Optimal. Leaf size=32 \[ 9+e^{4-e^4}-e^{\frac {-x^3+\frac {x}{\log (x)}}{\log (x)}} \]
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Rubi [F] time = 0.78, 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 {e^{\frac {x-x^3 \log (x)}{\log ^2(x)}} \left (2+\left (-1-x^2\right ) \log (x)+3 x^2 \log ^2(x)\right )}{\log ^3(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2 e^{\frac {x-x^3 \log (x)}{\log ^2(x)}}}{\log ^3(x)}+\frac {e^{\frac {x-x^3 \log (x)}{\log ^2(x)}} \left (-1-x^2\right )}{\log ^2(x)}+\frac {3 e^{\frac {x-x^3 \log (x)}{\log ^2(x)}} x^2}{\log (x)}\right ) \, dx\\ &=2 \int \frac {e^{\frac {x-x^3 \log (x)}{\log ^2(x)}}}{\log ^3(x)} \, dx+3 \int \frac {e^{\frac {x-x^3 \log (x)}{\log ^2(x)}} x^2}{\log (x)} \, dx+\int \frac {e^{\frac {x-x^3 \log (x)}{\log ^2(x)}} \left (-1-x^2\right )}{\log ^2(x)} \, dx\\ &=2 \int \frac {e^{\frac {x-x^3 \log (x)}{\log ^2(x)}}}{\log ^3(x)} \, dx+3 \int \frac {e^{\frac {x-x^3 \log (x)}{\log ^2(x)}} x^2}{\log (x)} \, dx+\int \left (-\frac {e^{\frac {x-x^3 \log (x)}{\log ^2(x)}}}{\log ^2(x)}-\frac {e^{\frac {x-x^3 \log (x)}{\log ^2(x)}} x^2}{\log ^2(x)}\right ) \, dx\\ &=2 \int \frac {e^{\frac {x-x^3 \log (x)}{\log ^2(x)}}}{\log ^3(x)} \, dx+3 \int \frac {e^{\frac {x-x^3 \log (x)}{\log ^2(x)}} x^2}{\log (x)} \, dx-\int \frac {e^{\frac {x-x^3 \log (x)}{\log ^2(x)}}}{\log ^2(x)} \, dx-\int \frac {e^{\frac {x-x^3 \log (x)}{\log ^2(x)}} x^2}{\log ^2(x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.17, size = 20, normalized size = 0.62 \begin {gather*} -e^{\frac {x}{\log ^2(x)}-\frac {x^3}{\log (x)}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 19, normalized size = 0.59 \begin {gather*} -e^{\left (-\frac {x^{3} \log \relax (x) - x}{\log \relax (x)^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 19, normalized size = 0.59 \begin {gather*} -e^{\left (-\frac {x^{3}}{\log \relax (x)} + \frac {x}{\log \relax (x)^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 19, normalized size = 0.59
method | result | size |
risch | \(-{\mathrm e}^{-\frac {x \left (x^{2} \ln \relax (x )-1\right )}{\ln \relax (x )^{2}}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.62, size = 17, normalized size = 0.53 \begin {gather*} -{\mathrm {e}}^{\frac {x-x^3\,\ln \relax (x)}{{\ln \relax (x)}^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.43, size = 15, normalized size = 0.47 \begin {gather*} - e^{\frac {- x^{3} \log {\relax (x )} + x}{\log {\relax (x )}^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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