3.40.39 \(\int \frac {e^{-2-e^{\frac {-x+(4-\log (3)) \log (x^3)}{\log (x^3)}}-x} (e^{\frac {-x+(4-\log (3)) \log (x^3)}{\log (x^3)}} (-3+\log (x^3))-\log ^2(x^3))}{\log ^2(x^3)} \, dx\)

Optimal. Leaf size=24 \[ e^{-2-\frac {1}{3} e^{4-\frac {x}{\log \left (x^3\right )}}-x} \]

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Rubi [F]  time = 1.19, 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*} \int \frac {\exp \left (-2-e^{\frac {-x+(4-\log (3)) \log \left (x^3\right )}{\log \left (x^3\right )}}-x\right ) \left (e^{\frac {-x+(4-\log (3)) \log \left (x^3\right )}{\log \left (x^3\right )}} \left (-3+\log \left (x^3\right )\right )-\log ^2\left (x^3\right )\right )}{\log ^2\left (x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(-2 - E^((-x + (4 - Log[3])*Log[x^3])/Log[x^3]) - x)*(E^((-x + (4 - Log[3])*Log[x^3])/Log[x^3])*(-3 + L
og[x^3]) - Log[x^3]^2))/Log[x^3]^2,x]

[Out]

-Defer[Int][E^(-2 - E^(4 - x/Log[x^3])/3 - x), x] - Defer[Int][E^(2 - E^((-x + (4 - Log[3])*Log[x^3])/Log[x^3]
) - x - x/Log[x^3])/Log[x^3]^2, x] + Defer[Int][E^(2 - E^((-x + (4 - Log[3])*Log[x^3])/Log[x^3]) - x - x/Log[x
^3])/Log[x^3], x]/3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\exp \left (-2-e^{\frac {-x+(4-\log (3)) \log \left (x^3\right )}{\log \left (x^3\right )}}-x\right )+\frac {\exp \left (2-e^{\frac {-x+(4-\log (3)) \log \left (x^3\right )}{\log \left (x^3\right )}}-x-\frac {x}{\log \left (x^3\right )}\right ) \left (-3+\log \left (x^3\right )\right )}{3 \log ^2\left (x^3\right )}\right ) \, dx\\ &=\frac {1}{3} \int \frac {\exp \left (2-e^{\frac {-x+(4-\log (3)) \log \left (x^3\right )}{\log \left (x^3\right )}}-x-\frac {x}{\log \left (x^3\right )}\right ) \left (-3+\log \left (x^3\right )\right )}{\log ^2\left (x^3\right )} \, dx-\int \exp \left (-2-e^{\frac {-x+(4-\log (3)) \log \left (x^3\right )}{\log \left (x^3\right )}}-x\right ) \, dx\\ &=\frac {1}{3} \int \left (-\frac {3 \exp \left (2-e^{\frac {-x+(4-\log (3)) \log \left (x^3\right )}{\log \left (x^3\right )}}-x-\frac {x}{\log \left (x^3\right )}\right )}{\log ^2\left (x^3\right )}+\frac {\exp \left (2-e^{\frac {-x+(4-\log (3)) \log \left (x^3\right )}{\log \left (x^3\right )}}-x-\frac {x}{\log \left (x^3\right )}\right )}{\log \left (x^3\right )}\right ) \, dx-\int e^{-2-\frac {1}{3} e^{4-\frac {x}{\log \left (x^3\right )}}-x} \, dx\\ &=\frac {1}{3} \int \frac {\exp \left (2-e^{\frac {-x+(4-\log (3)) \log \left (x^3\right )}{\log \left (x^3\right )}}-x-\frac {x}{\log \left (x^3\right )}\right )}{\log \left (x^3\right )} \, dx-\int e^{-2-\frac {1}{3} e^{4-\frac {x}{\log \left (x^3\right )}}-x} \, dx-\int \frac {\exp \left (2-e^{\frac {-x+(4-\log (3)) \log \left (x^3\right )}{\log \left (x^3\right )}}-x-\frac {x}{\log \left (x^3\right )}\right )}{\log ^2\left (x^3\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.78, size = 24, normalized size = 1.00 \begin {gather*} e^{-2-\frac {1}{3} e^{4-\frac {x}{\log \left (x^3\right )}}-x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-2 - E^((-x + (4 - Log[3])*Log[x^3])/Log[x^3]) - x)*(E^((-x + (4 - Log[3])*Log[x^3])/Log[x^3])*(
-3 + Log[x^3]) - Log[x^3]^2))/Log[x^3]^2,x]

[Out]

E^(-2 - E^(4 - x/Log[x^3])/3 - x)

