\(\int x^2 \sin ^4(a+b \log (c x^n)) \, dx\) [19]

Optimal result

Integrand size = 17, antiderivative size = 202 \[ \int x^2 \sin ^4\left (a+b \log \left (c x^n\right )\right ) \, dx=\frac {8 b^4 n^4 x^3}{81+180 b^2 n^2+64 b^4 n^4}-\frac {24 b^3 n^3 x^3 \cos \left (a+b \log \left (c x^n\right )\right ) \sin \left (a+b \log \left (c x^n\right )\right )}{81+180 b^2 n^2+64 b^4 n^4}+\frac {36 b^2 n^2 x^3 \sin ^2\left (a+b \log \left (c x^n\right )\right )}{81+180 b^2 n^2+64 b^4 n^4}-\frac {4 b n x^3 \cos \left (a+b \log \left (c x^n\right )\right ) \sin ^3\left (a+b \log \left (c x^n\right )\right )}{9+16 b^2 n^2}+\frac {3 x^3 \sin ^4\left (a+b \log \left (c x^n\right )\right )}{9+16 b^2 n^2} \]

[Out]

8*b^4*n^4*x^3/(64*b^4*n^4+180*b^2*n^2+81)-24*b^3*n^3*x^3*cos(a+b*ln(c*x^n))*sin(a+b*ln(c*x^n))/(64*b^4*n^4+180
*b^2*n^2+81)+36*b^2*n^2*x^3*sin(a+b*ln(c*x^n))^2/(64*b^4*n^4+180*b^2*n^2+81)-4*b*n*x^3*cos(a+b*ln(c*x^n))*sin(
a+b*ln(c*x^n))^3/(16*b^2*n^2+9)+3*x^3*sin(a+b*ln(c*x^n))^4/(16*b^2*n^2+9)

Rubi [A] (verified)

Time = 0.09 (sec) , antiderivative size = 202, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {4575, 30} \[ \int x^2 \sin ^4\left (a+b \log \left (c x^n\right )\right ) \, dx=\frac {3 x^3 \sin ^4\left (a+b \log \left (c x^n\right )\right )}{16 b^2 n^2+9}-\frac {4 b n x^3 \sin ^3\left (a+b \log \left (c x^n\right )\right ) \cos \left (a+b \log \left (c x^n\right )\right )}{16 b^2 n^2+9}+\frac {36 b^2 n^2 x^3 \sin ^2\left (a+b \log \left (c x^n\right )\right )}{64 b^4 n^4+180 b^2 n^2+81}-\frac {24 b^3 n^3 x^3 \sin \left (a+b \log \left (c x^n\right )\right ) \cos \left (a+b \log \left (c x^n\right )\right )}{64 b^4 n^4+180 b^2 n^2+81}+\frac {8 b^4 n^4 x^3}{64 b^4 n^4+180 b^2 n^2+81} \]

[In]

Int[x^2*Sin[a + b*Log[c*x^n]]^4,x]

[Out]

(8*b^4*n^4*x^3)/(81 + 180*b^2*n^2 + 64*b^4*n^4) - (24*b^3*n^3*x^3*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])
/(81 + 180*b^2*n^2 + 64*b^4*n^4) + (36*b^2*n^2*x^3*Sin[a + b*Log[c*x^n]]^2)/(81 + 180*b^2*n^2 + 64*b^4*n^4) -
(4*b*n*x^3*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]]^3)/(9 + 16*b^2*n^2) + (3*x^3*Sin[a + b*Log[c*x^n]]^4)/(
9 + 16*b^2*n^2)

