Optimal. Leaf size=21 \[ e^{4+x-\frac {x}{3+x-\log \left (4 x^2\right )}} \]
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Rubi [F] time = 3.66, 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 (\frac {-12-6 x-x^2+(4+x) \log \left (4 x^2\right )}{-3-x+\log \left (4 x^2\right )}\right ) \left (4+6 x+x^2+(-5-2 x) \log \left (4 x^2\right )+\log ^2\left (4 x^2\right )\right )}{9+6 x+x^2+(-6-2 x) \log \left (4 x^2\right )+\log ^2\left (4 x^2\right )} \, 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 {-12-6 x-x^2+(4+x) \log \left (4 x^2\right )}{-3-x+\log \left (4 x^2\right )}\right ) \left (4+6 x+x^2+(-5-2 x) \log \left (4 x^2\right )+\log ^2\left (4 x^2\right )\right )}{\left (3+x-\log \left (4 x^2\right )\right )^2} \, dx\\ &=\int \left (\exp \left (\frac {-12-6 x-x^2+(4+x) \log \left (4 x^2\right )}{-3-x+\log \left (4 x^2\right )}\right )+\frac {\exp \left (\frac {-12-6 x-x^2+(4+x) \log \left (4 x^2\right )}{-3-x+\log \left (4 x^2\right )}\right ) (-2+x)}{\left (3+x-\log \left (4 x^2\right )\right )^2}+\frac {\exp \left (\frac {-12-6 x-x^2+(4+x) \log \left (4 x^2\right )}{-3-x+\log \left (4 x^2\right )}\right )}{-3-x+\log \left (4 x^2\right )}\right ) \, dx\\ &=\int \exp \left (\frac {-12-6 x-x^2+(4+x) \log \left (4 x^2\right )}{-3-x+\log \left (4 x^2\right )}\right ) \, dx+\int \frac {\exp \left (\frac {-12-6 x-x^2+(4+x) \log \left (4 x^2\right )}{-3-x+\log \left (4 x^2\right )}\right ) (-2+x)}{\left (3+x-\log \left (4 x^2\right )\right )^2} \, dx+\int \frac {\exp \left (\frac {-12-6 x-x^2+(4+x) \log \left (4 x^2\right )}{-3-x+\log \left (4 x^2\right )}\right )}{-3-x+\log \left (4 x^2\right )} \, dx\\ &=\int \exp \left (\frac {-12-6 x-x^2+(4+x) \log \left (4 x^2\right )}{-3-x+\log \left (4 x^2\right )}\right ) \, dx+\int \left (-\frac {2 \exp \left (\frac {-12-6 x-x^2+(4+x) \log \left (4 x^2\right )}{-3-x+\log \left (4 x^2\right )}\right )}{\left (3+x-\log \left (4 x^2\right )\right )^2}+\frac {\exp \left (\frac {-12-6 x-x^2+(4+x) \log \left (4 x^2\right )}{-3-x+\log \left (4 x^2\right )}\right ) x}{\left (3+x-\log \left (4 x^2\right )\right )^2}\right ) \, dx+\int \frac {\exp \left (\frac {-12-6 x-x^2+(4+x) \log \left (4 x^2\right )}{-3-x+\log \left (4 x^2\right )}\right )}{-3-x+\log \left (4 x^2\right )} \, dx\\ &=-\left (2 \int \frac {\exp \left (\frac {-12-6 x-x^2+(4+x) \log \left (4 x^2\right )}{-3-x+\log \left (4 x^2\right )}\right )}{\left (3+x-\log \left (4 x^2\right )\right )^2} \, dx\right )+\int \exp \left (\frac {-12-6 x-x^2+(4+x) \log \left (4 x^2\right )}{-3-x+\log \left (4 x^2\right )}\right ) \, dx+\int \frac {\exp \left (\frac {-12-6 x-x^2+(4+x) \log \left (4 x^2\right )}{-3-x+\log \left (4 x^2\right )}\right ) x}{\left (3+x-\log \left (4 x^2\right )\right )^2} \, dx+\int \frac {\exp \left (\frac {-12-6 x-x^2+(4+x) \log \left (4 x^2\right )}{-3-x+\log \left (4 x^2\right )}\right )}{-3-x+\log \left (4 x^2\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.82, size = 20, normalized size = 0.95 \begin {gather*} e^{4+x+\frac {x}{-3-x+\log \left (4 x^2\right )}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 34, normalized size = 1.62 \begin {gather*} e^{\left (\frac {x^{2} - {\left (x + 4\right )} \log \left (4 \, x^{2}\right ) + 6 \, x + 12}{x - \log \left (4 \, x^{2}\right ) + 3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.07, size = 93, normalized size = 4.43 \begin {gather*} e^{\left (\frac {x^{2}}{x - \log \left (4 \, x^{2}\right ) + 3} - \frac {x \log \left (4 \, x^{2}\right )}{x - \log \left (4 \, x^{2}\right ) + 3} + \frac {6 \, x}{x - \log \left (4 \, x^{2}\right ) + 3} - \frac {4 \, \log \left (4 \, x^{2}\right )}{x - \log \left (4 \, x^{2}\right ) + 3} + \frac {12}{x - \log \left (4 \, x^{2}\right ) + 3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.30, size = 41, normalized size = 1.95
method | result | size |
risch | \({\mathrm e}^{\frac {-x \ln \left (4 x^{2}\right )+x^{2}-4 \ln \left (4 x^{2}\right )+6 x +12}{x -\ln \left (4 x^{2}\right )+3}}\) | \(41\) |
norman | \(\frac {x \,{\mathrm e}^{\frac {\left (4+x \right ) \ln \left (4 x^{2}\right )-x^{2}-6 x -12}{\ln \left (4 x^{2}\right )-3-x}}-\ln \left (4 x^{2}\right ) {\mathrm e}^{\frac {\left (4+x \right ) \ln \left (4 x^{2}\right )-x^{2}-6 x -12}{\ln \left (4 x^{2}\right )-3-x}}+3 \,{\mathrm e}^{\frac {\left (4+x \right ) \ln \left (4 x^{2}\right )-x^{2}-6 x -12}{\ln \left (4 x^{2}\right )-3-x}}}{x -\ln \left (4 x^{2}\right )+3}\) | \(133\) |
default | \(\frac {x \,{\mathrm e}^{\frac {\left (4+x \right ) \ln \left (4 x^{2}\right )-x^{2}-6 x -12}{\ln \left (4 x^{2}\right )-3-x}}+\left (-\ln \left (4 x^{2}\right )+2 \ln \relax (x )+3\right ) {\mathrm e}^{\frac {\left (4+x \right ) \ln \left (4 x^{2}\right )-x^{2}-6 x -12}{\ln \left (4 x^{2}\right )-3-x}}-2 \ln \relax (x ) {\mathrm e}^{\frac {\left (4+x \right ) \ln \left (4 x^{2}\right )-x^{2}-6 x -12}{\ln \left (4 x^{2}\right )-3-x}}}{x -\ln \left (4 x^{2}\right )+3}\) | \(142\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.67, size = 53, normalized size = 2.52 \begin {gather*} e^{\left (x - \frac {2 \, \log \relax (2)}{x - 2 \, \log \relax (2) - 2 \, \log \relax (x) + 3} - \frac {2 \, \log \relax (x)}{x - 2 \, \log \relax (2) - 2 \, \log \relax (x) + 3} + \frac {3}{x - 2 \, \log \relax (2) - 2 \, \log \relax (x) + 3} + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.54, size = 83, normalized size = 3.95 \begin {gather*} {\mathrm {e}}^{\frac {x^2}{x-\ln \left (x^2\right )-2\,\ln \relax (2)+3}}\,{\mathrm {e}}^{\frac {12}{x-\ln \left (x^2\right )-2\,\ln \relax (2)+3}}\,{\mathrm {e}}^{\frac {6\,x}{x-\ln \left (x^2\right )-2\,\ln \relax (2)+3}}\,{\left (\frac {1}{4\,x^2}\right )}^{\frac {x+4}{x-\ln \left (x^2\right )-2\,\ln \relax (2)+3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.67, size = 29, normalized size = 1.38 \begin {gather*} e^{\frac {- x^{2} - 6 x + \left (x + 4\right ) \log {\left (4 x^{2} \right )} - 12}{- x + \log {\left (4 x^{2} \right )} - 3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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