Optimal. Leaf size=32 \[ \log \left (\left (3-e^{5/3}-x-\frac {4 x}{\log (3)}-\log \left (-e^x+x\right )\right )^4\right ) \]
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Rubi [A]
time = 0.27, antiderivative size = 34, normalized size of antiderivative = 1.06, number of steps
used = 2, number of rules used = 2, integrand size = 91, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.022, Rules used = {6820, 6816}
\begin {gather*} 4 \log \left (x (4+\log (3))+\log (3) \log \left (x-e^x\right )-\left (3-e^{5/3}\right ) \log (3)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-4 (\log (3)+x (4+\log (3)))+4 e^x (4+\log (9))}{\left (e^x-x\right ) \left (\left (-3+e^{5/3}\right ) \log (3)+x (4+\log (3))+\log (3) \log \left (-e^x+x\right )\right )} \, dx\\ &=4 \log \left (-\left (\left (3-e^{5/3}\right ) \log (3)\right )+x (4+\log (3))+\log (3) \log \left (-e^x+x\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [F]
time = 0.21, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-16 x+(-4-4 x) \log (3)+e^x (16+8 \log (3))}{-4 x^2+\left (3 x-e^{5/3} x-x^2\right ) \log (3)+e^x \left (4 x+\left (-3+e^{5/3}+x\right ) \log (3)\right )+\left (e^x \log (3)-x \log (3)\right ) \log \left (-e^x+x\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.45, size = 31, normalized size = 0.97
method | result | size |
norman | \(4 \ln \left ({\mathrm e}^{\frac {5}{3}} \ln \left (3\right )+\ln \left (x -{\mathrm e}^{x}\right ) \ln \left (3\right )+x \ln \left (3\right )-3 \ln \left (3\right )+4 x \right )\) | \(31\) |
risch | \(4 \ln \left (\ln \left (x -{\mathrm e}^{x}\right )+\frac {{\mathrm e}^{\frac {5}{3}} \ln \left (3\right )+x \ln \left (3\right )-3 \ln \left (3\right )+4 x}{\ln \left (3\right )}\right )\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 25, normalized size = 0.78 \begin {gather*} 4 \, \log \left ({\left (x + e^{\frac {5}{3}} - 3\right )} \log \left (3\right ) + \log \left (3\right ) \log \left (x - e^{x}\right ) + 4 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.21, size = 34, normalized size = 1.06 \begin {gather*} 4 \log {\left (\frac {x \log {\left (3 \right )} + 4 x - 3 \log {\left (3 \right )} + e^{\frac {5}{3}} \log {\left (3 \right )}}{\log {\left (3 \right )}} + \log {\left (x - e^{x} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 30, normalized size = 0.94 \begin {gather*} 4 \, \log \left (x \log \left (3\right ) + e^{\frac {5}{3}} \log \left (3\right ) + \log \left (3\right ) \log \left (x - e^{x}\right ) + 4 \, x - 3 \, \log \left (3\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.94, size = 28, normalized size = 0.88 \begin {gather*} 4\,\ln \left (4\,x+x\,\ln \left (3\right )+\ln \left (3\right )\,\ln \left (x-{\mathrm {e}}^x\right )+\ln \left (3\right )\,\left ({\mathrm {e}}^{5/3}-3\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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