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rule 4575

Int[((e_.)*(x_))^(m_.)*Sin[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*(d_.)]^(p_), x_Symbol] :> Simp[(m + 1)*(e*x)^
(m + 1)*(Sin[d*(a + b*Log[c*x^n])]^p/(b^2*d^2*e*n^2*p^2 + e*(m + 1)^2)), x] + (Dist[b^2*d^2*n^2*p*((p - 1)/(b^
2*d^2*n^2*p^2 + (m + 1)^2)), Int[(e*x)^m*Sin[d*(a + b*Log[c*x^n])]^(p - 2), x], x] - Simp[b*d*n*p*(e*x)^(m + 1
)*Cos[d*(a + b*Log[c*x^n])]*(Sin[d*(a + b*Log[c*x^n])]^(p - 1)/(b^2*d^2*e*n^2*p^2 + e*(m + 1)^2)), x]) /; Free
Q[{a, b, c, d, e, m, n}, x] && IGtQ[p, 1] && NeQ[b^2*d^2*n^2*p^2 + (m + 1)^2, 0]

Rubi steps \begin{align*} \text {integral}& = -\frac {4 b n x^3 \cos \left (a+b \log \left (c x^n\right )\right ) \sin ^3\left (a+b \log \left (c x^n\right )\right )}{9+16 b^2 n^2}+\frac {3 x^3 \sin ^4\left (a+b \log \left (c x^n\right )\right )}{9+16 b^2 n^2}+\frac {\left (12 b^2 n^2\right ) \int x^2 \sin ^2\left (a+b \log \left (c x^n\right )\right ) \, dx}{9+16 b^2 n^2} \\ & = -\frac {24 b^3 n^3 x^3 \cos \left (a+b \log \left (c x^n\right )\right ) \sin \left (a+b \log \left (c x^n\right )\right )}{81+180 b^2 n^2+64 b^4 n^4}+\frac {36 b^2 n^2 x^3 \sin ^2\left (a+b \log \left (c x^n\right )\right )}{81+180 b^2 n^2+64 b^4 n^4}-\frac {4 b n x^3 \cos \left (a+b \log \left (c x^n\right )\right ) \sin ^3\left (a+b \log \left (c x^n\right )\right )}{9+16 b^2 n^2}+\frac {3 x^3 \sin ^4\left (a+b \log \left (c x^n\right )\right )}{9+16 b^2 n^2}+\frac {\left (24 b^4 n^4\right ) \int x^2 \, dx}{81+180 b^2 n^2+64 b^4 n^4} \\ & = \frac {8 b^4 n^4 x^3}{81+180 b^2 n^2+64 b^4 n^4}-\frac {24 b^3 n^3 x^3 \cos \left (a+b \log \left (c x^n\right )\right ) \sin \left (a+b \log \left (c x^n\right )\right )}{81+180 b^2 n^2+64 b^4 n^4}+\frac {36 b^2 n^2 x^3 \sin ^2\left (a+b \log \left (c x^n\right )\right )}{81+180 b^2 n^2+64 b^4 n^4}-\frac {4 b n x^3 \cos \left (a+b \log \left (c x^n\right )\right ) \sin ^3\left (a+b \log \left (c x^n\right )\right )}{9+16 b^2 n^2}+\frac {3 x^3 \sin ^4\left (a+b \log \left (c x^n\right )\right )}{9+16 b^2 n^2} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.38 (sec) , antiderivative size = 171, normalized size of antiderivative = 0.85 \[ \int x^2 \sin ^4\left (a+b \log \left (c x^n\right )\right ) \, dx=\frac {x^3 \left (81+180 b^2 n^2+64 b^4 n^4-12 \left (9+16 b^2 n^2\right ) \cos \left (2 \left (a+b \log \left (c x^n\right )\right )\right )+3 \left (9+4 b^2 n^2\right ) \cos \left (4 \left (a+b \log \left (c x^n\right )\right )\right )-72 b n \sin \left (2 \left (a+b \log \left (c x^n\right )\right )\right )-128 b^3 n^3 \sin \left (2 \left (a+b \log \left (c x^n\right )\right )\right )+36 b n \sin \left (4 \left (a+b \log \left (c x^n\right )\right )\right )+16 b^3 n^3 \sin \left (4 \left (a+b \log \left (c x^n\right )\right )\right )\right )}{8 \left (81+180 b^2 n^2+64 b^4 n^4\right )} \]

