\(\int \frac {A+C \sec ^2(c+d x)}{\cos ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx\) [1165]
Optimal result
Integrand size = 37, antiderivative size = 228 \[
\int \frac {A+C \sec ^2(c+d x)}{\cos ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx=-\frac {3 C \text {arcsinh}\left (\frac {\sqrt {a} \tan (c+d x)}{\sqrt {a+a \sec (c+d x)}}\right ) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}}{a^{3/2} d}+\frac {(A+9 C) \text {arctanh}\left (\frac {\sqrt {a} \sqrt {\sec (c+d x)} \sin (c+d x)}{\sqrt {2} \sqrt {a+a \sec (c+d x)}}\right ) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}}{2 \sqrt {2} a^{3/2} d}-\frac {(A+C) \sin (c+d x)}{2 d \cos ^{\frac {5}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}}+\frac {(A+3 C) \sin (c+d x)}{2 a d \cos ^{\frac {3}{2}}(c+d x) \sqrt {a+a \sec (c+d x)}}
\]
[Out]
-1/2*(A+C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2)-3*C*arcsinh(a^(1/2)*tan(d*x+c)/(a+a*sec(d*x+c)
)^(1/2))*cos(d*x+c)^(1/2)*sec(d*x+c)^(1/2)/a^(3/2)/d+1/4*(A+9*C)*arctanh(1/2*sin(d*x+c)*a^(1/2)*sec(d*x+c)^(1/
2)*2^(1/2)/(a+a*sec(d*x+c))^(1/2))*cos(d*x+c)^(1/2)*sec(d*x+c)^(1/2)/a^(3/2)/d*2^(1/2)+1/2*(A+3*C)*sin(d*x+c)/
a/d/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2)
Rubi [A] (verified)
Time = 0.85 (sec) , antiderivative size = 228, normalized size of antiderivative = 1.00, number of
steps used = 8, number of rules used = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.216, Rules used = {4350, 4170, 4106, 4108, 3893,
212, 3886, 221} \[
\int \frac {A+C \sec ^2(c+d x)}{\cos ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx=\frac {(A+9 C) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)} \text {arctanh}\left (\frac {\sqrt {a} \sin (c+d x) \sqrt {\sec (c+d x)}}{\sqrt {2} \sqrt {a \sec (c+d x)+a}}\right )}{2 \sqrt {2} a^{3/2} d}-\frac {3 C \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)} \text {arcsinh}\left (\frac {\sqrt {a} \tan (c+d x)}{\sqrt {a \sec (c+d x)+a}}\right )}{a^{3/2} d}+\frac {(A+3 C) \sin (c+d x)}{2 a d \cos ^{\frac {3}{2}}(c+d x) \sqrt {a \sec (c+d x)+a}}-\frac {(A+C) \sin (c+d x)}{2 d \cos ^{\frac {5}{2}}(c+d x) (a \sec (c+d x)+a)^{3/2}}
\]
[In]
Int[(A + C*Sec[c + d*x]^2)/(Cos[c + d*x]^(3/2)*(a + a*Sec[c + d*x])^(3/2)),x]
[Out]
(-3*C*ArcSinh[(Sqrt[a]*Tan[c + d*x])/Sqrt[a + a*Sec[c + d*x]]]*Sqrt[Cos[c + d*x]]*Sqrt[Sec[c + d*x]])/(a^(3/2)
*d) + ((A + 9*C)*ArcTanh[(Sqrt[a]*Sqrt[Sec[c + d*x]]*Sin[c + d*x])/(Sqrt[2]*Sqrt[a + a*Sec[c + d*x]])]*Sqrt[Co
s[c + d*x]]*Sqrt[Sec[c + d*x]])/(2*Sqrt[2]*a^(3/2)*d) - ((A + C)*Sin[c + d*x])/(2*d*Cos[c + d*x]^(5/2)*(a + a*
Sec[c + d*x])^(3/2)) + ((A + 3*C)*Sin[c + d*x])/(2*a*d*Cos[c + d*x]^(3/2)*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 221
Int[1/Sqrt[(a_) + (b_.)*(x_)^2], x_Symbol] :> Simp[ArcSinh[Rt[b, 2]*(x/Sqrt[a])]/Rt[b, 2], x] /; FreeQ[{a, b},
x] && GtQ[a, 0] && PosQ[b]
Rule 3886
Int[Sqrt[csc[(e_.) + (f_.)*(x_)]*(d_.)]*Sqrt[csc[(e_.) + (f_.)*(x_)]*(b_.) + (a_)], x_Symbol] :> Dist[-2*(a/(b
*f))*Sqrt[a*(d/b)], Subst[Int[1/Sqrt[1 + x^2/a], x], x, b*(Cot[e + f*x]/Sqrt[a + b*Csc[e + f*x]])], x] /; Free
Q[{a, b, d, e, f}, x] && EqQ[a^2 - b^2, 0] && GtQ[a*(d/b), 0]
Rule 3893
Int[Sqrt[csc[(e_.) + (f_.)*(x_)]*(d_.)]/Sqrt[csc[(e_.) + (f_.)*(x_)]*(b_.) + (a_)], x_Symbol] :> Dist[-2*b*(d/
(a*f)), Subst[Int[1/(2*b - d*x^2), x], x, b*(Cot[e + f*x]/(Sqrt[a + b*Csc[e + f*x]]*Sqrt[d*Csc[e + f*x]]))], x
] /; FreeQ[{a, b, d, e, f}, x] && EqQ[a^2 - b^2, 0]
Rule 4106
Int[(csc[(e_.) + (f_.)*(x_)]*(d_.))^(n_)*(csc[(e_.) + (f_.)*(x_)]*(b_.) + (a_))^(m_)*(csc[(e_.) + (f_.)*(x_)]*
(B_.) + (A_)), x_Symbol] :> Simp[(-B)*d*Cot[e + f*x]*(a + b*Csc[e + f*x])^m*((d*Csc[e + f*x])^(n - 1)/(f*(m +
n))), x] + Dist[d/(b*(m + n)), Int[(a + b*Csc[e + f*x])^m*(d*Csc[e + f*x])^(n - 1)*Simp[b*B*(n - 1) + (A*b*(m
+ n) + a*B*m)*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] && GtQ[n, 1]
Rule 4108
Int[(csc[(e_.) + (f_.)*(x_)]*(d_.))^(n_)*(csc[(e_.) + (f_.)*(x_)]*(b_.) + (a_))^(m_)*(csc[(e_.) + (f_.)*(x_)]*
(B_.) + (A_)), x_Symbol] :> Dist[(A*b - a*B)/b, Int[(a + b*Csc[e + f*x])^m*(d*Csc[e + f*x])^n, x], x] + Dist[B
/b, Int[(a + b*Csc[e + f*x])^(m + 1)*(d*Csc[e + f*x])^n, x], x] /; FreeQ[{a, b, d, e, f, A, B, m}, x] && NeQ[A
*b - a*B, 0] && EqQ[a^2 - b^2, 0]
Rule 4170
Int[((A_.) + csc[(e_.) + (f_.)*(x_)]^2*(C_.))*(csc[(e_.) + (f_.)*(x_)]*(d_.))^(n_)*(csc[(e_.) + (f_.)*(x_)]*(b
_.) + (a_))^(m_), x_Symbol] :> Simp[(-a)*(A + C)*Cot[e + f*x]*(a + b*Csc[e + f*x])^m*((d*Csc[e + f*x])^n/(a*f*
(2*m + 1))), x] + Dist[1/(a*b*(2*m + 1)), Int[(a + b*Csc[e + f*x])^(m + 1)*(d*Csc[e + f*x])^n*Simp[b*C*n + A*b
*(2*m + n + 1) - (a*(A*(m + n + 1) - C*(m - n)))*Csc[e + f*x], x], x], x] /; FreeQ[{a, b, d, e, f, A, C, n}, x
] && EqQ[a^2 - b^2, 0] && LtQ[m, -2^(-1)]
Rule 4350
Int[(cos[(a_.) + (b_.)*(x_)]*(c_.))^(m_.)*(u_), x_Symbol] :> Dist[(c*Cos[a + b*x])^m*(c*Sec[a + b*x])^m, Int[A
ctivateTrig[u]/(c*Sec[a + b*x])^m, x], x] /; FreeQ[{a, b, c, m}, x] && !IntegerQ[m] && KnownSecantIntegrandQ[
u, x]
Rubi steps \begin{align*}
\text {integral}& = \left (\sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \int \frac {\sec ^{\frac {3}{2}}(c+d x) \left (A+C \sec ^2(c+d x)\right )}{(a+a \sec (c+d x))^{3/2}} \, dx \\ & = -\frac {(A+C) \sin (c+d x)}{2 d \cos ^{\frac {5}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}}-\frac {\left (\sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \int \frac {\sec ^{\frac {3}{2}}(c+d x) \left (-\frac {1}{2} a (A-3 C)-a (A+3 C) \sec (c+d x)\right )}{\sqrt {a+a \sec (c+d x)}} \, dx}{2 a^2} \\ & = -\frac {(A+C) \sin (c+d x)}{2 d \cos ^{\frac {5}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}}+\frac {(A+3 C) \sin (c+d x)}{2 a d \cos ^{\frac {3}{2}}(c+d x) \sqrt {a+a \sec (c+d x)}}-\frac {\left (\sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \int \frac {\sqrt {\sec (c+d x)} \left (-\frac {1}{2} a^2 (A+3 C)+3 a^2 C \sec (c+d x)\right )}{\sqrt {a+a \sec (c+d x)}} \, dx}{2 a^3} \\ & = -\frac {(A+C) \sin (c+d x)}{2 d \cos ^{\frac {5}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}}+\frac {(A+3 C) \sin (c+d x)}{2 a d \cos ^{\frac {3}{2}}(c+d x) \sqrt {a+a \sec (c+d x)}}-\frac {\left (3 C \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \int \sqrt {\sec (c+d x)} \sqrt {a+a \sec (c+d x)} \, dx}{2 a^2}+\frac {\left ((A+9 C) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \int \frac {\sqrt {\sec (c+d x)}}{\sqrt {a+a \sec (c+d x)}} \, dx}{4 a} \\ & = -\frac {(A+C) \sin (c+d x)}{2 d \cos ^{\frac {5}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}}+\frac {(A+3 C) \sin (c+d x)}{2 a d \cos ^{\frac {3}{2}}(c+d x) \sqrt {a+a \sec (c+d x)}}+\frac {\left (3 C \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \text {Subst}\left (\int \frac {1}{\sqrt {1+\frac {x^2}{a}}} \, dx,x,-\frac {a \tan (c+d x)}{\sqrt {a+a \sec (c+d x)}}\right )}{a^2 d}-\frac {\left ((A+9 C) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}\right ) \text {Subst}\left (\int \frac {1}{2 a-x^2} \, dx,x,-\frac {a \sqrt {\sec (c+d x)} \sin (c+d x)}{\sqrt {a+a \sec (c+d x)}}\right )}{2 a d} \\ & = -\frac {3 C \text {arcsinh}\left (\frac {\sqrt {a} \tan (c+d x)}{\sqrt {a+a \sec (c+d x)}}\right ) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}}{a^{3/2} d}+\frac {(A+9 C) \text {arctanh}\left (\frac {\sqrt {a} \sqrt {\sec (c+d x)} \sin (c+d x)}{\sqrt {2} \sqrt {a+a \sec (c+d x)}}\right ) \sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)}}{2 \sqrt {2} a^{3/2} d}-\frac {(A+C) \sin (c+d x)}{2 d \cos ^{\frac {5}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}}+\frac {(A+3 C) \sin (c+d x)}{2 a d \cos ^{\frac {3}{2}}(c+d x) \sqrt {a+a \sec (c+d x)}} \\
\end{align*}
Mathematica [A] (verified)
Time = 7.11 (sec) , antiderivative size = 447, normalized size of antiderivative = 1.96
\[
\int \frac {A+C \sec ^2(c+d x)}{\cos ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx=\frac {\sqrt {\cos (c+d x)} \sqrt {\sec (c+d x)} \left (8 (A+3 C) \arcsin \left (\sqrt {1-\sec (c+d x)}\right ) \cos ^3\left (\frac {1}{2} (c+d x)\right ) \sec ^2(c+d x) \sin \left (\frac {1}{2} (c+d x)\right )+8 (A+9 C) \arcsin \left (\sqrt {\sec (c+d x)}\right ) \cos ^3\left (\frac {1}{2} (c+d x)\right ) \sec ^2(c+d x) \sin \left (\frac {1}{2} (c+d x)\right )+2 A \sqrt {1-\sec (c+d x)} \sec ^{\frac {3}{2}}(c+d x) \sin (c+d x)+6 C \sqrt {1-\sec (c+d x)} \sec ^{\frac {3}{2}}(c+d x) \sin (c+d x)+4 C \sqrt {1-\sec (c+d x)} \sec ^{\frac {5}{2}}(c+d x) \sin (c+d x)-\sqrt {2} A \arctan \left (\frac {\sqrt {2} \sqrt {\sec (c+d x)}}{\sqrt {1-\sec (c+d x)}}\right ) \tan (c+d x)-9 \sqrt {2} C \arctan \left (\frac {\sqrt {2} \sqrt {\sec (c+d x)}}{\sqrt {1-\sec (c+d x)}}\right ) \tan (c+d x)-\sqrt {2} A \arctan \left (\frac {\sqrt {2} \sqrt {\sec (c+d x)}}{\sqrt {1-\sec (c+d x)}}\right ) \sec (c+d x) \tan (c+d x)-9 \sqrt {2} C \arctan \left (\frac {\sqrt {2} \sqrt {\sec (c+d x)}}{\sqrt {1-\sec (c+d x)}}\right ) \sec (c+d x) \tan (c+d x)\right )}{4 d \sqrt {1-\sec (c+d x)} (a (1+\sec (c+d x)))^{3/2}}
\]
[In]
Integrate[(A + C*Sec[c + d*x]^2)/(Cos[c + d*x]^(3/2)*(a + a*Sec[c + d*x])^(3/2)),x]
[Out]
(Sqrt[Cos[c + d*x]]*Sqrt[Sec[c + d*x]]*(8*(A + 3*C)*ArcSin[Sqrt[1 - Sec[c + d*x]]]*Cos[(c + d*x)/2]^3*Sec[c +
d*x]^2*Sin[(c + d*x)/2] + 8*(A + 9*C)*ArcSin[Sqrt[Sec[c + d*x]]]*Cos[(c + d*x)/2]^3*Sec[c + d*x]^2*Sin[(c + d*
x)/2] + 2*A*Sqrt[1 - Sec[c + d*x]]*Sec[c + d*x]^(3/2)*Sin[c + d*x] + 6*C*Sqrt[1 - Sec[c + d*x]]*Sec[c + d*x]^(
3/2)*Sin[c + d*x] + 4*C*Sqrt[1 - Sec[c + d*x]]*Sec[c + d*x]^(5/2)*Sin[c + d*x] - Sqrt[2]*A*ArcTan[(Sqrt[2]*Sqr
t[Sec[c + d*x]])/Sqrt[1 - Sec[c + d*x]]]*Tan[c + d*x] - 9*Sqrt[2]*C*ArcTan[(Sqrt[2]*Sqrt[Sec[c + d*x]])/Sqrt[1
- Sec[c + d*x]]]*Tan[c + d*x] - Sqrt[2]*A*ArcTan[(Sqrt[2]*Sqrt[Sec[c + d*x]])/Sqrt[1 - Sec[c + d*x]]]*Sec[c +
d*x]*Tan[c + d*x] - 9*Sqrt[2]*C*ArcTan[(Sqrt[2]*Sqrt[Sec[c + d*x]])/Sqrt[1 - Sec[c + d*x]]]*Sec[c + d*x]*Tan[
c + d*x]))/(4*d*Sqrt[1 - Sec[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. \(536\) vs. \(2(189)=378\).
Time = 0.82 (sec) , antiderivative size = 537, normalized size of antiderivative = 2.36
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method | result | size |
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\(-\frac {\left (A \sqrt {2}\, \cos \left (d x +c \right )^{2} \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (1+\cos \left (d x +c \right )\right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}}\right )+9 C \sqrt {2}\, \cos \left (d x +c \right )^{2} \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (1+\cos \left (d x +c \right )\right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}}\right )+A \cos \left (d x +c \right ) \sqrt {2}\, \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (1+\cos \left (d x +c \right )\right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}}\right )-2 A \cos \left (d x +c \right ) \sin \left (d x +c \right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}+9 C \cos \left (d x +c \right ) \sqrt {2}\, \arctan \left (\frac {\sin \left (d x +c \right ) \sqrt {2}}{2 \left (1+\cos \left (d x +c \right )\right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}}\right )+6 C \cos \left (d x +c \right )^{2} \arctan \left (\frac {\cos \left (d x +c \right )-\sin \left (d x +c \right )+1}{2 \left (1+\cos \left (d x +c \right )\right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}}\right )-6 C \cos \left (d x +c \right )^{2} \arctan \left (\frac {\cos \left (d x +c \right )+\sin \left (d x +c \right )+1}{2 \left (1+\cos \left (d x +c \right )\right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}}\right )-6 C \cos \left (d x +c \right ) \sin \left (d x +c \right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}+6 C \arctan \left (\frac {\cos \left (d x +c \right )-\sin \left (d x +c \right )+1}{2 \left (1+\cos \left (d x +c \right )\right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}}\right ) \cos \left (d x +c \right )-6 C \cos \left (d x +c \right ) \arctan \left (\frac {\cos \left (d x +c \right )+\sin \left (d x +c \right )+1}{2 \left (1+\cos \left (d x +c \right )\right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}}\right )-4 C \sin \left (d x +c \right ) \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}\right ) \sqrt {a \left (1+\sec \left (d x +c \right )\right )}}{4 a^{2} d \left (1+\cos \left (d x +c \right )\right )^{2} \sqrt {-\frac {1}{1+\cos \left (d x +c \right )}}\, \sqrt {\cos \left (d x +c \right )}}\) |
\(537\) |
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[In]
int((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x,method=_RETURNVERBOSE)
[Out]
-1/4/a^2/d*(A*2^(1/2)*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*2^(1/2)/(1+cos(d*x+c))/(-1/(1+cos(d*x+c)))^(1/2))+9*C
*2^(1/2)*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*2^(1/2)/(1+cos(d*x+c))/(-1/(1+cos(d*x+c)))^(1/2))+A*cos(d*x+c)*2^(
1/2)*arctan(1/2*sin(d*x+c)*2^(1/2)/(1+cos(d*x+c))/(-1/(1+cos(d*x+c)))^(1/2))-2*A*cos(d*x+c)*sin(d*x+c)*(-1/(1+
cos(d*x+c)))^(1/2)+9*C*cos(d*x+c)*2^(1/2)*arctan(1/2*sin(d*x+c)*2^(1/2)/(1+cos(d*x+c))/(-1/(1+cos(d*x+c)))^(1/
2))+6*C*cos(d*x+c)^2*arctan(1/2*(cos(d*x+c)-sin(d*x+c)+1)/(1+cos(d*x+c))/(-1/(1+cos(d*x+c)))^(1/2))-6*C*cos(d*
x+c)^2*arctan(1/2*(cos(d*x+c)+sin(d*x+c)+1)/(1+cos(d*x+c))/(-1/(1+cos(d*x+c)))^(1/2))-6*C*cos(d*x+c)*sin(d*x+c
)*(-1/(1+cos(d*x+c)))^(1/2)+6*C*arctan(1/2*(cos(d*x+c)-sin(d*x+c)+1)/(1+cos(d*x+c))/(-1/(1+cos(d*x+c)))^(1/2))
*cos(d*x+c)-6*C*cos(d*x+c)*arctan(1/2*(cos(d*x+c)+sin(d*x+c)+1)/(1+cos(d*x+c))/(-1/(1+cos(d*x+c)))^(1/2))-4*C*
sin(d*x+c)*(-1/(1+cos(d*x+c)))^(1/2))*(a*(1+sec(d*x+c)))^(1/2)/(1+cos(d*x+c))^2/(-1/(1+cos(d*x+c)))^(1/2)/cos(
d*x+c)^(1/2)
Fricas [A] (verification not implemented)
none
Time = 0.34 (sec) , antiderivative size = 668, normalized size of antiderivative = 2.93
\[
\int \frac {A+C \sec ^2(c+d x)}{\cos ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx=\left [\frac {\sqrt {2} {\left ({\left (A + 9 \, C\right )} \cos \left (d x + c\right )^{3} + 2 \, {\left (A + 9 \, C\right )} \cos \left (d x + c\right )^{2} + {\left (A + 9 \, C\right )} \cos \left (d x + c\right )\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 ({\left (A + 3 \, C\right )} \cos \left (d x + c\right ) + 2 \, C\right )} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sqrt {\cos \left (d x + c\right )} \sin \left (d x + c\right ) + 6 \, {\left (C \cos \left (d x + c\right )^{3} + 2 \, C \cos \left (d x + c\right )^{2} + C \cos \left (d x + c\right )\right )} \sqrt {a} \log \left (\frac {a \cos \left (d x + c\right )^{3} + 4 \, \sqrt {a} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} {\left (\cos \left (d x + c\right ) - 2\right )} \sqrt {\cos \left (d x + c\right )} \sin \left (d x + c\right ) - 7 \, a \cos \left (d x + c\right )^{2} + 8 \, a}{\cos \left (d x + c\right )^{3} + \cos \left (d x + c\right )^{2}}\right )}{8 \, {\left (a^{2} d \cos \left (d x + c\right )^{3} + 2 \, a^{2} d \cos \left (d x + c\right )^{2} + a^{2} d \cos \left (d x + c\right )\right )}}, -\frac {\sqrt {2} {\left ({\left (A + 9 \, C\right )} \cos \left (d x + c\right )^{3} + 2 \, {\left (A + 9 \, C\right )} \cos \left (d x + c\right )^{2} + {\left (A + 9 \, C\right )} \cos \left (d x + c\right )\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 ({\left (A + 3 \, C\right )} \cos \left (d x + c\right ) + 2 \, C\right )} \sqrt {\frac {a \cos \left (d x + c\right ) + a}{\cos \left (d x + c\right )}} \sqrt {\cos \left (d x + c\right )} \sin \left (d x + c\right ) + 6 \, {\left (C \cos \left (d x + c\right )^{3} + 2 \, C \cos \left (d x + c\right )^{2} + C \cos \left (d x + c\right )\right )} \sqrt {-a} \arctan \left (\frac {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 )}{a \cos \left (d x + c\right )^{2} - a \cos \left (d x + c\right ) - 2 \, a}\right )}{4 \, {\left (a^{2} d \cos \left (d x + c\right )^{3} + 2 \, a^{2} d \cos \left (d x + c\right )^{2} + a^{2} d \cos \left (d x + c\right )\right )}}\right ]
\]
[In]
integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm="fricas")
[Out]
[1/8*(sqrt(2)*((A + 9*C)*cos(d*x + c)^3 + 2*(A + 9*C)*cos(d*x + c)^2 + (A + 9*C)*cos(d*x + c))*sqrt(a)*log(-(a
*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) -
2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*((A + 3*C)*cos(d*x + c) + 2*C)*sqrt((a*cos(
d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 6*(C*cos(d*x + c)^3 + 2*C*cos(d*x + c)^2 + C*cos
(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 + 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2
)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(a^2*d*cos(d
*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c)), -1/4*(sqrt(2)*((A + 9*C)*cos(d*x + c)^3 + 2*(A + 9*C
)*cos(d*x + c)^2 + (A + 9*C)*cos(d*x + c))*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x
+ c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*((A + 3*C)*cos(d*x + c) + 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*
x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 6*(C*cos(d*x + c)^3 + 2*C*cos(d*x + c)^2 + C*cos(d*x + c))*sqrt(-a)*
arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 -
a*cos(d*x + c) - 2*a)))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c))]
Sympy [F(-1)]
Timed out. \[
\int \frac {A+C \sec ^2(c+d x)}{\cos ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx=\text {Timed out}
\]
[In]
integrate((A+C*sec(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+a*sec(d*x+c))**(3/2),x)
[Out]
Timed out
Maxima [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 63653 vs. \(2 (189) = 378\).
