3.54 \(\int F^{c (a+b x)} (d+e x+f x^2+g x^3+h x^4) \, dx\)

Optimal. Leaf size=348 \[ -\frac{e F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}-\frac{2 f x F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}+\frac{2 f F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}-\frac{3 g x^2 F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}+\frac{6 g x F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}-\frac{6 g F^{c (a+b x)}}{b^4 c^4 \log ^4(F)}-\frac{4 h x^3 F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}+\frac{12 h x^2 F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}-\frac{24 h x F^{c (a+b x)}}{b^4 c^4 \log ^4(F)}+\frac{24 h F^{c (a+b x)}}{b^5 c^5 \log ^5(F)}+\frac{d F^{c (a+b x)}}{b c \log (F)}+\frac{e x F^{c (a+b x)}}{b c \log (F)}+\frac{f x^2 F^{c (a+b x)}}{b c \log (F)}+\frac{g x^3 F^{c (a+b x)}}{b c \log (F)}+\frac{h x^4 F^{c (a+b x)}}{b c \log (F)} \]

[Out]

(24*F^(c*(a + b*x))*h)/(b^5*c^5*Log[F]^5) - (6*F^(c*(a + b*x))*g)/(b^4*c^4*Log[F]^4) - (24*F^(c*(a + b*x))*h*x
)/(b^4*c^4*Log[F]^4) + (2*f*F^(c*(a + b*x)))/(b^3*c^3*Log[F]^3) + (6*F^(c*(a + b*x))*g*x)/(b^3*c^3*Log[F]^3) +
(12*F^(c*(a + b*x))*h*x^2)/(b^3*c^3*Log[F]^3) - (e*F^(c*(a + b*x)))/(b^2*c^2*Log[F]^2) - (2*f*F^(c*(a + b*x))
*x)/(b^2*c^2*Log[F]^2) - (3*F^(c*(a + b*x))*g*x^2)/(b^2*c^2*Log[F]^2) - (4*F^(c*(a + b*x))*h*x^3)/(b^2*c^2*Log
[F]^2) + (d*F^(c*(a + b*x)))/(b*c*Log[F]) + (e*F^(c*(a + b*x))*x)/(b*c*Log[F]) + (f*F^(c*(a + b*x))*x^2)/(b*c*
Log[F]) + (F^(c*(a + b*x))*g*x^3)/(b*c*Log[F]) + (F^(c*(a + b*x))*h*x^4)/(b*c*Log[F])

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Rubi [A]  time = 0.312263, antiderivative size = 348, normalized size of antiderivative = 1., number of steps used = 17, number of rules used = 3, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {2196, 2194, 2176} \[ -\frac{e F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}-\frac{2 f x F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}+\frac{2 f F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}-\frac{3 g x^2 F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}+\frac{6 g x F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}-\frac{6 g F^{c (a+b x)}}{b^4 c^4 \log ^4(F)}-\frac{4 h x^3 F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}+\frac{12 h x^2 F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}-\frac{24 h x F^{c (a+b x)}}{b^4 c^4 \log ^4(F)}+\frac{24 h F^{c (a+b x)}}{b^5 c^5 \log ^5(F)}+\frac{d F^{c (a+b x)}}{b c \log (F)}+\frac{e x F^{c (a+b x)}}{b c \log (F)}+\frac{f x^2 F^{c (a+b x)}}{b c \log (F)}+\frac{g x^3 F^{c (a+b x)}}{b c \log (F)}+\frac{h x^4 F^{c (a+b x)}}{b c \log (F)} \]

Antiderivative was successfully verified.

[In]

Int[F^(c*(a + b*x))*(d + e*x + f*x^2 + g*x^3 + h*x^4),x]

[Out]

(24*F^(c*(a + b*x))*h)/(b^5*c^5*Log[F]^5) - (6*F^(c*(a + b*x))*g)/(b^4*c^4*Log[F]^4) - (24*F^(c*(a + b*x))*h*x
)/(b^4*c^4*Log[F]^4) + (2*f*F^(c*(a + b*x)))/(b^3*c^3*Log[F]^3) + (6*F^(c*(a + b*x))*g*x)/(b^3*c^3*Log[F]^3) +
(12*F^(c*(a + b*x))*h*x^2)/(b^3*c^3*Log[F]^3) - (e*F^(c*(a + b*x)))/(b^2*c^2*Log[F]^2) - (2*f*F^(c*(a + b*x))
*x)/(b^2*c^2*Log[F]^2) - (3*F^(c*(a + b*x))*g*x^2)/(b^2*c^2*Log[F]^2) - (4*F^(c*(a + b*x))*h*x^3)/(b^2*c^2*Log
[F]^2) + (d*F^(c*(a + b*x)))/(b*c*Log[F]) + (e*F^(c*(a + b*x))*x)/(b*c*Log[F]) + (f*F^(c*(a + b*x))*x^2)/(b*c*
Log[F]) + (F^(c*(a + b*x))*g*x^3)/(b*c*Log[F]) + (F^(c*(a + b*x))*h*x^4)/(b*c*Log[F])

Rule 2196

Int[(F_)^((c_.)*(v_))*(u_), x_Symbol] :> Int[ExpandIntegrand[F^(c*ExpandToSum[v, x]), u, x], x] /; FreeQ[{F, c
}, x] && PolynomialQ[u, x] && LinearQ[v, x] &&  !$UseGamma === True

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rule 2176

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Simp[((c + d*x)^m
*(b*F^(g*(e + f*x)))^n)/(f*g*n*Log[F]), x] - Dist[(d*m)/(f*g*n*Log[F]), Int[(c + d*x)^(m - 1)*(b*F^(g*(e + f*x
)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && GtQ[m, 0] && IntegerQ[2*m] &&  !$UseGamma === True