[In]

Integrate[x^2*Sin[a + b*Log[c*x^n]]^4,x]

[Out]

(x^3*(81 + 180*b^2*n^2 + 64*b^4*n^4 - 12*(9 + 16*b^2*n^2)*Cos[2*(a + b*Log[c*x^n])] + 3*(9 + 4*b^2*n^2)*Cos[4*
(a + b*Log[c*x^n])] - 72*b*n*Sin[2*(a + b*Log[c*x^n])] - 128*b^3*n^3*Sin[2*(a + b*Log[c*x^n])] + 36*b*n*Sin[4*
(a + b*Log[c*x^n])] + 16*b^3*n^3*Sin[4*(a + b*Log[c*x^n])]))/(8*(81 + 180*b^2*n^2 + 64*b^4*n^4))

Maple [F]

\[\int x^{2} {\sin \left (a +b \ln \left (c \,x^{n}\right )\right )}^{4}d x\]

[In]

int(x^2*sin(a+b*ln(c*x^n))^4,x)

[Out]

int(x^2*sin(a+b*ln(c*x^n))^4,x)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 178, normalized size of antiderivative = 0.88 \[ \int x^2 \sin ^4\left (a+b \log \left (c x^n\right )\right ) \, dx=\frac {3 \, {\left (4 \, b^{2} n^{2} + 9\right )} x^{3} \cos \left (b n \log \left (x\right ) + b \log \left (c\right ) + a\right )^{4} - 6 \, {\left (10 \, b^{2} n^{2} + 9\right )} x^{3} \cos \left (b n \log \left (x\right ) + b \log \left (c\right ) + a\right )^{2} + {\left (8 \, b^{4} n^{4} + 48 \, b^{2} n^{2} + 27\right )} x^{3} + 4 \, {\left ({\left (4 \, b^{3} n^{3} + 9 \, b n\right )} x^{3} \cos \left (b n \log \left (x\right ) + b \log \left (c\right ) + a\right )^{3} - {\left (10 \, b^{3} n^{3} + 9 \, b n\right )} x^{3} \cos \left (b n \log \left (x\right ) + b \log \left (c\right ) + a\right )\right )} \sin \left (b n \log \left (x\right ) + b \log \left (c\right ) + a\right )}{64 \, b^{4} n^{4} + 180 \, b^{2} n^{2} + 81} \]

[In]

integrate(x^2*sin(a+b*log(c*x^n))^4,x, algorithm="fricas")

[Out]

(3*(4*b^2*n^2 + 9)*x^3*cos(b*n*log(x) + b*log(c) + a)^4 - 6*(10*b^2*n^2 + 9)*x^3*cos(b*n*log(x) + b*log(c) + a
)^2 + (8*b^4*n^4 + 48*b^2*n^2 + 27)*x^3 + 4*((4*b^3*n^3 + 9*b*n)*x^3*cos(b*n*log(x) + b*log(c) + a)^3 - (10*b^
3*n^3 + 9*b*n)*x^3*cos(b*n*log(x) + b*log(c) + a))*sin(b*n*log(x) + b*log(c) + a))/(64*b^4*n^4 + 180*b^2*n^2 +
81)

Sympy [F(-1)]

Timed out. \[ \int x^2 \sin ^4\left (a+b \log \left (c x^n\right )\right ) \, dx=\text {Timed out} \]

[In]

integrate(x**2*sin(a+b*ln(c*x**n))**4,x)

[Out]

Timed out

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1107 vs. \(2 (202) = 404\).

