\(\int \sin ^4(a+b \log (c x^n)) \, dx\) [21]
Optimal result
Integrand size = 13, antiderivative size = 191 \[
\int \sin ^4\left (a+b \log \left (c x^n\right )\right ) \, dx=\frac {24 b^4 n^4 x}{1+20 b^2 n^2+64 b^4 n^4}-\frac {24 b^3 n^3 x \cos \left (a+b \log \left (c x^n\right )\right ) \sin \left (a+b \log \left (c x^n\right )\right )}{1+20 b^2 n^2+64 b^4 n^4}+\frac {12 b^2 n^2 x \sin ^2\left (a+b \log \left (c x^n\right )\right )}{1+20 b^2 n^2+64 b^4 n^4}-\frac {4 b n x \cos \left (a+b \log \left (c x^n\right )\right ) \sin ^3\left (a+b \log \left (c x^n\right )\right )}{1+16 b^2 n^2}+\frac {x \sin ^4\left (a+b \log \left (c x^n\right )\right )}{1+16 b^2 n^2}
\]
[Out]
24*b^4*n^4*x/(64*b^4*n^4+20*b^2*n^2+1)-24*b^3*n^3*x*cos(a+b*ln(c*x^n))*sin(a+b*ln(c*x^n))/(64*b^4*n^4+20*b^2*n
^2+1)+12*b^2*n^2*x*sin(a+b*ln(c*x^n))^2/(64*b^4*n^4+20*b^2*n^2+1)-4*b*n*x*cos(a+b*ln(c*x^n))*sin(a+b*ln(c*x^n)
)^3/(16*b^2*n^2+1)+x*sin(a+b*ln(c*x^n))^4/(16*b^2*n^2+1)
Rubi [A] (verified)
Time = 0.06 (sec) , antiderivative size = 191, normalized size of antiderivative = 1.00,
number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {4565, 8}
\[
\int \sin ^4\left (a+b \log \left (c x^n\right )\right ) \, dx=\frac {x \sin ^4\left (a+b \log \left (c x^n\right )\right )}{16 b^2 n^2+1}-\frac {4 b n x \sin ^3\left (a+b \log \left (c x^n\right )\right ) \cos \left (a+b \log \left (c x^n\right )\right )}{16 b^2 n^2+1}+\frac {12 b^2 n^2 x \sin ^2\left (a+b \log \left (c x^n\right )\right )}{64 b^4 n^4+20 b^2 n^2+1}-\frac {24 b^3 n^3 x \sin \left (a+b \log \left (c x^n\right )\right ) \cos \left (a+b \log \left (c x^n\right )\right )}{64 b^4 n^4+20 b^2 n^2+1}+\frac {24 b^4 n^4 x}{64 b^4 n^4+20 b^2 n^2+1}
\]
[In]
Int[Sin[a + b*Log[c*x^n]]^4,x]
[Out]
(24*b^4*n^4*x)/(1 + 20*b^2*n^2 + 64*b^4*n^4) - (24*b^3*n^3*x*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(1 +
20*b^2*n^2 + 64*b^4*n^4) + (12*b^2*n^2*x*Sin[a + b*Log[c*x^n]]^2)/(1 + 20*b^2*n^2 + 64*b^4*n^4) - (4*b*n*x*Co
s[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]]^3)/(1 + 16*b^2*n^2) + (x*Sin[a + b*Log[c*x^n]]^4)/(1 + 16*b^2*n^2)
Rule 8
Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]
Rule 4565
Int[Sin[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*(d_.)]^(p_), x_Symbol] :> Simp[x*(Sin[d*(a + b*Log[c*x^n])]^p/(b
^2*d^2*n^2*p^2 + 1)), x] + (Dist[b^2*d^2*n^2*p*((p - 1)/(b^2*d^2*n^2*p^2 + 1)), Int[Sin[d*(a + b*Log[c*x^n])]^
(p - 2), x], x] - Simp[b*d*n*p*x*Cos[d*(a + b*Log[c*x^n])]*(Sin[d*(a + b*Log[c*x^n])]^(p - 1)/(b^2*d^2*n^2*p^2
+ 1)), x]) /; FreeQ[{a, b, c, d, n}, x] && IGtQ[p, 1] && NeQ[b^2*d^2*n^2*p^2 + 1, 0]
Rubi steps \begin{align*}
\text {integral}& = -\frac {4 b n x \cos \left (a+b \log \left (c x^n\right )\right ) \sin ^3\left (a+b \log \left (c x^n\right )\right )}{1+16 b^2 n^2}+\frac {x \sin ^4\left (a+b \log \left (c x^n\right )\right )}{1+16 b^2 n^2}+\frac {\left (12 b^2 n^2\right ) \int \sin ^2\left (a+b \log \left (c x^n\right )\right ) \, dx}{1+16 b^2 n^2} \\ & = -\frac {24 b^3 n^3 x \cos \left (a+b \log \left (c x^n\right )\right ) \sin \left (a+b \log \left (c x^n\right )\right )}{1+20 b^2 n^2+64 b^4 n^4}+\frac {12 b^2 n^2 x \sin ^2\left (a+b \log \left (c x^n\right )\right )}{1+20 b^2 n^2+64 b^4 n^4}-\frac {4 b n x \cos \left (a+b \log \left (c x^n\right )\right ) \sin ^3\left (a+b \log \left (c x^n\right )\right )}{1+16 b^2 n^2}+\frac {x \sin ^4\left (a+b \log \left (c x^n\right )\right )}{1+16 b^2 n^2}+\frac {\left (24 b^4 n^4\right ) \int 1 \, dx}{1+20 b^2 n^2+64 b^4 n^4} \\ & = \frac {24 b^4 n^4 x}{1+20 b^2 n^2+64 b^4 n^4}-\frac {24 b^3 n^3 x \cos \left (a+b \log \left (c x^n\right )\right ) \sin \left (a+b \log \left (c x^n\right )\right )}{1+20 b^2 n^2+64 b^4 n^4}+\frac {12 b^2 n^2 x \sin ^2\left (a+b \log \left (c x^n\right )\right )}{1+20 b^2 n^2+64 b^4 n^4}-\frac {4 b n x \cos \left (a+b \log \left (c x^n\right )\right ) \sin ^3\left (a+b \log \left (c x^n\right )\right )}{1+16 b^2 n^2}+\frac {x \sin ^4\left (a+b \log \left (c x^n\right )\right )}{1+16 b^2 n^2} \\
