\(\int \frac {\cos ^{\frac {3}{2}}(c+d x) (A+B \sec (c+d x))}{(a+a \sec (c+d x))^{3/2}} \, dx\) [549]
Optimal result
Integrand size = 35, antiderivative size = 223 \[
\int \frac {\cos ^{\frac {3}{2}}(c+d x) (A+B \sec (c+d x))}{(a+a \sec (c+d x))^{3/2}} \, dx=\frac {(11 A-7 B) \text {arctanh}\left (\frac {\sqrt {a} \sqrt {\sec (c+d x)} \sin (c+d x)}{\sqrt {2} \sqrt {a+a \sec (c+d x)}}\right ) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}}{2 \sqrt {2} a^{3/2} d}-\frac {(A-B) \sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}-\frac {(19 A-15 B) \sin (c+d x)}{6 a d \sqrt {\cos (c+d x)} \sqrt {a+a \sec (c+d x)}}+\frac {(7 A-3 B) \sqrt {\cos (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}}
\]
[Out]
-1/2*(A-B)*sin(d*x+c)*cos(d*x+c)^(1/2)/d/(a+a*sec(d*x+c))^(3/2)+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))*cos(d*x+c)^(1/2)*sec(d*x+c)^(1/2)/a^(3/2)/d*2^(1/2)-1/6*(19*A
-15*B)*sin(d*x+c)/a/d/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2)+1/6*(7*A-3*B)*sin(d*x+c)*cos(d*x+c)^(1/2)/a/d/(a
+a*sec(d*x+c))^(1/2)
Rubi [A] (verified)
Time = 1.10 (sec) , antiderivative size = 223, normalized size of antiderivative = 1.00, number of
steps used = 6, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.171, Rules used = {3034, 4105, 4107, 4098, 3893,
212} \[
\int \frac {\cos ^{\frac {3}{2}}(c+d x) (A+B \sec (c+d x))}{(a+a \sec (c+d x))^{3/2}} \, dx=\frac {(11 A-7 B) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)} \text {arctanh}\left (\frac {\sqrt {a} \sin (c+d x) \sqrt {\sec (c+d x)}}{\sqrt {2} \sqrt {a \sec (c+d x)+a}}\right )}{2 \sqrt {2} a^{3/2} d}+\frac {(7 A-3 B) \sin (c+d x) \sqrt {\cos (c+d x)}}{6 a d \sqrt {a \sec (c+d x)+a}}-\frac {(19 A-15 B) \sin (c+d x)}{6 a d \sqrt {\cos (c+d x)} \sqrt {a \sec (c+d x)+a}}-\frac {(A-B) \sin (c+d x) \sqrt {\cos (c+d x)}}{2 d (a \sec (c+d x)+a)^{3/2}}
\]
[In]
Int[(Cos[c + d*x]^(3/2)*(A + B*Sec[c + d*x]))/(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]])]*Sqrt[Cos[c
+ d*x]]*Sqrt[Sec[c + d*x]])/(2*Sqrt[2]*a^(3/2)*d) - ((A - B)*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(2*d*(a + a*Sec
[c + d*x])^(3/2)) - ((19*A - 15*B)*Sin[c + d*x])/(6*a*d*Sqrt[Cos[c + d*x]]*Sqrt[a + a*Sec[c + d*x]]) + ((7*A -
3*B)*Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(6*a*d*Sqrt[a + a*Sec[c + d*x]])
Rule 212
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1/(Rt[a, 2]*Rt[-b, 2]))*ArcTanh[Rt[-b, 2]*(x/Rt[a, 2])], x]
/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])
Rule 3034
Int[((a_.) + csc[(e_.) + (f_.)*(x_)]*(b_.))^(m_.)*(csc[(e_.) + (f_.)*(x_)]*(d_.) + (c_))^(n_.)*((g_.)*sin[(e_.
