Optimal. Leaf size=22 \[ \log \left (x \left (9+x \left (-\frac {2}{3}+x^2\right )+\log \left (\frac {x^2}{2}\right )\right )\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 26, normalized size of antiderivative = 1.18, number of steps used = 1, number of rules used = 1, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {6684} \begin {gather*} \log \left (3 x^4-2 x^2+3 x \log \left (\frac {x^2}{2}\right )+27 x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (27 x-2 x^2+3 x^4+3 x \log \left (\frac {x^2}{2}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.30, size = 24, normalized size = 1.09 \begin {gather*} \log (x)+\log \left (27-2 x+3 x^3+3 \log \left (\frac {x^2}{2}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 28, normalized size = 1.27 \begin {gather*} \log \left (3 \, x^{3} - 2 \, x + 3 \, \log \left (\frac {1}{2} \, x^{2}\right ) + 27\right ) + \frac {1}{2} \, \log \left (\frac {1}{2} \, x^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 22, normalized size = 1.00 \begin {gather*} \log \left (3 \, x^{3} - 2 \, x + 3 \, \log \left (\frac {1}{2} \, x^{2}\right ) + 27\right ) + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 19, normalized size = 0.86
method | result | size |
risch | \(\ln \relax (x )+\ln \left (x^{3}-\frac {2 x}{3}+\ln \left (\frac {x^{2}}{2}\right )+9\right )\) | \(19\) |
norman | \(\ln \relax (x )+\ln \left (3 x^{3}+3 \ln \left (\frac {x^{2}}{2}\right )-2 x +27\right )\) | \(23\) |
derivativedivides | \(\ln \left (3 x \ln \left (\frac {x^{2}}{2}\right )+3 x^{4}-2 x^{2}+27 x \right )\) | \(25\) |
default | \(\ln \left (3 x \ln \left (\frac {x^{2}}{2}\right )+3 x^{4}-2 x^{2}+27 x \right )\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 24, normalized size = 1.09 \begin {gather*} \log \left (3 \, x^{4} - 2 \, x^{2} + 3 \, x \log \left (\frac {1}{2} \, x^{2}\right ) + 27 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.16, size = 22, normalized size = 1.00 \begin {gather*} \ln \left (\ln \left (\frac {x^2}{2}\right )-\frac {2\,x}{3}+x^3+9\right )+\frac {\ln \left (x^2\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 20, normalized size = 0.91 \begin {gather*} \log {\relax (x )} + \log {\left (x^{3} - \frac {2 x}{3} + \log {\left (\frac {x^{2}}{2} \right )} + 9 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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