Rubi steps

\begin{align*} \int F^{c (a+b x)} \left (d+e x+f x^2+g x^3+h x^4\right ) \, dx &=\int \left (d F^{c (a+b x)}+e F^{c (a+b x)} x+f F^{c (a+b x)} x^2+F^{c (a+b x)} g x^3+F^{c (a+b x)} h x^4\right ) \, dx\\ &=d \int F^{c (a+b x)} \, dx+e \int F^{c (a+b x)} x \, dx+f \int F^{c (a+b x)} x^2 \, dx+g \int F^{c (a+b x)} x^3 \, dx+h \int F^{c (a+b x)} x^4 \, dx\\ &=\frac{d F^{c (a+b x)}}{b c \log (F)}+\frac{e F^{c (a+b x)} x}{b c \log (F)}+\frac{f F^{c (a+b x)} x^2}{b c \log (F)}+\frac{F^{c (a+b x)} g x^3}{b c \log (F)}+\frac{F^{c (a+b x)} h x^4}{b c \log (F)}-\frac{e \int F^{c (a+b x)} \, dx}{b c \log (F)}-\frac{(2 f) \int F^{c (a+b x)} x \, dx}{b c \log (F)}-\frac{(3 g) \int F^{c (a+b x)} x^2 \, dx}{b c \log (F)}-\frac{(4 h) \int F^{c (a+b x)} x^3 \, dx}{b c \log (F)}\\ &=-\frac{e F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}-\frac{2 f F^{c (a+b x)} x}{b^2 c^2 \log ^2(F)}-\frac{3 F^{c (a+b x)} g x^2}{b^2 c^2 \log ^2(F)}-\frac{4 F^{c (a+b x)} h x^3}{b^2 c^2 \log ^2(F)}+\frac{d F^{c (a+b x)}}{b c \log (F)}+\frac{e F^{c (a+b x)} x}{b c \log (F)}+\frac{f F^{c (a+b x)} x^2}{b c \log (F)}+\frac{F^{c (a+b x)} g x^3}{b c \log (F)}+\frac{F^{c (a+b x)} h x^4}{b c \log (F)}+\frac{(2 f) \int F^{c (a+b x)} \, dx}{b^2 c^2 \log ^2(F)}+\frac{(6 g) \int F^{c (a+b x)} x \, dx}{b^2 c^2 \log ^2(F)}+\frac{(12 h) \int F^{c (a+b x)} x^2 \, dx}{b^2 c^2 \log ^2(F)}\\ &=\frac{2 f F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}+\frac{6 F^{c (a+b x)} g x}{b^3 c^3 \log ^3(F)}+\frac{12 F^{c (a+b x)} h x^2}{b^3 c^3 \log ^3(F)}-\frac{e F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}-\frac{2 f F^{c (a+b x)} x}{b^2 c^2 \log ^2(F)}-\frac{3 F^{c (a+b x)} g x^2}{b^2 c^2 \log ^2(F)}-\frac{4 F^{c (a+b x)} h x^3}{b^2 c^2 \log ^2(F)}+\frac{d F^{c (a+b x)}}{b c \log (F)}+\frac{e F^{c (a+b x)} x}{b c \log (F)}+\frac{f F^{c (a+b x)} x^2}{b c \log (F)}+\frac{F^{c (a+b x)} g x^3}{b c \log (F)}+\frac{F^{c (a+b x)} h x^4}{b c \log (F)}-\frac{(6 g) \int F^{c (a+b x)} \, dx}{b^3 c^3 \log ^3(F)}-\frac{(24 h) \int F^{c (a+b x)} x \, dx}{b^3 c^3 \log ^3(F)}\\ &=-\frac{6 F^{c (a+b x)} g}{b^4 c^4 \log ^4(F)}-\frac{24 F^{c (a+b x)} h x}{b^4 c^4 \log ^4(F)}+\frac{2 f F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}+\frac{6 F^{c (a+b x)} g x}{b^3 c^3 \log ^3(F)}+\frac{12 F^{c (a+b x)} h x^2}{b^3 c^3 \log ^3(F)}-\frac{e F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}-\frac{2 f F^{c (a+b x)} x}{b^2 c^2 \log ^2(F)}-\frac{3 F^{c (a+b x)} g x^2}{b^2 c^2 \log ^2(F)}-\frac{4 F^{c (a+b x)} h x^3}{b^2 c^2 \log ^2(F)}+\frac{d F^{c (a+b x)}}{b c \log (F)}+\frac{e F^{c (a+b x)} x}{b c \log (F)}+\frac{f F^{c (a+b x)} x^2}{b c \log (F)}+\frac{F^{c (a+b x)} g x^3}{b c \log (F)}+\frac{F^{c (a+b x)} h x^4}{b c \log (F)}+\frac{(24 h) \int F^{c (a+b x)} \, dx}{b^4 c^4 \log ^4(F)}\\ &=\frac{24 F^{c (a+b x)} h}{b^5 c^5 \log ^5(F)}-\frac{6 F^{c (a+b x)} g}{b^4 c^4 \log ^4(F)}-\frac{24 F^{c (a+b x)} h x}{b^4 c^4 \log ^4(F)}+\frac{2 f F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}+\frac{6 F^{c (a+b x)} g x}{b^3 c^3 \log ^3(F)}+\frac{12 F^{c (a+b x)} h x^2}{b^3 c^3 \log ^3(F)}-\frac{e F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}-\frac{2 f F^{c (a+b x)} x}{b^2 c^2 \log ^2(F)}-\frac{3 F^{c (a+b x)} g x^2}{b^2 c^2 \log ^2(F)}-\frac{4 F^{c (a+b x)} h x^3}{b^2 c^2 \log ^2(F)}+\frac{d F^{c (a+b x)}}{b c \log (F)}+\frac{e F^{c (a+b x)} x}{b c \log (F)}+\frac{f F^{c (a+b x)} x^2}{b c \log (F)}+\frac{F^{c (a+b x)} g x^3}{b c \log (F)}+\frac{F^{c (a+b x)} h x^4}{b c \log (F)}\\ \end{align*}

Mathematica [A]  time = 0.161942, size = 117, normalized size = 0.34 \[ \frac{F^{c (a+b x)} \left (b^4 c^4 \log ^4(F) (d+x (e+x (f+x (g+h x))))-b^3 c^3 \log ^3(F) \left (e+x \left (2 f+3 g x+4 h x^2\right )\right )+2 b^2 c^2 \log ^2(F) (f+3 x (g+2 h x))-6 b c \log (F) (g+4 h x)+24 h\right )}{b^5 c^5 \log ^5(F)} \]

Antiderivative was successfully verified.

[In]

Integrate[F^(c*(a + b*x))*(d + e*x + f*x^2 + g*x^3 + h*x^4),x]

[Out]

(F^(c*(a + b*x))*(24*h - 6*b*c*(g + 4*h*x)*Log[F] + 2*b^2*c^2*(f + 3*x*(g + 2*h*x))*Log[F]^2 - b^3*c^3*(e + x*
(2*f + 3*g*x + 4*h*x^2))*Log[F]^3 + b^4*c^4*(d + x*(e + x*(f + x*(g + h*x))))*Log[F]^4))/(b^5*c^5*Log[F]^5)

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Maple [A]  time = 0.005, size = 212, normalized size = 0.6 \begin{align*}{\frac{ \left ( h{x}^{4}{b}^{4}{c}^{4} \left ( \ln \left ( F \right ) \right ) ^{4}+ \left ( \ln \left ( F \right ) \right ) ^{4}{b}^{4}{c}^{4}g{x}^{3}+ \left ( \ln \left ( F \right ) \right ) ^{4}{b}^{4}{c}^{4}f{x}^{2}+ \left ( \ln \left ( F \right ) \right ) ^{4}{b}^{4}{c}^{4}ex+ \left ( \ln \left ( F \right ) \right ) ^{4}{b}^{4}{c}^{4}d-4\, \left ( \ln \left ( F \right ) \right ) ^{3}{b}^{3}{c}^{3}h{x}^{3}-3\, \left ( \ln \left ( F \right ) \right ) ^{3}{b}^{3}{c}^{3}g{x}^{2}-2\, \left ( \ln \left ( F \right ) \right ) ^{3}{b}^{3}{c}^{3}fx- \left ( \ln \left ( F \right ) \right ) ^{3}{b}^{3}{c}^{3}e+12\, \left ( \ln \left ( F \right ) \right ) ^{2}{b}^{2}{c}^{2}h{x}^{2}+6\, \left ( \ln \left ( F \right ) \right ) ^{2}{b}^{2}{c}^{2}gx+2\,{b}^{2}{c}^{2} \left ( \ln \left ( F \right ) \right ) ^{2}f-24\,\ln \left ( F \right ) bchx-6\,gbc\ln \left ( F \right ) +24\,h \right ){F}^{c \left ( bx+a \right ) }}{{b}^{5}{c}^{5} \left ( \ln \left ( F \right ) \right ) ^{5}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F^(c*(b*x+a))*(h*x^4+g*x^3+f*x^2+e*x+d),x)

