3.32 \(\int f F^{c (a+b x)} (f x)^m (e x \cos (d+e x)+(1+m+b c x \log (F)) \sin (d+e x)) \, dx\)
Optimal. Leaf size=23 \[ f x (f x)^m \sin (d+e x) F^{c (a+b x)} \]
[Out]
f*F^(c*(a + b*x))*x*(f*x)^m*Sin[d + e*x]
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Rubi [F] time = 2.34032, antiderivative size = 0, normalized size of antiderivative = 0.,
number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {}
\[ \int f F^{c (a+b x)} (f x)^m (e x \cos (d+e x)+(1+m+b c x \log (F)) \sin (d+e x)) \, dx \]
Verification is Not applicable to the result.
[In]
Int[f*F^(c*(a + b*x))*(f*x)^m*(e*x*Cos[d + e*x] + (1 + m + b*c*x*Log[F])*Sin[d + e*x]),x]
[Out]
e*Defer[Int][F^(a*c + b*c*x)*(f*x)^(1 + m)*Cos[d + e*x], x] + f*(1 + m)*Defer[Int][F^(a*c + b*c*x)*(f*x)^m*Sin
[d + e*x], x] + b*c*Log[F]*Defer[Int][F^(a*c + b*c*x)*(f*x)^(1 + m)*Sin[d + e*x], x]
Rubi steps
\begin{align*} \int f F^{c (a+b x)} (f x)^m (e x \cos (d+e x)+(1+m+b c x \log (F)) \sin (d+e x)) \, dx &=f \int F^{c (a+b x)} (f x)^m (e x \cos (d+e x)+(1+m+b c x \log (F)) \sin (d+e x)) \, dx\\ &=f \int F^{a c+b c x} (f x)^m (e x \cos (d+e x)+(1+m+b c x \log (F)) \sin (d+e x)) \, dx\\ &=f \int \left (\frac{e F^{a c+b c x} (f x)^{1+m} \cos (d+e x)}{f}+F^{a c+b c x} (f x)^m (1+m+b c x \log (F)) \sin (d+e x)\right ) \, dx\\ &=e \int F^{a c+b c x} (f x)^{1+m} \cos (d+e x) \, dx+f \int F^{a c+b c x} (f x)^m (1+m+b c x \log (F)) \sin (d+e x) \, dx\\ &=e \int F^{a c+b c x} (f x)^{1+m} \cos (d+e x) \, dx+f \int \left (F^{a c+b c x} (1+m) (f x)^m \sin (d+e x)+\frac{b c F^{a c+b c x} (f x)^{1+m} \log (F) \sin (d+e x)}{f}\right ) \, dx\\ &=e \int F^{a c+b c x} (f x)^{1+m} \cos (d+e x) \, dx+(f (1+m)) \int F^{a c+b c x} (f x)^m \sin (d+e x) \, dx+(b c \log (F)) \int F^{a c+b c x} (f x)^{1+m} \sin (d+e x) \, dx\\ \end{align*}
Mathematica [A] time = 0.897916, size = 23, normalized size = 1. \[ f x (f x)^m \sin (d+e x) F^{c (a+b x)} \]
Antiderivative was successfully verified.
