\(\int \frac {A+B \sec (c+d x)}{\sec ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx\) [260]

Optimal result

Integrand size = 35, antiderivative size = 203 \[ \int \frac {A+B \sec (c+d x)}{\sec ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx=\frac {(11 A-7 B) \text {arctanh}\left (\frac {\sqrt {a} \sqrt {\sec (c+d x)} \sin (c+d x)}{\sqrt {2} \sqrt {a+a \sec (c+d x)}}\right )}{2 \sqrt {2} a^{3/2} d}-\frac {(A-B) \sin (c+d x)}{2 d \sqrt {\sec (c+d x)} (a+a \sec (c+d x))^{3/2}}+\frac {(7 A-3 B) \sin (c+d x)}{6 a d \sqrt {\sec (c+d x)} \sqrt {a+a \sec (c+d x)}}-\frac {(19 A-15 B) \sqrt {\sec (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}} \]

[Out]

1/4*(11*A-7*B)*arctanh(1/2*sin(d*x+c)*a^(1/2)*sec(d*x+c)^(1/2)*2^(1/2)/(a+a*sec(d*x+c))^(1/2))/a^(3/2)/d*2^(1/
2)-1/2*(A-B)*sin(d*x+c)/d/(a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2)+1/6*(7*A-3*B)*sin(d*x+c)/a/d/sec(d*x+c)^(1/2
)/(a+a*sec(d*x+c))^(1/2)-1/6*(19*A-15*B)*sin(d*x+c)*sec(d*x+c)^(1/2)/a/d/(a+a*sec(d*x+c))^(1/2)

Rubi [A] (verified)

Time = 0.90 (sec) , antiderivative size = 203, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {4105, 4107, 4098, 3893, 212} \[ \int \frac {A+B \sec (c+d x)}{\sec ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx=\frac {(11 A-7 B) \text {arctanh}\left (\frac {\sqrt {a} \sin (c+d x) \sqrt {\sec (c+d x)}}{\sqrt {2} \sqrt {a \sec (c+d x)+a}}\right )}{2 \sqrt {2} a^{3/2} d}-\frac {(19 A-15 B) \sin (c+d x) \sqrt {\sec (c+d x)}}{6 a d \sqrt {a \sec (c+d x)+a}}+\frac {(7 A-3 B) \sin (c+d x)}{6 a d \sqrt {\sec (c+d x)} \sqrt {a \sec (c+d x)+a}}-\frac {(A-B) \sin (c+d x)}{2 d \sqrt {\sec (c+d x)} (a \sec (c+d x)+a)^{3/2}} \]

[In]

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

[Out]

((11*A - 7*B)*ArcTanh[(Sqrt[a]*Sqrt[Sec[c + d*x]]*Sin[c + d*x])/(Sqrt[2]*Sqrt[a + a*Sec[c + d*x]])])/(2*Sqrt[2
]*a^(3/2)*d) - ((A - B)*Sin[c + d*x])/(2*d*Sqrt[Sec[c + d*x]]*(a + a*Sec[c + d*x])^(3/2)) + ((7*A - 3*B)*Sin[c
+ d*x])/(6*a*d*Sqrt[Sec[c + d*x]]*Sqrt[a + a*Sec[c + d*x]]) - ((19*A - 15*B)*Sqrt[Sec[c + d*x]]*Sin[c + d*x])
/(6*a*d*Sqrt[a + a*Sec[c + d*x]])

Rule 212

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

Rule 3893

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

Rule 4098

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

Rule 4105

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

Rule 4107

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

Rubi steps \begin{align*} \text {integral}& = -\frac {(A-B) \sin (c+d x)}{2 d \sqrt {\sec (c+d x)} (a+a \sec (c+d x))^{3/2}}+\frac {\int \frac {\frac {1}{2} a (7 A-3 B)-2 a (A-B) \sec (c+d x)}{\sec ^{\frac {3}{2}}(c+d x) \sqrt {a+a \sec (c+d x)}} \, dx}{2 a^2} \\ & = -\frac {(A-B) \sin (c+d x)}{2 d \sqrt {\sec (c+d x)} (a+a \sec (c+d x))^{3/2}}+\frac {(7 A-3 B) \sin (c+d x)}{6 a d \sqrt {\sec (c+d x)} \sqrt {a+a \sec (c+d x)}}+\frac {\int \frac {-\frac {1}{4} a^2 (19 A-15 B)+\frac {1}{2} a^2 (7 A-3 B) \sec (c+d x)}{\sqrt {\sec (c+d x)} \sqrt {a+a \sec (c+d x)}} \, dx}{3 a^3} \\ & = -\frac {(A-B) \sin (c+d x)}{2 d \sqrt {\sec (c+d x)} (a+a \sec (c+d x))^{3/2}}+\frac {(7 A-3 B) \sin (c+d x)}{6 a d \sqrt {\sec (c+d x)} \sqrt {a+a \sec (c+d x)}}-\frac {(19 A-15 B) \sqrt {\sec (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}}+\frac {(11 A-7 B) \int \frac {\sqrt {\sec (c+d x)}}{\sqrt {a+a \sec (c+d x)}} \, dx}{4 a} \\ & = -\frac {(A-B) \sin (c+d x)}{2 d \sqrt {\sec (c+d x)} (a+a \sec (c+d x))^{3/2}}+\frac {(7 A-3 B) \sin (c+d x)}{6 a d \sqrt {\sec (c+d x)} \sqrt {a+a \sec (c+d x)}}-\frac {(19 A-15 B) \sqrt {\sec (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}}-\frac {(11 A-7 B) \text {Subst}\left (\int \frac {1}{2 a-x^2} \, dx,x,-\frac {a \sqrt {\sec (c+d x)} \sin (c+d x)}{\sqrt {a+a \sec (c+d x)}}\right )}{2 a d} \\ & = \frac {(11 A-7 B) \text {arctanh}\left (\frac {\sqrt {a} \sqrt {\sec (c+d x)} \sin (c+d x)}{\sqrt {2} \sqrt {a+a \sec (c+d x)}}\right )}{2 \sqrt {2} a^{3/2} d}-\frac {(A-B) \sin (c+d x)}{2 d \sqrt {\sec (c+d x)} (a+a \sec (c+d x))^{3/2}}+\frac {(7 A-3 B) \sin (c+d x)}{6 a d \sqrt {\sec (c+d x)} \sqrt {a+a \sec (c+d x)}}-\frac {(19 A-15 B) \sqrt {\sec (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}} \\ \end{align*}

Mathematica [A] (verified)