Time = 2.41 (sec) , antiderivative size = 63653, normalized size of antiderivative = 279.18
\[
\int \frac {A+C \sec ^2(c+d x)}{\cos ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx=\text {Too large to display}
\]
[In]
integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm="maxima")
[Out]
1/4*((32*(cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) + cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + cos(d*x + c)*sin(3/2
*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(d*x + c))*cos(3*d*x + 3*c)^2 + 96*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3
*c) + 3*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) - (3*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) - cos(3*d*x + 3*c)*s
in(3/2*d*x + 3/2*c) - 3*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 3*cos(3/2*d*x + 3/2*c)*sin(d*x + c))*cos(4/3*a
rctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 96*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) + 3*cos(3/2*
d*x + 3/2*c)*sin(2*d*x + 2*c) - (3*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2
*c) - 3*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 3*cos(3/2*d*x + 3/2*c)*sin(d*x + c))*cos(2/3*arctan2(sin(3/2*d
*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 32*(cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) + cos(2*d*x + 2*c)*sin(3/2*d
*x + 3/2*c) + cos(d*x + c)*sin(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(d*x + c))*sin(3*d*x + 3*c)^2 + 32*(
6*cos(d*x + c) + 1)*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 96*cos(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 96*si
n(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 96*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) + 3*cos(3/2*d*x + 3/2*c)*sin
(2*d*x + 2*c) - (3*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 3*cos(2*d*
x + 2*c)*sin(3/2*d*x + 3/2*c) + 3*cos(3/2*d*x + 3/2*c)*sin(d*x + c))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos
(3/2*d*x + 3/2*c)))^2 + 96*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) + 3*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) -
(3*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 3*cos(2*d*x + 2*c)*sin(3/2
*d*x + 3/2*c) + 3*cos(3/2*d*x + 3/2*c)*sin(d*x + c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c
)))^2 + 32*(2*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 3*cos(2*d*x + 2*c)^2*sin(3/2*d*x +
3/2*c) + 3*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 2*(3*sin(3/2*d*x + 3/2*c)*sin(d*x + c) + cos(3/2*d*x + 3/
2*c))*sin(2*d*x + 2*c) + (3*cos(d*x + c)^2 + 3*sin(d*x + c)^2 + 2*cos(d*x + c))*sin(3/2*d*x + 3/2*c) + 2*cos(3
/2*d*x + 3/2*c)*sin(d*x + c))*cos(3*d*x + 3*c) - 4*(6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c)^2 + s
in(3*d*x + 3*c)^3 + (2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*
cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2
*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(3*d*x + 3*c) + 3*(2*(3*cos(2*d*x + 2*c)
+ 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(
2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2
+ 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(4/3*arc
tan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 3*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x +
3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2
+ 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2
*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*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))) - 4*(8*cos(3*d*x + 3*c)^2*sin(3
/2*d*x + 3/2*c) - 72*cos(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) - 144*cos(2*d*x + 2*c)*cos(d*x + c)*sin(3/2*d*x +
3/2*c) - 8*sin(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 72*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) - 16*(3*cos(3
/2*d*x + 3/2*c)*sin(2*d*x + 2*c) + 3*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c
) - 48*(cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) + 3*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) - (3*cos(d*x + c) + 1)
*sin(3/2*d*x + 3/2*c) - cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 3*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 3*co
s(3/2*d*x + 3/2*c)*sin(d*x + c))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 16*(cos(3*d*x
+ 3*c)*cos(3/2*d*x + 3/2*c) + 3*sin(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 3*sin(3/2*d*x + 3/2*c)*sin(d*x + c) +
cos(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) - 48*(3*sin(3/2*d*x + 3/2*c)*sin(d*x + c) + cos(3/2*d*x + 3/2*c))*sin(2
*d*x + 2*c) - 8*(9*cos(d*x + c)^2 + 9*sin(d*x + c)^2 - 1)*sin(3/2*d*x + 3/2*c) - 48*cos(3/2*d*x + 3/2*c)*sin(d
*x + c) + 3*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x
+ c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin
(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^
2 + 6*cos(d*x + c) + 1)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(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))) - 4*(8*cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) - 72*cos(2*d*x + 2*c)^2*si
n(3/2*d*x + 3/2*c) - 144*cos(2*d*x + 2*c)*cos(d*x + c)*sin(3/2*d*x + 3/2*c) - 8*sin(3*d*x + 3*c)^2*sin(3/2*d*x
+ 3/2*c) - 72*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) - 16*(3*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) + 3*cos(3
/2*d*x + 3/2*c)*sin(d*x + c) - sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c) - 16*(cos(3*d*x + 3*c)*cos(3/2*d*x + 3/2
*c) + 3*sin(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 3*sin(3/2*d*x + 3/2*c)*sin(d*x + c) + cos(3/2*d*x + 3/2*c))*si
n(3*d*x + 3*c) - 48*(3*sin(3/2*d*x + 3/2*c)*sin(d*x + c) + cos(3/2*d*x + 3/2*c))*sin(2*d*x + 2*c) - 8*(9*cos(d
*x + c)^2 + 9*sin(d*x + c)^2 - 1)*sin(3/2*d*x + 3/2*c) - 48*cos(3/2*d*x + 3/2*c)*sin(d*x + c) + 3*(2*(3*cos(2*
d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*
c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*
x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*
sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(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*(6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^3 + (2*(3*cos(2*d*
x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)
+ 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d
*x + c)^2 + 6*cos(d*x + c) + 1)*sin(3*d*x + 3*c))*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
+ (2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 2)*cos(3*d*x + 3*c)^3 + cos(3*d*x + 3*c)^4 + 6*(sin(2*d*x + 2*c)
+ sin(d*x + c))*sin(3*d*x + 3*c)^3 + sin(3*d*x + 3*c)^4 + 3*(6*(cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 3*cos(2*d
*x + 2*c)^2 + 3*cos(d*x + c)^2 + 3*sin(2*d*x + 2*c)^2 + 6*sin(2*d*x + 2*c)*sin(d*x + c) + 3*sin(d*x + c)^2 + 6
*cos(d*x + c) + 2)*cos(3*d*x + 3*c)^2 + 9*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(
3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*
d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*
sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*
c)))^2 + 9*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x +
c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(
3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2
+ 6*cos(d*x + c) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + (2*(3*cos(2*d*x + 2*c)
+ 3*cos(d*x + c) + 2)*cos(3*d*x + 3*c) + 2*cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*c
os(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c
)^2 + 6*cos(d*x + c) + 2)*sin(3*d*x + 3*c)^2 + 9*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c)
+ cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*
(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x
+ 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x
+ 3/2*c)))^2 + 9*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*co
s(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c
))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x
+ c)^2 + 6*cos(d*x + c) + 1)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(9*(2*cos(d*x
+ c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x +
2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 9*cos(d*x + c) + 2)*cos(3*d*x + 3*c) + 6*(3*cos(d*x + c) + 1)*cos(2*d*x
+ 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(3*(2*cos(2*d*x + 2*c) + 2*cos(d*x + c) + 1)*cos(3*d*x +
3*c)^2 + cos(3*d*x + 3*c)^3 + (cos(3*d*x + 3*c) + 1)*sin(3*d*x + 3*c)^2 + 3*(2*(3*cos(d*x + c) + 2)*cos(2*d*x
+ 2*c) + 3*cos(2*d*x + 2*c)^2 + 3*cos(d*x + c)^2 + 3*sin(2*d*x + 2*c)^2 + 6*sin(2*d*x + 2*c)*sin(d*x + c) + 3
*sin(d*x + c)^2 + 4*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x
+ 2*c)^2 + 9*cos(d*x + c)^2 + 3*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3
*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c
) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x +
c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*
((sin(2*d*x + 2*c) + sin(d*x + c))*cos(3*d*x + 3*c) + sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + 9*si
n(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(4/3*arctan2(s
in(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(3*(2*cos(2*d*x + 2*c) + 2*cos(d*x + c) + 1)*cos(3*d*x + 3*c)^
2 + cos(3*d*x + 3*c)^3 + (cos(3*d*x + 3*c) + 1)*sin(3*d*x + 3*c)^2 + 3*(2*(3*cos(d*x + c) + 2)*cos(2*d*x + 2*c
) + 3*cos(2*d*x + 2*c)^2 + 3*cos(d*x + c)^2 + 3*sin(2*d*x + 2*c)^2 + 6*sin(2*d*x + 2*c)*sin(d*x + c) + 3*sin(d
*x + c)^2 + 4*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c
)^2 + 9*cos(d*x + c)^2 + 6*((sin(2*d*x + 2*c) + sin(d*x + c))*cos(3*d*x + 3*c) + sin(2*d*x + 2*c) + sin(d*x +
c))*sin(3*d*x + 3*c) + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x
+ c) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*((sin(2*d*x + 2*c) + sin(d*x + c))*
cos(3*d*x + 3*c)^2 + 2*(sin(2*d*x + 2*c) + sin(d*x + c))*cos(3*d*x + 3*c) + sin(2*d*x + 2*c) + sin(d*x + c))*s
in(3*d*x + 3*c) + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*(6*(sin(2*d*x
+ 2*c) + sin(d*x + c))*sin(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^3 + (2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)
*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*co
s(d*x + c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1
)*sin(3*d*x + 3*c) + 3*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*
(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*
x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*si
n(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arcta
n2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c)^2 +
sin(3*d*x + 3*c)^3 + (2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3
*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(
2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(3*d*x + 3*c))*sin(2/3*arctan2(sin(3/2*d
*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*cos(d*x + c) + 1)*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) - (2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 2)*cos(3*d*x + 3*c)^3 + co
s(3*d*x + 3*c)^4 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c)^3 + sin(3*d*x + 3*c)^4 + 3*(6*(cos(d*x
+ c) + 1)*cos(2*d*x + 2*c) + 3*cos(2*d*x + 2*c)^2 + 3*cos(d*x + c)^2 + 3*sin(2*d*x + 2*c)^2 + 6*sin(2*d*x + 2
*c)*sin(d*x + c) + 3*sin(d*x + c)^2 + 6*cos(d*x + c) + 2)*cos(3*d*x + 3*c)^2 + 9*(2*(3*cos(2*d*x + 2*c) + 3*co
s(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x
+ 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*si
n(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(4/3*arctan2(s
in(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 9*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c
) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6
*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x
+ 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*
x + 3/2*c)))^2 + (2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 2)*cos(3*d*x + 3*c) + 2*cos(3*d*x + 3*c)^2 + 6*(3*c
os(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*
d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 2)*sin(3*d*x + 3*c)^2 + 9*(2*(3*cos(2*d*x + 2*c)
+ 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos
(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2
+ 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(4/3*ar
ctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 9*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*
x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c
)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*si
n(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos
(3/2*d*x + 3/2*c)))^2 + 2*(9*(2*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 +
9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 9*cos(d*x + c) + 2)*cos(3*d*x +
3*c) + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(3*(2*cos(2*d*x +
2*c) + 2*cos(d*x + c) + 1)*cos(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)^3 + (cos(3*d*x + 3*c) + 1)*sin(3*d*x + 3*c)^
2 + 3*(2*(3*cos(d*x + c) + 2)*cos(2*d*x + 2*c) + 3*cos(2*d*x + 2*c)^2 + 3*cos(d*x + c)^2 + 3*sin(2*d*x + 2*c)^
2 + 6*sin(2*d*x + 2*c)*sin(d*x + c) + 3*sin(d*x + c)^2 + 4*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + 6*(3*cos(d*x +
c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 3*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c
) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2
+ 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x +
2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(2/3*arctan2(sin(3/2*d*
x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*((sin(2*d*x + 2*c) + sin(d*x + c))*cos(3*d*x + 3*c) + sin(2*d*x + 2*c)
+ sin(d*x + c))*sin(3*d*x + 3*c) + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2
+ 6*cos(d*x + c) + 1)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(3*(2*cos(2*d*x + 2*c)
+ 2*cos(d*x + c) + 1)*cos(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)^3 + (cos(3*d*x + 3*c) + 1)*sin(3*d*x + 3*c)^2 + 3*
(2*(3*cos(d*x + c) + 2)*cos(2*d*x + 2*c) + 3*cos(2*d*x + 2*c)^2 + 3*cos(d*x + c)^2 + 3*sin(2*d*x + 2*c)^2 + 6*
sin(2*d*x + 2*c)*sin(d*x + c) + 3*sin(d*x + c)^2 + 4*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + 6*(3*cos(d*x + c) +
1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*((sin(2*d*x + 2*c) + sin(d*x + c))*cos(3*d*x
+ 3*c) + sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d
*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
+ 6*((sin(2*d*x + 2*c) + sin(d*x + c))*cos(3*d*x + 3*c)^2 + 2*(sin(2*d*x + 2*c) + sin(d*x + c))*cos(3*d*x + 3*
c) + sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x +
c) + 9*sin(d*x + c)^2 + 6*(6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^3 + (2*(3
*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d
*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c)
+ 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(3*d*x + 3*c) + 3*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos
(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*
x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 +
18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c)
, cos(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))) + 6*(6*(sin(2*d*x + 2*c
) + sin(d*x + c))*sin(3*d*x + 3*c)^2 + sin(3*d*x + 3*c)^3 + (2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3
*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x
+ c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(
3*d*x + 3*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*cos(d*x + c) + 1)*log(cos(1/3*a
rctan2(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) - 32*(2*(3*cos(d*x + c) + 1)*co
s(2*d*x + 2*c)*cos(3/2*d*x + 3/2*c) + 3*cos(2*d*x + 2*c)^2*cos(3/2*d*x + 3/2*c) + 3*cos(3/2*d*x + 3/2*c)*sin(2
*d*x + 2*c)^2 + 2*(cos(2*d*x + 2*c)*cos(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*cos(d*x + c) - sin(2*d*x + 2*c
)*sin(3/2*d*x + 3/2*c) - sin(3/2*d*x + 3/2*c)*sin(d*x + c))*cos(3*d*x + 3*c) + (3*cos(d*x + c)^2 + 3*sin(d*x +
c)^2 + 2*cos(d*x + c))*cos(3/2*d*x + 3/2*c) + 2*(3*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - sin(3/2*d*x + 3/2*c))*
sin(2*d*x + 2*c) - 2*sin(3/2*d*x + 3/2*c)*sin(d*x + c))*sin(3*d*x + 3*c) + 32*(6*sin(3/2*d*x + 3/2*c)*sin(d*x
+ c) + cos(3/2*d*x + 3/2*c))*sin(2*d*x + 2*c) + 32*(3*cos(d*x + c)^2 + 3*sin(d*x + c)^2 + cos(d*x + c))*sin(3/
2*d*x + 3/2*c) + 32*cos(3/2*d*x + 3/2*c)*sin(d*x + c) + 4*(3*(2*cos(2*d*x + 2*c) + 2*cos(d*x + c) + 1)*cos(3*d
*x + 3*c)^2 + cos(3*d*x + 3*c)^3 + (cos(3*d*x + 3*c) + 1)*sin(3*d*x + 3*c)^2 + 3*(2*(3*cos(d*x + c) + 2)*cos(2
*d*x + 2*c) + 3*cos(2*d*x + 2*c)^2 + 3*cos(d*x + c)^2 + 3*sin(2*d*x + 2*c)^2 + 6*sin(2*d*x + 2*c)*sin(d*x + c)
+ 3*sin(d*x + c)^2 + 4*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2
*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 3*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x
+ 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x +
2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d
*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))
+ 3*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1
)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x +
3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*co
s(d*x + c) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*((sin(2*d*x + 2*c) + sin(d*x
+ c))*cos(3*d*x + 3*c) + sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d
*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*
d*x + 3/2*c))) - 4*(8*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + 48*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)*cos(3
/2*d*x + 3/2*c) + 72*cos(2*d*x + 2*c)^2*cos(3/2*d*x + 3/2*c) - 8*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + 72*
cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c)^2 + 144*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c)*sin(d*x + c) + 16*((3*cos(
d*x + c) + 1)*cos(3/2*d*x + 3/2*c) + 3*cos(2*d*x + 2*c)*cos(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c) + 8*(9*cos(d*x
+ c)^2 + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(3/2*d*x + 3/2*c) - 3*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x +
