Optimal. Leaf size=24 \[ 5-e^{x+\frac {1}{3} \left (-2 x-e^x \log (x)\right )}+x \]
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Rubi [A]
time = 0.06, antiderivative size = 26, normalized size of antiderivative = 1.08, number of steps
used = 4, number of rules used = 3, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.073, Rules used = {12, 14, 2326}
\begin {gather*} x-e^{x/3} x^{\frac {1}{3} \left (-e^x-3\right )+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {3 x+e^{\frac {1}{3} \left (x-e^x \log (x)\right )} \left (e^x-x+e^x x \log (x)\right )}{x} \, dx\\ &=\frac {1}{3} \int \left (3+e^{x/3} x^{\frac {1}{3} \left (-3-e^x\right )} \left (e^x-x+e^x x \log (x)\right )\right ) \, dx\\ &=x+\frac {1}{3} \int e^{x/3} x^{\frac {1}{3} \left (-3-e^x\right )} \left (e^x-x+e^x x \log (x)\right ) \, dx\\ &=x-e^{x/3} x^{1+\frac {1}{3} \left (-3-e^x\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 20, normalized size = 0.83 \begin {gather*} x-e^{x/3} x^{-\frac {e^x}{3}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 15, normalized size = 0.62
method | result | size |
risch | \(x -x^{-\frac {{\mathrm e}^{x}}{3}} {\mathrm e}^{\frac {x}{3}}\) | \(15\) |
norman | \(x -{\mathrm e}^{-\frac {{\mathrm e}^{x} \ln \left (x \right )}{3}+\frac {x}{3}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 15, normalized size = 0.62 \begin {gather*} x - e^{\left (-\frac {1}{3} \, e^{x} \log \left (x\right ) + \frac {1}{3} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.17, size = 14, normalized size = 0.58 \begin {gather*} x - e^{\frac {x}{3} - \frac {e^{x} \log {\left (x \right )}}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.69, size = 15, normalized size = 0.62 \begin {gather*} x-{\mathrm {e}}^{\frac {x}{3}-\frac {{\mathrm {e}}^x\,\ln \left (x\right )}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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