[Out]

(h*x^4*b^4*c^4*ln(F)^4+ln(F)^4*b^4*c^4*g*x^3+ln(F)^4*b^4*c^4*f*x^2+ln(F)^4*b^4*c^4*e*x+ln(F)^4*b^4*c^4*d-4*ln(
F)^3*b^3*c^3*h*x^3-3*ln(F)^3*b^3*c^3*g*x^2-2*ln(F)^3*b^3*c^3*f*x-ln(F)^3*b^3*c^3*e+12*ln(F)^2*b^2*c^2*h*x^2+6*
ln(F)^2*b^2*c^2*g*x+2*b^2*c^2*ln(F)^2*f-24*ln(F)*b*c*h*x-6*g*b*c*ln(F)+24*h)*F^(c*(b*x+a))/b^5/c^5/ln(F)^5

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Maxima [A]  time = 1.06509, size = 393, normalized size = 1.13 \begin{align*} \frac{F^{b c x + a c} d}{b c \log \left (F\right )} + \frac{{\left (F^{a c} b c x \log \left (F\right ) - F^{a c}\right )} F^{b c x} e}{b^{2} c^{2} \log \left (F\right )^{2}} + \frac{{\left (F^{a c} b^{2} c^{2} x^{2} \log \left (F\right )^{2} - 2 \, F^{a c} b c x \log \left (F\right ) + 2 \, F^{a c}\right )} F^{b c x} f}{b^{3} c^{3} \log \left (F\right )^{3}} + \frac{{\left (F^{a c} b^{3} c^{3} x^{3} \log \left (F\right )^{3} - 3 \, F^{a c} b^{2} c^{2} x^{2} \log \left (F\right )^{2} + 6 \, F^{a c} b c x \log \left (F\right ) - 6 \, F^{a c}\right )} F^{b c x} g}{b^{4} c^{4} \log \left (F\right )^{4}} + \frac{{\left (F^{a c} b^{4} c^{4} x^{4} \log \left (F\right )^{4} - 4 \, F^{a c} b^{3} c^{3} x^{3} \log \left (F\right )^{3} + 12 \, F^{a c} b^{2} c^{2} x^{2} \log \left (F\right )^{2} - 24 \, F^{a c} b c x \log \left (F\right ) + 24 \, F^{a c}\right )} F^{b c x} h}{b^{5} c^{5} \log \left (F\right )^{5}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(c*(b*x+a))*(h*x^4+g*x^3+f*x^2+e*x+d),x, algorithm="maxima")

[Out]

F^(b*c*x + a*c)*d/(b*c*log(F)) + (F^(a*c)*b*c*x*log(F) - F^(a*c))*F^(b*c*x)*e/(b^2*c^2*log(F)^2) + (F^(a*c)*b^
2*c^2*x^2*log(F)^2 - 2*F^(a*c)*b*c*x*log(F) + 2*F^(a*c))*F^(b*c*x)*f/(b^3*c^3*log(F)^3) + (F^(a*c)*b^3*c^3*x^3
*log(F)^3 - 3*F^(a*c)*b^2*c^2*x^2*log(F)^2 + 6*F^(a*c)*b*c*x*log(F) - 6*F^(a*c))*F^(b*c*x)*g/(b^4*c^4*log(F)^4
) + (F^(a*c)*b^4*c^4*x^4*log(F)^4 - 4*F^(a*c)*b^3*c^3*x^3*log(F)^3 + 12*F^(a*c)*b^2*c^2*x^2*log(F)^2 - 24*F^(a
*c)*b*c*x*log(F) + 24*F^(a*c))*F^(b*c*x)*h/(b^5*c^5*log(F)^5)

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Fricas [A]  time = 1.56461, size = 396, normalized size = 1.14 \begin{align*} \frac{{\left ({\left (b^{4} c^{4} h x^{4} + b^{4} c^{4} g x^{3} + b^{4} c^{4} f x^{2} + b^{4} c^{4} e x + b^{4} c^{4} d\right )} \log \left (F\right )^{4} -{\left (4 \, b^{3} c^{3} h x^{3} + 3 \, b^{3} c^{3} g x^{2} + 2 \, b^{3} c^{3} f x + b^{3} c^{3} e\right )} \log \left (F\right )^{3} + 2 \,{\left (6 \, b^{2} c^{2} h x^{2} + 3 \, b^{2} c^{2} g x + b^{2} c^{2} f\right )} \log \left (F\right )^{2} - 6 \,{\left (4 \, b c h x + b c g\right )} \log \left (F\right ) + 24 \, h\right )} F^{b c x + a c}}{b^{5} c^{5} \log \left (F\right )^{5}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(c*(b*x+a))*(h*x^4+g*x^3+f*x^2+e*x+d),x, algorithm="fricas")

[Out]

((b^4*c^4*h*x^4 + b^4*c^4*g*x^3 + b^4*c^4*f*x^2 + b^4*c^4*e*x + b^4*c^4*d)*log(F)^4 - (4*b^3*c^3*h*x^3 + 3*b^3
*c^3*g*x^2 + 2*b^3*c^3*f*x + b^3*c^3*e)*log(F)^3 + 2*(6*b^2*c^2*h*x^2 + 3*b^2*c^2*g*x + b^2*c^2*f)*log(F)^2 -
6*(4*b*c*h*x + b*c*g)*log(F) + 24*h)*F^(b*c*x + a*c)/(b^5*c^5*log(F)^5)

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Sympy [A]  time = 0.216861, size = 284, normalized size = 0.82 \begin{align*} \begin{cases} \frac{F^{c \left (a + b x\right )} \left (b^{4} c^{4} d \log{\left (F \right )}^{4} + b^{4} c^{4} e x \log{\left (F \right )}^{4} + b^{4} c^{4} f x^{2} \log{\left (F \right )}^{4} + b^{4} c^{4} g x^{3} \log{\left (F \right )}^{4} + b^{4} c^{4} h x^{4} \log{\left (F \right )}^{4} - b^{3} c^{3} e \log{\left (F \right )}^{3} - 2 b^{3} c^{3} f x \log{\left (F \right )}^{3} - 3 b^{3} c^{3} g x^{2} \log{\left (F \right )}^{3} - 4 b^{3} c^{3} h x^{3} \log{\left (F \right )}^{3} + 2 b^{2} c^{2} f \log{\left (F \right )}^{2} + 6 b^{2} c^{2} g x \log{\left (F \right )}^{2} + 12 b^{2} c^{2} h x^{2} \log{\left (F \right )}^{2} - 6 b c g \log{\left (F \right )} - 24 b c h x \log{\left (F \right )} + 24 h\right )}{b^{5} c^{5} \log{\left (F \right )}^{5}} & \text{for}\: b^{5} c^{5} \log{\left (F \right )}^{5} \neq 0 \\d x + \frac{e x^{2}}{2} + \frac{f x^{3}}{3} + \frac{g x^{4}}{4} + \frac{h x^{5}}{5} & \text{otherwise} \end{cases} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F**(c*(b*x+a))*(h*x**4+g*x**3+f*x**2+e*x+d),x)

