\(\int \frac {(A+C \cos ^2(c+d x)) \sec (c+d x)}{(a+a \cos (c+d x))^{3/2}} \, dx\) [115]

Optimal result

Integrand size = 33, antiderivative size = 125 \[ \int \frac {\left (A+C \cos ^2(c+d x)\right ) \sec (c+d x)}{(a+a \cos (c+d x))^{3/2}} \, dx=\frac {2 A \text {arctanh}\left (\frac {\sqrt {a} \sin (c+d x)}{\sqrt {a+a \cos (c+d x)}}\right )}{a^{3/2} d}-\frac {(5 A-3 C) \text {arctanh}\left (\frac {\sqrt {a} \sin (c+d x)}{\sqrt {2} \sqrt {a+a \cos (c+d x)}}\right )}{2 \sqrt {2} a^{3/2} d}-\frac {(A+C) \sin (c+d x)}{2 d (a+a \cos (c+d x))^{3/2}} \]

[Out]

2*A*arctanh(sin(d*x+c)*a^(1/2)/(a+a*cos(d*x+c))^(1/2))/a^(3/2)/d-1/2*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)
-1/4*(5*A-3*C)*arctanh(1/2*sin(d*x+c)*a^(1/2)*2^(1/2)/(a+a*cos(d*x+c))^(1/2))/a^(3/2)/d*2^(1/2)

Rubi [A] (verified)

Time = 0.53 (sec) , antiderivative size = 125, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.152, Rules used = {3121, 3064, 2728, 212, 2852} \[ \int \frac {\left (A+C \cos ^2(c+d x)\right ) \sec (c+d x)}{(a+a \cos (c+d x))^{3/2}} \, dx=-\frac {(5 A-3 C) \text {arctanh}\left (\frac {\sqrt {a} \sin (c+d x)}{\sqrt {2} \sqrt {a \cos (c+d x)+a}}\right )}{2 \sqrt {2} a^{3/2} d}+\frac {2 A \text {arctanh}\left (\frac {\sqrt {a} \sin (c+d x)}{\sqrt {a \cos (c+d x)+a}}\right )}{a^{3/2} d}-\frac {(A+C) \sin (c+d x)}{2 d (a \cos (c+d x)+a)^{3/2}} \]

[In]

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

[Out]

(2*A*ArcTanh[(Sqrt[a]*Sin[c + d*x])/Sqrt[a + a*Cos[c + d*x]]])/(a^(3/2)*d) - ((5*A - 3*C)*ArcTanh[(Sqrt[a]*Sin
[c + d*x])/(Sqrt[2]*Sqrt[a + a*Cos[c + d*x]])])/(2*Sqrt[2]*a^(3/2)*d) - ((A + C)*Sin[c + d*x])/(2*d*(a + a*Cos
[c + d*x])^(3/2))

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 2728

Int[1/Sqrt[(a_) + (b_.)*sin[(c_.) + (d_.)*(x_)]], x_Symbol] :> Dist[-2/d, Subst[Int[1/(2*a - x^2), x], x, b*(C
os[c + d*x]/Sqrt[a + b*Sin[c + d*x]])], x] /; FreeQ[{a, b, c, d}, x] && EqQ[a^2 - b^2, 0]

Rule 2852

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

Rule 3064

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

Rule 3121

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

Rubi steps \begin{align*} \text {integral}& = -\frac {(A+C) \sin (c+d x)}{2 d (a+a \cos (c+d x))^{3/2}}+\frac {\int \frac {\left (2 a A-\frac {1}{2} a (A-3 C) \cos (c+d x)\right ) \sec (c+d x)}{\sqrt {a+a \cos (c+d x)}} \, dx}{2 a^2} \\ & = -\frac {(A+C) \sin (c+d x)}{2 d (a+a \cos (c+d x))^{3/2}}+\frac {A \int \sqrt {a+a \cos (c+d x)} \sec (c+d x) \, dx}{a^2}-\frac {(5 A-3 C) \int \frac {1}{\sqrt {a+a \cos (c+d x)}} \, dx}{4 a} \\ & = -\frac {(A+C) \sin (c+d x)}{2 d (a+a \cos (c+d x))^{3/2}}-\frac {(2 A) \text {Subst}\left (\int \frac {1}{a-x^2} \, dx,x,-\frac {a \sin (c+d x)}{\sqrt {a+a \cos (c+d x)}}\right )}{a d}+\frac {(5 A-3 C) \text {Subst}\left (\int \frac {1}{2 a-x^2} \, dx,x,-\frac {a \sin (c+d x)}{\sqrt {a+a \cos (c+d x)}}\right )}{2 a d} \\ & = \frac {2 A \text {arctanh}\left (\frac {\sqrt {a} \sin (c+d x)}{\sqrt {a+a \cos (c+d x)}}\right )}{a^{3/2} d}-\frac {(5 A-3 C) \text {arctanh}\left (\frac {\sqrt {a} \sin (c+d x)}{\sqrt {2} \sqrt {a+a \cos (c+d x)}}\right )}{2 \sqrt {2} a^{3/2} d}-\frac {(A+C) \sin (c+d x)}{2 d (a+a \cos (c+d x))^{3/2}} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.52 (sec) , antiderivative size = 129, normalized size of antiderivative = 1.03 \[ \int \frac {\left (A+C \cos ^2(c+d x)\right ) \sec (c+d x)}{(a+a \cos (c+d x))^{3/2}} \, dx=\frac {(5 A-3 C) \text {arctanh}\left (\sin \left (\frac {1}{2} (c+d x)\right )\right ) \cos ^5\left (\frac {1}{2} (c+d x)\right )-4 \sqrt {2} A \text {arctanh}\left (\sqrt {2} \sin \left (\frac {1}{2} (c+d x)\right )\right ) \cos ^5\left (\frac {1}{2} (c+d x)\right )+(A+C) \cos ^3\left (\frac {1}{2} (c+d x)\right ) \sin \left (\frac {1}{2} (c+d x)\right )}{d (a (1+\cos (c+d x)))^{3/2} \left (-1+\sin ^2\left (\frac {1}{2} (c+d x)\right )\right )} \]

[In]

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

[Out]

((5*A - 3*C)*ArcTanh[Sin[(c + d*x)/2]]*Cos[(c + d*x)/2]^5 - 4*Sqrt[2]*A*ArcTanh[Sqrt[2]*Sin[(c + d*x)/2]]*Cos[
(c + d*x)/2]^5 + (A + C)*Cos[(c + d*x)/2]^3*Sin[(c + d*x)/2])/(d*(a*(1 + Cos[c + d*x]))^(3/2)*(-1 + Sin[(c + d
*x)/2]^2))

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(372\) vs. \(2(104)=208\).