Time = 1.28 (sec) , antiderivative size = 173, normalized size of antiderivative = 0.85 \[ \int \frac {A+B \sec (c+d x)}{\sec ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx=\frac {-6 \sqrt {2} (11 A-7 B) \arctan \left (\frac {\sqrt {2} \sqrt {\sec (c+d x)}}{\sqrt {1-\sec (c+d x)}}\right ) \cos ^3\left (\frac {1}{2} (c+d x)\right ) \sec ^{\frac {5}{2}}(c+d x) \sin \left (\frac {1}{2} (c+d x)\right )+\sqrt {1-\sec (c+d x)} (12 (-A+B)+(-17 A+15 B+2 A \cos (2 (c+d x))) \sec (c+d x)) \tan (c+d x)}{6 d \sqrt {-((-1+\sec (c+d x)) \sec (c+d x))} (a (1+\sec (c+d x)))^{3/2}} \]

[In]

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

[Out]

(-6*Sqrt[2]*(11*A - 7*B)*ArcTan[(Sqrt[2]*Sqrt[Sec[c + d*x]])/Sqrt[1 - Sec[c + d*x]]]*Cos[(c + d*x)/2]^3*Sec[c
+ d*x]^(5/2)*Sin[(c + d*x)/2] + Sqrt[1 - Sec[c + d*x]]*(12*(-A + B) + (-17*A + 15*B + 2*A*Cos[2*(c + d*x)])*Se
c[c + d*x])*Tan[c + d*x])/(6*d*Sqrt[-((-1 + Sec[c + d*x])*Sec[c + d*x])]*(a*(1 + Sec[c + d*x]))^(3/2))

Maple [B] (warning: unable to verify)

Leaf count of result is larger than twice the leaf count of optimal. \(449\) vs. \(2(172)=344\).

Time = 4.56 (sec) , antiderivative size = 450, normalized size of antiderivative = 2.22

method	result	size
parts	\(\frac {A \sqrt {a \left (1+\sec \left (d x +c \right )\right )}\, \left (33 \sqrt {2}\, \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (\cos \left (d x +c \right )+1\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}}\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}\, \cos \left (d x +c \right )+66 \sqrt {2}\, \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (\cos \left (d x +c \right )+1\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}}\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}+33 \sqrt {2}\, \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (\cos \left (d x +c \right )+1\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}}\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}\, \sec \left (d x +c \right )+8 \cos \left (d x +c \right ) \sin \left (d x +c \right )-24 \sin \left (d x +c \right )-38 \tan \left (d x +c \right )\right )}{12 d \,a^{2} \left (\cos \left (d x +c \right )+1\right )^{2} \sec \left (d x +c \right )^{\frac {3}{2}}}-\frac {B \left (-\left (1-\cos \left (d x +c \right )\right )^{3} \csc \left (d x +c \right )^{3}+7 \arctan \left (\frac {-\cot \left (d x +c \right )+\csc \left (d x +c \right )}{\sqrt {-\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-1}}\right ) \sqrt {-\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-1}-9 \csc \left (d x +c \right )+9 \cot \left (d x +c \right )\right ) \sqrt {-\frac {2 a}{\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-1}}}{4 d \,a^{2} \sqrt {-\frac {\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}+1}{\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-1}}}\)	\(450\)
default	\(-\frac {\left (-3 A \left (1-\cos \left (d x +c \right )\right )^{5} \csc \left (d x +c \right )^{5}+3 B \left (1-\cos \left (d x +c \right )\right )^{5} \csc \left (d x +c \right )^{5}+33 A \arctan \left (\frac {-\cot \left (d x +c \right )+\csc \left (d x +c \right )}{\sqrt {-\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-1}}\right ) \sqrt {-\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-1}\, \left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-21 B \arctan \left (\frac {-\cot \left (d x +c \right )+\csc \left (d x +c \right )}{\sqrt {-\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-1}}\right ) \sqrt {-\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-1}\, \left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-46 A \left (1-\cos \left (d x +c \right )\right )^{3} \csc \left (d x +c \right )^{3}+30 B \left (1-\cos \left (d x +c \right )\right )^{3} \csc \left (d x +c \right )^{3}+33 \arctan \left (\frac {-\cot \left (d x +c \right )+\csc \left (d x +c \right )}{\sqrt {-\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-1}}\right ) \sqrt {-\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-1}\, A -21 \arctan \left (\frac {-\cot \left (d x +c \right )+\csc \left (d x +c \right )}{\sqrt {-\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-1}}\right ) \sqrt {-\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-1}\, B -27 A \left (-\cot \left (d x +c \right )+\csc \left (d x +c \right )\right )+27 B \left (-\cot \left (d x +c \right )+\csc \left (d x +c \right )\right )\right ) \sqrt {-\frac {2 a}{\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-1}}}{12 a^{2} d \left (\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-1\right ) \left (-\frac {\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}+1}{\left (1-\cos \left (d x +c \right )\right )^{2} \csc \left (d x +c \right )^{2}-1}\right )^{\frac {3}{2}}}\)	\(573\)

[In]

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

[Out]

1/12*A/d/a^2*(a*(1+sec(d*x+c)))^(1/2)/(cos(d*x+c)+1)^2/sec(d*x+c)^(3/2)*(33*2^(1/2)*arctan(1/2*sin(d*x+c)*2^(1
/2)/(cos(d*x+c)+1)/(-1/(cos(d*x+c)+1))^(1/2))*(-1/(cos(d*x+c)+1))^(1/2)*cos(d*x+c)+66*2^(1/2)*arctan(1/2*sin(d
*x+c)*2^(1/2)/(cos(d*x+c)+1)/(-1/(cos(d*x+c)+1))^(1/2))*(-1/(cos(d*x+c)+1))^(1/2)+33*2^(1/2)*arctan(1/2*sin(d*
x+c)*2^(1/2)/(cos(d*x+c)+1)/(-1/(cos(d*x+c)+1))^(1/2))*(-1/(cos(d*x+c)+1))^(1/2)*sec(d*x+c)+8*cos(d*x+c)*sin(d
*x+c)-24*sin(d*x+c)-38*tan(d*x+c))-1/4*B/d/a^2*(-(1-cos(d*x+c))^3*csc(d*x+c)^3+7*arctan(1/(-(1-cos(d*x+c))^2*c
sc(d*x+c)^2-1)^(1/2)*(-cot(d*x+c)+csc(d*x+c)))*(-(1-cos(d*x+c))^2*csc(d*x+c)^2-1)^(1/2)-9*csc(d*x+c)+9*cot(d*x
+c))*(-2*a/((1-cos(d*x+c))^2*csc(d*x+c)^2-1))^(1/2)/(-((1-cos(d*x+c))^2*csc(d*x+c)^2+1)/((1-cos(d*x+c))^2*csc(
d*x+c)^2-1))^(1/2)