[Out]

Piecewise((F**(c*(a + b*x))*(b**4*c**4*d*log(F)**4 + b**4*c**4*e*x*log(F)**4 + b**4*c**4*f*x**2*log(F)**4 + b*
*4*c**4*g*x**3*log(F)**4 + b**4*c**4*h*x**4*log(F)**4 - b**3*c**3*e*log(F)**3 - 2*b**3*c**3*f*x*log(F)**3 - 3*
b**3*c**3*g*x**2*log(F)**3 - 4*b**3*c**3*h*x**3*log(F)**3 + 2*b**2*c**2*f*log(F)**2 + 6*b**2*c**2*g*x*log(F)**
2 + 12*b**2*c**2*h*x**2*log(F)**2 - 6*b*c*g*log(F) - 24*b*c*h*x*log(F) + 24*h)/(b**5*c**5*log(F)**5), Ne(b**5*
c**5*log(F)**5, 0)), (d*x + e*x**2/2 + f*x**3/3 + g*x**4/4 + h*x**5/5, True))

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Giac [C]  time = 1.51238, size = 10024, normalized size = 28.8 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(c*(b*x+a))*(h*x^4+g*x^3+f*x^2+e*x+d),x, algorithm="giac")

[Out]

(2*((pi*b^2*c^2*log(abs(F))*sgn(F) - pi*b^2*c^2*log(abs(F)))*(pi*b*c*x*sgn(F) - pi*b*c*x)/((pi^2*b^2*c^2*sgn(F
) - pi^2*b^2*c^2 + 2*b^2*c^2*log(abs(F))^2)^2 + 4*(pi*b^2*c^2*log(abs(F))*sgn(F) - pi*b^2*c^2*log(abs(F)))^2)
+ (pi^2*b^2*c^2*sgn(F) - pi^2*b^2*c^2 + 2*b^2*c^2*log(abs(F))^2)*(b*c*x*log(abs(F)) - 1)/((pi^2*b^2*c^2*sgn(F)
- pi^2*b^2*c^2 + 2*b^2*c^2*log(abs(F))^2)^2 + 4*(pi*b^2*c^2*log(abs(F))*sgn(F) - pi*b^2*c^2*log(abs(F)))^2))*
cos(-1/2*pi*b*c*x*sgn(F) + 1/2*pi*b*c*x - 1/2*pi*a*c*sgn(F) + 1/2*pi*a*c) + ((pi^2*b^2*c^2*sgn(F) - pi^2*b^2*c
^2 + 2*b^2*c^2*log(abs(F))^2)*(pi*b*c*x*sgn(F) - pi*b*c*x)/((pi^2*b^2*c^2*sgn(F) - pi^2*b^2*c^2 + 2*b^2*c^2*lo
g(abs(F))^2)^2 + 4*(pi*b^2*c^2*log(abs(F))*sgn(F) - pi*b^2*c^2*log(abs(F)))^2) - 4*(pi*b^2*c^2*log(abs(F))*sgn
(F) - pi*b^2*c^2*log(abs(F)))*(b*c*x*log(abs(F)) - 1)/((pi^2*b^2*c^2*sgn(F) - pi^2*b^2*c^2 + 2*b^2*c^2*log(abs
(F))^2)^2 + 4*(pi*b^2*c^2*log(abs(F))*sgn(F) - pi*b^2*c^2*log(abs(F)))^2))*sin(-1/2*pi*b*c*x*sgn(F) + 1/2*pi*b
*c*x - 1/2*pi*a*c*sgn(F) + 1/2*pi*a*c))*e^(b*c*x*log(abs(F)) + a*c*log(abs(F)) + 1) - 1/2*I*((2*pi*b*c*x*sgn(F
) - 2*pi*b*c*x - 4*I*b*c*x*log(abs(F)) + 4*I)*e^(1/2*I*pi*b*c*x*sgn(F) - 1/2*I*pi*b*c*x + 1/2*I*pi*a*c*sgn(F)
- 1/2*I*pi*a*c)/(2*pi^2*b^2*c^2*sgn(F) + 4*I*pi*b^2*c^2*log(abs(F))*sgn(F) - 2*pi^2*b^2*c^2 - 4*I*pi*b^2*c^2*l
og(abs(F)) + 4*b^2*c^2*log(abs(F))^2) + (2*pi*b*c*x*sgn(F) - 2*pi*b*c*x + 4*I*b*c*x*log(abs(F)) - 4*I)*e^(-1/2
*I*pi*b*c*x*sgn(F) + 1/2*I*pi*b*c*x - 1/2*I*pi*a*c*sgn(F) + 1/2*I*pi*a*c)/(2*pi^2*b^2*c^2*sgn(F) - 4*I*pi*b^2*
c^2*log(abs(F))*sgn(F) - 2*pi^2*b^2*c^2 + 4*I*pi*b^2*c^2*log(abs(F)) + 4*b^2*c^2*log(abs(F))^2))*e^(b*c*x*log(
abs(F)) + a*c*log(abs(F)) + 1) - (((4*pi^3*b^4*c^4*h*x^4*log(abs(F))*sgn(F) - 4*pi*b^4*c^4*h*x^4*log(abs(F))^3
*sgn(F) - 4*pi^3*b^4*c^4*h*x^4*log(abs(F)) + 4*pi*b^4*c^4*h*x^4*log(abs(F))^3 + 4*pi^3*b^4*c^4*g*x^3*log(abs(F
))*sgn(F) - 4*pi*b^4*c^4*g*x^3*log(abs(F))^3*sgn(F) - 4*pi^3*b^4*c^4*g*x^3*log(abs(F)) + 4*pi*b^4*c^4*g*x^3*lo
g(abs(F))^3 + 4*pi^3*b^4*c^4*f*x^2*log(abs(F))*sgn(F) - 4*pi*b^4*c^4*f*x^2*log(abs(F))^3*sgn(F) - 4*pi^3*b^4*c
^4*f*x^2*log(abs(F)) + 4*pi*b^4*c^4*f*x^2*log(abs(F))^3 - 4*pi^3*b^3*c^3*h*x^3*sgn(F) + 4*pi^3*b^4*c^4*d*log(a
bs(F))*sgn(F) + 12*pi*b^3*c^3*h*x^3*log(abs(F))^2*sgn(F) - 4*pi*b^4*c^4*d*log(abs(F))^3*sgn(F) + 4*pi^3*b^3*c^
3*h*x^3 - 4*pi^3*b^4*c^4*d*log(abs(F)) - 12*pi*b^3*c^3*h*x^3*log(abs(F))^2 + 4*pi*b^4*c^4*d*log(abs(F))^3 - 3*