Time = 0.25 (sec) , antiderivative size = 1107, normalized size of antiderivative = 5.48 \[ \int x^2 \sin ^4\left (a+b \log \left (c x^n\right )\right ) \, dx=\text {Too large to display} \]

[In]

integrate(x^2*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 + 12*(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 +
36*(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 + 27*cos(8*b
*log(c))*cos(4*b*log(c)) + 27*sin(8*b*log(c))*sin(4*b*log(c)) + 27*cos(4*b*log(c)))*x^3*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 + 48*(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 + 1
8*(b*cos(4*b*log(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 + 27*cos(6*b*log(c))*cos(4*b*log(c)) + 27*cos(4*b*log(c))*cos(2*b*log(c)
) + 27*sin(6*b*log(c))*sin(4*b*log(c)) + 27*sin(4*b*log(c))*sin(2*b*log(c)))*x^3*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 - 12*(b
^2*cos(4*b*log(c))*sin(8*b*log(c)) - b^2*cos(8*b*log(c))*sin(4*b*log(c)) + b^2*sin(4*b*log(c)))*n^2 + 36*(b*co
s(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 - 27*cos(4*b*log(c))*
sin(8*b*log(c)) + 27*cos(8*b*log(c))*sin(4*b*log(c)) - 27*sin(4*b*log(c)))*x^3*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 - 48*(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))*sin(4*b*log(c)) - b^2*cos(4*b*log(c))*sin(2*b*log(c)))*n^2 + 18*(b*cos(
6*b*log(c))*cos(4*b*log(c)) + b*cos(4*b*log(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 - 27*cos(4*b*log(c))*sin(6*b*log(c)) + 27*cos(6*b*log(c))*sin(4*b*log(c)) - 27*co
s(2*b*log(c))*sin(4*b*log(c)) + 27*cos(4*b*log(c))*sin(2*b*log(c)))*x^3*sin(2*b*log(x^n) + 2*a) + 2*(64*(b^4*c
os(4*b*log(c))^2 + b^4*sin(4*b*log(c))^2)*n^4 + 180*(b^2*cos(4*b*log(c))^2 + b^2*sin(4*b*log(c))^2)*n^2 + 81*c
os(4*b*log(c))^2 + 81*sin(4*b*log(c))^2)*x^3)/(64*(b^4*cos(4*b*log(c))^2 + b^4*sin(4*b*log(c))^2)*n^4 + 180*(b
^2*cos(4*b*log(c))^2 + b^2*sin(4*b*log(c))^2)*n^2 + 81*cos(4*b*log(c))^2 + 81*sin(4*b*log(c))^2)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 17035 vs. \(2 (202) = 404\).

Time = 1.30 (sec) , antiderivative size = 17035, normalized size of antiderivative = 84.33 \[ \int x^2 \sin ^4\left (a+b \log \left (c x^n\right )\right ) \, dx=\text {Too large to display} \]

[In]

integrate(x^2*sin(a+b*log(c*x^n))^4,x, algorithm="giac")

[Out]

