3.80.5 \(\int \frac {8 x+32 x^3+e^{e^5} (-4-24 x^2)+4 (i \pi +\log (5))}{x^4+4 x^6+4 x^8+(2 x^3+4 x^5) (i \pi +\log (5))+x^2 (i \pi +\log (5))^2+e^{2 e^5} (x^2+4 x^4+4 x^6+(2 x+4 x^3) (i \pi +\log (5))+(i \pi +\log (5))^2)+e^{e^5} (-2 x^3-8 x^5-8 x^7+(-4 x^2-8 x^4) (i \pi +\log (5))-2 x (i \pi +\log (5))^2)} \, dx\)

Optimal. Leaf size=29 \[ \frac {4}{\left (e^{e^5}-x\right ) \left (i \pi +x+2 x^3+\log (5)\right )} \]

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Rubi [F]  time = 180.00, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(8*x + 32*x^3 + E^E^5*(-4 - 24*x^2) + 4*(I*Pi + Log[5]))/(x^4 + 4*x^6 + 4*x^8 + (2*x^3 + 4*x^5)*(I*Pi + Lo
g[5]) + x^2*(I*Pi + Log[5])^2 + E^(2*E^5)*(x^2 + 4*x^4 + 4*x^6 + (2*x + 4*x^3)*(I*Pi + Log[5]) + (I*Pi + Log[5
])^2) + E^E^5*(-2*x^3 - 8*x^5 - 8*x^7 + (-4*x^2 - 8*x^4)*(I*Pi + Log[5]) - 2*x*(I*Pi + Log[5])^2)),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.23, size = 29, normalized size = 1.00 \begin {gather*} \frac {4}{\left (e^{e^5}-x\right ) \left (i \pi +x+2 x^3+\log (5)\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(8*x + 32*x^3 + E^E^5*(-4 - 24*x^2) + 4*(I*Pi + Log[5]))/(x^4 + 4*x^6 + 4*x^8 + (2*x^3 + 4*x^5)*(I*P
i + Log[5]) + x^2*(I*Pi + Log[5])^2 + E^(2*E^5)*(x^2 + 4*x^4 + 4*x^6 + (2*x + 4*x^3)*(I*Pi + Log[5]) + (I*Pi +
Log[5])^2) + E^E^5*(-2*x^3 - 8*x^5 - 8*x^7 + (-4*x^2 - 8*x^4)*(I*Pi + Log[5]) - 2*x*(I*Pi + Log[5])^2)),x]

[Out]

4/((E^E^5 - x)*(I*Pi + x + 2*x^3 + Log[5]))

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fricas [A]  time = 0.86, size = 38, normalized size = 1.31 \begin {gather*} -\frac {4}{2 \, x^{4} + i \, \pi x + x^{2} - {\left (i \, \pi + 2 \, x^{3} + x + \log \relax (5)\right )} e^{\left (e^{5}\right )} + x \log \relax (5)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-24*x^2-4)*exp(exp(5))+4*log(5)+4*I*pi+32*x^3+8*x)/(((log(5)+I*pi)^2+(4*x^3+2*x)*(log(5)+I*pi)+4*x
^6+4*x^4+x^2)*exp(exp(5))^2+(-2*x*(log(5)+I*pi)^2+(-8*x^4-4*x^2)*(log(5)+I*pi)-8*x^7-8*x^5-2*x^3)*exp(exp(5))+
x^2*(log(5)+I*pi)^2+(4*x^5+2*x^3)*(log(5)+I*pi)+4*x^8+4*x^6+x^4),x, algorithm="fricas")

[Out]

-4/(2*x^4 + I*pi*x + x^2 - (I*pi + 2*x^3 + x + log(5))*e^(e^5) + x*log(5))

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-24*x^2-4)*exp(exp(5))+4*log(5)+4*I*pi+32*x^3+8*x)/(((log(5)+I*pi)^2+(4*x^3+2*x)*(log(5)+I*pi)+4*x
^6+4*x^4+x^2)*exp(exp(5))^2+(-2*x*(log(5)+I*pi)^2+(-8*x^4-4*x^2)*(log(5)+I*pi)-8*x^7-8*x^5-2*x^3)*exp(exp(5))+
x^2*(log(5)+I*pi)^2+(4*x^5+2*x^3)*(log(5)+I*pi)+4*x^8+4*x^6+x^4),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 3.59, size = 58, normalized size = 2.00