[In]
Integrate[f*F^(c*(a + b*x))*(f*x)^m*(e*x*Cos[d + e*x] + (1 + m + b*c*x*Log[F])*Sin[d + e*x]),x]
[Out]
f*F^(c*(a + b*x))*x*(f*x)^m*Sin[d + e*x]
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Maple [C] time = 0.161, size = 201, normalized size = 8.7 \begin{align*} -{\frac{i}{2}}{F}^{c \left ( bx+a \right ) }xf \left ({x}^{m}{f}^{m}{{\rm e}^{iex}}{{\rm e}^{id}}{{\rm e}^{-{\frac{i}{2}}\pi \, \left ({\it csgn} \left ( ifx \right ) \right ) ^{3}m}}{{\rm e}^{{\frac{i}{2}}\pi \, \left ({\it csgn} \left ( ifx \right ) \right ) ^{2}{\it csgn} \left ( if \right ) m}}{{\rm e}^{{\frac{i}{2}}\pi \, \left ({\it csgn} \left ( ifx \right ) \right ) ^{2}{\it csgn} \left ( ix \right ) m}}{{\rm e}^{-{\frac{i}{2}}\pi \,{\it csgn} \left ( ifx \right ){\it csgn} \left ( if \right ){\it csgn} \left ( ix \right ) m}}-{x}^{m}{f}^{m}{{\rm e}^{-iex}}{{\rm e}^{-id}}{{\rm e}^{-{\frac{i}{2}}\pi \, \left ({\it csgn} \left ( ifx \right ) \right ) ^{3}m}}{{\rm e}^{{\frac{i}{2}}\pi \, \left ({\it csgn} \left ( ifx \right ) \right ) ^{2}{\it csgn} \left ( if \right ) m}}{{\rm e}^{{\frac{i}{2}}\pi \, \left ({\it csgn} \left ( ifx \right ) \right ) ^{2}{\it csgn} \left ( ix \right ) m}}{{\rm e}^{-{\frac{i}{2}}\pi \,{\it csgn} \left ( ifx \right ){\it csgn} \left ( if \right ){\it csgn} \left ( ix \right ) m}} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(f*F^(c*(b*x+a))*(f*x)^m*(e*x*cos(e*x+d)+(1+m+b*c*x*ln(F))*sin(e*x+d)),x)
[Out]
-1/2*I*F^(c*(b*x+a))*x*f*(x^m*f^m*exp(I*e*x)*exp(I*d)*exp(-1/2*I*Pi*csgn(I*f*x)^3*m)*exp(1/2*I*Pi*csgn(I*f*x)^
2*csgn(I*f)*m)*exp(1/2*I*Pi*csgn(I*f*x)^2*csgn(I*x)*m)*exp(-1/2*I*Pi*csgn(I*f*x)*csgn(I*f)*csgn(I*x)*m)-x^m*f^
m*exp(-I*e*x)*exp(-I*d)*exp(-1/2*I*Pi*csgn(I*f*x)^3*m)*exp(1/2*I*Pi*csgn(I*f*x)^2*csgn(I*f)*m)*exp(1/2*I*Pi*cs
gn(I*f*x)^2*csgn(I*x)*m)*exp(-1/2*I*Pi*csgn(I*f*x)*csgn(I*f)*csgn(I*x)*m))
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Maxima [A] time = 2.13198, size = 41, normalized size = 1.78 \begin{align*} F^{a c} f^{m + 1} x e^{\left (b c x \log \left (F\right ) + m \log \left (x\right )\right )} \sin \left (e x + d\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(f*F^(c*(b*x+a))*(f*x)^m*(e*x*cos(e*x+d)+(1+m+b*c*x*log(F))*sin(e*x+d)),x, algorithm="maxima")
[Out]
F^(a*c)*f^(m + 1)*x*e^(b*c*x*log(F) + m*log(x))*sin(e*x + d)
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Fricas [A] time = 0.494808, size = 57, normalized size = 2.48 \begin{align*} \left (f x\right )^{m} F^{b c x + a c} f x \sin \left (e x + d\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(f*F^(c*(b*x+a))*(f*x)^m*(e*x*cos(e*x+d)+(1+m+b*c*x*log(F))*sin(e*x+d)),x, algorithm="fricas")
[Out]
(f*x)^m*F^(b*c*x + a*c)*f*x*sin(e*x + d)
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(f*F**(c*(b*x+a))*(f*x)**m*(e*x*cos(e*x+d)+(1+m+b*c*x*ln(F))*sin(e*x+d)),x)
[Out]
Timed out
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Giac [B] time = 1.88481, size = 6483, normalized size = 281.87 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(f*F^(c*(b*x+a))*(f*x)^m*(e*x*cos(e*x+d)+(1+m+b*c*x*log(F))*sin(e*x+d)),x, algorithm="giac")
[Out]
(x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*flo
or(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)^2*tan(1/4*pi*b*c*x*
sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*
m - 1/2*x*e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d) - x*a
bs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-
1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)^2*tan(1/4*pi*b*c*x*sgn(
F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m -
1/2*x*e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d)^2 + x*abs(F
)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*
sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)^2*tan(1/4*pi*b*c*x*sgn(F) -
1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*
x*e)*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d)^2 - x*abs(F)^(a
*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(
f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)*tan(1/4*pi*b*c*x*sgn(F) - 1/4*p
i*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)^2
*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d)^2 - x*abs(F)^(a*c)*
e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) -
1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)^2*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*
b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)^2*t
an(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d) - x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1
/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(
x) - 1/2*pi*m + 1/2*x*e)^2*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) +
1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)^2 - x*abs
(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/
4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)*tan(1/4*pi*b*c*x*sgn(F) -
1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*
x*e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)^2 + x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(
x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4
*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)^2*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn
(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*
d) - x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m
*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)^2*tan(1/4*pi*a*
c*sgn(F) - 1/4*pi*a*c + 1/2*d)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d) + x*abs(F)^(a*c)*e^(b*c*x*log(abs
(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1)
+ 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)^2*tan
(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d) + x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4
*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x)
- 1/2*pi*m + 1/2*x*e)^2*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1
/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d)^2 + x*abs(F
)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*
sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)*tan(1/4*pi*b*c*x*sgn(F) - 1
/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*
e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d)^2 - x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)
))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*p
i*m*sgn(x) - 1/2*pi*m + 1/2*x*e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*
a*c - 1/2*d)^2 + x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*
b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)^2*t
an(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d)^2 - x*abs(F)^(a*c)*e^(b
*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4
*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/
2*d)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d)^2 + x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(
x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4
*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*p
i*a*c - 1/2*d)^2 - x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*p
i*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)^2
*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*
m*sgn(x) - 1/2*pi*m - 1/2*x*e) + x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*
sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*
m + 1/2*x*e)*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(
f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)^2 - x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan
(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sg
n(x) - 1/2*pi*m + 1/2*x*e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d) + x*abs(F)^(a*c)*e^(b*c*x*log(abs(F))
+ m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1
/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d) - x*abs(F
)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*
sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)*tan(1/4*pi*a*c*sgn(F) - 1/4
*pi*a*c + 1/2*d)^2 - x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4
*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)
*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)^2 - x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*t
an(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*
sgn(x) - 1/2*pi*m + 1/2*x*e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d) + x*abs(F)^(a*c)*e^(b*c*x*log(abs(F
)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) +
1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d) - x*abs
(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)^2*tan(1/4*p
i*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d) + x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*
c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2
*pi*m + 1/2*x*e)*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d)^2 + x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(a
bs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sg
n(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d)^2 + x*abs(F)^(a*c)*e^
(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)*tan(1/4*pi*a*c*sgn(F) -
1/4*pi*a*c - 1/2*d)^2 + x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) -
1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*
x*e) - x*abs(F)^(a*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi
*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e) + x*abs(F)^(a
*c)*e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d) - x*abs(F)^(a*c)*
e^(b*c*x*log(abs(F)) + m*log(abs(f)*abs(x)))*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d))*f/(tan(1/4*pi*b*c*x*
sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*
m + 1/2*x*e)^2*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sg
n(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)^2*tan(1/4*pi*a*c*sg
n(F) - 1/4*pi*a*c - 1/2*d)^2 + tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) +
1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)^2*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*f
loor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)^2*tan(1/4*pi*a*c*
sgn(F) - 1/4*pi*a*c + 1/2*d)^2 + tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x)
+ 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)^2*tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m
*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)^2*tan(1/4*pi*a*
c*sgn(F) - 1/4*pi*a*c - 1/2*d)^2 + tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x
) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)
^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d)^2 + tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sg
n(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4
*pi*a*c + 1/2*d)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d)^2 + tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi
*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)^2*tan(1/4*pi*
b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1
/2*pi*m - 1/2*x*e)^2 + tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4
*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)^2 + tan(1/4
*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x)
- 1/2*pi*m - 1/2*x*e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)^2 + tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*
x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m + 1/2*x*e)^2*tan(1
/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d)^2 + tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1
/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c
- 1/2*d)^2 + tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)^2*tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d)^2 + tan
(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) + 1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sg
n(x) - 1/2*pi*m + 1/2*x*e)^2 + tan(1/4*pi*b*c*x*sgn(F) - 1/4*pi*b*c*x + pi*m*floor(-1/4*sgn(f) - 1/4*sgn(x) +
1) + 1/4*pi*m*sgn(f) + 1/4*pi*m*sgn(x) - 1/2*pi*m - 1/2*x*e)^2 + tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c + 1/2*d)^2
+ tan(1/4*pi*a*c*sgn(F) - 1/4*pi*a*c - 1/2*d)^2 + 1)