) + (f_.)*(x_)])^(p_.), x_Symbol] :> Dist[(g*Csc[e + f*x])^p*(g*Sin[e + f*x])^p, Int[(a + b*Csc[e + f*x])^m*((
c + d*Csc[e + f*x])^n/(g*Csc[e + f*x])^p), x], x] /; FreeQ[{a, b, c, d, e, f, g, m, n, p}, x] && NeQ[b*c - a*d
, 0] && !IntegerQ[p] && !(IntegerQ[m] && IntegerQ[n])
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}& = \left (\sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \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 {(A-B) \sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}+\frac {\left (\sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \int \frac {\frac {1}{2} a (7 A-3 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) \sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}+\frac {(7 A-3 B) \sqrt {\cos (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}}+\frac {\left (\sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \int \frac {-\frac {1}{4} a^2 (19 A-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) \sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}-\frac {(19 A-15 B) \sin (c+d x)}{6 a d \sqrt {\cos (c+d x)} \sqrt {a+a \sec (c+d x)}}+\frac {(7 A-3 B) \sqrt {\cos (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}}+\frac {\left ((11 A-7 B) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \int \frac {\sqrt {\sec (c+d x)}}{\sqrt {a+a \sec (c+d x)}} \, dx}{4 a} \\ & = -\frac {(A-B) \sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}-\frac {(19 A-15 B) \sin (c+d x)}{6 a d \sqrt {\cos (c+d x)} \sqrt {a+a \sec (c+d x)}}+\frac {(7 A-3 B) \sqrt {\cos (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}}-\frac {\left ((11 A-7 B) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \text {Subst}\left (\int \frac {1}{2 a-x^2} \, dx,x,-\frac {a \sqrt {\sec (c+d x)} \sin (c+d x)}{\sqrt {a+a \sec (c+d x)}}\right )}{2 a d} \\ & = \frac {(11 A-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 ) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}}{2 \sqrt {2} a^{3/2} d}-\frac {(A-B) \sqrt {\cos (c+d x)} \sin (c+d x)}{2 d (a+a \sec (c+d x))^{3/2}}-\frac {(19 A-15 B) \sin (c+d x)}{6 a d \sqrt {\cos (c+d x)} \sqrt {a+a \sec (c+d x)}}+\frac {(7 A-3 B) \sqrt {\cos (c+d x)} \sin (c+d x)}{6 a d \sqrt {a+a \sec (c+d x)}} \\
\end{align*}
Mathematica [A] (verified)
Time = 1.30 (sec) , antiderivative size = 155, normalized size of antiderivative = 0.70
\[
\int \frac {\cos ^{\frac {3}{2}}(c+d x) (A+B \sec (c+d x))}{(a+a \sec (c+d x))^{3/2}} \, dx=\frac {\left (-3 \sqrt {2} (11 A-7 B) \arctan \left (\frac {\sqrt {2} \sqrt {\sec (c+d x)}}{\sqrt {1-\sec (c+d x)}}\right ) \cos ^2\left (\frac {1}{2} (c+d x)\right ) \sec ^{\frac {3}{2}}(c+d x)+\sqrt {1-\sec (c+d x)} (12 (-A+B)+(-17 A+15 B+2 A \cos (2 (c+d x))) \sec (c+d x))\right ) \sin (c+d x)}{6 d \sqrt {-1+\cos (c+d x)} (a (1+\sec (c+d x)))^{3/2}}
\]
[In]
Integrate[(Cos[c + d*x]^(3/2)*(A + B*Sec[c + d*x]))/(a + a*Sec[c + d*x])^(3/2),x]
[Out]
((-3*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]^2*Sec[c
+ d*x]^(3/2) + Sqrt[1 - Sec[c + d*x]]*(12*(-A + B) + (-17*A + 15*B + 2*A*Cos[2*(c + d*x)])*Sec[c + d*x]))*Sin
[c + d*x])/(6*d*Sqrt[-1 + Cos[c + d*x]]*(a*(1 + Sec[c + d*x]))^(3/2))
Maple [B] (verified)
Leaf count of result is larger than twice the leaf count of optimal. \(468\) vs. \(2(188)=376\).