c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2
+ 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x
+ 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(1/3*arctan2(sin(3/2*d
*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*((3*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) + cos(3*d*x + 3*c)*sin(3/2
*d*x + 3/2*c) + 3*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c) - 48*(cos(3/2*d*x + 3/2*c)*sin(3*d*x
+ 3*c) + 3*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) - (3*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) - cos(3*d*x + 3*
c)*sin(3/2*d*x + 3/2*c) - 3*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 3*cos(3/2*d*x + 3/2*c)*sin(d*x + c))*sin(2
/3*arctan2(sin(3/2*d*x + 3/2*c), cos(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))) - 4*(8*cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + 48*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)*cos(3/2*d*x
+ 3/2*c) + 72*cos(2*d*x + 2*c)^2*cos(3/2*d*x + 3/2*c) - 8*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + 72*cos(3/2
*d*x + 3/2*c)*sin(2*d*x + 2*c)^2 + 144*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c)*sin(d*x + c) + 16*((3*cos(d*x + c
) + 1)*cos(3/2*d*x + 3/2*c) + 3*cos(2*d*x + 2*c)*cos(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c) + 8*(9*cos(d*x + c)^2
+ 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(3/2*d*x + 3/2*c) - 3*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)
*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*co
s(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^
2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(1/3*arctan2(sin(3/2*d*x + 3/
2*c), cos(3/2*d*x + 3/2*c))) + 16*((3*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) + cos(3*d*x + 3*c)*sin(3/2*d*x +
3/2*c) + 3*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c))*sin(3*d*x + 3*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(
3/2*d*x + 3/2*c))) - 4*(3*(2*cos(2*d*x + 2*c) + 2*cos(d*x + c) + 1)*cos(3*d*x + 3*c)^2 + cos(3*d*x + 3*c)^3 +
(cos(3*d*x + 3*c) + 1)*sin(3*d*x + 3*c)^2 + 3*(2*(3*cos(d*x + c) + 2)*cos(2*d*x + 2*c) + 3*cos(2*d*x + 2*c)^2
+ 3*cos(d*x + c)^2 + 3*sin(2*d*x + 2*c)^2 + 6*sin(2*d*x + 2*c)*sin(d*x + c) + 3*sin(d*x + c)^2 + 4*cos(d*x + c
) + 1)*cos(3*d*x + 3*c) + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 +
6*((sin(2*d*x + 2*c) + sin(d*x + c))*cos(3*d*x + 3*c) + sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + 9*
sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*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*d*x + 3*c)^4 + sqrt(2)*a*sin(3*d*x + 3*c)^4
+ 2*(3*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + 2*sqrt(2)*a)*cos(3*d*x + 3*c)^3 + 6*(sqrt(2)*a
*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x + c))*sin(3*d*x + 3*c)^3 + 9*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*a*
cos(d*x + c)^2 + 9*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*a*sin
(d*x + c)^2 + 3*(3*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 3*sqrt(2)*a*cos(d*x + c)^2 + 3*sqrt(2)*a*sin(2*d*x + 2*c)^2
+ 6*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 3*sqrt(2)*a*sin(d*x + c)^2 + 6*sqrt(2)*a*cos(d*x + c) + 6*(sqrt(
2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 2*sqrt(2)*a)*cos(3*d*x + 3*c)^2 + 9*(sqrt(2)*a*cos(3*d*x + 3
*c)^2 + 9*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*a*cos(d*x + c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2 + 9*sqrt(2)
*a*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*a*sin(d*x + c)^2 + 6*sqrt(2)*a*
cos(d*x + c) + 2*(3*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(3*d*x + 3*c) + 6*(3
*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 6*(sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x + c)
)*sin(3*d*x + 3*c) + sqrt(2)*a)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 9*(sqrt(2)*a*
cos(3*d*x + 3*c)^2 + 9*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*a*cos(d*x + c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^
2 + 9*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*a*sin(d*x + c)^2 +
6*sqrt(2)*a*cos(d*x + c) + 2*(3*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(3*d*x
+ 3*c) + 6*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 6*(sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a
*sin(d*x + c))*sin(3*d*x + 3*c) + sqrt(2)*a)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 +
(2*sqrt(2)*a*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*a*cos(d*x + c)^2 + 9*sqrt(2)*a*si
n(2*d*x + 2*c)^2 + 18*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*a*sin(d*x + c)^2 + 6*sqrt(2)*a*cos(d
*x + c) + 2*(3*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + 2*sqrt(2)*a)*cos(3*d*x + 3*c) + 6*(3*sq
rt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 2*sqrt(2)*a)*sin(3*d*x + 3*c)^2 + 9*(sqrt(2)*a*cos(3*d*x
+ 3*c)^2 + 9*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*a*cos(d*x + c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2 + 9*sqrt
(2)*a*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*a*sin(d*x + c)^2 + 6*sqrt(2)
*a*cos(d*x + c) + 2*(3*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(3*d*x + 3*c) + 6
*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 6*(sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x +
c))*sin(3*d*x + 3*c) + sqrt(2)*a)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 9*(sqrt(2)
*a*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*a*cos(d*x + c)^2 + sqrt(2)*a*sin(3*d*x + 3*
c)^2 + 9*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*a*sin(d*x + c)^
2 + 6*sqrt(2)*a*cos(d*x + c) + 2*(3*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(3*d
*x + 3*c) + 6*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 6*(sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2
)*a*sin(d*x + c))*sin(3*d*x + 3*c) + sqrt(2)*a)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2
+ 6*sqrt(2)*a*cos(d*x + c) + 2*(9*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*a*cos(d*x + c)^2 + 9*sqrt(2)*a*sin
(2*d*x + 2*c)^2 + 18*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*a*sin(d*x + c)^2 + 9*sqrt(2)*a*cos(d*
x + c) + 9*(2*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 2*sqrt(2)*a)*cos(3*d*x + 3*c) + 6*(3*sqrt
(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 6*(sqrt(2)*a*cos(3*d*x + 3*c)^3 + 9*sqrt(2)*a*cos(2*d*x + 2
*c)^2 + 9*sqrt(2)*a*cos(d*x + c)^2 + 9*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x +
c) + 9*sqrt(2)*a*sin(d*x + c)^2 + 3*(2*sqrt(2)*a*cos(2*d*x + 2*c) + 2*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(
3*d*x + 3*c)^2 + (sqrt(2)*a*cos(3*d*x + 3*c) + sqrt(2)*a)*sin(3*d*x + 3*c)^2 + 6*sqrt(2)*a*cos(d*x + c) + 3*(3
*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 3*sqrt(2)*a*cos(d*x + c)^2 + 3*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 6*sqrt(2)*a*sin(
2*d*x + 2*c)*sin(d*x + c) + 3*sqrt(2)*a*sin(d*x + c)^2 + 4*sqrt(2)*a*cos(d*x + c) + 2*(3*sqrt(2)*a*cos(d*x + c
) + 2*sqrt(2)*a)*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos
(2*d*x + 2*c) + 3*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*a*cos(d*x + c)^2
+ sqrt(2)*a*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) +
9*sqrt(2)*a*sin(d*x + c)^2 + 6*sqrt(2)*a*cos(d*x + c) + 2*(3*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x
+ c) + sqrt(2)*a)*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 6*(sqrt(2)*a
*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x + c))*sin(3*d*x + 3*c) + sqrt(2)*a)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c)
, cos(3/2*d*x + 3/2*c))) + 6*(sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x + c) + (sqrt(2)*a*sin(2*d*x + 2*c
) + sqrt(2)*a*sin(d*x + c))*cos(3*d*x + 3*c))*sin(3*d*x + 3*c) + sqrt(2)*a)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*
c), cos(3/2*d*x + 3/2*c))) + 6*(sqrt(2)*a*cos(3*d*x + 3*c)^3 + 9*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*a*co
s(d*x + c)^2 + 9*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*a*sin(d
*x + c)^2 + 3*(2*sqrt(2)*a*cos(2*d*x + 2*c) + 2*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(3*d*x + 3*c)^2 + (sqrt
(2)*a*cos(3*d*x + 3*c) + sqrt(2)*a)*sin(3*d*x + 3*c)^2 + 6*sqrt(2)*a*cos(d*x + c) + 3*(3*sqrt(2)*a*cos(2*d*x +
2*c)^2 + 3*sqrt(2)*a*cos(d*x + c)^2 + 3*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 6*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x +
c) + 3*sqrt(2)*a*sin(d*x + c)^2 + 4*sqrt(2)*a*cos(d*x + c) + 2*(3*sqrt(2)*a*cos(d*x + c) + 2*sqrt(2)*a)*cos(2
*d*x + 2*c) + sqrt(2)*a)*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 6*(sqr
t(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x + c) + (sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x + c))*cos(3
*d*x + 3*c))*sin(3*d*x + 3*c) + sqrt(2)*a)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*((
sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x + c))*cos(3*d*x + 3*c)^2 + sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)
*a*sin(d*x + c) + 2*(sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x + c))*cos(3*d*x + 3*c))*sin(3*d*x + 3*c) +
6*(sqrt(2)*a*sin(3*d*x + 3*c)^3 + 6*(sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x + c))*sin(3*d*x + 3*c)^2
+ (sqrt(2)*a*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*a*cos(d*x + c)^2 + 9*sqrt(2)*a*si
n(2*d*x + 2*c)^2 + 18*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*a*sin(d*x + c)^2 + 6*sqrt(2)*a*cos(d
*x + c) + 2*(3*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(3*d*x + 3*c) + 6*(3*sqrt
(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(3*d*x + 3*c) + 3*(sqrt(2)*a*cos(3*d*x + 3*c)
^2 + 9*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*a*cos(d*x + c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*a*
sin(2*d*x + 2*c)^2 + 18*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*a*sin(d*x + c)^2 + 6*sqrt(2)*a*cos
(d*x + c) + 2*(3*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(3*d*x + 3*c) + 6*(3*sq
rt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 6*(sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x + c))*s
in(3*d*x + 3*c) + sqrt(2)*a)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(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))) + 6*(sqrt(2)*a*sin(3*d*x + 3*c)^3 + 6*(sqrt(2)*a*sin(2*d*x + 2*c) +
sqrt(2)*a*sin(d*x + c))*sin(3*d*x + 3*c)^2 + (sqrt(2)*a*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*a*cos(2*d*x + 2*c)^2 +
9*sqrt(2)*a*cos(d*x + c)^2 + 9*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 9*s
qrt(2)*a*sin(d*x + c)^2 + 6*sqrt(2)*a*cos(d*x + c) + 2*(3*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c
) + sqrt(2)*a)*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(3
*d*x + 3*c))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sqrt(a)) + (128*cos(3/2
*d*x + 3/2*c)*sin(3*d*x + 3*c)^3 + 1152*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c)^3 - 128*cos(3*d*x + 3*c)^3*sin(3
/2*d*x + 3/2*c) - 1152*cos(2*d*x + 2*c)^3*sin(3/2*d*x + 3/2*c) + 32*(4*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) -
9*(3*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) - 28*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 3*cos(3/2*d*x + 3/2*
c)*sin(d*x + c))*cos(3*d*x + 3*c)^2 - 96*(11*(3*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) - 9*cos(3/2*d*x + 3/2*c
)*sin(d*x + c))*cos(2*d*x + 2*c)^2 + 32*(28*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) - (3*cos(d*x + c) + 1)*sin(3
/2*d*x + 3/2*c) - 4*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 27*cos(3
/2*d*x + 3/2*c)*sin(d*x + c))*sin(3*d*x + 3*c)^2 - 288*((3*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) + 4*cos(2*d*
x + 2*c)*sin(3/2*d*x + 3/2*c) - 11*cos(3/2*d*x + 3/2*c)*sin(d*x + c))*sin(2*d*x + 2*c)^2 - 32*(cos(3*d*x + 3*c
)^2*sin(3/2*d*x + 3/2*c) + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 9*cos(2*d*x + 2*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*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) +
18*sin(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c)*sin(d*x + c) + 2*((3*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) + 3*cos(2
*d*x + 2*c)*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c) + 6*(sin(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x +
3/2*c)*sin(d*x + c))*sin(3*d*x + 3*c) + (9*cos(d*x + c)^2 + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(3/2*d*x
+ 3/2*c))*cos(5*d*x + 5*c) - 96*(cos(3*d*x + 3*c)^2*sin(3/2*d*x + 3/2*c) + 6*(3*cos(d*x + c) + 1)*cos(2*d*x +
2*c)*sin(3/2*d*x + 3/2*c) + 9*cos(2*d*x + 2*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*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 18*sin(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c)*sin(d*x + c) + 2*((3
*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) + 3*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c) + 6*(sin(2
*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + sin(3/2*d*x + 3/2*c)*sin(d*x + c))*sin(3*d*x + 3*c) + (9*cos(d*x + c)^2 + 9
*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c))*cos(4*d*x + 4*c) - 64*(30*cos(2*d*x + 2*c)^2*sin(3
/2*d*x + 3/2*c) + 18*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) - 3*(3*cos(d*x + c) + 1)*cos(3/2*d*x + 3/2*c)*sin
(d*x + c) + (19*(3*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) - 9*cos(3/2*d*x + 3/2*c)*sin(d*x + c))*cos(2*d*x + 2
*c) - 4*((3*cos(d*x + c) + 1)*cos(3/2*d*x + 3/2*c) + 3*cos(2*d*x + 2*c)*cos(3/2*d*x + 3/2*c) - 9*sin(3/2*d*x +
3/2*c)*sin(d*x + c))*sin(2*d*x + 2*c) + 3*(9*cos(d*x + c)^2 + 6*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(3/2*
d*x + 3/2*c))*cos(3*d*x + 3*c) + 64*(9*(3*cos(d*x + c) + 1)*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - (45*cos(d*x +
c)^2 + 18*sin(d*x + c)^2 + 30*cos(d*x + c) + 5)*sin(3/2*d*x + 3/2*c))*cos(2*d*x + 2*c) + 96*(9*sin(d*x + c)^3
+ (9*cos(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(d*x + c))*cos(3/2*d*x + 3/2*c) - 12*((sin(3*d*x + 3*c) + 3*sin(2
*d*x + 2*c) + 3*sin(d*x + c))*cos(5*d*x + 5*c)^2 + 9*(sin(3*d*x + 3*c) + 3*sin(2*d*x + 2*c) + 3*sin(d*x + c))*
cos(4*d*x + 4*c)^2 + 48*(sin(2*d*x + 2*c) + sin(d*x + c))*cos(3*d*x + 3*c)^2 + (sin(3*d*x + 3*c) + 3*sin(2*d*x
+ 2*c) + 3*sin(d*x + c))*sin(5*d*x + 5*c)^2 + 9*(sin(3*d*x + 3*c) + 3*sin(2*d*x + 2*c) + 3*sin(d*x + c))*sin(
4*d*x + 4*c)^2 + 8*(10*sin(2*d*x + 2*c) + 9*sin(d*x + c))*sin(3*d*x + 3*c)^2 + 16*sin(3*d*x + 3*c)^3 + 48*sin(
2*d*x + 2*c)^3 + 24*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)*sin(d*x + c) + 48*cos(2*d*x + 2*c)^2*sin(d*x + c) +
120*sin(2*d*x + 2*c)^2*sin(d*x + c) + 27*sin(d*x + c)^3 + 2*(3*(sin(3*d*x + 3*c) + 3*sin(2*d*x + 2*c) + 3*sin(
d*x + c))*cos(4*d*x + 4*c) + 12*(sin(2*d*x + 2*c) + sin(d*x + c))*cos(3*d*x + 3*c) + (4*cos(3*d*x + 3*c) + 4*c
os(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(3*d*x + 3*c) + 3*(4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x
+ 2*c) + 3*(3*cos(d*x + c) + 1)*sin(d*x + c) + 12*cos(2*d*x + 2*c)*sin(d*x + c))*cos(5*d*x + 5*c) + 6*(12*(si
n(2*d*x + 2*c) + sin(d*x + c))*cos(3*d*x + 3*c) + (4*cos(3*d*x + 3*c) + 4*cos(2*d*x + 2*c) + 3*cos(d*x + c) +
1)*sin(3*d*x + 3*c) + 3*(4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + 3*(3*cos(d*x + c) + 1)*si
n(d*x + c) + 12*cos(2*d*x + 2*c)*sin(d*x + c))*cos(4*d*x + 4*c) + 24*((4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1
)*sin(2*d*x + 2*c) + (3*cos(d*x + c) + 1)*sin(d*x + c) + 4*cos(2*d*x + 2*c)*sin(d*x + c))*cos(3*d*x + 3*c) + 2
*(3*(sin(3*d*x + 3*c) + 3*sin(2*d*x + 2*c) + 3*sin(d*x + c))*sin(4*d*x + 4*c) + (16*sin(2*d*x + 2*c) + 15*sin(
d*x + c))*sin(3*d*x + 3*c) + 4*sin(3*d*x + 3*c)^2 + 12*sin(2*d*x + 2*c)^2 + 21*sin(2*d*x + 2*c)*sin(d*x + c) +
9*sin(d*x + c)^2)*sin(5*d*x + 5*c) + 6*((16*sin(2*d*x + 2*c) + 15*sin(d*x + c))*sin(3*d*x + 3*c) + 4*sin(3*d*
x + 3*c)^2 + 12*sin(2*d*x + 2*c)^2 + 21*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2)*sin(4*d*x + 4*c) + (
8*(4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + 16*cos(3*d*x + 3*c)^2 + 8*(3*cos(d*x + c) + 1)*
cos(2*d*x + 2*c) + 16*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 112*sin(2*d*x + 2*c)^2 + 192*sin(2*d*x + 2*c)*si
n(d*x + c) + 81*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(3*d*x + 3*c) + 3*(8*(3*cos(d*x + c) + 1)*cos(2*d*x +
2*c) + 16*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 33*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + 3
*(9*cos(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(d*x + c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 16*((sin
(3*d*x + 3*c) + 3*sin(2*d*x + 2*c) + 3*sin(d*x + c))*cos(5*d*x + 5*c)^2 + 9*(sin(3*d*x + 3*c) + 3*sin(2*d*x +
2*c) + 3*sin(d*x + c))*cos(4*d*x + 4*c)^2 + 48*(sin(2*d*x + 2*c) + sin(d*x + c))*cos(3*d*x + 3*c)^2 + (sin(3*d
*x + 3*c) + 3*sin(2*d*x + 2*c) + 3*sin(d*x + c))*sin(5*d*x + 5*c)^2 + 9*(sin(3*d*x + 3*c) + 3*sin(2*d*x + 2*c)
+ 3*sin(d*x + c))*sin(4*d*x + 4*c)^2 + 8*(10*sin(2*d*x + 2*c) + 9*sin(d*x + c))*sin(3*d*x + 3*c)^2 + 16*sin(3
*d*x + 3*c)^3 + 48*sin(2*d*x + 2*c)^3 + 24*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)*sin(d*x + c) + 48*cos(2*d*x +
2*c)^2*sin(d*x + c) + 120*sin(2*d*x + 2*c)^2*sin(d*x + c) + 27*sin(d*x + c)^3 + 2*(3*(sin(3*d*x + 3*c) + 3*si
n(2*d*x + 2*c) + 3*sin(d*x + c))*cos(4*d*x + 4*c) + 12*(sin(2*d*x + 2*c) + sin(d*x + c))*cos(3*d*x + 3*c) + (4
*cos(3*d*x + 3*c) + 4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(3*d*x + 3*c) + 3*(4*cos(2*d*x + 2*c) + 3*cos(
d*x + c) + 1)*sin(2*d*x + 2*c) + 3*(3*cos(d*x + c) + 1)*sin(d*x + c) + 12*cos(2*d*x + 2*c)*sin(d*x + c))*cos(5
*d*x + 5*c) + 6*(12*(sin(2*d*x + 2*c) + sin(d*x + c))*cos(3*d*x + 3*c) + (4*cos(3*d*x + 3*c) + 4*cos(2*d*x + 2
*c) + 3*cos(d*x + c) + 1)*sin(3*d*x + 3*c) + 3*(4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + 3*
(3*cos(d*x + c) + 1)*sin(d*x + c) + 12*cos(2*d*x + 2*c)*sin(d*x + c))*cos(4*d*x + 4*c) + 24*((4*cos(2*d*x + 2*
c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + (3*cos(d*x + c) + 1)*sin(d*x + c) + 4*cos(2*d*x + 2*c)*sin(d*x + c