1/8*x^3 + 1/16*(256*b^3*n^3*x^3*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(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)^2*tan(a) + 256*b^3*n^3*x^3*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*t
an(2*a)^2*tan(a) - 32*b^3*n^3*x^3*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^3*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^3*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^3*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^3*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 - 32*b^3*n
^3*x^3*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 + 12*b^2*n^2*x^3*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 - 192*b^2*n^2*x^3*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 - 192*b^2*n^2*x^3*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 + 12*b^2*n^2*x^3*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^3*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^3*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) - 256*b^3*n^3*x^3*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(b*n*log(abs(x)) + b*log(ab
s(c)))*tan(2*a)^2 - 256*b^3*n^3*x^3*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^3*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*t
an(2*a)^2 - 32*b^3*n^3*x^3*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 + 256*b^3*n^3*x^3*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^3*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^3*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^3*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^3*e^(pi*b*n*s
gn(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^
3*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^3*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^3*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^3*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^3*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^3*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^3*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^3*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(b*n*log(ab
s(x)) + b*log(abs(c)))^2*tan(2*a)*tan(a)^2 + 32*b^3*n^3*x^3*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^3*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^3*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^3*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^3*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 + 12*b^2*n^2*x^3*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 + 192*b^2*n^2*x^3*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*l
og(abs(c)))^2*tan(2*a)^2 + 192*b^2*n^2*x^3*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 + 12*b^2*n^2*x^3*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 + 768*b^2*n^2*x^3*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) + 768*b^2*n^2*x^3*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) - 12*b^2*n^2*x^3*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)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a)^2 - 192*b^2*n^2*x^3*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 - 192*b^2*n^2*x^3*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 - 12*b^2*n^2*x^3*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 - 48*b^2*n^2*x^3*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 - 48*b^2*n^2*x^3*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 + 12*b^2*n^2*x^3*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 + 192*b^2*n^2*x^3*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 + 192*b^2*n^2*x^3*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 + 12*b^2*n^2*x^3*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
- 12*b^2*n^2*x^3*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 - 192*b^2*n^2*x^3*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 - 192*b^2*n^2*x^3*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 - 12*b^2*n^2*x^3*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^3*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^3*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))) + 32*b^3*n^3*x^3*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^3*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^3*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^3*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^3*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^3*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^3*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^3*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 - 256*b^3
*n^3*x^3*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^3*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^3*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*t
an(a) - 256*b^3*n^3*x^3*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^3*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^3*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^3*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^3*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*a)^2*tan(a) + 144*b*n*x^3*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) + 144*b*n*x^3*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^3*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 + 32*b^3*n^3*x^3*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^3*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^3*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^3*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^3*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 - 72*b*n*x^3*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*ta
n(2*a)*tan(a)^2 - 72*b*n*x^3*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 + 144*b*n*x^3*e^(pi*b*n*sgn(x) - p
i*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)))*ta
n(2*a)^2*tan(a)^2 + 144*b*n*x^3*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*log(abs(x)) + 2*b*l
og(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(2*a)^2*tan(a)^2 - 72*b*n*x^3*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 - 72*b*n*x^3*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 - 12*b^2*n^2*x^3*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)))^2*tan(b*n*log(abs(x)) + b*
log(abs(c)))^2 + 192*b^2*n^2*x^3*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*b*n*log(abs(x)) + 2*b*l
og(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2 + 192*b^2*n^2*x^3*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 - 12*b^2*n^2*x^3*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 - 48*b^2*n^2*x^3*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) - 48*b^2*n^2*x^3*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*l
og(abs(c)))^2*tan(2*a) + 12*b^2*n^2*x^3*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 - 192*b^2*n^2*x^3*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 - 192*b^2*n^2*x^3*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 + 12*b^2*n^2*x^3*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 - 12*b^2*n^2*x^3*e^(2*pi*b*n*sg
n(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 + 192*b^2*n^2*x^3*
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 + 192*b^2*n^
2*x^3*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 - 12*
b^2*n^2*x^3*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*ta
n(2*a)^2 + 768*b^2*n^2*x^3*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) + 768*b^2*n^2*x^3*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) + 768*b^2*n^2*
x^3*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) + 7