\end{align*}
Mathematica [A] (verified)
Time = 0.30 (sec) , antiderivative size = 168, normalized size of antiderivative = 0.88
\[
\int \sin ^4\left (a+b \log \left (c x^n\right )\right ) \, dx=\frac {x \left (3+60 b^2 n^2+192 b^4 n^4-4 \left (1+16 b^2 n^2\right ) \cos \left (2 \left (a+b \log \left (c x^n\right )\right )\right )+\left (1+4 b^2 n^2\right ) \cos \left (4 \left (a+b \log \left (c x^n\right )\right )\right )-8 b n \sin \left (2 \left (a+b \log \left (c x^n\right )\right )\right )-128 b^3 n^3 \sin \left (2 \left (a+b \log \left (c x^n\right )\right )\right )+4 b n \sin \left (4 \left (a+b \log \left (c x^n\right )\right )\right )+16 b^3 n^3 \sin \left (4 \left (a+b \log \left (c x^n\right )\right )\right )\right )}{8 \left (1+20 b^2 n^2+64 b^4 n^4\right )}
\]
[In]
Integrate[Sin[a + b*Log[c*x^n]]^4,x]
[Out]
(x*(3 + 60*b^2*n^2 + 192*b^4*n^4 - 4*(1 + 16*b^2*n^2)*Cos[2*(a + b*Log[c*x^n])] + (1 + 4*b^2*n^2)*Cos[4*(a + b
*Log[c*x^n])] - 8*b*n*Sin[2*(a + b*Log[c*x^n])] - 128*b^3*n^3*Sin[2*(a + b*Log[c*x^n])] + 4*b*n*Sin[4*(a + b*L
og[c*x^n])] + 16*b^3*n^3*Sin[4*(a + b*Log[c*x^n])]))/(8*(1 + 20*b^2*n^2 + 64*b^4*n^4))
Maple [A] (verified)
Time = 4.41 (sec) , antiderivative size = 184, normalized size of antiderivative = 0.96
| | |
| method | result | size |
| | |
| parallelrisch |
\(\frac {x \left (4 \left (-16 b^{2} n^{2}-1\right ) \cos \left (2 b \ln \left (c \,x^{n}\right )+2 a \right )+192 b^{4} n^{4}-128 b^{3} n^{3} \sin \left (2 b \ln \left (c \,x^{n}\right )+2 a \right )+16 b^{3} n^{3} \sin \left (4 b \ln \left (c \,x^{n}\right )+4 a \right )+4 b^{2} n^{2} \cos \left (4 b \ln \left (c \,x^{n}\right )+4 a \right )+60 b^{2} n^{2}-8 b n \sin \left (2 b \ln \left (c \,x^{n}\right )+2 a \right )+4 b n \sin \left (4 b \ln \left (c \,x^{n}\right )+4 a \right )+\cos \left (4 b \ln \left (c \,x^{n}\right )+4 a \right )+3\right )}{512 b^{4} n^{4}+160 b^{2} n^{2}+8}\) |
\(184\) |
| default |
\(\frac {3 x}{8}-\frac {{\mathrm e}^{\frac {\ln \left (c \,x^{n}\right )}{n}-\frac {\ln \left (c \right )}{n}} \cos \left (2 b \ln \left (c \,x^{n}\right )+2 a \right )}{2 n^{2} \left (\frac {1}{n^{2}}+4 b^{2}\right )}-\frac {b \,{\mathrm e}^{\frac {\ln \left (c \,x^{n}\right )}{n}-\frac {\ln \left (c \right )}{n}} \sin \left (2 b \ln \left (c \,x^{n}\right )+2 a \right )}{n \left (\frac {1}{n^{2}}+4 b^{2}\right )}+\frac {{\mathrm e}^{\frac {\ln \left (c \,x^{n}\right )}{n}-\frac {\ln \left (c \right )}{n}} \cos \left (4 b \ln \left (c \,x^{n}\right )+4 a \right )}{8 n^{2} \left (\frac {1}{n^{2}}+16 b^{2}\right )}+\frac {b \,{\mathrm e}^{\frac {\ln \left (c \,x^{n}\right )}{n}-\frac {\ln \left (c \right )}{n}} \sin \left (4 b \ln \left (c \,x^{n}\right )+4 a \right )}{2 n \left (\frac {1}{n^{2}}+16 b^{2}\right )}\) |
\(203\) |
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[In]
int(sin(a+b*ln(c*x^n))^4,x,method=_RETURNVERBOSE)
[Out]
1/8*x*(4*(-16*b^2*n^2-1)*cos(2*b*ln(c*x^n)+2*a)+192*b^4*n^4-128*b^3*n^3*sin(2*b*ln(c*x^n)+2*a)+16*b^3*n^3*sin(
4*b*ln(c*x^n)+4*a)+4*b^2*n^2*cos(4*b*ln(c*x^n)+4*a)+60*b^2*n^2-8*b*n*sin(2*b*ln(c*x^n)+2*a)+4*b*n*sin(4*b*ln(c
*x^n)+4*a)+cos(4*b*ln(c*x^n)+4*a)+3)/(64*b^4*n^4+20*b^2*n^2+1)
Fricas [A] (verification not implemented)
none
Time = 0.25 (sec) , antiderivative size = 165, normalized size of antiderivative = 0.86
\[
\int \sin ^4\left (a+b \log \left (c x^n\right )\right ) \, dx=\frac {{\left (4 \, b^{2} n^{2} + 1\right )} x \cos \left (b n \log \left (x\right ) + b \log \left (c\right ) + a\right )^{4} - 2 \, {\left (10 \, b^{2} n^{2} + 1\right )} x \cos \left (b n \log \left (x\right ) + b \log \left (c\right ) + a\right )^{2} + {\left (24 \, b^{4} n^{4} + 16 \, b^{2} n^{2} + 1\right )} x + 4 \, {\left ({\left (4 \, b^{3} n^{3} + b n\right )} x \cos \left (b n \log \left (x\right ) + b \log \left (c\right ) + a\right )^{3} - {\left (10 \, b^{3} n^{3} + b n\right )} x \cos \left (b n \log \left (x\right ) + b \log \left (c\right ) + a\right )\right )} \sin \left (b n \log \left (x\right ) + b \log \left (c\right ) + a\right )}{64 \, b^{4} n^{4} + 20 \, b^{2} n^{2} + 1}