method	result	size
risch	\(-\frac {4 i}{-2 i {\mathrm e}^{{\mathrm e}^{5}} x^{3}+2 i x^{4}-i \ln \relax (5) {\mathrm e}^{{\mathrm e}^{5}}+i x \ln \relax (5)-i {\mathrm e}^{{\mathrm e}^{5}} x +i x^{2}+\pi \,{\mathrm e}^{{\mathrm e}^{5}}-\pi x}\)	\(58\)
norman	\(\frac {8 x^{3}+4 x -4 i \pi +4 \ln \relax (5)}{\left ({\mathrm e}^{{\mathrm e}^{5}}-x \right ) \left (4 x^{6}+4 x^{3} \ln \relax (5)+4 x^{4}+\pi ^{2}+\ln \relax (5)^{2}+2 x \ln \relax (5)+x^{2}\right )}\)	\(63\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-24*x^2-4)*exp(exp(5))+4*ln(5)+4*I*Pi+32*x^3+8*x)/(((ln(5)+I*Pi)^2+(4*x^3+2*x)*(ln(5)+I*Pi)+4*x^6+4*x^4+
x^2)*exp(exp(5))^2+(-2*x*(ln(5)+I*Pi)^2+(-8*x^4-4*x^2)*(ln(5)+I*Pi)-8*x^7-8*x^5-2*x^3)*exp(exp(5))+x^2*(ln(5)+
I*Pi)^2+(4*x^5+2*x^3)*(ln(5)+I*Pi)+4*x^8+4*x^6+x^4),x,method=_RETURNVERBOSE)

[Out]

-4*I/(-2*I*exp(exp(5))*x^3+2*I*x^4-I*ln(5)*exp(exp(5))+I*x*ln(5)-I*exp(exp(5))*x+I*x^2+Pi*exp(exp(5))-Pi*x)

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maxima [A]  time = 0.39, size = 47, normalized size = 1.62 \begin {gather*} -\frac {4}{2 \, x^{4} - 2 \, x^{3} e^{\left (e^{5}\right )} + {\left (i \, \pi - e^{\left (e^{5}\right )} + \log \relax (5)\right )} x + x^{2} - i \, \pi e^{\left (e^{5}\right )} - e^{\left (e^{5}\right )} \log \relax (5)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-24*x^2-4)*exp(exp(5))+4*log(5)+4*I*pi+32*x^3+8*x)/(((log(5)+I*pi)^2+(4*x^3+2*x)*(log(5)+I*pi)+4*x
^6+4*x^4+x^2)*exp(exp(5))^2+(-2*x*(log(5)+I*pi)^2+(-8*x^4-4*x^2)*(log(5)+I*pi)-8*x^7-8*x^5-2*x^3)*exp(exp(5))+
x^2*(log(5)+I*pi)^2+(4*x^5+2*x^3)*(log(5)+I*pi)+4*x^8+4*x^6+x^4),x, algorithm="maxima")

[Out]

-4/(2*x^4 - 2*x^3*e^(e^5) + (I*pi - e^(e^5) + log(5))*x + x^2 - I*pi*e^(e^5) - e^(e^5)*log(5))

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mupad [B]  time = 11.38, size = 53, normalized size = 1.83 \begin {gather*} \frac {2}{-x^4+{\mathrm {e}}^{{\mathrm {e}}^5}\,x^3-\frac {x^2}{2}+\left (\frac {{\mathrm {e}}^{{\mathrm {e}}^5}}{2}-\frac {\ln \relax (5)}{2}-\frac {\Pi \,1{}\mathrm {i}}{2}\right )\,x+\frac {\Pi \,{\mathrm {e}}^{{\mathrm {e}}^5}\,1{}\mathrm {i}}{2}+\frac {{\mathrm {e}}^{{\mathrm {e}}^5}\,\ln \relax (5)}{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((Pi*4i + 8*x + 4*log(5) - exp(exp(5))*(24*x^2 + 4) + 32*x^3)/(x^2*(Pi*1i + log(5))^2 + exp(2*exp(5))*((2*x
+ 4*x^3)*(Pi*1i + log(5)) + x^2 + 4*x^4 + 4*x^6 + (Pi*1i + log(5))^2) - exp(exp(5))*((Pi*1i + log(5))*(4*x^2
+ 8*x^4) + 2*x*(Pi*1i + log(5))^2 + 2*x^3 + 8*x^5 + 8*x^7) + (Pi*1i + log(5))*(2*x^3 + 4*x^5) + x^4 + 4*x^6 +
4*x^8),x)

[Out]

2/(x^3*exp(exp(5)) + (Pi*exp(exp(5))*1i)/2 + (exp(exp(5))*log(5))/2 - x^2/2 - x^4 - x*((Pi*1i)/2 + log(5)/2 -
exp(exp(5))/2))

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-24*x**2-4)*exp(exp(5))+4*ln(5)+4*I*pi+32*x**3+8*x)/(((ln(5)+I*pi)**2+(4*x**3+2*x)*(ln(5)+I*pi)+4*
x**6+4*x**4+x**2)*exp(exp(5))**2+(-2*x*(ln(5)+I*pi)**2+(-8*x**4-4*x**2)*(ln(5)+I*pi)-8*x**7-8*x**5-2*x**3)*exp
(exp(5))+x**2*(ln(5)+I*pi)**2+(4*x**5+2*x**3)*(ln(5)+I*pi)+4*x**8+4*x**6+x**4),x)

[Out]

Timed out

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