68*b^2*n^2*x^3*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) - 12*b^2*n^2*x^3*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 + 192*b^2*n^2*x^3*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 + 192*b^2*n^2*x^3*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*l
og(abs(x)) + 2*b*log(abs(c)))^2*tan(a)^2 - 12*b^2*n^2*x^3*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)))^2*tan(a)^2 + 12*b^2*n^2*x^3*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 - 192*b^2*n^2*x^3*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 - 192*b^2*n^2*x^3*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 + 12*b^2*n^2*x^3*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 - 48*b^2*n^2*x^3*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
- 48*b^2*n^2*x^3*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 - 12*b^2*n^2*x^3*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*a)^2*ta
n(a)^2 + 192*b^2*n^2*x^3*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*a)^2*tan(a)^2 + 192*b^2*n^2*x^3
*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*a)^2*tan(a)^2 - 12*b^2*n^2*x^3*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 + 27*x^3*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
- 108*x^3*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 - 108*x^3*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 + 27*x^3
*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*tan(2*a)^2*tan(a)^2 + 32*b^3*n^3*x^3*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^3*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))) - 256*b^3*n^3*x^3*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^3*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))) + 32*b^3*n^3*x^3*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^3*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*a) - 72*b*n*
x^3*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) - 72*b*n*x^3*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) - 144*b*n*x^3*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)))*tan(2*a)^2 - 144*b*n*x^3*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 - 72*b*n*x^3*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*ta
n(2*a)^2 - 72*b*n*x^3*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 - 256*b^3*n^3*x^3*e^(pi*b*n*sgn(x) - pi*b*n + pi*b
*sgn(c) - pi*b)*tan(a) - 256*b^3*n^3*x^3*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(a) + 144*b*n*x^3
*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) + 144*b*n*x^3*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) - 144*b*n*x^3*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) - 144*b*n*x^3*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*tan(a) + 144*b*n*x^3
*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) + 14
4*b*n*x^3*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*t
an(a) + 144*b*n*x^3*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 + 144*b*n*x^3*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 + 72*b*n*x^3*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 + 72*b*n*x^3*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 - 72*b*n*x^3*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 - 72*b*n*x^3*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)*ta
n(a)^2 + 72*b*n*x^3*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 + 72*b*n*x^3*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 - 72*b*n*x^3*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)))*tan(2*a)^2*tan(a)^2 - 72*b*n*x^3*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 + 144*b*n*x^3*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 + 144*b*n*x^3*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 - 12*b^2*n
^2*x^3*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 - 19
2*b^2*n^2*x^3*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 - 192
*b^2*n^2*x^3*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 - 12*
b^2*n^2*x^3*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 + 12*b^2*n^2*x^3*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 + 192*b^2*n^2*x^3*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 +
192*b^2*n^2*x^3*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 + 12*
b^2*n^2*x^3*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 -
48*b^2*n^2*x^3*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) - 48*b^2*n^2*x^3*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) - 12*b^2*n^2*x^3*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*a)^2 -
192*b^2*n^2*x^3*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*a)^2 - 192*b^2*n^2*x^3*e^(-pi*b*n*sgn(x
) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*a)^2 - 12*b^2*n^2*x^3*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) +
2*pi*b)*tan(2*a)^2 + 27*x^3*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 + 108*x^3*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 +
108*x^3*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)))^2*tan(2*a)^2 + 27*x^3*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 + 768*b^2*n^2*x^3*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) + 768*b^2*n^2*x^3*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) + 432*x^3*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(a
bs(c)))*tan(2*a)^2*tan(a) + 432*x^3*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) + 12*b^2*n^2*x^3*e^(2*pi*b*n*sgn(x) -
2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(a)^2 + 192*b^2*n^2*x^3*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)
*tan(a)^2 + 192*b^2*n^2*x^3*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(a)^2 + 12*b^2*n^2*x^3*e^(-2*p
i*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(a)^2 - 27*x^3*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 - 108
*x^3*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(ab
s(x)) + b*log(abs(c)))^2*tan(a)^2 - 108*x^3*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 - 27*x^3*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 - 108*x^3*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(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(2*a)*tan(a)^2 - 108*x^3*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 + 27*x^3*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 + 108*x^3*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 + 108*x^3*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*tan(a)^2 + 27*x^3*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 - 27*x^3*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 - 108*x^3*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 - 108*x^3*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 - 27*x^3*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 - 144*b*n*x^3*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*t
an(b*n*log(abs(x)) + b*log(abs(c))) - 144*b*n*x^3*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(2*b*n*l
og(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log(abs(c))) + 72*b*n*x^3*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 +
72*b*n*x^3*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 - 72*b*n*x^3*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) - 72*b*n*x^3*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) + 72*b*n*x^3*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) + 72*b*n*x^3*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) - 72*b*n*x^3*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 - 72*b*n*x^3*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 - 144*b*n*x
^3*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 - 144*b*n*x
^3*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 - 144*b*n*
x^3*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) - 144*b*