Fricas [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 464, normalized size of antiderivative = 2.29 \[ \int \frac {A+B \sec (c+d x)}{\sec ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx=\left [-\frac {3 \, \sqrt {2} {\left ({\left (11 \, A - 7 \, B\right )} \cos \left (d x + c\right )^{2} + 2 \, {\left (11 \, A - 7 \, B\right )} \cos \left (d x + c\right ) + 11 \, A - 7 \, B\right )} \sqrt {a} \log \left (-\frac {a \cos \left (d x + c\right )^{2} + 2 \, \sqrt {2} \sqrt {a} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sqrt {\cos \left (d x + c\right )} \sin \left (d x + c\right ) - 2 \, a \cos \left (d x + c\right ) - 3 \, a}{\cos \left (d x + c\right )^{2} + 2 \, \cos \left (d x + c\right ) + 1}\right ) - \frac {4 \, {\left (4 \, A \cos \left (d x + c\right )^{3} - 12 \, {\left (A - B\right )} \cos \left (d x + c\right )^{2} - {\left (19 \, A - 15 \, B\right )} \cos \left (d x + c\right )\right )} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sin \left (d x + c\right )}{\sqrt {\cos \left (d x + c\right )}}}{24 \, {\left (a^{2} d \cos \left (d x + c\right )^{2} + 2 \, a^{2} d \cos \left (d x + c\right ) + a^{2} d\right )}}, -\frac {3 \, \sqrt {2} {\left ({\left (11 \, A - 7 \, B\right )} \cos \left (d x + c\right )^{2} + 2 \, {\left (11 \, A - 7 \, B\right )} \cos \left (d x + c\right ) + 11 \, A - 7 \, B\right )} \sqrt {-a} \arctan \left (\frac {\sqrt {2} \sqrt {-a} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sqrt {\cos \left (d x + c\right )}}{a \sin \left (d x + c\right )}\right ) - \frac {2 \, {\left (4 \, A \cos \left (d x + c\right )^{3} - 12 \, {\left (A - B\right )} \cos \left (d x + c\right )^{2} - {\left (19 \, A - 15 \, B\right )} \cos \left (d x + c\right )\right )} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sin \left (d x + c\right )}{\sqrt {\cos \left (d x + c\right )}}}{12 \, {\left (a^{2} d \cos \left (d x + c\right )^{2} + 2 \, a^{2} d \cos \left (d x + c\right ) + a^{2} d\right )}}\right ] \]

[In]

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

[Out]

[-1/24*(3*sqrt(2)*((11*A - 7*B)*cos(d*x + c)^2 + 2*(11*A - 7*B)*cos(d*x + c) + 11*A - 7*B)*sqrt(a)*log(-(a*cos
(d*x + c)^2 + 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*
cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(4*A*cos(d*x + c)^3 - 12*(A - B)*cos(d*x + c)^2
- (19*A - 15*B)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d
*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), -1/12*(3*sqrt(2)*((11*A - 7*B)*cos(d*x + c)^2 + 2*(11*A - 7*B
)*cos(d*x + c) + 11*A - 7*B)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos
(d*x + c))/(a*sin(d*x + c))) - 2*(4*A*cos(d*x + c)^3 - 12*(A - B)*cos(d*x + c)^2 - (19*A - 15*B)*cos(d*x + c))
*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(
d*x + c) + a^2*d)]

Sympy [F]

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

[In]

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

[Out]

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

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 41138 vs. \(2 (172) = 344\).

Time = 0.98 (sec) , antiderivative size = 41138, normalized size of antiderivative = 202.65 \[ \int \frac {A+B \sec (c+d x)}{\sec ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx=\text {Too large to display} \]

[In]

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

[Out]