Time = 8.11 (sec) , antiderivative size = 373, normalized size of antiderivative = 2.98

method	result	size
default	\(-\frac {\sqrt {a \left (\sin ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}\, \left (5 A \ln \left (\frac {4 \sqrt {a}\, \sqrt {a \left (\sin ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}+4 a}{\cos \left (\frac {d x}{2}+\frac {c}{2}\right )}\right ) \sqrt {2}\, \left (\cos ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right ) a -3 C \sqrt {2}\, \ln \left (\frac {4 \sqrt {a}\, \sqrt {a \left (\sin ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}+4 a}{\cos \left (\frac {d x}{2}+\frac {c}{2}\right )}\right ) \left (\cos ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right ) a -4 A \ln \left (\frac {4 \sqrt {2}\, a \cos \left (\frac {d x}{2}+\frac {c}{2}\right )+4 \sqrt {2}\, \sqrt {a \left (\sin ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}\, \sqrt {a}+8 a}{2 \cos \left (\frac {d x}{2}+\frac {c}{2}\right )+\sqrt {2}}\right ) \left (\cos ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right ) a -4 A \ln \left (-\frac {4 \left (\sqrt {2}\, a \cos \left (\frac {d x}{2}+\frac {c}{2}\right )-\sqrt {2}\, \sqrt {a \left (\sin ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}\, \sqrt {a}-2 a \right )}{2 \cos \left (\frac {d x}{2}+\frac {c}{2}\right )-\sqrt {2}}\right ) \left (\cos ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right ) a +A \sqrt {a}\, \sqrt {2}\, \sqrt {a \left (\sin ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}+C \sqrt {2}\, \sqrt {a \left (\sin ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}\, \sqrt {a}\right )}{4 a^{\frac {5}{2}} \cos \left (\frac {d x}{2}+\frac {c}{2}\right ) \sin \left (\frac {d x}{2}+\frac {c}{2}\right ) \sqrt {a \left (\cos ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}\, d}\)	\(373\)
parts	\(-\frac {A \sqrt {a \left (\sin ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}\, \left (5 \sqrt {2}\, \ln \left (\frac {4 \sqrt {a}\, \sqrt {a \left (\sin ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}+4 a}{\cos \left (\frac {d x}{2}+\frac {c}{2}\right )}\right ) a \left (\cos ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )-4 \ln \left (\frac {4 \sqrt {2}\, a \cos \left (\frac {d x}{2}+\frac {c}{2}\right )+4 \sqrt {2}\, \sqrt {a \left (\sin ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}\, \sqrt {a}+8 a}{2 \cos \left (\frac {d x}{2}+\frac {c}{2}\right )+\sqrt {2}}\right ) \left (\cos ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right ) a -4 \ln \left (-\frac {4 \left (\sqrt {2}\, a \cos \left (\frac {d x}{2}+\frac {c}{2}\right )-\sqrt {2}\, \sqrt {a \left (\sin ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}\, \sqrt {a}-2 a \right )}{2 \cos \left (\frac {d x}{2}+\frac {c}{2}\right )-\sqrt {2}}\right ) \left (\cos ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right ) a +\sqrt {2}\, \sqrt {a \left (\sin ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}\, \sqrt {a}\right )}{4 a^{\frac {5}{2}} \cos \left (\frac {d x}{2}+\frac {c}{2}\right ) \sin \left (\frac {d x}{2}+\frac {c}{2}\right ) \sqrt {a \left (\cos ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}\, d}+\frac {C \sqrt {a \left (\sin ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}\, \left (3 \ln \left (\frac {2 \sqrt {a}\, \sqrt {a \left (\sin ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}+2 a}{\cos \left (\frac {d x}{2}+\frac {c}{2}\right )}\right ) \left (\cos ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right ) a -\sqrt {a}\, \sqrt {a \left (\sin ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}\right ) \sqrt {2}}{4 \cos \left (\frac {d x}{2}+\frac {c}{2}\right ) a^{\frac {5}{2}} \sin \left (\frac {d x}{2}+\frac {c}{2}\right ) \sqrt {a \left (\cos ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}\, d}\)	\(426\)

[In]

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

[Out]

-1/4/a^(5/2)/cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*A*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(
1/2)+2*a)/cos(1/2*d*x+1/2*c))*2^(1/2)*cos(1/2*d*x+1/2*c)^2*a-3*C*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)
^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*cos(1/2*d*x+1/2*c)^2*a-4*A*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*a*c
os(1/2*d*x+1/2*c)+2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+2*a))*cos(1/2*d*x+1/2*c)^2*a-4*A*ln(-4/(2*cos
(1/2*d*x+1/2*c)-2^(1/2))*(2^(1/2)*a*cos(1/2*d*x+1/2*c)-2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-2*a))*co
s(1/2*d*x+1/2*c)^2*a+A*a^(1/2)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+C*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)
*a^(1/2))/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 279 vs. \(2 (104) = 208\).

Time = 0.31 (sec) , antiderivative size = 279, normalized size of antiderivative = 2.23 \[ \int \frac {\left (A+C \cos ^2(c+d x)\right ) \sec (c+d x)}{(a+a \cos (c+d x))^{3/2}} \, dx=-\frac {\sqrt {2} {\left ({\left (5 \, A - 3 \, C\right )} \cos \left (d x + c\right )^{2} + 2 \, {\left (5 \, A - 3 \, C\right )} \cos \left (d x + c\right ) + 5 \, A - 3 \, C\right )} \sqrt {a} \log \left (-\frac {a \cos \left (d x + c\right )^{2} - 2 \, \sqrt {2} \sqrt {a \cos \left (d x + c\right ) + a} \sqrt {a} \sin \left (d x + c\right ) - 2 \, a \cos \left (d x + c\right ) - 3 \, a}{\cos \left (d x + c\right )^{2} + 2 \, \cos \left (d x + c\right ) + 1}\right ) - 4 \, {\left (A \cos \left (d x + c\right )^{2} + 2 \, A \cos \left (d x + c\right ) + A\right )} \sqrt {a} \log \left (\frac {a \cos \left (d x + c\right )^{3} - 7 \, a \cos \left (d x + c\right )^{2} - 4 \, \sqrt {a \cos \left (d x + c\right ) + a} \sqrt {a} {\left (\cos \left (d x + c\right ) - 2\right )} \sin \left (d x + c\right ) + 8 \, a}{\cos \left (d x + c\right )^{3} + \cos \left (d x + c\right )^{2}}\right ) + 4 \, \sqrt {a \cos \left (d x + c\right ) + a} {\left (A + C\right )} \sin \left (d x + c\right )}{8 \, {\left (a^{2} d \cos \left (d x + c\right )^{2} + 2 \, a^{2} d \cos \left (d x + c\right ) + a^{2} d\right )}} \]

[In]

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

[Out]

-1/8*(sqrt(2)*((5*A - 3*C)*cos(d*x + c)^2 + 2*(5*A - 3*C)*cos(d*x + c) + 5*A - 3*C)*sqrt(a)*log(-(a*cos(d*x +
c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*c
os(d*x + c) + 1)) - 4*(A*cos(d*x + c)^2 + 2*A*cos(d*x + c) + A)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x +
c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c
)^2)) + 4*sqrt(a*cos(d*x + c) + a)*(A + C)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)

Sympy [F]

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

[In]

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

[Out]

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

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 46533 vs. \(2 (104) = 208\).