n*x^3*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) + 144
*b*n*x^3*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) + 144*b
*n*x^3*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) - 144*b*
n*x^3*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*a)^2*tan(a) - 144*b*n*x^3*e^(-pi*b*n*sgn(x) + pi*b
*n - pi*b*sgn(c) + pi*b)*tan(2*a)^2*tan(a) + 72*b*n*x^3*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 + 72*b*n*x^3*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 + 144*b*n*x^3*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(a)^2 + 144*b*n*x^3*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sg
n(c) + pi*b)*tan(b*n*log(abs(x)) + b*log(abs(c)))*tan(a)^2 + 72*b*n*x^3*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 + 72*b*n*x^3*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 + 12*b^2*n^2*x^3*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b) - 192*b^2*n^2*x^3*e^(pi
*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b) - 192*b^2*n^2*x^3*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)
+ 12*b^2*n^2*x^3*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b) - 27*x^3*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
+ 108*x^3*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 + 108*x^3*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 - 27*x^3*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 - 108*x^3*
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(a
bs(x)) + b*log(abs(c)))^2*tan(2*a) - 108*x^3*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) + 27*x^3*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 - 108*x^3*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 - 108*x^3*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 + 27*x^3*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 - 27*
x^3*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
+ 108*x^3*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 +
108*x^3*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 - 2
7*x^3*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 + 432*x^3*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) + 432*x^3*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) + 432*x^3*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) + 432*x^3*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) - 27*x^3*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 + 108*x^3*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(a)^2 + 108*x^3*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(a)^2 - 27*x^3*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 + 27*x^3*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 - 108*x^3*
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 - 108*x^3*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 + 27*x^3*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 - 108*x^3*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 - 108*x^3*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 - 27*x^3*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 + 108*x
^3*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*a)^2*tan(a)^2 + 108*x^3*e^(-pi*b*n*sgn(x) + pi*b*n -
pi*b*sgn(c) + pi*b)*tan(2*a)^2*tan(a)^2 - 27*x^3*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 + 72*b*n*x^3*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))) + 72*b*n*x^3*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))) - 144*b*n*x^3*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))) - 144*b*n*x^3*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))) + 72
*b*n*x^3*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*a) + 72*b*n*x^3*e^(-2*pi*b*n*sgn(x) + 2
*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*a) - 144*b*n*x^3*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(a
) - 144*b*n*x^3*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(a) - 27*x^3*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 - 108*x^3*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 - 108*x^3*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 - 27*x^3*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 + 27*x^3*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 + 108*x^3*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 + 108*x^3*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 + 27*x^3*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 - 108*x^3*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) - 108*x^3*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) - 27*x^3*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(2*a)^2 - 108
*x^3*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*tan(2*a)^2 - 108*x^3*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sg
n(c) + pi*b)*tan(2*a)^2 - 27*x^3*e^(-2*pi*b*n*sgn(x) + 2*pi*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(2*a)^2 + 432*x^3
*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) + 432*x^3*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) + 27*x^3*e^(2*pi*b*n*sgn
(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b)*tan(a)^2 + 108*x^3*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b)*ta
n(a)^2 + 108*x^3*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b)*tan(a)^2 + 27*x^3*e^(-2*pi*b*n*sgn(x) + 2*pi
*b*n - 2*pi*b*sgn(c) + 2*pi*b)*tan(a)^2 + 27*x^3*e^(2*pi*b*n*sgn(x) - 2*pi*b*n + 2*pi*b*sgn(c) - 2*pi*b) - 108
*x^3*e^(pi*b*n*sgn(x) - pi*b*n + pi*b*sgn(c) - pi*b) - 108*x^3*e^(-pi*b*n*sgn(x) + pi*b*n - pi*b*sgn(c) + pi*b
) + 27*x^3*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*l
og(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*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(ab
s(c)))^2*tan(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*l
og(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*tan(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 + 180*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 + 6
4*b^4*n^4*tan(b*n*log(abs(x)) + b*log(abs(c)))^2 + 64*b^4*n^4*tan(2*a)^2 + 180*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 + 180*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 + 180*b^2*n^2*tan(2*b*n
*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + 180*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 + 180*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 + 180*b^2*n^2*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2 + 180*b^2*n^2*tan(b*n*log(
abs(x)) + b*log(abs(c)))^2*tan(2*a)^2 + 180*b^2*n^2*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(a)^2 + 180*
b^2*n^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2*tan(a)^2 + 180*b^2*n^2*tan(2*a)^2*tan(a)^2 + 81*tan(2*b*n*log(a
bs(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 + 180*b^2*n^2*tan(2*b*n
*log(abs(x)) + 2*b*log(abs(c)))^2 + 180*b^2*n^2*tan(b*n*log(abs(x)) + b*log(abs(c)))^2 + 180*b^2*n^2*tan(2*a)^
2 + 81*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 + 180*b^2*
n^2*tan(a)^2 + 81*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 +
81*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2*tan(a)^2 + 81*tan(b*n*log(abs(x)) + b*log(abs(c)))^2
*tan(2*a)^2*tan(a)^2 + 180*b^2*n^2 + 81*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(b*n*log(abs(x)) + b*log
(abs(c)))^2 + 81*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(2*a)^2 + 81*tan(b*n*log(abs(x)) + b*log(abs(c)
))^2*tan(2*a)^2 + 81*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2*tan(a)^2 + 81*tan(b*n*log(abs(x)) + b*log(abs(
c)))^2*tan(a)^2 + 81*tan(2*a)^2*tan(a)^2 + 81*tan(2*b*n*log(abs(x)) + 2*b*log(abs(c)))^2 + 81*tan(b*n*log(abs(
x)) + b*log(abs(c)))^2 + 81*tan(2*a)^2 + 81*tan(a)^2 + 81)