-1/12*(3*(4*(7*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 7*log(cos(1
/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x
+ 3/2*c)^4 + 63*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(
1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x + 1/2*c)^4 + 4*(7*log(c
os(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 7*log(cos(1/2*d*x + 1/2*c)^2 +
sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 8*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^4 + 70*(lo
g(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 +
sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x + 1/2*c)^2*sin(1/2*d*x + 1/2*c)^2 + 7*(log(
cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + s
in(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(1/2*d*x + 1/2*c)^4 - 8*sin(1/2*d*x + 1/2*c)^5 + 28*(7
*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)
^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1
/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^3 + 4*(21*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1
/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(
1/2*d*x + 1/2*c) - 24*sin(1/2*d*x + 1/2*c)^2 - 20)*sin(3/2*d*x + 3/2*c)^3 - 8*(10*cos(1/2*d*x + 1/2*c)^2 + 3)*
sin(1/2*d*x + 1/2*c)^3 + ((7*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1)
- 7*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 8*sin(1/2*d*x + 1/2*c
))*cos(3/2*d*x + 3/2*c)^2 + 63*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) +
1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x + 1/2*c)^
2 + (7*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 7*log(cos(1/2*d*x +
1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 8*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c
)^2 + 7*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x +
1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(1/2*d*x + 1/2*c)^2 - 8*sin(1/2*d*x + 1/2
*c)^3 + 6*(7*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*
d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x +
1/2*c)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) + 2*(7*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2
+ 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) +
1))*sin(1/2*d*x + 1/2*c) - 8*sin(1/2*d*x + 1/2*c)^2 - 8)*sin(3/2*d*x + 3/2*c) - 8*(9*cos(1/2*d*x + 1/2*c)^2 +
2)*sin(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c)^2 + (427*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 +
2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) +
1))*cos(1/2*d*x + 1/2*c)^2 + 35*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)
+ 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(1/2*d*x + 1/2*c)
^2 - 40*sin(1/2*d*x + 1/2*c)^3 - 8*(61*cos(1/2*d*x + 1/2*c)^2 + 9)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^
2 + ((7*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 7*log(cos(1/2*d*x
+ 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*
c)^2 + 63*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x
+ 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x + 1/2*c)^2 + (7*log(cos(1/2*d*
x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 7*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d
*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 8*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^2 + 7*(log(cos(1/2*
d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d
*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(1/2*d*x + 1/2*c)^2 - 8*sin(1/2*d*x + 1/2*c)^3 + 6*(7*(log(cos
(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(
1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x +
1/2*c))*cos(3/2*d*x + 3/2*c) + 2*(7*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2
*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(1/2*d*x + 1/
2*c) - 8*sin(1/2*d*x + 1/2*c)^2 - 8)*sin(3/2*d*x + 3/2*c) - 8*(9*cos(1/2*d*x + 1/2*c)^2 + 2)*sin(1/2*d*x + 1/2
*c))*sin(5/2*d*x + 5/2*c)^2 + (8*(7*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*
c) + 1) - 7*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 8*sin(1/2*d*x
+ 1/2*c))*cos(3/2*d*x + 3/2*c)^2 + 259*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x +
1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x +
1/2*c)^2 + 91*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/
2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(1/2*d*x + 1/2*c)^2 - 104*sin(1/2*
d*x + 1/2*c)^3 + 28*(7*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - lo
g(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x + 1/2*c) - 8*cos(
1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) - 8*(37*cos(1/2*d*x + 1/2*c)^2 + 21)*sin(1/2*d*x +
1/2*c))*sin(3/2*d*x + 3/2*c)^2 + 2*(2*(7*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x
+ 1/2*c) + 1) - 7*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 8*sin(1/
2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^3 + 63*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d
*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*
d*x + 1/2*c)^3 + 7*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(co
s(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x
+ 1/2*c)^2 - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^3 + 13*(7*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x +
1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x
+ 1/2*c) + 1))*cos(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^2 + (2
*(7*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 7*log(cos(1/2*d*x + 1/
2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) +
7*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*
c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin
(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^2 + 2*(84*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin
(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*co
s(1/2*d*x + 1/2*c)^2 + 7*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) -
log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(1/2*d*x + 1/2*c)^2 - 8*
sin(1/2*d*x + 1/2*c)^3 - 16*(6*cos(1/2*d*x + 1/2*c)^2 + 1)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) + 2*(7*(
log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2
+ sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) - 8*cos(1/2
*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 + 2*(7*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d
*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(1/2*
d*x + 1/2*c) - 8*sin(1/2*d*x + 1/2*c)^2 - 8)*cos(3/2*d*x + 3/2*c) - 8*cos(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*
c) - 8*(9*cos(1/2*d*x + 1/2*c)^3 + 2*cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(147
*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)
^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x + 1/2*c)^3 + 35*(log(cos(1/2*d*x + 1/2*
c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c
)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 - 40*cos(1/2*d*x + 1/2*c)*sin(1
/2*d*x + 1/2*c)^3 - 56*(3*cos(1/2*d*x + 1/2*c)^3 + cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3
/2*c) + 2*(2*(7*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 7*log(cos(
1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 8*sin(1/2*d*x + 1/2*c))*sin(3/2*d*
x + 3/2*c)^3 + 63*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos
(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x + 1/2*c)^2*sin(1/2*d*x
+ 1/2*c) + 7*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2
*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(1/2*d*x + 1/2*c)^3 - 8*sin(1/2*d*x
+ 1/2*c)^4 + (7*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(
1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(1/2*d*x + 1/2*c) - 8*sin(1/2*d*
x + 1/2*c)^2 - 4)*cos(3/2*d*x + 3/2*c)^2 + (35*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/
2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(1
/2*d*x + 1/2*c) - 40*sin(1/2*d*x + 1/2*c)^2 - 36)*sin(3/2*d*x + 3/2*c)^2 - 4*(18*cos(1/2*d*x + 1/2*c)^2 + 5)*s
in(1/2*d*x + 1/2*c)^2 + 6*(7*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1
) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x + 1/2*c)*si
n(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 - 4*cos(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2
*c) - 36*cos(1/2*d*x + 1/2*c)^2 + 2*((7*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x +
1/2*c) + 1) - 7*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 8*sin(1/2*
d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^2 + 63*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x
+ 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*
x + 1/2*c)^2 + 14*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos
(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(1/2*d*x + 1/2*c)^2 - 16*sin(1/
2*d*x + 1/2*c)^3 + 6*(7*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - l
og(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(1/2*d*x + 1/2*c) - 8*cos
(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) - 4*(18*cos(1/2*d*x + 1/2*c)^2 + 7)*sin(1/2*d*x +
1/2*c))*sin(3/2*d*x + 3/2*c))*sin(5/2*d*x + 5/2*c) + 2*(133*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c
)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*
c) + 1))*cos(1/2*d*x + 1/2*c)^2*sin(1/2*d*x + 1/2*c) + 21*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2
+ 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c)
+ 1))*sin(1/2*d*x + 1/2*c)^3 - 24*sin(1/2*d*x + 1/2*c)^4 + 2*(21*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1
/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x +
1/2*c) + 1))*sin(1/2*d*x + 1/2*c) - 24*sin(1/2*d*x + 1/2*c)^2 - 20)*cos(3/2*d*x + 3/2*c)^2 - 8*(19*cos(1/2*d*x
+ 1/2*c)^2 + 7)*sin(1/2*d*x + 1/2*c)^2 + 16*(7*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1
/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(
1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 - 5*cos(1/2*d*x + 1/2*c)
)*cos(3/2*d*x + 3/2*c) - 80*cos(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c) - 8*(9*cos(1/2*d*x + 1/2*c)^4 + 11*co
s(1/2*d*x + 1/2*c)^2)*sin(1/2*d*x + 1/2*c))*B*sqrt(a)/(4*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^4 + 28*sqrt(2)*a^2*c
os(3/2*d*x + 3/2*c)^3*cos(1/2*d*x + 1/2*c) + 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^4 + 4*sqrt(2)*a^2*sin(3/2*d*x
+ 3/2*c)^4 + 12*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)^3*sin(1/2*d*x + 1/2*c) + 10*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^
2*sin(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^4 + (sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2 + 6*sqrt(2
)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c) + 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(3/2*d
*x + 3/2*c)^2 + 2*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*
cos(5/2*d*x + 5/2*c)^2 + (61*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 5*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(3/
2*d*x + 3/2*c)^2 + (sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2 + 6*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*
c) + 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)^2 + 2*sqrt(2)*a^2*sin(3/2*d*x + 3
/2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(5/2*d*x + 5/2*c)^2 + (8*sqrt(2)*a^2*cos(3
/2*d*x + 3/2*c)^2 + 28*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c) + 37*sqrt(2)*a^2*cos(1/2*d*x + 1/
2*c)^2 + 13*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c)^2 + 2*(2*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)
^3 + 13*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2*cos(1/2*d*x + 1/2*c) + 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^3 + sqrt(
2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 + (2*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a^2*cos(1/2
*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^2 + 2*(12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1
/2*c)^2)*cos(3/2*d*x + 3/2*c) + 2*(2*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1
/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c))*cos(5/2*d*x + 5/2*c) + 2*(21*sqrt(2)*a^2*cos(1/2*d
*x + 1/2*c)^3 + 5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2)*cos(3/2*d*x + 3/2*c) + 2*(2*sqrt(2)
*a^2*sin(3/2*d*x + 3/2*c)^3 + sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2*sin(1/2*d*x + 1/2*c) + 6*sqrt(2)*a^2*cos(3/2*
d*x + 3/2*c)*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) + 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2*sin(1/2*d*x + 1/
2*c) + 5*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)^2*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^3 + 2*(sqr