Time = 1.92 (sec) , antiderivative size = 46533, normalized size of antiderivative = 372.26 \[ \int \frac {\left (A+C \cos ^2(c+d x)\right ) \sec (c+d x)}{(a+a \cos (c+d x))^{3/2}} \, dx=\text {Too large to display} \]

[In]

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

[Out]

1/16*(3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*l
og(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 4*sqrt(2)*sin(5/2*d*x + 5/2
*c))*cos(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/
2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d
*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) -
sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + (3
*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(
1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(3*d*x + 3*c)^2 + 27*(sqrt(2)*lo
g(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/
2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*
x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin
(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + si
n(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)
^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x +
1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1
/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2
*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2
*c) + 1))*sin(d*x + c)^2 - 96*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 60*sqrt(2)*cos(1/2*d*x + 1/2*c)*sin(
d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - s
qrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c) + 9
*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(
1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/
2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2
+ sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 10*sqrt(2)*sin(5/2*d*x + 5/2*c) + 16*sqrt(2)*sin(3/2
*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(3*d*x + 3*c) + 60*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin
(d*x + c))*cos(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/
2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1
))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1)
- 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 16*sqrt(2)*sin
(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 6*(3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^
2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x
+ 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(d*x + c) + 2*(9*(sqrt(2)*log(c
os(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c
)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/
2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d
*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + 10*sqrt(2)*cos(5/2*d*x + 5/2*c) - 16*sqrt(2)*cos(3
/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(3*d*x + 3*c) - 20*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(
2)*cos(d*x + c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2
*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*
d*x + 1/2*c) + 1))*sin(d*x + c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(2*d*x
+ 2*c) + 32*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 +
sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/
2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 20*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(6/5*arctan2(sin(5/2*d*x + 5/2*c),
cos(5/2*d*x + 5/2*c)))^2 + 9*(3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x +
1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(
3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1)
- sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c)
^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*l
og(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 3*(sqrt(2)*
log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x +
1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*
d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + s
in(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)
^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x +
1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 - 96*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 60*sq
rt(2)*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 +
2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/
2*c) + 1))*cos(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x +
1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(
d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqr
t(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 10*sqrt(2)*sin(5/2*d*
x + 5/2*c) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(3*d*x + 3*c) + 60*(sqrt(2)
*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + si
n(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)
^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2
+ 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x
+ 1/2*c) + 1) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 6*(3*sq
rt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/
2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos
(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) -
sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c) +
9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos
(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + 10*sqrt(2)*cos(5/2*
d*x + 5/2*c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(3*d*x + 3*c) - 20*(3*sqr
t(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x
+ 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(
1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*
cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) + 32*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3/2*d*x + 3/2*c) + 3*sqrt(2
)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*
x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 20*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(4/5
*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + 9*(3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d
*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*
sin(1/2*d*x + 1/2*c) + 1))*cos(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^
2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x
+ 1/2*c) + 1))*cos(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/
2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1
))*cos(d*x + c)^2 + 3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) +
1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(3*d*x + 3*
c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)
*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 27*(s
qrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2
*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 - 96*sqrt(2)*cos(3/2*d*
x + 3/2*c)*sin(d*x + c) - 60*sqrt(2)*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c
)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x
+ 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d
*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*
sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*si
n(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*
c) + 1) - 10*sqrt(2)*sin(5/2*d*x + 5/2*c) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))
*cos(3*d*x + 3*c) + 60*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*
log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x +
1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/
2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2
*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2
*c))*cos(2*d*x + 2*c) + 6*(3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2
*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 10*sq
rt(2)*sin(1/2*d*x + 1/2*c))*cos(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 +
2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1
/2*c) + 1))*sin(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x
+ 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin
(d*x + c) + 10*sqrt(2)*cos(5/2*d*x + 5/2*c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c
))*sin(3*d*x + 3*c) - 20*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(5/2*d*x + 5/2*c)
+ 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*lo
g(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) - 16*sqrt(2)*cos
(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) + 32*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*
sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)
+ 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 20*sqrt(2
)*sin(1/2*d*x + 1/2*c))*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + 3*(sqrt(2)*log(cos(1/
2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 +
sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 4*sqrt(2)*sin(5/2*d*x + 5/2*c))*sin(3*d*x + 3*c)^2 + 2
7*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos
(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 27*(sqrt(2)*l
og(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1
/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 + (3*(sqrt(2)*log(cos(1/2*d*x +
1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/
2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 +
sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*
c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x
+ 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin
(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*si
n(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c)
+ 1))*sin(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x +
1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2
*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1)
- sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 -
96*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 60*sqrt(2)*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 2*(9*(sqrt(2)*lo
g(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/
2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x +
1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/
2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*
d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 -
2*sin(1/2*d*x + 1/2*c) + 1) - 10*sqrt(2)*sin(5/2*d*x + 5/2*c) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*
sin(1/2*d*x + 1/2*c))*cos(3*d*x + 3*c) + 60*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(5/2*d*x + 5/
2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(
2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)
*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x
+ 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt
(2)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 6*(3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2
+ 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x
+ 1/2*c) + 1) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin
(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^
2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*
c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d
*x + 1/2*c) + 1))*sin(d*x + c) + 10*sqrt(2)*cos(5/2*d*x + 5/2*c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2
)*cos(1/2*d*x + 1/2*c))*sin(3*d*x + 3*c) - 20*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*
sin(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2
*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x
+ c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) + 32*(3*sqrt(2)*cos
(d*x + c) + sqrt(2))*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*
sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/
2*c) + 1) + 20*sqrt(2)*sin(1/2*d*x + 1/2*c))*sin(6/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 +
9*(3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(
cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(3*d*x + 3*c)^2 + 27*(sqrt(2
)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x
+ 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/
2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 +
sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2
+ sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/
2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*
x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*s
in(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2