))*cos(3*d*x + 3*c) + 2*(3*(sin(3*d*x + 3*c) + 3*sin(2*d*x + 2*c) + 3*sin(d*x + c))*sin(4*d*x + 4*c) + (16*sin
(2*d*x + 2*c) + 15*sin(d*x + c))*sin(3*d*x + 3*c) + 4*sin(3*d*x + 3*c)^2 + 12*sin(2*d*x + 2*c)^2 + 21*sin(2*d*
x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2)*sin(5*d*x + 5*c) + 6*((16*sin(2*d*x + 2*c) + 15*sin(d*x + c))*sin(3*
d*x + 3*c) + 4*sin(3*d*x + 3*c)^2 + 12*sin(2*d*x + 2*c)^2 + 21*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^
2)*sin(4*d*x + 4*c) + (8*(4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + 16*cos(3*d*x + 3*c)^2 +
8*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 16*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 112*sin(2*d*x + 2*c)^2 +
192*sin(2*d*x + 2*c)*sin(d*x + c) + 81*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(3*d*x + 3*c) + 3*(8*(3*cos(d*x
+ c) + 1)*cos(2*d*x + 2*c) + 16*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 33*sin(d*x + c)^2 + 6*cos(d*x + c) +
1)*sin(2*d*x + 2*c) + 3*(9*cos(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(d*x + c))*cos(3/2*arctan2(sin(d*x + c), co
s(d*x + c))) + 12*((sin(3*d*x + 3*c) + 3*sin(2*d*x + 2*c) + 3*sin(d*x + c))*cos(5*d*x + 5*c)^2 + 9*(sin(3*d*x
+ 3*c) + 3*sin(2*d*x + 2*c) + 3*sin(d*x + c))*cos(4*d*x + 4*c)^2 + 48*(sin(2*d*x + 2*c) + sin(d*x + c))*cos(3*
d*x + 3*c)^2 + (sin(3*d*x + 3*c) + 3*sin(2*d*x + 2*c) + 3*sin(d*x + c))*sin(5*d*x + 5*c)^2 + 9*(sin(3*d*x + 3*
c) + 3*sin(2*d*x + 2*c) + 3*sin(d*x + c))*sin(4*d*x + 4*c)^2 + 8*(10*sin(2*d*x + 2*c) + 9*sin(d*x + c))*sin(3*
d*x + 3*c)^2 + 16*sin(3*d*x + 3*c)^3 + 48*sin(2*d*x + 2*c)^3 + 24*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)*sin(d*
x + c) + 48*cos(2*d*x + 2*c)^2*sin(d*x + c) + 120*sin(2*d*x + 2*c)^2*sin(d*x + c) + 27*sin(d*x + c)^3 + 2*(3*(
sin(3*d*x + 3*c) + 3*sin(2*d*x + 2*c) + 3*sin(d*x + c))*cos(4*d*x + 4*c) + 12*(sin(2*d*x + 2*c) + sin(d*x + c)
)*cos(3*d*x + 3*c) + (4*cos(3*d*x + 3*c) + 4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(3*d*x + 3*c) + 3*(4*co
s(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + 3*(3*cos(d*x + c) + 1)*sin(d*x + c) + 12*cos(2*d*x + 2
*c)*sin(d*x + c))*cos(5*d*x + 5*c) + 6*(12*(sin(2*d*x + 2*c) + sin(d*x + c))*cos(3*d*x + 3*c) + (4*cos(3*d*x +
3*c) + 4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(3*d*x + 3*c) + 3*(4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1
)*sin(2*d*x + 2*c) + 3*(3*cos(d*x + c) + 1)*sin(d*x + c) + 12*cos(2*d*x + 2*c)*sin(d*x + c))*cos(4*d*x + 4*c)
+ 24*((4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + (3*cos(d*x + c) + 1)*sin(d*x + c) + 4*cos(2
*d*x + 2*c)*sin(d*x + c))*cos(3*d*x + 3*c) + 2*(3*(sin(3*d*x + 3*c) + 3*sin(2*d*x + 2*c) + 3*sin(d*x + c))*sin
(4*d*x + 4*c) + (16*sin(2*d*x + 2*c) + 15*sin(d*x + c))*sin(3*d*x + 3*c) + 4*sin(3*d*x + 3*c)^2 + 12*sin(2*d*x
+ 2*c)^2 + 21*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2)*sin(5*d*x + 5*c) + 6*((16*sin(2*d*x + 2*c) +
15*sin(d*x + c))*sin(3*d*x + 3*c) + 4*sin(3*d*x + 3*c)^2 + 12*sin(2*d*x + 2*c)^2 + 21*sin(2*d*x + 2*c)*sin(d*x
+ c) + 9*sin(d*x + c)^2)*sin(4*d*x + 4*c) + (8*(4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + 1
6*cos(3*d*x + 3*c)^2 + 8*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 16*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 11
2*sin(2*d*x + 2*c)^2 + 192*sin(2*d*x + 2*c)*sin(d*x + c) + 81*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(3*d*x +
3*c) + 3*(8*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 16*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 33*sin(d*x + c
)^2 + 6*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + 3*(9*cos(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(d*x + c))*cos(1/2*a
rctan2(sin(d*x + c), cos(d*x + c))) - 3*(16*sqrt(2)*cos(3*d*x + 3*c)^4 + 144*sqrt(2)*cos(2*d*x + 2*c)^4 + 81*s
qrt(2)*cos(d*x + c)^4 + 16*sqrt(2)*sin(3*d*x + 3*c)^4 + 144*sqrt(2)*sin(2*d*x + 2*c)^4 + 504*sqrt(2)*sin(2*d*x
+ 2*c)^3*sin(d*x + c) + 81*sqrt(2)*sin(d*x + c)^4 + 8*(16*sqrt(2)*cos(2*d*x + 2*c) + 15*sqrt(2)*cos(d*x + c)
+ 5*sqrt(2))*cos(3*d*x + 3*c)^3 + 168*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)^3 + 8*(16*sqrt(2)*si
n(2*d*x + 2*c) + 15*sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c)^3 + 108*sqrt(2)*cos(d*x + c)^3 + (sqrt(2)*cos(3*d*x
+ 3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*s
in(2*d*x + 2*c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d
*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*
x + 2*c) + 6*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqr
t(2))*cos(5*d*x + 5*c)^2 + 9*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x +
c)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) +
9*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c)
+ 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*
sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(4*d*x + 4*c)^2 + (352*sqrt(2)*cos(2*d*x + 2*c)^2 + 29
7*sqrt(2)*cos(d*x + c)^2 + 160*sqrt(2)*sin(2*d*x + 2*c)^2 + 312*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 153*sq
rt(2)*sin(d*x + c)^2 + 216*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 198*sqrt(2)*cos(d*x + c) + 33
*sqrt(2))*cos(3*d*x + 3*c)^2 + (657*sqrt(2)*cos(d*x + c)^2 + 225*sqrt(2)*sin(d*x + c)^2 + 438*sqrt(2)*cos(d*x
+ c) + 73*sqrt(2))*cos(2*d*x + 2*c)^2 + (sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)
*cos(d*x + c)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(
d*x + c) + 9*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*
d*x + 3*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin
(d*x + c))*sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(5*d*x + 5*c)^2 + 9*(sqrt(2)*cos(3*d*x + 3*
c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*
d*x + 2*c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x +
2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2
*c) + 6*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))
*sin(4*d*x + 4*c)^2 + (32*sqrt(2)*cos(3*d*x + 3*c)^2 + 160*sqrt(2)*cos(2*d*x + 2*c)^2 + 153*sqrt(2)*cos(d*x +
c)^2 + 352*sqrt(2)*sin(2*d*x + 2*c)^2 + 648*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 297*sqrt(2)*sin(d*x + c)^2
+ 8*(16*sqrt(2)*cos(2*d*x + 2*c) + 15*sqrt(2)*cos(d*x + c) + 5*sqrt(2))*cos(3*d*x + 3*c) + 104*(3*sqrt(2)*cos
(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 102*sqrt(2)*cos(d*x + c) + 17*sqrt(2))*sin(3*d*x + 3*c)^2 + (288*sqrt(
2)*cos(2*d*x + 2*c)^2 + 225*sqrt(2)*cos(d*x + c)^2 + 657*sqrt(2)*sin(d*x + c)^2 + 168*(3*sqrt(2)*cos(d*x + c)
+ sqrt(2))*cos(2*d*x + 2*c) + 150*sqrt(2)*cos(d*x + c) + 25*sqrt(2))*sin(2*d*x + 2*c)^2 + 18*(9*sqrt(2)*cos(d*
x + c)^2 + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c)^2 + 54*sqrt(2)*cos(d*x + c)^2 + 2*(4*sqrt(2)*cos(3*d
*x + 3*c)^3 + 36*sqrt(2)*cos(2*d*x + 2*c)^3 + 27*sqrt(2)*cos(d*x + c)^3 + (28*sqrt(2)*cos(2*d*x + 2*c) + 27*sq
rt(2)*cos(d*x + c) + 9*sqrt(2))*cos(3*d*x + 3*c)^2 + 33*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)^2
+ (4*sqrt(2)*cos(3*d*x + 3*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3*d*x + 3*c
)^2 + 9*(4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c)^2 + 9*(3*sqrt(2)*cos(
d*x + c) + sqrt(2))*sin(d*x + c)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 3*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos
(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 18*sq
rt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos
(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(sqrt(2)*sin
(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(4*d*x + 4*c) +
2*(30*sqrt(2)*cos(2*d*x + 2*c)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)^2 + 36*sqrt(2)*sin(
2*d*x + 2*c)*sin(d*x + c) + 18*sqrt(2)*sin(d*x + c)^2 + 19*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)
+ 18*sqrt(2)*cos(d*x + c) + 3*sqrt(2))*cos(3*d*x + 3*c) + 2*(45*sqrt(2)*cos(d*x + c)^2 + 18*sqrt(2)*sin(d*x +
c)^2 + 30*sqrt(2)*cos(d*x + c) + 5*sqrt(2))*cos(2*d*x + 2*c) + 6*(4*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + 4
*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(3*d*x + 3*c) + (4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*
cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c) + (3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(3*d*x + 3*c) +
18*(4*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + (3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(2*d*x + 2*
c) + 9*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(5*d*x + 5*c) + 6*(4*sqrt(2)*cos(3*d*x + 3*c)^3 + 36*sqrt(2)*cos(2*d
*x + 2*c)^3 + 27*sqrt(2)*cos(d*x + c)^3 + (28*sqrt(2)*cos(2*d*x + 2*c) + 27*sqrt(2)*cos(d*x + c) + 9*sqrt(2))*
cos(3*d*x + 3*c)^2 + 33*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)^2 + (4*sqrt(2)*cos(3*d*x + 3*c) +
4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3*d*x + 3*c)^2 + 9*(4*sqrt(2)*cos(2*d*x + 2
*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c)^2 + 9*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c)
^2 + 27*sqrt(2)*cos(d*x + c)^2 + 2*(30*sqrt(2)*cos(2*d*x + 2*c)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 18*sqrt(2)*sin
(2*d*x + 2*c)^2 + 36*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 18*sqrt(2)*sin(d*x + c)^2 + 19*(3*sqrt(2)*cos(d*x
+ c) + sqrt(2))*cos(2*d*x + 2*c) + 18*sqrt(2)*cos(d*x + c) + 3*sqrt(2))*cos(3*d*x + 3*c) + 2*(45*sqrt(2)*cos(
d*x + c)^2 + 18*sqrt(2)*sin(d*x + c)^2 + 30*sqrt(2)*cos(d*x + c) + 5*sqrt(2))*cos(2*d*x + 2*c) + 6*(4*sqrt(2)*
cos(2*d*x + 2*c)*sin(d*x + c) + 4*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(3*d*x + 3*c) + (4*sqrt
(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c) + (3*sqrt(2)*cos(d*x + c) + sqrt(2))
*sin(d*x + c))*sin(3*d*x + 3*c) + 18*(4*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + (3*sqrt(2)*cos(d*x + c) + sqrt
(2))*sin(d*x + c))*sin(2*d*x + 2*c) + 9*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(4*d*x + 4*c) + 2*(192*sqrt(2)*cos(
2*d*x + 2*c)^3 + 135*sqrt(2)*cos(d*x + c)^3 + 172*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)^2 + 4*(4
8*sqrt(2)*cos(2*d*x + 2*c) + 39*sqrt(2)*cos(d*x + c) + 13*sqrt(2))*sin(2*d*x + 2*c)^2 + 45*(3*sqrt(2)*cos(d*x
+ c) + sqrt(2))*sin(d*x + c)^2 + 135*sqrt(2)*cos(d*x + c)^2 + 3*(153*sqrt(2)*cos(d*x + c)^2 + 57*sqrt(2)*sin(d
*x + c)^2 + 102*sqrt(2)*cos(d*x + c) + 17*sqrt(2))*cos(2*d*x + 2*c) + 24*(15*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x
+ c) + 4*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(2*d*x + 2*c) + 45*sqrt(2)*cos(d*x + c) + 5*sqrt(
2))*cos(3*d*x + 3*c) + 14*(27*sqrt(2)*cos(d*x + c)^3 + 9*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c)^2 + 2
7*sqrt(2)*cos(d*x + c)^2 + 9*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 2*(4*sqrt(2)*sin(3*d*x + 3*c)^
3 + 36*sqrt(2)*sin(2*d*x + 2*c)^3 + 27*sqrt(2)*cos(2*d*x + 2*c)^2*sin(d*x + c) + 99*sqrt(2)*sin(2*d*x + 2*c)^2
*sin(d*x + c) + 27*sqrt(2)*sin(d*x + c)^3 + (4*sqrt(2)*sin(2*d*x + 2*c) + 3*sqrt(2)*sin(d*x + c))*cos(3*d*x +
3*c)^2 + (28*sqrt(2)*sin(2*d*x + 2*c) + 27*sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c)^2 + 18*(3*sqrt(2)*cos(d*x +
c) + sqrt(2))*cos(2*d*x + 2*c)*sin(d*x + c) + 2*(9*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(3*sqrt(2)*cos(2*
d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c) + 3*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x
+ c))*cos(3*d*x + 3*c) + 3*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c
)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9
*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) +
6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*s
in(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(4*d*x + 4*c) + 2*(2*sqrt(2)*cos(3*d*x + 3*c)^2 + 18*sq
rt(2)*cos(2*d*x + 2*c)^2 + 18*sqrt(2)*cos(d*x + c)^2 + 30*sqrt(2)*sin(2*d*x + 2*c)^2 + 57*sqrt(2)*sin(2*d*x +
2*c)*sin(d*x + c) + 27*sqrt(2)*sin(d*x + c)^2 + 4*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(
2))*cos(3*d*x + 3*c) + 12*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 12*sqrt(2)*cos(d*x + c) + 2*sq
rt(2))*sin(3*d*x + 3*c) + 2*(18*sqrt(2)*cos(2*d*x + 2*c)^2 + 18*sqrt(2)*cos(d*x + c)^2 + 45*sqrt(2)*sin(d*x +
c)^2 + 12*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 12*sqrt(2)*cos(d*x + c) + 2*sqrt(2))*sin(2*d*x
+ 2*c) + 3*(9*sqrt(2)*cos(d*x + c)^2 + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(5*d*x + 5*c) + 6*(
4*sqrt(2)*sin(3*d*x + 3*c)^3 + 36*sqrt(2)*sin(2*d*x + 2*c)^3 + 27*sqrt(2)*cos(2*d*x + 2*c)^2*sin(d*x + c) + 99
*sqrt(2)*sin(2*d*x + 2*c)^2*sin(d*x + c) + 27*sqrt(2)*sin(d*x + c)^3 + (4*sqrt(2)*sin(2*d*x + 2*c) + 3*sqrt(2)
*sin(d*x + c))*cos(3*d*x + 3*c)^2 + (28*sqrt(2)*sin(2*d*x + 2*c) + 27*sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c)^2
+ 18*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)*sin(d*x + c) + 2*(9*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x
+ c) + 4*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c) + 3*(3*sqrt(2)*cos(
d*x + c) + sqrt(2))*sin(d*x + c))*cos(3*d*x + 3*c) + 2*(2*sqrt(2)*cos(3*d*x + 3*c)^2 + 18*sqrt(2)*cos(2*d*x +
2*c)^2 + 18*sqrt(2)*cos(d*x + c)^2 + 30*sqrt(2)*sin(2*d*x + 2*c)^2 + 57*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c)
+ 27*sqrt(2)*sin(d*x + c)^2 + 4*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*
c) + 12*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 12*sqrt(2)*cos(d*x + c) + 2*sqrt(2))*sin(3*d*x +
3*c) + 2*(18*sqrt(2)*cos(2*d*x + 2*c)^2 + 18*sqrt(2)*cos(d*x + c)^2 + 45*sqrt(2)*sin(d*x + c)^2 + 12*(3*sqrt(
2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 12*sqrt(2)*cos(d*x + c) + 2*sqrt(2))*sin(2*d*x + 2*c) + 3*(9*sqr
t(2)*cos(d*x + c)^2 + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(4*d*x + 4*c) + 2*(192*sqrt(2)*sin(2*
d*x + 2*c)^3 + 156*sqrt(2)*cos(2*d*x + 2*c)^2*sin(d*x + c) + 516*sqrt(2)*sin(2*d*x + 2*c)^2*sin(d*x + c) + 135
*sqrt(2)*sin(d*x + c)^3 + 4*(16*sqrt(2)*sin(2*d*x + 2*c) + 15*sqrt(2)*sin(d*x + c))*cos(3*d*x + 3*c)^2 + 96*(3
*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)*sin(d*x + c) + 8*(21*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) +
(24*sqrt(2)*cos(2*d*x + 2*c) + 21*sqrt(2)*cos(d*x + c) + 7*sqrt(2))*sin(2*d*x + 2*c) + 6*(3*sqrt(2)*cos(d*x +
c) + sqrt(2))*sin(d*x + c))*cos(3*d*x + 3*c) + (192*sqrt(2)*cos(2*d*x + 2*c)^2 + 171*sqrt(2)*cos(d*x + c)^2 +
459*sqrt(2)*sin(d*x + c)^2 + 120*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 114*sqrt(2)*cos(d*x +
c) + 19*sqrt(2))*sin(2*d*x + 2*c) + 15*(9*sqrt(2)*cos(d*x + c)^2 + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x +
c))*sin(3*d*x + 3*c) + 6*(84*sqrt(2)*cos(2*d*x + 2*c)^2*sin(d*x + c) + 63*sqrt(2)*sin(d*x + c)^3 + 48*(3*sqrt
(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)*sin(d*x + c) + 7*(9*sqrt(2)*cos(d*x + c)^2 + 6*sqrt(2)*cos(d*x +
c) + sqrt(2))*sin(d*x + c))*sin(2*d*x + 2*c) + 12*sqrt(2)*cos(d*x + c) + sqrt(2))*log(2*cos(1/2*arctan2(sin(d*
x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*
x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(16*sqrt(2)*cos(3*d*x
+ 3*c)^4 + 144*sqrt(2)*cos(2*d*x + 2*c)^4 + 81*sqrt(2)*cos(d*x + c)^4 + 16*sqrt(2)*sin(3*d*x + 3*c)^4 + 144*s
qrt(2)*sin(2*d*x + 2*c)^4 + 504*sqrt(2)*sin(2*d*x + 2*c)^3*sin(d*x + c) + 81*sqrt(2)*sin(d*x + c)^4 + 8*(16*sq
rt(2)*cos(2*d*x + 2*c) + 15*sqrt(2)*cos(d*x + c) + 5*sqrt(2))*cos(3*d*x + 3*c)^3 + 168*(3*sqrt(2)*cos(d*x + c)
+ sqrt(2))*cos(2*d*x + 2*c)^3 + 8*(16*sqrt(2)*sin(2*d*x + 2*c) + 15*sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c)^3
+ 108*sqrt(2)*cos(d*x + c)^3 + (sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x
+ c)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c)
+ 9*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c
) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c)
)*sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(5*d*x + 5*c)^2 + 9*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*
sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c
)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*
sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(
sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(4*d*
x + 4*c)^2 + (352*sqrt(2)*cos(2*d*x + 2*c)^2 + 297*sqrt(2)*cos(d*x + c)^2 + 160*sqrt(2)*sin(2*d*x + 2*c)^2 + 3
12*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 153*sqrt(2)*sin(d*x + c)^2 + 216*(3*sqrt(2)*cos(d*x + c) + sqrt(2))
*cos(2*d*x + 2*c) + 198*sqrt(2)*cos(d*x + c) + 33*sqrt(2))*cos(3*d*x + 3*c)^2 + (657*sqrt(2)*cos(d*x + c)^2 +
225*sqrt(2)*sin(d*x + c)^2 + 438*sqrt(2)*cos(d*x + c) + 73*sqrt(2))*cos(2*d*x + 2*c)^2 + (sqrt(2)*cos(3*d*x +
3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(
2*d*x + 2*c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x
+ 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x +
2*c) + 6*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2
))*sin(5*d*x + 5*c)^2 + 9*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^
2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*s
qrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6
*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin
(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(4*d*x + 4*c)^2 + (32*sqrt(2)*cos(3*d*x + 3*c)^2 + 160*sq
rt(2)*cos(2*d*x + 2*c)^2 + 153*sqrt(2)*cos(d*x + c)^2 + 352*sqrt(2)*sin(2*d*x + 2*c)^2 + 648*sqrt(2)*sin(2*d*x
+ 2*c)*sin(d*x + c) + 297*sqrt(2)*sin(d*x + c)^2 + 8*(16*sqrt(2)*cos(2*d*x + 2*c) + 15*sqrt(2)*cos(d*x + c) +
5*sqrt(2))*cos(3*d*x + 3*c) + 104*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 102*sqrt(2)*cos(d*x +
c) + 17*sqrt(2))*sin(3*d*x + 3*c)^2 + (288*sqrt(2)*cos(2*d*x + 2*c)^2 + 225*sqrt(2)*cos(d*x + c)^2 + 657*sqrt
(2)*sin(d*x + c)^2 + 168*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 150*sqrt(2)*cos(d*x + c) + 25*s
qrt(2))*sin(2*d*x + 2*c)^2 + 18*(9*sqrt(2)*cos(d*x + c)^2 + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c)^2 +
54*sqrt(2)*cos(d*x + c)^2 + 2*(4*sqrt(2)*cos(3*d*x + 3*c)^3 + 36*sqrt(2)*cos(2*d*x + 2*c)^3 + 27*sqrt(2)*cos(