t(2)*a^2*cos(3/2*d*x + 3/2*c)^2 + 6*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c) + 9*sqrt(2)*a^2*cos(
1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c))*sin(5/2*d*x + 5/2*c) + 2*(6*s
qrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2*sin(1/2*d*x + 1/2*c) + 16*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2
*c)*sin(1/2*d*x + 1/2*c) + 19*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2*sin(1/2*d*x + 1/2*c) + 3*sqrt(2)*a^2*sin(1/2*
d*x + 1/2*c)^3)*sin(3/2*d*x + 3/2*c)) - (4*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3
/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*
x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 64*(cos(3*d*x + 3*c)^2*sin(3/2*
d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*a
rctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c
)))^4 + 4*sin(3/2*d*x + 3/2*c)^5 + 4*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x
+ 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/
2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 64*(cos(3*d*x + 3*c)^2*sin(3/2*d*x +
3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2
(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4
+ 4*(2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^
2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 8*(cos(3*d*x + 3*c)^2*
sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*s
in(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c))) + 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*s
in(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(
2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3
/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/
2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(
3/2*d*x + 3/2*c)))^3 + 32*(2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/
2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) +
2*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2
(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(si
n(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c
)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*
arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*
c)))^3 + 4*(2*cos(3/2*d*x + 3/2*c)^2 + 7)*sin(3/2*d*x + 3/2*c)^3 + 4*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x
+ 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/
2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2
)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*c
os(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin
(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*
x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3
*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin
(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 32*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3
*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*
x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*co
s(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(2
/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*
d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2
*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3
/2*d*x + 3/2*c)))^3 + 4*(4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + (sin(3/2*d*x + 3/2*c
)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c)^2 + 24*(cos(3*d*x + 3*c)^2*sin(3/2*d
*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*ar
ctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)
))^2 + (sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c)^2 + sin(3
/2*d*x + 3/2*c)^3 + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(
cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3
*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 6*(2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2
*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*
x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + s
in(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(
3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*
d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3
*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/
2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 20*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(
3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2*sin(3/2
*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3
/2*c))) + 4*(cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + 3*cos(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + (cos(3/2
*d*x + 3/2*c)^2 + 6)*sin(3/2*d*x + 3/2*c) + 2*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*
d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin
(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3
/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(2/3*arctan2(sin(3/2*
d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/
2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan
2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) +
20*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + 2*cos(3*d*x + 3*c)*co
s(3/2*d*x + 3/2*c) + 2*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*
x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + 2*cos(3*
d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 2*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c
), cos(3/2*d*x + 3/2*c))) - 9*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*
d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*c
os(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*s
in(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c)))^2 + 16*(4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + (sin(3/2*d*x + 3/2*c)^3 +
(cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c)^2 + (sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*
x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c)^2 + sin(3/2*d*x + 3/2*c)^3 - 20*(cos(3*d*x + 3*c)^2*s
in(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d
*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c))*cos(2/3*
arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + 3*cos(
3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2 + 6)*sin(3/2*d*x + 3/2*c) + 20*(cos(3*d*x + 3*c)^
2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 2
*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(
3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + 2*cos(3*d*x + 3*c)*cos(3/2*d*x
+ 3/2*c) + 2*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c
))) - 9*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)*cos(3/2*d*x
+ 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*si
n(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(1/3*arctan2(sin(3/2
*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*((si
n(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c)^2 + 2*(cos(3*d*x +
3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*
c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(
3/2*d*x + 3/2*c)))^2 + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) -
9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(
5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2
+ 1)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c)^2 + sin(3/2*d*x + 3/2*c)^3 + 24*(cos(3*d*x + 3*c)^2*sin(3/2*d*x +
3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan
2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2
- 2*(2*sin(3/2*d*x + 3/2*c)^3 + 7*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c) + (2*cos(3*d*x + 3*c)^2*cos(3/2*d*x
+ 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x +
3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c
)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), c
os(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(sin(3/2*d*x + 3/2*c)^
2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), c
os(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(
3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + c
os(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/
2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(2*cos(3*d*x +
3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2
*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x
+ 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*
c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))
) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*c
os(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 20*(cos(3*d*x + 3*c)^2*sin(3/2*d*x
+ 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - 2*cos(3*d*x +
3*c)*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^
2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - 2
*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(2*co
s(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2 +
6)*sin(3/2*d*x + 3/2*c) + 6*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 +
1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)
^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c),
cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos
(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) +
cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3
/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 20*(cos(3*d*x +
3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), c
os(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2)*
sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 9*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*
c)^2)*cos(3*d*x + 3*c)^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*
x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3
/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan
2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 16*((sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*
sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c)^2 + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin
(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*
d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sin(3/2*d*x + 3/2*c)^3 + (co
s(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c)^2 + sin(3/2*d*x + 3/2*c)^3 - 2*(2*sin(3/2*d*x
+ 3/2*c)^3 + 7*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c) + 2*(2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*
d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x
+ 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + si
n(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3
*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d
*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*
c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2
*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 20*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3
/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - 2*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(4/3*a
rctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x +
3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - 2*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*
c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2
*c)^2 + cos(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2 + 6)*sin(3/2*d*x + 3/2*c) + 20*(cos(3
*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/
2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3
*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 9*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x
+ 3/2*c)^2)*cos(3*d*x + 3*c)^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos
(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*
d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3
*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(32*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin
(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 2*cos(3/2*
d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^3 + 12*(2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*c
os(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*
d*x + 3/2*c) + 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*
sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin
(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(
3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3
/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos
(3/2*d*x + 3/2*c)))^2 + 4*(2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/
2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) +
8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 +
sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 +
sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + si
n(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/
2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x +
3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(