+ 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x +
1/2*c) + 1))*sin(d*x + c)^2 - 96*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 60*sqrt(2)*cos(1/2*d*x + 1/2*c)*
sin(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1)
- sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c)
+ 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(
cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(co
s(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*
c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 10*sqrt(2)*sin(5/2*d*x + 5/2*c) + 16*sqrt(2)*sin
(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(3*d*x + 3*c) + 60*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)
*sin(d*x + c))*cos(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*si
n(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c)
+ 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) +
1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 16*sqrt(2)
*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 6*(3*sqrt(2)*log(cos(1/2*d*x + 1/2
*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*
d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(d*x + c) + 2*(9*(sqrt(2)*l
og(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1
/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x
+ 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1
/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + 10*sqrt(2)*cos(5/2*d*x + 5/2*c) - 16*sqrt(2)*c
os(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(3*d*x + 3*c) - 20*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*s
qrt(2)*cos(d*x + c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x +
1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(
1/2*d*x + 1/2*c) + 1))*sin(d*x + c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(2
*d*x + 2*c) + 32*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^
2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x
+ 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 20*sqrt(2)*sin(1/2*d*x + 1/2*c))*sin(4/5*arctan2(sin(5/2*d*x + 5/2*
c), cos(5/2*d*x + 5/2*c)))^2 + 96*(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(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x +
5/2*c)))*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 9*(3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)
^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x +
1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2
*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 -
2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c
)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*
x + 1/2*c) + 1))*cos(d*x + c)^2 + 3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d
*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*
sin(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)
+ 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x +
2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(
2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 - 96*sqrt
(2)*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 60*sqrt(2)*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 2*(9*(sqrt(2)*log(cos(1
/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2
+ sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)
^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x +
1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1
/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(
1/2*d*x + 1/2*c) + 1) - 10*sqrt(2)*sin(5/2*d*x + 5/2*c) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2
*d*x + 1/2*c))*cos(3*d*x + 3*c) + 60*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(5/2*d*x + 5/2*c) +
6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(
cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(co
s(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*
c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin
(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 6*(3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin
(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c
) + 1) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*
x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*s
in(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 +
2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/
2*c) + 1))*sin(d*x + c) + 10*sqrt(2)*cos(5/2*d*x + 5/2*c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1
/2*d*x + 1/2*c))*sin(3*d*x + 3*c) - 20*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(5/2
*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1
) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) -
16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) + 32*(3*sqrt(2)*cos(d*x +
c) + sqrt(2))*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2
*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) +
1) + 20*sqrt(2)*sin(1/2*d*x + 1/2*c))*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 - 96*sqrt
(2)*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 60*sqrt(2)*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 2*(9*(sqrt(2)*log(cos(1
/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2
+ sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)
^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x +
1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 2*(18*sqrt(2)*cos(2*d*x + 2*c) + 18*sqrt(2)*cos(d*x +
c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2
*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) +
1) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(3*d*x + 3*c) + 60*(sqrt(2)*sin(2*d
*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*
x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*s
in(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin
(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c
) + 1) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 6*(3*sqrt(2)*lo
g(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x +
1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(d*x + c
) + 2*(3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*
log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 2*sqrt(2)*sin(5/2*d*x + 5/
2*c))*cos(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1
/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*
d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) -
sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 3
*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(
1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 2*sqrt(2)*sin(5/2*d*x + 5/2*c))*si
n(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) +
1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*
c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)
*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 - 96*sqrt(2
)*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 60*sqrt(2)*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2
*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 +
sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2
+ sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1
/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 2*(9*sqrt(2)*cos(2*d*x + 2*c) + 9*sqrt(2)*cos(d*x + c) -
2*sqrt(2))*sin(5/2*d*x + 5/2*c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d
*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1)
+ 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(3*d*x + 3*c) + 60*(sqrt(2)*sin(2*d*x
+ 2*c) + sqrt(2)*sin(d*x + c))*cos(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x
+ 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin
(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1
/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c)
+ 1) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 6*(3*sqrt(2)*log(
cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/
2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(d*x + c)
+ 3*(3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*lo
g(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(3*d*x + 3*c)^2 + 27*(sqrt
(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*
x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(
1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2
+ sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^
2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x +
1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*
d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2
*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)
^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x
+ 1/2*c) + 1))*sin(d*x + c)^2 - 96*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 60*sqrt(2)*cos(1/2*d*x + 1/2*c
)*sin(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) +
1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*
c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*lo
g(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(
cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/
2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 10*sqrt(2)*sin(5/2*d*x + 5/2*c) + 16*sqrt(2)*s
in(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(3*d*x + 3*c) + 60*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(
2)*sin(d*x + c))*cos(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*
sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*
c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)
+ 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 16*sqrt(
2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 6*(3*sqrt(2)*log(cos(1/2*d*x + 1
/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/
2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(d*x + c) + 2*(9*(sqrt(2)
*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x +
1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*
x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin
(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + 10*sqrt(2)*cos(5/2*d*x + 5/2*c) - 16*sqrt(2)
*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(3*d*x + 3*c) - 20*(3*sqrt(2)*cos(2*d*x + 2*c) + 3
*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x
+ 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*si
n(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin
(2*d*x + 2*c) + 32*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c
)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*
x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 20*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(4/5*arctan2(sin(5/2*d*x + 5/
2*c), cos(5/2*d*x + 5/2*c))) + 3*(3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d
*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*
cos(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)
+ 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x +
2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(
2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 3*(sqrt
(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*
x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(
1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2
+ sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/
2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d
*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 - 96*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 6
0*sqrt(2)*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^
2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x
+ 1/2*c) + 1))*cos(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d
*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*
cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3
*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 10*sqrt(2)*sin(5/
2*d*x + 5/2*c) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(3*d*x + 3*c) + 60*(sqr
t(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2
+ sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/
2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*
c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2
*d*x + 1/2*c) + 1) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 6*(
3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(co
s(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))
*cos(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1
) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c
) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log
(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + 10*sqrt(2)*cos(
5/2*d*x + 5/2*c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(3*d*x + 3*c) - 20*(3
*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2
*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 +
sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt
(2)*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) + 32*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3/2*d*x + 3/2*c) + 3*sq
rt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/
2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 20*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos
(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 2*(18*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x
+ c))*sin(5/2*d*x + 5/2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x +
1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2
*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - s
qrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + 10*sq
rt(2)*cos(5/2*d*x + 5/2*c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(3*d*x + 3*
c) + 2*(27*sqrt(2)*cos(2*d*x + 2*c)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 27*sqrt(2)*sin(2*d*x + 2*c)^2 + 54*sqrt(2)
*sin(2*d*x + 2*c)*sin(d*x + c) + 27*sqrt(2)*sin(d*x + c)^2 + 6*(9*sqrt(2)*cos(d*x + c) - 2*sqrt(2))*cos(2*d*x
+ 2*c) - 12*sqrt(2)*cos(d*x + c) - 7*sqrt(2))*sin(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2
+ sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/
2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x
+ 1/2*c))*sin(2*d*x + 2*c) + 32*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3/2*d*x + 3/2*c) - 16*(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) + sq
rt(2))*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 6*(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(1/5*arctan
2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2
+ 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x
+ 1/2*c) + 1) + 20*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(6/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))
+ 6*(3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*l
og(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 2*sqrt(2)*sin(5/2*d*x + 5/2
*c))*cos(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/
2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d
*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) -
sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 3*
(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1
/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 2*sqrt(2)*sin(5/2*d*x + 5/2*c))*sin
(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1
) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c
)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*
log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 - 96*sqrt(2)
*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 60*sqrt(2)*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*
d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + s
in(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2
+ sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/
2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 2*(9*sqrt(2)*cos(2*d*x + 2*c) + 9*sqrt(2)*cos(d*x + c) -
2*sqrt(2))*sin(5/2*d*x + 5/2*c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*
x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1)
+ 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(3*d*x + 3*c) + 60*(sqrt(2)*sin(2*d*x
+ 2*c) + sqrt(2)*sin(d*x + c))*cos(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x +
1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(
1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/
2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) +
1) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 6*(3*sqrt(2)*log(c
os(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2
*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(d*x + c) +
3*(3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log
(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(3*d*x + 3*c)^2 + 27*(sqrt(
2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x
+ 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1
/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2
+ sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2
+ sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1
/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d
*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*
sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^
2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x
+ 1/2*c) + 1))*sin(d*x + c)^2 - 96*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 60*sqrt(2)*cos(1/2*d*x + 1/2*c)
*sin(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1
) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c
) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log
(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(c
os(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2
*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 10*sqrt(2)*sin(5/2*d*x + 5/2*c) + 16*sqrt(2)*si
n(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(3*d*x + 3*c) + 60*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2
)*sin(d*x + c))*cos(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*s
in(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c
) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)
+ 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 16*sqrt(2
)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 6*(3*sqrt(2)*log(cos(1/2*d*x + 1/
2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2
*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(d*x + c) + 2*(9*(sqrt(2)*
log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x +
1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x
+ 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(
1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + 10*sqrt(2)*cos(5/2*d*x + 5/2*c) - 16*sqrt(2)*
cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(3*d*x + 3*c) - 20*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*
sqrt(2)*cos(d*x + c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x
+ 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin
(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(
2*d*x + 2*c) + 32*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)
^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x
+ 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 20*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(2/5*arctan2(sin(5/2*d*x + 5/2
*c), cos(5/2*d*x + 5/2*c))) + 2*(18*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(5/2*d*x + 5/2*c) + 9
*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(
1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c) + 9*(sqrt(2)*log(c
os(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c
)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + 10*sqrt(2)*cos(5/2*d*x + 5/2*c) - 1
6*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(3*d*x + 3*c) + 2*(27*sqrt(2)*cos(2*d*x +
2*c)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 27*sqrt(2)*sin(2*d*x + 2*c)^2 + 54*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c)
+ 27*sqrt(2)*sin(d*x + c)^2 + 6*(9*sqrt(2)*cos(d*x + c) - 2*sqrt(2))*cos(2*d*x + 2*c) - 12*sqrt(2)*cos(d*x +
c) - 7*sqrt(2))*sin(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*s
in(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c
) + 1))*sin(d*x + c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) + 3
2*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3/2*d*x + 3/2*c) - 16*(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(3/5*arctan2(sin(5/2
*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 6*(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)*si
n(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)*s
in(d*x + c))*sin(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/
2*d*x + 5/2*c))) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1)
- 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 20*sqrt(2)*si
n(1/2*d*x + 1/2*c))*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 6*(3*(sqrt(2)*log(cos(1/2*d
*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + si
n(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 2*sqrt(2)*sin(5/2*d*x + 5/2*c))*cos(3*d*x + 3*c)^2 + 27*(
sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/
2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(
cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*
c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 3*(sqrt(2)*log(cos(1/2*d*x + 1/2
*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*
x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 2*sqrt(2)*sin(5/2*d*x + 5/2*c))*sin(3*d*x + 3*c)^2 + 27*(sqrt(2)*
log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x +
1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*
d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + s
in(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 - 96*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(d*x
+ c) - 60*sqrt(2)*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x +
1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(
1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*s
in(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c
) + 1))*cos(d*x + c) + 2*(9*sqrt(2)*cos(2*d*x + 2*c) + 9*sqrt(2)*cos(d*x + c) - 2*sqrt(2))*sin(5/2*d*x + 5/2*c
) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*lo
g(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 16*sqrt(2)*sin(3/2*d*x + 3/2
*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(3*d*x + 3*c) + 60*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))
*cos(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/
2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x
+ c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2
)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 16*sqrt(2)*sin(3/2*d*x +
3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 6*(3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/
2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2
- 2*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(d*x + c) + 2*(18*(sqrt(2)*sin(2*d*x + 2*
c) + sqrt(2)*sin(d*x + c))*sin(5/2*d*x + 5/2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)
^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x
+ 1/2*c) + 1))*sin(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*
d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))
*sin(d*x + c) + 10*sqrt(2)*cos(5/2*d*x + 5/2*c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1
/2*c))*sin(3*d*x + 3*c) + 2*(27*sqrt(2)*cos(2*d*x + 2*c)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 27*sqrt(2)*sin(2*d*x
+ 2*c)^2 + 54*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 27*sqrt(2)*sin(d*x + c)^2 + 6*(9*sqrt(2)*cos(d*x + c) -
2*sqrt(2))*cos(2*d*x + 2*c) - 12*sqrt(2)*cos(d*x + c) - 7*sqrt(2))*sin(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(co
s(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)
^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10
*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) + 32*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3/2*d*x + 3/2*c) -
6*(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(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 3*sqrt(2)*log(cos(1/
2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2
+ sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 20*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(2/5*arctan2(sin
(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*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(6/5*arctan2(sin(5/2*d*x + 5/2*c), c
os(5/2*d*x + 5/2*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))*s
in(3*d*x + 3*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*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(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*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*sqr