\]
[In]
integrate(sin(a+b*log(c*x^n))^4,x, algorithm="fricas")
[Out]
((4*b^2*n^2 + 1)*x*cos(b*n*log(x) + b*log(c) + a)^4 - 2*(10*b^2*n^2 + 1)*x*cos(b*n*log(x) + b*log(c) + a)^2 +
(24*b^4*n^4 + 16*b^2*n^2 + 1)*x + 4*((4*b^3*n^3 + b*n)*x*cos(b*n*log(x) + b*log(c) + a)^3 - (10*b^3*n^3 + b*n)
*x*cos(b*n*log(x) + b*log(c) + a))*sin(b*n*log(x) + b*log(c) + a))/(64*b^4*n^4 + 20*b^2*n^2 + 1)
Sympy [F]
\[
\int \sin ^4\left (a+b \log \left (c x^n\right )\right ) \, dx=\begin {cases} \int \sin ^{4}{\left (a - \frac {i \log {\left (c x^{n} \right )}}{2 n} \right )}\, dx & \text {for}\: b = - \frac {i}{2 n} \\\int \sin ^{4}{\left (a - \frac {i \log {\left (c x^{n} \right )}}{4 n} \right )}\, dx & \text {for}\: b = - \frac {i}{4 n} \\\int \sin ^{4}{\left (a + \frac {i \log {\left (c x^{n} \right )}}{4 n} \right )}\, dx & \text {for}\: b = \frac {i}{4 n} \\\int \sin ^{4}{\left (a + \frac {i \log {\left (c x^{n} \right )}}{2 n} \right )}\, dx & \text {for}\: b = \frac {i}{2 n} \\\frac {24 b^{4} n^{4} x \sin ^{4}{\left (a + b \log {\left (c x^{n} \right )} \right )}}{64 b^{4} n^{4} + 20 b^{2} n^{2} + 1} + \frac {48 b^{4} n^{4} x \sin ^{2}{\left (a + b \log {\left (c x^{n} \right )} \right )} \cos ^{2}{\left (a + b \log {\left (c x^{n} \right )} \right )}}{64 b^{4} n^{4} + 20 b^{2} n^{2} + 1} + \frac {24 b^{4} n^{4} x \cos ^{4}{\left (a + b \log {\left (c x^{n} \right )} \right )}}{64 b^{4} n^{4} + 20 b^{2} n^{2} + 1} - \frac {40 b^{3} n^{3} x \sin ^{3}{\left (a + b \log {\left (c x^{n} \right )} \right )} \cos {\left (a + b \log {\left (c x^{n} \right )} \right )}}{64 b^{4} n^{4} + 20 b^{2} n^{2} + 1} - \frac {24 b^{3} n^{3} x \sin {\left (a + b \log {\left (c x^{n} \right )} \right )} \cos ^{3}{\left (a + b \log {\left (c x^{n} \right )} \right )}}{64 b^{4} n^{4} + 20 b^{2} n^{2} + 1} + \frac {16 b^{2} n^{2} x \sin ^{4}{\left (a + b \log {\left (c x^{n} \right )} \right )}}{64 b^{4} n^{4} + 20 b^{2} n^{2} + 1} + \frac {12 b^{2} n^{2} x \sin ^{2}{\left (a + b \log {\left (c x^{n} \right )} \right )} \cos ^{2}{\left (a + b \log {\left (c x^{n} \right )} \right )}}{64 b^{4} n^{4} + 20 b^{2} n^{2} + 1} - \frac {4 b n x \sin ^{3}{\left (a + b \log {\left (c x^{n} \right )} \right )} \cos {\left (a + b \log {\left (c x^{n} \right )} \right )}}{64 b^{4} n^{4} + 20 b^{2} n^{2} + 1} + \frac {x \sin ^{4}{\left (a + b \log {\left (c x^{n} \right )} \right )}}{64 b^{4} n^{4} + 20 b^{2} n^{2} + 1} & \text {otherwise} \end {cases}
\]
[In]
integrate(sin(a+b*ln(c*x**n))**4,x)
[Out]
Piecewise((Integral(sin(a - I*log(c*x**n)/(2*n))**4, x), Eq(b, -I/(2*n))), (Integral(sin(a - I*log(c*x**n)/(4*
n))**4, x), Eq(b, -I/(4*n))), (Integral(sin(a + I*log(c*x**n)/(4*n))**4, x), Eq(b, I/(4*n))), (Integral(sin(a
+ I*log(c*x**n)/(2*n))**4, x), Eq(b, I/(2*n))), (24*b**4*n**4*x*sin(a + b*log(c*x**n))**4/(64*b**4*n**4 + 20*b
**2*n**2 + 1) + 48*b**4*n**4*x*sin(a + b*log(c*x**n))**2*cos(a + b*log(c*x**n))**2/(64*b**4*n**4 + 20*b**2*n**
2 + 1) + 24*b**4*n**4*x*cos(a + b*log(c*x**n))**4/(64*b**4*n**4 + 20*b**2*n**2 + 1) - 40*b**3*n**3*x*sin(a + b
*log(c*x**n))**3*cos(a + b*log(c*x**n))/(64*b**4*n**4 + 20*b**2*n**2 + 1) - 24*b**3*n**3*x*sin(a + b*log(c*x**
n))*cos(a + b*log(c*x**n))**3/(64*b**4*n**4 + 20*b**2*n**2 + 1) + 16*b**2*n**2*x*sin(a + b*log(c*x**n))**4/(64
*b**4*n**4 + 20*b**2*n**2 + 1) + 12*b**2*n**2*x*sin(a + b*log(c*x**n))**2*cos(a + b*log(c*x**n))**2/(64*b**4*n
**4 + 20*b**2*n**2 + 1) - 4*b*n*x*sin(a + b*log(c*x**n))**3*cos(a + b*log(c*x**n))/(64*b**4*n**4 + 20*b**2*n**
2 + 1) + x*sin(a + b*log(c*x**n))**4/(64*b**4*n**4 + 20*b**2*n**2 + 1), True))
Maxima [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 1078 vs. \(2 (191) = 382\).
