Optimal. Leaf size=18 \[ \frac {5}{2} x \log (2) \left (18-2 x^2 \log \left (x^3\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.94, number of steps used = 3, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {2304} \begin {gather*} 45 x \log (2)-5 x^3 \log (2) \log \left (x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2304
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log (2) \int \left (45-15 x^2\right ) \, dx-(15 \log (2)) \int x^2 \log \left (x^3\right ) \, dx\\ &=45 x \log (2)-5 x^3 \log (2) \log \left (x^3\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 0.94 \begin {gather*} 45 x \log (2)-5 x^3 \log (2) \log \left (x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 17, normalized size = 0.94 \begin {gather*} -5 \, x^{3} \log \relax (2) \log \left (x^{3}\right ) + 45 \, x \log \relax (2) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 30, normalized size = 1.67 \begin {gather*} -5 \, {\left (x^{3} \log \left (x^{3}\right ) - x^{3}\right )} \log \relax (2) - 5 \, {\left (x^{3} - 9 \, x\right )} \log \relax (2) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 18, normalized size = 1.00
method | result | size |
default | \(45 x \ln \relax (2)-5 \ln \relax (2) x^{3} \ln \left (x^{3}\right )\) | \(18\) |
norman | \(45 x \ln \relax (2)-5 \ln \relax (2) x^{3} \ln \left (x^{3}\right )\) | \(18\) |
risch | \(45 x \ln \relax (2)-5 \ln \relax (2) x^{3} \ln \left (x^{3}\right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 30, normalized size = 1.67 \begin {gather*} -5 \, {\left (x^{3} \log \left (x^{3}\right ) - x^{3}\right )} \log \relax (2) - 5 \, {\left (x^{3} - 9 \, x\right )} \log \relax (2) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.62, size = 15, normalized size = 0.83 \begin {gather*} -5\,x\,\ln \relax (2)\,\left (x^2\,\ln \left (x^3\right )-9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 19, normalized size = 1.06 \begin {gather*} - 5 x^{3} \log {\relax (2 )} \log {\left (x^{3} \right )} + 45 x \log {\relax (2 )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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