t(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)*c
os(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))*co
s(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(6/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*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(4/5
*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + 18*(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(4/5*arctan2(sin(5/2*d
*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 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(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*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) + 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) + 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(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2
*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(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 6*(sqrt(2)*si
n(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(6/5*arctan2(si
n(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 6*(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) + 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(2/5*
arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*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(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))
+ 6*(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*sqr
t(2)*cos(d*x + c) + sqrt(2))*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*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(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(4/5*arctan2(sin(5/2*d*x +
5/2*c), cos(5/2*d*x + 5/2*c))) + (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(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5
/2*c))))*sin(6/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*log(
cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2
*d*x + 5/2*c)))^2 + 2*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 1) - 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) + sq
rt(2))*cos(6/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*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(4/5*arct
an2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*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(2/5*arctan2(sin(5/2*d*x + 5
/2*c), cos(5/2*d*x + 5/2*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(6/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x +
5/2*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(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + 18*(sq
rt(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) + sq
rt(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(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(2/5*arctan2(sin(5/2*d*x
+ 5/2*c), cos(5/2*d*x + 5/2*c))) + 9*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*co
s(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(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x
+ 5/2*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) + 2*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*s
qrt(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) + 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))*cos(4/5*a
rctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*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(2/5*arctan2(sin(5/2*d*x +
5/2*c), cos(5/2*d*x + 5/2*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(6/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 6*(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) + 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(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*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(4/5*arctan
2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 6*(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(2/5*arctan2(sin(5/2*d*x + 5/2*c
), cos(5/2*d*x + 5/2*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(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(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + (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(2/5
*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*sin(6/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2
*c))) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*log(cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 +
sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 - 2*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(
5/2*d*x + 5/2*c))) + 1) + 2*(36*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*sin(5/2*d*x + 5/2*c) + 9*(sq
rt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*
d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1
/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2
+ sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + 10*sqrt(2)*cos(5/2*d*x + 5/2*c) - 16*sq
rt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(3*d*x + 3*c) + 4*(27*sqrt(2)*cos(2*d*x + 2*c
)^2 + 27*sqrt(2)*cos(d*x + c)^2 + 27*sqrt(2)*sin(2*d*x + 2*c)^2 + 54*sqrt(2)*sin(2*d*x + 2*c)*sin(d*x + c) + 2
7*sqrt(2)*sin(d*x + c)^2 + 3*(18*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) - 2
*sqrt(2))*sin(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2
*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1)
)*sin(d*x + c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) + 32*(3*s
qrt(2)*cos(d*x + c) + sqrt(2))*sin(3/2*d*x + 3/2*c) - 2*(6*sqrt(2)*cos(3*d*x + 3*c)^2*cos(5/2*d*x + 5/2*c) + 6
*sqrt(2)*cos(5/2*d*x + 5/2*c)*sin(3*d*x + 3*c)^2 + 12*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + s
qrt(2))*cos(3*d*x + 3*c)*cos(5/2*d*x + 5/2*c) + 36*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(5/2*d
*x + 5/2*c)*sin(3*d*x + 3*c) + 6*(9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + 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 + 6*(3*sqrt(2)*cos(d*x + c) +
sqrt(2))*cos(2*d*x + 2*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(5/2*d*x + 5/2*c) - 16*(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(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 6*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*co
s(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*s
qrt(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)*co
s(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)*si
n(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(1/5*arctan2(si
n(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 3*(3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2
+ 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x +
1/2*c) + 1))*cos(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2
*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1)
)*cos(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c
) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x +
c)^2 + 3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*
log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(3*d*x + 3*c)^2 + 27*(sq
rt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*
d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(co
s(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)
^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 - 96*sqrt(2)*cos(3/2*d*x + 3/2*c)*si
n(d*x + c) - 60*sqrt(2)*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2
*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 -
2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2
+ 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x +
1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1
/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 10*
sqrt(2)*sin(5/2*d*x + 5/2*c) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(3*d*x +
3*c) + 60*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d
*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + si
n(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(
1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)
^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(2*d*
x + 2*c) + 6*(3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*
sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*sin(1/2
*d*x + 1/2*c))*cos(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*
x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*s
in(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1)
- sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + 1
0*sqrt(2)*cos(5/2*d*x + 5/2*c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(3*d*x
+ 3*c) - 20*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 6*(9*(sqrt(
2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x
+ 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) - 16*sqrt(2)*cos(3/2*d*x + 3/
2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) + 32*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3/2*d*x +
3/2*c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt
(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 20*sqrt(2)*sin(1/2*d*x
+ 1/2*c))*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 3*(3*(sqrt(2)*log(cos(1/2*d*x + 1/2*
c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x
+ 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1
/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2
- 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2
*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*
d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2
*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1)
)*sin(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c
) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x
+ 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqr
t(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 - 96*sq
rt(2)*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 60*sqrt(2)*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 2*(9*(sqrt(2)*log(cos
(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^
2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*
c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x
+ 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x +
1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*si
n(1/2*d*x + 1/2*c) + 1) - 10*sqrt(2)*sin(5/2*d*x + 5/2*c) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1
/2*d*x + 1/2*c))*cos(3*d*x + 3*c) + 60*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(5/2*d*x + 5/2*c)
+ 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*lo
g(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(
cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/
2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*s
in(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 6*(3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*s
in(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2
*c) + 1) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*
d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2
*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2
+ 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x +
1/2*c) + 1))*sin(d*x + c) + 10*sqrt(2)*cos(5/2*d*x + 5/2*c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos
(1/2*d*x + 1/2*c))*sin(3*d*x + 3*c) - 20*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(5
/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) +
1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)
- 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) + 32*(3*sqrt(2)*cos(d*x
+ c) + sqrt(2))*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1
/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c)
+ 1) + 20*sqrt(2)*sin(1/2*d*x + 1/2*c))*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*sin(6/5*
arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 6*(6*sqrt(2)*cos(3*d*x + 3*c)^2*cos(5/2*d*x + 5/2*c) +
6*sqrt(2)*cos(5/2*d*x + 5/2*c)*sin(3*d*x + 3*c)^2 + 12*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) +
sqrt(2))*cos(3*d*x + 3*c)*cos(5/2*d*x + 5/2*c) + 36*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(5/2*
d*x + 5/2*c)*sin(3*d*x + 3*c) + 6*(9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*cos(d*x + 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 + 6*(3*sqrt(2)*cos(d*x + c)