Time = 0.25 (sec) , antiderivative size = 1078, normalized size of antiderivative = 5.64
\[
\int \sin ^4\left (a+b \log \left (c x^n\right )\right ) \, dx=\text {Too large to display}
\]
[In]
integrate(sin(a+b*log(c*x^n))^4,x, algorithm="maxima")
[Out]
1/16*((16*(b^3*cos(4*b*log(c))*sin(8*b*log(c)) - b^3*cos(8*b*log(c))*sin(4*b*log(c)) + b^3*sin(4*b*log(c)))*n^
3 + 4*(b^2*cos(8*b*log(c))*cos(4*b*log(c)) + b^2*sin(8*b*log(c))*sin(4*b*log(c)) + b^2*cos(4*b*log(c)))*n^2 +
4*(b*cos(4*b*log(c))*sin(8*b*log(c)) - b*cos(8*b*log(c))*sin(4*b*log(c)) + b*sin(4*b*log(c)))*n + cos(8*b*log(
c))*cos(4*b*log(c)) + sin(8*b*log(c))*sin(4*b*log(c)) + cos(4*b*log(c)))*x*cos(4*b*log(x^n) + 4*a) - 4*(32*(b^
3*cos(4*b*log(c))*sin(6*b*log(c)) - b^3*cos(6*b*log(c))*sin(4*b*log(c)) + b^3*cos(2*b*log(c))*sin(4*b*log(c))
- b^3*cos(4*b*log(c))*sin(2*b*log(c)))*n^3 + 16*(b^2*cos(6*b*log(c))*cos(4*b*log(c)) + b^2*cos(4*b*log(c))*cos
(2*b*log(c)) + b^2*sin(6*b*log(c))*sin(4*b*log(c)) + b^2*sin(4*b*log(c))*sin(2*b*log(c)))*n^2 + 2*(b*cos(4*b*l
og(c))*sin(6*b*log(c)) - b*cos(6*b*log(c))*sin(4*b*log(c)) + b*cos(2*b*log(c))*sin(4*b*log(c)) - b*cos(4*b*log
(c))*sin(2*b*log(c)))*n + cos(6*b*log(c))*cos(4*b*log(c)) + cos(4*b*log(c))*cos(2*b*log(c)) + sin(6*b*log(c))*
sin(4*b*log(c)) + sin(4*b*log(c))*sin(2*b*log(c)))*x*cos(2*b*log(x^n) + 2*a) + (16*(b^3*cos(8*b*log(c))*cos(4*
b*log(c)) + b^3*sin(8*b*log(c))*sin(4*b*log(c)) + b^3*cos(4*b*log(c)))*n^3 - 4*(b^2*cos(4*b*log(c))*sin(8*b*lo
g(c)) - b^2*cos(8*b*log(c))*sin(4*b*log(c)) + b^2*sin(4*b*log(c)))*n^2 + 4*(b*cos(8*b*log(c))*cos(4*b*log(c))
+ b*sin(8*b*log(c))*sin(4*b*log(c)) + b*cos(4*b*log(c)))*n - cos(4*b*log(c))*sin(8*b*log(c)) + cos(8*b*log(c))
*sin(4*b*log(c)) - sin(4*b*log(c)))*x*sin(4*b*log(x^n) + 4*a) - 4*(32*(b^3*cos(6*b*log(c))*cos(4*b*log(c)) + b
^3*cos(4*b*log(c))*cos(2*b*log(c)) + b^3*sin(6*b*log(c))*sin(4*b*log(c)) + b^3*sin(4*b*log(c))*sin(2*b*log(c))
)*n^3 - 16*(b^2*cos(4*b*log(c))*sin(6*b*log(c)) - b^2*cos(6*b*log(c))*sin(4*b*log(c)) + b^2*cos(2*b*log(c))*si
n(4*b*log(c)) - b^2*cos(4*b*log(c))*sin(2*b*log(c)))*n^2 + 2*(b*cos(6*b*log(c))*cos(4*b*log(c)) + b*cos(4*b*lo
g(c))*cos(2*b*log(c)) + b*sin(6*b*log(c))*sin(4*b*log(c)) + b*sin(4*b*log(c))*sin(2*b*log(c)))*n - cos(4*b*log
(c))*sin(6*b*log(c)) + cos(6*b*log(c))*sin(4*b*log(c)) - cos(2*b*log(c))*sin(4*b*log(c)) + cos(4*b*log(c))*sin
(2*b*log(c)))*x*sin(2*b*log(x^n) + 2*a) + 6*(64*(b^4*cos(4*b*log(c))^2 + b^4*sin(4*b*log(c))^2)*n^4 + 20*(b^2*
cos(4*b*log(c))^2 + b^2*sin(4*b*log(c))^2)*n^2 + cos(4*b*log(c))^2 + sin(4*b*log(c))^2)*x)/(64*(b^4*cos(4*b*lo
g(c))^2 + b^4*sin(4*b*log(c))^2)*n^4 + 20*(b^2*cos(4*b*log(c))^2 + b^2*sin(4*b*log(c))^2)*n^2 + cos(4*b*log(c)
)^2 + sin(4*b*log(c))^2)
Giac [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 16422 vs. \(2 (191) = 382\).
