Optimal. Leaf size=24 \[ \frac {\left (x+x^2-(6 (-8+x)+x) (x+\log (2))\right ) \log (3)}{x} \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.62, number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 14} \begin {gather*} \frac {48 \log (2) \log (3)}{x}-6 x \log (3) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log (3) \int \frac {-6 x^2-48 \log (2)}{x^2} \, dx\\ &=\log (3) \int \left (-6-\frac {48 \log (2)}{x^2}\right ) \, dx\\ &=-6 x \log (3)+\frac {48 \log (2) \log (3)}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 0.54 \begin {gather*} -6 \log (3) \left (x-\frac {\log (256)}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.11, size = 15, normalized size = 0.62 \begin {gather*} -\frac {6 \, {\left (x^{2} - 8 \, \log \relax (2)\right )} \log \relax (3)}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.11, size = 13, normalized size = 0.54 \begin {gather*} -6 \, {\left (x - \frac {8 \, \log \relax (2)}{x}\right )} \log \relax (3) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 16, normalized size = 0.67
method | result | size |
default | \(6 \ln \relax (3) \left (-x +\frac {8 \ln \relax (2)}{x}\right )\) | \(16\) |
risch | \(-6 x \ln \relax (3)+\frac {48 \ln \relax (3) \ln \relax (2)}{x}\) | \(16\) |
gosper | \(\frac {6 \ln \relax (3) \left (-x^{2}+8 \ln \relax (2)\right )}{x}\) | \(18\) |
norman | \(\frac {-6 x^{2} \ln \relax (3)+48 \ln \relax (2) \ln \relax (3)}{x}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 13, normalized size = 0.54 \begin {gather*} -6 \, {\left (x - \frac {8 \, \log \relax (2)}{x}\right )} \log \relax (3) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 17, normalized size = 0.71 \begin {gather*} \frac {6\,\ln \relax (3)\,\left (8\,\ln \relax (2)-x^2\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 15, normalized size = 0.62 \begin {gather*} - 6 x \log {\relax (3 )} + \frac {48 \log {\relax (2 )} \log {\relax (3 )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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