+ sqrt(2))*cos(2*d*x + 2*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(5/2*d*x + 5/2*c) - 16*(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(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 6*(sqrt(2)*cos(3*d*x + 3*c)^2 + 9*sqrt(2)*c
os(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)*c
os(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)*s
in(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(1/5*arctan2(s
in(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 3*(3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^
2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x
+ 1/2*c) + 1))*cos(3*d*x + 3*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/
2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1
))*cos(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*
c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x +
c)^2 + 3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)
*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(3*d*x + 3*c)^2 + 27*(s
qrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2
*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 27*(sqrt(2)*log(c
os(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c
)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 - 96*sqrt(2)*cos(3/2*d*x + 3/2*c)*s
in(d*x + c) - 60*sqrt(2)*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/
2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 -
2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^
2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x
+ 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x +
1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 10
*sqrt(2)*sin(5/2*d*x + 5/2*c) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(3*d*x +
3*c) + 60*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2)*sin(d*x + c))*cos(5/2*d*x + 5/2*c) + 6*(9*(sqrt(2)*log(cos(1/2*
d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + s
in(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin
(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c
)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 16*sqrt(2)*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*sin(1/2*d*x + 1/2*c))*cos(2*d
*x + 2*c) + 6*(3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3
*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*sin(1/
2*d*x + 1/2*c))*cos(d*x + c) + 2*(9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d
*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*
sin(2*d*x + 2*c) + 9*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1
) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) +
10*sqrt(2)*cos(5/2*d*x + 5/2*c) - 16*sqrt(2)*cos(3/2*d*x + 3/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(3*d*x
+ 3*c) - 20*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 6*(9*(sqrt
(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*
x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) - 16*sqrt(2)*cos(3/2*d*x + 3
/2*c) - 10*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) + 32*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*sin(3/2*d*x
+ 3/2*c) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*sqr
t(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 20*sqrt(2)*sin(1/2*d*
x + 1/2*c))*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c)
, cos(5/2*d*x + 5/2*c))) - 32*(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) + 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(2/5*arctan2(sin(5/2*d
*x + 5/2*c), cos(5/2*d*x + 5/2*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(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 36*(sqrt(2)*co
s(3*d*x + 3*c)^2*cos(5/2*d*x + 5/2*c) + sqrt(2)*cos(5/2*d*x + 5/2*c)*sin(3*d*x + 3*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)*cos(5/2*d*x + 5/2*c) + 6*(sqrt(2)*sin(2*d*x + 2
*c) + sqrt(2)*sin(d*x + c))*cos(5/2*d*x + 5/2*c)*sin(3*d*x + 3*c) + (9*sqrt(2)*cos(2*d*x + 2*c)^2 + 9*sqrt(2)*
cos(d*x + 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 + 6*(3*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(2*d*x + 2*c) + 6*sqrt(2)*cos(d*x + c) + sqrt(2))*cos(5/2*d*x
+ 5/2*c) - (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(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*sin(2/5*arcta
n2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 12*(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) + sq
rt(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(1/5*arctan2(sin(5/2*d*x + 5/2
*c), cos(5/2*d*x + 5/2*c))) + 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x +
1/2*c) + 1) - 3*sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 20
*sqrt(2)*sin(1/2*d*x + 1/2*c))*C*sqrt(a)/((a^2*cos(3*d*x + 3*c)^2 + 9*a^2*cos(2*d*x + 2*c)^2 + 9*a^2*cos(d*x +
c)^2 + a^2*sin(3*d*x + 3*c)^2 + 9*a^2*sin(2*d*x + 2*c)^2 + 18*a^2*sin(2*d*x + 2*c)*sin(d*x + c) + 9*a^2*sin(d
*x + c)^2 + 6*a^2*cos(d*x + c) + (a^2*cos(3*d*x + 3*c)^2 + 9*a^2*cos(2*d*x + 2*c)^2 + 9*a^2*cos(d*x + c)^2 + a
^2*sin(3*d*x + 3*c)^2 + 9*a^2*sin(2*d*x + 2*c)^2 + 18*a^2*sin(2*d*x + 2*c)*sin(d*x + c) + 9*a^2*sin(d*x + c)^2
+ 6*a^2*cos(d*x + c) + a^2 + 2*(3*a^2*cos(2*d*x + 2*c) + 3*a^2*cos(d*x + c) + a^2)*cos(3*d*x + 3*c) + 6*(3*a^
2*cos(d*x + c) + a^2)*cos(2*d*x + 2*c) + 6*(a^2*sin(2*d*x + 2*c) + a^2*sin(d*x + c))*sin(3*d*x + 3*c))*cos(6/5
*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + 9*(a^2*cos(3*d*x + 3*c)^2 + 9*a^2*cos(2*d*x + 2*c)^2
+ 9*a^2*cos(d*x + c)^2 + a^2*sin(3*d*x + 3*c)^2 + 9*a^2*sin(2*d*x + 2*c)^2 + 18*a^2*sin(2*d*x + 2*c)*sin(d*x
+ c) + 9*a^2*sin(d*x + c)^2 + 6*a^2*cos(d*x + c) + a^2 + 2*(3*a^2*cos(2*d*x + 2*c) + 3*a^2*cos(d*x + c) + a^2)
*cos(3*d*x + 3*c) + 6*(3*a^2*cos(d*x + c) + a^2)*cos(2*d*x + 2*c) + 6*(a^2*sin(2*d*x + 2*c) + a^2*sin(d*x + c)
)*sin(3*d*x + 3*c))*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + 9*(a^2*cos(3*d*x + 3*c)^2
+ 9*a^2*cos(2*d*x + 2*c)^2 + 9*a^2*cos(d*x + c)^2 + a^2*sin(3*d*x + 3*c)^2 + 9*a^2*sin(2*d*x + 2*c)^2 + 18*a^
2*sin(2*d*x + 2*c)*sin(d*x + c) + 9*a^2*sin(d*x + c)^2 + 6*a^2*cos(d*x + c) + a^2 + 2*(3*a^2*cos(2*d*x + 2*c)
+ 3*a^2*cos(d*x + c) + a^2)*cos(3*d*x + 3*c) + 6*(3*a^2*cos(d*x + c) + a^2)*cos(2*d*x + 2*c) + 6*(a^2*sin(2*d*
x + 2*c) + a^2*sin(d*x + c))*sin(3*d*x + 3*c))*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2
+ (a^2*cos(3*d*x + 3*c)^2 + 9*a^2*cos(2*d*x + 2*c)^2 + 9*a^2*cos(d*x + c)^2 + a^2*sin(3*d*x + 3*c)^2 + 9*a^2*s
in(2*d*x + 2*c)^2 + 18*a^2*sin(2*d*x + 2*c)*sin(d*x + c) + 9*a^2*sin(d*x + c)^2 + 6*a^2*cos(d*x + c) + a^2 + 2
*(3*a^2*cos(2*d*x + 2*c) + 3*a^2*cos(d*x + c) + a^2)*cos(3*d*x + 3*c) + 6*(3*a^2*cos(d*x + c) + a^2)*cos(2*d*x
+ 2*c) + 6*(a^2*sin(2*d*x + 2*c) + a^2*sin(d*x + c))*sin(3*d*x + 3*c))*sin(6/5*arctan2(sin(5/2*d*x + 5/2*c),
cos(5/2*d*x + 5/2*c)))^2 + 9*(a^2*cos(3*d*x + 3*c)^2 + 9*a^2*cos(2*d*x + 2*c)^2 + 9*a^2*cos(d*x + c)^2 + a^2*s
in(3*d*x + 3*c)^2 + 9*a^2*sin(2*d*x + 2*c)^2 + 18*a^2*sin(2*d*x + 2*c)*sin(d*x + c) + 9*a^2*sin(d*x + c)^2 + 6
*a^2*cos(d*x + c) + a^2 + 2*(3*a^2*cos(2*d*x + 2*c) + 3*a^2*cos(d*x + c) + a^2)*cos(3*d*x + 3*c) + 6*(3*a^2*co
s(d*x + c) + a^2)*cos(2*d*x + 2*c) + 6*(a^2*sin(2*d*x + 2*c) + a^2*sin(d*x + c))*sin(3*d*x + 3*c))*sin(4/5*arc
tan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + 18*(a^2*cos(3*d*x + 3*c)^2 + 9*a^2*cos(2*d*x + 2*c)^2 +
9*a^2*cos(d*x + c)^2 + a^2*sin(3*d*x + 3*c)^2 + 9*a^2*sin(2*d*x + 2*c)^2 + 18*a^2*sin(2*d*x + 2*c)*sin(d*x + c
) + 9*a^2*sin(d*x + c)^2 + 6*a^2*cos(d*x + c) + a^2 + 2*(3*a^2*cos(2*d*x + 2*c) + 3*a^2*cos(d*x + c) + a^2)*co
s(3*d*x + 3*c) + 6*(3*a^2*cos(d*x + c) + a^2)*cos(2*d*x + 2*c) + 6*(a^2*sin(2*d*x + 2*c) + a^2*sin(d*x + c))*s
in(3*d*x + 3*c))*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(2/5*arctan2(sin(5/2*d*x + 5/
2*c), cos(5/2*d*x + 5/2*c))) + 9*(a^2*cos(3*d*x + 3*c)^2 + 9*a^2*cos(2*d*x + 2*c)^2 + 9*a^2*cos(d*x + c)^2 + a
^2*sin(3*d*x + 3*c)^2 + 9*a^2*sin(2*d*x + 2*c)^2 + 18*a^2*sin(2*d*x + 2*c)*sin(d*x + c) + 9*a^2*sin(d*x + c)^2
+ 6*a^2*cos(d*x + c) + a^2 + 2*(3*a^2*cos(2*d*x + 2*c) + 3*a^2*cos(d*x + c) + a^2)*cos(3*d*x + 3*c) + 6*(3*a^
2*cos(d*x + c) + a^2)*cos(2*d*x + 2*c) + 6*(a^2*sin(2*d*x + 2*c) + a^2*sin(d*x + c))*sin(3*d*x + 3*c))*sin(2/5
*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + a^2 + 2*(3*a^2*cos(2*d*x + 2*c) + 3*a^2*cos(d*x + c)
+ a^2)*cos(3*d*x + 3*c) + 6*(3*a^2*cos(d*x + c) + a^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(3*d*x + 3*c)^2 + 9*a^2*c
os(2*d*x + 2*c)^2 + 9*a^2*cos(d*x + c)^2 + a^2*sin(3*d*x + 3*c)^2 + 9*a^2*sin(2*d*x + 2*c)^2 + 18*a^2*sin(2*d*
x + 2*c)*sin(d*x + c) + 9*a^2*sin(d*x + c)^2 + 6*a^2*cos(d*x + c) + a^2 + 2*(3*a^2*cos(2*d*x + 2*c) + 3*a^2*co
s(d*x + c) + a^2)*cos(3*d*x + 3*c) + 6*(3*a^2*cos(d*x + c) + a^2)*cos(2*d*x + 2*c) + 3*(a^2*cos(3*d*x + 3*c)^2
+ 9*a^2*cos(2*d*x + 2*c)^2 + 9*a^2*cos(d*x + c)^2 + a^2*sin(3*d*x + 3*c)^2 + 9*a^2*sin(2*d*x + 2*c)^2 + 18*a^
2*sin(2*d*x + 2*c)*sin(d*x + c) + 9*a^2*sin(d*x + c)^2 + 6*a^2*cos(d*x + c) + a^2 + 2*(3*a^2*cos(2*d*x + 2*c)
+ 3*a^2*cos(d*x + c) + a^2)*cos(3*d*x + 3*c) + 6*(3*a^2*cos(d*x + c) + a^2)*cos(2*d*x + 2*c) + 6*(a^2*sin(2*d*
x + 2*c) + a^2*sin(d*x + c))*sin(3*d*x + 3*c))*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) +
3*(a^2*cos(3*d*x + 3*c)^2 + 9*a^2*cos(2*d*x + 2*c)^2 + 9*a^2*cos(d*x + c)^2 + a^2*sin(3*d*x + 3*c)^2 + 9*a^2*s
in(2*d*x + 2*c)^2 + 18*a^2*sin(2*d*x + 2*c)*sin(d*x + c) + 9*a^2*sin(d*x + c)^2 + 6*a^2*cos(d*x + c) + a^2 + 2
*(3*a^2*cos(2*d*x + 2*c) + 3*a^2*cos(d*x + c) + a^2)*cos(3*d*x + 3*c) + 6*(3*a^2*cos(d*x + c) + a^2)*cos(2*d*x
+ 2*c) + 6*(a^2*sin(2*d*x + 2*c) + a^2*sin(d*x + c))*sin(3*d*x + 3*c))*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c),
cos(5/2*d*x + 5/2*c))) + 6*(a^2*sin(2*d*x + 2*c) + a^2*sin(d*x + c))*sin(3*d*x + 3*c))*cos(6/5*arctan2(sin(5/2
*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 6*(a^2*cos(3*d*x + 3*c)^2 + 9*a^2*cos(2*d*x + 2*c)^2 + 9*a^2*cos(d*x +
c)^2 + a^2*sin(3*d*x + 3*c)^2 + 9*a^2*sin(2*d*x + 2*c)^2 + 18*a^2*sin(2*d*x + 2*c)*sin(d*x + c) + 9*a^2*sin(d
*x + c)^2 + 6*a^2*cos(d*x + c) + a^2 + 2*(3*a^2*cos(2*d*x + 2*c) + 3*a^2*cos(d*x + c) + a^2)*cos(3*d*x + 3*c)
+ 6*(3*a^2*cos(d*x + c) + a^2)*cos(2*d*x + 2*c) + 3*(a^2*cos(3*d*x + 3*c)^2 + 9*a^2*cos(2*d*x + 2*c)^2 + 9*a^2
*cos(d*x + c)^2 + a^2*sin(3*d*x + 3*c)^2 + 9*a^2*sin(2*d*x + 2*c)^2 + 18*a^2*sin(2*d*x + 2*c)*sin(d*x + c) + 9
*a^2*sin(d*x + c)^2 + 6*a^2*cos(d*x + c) + a^2 + 2*(3*a^2*cos(2*d*x + 2*c) + 3*a^2*cos(d*x + c) + a^2)*cos(3*d
*x + 3*c) + 6*(3*a^2*cos(d*x + c) + a^2)*cos(2*d*x + 2*c) + 6*(a^2*sin(2*d*x + 2*c) + a^2*sin(d*x + c))*sin(3*
d*x + 3*c))*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 6*(a^2*sin(2*d*x + 2*c) + a^2*sin(d
*x + c))*sin(3*d*x + 3*c))*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 6*(a^2*cos(3*d*x + 3
*c)^2 + 9*a^2*cos(2*d*x + 2*c)^2 + 9*a^2*cos(d*x + c)^2 + a^2*sin(3*d*x + 3*c)^2 + 9*a^2*sin(2*d*x + 2*c)^2 +
18*a^2*sin(2*d*x + 2*c)*sin(d*x + c) + 9*a^2*sin(d*x + c)^2 + 6*a^2*cos(d*x + c) + a^2 + 2*(3*a^2*cos(2*d*x +
2*c) + 3*a^2*cos(d*x + c) + a^2)*cos(3*d*x + 3*c) + 6*(3*a^2*cos(d*x + c) + a^2)*cos(2*d*x + 2*c) + 6*(a^2*sin
(2*d*x + 2*c) + a^2*sin(d*x + c))*sin(3*d*x + 3*c))*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)
)) + 6*(a^2*sin(2*d*x + 2*c) + a^2*sin(d*x + c))*sin(3*d*x + 3*c) + 6*((a^2*cos(3*d*x + 3*c)^2 + 9*a^2*cos(2*d
*x + 2*c)^2 + 9*a^2*cos(d*x + c)^2 + a^2*sin(3*d*x + 3*c)^2 + 9*a^2*sin(2*d*x + 2*c)^2 + 18*a^2*sin(2*d*x + 2*
c)*sin(d*x + c) + 9*a^2*sin(d*x + c)^2 + 6*a^2*cos(d*x + c) + a^2 + 2*(3*a^2*cos(2*d*x + 2*c) + 3*a^2*cos(d*x
+ c) + a^2)*cos(3*d*x + 3*c) + 6*(3*a^2*cos(d*x + c) + a^2)*cos(2*d*x + 2*c) + 6*(a^2*sin(2*d*x + 2*c) + a^2*s
in(d*x + c))*sin(3*d*x + 3*c))*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + (a^2*cos(3*d*x +
3*c)^2 + 9*a^2*cos(2*d*x + 2*c)^2 + 9*a^2*cos(d*x + c)^2 + a^2*sin(3*d*x + 3*c)^2 + 9*a^2*sin(2*d*x + 2*c)^2
+ 18*a^2*sin(2*d*x + 2*c)*sin(d*x + c) + 9*a^2*sin(d*x + c)^2 + 6*a^2*cos(d*x + c) + a^2 + 2*(3*a^2*cos(2*d*x
+ 2*c) + 3*a^2*cos(d*x + c) + a^2)*cos(3*d*x + 3*c) + 6*(3*a^2*cos(d*x + c) + a^2)*cos(2*d*x + 2*c) + 6*(a^2*s
in(2*d*x + 2*c) + a^2*sin(d*x + c))*sin(3*d*x + 3*c))*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*
c))))*sin(6/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*d)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 219 vs. \(2 (104) = 208\).