pi^3*b^3*c^3*g*x^2*sgn(F) + 9*pi*b^3*c^3*g*x^2*log(abs(F))^2*sgn(F) + 3*pi^3*b^3*c^3*g*x^2 - 9*pi*b^3*c^3*g*x^
2*log(abs(F))^2 - 2*pi^3*b^3*c^3*f*x*sgn(F) + 6*pi*b^3*c^3*f*x*log(abs(F))^2*sgn(F) + 2*pi^3*b^3*c^3*f*x - 6*p
i*b^3*c^3*f*x*log(abs(F))^2 - 24*pi*b^2*c^2*h*x^2*log(abs(F))*sgn(F) + 24*pi*b^2*c^2*h*x^2*log(abs(F)) - 12*pi
*b^2*c^2*g*x*log(abs(F))*sgn(F) + 12*pi*b^2*c^2*g*x*log(abs(F)) - 4*pi*b^2*c^2*f*log(abs(F))*sgn(F) + 4*pi*b^2
*c^2*f*log(abs(F)) + 24*pi*b*c*h*x*sgn(F) - 24*pi*b*c*h*x + 6*pi*b*c*g*sgn(F) - 6*pi*b*c*g)*(pi^5*b^5*c^5*sgn(
F) - 10*pi^3*b^5*c^5*log(abs(F))^2*sgn(F) + 5*pi*b^5*c^5*log(abs(F))^4*sgn(F) - pi^5*b^5*c^5 + 10*pi^3*b^5*c^5
*log(abs(F))^2 - 5*pi*b^5*c^5*log(abs(F))^4)/((pi^5*b^5*c^5*sgn(F) - 10*pi^3*b^5*c^5*log(abs(F))^2*sgn(F) + 5*
pi*b^5*c^5*log(abs(F))^4*sgn(F) - pi^5*b^5*c^5 + 10*pi^3*b^5*c^5*log(abs(F))^2 - 5*pi*b^5*c^5*log(abs(F))^4)^2
+ (5*pi^4*b^5*c^5*log(abs(F))*sgn(F) - 10*pi^2*b^5*c^5*log(abs(F))^3*sgn(F) - 5*pi^4*b^5*c^5*log(abs(F)) + 10
*pi^2*b^5*c^5*log(abs(F))^3 - 2*b^5*c^5*log(abs(F))^5)^2) - (pi^4*b^4*c^4*h*x^4*sgn(F) - 6*pi^2*b^4*c^4*h*x^4*
log(abs(F))^2*sgn(F) - pi^4*b^4*c^4*h*x^4 + 6*pi^2*b^4*c^4*h*x^4*log(abs(F))^2 - 2*b^4*c^4*h*x^4*log(abs(F))^4
+ pi^4*b^4*c^4*g*x^3*sgn(F) - 6*pi^2*b^4*c^4*g*x^3*log(abs(F))^2*sgn(F) - pi^4*b^4*c^4*g*x^3 + 6*pi^2*b^4*c^4
*g*x^3*log(abs(F))^2 - 2*b^4*c^4*g*x^3*log(abs(F))^4 + pi^4*b^4*c^4*f*x^2*sgn(F) - 6*pi^2*b^4*c^4*f*x^2*log(ab
s(F))^2*sgn(F) - pi^4*b^4*c^4*f*x^2 + 6*pi^2*b^4*c^4*f*x^2*log(abs(F))^2 - 2*b^4*c^4*f*x^2*log(abs(F))^4 + pi^
4*b^4*c^4*d*sgn(F) + 12*pi^2*b^3*c^3*h*x^3*log(abs(F))*sgn(F) - 6*pi^2*b^4*c^4*d*log(abs(F))^2*sgn(F) - pi^4*b
^4*c^4*d - 12*pi^2*b^3*c^3*h*x^3*log(abs(F)) + 6*pi^2*b^4*c^4*d*log(abs(F))^2 + 8*b^3*c^3*h*x^3*log(abs(F))^3
- 2*b^4*c^4*d*log(abs(F))^4 + 9*pi^2*b^3*c^3*g*x^2*log(abs(F))*sgn(F) - 9*pi^2*b^3*c^3*g*x^2*log(abs(F)) + 6*b
^3*c^3*g*x^2*log(abs(F))^3 + 6*pi^2*b^3*c^3*f*x*log(abs(F))*sgn(F) - 6*pi^2*b^3*c^3*f*x*log(abs(F)) + 4*b^3*c^
3*f*x*log(abs(F))^3 - 12*pi^2*b^2*c^2*h*x^2*sgn(F) + 12*pi^2*b^2*c^2*h*x^2 - 24*b^2*c^2*h*x^2*log(abs(F))^2 -
6*pi^2*b^2*c^2*g*x*sgn(F) + 6*pi^2*b^2*c^2*g*x - 12*b^2*c^2*g*x*log(abs(F))^2 - 2*pi^2*b^2*c^2*f*sgn(F) + 2*pi
^2*b^2*c^2*f - 4*b^2*c^2*f*log(abs(F))^2 + 48*b*c*h*x*log(abs(F)) + 12*b*c*g*log(abs(F)) - 48*h)*(5*pi^4*b^5*c
^5*log(abs(F))*sgn(F) - 10*pi^2*b^5*c^5*log(abs(F))^3*sgn(F) - 5*pi^4*b^5*c^5*log(abs(F)) + 10*pi^2*b^5*c^5*lo
g(abs(F))^3 - 2*b^5*c^5*log(abs(F))^5)/((pi^5*b^5*c^5*sgn(F) - 10*pi^3*b^5*c^5*log(abs(F))^2*sgn(F) + 5*pi*b^5
*c^5*log(abs(F))^4*sgn(F) - pi^5*b^5*c^5 + 10*pi^3*b^5*c^5*log(abs(F))^2 - 5*pi*b^5*c^5*log(abs(F))^4)^2 + (5*
pi^4*b^5*c^5*log(abs(F))*sgn(F) - 10*pi^2*b^5*c^5*log(abs(F))^3*sgn(F) - 5*pi^4*b^5*c^5*log(abs(F)) + 10*pi^2*
b^5*c^5*log(abs(F))^3 - 2*b^5*c^5*log(abs(F))^5)^2))*cos(-1/2*pi*b*c*x*sgn(F) + 1/2*pi*b*c*x - 1/2*pi*a*c*sgn(
F) + 1/2*pi*a*c) - ((pi^4*b^4*c^4*h*x^4*sgn(F) - 6*pi^2*b^4*c^4*h*x^4*log(abs(F))^2*sgn(F) - pi^4*b^4*c^4*h*x^
4 + 6*pi^2*b^4*c^4*h*x^4*log(abs(F))^2 - 2*b^4*c^4*h*x^4*log(abs(F))^4 + pi^4*b^4*c^4*g*x^3*sgn(F) - 6*pi^2*b^
4*c^4*g*x^3*log(abs(F))^2*sgn(F) - pi^4*b^4*c^4*g*x^3 + 6*pi^2*b^4*c^4*g*x^3*log(abs(F))^2 - 2*b^4*c^4*g*x^3*l