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fricas [A]  time = 0.90, size = 28, normalized size = 1.17 \begin {gather*} e^{\left (-x - e^{\left (-\frac {{\left (\log \relax (3) - 4\right )} \log \left (x^{3}\right ) + x}{\log \left (x^{3}\right )}\right )} - 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((log(x^3)-3)*exp(((-log(3)+4)*log(x^3)-x)/log(x^3))-log(x^3)^2)*exp(-exp(((-log(3)+4)*log(x^3)-x)/l
og(x^3))-x-2)/log(x^3)^2,x, algorithm="fricas")

[Out]

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

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giac [A]  time = 0.18, size = 24, normalized size = 1.00 \begin {gather*} e^{\left (-x - e^{\left (-\frac {x}{\log \left (x^{3}\right )} - \log \relax (3) + 4\right )} - 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((log(x^3)-3)*exp(((-log(3)+4)*log(x^3)-x)/log(x^3))-log(x^3)^2)*exp(-exp(((-log(3)+4)*log(x^3)-x)/l
og(x^3))-x-2)/log(x^3)^2,x, algorithm="giac")

[Out]

e^(-x - e^(-x/log(x^3) - log(3) + 4) - 2)

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maple [A]  time = 0.78, size = 27, normalized size = 1.12

method	result	size
risch	\({\mathrm e}^{-\frac {{\mathrm e}^{\frac {4 \ln \left (x^{3}\right )-x}{\ln \left (x^{3}\right )}}}{3}-x -2}\)	\(27\)
norman	\({\mathrm e}^{-{\mathrm e}^{\frac {\left (-\ln \relax (3)+4\right ) \ln \left (x^{3}\right )-x}{\ln \left (x^{3}\right )}}-x -2}\)	\(32\)
default	\(\frac {\left (\ln \left (x^{3}\right )-3 \ln \relax (x )\right ) {\mathrm e}^{-{\mathrm e}^{\frac {\left (-\ln \relax (3)+4\right ) \ln \left (x^{3}\right )-x}{\ln \left (x^{3}\right )}}-x -2}+3 \ln \relax (x ) {\mathrm e}^{-{\mathrm e}^{\frac {\left (-\ln \relax (3)+4\right ) \ln \left (x^{3}\right )-x}{\ln \left (x^{3}\right )}}-x -2}}{\ln \left (x^{3}\right )}\)	\(85\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((ln(x^3)-3)*exp(((-ln(3)+4)*ln(x^3)-x)/ln(x^3))-ln(x^3)^2)*exp(-exp(((-ln(3)+4)*ln(x^3)-x)/ln(x^3))-x-2)/
ln(x^3)^2,x,method=_RETURNVERBOSE)

[Out]

exp(-1/3*exp((4*ln(x^3)-x)/ln(x^3))-x-2)

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maxima [A]  time = 0.56, size = 18, normalized size = 0.75 \begin {gather*} e^{\left (-x - \frac {1}{3} \, e^{\left (-\frac {x}{3 \, \log \relax (x)} + 4\right )} - 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((log(x^3)-3)*exp(((-log(3)+4)*log(x^3)-x)/log(x^3))-log(x^3)^2)*exp(-exp(((-log(3)+4)*log(x^3)-x)/l
og(x^3))-x-2)/log(x^3)^2,x, algorithm="maxima")

[Out]

e^(-x - 1/3*e^(-1/3*x/log(x) + 4) - 2)

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mupad [B]  time = 2.42, size = 22, normalized size = 0.92 \begin {gather*} {\mathrm {e}}^{-\frac {{\mathrm {e}}^4\,{\mathrm {e}}^{-\frac {x}{\ln \left (x^3\right )}}}{3}}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(- x - exp(-(x + log(x^3)*(log(3) - 4))/log(x^3)) - 2)*(log(x^3)^2 - exp(-(x + log(x^3)*(log(3) - 4))
/log(x^3))*(log(x^3) - 3)))/log(x^3)^2,x)

[Out]

exp(-(exp(4)*exp(-x/log(x^3)))/3)*exp(-x)*exp(-2)

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sympy [A]  time = 0.69, size = 24, normalized size = 1.00 \begin {gather*} e^{- x - e^{\frac {- x + \left (4 - \log {\relax (3 )}\right ) \log {\left (x^{3} \right )}}{\log {\left (x^{3} \right )}}} - 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((ln(x**3)-3)*exp(((-ln(3)+4)*ln(x**3)-x)/ln(x**3))-ln(x**3)**2)*exp(-exp(((-ln(3)+4)*ln(x**3)-x)/ln
(x**3))-x-2)/ln(x**3)**2,x)

[Out]

exp(-x - exp((-x + (4 - log(3))*log(x**3))/log(x**3)) - 2)

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