d x)} \, dx=\int \frac {\left (C\,{\cos \left (c+d\,x\right )}^2+A\right )\,{\left (a+a\,\cos \left (c+d\,x\right )\right )}^{5/2}}{{\left (\frac {1}{\cos \left (c+d\,x\right )}\right )}^{3/2}} \,d x \]

[In]

int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(3/2),x)

[Out]

int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(3/2), x)