Time = 0.73 (sec) , antiderivative size = 16422, normalized size of antiderivative = 85.98
\[
\int \sin ^4\left (a+b \log \left (c x^n\right )\right ) \, dx=\text {Too large to display}
\]
[In]
integrate(sin(a+b*log(c*x^n))^4,x, algorithm="giac")
[Out]
3/8*x + 1/16*(256*b^3*n^3*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(ab
s(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a) + 256*b^3*n^3*x*e^(-pi*b*n*sgn(x) + pi*b*n -
pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a
)^2*tan(a) - 32*b^3*n^3*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*
log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)*tan(a)^2 - 32*b^3*n^3*x*e^(-2*pi*b*n*sgn(x) + 2
*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c
)))^2*tan(2*a)*tan(a)^2 + 256*b^3*n^3*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x))
+ 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(2*a)^2*tan(a)^2 + 256*b^3*n^3*x*e^(-pi*b*n*sgn(x
) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)
))*tan(2*a)^2*tan(a)^2 - 32*b^3*n^3*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(ab
s(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 - 32*b^3*n^3*x*e^(-2*pi*b*
n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) + b
*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + 4*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(
2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 - 64*b^2*n^2
*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(
x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 - 64*b^2*n^2*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan
(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + 4*b^2*n^2
*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n
*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 - 32*b^3*n^3*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(
c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a) - 32*b
^3*n^3*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*t
an(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a) - 256*b^3*n^3*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)
*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(2*a)^2 - 256*b^3*n^3*x*e^
(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x))
+ b*log(abs(c)))*tan(2*a)^2 - 32*b^3*n^3*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*l
og(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 - 32*b^3*n^3*x*e^(-2*pi*b*n*sg
n(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) + b*log
(abs(c)))^2*tan(2*a)^2 + 256*b^3*n^3*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) +
2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a) + 256*b^3*n^3*x*e^(-pi*b*n*sgn(x) + pi*b*n -
pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a)
- 256*b^3*n^3*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan
(2*a)^2*tan(a) - 256*b^3*n^3*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*lo
g(abs(c)))^2*tan(2*a)^2*tan(a) + 256*b^3*n^3*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs
(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a) + 256*b^3*n^3*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan
(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a) + 256*b^3*n^3*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c)
- pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(a)^2 + 256*b^3*n^3
*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs
(x)) + b*log(abs(c)))*tan(a)^2 + 32*b^3*n^3*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*
n*log(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a)^2 + 32*b^3*n^3*x*e^(-2*pi*b*n*s
gn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) + b*lo
g(abs(c)))^2*tan(a)^2 - 32*b^3*n^3*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs
(x)) + 2*b*log(abs(c)))^2*tan(2*a)*tan(a)^2 - 32*b^3*n^3*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*
pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)*tan(a)^2 + 32*b^3*n^3*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*
n + 2*pi*b*sgn(c) - 2*pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)*tan(a)^2 + 32*b^3*n^3*x*e^(-2*pi*b
*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)*tan(a)^2 - 32*b
^3*n^3*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(
2*a)^2*tan(a)^2 - 32*b^3*n^3*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x))
+ 2*b*log(abs(c)))*tan(2*a)^2*tan(a)^2 + 256*b^3*n^3*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(b*n
*log(abs(x)) + b*log(abs(c)))*tan(2*a)^2*tan(a)^2 + 256*b^3*n^3*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + p
i*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(2*a)^2*tan(a)^2 + 4*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*
pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*
a)^2 + 64*b^2*n^2*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2
*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 64*b^2*n^2*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + p
i*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 4*b^2*n^2*
x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*
log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 256*b^2*n^2*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(
2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(2*a)^2*tan(a) + 256*b^2*n^2*x*
e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)
) + b*log(abs(c)))*tan(2*a)^2*tan(a) - 4*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan
(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a)^2 - 64*b^2*n^2*x*e^(pi*b
*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*lo
g(abs(c)))^2*tan(a)^2 - 64*b^2*n^2*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) +
2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a)^2 - 4*b^2*n^2*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*
n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*
tan(a)^2 - 16*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*lo
g(abs(c)))*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)*tan(a)^2 - 16*b^2*n^2*x*e^(-2*pi*b*n*sgn(x) + 2*pi*
b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*
tan(2*a)*tan(a)^2 + 4*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x))
+ 2*b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + 64*b^2*n^2*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*
b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + 64*b^2*n^2*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(
c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + 4*b^2*n^2*x*e^(-2*pi*b*n*sgn(x) +
2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 - 4*b^2*n^2*
x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*ta
n(a)^2 - 64*b^2*n^2*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*t
an(2*a)^2*tan(a)^2 - 64*b^2*n^2*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log
(abs(c)))^2*tan(2*a)^2*tan(a)^2 - 4*b^2*n^2*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(b*n
*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 - 256*b^3*n^3*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) -
pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c))) - 256*b^3*n^3*x*e^(-pi*b
*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*lo
g(abs(c))) + 32*b^3*n^3*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*
log(abs(c)))*tan(b*n*log(abs(x)) + b*log(abs(c)))^2 + 32*b^3*n^3*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn
(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) + b*log(abs(c)))^2 - 32*b^3*n^3*x*e
^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a) - 3
2*b^3*n^3*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^
2*tan(2*a) + 32*b^3*n^3*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(b*n*log(abs(x)) + b*log(
abs(c)))^2*tan(2*a) + 32*b^3*n^3*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(b*n*log(abs(x)
) + b*log(abs(c)))^2*tan(2*a) - 32*b^3*n^3*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n
*log(abs(x)) + 2*b*log(abs(c)))*tan(2*a)^2 - 32*b^3*n^3*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*p
i*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(2*a)^2 - 256*b^3*n^3*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(
c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(2*a)^2 - 256*b^3*n^3*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*s
gn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(2*a)^2 - 256*b^3*n^3*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b
