Optimal. Leaf size=18 \[ -x-\log \left (3-x^2+3 \log (x)\right ) \]
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Rubi [A]
time = 0.17, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {6874, 6816}
\begin {gather*} -\log \left (-x^2+3 \log (x)+3\right )-x \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+\frac {3-2 x^2}{x \left (-3+x^2-3 \log (x)\right )}\right ) \, dx\\ &=-x+\int \frac {3-2 x^2}{x \left (-3+x^2-3 \log (x)\right )} \, dx\\ &=-x-\log \left (3-x^2+3 \log (x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 18, normalized size = 1.00 \begin {gather*} -x-\log \left (3-x^2+3 \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 7.94, size = 19, normalized size = 1.06
method | result | size |
norman | \(-x -\ln \left (x^{2}-3 \ln \left (x \right )-3\right )\) | \(17\) |
risch | \(-x -\ln \left (-\frac {x^{2}}{3}+\ln \left (x \right )+1\right )\) | \(17\) |
default | \(-x -\ln \left (3+3 \ln \left (x \right )-x^{2}\right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 16, normalized size = 0.89 \begin {gather*} -x - \log \left (-\frac {1}{3} \, x^{2} + \log \left (x\right ) + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 18, normalized size = 1.00 \begin {gather*} -x - \log \left (-x^{2} + 3 \, \log \left (x\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 14, normalized size = 0.78 \begin {gather*} - x - \log {\left (- \frac {x^{2}}{3} + \log {\left (x \right )} + 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 18, normalized size = 1.00 \begin {gather*} -x - \log \left (-x^{2} + 3 \, \log \left (x\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.47, size = 16, normalized size = 0.89 \begin {gather*} -x-\ln \left (x^2-3\,\ln \left (x\right )-3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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