Optimal. Leaf size=31 \[ \frac {2 x+4 e^{-e^{x^2}+x} x-\frac {4+x}{\log (3)}}{x} \]
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Rubi [F] time = 1.25, 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^{-e^{x^2}+x} \left (4 e^{e^{x^2}-x}+4 x^2 \log (3)-8 e^{x^2} x^3 \log (3)\right )}{x^2 \log (3)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^{-e^{x^2}+x} \left (4 e^{e^{x^2}-x}+4 x^2 \log (3)-8 e^{x^2} x^3 \log (3)\right )}{x^2} \, dx}{\log (3)}\\ &=\frac {\int \left (-8 e^{-e^{x^2}+x+x^2} x \log (3)+\frac {4 e^{-e^{x^2}} \left (e^{e^{x^2}}+e^x x^2 \log (3)\right )}{x^2}\right ) \, dx}{\log (3)}\\ &=-\left (8 \int e^{-e^{x^2}+x+x^2} x \, dx\right )+\frac {4 \int \frac {e^{-e^{x^2}} \left (e^{e^{x^2}}+e^x x^2 \log (3)\right )}{x^2} \, dx}{\log (3)}\\ &=-\left (8 \int e^{-e^{x^2}+x+x^2} x \, dx\right )+\frac {4 \int \left (\frac {1}{x^2}+e^{-e^{x^2}+x} \log (3)\right ) \, dx}{\log (3)}\\ &=-\frac {4}{x \log (3)}+4 \int e^{-e^{x^2}+x} \, dx-8 \int e^{-e^{x^2}+x+x^2} x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.28, size = 23, normalized size = 0.74 \begin {gather*} 4 \left (e^{-e^{x^2}+x}-\frac {1}{x \log (3)}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.88, size = 34, normalized size = 1.10 \begin {gather*} \frac {4 \, {\left (x \log \relax (3) - e^{\left (-x + e^{\left (x^{2}\right )}\right )}\right )} e^{\left (x - e^{\left (x^{2}\right )}\right )}}{x \log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.43, size = 24, normalized size = 0.77 \begin {gather*} \frac {4 \, {\left (x e^{\left (x - e^{\left (x^{2}\right )}\right )} \log \relax (3) - 1\right )}}{x \log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 22, normalized size = 0.71
method | result | size |
risch | \(-\frac {4}{x \ln \relax (3)}+4 \,{\mathrm e}^{-{\mathrm e}^{x^{2}}+x}\) | \(22\) |
norman | \(\frac {\left (4 x -\frac {4 \,{\mathrm e}^{{\mathrm e}^{x^{2}}-x}}{\ln \relax (3)}\right ) {\mathrm e}^{-{\mathrm e}^{x^{2}}+x}}{x}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.85, size = 24, normalized size = 0.77 \begin {gather*} \frac {4 \, {\left (e^{\left (x - e^{\left (x^{2}\right )}\right )} \log \relax (3) - \frac {1}{x}\right )}}{\log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.86, size = 21, normalized size = 0.68 \begin {gather*} 4\,{\mathrm {e}}^{x-{\mathrm {e}}^{x^2}}-\frac {4}{x\,\ln \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.31, size = 15, normalized size = 0.48 \begin {gather*} 4 e^{x - e^{x^{2}}} - \frac {4}{x \log {\relax (3 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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