Time = 5.16 (sec) , antiderivative size = 469, normalized size of antiderivative = 2.10
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method | result | size |
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\(\frac {\left (33 A \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}\, \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (\cos \left (d x +c \right )+1\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}}\right ) \sqrt {2}\, \cos \left (d x +c \right )^{2}-21 B \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}\, \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (\cos \left (d x +c \right )+1\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}}\right ) \sqrt {2}\, \cos \left (d x +c \right )^{2}+66 A \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (\cos \left (d x +c \right )+1\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}}\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}\, \sqrt {2}\, \cos \left (d x +c \right )-42 B \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (\cos \left (d x +c \right )+1\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}}\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}\, \sqrt {2}\, \cos \left (d x +c \right )+33 A \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (\cos \left (d x +c \right )+1\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}}\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}\, \sqrt {2}+8 A \cos \left (d x +c \right )^{2} \sin \left (d x +c \right )-21 B \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (\cos \left (d x +c \right )+1\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}}\right ) \sqrt {-\frac {1}{\cos \left (d x +c \right )+1}}\, \sqrt {2}-24 A \cos \left (d x +c \right ) \sin \left (d x +c \right )+24 B \cos \left (d x +c \right ) \sin \left (d x +c \right )-38 A \sin \left (d x +c \right )+30 B \sin \left (d x +c \right )\right ) \sqrt {\cos \left (d x +c \right )}\, \sqrt {a \left (1+\sec \left (d x +c \right )\right )}}{12 a^{2} d \left (\cos \left (d x +c \right )+1\right )^{2}}\) |
\(469\) |
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[In]
int(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x,method=_RETURNVERBOSE)
[Out]
1/12/a^2/d*(33*A*(-1/(cos(d*x+c)+1))^(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))*2^(1/2)*cos(d*x+c)^2-21*B*(-1/(cos(d*x+c)+1))^(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))*2^(1/2)*cos(d*x+c)^2+66*A*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)*2^(1/2)*cos(d*x+c)-42*B*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)*2^(1/2)*cos(d*x+c)+33*A*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)*2^(1/2)+8*A*cos(d*x+c)^2*sin(d*x+c)-21*B*arctan(1/2*s
in(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)*2^(1/2)-24*A*cos(d*x+c)*
sin(d*x+c)+24*B*cos(d*x+c)*sin(d*x+c)-38*A*sin(d*x+c)+30*B*sin(d*x+c))*cos(d*x+c)^(1/2)*(a*(1+sec(d*x+c)))^(1/
2)/(cos(d*x+c)+1)^2
Fricas [A] (verification not implemented)
none
Time = 0.30 (sec) , antiderivative size = 442, normalized size of antiderivative = 1.98
\[
\int \frac {\cos ^{\frac {3}{2}}(c+d x) (A+B \sec (c+d x))}{(a+a \sec (c+d x))^{3/2}} \, dx=\left [-\frac {3 \, \sqrt {2} {\left ({\left (11 \, A - 7 \, B\right )} \cos \left (d x + c\right )^{2} + 2 \, {\left (11 \, A - 7 \, B\right )} \cos \left (d x + c\right ) + 11 \, A - 7 \, B\right )} \sqrt {a} \log \left (-\frac {a \cos \left (d x + c\right )^{2} + 2 \, \sqrt {2} \sqrt {a} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sqrt {\cos \left (d x + c\right )} \sin \left (d x + c\right ) - 2 \, a \cos \left (d x + c\right ) - 3 \, a}{\cos \left (d x + c\right )^{2} + 2 \, \cos \left (d x + c\right ) + 1}\right ) - 4 \, {\left (4 \, A \cos \left (d x + c\right )^{2} - 12 \, {\left (A - B\right )} \cos \left (d x + c\right ) - 19 \, A + 15 \, B\right )} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sqrt {\cos \left (d x + c\right )} \sin \left (d x + c\right )}{24 \, {\left (a^{2} d \cos \left (d x + c\right )^{2} + 2 \, a^{2} d \cos \left (d x + c\right ) + a^{2} d\right )}}, -\frac {3 \, \sqrt {2} {\left ({\left (11 \, A - 7 \, B\right )} \cos \left (d x + c\right )^{2} + 2 \, {\left (11 \, A - 7 \, B\right )} \cos \left (d x + c\right ) + 11 \, A - 7 \, B\right )} \sqrt {-a} \arctan \left (\frac {\sqrt {2} \sqrt {-a} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sqrt {\cos \left (d x + c\right )}}{a \sin \left (d x + c\right )}\right ) - 2 \, {\left (4 \, A \cos \left (d x + c\right )^{2} - 12 \, {\left (A - B\right )} \cos \left (d x + c\right ) - 19 \, A + 15 \, B\right )} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sqrt {\cos \left (d x + c\right )} \sin \left (d x + c\right )}{12 \, {\left (a^{2} d \cos \left (d x + c\right )^{2} + 2 \, a^{2} d \cos \left (d x + c\right ) + a^{2} d\right )}}\right ]
\]
[In]
integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(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)^2 - 12*(A - B)*cos(d*x + c) -
19*A + 15*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 +
2*a^2*d*cos(d*x + c) + a^2*d), -1/12*(3*sqrt(2)*((11*A - 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)^2 - 12*(A - B)*cos(d*x + c) - 19*A + 15*B)*sqrt((a*cos(d*x + c) + a)/cos(d*x
+ c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]
Sympy [F(-1)]
Timed out. \[
\int \frac {\cos ^{\frac {3}{2}}(c+d x) (A+B \sec (c+d x))}{(a+a \sec (c+d x))^{3/2}} \, dx=\text {Timed out}
\]
[In]
integrate(cos(d*x+c)**(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))**(3/2),x)
[Out]
Timed out
Maxima [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 36231 vs. \(2 (188) = 376\).
