Optimal. Leaf size=17 \[ -1+x-x^2 \log (x) \log \left (\frac {\log (2)}{3}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps
used = 3, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {2341}
\begin {gather*} x-x^2 \log \left (\frac {\log (2)}{3}\right ) \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2341
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+\log \left (\frac {\log (2)}{3}\right ) \int (-x-2 x \log (x)) \, dx\\ &=x-\frac {1}{2} x^2 \log \left (\frac {\log (2)}{3}\right )-\left (2 \log \left (\frac {\log (2)}{3}\right )\right ) \int x \log (x) \, dx\\ &=x-x^2 \log (x) \log \left (\frac {\log (2)}{3}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 0.94 \begin {gather*} x-x^2 \log (x) \log \left (\frac {\log (2)}{3}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 15, normalized size = 0.88
method | result | size |
default | \(x -x^{2} \ln \left (x \right ) \ln \left (\frac {\ln \left (2\right )}{3}\right )\) | \(15\) |
norman | \(x +\left (\ln \left (3\right )-\ln \left (\ln \left (2\right )\right )\right ) x^{2} \ln \left (x \right )\) | \(17\) |
risch | \(-\left (-\ln \left (3\right )+\ln \left (\ln \left (2\right )\right )\right ) x^{2} \ln \left (x \right )+x\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 14, normalized size = 0.82 \begin {gather*} -x^{2} \log \left (x\right ) \log \left (\frac {1}{3} \, \log \left (2\right )\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 14, normalized size = 0.82 \begin {gather*} -x^{2} \log \left (x\right ) \log \left (\frac {1}{3} \, \log \left (2\right )\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 19, normalized size = 1.12 \begin {gather*} x + \left (- x^{2} \log {\left (\log {\left (2 \right )} \right )} + x^{2} \log {\left (3 \right )}\right ) \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 14, normalized size = 0.82 \begin {gather*} -x^{2} \log \left (x\right ) \log \left (\frac {1}{3} \, \log \left (2\right )\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.77, size = 14, normalized size = 0.82 \begin {gather*} x-x^2\,\ln \left (\frac {\ln \left (2\right )}{3}\right )\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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