d*x + c)^3 + (28*sqrt(2)*cos(2*d*x + 2*c) + 27*sqrt(2)*cos(d*x + c) + 9*sqrt(2))*cos(3*d*x + 3*c)^2 + 33*(3*sq
rt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)^2 + (4*sqrt(2)*cos(3*d*x + 3*c) + 4*sqrt(2)*cos(2*d*x + 2*c) +
3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3*d*x + 3*c)^2 + 9*(4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c)
+ sqrt(2))*sin(2*d*x + 2*c)^2 + 9*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c)^2 + 27*sqrt(2)*cos(d*x + c)^
2 + 3*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(2)*sin(3*d*
x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*sin(d*x + c)^
2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*cos(d*x
+ c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c) + 6*sq
rt(2)*cos(d*x + c) + sqrt(2))*cos(4*d*x + 4*c) + 2*(30*sqrt(2)*cos(2*d*x + 2*c)^2 + 27*sqrt(2)*cos(d*x + c)^2
+ 18*sqrt(2)*sin(2*d*x + 2*c)^2 + 36*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 18*sqrt(2)*sin(d*x + c)^2 + 19*(3
*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 18*sqrt(2)*cos(d*x + c) + 3*sqrt(2))*cos(3*d*x + 3*c) + 2*
(45*sqrt(2)*cos(d*x + c)^2 + 18*sqrt(2)*sin(d*x + c)^2 + 30*sqrt(2)*cos(d*x + c) + 5*sqrt(2))*cos(2*d*x + 2*c)
+ 6*(4*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(3*d*x
+ 3*c) + (4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c) + (3*sqrt(2)*cos(d*x
+ c) + sqrt(2))*sin(d*x + c))*sin(3*d*x + 3*c) + 18*(4*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + (3*sqrt(2)*cos
(d*x + c) + sqrt(2))*sin(d*x + c))*sin(2*d*x + 2*c) + 9*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(5*d*x + 5*c) + 6*(
4*sqrt(2)*cos(3*d*x + 3*c)^3 + 36*sqrt(2)*cos(2*d*x + 2*c)^3 + 27*sqrt(2)*cos(d*x + c)^3 + (28*sqrt(2)*cos(2*d
*x + 2*c) + 27*sqrt(2)*cos(d*x + c) + 9*sqrt(2))*cos(3*d*x + 3*c)^2 + 33*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*co
s(2*d*x + 2*c)^2 + (4*sqrt(2)*cos(3*d*x + 3*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2)
)*sin(3*d*x + 3*c)^2 + 9*(4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c)^2 +
9*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 2*(30*sqrt(2)*cos(2*d*x + 2*
c)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)^2 + 36*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) +
18*sqrt(2)*sin(d*x + c)^2 + 19*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 18*sqrt(2)*cos(d*x + c) +
3*sqrt(2))*cos(3*d*x + 3*c) + 2*(45*sqrt(2)*cos(d*x + c)^2 + 18*sqrt(2)*sin(d*x + c)^2 + 30*sqrt(2)*cos(d*x +
c) + 5*sqrt(2))*cos(2*d*x + 2*c) + 6*(4*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(sqrt(2)*sin(2*d*x + 2*c) +
sqrt(2)*sin(d*x + c))*cos(3*d*x + 3*c) + (4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(
2*d*x + 2*c) + (3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(3*d*x + 3*c) + 18*(4*sqrt(2)*cos(2*d*x + 2
*c)*sin(d*x + c) + (3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(2*d*x + 2*c) + 9*sqrt(2)*cos(d*x + c)
+ sqrt(2))*cos(4*d*x + 4*c) + 2*(192*sqrt(2)*cos(2*d*x + 2*c)^3 + 135*sqrt(2)*cos(d*x + c)^3 + 172*(3*sqrt(2)*
cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)^2 + 4*(48*sqrt(2)*cos(2*d*x + 2*c) + 39*sqrt(2)*cos(d*x + c) + 13*sqr
t(2))*sin(2*d*x + 2*c)^2 + 45*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c)^2 + 135*sqrt(2)*cos(d*x + c)^2 +
3*(153*sqrt(2)*cos(d*x + c)^2 + 57*sqrt(2)*sin(d*x + c)^2 + 102*sqrt(2)*cos(d*x + c) + 17*sqrt(2))*cos(2*d*x
+ 2*c) + 24*(15*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin
(2*d*x + 2*c) + 45*sqrt(2)*cos(d*x + c) + 5*sqrt(2))*cos(3*d*x + 3*c) + 14*(27*sqrt(2)*cos(d*x + c)^3 + 9*(3*s
qrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 9*sqrt(2)*cos(d*x + c) + sqrt(2))*
cos(2*d*x + 2*c) + 2*(4*sqrt(2)*sin(3*d*x + 3*c)^3 + 36*sqrt(2)*sin(2*d*x + 2*c)^3 + 27*sqrt(2)*cos(2*d*x + 2*
c)^2*sin(d*x + c) + 99*sqrt(2)*sin(2*d*x + 2*c)^2*sin(d*x + c) + 27*sqrt(2)*sin(d*x + c)^3 + (4*sqrt(2)*sin(2*
d*x + 2*c) + 3*sqrt(2)*sin(d*x + c))*cos(3*d*x + 3*c)^2 + (28*sqrt(2)*sin(2*d*x + 2*c) + 27*sqrt(2)*sin(d*x +
c))*sin(3*d*x + 3*c)^2 + 18*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)*sin(d*x + c) + 2*(9*sqrt(2)*co
s(2*d*x + 2*c)*sin(d*x + c) + 4*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*
c) + 3*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*cos(3*d*x + 3*c) + 3*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*s
qrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)
^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*s
qrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(s
qrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(4*d*x
+ 4*c) + 2*(2*sqrt(2)*cos(3*d*x + 3*c)^2 + 18*sqrt(2)*cos(2*d*x + 2*c)^2 + 18*sqrt(2)*cos(d*x + c)^2 + 30*sqr
t(2)*sin(2*d*x + 2*c)^2 + 57*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 27*sqrt(2)*sin(d*x + c)^2 + 4*(3*sqrt(2)*
cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 12*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*
cos(2*d*x + 2*c) + 12*sqrt(2)*cos(d*x + c) + 2*sqrt(2))*sin(3*d*x + 3*c) + 2*(18*sqrt(2)*cos(2*d*x + 2*c)^2 +
18*sqrt(2)*cos(d*x + c)^2 + 45*sqrt(2)*sin(d*x + c)^2 + 12*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)
+ 12*sqrt(2)*cos(d*x + c) + 2*sqrt(2))*sin(2*d*x + 2*c) + 3*(9*sqrt(2)*cos(d*x + c)^2 + 6*sqrt(2)*cos(d*x + c
) + sqrt(2))*sin(d*x + c))*sin(5*d*x + 5*c) + 6*(4*sqrt(2)*sin(3*d*x + 3*c)^3 + 36*sqrt(2)*sin(2*d*x + 2*c)^3
+ 27*sqrt(2)*cos(2*d*x + 2*c)^2*sin(d*x + c) + 99*sqrt(2)*sin(2*d*x + 2*c)^2*sin(d*x + c) + 27*sqrt(2)*sin(d*x
+ c)^3 + (4*sqrt(2)*sin(2*d*x + 2*c) + 3*sqrt(2)*sin(d*x + c))*cos(3*d*x + 3*c)^2 + (28*sqrt(2)*sin(2*d*x + 2
*c) + 27*sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c)^2 + 18*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)*sin
(d*x + c) + 2*(9*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c
) + sqrt(2))*sin(2*d*x + 2*c) + 3*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*cos(3*d*x + 3*c) + 2*(2*sqr
t(2)*cos(3*d*x + 3*c)^2 + 18*sqrt(2)*cos(2*d*x + 2*c)^2 + 18*sqrt(2)*cos(d*x + c)^2 + 30*sqrt(2)*sin(2*d*x + 2
*c)^2 + 57*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 27*sqrt(2)*sin(d*x + c)^2 + 4*(3*sqrt(2)*cos(2*d*x + 2*c) +
3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 12*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) +
12*sqrt(2)*cos(d*x + c) + 2*sqrt(2))*sin(3*d*x + 3*c) + 2*(18*sqrt(2)*cos(2*d*x + 2*c)^2 + 18*sqrt(2)*cos(d*x
+ c)^2 + 45*sqrt(2)*sin(d*x + c)^2 + 12*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 12*sqrt(2)*cos(
d*x + c) + 2*sqrt(2))*sin(2*d*x + 2*c) + 3*(9*sqrt(2)*cos(d*x + c)^2 + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d
*x + c))*sin(4*d*x + 4*c) + 2*(192*sqrt(2)*sin(2*d*x + 2*c)^3 + 156*sqrt(2)*cos(2*d*x + 2*c)^2*sin(d*x + c) +
516*sqrt(2)*sin(2*d*x + 2*c)^2*sin(d*x + c) + 135*sqrt(2)*sin(d*x + c)^3 + 4*(16*sqrt(2)*sin(2*d*x + 2*c) + 15
*sqrt(2)*sin(d*x + c))*cos(3*d*x + 3*c)^2 + 96*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)*sin(d*x + c
) + 8*(21*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + (24*sqrt(2)*cos(2*d*x + 2*c) + 21*sqrt(2)*cos(d*x + c) + 7*s
qrt(2))*sin(2*d*x + 2*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*cos(3*d*x + 3*c) + (192*sqrt(2)*
cos(2*d*x + 2*c)^2 + 171*sqrt(2)*cos(d*x + c)^2 + 459*sqrt(2)*sin(d*x + c)^2 + 120*(3*sqrt(2)*cos(d*x + c) + s
qrt(2))*cos(2*d*x + 2*c) + 114*sqrt(2)*cos(d*x + c) + 19*sqrt(2))*sin(2*d*x + 2*c) + 15*(9*sqrt(2)*cos(d*x + c
)^2 + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(3*d*x + 3*c) + 6*(84*sqrt(2)*cos(2*d*x + 2*c)^2*sin(
d*x + c) + 63*sqrt(2)*sin(d*x + c)^3 + 48*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)*sin(d*x + c) + 7
*(9*sqrt(2)*cos(d*x + c)^2 + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(2*d*x + 2*c) + 12*sqrt(2)*cos
(d*x + c) + sqrt(2))*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), co
s(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x +
c), cos(d*x + c))) + 2) - 3*(16*sqrt(2)*cos(3*d*x + 3*c)^4 + 144*sqrt(2)*cos(2*d*x + 2*c)^4 + 81*sqrt(2)*cos(d
*x + c)^4 + 16*sqrt(2)*sin(3*d*x + 3*c)^4 + 144*sqrt(2)*sin(2*d*x + 2*c)^4 + 504*sqrt(2)*sin(2*d*x + 2*c)^3*si
n(d*x + c) + 81*sqrt(2)*sin(d*x + c)^4 + 8*(16*sqrt(2)*cos(2*d*x + 2*c) + 15*sqrt(2)*cos(d*x + c) + 5*sqrt(2))
*cos(3*d*x + 3*c)^3 + 168*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)^3 + 8*(16*sqrt(2)*sin(2*d*x + 2*
c) + 15*sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c)^3 + 108*sqrt(2)*cos(d*x + c)^3 + (sqrt(2)*cos(3*d*x + 3*c)^2 +
9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2
*c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) +
3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6
*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(5*
d*x + 5*c)^2 + 9*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(
2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*si
n(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(
2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x +
3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(4*d*x + 4*c)^2 + (352*sqrt(2)*cos(2*d*x + 2*c)^2 + 297*sqrt(2)*co
s(d*x + c)^2 + 160*sqrt(2)*sin(2*d*x + 2*c)^2 + 312*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 153*sqrt(2)*sin(d*
x + c)^2 + 216*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 198*sqrt(2)*cos(d*x + c) + 33*sqrt(2))*co
s(3*d*x + 3*c)^2 + (657*sqrt(2)*cos(d*x + c)^2 + 225*sqrt(2)*sin(d*x + c)^2 + 438*sqrt(2)*cos(d*x + c) + 73*sq
rt(2))*cos(2*d*x + 2*c)^2 + (sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c
)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9
*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) +
6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*s
in(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(5*d*x + 5*c)^2 + 9*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqr
t(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)^2
+ 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqr
t(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(sqr
t(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(4*d*x +
4*c)^2 + (32*sqrt(2)*cos(3*d*x + 3*c)^2 + 160*sqrt(2)*cos(2*d*x + 2*c)^2 + 153*sqrt(2)*cos(d*x + c)^2 + 352*s
qrt(2)*sin(2*d*x + 2*c)^2 + 648*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 297*sqrt(2)*sin(d*x + c)^2 + 8*(16*sqr
t(2)*cos(2*d*x + 2*c) + 15*sqrt(2)*cos(d*x + c) + 5*sqrt(2))*cos(3*d*x + 3*c) + 104*(3*sqrt(2)*cos(d*x + c) +
sqrt(2))*cos(2*d*x + 2*c) + 102*sqrt(2)*cos(d*x + c) + 17*sqrt(2))*sin(3*d*x + 3*c)^2 + (288*sqrt(2)*cos(2*d*x
+ 2*c)^2 + 225*sqrt(2)*cos(d*x + c)^2 + 657*sqrt(2)*sin(d*x + c)^2 + 168*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*c
os(2*d*x + 2*c) + 150*sqrt(2)*cos(d*x + c) + 25*sqrt(2))*sin(2*d*x + 2*c)^2 + 18*(9*sqrt(2)*cos(d*x + c)^2 + 6
*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c)^2 + 54*sqrt(2)*cos(d*x + c)^2 + 2*(4*sqrt(2)*cos(3*d*x + 3*c)^3
+ 36*sqrt(2)*cos(2*d*x + 2*c)^3 + 27*sqrt(2)*cos(d*x + c)^3 + (28*sqrt(2)*cos(2*d*x + 2*c) + 27*sqrt(2)*cos(d*
x + c) + 9*sqrt(2))*cos(3*d*x + 3*c)^2 + 33*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)^2 + (4*sqrt(2)
*cos(3*d*x + 3*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3*d*x + 3*c)^2 + 9*(4*s
qrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c)^2 + 9*(3*sqrt(2)*cos(d*x + c) + s
qrt(2))*sin(d*x + c)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 3*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c
)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*sin(2*
d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) +
sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(sqrt(2)*sin(2*d*x + 2*c
) + sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(4*d*x + 4*c) + 2*(30*sqrt(2
)*cos(2*d*x + 2*c)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)^2 + 36*sqrt(2)*sin(2*d*x + 2*c)
*sin(d*x + c) + 18*sqrt(2)*sin(d*x + c)^2 + 19*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 18*sqrt(2
)*cos(d*x + c) + 3*sqrt(2))*cos(3*d*x + 3*c) + 2*(45*sqrt(2)*cos(d*x + c)^2 + 18*sqrt(2)*sin(d*x + c)^2 + 30*s
qrt(2)*cos(d*x + c) + 5*sqrt(2))*cos(2*d*x + 2*c) + 6*(4*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(sqrt(2)*si
n(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(3*d*x + 3*c) + (4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c)
+ sqrt(2))*sin(2*d*x + 2*c) + (3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(3*d*x + 3*c) + 18*(4*sqrt(
2)*cos(2*d*x + 2*c)*sin(d*x + c) + (3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(2*d*x + 2*c) + 9*sqrt(
2)*cos(d*x + c) + sqrt(2))*cos(5*d*x + 5*c) + 6*(4*sqrt(2)*cos(3*d*x + 3*c)^3 + 36*sqrt(2)*cos(2*d*x + 2*c)^3
+ 27*sqrt(2)*cos(d*x + c)^3 + (28*sqrt(2)*cos(2*d*x + 2*c) + 27*sqrt(2)*cos(d*x + c) + 9*sqrt(2))*cos(3*d*x +
3*c)^2 + 33*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)^2 + (4*sqrt(2)*cos(3*d*x + 3*c) + 4*sqrt(2)*co
s(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3*d*x + 3*c)^2 + 9*(4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt
(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c)^2 + 9*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c)^2 + 27*sqrt
(2)*cos(d*x + c)^2 + 2*(30*sqrt(2)*cos(2*d*x + 2*c)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c
)^2 + 36*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 18*sqrt(2)*sin(d*x + c)^2 + 19*(3*sqrt(2)*cos(d*x + c) + sqrt
(2))*cos(2*d*x + 2*c) + 18*sqrt(2)*cos(d*x + c) + 3*sqrt(2))*cos(3*d*x + 3*c) + 2*(45*sqrt(2)*cos(d*x + c)^2 +
18*sqrt(2)*sin(d*x + c)^2 + 30*sqrt(2)*cos(d*x + c) + 5*sqrt(2))*cos(2*d*x + 2*c) + 6*(4*sqrt(2)*cos(2*d*x +
2*c)*sin(d*x + c) + 4*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(3*d*x + 3*c) + (4*sqrt(2)*cos(2*d*
x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c) + (3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c
))*sin(3*d*x + 3*c) + 18*(4*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + (3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x
+ c))*sin(2*d*x + 2*c) + 9*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(4*d*x + 4*c) + 2*(192*sqrt(2)*cos(2*d*x + 2*c)
^3 + 135*sqrt(2)*cos(d*x + c)^3 + 172*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)^2 + 4*(48*sqrt(2)*co
s(2*d*x + 2*c) + 39*sqrt(2)*cos(d*x + c) + 13*sqrt(2))*sin(2*d*x + 2*c)^2 + 45*(3*sqrt(2)*cos(d*x + c) + sqrt(
2))*sin(d*x + c)^2 + 135*sqrt(2)*cos(d*x + c)^2 + 3*(153*sqrt(2)*cos(d*x + c)^2 + 57*sqrt(2)*sin(d*x + c)^2 +
102*sqrt(2)*cos(d*x + c) + 17*sqrt(2))*cos(2*d*x + 2*c) + 24*(15*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(3*
sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(2*d*x + 2*c) + 45*sqrt(2)*cos(d*x + c) + 5*sqrt(2))*cos(3*d*
x + 3*c) + 14*(27*sqrt(2)*cos(d*x + c)^3 + 9*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c)^2 + 27*sqrt(2)*co
s(d*x + c)^2 + 9*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 2*(4*sqrt(2)*sin(3*d*x + 3*c)^3 + 36*sqrt(
2)*sin(2*d*x + 2*c)^3 + 27*sqrt(2)*cos(2*d*x + 2*c)^2*sin(d*x + c) + 99*sqrt(2)*sin(2*d*x + 2*c)^2*sin(d*x + c
) + 27*sqrt(2)*sin(d*x + c)^3 + (4*sqrt(2)*sin(2*d*x + 2*c) + 3*sqrt(2)*sin(d*x + c))*cos(3*d*x + 3*c)^2 + (28
*sqrt(2)*sin(2*d*x + 2*c) + 27*sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c)^2 + 18*(3*sqrt(2)*cos(d*x + c) + sqrt(2)
)*cos(2*d*x + 2*c)*sin(d*x + c) + 2*(9*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(3*sqrt(2)*cos(2*d*x + 2*c) +
3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c) + 3*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*cos(3
*d*x + 3*c) + 3*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(2
)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*sin
(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(2
)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x + 3
*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(4*d*x + 4*c) + 2*(2*sqrt(2)*cos(3*d*x + 3*c)^2 + 18*sqrt(2)*cos(2*
d*x + 2*c)^2 + 18*sqrt(2)*cos(d*x + c)^2 + 30*sqrt(2)*sin(2*d*x + 2*c)^2 + 57*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x
+ c) + 27*sqrt(2)*sin(d*x + c)^2 + 4*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*
x + 3*c) + 12*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 12*sqrt(2)*cos(d*x + c) + 2*sqrt(2))*sin(3
*d*x + 3*c) + 2*(18*sqrt(2)*cos(2*d*x + 2*c)^2 + 18*sqrt(2)*cos(d*x + c)^2 + 45*sqrt(2)*sin(d*x + c)^2 + 12*(3
*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 12*sqrt(2)*cos(d*x + c) + 2*sqrt(2))*sin(2*d*x + 2*c) + 3*
(9*sqrt(2)*cos(d*x + c)^2 + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(5*d*x + 5*c) + 6*(4*sqrt(2)*si
n(3*d*x + 3*c)^3 + 36*sqrt(2)*sin(2*d*x + 2*c)^3 + 27*sqrt(2)*cos(2*d*x + 2*c)^2*sin(d*x + c) + 99*sqrt(2)*sin
(2*d*x + 2*c)^2*sin(d*x + c) + 27*sqrt(2)*sin(d*x + c)^3 + (4*sqrt(2)*sin(2*d*x + 2*c) + 3*sqrt(2)*sin(d*x + c
))*cos(3*d*x + 3*c)^2 + (28*sqrt(2)*sin(2*d*x + 2*c) + 27*sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c)^2 + 18*(3*sqr
t(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)*sin(d*x + c) + 2*(9*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(3
*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c) + 3*(3*sqrt(2)*cos(d*x + c) + s
qrt(2))*sin(d*x + c))*cos(3*d*x + 3*c) + 2*(2*sqrt(2)*cos(3*d*x + 3*c)^2 + 18*sqrt(2)*cos(2*d*x + 2*c)^2 + 18*
sqrt(2)*cos(d*x + c)^2 + 30*sqrt(2)*sin(2*d*x + 2*c)^2 + 57*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 27*sqrt(2)
*sin(d*x + c)^2 + 4*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 12*(3*s
qrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 12*sqrt(2)*cos(d*x + c) + 2*sqrt(2))*sin(3*d*x + 3*c) + 2*(1
8*sqrt(2)*cos(2*d*x + 2*c)^2 + 18*sqrt(2)*cos(d*x + c)^2 + 45*sqrt(2)*sin(d*x + c)^2 + 12*(3*sqrt(2)*cos(d*x +
c) + sqrt(2))*cos(2*d*x + 2*c) + 12*sqrt(2)*cos(d*x + c) + 2*sqrt(2))*sin(2*d*x + 2*c) + 3*(9*sqrt(2)*cos(d*x
+ c)^2 + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(4*d*x + 4*c) + 2*(192*sqrt(2)*sin(2*d*x + 2*c)^3
+ 156*sqrt(2)*cos(2*d*x + 2*c)^2*sin(d*x + c) + 516*sqrt(2)*sin(2*d*x + 2*c)^2*sin(d*x + c) + 135*sqrt(2)*sin