Time = 0.95 (sec) , antiderivative size = 36231, normalized size of antiderivative = 162.47
\[
\int \frac {\cos ^{\frac {3}{2}}(c+d x) (A+B \sec (c+d x))}{(a+a \sec (c+d x))^{3/2}} \, dx=\text {Too large to display}
\]
[In]
integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm="maxima")
[Out]
1/12*(3*(8*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x
+ 2*c))) + 32*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d
*x + 2*c))) + 8*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2
*d*x + 2*c))) + 32*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2*sin(1/4*arctan2(sin(2*d*x + 2*c), co
s(2*d*x + 2*c))) + 8*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^3 + 4*(8*cos(3/4*arctan2(sin(2*d*x +
2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*cos(1/4*arctan2(sin(2*d*x +
2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - sin(2*d*x + 2*c) - 5*sin(1/2*
arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(4*cos(
1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - sin(2*
d*x + 2*c) - 5*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d
*x + 2*c))) - 7*(2*(2*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + cos(1/4*arctan2(sin(2*d*x + 2*c),
cos(2*d*x + 2*c))))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + cos(5/4*arctan2(sin(2*d*x + 2*c),
cos(2*d*x + 2*c)))^2 + 4*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*cos(3/4*arctan2(sin(2*d*x
+ 2*c), cos(2*d*x + 2*c)))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + cos(1/4*arctan2(sin(2*d*x +
2*c), cos(2*d*x + 2*c)))^2 + 2*(2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/4*arctan2(sin(2
*d*x + 2*c), cos(2*d*x + 2*c))))*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(5/4*arctan2(sin(2*
d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sin(3/4*arctan
2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/4*arctan2(
sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*a
rctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) +
7*(2*(2*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2
*c))))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*
c)))^2 + 4*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*
d*x + 2*c)))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*
x + 2*c)))^2 + 2*(2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/4*arctan2(sin(2*d*x + 2*c), c
os(2*d*x + 2*c))))*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(5/4*arctan2(sin(2*d*x + 2*c), co
s(2*d*x + 2*c)))^2 + 4*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sin(3/4*arctan2(sin(2*d*x +
2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/4*arctan2(sin(2*d*x + 2*
c), cos(2*d*x + 2*c)))^2)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d
*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*cos(1/4*arct
an2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) + 4*(8*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x +
2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x +
2*c)))^2 + cos(2*d*x + 2*c) + 5*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2)*sin(5/4*arctan2(sin
(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(4*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + cos(2*d*x +
2*c) + 5*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x
+ 2*c))) - 20*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*
x + 2*c))) + 4*(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + cos(2*d*x + 2*c) + 2)*sin(1/4*arcta
n2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 20*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arct
an2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B*sqrt(a)/(sqrt(2)*a^2*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x +
2*c)))^2 + 4*sqrt(2)*a^2*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sqrt(2)*a^2*cos(3/4*arcta
n2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2)*a^2*cos
(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x
+ 2*c)))^2 + 4*sqrt(2)*a^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sqrt(2)*a^2*sin(3/4*arct
an2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2)*a^2*si
n(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(2*sqrt(2)*a^2*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(
2*d*x + 2*c))) + sqrt(2)*a^2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(5/4*arctan2(sin(2*d*x +
2*c), cos(2*d*x + 2*c))) + 2*(2*sqrt(2)*a^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2)*a^
2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 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*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d
*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 4*sin(3/2*d*x + 3/2*c)^5 + 4*(
cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + si
n(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x +
3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 64*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*
x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3
/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 4*(2*cos(3*d*x + 3*c)^2*cos(3/2*d*x
+ 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x +
3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c
)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), 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)))^3 + 32*(2*cos(3*d*x
+ 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x +
3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d
*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3
/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*
c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c
)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*
d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 4*(2*cos(3/2*d*x + 3/2*c)^2 +
7)*sin(3/2*d*x + 3/2*c)^3 + 4*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2
+ 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*
c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c)
, cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), c
os(3/2*d*x + 3/2*c))) + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) -
9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin
(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(
3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3
/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos
(3/2*d*x + 3/2*c)))^3 + 32*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)
*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2
+ 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), co
s(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) + 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(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*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*
x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sin(3/2*d*x + 3/2*c)^3 + (cos(
3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c)^2 + sin(3/2*d*x + 3/2*c)^3 + 8*(cos(3*d*x + 3*c
)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^
2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2
*d*x + 3/2*c)))^2 + 6*(2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)
*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*(s
in(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)*si
n(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*arct
an2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
- 20*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(
3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin
(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(cos(3/2*d*x + 3/2*c)*sin(
3/2*d*x + 3/2*c)^2 + 3*cos(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2 + 6)*sin(3/2*d*x + 3/2
*c) + 2*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2
+ 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3
*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))
) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) -
18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*
sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 20*(cos(3*d*x + 3*c)^2*cos(3/2*d*x +
3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 2*sin(3*d*x + 3*c
)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2*c
os(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*si
n(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 + (c
os(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)*s
in(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), c
os(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 16*(4*cos(3*d*x + 3*c)
*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + (sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*
d*x + 3/2*c))*cos(3*d*x + 3*c)^2 + (sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c)
)*sin(3*d*x + 3*c)^2 + sin(3/2*d*x + 3/2*c)^3 - 20*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)
^2*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2*
sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*
d*x + 3/2*c))) + 4*(cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + 3*cos(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + (
cos(3/2*d*x + 3/2*c)^2 + 6)*sin(3/2*d*x + 3/2*c) + 20*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x +
3/2*c)*sin(3*d*x + 3*c)^2 + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 2*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)
)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) +
cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 2*sin(3*d*x + 3*c)*sin(3/2
*d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 9*((cos(3/2*d*x + 3/2*c)^2 + sin
(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^2
+ sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) +
cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))
*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*((sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x +
3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c)^2 + 2*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*
x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/
2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*(cos(3*d*x +
3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*
c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(
3/2*d*x + 3/2*c)))^2 + (sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*sin(3*d*x
+ 3*c)^2 + sin(3/2*d*x + 3/2*c)^3 + 24*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d
*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*(2*sin(3/2*d*x + 3/2*c)^3 + 7*sin
(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c) + (2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(
3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x
+ 3/2*c) + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*
x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2
(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*
x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x +
3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3
*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) +
sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*
arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 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*arc
tan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3
*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - 2*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)
)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c
)^2 + cos(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2 + 6)*sin(3/2*d*x + 3/2*c) + 6*((2*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), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x +
3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c),
cos(3/2*d*x + 3/2*c))) - 9*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + (cos(3/2*d*
x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*
x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(
1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c)))^2 + 16*((sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c)
^2 + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c
)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(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*(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))))*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) + c
os(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(
3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3
/2*c), cos(3/2*d*x + 3/2*c))) - 9*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + (cos
(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin
(3/2*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^
2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2
*d*x + 3/2*c)))^2 + 4*(32*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) -
9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos
(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^3 +
12*(2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2
*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*(sin(3/2*d*x + 3/2*c)
^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c),
cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos
(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 +
cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3
/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(2*cos(3*d*x
+ 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x +
3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/
2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(s
in(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*
(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x + 3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(s
in(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(
3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*
sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*ar
ctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)
))^2 + 2*(cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c))*sin(3/
2*d*x + 3/2*c))*cos(3*d*x + 3*c) + 4*(4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + (sin(3/
2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c)^2 + (sin(3/2*d*x + 3/2*
c)^3 + (cos(3/2*d*x + 3/2*c)^2 + 1)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c)^2 + sin(3/2*d*x + 3/2*c)^3 - 20*(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(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), c
os(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) + s
in(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x
+ 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*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))*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)*cos(3/2*d*x + 3/2*c) + sin(3*
d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - (2*sin(3/2*d*x
+ 3/2*c)^3 + (2*cos(3/2*d*x + 3/2*c)^2 + 7)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) - 20*(cos(3/2*d*x + 3/2*c)
*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c))) - 7*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(2/3*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
0*(2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) +
cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
+ 7*(2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)
+ cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))
) - 18*(cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^3 + cos(3
/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(
3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*ar
ctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^3 + 2*(cos
(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c))*sin(3/2*d*x + 3/2*c
))*cos(3*d*x + 3*c) - 40*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/