og(abs(F))^4 + pi^4*b^4*c^4*f*x^2*sgn(F) - 6*pi^2*b^4*c^4*f*x^2*log(abs(F))^2*sgn(F) - pi^4*b^4*c^4*f*x^2 + 6*
pi^2*b^4*c^4*f*x^2*log(abs(F))^2 - 2*b^4*c^4*f*x^2*log(abs(F))^4 + pi^4*b^4*c^4*d*sgn(F) + 12*pi^2*b^3*c^3*h*x
^3*log(abs(F))*sgn(F) - 6*pi^2*b^4*c^4*d*log(abs(F))^2*sgn(F) - pi^4*b^4*c^4*d - 12*pi^2*b^3*c^3*h*x^3*log(abs
(F)) + 6*pi^2*b^4*c^4*d*log(abs(F))^2 + 8*b^3*c^3*h*x^3*log(abs(F))^3 - 2*b^4*c^4*d*log(abs(F))^4 + 9*pi^2*b^3
*c^3*g*x^2*log(abs(F))*sgn(F) - 9*pi^2*b^3*c^3*g*x^2*log(abs(F)) + 6*b^3*c^3*g*x^2*log(abs(F))^3 + 6*pi^2*b^3*
c^3*f*x*log(abs(F))*sgn(F) - 6*pi^2*b^3*c^3*f*x*log(abs(F)) + 4*b^3*c^3*f*x*log(abs(F))^3 - 12*pi^2*b^2*c^2*h*
x^2*sgn(F) + 12*pi^2*b^2*c^2*h*x^2 - 24*b^2*c^2*h*x^2*log(abs(F))^2 - 6*pi^2*b^2*c^2*g*x*sgn(F) + 6*pi^2*b^2*c
^2*g*x - 12*b^2*c^2*g*x*log(abs(F))^2 - 2*pi^2*b^2*c^2*f*sgn(F) + 2*pi^2*b^2*c^2*f - 4*b^2*c^2*f*log(abs(F))^2
+ 48*b*c*h*x*log(abs(F)) + 12*b*c*g*log(abs(F)) - 48*h)*(pi^5*b^5*c^5*sgn(F) - 10*pi^3*b^5*c^5*log(abs(F))^2*
sgn(F) + 5*pi*b^5*c^5*log(abs(F))^4*sgn(F) - pi^5*b^5*c^5 + 10*pi^3*b^5*c^5*log(abs(F))^2 - 5*pi*b^5*c^5*log(a
bs(F))^4)/((pi^5*b^5*c^5*sgn(F) - 10*pi^3*b^5*c^5*log(abs(F))^2*sgn(F) + 5*pi*b^5*c^5*log(abs(F))^4*sgn(F) - p
i^5*b^5*c^5 + 10*pi^3*b^5*c^5*log(abs(F))^2 - 5*pi*b^5*c^5*log(abs(F))^4)^2 + (5*pi^4*b^5*c^5*log(abs(F))*sgn(
F) - 10*pi^2*b^5*c^5*log(abs(F))^3*sgn(F) - 5*pi^4*b^5*c^5*log(abs(F)) + 10*pi^2*b^5*c^5*log(abs(F))^3 - 2*b^5
*c^5*log(abs(F))^5)^2) + (4*pi^3*b^4*c^4*h*x^4*log(abs(F))*sgn(F) - 4*pi*b^4*c^4*h*x^4*log(abs(F))^3*sgn(F) -
4*pi^3*b^4*c^4*h*x^4*log(abs(F)) + 4*pi*b^4*c^4*h*x^4*log(abs(F))^3 + 4*pi^3*b^4*c^4*g*x^3*log(abs(F))*sgn(F)
- 4*pi*b^4*c^4*g*x^3*log(abs(F))^3*sgn(F) - 4*pi^3*b^4*c^4*g*x^3*log(abs(F)) + 4*pi*b^4*c^4*g*x^3*log(abs(F))^
3 + 4*pi^3*b^4*c^4*f*x^2*log(abs(F))*sgn(F) - 4*pi*b^4*c^4*f*x^2*log(abs(F))^3*sgn(F) - 4*pi^3*b^4*c^4*f*x^2*l
og(abs(F)) + 4*pi*b^4*c^4*f*x^2*log(abs(F))^3 - 4*pi^3*b^3*c^3*h*x^3*sgn(F) + 4*pi^3*b^4*c^4*d*log(abs(F))*sgn
(F) + 12*pi*b^3*c^3*h*x^3*log(abs(F))^2*sgn(F) - 4*pi*b^4*c^4*d*log(abs(F))^3*sgn(F) + 4*pi^3*b^3*c^3*h*x^3 -
4*pi^3*b^4*c^4*d*log(abs(F)) - 12*pi*b^3*c^3*h*x^3*log(abs(F))^2 + 4*pi*b^4*c^4*d*log(abs(F))^3 - 3*pi^3*b^3*c
^3*g*x^2*sgn(F) + 9*pi*b^3*c^3*g*x^2*log(abs(F))^2*sgn(F) + 3*pi^3*b^3*c^3*g*x^2 - 9*pi*b^3*c^3*g*x^2*log(abs(
F))^2 - 2*pi^3*b^3*c^3*f*x*sgn(F) + 6*pi*b^3*c^3*f*x*log(abs(F))^2*sgn(F) + 2*pi^3*b^3*c^3*f*x - 6*pi*b^3*c^3*
f*x*log(abs(F))^2 - 24*pi*b^2*c^2*h*x^2*log(abs(F))*sgn(F) + 24*pi*b^2*c^2*h*x^2*log(abs(F)) - 12*pi*b^2*c^2*g
*x*log(abs(F))*sgn(F) + 12*pi*b^2*c^2*g*x*log(abs(F)) - 4*pi*b^2*c^2*f*log(abs(F))*sgn(F) + 4*pi*b^2*c^2*f*log
(abs(F)) + 24*pi*b*c*h*x*sgn(F) - 24*pi*b*c*h*x + 6*pi*b*c*g*sgn(F) - 6*pi*b*c*g)*(5*pi^4*b^5*c^5*log(abs(F))*
sgn(F) - 10*pi^2*b^5*c^5*log(abs(F))^3*sgn(F) - 5*pi^4*b^5*c^5*log(abs(F)) + 10*pi^2*b^5*c^5*log(abs(F))^3 - 2
*b^5*c^5*log(abs(F))^5)/((pi^5*b^5*c^5*sgn(F) - 10*pi^3*b^5*c^5*log(abs(F))^2*sgn(F) + 5*pi*b^5*c^5*log(abs(F)
)^4*sgn(F) - pi^5*b^5*c^5 + 10*pi^3*b^5*c^5*log(abs(F))^2 - 5*pi*b^5*c^5*log(abs(F))^4)^2 + (5*pi^4*b^5*c^5*lo
g(abs(F))*sgn(F) - 10*pi^2*b^5*c^5*log(abs(F))^3*sgn(F) - 5*pi^4*b^5*c^5*log(abs(F)) + 10*pi^2*b^5*c^5*log(abs
(F))^3 - 2*b^5*c^5*log(abs(F))^5)^2))*sin(-1/2*pi*b*c*x*sgn(F) + 1/2*pi*b*c*x - 1/2*pi*a*c*sgn(F) + 1/2*pi*a*c