3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3
/2*c)^3 + cos(3/2*d*x + 3/2*c))*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c) + 4*(4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3
/2*c)^2*sin(3/2*d*x + 3/2*c) + (sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*co
s(3*d*x + 3*c)^2 + (sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*
c)^2 + sin(3/2*d*x + 3/2*c)^3 - 20*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x +
3/2*c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/
2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) +
4*(cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + 3*cos(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + (cos(3/2*d*x + 3/
2*c)^2 + 6)*sin(3/2*d*x + 3/2*c) + 20*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*
x + 3*c)^2 + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 2*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan
2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/
2*c)*sin(3*d*x + 3*c)^2 + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 2*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*s
in(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 9*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c
)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x +
3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/
2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2
(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 40*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)
+ sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 14*
(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2)*cos(2/3
*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(sin(3/2*d*x + 3/2*c)^4 + (cos(3/2*d*x + 3/2*c)^2 +
4)*sin(3/2*d*x + 3/2*c)^2 + 3*cos(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c) + 2*(cos(3/2*d*x + 3/2*c)^3 + 6*cos(3/2
*d*x + 3/2*c))*sin(3/2*d*x + 3/2*c) - 4*(18*(cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)
*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 5*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) - 2*((
2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3
/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(
cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos
(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3
*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x
+ 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*
cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 20*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin
(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*
x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), c
os(3/2*d*x + 3/2*c))) - (2*sin(3/2*d*x + 3/2*c)^3 + (2*cos(3/2*d*x + 3/2*c)^2 + 7)*sin(3/2*d*x + 3/2*c))*sin(3
*d*x + 3*c) - 20*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arcta
n2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*
sin(3/2*d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*
x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 20*(2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 2*cos(3/2*d*x + 3/2*c)*si
n(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(4/3*arctan2(sin(3/2
*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 2*cos(3/2*d*x + 3/2*c)*
sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(2/3*arctan2(sin(3
/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*
c)^2 + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + (cos(3/2*d*x
+ 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*
c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(2*cos(3/2*d*x +
3/2*c)*sin(3/2*d*x + 3/2*c)^3 + 2*(cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^3 + cos
(3/2*d*x + 3/2*c))*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c) - 40*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*
d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/
2*c))) - 14*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c
)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(sin(3/2*d*x + 3/2*c)^4 + (cos(3/2*d*x +
3/2*c)^2 + 4)*sin(3/2*d*x + 3/2*c)^2 + 3*cos(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c) + 2*(cos(3/2*d*x + 3/2*c)^3
+ 6*cos(3/2*d*x + 3/2*c))*sin(3/2*d*x + 3/2*c) + 20*(2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 2*cos(3/2*d*
x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(4/3*ar
ctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 2*cos(3/2*
d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(2/3*
arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3
/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) +
(cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c))*sin(1/3*arctan2(sin(3
/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 80*(co
s(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(
3/2*d*x + 3/2*c))) - 28*(cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*cos(2/3*arctan2
(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 33*((cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(7/3*arctan2(
sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 16*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(
sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + (cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(7/3*arctan2(sin
(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 16*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin
(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + cos(3/2*d*x + 3/2*c)^4 + 2*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2
*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2
+ sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3*d*x + 3*c)*sin(3/2*
d*x + 3/2*c))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 16*(cos(3*d*x + 3*c)^2*cos(3/2*
d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3
*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 2*cos(3/2*d*x + 3/2
*c)^2*sin(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^4 + 2*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x
+ 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)
+ 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*s
in(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 16*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) +
sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x
+ 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + ((cos(3/2*d*x + 3/2*c)^2 + sin(3/2
*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 24*(cos(3*d*x + 3*c)^2 + sin
(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^2 + si
n(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 8*(c
os(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + cos(3
/2*d*x + 3/2*c)^2 + 12*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + co
s(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2
*c), cos(3/2*d*x + 3/2*c))) + sin(3/2*d*x + 3/2*c)^2 + 4*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x
+ 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))
*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d
*x + 3/2*c)))^2 + 4*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)
*cos(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x
+ 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arc
tan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + ((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3
*d*x + 3*c)^2 + 2*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c)))^2 + 8*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*si
n(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + 24*(cos(3*d*x + 3*c)^2 + sin
(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + cos(3/2*d*x + 3/2*c)^2 + 2*(
cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d
*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c))) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
+ 4*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos
(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c))) + sin(3/2*d*x + 3/2*c)^2 + 12*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*
d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(
sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 +
4*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 8*(cos(3*d*x + 3*c)^2 + sin(3*d*x +
3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*
x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*cos(3*d*x
+ 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + 4*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*
d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c
))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3/2*d*x + 3/2*c)^2)*sin(5/3*arctan2(sin(
3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(16*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(s
in(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + cos(3/2*d*x + 3/2*c)^3 + 12*(cos(3*d*x + 3*c)^2*cos(3/2*d*x +
3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*si
n(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + cos(3/2*d*x + 3/2*c)*sin(
3/2*d*x + 3/2*c)^2 + 4*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + co
s(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c)
, cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x
+ 3*c) + 2*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)*cos(3/2*
d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)
*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(sin(
3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)
^3)*sin(3*d*x + 3*c) + 4*(2*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c)
+ cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))) + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c))*sin(5/3
*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2
*c))) + 4*(cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^3 + co
s(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + s
in(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(16*
(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + (co
s(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d
*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan
2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2
+ 4*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)
*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c)))^2 + 4*(cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/
2*d*x + 3/2*c)))*sin(3*d*x + 3*c) + cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3 + 12*
(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(
3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*
c)))^2 - (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*cos(3*d*x + 3*c) + 2*(2*(cos(3
*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x
+ 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) +
(cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c) + 2*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*
c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 +
sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3*d*x + 3*c)*sin(3/2*d
*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c
), cos(3/2*d*x + 3/2*c))) + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x +
3*c) + 2*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 8*(cos(3*d*x + 3*c)^2 + sin(
3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^2 + sin
(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*cos
(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + 4*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + c
os(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x
+ 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3/2*d*x + 3/2*c)^2)*sin(5/3*arcta
n2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
+ 4*(4*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*
c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c)))^2 + 4*(cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(
3/2*d*x + 3/2*c)))*sin(3*d*x + 3*c) + cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3 - (
cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)
^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(
3/2*d*x + 3/2*c))))*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3
/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1
) - 33*((cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
^4 + 16*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
^4 + (cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4
+ 16*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4
+ cos(3/2*d*x + 3/2*c)^4 + 2*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^
2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/