2*d*x + 3/2*c)^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 14*(cos(3*d*x + 3*c)*cos(3/2*
d*x + 3/2*c)*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2
*c), cos(3/2*d*x + 3/2*c))) + 2*(sin(3/2*d*x + 3/2*c)^4 + (cos(3/2*d*x + 3/2*c)^2 + 4)*sin(3/2*d*x + 3/2*c)^2
+ 3*cos(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c) + 2*(cos(3/2*d*x + 3/2*c)^3 + 6*cos(3/2*d*x + 3/2*c))*sin(3/2*d*x
+ 3/2*c) + 20*(2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*
x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*
x + 3/2*c))) + 7*(2*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*
d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*
d*x + 3/2*c))) - 18*(cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2
*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x +
3/2*c) + sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))
))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 80*(cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2
*c) + sin(3/2*d*x + 3/2*c)^3)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 28*(cos(3/2*d*x +
3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3
/2*c))) + 33*((cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/
2*c)))^4 + 16*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/
2*c)))^4 + (cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c
)))^4 + 16*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c
)))^4 + cos(3/2*d*x + 3/2*c)^4 + 2*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x +
3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*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)*si
n(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*arct
an2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 2*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c)^2 + sin(3/2
*d*x + 3/2*c)^4 + 2*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3
/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x +
3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), c
os(3/2*d*x + 3/2*c)))^3 + 16*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c
) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + ((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 +
4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 24*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3
/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)
^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 8*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2
)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + cos(3/2*d*x + 3/2*c)^2 + 12*(cos(3*d*x + 3*
c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) +
sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*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
) + 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)*s
in(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3/2*d*x + 3/2*c)^2 + 1
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)*si
n(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*c
os(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(si
n(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 + 4*(cos(3*d*x + 3*
c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) +
4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin
(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*
d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + 2*((cos(3/2*d*x + 3/2*c)^2 +
sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)
^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)
+ cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)
)) + (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c) + 4*(2*(cos(3*d*x
+ 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*
c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (co
s(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c))*sin(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 + 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)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c
)^2)*cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c
))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(16*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)
^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + (cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c)
+ sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d
*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(cos(3*d*x + 3*c)^2*sin(3/2*d*x +
3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*s
in(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(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) + 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 + 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) + 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))*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(s
in(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 + s
in(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*arctan
2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))
)^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 33*((cos(3*d*x + 3*c)^2 + sin(3*d*
x + 3*c)^2)*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 16*(cos(3*d*x + 3*c)^2 + sin(3*d*
x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + (cos(3*d*x + 3*c)^2 + sin(3*d*x +
3*c)^2)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + 16*(cos(3*d*x + 3*c)^2 + sin(3*d*x +
3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^4 + cos(3/2*d*x + 3/2*c)^4 + 2*(cos(3*d*
x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2
*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
+ sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 16*
(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*
d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*
c)))^3 + 2*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^4 + 2*(cos(3*d*x + 3*c)^2*sin(
3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x
+ 3*c)*sin(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c
), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 16*(cos(3*d*x + 3*
c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) -
cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + ((cos(
3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 +
24*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 +
(cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)
*sin(3/2*d*x + 3/2*c) + 8*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(
3/2*d*x + 3/2*c)))^2 + cos(3/2*d*x + 3/2*c)^2 + 12*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/
2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*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 + s
in(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 2*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(7/3*arctan2(sin(3/
2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2
*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2
+ 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 +
24*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 +
cos(3/2*d*x + 3/2*c)^2 + 2*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2
+ cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*
d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(7/3*arctan2(sin(3/2*d*x + 3/
2*c), cos(3/2*d*x + 3/2*c))) + 4*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3
*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2
*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3/2*d*x + 3/2*c)^2 + 12*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) +
sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*
x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c)
, cos(3/2*d*x + 3/2*c)))^2 + 4*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + 8*(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*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/
