Optimal. Leaf size=19 \[ \log \left (e^{-2 e^{x/3}} \left (\frac {5}{86}+e\right ) x\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 12, normalized size of antiderivative = 0.63, number of steps
used = 4, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {12, 14, 2225}
\begin {gather*} \log (x)-2 e^{x/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {3-2 e^{x/3} x}{x} \, dx\\ &=\frac {1}{3} \int \left (-2 e^{x/3}+\frac {3}{x}\right ) \, dx\\ &=\log (x)-\frac {2}{3} \int e^{x/3} \, dx\\ &=-2 e^{x/3}+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 12, normalized size = 0.63 \begin {gather*} -2 e^{x/3}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.25, size = 12, normalized size = 0.63
method | result | size |
norman | \(-2 \,{\mathrm e}^{\frac {x}{3}}+\ln \left (x \right )\) | \(10\) |
risch | \(-2 \,{\mathrm e}^{\frac {x}{3}}+\ln \left (x \right )\) | \(10\) |
derivativedivides | \(\ln \left (\frac {x}{3}\right )-2 \,{\mathrm e}^{\frac {x}{3}}\) | \(12\) |
default | \(\ln \left (\frac {x}{3}\right )-2 \,{\mathrm e}^{\frac {x}{3}}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 9, normalized size = 0.47 \begin {gather*} -2 \, e^{\left (\frac {1}{3} \, x\right )} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 9, normalized size = 0.47 \begin {gather*} -2 \, e^{\left (\frac {1}{3} \, x\right )} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 8, normalized size = 0.42 \begin {gather*} - 2 e^{\frac {x}{3}} + \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 11, normalized size = 0.58 \begin {gather*} -2 \, e^{\left (\frac {1}{3} \, x\right )} + \log \left (\frac {1}{3} \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 9, normalized size = 0.47 \begin {gather*} \ln \left (x\right )-2\,{\mathrm {e}}^{x/3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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