Optimal. Leaf size=23 \[ 3 \left (3+(1-x)^2+2 x+x^2\right ) (-5+\log (3 x)) \]
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Rubi [A] time = 0.02, antiderivative size = 19, normalized size of antiderivative = 0.83, number of steps used = 5, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {14, 2304} \begin {gather*} -30 x^2+6 x^2 \log (3 x)+12 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2304
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {6 \left (-2+9 x^2\right )}{x}+12 x \log (3 x)\right ) \, dx\\ &=-\left (6 \int \frac {-2+9 x^2}{x} \, dx\right )+12 \int x \log (3 x) \, dx\\ &=-3 x^2+6 x^2 \log (3 x)-6 \int \left (-\frac {2}{x}+9 x\right ) \, dx\\ &=-30 x^2+12 \log (x)+6 x^2 \log (3 x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 0.83 \begin {gather*} -30 x^2+12 \log (x)+6 x^2 \log (3 x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 17, normalized size = 0.74 \begin {gather*} -30 \, x^{2} + 6 \, {\left (x^{2} + 2\right )} \log \left (3 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 19, normalized size = 0.83 \begin {gather*} 6 \, x^{2} \log \left (3 \, x\right ) - 30 \, x^{2} + 12 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 20, normalized size = 0.87
method | result | size |
risch | \(6 x^{2} \ln \left (3 x \right )-30 x^{2}+12 \ln \relax (x )\) | \(20\) |
derivativedivides | \(6 x^{2} \ln \left (3 x \right )-30 x^{2}+12 \ln \left (3 x \right )\) | \(22\) |
default | \(6 x^{2} \ln \left (3 x \right )-30 x^{2}+12 \ln \left (3 x \right )\) | \(22\) |
norman | \(6 x^{2} \ln \left (3 x \right )-30 x^{2}+12 \ln \left (3 x \right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 19, normalized size = 0.83 \begin {gather*} 6 \, x^{2} \log \left (3 \, x\right ) - 30 \, x^{2} + 12 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.13, size = 24, normalized size = 1.04 \begin {gather*} 12\,\ln \relax (x)+6\,x^2\,\ln \relax (x)+6\,x^2\,\ln \relax (3)-30\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 19, normalized size = 0.83 \begin {gather*} 6 x^{2} \log {\left (3 x \right )} - 30 x^{2} + 12 \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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