Optimal. Leaf size=22 \[ \frac {x+\frac {1}{2} (-2+x+4 \log (2))-x \log (x)}{e} \]
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Rubi [A]
time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.77, number of steps
used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 2332}
\begin {gather*} \frac {3 x}{2 e}-\frac {x \log (x)}{e} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2332
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int (1-2 \log (x)) \, dx}{2 e}\\ &=\frac {x}{2 e}-\frac {\int \log (x) \, dx}{e}\\ &=\frac {3 x}{2 e}-\frac {x \log (x)}{e}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 0.73 \begin {gather*} \frac {3 x-2 x \log (x)}{2 e} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.19, size = 16, normalized size = 0.73
method | result | size |
risch | \(\frac {3 \,{\mathrm e}^{-1} x}{2}-x \,{\mathrm e}^{-1} \ln \left (x \right )\) | \(14\) |
default | \(\frac {{\mathrm e}^{-1} \left (3 x -2 x \ln \left (x \right )\right )}{2}\) | \(16\) |
norman | \(\frac {3 \,{\mathrm e}^{-1} x}{2}-x \,{\mathrm e}^{-1} \ln \left (x \right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 13, normalized size = 0.59 \begin {gather*} -\frac {1}{2} \, {\left (2 \, x \log \left (x\right ) - 3 \, x\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 13, normalized size = 0.59 \begin {gather*} -\frac {1}{2} \, {\left (2 \, x \log \left (x\right ) - 3 \, x\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 15, normalized size = 0.68 \begin {gather*} - \frac {x \log {\left (x \right )}}{e} + \frac {3 x}{2 e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 13, normalized size = 0.59 \begin {gather*} -\frac {1}{2} \, {\left (2 \, x \log \left (x\right ) - 3 \, x\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.30, size = 11, normalized size = 0.50 \begin {gather*} -\frac {x\,{\mathrm {e}}^{-1}\,\left (2\,\ln \left (x\right )-3\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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