*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(a) - 256*b^3*n^3*x*e^(-pi*b*n*sgn(x) + pi*b*n -
pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(a) + 256*b^3*n^3*x*e^(pi*b*n*sgn(x) - pi*b
*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a) + 256*b^3*n^3*x*e^(-pi*b*n*sgn(x) + pi*
b*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a) - 256*b^3*n^3*x*e^(pi*b*n*sgn(x) - pi*
b*n + pi*b*sgn(c) - pi*b)*tan(2*a)^2*tan(a) - 256*b^3*n^3*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*t
an(2*a)^2*tan(a) + 16*b*n*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(ab
s(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a) + 16*b*n*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b
*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*t
an(a) + 32*b^3*n^3*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(a
bs(c)))*tan(a)^2 + 32*b^3*n^3*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x))
+ 2*b*log(abs(c)))*tan(a)^2 + 256*b^3*n^3*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x
)) + b*log(abs(c)))*tan(a)^2 + 256*b^3*n^3*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(
x)) + b*log(abs(c)))*tan(a)^2 + 32*b^3*n^3*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*a)*
tan(a)^2 + 32*b^3*n^3*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*a)*tan(a)^2 - 8*b*n*x*e
^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(
abs(x)) + b*log(abs(c)))^2*tan(2*a)*tan(a)^2 - 8*b*n*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b
)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)*tan(a)^2 + 16*b*n
*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(
x)) + b*log(abs(c)))*tan(2*a)^2*tan(a)^2 + 16*b*n*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n
*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(2*a)^2*tan(a)^2 - 8*b*n*x*e^(2*pi*b
*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) +
b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 - 8*b*n*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*
b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 - 4*b^2*n^2*x*e^
(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(a
bs(x)) + b*log(abs(c)))^2 + 64*b^2*n^2*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x))
+ 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2 + 64*b^2*n^2*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*
sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2 - 4*b^2*n^2*x
*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*l
og(abs(x)) + b*log(abs(c)))^2 - 16*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n
*log(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a) - 16*b^2*n^2*x*e^(-2*pi*b*n*sg
n(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) + b*log
(abs(c)))^2*tan(2*a) + 4*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x
)) + 2*b*log(abs(c)))^2*tan(2*a)^2 - 64*b^2*n^2*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*lo
g(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2 - 64*b^2*n^2*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(
2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2 + 4*b^2*n^2*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c)
+ 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2 - 4*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n +
2*pi*b*sgn(c) - 2*pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 64*b^2*n^2*x*e^(pi*b*n*sgn(x) - p
i*b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 64*b^2*n^2*x*e^(-pi*b*n*sgn(x)
+ pi*b*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 - 4*b^2*n^2*x*e^(-2*pi*b*n*s
gn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 256*b^2*n^2*x*e
^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x))
+ b*log(abs(c)))*tan(a) + 256*b^2*n^2*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x))
+ 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(a) + 256*b^2*n^2*x*e^(pi*b*n*sgn(x) - pi*b*n +
pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(2*a)^2*tan(a) + 256*b^2*n^2*x*e^(-pi*b*n*sgn(x) +
pi*b*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(2*a)^2*tan(a) - 4*b^2*n^2*x*e^(2*pi*b*n
*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(a)^2 + 64*b^2*n^2*
x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(a)^2 + 64*b^2
*n^2*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(a)^2 -
4*b^2*n^2*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^
2*tan(a)^2 + 4*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(b*n*log(abs(x)) + b*log(a
bs(c)))^2*tan(a)^2 - 64*b^2*n^2*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(
abs(c)))^2*tan(a)^2 - 64*b^2*n^2*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*lo
g(abs(c)))^2*tan(a)^2 + 4*b^2*n^2*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(b*n*log(abs(x
)) + b*log(abs(c)))^2*tan(a)^2 - 16*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*
n*log(abs(x)) + 2*b*log(abs(c)))*tan(2*a)*tan(a)^2 - 16*b^2*n^2*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(
c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(2*a)*tan(a)^2 - 4*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*p
i*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*a)^2*tan(a)^2 + 64*b^2*n^2*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - p
i*b)*tan(2*a)^2*tan(a)^2 + 64*b^2*n^2*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*a)^2*tan(a)^2 -
4*b^2*n^2*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*a)^2*tan(a)^2 + x*e^(2*pi*b*n*sgn(
x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log
(abs(c)))^2*tan(2*a)^2*tan(a)^2 - 4*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) +
2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 - 4*x*e^(-pi*b*n*sgn(x) + pi*b*n
- pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2
*a)^2*tan(a)^2 + x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(ab
s(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + 32*b^3*n^3*x*e^(2*pi*b*n*sgn(x) - 2*pi*b
*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c))) + 32*b^3*n^3*x*e^(-2*pi*b*n*sgn(x) + 2*p
i*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c))) - 256*b^3*n^3*x*e^(pi*b*n*sgn(x) - pi
*b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c))) - 256*b^3*n^3*x*e^(-pi*b*n*sgn(x) + pi*b*n - p
i*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c))) + 32*b^3*n^3*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*
sgn(c) - 2*pi*b)*tan(2*a) + 32*b^3*n^3*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*a) - 8
*b*n*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(
b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a) - 8*b*n*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)
*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a) - 16*b*n*x*e^(pi*b
*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*lo
g(abs(c)))*tan(2*a)^2 - 16*b*n*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*
log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(2*a)^2 - 8*b*n*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*
b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2
- 8*b*n*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*ta
n(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 - 256*b^3*n^3*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b
)*tan(a) - 256*b^3*n^3*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(a) + 16*b*n*x*e^(pi*b*n*sgn(x) -
pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^
2*tan(a) + 16*b*n*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^
2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a) - 16*b*n*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan
(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2*tan(a) - 16*b*n*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c)
+ pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2*tan(a) + 16*b*n*x*e^(pi*b*n*sgn(x) - pi*b*n + pi
*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a) + 16*b*n*x*e^(-pi*b*n*sgn(x) + pi*b
*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a) + 16*b*n*x*e^(pi*b*n*sgn(x)
- pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))
*tan(a)^2 + 16*b*n*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))
^2*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(a)^2 + 8*b*n*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*p
i*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a)^2 + 8*b*n*x*e^(-2*
pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)