Mupad [B] (verification not implemented)

Time = 27.24 (sec) , antiderivative size = 127, normalized size of antiderivative = 0.63 \[ \int x^2 \sin ^4\left (a+b \log \left (c x^n\right )\right ) \, dx=\frac {x^3}{8}-\frac {x^3\,{\mathrm {e}}^{-a\,2{}\mathrm {i}}\,\frac {1}{{\left (c\,x^n\right )}^{b\,2{}\mathrm {i}}}\,1{}\mathrm {i}}{8\,b\,n+12{}\mathrm {i}}-\frac {x^3\,{\mathrm {e}}^{a\,2{}\mathrm {i}}\,{\left (c\,x^n\right )}^{b\,2{}\mathrm {i}}}{12+b\,n\,8{}\mathrm {i}}+\frac {x^3\,{\mathrm {e}}^{-a\,4{}\mathrm {i}}\,\frac {1}{{\left (c\,x^n\right )}^{b\,4{}\mathrm {i}}}\,1{}\mathrm {i}}{64\,b\,n+48{}\mathrm {i}}+\frac {x^3\,{\mathrm {e}}^{a\,4{}\mathrm {i}}\,{\left (c\,x^n\right )}^{b\,4{}\mathrm {i}}}{48+b\,n\,64{}\mathrm {i}} \]

[In]

int(x^2*sin(a + b*log(c*x^n))^4,x)

[Out]

x^3/8 - (x^3*exp(-a*2i)/(c*x^n)^(b*2i)*1i)/(8*b*n + 12i) - (x^3*exp(a*2i)*(c*x^n)^(b*2i))/(b*n*8i + 12) + (x^3
*exp(-a*4i)/(c*x^n)^(b*4i)*1i)/(64*b*n + 48i) + (x^3*exp(a*4i)*(c*x^n)^(b*4i))/(b*n*64i + 48)