Optimal. Leaf size=23 \[ \log ^2\left (e^{\frac {x}{\log (x)}}+\frac {1}{2} \left (4-e^5\right )\right ) \]
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Rubi [A] time = 0.82, antiderivative size = 24, normalized size of antiderivative = 1.04, number of steps used = 1, number of rules used = 4, integrand size = 66, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {6741, 12, 6684, 6686} \begin {gather*} \log ^2\left (\frac {1}{2} \left (2 e^{\frac {x}{\log (x)}}+4-e^5\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6684
Rule 6686
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log ^2\left (\frac {1}{2} \left (4-e^5+2 e^{\frac {x}{\log (x)}}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.11, size = 20, normalized size = 0.87 \begin {gather*} \log ^2\left (2-\frac {e^5}{2}+e^{\frac {x}{\log (x)}}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.17, size = 16, normalized size = 0.70 \begin {gather*} \log \left (-\frac {1}{2} \, e^{5} + e^{\frac {x}{\log \relax (x)}} + 2\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.30, size = 39, normalized size = 1.70 \begin {gather*} -2 \, \log \relax (2) \log \left (-e^{5} + 2 \, e^{\frac {x}{\log \relax (x)}} + 4\right ) + \log \left (-e^{5} + 2 \, e^{\frac {x}{\log \relax (x)}} + 4\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 17, normalized size = 0.74
method | result | size |
risch | \(\ln \left ({\mathrm e}^{\frac {x}{\ln \relax (x )}}+2-\frac {{\mathrm e}^{5}}{2}\right )^{2}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.73, size = 53, normalized size = 2.30 \begin {gather*} 2 \, \log \left (-\frac {1}{2} \, e^{5} + e^{\frac {x}{\log \relax (x)}} + 2\right ) \log \left (-e^{5} + 2 \, e^{\frac {x}{\log \relax (x)}} + 4\right ) - \log \left (-e^{5} + 2 \, e^{\frac {x}{\log \relax (x)}} + 4\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.88, size = 16, normalized size = 0.70 \begin {gather*} {\ln \left ({\mathrm {e}}^{\frac {x}{\ln \relax (x)}}-\frac {{\mathrm {e}}^5}{2}+2\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.63, size = 15, normalized size = 0.65 \begin {gather*} \log {\left (e^{\frac {x}{\log {\relax (x )}}} - \frac {e^{5}}{2} + 2 \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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