Optimal. Leaf size=30 \[ e^{x-x^2+\frac {3 x^2 \left (-e^{-x} x+x^2\right )}{\log (x)}} \]
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Rubi [F] time = 9.49, 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 (-x+\frac {e^{-x} \left (-3 x^3+3 e^x x^4+e^x \left (x-x^2\right ) \log (x)\right )}{\log (x)}\right ) \left (3 x^2-3 e^x x^3+\left (-9 x^2+3 x^3+12 e^x x^3\right ) \log (x)+e^x (1-2 x) \log ^2(x)\right )}{\log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) \left (3 x^2-3 e^x x^3+\left (-9 x^2+3 x^3+12 e^x x^3\right ) \log (x)+e^x (1-2 x) \log ^2(x)\right )}{\log ^2(x)} \, dx\\ &=\int \left (\frac {3 \exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^2 (1-3 \log (x)+x \log (x))}{\log ^2(x)}-\frac {\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) \left (3 x^3-12 x^3 \log (x)-\log ^2(x)+2 x \log ^2(x)\right )}{\log ^2(x)}\right ) \, dx\\ &=3 \int \frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^2 (1-3 \log (x)+x \log (x))}{\log ^2(x)} \, dx-\int \frac {\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) \left (3 x^3-12 x^3 \log (x)-\log ^2(x)+2 x \log ^2(x)\right )}{\log ^2(x)} \, dx\\ &=3 \int \left (\frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^2}{\log ^2(x)}+\frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) (-3+x) x^2}{\log (x)}\right ) \, dx-\int \left (-\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right )+2 \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x+\frac {3 \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log ^2(x)}-\frac {12 \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log (x)}\right ) \, dx\\ &=-\left (2 \int \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x \, dx\right )+3 \int \frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^2}{\log ^2(x)} \, dx-3 \int \frac {\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log ^2(x)} \, dx+3 \int \frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) (-3+x) x^2}{\log (x)} \, dx+12 \int \frac {\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log (x)} \, dx+\int \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) \, dx\\ &=-\left (2 \int \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x \, dx\right )+3 \int \left (-\frac {3 \exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^2}{\log (x)}+\frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log (x)}\right ) \, dx+3 \int \frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^2}{\log ^2(x)} \, dx-3 \int \frac {\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log ^2(x)} \, dx+12 \int \frac {\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log (x)} \, dx+\int \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) \, dx\\ &=-\left (2 \int \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x \, dx\right )+3 \int \frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^2}{\log ^2(x)} \, dx-3 \int \frac {\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log ^2(x)} \, dx+3 \int \frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log (x)} \, dx-9 \int \frac {\exp \left (\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^2}{\log (x)} \, dx+12 \int \frac {\exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) x^3}{\log (x)} \, dx+\int \exp \left (x+\frac {e^{-x} x^2 \left (-3 x+3 e^x x^2-e^x \log (x)\right )}{\log (x)}\right ) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 2.82, size = 27, normalized size = 0.90 \begin {gather*} e^{x-x^2-\frac {3 \left (e^{-x}-x\right ) x^3}{\log (x)}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 34, normalized size = 1.13 \begin {gather*} e^{\left (x + \frac {{\left (3 \, x^{4} e^{x} - x^{2} e^{x} \log \relax (x) - 3 \, x^{3}\right )} e^{\left (-x\right )}}{\log \relax (x)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left (3 \, x^{3} e^{x} + {\left (2 \, x - 1\right )} e^{x} \log \relax (x)^{2} - 3 \, x^{2} - 3 \, {\left (4 \, x^{3} e^{x} + x^{3} - 3 \, x^{2}\right )} \log \relax (x)\right )} e^{\left (-x + \frac {{\left (3 \, x^{4} e^{x} - 3 \, x^{3} - {\left (x^{2} - x\right )} e^{x} \log \relax (x)\right )} e^{\left (-x\right )}}{\log \relax (x)}\right )}}{\log \relax (x)^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.15, size = 38, normalized size = 1.27
method | result | size |
risch | \({\mathrm e}^{-\frac {x \left (-3 \,{\mathrm e}^{x} x^{3}+x \,{\mathrm e}^{x} \ln \relax (x )-{\mathrm e}^{x} \ln \relax (x )+3 x^{2}\right ) {\mathrm e}^{-x}}{\ln \relax (x )}}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.82, size = 30, normalized size = 1.00 \begin {gather*} e^{\left (\frac {3 \, x^{4}}{\log \relax (x)} - \frac {3 \, x^{3} e^{\left (-x\right )}}{\log \relax (x)} - x^{2} + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.59, size = 33, normalized size = 1.10 \begin {gather*} {\mathrm {e}}^{-\frac {3\,x^3\,{\mathrm {e}}^{-x}}{\ln \relax (x)}}\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^x\,{\mathrm {e}}^{\frac {3\,x^4}{\ln \relax (x)}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.84, size = 32, normalized size = 1.07 \begin {gather*} e^{\frac {\left (3 x^{4} e^{x} - 3 x^{3} + \left (- x^{2} + x\right ) e^{x} \log {\relax (x )}\right ) e^{- x}}{\log {\relax (x )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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