) + b*log(abs(c)))^2*tan(a)^2 - 8*b*n*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(
abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)*tan(a)^2 - 8*b*n*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi
*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)*tan(a)^2 + 8*b*n*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*p
i*b*sgn(c) - 2*pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)*tan(a)^2 + 8*b*n*x*e^(-2*pi*b*n*sgn(x) +
2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)*tan(a)^2 - 8*b*n*x*e^(2*pi*
b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(2*a)^2*tan(a)^2 -
8*b*n*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan
(2*a)^2*tan(a)^2 + 16*b*n*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)
))*tan(2*a)^2*tan(a)^2 + 16*b*n*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log
(abs(c)))*tan(2*a)^2*tan(a)^2 - 4*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*
log(abs(x)) + 2*b*log(abs(c)))^2 - 64*b^2*n^2*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(
abs(x)) + 2*b*log(abs(c)))^2 - 64*b^2*n^2*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs
(x)) + 2*b*log(abs(c)))^2 - 4*b^2*n^2*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log
(abs(x)) + 2*b*log(abs(c)))^2 + 4*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(b*n*lo
g(abs(x)) + b*log(abs(c)))^2 + 64*b^2*n^2*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)
) + b*log(abs(c)))^2 + 64*b^2*n^2*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*l
og(abs(c)))^2 + 4*b^2*n^2*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(b*n*log(abs(x)) + b*l
og(abs(c)))^2 - 16*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2
*b*log(abs(c)))*tan(2*a) - 16*b^2*n^2*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log
(abs(x)) + 2*b*log(abs(c)))*tan(2*a) - 4*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan
(2*a)^2 - 64*b^2*n^2*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*a)^2 - 64*b^2*n^2*x*e^(-pi*b*n*sg
n(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*a)^2 - 4*b^2*n^2*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) +
2*pi*b)*tan(2*a)^2 + x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log
(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 4*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) -
pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 4*x*e^(-p
i*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b
*log(abs(c)))^2*tan(2*a)^2 + x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x))
+ 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 256*b^2*n^2*x*e^(pi*b*n*sgn(x) - pi*b
*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(a) + 256*b^2*n^2*x*e^(-pi*b*n*sgn(x) + pi*b*
n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(a) + 16*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sg
n(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(2*a)^2*tan(a)
+ 16*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*lo
g(abs(x)) + b*log(abs(c)))*tan(2*a)^2*tan(a) + 4*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*p
i*b)*tan(a)^2 + 64*b^2*n^2*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(a)^2 + 64*b^2*n^2*x*e^(-pi*b*
n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(a)^2 + 4*b^2*n^2*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c)
+ 2*pi*b)*tan(a)^2 - x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log
(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a)^2 - 4*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi
*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a)^2 - 4*x*e^(-pi*b*
n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log
(abs(c)))^2*tan(a)^2 - x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*
log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a)^2 - 4*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sg
n(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)*tan(a)
^2 - 4*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan
(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)*tan(a)^2 + x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi
*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + 4*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(
c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + 4*x*e^(-pi*b*n*sgn(x) + pi*b*n - p
i*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + x*e^(-2*pi*b*n*sgn(x) + 2*
pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 - x*e^(2*pi*b*
n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 - 4*x
*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 -
4*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^
2 - x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)
^2*tan(a)^2 - 16*b*n*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c))
)^2*tan(b*n*log(abs(x)) + b*log(abs(c))) - 16*b*n*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n
*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c))) + 8*b*n*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n
+ 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) + b*log(abs(c)))^2 + 8
*b*n*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(b
*n*log(abs(x)) + b*log(abs(c)))^2 - 8*b*n*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*
log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a) - 8*b*n*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*t
an(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a) + 8*b*n*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2
*pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a) + 8*b*n*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c
) + 2*pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a) - 8*b*n*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*s
gn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(2*a)^2 - 8*b*n*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n -
2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(2*a)^2 - 16*b*n*x*e^(pi*b*n*sgn(x) - pi*
b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(2*a)^2 - 16*b*n*x*e^(-pi*b*n*sgn(x) + pi*b*
n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(2*a)^2 - 16*b*n*x*e^(pi*b*n*sgn(x) - pi*b*n +
pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(a) - 16*b*n*x*e^(-pi*b*n*sgn(x) + pi*b*n -
pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(a) + 16*b*n*x*e^(pi*b*n*sgn(x) - pi*b*n +
pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a) + 16*b*n*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b
*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a) - 16*b*n*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(
c) - pi*b)*tan(2*a)^2*tan(a) - 16*b*n*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*a)^2*tan(a) + 8
*b*n*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(a)
^2 + 8*b*n*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))
*tan(a)^2 + 16*b*n*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(
a)^2 + 16*b*n*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(a)^2
+ 8*b*n*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*a)*tan(a)^2 + 8*b*n*x*e^(-2*pi*b*n*sg
n(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*a)*tan(a)^2 + 4*b^2*n^2*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi
*b*sgn(c) - 2*pi*b) - 64*b^2*n^2*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b) - 64*b^2*n^2*x*e^(-pi*b*n*s
gn(x) + pi*b*n - pi*b*sgn(c) + pi*b) + 4*b^2*n^2*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b) -
x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*l
og(abs(x)) + b*log(abs(c)))^2 + 4*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*
b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2 + 4*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)
*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2 - x*e^(-2*pi*b*n*sgn(x) + 2
*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c
)))^2 - 4*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*t
an(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a) - 4*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*
tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a) + x*e^(2*pi*b*n*sgn(x
) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2 - 4*x*e^(pi*b*n*s
gn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2 - 4*x*e^(-pi*b*n*sg
n(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2 + x*e^(-2*pi*b*n*sgn
(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2 - x*e^(2*pi*b*n