2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*
cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*
arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/
2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + 2*((cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 +
4*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c
)^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/
2*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3
/2*c) + sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c) + 4*(2*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x +
3*c)^2*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*
cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^
2)*sin(3*d*x + 3*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2 +
(cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c
)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*sin(3*d*x + 3*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos
(3/2*d*x + 3/2*c))) + 2*(16*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), co
s(3/2*d*x + 3/2*c)))^3 + (cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) +
cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(cos(3*d*x + 3*c)^2 + sin(3*
d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*
c), cos(3/2*d*x + 3/2*c)))^2 + 4*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3
/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2
*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(5/3*arctan2(
sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3*d*x + 3*c) + cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) +
sin(3/2*d*x + 3/2*c)^3 + 12*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c)
+ cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*co
s(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) + s
in(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*arctan
2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3*d*x + 3*c) + cos(3/2*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*arctan
2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)
))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c)
, cos(3/2*d*x + 3/2*c))) + 1) + 4*(cos(3/2*d*x + 3/2*c)^4 + 7*cos(3/2*d*x + 3/2*c)^2)*sin(3/2*d*x + 3/2*c) + 4
*(2*sin(3/2*d*x + 3/2*c)^4 + 32*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/
2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))
))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + ((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x
+ 3*c)^2 + (2*sin(3/2*d*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2
*d*x + 3/2*c) - 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)
*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*co
s(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)*si
n(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*(sin(3/2*d*x + 3/2*c)^4 + (cos(3/2*d*x + 3/2*c)^2 + 4)*sin(3/2*d*x + 3/
2*c)^2 + 3*cos(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c) + cos(3/2*d*x + 3/2*c)^2 - 2*(18*(cos(3/2*d*x + 3/2*c)^2 +
sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 5*cos
(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) - 2*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d*x + 3
/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(3/2*d*
x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(2/3*arctan2(sin(3/2*d*x + 3
/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x +
3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(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*(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(4/3*arctan2(sin(3/2*d*x + 3/2
*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)
)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - (2*sin(3/2*d*x + 3/2*c)^3 + (2*cos(3/2*d*x +
3/2*c)^2 + 7)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) - 2*(2*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c)*sin(3/2*d*
x + 3/2*c) + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 2*cos(3*d*x + 3*c)*cos(3/2*d*x +
3/2*c)*sin(3/2*d*x + 3/2*c) + 8*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3
/2*c) - 9*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)
)))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(sin(3/2*d*x + 3/2*c)^2 + 3)*sin(3*d*x +
3*c) + 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)
)) + 7*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
- 18*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)*cos
(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 20*(cos(3/2*d*x + 3/2*c)*sin(3*d*x +
3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) -
7*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 4*(18*(cos(3/
2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c))) + 5*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 20*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x +
3*c)*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x + 3*c)
*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d
*x + 3/2*c))) - (2*sin(3/2*d*x + 3/2*c)^3 + (2*cos(3/2*d*x + 3/2*c)^2 + 7)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3
*c) - 20*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(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 + c
os(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*s
in(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)*c
os(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*arcta
n2(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) + s
in(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 + s
in(3/2*d*x + 3/2*c)^2)*cos(3*d*x + 3*c)^2 + (cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)
^2 + 4*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2
+ cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))
))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 40*(cos(3/2*d*x + 3/2*c)^2*sin(3*d*x + 3*c)
- cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*
x + 3/2*c))) + 14*(cos(3/2*d*x + 3/2*c)^2*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x
+ 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3/2*d*x + 3/2*c)^2*sin(3/2*d
*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3 - (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*
cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c))*si
n(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c))) + 8*(2*sin(3/2*d*x + 3/2*c)^4 + 4*((2*sin(3/2*d*x + 3/2*c)^2 + 1)*cos(3*d*x + 3*c)^2 + (2*sin(3/2*d
*x + 3/2*c)^2 + 1)*sin(3*d*x + 3*c)^2 + 2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*(sin(
3/2*d*x + 3/2*c)^2 + 3)*cos(3*d*x + 3*c) - 20*(cos(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^2)*cos(4/3*arctan2(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*(co
s(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*
d*x + 3/2*c))) + 5*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + 20*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d
*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*(cos(3*d*x +
3*c)*cos(3/2*d*x + 3/2*c) + sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3
/2*d*x + 3/2*c))) - (2*sin(3/2*d*x + 3/2*c)^3 + (2*cos(3/2*d*x + 3/2*c)^2 + 7)*sin(3/2*d*x + 3/2*c))*sin(3*d*x
+ 3*c) - 20*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(s
in(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*sin(
3/2*d*x + 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x +
3/2*c), cos(3/2*d*x + 3/2*c))) - 20*(2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*cos(3*d*
x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(4/3*arctan2(sin(3/2*d*x
+ 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(2*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 2*cos(3*
d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + cos(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^2)*cos(2/3*arctan2(sin(3/2*d
*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^3 + (cos(3/2*d*x + 3/2*c)^3
