Optimal. Leaf size=21 \[ \log \left (\frac {1}{1-e+x+\frac {1}{3} \left (\frac {4}{3}+e^x\right ) x}\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 20, normalized size of antiderivative = 0.95, number of steps used = 1, number of rules used = 1, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {6684} \begin {gather*} -\log \left (3 e^x x+13 x+9 (1-e)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\log \left (9 (1-e)+13 x+3 e^x x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.18, size = 17, normalized size = 0.81 \begin {gather*} -\log \left (9-9 e+13 x+3 e^x x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 26, normalized size = 1.24 \begin {gather*} -\log \relax (x) - \log \left (\frac {3 \, x e^{x} + 13 \, x - 9 \, e + 9}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.30, size = 17, normalized size = 0.81 \begin {gather*} -\log \left (3 \, x e^{x} + 13 \, x - 9 \, e + 9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 18, normalized size = 0.86
method | result | size |
norman | \(-\ln \left (-3 \,{\mathrm e}^{x} x +9 \,{\mathrm e}-13 x -9\right )\) | \(18\) |
risch | \(-\ln \relax (x )-\ln \left ({\mathrm e}^{x}-\frac {9 \,{\mathrm e}-13 x -9}{3 x}\right )\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 27, normalized size = 1.29 \begin {gather*} -\log \relax (x) - \log \left (\frac {3 \, x e^{x} + 13 \, x - 9 \, e + 9}{3 \, x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 17, normalized size = 0.81 \begin {gather*} -\ln \left (13\,x-9\,\mathrm {e}+3\,x\,{\mathrm {e}}^x+9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 22, normalized size = 1.05 \begin {gather*} - \log {\relax (x )} - \log {\left (e^{x} + \frac {13 x - 9 e + 9}{3 x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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