*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 4*x*e^(pi*b*n
*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 4*x*e^(-pi*b*n*sgn(
x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 - x*e^(-2*pi*b*n*sgn(x) +
2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 16*x*e^(pi*b*n*sgn(x) -
pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))*
tan(a) + 16*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(
b*n*log(abs(x)) + b*log(abs(c)))*tan(a) + 16*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs
(x)) + b*log(abs(c)))*tan(2*a)^2*tan(a) + 16*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(ab
s(x)) + b*log(abs(c)))*tan(2*a)^2*tan(a) - x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n
*log(abs(x)) + 2*b*log(abs(c)))^2*tan(a)^2 + 4*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log
(abs(x)) + 2*b*log(abs(c)))^2*tan(a)^2 + 4*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(ab
s(x)) + 2*b*log(abs(c)))^2*tan(a)^2 - x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log
(abs(x)) + 2*b*log(abs(c)))^2*tan(a)^2 + x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(b*n*log
(abs(x)) + b*log(abs(c)))^2*tan(a)^2 - 4*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x))
+ b*log(abs(c)))^2*tan(a)^2 - 4*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*lo
g(abs(c)))^2*tan(a)^2 + x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(b*n*log(abs(x)) + b*log
(abs(c)))^2*tan(a)^2 - 4*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b
*log(abs(c)))*tan(2*a)*tan(a)^2 - 4*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(a
bs(x)) + 2*b*log(abs(c)))*tan(2*a)*tan(a)^2 - x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*
a)^2*tan(a)^2 + 4*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*a)^2*tan(a)^2 + 4*x*e^(-pi*b*n*sgn(x
) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*a)^2*tan(a)^2 - x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi
*b)*tan(2*a)^2*tan(a)^2 + 8*b*n*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)
) + 2*b*log(abs(c))) + 8*b*n*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x))
+ 2*b*log(abs(c))) - 16*b*n*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(
c))) - 16*b*n*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c))) + 8*b*n*
x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*a) + 8*b*n*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n -
2*pi*b*sgn(c) + 2*pi*b)*tan(2*a) - 16*b*n*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(a) - 16*b*n*x*
e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(a) - x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*
pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2 - 4*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b
*n*log(abs(x)) + 2*b*log(abs(c)))^2 - 4*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x
)) + 2*b*log(abs(c)))^2 - x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2
*b*log(abs(c)))^2 + x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(b*n*log(abs(x)) + b*log(abs(
c)))^2 + 4*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2 + 4*x*e^(-
pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2 + x*e^(-2*pi*b*n*sgn(x) +
2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))^2 - 4*x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n
+ 2*pi*b*sgn(c) - 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(2*a) - 4*x*e^(-2*pi*b*n*sgn(x) + 2*pi*b
*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))*tan(2*a) - x*e^(2*pi*b*n*sgn(x) - 2*pi*b
*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*a)^2 - 4*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*a)^2 - 4*x
*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*a)^2 - x*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c
) + 2*pi*b)*tan(2*a)^2 + 16*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(b*n*log(abs(x)) + b*log(abs(
c)))*tan(a) + 16*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(a
) + x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(a)^2 + 4*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*
sgn(c) - pi*b)*tan(a)^2 + 4*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(a)^2 + x*e^(-2*pi*b*n*sgn(x
) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(a)^2 + x*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b) -
4*x*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b) - 4*x*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b) + x
*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b))/(64*b^4*n^4*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c))
)^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + 64*b^4*n^4*tan(2*b*n*log(abs(x)) + 2*b*log(ab
s(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 64*b^4*n^4*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)
))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a)^2 + 64*b^4*n^4*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*t
an(2*a)^2*tan(a)^2 + 64*b^4*n^4*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + 64*b^4*n^4*tan(2*
b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2 + 64*b^4*n^4*tan(2*b*n*log(abs(x))
+ 2*b*log(abs(c)))^2*tan(2*a)^2 + 64*b^4*n^4*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 64*b^4*n^4*t
an(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(a)^2 + 64*b^4*n^4*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a)^
2 + 64*b^4*n^4*tan(2*a)^2*tan(a)^2 + 20*b^2*n^2*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x))
+ b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + 64*b^4*n^4*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2 + 64*b^4*n^4*t
an(b*n*log(abs(x)) + b*log(abs(c)))^2 + 64*b^4*n^4*tan(2*a)^2 + 20*b^2*n^2*tan(2*b*n*log(abs(x)) + 2*b*log(abs
(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 64*b^4*n^4*tan(a)^2 + 20*b^2*n^2*tan(2*b*n*log(abs
(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a)^2 + 20*b^2*n^2*tan(2*b*n*log(abs(x)) +
2*b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + 20*b^2*n^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^
2 + 64*b^4*n^4 + 20*b^2*n^2*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2
+ 20*b^2*n^2*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2 + 20*b^2*n^2*tan(b*n*log(abs(x)) + b*log(ab
s(c)))^2*tan(2*a)^2 + 20*b^2*n^2*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(a)^2 + 20*b^2*n^2*tan(b*n*log(
abs(x)) + b*log(abs(c)))^2*tan(a)^2 + 20*b^2*n^2*tan(2*a)^2*tan(a)^2 + tan(2*b*n*log(abs(x)) + 2*b*log(abs(c))
)^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + 20*b^2*n^2*tan(2*b*n*log(abs(x)) + 2*b*log(ab
s(c)))^2 + 20*b^2*n^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2 + 20*b^2*n^2*tan(2*a)^2 + tan(2*b*n*log(abs(x)) +
2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 20*b^2*n^2*tan(a)^2 + tan(2*b*n*log(ab
s(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a)^2 + tan(2*b*n*log(abs(x)) + 2*b*log(a
bs(c)))^2*tan(2*a)^2*tan(a)^2 + tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + 20*b^2*n^2 + tan(
2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2 + tan(2*b*n*log(abs(x)) + 2*b*lo
g(abs(c)))^2*tan(2*a)^2 + tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + tan(2*b*n*log(abs(x)) + 2*b*log(
abs(c)))^2*tan(a)^2 + tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a)^2 + tan(2*a)^2*tan(a)^2 + tan(2*b*n*log(ab
s(x)) + 2*b*log(abs(c)))^2 + tan(b*n*log(abs(x)) + b*log(abs(c)))^2 + tan(2*a)^2 + tan(a)^2 + 1)
Mupad [B] (verification not implemented)
Time = 28.64 (sec) , antiderivative size = 117, normalized size of antiderivative = 0.61
\[
\int \sin ^4\left (a+b \log \left (c x^n\right )\right ) \, dx=\frac {3\,x}{8}-\frac {x\,{\mathrm {e}}^{-a\,2{}\mathrm {i}}\,\frac {1}{{\left (c\,x^n\right )}^{b\,2{}\mathrm {i}}}\,1{}\mathrm {i}}{8\,b\,n+4{}\mathrm {i}}-\frac {x\,{\mathrm {e}}^{a\,2{}\mathrm {i}}\,{\left (c\,x^n\right )}^{b\,2{}\mathrm {i}}}{4+b\,n\,8{}\mathrm {i}}+\frac {x\,{\mathrm {e}}^{-a\,4{}\mathrm {i}}\,\frac {1}{{\left (c\,x^n\right )}^{b\,4{}\mathrm {i}}}\,1{}\mathrm {i}}{64\,b\,n+16{}\mathrm {i}}+\frac {x\,{\mathrm {e}}^{a\,4{}\mathrm {i}}\,{\left (c\,x^n\right )}^{b\,4{}\mathrm {i}}}{16+b\,n\,64{}\mathrm {i}}
\]
[In]
int(sin(a + b*log(c*x^n))^4,x)
[Out]
(3*x)/8 - (x*exp(-a*2i)/(c*x^n)^(b*2i)*1i)/(8*b*n + 4i) - (x*exp(a*2i)*(c*x^n)^(b*2i))/(b*n*8i + 4) + (x*exp(-
a*4i)/(c*x^n)^(b*4i)*1i)/(64*b*n + 16i) + (x*exp(a*4i)*(c*x^n)^(b*4i))/(b*n*64i + 16)