Optimal. Leaf size=30 \[ \frac {2 x \log (x)}{e^{e^{\log ^2(2)}-e^{x^2} (-3+x)}-x} \]
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Rubi [F] time = 12.75, 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 {-2 e^{2 e^{x^2} (-3+x)} x+e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \left (2+\left (2+e^{x^2} \left (2 x-12 x^2+4 x^3\right )\right ) \log (x)\right )}{e^{2 e^{\log ^2(2)}}-2 e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} x+e^{2 e^{x^2} (-3+x)} x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-2 e^{2 e^{x^2} (-3+x)} x+e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \left (2+\left (2+e^{x^2} \left (2 x-12 x^2+4 x^3\right )\right ) \log (x)\right )}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx\\ &=\int \left (\frac {2 e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x \left (1-6 x+2 x^2\right ) \log (x)}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2}-\frac {2 e^{e^{x^2} (-3+x)} \left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x-e^{e^{\log ^2(2)}} \log (x)\right )}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2}\right ) \, dx\\ &=2 \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x \left (1-6 x+2 x^2\right ) \log (x)}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx-2 \int \frac {e^{e^{x^2} (-3+x)} \left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x-e^{e^{\log ^2(2)}} \log (x)\right )}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx\\ &=-\left (2 \int \left (-\frac {e^{e^{x^2} (-3+x)}}{e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x}-\frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \log (x)}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2}\right ) \, dx\right )-2 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx-6 \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx+2 \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx+(2 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx+(4 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx-(12 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx\\ &=2 \int \frac {e^{e^{x^2} (-3+x)}}{e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x} \, dx+2 \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \log (x)}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx-2 \int \left (\frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx-6 \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x}+\frac {2 \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x}\right ) \, dx+(2 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx+(4 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx-(12 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx\\ &=2 \int \frac {e^{e^{x^2} (-3+x)}}{e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x} \, dx-2 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)}}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx-2 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx-6 \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx-4 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx+(2 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)}}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx+(2 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx+(4 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx-(12 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx\\ &=2 \int \frac {e^{e^{x^2} (-3+x)}}{e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x} \, dx-2 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)}}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx-2 \int \left (\frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x}-\frac {6 \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x}\right ) \, dx-4 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx+(2 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)}}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx+(2 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx+(4 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx-(12 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx\\ &=2 \int \frac {e^{e^{x^2} (-3+x)}}{e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x} \, dx-2 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)}}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx-2 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx-4 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx+12 \int \frac {\int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx}{x} \, dx+(2 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)}}{\left (e^{e^{\log ^2(2)}}-e^{e^{x^2} (-3+x)} x\right )^2} \, dx+(2 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx+(4 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^3}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx-(12 \log (x)) \int \frac {e^{e^{\log ^2(2)}+e^{x^2} (-3+x)+x^2} x^2}{\left (-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.29, size = 45, normalized size = 1.50 \begin {gather*} 2 \left (-\log (x)-\frac {e^{e^{\log ^2(2)}} \log (x)}{-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 50, normalized size = 1.67 \begin {gather*} -\frac {2 \, x e^{\left ({\left (x - 3\right )} e^{\left (x^{2}\right )} + e^{\left (\log \relax (2)^{2}\right )}\right )} \log \relax (x)}{x e^{\left ({\left (x - 3\right )} e^{\left (x^{2}\right )} + e^{\left (\log \relax (2)^{2}\right )}\right )} - e^{\left (2 \, e^{\left (\log \relax (2)^{2}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.59, size = 46, normalized size = 1.53 \begin {gather*} -\frac {2 \, x e^{\left (x e^{\left (x^{2}\right )} - 3 \, e^{\left (x^{2}\right )}\right )} \log \relax (x)}{x e^{\left (x e^{\left (x^{2}\right )} - 3 \, e^{\left (x^{2}\right )}\right )} - e^{\left (e^{\left (\log \relax (2)^{2}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.40, size = 37, normalized size = 1.23
method | result | size |
risch | \(-2 \ln \relax (x )+\frac {2 \,{\mathrm e}^{{\mathrm e}^{\ln \relax (2)^{2}}} \ln \relax (x )}{-x \,{\mathrm e}^{\left (x -3\right ) {\mathrm e}^{x^{2}}}+{\mathrm e}^{{\mathrm e}^{\ln \relax (2)^{2}}}}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.74, size = 49, normalized size = 1.63 \begin {gather*} -\frac {2 \, e^{\left (3 \, e^{\left (x^{2}\right )} + e^{\left (\log \relax (2)^{2}\right )}\right )} \log \relax (x)}{x e^{\left (x e^{\left (x^{2}\right )}\right )} - e^{\left (3 \, e^{\left (x^{2}\right )} + e^{\left (\log \relax (2)^{2}\right )}\right )}} - 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.25, size = 161, normalized size = 5.37 \begin {gather*} -2\,\ln \relax (x)-\frac {2\,\left (x^2\,{\mathrm {e}}^{x^2+2\,{\mathrm {e}}^{{\ln \relax (2)}^2}}\,\ln \relax (x)-6\,x^3\,{\mathrm {e}}^{x^2+2\,{\mathrm {e}}^{{\ln \relax (2)}^2}}\,\ln \relax (x)+2\,x^4\,{\mathrm {e}}^{x^2+2\,{\mathrm {e}}^{{\ln \relax (2)}^2}}\,\ln \relax (x)+x\,{\mathrm {e}}^{2\,{\mathrm {e}}^{{\ln \relax (2)}^2}}\,\ln \relax (x)\right )}{\left ({\mathrm {e}}^{x\,{\mathrm {e}}^{x^2}-3\,{\mathrm {e}}^{x^2}}-\frac {{\mathrm {e}}^{{\mathrm {e}}^{{\ln \relax (2)}^2}}}{x}\right )\,\left (x^3\,{\mathrm {e}}^{x^2+{\mathrm {e}}^{{\ln \relax (2)}^2}}-6\,x^4\,{\mathrm {e}}^{x^2+{\mathrm {e}}^{{\ln \relax (2)}^2}}+2\,x^5\,{\mathrm {e}}^{x^2+{\mathrm {e}}^{{\ln \relax (2)}^2}}+x^2\,{\mathrm {e}}^{{\mathrm {e}}^{{\ln \relax (2)}^2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.45, size = 39, normalized size = 1.30 \begin {gather*} - 2 \log {\relax (x )} - \frac {2 e^{e^{\log {\relax (2 )}^{2}}} \log {\relax (x )}}{x e^{\left (x - 3\right ) e^{x^{2}}} - e^{e^{\log {\relax (2 )}^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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