Optimal. Leaf size=22 \[ 5+x \left (3-\log (x)-\log \left (\frac {\log (2)}{5 x}\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2295} \begin {gather*} 3 x+x (-\log (x))-x \log \left (\frac {\log (2)}{5 x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2295
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=3 x-\int \log (x) \, dx-\int \log \left (\frac {\log (2)}{5 x}\right ) \, dx\\ &=3 x-x \log (x)-x \log \left (\frac {\log (2)}{5 x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 22, normalized size = 1.00 \begin {gather*} 3 x-x \log (x)-x \log \left (\frac {\log (2)}{5 x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 12, normalized size = 0.55 \begin {gather*} -x \log \left (\frac {1}{5} \, \log \relax (2)\right ) + 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 15, normalized size = 0.68 \begin {gather*} -x {\left (\log \relax (x) + \log \left (\frac {\log \relax (2)}{5 \, x}\right ) - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 21, normalized size = 0.95
method | result | size |
default | \(-x \ln \relax (x )+3 x -\ln \left (\frac {\ln \relax (2)}{5 x}\right ) x\) | \(21\) |
norman | \(-x \ln \relax (x )+3 x -\ln \left (\frac {\ln \relax (2)}{5 x}\right ) x\) | \(21\) |
risch | \(-x \ln \relax (x )+3 x -\ln \left (\frac {\ln \relax (2)}{5 x}\right ) x\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 20, normalized size = 0.91 \begin {gather*} -x \log \relax (x) - x \log \left (\frac {\log \relax (2)}{5 \, x}\right ) + 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.83, size = 15, normalized size = 0.68 \begin {gather*} -x\,\left (\ln \left (\frac {\ln \relax (2)}{5\,x}\right )+\ln \relax (x)-3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 10, normalized size = 0.45 \begin {gather*} x \left (- \log {\left (\log {\relax (2 )} \right )} + \log {\relax (5 )} + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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