(d*x + c)^3 + 4*(16*sqrt(2)*sin(2*d*x + 2*c) + 15*sqrt(2)*sin(d*x + c))*cos(3*d*x + 3*c)^2 + 96*(3*sqrt(2)*cos
(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)*sin(d*x + c) + 8*(21*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + (24*sqrt(2)
*cos(2*d*x + 2*c) + 21*sqrt(2)*cos(d*x + c) + 7*sqrt(2))*sin(2*d*x + 2*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2
))*sin(d*x + c))*cos(3*d*x + 3*c) + (192*sqrt(2)*cos(2*d*x + 2*c)^2 + 171*sqrt(2)*cos(d*x + c)^2 + 459*sqrt(2)
*sin(d*x + c)^2 + 120*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 114*sqrt(2)*cos(d*x + c) + 19*sqrt
(2))*sin(2*d*x + 2*c) + 15*(9*sqrt(2)*cos(d*x + c)^2 + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(3*d
*x + 3*c) + 6*(84*sqrt(2)*cos(2*d*x + 2*c)^2*sin(d*x + c) + 63*sqrt(2)*sin(d*x + c)^3 + 48*(3*sqrt(2)*cos(d*x
+ c) + sqrt(2))*cos(2*d*x + 2*c)*sin(d*x + c) + 7*(9*sqrt(2)*cos(d*x + c)^2 + 6*sqrt(2)*cos(d*x + c) + sqrt(2)
)*sin(d*x + c))*sin(2*d*x + 2*c) + 12*sqrt(2)*cos(d*x + c) + sqrt(2))*log(2*cos(1/2*arctan2(sin(d*x + c), cos(
d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(
d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(16*sqrt(2)*cos(3*d*x + 3*c)^4 +
144*sqrt(2)*cos(2*d*x + 2*c)^4 + 81*sqrt(2)*cos(d*x + c)^4 + 16*sqrt(2)*sin(3*d*x + 3*c)^4 + 144*sqrt(2)*sin(2
*d*x + 2*c)^4 + 504*sqrt(2)*sin(2*d*x + 2*c)^3*sin(d*x + c) + 81*sqrt(2)*sin(d*x + c)^4 + 8*(16*sqrt(2)*cos(2*
d*x + 2*c) + 15*sqrt(2)*cos(d*x + c) + 5*sqrt(2))*cos(3*d*x + 3*c)^3 + 168*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*
cos(2*d*x + 2*c)^3 + 8*(16*sqrt(2)*sin(2*d*x + 2*c) + 15*sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c)^3 + 108*sqrt(2
)*cos(d*x + c)^3 + (sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqr
t(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*
sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqr
t(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x
+ 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(5*d*x + 5*c)^2 + 9*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(
2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 18*sqr
t(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(
d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(sqrt(2)*sin(
2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(4*d*x + 4*c)^2 +
(352*sqrt(2)*cos(2*d*x + 2*c)^2 + 297*sqrt(2)*cos(d*x + c)^2 + 160*sqrt(2)*sin(2*d*x + 2*c)^2 + 312*sqrt(2)*s
in(2*d*x + 2*c)*sin(d*x + c) + 153*sqrt(2)*sin(d*x + c)^2 + 216*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x +
2*c) + 198*sqrt(2)*cos(d*x + c) + 33*sqrt(2))*cos(3*d*x + 3*c)^2 + (657*sqrt(2)*cos(d*x + c)^2 + 225*sqrt(2)*
sin(d*x + c)^2 + 438*sqrt(2)*cos(d*x + c) + 73*sqrt(2))*cos(2*d*x + 2*c)^2 + (sqrt(2)*cos(3*d*x + 3*c)^2 + 9*s
qrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)
^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*s
qrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(s
qrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(5*d*x
+ 5*c)^2 + 9*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(2)*
sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*sin(d
*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*
cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c
) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(4*d*x + 4*c)^2 + (32*sqrt(2)*cos(3*d*x + 3*c)^2 + 160*sqrt(2)*cos(2*
d*x + 2*c)^2 + 153*sqrt(2)*cos(d*x + c)^2 + 352*sqrt(2)*sin(2*d*x + 2*c)^2 + 648*sqrt(2)*sin(2*d*x + 2*c)*sin(
d*x + c) + 297*sqrt(2)*sin(d*x + c)^2 + 8*(16*sqrt(2)*cos(2*d*x + 2*c) + 15*sqrt(2)*cos(d*x + c) + 5*sqrt(2))*
cos(3*d*x + 3*c) + 104*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 102*sqrt(2)*cos(d*x + c) + 17*sqr
t(2))*sin(3*d*x + 3*c)^2 + (288*sqrt(2)*cos(2*d*x + 2*c)^2 + 225*sqrt(2)*cos(d*x + c)^2 + 657*sqrt(2)*sin(d*x
+ c)^2 + 168*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 150*sqrt(2)*cos(d*x + c) + 25*sqrt(2))*sin(
2*d*x + 2*c)^2 + 18*(9*sqrt(2)*cos(d*x + c)^2 + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c)^2 + 54*sqrt(2)*
cos(d*x + c)^2 + 2*(4*sqrt(2)*cos(3*d*x + 3*c)^3 + 36*sqrt(2)*cos(2*d*x + 2*c)^3 + 27*sqrt(2)*cos(d*x + c)^3 +
(28*sqrt(2)*cos(2*d*x + 2*c) + 27*sqrt(2)*cos(d*x + c) + 9*sqrt(2))*cos(3*d*x + 3*c)^2 + 33*(3*sqrt(2)*cos(d*
x + c) + sqrt(2))*cos(2*d*x + 2*c)^2 + (4*sqrt(2)*cos(3*d*x + 3*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*co
s(d*x + c) + sqrt(2))*sin(3*d*x + 3*c)^2 + 9*(4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*s
in(2*d*x + 2*c)^2 + 9*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 3*(sqrt(
2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 +
9*sqrt(2)*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqr
t(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(
2))*cos(2*d*x + 2*c) + 6*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*
x + c) + sqrt(2))*cos(4*d*x + 4*c) + 2*(30*sqrt(2)*cos(2*d*x + 2*c)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 18*sqrt(2)
*sin(2*d*x + 2*c)^2 + 36*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 18*sqrt(2)*sin(d*x + c)^2 + 19*(3*sqrt(2)*cos
(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 18*sqrt(2)*cos(d*x + c) + 3*sqrt(2))*cos(3*d*x + 3*c) + 2*(45*sqrt(2)*
cos(d*x + c)^2 + 18*sqrt(2)*sin(d*x + c)^2 + 30*sqrt(2)*cos(d*x + c) + 5*sqrt(2))*cos(2*d*x + 2*c) + 6*(4*sqrt
(2)*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(3*d*x + 3*c) + (4*
sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c) + (3*sqrt(2)*cos(d*x + c) + sqrt
(2))*sin(d*x + c))*sin(3*d*x + 3*c) + 18*(4*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + (3*sqrt(2)*cos(d*x + c) +
sqrt(2))*sin(d*x + c))*sin(2*d*x + 2*c) + 9*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(5*d*x + 5*c) + 6*(4*sqrt(2)*co
s(3*d*x + 3*c)^3 + 36*sqrt(2)*cos(2*d*x + 2*c)^3 + 27*sqrt(2)*cos(d*x + c)^3 + (28*sqrt(2)*cos(2*d*x + 2*c) +
27*sqrt(2)*cos(d*x + c) + 9*sqrt(2))*cos(3*d*x + 3*c)^2 + 33*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*
c)^2 + (4*sqrt(2)*cos(3*d*x + 3*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3*d*x
+ 3*c)^2 + 9*(4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c)^2 + 9*(3*sqrt(2)
*cos(d*x + c) + sqrt(2))*sin(d*x + c)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 2*(30*sqrt(2)*cos(2*d*x + 2*c)^2 + 27*sq
rt(2)*cos(d*x + c)^2 + 18*sqrt(2)*sin(2*d*x + 2*c)^2 + 36*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 18*sqrt(2)*s
in(d*x + c)^2 + 19*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 18*sqrt(2)*cos(d*x + c) + 3*sqrt(2))*
cos(3*d*x + 3*c) + 2*(45*sqrt(2)*cos(d*x + c)^2 + 18*sqrt(2)*sin(d*x + c)^2 + 30*sqrt(2)*cos(d*x + c) + 5*sqrt
(2))*cos(2*d*x + 2*c) + 6*(4*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin
(d*x + c))*cos(3*d*x + 3*c) + (4*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c)
+ (3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(3*d*x + 3*c) + 18*(4*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x
+ c) + (3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(2*d*x + 2*c) + 9*sqrt(2)*cos(d*x + c) + sqrt(2))*c
os(4*d*x + 4*c) + 2*(192*sqrt(2)*cos(2*d*x + 2*c)^3 + 135*sqrt(2)*cos(d*x + c)^3 + 172*(3*sqrt(2)*cos(d*x + c)
+ sqrt(2))*cos(2*d*x + 2*c)^2 + 4*(48*sqrt(2)*cos(2*d*x + 2*c) + 39*sqrt(2)*cos(d*x + c) + 13*sqrt(2))*sin(2*
d*x + 2*c)^2 + 45*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c)^2 + 135*sqrt(2)*cos(d*x + c)^2 + 3*(153*sqrt
(2)*cos(d*x + c)^2 + 57*sqrt(2)*sin(d*x + c)^2 + 102*sqrt(2)*cos(d*x + c) + 17*sqrt(2))*cos(2*d*x + 2*c) + 24*
(15*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(2*d*x + 2*c
) + 45*sqrt(2)*cos(d*x + c) + 5*sqrt(2))*cos(3*d*x + 3*c) + 14*(27*sqrt(2)*cos(d*x + c)^3 + 9*(3*sqrt(2)*cos(d
*x + c) + sqrt(2))*sin(d*x + c)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 9*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x +
2*c) + 2*(4*sqrt(2)*sin(3*d*x + 3*c)^3 + 36*sqrt(2)*sin(2*d*x + 2*c)^3 + 27*sqrt(2)*cos(2*d*x + 2*c)^2*sin(d*x
+ c) + 99*sqrt(2)*sin(2*d*x + 2*c)^2*sin(d*x + c) + 27*sqrt(2)*sin(d*x + c)^3 + (4*sqrt(2)*sin(2*d*x + 2*c) +
3*sqrt(2)*sin(d*x + c))*cos(3*d*x + 3*c)^2 + (28*sqrt(2)*sin(2*d*x + 2*c) + 27*sqrt(2)*sin(d*x + c))*sin(3*d*
x + 3*c)^2 + 18*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)*sin(d*x + c) + 2*(9*sqrt(2)*cos(2*d*x + 2*
c)*sin(d*x + c) + 4*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(2*d*x + 2*c) + 3*(3*sq
rt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*cos(3*d*x + 3*c) + 3*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(2
*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + c)^2 + sqrt(2)*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 18*sqrt
(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*sin(d*x + c)^2 + 2*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d
*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*(sqrt(2)*sin(2
*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(4*d*x + 4*c) + 2*
(2*sqrt(2)*cos(3*d*x + 3*c)^2 + 18*sqrt(2)*cos(2*d*x + 2*c)^2 + 18*sqrt(2)*cos(d*x + c)^2 + 30*sqrt(2)*sin(2*d
*x + 2*c)^2 + 57*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 27*sqrt(2)*sin(d*x + c)^2 + 4*(3*sqrt(2)*cos(2*d*x +
2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 12*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x +
2*c) + 12*sqrt(2)*cos(d*x + c) + 2*sqrt(2))*sin(3*d*x + 3*c) + 2*(18*sqrt(2)*cos(2*d*x + 2*c)^2 + 18*sqrt(2)*c
os(d*x + c)^2 + 45*sqrt(2)*sin(d*x + c)^2 + 12*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 12*sqrt(2
)*cos(d*x + c) + 2*sqrt(2))*sin(2*d*x + 2*c) + 3*(9*sqrt(2)*cos(d*x + c)^2 + 6*sqrt(2)*cos(d*x + c) + sqrt(2))
*sin(d*x + c))*sin(5*d*x + 5*c) + 6*(4*sqrt(2)*sin(3*d*x + 3*c)^3 + 36*sqrt(2)*sin(2*d*x + 2*c)^3 + 27*sqrt(2)
*cos(2*d*x + 2*c)^2*sin(d*x + c) + 99*sqrt(2)*sin(2*d*x + 2*c)^2*sin(d*x + c) + 27*sqrt(2)*sin(d*x + c)^3 + (4
*sqrt(2)*sin(2*d*x + 2*c) + 3*sqrt(2)*sin(d*x + c))*cos(3*d*x + 3*c)^2 + (28*sqrt(2)*sin(2*d*x + 2*c) + 27*sqr
t(2)*sin(d*x + c))*sin(3*d*x + 3*c)^2 + 18*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)*sin(d*x + c) +
2*(9*sqrt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))
*sin(2*d*x + 2*c) + 3*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*cos(3*d*x + 3*c) + 2*(2*sqrt(2)*cos(3*d
*x + 3*c)^2 + 18*sqrt(2)*cos(2*d*x + 2*c)^2 + 18*sqrt(2)*cos(d*x + c)^2 + 30*sqrt(2)*sin(2*d*x + 2*c)^2 + 57*s
qrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 27*sqrt(2)*sin(d*x + c)^2 + 4*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*c
os(d*x + c) + sqrt(2))*cos(3*d*x + 3*c) + 12*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 12*sqrt(2)*
cos(d*x + c) + 2*sqrt(2))*sin(3*d*x + 3*c) + 2*(18*sqrt(2)*cos(2*d*x + 2*c)^2 + 18*sqrt(2)*cos(d*x + c)^2 + 45
*sqrt(2)*sin(d*x + c)^2 + 12*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 12*sqrt(2)*cos(d*x + c) + 2
*sqrt(2))*sin(2*d*x + 2*c) + 3*(9*sqrt(2)*cos(d*x + c)^2 + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin
(4*d*x + 4*c) + 2*(192*sqrt(2)*sin(2*d*x + 2*c)^3 + 156*sqrt(2)*cos(2*d*x + 2*c)^2*sin(d*x + c) + 516*sqrt(2)*
sin(2*d*x + 2*c)^2*sin(d*x + c) + 135*sqrt(2)*sin(d*x + c)^3 + 4*(16*sqrt(2)*sin(2*d*x + 2*c) + 15*sqrt(2)*sin
(d*x + c))*cos(3*d*x + 3*c)^2 + 96*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)*sin(d*x + c) + 8*(21*sq
rt(2)*cos(2*d*x + 2*c)*sin(d*x + c) + (24*sqrt(2)*cos(2*d*x + 2*c) + 21*sqrt(2)*cos(d*x + c) + 7*sqrt(2))*sin(
2*d*x + 2*c) + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*cos(3*d*x + 3*c) + (192*sqrt(2)*cos(2*d*x +
2*c)^2 + 171*sqrt(2)*cos(d*x + c)^2 + 459*sqrt(2)*sin(d*x + c)^2 + 120*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(
2*d*x + 2*c) + 114*sqrt(2)*cos(d*x + c) + 19*sqrt(2))*sin(2*d*x + 2*c) + 15*(9*sqrt(2)*cos(d*x + c)^2 + 6*sqrt
(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(3*d*x + 3*c) + 6*(84*sqrt(2)*cos(2*d*x + 2*c)^2*sin(d*x + c) + 6
3*sqrt(2)*sin(d*x + c)^3 + 48*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c)*sin(d*x + c) + 7*(9*sqrt(2)*
cos(d*x + c)^2 + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(d*x + c))*sin(2*d*x + 2*c) + 12*sqrt(2)*cos(d*x + c) +
sqrt(2))*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))
^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x
+ c))) + 2) + 9*(8*(16*cos(2*d*x + 2*c) + 15*cos(d*x + c) + 5)*cos(3*d*x + 3*c)^3 + 16*cos(3*d*x + 3*c)^4 + 16
8*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)^3 + 144*cos(2*d*x + 2*c)^4 + 81*cos(d*x + c)^4 + 8*(16*sin(2*d*x + 2*c
) + 15*sin(d*x + c))*sin(3*d*x + 3*c)^3 + 16*sin(3*d*x + 3*c)^4 + 144*sin(2*d*x + 2*c)^4 + 504*sin(2*d*x + 2*c
)^3*sin(d*x + c) + 81*sin(d*x + c)^4 + (2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d
*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x
+ 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin
(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(5*d*x + 5*c)^2 + 9*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x +
c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^
2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x
+ 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(4*d*x + 4*c)^2 + (21
6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 352*cos(2*d*x + 2*c)^2 + 297*cos(d*x + c)^2 + 160*sin(2*d*x + 2*c)^2
+ 312*sin(2*d*x + 2*c)*sin(d*x + c) + 153*sin(d*x + c)^2 + 198*cos(d*x + c) + 33)*cos(3*d*x + 3*c)^2 + (657*c
os(d*x + c)^2 + 225*sin(d*x + c)^2 + 438*cos(d*x + c) + 73)*cos(2*d*x + 2*c)^2 + 108*cos(d*x + c)^3 + (2*(3*co
s(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x
+ 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(
3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) +
1)*sin(5*d*x + 5*c)^2 + 9*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2
+ 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + si
n(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) +
9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(4*d*x + 4*c)^2 + (8*(16*cos(2*d*x + 2*c) + 15*cos(d*x + c) + 5)*cos
(3*d*x + 3*c) + 32*cos(3*d*x + 3*c)^2 + 104*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 160*cos(2*d*x + 2*c)^2 + 1
53*cos(d*x + c)^2 + 352*sin(2*d*x + 2*c)^2 + 648*sin(2*d*x + 2*c)*sin(d*x + c) + 297*sin(d*x + c)^2 + 102*cos(
d*x + c) + 17)*sin(3*d*x + 3*c)^2 + (168*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 288*cos(2*d*x + 2*c)^2 + 225*
cos(d*x + c)^2 + 657*sin(d*x + c)^2 + 150*cos(d*x + c) + 25)*sin(2*d*x + 2*c)^2 + 18*(9*cos(d*x + c)^2 + 6*cos
(d*x + c) + 1)*sin(d*x + c)^2 + 2*((28*cos(2*d*x + 2*c) + 27*cos(d*x + c) + 9)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*
x + 3*c)^3 + 33*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)^2 + 36*cos(2*d*x + 2*c)^3 + 27*cos(d*x + c)^3 + (4*cos(3
*d*x + 3*c) + 4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(3*d*x + 3*c)^2 + 9*(4*cos(2*d*x + 2*c) + 3*cos(d*x
+ c) + 1)*sin(2*d*x + 2*c)^2 + 9*(3*cos(d*x + c) + 1)*sin(d*x + c)^2 + 3*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x +
c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2
+ 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x
+ 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(4*d*x + 4*c) + 2*(19*
(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 30*cos(2*d*x + 2*c)^2 + 27*cos(d*x + c)^2 + 18*sin(2*d*x + 2*c)^2 + 36
*sin(2*d*x + 2*c)*sin(d*x + c) + 18*sin(d*x + c)^2 + 18*cos(d*x + c) + 3)*cos(3*d*x + 3*c) + 2*(45*cos(d*x + c
)^2 + 18*sin(d*x + c)^2 + 30*cos(d*x + c) + 5)*cos(2*d*x + 2*c) + 27*cos(d*x + c)^2 + 6*(4*(sin(2*d*x + 2*c) +
sin(d*x + c))*cos(3*d*x + 3*c) + (4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + (3*cos(d*x + c)
+ 1)*sin(d*x + c) + 4*cos(2*d*x + 2*c)*sin(d*x + c))*sin(3*d*x + 3*c) + 18*((3*cos(d*x + c) + 1)*sin(d*x + c)
+ 4*cos(2*d*x + 2*c)*sin(d*x + c))*sin(2*d*x + 2*c) + 9*cos(d*x + c) + 1)*cos(5*d*x + 5*c) + 6*((28*cos(2*d*x
+ 2*c) + 27*cos(d*x + c) + 9)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)^3 + 33*(3*cos(d*x + c) + 1)*cos(2*d*x +
2*c)^2 + 36*cos(2*d*x + 2*c)^3 + 27*cos(d*x + c)^3 + (4*cos(3*d*x + 3*c) + 4*cos(2*d*x + 2*c) + 3*cos(d*x + c
) + 1)*sin(3*d*x + 3*c)^2 + 9*(4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c)^2 + 9*(3*cos(d*x + c)
+ 1)*sin(d*x + c)^2 + 2*(19*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 30*cos(2*d*x + 2*c)^2 + 27*cos(d*x + c)^2
+ 18*sin(2*d*x + 2*c)^2 + 36*sin(2*d*x + 2*c)*sin(d*x + c) + 18*sin(d*x + c)^2 + 18*cos(d*x + c) + 3)*cos(3*d
*x + 3*c) + 2*(45*cos(d*x + c)^2 + 18*sin(d*x + c)^2 + 30*cos(d*x + c) + 5)*cos(2*d*x + 2*c) + 27*cos(d*x + c)
^2 + 6*(4*(sin(2*d*x + 2*c) + sin(d*x + c))*cos(3*d*x + 3*c) + (4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2
*d*x + 2*c) + (3*cos(d*x + c) + 1)*sin(d*x + c) + 4*cos(2*d*x + 2*c)*sin(d*x + c))*sin(3*d*x + 3*c) + 18*((3*c
os(d*x + c) + 1)*sin(d*x + c) + 4*cos(2*d*x + 2*c)*sin(d*x + c))*sin(2*d*x + 2*c) + 9*cos(d*x + c) + 1)*cos(4*
d*x + 4*c) + 2*(172*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)^2 + 192*cos(2*d*x + 2*c)^3 + 135*cos(d*x + c)^3 + 4*
(48*cos(2*d*x + 2*c) + 39*cos(d*x + c) + 13)*sin(2*d*x + 2*c)^2 + 45*(3*cos(d*x + c) + 1)*sin(d*x + c)^2 + 3*(
153*cos(d*x + c)^2 + 57*sin(d*x + c)^2 + 102*cos(d*x + c) + 17)*cos(2*d*x + 2*c) + 135*cos(d*x + c)^2 + 24*(4*
(3*cos(d*x + c) + 1)*sin(d*x + c) + 15*cos(2*d*x + 2*c)*sin(d*x + c))*sin(2*d*x + 2*c) + 45*cos(d*x + c) + 5)*
cos(3*d*x + 3*c) + 14*(27*cos(d*x + c)^3 + 9*(3*cos(d*x + c) + 1)*sin(d*x + c)^2 + 27*cos(d*x + c)^2 + 9*cos(d
*x + c) + 1)*cos(2*d*x + 2*c) + 54*cos(d*x + c)^2 + 2*((4*sin(2*d*x + 2*c) + 3*sin(d*x + c))*cos(3*d*x + 3*c)^
2 + (28*sin(2*d*x + 2*c) + 27*sin(d*x + c))*sin(3*d*x + 3*c)^2 + 4*sin(3*d*x + 3*c)^3 + 36*sin(2*d*x + 2*c)^3
+ 18*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)*sin(d*x + c) + 27*cos(2*d*x + 2*c)^2*sin(d*x + c) + 99*sin(2*d*x +
2*c)^2*sin(d*x + c) + 27*sin(d*x + c)^3 + 2*(4*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + 3*
(3*cos(d*x + c) + 1)*sin(d*x + c) + 9*cos(2*d*x + 2*c)*sin(d*x + c))*cos(3*d*x + 3*c) + 3*(2*(3*cos(2*d*x + 2*
c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*c
