Optimal. Leaf size=15 \[ -9+x \left (1-e^3 (3+\log (x))\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.53, number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2295} \begin {gather*} \left (1-4 e^3\right ) x+e^3 x-e^3 x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2295
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\left (1-4 e^3\right ) x-e^3 \int \log (x) \, dx\\ &=e^3 x+\left (1-4 e^3\right ) x-e^3 x \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.07 \begin {gather*} x-3 e^3 x-e^3 x \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 14, normalized size = 0.93 \begin {gather*} -x e^{3} \log \relax (x) - 3 \, x e^{3} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 19, normalized size = 1.27 \begin {gather*} -{\left (x \log \relax (x) - x\right )} e^{3} - 4 \, x e^{3} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 15, normalized size = 1.00
method | result | size |
default | \(x -x \,{\mathrm e}^{3} \ln \relax (x )-3 x \,{\mathrm e}^{3}\) | \(15\) |
risch | \(x -x \,{\mathrm e}^{3} \ln \relax (x )-3 x \,{\mathrm e}^{3}\) | \(15\) |
norman | \(\left (1-3 \,{\mathrm e}^{3}\right ) x -x \,{\mathrm e}^{3} \ln \relax (x )\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 19, normalized size = 1.27 \begin {gather*} -{\left (x \log \relax (x) - x\right )} e^{3} - 4 \, x e^{3} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.54, size = 14, normalized size = 0.93 \begin {gather*} -x\,\left (3\,{\mathrm {e}}^3+{\mathrm {e}}^3\,\ln \relax (x)-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 15, normalized size = 1.00 \begin {gather*} - x e^{3} \log {\relax (x )} + x \left (1 - 3 e^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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