Optimal. Leaf size=23 \[ 5-\log \left (-\frac {5}{2}+\log \left (4 \left (e^{-4+x+x^2}+\log (x)\right )\right )\right ) \]
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Rubi [A] time = 0.65, antiderivative size = 21, normalized size of antiderivative = 0.91, number of steps used = 3, number of rules used = 3, integrand size = 74, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.041, Rules used = {6741, 12, 6684} \begin {gather*} -\log \left (5-2 \log \left (4 \left (e^{x^2+x-4}+\log (x)\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6684
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^4 \left (2-e^{-4+x+x^2} \left (-2 x-4 x^2\right )\right )}{x \left (e^{x+x^2}+e^4 \log (x)\right ) \left (5-2 \log \left (4 \left (e^{-4+x+x^2}+\log (x)\right )\right )\right )} \, dx\\ &=e^4 \int \frac {2-e^{-4+x+x^2} \left (-2 x-4 x^2\right )}{x \left (e^{x+x^2}+e^4 \log (x)\right ) \left (5-2 \log \left (4 \left (e^{-4+x+x^2}+\log (x)\right )\right )\right )} \, dx\\ &=-\log \left (5-2 \log \left (4 \left (e^{-4+x+x^2}+\log (x)\right )\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.41, size = 21, normalized size = 0.91 \begin {gather*} -\log \left (-5+2 \log \left (4 \left (e^{-4+x+x^2}+\log (x)\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 22, normalized size = 0.96 \begin {gather*} -\log \left (2 \, \log \left (4 \, e^{\left (x^{2} + x - 4\right )} + 4 \, \log \relax (x)\right ) - 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.45, size = 23, normalized size = 1.00 \begin {gather*} -\log \left (2 \, \log \left (4 \, e^{4} \log \relax (x) + 4 \, e^{\left (x^{2} + x\right )}\right ) - 13\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 21, normalized size = 0.91
method | result | size |
risch | \(-\ln \left (\ln \left (4 \ln \relax (x )+4 \,{\mathrm e}^{x^{2}+x -4}\right )-\frac {5}{2}\right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.66, size = 22, normalized size = 0.96 \begin {gather*} -\log \left (2 \, \log \relax (2) + \log \left (e^{4} \log \relax (x) + e^{\left (x^{2} + x\right )}\right ) - \frac {13}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.93, size = 21, normalized size = 0.91 \begin {gather*} -\ln \left (\ln \left (4\,\ln \relax (x)+4\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-4}\,{\mathrm {e}}^x\right )-\frac {5}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.92, size = 22, normalized size = 0.96 \begin {gather*} - \log {\left (\log {\left (4 e^{x^{2} + x - 4} + 4 \log {\relax (x )} \right )} - \frac {5}{2} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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