Optimal. Leaf size=26 \[ e^{5 \left (-4+\frac {1}{5} \left (2+e^x\right )+\log (9)\right )} \left (4+\frac {4}{\log (x)}\right ) \]
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Rubi [A] time = 0.20, antiderivative size = 36, normalized size of antiderivative = 1.38, number of steps used = 2, number of rules used = 2, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {12, 2288} \begin {gather*} \frac {236196 e^{-x+e^x-18} \left (e^x x \log ^2(x)+e^x x \log (x)\right )}{x \log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=59049 \int \frac {e^{-18+e^x} \left (-4+4 e^x x \log (x)+4 e^x x \log ^2(x)\right )}{x \log ^2(x)} \, dx\\ &=\frac {236196 e^{-18+e^x-x} \left (e^x x \log (x)+e^x x \log ^2(x)\right )}{x \log ^2(x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 17, normalized size = 0.65 \begin {gather*} \frac {236196 e^{-18+e^x} (1+\log (x))}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 19, normalized size = 0.73 \begin {gather*} \frac {4 \, {\left (\log \relax (x) + 1\right )} e^{\left (e^{x} + 10 \, \log \relax (3) - 18\right )}}{\log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 26, normalized size = 1.00 \begin {gather*} \frac {236196 \, {\left (e^{\left (x + e^{x}\right )} \log \relax (x) + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x - 18\right )}}{\log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 16, normalized size = 0.62
method | result | size |
risch | \(\frac {236196 \left (\ln \relax (x )+1\right ) {\mathrm e}^{{\mathrm e}^{x}-18}}{\ln \relax (x )}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 19, normalized size = 0.73 \begin {gather*} \frac {236196 \, e^{\left (e^{x} - 18\right )}}{\log \relax (x)} + 236196 \, e^{\left (e^{x} - 18\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.06, size = 15, normalized size = 0.58 \begin {gather*} \frac {236196\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{-18}\,\left (\ln \relax (x)+1\right )}{\ln \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 15, normalized size = 0.58 \begin {gather*} \frac {\left (236196 \log {\relax (x )} + 236196\right ) e^{e^{x} - 18}}{\log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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