2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(7/3*arctan2(sin(3/2*d*x +
3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 16*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*
x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(si
n(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 2*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x +
3/2*c)^4 + 2*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x
+ 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^
2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2
*d*x + 3/2*c)))^3 + 16*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + co
s(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2
*c), cos(3/2*d*x + 3/2*c)))^3 + ((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(
3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 24*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4
*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 8*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(
5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + cos(3/2*d*x + 3/2*c)^2 + 12*(cos(3*d*x + 3*c)^2*c
os(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*
d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3/2*d*x +
3/2*c)^2 + 4*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x
+ 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3
/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*((cos(3/2*d*x + 3/2*c)^2
+ sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2
*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2
*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2
*c)))^2 + ((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 2*(cos(3*d*x + 3*c)^2 + sin(
3*d*x + 3*c)^2)*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*(cos(3*d*x + 3*c)^2 + sin(3
*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(
3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*cos(
3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + 24*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + cos(3/2*d*x + 3/2*c)^2 + 2*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + co
s(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*
d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/
2*c))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c
) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2
*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3/2*d*x + 3/2*c)^2 + 12*(cos
(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*
x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x +
3/2*c)^2)*cos(3*d*x + 3*c)^2 + 8*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c
), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2
*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x
+ 3/2*c)^2 + 4*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x
+ 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos
(3/2*d*x + 3/2*c))) + sin(3/2*d*x + 3/2*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 +
2*(16*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^
3 + cos(3/2*d*x + 3/2*c)^3 + 12*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*
c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*
d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + 4*(cos(3*d*x + 3*c)^2*c
os(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 4*(cos
(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3*d*x
+ 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x +
3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + 2*((cos(3/2*d*x + 3/2*c)^2 + sin(3/
2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^2 + s
in(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + cos
(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (
cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c) + 4*(2*(cos(3*d*x + 3*c
)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - c
os(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (cos(3/2*
d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(cos(3/2*d*x + 3/2*c)^3 + cos(3/2*
d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*c
os(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c))*cos
(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(16*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*si
n(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + (cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(
3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3
/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)
)))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c
) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2
*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(cos(3/2*d*x + 3/2*c)^2 + si
n(3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3*d*x + 3*c) + cos(3/2*
d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3 + 12*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + s
in(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x
+ 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x
+ 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*cos(3*d*x + 3*c) + 2*(2*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d
*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*
c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2
*c)^2)*sin(3*d*x + 3*c) + 2*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2
+ cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2
*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3
/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (cos(3/2*d*x + 3
/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c) + 2*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2
*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 8*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*
cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3
/2*d*x + 3/2*c)^2 + 4*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos
(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*
c), cos(3/2*d*x + 3/2*c))) + sin(3/2*d*x + 3/2*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c
))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(4*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2
*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3
/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(cos(3/2*d*x + 3/2*c)^2 +
sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3*d*x + 3*c) + cos(3/
2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3 - (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c)
+ sin(3/2*d*x + 3/2*c)^3)*cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*
c)^2)*sin(3*d*x + 3*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*log(cos(1/3*arctan2(sin(
3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 -
2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 4*(cos(3/2*d*x + 3/2*c)^4 + 7*cos(3/2*d*
x + 3/2*c)^2)*sin(3/2*d*x + 3/2*c) + 4*(2*sin(3/2*d*x + 3/2*c)^4 + 32*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c)
+ sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3
/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + ((2*
sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2
*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(co
s(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3
*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(cos(3*d*
x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x
+ 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c),
cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c)
+ cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*((2*sin(3
/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x
+ 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d
*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x
+ 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x +
3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)
- cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3
*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (2*cos(3/2*d*x + 3/2*c)^2 + 13)*sin(3/2*d*x + 3/2*c)
^2 + 12*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2
+ 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3
*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))
) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) -
18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*
sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*(sin(3/2*d*x + 3/2*c)^4 + (cos(3/
2*d*x + 3/2*c)^2 + 4)*sin(3/2*d*x + 3/2*c)^2 + 3*cos(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + cos(3/2*d*x + 3/2*
c)^2 - 2*(18*(cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)*sin(1/3*arctan2(sin(3/2*d*x +
3/2*c), cos(3/2*d*x + 3/2*c))) + 5*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) - 2*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*c
os(3*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c
)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x
+ 3*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3
*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2
*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3
/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3
/2*c), cos(3/2*d*x + 3/2*c))) + 20*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2
*c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) +
sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - (2*sin(
3/2*d*x + 3/2*c)^3 + (2*cos(3/2*d*x + 3/2*c)^2 + 7)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) - 2*(2*cos(3*d*x +
3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2
*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c
) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(
3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(si
n(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(
3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2
*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin
(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arcta
n2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
- 20*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(sin(3/2*d
*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x
+ 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c),
cos(3/2*d*x + 3/2*c))) - 4*(18*(cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)*sin(1/3*arct
an2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 5*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 20*(cos(3*d*x + 3
*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/
2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(2/3*a
rctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - (2*sin(3/2*d*x + 3/2*c)^3 + (2*cos(3/2*d*x + 3/2*c)^2 +
7)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) - 20*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3
/2*d*x + 3/2*c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3/2*d*x + 3/2*c)*sin(3*
d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)
)))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 20*(2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)
*sin(3/2*d*x + 3/2*c) - 2*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2
*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*
c)*sin(3/2*d*x + 3/2*c) - 2*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3
/2*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(cos(3/2*d*x + 3/2*c)*sin(3/2*d*x +
3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c))*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + 4*((sin(3/
2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c)^2 + 8*(cos(3*d*x + 3*c)
^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2
)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*
d*x + 3/2*c)))^2 + (sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*
c)^2 + sin(3/2*d*x + 3/2*c)^3 - 2*(2*sin(3/2*d*x + 3/2*c)^3 + 7*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c) + 2*(2*
cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3
/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*(sin(3/2*d*x + 3/2*c)^2 + 3
)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/
2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d
*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*
d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c),
cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 20*(cos(3*d*x + 3*c)^2
*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - 2*
cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3
*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*
x + 3*c) - 2*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)
)) + 2*(2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + (cos(3/2*d*x
+ 3/2*c)^2 + 6)*sin(3/2*d*x + 3/2*c) + 20*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(