))*e^(b*c*x*log(abs(F)) + a*c*log(abs(F))) + 1/2*I*((-16*I*pi^4*b^4*c^4*h*x^4*sgn(F) + 64*pi^3*b^4*c^4*h*x^4*l
og(abs(F))*sgn(F) + 96*I*pi^2*b^4*c^4*h*x^4*log(abs(F))^2*sgn(F) - 64*pi*b^4*c^4*h*x^4*log(abs(F))^3*sgn(F) +
16*I*pi^4*b^4*c^4*h*x^4 - 64*pi^3*b^4*c^4*h*x^4*log(abs(F)) - 96*I*pi^2*b^4*c^4*h*x^4*log(abs(F))^2 + 64*pi*b^
4*c^4*h*x^4*log(abs(F))^3 + 32*I*b^4*c^4*h*x^4*log(abs(F))^4 - 16*I*pi^4*b^4*c^4*g*x^3*sgn(F) + 64*pi^3*b^4*c^
4*g*x^3*log(abs(F))*sgn(F) + 96*I*pi^2*b^4*c^4*g*x^3*log(abs(F))^2*sgn(F) - 64*pi*b^4*c^4*g*x^3*log(abs(F))^3*
sgn(F) + 16*I*pi^4*b^4*c^4*g*x^3 - 64*pi^3*b^4*c^4*g*x^3*log(abs(F)) - 96*I*pi^2*b^4*c^4*g*x^3*log(abs(F))^2 +
64*pi*b^4*c^4*g*x^3*log(abs(F))^3 + 32*I*b^4*c^4*g*x^3*log(abs(F))^4 - 16*I*pi^4*b^4*c^4*f*x^2*sgn(F) + 64*pi
^3*b^4*c^4*f*x^2*log(abs(F))*sgn(F) + 96*I*pi^2*b^4*c^4*f*x^2*log(abs(F))^2*sgn(F) - 64*pi*b^4*c^4*f*x^2*log(a
bs(F))^3*sgn(F) + 16*I*pi^4*b^4*c^4*f*x^2 - 64*pi^3*b^4*c^4*f*x^2*log(abs(F)) - 96*I*pi^2*b^4*c^4*f*x^2*log(ab
s(F))^2 + 64*pi*b^4*c^4*f*x^2*log(abs(F))^3 + 32*I*b^4*c^4*f*x^2*log(abs(F))^4 - 16*I*pi^4*b^4*c^4*d*sgn(F) -
64*pi^3*b^3*c^3*h*x^3*sgn(F) + 64*pi^3*b^4*c^4*d*log(abs(F))*sgn(F) - 192*I*pi^2*b^3*c^3*h*x^3*log(abs(F))*sgn
(F) + 96*I*pi^2*b^4*c^4*d*log(abs(F))^2*sgn(F) + 192*pi*b^3*c^3*h*x^3*log(abs(F))^2*sgn(F) - 64*pi*b^4*c^4*d*l
og(abs(F))^3*sgn(F) + 16*I*pi^4*b^4*c^4*d + 64*pi^3*b^3*c^3*h*x^3 - 64*pi^3*b^4*c^4*d*log(abs(F)) + 192*I*pi^2
*b^3*c^3*h*x^3*log(abs(F)) - 96*I*pi^2*b^4*c^4*d*log(abs(F))^2 - 192*pi*b^3*c^3*h*x^3*log(abs(F))^2 + 64*pi*b^
4*c^4*d*log(abs(F))^3 - 128*I*b^3*c^3*h*x^3*log(abs(F))^3 + 32*I*b^4*c^4*d*log(abs(F))^4 - 48*pi^3*b^3*c^3*g*x
^2*sgn(F) - 144*I*pi^2*b^3*c^3*g*x^2*log(abs(F))*sgn(F) + 144*pi*b^3*c^3*g*x^2*log(abs(F))^2*sgn(F) + 48*pi^3*
b^3*c^3*g*x^2 + 144*I*pi^2*b^3*c^3*g*x^2*log(abs(F)) - 144*pi*b^3*c^3*g*x^2*log(abs(F))^2 - 96*I*b^3*c^3*g*x^2
*log(abs(F))^3 - 32*pi^3*b^3*c^3*f*x*sgn(F) - 96*I*pi^2*b^3*c^3*f*x*log(abs(F))*sgn(F) + 96*pi*b^3*c^3*f*x*log
(abs(F))^2*sgn(F) + 32*pi^3*b^3*c^3*f*x + 96*I*pi^2*b^3*c^3*f*x*log(abs(F)) - 96*pi*b^3*c^3*f*x*log(abs(F))^2
- 64*I*b^3*c^3*f*x*log(abs(F))^3 + 192*I*pi^2*b^2*c^2*h*x^2*sgn(F) - 384*pi*b^2*c^2*h*x^2*log(abs(F))*sgn(F) -
192*I*pi^2*b^2*c^2*h*x^2 + 384*pi*b^2*c^2*h*x^2*log(abs(F)) + 384*I*b^2*c^2*h*x^2*log(abs(F))^2 + 96*I*pi^2*b
^2*c^2*g*x*sgn(F) - 192*pi*b^2*c^2*g*x*log(abs(F))*sgn(F) - 96*I*pi^2*b^2*c^2*g*x + 192*pi*b^2*c^2*g*x*log(abs
(F)) + 192*I*b^2*c^2*g*x*log(abs(F))^2 + 32*I*pi^2*b^2*c^2*f*sgn(F) - 64*pi*b^2*c^2*f*log(abs(F))*sgn(F) - 32*
I*pi^2*b^2*c^2*f + 64*pi*b^2*c^2*f*log(abs(F)) + 64*I*b^2*c^2*f*log(abs(F))^2 + 384*pi*b*c*h*x*sgn(F) - 384*pi
*b*c*h*x - 768*I*b*c*h*x*log(abs(F)) + 96*pi*b*c*g*sgn(F) - 96*pi*b*c*g - 192*I*b*c*g*log(abs(F)) + 768*I*h)*e
^(1/2*I*pi*b*c*x*sgn(F) - 1/2*I*pi*b*c*x + 1/2*I*pi*a*c*sgn(F) - 1/2*I*pi*a*c)/(16*I*pi^5*b^5*c^5*sgn(F) - 80*
pi^4*b^5*c^5*log(abs(F))*sgn(F) - 160*I*pi^3*b^5*c^5*log(abs(F))^2*sgn(F) + 160*pi^2*b^5*c^5*log(abs(F))^3*sgn
(F) + 80*I*pi*b^5*c^5*log(abs(F))^4*sgn(F) - 16*I*pi^5*b^5*c^5 + 80*pi^4*b^5*c^5*log(abs(F)) + 160*I*pi^3*b^5*
c^5*log(abs(F))^2 - 160*pi^2*b^5*c^5*log(abs(F))^3 - 80*I*pi*b^5*c^5*log(abs(F))^4 + 32*b^5*c^5*log(abs(F))^5)