os(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)
^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(4*d*
x + 4*c) + 2*(4*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + 2*cos(3*d*x + 3*c)^2 + 12*(3*cos(
d*x + c) + 1)*cos(2*d*x + 2*c) + 18*cos(2*d*x + 2*c)^2 + 18*cos(d*x + c)^2 + 30*sin(2*d*x + 2*c)^2 + 57*sin(2*
d*x + 2*c)*sin(d*x + c) + 27*sin(d*x + c)^2 + 12*cos(d*x + c) + 2)*sin(3*d*x + 3*c) + 2*(12*(3*cos(d*x + c) +
1)*cos(2*d*x + 2*c) + 18*cos(2*d*x + 2*c)^2 + 18*cos(d*x + c)^2 + 45*sin(d*x + c)^2 + 12*cos(d*x + c) + 2)*sin
(2*d*x + 2*c) + 3*(9*cos(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(d*x + c))*sin(5*d*x + 5*c) + 6*((4*sin(2*d*x + 2
*c) + 3*sin(d*x + c))*cos(3*d*x + 3*c)^2 + (28*sin(2*d*x + 2*c) + 27*sin(d*x + c))*sin(3*d*x + 3*c)^2 + 4*sin(
3*d*x + 3*c)^3 + 36*sin(2*d*x + 2*c)^3 + 18*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)*sin(d*x + c) + 27*cos(2*d*x
+ 2*c)^2*sin(d*x + c) + 99*sin(2*d*x + 2*c)^2*sin(d*x + c) + 27*sin(d*x + c)^3 + 2*(4*(3*cos(2*d*x + 2*c) + 3*
cos(d*x + c) + 1)*sin(2*d*x + 2*c) + 3*(3*cos(d*x + c) + 1)*sin(d*x + c) + 9*cos(2*d*x + 2*c)*sin(d*x + c))*co
s(3*d*x + 3*c) + 2*(4*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + 2*cos(3*d*x + 3*c)^2 + 12*(
3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 18*cos(2*d*x + 2*c)^2 + 18*cos(d*x + c)^2 + 30*sin(2*d*x + 2*c)^2 + 57*
sin(2*d*x + 2*c)*sin(d*x + c) + 27*sin(d*x + c)^2 + 12*cos(d*x + c) + 2)*sin(3*d*x + 3*c) + 2*(12*(3*cos(d*x +
c) + 1)*cos(2*d*x + 2*c) + 18*cos(2*d*x + 2*c)^2 + 18*cos(d*x + c)^2 + 45*sin(d*x + c)^2 + 12*cos(d*x + c) +
2)*sin(2*d*x + 2*c) + 3*(9*cos(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(d*x + c))*sin(4*d*x + 4*c) + 2*(4*(16*sin(
2*d*x + 2*c) + 15*sin(d*x + c))*cos(3*d*x + 3*c)^2 + 192*sin(2*d*x + 2*c)^3 + 96*(3*cos(d*x + c) + 1)*cos(2*d*
x + 2*c)*sin(d*x + c) + 156*cos(2*d*x + 2*c)^2*sin(d*x + c) + 516*sin(2*d*x + 2*c)^2*sin(d*x + c) + 135*sin(d*
x + c)^3 + 8*((24*cos(2*d*x + 2*c) + 21*cos(d*x + c) + 7)*sin(2*d*x + 2*c) + 6*(3*cos(d*x + c) + 1)*sin(d*x +
c) + 21*cos(2*d*x + 2*c)*sin(d*x + c))*cos(3*d*x + 3*c) + (120*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 192*cos
(2*d*x + 2*c)^2 + 171*cos(d*x + c)^2 + 459*sin(d*x + c)^2 + 114*cos(d*x + c) + 19)*sin(2*d*x + 2*c) + 15*(9*co
s(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(d*x + c))*sin(3*d*x + 3*c) + 6*(48*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c
)*sin(d*x + c) + 84*cos(2*d*x + 2*c)^2*sin(d*x + c) + 63*sin(d*x + c)^3 + 7*(9*cos(d*x + c)^2 + 6*cos(d*x + c)
+ 1)*sin(d*x + c))*sin(2*d*x + 2*c) + 12*cos(d*x + c) + 1)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2
+ sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - 9*(8
*(16*cos(2*d*x + 2*c) + 15*cos(d*x + c) + 5)*cos(3*d*x + 3*c)^3 + 16*cos(3*d*x + 3*c)^4 + 168*(3*cos(d*x + c)
+ 1)*cos(2*d*x + 2*c)^3 + 144*cos(2*d*x + 2*c)^4 + 81*cos(d*x + c)^4 + 8*(16*sin(2*d*x + 2*c) + 15*sin(d*x + c
))*sin(3*d*x + 3*c)^3 + 16*sin(3*d*x + 3*c)^4 + 144*sin(2*d*x + 2*c)^4 + 504*sin(2*d*x + 2*c)^3*sin(d*x + c) +
81*sin(d*x + c)^4 + (2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3
*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x
+ c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(
d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(5*d*x + 5*c)^2 + 9*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x
+ 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)
^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin
(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(4*d*x + 4*c)^2 + (216*(3*cos(d*x + c)
+ 1)*cos(2*d*x + 2*c) + 352*cos(2*d*x + 2*c)^2 + 297*cos(d*x + c)^2 + 160*sin(2*d*x + 2*c)^2 + 312*sin(2*d*x +
2*c)*sin(d*x + c) + 153*sin(d*x + c)^2 + 198*cos(d*x + c) + 33)*cos(3*d*x + 3*c)^2 + (657*cos(d*x + c)^2 + 22
5*sin(d*x + c)^2 + 438*cos(d*x + c) + 73)*cos(2*d*x + 2*c)^2 + 108*cos(d*x + c)^3 + (2*(3*cos(2*d*x + 2*c) + 3
*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d
*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9
*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(5*d*x + 5*
c)^2 + 9*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c
) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*
d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 +
6*cos(d*x + c) + 1)*sin(4*d*x + 4*c)^2 + (8*(16*cos(2*d*x + 2*c) + 15*cos(d*x + c) + 5)*cos(3*d*x + 3*c) + 32
*cos(3*d*x + 3*c)^2 + 104*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 160*cos(2*d*x + 2*c)^2 + 153*cos(d*x + c)^2
+ 352*sin(2*d*x + 2*c)^2 + 648*sin(2*d*x + 2*c)*sin(d*x + c) + 297*sin(d*x + c)^2 + 102*cos(d*x + c) + 17)*sin
(3*d*x + 3*c)^2 + (168*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 288*cos(2*d*x + 2*c)^2 + 225*cos(d*x + c)^2 + 6
57*sin(d*x + c)^2 + 150*cos(d*x + c) + 25)*sin(2*d*x + 2*c)^2 + 18*(9*cos(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin
(d*x + c)^2 + 2*((28*cos(2*d*x + 2*c) + 27*cos(d*x + c) + 9)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)^3 + 33*(3
*cos(d*x + c) + 1)*cos(2*d*x + 2*c)^2 + 36*cos(2*d*x + 2*c)^3 + 27*cos(d*x + c)^3 + (4*cos(3*d*x + 3*c) + 4*co
s(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(3*d*x + 3*c)^2 + 9*(4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*
x + 2*c)^2 + 9*(3*cos(d*x + c) + 1)*sin(d*x + c)^2 + 3*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x
+ 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^
2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x + 2*c)^2 + 18*sin(
2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(4*d*x + 4*c) + 2*(19*(3*cos(d*x + c) +
1)*cos(2*d*x + 2*c) + 30*cos(2*d*x + 2*c)^2 + 27*cos(d*x + c)^2 + 18*sin(2*d*x + 2*c)^2 + 36*sin(2*d*x + 2*c)*
sin(d*x + c) + 18*sin(d*x + c)^2 + 18*cos(d*x + c) + 3)*cos(3*d*x + 3*c) + 2*(45*cos(d*x + c)^2 + 18*sin(d*x +
c)^2 + 30*cos(d*x + c) + 5)*cos(2*d*x + 2*c) + 27*cos(d*x + c)^2 + 6*(4*(sin(2*d*x + 2*c) + sin(d*x + c))*cos
(3*d*x + 3*c) + (4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + (3*cos(d*x + c) + 1)*sin(d*x + c)
+ 4*cos(2*d*x + 2*c)*sin(d*x + c))*sin(3*d*x + 3*c) + 18*((3*cos(d*x + c) + 1)*sin(d*x + c) + 4*cos(2*d*x + 2
*c)*sin(d*x + c))*sin(2*d*x + 2*c) + 9*cos(d*x + c) + 1)*cos(5*d*x + 5*c) + 6*((28*cos(2*d*x + 2*c) + 27*cos(d
*x + c) + 9)*cos(3*d*x + 3*c)^2 + 4*cos(3*d*x + 3*c)^3 + 33*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)^2 + 36*cos(2
*d*x + 2*c)^3 + 27*cos(d*x + c)^3 + (4*cos(3*d*x + 3*c) + 4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(3*d*x +
3*c)^2 + 9*(4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c)^2 + 9*(3*cos(d*x + c) + 1)*sin(d*x + c)
^2 + 2*(19*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 30*cos(2*d*x + 2*c)^2 + 27*cos(d*x + c)^2 + 18*sin(2*d*x +
2*c)^2 + 36*sin(2*d*x + 2*c)*sin(d*x + c) + 18*sin(d*x + c)^2 + 18*cos(d*x + c) + 3)*cos(3*d*x + 3*c) + 2*(45*
cos(d*x + c)^2 + 18*sin(d*x + c)^2 + 30*cos(d*x + c) + 5)*cos(2*d*x + 2*c) + 27*cos(d*x + c)^2 + 6*(4*(sin(2*d
*x + 2*c) + sin(d*x + c))*cos(3*d*x + 3*c) + (4*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + (3*c
os(d*x + c) + 1)*sin(d*x + c) + 4*cos(2*d*x + 2*c)*sin(d*x + c))*sin(3*d*x + 3*c) + 18*((3*cos(d*x + c) + 1)*s
in(d*x + c) + 4*cos(2*d*x + 2*c)*sin(d*x + c))*sin(2*d*x + 2*c) + 9*cos(d*x + c) + 1)*cos(4*d*x + 4*c) + 2*(17
2*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)^2 + 192*cos(2*d*x + 2*c)^3 + 135*cos(d*x + c)^3 + 4*(48*cos(2*d*x + 2*
c) + 39*cos(d*x + c) + 13)*sin(2*d*x + 2*c)^2 + 45*(3*cos(d*x + c) + 1)*sin(d*x + c)^2 + 3*(153*cos(d*x + c)^2
+ 57*sin(d*x + c)^2 + 102*cos(d*x + c) + 17)*cos(2*d*x + 2*c) + 135*cos(d*x + c)^2 + 24*(4*(3*cos(d*x + c) +
1)*sin(d*x + c) + 15*cos(2*d*x + 2*c)*sin(d*x + c))*sin(2*d*x + 2*c) + 45*cos(d*x + c) + 5)*cos(3*d*x + 3*c) +
14*(27*cos(d*x + c)^3 + 9*(3*cos(d*x + c) + 1)*sin(d*x + c)^2 + 27*cos(d*x + c)^2 + 9*cos(d*x + c) + 1)*cos(2
*d*x + 2*c) + 54*cos(d*x + c)^2 + 2*((4*sin(2*d*x + 2*c) + 3*sin(d*x + c))*cos(3*d*x + 3*c)^2 + (28*sin(2*d*x
+ 2*c) + 27*sin(d*x + c))*sin(3*d*x + 3*c)^2 + 4*sin(3*d*x + 3*c)^3 + 36*sin(2*d*x + 2*c)^3 + 18*(3*cos(d*x +
c) + 1)*cos(2*d*x + 2*c)*sin(d*x + c) + 27*cos(2*d*x + 2*c)^2*sin(d*x + c) + 99*sin(2*d*x + 2*c)^2*sin(d*x + c
) + 27*sin(d*x + c)^3 + 2*(4*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + 3*(3*cos(d*x + c) +
1)*sin(d*x + c) + 9*cos(2*d*x + 2*c)*sin(d*x + c))*cos(3*d*x + 3*c) + 3*(2*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c
) + 1)*cos(3*d*x + 3*c) + cos(3*d*x + 3*c)^2 + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 9*cos(2*d*x + 2*c)^2
+ 9*cos(d*x + c)^2 + 6*(sin(2*d*x + 2*c) + sin(d*x + c))*sin(3*d*x + 3*c) + sin(3*d*x + 3*c)^2 + 9*sin(2*d*x +
2*c)^2 + 18*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(4*d*x + 4*c) + 2*(4*(3
*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + 2*cos(3*d*x + 3*c)^2 + 12*(3*cos(d*x + c) + 1)*cos(
2*d*x + 2*c) + 18*cos(2*d*x + 2*c)^2 + 18*cos(d*x + c)^2 + 30*sin(2*d*x + 2*c)^2 + 57*sin(2*d*x + 2*c)*sin(d*x
+ c) + 27*sin(d*x + c)^2 + 12*cos(d*x + c) + 2)*sin(3*d*x + 3*c) + 2*(12*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c
) + 18*cos(2*d*x + 2*c)^2 + 18*cos(d*x + c)^2 + 45*sin(d*x + c)^2 + 12*cos(d*x + c) + 2)*sin(2*d*x + 2*c) + 3*
(9*cos(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(d*x + c))*sin(5*d*x + 5*c) + 6*((4*sin(2*d*x + 2*c) + 3*sin(d*x +
c))*cos(3*d*x + 3*c)^2 + (28*sin(2*d*x + 2*c) + 27*sin(d*x + c))*sin(3*d*x + 3*c)^2 + 4*sin(3*d*x + 3*c)^3 + 3
6*sin(2*d*x + 2*c)^3 + 18*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)*sin(d*x + c) + 27*cos(2*d*x + 2*c)^2*sin(d*x +
c) + 99*sin(2*d*x + 2*c)^2*sin(d*x + c) + 27*sin(d*x + c)^3 + 2*(4*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*
sin(2*d*x + 2*c) + 3*(3*cos(d*x + c) + 1)*sin(d*x + c) + 9*cos(2*d*x + 2*c)*sin(d*x + c))*cos(3*d*x + 3*c) + 2
*(4*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(3*d*x + 3*c) + 2*cos(3*d*x + 3*c)^2 + 12*(3*cos(d*x + c) + 1
)*cos(2*d*x + 2*c) + 18*cos(2*d*x + 2*c)^2 + 18*cos(d*x + c)^2 + 30*sin(2*d*x + 2*c)^2 + 57*sin(2*d*x + 2*c)*s
in(d*x + c) + 27*sin(d*x + c)^2 + 12*cos(d*x + c) + 2)*sin(3*d*x + 3*c) + 2*(12*(3*cos(d*x + c) + 1)*cos(2*d*x
+ 2*c) + 18*cos(2*d*x + 2*c)^2 + 18*cos(d*x + c)^2 + 45*sin(d*x + c)^2 + 12*cos(d*x + c) + 2)*sin(2*d*x + 2*c
) + 3*(9*cos(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(d*x + c))*sin(4*d*x + 4*c) + 2*(4*(16*sin(2*d*x + 2*c) + 15*
sin(d*x + c))*cos(3*d*x + 3*c)^2 + 192*sin(2*d*x + 2*c)^3 + 96*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)*sin(d*x +
c) + 156*cos(2*d*x + 2*c)^2*sin(d*x + c) + 516*sin(2*d*x + 2*c)^2*sin(d*x + c) + 135*sin(d*x + c)^3 + 8*((24*
cos(2*d*x + 2*c) + 21*cos(d*x + c) + 7)*sin(2*d*x + 2*c) + 6*(3*cos(d*x + c) + 1)*sin(d*x + c) + 21*cos(2*d*x
+ 2*c)*sin(d*x + c))*cos(3*d*x + 3*c) + (120*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 192*cos(2*d*x + 2*c)^2 +
171*cos(d*x + c)^2 + 459*sin(d*x + c)^2 + 114*cos(d*x + c) + 19)*sin(2*d*x + 2*c) + 15*(9*cos(d*x + c)^2 + 6*c
os(d*x + c) + 1)*sin(d*x + c))*sin(3*d*x + 3*c) + 6*(48*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)*sin(d*x + c) + 8
4*cos(2*d*x + 2*c)^2*sin(d*x + c) + 63*sin(d*x + c)^3 + 7*(9*cos(d*x + c)^2 + 6*cos(d*x + c) + 1)*sin(d*x + c)
)*sin(2*d*x + 2*c) + 12*cos(d*x + c) + 1)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2
(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) + 32*(cos(3*d*x + 3*c)^2
*cos(3/2*d*x + 3/2*c) + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)*cos(3/2*d*x + 3/2*c) + 9*cos(2*d*x + 2*c)^2*co
s(3/2*d*x + 3/2*c) + cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c)^2 + 9*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c)^2 + 18*
cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c)*sin(d*x + c) + 2*((3*cos(d*x + c) + 1)*cos(3/2*d*x + 3/2*c) + 3*cos(2*d*
x + 2*c)*cos(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c) + (9*cos(d*x + c)^2 + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*c
os(3/2*d*x + 3/2*c) + 6*(cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) + cos(3/2*d*x + 3/2*c)*sin(d*x + c))*sin(3*d*x
+ 3*c))*sin(5*d*x + 5*c) + 96*(cos(3*d*x + 3*c)^2*cos(3/2*d*x + 3/2*c) + 6*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*
c)*cos(3/2*d*x + 3/2*c) + 9*cos(2*d*x + 2*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
+ 9*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c)^2 + 18*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c)*sin(d*x + c) + 2*((3*co
s(d*x + c) + 1)*cos(3/2*d*x + 3/2*c) + 3*cos(2*d*x + 2*c)*cos(3/2*d*x + 3/2*c))*cos(3*d*x + 3*c) + (9*cos(d*x
+ c)^2 + 9*sin(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(3/2*d*x + 3/2*c) + 6*(cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c
) + cos(3/2*d*x + 3/2*c)*sin(d*x + c))*sin(3*d*x + 3*c))*sin(4*d*x + 4*c) + 64*(2*cos(3*d*x + 3*c)^2*cos(3/2*d
*x + 3/2*c) + 18*cos(2*d*x + 2*c)^2*cos(3/2*d*x + 3/2*c) + 30*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c)^2 - 3*(3*c
os(d*x + c) + 1)*sin(3/2*d*x + 3/2*c)*sin(d*x + c) + 4*((3*cos(d*x + c) + 1)*cos(3/2*d*x + 3/2*c) + 3*cos(2*d*
x + 2*c)*cos(3/2*d*x + 3/2*c) - 3*sin(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - 3*sin(3/2*d*x + 3/2*c)*sin(d*x + c))
*cos(3*d*x + 3*c) + 12*((3*cos(d*x + c) + 1)*cos(3/2*d*x + 3/2*c) - sin(3/2*d*x + 3/2*c)*sin(d*x + c))*cos(2*d
*x + 2*c) + (18*cos(d*x + c)^2 + 27*sin(d*x + c)^2 + 12*cos(d*x + c) + 2)*cos(3/2*d*x + 3/2*c) - 3*((3*cos(d*x
+ c) + 1)*sin(3/2*d*x + 3/2*c) + 4*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - 19*cos(3/2*d*x + 3/2*c)*sin(d*x +
c))*sin(2*d*x + 2*c))*sin(3*d*x + 3*c) + 64*(18*cos(2*d*x + 2*c)^2*cos(3/2*d*x + 3/2*c) - 9*(3*cos(d*x + c) +
1)*sin(3/2*d*x + 3/2*c)*sin(d*x + c) + 12*((3*cos(d*x + c) + 1)*cos(3/2*d*x + 3/2*c) - 3*sin(3/2*d*x + 3/2*c)*
sin(d*x + c))*cos(2*d*x + 2*c) + (18*cos(d*x + c)^2 + 45*sin(d*x + c)^2 + 12*cos(d*x + c) + 2)*cos(3/2*d*x + 3
/2*c))*sin(2*d*x + 2*c) - 32*(27*cos(d*x + c)^3 + 9*(3*cos(d*x + c) + 1)*sin(d*x + c)^2 + 27*cos(d*x + c)^2 +
9*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) + 12*((cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*co
s(5*d*x + 5*c)^2 + 9*(cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(4*d*x + 4*c)^2 + 8*(10*c
os(2*d*x + 2*c) + 9*cos(d*x + c) + 3)*cos(3*d*x + 3*c)^2 + 16*cos(3*d*x + 3*c)^3 + 40*(3*cos(d*x + c) + 1)*cos
(2*d*x + 2*c)^2 + 48*cos(2*d*x + 2*c)^3 + 27*cos(d*x + c)^3 + (cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d
*x + c) + 1)*sin(5*d*x + 5*c)^2 + 9*(cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(4*d*x + 4
*c)^2 + 16*(cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(3*d*x + 3*c)^2 + 16*(3*cos(2*d*x +
2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c)^2 + 9*(3*cos(d*x + c) + 1)*sin(d*x + c)^2 + 2*(3*(cos(3*d*x + 3*c
) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(4*d*x + 4*c) + (16*cos(2*d*x + 2*c) + 15*cos(d*x + c) + 5)*co
s(3*d*x + 3*c) + 4*cos(3*d*x + 3*c)^2 + 7*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 12*cos(2*d*x + 2*c)^2 + 9*co
s(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(5*d*x + 5*c) + 6*((16*cos(2*d*x + 2*c) + 15*cos(d*x + c) + 5)*cos(3*d*x
+ 3*c) + 4*cos(3*d*x + 3*c)^2 + 7*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 12*cos(2*d*x + 2*c)^2 + 9*cos(d*x +
c)^2 + 6*cos(d*x + c) + 1)*cos(4*d*x + 4*c) + (64*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 112*cos(2*d*x + 2*c
)^2 + 81*cos(d*x + c)^2 + 16*sin(2*d*x + 2*c)^2 + 24*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 54*cos
(d*x + c) + 9)*cos(3*d*x + 3*c) + (99*cos(d*x + c)^2 + 27*sin(d*x + c)^2 + 66*cos(d*x + c) + 11)*cos(2*d*x + 2
*c) + 27*cos(d*x + c)^2 + 2*((4*sin(2*d*x + 2*c) + 3*sin(d*x + c))*cos(3*d*x + 3*c) + 3*(cos(3*d*x + 3*c) + 3*
cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(4*d*x + 4*c) + 4*(cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x
+ c) + 1)*sin(3*d*x + 3*c) + 4*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + 3*(3*cos(d*x + c)
+ 1)*sin(d*x + c) + 9*cos(2*d*x + 2*c)*sin(d*x + c))*sin(5*d*x + 5*c) + 6*((4*sin(2*d*x + 2*c) + 3*sin(d*x +
c))*cos(3*d*x + 3*c) + 4*(cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(3*d*x + 3*c) + 4*(3*
cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + 3*(3*cos(d*x + c) + 1)*sin(d*x + c) + 9*cos(2*d*x +
2*c)*sin(d*x + c))*sin(4*d*x + 4*c) + 8*((4*sin(2*d*x + 2*c) + 3*sin(d*x + c))*cos(3*d*x + 3*c) + 4*(3*cos(2*d
*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + 3*(3*cos(d*x + c) + 1)*sin(d*x + c) + 9*cos(2*d*x + 2*c)*si
n(d*x + c))*sin(3*d*x + 3*c) + 24*((3*cos(d*x + c) + 1)*sin(d*x + c) + 3*cos(2*d*x + 2*c)*sin(d*x + c))*sin(2*
d*x + 2*c) + 9*cos(d*x + c) + 1)*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 16*((cos(3*d*x + 3*c) + 3*cos(
2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(5*d*x + 5*c)^2 + 9*(cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x +
c) + 1)*cos(4*d*x + 4*c)^2 + 8*(10*cos(2*d*x + 2*c) + 9*cos(d*x + c) + 3)*cos(3*d*x + 3*c)^2 + 16*cos(3*d*x +
3*c)^3 + 40*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)^2 + 48*cos(2*d*x + 2*c)^3 + 27*cos(d*x + c)^3 + (cos(3*d*x
+ 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(5*d*x + 5*c)^2 + 9*(cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c
) + 3*cos(d*x + c) + 1)*sin(4*d*x + 4*c)^2 + 16*(cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*s
in(3*d*x + 3*c)^2 + 16*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c)^2 + 9*(3*cos(d*x + c) + 1)*s
in(d*x + c)^2 + 2*(3*(cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(4*d*x + 4*c) + (16*cos(2
*d*x + 2*c) + 15*cos(d*x + c) + 5)*cos(3*d*x + 3*c) + 4*cos(3*d*x + 3*c)^2 + 7*(3*cos(d*x + c) + 1)*cos(2*d*x
+ 2*c) + 12*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(5*d*x + 5*c) + 6*((16*cos(2*d*x +
2*c) + 15*cos(d*x + c) + 5)*cos(3*d*x + 3*c) + 4*cos(3*d*x + 3*c)^2 + 7*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)