Time = 1.49 (sec) , antiderivative size = 219, normalized size of antiderivative = 1.75 \[ \int \frac {\left (A+C \cos ^2(c+d x)\right ) \sec (c+d x)}{(a+a \cos (c+d x))^{3/2}} \, dx=-\frac {\frac {8 \, A \log \left (\frac {{\left | -2 \, \sqrt {2} + 4 \, \sin \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) \right |}}{{\left | 2 \, \sqrt {2} + 4 \, \sin \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) \right |}}\right )}{a^{\frac {3}{2}} \mathrm {sgn}\left (\cos \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )\right )} + \frac {\sqrt {2} {\left (5 \, A \sqrt {a} - 3 \, C \sqrt {a}\right )} \log \left (\sin \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + 1\right )}{a^{2} \mathrm {sgn}\left (\cos \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )\right )} - \frac {\sqrt {2} {\left (5 \, A \sqrt {a} - 3 \, C \sqrt {a}\right )} \log \left (-\sin \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + 1\right )}{a^{2} \mathrm {sgn}\left (\cos \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )\right )} - \frac {2 \, \sqrt {2} {\left (A \sqrt {a} \sin \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + C \sqrt {a} \sin \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )\right )}}{{\left (\sin \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{2} - 1\right )} a^{2} \mathrm {sgn}\left (\cos \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )\right )}}{8 \, d} \]

[In]

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

[Out]

-1/8*(8*A*log(abs(-2*sqrt(2) + 4*sin(1/2*d*x + 1/2*c))/abs(2*sqrt(2) + 4*sin(1/2*d*x + 1/2*c)))/(a^(3/2)*sgn(c
os(1/2*d*x + 1/2*c))) + sqrt(2)*(5*A*sqrt(a) - 3*C*sqrt(a))*log(sin(1/2*d*x + 1/2*c) + 1)/(a^2*sgn(cos(1/2*d*x
+ 1/2*c))) - sqrt(2)*(5*A*sqrt(a) - 3*C*sqrt(a))*log(-sin(1/2*d*x + 1/2*c) + 1)/(a^2*sgn(cos(1/2*d*x + 1/2*c)
)) - 2*sqrt(2)*(A*sqrt(a)*sin(1/2*d*x + 1/2*c) + C*sqrt(a)*sin(1/2*d*x + 1/2*c))/((sin(1/2*d*x + 1/2*c)^2 - 1)
*a^2*sgn(cos(1/2*d*x + 1/2*c))))/d

Mupad [F(-1)]

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

[In]

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

[Out]

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