- (-16*I*pi^4*b^4*c^4*h*x^4*sgn(F) - 64*pi^3*b^4*c^4*h*x^4*log(abs(F))*sgn(F) + 96*I*pi^2*b^4*c^4*h*x^4*log(a
bs(F))^2*sgn(F) + 64*pi*b^4*c^4*h*x^4*log(abs(F))^3*sgn(F) + 16*I*pi^4*b^4*c^4*h*x^4 + 64*pi^3*b^4*c^4*h*x^4*l
og(abs(F)) - 96*I*pi^2*b^4*c^4*h*x^4*log(abs(F))^2 - 64*pi*b^4*c^4*h*x^4*log(abs(F))^3 + 32*I*b^4*c^4*h*x^4*lo
g(abs(F))^4 - 16*I*pi^4*b^4*c^4*g*x^3*sgn(F) - 64*pi^3*b^4*c^4*g*x^3*log(abs(F))*sgn(F) + 96*I*pi^2*b^4*c^4*g*
x^3*log(abs(F))^2*sgn(F) + 64*pi*b^4*c^4*g*x^3*log(abs(F))^3*sgn(F) + 16*I*pi^4*b^4*c^4*g*x^3 + 64*pi^3*b^4*c^
4*g*x^3*log(abs(F)) - 96*I*pi^2*b^4*c^4*g*x^3*log(abs(F))^2 - 64*pi*b^4*c^4*g*x^3*log(abs(F))^3 + 32*I*b^4*c^4
*g*x^3*log(abs(F))^4 - 16*I*pi^4*b^4*c^4*f*x^2*sgn(F) - 64*pi^3*b^4*c^4*f*x^2*log(abs(F))*sgn(F) + 96*I*pi^2*b
^4*c^4*f*x^2*log(abs(F))^2*sgn(F) + 64*pi*b^4*c^4*f*x^2*log(abs(F))^3*sgn(F) + 16*I*pi^4*b^4*c^4*f*x^2 + 64*pi
^3*b^4*c^4*f*x^2*log(abs(F)) - 96*I*pi^2*b^4*c^4*f*x^2*log(abs(F))^2 - 64*pi*b^4*c^4*f*x^2*log(abs(F))^3 + 32*
I*b^4*c^4*f*x^2*log(abs(F))^4 - 16*I*pi^4*b^4*c^4*d*sgn(F) + 64*pi^3*b^3*c^3*h*x^3*sgn(F) - 64*pi^3*b^4*c^4*d*
log(abs(F))*sgn(F) - 192*I*pi^2*b^3*c^3*h*x^3*log(abs(F))*sgn(F) + 96*I*pi^2*b^4*c^4*d*log(abs(F))^2*sgn(F) -
192*pi*b^3*c^3*h*x^3*log(abs(F))^2*sgn(F) + 64*pi*b^4*c^4*d*log(abs(F))^3*sgn(F) + 16*I*pi^4*b^4*c^4*d - 64*pi
^3*b^3*c^3*h*x^3 + 64*pi^3*b^4*c^4*d*log(abs(F)) + 192*I*pi^2*b^3*c^3*h*x^3*log(abs(F)) - 96*I*pi^2*b^4*c^4*d*
log(abs(F))^2 + 192*pi*b^3*c^3*h*x^3*log(abs(F))^2 - 64*pi*b^4*c^4*d*log(abs(F))^3 - 128*I*b^3*c^3*h*x^3*log(a
bs(F))^3 + 32*I*b^4*c^4*d*log(abs(F))^4 + 48*pi^3*b^3*c^3*g*x^2*sgn(F) - 144*I*pi^2*b^3*c^3*g*x^2*log(abs(F))*
sgn(F) - 144*pi*b^3*c^3*g*x^2*log(abs(F))^2*sgn(F) - 48*pi^3*b^3*c^3*g*x^2 + 144*I*pi^2*b^3*c^3*g*x^2*log(abs(
F)) + 144*pi*b^3*c^3*g*x^2*log(abs(F))^2 - 96*I*b^3*c^3*g*x^2*log(abs(F))^3 + 32*pi^3*b^3*c^3*f*x*sgn(F) - 96*
I*pi^2*b^3*c^3*f*x*log(abs(F))*sgn(F) - 96*pi*b^3*c^3*f*x*log(abs(F))^2*sgn(F) - 32*pi^3*b^3*c^3*f*x + 96*I*pi
^2*b^3*c^3*f*x*log(abs(F)) + 96*pi*b^3*c^3*f*x*log(abs(F))^2 - 64*I*b^3*c^3*f*x*log(abs(F))^3 + 192*I*pi^2*b^2
*c^2*h*x^2*sgn(F) + 384*pi*b^2*c^2*h*x^2*log(abs(F))*sgn(F) - 192*I*pi^2*b^2*c^2*h*x^2 - 384*pi*b^2*c^2*h*x^2*
log(abs(F)) + 384*I*b^2*c^2*h*x^2*log(abs(F))^2 + 96*I*pi^2*b^2*c^2*g*x*sgn(F) + 192*pi*b^2*c^2*g*x*log(abs(F)
)*sgn(F) - 96*I*pi^2*b^2*c^2*g*x - 192*pi*b^2*c^2*g*x*log(abs(F)) + 192*I*b^2*c^2*g*x*log(abs(F))^2 + 32*I*pi^
2*b^2*c^2*f*sgn(F) + 64*pi*b^2*c^2*f*log(abs(F))*sgn(F) - 32*I*pi^2*b^2*c^2*f - 64*pi*b^2*c^2*f*log(abs(F)) +
64*I*b^2*c^2*f*log(abs(F))^2 - 384*pi*b*c*h*x*sgn(F) + 384*pi*b*c*h*x - 768*I*b*c*h*x*log(abs(F)) - 96*pi*b*c*
g*sgn(F) + 96*pi*b*c*g - 192*I*b*c*g*log(abs(F)) + 768*I*h)*e^(-1/2*I*pi*b*c*x*sgn(F) + 1/2*I*pi*b*c*x - 1/2*I
*pi*a*c*sgn(F) + 1/2*I*pi*a*c)/(-16*I*pi^5*b^5*c^5*sgn(F) - 80*pi^4*b^5*c^5*log(abs(F))*sgn(F) + 160*I*pi^3*b^
5*c^5*log(abs(F))^2*sgn(F) + 160*pi^2*b^5*c^5*log(abs(F))^3*sgn(F) - 80*I*pi*b^5*c^5*log(abs(F))^4*sgn(F) + 16
*I*pi^5*b^5*c^5 + 80*pi^4*b^5*c^5*log(abs(F)) - 160*I*pi^3*b^5*c^5*log(abs(F))^2 - 160*pi^2*b^5*c^5*log(abs(F)
)^3 + 80*I*pi*b^5*c^5*log(abs(F))^4 + 32*b^5*c^5*log(abs(F))^5))*e^(b*c*x*log(abs(F)) + a*c*log(abs(F)))