+ cos(3/2*d*x + 3/2*c))*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) + 40*(cos(3/2*d*x + 3/2*c)^2*sin(3*d*x + 3*c)
- cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*
x + 3/2*c))) + 14*(cos(3/2*d*x + 3/2*c)^2*sin(3*d*x + 3*c) - cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x
+ 3/2*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 18*(cos(3/2*d*x + 3/2*c)^2*sin(3/2*d
*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3 - (cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)^3)*
cos(3*d*x + 3*c) + (cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c))*si
n(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c))) + 80*(cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(4/3*arctan2(sin(3/2
*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 28*(cos(3/2*d*x + 3/2*c)^3 + cos(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)
^2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 36*(cos(3/2*d*x + 3/2*c)^4 + 2*cos(3/2*d*x
+ 3/2*c)^2*sin(3/2*d*x + 3/2*c)^2 + sin(3/2*d*x + 3/2*c)^4)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c))))*A/((sqrt(2)*a*cos(3/2*d*x + 3/2*c)^4 + 2*sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c)^2 +
sqrt(2)*a*sin(3/2*d*x + 3/2*c)^4 + (sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(7/3*arct
an2(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 + sqr
t(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(sqrt(2)*a*
cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))
))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 16*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d
*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2
*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2
*c)))^3 + 2*(sqrt(2)*a*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/
2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) + 4*(
sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^3 + 16*(sqrt(2)*a*cos(3*d*x + 3*c)^2
*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin
(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2
*d*x + 3/2*c)))^3 + (4*sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c)^2 + 4*sqrt(2)*a*cos(3/2*d*x + 3/2*c)*si
n(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 + (s
qrt(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 + 1
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 + sqr
t(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*arctan
2(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*arcta
n2(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 + sqr
t(2)*a*sin(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*cos(3*d*
x + 3*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2)*cos(5/3
*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (4*sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)*s
in(3/2*d*x + 3/2*c) - 4*sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 +
sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*cos(
3*d*x + 3*c)^2 + 2*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(7/3*arctan2(sin(3/2*d*x +
3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*ar
ctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d
*x + 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 24*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*sin(5/3*a
rctan2(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*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x +
3/2*c))) + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x +
3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*co
s(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) - s
qrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*
sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(4*sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x
+ 3*c)*sin(3/2*d*x + 3/2*c) - 4*sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*cos(3/2*d*x + 3
/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c
)^2)*cos(3*d*x + 3*c)^2 + 8*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(
3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c
)^2)*sin(3*d*x + 3*c)^2 + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c
)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin(3/2*d*
x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c)
, cos(3/2*d*x + 3/2*c)))^2 + 2*(sqrt(2)*a*cos(3/2*d*x + 3/2*c)^3 + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3/2*d*x
+ 3/2*c)^2 + 16*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2)*cos(5/3*arctan2(sin(3/2*d*x + 3/
2*c), cos(3/2*d*x + 3/2*c)))^3 + 12*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x
+ 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*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 + 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)*c
os(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*si
n(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), cos(3/2*d*x + 3/2*c)))^2 + 4*(sqrt(2)*a
*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3
/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*
x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*(sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)
*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3*d*x + 3*c) + 12*(sqrt(2)*a*cos(3*d*x + 3*c
)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*
sin(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(
3/2*d*x + 3/2*c)))^2 - (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3/2*d*x + 3/2*c)
^3)*cos(3*d*x + 3*c) + 2*(2*(sqrt(2)*a*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)^2*
sin(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) - sqrt(2)*a*cos(3*d*x + 3*c)*sin(3/2*d*
x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 +
sqrt(2)*a*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c) + 2*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + s
qrt(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 + sq
rt(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)*si
n(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*arcta
n2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (sqrt(2)*a*cos(3/2*d*x + 3/2*c)^2 + sqrt(2)*a*sin(3/2*d*x
+ 3/2*c)^2)*sin(3*d*x + 3*c)^2 + 4*(sqrt(2)*a*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(3/2*d*x
+ 3/2*c)*sin(3*d*x + 3*c)^2 + sqrt(2)*a*cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*sin(3*d*x + 3*c)*sin
(3/2*d*x + 3/2*c))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(5/3*arctan2(sin(3/2*d*x +
3/2*c), cos(3/2*d*x + 3/2*c))))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(sqrt(2)*a*c
os(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)*si
n(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(s
in(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*c
os(3/2*d*x + 3/2*c)*sin(3/2*d*x + 3/2*c)^2)*sin(3*d*x + 3*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*
x + 3/2*c))))*sqrt(a)))/d
Giac [F]
\[
\int \frac {\cos ^{\frac {3}{2}}(c+d x) (A+B \sec (c+d x))}{(a+a \sec (c+d x))^{3/2}} \, dx=\int { \frac {{\left (B \sec \left (d x + c\right ) + A\right )} \cos \left (d x + c\right )^{\frac {3}{2}}}{{\left (a \sec \left (d x + c\right ) + a\right )}^{\frac {3}{2}}} \,d x }
\]
[In]
integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm="giac")
[Out]
integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(3/2), x)
Mupad [F(-1)]
Timed out. \[
\int \frac {\cos ^{\frac {3}{2}}(c+d x) (A+B \sec (c+d x))}{(a+a \sec (c+d x))^{3/2}} \, dx=\int \frac {{\cos \left (c+d\,x\right )}^{3/2}\,\left (A+\frac {B}{\cos \left (c+d\,x\right )}\right )}{{\left (a+\frac {a}{\cos \left (c+d\,x\right )}\right )}^{3/2}} \,d x
\]
[In]
int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x)))/(a + a/cos(c + d*x))^(3/2),x)
[Out]
int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x)))/(a + a/cos(c + d*x))^(3/2), x)