+ 12*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(4*d*x + 4*c) + (64*(3*cos(d*x + c) + 1)*c
os(2*d*x + 2*c) + 112*cos(2*d*x + 2*c)^2 + 81*cos(d*x + c)^2 + 16*sin(2*d*x + 2*c)^2 + 24*sin(2*d*x + 2*c)*sin
(d*x + c) + 9*sin(d*x + c)^2 + 54*cos(d*x + c) + 9)*cos(3*d*x + 3*c) + (99*cos(d*x + c)^2 + 27*sin(d*x + c)^2
+ 66*cos(d*x + c) + 11)*cos(2*d*x + 2*c) + 27*cos(d*x + c)^2 + 2*((4*sin(2*d*x + 2*c) + 3*sin(d*x + c))*cos(3*
d*x + 3*c) + 3*(cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(4*d*x + 4*c) + 4*(cos(3*d*x +
3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(3*d*x + 3*c) + 4*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)
*sin(2*d*x + 2*c) + 3*(3*cos(d*x + c) + 1)*sin(d*x + c) + 9*cos(2*d*x + 2*c)*sin(d*x + c))*sin(5*d*x + 5*c) +
6*((4*sin(2*d*x + 2*c) + 3*sin(d*x + c))*cos(3*d*x + 3*c) + 4*(cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d
*x + c) + 1)*sin(3*d*x + 3*c) + 4*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + 3*(3*cos(d*x +
c) + 1)*sin(d*x + c) + 9*cos(2*d*x + 2*c)*sin(d*x + c))*sin(4*d*x + 4*c) + 8*((4*sin(2*d*x + 2*c) + 3*sin(d*x
+ c))*cos(3*d*x + 3*c) + 4*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + 3*(3*cos(d*x + c) + 1)
*sin(d*x + c) + 9*cos(2*d*x + 2*c)*sin(d*x + c))*sin(3*d*x + 3*c) + 24*((3*cos(d*x + c) + 1)*sin(d*x + c) + 3*
cos(2*d*x + 2*c)*sin(d*x + c))*sin(2*d*x + 2*c) + 9*cos(d*x + c) + 1)*sin(3/2*arctan2(sin(d*x + c), cos(d*x +
c))) - 12*((cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(5*d*x + 5*c)^2 + 9*(cos(3*d*x + 3*
c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*cos(4*d*x + 4*c)^2 + 8*(10*cos(2*d*x + 2*c) + 9*cos(d*x + c) + 3
)*cos(3*d*x + 3*c)^2 + 16*cos(3*d*x + 3*c)^3 + 40*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c)^2 + 48*cos(2*d*x + 2*c
)^3 + 27*cos(d*x + c)^3 + (cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(5*d*x + 5*c)^2 + 9*
(cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(4*d*x + 4*c)^2 + 16*(cos(3*d*x + 3*c) + 3*cos
(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(3*d*x + 3*c)^2 + 16*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*
x + 2*c)^2 + 9*(3*cos(d*x + c) + 1)*sin(d*x + c)^2 + 2*(3*(cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x +
c) + 1)*cos(4*d*x + 4*c) + (16*cos(2*d*x + 2*c) + 15*cos(d*x + c) + 5)*cos(3*d*x + 3*c) + 4*cos(3*d*x + 3*c)^
2 + 7*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 12*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*cos(d*x + c) + 1)*c
os(5*d*x + 5*c) + 6*((16*cos(2*d*x + 2*c) + 15*cos(d*x + c) + 5)*cos(3*d*x + 3*c) + 4*cos(3*d*x + 3*c)^2 + 7*(
3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 12*cos(2*d*x + 2*c)^2 + 9*cos(d*x + c)^2 + 6*cos(d*x + c) + 1)*cos(4*d*
x + 4*c) + (64*(3*cos(d*x + c) + 1)*cos(2*d*x + 2*c) + 112*cos(2*d*x + 2*c)^2 + 81*cos(d*x + c)^2 + 16*sin(2*d
*x + 2*c)^2 + 24*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sin(d*x + c)^2 + 54*cos(d*x + c) + 9)*cos(3*d*x + 3*c) + (9
9*cos(d*x + c)^2 + 27*sin(d*x + c)^2 + 66*cos(d*x + c) + 11)*cos(2*d*x + 2*c) + 27*cos(d*x + c)^2 + 2*((4*sin(
2*d*x + 2*c) + 3*sin(d*x + c))*cos(3*d*x + 3*c) + 3*(cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) +
1)*sin(4*d*x + 4*c) + 4*(cos(3*d*x + 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(3*d*x + 3*c) + 4*(3*c
os(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(2*d*x + 2*c) + 3*(3*cos(d*x + c) + 1)*sin(d*x + c) + 9*cos(2*d*x + 2
*c)*sin(d*x + c))*sin(5*d*x + 5*c) + 6*((4*sin(2*d*x + 2*c) + 3*sin(d*x + c))*cos(3*d*x + 3*c) + 4*(cos(3*d*x
+ 3*c) + 3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(3*d*x + 3*c) + 4*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) +
1)*sin(2*d*x + 2*c) + 3*(3*cos(d*x + c) + 1)*sin(d*x + c) + 9*cos(2*d*x + 2*c)*sin(d*x + c))*sin(4*d*x + 4*c)
+ 8*((4*sin(2*d*x + 2*c) + 3*sin(d*x + c))*cos(3*d*x + 3*c) + 4*(3*cos(2*d*x + 2*c) + 3*cos(d*x + c) + 1)*sin(
2*d*x + 2*c) + 3*(3*cos(d*x + c) + 1)*sin(d*x + c) + 9*cos(2*d*x + 2*c)*sin(d*x + c))*sin(3*d*x + 3*c) + 24*((
3*cos(d*x + c) + 1)*sin(d*x + c) + 3*cos(2*d*x + 2*c)*sin(d*x + c))*sin(2*d*x + 2*c) + 9*cos(d*x + c) + 1)*sin
(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C/((16*sqrt(2)*a*cos(3*d*x + 3*c)^4 + 144*sqrt(2)*a*cos(2*d*x + 2*c
)^4 + 81*sqrt(2)*a*cos(d*x + c)^4 + 16*sqrt(2)*a*sin(3*d*x + 3*c)^4 + 144*sqrt(2)*a*sin(2*d*x + 2*c)^4 + 504*s
qrt(2)*a*sin(2*d*x + 2*c)^3*sin(d*x + c) + 81*sqrt(2)*a*sin(d*x + c)^4 + 108*sqrt(2)*a*cos(d*x + c)^3 + 8*(16*
sqrt(2)*a*cos(2*d*x + 2*c) + 15*sqrt(2)*a*cos(d*x + c) + 5*sqrt(2)*a)*cos(3*d*x + 3*c)^3 + 168*(3*sqrt(2)*a*co
s(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c)^3 + 8*(16*sqrt(2)*a*sin(2*d*x + 2*c) + 15*sqrt(2)*a*sin(d*x + c))*sin
(3*d*x + 3*c)^3 + 54*sqrt(2)*a*cos(d*x + c)^2 + (sqrt(2)*a*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*a*cos(2*d*x + 2*c)^2
+ 9*sqrt(2)*a*cos(d*x + c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*a*s
in(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*a*sin(d*x + c)^2 + 6*sqrt(2)*a*cos(d*x + c) + 2*(3*sqrt(2)*a*cos(2*d*
x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*c
os(2*d*x + 2*c) + 6*(sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x + c))*sin(3*d*x + 3*c) + sqrt(2)*a)*cos(5*
d*x + 5*c)^2 + 9*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*a*cos(d*x + c)^2 +
sqrt(2)*a*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) +
9*sqrt(2)*a*sin(d*x + c)^2 + 6*sqrt(2)*a*cos(d*x + c) + 2*(3*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x
+ c) + sqrt(2)*a)*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 6*(sqrt(2)*a*
sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x + c))*sin(3*d*x + 3*c) + sqrt(2)*a)*cos(4*d*x + 4*c)^2 + (352*sqrt(2)*a*c
os(2*d*x + 2*c)^2 + 297*sqrt(2)*a*cos(d*x + c)^2 + 160*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 312*sqrt(2)*a*sin(2*d*x
+ 2*c)*sin(d*x + c) + 153*sqrt(2)*a*sin(d*x + c)^2 + 198*sqrt(2)*a*cos(d*x + c) + 216*(3*sqrt(2)*a*cos(d*x + c
) + sqrt(2)*a)*cos(2*d*x + 2*c) + 33*sqrt(2)*a)*cos(3*d*x + 3*c)^2 + (657*sqrt(2)*a*cos(d*x + c)^2 + 225*sqrt(
2)*a*sin(d*x + c)^2 + 438*sqrt(2)*a*cos(d*x + c) + 73*sqrt(2)*a)*cos(2*d*x + 2*c)^2 + (sqrt(2)*a*cos(3*d*x + 3
*c)^2 + 9*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*a*cos(d*x + c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2 + 9*sqrt(2)
*a*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*a*sin(d*x + c)^2 + 6*sqrt(2)*a*
cos(d*x + c) + 2*(3*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(3*d*x + 3*c) + 6*(3
*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 6*(sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x + c)
)*sin(3*d*x + 3*c) + sqrt(2)*a)*sin(5*d*x + 5*c)^2 + 9*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*a*cos(2*d*x +
2*c)^2 + 9*sqrt(2)*a*cos(d*x + c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 18*sqrt
(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*a*sin(d*x + c)^2 + 6*sqrt(2)*a*cos(d*x + c) + 2*(3*sqrt(2)*a*c
os(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*a*cos(d*x + c) + sqrt(
2)*a)*cos(2*d*x + 2*c) + 6*(sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x + c))*sin(3*d*x + 3*c) + sqrt(2)*a)
*sin(4*d*x + 4*c)^2 + (32*sqrt(2)*a*cos(3*d*x + 3*c)^2 + 160*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 153*sqrt(2)*a*cos(
d*x + c)^2 + 352*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 648*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 297*sqrt(2)*a*si
n(d*x + c)^2 + 102*sqrt(2)*a*cos(d*x + c) + 8*(16*sqrt(2)*a*cos(2*d*x + 2*c) + 15*sqrt(2)*a*cos(d*x + c) + 5*s
qrt(2)*a)*cos(3*d*x + 3*c) + 104*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 17*sqrt(2)*a)*sin(3
*d*x + 3*c)^2 + (288*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 225*sqrt(2)*a*cos(d*x + c)^2 + 657*sqrt(2)*a*sin(d*x + c)^
2 + 150*sqrt(2)*a*cos(d*x + c) + 168*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 25*sqrt(2)*a)*s
in(2*d*x + 2*c)^2 + 18*(9*sqrt(2)*a*cos(d*x + c)^2 + 6*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(d*x + c)^2 + 12
*sqrt(2)*a*cos(d*x + c) + 2*(4*sqrt(2)*a*cos(3*d*x + 3*c)^3 + 36*sqrt(2)*a*cos(2*d*x + 2*c)^3 + 27*sqrt(2)*a*c
os(d*x + c)^3 + 27*sqrt(2)*a*cos(d*x + c)^2 + (28*sqrt(2)*a*cos(2*d*x + 2*c) + 27*sqrt(2)*a*cos(d*x + c) + 9*s
qrt(2)*a)*cos(3*d*x + 3*c)^2 + 33*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c)^2 + (4*sqrt(2)*a*cos
(3*d*x + 3*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(3*d*x + 3*c)^2 + 9*(4
*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(2*d*x + 2*c)^2 + 9*(3*sqrt(2)*a*cos(d*
x + c) + sqrt(2)*a)*sin(d*x + c)^2 + 9*sqrt(2)*a*cos(d*x + c) + 3*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*a*
cos(2*d*x + 2*c)^2 + 9*sqrt(2)*a*cos(d*x + c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*a*sin(2*d*x + 2*c)^
2 + 18*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 9*sqrt(2)*a*sin(d*x + c)^2 + 6*sqrt(2)*a*cos(d*x + c) + 2*(3*
sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*a*cos(d*x +
c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 6*(sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x + c))*sin(3*d*x + 3*c) +
sqrt(2)*a)*cos(4*d*x + 4*c) + 2*(30*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 27*sqrt(2)*a*cos(d*x + c)^2 + 18*sqrt(2)*a
*sin(2*d*x + 2*c)^2 + 36*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 18*sqrt(2)*a*sin(d*x + c)^2 + 18*sqrt(2)*a*
cos(d*x + c) + 19*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 3*sqrt(2)*a)*cos(3*d*x + 3*c) + 2*
(45*sqrt(2)*a*cos(d*x + c)^2 + 18*sqrt(2)*a*sin(d*x + c)^2 + 30*sqrt(2)*a*cos(d*x + c) + 5*sqrt(2)*a)*cos(2*d*
x + 2*c) + 6*(4*sqrt(2)*a*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x +
c))*cos(3*d*x + 3*c) + (4*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(2*d*x + 2*c)
+ (3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(d*x + c))*sin(3*d*x + 3*c) + 18*(4*sqrt(2)*a*cos(2*d*x + 2*c)*sin
(d*x + c) + (3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(d*x + c))*sin(2*d*x + 2*c) + sqrt(2)*a)*cos(5*d*x + 5*c
) + 6*(4*sqrt(2)*a*cos(3*d*x + 3*c)^3 + 36*sqrt(2)*a*cos(2*d*x + 2*c)^3 + 27*sqrt(2)*a*cos(d*x + c)^3 + 27*sqr
t(2)*a*cos(d*x + c)^2 + (28*sqrt(2)*a*cos(2*d*x + 2*c) + 27*sqrt(2)*a*cos(d*x + c) + 9*sqrt(2)*a)*cos(3*d*x +
3*c)^2 + 33*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c)^2 + (4*sqrt(2)*a*cos(3*d*x + 3*c) + 4*sqrt
(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(3*d*x + 3*c)^2 + 9*(4*sqrt(2)*a*cos(2*d*x +
2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(2*d*x + 2*c)^2 + 9*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*si
n(d*x + c)^2 + 9*sqrt(2)*a*cos(d*x + c) + 2*(30*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 27*sqrt(2)*a*cos(d*x + c)^2 + 1
8*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 36*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 18*sqrt(2)*a*sin(d*x + c)^2 + 18
*sqrt(2)*a*cos(d*x + c) + 19*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 3*sqrt(2)*a)*cos(3*d*x
+ 3*c) + 2*(45*sqrt(2)*a*cos(d*x + c)^2 + 18*sqrt(2)*a*sin(d*x + c)^2 + 30*sqrt(2)*a*cos(d*x + c) + 5*sqrt(2)*
a)*cos(2*d*x + 2*c) + 6*(4*sqrt(2)*a*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a
*sin(d*x + c))*cos(3*d*x + 3*c) + (4*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(2*
d*x + 2*c) + (3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(d*x + c))*sin(3*d*x + 3*c) + 18*(4*sqrt(2)*a*cos(2*d*x
+ 2*c)*sin(d*x + c) + (3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(d*x + c))*sin(2*d*x + 2*c) + sqrt(2)*a)*cos(
4*d*x + 4*c) + 2*(192*sqrt(2)*a*cos(2*d*x + 2*c)^3 + 135*sqrt(2)*a*cos(d*x + c)^3 + 135*sqrt(2)*a*cos(d*x + c)
^2 + 172*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c)^2 + 4*(48*sqrt(2)*a*cos(2*d*x + 2*c) + 39*sqr
t(2)*a*cos(d*x + c) + 13*sqrt(2)*a)*sin(2*d*x + 2*c)^2 + 45*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(d*x + c
)^2 + 45*sqrt(2)*a*cos(d*x + c) + 3*(153*sqrt(2)*a*cos(d*x + c)^2 + 57*sqrt(2)*a*sin(d*x + c)^2 + 102*sqrt(2)*
a*cos(d*x + c) + 17*sqrt(2)*a)*cos(2*d*x + 2*c) + 24*(15*sqrt(2)*a*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(3*sqrt(2
)*a*cos(d*x + c) + sqrt(2)*a)*sin(d*x + c))*sin(2*d*x + 2*c) + 5*sqrt(2)*a)*cos(3*d*x + 3*c) + 14*(27*sqrt(2)*
a*cos(d*x + c)^3 + 27*sqrt(2)*a*cos(d*x + c)^2 + 9*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(d*x + c)^2 + 9*s
qrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 2*(4*sqrt(2)*a*sin(3*d*x + 3*c)^3 + 36*sqrt(2)*a*sin(2*d
*x + 2*c)^3 + 27*sqrt(2)*a*cos(2*d*x + 2*c)^2*sin(d*x + c) + 99*sqrt(2)*a*sin(2*d*x + 2*c)^2*sin(d*x + c) + 27
*sqrt(2)*a*sin(d*x + c)^3 + (4*sqrt(2)*a*sin(2*d*x + 2*c) + 3*sqrt(2)*a*sin(d*x + c))*cos(3*d*x + 3*c)^2 + (28
*sqrt(2)*a*sin(2*d*x + 2*c) + 27*sqrt(2)*a*sin(d*x + c))*sin(3*d*x + 3*c)^2 + 18*(3*sqrt(2)*a*cos(d*x + c) + s
qrt(2)*a)*cos(2*d*x + 2*c)*sin(d*x + c) + 2*(9*sqrt(2)*a*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(3*sqrt(2)*a*cos(2*
d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(2*d*x + 2*c) + 3*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)
*sin(d*x + c))*cos(3*d*x + 3*c) + 3*(sqrt(2)*a*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 9*sqrt(2)
*a*cos(d*x + c)^2 + sqrt(2)*a*sin(3*d*x + 3*c)^2 + 9*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 18*sqrt(2)*a*sin(2*d*x + 2
*c)*sin(d*x + c) + 9*sqrt(2)*a*sin(d*x + c)^2 + 6*sqrt(2)*a*cos(d*x + c) + 2*(3*sqrt(2)*a*cos(2*d*x + 2*c) + 3
*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(3*d*x + 3*c) + 6*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2
*c) + 6*(sqrt(2)*a*sin(2*d*x + 2*c) + sqrt(2)*a*sin(d*x + c))*sin(3*d*x + 3*c) + sqrt(2)*a)*sin(4*d*x + 4*c) +
2*(2*sqrt(2)*a*cos(3*d*x + 3*c)^2 + 18*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 18*sqrt(2)*a*cos(d*x + c)^2 + 30*sqrt(2
)*a*sin(2*d*x + 2*c)^2 + 57*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 27*sqrt(2)*a*sin(d*x + c)^2 + 12*sqrt(2)
*a*cos(d*x + c) + 4*(3*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(3*d*x + 3*c) + 1
2*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 2*sqrt(2)*a)*sin(3*d*x + 3*c) + 2*(18*sqrt(2)*a*co
s(2*d*x + 2*c)^2 + 18*sqrt(2)*a*cos(d*x + c)^2 + 45*sqrt(2)*a*sin(d*x + c)^2 + 12*sqrt(2)*a*cos(d*x + c) + 12*
(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 2*sqrt(2)*a)*sin(2*d*x + 2*c) + 3*(9*sqrt(2)*a*cos(d
*x + c)^2 + 6*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(d*x + c))*sin(5*d*x + 5*c) + 6*(4*sqrt(2)*a*sin(3*d*x +
3*c)^3 + 36*sqrt(2)*a*sin(2*d*x + 2*c)^3 + 27*sqrt(2)*a*cos(2*d*x + 2*c)^2*sin(d*x + c) + 99*sqrt(2)*a*sin(2*d
*x + 2*c)^2*sin(d*x + c) + 27*sqrt(2)*a*sin(d*x + c)^3 + (4*sqrt(2)*a*sin(2*d*x + 2*c) + 3*sqrt(2)*a*sin(d*x +
c))*cos(3*d*x + 3*c)^2 + (28*sqrt(2)*a*sin(2*d*x + 2*c) + 27*sqrt(2)*a*sin(d*x + c))*sin(3*d*x + 3*c)^2 + 18*
(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c)*sin(d*x + c) + 2*(9*sqrt(2)*a*cos(2*d*x + 2*c)*sin(d*x
+ c) + 4*(3*sqrt(2)*a*cos(2*d*x + 2*c) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(2*d*x + 2*c) + 3*(3*sqrt(2
)*a*cos(d*x + c) + sqrt(2)*a)*sin(d*x + c))*cos(3*d*x + 3*c) + 2*(2*sqrt(2)*a*cos(3*d*x + 3*c)^2 + 18*sqrt(2)*
a*cos(2*d*x + 2*c)^2 + 18*sqrt(2)*a*cos(d*x + c)^2 + 30*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 57*sqrt(2)*a*sin(2*d*x
+ 2*c)*sin(d*x + c) + 27*sqrt(2)*a*sin(d*x + c)^2 + 12*sqrt(2)*a*cos(d*x + c) + 4*(3*sqrt(2)*a*cos(2*d*x + 2*c
) + 3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(3*d*x + 3*c) + 12*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d
*x + 2*c) + 2*sqrt(2)*a)*sin(3*d*x + 3*c) + 2*(18*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 18*sqrt(2)*a*cos(d*x + c)^2 +
45*sqrt(2)*a*sin(d*x + c)^2 + 12*sqrt(2)*a*cos(d*x + c) + 12*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x
+ 2*c) + 2*sqrt(2)*a)*sin(2*d*x + 2*c) + 3*(9*sqrt(2)*a*cos(d*x + c)^2 + 6*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a
)*sin(d*x + c))*sin(4*d*x + 4*c) + 2*(192*sqrt(2)*a*sin(2*d*x + 2*c)^3 + 156*sqrt(2)*a*cos(2*d*x + 2*c)^2*sin(
d*x + c) + 516*sqrt(2)*a*sin(2*d*x + 2*c)^2*sin(d*x + c) + 135*sqrt(2)*a*sin(d*x + c)^3 + 4*(16*sqrt(2)*a*sin(
2*d*x + 2*c) + 15*sqrt(2)*a*sin(d*x + c))*cos(3*d*x + 3*c)^2 + 96*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2
*d*x + 2*c)*sin(d*x + c) + 8*(21*sqrt(2)*a*cos(2*d*x + 2*c)*sin(d*x + c) + (24*sqrt(2)*a*cos(2*d*x + 2*c) + 21
*sqrt(2)*a*cos(d*x + c) + 7*sqrt(2)*a)*sin(2*d*x + 2*c) + 6*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(d*x + c
))*cos(3*d*x + 3*c) + (192*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 171*sqrt(2)*a*cos(d*x + c)^2 + 459*sqrt(2)*a*sin(d*x
+ c)^2 + 114*sqrt(2)*a*cos(d*x + c) + 120*(3*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + 19*sqrt(2
)*a)*sin(2*d*x + 2*c) + 15*(9*sqrt(2)*a*cos(d*x + c)^2 + 6*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*sin(d*x + c))*s
in(3*d*x + 3*c) + 6*(84*sqrt(2)*a*cos(2*d*x + 2*c)^2*sin(d*x + c) + 63*sqrt(2)*a*sin(d*x + c)^3 + 48*(3*sqrt(2
)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c)*sin(d*x + c) + 7*(9*sqrt(2)*a*cos(d*x + c)^2 + 6*sqrt(2)*a*cos(
d*x + c) + sqrt(2)*a)*sin(d*x + c))*sin(2*d*x + 2*c) + sqrt(2)*a)*sqrt(a)))/d
Giac [F]
\[
\int \frac {A+C \sec ^2(c+d x)}{\cos ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx=\int { \frac {C \sec \left (d x + c\right )^{2} + A}{{\left (a \sec \left (d x + c\right ) + a\right )}^{\frac {3}{2}} \cos \left (d x + c\right )^{\frac {3}{2}}} \,d x }
\]
[In]
integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm="giac")
[Out]
integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)
Mupad [F(-1)]
Timed out. \[
\int \frac {A+C \sec ^2(c+d x)}{\cos ^{\frac {3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx=\int \frac {A+\frac {C}{{\cos \left (c+d\,x\right )}^2}}{{\cos \left (c+d\,x\right )}^{3/2}\,{\left (a+\frac {a}{\cos \left (c+d\,x\right )}\right )}^{3/2}} \,d x
\]
[In]
int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(3/2)),x)
[Out]
int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(3/2)), x)