3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2*cos(3/2*d
*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2
*c))) - 9*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + (cos(3/2*d*x + 3/2*c)^2 + si
n(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*co
s(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(1/3*arctan2(sin(3
/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 40*(co
s(3/2*d*x + 3/2*c)^2*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*ar
ctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 14*(cos(3/2*d*x + 3/2*c)^2*sin(3*d*x + 3*c) - cos(3*d*x +
3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
- 18*(cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3 - (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d
*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/
2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arct
an2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(2*sin(3/2*d*x + 3/2*c)^4 + 4*((2*sin(3/2*d*x + 3/2*c)^2
+ 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x
+ 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(
3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d
*x + 3*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x
+ 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)
*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d
*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (2*cos(3/2*d*x + 3/2*c)^2 + 13)*sin(3/2*d*x + 3/2*c)^2 - 2*(sin(3/2*d*
x + 3/2*c)^4 + (cos(3/2*d*x + 3/2*c)^2 + 4)*sin(3/2*d*x + 3/2*c)^2 + 3*cos(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c
) + cos(3/2*d*x + 3/2*c)^2 - 4*(18*(cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)*sin(1/3*
arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 5*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 20*(cos(3*d*x
+ 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), co
s(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(2
/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - (2*sin(3/2*d*x + 3/2*c)^3 + (2*cos(3/2*d*x + 3/2*c)^
2 + 7)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) - 20*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*s
in(3/2*d*x + 3/2*c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3/2*d*x + 3/2*c)*si
n(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/
2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 20*(2*cos(3/2*d*x + 3/2*c)*sin(3*d*x +
3*c)*sin(3/2*d*x + 3/2*c) - 2*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x +
3/2*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(2*cos(3/2*d*x + 3/2*c)*sin(3*d*x
+ 3*c)*sin(3/2*d*x + 3/2*c) - 2*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x
+ 3/2*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(cos(3/2*d*x + 3/2*c)*sin(3/2*d*
x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c))*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + 40*(co
s(3/2*d*x + 3/2*c)^2*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*ar
ctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 14*(cos(3/2*d*x + 3/2*c)^2*sin(3*d*x + 3*c) - cos(3*d*x +
3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
- 18*(cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3 - (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d
*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/
2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arct
an2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 80*(cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d
*x + 3/2*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 28*(cos(3/2*d*x + 3/2*c)^3 + cos
(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 36*(c
os(3/2*d*x + 3/2*c)^4 + 2*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^4)*sin(1/3*arct
an2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A/((sqrt(2)*a*cos(3/2*d*x + 3/2*c)^4 + 2*sqrt(2)*a*cos(3/2*d
*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^4 + (sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt
(2)*a*sin(3*d*x + 3*c)^2)*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 16*(sqrt(2)*a*cos(3
*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 +
(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d
*x + 3/2*c)))^4 + 16*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 2*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2
*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c
)*sin(3/2*d*x + 3/2*c) + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3
/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 16*(
sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2
)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(s
in(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 2*(sqrt(2)*a*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)
*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*cos(3
*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*sin(5/3*arc
tan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))
)^3 + 16*(sqrt(2)*a*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c
) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3
*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + (4*sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2
+ 4*sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 +
sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*cos(
3*d*x + 3*c)^2 + 24*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*sin
(3*d*x + 3*c)^2 + 8*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 12*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2
*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c
)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(sqrt(2)*a*cos(3*d*x
+ 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/
2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c),
cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(4*sqrt(2)*a*cos(3
*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 4*sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) +
sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt
(2)*a*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x +
3/2*c)^2)*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (4*sqrt(2)*a*c
os(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^
2 + sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 +
sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 2*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x +
3*c)^2)*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sq
rt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sqrt(2)*a*cos(3/
2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 24*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + s
qrt(2)*a*sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(sqrt(2)*a*cos
(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x
+ 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(sqrt(2)*a*cos(3*d*x + 3*c)
^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arcta
n2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(
2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin
(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(sqrt(2)
*a*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos
(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*
d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(4*sq
rt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x
+ 3/2*c)^2 + sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/
2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 8*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*si
n(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sqrt(2)*a*cos(3/2*d*x + 3/
2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x +
3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) +
sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(sqrt(2)*a*cos(3/2*d*x + 3/2*c)^3 + sqrt(
2)*a*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + 16*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*
c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 12*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/
2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x +
3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c)))^2 + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x +
3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) +
4*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*
d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*
c)^3 + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + 2*(4*sqrt(2)*a*cos(3*d*x + 3*
c)*cos(3/2*d*x + 3/2*c)^2 + 4*sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + sqrt(2)*a
*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin
(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2
)*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (sqrt(2)*a*cos(3/2*d*x +
3/2*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c) + 4*(2*(sqrt(2)*a*cos(3*d*x
+ 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3
/2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c)
, cos(3/2*d*x + 3/2*c))) + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3
*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3
/2*d*x + 3/2*c))) + 4*(sqrt(2)*a*cos(3/2*d*x + 3/2*c)^3 + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^
2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^3 + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c
) + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c
))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2*sin(3/2*
d*x + 3/2*c) + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^3 + 16*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c
)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + (sqrt(2)*a*cos(3*d*x + 3*c)^2*sin(3/2*d*
x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*
c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x +
3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), c
os(3/2*d*x + 3/2*c)))^2 + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*
sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*
x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(sqrt(2)*a*cos(3/2*d*x + 3/2*c)
^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3*d*x
+ 3*c) + 12*(sqrt(2)*a*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/
2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(
5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3
/2*c) + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^3)*cos(3*d*x + 3*c) + 2*(2*(sqrt(2)*a*cos(3*d*x + 3*c)^2*sin(3/2*d*x +
3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) -
sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
+ (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c) + 2*(sqrt(2)*a*cos(3
*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x +
3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2
+ sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2
(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) +
(sqrt(2)*a*cos(3/2*d*x + 3/2*c)^3 + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c) +
2*(4*sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*sqrt(2)*a*cos(3*d*x + 3*c)*sin(3
/2*d*x + 3/2*c)^2 + sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a*cos(3/2*d
*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 8*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(
2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sqrt(2)*a*cos(3/2*d
*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2
*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3
/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3
/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), c
os(3/2*d*x + 3/2*c))) + 4*(sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3/2*d*x + 3/2
*c)^3 + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*
c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/
3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin
(3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3*d*x + 3*c) - (sqrt(2)*
a*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^3)*cos(3*d*x + 3*c) + (sqrt(2)*
a*cos(3/2*d*x + 3/2*c)^3 + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c))*sin(5/3*ar
ctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sqrt(a)))/d

Giac [F]

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

[In]

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

[Out]

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

Mupad [F(-1)]

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

[In]

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

[Out]

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